Modelling in Hydrogeology

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Modelling in Hydrogeology, Eds: L. Elango and R. Jayakumar, UNESCO-IHP,

Allied Publishers, 2001, pp.3-16

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Ground Water Modelling: Issues and Requirements

S. Mohan

Abstract

The progress of research in groundwater modelling from the past and basic

aspects of modelling techniques and requirements for modelling areexplained in this paper. The application of groundwater techniques in twodifferent regions are given. The first study explain the use of groundwatermodelling studies in to evaluate the effectiveness of percolation ponds. The

second can study demonstrate the application of groundwater modelling to study seawater intrusion in coastal aquifer.

Keywords : Groundwater modelling, Requirements, Percolation ponds,

Seawater intrusion.

1. INTRODUCTION

Throughout the world, there has been a growing concern about the water resources,

especially water crisis, and a re examination of the relationship between different waterresources and the relationship between water and environment assume a great role. The

United Nations recently surveyed a group of leading thinkers from many disciplines on themost important issues facing humankind in the next century. In its report, the scarcity offreshwater in localized areas ranked as the world’s second most priming concern (after population growth) in area where people can least afford the necessities of like. To meet

the increasing demand of water, there is a need to tap the groundwater resources consignedover the world. This process causes concern over the sustainable use of this resources andthe reservation of environment.

India is vast country with a geographical area of 328 million hectares (M.Ha.m.). It

receives an average annual rainfall of 1170 millimeters (mm), which is the highest inthe world among countries of comparable size. India receives most of its rainfallfrom the southwest monsoon originating in the Indian Ocean and having two distinct branches; the Arabian sea branch and the Bay of Bengal branch. The Arabian Sea branch produces rainfall in Peninsular India and part of Gujarat and Rajasthan. Therest of India receives rainfall from the Bay of Bengal branch. The windward sides



Modelling in Hydrogeology

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of the hills and mountain ranges receive high rainfall while the leeward side and theinterior of the vast plains receive less rainfall. For example, the Khasi and Jaintiahill areas in the northeast of the country receive as much as 10,000mm of rainfallwhere as western Rajasthan receives only 150 to 200 mm. About 75% of the rainfalltakes place in the four monsoon months of June to September. Another 10% to 11%

each occur in the pre-monsoon and post-monsoon months of March to May andOctober to December respectively, the winter rainfall (January-February) being onlyof the order of 4 to 5%. There is thus a large variation exists between differentseasons. There is also large variation in the rainfall from year to year, usually incycles of wet years followed by dry years

There have been varying estimates about the total precipitation in the country and itssub-distribution into evaporation and transpiration, surface flow, sub-surface flowand regeneration and contribution to ground water recharge. I am quoting here thecomprehensive set of figures assessed by the National Agricultural Commission in

1976. According to them, the average annual precipitation over the whole county,(including snow fall which constitutes only a small part, about 2 to 3%) is 400

million hectare meters (M.ha.m.) of which about 70 M.ha.m. evaporate immediatelyfrom the top soil, 215 M.ha.m infiltrate into the ground out of which 165 M.ha.m. go back to the atmosphere as evaporation and transpiration and 50 M.ha.m go down torecharge the ground water. It is also envisaged that 5 to 10 M.ha.m will go fromstream flows to found water during floods and further that about 50% of the

irrigation water will also go to ground water. At the same time, 45 M.ha.m ofground water is estimated to reappear as surface flow (regeneration) in streams and

rivers during the low-flow season. The resultant surface flow including 20 M.ha.mreceived from adjoining countries estimated to be 185 M.ha.m on full harnessing

and mobilization of these water resources, say, by 2025 AD, (Techno-economicallyfeasible development), it is envisaged that 70 M.ha.m of surface water and 35

M.ha.m of groundwater can be mobilized for-consumptive use. The projected useout of this 105 M.ha.m. water is 77 M.ha.m for irrigation and 28 M.ha.m fordomestic and industrial water supply and all other purposes.

It is relevant to emphasis that the return flow from ground water (45 M.ha.m) is themain contributor to the dry-weather flow in streams and rivers. It is also important todraw attention to the postulation that in the time ultimate stage 25 M.ha.m of groundwater is to be contributed by surface irrigation. It is on this premise that 35 M.ha.mof groundwater has been considered extractable annually for consumptive use. If in

the long run, all the canal system are progressively lined and more efficient methodsof irrigation like sprinkler and drip irrigation are adopted, the contribution fromirrigation to ground water may be only of the order of 20 to 25 M. ha.m. Any over-extraction of ground water will correspondingly reduce the precious dry weatherflows in streams and rivers and lower the permanent ground water table, therebyupsetting the ground water regime. The often-profounded idea that there exists an

infinite quantum of ground water, which can readily be extracted for consumptive




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use without any detriment to the surface water regime, does not have any scientific backing.

Consequent to the seasonal concentration of rainfall, the river flows are alsoconcentrated (about 85%) in the period June to November, and that too during four

or five flood spells of 5to 10 days each. On the other hand, during the months ofApril, May and part of June, consequent to the progressively decreasing ground-water return flow, the river flows dwindle to a trickle.

In a country like India, where more than 70 percent of the total area is underlain byhard rocks, formations like granites, gneisses and other consolidated rocks which for

in shallow aquifers of limited thickness. It is essential to tap this ground water inwhatever available quantity. Due to the poor availability of water and complexhydrogeology of hard rock aquifers, exploration is a very difficult job in these areas.However some ground water is often available in areas underlain by hard rocks,

though the quantity available is very small as compared to unconsolidated aquifers.

2. GROUND WATER RESEARCH

The progress of research in ground water area is briefly outlined below.

During sixties one could count the number of groundwater professionals and

whatever the number one came up with; there was one less available job. Thosedays practically every one of them was involved in water supply problems. And the

tools of the trade were primitive by today’s standards. Wells were usually percussion drill rigs and the only quantitative analysis was carried out involving

analyzing water-level changes induced by a pumping test to obtain aquifer parameters.

All that changed in the mid seventies, thanks to the discovery of organic solvents inground water and the resulting concern about cancer risk and overnight a newindustry was formed. Also the sudden increase in interest in ground water caused by

that discovery spawned a number of important improvements in the field methods.The concepts of water-quality sampling for example, changed overnight. Instead ofworrying about ground water concentrations of parts per thousand of salt in coastalaquifers, we were suddenly concerned about concentrations of parts of per million oforganic compounds that had never even heard of before.

There was a similar revolution in the area of analysis. Until chlorinated organicscompounds were found in ground water, there was practically no interest at all instudying groundwater transport. People were casually interested in water supplied being contaminated by salt water, but that was not the concern cancer-causingcompound that exists today in most developed countries.




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The vast majority of research activities and field applications we see today arededicated to ground water contamination problems. Chlorinated hydrocarboncontamination, in particular, is of enormous interest, whether in the aqueous phaseor the non-aqueous phase. DNAPL (Dense Non-Aqueous Phase Liquids)contamination is probably the number one ground water contamination problem.

Just twenty-five years ago, no one had any idea that such compounds even existed inthe subsurface.

There has not only been an evaluation in the kinds of problems that we are facedwith, but there has also been a significant change in tools we use to address them.Thanks to research community, we now have many new techniques and

technologies for tackling field problems.

The quality of data provided to the groundwater professional has improvedenormously too. The sample was not properly sealed and much of the contaminant

of concern was permitted to escape before the samples even got to the laboratory.And boring logs were not nearly as carefully prepared as they are today. Not to

mention that there was too little concern about the location of piezometers and wellscreens. Another problem that was not recognized early was the importance ofaccurate water-level measurements.

Recent past has been witnessing the “dowsing” technology in locating ground water

availability. Dowsing is the art of using a divining rod to locate water. Dowsing isalso known as water witching. Although lacking scientific justification, water

witches diligently follow the dictation of their divining rods wherever people can be persuaded of their potential value. As they dowse the cone on top of ground they

can get water-availability and in some cases water quality measurements. Acomplete investigation of a site can be completed in a matter of hours rather than

weeks. A recent research established that a good correlation exists between the blood groups of the dowsing persons and the success of the dowsing technology.

It is to be noted that the advances made in the analysis and utilization of data is even

more impressive than the technology itself. In earlier days the only way to forecastthe impact of a new well on neighboring wells was to be of a simple and usuallyunrealistic geometry. Not only that, but also one had to assume the entire aquifer hasuniform permeability, net infiltration and storativity. In early days it was alsoimpossible to simulate unsaturated flow because the equations describing the system

were non-linear. Of course, the idea of representing chemical or biological reactionswas unheard of in those days.

It is evident that a sea change in the field of groundwater hydrology in the next fewyears and the following are being envisaged. One is the convergence of two verystrong forces. The other is that the agencies charged with defining and enforcing

our environmental laws are re-examining the effectiveness of past practices and,having done so are in some sense, changing course. On the other hand, industries




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strongly influenced by international competition, are reticent to invest scarce capitalin activities that do not enhance short-term profits. Environmental protection andremediation programs do not generally improve short-term profits. The obvious neteffect of the convergence of these two forces is a retreat from the aggressive program of groundwater contamination identification and remediation.

Groundwater contamination problems, while constituting an enormous national problem, nevertheless exhibit the normal evolutionary sequence of youth, maturity,and well, death. While there are still a significant number of problems that have not been characterized, or even found for that matter, many have been characterized,evaluated and in some sense remediated.

Certainly there are gargantuan environmental and water supply challenges indeveloping countries lives. Just think of the impact that a solution to the soilsalinization problem would have on society!. However, the countries that have the

greatest environmental challenges do not necessarily have, or not willing to committhe resources necessary to address these problems. They may tend to depend on

local professional rather than seek international expertise. If this is the case, there isa potential market internationally, but to be realized, it may be essential to involvelocal firms to gain access.

3. GROUND WATER MODELING

In ground water management, a through understanding of the physical, chemical and

biological processes in complex environment and their modeling are greatchallenges. Mathematical models provide a quantitative framework for analyzing

data from monitoring and assess quantitatively responses of the ground watersystems subjected to external stresses. Over the last four decades there has been a

continuous improvement in the development of numerical ground water models.Earlier models concentrated on the analysis of flow behaviour in ground watersystems where as the recent attempts aim at addressing the water quality problemsand to simulate the transport contaminants in ground water. Even through there has

been significant development in modeling tools and techniques, scientific challengesexist as the credibility of field level application of models has to be ascertained dueto the existence of uncertainty in the conceptualization of the system like the boundary conditions, aquifer heterogeneity, natural recharge and others. Anderson(1995) provided a chronological time line of significant theoretical development

representing the processes in groundwater systems, on the basis of whichmathematical models are developed. All through 1990s there has been muchresearch devoted to analysis of uncertainty in modeling both groundwater flow andtransport of solutes using geostatisitcal concepts and stochastic methods (Dagan and Neuman, 1997). This will be the major thrust of research and challenge in thecoming decades, especially when one has to ascertain the reliability of the modeling

on a regional scale.




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Groundwater modeling softwares are now easily available. Also graphical userinterface (GUI) processors for these models are available at reasonable cost. Manyof these pre- and post-processors work with the popular computer code likeMODFLOW, which has been extensively used for analyzing field problems. Withthese processing tools, the water resources professionals now find it easy to carry

out the modeling work. Complex arrays of data can now be created quickly fromexternal databases. Geostatistical routines embedded in GUI software facilitateautomatic interpolation and extrapolation of scattered data. Input data and themodel results can now be visualized for better perception and understanding. Thisin turn has lead to situations, mostly in developing countries, where overemphasis isgiven on the requirement of model study for resource evaluation and prediction

wherein most of the cases, field data and information are not adequate for properconceptualization of the system. It has come to a stage where the model applicationis carried out by the so-called modelers who do not need to have properunderstanding of the basic operational function of the models. Unfortunately, this

trend in modeling will have a serious consequence when the beneficiaries will startquestioning the creditability of modeling as the fault lies not with the model itself

but with the conceptualization of the physical system for model application.

4. REQUIREMENTS FOR REGIONAL GROUNDWATER MODEL

Regional groundwater models need to be developed meeting the important

requirements on many aspects. These requirements were based on the review ongroundwater modeling applications, as well as consideration of the future

applications of the groundwater model. The requirements for the regionalgroundwater model address the key elements of the conceptual model of the aquifer

system, anticipated future flow conditions, the types of contaminant transport, andthe spatial and temporal scales of potential applications.

The requirements for regional groundwater model were outlined by Mann andMyers (1998) to develop technical and administrative requirements for selecting acomputer code that will be used in the implementation of the comprehensive model.

A brief discussion of the rationale is provided with each requirement. The review offuture groundwater analyses that will be performed by any regional ground watermodel could cover a wide range of problems. The range of analyses include

• evaluations of current and near-term impacts of operations facilities and

proposed waste-disposal facilities• planning, design, and evaluation of remediation strategies, including

monitoring, natural attenuation, hydraulic control/containment, and contaminantremoval/cleanup

• long-term planning involving risk assessment and management

• assessment of cumulative environmental impacts.




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of driving hydrologic processes and mass-transport phenomena, including advection,hydrodynamic dispersion, adsorption, and radiological decay.

Rationale. The ability to simulate transport of contaminants in the aquifer system isthe main technical reason for the regional groundwater model. It is acknowledged by

many researchers that the transport of some contaminants in close proximity towaste sources or at local scales are subject to more complex transport phenomena,and other processes for which the linear sorption isotherm approach is inadequatemay be affecting contaminant mobility. These phenomena include

• reactive transport

• complexation

•

pH controls• volatilization

• occurrence of non-aqueous phase liquids

Technical understanding and techniques for simulating these processes are still amatter of scientific inquiry. As understanding of the processes themselves and

acceptance for techniques to model these processes grow, it is anticipated that themodel may be enhanced to include these techniques.

d. Hydrologic Boundaries

Requirement . The regional groundwater model shall be capable of evaluating thenear-term and long-term impacts of major lateral, upper, and lower hydrologic boundaries of the aquifer system.

Rationale. Consideration of all major hydrologic boundaries is critical to addressnear-term and long-term predictions of groundwater flow and contaminant transport.

e. Recharge

Requirement . The regional groundwater model shall consider all sources of

significant recharge to the aquifer system including

• artificial recharge to the unconfined aquifer system from past and currentoperations

• natural recharge from direct infiltration of precipitation falling across

• recharge from runoff that infiltrate the aquifer

Rationale. Artificial recharge to the aquifer system has and continues to havesignificant impact on water table conditions. As the transient effects of past artificialrecharge to the aquifer dissipate, the effect of natural recharge on flow conditions in

the aquifer will become more important. In addition to natural recharge from onsiteinfiltration, the aquifer receives recharge from infiltration of runoff and springdischarges originating in elevated regions offsite.




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f. Anticipated Future Flow Conditions

Requirement . The regional groundwater model shall be able to evaluate transientand steady state future flow conditions in the aquifer system.

Rationale. The future pumping requirements for irrigation, domestic and industrial purposes need to be assessed and the utilization plans need to be evolved so that thesustained use of ground water is possible without any damage to the quality ofground water. Usually the prediction of conditions for next 50-100 years is adopted.

g. Existing Chemical Contamination and Potential Future Transport

Requirement . The regional groundwater model shall be able to simulatecontaminant transport of a variety of chemical constituents. The regionalgroundwater model shall also be able to evaluate potential future releases of

chemical contaminants to the groundwater that may occur from a variety of wastesources.

Rationale. Monitoring of groundwater across site may reveal presence of a numberof contaminant plumes emanating from various operational areas. The extent ofmajor chemical constituents at levels above the primary concentration limits in theaquifer system needs to be analyzed.

h. Spatial and Temporal Scales of Analysis

Requirement . The regional groundwater model shall be able to support a variety of

spatial and temporal scales of analysis to adequately meet project-specific needs.

Rationale. Review of anticipated future applications of the site-wide groundwatermodel indicated that the model would need a variety of spatial and temporal scalesof analysis to adequately meet project-specific needs. The distribution of hydro-geologic data and the nature of the specific problem to be solved are both controlling

factors in determining the appropriate spatial and temporal scale for a groundwaterflow and transport model.

i. Configuration Control

Requirement . The regional groundwater model, including the databases supportingthe conceptual model and its numerical implementation, shall be maintained underconfiguration control.

Rationale. Since the regional groundwater model will provide the framework for allgroundwater modeling analysis performed on the site and a common site-wide

groundwater model database will be maintained containing all the informationnecessary, needs to be maintained. Such a database will contain




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• ·the basic geologic and hydrologic information that provides the basis for theconceptual model

• the key interpretations of geologic and hydrologic data and information,including descriptions of methods and approaches used to make interpretations.

The database and data interpretations will be updated, as new data, on both the local

and regional scale, become available. The modeling database should be stored in aform independent of the computer code used or the assumptions made for a particular modeling study. By storing high resolution, regularly gridded information,it is possible to use the model information at different scales (e.g., in sub-models) orwith different groundwater computer codes. This allows for use of the numerical

representation and computer code that is most appropriate for simulating the problem being considered. The database should include all information necessary todevelop parameter distributions based on geologic data (e.g., geometry of the mainhydro-geologic units), hydraulic property estimates, boundary conditions, initialconditions, locations and volumes of sources and sinks, and natural rechargeestimates.

The regional groundwater model must be a flexible and evolving platform foranalyzing groundwater flow and contaminant transport. As more data are collected,it is likely that the site-wide groundwater model must be a flexible and evolving platform for analyzing groundwater conceptual model of the groundwater system

will change, and new predictive capabilities will be desired and available. Theadopted model framework must be one in which new concepts can be tested and

enhancements readily included. The data used in the site-wide groundwater modelare stored in a geographic information system (GIS), which allows for easy dataretrieval, display and update. Collections of raw data (measured data) will bedescribed as databases, and interpretations will be described as information bases.

The configuration control system should make optimal use of existing site resources.Much of the data in use can be linked to ARC-INFO, a GIS, which allows for easydata retrieval, display and update. Because data continue to be gathered and becausenewly gathered data do not always fit the existing conceptual model, a continuous

effort is required to continually evaluate the data and refine the geologic and hydro-geologic conceptual models.

Any modeling applications that make simplifications to the conceptual model andmodeling database for use in their specific analyses should include adequate

documentation to demonstrate the consistency of their modeling assessment with theaccepted conceptual model. Such documentation may include a list of assumptions

made, their justification, and comparisons with simulation results based on the mostcomplete and complex conceptual model.




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j. Model Uncertainty

Requirement . The regional groundwater model will provide for explicitacknowledgement and estimation of uncertainty. A more specific requirement will be promulgated after additional evaluation of alternatives and methodologies for

addressing uncertainty have been proposed and evaluated.

Rationale. Ultimately, the regional groundwater model must embrace uncertainty.Implementation of an uncertainty framework with respect to the databases, modeland code will require a long commitment of resources and model development.

5. CASE STUDIES

Two recent studies carried out by IIT Madras, connected with ground waterassessment and modeling are briefly discussed below.

a. Effectiveness of percolation ponds

Recharging ground water is of very great significance because it providesreadymade storage reservoir free from evaporation and protected against pollutionand because replenishing ground water resources keeps neighboring saline watersfrom intruding into the aquifers and helps prevent land subsidence in a depleted

aquifer. It can also be used to reclaim wastewater. Rainwater harvesting can also beused for recharging ground water.

The selection of the methods for artificial recharging depends upon the hydrological

characteristics of aquifers; sediment contents in recharge waters, fluctuations inwater levels and rates of recharge in relation to water levels. Since there is limited

requisite data available there is a need for systematic investigations, research anddevelopment in this direction especially in the water deficit regions.

A study was taken up by IIT Madras to study the effectiveness of percolation ponds

in sustaining recharge of ground water. Two ponds one at Karthikeyapuram (at 4Km from Tirutani) and another one at Santhana Venu Gopalapuram (at 15 Km fromTirutani) were selected for detailed field study. However performance of one pond,Santhana Venu Gopalapuram (SVG Puram) pond, is discussed below:

This pond is in Pallipatu taluk of Chengalpattu district constructed during 1986 bythe Tamil Nadu Agricultural Engineering Department. This pond is constructedacross a nallah flowing from a mountain of an estimated catchments area of 100ha.Red soil is found in and around the pond with depth varying from 50 cm to sixmeters. In a reconnaissance survey conducted during the starting period of the project, only 16 wells were selected; as further detailed study was carried out,

another 12 wells were added. Hence a total 28 wells were observed. The wells are




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located at distances varying from 172 m to 840 m. the depths of wells vary from 7mto 16m.

The pond has a capacity of 0.01 Mm3 spreading over an area of 4521 m2, themaximum pond depth is 2.3 m. There are three rain gauge stations located near by,one at Ramakrishnarajupet, 3 km from the pond, the second one at Pallipatu nearly

20 km and the third one at Sholingur 10 km from the pond. All these are maintained by the Revenue Department. The maximum rainfall occurs during the Northeastmonsoon at an average of 500 mm to annual average of 1000mm. The maximumnumber of fillings that occurred during the study period is 3 per year. The studyshows that the potential infiltration rate is of 190mm/hour with basic infiltration rate

of 60mm/hr. Under this pond, the cropping pattern is of two crops mainly paddyfollowed by groundnut. Also flower plants are nursed, mainly (Lilly). During thefiled study, it was found that due to availability of sufficient water some farmers areswitching over to sugarcane also.

To assess the efficiency of the existing percolation pond systems two mathematical

models, namely lumped model and distributed models were developed. The zone ofinfluence is an ideal choice for defining the control volume. In the case of the percolation pond, this control volume is strictly a deformable one, in the sense thatthe zone of influence is a variable in space and time. In this study five differentapproaches were adopted to delineate the zone of influence, both spatially and

temporally. They are based on (I) water level variations (temporal), (ii) water levelcontours (spatial), (iii) water level profile (spatial), (iv) conductivity fluctuation

(temporal) and (v) conductivity contours (spatial). A water balance study was alsocarried out with the pond and without the pond effect, a gross additional quantity ofwater to the extent of three fold to four fold increase in the pump age is estimated asrealized due to the presence of the pond.

The two percolation ponds investigated indicate that they are contributingsubstantially by augmentation of the sub-surface water availability. The zone ofinfluence can be substantially different from a regular geometry such as a sector of a

circle. In Santhana Venu Gopalapuram (SVG Puram) the zone of influence is 800mfrom the pond out of which 400m lengths is strongly influenced. The wells closer in

the range of 400 to 500m get substantial contribution.

b. Modelling of salt water Intrusion

In the urban and agricultural areas bordering the seas, the coastal aquifers prove to be an important source of groundwater resource. It is seen that seawater is he mostcommon pollutant of freshwater in coastal aquifers. Seawater intrusion in freshwateraquifers generally results from the activities of man. If groundwater withdrawal ismoderate, no problems should arise. But once the groundwater is excessively

withdrawn, the quality of the water may deteriorate, dictating expensive remediesunless proper management is considered.




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One of the goals of coastal aquifer management is to maximize freshwater extractionwithout causing the invasion of saltwater into the wells. A number of managementquestions can be asked during such considerations. For existing wells, how shouldthe pumping rate be apportioned so as to achieve the maximum total extraction? Fornew wells, where should they be located? How can recharge wells and canals be

effectively used to protect pumping wells? How can we maximize the recovery percentage of recharged water? These and other questions may be answered usingthe mathematical tool of optimization.

Coastal aquifers that have their end boundaries in contact with sea or other saltwater bodies often get intruded by saltwater, as a result of over exploration, and due to

their various other activities of human beings. The main objective of the presentstudy is to evaluate the saltwater intrusion in the south Chennai Aquifer system,Tamilnadu, India. The main reason for the intrusion in this aquifer is due to overexploration of groundwater to meet various demands. The area is characterized by

an unconfined aquifer.

The water table contour reveals the zero M.S.L line gradually shifting inland duringthe successive years from 1996. There also exists a reverse hydraulic gradient incertain areas. The seawater intrusion is assessed by studying the water tablecontours and the water level fluctuation plots. These plots indicate that there is agradual reduction on water table in all the wells studied during successive years.

The seawater intrusion in the area is also validated by the chemical analysis of thegroundwater.

The exact location of the interface in the study area is determined with the help of an

existing numerical model, namely SHARP. It was observed that there is a heavyextraction of groundwater in the study area by various agencies. It is also seen that

the aquifer gets replenished to some extent immediately after the monsoon. Adetailed analysis of the water balance in the study area was also carried out. Thesubsurface outflows are calculated for various cross sections and the rate intrusionwith pumping was assessed. The study clearly reveals that there should not be any

increase in pumping from the aquifer.

6. FINAL REMARKS

There is some good news!. Population growth is slowing. Alternative and less

expensive sources of energy may reduce the cost of desalination. Advances in biotechnology will soon make it possible to grow food crops using less water.Evolving systems of governance may allow stakeholders greater influence over thechoice of investments. The important role of women in water management isrecognized and widely accepted. Remote sensing satellites and globalcommunications will help locate water and track rainfall for optimum use.




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The same technology will encourage sharing of best practices and has the potentialfor creasing solidarity around proposed solutions. Among water experts there is agrowing recognition that a ‘business as usual’ approach to managing this most precious resources is no longer tenable. Indeed, the so-called Dublin-Rio Principlesreflect a sea change in the way we seek to mange water. There are also widespread

calls for new water ‘ethic’. Not enough is known about the dynamics of waterdemand and supply to make long-term decisions. How will economic, social,demographic and scientific forces come together to affect water and what policiesand investments should be fashioned in response. In seeking answers to thesequestions we must also grapple with another, fundamental, query. That is, what kindof future do we want? As Glieck states in his recent book on water (Glieck, 1998)

“ Many different dreams and visions can be described. Without some positive vision,without some thought about truly sustainable water use means, society riskscontinuing on a path that will take us further and further in the wrong direction. We

can choose a different path and try to define and attain a different future. But wemust make that choice soon”.

It may also be noted that the development of groundwater models provided tools forintegrating al the available data together and for evaluation of the response of the physical system when subjected to changes in conditions and external stresses.However, it has to be realized that the hydrologist, hydro geologist or

geohydrologist has to work with a very heterogeneous and anisotropic system at thefiled scale.

REFERENCES

Anderson, M.P., (1995), "Groundwater modeling in the 21 st

Century, Groundwater Models for Resources Analysis and management" Aly I.EL-Kadi, Ed., LewisPublishers, London, pp. 79-93.

Dagan, G. and S.P. Neuman, (1997). "Subsurface Flow and Transport" :A Stochastic Approach Cambridge Univ. Press.

Dowdeswell, E. (1998). "where peaceful water flow" water International, 23 (1998),

13-16.

Glieck, P. (1998). “Moving toward a sustainable vision for the Earth’s fresh water”.

In Gleick, The world’s water: 1998:1999. Washington Dc: Island Press.

Todd, D.K. (1995). "Groundwater Hydrology," 2nd edition, John Wiley and Sons,Singapore.

Mann, F. M. and D. A. Myers. (1998). "Computer Code Selection Criteria for Flow

and Transport Code(s) to be used in Undisturbed Vadose Zone Calculations forTWRS Environmental Analyses" . (HNF-1839,Rev. B). Lockheed-Martin HanfordCompany, Richland, Washington.





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Overview of Groundwater Models

A. Balasubramanian

Abstract

Groundwater models are mathematical and digital tools of analysing and predicting the behavior of aquifer systems on local and regional scale,under varying geological environments. Groundwater modelling has alsobecome a widely used environmental tool, since the development of digitalcomputers and appropriate numerical models during 1960-1990's. Thesemodels solve the basic partial differential equations that govern the flow of

groundwater and solute transport through the saturated and unsaturated porous medium. Models solve the equations analytically for simple geometric problems and applies numerical simulation to solve the

equations of more complex hydrogeological problems involving aquiferheterogeneities, anisotropic aquifer properties and complicated boundary

conditions. Many references describe the development of the governingequations and methods of solution in detail. Groundwater models are of several categories developed for specific purposes. Flow and solutetransport problems vary in 2 or 3 dimensions. The solution strategies mayadopt techniques like finite difference, finite element and integrated finitedifference approaches. Models can handle single or multiple fluid

properties. The development of a model requires the definition andmanipulation of many physical parameters (e.g., aquifer characteristics)and time varying inflow and outflow data. The choice of a modeldetermines the nature and quantity of the output information required.

Groundwater modelling requires the following domain specific

information: physical units, model domain hydrologic conditions, aquifer parameters , time varying inputs and boundary conditions. Detailed reviewof modelling approaches has been made by several workers. This paperreviews and highlights the applications of various groundwater models.

Keywords : Mathematical models, Groundwater, Analytical, Numericalsolutions.




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1. INTRODUCTION

The quantitative occurrence, flow and qualitative availability of groundwaterresources in different aquifer systems( coastal, hard-rock, arid, semi-arid,etc) arecontrolled by the local or regional physiographic, hydrological and subsurface

geological conditions and man-made influences over the aquifers. Aquifer parameters and quantities of recharge and discharge play a significant role ingroundwater resources evaluation and development. Most of these parameters varywith reference to space and time. The flow and occurrence of groundwater aregoverned by several numerical principles and site-specific hydrogeology.Mathematical models are based on the real hydrogeologic properties of the idealised

aquifer. Groundwater models are mathematical and digital tools of analysing and predicting the behavior of aquifer systems on local and regional scale, under varyinggeological environments. Groundwater modelling has also become a widely usedenvironmental tool, since the development of digital computers and appropriate

numerical models during 1960-1990's.

Groundwater models are constructed using these parameters for solving many field problems, predicting the aquifers’ response to the imposed stress or strain, and forevolving the appropriate water management strategies. The perfect analysis of anaquifer environment and its processes depend on one of the following four aspectsand the method of modelling:

1. Analysis pertaining to groundwater occurrence and flow, sources of

recharge - discharge and their impacts( Single phase or multi-phase; steady

or transient groundwater flow models)2. Analysis of the dispersal, mobility and distribution of solutes(

contaminants) in the groundwater systems( Chemical mass or solute; steadyor transient transport models)

3. Analysis of the mechanisms of rock-water geochemical interactionscontrolling the distribution of solute species( Aqueous geochemicalmodels) and the

4. Analysis of salinity intrusions in the complex coastal ecosystems(saltwaterintrusion ; steady or transient; sharp or dispersed interface models).

Each one of these, require careful application of unique numerical principles,typical databases and complicated solution strategies. Despite the limitations,

attempts have been made so far by several eminent workers in using themathematical models for various field and laboratory applications. This paper presents an overview of the groundwater flow models and their applications.

1.1 State of the art of modelling:

Mathematical modelling involves four basic steps namely (i) formulation, (ii)approximation and transformation (iii) computation and (iv) application.




19

Formulation: Formulation refers to the process of deriving or selecting the basicequation (s) governing the flow and solute transport of groundwater, with thedomain specification and initial boundary conditions.

Approximation: Approximation refers to the selection of a numerical method whichcan be used to solve the system of algebraic equations. Finite Difference, Finiteelement and Integrated Finite difference (IFD), methods are the widely used solutionstrategies for modelling the groundwater systems.

Computation: Computation is the most important step in the process of modelling.

This part refers to the process of obtaining a solution to a large number ofdifferential equations. This is done using a digital computer and a method of codingthe steps, in a computer programming language.

Application: The application part of groundwater modelling includes calibration orhistory matching of the observed and simulated heads, sensitivity analysis and

prediction, sensitivity tests are to show how the model reacts to various extremevalues of transmissivity, storage coefficient and recharge/discharge volumes.

1.2 Groundwater flow models:

Walton (1962) presented the analytical methods of aquifer evaluation which formedthe basis for all the later orientations towards the numerical approaches. Prickett

(1975) gave a comprehensive outlook on the modelling techniques for groundwater

evaluation by properly explaining the equations of flow, given an overview of thetypes of analog and numerical models used prior to 1975 .

It has been understood that the occurrence and flow of groundwater in a non-homogeneous anisotropic aquifer system can be represented by the following

partial difference equations, applicable for two-or three- dimensions(x,y &z):

Two-dimensional case:

d (Tx - dh) + d (Ty dh) = S dh + w(x,y,t)

dx dx dy dy dy

Three-dimensional case:

d (Tx - dh) + d (Ty dh) + d (Tz dh) = S dh + w(x,y,z, t)dx dx dy dy dz dz dy

whereTx , Ty and Tz = Transmissivity tensors in X , Y and Z co ordinates (L2/T)

S = Approximate storage Coefficienth = Hydraulic head

t = time increments andw = fraction of recharge or discharge (L/T) with reference to space and time




20

These equations can not be solved directly. They can be solved through finitedifference or finite element approaches. Rushton and Redshaw (1979) explains thesolution strategies of solving these equations in two dimensions.

2. DATA REQUIREMENTS FOR MODELLING

There are several aquifer parameters which are of much use in modelling studies.Groundwater modelling requires the basic information pertaining to physical units,model domain, aquifer parameters, time varying inputs, and boundary conditions.The sets of hydrogeological data required for any type of modelling are:

a. Geomorphology- Topography - (Watershed/Basin/District/block ) –Basin Boundary Drainage - River Course, Canals (Lined/Unlined) – Channel MorphologySurface Water Bodies - Reservoirs - Rainfed Tanks/ Ponds/Cess Pools / Lakes /Estuaries / Impoundments / Landuse/Land Cover/Soil/Vegetation/Developmental Features

b. Hydrometeorology -- Rainfall - Pattern - Point measurements - Long termRecords - (Polygon / Isohyets) -Specified intervals/ Evapotranspiration - Pointmeasurements - Areal distribution - Surface Runoff - Volumes - Specified intervals

– Soil thickness - Types - Moisture – Point measurements - Infiltration rate ofSoils - Point measurements

c. Hydrogeology-- Geology and structures - boundaries - variations - Aquifer types – boundaries/geometry – weathered / fractured / lateritic / volcanic / alluvial

/coastal/ Aquifer thickness - areal distribution - depth to the basement (bedrock)/Distribution of deep/shallow fractures/ Water table elevation - long term records -closed network Aquifer parameters - point measurements - areal distribution - /(transmissivity (sp.yield) Confining/leaky layers - physical frame work andcharacteristics/ Source of seepage/recharge - flow rates (irrigated open areas -

Location of recharge basins/wells/ Sinks - location of wells - pumping rates/shedules - spatial and time variant data

d. Others-- Consumption Pattern - Changes In Space/Time / Environmental Factors- Quality

3. APPLICATIONS

Groundwater flow models can provide valuable directions in solving specific problems like:

• Groundwater balance estimation- assessment of regional inflow and

outflow patterns of groundwater , surface waters within and fromneighboring reservoirs

• Well withdrawals-prediction of effects of groundwater withdrawals overthe piezometric head levels and stream flow discharge; assessment of safe




21

yield; prediction and movement of saline water interface; prediction ofeffects of scattered groundwater withdrawal for irrigation;

• Changes in aquifer recharge- prediction of effects of urbanization; prediction of changes resulting from irrigation return f low and canalleakage; analysis of long-term climatologically related trends in

piezometric levels and separation of man induced changes.

• Parameter estimation- determination of regional distribution of thehydraulic parameters (inverse modelling).

• Planning of field investigations- rationalization of data collectionrequirements by identifying the measurements most needed

•Prediction of seepage velocities for subsequent use in transports modelling.

• Groundwater management- estimation of optimal yield of basins for thedevelopment of groundwater resources using the concepts of conjunctive

and consumptive usage.

4. GEOCHEMICAL MODELLING

Geochemical modelling attempts to interpret and predict the chemical reactions of

minerals, gases and organic matter with aqueous solutions in real or hypotheticalwater-rock systems have been attempted by many. It can also help to identify

geochemical processes that regulate the concentration of dissolved constituents andmay help to quantify the effects of temperature, speciation, sorption and solubilityon the concentrations of dissolved constituents. Geochemical models can be utilized

in sensitivity analysis mode to assist in assigning priorities among additionalchemical characterizations of water from field to laboratory studies. The approachincludes the calculation of the degree of saturation of an aqueous media with regardto both meta stable and equilibrium solids. The advent of digital computers allowedthe development of a lot of sophisticated geochemical models for describing and

predicting the chemical behaviour of complex natural waters. More than 50 suchmodels have been developed and are available in literature. Much of the impetus forthe development of geochemical computer models comes from the need to protectthe chemical quality of groundwater, and from a search for safe methods of geologicdisposal of nuclear wastes.

5. SIMULATION OF SALTWATER ENCROACHMENT IN COASTAL

AQUIFERS

Coastal aquifers are an important resource for urban and agricultural development inareas bordering seas and oceans. Coastal hydrogeological conditions can be simplyrepresented by an unconfined, island or confined aquifer. In coastal zones,

freshwater body will overlie the saltwater body because the unit weight offreshwater (1 gm/ml) is less than that of saltwater (1.022 to 1.031 gm/ml). The

boundary surface between the two types of water is known as the saltwater-freshwater interface or the interface. The hydrodynamic balance of the fluids




22

governs the shape and movement of the interface. If the coastal zone consists of twoor more distinct layers, each aquifer will have an independent interface. Successfulinvestigations have enabled the control of this hydrodynamic balance. Thetransition from fresh to saltwater is not a sharp one due to the effects of mechanicaldispersion.

Cooper (1959) and Kohout (1964) have shown that in the zone of mixing, thediluted seawater is less dense than the original seawater, causing it to rise and moveseaward along this interface. This involves a cyclic flow of saltwater from the seathrough the ocean floor, to the zone of mixing and back to the sea. This cyclic flowoccurs even under steady-state conditions. Due to pumping of fresh groundwater,

the natural equilibrium is disturbed and the saltwater moves inland until a newequilibrium is established. Conversely, an increase in freshwater flow pushes theinterface seaward. The location, shape and extent of the diffused zone depend uponseveral factors including (1) the relative densities of fresh and saltwater, (2) the rate

of discharge of groundwater, and (3) the dispersion and hydraulic parameters of theaquifer. An integrated study involving geophysical and hydrogeochemical

techniques can give a clear picture about the spatial disposition of the two zones. Asystematic hydrogeological study can show the movement of this interface in spaceand time.

6. MATHEMATICAL MODELS

Mathematical models are an attempt to represent certain processes by mathematicalequations. In the case of contaminant transport, a number of diverse and

complicated processes like advection, diffusion and dispersion are involved.Various numerical models have been used in the past to predict the location of the

saltwater interface for a given set of hydrologic conditions. These models,depending upon the way they treat the interface, are broadly classified into 2 types,namely sharp (abrupt) interface models and diffuse (disperse) interface models. Thecommon solution strategies adopted in these models are finite-difference, finite-

element, and boundary integral methods, using either Ghyben-Herzberg principle orDupuit approximation.

The diffuse interface approach explicitly represents the transition zone, where thereis mixing of freshwater and saltwater due to the effects of hydrodynamic dispersion

(molecular diffusion and mechanical dispersion). The sharp interface approachsimplifies the analysis by assuming that freshwater and saltwater do not mix and arerepresented by an abrupt interface. Both approaches have been used to developnumerical models to study and predict the flow of groundwater in coastal aquifers.These type of models consider two fluid or only the saltwater. Further the modelscan also be based on dispersed interface approaches. Seawater intrusion models can

also be classified as non-density dependent and density dependent models.




23

7. DISCUSSION OF APPROACHES

Each of these approaches has advantages and limitations and can be successfullyemployed only under appropriate conditions. The dispersed interface approach isnecessary in areas where the transition zone is wide. Density effects can beneglected when chloride concentration gradients are low and the governing

equations can be solved areally on a basin-wide scale. However, when the flow isdensity-dependent, the vertical dimension must be included. Volker and Rushton(1982) compared steady-state solutions for both the dispersed interface and sharpinterface approaches and showed that as the coefficient of hydrodynamic dispersiondecreases, the two solutions approach each other. Volker and Young (1979)

compared the applications of boundary integral and finite-element methods for freesurface flows in porous media, including the saltwater intrusion in aquifers.

The choice of the approach used to model a particular system will depend on the

nature of the system as well as the goals of the modelling effort. The sharp interfaceapproach can represent the overall flow characteristics of the system, but does not

give details concerning the nature of the transition zone. When studying an aquifersystem, it is important first to understand its overall behaviour before examiningsmaller scale effects. Therefore, the ideal characterization of such systems mayinvolve a two-step process integrating the sharp interface and dispersed interfacemodelling approaches.

8. CONCLUSION

Modelling is a digital tool used for predictive and management simulations ofaquifer environments. Models are unique in their applications. All models havecertain assumptions. This paper enumerates the simple and applicable models for

various ecosystems. The database requirement is also highlighted. Due to enormousnumber of references (more than the pages of this paper), the reader is requested tocontact the author for the detailed bibliography.

REFERENCES:

Prickett, T.A. (1975), " Modelling techniques for groundwater evaluation", InAdvances in hydroscience, Vol.10 ed., V.T. Chow, New York : Academic press.

Walton, W.C (1962), "Groundwater Resources Evaluation" . Mcgraw-Hill, New

York.

Rushton.K.R and Redshaw.S.C (1979). “Seepage and groundwater flow”. John

Wiley and Sons Ltd. NY 330 pp.

Cooper, H. H. Jr., 1959. " A hypothesis concerning the dynamic balance of freshwater and saltwater in a coastal aquifer :" Journal of Geophysics Research,v. 64, no. 4, p. 461-467.




24

Volker, R.E. and K.R. Rushton, 1982. " An assessment of the importance of someparameters for seawater intrusion in aquifers and a comparison of dispersiveand sharpinterface modelling approaches:" Journal of Hydrology, v. 56, p. 239 -250.

Kohout, F.A., 1964, "The flow of freshwater and salt water in the Biscayneaquifer ofthe Miami area," Florida:U.S. Geological Survey Water-SupplyPaper 1613–C, p.C12–C32.





25

Artificial Recharging of Ground Water Aquifers and

Groundwater Modelling in the Context of

Basin Water Management

R. Sakthivadivel

Abstract

Ground water as a source of supply for meeting the rapidly expanding urban,industrial and agricultural water requirements has received a major boost in itsdevelopment and utilization in the recent past, creating some negative externalities

such as rapid ground water decline. This rapid depletion of ground water has given rise to artificial recharging of ground water aquifers, which has off-siteimplications in the basin context. This paper describes different types of recharges, provides a classification of several ground water recharge estimation techniques,argues the need for ground water recharge estimation and modelling in the basincontext and discusses three types of simple models used for ground water

estimation and managing the ground water aquifers. The importance of simple andcost-effective models for practicing professionals and the need for reliable database for modelling exercise are highlighted.

Keywords : Artificial recharging, Groundwater, groundwater models.

1. INTRODUCTION

One third of world’s land surface has been classified as arid or semi-arid.

Approximately half the countries of globe are directly affected in someway by

problems of aridity. Easily developed land and water resources have in largemeasures already been developed and attention is thus increasingly towards morearid region for human survival. However, soil and water resources of arid and semi-

arid regions are limited, often being in a delicate environmental balance. Surfacewater supplies are normally critically unreliable, poorly distributed and subject tohigh evaporation losses. For the rapidly expanding urban, industrial and agriculturalwater requirements, ground water has assumed greater significance.




26

Ground water as a source of supply for meeting the above needs has received amajor boost in the recent past as ground water development schemes require lowinvestments, have a short gestation period, and the resource is directly under thecontrol of users. Moreover, ground water development has been phenomenalespecially after the advent of electrical and diesel abstraction machines. The two

most populous countries:China and India are facing a huge water crisis and are overexploiting their ground water resources.

In China, according to historical records, during 1950s and 1960s, Fuyang river inHebei province was an important shipping channel. In contrast, from 1990 onwards,the river had over 300 dry days annually. The outflow from the basin dramatically

decreased from the late 1970s to less than 100 Mm3 of annual flow with no outflowin 1997. The basin has become a closed basin for all practical purposes

Fig. 1: Variations of discharge measured at Aixinzhuang

Hydrology Station from 1957 to 1998

In Fuyang, ground water accounts for 80 percent of supply. As a consciousallocation decision, water managers of Fuyang have allowed cities and industries

first priority on reservoir water, and hence supported farmers in their efforts to tapground water. Ground water overdraft led to a dramatic drop of ground water level,

especially in the recent two decades. The ground water table dropped at a rate of0.68m/ year for the county located at the upstream and at a rate exceeding 1m/year

for the middle and downstream counties.




27

Fig. 2: Variations of groundwater depth from the surface, 1980 to 1998,

Jiuzhou Station, Renxian County, Hebei Province

In India, there are about 10 million tube wells in the country, which were only a fewthousand in 1961-62. With the increasing number of wells, the consumption of electricity

by these abstraction devices also increased. In 1994-95, consumption of electricity inagricultural sector was 30.54 percent of total electricity consumption amounting to 79300

GWH, which was mostly consumed by 10.72 million electric pump sets. Similarly, billionsof liters of diesel oil per year are consumed by diesel pump sets installed for lifting waterthrough tube wells. In its development stride with focus on irrigated agriculture usingground water, India has successfully staged a comeback from a country at the verge of

famine in 1950’s to that of a food self sufficient one in the 90’s with a proviso even toexport some food grains to other countries. These gains have mainly come from increasingthe irrigated area from 22.6 m.ha in 1951 to about 90 m.ha in 1995-96 with more than 60 percent increase in irrigated area from unorganized groundwater development by privatesector. While ground water development has increased the productivity of land by as much

as 200 percent or more from that of surface water irrigation, it has also brought with it somenegative externalities such as rapid ground water decline, increase in pumping cost anddeterioration of ground water quality. The alarming rate of ground water decline (1 to 2 m per year) in pockets of north western, western and southern regions of the country and its

impact on agricultural productivity and profitability has sounded an alarming bell for policymakers and stakeholders to reappraise the ground water development and management.

While the Government has recognized the importance of ground water development forincreasing the agricultural production to meet the challenging demand for food for burgeoning population in the next two to three decades, its focus on managing the groundwater resources in a sustainable way has not been commensurate with the gravity of problems that India faces at this moment.




28

2. RAIN WATER HARVESTING AND RECHARGING IN INDIA

While this is the situation at government and policy making level, there is plethoraof activities going on at the local levels with respect to rainwater harvesting andrecharging the aquifers. In States such as Gujarat, Rajasthan and Madhya Pradesh ,

after the recent droughts in 1999 and 2000, there are increased level of waterharvesting and recharging activities where the government is also trying to provideassistance to carry out these activities. A quick survey of these activities indicates:

• Water harvesting at village level or at micro-watershed level seems to besporadic activity not coordinated well at the watershed level;

•

People based on their perception and understanding have implemented theseactivities without much of integrated planning and coordination;

• These unplanned development have lead to interference among structures,

resulted in costly harnessing structures and conflict among stakeholders;

• No guidelines exist for systematic planning, investigation, selection ofstructures, minimization of cost of construction, operation and maintenance,

monitoring and conflict resolution.

• Water harvesting has been considered as a separate activity without muchrelation to watershed level resource development and management and without

much consideration to off-site impacts.

In the present scenario of haphazard development of recharge structures a number ofquestions such as the following remain unanswered:

• How much of water harvested gets recharged and percentage of it is extractedout? What is the productivity of extracted water?

• When a farmer recharges through a well, how does a free rider prevented fromusing that water?

• What type of water harvesting and recharge structures is used at a village level?

Are these patterns same or are they differ? If differs why?

• What kind of organization at village level exists for implementation andmonitoring of these activities?

• What kind of modelling efforts are attempted to develop strategies and policies

for recharge activities?

• What are the key characteristics which prompt individual farmers or group offarmers to undertake water harnessing activities? How do they decide aboutlocation, type of structure, method of construction and operation and costsharing?

• What kind of planning and technical considerations go into it beforeconstruction and operation?

• Who are the people really benefited by installing these structures? How are poor, landless and women are affected/benefited by water harvesting activities?




29

3. GROUND WATER RECHARGE

Groundwater recharge may be defined in a general sense as the downward flow ofwater reaching the water table, forming an addition to the ground water reservoir.Recharge of ground water may occur naturally from precipitation, rivers, canals,

drains and lakes and as man-induced phenomenon via such activities as irrigationand pumping regulations.

Three basic types of recharge are recognized, categorized here (Figure 3: SchematicDiagram of the hydrological Processes involved in Runoff, natural, indirect andartificial recharges and its conjunctive management) as direct, indirect, and man-

induced (artificial):

• Direct recharge is defined as water added to the ground water reservoir in

excess of soil moisture deficit and evapotranspiration, by direct vertical percolation of precipitation through the unsaturated zone.

• Indirect recharge results from percolation to the water table following runoff,

flood out and localization in ponding in low lying areas or through the beds ofwater courses.

• Man induced recharge is the percolation of water conserved from rainfall or

transported through ponding, spreading such as irrigation ,and injecting throughtube wells etc.,This is also called artificial recharge.

A major difficulty in arid areas is that although basic recharge mechanisms are

reasonably well known, deficiencies are evident in quantifying the various elements.Although direct recharge is known to be of decreasing significance with increasingaridity, the processes involved are conceptually the easiest to define and form the basis of numerous recharge estimation techniques currently in common use.Assuming a dominate vertical moisture flux ,a single porous medium and a watertable which is not close to the surface, water is postulated to move by Darcian flowin the unsaturated zone to the ground water body. However, field experiments show

that volumetric water content and flow mechanisms in the unsaturated zone vary in acomplex manner, the main problem being that the parameters, moisture content,matrix potential, and hydraulic conductivity are sensitively interrelated. Further,material in the unsaturated zone rarely displays homogeneous properties, oftenconsisting of layered sands, silt, and clays with widely varying saturated hydraulic

conductivities, and a strong potential for lateral rather than vertical flow above

lithological discontinuities. In short, quantification of ground water recharge isfraught with problems of varying magnitude and hence substantial uncertainties.

Variations in ground water recharge with time and in space (both laterally andvertically) are well documented and are consequences of such factors as differing

precipitation, soil characteristics, vegetation, land use and topography.



2 5

P p o m S o

I n j e c t i o n

r e c h a r e

S p r e a d i n g

r e c h a r e

P o n d i n g

r e c h a r g e

A t m o s p h

e r i c f a c t o r s

f o r c i n e v a o r a t i o n

E v a p o r a t i o n a n d

t r a n s

i r a t i o n

P r e c i p i t a t i o n

I n t e r c e p t i o n

I n f i l t r a

t i o n

O v e r l a n d

f l o w

S t r e a m

f l o w

S o i l w a t e

r

I n t e r f l o w

P e r c o l a t i o n

G r o u n d

W a t e r

B a s e f l o w

T r a n s m i s s i o n

l o s s e s &

f l o o d o u t

S h e e t - r u n o

f f

L o c a l i z e d

p o n d i n g

V e r t i c a l

i n f i l t r a t i o n

o i n t s &

c r a c k f l o w

L a t e r a l a n d

v e r t i c a l


I n d i r e c t

r e c h a r g e

V e r t i c a l


I n d i r e c t r e c h a r g e

I n d i r e c t r e c h a r g e

W a t e r t r a n s p o r t e d f o r

r e c h .

S u r f a c e w a t e r

s t o r a e

E v a p o r a t i o n

a n d

t r a n s p i r a t i o n

I n f i l t r a t i o n

S o i l w a t e r

W a t e r d i v e r t e d

f o r r e c h a r g e

P e r c o l a t i o n

G r o u n d w a t e r

B a l a n c e

s t r e a m f l o w

D o w n s t r e a m

i m p a c t

C o n j u n c . M a n a g .

O f G W

w i t h

o t h e r s o u r c e s

G W

i n s t i t u t i o n

G W

m o n i t o r i

n g

I n c r e a s i n g

p r o d u c t i v i t y o f

w a t e r

S u s t a i n i

n g G W

r e g i m e

M a i n t a i n i n g

w a t e r

q u a l i t y

P r e v e n t i n g

H y d .

d r o u g h t

N A T U R A L R E C H A R G E

I N D I R E C T R E C H A R G E

A R T I F I C I A L R E C H A R G E

S c h e m a t i c D i a g r a m o f t h e h y d r o l o g i c a l P r o c e s s e s i n v o l v e d i n R u n o f f , n a t u r a l , i n d i r e c t a n d a r t i f i c i a l r e c h a r g e s a n d i t s c o n

j u n c t i v e m a n a g e m e n t




31

Given the variability, the obviously interrelated question is what techniques should be usedto derive reliable recharge estimates. Table 1 gives classification of several ground waterrecharge estimation techniques according to result resolution in time and space:

Time Scale

Estimation Technique Instataneous

Event Monthly

Seasonal Annual Longterm

averages

A) Point recharge

value

-direct measurement

(Lysimeter)-soil moisture balance-Darcian models

(unsaturated)-Tracers in

unsaturated zone

B) Areally

Integrated net

Recharge values

-Ground waterchloride balance

-Ground water Flow

Equation-Ground waterFluctuation

-Spring Discharge-Hydrograph

Separation-Catchment Water

balance-Conceptual

Catchment Models

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

4 NEED FOR GROUND WATER MODELS IN THE BASIN CONTEXT

Water scarcity in many countries has become endemic. Many river basins are

becoming closed or closing* In such basins, additional water conservation atupstream point affects the downstream people who are already using that water. The off -site effect of water conservation has both economic and environmental consequences in

*In open basins, more water could be developed and beneficially depleted upstream without diminishing existing uses: in other words, the

opportunity cost of additional depletion is zero. A closing basin has no more remaining available water flowing out of the basin during part of the

year, typically a dry season. In a completely closed basin, all water is committed to environmental and process uses.




32

addition to hydrologic impacts. Therefore, any water conservation such as artificial rechargeshould be viewed in the basin context In this case regional model such as basin models play asignificant role in guiding the policy makers where to encourage ground water recharging and

where to prevent going for artificial recharging which will affect the downstream people.Haphazard development of recharging that is going on in many states in India will bring inlarge conflicts between upstream and downstream stakeholders. Clear water rights are to be put in place, enforced and monitored Hydro-economic conjunctive management models will play a crucial role in the years to come in better managing the river basins.

5. GROUND WATER MODELS

In this section, I will present the following three types of models currently developed and

used for estimating ground water recharge and managing the aquifer systems:1. Ground water balance model,2. Ground water chloride balance model, and

3. Finite difference ground water simulation model.

A spatially distributed water balance model that can be used to estimate the time series andspatial distribution of ground water recharge in semi-arid conditions, developed by the

Institute of Water Studies, Wallingford, U.K. is presented (Finch,1999).Water balance models have the following advantages:

• They use readily available meteorological data as the primary source of data.

• They are capable of providing arieal estimates.

• They are capable of predicting the impact of change, e.g., of land cover.The main potential disadvantage of these models is that they rely on mass balance and sothe recharge estimate is a result of subtracting all other losses of water from the rainfall with

the result that errors tend to accumulate into the estimates of recharge.Direct Recharge is calculated using a simple daily water balance equation

Fig. 4: Schematic Diagram of the hydrological Processes involved in Runoff,

natural, indirect and artificial recharges and its conjunctive management

B+DS=P-Ea- I- Ro-RiWhere P= rainfall (mm),

Ea= actual evapotranspiration (mm),I= interception loss (mm),




33

Ro= surface runoff (mm),Ri= interflow (mm),B= bypass flow (mm),

DS= change in soil water content (mm).

Recharge is the sum of the bypass flow and positive values of the changes in soilwater content, once the soil water content exceeds the water content of the soil atwhich drainage can occur ( field capacity).

The model consists of several sub models dealing with interception, overland flow,interflow, evaporation from vegetation and soil, soil moisture and transfer throughthe unsaturated zone The model uses a 2- dimensional rectangular grid of cells torepresent the spatial variability of the land surface and is best used for conditions

where vertical drainage is dominant over horizontal processes in the soils.

Fig. 5: Schematic representation of the sub-models forming the water balance model

RAINFALL

RECHARGE

CANOPYINCEPTION

EVAPORATION

SOIL-VEGETATION

EVAPORATION

SOIL MOISTURE

UNSATURATED ZONE

OVERLAND FLOW

INTERFLOW

SOIL STORE BYPASS

RUNOFF




34

The minimum data required by the model are:1. Time series of rainfall from rain gauges.2. Time series of meteorological data from weather stations.

3. A map of aquifer outcrop areas.4. A map of the soil types.5. A map of the land cover classes.6. A topogarphical map

Additional data that will improve the accuracy of the model predictions are:-measurement of the soil hydraulic properties,-measurements of the land cover physical properties,

-measurements of the aquifer unsaturated zone response function.

The model was tested at the site of HAPEX-SAHEL experiment (13-o14.63N: 2-

o

14.65E) in Niger.The area has not been cropped sine 1986 allowing the naturalsavannah vegetation to regenerate. Soils at the site are very sandy, approximately 2to 3 m deep and underlain by a hard laterite. The water table is at a depth ofapproximately 32 m. Table 2 gives the annual water balance predicted by the model.

Table 2: Annual Water Balance Predicted by the Model

Year Rainfall(mm)

PotentialEvaporation(mm)

Actual

Evaporation(mm)

Recharge(mm)

1992 706 1754 614 89

1993 545 1843 554 0

1994 650 1770 583 61Mean 633 1789 584 50

Fig. 6: Observed and modelled soil water contents for Niger




35

5.1 Ground Water Chloride Balance Model

Physical approaches have traditionally been more widely used than tracer

techniques. In semi-arid regions, however, there is acceptance of the limitations ofthe physical approaches and tracer techniques are becoming more widely used. Ofthe three possible tracer methods( tritium, stable isotopes, and chloride) the use ofchloride proves especially attractive as a low –cost tracer for recharge estimation.

For a catchment area the most basic approach for using cl is through the water

balance equation:

P=E+R+QWhere P= precipitation amount,

E= evaporation,R= recharge to ground water

Q= runoff to stream.

If we assume cl is neither gained nor lost via weathering, and that anthropogenicinputs are zero, we can include cl concentration in the above equation:P. cl pptn = E. cl evap + R.cl rec + Q.clroff

Where Cl pptn= chloride concentration in precipitationCl evap= chloride concentration in evaporationCl rec = chloride concentration in recharge to ground waterCl roff = chloride concentration in run off

Assuming no significant clroff removed via evapotranspiration and clroff is equal tocl pptn, the above equation can be reduced to: R= ( P-Q)*(Cl pptn/Clrec) ----(1)

for Romwe catchment in Zimbabwe (MacDonald,1999). This gives the totaldeposition of chloride for each of the three seasons in which samples were taken.

The rainfall chloride concentrations in three years are: 0.78; 1.39; and 0.68 mg/lrespectively, giving an averaged chloride concentration in rainfall of 1mg/l over theseason. To calculate the mass of chloride entering the ground, we must know theeffective rainfall (rainfall-surface runoff) and the spatially averaged ground waterconcentration. Then using Equation (1),we can compute the mean ground waterrecharge. The mean ground water recharge computed for the Romwe catchment in

Zimbabwe is shown in Table 3.

Table 3: Calculation of ground water Recharge in the Romwe Catchment

Aquifer Effectiverainfall

(mm)

Mass chlorideentering

ground (mg)

Ave.Groundchloride

concentration(mg/l).

Mean Ground

waterRecharge(mm)

Melanocratic 548 548 19 29

Leucocratic 390 390 68 6




36

Fig. 7 : Cumulative fractional chloride mass in rainfall versus cumulative

rainfall from a raingauge in the Romwe catchment for dry seasons 1993/94,

1994/95 and 1995/96 (missing data for the period February to April 1994 has

been estimated using daily volume, chloride concentration rations for the

rainfall from the rest of the 1994/95 wet season)

5.2 Finite Difference Ground Water Simulation Model

Ground water models are used to understand the behavior of ground water regimesand predict response of aquifer to any external changes such as extraction, rechargeetc., The model can also be used to select the best management plan for a ground

water basin.

Dr Sondhi et al from Punjab Agricultural University, Ludhiana, have applied water balance analysis and finite difference ground water simulation models for falling andraising ground water regions of the state of Punjab to assess the ground waterresources and plan the management strategies for its exploitation on sustainable

basis.

Digital simulation model developed by Pricket and Lonquist (1971) was used forground water simulation and management. The impact of crop diversification on the

ground water behavior was studied by shifting 5,10,20 and 30 percent paddy areawith cotton, maize, and groundnut in the ratio of 3:1:1 respectively. It was found

after reducing the paddy area the area under falling water table condition hasdiminished. The area under depth range of 10 to 15m diminished from 48% to 40 %

when the paddy area was reduced to 30%.

The authors have also developed an integrated simulation-optimization model byembedding finite difference form of linear algebraic equations of groundwater flowmodel (MODFLOW) as constraints in linear programming formulation for optimalmanagement of ground water resources. The objective was to maximize pumpageover the whole tract and to study the impact of management alternatives on water




37

table depth. The studies show that it is possible to arrest the rising trend of watertable depth in south west Punjab by seasonal and inter-seasonal redistribution ofcanal water releases and enhancing the ground water pumpage by74% during karif

and 135 percent during rabi from existing level.

6. CONCLUDING REMARKS

Advent of fast computing techniques together with availability of large scale storagefacilities in PC’s, availability of less costly remote sensed data with acceptable

resolution and shorter turnaround time, introduction of new tools such asGeographical Information System (GIS) and digital elevation model (DEM) and public domain data available through Internet have all helped to develop and useground water models of complex and sophisticated nature having regional andglobal character. These developments augur a good sign to understand the regionaland basin level variability of ground water situations. Once the global picture and

trends are identified, then one can use a more refined methodology to track down thevariables to acceptable level of accuracy at a local scale such as an irrigation systemor sub-system level underlain with an aquifer.

As models become sophisticated, the data requirement also increases. In many

situations, we do not have adequate data making us to go for simple models.Selection of model to achieve an objective is an art by itself. Some time simple, andcost effective models would provide the necessary answer, avoiding the need to gofor complicated models. Developing such simple and cost effective models require

great skill and understanding of the problem being attempted to solve throughmodelling.

Simple water balance models such as the ones referred in this paper are needed toestimate the basin recharge before we take up complicated regional level models tomanage groundwater aquifers in the basin context. Such models would then bring

out the on-site/off site impact of artificial recharging.

ACKNOWLEDGEMENT

Apart of the work reported herein is carried out under IWMI-TATA program under project titled “Groundwater Re-charge and Conjunctive Management in India.”

REFERENCES:

Finch JW (1999) " Regional groundwater recharge assessment in semi-arid areas."DFID Report 99/6, Institute of Hydrology, U.K.

MacDonald D, Edmunds WM, Moriarty P (1999) "The use of chloride balancemethod in weathered basement aquifers: A case study from Southern Zimbabwe."DFID 99/6, Institute of Hydrology, U.K.




38

Sondhi SK, Kaushal MP, Aggarwal Rajan (2001) " Management of groundwaterresources in Punjab." Proceedings of IWMI-ICAR workshop on groundwaterresearch in India, Karnal, Haryana, India, 6-7 November 2001.

Abernethy CL (2001) Inter sectoral management of river basin, International WaterManagement Institute (IWMI), Sri Lanka: Proceedings of an international workshopon “Integrated water management in water-stressed river basins in developing

countries: strategies for poverty alleviation and agricultural growth” Loskop Dam,South Africa, 16-21 October.




Allied Publishers, 2001,pp.39-57

39

Regionalization of Aquifer Parameters for Aquifer

Modelling Including Monitoring Network Design

Shakeel Ahmed

Abstract

Appropriate and adequate data are essential for the success of any scientific study. Scarcity ofdata and their collection on isolated location particularly in the field of hydrology, makes it

necessary to adopt special procedures such as geostatistical estimation technique for

bridging the gap between field measurements and numerical aquifer modelling. However,

these estimations are based on a crucial criterion of the structural analysis known asvariography and obtaining a true and representative variogram is extremely ambiguous fromlimited field data. Cross-validation test to determine a representative and optimal variogram

as well as to validate the other assumptions, has been found very useful in case of

hydrogeological parameters.

The application of Ordinary Kriging including variography is presented by taking a case

study on Fluoride concentration. In addition, multivariate geostatistical techniques viz.,Cokriging, Kriging with an External Drift have found better applications and are described. It is concluded that, depending upon the situation, geostatistical techniques could be applied

at each step of hydrogeological modelling studies i.e. from data collection network design, parameter estimation to the fabrication and calibration of aquifer models.

Key Words: Variography, Cross-validation, Cokriging, Kriging with an externaldrift, Aquifer Modelling, Transmissivity, Electrical Transverse Resistance, optimalnetwork.

1. INTRODUCTION

Numerical simulation of flow and transport processes in an aquifer necessitates, dividingand discretizing the natural heterogeneous system into a number of small parts called meshsupposed to be uniform with almost no variation of the aquifer properties. To satisfy this

condition, it is necessary to discretize the system into much finer and hence more numberof grids. Although with the availability of fast and strong computers, computation withlarge number of grids/mesh is not a problem but the data preparation that is to assign theaquifer parameters to each grid/mesh becomes cumbersome. Also an appropriate




40

estimation procedure is required to provide an unbiased, minimum variance and withunique value over the entire area of the mesh.

Geostatistical techniques in the form of "Theory of Regionalized Variables" weredeveloped to be applied to mining problems (Matheron, 1963). But soon after,

hydrogeologists have realized its applications to the groundwater hydrology and the firstwork was carried out by Delhomme (1974). Thereafter, number of studies have now beencarried out on hydrogeological parameters. Subsequently works of Aboufirassi andMarino (1983), Neuman (1984), Hoeksema and Kitanidis (1984), Ahmed (1987), Dong(1990), Roth (1995) etc. have shown more applications of geostatistics in groundwaterhydrology. However, multivariate and non-stationary geostatistics have got comparatively

more applications in groundwater hydrology. Also some of them have to be suitablymodified as well as some special procedures developed for a meaningful application ofgeostatistics in this field. Delhomme (1976) has developed the method of Kriging withLinear Regression, Kriging using erroneous data, Kriging in the presence of a fault etc.

Conditional simulation has also been applied in aquifer modelling (Delhomme, 1979).Galli and Meunier (1987) and Ahmed (1987) have worked on Kriging with an External

Drift. Ahmed and Marsily (1987) have compared a number of multivariate geostatisticalmethods in estimating transmissivity using data on transmissivity and specific capacity.Also Ahmed (1987) has developed a special antisymmetric and anisotropic cross-covariance between residuals of hydraulic head and transmissivity based on the work ofMizell (1980) and used coherent nature of various covariances to cokrige transmissivity

and hydraulic head in solving an Inverse Problem (Ahmed and Marsily, 1993). Bardossy et

al. (1986), Ahmed et al. (1988) and Kupfersberger and Bl !!o schl (1995) have combined

electrical and hydraulic parameters in a geostatistical analysis. Geohydrological data aremostly scattered and often subjected to errors. At each step special procedures havetherefore, to be adopted (Delhomme, 1976; !en, 1992 etc.).

Now geostatistics has found applications in almost all domain of Hydrogeology from

parameter estimation to predictive modelling for Groundwater Management e.g.,designing an optimal groundwater monitoring network, estimating parameters atunmeasured locations, groundwater model fabrication (optimal discretization), unbiasedmodel calibration using estimation errors and in deciding the best models for prediction.

2. VARIOGRAPHY OF A HYDROGEOLOGICAL PARAMETER

The theoretical part of the geostatistical techniques have already been dealt with earlier

workers e.g., Matheron, (1971), Journel and Huijbregts (1978), Marsily (1986), Isaaks andSrivastava (1989), Samper and Carrera (1990), Deutch and Journal (1992), Wackernagel

(1995) etc. Most of the hydrogeological parameters are defined and measured at points in a2D space. Therefore, all the derivations and examples in the chapter are given in 2D space

and point estimation is used. The main steps involved in a geostatistical technique appliedto hydrogeological parameters are: Variography i.e., structure analysis, cross-validation,estimation and backward transformation (if any). Variography in determining variability ofa parameter is an important step and quality of the estimation result depends on it. The




41

procedure involves calculation of experimental variogram, its modelling throughtheoretical variogram and its validation by reproducing the field data.

2.1 Calculation of Experimental variogram from scattered data

Unlike mining or airborne geophysical survey, hydrogeological parameters aremeasured on scattered locations due to the fact that most of the parameters are collectedfrom the wells that exist in the vicinity of a village and not on a grid pattern. Low costof the groundwater projects also restricts a systematic and extensive data collection. Ageneralised formula to calculate experimental variogram from a set of scattered data can be written as follows (Ahmed, 1995).

γ θ θ θ (d, ) = 12 N

[z ( x +d, )-z( x , ) ] (1)d

i=1 N

i i2d

! " " "

where

d - d d d + d , - + (2)∆ ∆ ∆ ∆≤ ≤ ≤ ≤" "θ θ θ θ θ

with

d =1

N d , =

1

N (3)

d

i=1 N

id

i=1 N

id d ! !" "θ θ

where d and θ are the initially chosen lag and direction of the variogram with ∆d and

∆θ as tolerance on lag and direction respectively. d and θ are actual lag and direction forthe corresponding calculated variogram. Nd is the number of pairs for a particular lag anddirection. The additional eqn (3) avoids the rounding off error of pre-decided lags

(multiples of the initial lag only are taken in conventional cases) and the direction. It isvery important to account for every term carefully while calculating variograms. If the

data are collected on a regular grid, and ∆d is taken zero, eqn (2) and eqn (3) will be

simplified only for θ. Often, geohydrological parameters exhibit anisotropy and hencevariograms should be calculated at least in 2 to 4 directions to ensure existence orabsence of anisotropy. Of course, sufficient numbers of samples are required in that case.

2.2 Modelling an experimental variogram

Calculation of experimental variogram is subjected to many approximations and its plot is

mostly irregular. A smooth curve is therefore, fitted to it. This fitting is called modellingand the fitted curve is called a theoretical variogram. A theoretical variogram is defined by

a number of parameters e.g., sill, range, nugget effect and model type. These parameters of

a variogram could approximately be decided by visualising the experimental variogram aswell as by nature of parameter. For example, a variogram of transmissivity posses usually,a nugget effect but that of the water-levels does not. Sometimes, an experimental variogramis not satisfactorily fitted by any of the limited available theoretical variograms. Thus a

combination of several variograms is fitted and the resultant variogram is called a nestedstructure. Following resultant variogram is only authorized as a nested structure.

(4) (d)a=(d)ii

k =1i

Rγ γ !




42

iawhere i0∀> 0 and

i(d) are individual variograms. Mostly the fitting is visual

but often an automatic fitting such as least squares etc. is also used. However, a

measure of difference between theoretical and experimental variograms is alwayscalculated to decide the best of several fits.

2.2.1 Cross-validation test

Theoretical variogram obtained by fitting an experimental variogram is usuallyambiguous. It is therefore, necessary to validate it against the measured value. Thecross-validation is performed by estimating the parameter at the points of measurementand comparing them with the field values in a statistical sense (Ahmed and Gupta,

1989). In this exercise, a measured value is removed from the data set one by one andthe same is estimated at that point using the remaining values and the structural model.

The process is repeated for the entire data set. Thus we will have, at all themeasurement points, measured value (z), estimated value (z

*) and variance of the

estimation error (σ2). This leads to computing following statistics.

1

n ( z - z ) 0 (5)i=1

ni i

*! ≅

1

n( z - z ) ..............(6)

i=1

n

i i* 2

! ≈ min

1

n

( z - z )

1 (7)i=1n i i

* 2

i

2! ≅

σ

i

i

z z i

−≤ ∀

*

..... .. .. .( )σ

2 8

Various parameters of the variogram model are gradually modified to obtain

satisfactory values of the eqns. 5 to 8. Therefore, during the cross-validation we testmany important points such as:

i. Inferring a structural model and removing its ambiguity.

ii. Deciding optimum neighbourhood.iii. Selecting suitable combination of additional information particularly in case of

multivariate estimation.

iv. Sorting out the unreliable data.

3. UNIVARIATE GEOSTATISTICAL ESTIMATION

Although due to scarcity of data or various other reasons Ordinary Kriging, a class ofsingle-variate geostatistical technique is not much practised, some work have been carriedout and it was thought useful to present one of them here. Moreover, in most of themultivariate estimation also, ordinary kriging is used particularly in cross-validation test.




43

3.1 Estimation of Fluoride content in an aquifer

Fluoride content in groundwater beyond a permissible limit has been a serious problem inaquifer in drought prone areas with granitic bed rocks. Also, this being a natural pollutant,its control including source identification is much more complicated. Fluoride contents (F)

have been monitored in 146 wells in the district of Anantpur in A.P., India (Fig. 1).Although this parameter varies with time; a slow varying one, we have tried to estimate aregional picture of this parameter to delineate zones of high and low fluoride at one time.Since the F data was showing log-normal distribution, the values were transformed bytaking logarithms of F. Experimental variogram of log-F was thus calculated and fittedwith a theoretical model which was cross-validated later. (Ahmed and Murali, 1992).

Fig. 1: Location of measurement points for Fluoride data

The variograms were also calculated in two perpendicular directions and it was found

that they do not exhibit any anisotropy. A mean variogram was therefore, calculatedand approximately fitted with the following variogram.

(d)=0 0.038+0.016 sph(7)

The whole area was divided into a uniform grid of 1 Km by 1 Km and log-F wasestimated at the centre of each grid using Ordinary Kriging with a changing

neighbourhood equal to 25. The estimated values and the corresponding estimationvariance are shown in Fig.s. 2 and 3 respectively. In Fig. 2 only three values of F viz.,




44

less than 1.5 ppm, between 1.5 and 2.0 ppm and greater than 2.0 ppm were considered.Areas with less than 1.5 ppm are safe for drinking, areas with more than 2.0 ppm should be abandoned but areas with F varying from 1.5 to 2.0 ppm could be used to treat waterfor drinking. Moreover, the map of variance of the estimation error has also

Fig. 2: Estimated value of Fluoride in Anantpur dist., A.P., India

Fig. 3: Standard deviation of Estimation error in Fluoride estimation

been divided into three values; viz., high moderate and low. A better decision could betaken by superimposing the two maps and arriving at the areas with F estimated to bewithin the permissible limit and the error map with highly reliable value etc.

4. MULTIVARIATE GEOSTATISTICAL ESTIMATION

As the data in groundwater hydrology is usually scarce, we must make use ofsupporting information and apply multivariate geostatistical techniques (Ahmed and




45

Marsily, 1987; 1988). Two common multivariate geostatistical techniques are describedhere which are mainly applied to groundwater hydrology.

4.1 Cokriging

It is a common technique of geostatistical estimation with many variable information.Theoretical part is very well dealt with Journel and Huijbregts (1978), Myers (1982,1984), Marsily (1986) etc. One very important point about this technique is that itrequires sufficient number of measurement points at which both the variables underconsideration are available to calculate the cross-variogram. Dong et al., (1990) hasdiscussed advantages of cokriging of related variables.

4.2 Estimation of Transmissivity in an aquifer in North-West Tunisia

In an area of 120 km2 of a semi-confined alluvial aquifer in Tunisia, many resistivity

sounding results (at 82 points) are available besides data on transmissivity (at 16 points) and specific capacity (at 17 points). A new variable viz., electrical transverseresistance was calculated from resistivity and thickness obtained from the VES in

the aquifer. The electrical transverse resistances were then corrected for the waterresistivity variation. All the three parameters show log-normal frequencydistribution and they have been transferred taking their logarithms (base 10). Thegeographical locations of these data are shown in Fig. 4. The regression between thevariables shows a fairly good correlation (Ahmed et al., 1988). The variograms do

not show any nugget effect and are fitted with spherical models with equal ranges

but different sill values. The numbers of pairs during calculation of the variogramswere not sufficient to perfectly fit theoretical models. Hence several trials forcross-validation have been made by varying variogram and cross-variogram parameters as well as the variogram type. Also the constrains of having positivedefinite kriging matrix were checked while modifying the cross-variogram

parameters. Finally it was found that the spherical models of variogram andcross-variogram have given the best results while using all the three variables inestimation of log-T through cokriging. The details are given in Table 1.

Fig. 4: Location of measurement points in Tunisian aquifer




46

Table 1: Results of cross-validation test

EstimatedVariable

Variable(s)used inestimation

Method Valueof eqn.5

Valueof eqn.6

Value ofeqn. 7

Log-T log-T Ordinary

Kriging

0.0232 0.1431 1.008

Log-SC log-SC ,, 0.2900 0.1655 1.256

LOG-TR log-TR ,, 0.0078 0.0253 1.337

Log-T log-T & log-SC Cokriging 0.0180 0.0710 1.184

Log-T log-T & log-TR ,, 0.0307 0.1180 0.997

Log-T log-T, log-SC &log-TR

,, 0.0178 0.673 1.116

Log-T log-T & log-SC KrigingwithExternaldrift

0.0131 0.0873 0.754

Log-T log-T & log-TR ,, 0.0023 0.1619 0.936

Log-T log-T, log-SC &log-TR

,, 0.0085 0.1459 0.951

The variogram parameters of variables Z (log of transmissivity / log-T), Y (log ofspecific capacity / log-SC) and W (log of electrical transverse resistance / log-TR) are

given below.

γ ZZ= 0.0 + 0.55 sph (6 Km), γ YY

= 0.0 + 0.60 sph (6 Km), γ WW= 0.0 +

0.14 sph (6 Km),

γ ZY= 0.0 + 0.45 sph (6 Km), γ ZW

= 0.0 + 0.16 sph (6 Km) & γ YW = 0.0 +

0.20 sph (6 Km).

The cross-validation tests clearly show that the best results are obtained using cokrigingwith all the three variables. It has been explained in the work of Ahmed and Marsily

(1987) that cokriging should be used when the variables have high correlationcoefficient and their residuals have spatial structure. This property of the residual to

have spatial structure is, however, found between transmissivity and electricaltransverse resistance but not between transmissivity and specific capacity. Thus anestimation of log-T has been carried out on the central points of square grids of 1 kmside using method of cokriging with all the three variables. Fig. 5 and Fig. 6 show theestimated log-T and the corresponding standard deviation. An inverse transform of the

estimated log-T values have given a regional distribution of T for siting a suitable welldrilling site as well as to used in numerical modelling.




47

Fig. 5: Estimated values of log-T in Tunisian Aquifer (through Cokriging)

Fig. 6: Standard deviation of the estimation error for log-T in Tunisian aquifer

4.3 Kriging with an external drift

Drift in a general sense, is a deterministic (linear quadratic or even higher order

polynomial as well as other regular functions) function of spatial co-ordinates. Thesetypes of drift functions are called internal drift or simply drift. However, according toMatheron (1971) a drift could be a random function also and may be represented byfunction of a different variable. This type of drift is called an external drift.Sometimes, two variables are very closely related and hence one completely or partiallycould represent the drift of the other. The expected value of a variable, knowing other

variables simultaneously can be written as the conditional expectation in the followingmanner:

E z y y ii i i x x a a x[ ( ) / ( )] ( ) .............( )= + ∀

0 19




48

Similarly if data on many variables are available a, combination of these values can beused to define the external drift of the main variable as:

where M is number of other variables. An estimator in this case is written as in case of

E [z ( x ) / y ( x ), j = 1,.. ,M ] = a + a y ( x ) i (10)i j i 0 j=1 M

j j i! ∀

Ordinary kriging i.e.*

0 i i z ( x )= z( x )!λ 0. But the weights associated with the data

values will be different as the conditions of unbiasedness in this case give the followingequations:

i=1n

i = 1 (11)! λ

i=1n

i j i j 0 y ( ) = y ( x ) j=1,...M (12) x! ∀λ

The system of kriging equations can be written as:

i=1n

i ij 0 k=1 M

k k 0 j0 + + ( x ) = , where j = 1,...n (13)! !λ γ µ µ γ γ

i=1n

i = 1 (14)! λ

i ji

n

i j y x y x j M λ =! = ∀ =

1 01 15( ) ( ) ,....... .........( )

The expression for the variance of the estimation error can be written as:

20 i=1

ni i0 0 k=1

M

k k 0( x ) = + + y ( x ) (16)σ λ γ µ µ ! !

It can, however, be seen that the values of all the additional variables are required notonly at the estimation points but also at those locations where values of the mainvariable are known. In practice, some of these values may not be available and we mayhave to use their estimated values, though it would affect the accuracy of estimation.The estimation variance in this method is generally higher than that in Cokriging or any

other multivariate kriging methods (Ahmed and Marsily, 1987). This is due to the factthat there are additional unbiased conditions (eqn 12) and the data to minimise thevariance are less.

Another important point to be borne in the mind here, is the calculation of theconditional variogram. A conditional variogram of a variable having other variables as

external drift, is a function of all the individual variograms as well as theircross-variograms (Ahmed, 1987). However, most of the authors e.g., Galli andMeunier (1987), Ahmed and Marsily (1987), Deutch and Journel (1992) etc. have usedthe variograms of the main variable only after verifying it through cross-validation.




49

5. DATA COLLECTION NETWORK DESIGN

Data collection from a finite number of observation/monitoring points randomly orsystematically distributed is necessary to infer the spatial variability of any parameter under study. The number and distribution of such stations are constrained

by numerous factors of which cost and feasibility are quite common to consider.Therefore, it is imperative that an optimal monitoring network be evolved usingminimum number of observations stations that can provide maximum information.At the same time configuration of a network also depends on the objectives and theend use of the project. One of the important and obvious end use of the datacollection is to infer or estimate the parameter at the intermediate and/or unmeasured

locations. Obviously even using the best available interpolation/estimationtechniques, there would certainly be an estimation error and the further objectiveshould be to improve upon this error in the form of minimization of variance of theestimation error. Based on this criterion a procedure of optimizing a temperature

measurement network using geostatistical technique is developed. There has been alarge amount of work using different statistical and geostatistical procedures in

monitoring network design. Langbein (1979) and Loaiciga et al (1992) have presented overview for such applications. However, Agnihotri and Ahmed (1997)have made a short review and highlighted ambiguities in the methods with suitableexamples.

The area of interest is thus divided into considerably finer grids of uniform size andusing the geostatistical estimation procedures, the kriging estimation variance are

calculated with suitable kriging method depending upon the nature of the parameter.Since we are interested in the coordinates of the optimal location of the

measurement points and since the objective function i.e. the variance of theestimation error without directly containing these coordinates, cannot be minimized

with respect to the coordinates, an indirect iterative procedure is therefore,developed to arrive at an optimal or near optimal network. Considering the formulafor the estimation error as follows:

γ γ λ σ µ vviv

n

i ik v −+= ! =1

2)( ∀ k =1,…N (17)

where N is the total number of estimation grids )(2

vk σ is the variance of the

estimation error at the k th grid v, γ

iv and γ

vv are average variograms between i

th

point and v as well as between v and v respectively, λi the kriging weights. It is clearthat more the number of points, less would be the variance of the estimation error.Beside the number, the position of the measurement points from the estimation

points/block also plays important role.

As mentioned earlier, the entire area was divided into a number of grids of equalsize. Using the block estimation of ordinary kriging, standard deviation of the




50

estimation error ( )(vk σ ) was calculated. A list of the points where )(v

k σ has

exceeded σ c, the pre-set values, was prepared. Also a few more norms as follows,were calculated.

Average of )(vk σ =σ k

(18)

Number of grids (M) where )(vk σ > σc (19)

and

Sum of squared difference (SSD) between )(vk σ and σc for all )(v

k σ > σc

(20)

Thus with the values of M, SSD and σ k a network is declared dense, sparse or near

optimal for a given σc and addition, deletion or shifting of measurement points aremade accordingly. After a few iteration of this procedure the network could be made

optimal for the given σc. In this procedure, it is also necessary that the optimality is

checked on a further fine grid. Other constraints should also be considered and amuch elaborate table of suitable additional measurement points could be prepared based on all other alternatives and the present method finally provides an optimal ornear optimal network for a desired accuracy for the regionalization of the parameter.

Optimization of water level monitoring network in a fractured granitic aquifer

In a small watershed of 60 Km2 area (Maheshwaram watershed) near Hyderabad, India(Fig. 7) groundwater is mainly found in a coupled system of weathered and fracturedgranitic rocks. However, due to over exploitation and successive reduction in the rainfallrecharge, the water table has declined and the saturated flow is mainly confined to aquifer

consisting of highly fractured rocks only. Crystalline rocks of Archaean age, comprisinggray and pink granites cover a major portion of the study area; porphyritic granites intruded

by dolerite dykes and quartz reefs. The granites have undergone variable degree ofweathering and fracturing. Large scale fracturing and jointing has resulted in formation ofhuge boulders of granite, which are also scattered randomly in the area.

The water levels are being monitored through a network of about 55 bore wells out ofwhich 25 have been specially drilled to observe comparatively undisturbed water tableand the other 30 bore wells are selected based on the drainage pattern and intervals etc.

from the existing private wells used for irrigation (Fig. 7). The water levelmeasurements have been carried out on monthly basis for a period of almost one

hydrological cycle.




51

Fig. 7: Location map of the study area for water level optimisation.

About 30 wells (indicated as IFW) out of the 600 irrigation wells existing in the areahave been selected for water level measurement based on the drainage pattern present,variation in rock formation covering the study area. Later 25 wells (indicated as IFP)taping the fractured aquifer have been drilled up to a depth of 45 m uniquely to monitor

the water levels. These wells have been drilled based on the recommendation fromgeophysical investigations. Thus it was thought to reduce the number of wells so that;

• all the wells are monitored in a shortest possible time say one single day,

• discard some of the irrigation wells fitted with pumps as it was difficult to monitorstatic levels in these wells and

• reduce the cost of monitoring also




52

without loosing the monitoring benefits. The objectives for geostatisticaloptimization of the monitoring network has been that the monitored water levelsshould (i) represent the true variability of the parameter and (ii) provide its estimateon unmeasured locations with a desired accuracy. Thus to obtain an optimalmonitoring network having 25 IFP wells and minimize the IFW wells such that the

kriging estimation of water levels provide standard deviation of the estimation errornot more than 8 m (against the average standard deviation of 12 m of the water leveldata) in the entire area. Through a special procedure as described through eqns 18-20 above the IFW wells were removed one by one and the impact with the aboveconstraints were studied. Finally a network with 25 IFP wells and 15 IFW wells

0 1000 2000 3000 4000 5000 6000 7000 8000

Easting in metres

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

N o r t h

i n g i n m e t r e s

IFW LOCATION

IFP LOCATION

Fig. 8: Map of estimation error from 40 wells




53

0 1000 2000 3000 4000 5000 6000 7000 8000

Easting in metres

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

N o r t h i n g i n m e t r e s

Contour Interval = 0.5 m

WELL LOCATION

Fig. 9: Map of estimation error from 55 wells

have been evolved for monitoring the water levels every month. The contour map of

the standard deviation of the estimation errors (σk ) from a network of 55 wells aswell as from a network of 40 wells are shown in Figs. 8 and 9 respectively using asuitable kriging method. It is very clear that using the optimized monitoring network

it is still possible to maintain the magnitudes of σk .

The constrained optimization of the monitoring network with only 40 wells will

ensure that all the wells are measured in the shortest possible time every month.Also that the revised network consists all the 25 wells without pumping and one hasto be careful for monitoring only 15 private wells fitted with pumps for irrigation.This provides a hydrogeologist much ease for an accurate water level measurement.The revised network will also provide almost same accuracy in estimation thatwould have been obtained from the network of 55 measurement wells.




54

6. CONCLUSION

The field heterogeneity of groundwater basins is often inextricable and very difficult toanalyse with deterministic methods. Another advantage of using geostatistical methodsis that it provides the variance of the estimation error together with the estimated values.

Of course, there are many advantages of these methods particularly in Groundwatermodelling:

• The closer the values of the aquifer parameters to reality, the faster will be themodel calibration. Better estimated values (with lower estimation variance) areinitially assigned to the nodes of aquifer model using geostatistical estimation.

• An assumption is made in Aquifer Modelling that a single value of system parameter represents the entire mesh (Of course, very small). Averaging over a block in two or three dimension can be obtained through block estimation.

• An optimal mesh size and number of nodes in discretizing aquifer system, can beobtained and best location of new control points can be predicted.

• A confidence interval given by the standard deviation of the estimation error

provides a useful guide to T modification at each mesh and to check that thecalculated heads fall inside the confidence interval of the observed heads.

• A performance analysis of the calibrated model can be achieved to decide the best

calibrated model using variance of the estimation error which can be used for prediction.

A few modifications and improvement to the existing techniques permit to utilisehydrogeological data successfully in prediction of aquifer parameters. One suchmodification in kriging techniques is called "kriging with an external drift". This

technique has been found quite useful in arriving at the estimation of hydrogeologic parameters. Cross-validation, though very cumbersome and not useful when data arenumerous as in case of mining, it is much more useful and almost necessary when thereare less data as in case of hydrogeological parameters.

A large number of works have been reported particularly using geostatisticalmethods in optimal data collection network design. However, very few have found

application in real field. It is therefore, useful to analyse and discuss the problems oftheir application. A number of ambiguities have been found in the methods so farapplied; some of them are quite severe. Since most of the network design is based on

the reduction of kriging variance which does not depend on the measured value ofthe parameter at a newly decided location, a common ambiguity is about themaximum value allowed of the variance or the standard deviation of the estimationerror (say a threshold). In the absence of an objective function directly involving thelocation of measurement points, it is difficult to minimize the variance of the

estimation error (σ 2k ) Either this value is arbitrarily chosen or optimization of a

data collection network may be terminated if the corresponding change in the σ 2k is

negligible.




55

It is finally recommeded that the method of estimating kriging variance on a block/area may be used in data collection network design but with the care asdescribed above. Of course, the better way of analysing and designing a network isto discretize the area into a number of blocks and design a network by reducing theestimation variance on an average basis. This procedure could be repeated by

reducing the size of discretized blocks until there is no change in the averagestatistics of the estimation variance.

ACKNOWLEDGEMENTS

Authors would like to thank the Director, NGRI for his kind permission to prepare the

paper. We thankfully acknowledge the discussion made with Dr. PSN Murthy ofAndhra Uiversity.

REFERENCES:

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Morocco" , Math. Geol., Vol. 15, No. 4, pp. 537-551.

Agnihotri, V. and Ahmed, S. (1997), " Analyzing ambiguities in data collection

network design using Geostatistical estimation variance reduction analysis" , Jour.of Environ. Hydrology, in press.

Ahmed, S. and Marsily, G. de., (1993), "Cokriged estimation of aquifer transmissivityas an indirect solution of inverse problem - A practical approach" , Water Resour. Res.,Vol. 29, No. 2, pp. 521-530.

Ahmed, S. (1987), " Estimation des transmissivites des aquiferes par methodes geostatistiques multivariables et resolution indirect du Probleme Inverse" , Doctoralthesis, Paris School of Mines, France.

Ahmed, S. (1995), ‘" An interactive software for computing and modelling avariograms" . In Mousavi and Karamooz (eds.) Proc. of a conference on "WaterResources Management (WRM'95)", August 28-30. Isfahan University of Technology,Iran, pp. 797-808.

Ahmed, S. and Murali, G. (1992), " Regionalization of fluoride content in an aquifer" . Jour. of Environmental Hydrology, Vol. 1, No. 1, pp. 35-39.

Ahmed, S. and Gupta, C.P. (1989), "Stochastic spatial prediction of hydrogeologic

parameters: Use of cross-validation in krigings" . In Gupta et al. (eds.) Proc. of Internat.

Groundwater Workshop (IGW-89), Hyderabad, India, Feb. 28 to March 4, Oxford &IBH Pub. Co., Vol. 3, pp. 77-90.

Ahmed, S. and Marsily, G. de. (1987), "Comparison of geostatistical methods forestimating transmissivity using data on transmissivity and specific capacity" , Water Resour. Res., Vol. 23, No. 9, pp. 1717-1737.

Ahmed, S. and Marsily, G. de (1988), "Some applications of multivariate kriging in

groundwater hydrology" , Science de la Terre, Serie Informatique, Vol. 28, pp. 1-25.




56

Ahmed, S., Marsily, G. de. and Alain Talbot (1988), "Combined use of hydraulic andelectrical properties of an aquifer in a geostatistical estimation of transmissivity", Ground Water , Vol. 26, No. 1, pp. 78-86.

Bardossy, A., Bogardi, I. and Kelly, W.E. (1986), "Geostatistical analysis of geolectric

estimates for specific capacity", J. Hydrol . Vol. 84, pp. 81-95.

Delhomme, J.P. (1974), "La cartographie d'une grandeur physique à partir desdonnées de différentes qualités" . In proc. of IAH congress, Montpelier, France, Tome

X, Part-1, pp. 185-194.

Delhomme, J.P. (1976), "Application de la théorie des variables régionalisées dans les sciences de l'eau" . Doctoral thesis, Paris School of Mines, France, 130pp.

Delhomme, J.P. (1979), "Spatial variability and uncertainty in groundwater flow parameters: a Geostatistical approach" . Water Resour. Res., Vol. 15, No. 2, pp. 269-280.

Deutsch, C.V. and Journel, A. G. (1992 ), "GSLIB, Geostatistical software library andUser's guide" . Oxford Univ. Press, New York, 340p.

Dong, A., S. Ahmed and Marsily, G. de (1990), " Development of Geostatistical Methodsdealing with the Boundary Condition Problem Encountered in Fluid Mechanics of Porous

Media’. In Guerillot and Guillon (eds.) Proc. of the 2nd European Conf. on "Mathematicsof Oil Recovery", Arles, France, Sept. 11-14, Technip, Paris, pp. 21-30.

Galli A. and Meunier, G. (1987), "Study of a gas reservoir using the external drift

method" . In Matheron and Armstrong (eds.) Geostatistical case studies, D. ReidelHingham, pp. 105-120.

Hoeksema, R.J. and Kitanidis, P.K., (1984), "An application of the geostasticalapproach to the inverse problem in two-dimentional ground water modelling" . Water

Resour,Res.,Vol 20, No. 7, pp. 1003-1020.

Isaaks, E.H. and Srivastava, R.M., (1989), "An introduction to Applied Geostatistics" ,Oxford Univ. Press, 561p.

Journel, A.G. and Huijbregts, C., (1978), "Mining Geostatistics" . Academic Press,600p.

Kupfersberger, H. and G. Bloschl (1995): "Estimating aquifer transmissivities" - On

value of auxilary data. J. Hydrol., Vol. 165, pp. 85-99.

Langbein, W. B., "Overview of Conference on Hydrologic Data Networks" , Water Resour. Res., Vol. 15, No. 6, pp 1867, 1979.

Loaiciga, H. A., Charbeneau, R. J. (1992), "Reiew of Groundwater Quality Monitoring Network Design", Jour. of Hydraulic Engineering , Vol. 118, No.1, pp11-37.

Marsily, G. de (1986), "Quantitative Hydrogeology, Groundwater Hydrology for Engineers" , Academic Press, 440p.

Matheron, G. (1963), "Traité de Géostatistique appliquée" . Vol. 1 and 2 EditionTechnip. Paris.




57

Matheron, G. (1971), "Theory of Regionalized Variables and their Applications" .Cahier du C.G.M.M., Fontainebleau, France, 211pp.

Mizell, S.A.(1980), "Stochastic analysis of spatial variability in two -dimentionalGroundwater flow with implications for observation-well network design". Doctoral

thesis, New maxico institute of mining and technology, U.S.A.,133 pp.

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Myers, D.E. (1984), "Cokriging - New developments. In Verly et al". (eds.) Geostatisticsfor natural resources characterization. D. Reidel Pub. Co., pp. 295-305.

Neuman, S.P. (1984), "Role of Geostatistics in subsurface hydrology" . In Verly et al.

(eds.) Geostatistics for natural resources characterization, Proc. NATO-ASI, D. ReidelPub. Co., pp. 787-816.

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Samper F.J. and Carrera, J. (1990), "Geoestadística - Aplicaciones la hidrología subterránea" . Bercelona Univ., 484p.

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Wackernagal, H.(1995), "Multivariate Geostatistics: An introduction with applications".

Springer, 256 pp.





59

Approaches for Modelling of Hard Rock

Aquifer System

M. Thangarajan

Abstract

The groundwater flow models so far used represents the porous mediahaving continuous interconnected pore space. The flow problem in the

fractured rocks has always been and will continue to be of interest tohydrologists. Evolving conceptual model of a fractured system requires eithera gross simplification or a detailed description of the aquifer propertiescontrolling the groundwater flow. At present, there is only a basic conceptualunderstanding of flow in the vicinity of weathered and fractured hard rock

aquifers. Normally this conceptual understanding is not translated in to thequantitative interpretation procedures; often, simple continuum models areapplied to analyse pumping test data, and the results then used to producequantitative calculations on a regional scale. Even if the regional system can

be represented using the continuum equivalent approach, it is unlikely thatthe results of applying continuum models at the local scale have any general

validity, and also aquifer parameters so derived, may be different to theaquifer parameters appropriate for describing regional flow in quantitativeterms. Hence, there is a need to develop appropriate methods for analysis of pumping test data and appropriate simulation technique to improve the success rate and yield of wells in fractured rock. The analysis should provide

cost-benefit analysis for new and / or in-fill wells. To do this, it is necessaryto investigate in detail the flow in the vicinity of a pumping borehole, and toapply appropriate non-continuum models. Fractured systems are typicallyusing one or more of the following conceptual models: (i) equivalent porousmedium, (ii) dual porosity medium, (iii) discrete fracture network model, and(iv) stochastic continuum model. This paper deals with the different

approaches used to simulate the fractured aquifer system.

Keywords: Dual porosity, discrete fracture network model, stochasticcontinuum model, discrete-fracture networks.




60

1. INTRODUCTION

Hard rocks are all those crystalline hard and massive rocks, which have no intergranular porosity. The most common types are the granites and basalts. The distribution of hardrocks of India is shown in Fig. 1 (Radhakrishna, 1970). The crystalline limestones,quartzite, sandstones, and many schistose rocks formed as a result of metamorphism are

also called hard rocks (Radhakrishna, 1970). However, due to tectonic disturbances,secondary porosity in the form of fissures, fractures, and joints have higher permeability. Number of fractures, if they connect to form networks, can be expected to form the principal pathways for fluid flow and mass transport. The hydraulic conductivity ofindividual fracture in granitic rock can vary over several orders of magnitude, and the

geometry of interconnection of the fracture is generally irregular. For these reasons, the properties of the fractured rock mass with respect to groundwater flow are, on a local scale,extremely heterogeneous. Hydrological testing methods that are commonly used tocharacterise less heterogeneous rock is of questionable value for characterising rock

masses. Traditional methods for interpretation of hydrological test results are based onassumption of flow through an approximately homogeneous porous medium with simple

flow geometry (e.g. radial or spherical flow). In fractured rock, the test results are, ingeneral, controlled by fracture properties on a very localised scale, and the flow geometrycan be very irregular.

Fig. 1: Hard rock regions of India (after B.P.Radhakrishna)

It is, thus, imperative to develop more reliable techniques for estimation of aquifer parameters in hard rock region and assessment of these resources for their hazard-free optimal exploitation. The ultimate objective would be to evolve an appropriate

methodology for a rational management of this precious natural resource andthereby find lasting solutions to the problems of water scarcity and water quality.




61

2. MODELLING APPROACH

Groundwater flow is expected to occur in crystalline rocks mainly through networks ofinterconnected fractures and joints. Discrete-fracture networks (DFN) models provide ameans of explicitly representing flow path geometry in such cases. The geometry ofinterconnection among fractures determines the locations and pathways. The statistical

geometry of fractures can be deduced directly from observation of fractures in borehole andat outcrops on the surface. Thus, the flow paths in DFN models arise as a directconsequence of observed fracture geometry, rather than as the result of conditioning oncross-hole hydrological data. The applicability of this model is limited in terms of scale ofthe area and volume to be simulated. The maximum volume (3D) that can be modelled

depends upon the intensity of fracturing and the resolution (in terms of minimum fractureconductivity) that is desired. Due to these limitations, DFN models must be used inconjunction with Stochastic Continuum (SC) and Channel Network (CN) models. SCmodel is used to model fluid flow in the larger scale by making use of probability

distribution of fracture properties (i.e., given a definite location, size, transmissivity etc). In practice, it is extremely difficult to characterise all hydraulically significant fractures in a

block of rock, in which case, stochastic modelling allows uncertainty to be representedexplicitly. Monte Carlo simulations resulting in multiple model realisations achieve this.Dual porosity stream tube modelling is used to predict mass transport. CN models are usedas an alternative model for transport within the dominant flow pathways. The DFN modelis used to provide information required for the other two modelling approaches.

The comparison between DFN, SC and CN modelling approach is shown in Fig. 2.

The data analysis and the conceptual model of the system are explained in Fig. 3.

The model validation and prediction is shown in Fig. 4.

Fig.2: Comparison of DFN, SC,and Fig. 3: Conceptual

CN Models (after Golder Associates Inc) model of flow systems




62

Fig. 4: Model Validation and prediction

(after Golder Associates Inc)

2.1 Equivalent Porous Medium

Fractured system is represented as an equivalent porous medium (EPM) by

replacing the primary and secondary porosity and hydraulic conductivity distributionwith a continuous porous medium having so called equivalent or effective hydraulic properties. The parameters are selected so that the flow pattern in the EPM is similarto the flow pattern in the fractured system. An EPM approach assumes that the

fractured material can be treated as a continuum and that a representative elementaryvolume (REV) of material characterised by effective hydraulic parameters can bedefined. Simulation of flow in fractured system using this concept requiresdefinition of effective values for hydraulic conductivity, specific storage, and

porosity, which are, in turn, determined from aquifer testing (Gingarten, 1982),estimated from water balance or inverse models, and or calculated from fielddescription of fracture apertures, lengths and interconnections, and unfractured rockvolumes and permeabilities (Cacas et al., 1990 a). When EPM is considered, thenstandard Finite Difference Method (FDM) or Finite Element Method (FEM) may be

applied to simulate groundwater flow in fractured system. This approach can beapplied, only if the system has high intensity of fractures, otherwise this concept isnot valid. Many research workers, however, have concluded that EPM approachmay adequately represent the behaviour of regional system, but poorly reproduceslocal condition.




63

2.2 Dual Porosity Medium

If the rock mass containing the fracture network has significant primary permeability, thena dual porosity approach may be used. Barrenblatt et al. (1960) have proposed this concept.In this conceptual model, flow through the fractures is accompanied by exchange of water

to and from the surrounding porous rock matrix. Obviously, the fracture network as well asthe properties of the porous blocks must be described prior to modelling. Exchange between the fracture network and the porous blocks is normally represented by masstransfer function (Huyakorn et al., 1983). The double porosity approach is primarilyapplicable to sedimentary formations such as sandstone, but may also be of interest in theinverse interpretation of the hydraulic properties of hard rock formation.

2.3 Discrete Fracture Network

A discrete fracture network model assumes that water moves only through the discrete

fracture network. This approach is typically applied to fractured media with low primary permeability such as crystalline rocks. The flow through single fracture may be identified

as occurring between two parallel plates with a uniform separation equal to the fractureaperture. The parallel plate fracture flow equation is derived from the Navier-Stokesgeneral equation for fluid flow in three dimensions of space as;

Where, ρ is fluid density

µ is viscosity of fluidu is groundwater flow velocityPT is total pressure

Flow through a single fracture may be idealised as occurring between two parallel plates.For the parallel plate situation, the relationship can be simplified in to 1-dimensionalequation. This is because the aperture is assumed infinite perpendicular to flow. Thiscondition is illustrated in Fig. 5.

Fig. 5: Parallel flow Approximation

)1.......(....................2u P g uut

uT ∇+∇−=∇+

∂

∂ µ ρ ρ ρ




64

From these simplifications, the relationship becomes:

Where,

dP/dx = -Gu is the groundwater velocity in x direction

Integrating equation 2 with respect to z twice gives

Where, A and B are arbitrary constants and they can be eliminated by applying boundary conditions: when z=0, u=0 and z=d, u=0 Where, d is the aperture size.Substituting these boundary equation in to equation (3)

Thus, the velocity profile across the fracture is parabolic, the maximum is located at

z=d/2.

Given the symmetry of the system, it is then possible to integrate this relationship

with respect to z in order to obtain a discharge per unit length of the fracture.

Where, G is pressure gradient. When using head gradient, one must use thefollowing relationship:

Where, i is the hydraulic gradient, ρ is density of fluid and µ is the viscosity of fluid.By making use of Darcy law, one can write

Q = -Aki - ( 7 )

)3.....(........................................2

2

B Az Gz

U ++−= µ

)4.....(..............................).........(2

2 z dz G

U −= µ

)5.........(........................................12

3

µ

Gd Q =

)6.(........................................12

3

i g d

Q µ

ρ =

)2..(........................................2

2

µ

G

z

u−=

∂

∂




65

Equations 6 & 7 show an analogy in terms of flow. Transmissivity is defined ashydraulic conductivity multiplied by saturated thickness, so that equation 7 can berewritten as:

Q = -Ti - (8)

for discharge per unit length in x direction. Thus, transmissivity of fracture can bewritten as

The above derivation has been taken from Alex Bond (1998).

2.4. Discrete-Fracture Network (DFN) Models are applied for --

(i) Small scale modelling.(ii) Explicit representation of flow path geometry.(iii) Process of flow and mass transport assumed to take place

primarily or entirely through network of discrete fractures.

2.5. Advantages of DFN Model

(i) Explicit representation of the geometry and physical properties of

fracture and fracture zones.(ii) Ability to incorporate fracture-geometry data in the model, and

thus give a basis for extrapolation from packer tests of uncertainflow geometry.

(iii) Possibility of modelling fracture zones on various scales,including undetected zones and other heterogeneities, based onobservations of structural patterns.

2.6. Disadvantages of DFN Model

(i) The approach is relatively new, so the modelling tools are not assophisticated as continuum tools. They have generally beendeveloped for specific applications e.g., deep repository or

reservoir studies, treatment of water table, unconfined aquifers,and surface water features is currently under active research. Needfor fracture geometrical data at sampling location distributedthroughout the region to be modelled, including data at depth.When sampling locations are not well distributed, extrapolation isrequired.

(ii) Need to simplify fracture patterns and / or restrict the range offracture transmissivity modelled to simulate large-scale region.

)9(..................................................12

3

µ

ρ g d

T =




66

This methodology is applied in advanced countries for identification of sites todispose nuclear wastes. Models based on DFN approach are computationallycomplicated. To date, applications are only to the oil industry, mining industry andnuclear waste disposal sites.

2.7 Stochastic Continuum Approach

The stochastic continuum theory treats the parameter heterogeneity in the context ofa statistical (probabilistic) framework. It is usually assumed that an effectivehydraulic conductivity tensor K exists on some averaging scales, and that it forms acontinuous random tensor field i.e.,

K s = K s(x) -- (10)

The assumed hydraulic conductivity field K s(x) is described by the expected value,the variance and the co-variance function, but possibly by trends. The followingsteps are involved in SC approach:

(i) Estimate the population statistics i.e., expected value, variance andco-variance.

(ii) Divide the flow domain in to blocks.(iii) Generate multiple realisation of the conductivity field(iv) Solve the flow problem for each realisation.

(v) Carry out statistical analysis of the results from the simulations.

Normally the conductivity is transformed so that the resulting value field will satisfythe theory of Regionalised Variables i.e., stationarity and Gaussian behaviour. Ingeneral, it is assumed that K s is locally isotropic at each point in the log-conductivityfield is a statistically stationary one.

Z (x) = ln (K(x )) .. (11)

The hypothesis of a multivariate normal distribution Z implies that the entire statistical

structure of the stationary Z(x) is completely defined with the aid of µ and σij= Cz(xi x j)

Where, µ denotes the mean and Cz the two point co-variance. Thus, we may write

Z (x) = ln(k(x)) ∈ (N (µ,σ,λz (or Iz)) (12)

Where, N ( ) denotes normal (Gaussian) distribution.

2.8. Advantages of SC Model

(i) An extensive theory and statistical procedure for analysis.(ii) Ability to model site scale regions.




67

(iii) The possibility of conditional simulation.(iv) A tendency to produce more structure than a purely random field.

2.9. Disadvantages of SC Model

(i) Simplistic structure of the conductivity field produced by thesemodels.

(ii) Inability to model discrete, heterogeneous connection.(iii) Uncertain relation of model parameters to the varying support

scales owing to the differing influence of radii when performing pumping tests.

A major problem with numerical simulation using stochastic continuum-approach isthat of framing representative model blocks in which the heterogeneous equivalentconductivity is spatially varying parameters for which spatial conductivity is defined

in geostatistical terms. This problem is particularly relevant to hard rocks, where theamount of test data is by far too small to the size of the regional flow domain to be

modelled. It is, therefore, proposed to use DFN model to characterise the discretefractures and use this as an input to stochastic continuum model to simulate regionalflow

3. NUMERICAL SOLUTION METHODS

Though analytical methods provide error free solution, it is applied only to

simplified flow conditions with regard to the physical and geometrical aspects of theaquifer system. Therefore, one has to resort to numerical methods. Groundwater

modellers are using both finite difference (FD) approximation and finite element(FE) techniques to solve groundwater flow equation. Computationally, FD is easier

than the FE method. Since the flow problem is heterogeneous in fractured rock, it is preferred to use FE technique.

4. PROCEDURE (STEP-WISE) FOR MODELLING DISCRETE

FRACTURE NETWORK

(i) Preliminary geological and geophysical investigations forselection of suitable sites.

(ii) Geological assessment [scan surveys on outcrops, borehole

logging (fluid logs, formation logs, calliper, CCTV, ideallyacoustic televiewer), surface geophysics, coring and trenching].

(iii) Selection of an appropriate conceptual model for discrete-fracturenetwork geometry.

(iv) Testing (core material / trench material, pumping tests, packertests and tracer tests).




68

(v) Derivation of statistics for fracture properties from sitecharacterisation data to conceptualise a preliminary DFN modelfor the rock mass.

(vi) Constant (pressure) head packer tests will be analysed usingfractional dimensional methods to estimate effectivetransmissivities and flow dimension for the packer test intervals.

(vii) Discrete fracture data on orientation, size, shape, and locationalong with hydrologic data will be used to evolve preliminaryconceptual model for the conductive fractures at the site.

(viii) The variability of fracture properties will be expressed by probability distributions.

(ix) The preliminary conceptual model will be used to simulate 3-

dimensional population of conductive fractures in a cube of rock.

(x) Transient packer tests will be simulated in these fracture

populations, and the simulated results will be used to validate the preliminary conceptual model.

(xi) The calibrated model will, then, be used to estimate thecomponents of effective conductivity tensors for the rock bysimulating steady state groundwater flow through cubes in threeorthogonal directions.

(xii) Monte Carlo stochastic simulations will be performed foralternative realisations of the conceptual model.

(xiii) Adaptation of software for discrete fracture network (DFN) flowmodel (FracMan or NapSac or Frac3dvs) based on observable,geometric, and hydrologic characteristic of the fracture population,

that can be used to predict groundwater flow through fractures ofthe crystalline rock. (Fig. 6)

Fig. 6: Oblique view of fractures generated in a 5m cube at Helsby using

NAPSAC computer code (after Allex Bond)




69

5 DATA REQUIREMENTS FOR DISCRETE FRACTURE NETWORK

MODEL

Due to fundamental limitations of site characterisation technology, the data neededto model the exact geometry and property is limited to a few boreholes and outcrops.

Although a few major conductive features can perhaps be identified within the rockmass by geophysical methods such as borehole radar, skin depth effects andinterference limit the resolution of these techniques. Since the locations and properties of most of the fractures in the rock cannot be measured by any availablemeans, an approach is needed that is based on some form of statistical

characterisation of the fractured population. The following data are required to

characterise the discrete fractures through the DFN model.

Fracture Property Data Source

1. Orientation Lineament and Fracture Maps,

Core Logs2. Conductive Fracture Intensity Core Logs and Packer Tests3. Location Lineament and Fracture Maps4. Size Lineament and Fracture Maps5. Shape Fracture Maps, Generic

Information6. Transmissivity Steady and Transient Packer

Test Data7. Dimensionality Transient Packer Test Data

8. Storativity Transient Packer Test Data andGeneric Information

9. Transmissivity Variability Generic Information

5.1 Information Needed for SC Modelling

(i) The minimal scale [the representative volume (REV)] if any, on which therock mass can be said to behave as an equivalent porous medium.

(ii) The variability of (average) rock mass effective hydraulic conductivity (K).

(iii) The variability of anisotropy, expressed in terms of the ratios of the

principal components of the (presumed) hydraulic conductivity tensor (Kx,Ky and Kz) to the average hydraulic conductivity K.

(iv) The form of spatial correlation of rock mass conductivity that results fromfracture network effects.

(v) The relationship between apparent hydraulic conductivities measured by borehole testing and the effective hydraulic conductivities of the rock masson the scale of blocks used in SC modelling.




70

5.2 Information Needed for CN Modelling

(i) The spatial intensity of channel (number per unit volume) as a function ofchannel length and channel conductivity, based upon the observablegeometric characteristics of the fracture population.

(ii) The interconnectivity of flow channels (number of intersection with other

channels per unit length of channel) in three dimensions.

The spatial intensity of channels can be estimated directly from packer test data, butDFN models may provide independent ways for deducing the same data.

All fracture properties can be viewed as stochastic variables, the variability of whichis characterised in terms of probability distributions. Because the quantity of data is

limited, and because a finite degree of error is associated with any single datameasurement, the estimated forms and parameters of probability distributions forfracture properties have an associated uncertainty.

5.3 Variability and Uncertainty

The variability and uncertainty are inherent in modelling a heterogeneous system.Variability in the model arises from the heterogeneity of the system. In the case of aDFN Model, variability is expressed in terms of probability distribution for fracture

properties (orientation, transmissivity etc.), the forms and parameters of which can be estimated from field data.

Uncertainty in a model of the heterogeneous system exists whether the simulationsare based on a SC, CN or DFN approach. The uncertainty arises from problemsinherent to data collection, such as sample size, sampling bias, sampling accuracy

and analysis limitations.

6. CONCLUSIONS

Assessment of the dynamic potential of groundwater resources throughmathematical modelling (discrete fractured network modelling) in a hard rock

region will be the first of its kind in this country.

The combined DFN and SC Model will be a potential tool to get answer for

(i) Borehole optimisation – orientation, location pumping regime, artificial

recharge, etc.

(ii) Yield estimation from a single borehole and / or a sub-basin

(iii) Contaminant prediction




71

It is suggested to establish a National facility to carry out research work onCharacterisation of Fracture geometry and Modelling of Fracture aquifer system.

ACKNOWLEDGEMENTS

Director, NGRI is thanked for his keen interest in this topic and according permission to present this paper. Prof. Rae Mackay, Dr. John Tellam, Alex Bond ofThe School of Earth Sciences, University of Birmingham, U.K. and Dr. A. MarkJones of Golder Associates Inc. (U.K. Ltd.), Nottingham are thanked for their personal interaction and providing technical information on the above subject whenthe author visited U.K. during July, 1999.

REFERENCES:

Alex Bond, 1998. " A preliminary investigation in to the effects of fracturing and

fluids in the Triassic sandstone of the North Chestire basin" . Unpublished M.Sc.Thesis of School of Earth Sciences, University of Birmingham, UK, p. 118.

Anderson M.P. and William W. Woessner, (1991). "Applied groundwatermodelling: Simulation of flow and advective transport" . Academic Press, London, New York, P.381.

Baecher, G.B., Lanncy, N.A. and Einstein, H.H., (1977). "Structural description ofrock properties and sampling" . Proc. of 18

th U.S. Symp. On Rock Mechanics,

American Instt. of Mining Engineers, 5C1-8.

Barker, J., (1988). "A generalised radial flow model for hydrologic tests in fracturedrock" . Water Resources Research, Vol.24, pp. 1796-1804.

Barrenblatt, G.I., Zheltov Iu, P., Kochina, I.N., (1960). "Basic concepts in the theoryof seepage of homogeneous liquids in fissured rocks" , PPM, Vol. 14, No. 5, pp. 853-864.

Bingham, C., (1964). "Distribution on the sphere and on the projective plane" .Ph.D. Dissertation, Yale University, New Haven, Connecticut, U.S.A.

Cacas, M.C., Ledoux, E., De Marsily, G. and Tillie, B., (1990). "Modelling fracture flow with stochastic discrete fracture network: calibration and validation-" (1) Theflow model. Water Resources Research, Vol. 26, pp. 479-489.

Dershowitz, W.S., (1979). "Probabilistic model for the deformability of jointed rockmasses". M.Sc. Thesis, Massachusetts Institute of Technology, Cambridge,

Massachusetts.

Dershowitz, W.S., Herbert, A. and Long, J., (1989). "Fracture flow code cross

verification plan". Stripa Project Technical Report SKB 89-02, Stockholm.

Dershowitz, W.S., Lee, G., Geier, J., Foxford, T., Laponte, P. and Thomas, A.,(1995). Fracman: "Interactive Discrete Fracture Data Analysis, Geometric Modelling, and Exploration Simulation", User Documentation. Golder AssociatesInc., Redmond, WA.




72

Deutch, C.V. and Journal, A.G. , 1992. "Geostatistical Software Library and User’sGuide", Oxford University Press, 340p

Geier, J.E. and Axelsson, C.L., (1991). "Discrete fracture modelling of Finnsjonrock mass; Phase I: Feasibility Study" . Swedish Nuclear Fuel and WasteManagement Co., Technical Report No. SKB 91-13, Stockholm.

Gingarten, A.C., (1982). "Flow test evaluation of fractured reservoirs", Geol. Soc.of America, Special Paper 189, pp. 237-263.

Hugakorn, P.S., Lester B.H. and Faust, C.R., (1983). "Finite element techniques formodelling groundwater flow in fractured aquifers". Water Resources Research, Vol.

19, No. 4, pp. 1019-1031.

Lee C. and Farmer, I., (1993). "Fluid flow in discontinuous rocks". Published byChapman and Hall, London & New York, P.169.

Long, J.C.S., Gilmour, P.S. and Witherspoon, P.A., (1985). "A model for steady state flow in random 3-dimensional network of disc-shaped fractures". Water

Resources Research, Vol. 21, pp. 1105-1115.

Mark A. Jones, Alec B. Pringle, Iain M. Fulton and Shane O’Neill, (1999). "Discrete fracture network modelling applied to groundwater resource exploitationin Southwest Ireland". Fractures, Fluid flow and Mineralization. Geological Society,London, Special Publications 155, pp. 83-103.

Osnes, J.D., A. Winberg, and J. Anderson, (1988). "Analysis of Well Test data – Application of Probabilistic Models to infer Hydraulic Properties of Fractures", Topical Report RSI – 0338, RE/SPEC Inc., Rapid City, South Dakota.

Radhakrishna, B.P., (1970). "Problems confronting the occurrence of groundwaterin Hard Rocks" , Proceedings of seminar on Groundwater potential in Hard Rocks ofIndia, Bangalore, pp.27-44.

Terzaghi, R., (1965). "Sources of error in joint surveys" . Geotechnique, Vol.15, pp.287-304.

Tsang, Y.W., and C.F. Tsang, (1987). "Channel Model of flow through fracturemedia", Water Resources Research, Vol. 23 (3), pp. 467-479.

UNESCO, (1999) – "Water Resources of hard rock aquifers in arid and semi-arid zones" , edited by J.W. Lloyd.




Allied Publishers, 2001,pp.73-80

73

Aquifer Flow Modelling by Numerical Simulation in

Mahi Right Bank Canal Command Area, Gujarat, India.

A.K. Rastogi

Abstract

The study area of Mahi Right Bank Canal Command (MRBC) is situated in

Kheda Dist. Gujarat State. The aquifer region covers an area of 2952 square

kilometer and is bounded by rivers Mahi and Shedi on the northern, easternand southern boundaries, and Alang Drain on the western boundary. In the

present study groundwater flow behaviour in the water table aquifer was

simulated over a period of two specific years (June 84 to May 85 and June 91to May 92) based upon the available information. During this time span

recharge to the aquifer from various sources involving rainfall, canal seepage, irrigation return flow and discharge due to evapotranspiration,

pumping withdrawals and outflow from the region were considered. Usingthe technique of recharge distribution coefficient finite element solutions in

terms of aquifer heads were obtained for the entire flow domain. A close

agreement was noted between the observed groundwater head contours and

the simulated contours for the period of May 1985 and May 1992respectively. The average rise of water table observed for the two years

1984-85 and 1991-92 was 1.732m and 2.241m respectively which compared

favourably with the simulated rise of water table of 1.815m and 2.163mrespectively for the corresponding years.

Keywords: Aquifer, Modelling, Finite element, Recharge distribution,

Water table

1. INTRODUCTION

With a phenomenal increase in the use of groundwater in recent years, the need hasarisen for a better understanding of the aquifer head behaviour in response to

recharge and pumping withdrawals from the system. This is essential for asustainable development of the groundwater reservoirs. The available analyticalsolutions derived on the basis of certain assumptions are restrictive in use, in as




74

much as the real systems are quite complex in the geometry and the stresses imposedon the system vary widely in space and time. Consequently groundwater flow

modelling plays an important role, particularly, in simulating the head behaviour in

large aquifer systems, and is an important tool for groundwater systems planningand management. This has ensured harmless and timely supply of water to meet the

ever increasing irrigation, industrial and municipal demand of water in many parts

of the world which rely on groundwater based supply schemes. In an aquifer host of

parameters cause dynamic stresses in the system which influence the groundwater

head which is an important state variable in the flow domain. Recharge from therainfall, return flow from the cultivated areas irrigated by canal water and tube wells,

seepage losses from tanks and canals, river discharge and recharge, inflows and

outflows from the flow domains and evapo transpiration loss continuously interactwith the aquifer and cause changes in the ground water tables. Normally it is very

difficult to exactly quantify the net recharge into an aquifer because except for

pumping and evapo transpiration losses, the other contributions to the aquifer asmentioned above can not be estimated with exactness. Presently the value for these

parameters is worked out based upon the recommendations of the Ground Water

Recharge Estimation Committee (1984) and Indian Agricultural Research Institute

(1983). These values are given by national experts after considerable research

experiments in various types of aquifer conditions.

Presently a groundwater flow model involving finite element method (FEM) is

developed for a field problem. Mahi Right Bank Canal (MRBC) command areasituated in Kheda and Anand districts, Gujarat state, India is chosen for the present

study.

2. THE STUDY AREA

The present study region of MRBC command area (Fig. 1) covers an area of 2997sq. km and is bounded by Shedi river in the north, Mahi river in the east and south

and Alang drain in west direction. The MRBC command area lies between north

latitudes 220 26′- 22

055′ and east longitudes 72

0 49′- 73

0 23′ and covers seven taluks

namely Thasra, Anand, Cambay, Nadiad, Petlad, Borsad and Matar. The climate of

the area is arid to semi arid with an average rainfall of 823 mm. About 96% ofrainfall occurs in the monsoon season (June-Sept) and there is substantial variation

in the monthly and annual rainfall.

Detailed field investigations of the region were carried out by the Gujarat Water

Resources Development Corporation (GWRDC), Gujarat state. Lithological crosssections of selected regions of the area have indicated the presence of a main water

table aquifer consisting mostly of a mixture of gravel and sand which exhibits a

large variation in the conductance properties. The transmissivity values range from

196 to 6830 m2

/d with the highest values occurring in the eastern part of the aquifer.These values in general also tend to increase from north to south. The applicable

value of specific yield within the aquifer region is 0.15.




75

LOCATION

MAP OF

STUDY AREA

MRBC COMMAND AREA

N

INDIA

Fig. 1: Location of study area

Analysis of water table maps of the past few years suggested that the recharge to the

aquifer from rainfall, canal seepage, and irrigation return flows exceeds the

groundwater withdrawals from the region resulting in a steady rise of water table.

For simulation purposes net annual recharge values over the area were considered.

However, spatial distribution of the net recharge over the region is influenced bydifferent surface runoff rates, changing evaporation and evapo transpiration rates

due to varying soil texture, vegetation cover and urban development. The values of

recharge from various sources are worked out presently using the norms given byGround Water Recharge Estimation Committee (1984) and the Indian Agricultural

Research Institute (1983). These are presented in Table 1 for the year June 84-

May85 and 91-92 respectively. The concept of recharge distribution coefficient(Sondhi et el 1989) is used presently to apply the appropriate recharge to various

nodal sub-domains. This has been considered a better way of distributing the

recharge adequately in the large aquifer systems.

The important steps involved in the computation of recharge distribution coefficients

(R d) are:

♦ Obtain the groundwater head contours of the flow domain for two successiveyears N and N+1 from the field observations.




76

♦ Compute the difference of nodal heads between N and N+1 year, which givesthe annual water table rise at a node due to the net nodal recharge.

♦ Multiply the above difference with the nodal area of influence and the specificyield, which gives the applicable annual nodal recharge (AANR) at the node.

♦ Compute the average annual nodal recharge (ANR) at the node by dividing the

net recharge in the flow domain by the total flow domain area and multiplied bythe nodal area.

♦ Ratio of applicable annual nodal recharge to the average annual nodal recharge

at the node gives the recharge distribution coefficient (R d) value for the nodal

area of the flow domain ! "

#$%

& =

ANR

AANR Rd .

It is also assumed that in the present model the average annual inflow is almost

insignificant (zero) compared to average annual outflow across the boundaries,

which is computed by subtracting pumping withdrawals and aquifer storage from

the net annual recharge. The no inflow assumption is justified in view of acontinuously rising trend of the water level in the MRBC region over the past

several years which suggests the only possibility of aquifer storage and outflows.

3. FINITE ELEMENT MODEL

The general governing equation for the groundwater flow in the MRBC commandarea can be given as

t hS R

yhh K

y xhh K

x y y x∂∂=+

'()

*+, ∂

∂−∂∂+

'()

*+, ∂

∂−∂∂ )()( η η (1)

where

h (x, y, t) is the hydraulic head (m),

Sy is the specific yield,

K x and K y are the hydraulic conductivity values (m/d) in the principal axes direction,

η(x,y) is the elevation of aquifer bottom (m),and R (x,y,t) is the net nodal recharge (m/d).

The initial and boundary conditions for the problem are given as,

h (x,y,0) = H (x,y) for all x,y ∈ Ω (2)

h (x,y,t) = HR (x,y,t) for all x,y ∈ Ω1 (3)




77

where, H is the initial groundwater head (m) in the aquifer domain Ω and HR is the

known head (m) along the Alang drain and the river boundaries Ω1.

The solution of the above governing equation (1) is obtained by Galerkin's finiteelement approach for which detailed formulation is presented. The study area is

divided into 171 nodes with 294 triangular elements (Fig. 2).

M A H I R I V E R

SHEDI RIVER

A L A N G D

R A I N

O Observation wells

No. of Nodes: 171,

No. of elements: 294

Fig. 2: Finite element grid

Aquifer properties and applicable net recharge are assigned to each element of the

domain. The resulting system of linear equations can be finally written in the matrix

form as,

[ ] [ ] [ ] LtL

ttL FhP

thP

tG +

∆=!

"

#$%

&

∆+ ∆+ 11

(4)

where [G] is the conductance matrix containing hydraulic conductivity terms, [P] is

the storage matrix with specific yield terms, ∆t is the size of timestep, vector FL is

the net flux at node L, ht+∆t

is the unknown head vector and ht is the known head

vector at time t. The solution is then carried out iteratively and during each timestep

size of one day the right hand side known vector and the conductance matrix is

updated with the latest head values to take care of the transient nature of the problem.




78

Using June 1991 initial water levels the FEM model was run for one year and thehead distribution at the end of a year using applicable recharge values was

computed. The observed head contours of May 1992 are in good agreement with the

computed head contours. The groundwater head values varies from 55 m in the Northeast to 5 m in the South. Further, analysis of the results show that for a large

area within the flow domain the difference in simulated and observed heads is not

large. It is observed that in over 97% MRBC command area the difference in model

and observed head values does not exceed 2 m and in about 70.% area this reduces

further within 1 m (Table 2).

Table 2. Percent area covered by various ranges of difference

in the simulated and the observed head distribution

Difference in the simulated and observed head (m)

< 0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0

(1) (2) (3) (4) (5) (6)

Year

May 92

May 85

35.04%

30.77%

37.64%

43.59%

12.8%

17.95%

11.97%

6.84%

1.7%

0.85%

0.85%

0.00%

The head contours (Fig. 3) show the comparison between observed and computed

head values within the MRBC flow domain. Further, defining the average watertable rise

- !! " #$$

% & =

171

1 domain flowtheof areaTotal nodethat at tablewater of rise xareanodal ,

it was found that the computed average water table rise in the region exhibits a closeagreement with the average observed water table rise (Table 3) for both the

simulation years.

Table 3. Average water table rise in the MRBC flow domain

Water table rise in mMay 1985 May 1992

Numerically Computed

1.8152.163

From field observation1.7322.241




79

Computed Head

- - - -Observed Head

Fig. 3: Regional groundwater head

4. CONCLUSION

A finite element model simulating water table aquifer in the Mahi Right Bank CanalCommand area was developed using the concept of recharge distribution coefficient.Available data constrained the model for simulation periods of 1984-85 and 1991-92

respectively. Agreement between the simulated and observed head distribution in

the area indicated the validity of the model. The average rise of water table observed

for the two years 1984-85 and 1991-92 was 1.732m and 2.241m respectively whichcompared favourably with the simulated rise of water table of 1.815m and 2.163m

respectively for the corresponding years. The dominant groundwater flow direction

in the region remained almost the same (southwest) throughout the study period

despite variation in the dynamic stresses on the aquifer system. Velocity magnitudes

and fluxes were highest in the eastern part of the aquifer indicating it to be the mostfavourable region for further groundwater development. However, a continuous rise

of water table recommends increased utilization of ground water to avoid situations

of water logging in the area.




80

ACKNOWLEDGEMENTS

Help of Groundwater Resources and Development Corporation Gandhinagar,

Gujarat and MIC Nadiad is thankfully acknowledged for securing the required fielddata.

REFERENCES:

"Ground Water Recharge Estimation Committee Report" (1984) Ministry of

Irrigation, Ground Water Estimation Methodology, Govt. of India, New Delhi.

Indian Agriculture Research Bulletin 42 (1983) Water Technology Centre, New

Delhi. Indian Agriculture Research Institute, "Resource analysis and plan forefficient water management" . A case study of Mahi Right Bank Canal Command

Area, Gujarat.

Sondhi S K, Rao N H and Sarma P B S (1989) "Assessment of ground water

potential for conjuctive water use in a large irrigation project in India". Journal of

Hydrology 107:283-295





81

Mathematical Modelling of Chennai Area

Aquifer System

R.Ravi , P.N.Ballukraya and M.Thangarajan

Abstract

Infiltration of surface water is the main mode of recharge to the shallow groundwater system

of the Chennai city area and thus plays a major role in the sustained development of

groundwater resources in shallow aquifers. Recharge to the deeper (lower) aquifer is mainly

through leakage from the overlying unconfined aquifer. A two layer aquifer system was

conceptualised by consolidating all the available geohydrological data in the area of study.

Lateral boundary demarcation was done based on the information gained from boreholes

drilled in the area. The model was constructed and calibrated in two stages viz. steady state

flow and transient state flow conditions. During model calibration, field values of hydraulic

conductivity and storage coefficient were appropriately modified to achieve a better match

between computed and observed groundwater levels. The computed well hydrographs were

found to be matching reasonably well with the field hydrographs. The modelling study helpedin characterizing the two-layer aquifer system.

Keywords: Modelling, Multiple Aquifer System.

1. INTRODUCTION

The objective of the present modelling exercise is to realize the optimum levels of

utilization of groundwater as well as to characterize the aquifer system of the Chennai city

area (East Cooum Basin), approximately 500 sq.km (Fig.1), through mathematical

modelling. The computer software used for this purpose is the USGS-MODFLOW. Water

levels for the upper (top) unconfined aquifer were monitored from January 1992 by

establishing 101 monitoring wells in equally spaced grid pattern. Post- and pre-recharge

levels recorded during the years 1992, 1993 & 1994 in addition to monthly water levels

recorded in 26 wells during the period April 1994 to June 1995 have been used as historicdata to calibrate the mathematical model developed for the study area. In the case of lower

aquifer, only a few field observations were available and with these as the data base, a

two-layer aquifer system




82

was conceptualized and an attempt made to understand the complex hydrodynamics of

the flow regime using the above said software

2. HYDROGEOLOGICAL SETTING

There are two principal aquifers in the study area, both of which are generally fresh

water bearing, except a small part of the lower aquifer in the east near the sea coast

(sea water intrusion)(Ballukraya and Ravi, 1998) as well as a few isolated pockets

of highly brackish groundwater in the west. Both the upper (top) and the lower

(bottom) aquifers are mainly made up of medium sand/clayey sand of alluvial origin

deposited during Pleistocene/Recent period (Ballukraya and Ravi, 1995). The

thickness of sand/clayey sand horizon of the upper aquifer ranges from 2 to 30




83

metres. The saturated thickness is variable and dependant upon recharge from

rainfall infiltration. The nature of response during controlled aquifer testing

indicates that this unit is an unconfined or water-table aquifer. Hydraulic

conductivity in the upper aquifer ranges from 6 to 150 m/day. These are based on

the values obtained from a limited number of pumping tests carried out in some

parts of the study area. The storativity (specific yield) calculated from the laboratory

tests for this unit ranges from 0.18 to 0.25 (unconfined). Considering the fact that

the aquifer samples collected from drill cuttings are not truly representative of in

situ conditions, most of the clay and silt in it having been washed away during

sample collection, the specific yield is likely to be over-estimated. Recharge to the

unconfined aquifer is predominantly from the infiltration of rain water. The

discharge from the aquifer is through pumping from the dugwells/shallow borewellsfor domestic and industrial needs in the east and for irrigation in the west. The land

use pattern of the area as observed in the field is classified as urban, semiurban,

agricultural and underdeveloped (Fig.2). The Total groundwater abstraction from

blocks of one square km area in each of these land cover types has been calculated

to be approximately 1080 m3/day; 270 m3/day; 2000 m3/day and 50 m3/day

respectively.

Fig. 2: Land use pattern and discharge in metre per day steady state condition

The lower aquifer is also made up of predominantly medium grained sand/clayeysand with a thickness of 1 to 43m. The hydraulic conductivity and storativity of this

aquifer as determined from the pumping tests are in the range of 5 to 150 m/d and

0.05 to 0.0002 respectively. The time-drawdown curves of these tests indicate a

semi-confined flow condition. Very little field data is available as to the piezometric

head of the second aquifer since the borewells tested tapped both the upper as well

as lower aquifers, hence independent heads for the lower aquifer is not available.

However it has been assumed that it is five to six metres lower than that of the upper




84

aquifer based on a few field measurements. The hydraulic conductivity and

storativity assumed for this model is 6 to 100 m/d and 0.0002 to 0.0005

respectively. Below the second aquifer compact clay/shales of Gondwana age in the

west and clays/crystallines in the east and south form the basement. The upper and

lower aquifers are separated by a clay/sandy clay aquitard with a thickness of 1 to 27

metres and forming a semi-confining/leaky layer. The hydraulic conductivity and

storativity assumed for this layer is 0.1 to 5m/day and 0.001 respectively. The locations

in which aquifer parameters are available are given in figure 1.

3. BASIC PRINCIPLES OF GROUNDWATER MODELLING

Groundwater modelling is concerned with the behaviour of subsurface systems. Themodels are simplified representations of these subsurface systems (aquifers). Modelling,

therefore, may be considered as an exercise in system analysis whereby theories

concerning the behavior of groundwater systems are organised into models and used for

their predictive capabilities.

A groundwater system is composed of interacting parts. While recognising the different

components of the system and their functions, the ultimate concern of modelling is with the

operation of the groundwater system as a whole in relation to its surrounding environment.

Models integrate fragmented knowledge of the system's components and develop a

comprehensive conception of the entire system. Some degree of simplicity or assumptions

are required in modelling to represent or simulate groundwater systems. Approximations

are factored into the analysis via the assumptions incorporated into the model after

considering (1) the purpose of model, (2) the available computer code and (3) the databaseto be used in developing and testing the model. Although a model by design may be less

complex than the real system it represents, over-simplifying a system is not always

justified. Complete and comprehensive data is normally lacking for any specific

groundwater system and the gap between data needs and availability increases with the

complexity of the groundwater regime (Thangarajanet al ., 1991). The effective application

of models to field problems requires the ability to fill the data gaps with estimated,

interpolated or extrapolated values. Considerable scientific judgement of a subjective or

intuitive nature is often necessary for any degree of success in modelling. Attempts on

modelling without a measure of experienced judgement could prove to be

counter-productive.

4. MODELLING OF GROUNDWATER SYSTEMS

The groundwater modelling procedure involves an appropriate discretization of the

aquifer in space and time. The partial differential equation describing groundwater flow

in three dimensions in a porous media of constant density can be described as (Rushton

and Redshaw, 1979)

δ/δx (K xx δh/δx) + δ/δy(K yy δh/δy) +δ/δz(K zz δh/δz)




85

= W +Ss δh/δt (1)

where

K xx, K yy & K zz are the hydraulic conductivity along x,y and z co-ordinates which are

assumed to be parallel to the major axes of hydraulic conductivity (LT-1)

h is the potentiometer head (L)

W volumetric flux per unit volume and represents source and/or sinks of water (T-1)

Ss is the specific storage of porous material (L-1)

t is the time (T)

Equation (1) describes groundwater flow under non-equilibrium condition in a

heterogeneous and anisotropic medium, provided the principal axes of hydraulicconductivity are aligned with the x-y cartesian co-ordinate axis. The ground water flow

equation together with specification of flow and/or initial head conditions at the

boundaries constitute a mathematical representation of the aquifer system. The

groundwater flow equation (1) can be solved either using analytical or numerical

techniques. Though analytical solutions are exact, they can be only applied to idealistic

conditions and not for complex field problems. Therefore various numerical methods

have been employed to obtain approximate solutions.

Finite Difference Method is one such approach wherein the continuous system

described by equation 1 is replaced by a finite set of discrete points in space and time,

and the partial derivatives are replaced by terms calculated from differences in head

values at these points. The process leads to systems of simultaneous linear algebraic

difference equations and their solution yield values of head at specific points and time.These values constitute an approximation of the time-varying head distribution that

would be given by an analytical solution of the partial differential flow equation.

A computer software MODFLOW developed by the United States Geological Survey

(USGS, 1988) was used for the present study. A pre and post processor viz. visual

MODFLOW v. 2.00 developed by Guigner and Franz of Waterloo Hydrologic Software

Inc., Waterloo, Ontario, Canada (1996) was used for the graphical inputting of the data

and for analysis and presentation of the output data. MODFLOW can be used to

simulate groundwater flow in two or three dimensions. Groundwater flow within the

aquifer is simulated using a block centered finite difference approach. Multilayers can

be simulated as confined, unconfined or combination of both. The flows associated with

external stresses, such as wells, aerial recharge, evapo-transpiration, lakes with surface

water, drains and rivers can be simulated through this computer code. The finite

difference equation can be solved using either strongly implicit procedure (SIP) or WHS

solver, developed by the Waterloo Hydrogeologic Group. The WHS solver uses a

Bi-conjugate gradient stabilised (Bi-CGSTAB) acceleration routine implemented with

some incomplete decomposition for pre-conditioning of the groundwater flow partial

differential flow equations. This solver, as all iterative solvers, approaches the solution

of a large set of partial differential equations iteratively through an approximate




86

solution. Successive Over Relaxation (SOR) method is also available for solving the

finite difference equations. WHS solver was used for the present study.

5. MODEL DESIGN

Chennai city aquifer system was conceptualised as a two-layer aquifer system separated

by an aquitard layer. The study area was divided into 508 square grids of 1000m by

1000m with grid interval of 1000m in each layer. The grid map of the study is shown in

figure 1. The grid interval was chosen based on the availability of data and information

required for the model. The following boundary conditions and initial conditions were

used.

1. The surface elevation, bottom of the upper aquifer, bottom of the aquitard, bottom

of the lower aquifer, in metres, with reference to mean sea level ranges between 2

and 40; -12 and 26; -21 and 15 and -33 and 5 respectively. Similarly the thickness

of upper aquifer, aquitard and lower aquifer varies from 2 to 30m; 1 to 27m and 1

to 39m respectively.

2. The western boundary of the upper (unconfined) and lower (semi/leaky confined)

aquifers were taken as subsurface inflow boundary. The quantum of inflow was

estimated at 9000 m3/day received in both top and bottom aquifer respectively

(steady state). The quantum of inflow was calculated based on the transmissivity

values and hydraulic gradient. Layer two (clay/sandy clay) is taken as aquitard. The

north and south boundaries were treated as no flow boundaries as the flow is

predominantly in eastern direction in both the aquifers.

3. The subsurface outflow towards the sea along the sea coast in the east was

simulated as time-varying fixed outflow of 29,218 m3/day in both top and bottom

aquifers (steady state). The time-varying head was fixed based on water level data

from wells along the coast which ranges from -0.5 to -3m (I layer); -1.5 to -6m (II

layer) and -2 to -6.5m (III layer).

4. For the upper aquifer, aerial recharge was assumed to be 15% of the annual rainfall

on an average and the discharge (aerial; Fig. 2) assigned in the model ranges from

0 to 0.006 m/day and 0.00005 to 0.0015 m/day per unit area respectively. The

discharge for the lower aquifer, assigned in wells is 2000 m3/day in the agricultural

area (west) and 1500 m3/day in other areas.

5. The transverse flow between the aquifers were calculated in the model by making

use of differential heads between the top and the bottom aquifer and theintervening aquitard permeability and thickness.

6. The aquifer parameters K and S were assigned zone-wise for each layer. The

storativity assigned for the aquitard is 0.001.

7. In general one tenth of the hydraulic conductivity of the aquifer/aquitard is

assigned as vertical hydraulic conductivity in this model. However, in some places

it is assigned with different values.




87

8. The porosity of upper and lower aquifer is taken as 0.2 and for the aquitard it is

taken as 0.3. Specific storage is taken as one tenth of storativity for all three layers

(i.e. upper & lower aquifers and aquitard).

9. The initial water levels for the model were taken as that of January 1992.

10. The abstraction from the wells/borewells were calculated based on field estimates.

11. Yearly input and output quantities were used in the present model.

6. MODEL CALIBRATION

The main method of testing the accuracy of a groundwater flow model is to simulate

historical water level conditions and compare the computed values with the values

measured in the field. This process is known as calibration. The model was calibrated in

two stages viz., for a steady state condition and a transient condition.

6.1 Steady State Calibration

The aquifer condition of January 1992 was assumed to be the initial condition for the

calibration of steady state model. The model calibration was started with the assumption

that the aquifer was in a steady state condition (actually it is not so). The difference

between the computed hydraulic heads and the field data were progressively minimised for

each observation point. A number of trial runs were made by varying the hydraulic

conductivity values of the upper and lower aquifers so that the root mean square (RMS)

error was kept below 1.73m and mean error was kept below 0.7m. The calculated heads

for the upper aquifer are shown in figure 3 along with observed water levels.

This figure indicates that there is a fairly good agreement between the calculated and

observed water levels in most of the wells. The aerial abstraction from upper aquifer

assigned under steady state conditions are 1. urban area - 0.0006 m/day 2. semi urban area

- 0.00025 m/day, 3. agriculture area - 0.00078 m/day and 4. underdeveloped area -

0.00005 m/day (Fig.2). The rainfall recharge assigned under steady state condition for area

I, II, III, IV & V are 0.0007 m/day; 0.00045 m/day; 0.0007 m/day; 0.00022 m/day and

0.00066 m/day respectively. The calibrated zonal storativity (specific yield for first aquifer)

values for the upper and lower aquifers ranges from 0.025 to 0.1 and 0.0002 to 0.0005

respectively. The storativity value for aquitard is 0.001.




88

Fig. 3. Computed potentiometric surfaces (Jan. 92)

for upper aquifer (Steady state)

6.2 Calibration of Transient Flow

The hydraulic conductivity values, boundary conditions and waterlevels arrived through

the steady state model calibration were then used as the initial condition in the

calibration of transient flow model. The above were used along with the storage

coefficient distribution and variable recharge distribution in space and time. Thetransient (dynamic) calibration was carried out for the time period January 1992 to

December 1995. A number of trial runs were made by varying the storage coefficient

and aquitard permeability values in a most appropriate way so that a reasonably good

match is obtained between computed and observed well hydrographs. The computed

heads in the upper and lower aquifers for transient condition, for various time periods,

show a good agreement with the field values.

The computed well hydrographs for these wells of upper aquifer show a fairly good

agreement with the field values (Fig. 4). The mismatch observed in some of the

observation points are generally attributed to the differences in the initial head

conditions arrived through steady state calibration. The root mean square (RMS) error is

2.22 and mean error is 0.041 for the transient period (1461 days). The high RMS error may

be due to the assumption of water level for the second aquifer as there is no accurate data

for Piezometric levels in the second aquifer. The rainfall recharge of the areas I, III, IV &

V is assigned as 10% for 0-366 days (1992); 20% for 366 to 1096 days (1993 & 1994);

10% for 1096 to 1461 days (1995) and for area II, 75% of that of area I is assigned.

Similarly abstraction for upper aquifer is also assigned suitably for various time steps.




89

7. THE UNCERTAINITIES IN THE MODEL

Due to either sparse data or no data available in specific instances, some assumptions

and estimates were made during the conceptualisation of the Chennai aquifer system.

Any error associated with these assumptions gets reflected during the model calibration.

The following uncertainities are inherent in the model and have to be verified through

additional field investigations.




90

1. The thickness of the upper aquifer in some parts of the city area (small portion in

the south east) is less hence the wells are tapping the second layer (aquitard).

Actual demarcation of boundaries of layers i.e. upper aquifer, aquitard and lower

aquifer is difficult as the lithology of the area is complex or varying at very short

distances.

2. The calibrated hydraulic conductivities assigned for the upper and lower aquifer

are based on sparse data. There is no field data available for the aquitard.

3. The recharge as percentage of rainfall is assigned with only five representative

values based on data from three rainfall station.

4. Only three values of specific yield are assigned for the upper aquifer (as three

zones only).

5. Only two values of storativity are assigned to the lower aquifer (as two zones

only).

6. There is no accurate water level (piezometric head) data available for the second

aquifer for calibration. Also no field estimation of hydraulic conductivities is

available for the aquitard.

7. The groundwater budget obtained from the model is only 60 to 75 % of the

values estimated from the field calculations. As per this modelling, the yearly

recharge over the entire area is 124 MCM (1992); 157 MCM (1993); 172 MCM

(1994) and 117 MCM (1995) and the same from the calculations of field data is

166 MCM (1992); 262 MCM (1993); 259 MCM (1994) and 165 MCM (1995).

8. Field data for vertical permeability and porosity of the three layers (two aquifers

and aquitard) are not available.9. There is no field data for the inflow in the west and outflow to the sea.

10. Under transient condition, same amount of abstraction is assigned in lower

aquifer (for 0 to 1461 days).

11. The recharge and discharge calculated for the upper aquifer, based on the field

data could be suitably assigned for each node (unlike what has been done now).

12. As the aquifers are with complex hydrodynamic and hydrologic characteristics,

the zonal assignment of input parameters of the model could be further refined

i.e., each zone should be further divided into smaller zones and appropriate

values should be assigned to make the model best fitting.

8. CONCLUSIONS

The modelling study helped to improve the understanding of the complex

hydrodynamics of the Chennai city aquifer system. The modelling exercise indicates

that there exits a two aquifer system and also that there are vertical leakages from the

first aquifer to the second aquifer. The land use pattern prepared based on field study

and the abstraction calculated in the field play a major role in constructing the model.

River Cooum and Adyar are essentially effluent streams, and this, along with the




91

impermeable layer of sediments they have formed on their beds, probably is the reason

why they have not contaminated the groundwater system to significant levels, inspite of

their carrying urban waste for most of the time. The velocity vectors of the first aquifer

brought out by this model show that the flow gradient is essentially eastward though

some local variations do exist. The study also shows that with a normal rainfall/more

number of rainy days (which allows a larger percentage of precipitation to infiltrate)

there may not be undue depletion in groundwater levels and that the water levels

recover to their original elevation after the recharge period. It is observed from the

modelling exercise that when the field data is sparse and/or approximate, a mathematical

model helps in understanding the true field conditions. However when the required field

data is available,the model ascertains the accuracy of the field data.

It needs to be pointed out that the model requires further refining. It could not be done at

the present stage for various reasons, most important of which being lack of

computer-time. This is reflected in the slightly high RMS errors reported. There is not

much doubt that with further work, a very accurate predictive model could be built

based on the present work.

ACKNOWLEDGEMENT

The first author gratefully acknowledges the Chief Engineer, State Ground and Surface

Water Resources Data Centre, Water Resources Organisation, Public Works

Department, Chennai for according permission for carrying out this research. The first

author also gratefully acknowledges the Director, National Geophysical Research

Institute, Hyderabad for permitting to work in the computer laboratory for carrying outthis mathematical modelling exercise.

REFERENCES

Ballukraya, P.N. and Ravi, R. (1995), "Hydrogeology of Madras city aquifers",

Jl. Geol. Soc. of India, Vol. 45, pp. 87- 96.

Ballukraya, P.N. and Ravi, R. (1998), "Natural fresh-water ridge as barrier against sea

water intrusion in Chennai city", Jl. Geol. Soc. of India, Vol. 52, pp. 279 to 286.

Guiger, N. and Franz, T, (1996), "Visual modflow Waterloo Hydrogeological

Software", Waterloo, Ontario, Canada.

Rushton, K.R. and Redshaw, (1979), "Seepage and Groundwater flow", Mc Graw Hill

Publishing Company, London.

Thangarajan, M., Singh, V.S. and Gupta, C.P. (1991), "Modelling leaky aquifer

systems: A case study", Water Resources Journal, Vol. 170, pp. 90-99.




94

irrigation districts including Wakool, Berriquin, Denimein and Cadell. Recharge tothe aquifer systems occurs principally from irrigation and rainfall recharge and in the

eastern parts as leakage from the bed of the Murray River. There are also major

contributions from the Wakool River, Edward Rivers and Billabong Creek, and thereis also significant leakage from major supply channels such as Mulwala Canal. A

limiting factor on the amount of water that can be extracted is the presence of saline

water within the Shepparton Formation overlying the low salinity aquifers. About 70

percent of the Shepparton has salinities in excess of 3000 EC. In addition, salinity of

the groundwater increases progressively in a westerly direction. Since 1971approximately 90 monitoring bores have been established which penetrate aquifers at

various depths and measurements of pressure levels are undertaken quarterly. There

are also 3500 shallow piezometers which are at depths less than 20 m which are usedto monitor water levels within and outside irrigation districts.

Groundwater is an important resource for rural and regional communities and forsustaining rural economies. It is also a vital resource for sustaining vital ecosystems.As surface water supplies are fully committed, demand for additional irrigation water

has placed greater pressure on limited groundwater resources. At present there are 210

pumping bores used for irrigation, and numerous shallow spear points which pump the

shallow groundwater in order to control rising water levels. Past estimates of wateravailable for extraction were around 400,000 ML and recent qualitative studies have

reduced that figure to 140,000 ML (Ross, 1999). Kulatunga (1999) reported that the

total groundwater entitlements for the Lower Murray region up to March 1999 was329840 ML. At present total entitlements for the Murray region stand at 273,000 ML.

Both groundwater users and the government agree that groundwater is a valuable

natural resource and should be used in a sustainable way. This means that present use

as well as any further development must be limited to the sustainable yield for theaquifer system. The development of the Murray Region groundwater model was

undertaken to provide estimates of sustainable yield which could then be used to bring present entitlements to a level within sustainable yields and to improve management of

the groundwater resource. The objectives of this study were to simulate groundwater

behaviour under varying climatic conditions and changing groundwater usage; toestimate net recharge, sustainable yield and water level simulations for various

pumping and climate scenarios; to predict response to groundwater pumping; and to

assist groundwater users and Resource Managers to prepare groundwatermanagement policies. This paper describes the development and calibration of the

model and presents the results of pumping scenarios.

2. THE LOWER MURRAY GROUNDWATER MODEL

The Lower Murray regional groundwater model covers an area of approximately

17,000 km2 equivalent to 5.7 percent of the Murray geological basin. The model

domain is bounded by Billabong Creek and the Murray River shown in Figure 1.Both form good boundary conditions for the shallow groundwater system. Although

the aquifers are large in areal extent as they form part of the Murray Basin, both




95

boundaries follow streamlines. The boundary along Billabong creek forms acommon boundary with the Lower Murrumbidgee groundwater model (Punthakey et

al 1996). In the deeper aquifers flow occurs across these boundaries with the flow

from Victoria crossing the southern boundary of GMA016 in a north westerlydirection. Similarly there is flow across the northern boundary flowing into the

Murrumbidgee region. The groundwater model used was MODFLOW and a grid of

2500 x 2500 m was imposed on the model area.

Billabong

Murray

Wakool

Edwards

Fig. 1: Model grid for the Lower Murray groundwater model.

The model comprises 3 layers and each layer represents a major regional aquifer system,

the Shepparton, Calivil and Renmark. The Shepparton Formation aquifer is mostwidespread, and because it essentially forms the land surface it has a major influence on

recharge conditions. It is not a high yielding aquifer however, with relatively low values of

hydraulic conductivity and storage. The Calivil aquifer is exposed at the land surface in

some areas, notably near the eastern margin of the Basin. It therefore also plays an

important feature in recharge to the regional aquifer system. It commonly has higher valuesof hydraulic conductivity than the Shepparton aquifer, and in the basin-margin areas where

the influence of the alluvial fan deposits is present the values are very high. In these areas it

can be the major water yielding part of the aquifer system. The Renmark aquifer is thedeepest of the aquifers, and is nowhere exposed at the land surface. Apart from the alluvial

fan areas, it is the most important of the aquifers, with greater thickness and generally high

values of hydraulic conductivity because of the high proportion of sand and gravel it

contains. Aquifer properties were determined from hydrogeologic database which includedinformation on drillers logs, depth of bore, location, and limited water quality information.

Water level and piezometric surfaces were generated for each of the layers using

monitoring data. The modelling time frame extended over fifteen years from March 1985to February 2000 and monthly stress periods with a total of 180 stress periods.




96

Fig. 2: Reported monthly usage pattern from 1975 to 1989 (ML/mo)

The transient packages used in the model were recharge, evaporation, river and well.

Recharge and evaporation were estimated from monthly rainfall records for sevenrainfall stations within the Murray region and estimates of surface irrigation. Soil

descriptions were used to identify zones of high, medium and low recharge and

appropriate factors were applied. Initial estimates were fine tuned during calibration.For evaporation estimates landuse, critical depth and topography were used to

identify areas where evaporation would occur if the water table in those cells rose

above specified critical depths. The river package was used to quantify theinteraction between the river and aquifer system. The flow to or from the aquifer is

controlled by the difference in head between the river and the aquifer within a celland the conductance of the river bed. Each river was divided into reaches such that

each reach is completely contained within a single cell, and stream-aquifer seepage

is simulated for each reach within that model cell. The model of stream-aquifer

interaction used here assumes the interaction is independent of the location of thestream reach within the cell, and the stream level is uniform over the reach and

constant over the stress period. The use of a single conductance term to describe

what is essentially a 3-dimensional flow process is a simplification which requiresadjustment during model calibration. Processors were developed to specify river

stage, bed conductance and river elevations for each river cell.

There were reasonable records of groundwater usage from 1975 to 1989 however

these were generally underestimated due to lack of metered data. Between 1989 and1999 usage data was minimal due in part to lack of monitoring and loss of data due

to database transition. In order make reasonable estimates of usage a methodology

was devised which was based on the ratio of reported usage to entitlements for each bore and the historical distribution of monthly usage from 1975 to 1989 shown in

Figure 2. Groundwater usage peaks between November and January during the

irrigation season and is lowest in winter during June and July. In addition during the

0

200

400

600

800

1000

jul aug sep oct nov dec jan feb mar apr may jun

U s a g e M L / m o

Monthly Usage Pattern (1975-89)




97

estimation period growth factors were used which approximated the increase inentitlements which grew from 52,700 ML in 1986 to 296,000 ML in 1999.0 During

the modelling period (1985 to 2000) groundwater pumping from all three layers

increased from 19,700 ML to 98,700 ML and from the deep aquifers (Calivil andRenmark) increased from 7400 ML to 77,800 ML indicating increased use of

groundwater for irrigation. The major growth in usage from the deeper aquifers

occurred during the past five years from 1995 to 2000.

3. CALIBRATION OF THE LOWER MURRAY GROUNDWATER MODEL

The Lower Murray groundwater flow model was calibrated using observed potentiometric data from 1985 to 2000. Comparison of contours of observed heads

and modelled heads for the Shepparton, Calivil and Renmark aquifers at the end of

the simulation period in March 2000 showed the modelled heads matched the

observed head contours closely. The RMS error for each layer was 0.99, 1.12, and0.98 m for the Shepparton, Calivil and Renmark layers respectively.

The model was also calibrated for the transient response at selected bore sites where

piezometric heads were monitored. For the shallow aquifer the trends in several

bores showed that water levels were continuing to rise as shown in Figure 3. Bore36391 in Figure 3 shows water levels continuing to rise over a fifteen year period

from 1985 to 2000, whereas bore 36744 shows a steep rise until 1993 after whichthe water levels seems to have stabilised between 101.5 and 102 m AHD. During

bore calibration emphasis was placed to ensure that trends were closely matched

particularly post 1995 when pumping stresses had increased significantly for both

Calivil and Renmark layers as shown in Figure 4. The Calivil bore 36585 in Figure4 shows piezometric levels are steady until 1994 after which there are steep declines

reflecting the increased pumping stress post 1995. The Renmark bore 36744 in

Figure 4 shows a similar trend to the Calivil bore, piezometric levels are steady until1994 after which there are steep declines reflecting the increased pumping stress

post 1995.

Fig. 3: Calibration of Shepparton bores 36391 and 36587

(observed – light line, and modelled – dark line)




98

Fig. 4: Calibration of Calivil bore 36585 and Renmark bores 36742 and 36744

(observed – light line, and modelled – dark line)

Improvement in model calibration and performance can be achieved in the future,since the Department of Land & Water Conservation has instituted a program for

metering all deep bores. Improvement in groundwater usage data quality and afterthe data is collected for a period of at least three years, the model can be re-adjusted

to better reflect the improved data quality and also to improve estimations of

sustainable yields and long term response to pumping.

3.2 Water Balance for the Calibrated Model

The water balance for the model averaged over 15 years from 1985 to 2000 is shownin Table 1 below. The water balance indicates that significant changes have

occurred in the 1998-2000 period compared to the average over the past 15 years.

Notable amongst these is that evaporation has increased reflecting higher watertables in some areas of the model. There has also been considerable decrease in

recharge from the river to the aquifer as head gradients between the river and aquifer

decrease in response to higher water tables. The increase in discharge to the river

system is also important as it will increase in saline inflows to the river system.

Table 1. Water balance for the Lower Murray model

for 1985-2000 and 1998-2000 (Gl/yr)

Inputs/Outputs +/- 1985-2000 1998-2000

Recharge + 213 243

River to aquifer + 76 51

Boundary flows in + 33 34

Evaporation - 18 35

Aquifer to river - 48 57

Boundary flows out - 14 13

Wells - 53 106

Net Storage change 189 117

The major increase in pumping stresses from an average of 53 GL/yr to 106 GL/yrhas implications on leakage from the shallow to the deeper system and on

piezometric heads in the deeper layers where most of the increased pumping has




99

occurred. This can be better illustrated by examining water balances for the shallowShepparton aquifer and the deeper Calivil/Renmark aquifers as shown in Table 2

and 3. The increase in pumping from the deeper aquifers from an average of 22

GL/yr to 73 GL/yr in 1998-2000 has resulted in a negative net storage of –36 Gl/yr.This has also resulted in sharp declines in piezometric levels in parts of the aquifer

where pumping stresses are concentrated. Based on the 1998-2000 water balance

and by considering all inputs to the deeper aquifers we arrived at a figure of 58 GL

as an initial estimate of sustainable yield. The rational for taking all inputs was that

out flow boundaries are far removed from where pumping is taking place. Alsodeep groundwater pumping plays an important role in inducing net leakage

downwards and also in reducing upward leakage to the shallow Shepparton aquifer

which is experiencing rising water levels due to irrigation recharge.

Table 2. Water balance for the Shepparton aquifer

for 1985-2000 and 1998-2000 (Gl/yr)

Inputs/Outputs +/- 1985-2000 1998-2000

Recharge + 203 232

River to aquifer + 76 51


Calivil/Renmark to Shepparton + 12 10

Evaporation - 18 35

Aquifer to river - 48 57


Shepparton to Calivil/Renmark - 17 21

Wells - 31 33

Net Storage change 184 153

Table 3. Water balance for the Calivil/Renmark aquifersfor 1985-2000 and 1998 –2000 (Gl/yr)

Inputs/Outputs +/- 1985-

2000

1998-

2000

Recharge + 10 11


Shepparton to Calivil/Renmark + 17 21


Calivil/Renmark to Shepparton - 12 10

Wells - 22 73

Net Storage change 5 -36




100

4. MODEL APPLICATION AND MANAGEMENT STRATEGIES

4.1 Management Strategies

Until the early nineties the focus was on continuing development of groundwater

resources. The impact that extraction of groundwater might have on its continuing

availability and dependent ecosystems was largely ignored. In addition, the rights of

groundwater users such as access rights and property rights were poorly defined.

Similarly users obligations were not clearly defined which led to the followingconsequences:

• Licensed entitlements for many aquifers were in excess of sustainable levels;

• Extraction of groundwater was approaching or exceeding natural recharge;

• Degradation of ecosystems that depend on groundwater;

• Perceived inequities within, and between, users; and

• Uncertainty about the impacts of groundwater use on other values – environmental,social or economic.

Groundwater resource management in Australia is undergoing extensive reform

under the umbrella of the Council of Australian Governments (COAG). In thiscontext the NSW Groundwater Quantity Management Policy and the Regional

groundwater strategies has been prepared. The strategies will guide the actions of

regional resource managers in their management of activities that can impact on

groundwater. Additionally, the strategy clarifies the context in which individuals,

businesses and others can use this valuable resource. It also seeks to protect theresource for present and future generations. The strategies are designed to meet the

following objectives:

• To achieve efficient, equitable and sustainable use of the State’s groundwaterresources;

• To prevent, halt, or reverse degradation of the States groundwater anddependent ecosystems;

• To provide opportunities for development which maximise cultural, social and

economic benefits to the community, region, state and nation, within the context

of environmental sustainability; and

• To involve the community in the management of groundwater resources.

The single most important long term change will be the active involvement of the

community in the management of natural resources as the communities that depend

on these resources take responsibility for sustainable levels of extraction. Access togroundwater will be managed within sustainable yield, so that groundwater is

available for future generations, and dependent ecological processes remain viable.

Sustainable yield has been defined as the long-term average annual recharge to theaquifer, less a portion that is set aside for environmental purposes. The policy is

intended to allow groundwater use without compromising the integrity of the aquiferor the surface ecosystems that it supports. Estimates of sustainable yields based on

the results of groundwater models will provide information on managing




101

groundwater resources on a long term sustainable basis. In addition groundwatermodels will also provide information on the impact of short term extraction in

excess of sustainable yields particularly in those periods when surface water

resources are fully committed.

4.2 Pumping Scenarios

Two long term pumping scenarios were tested in order to examine impacts on the

deep aquifers. The first scenario involved pumping of 73 GL per year which is the1998-2000 pumping rate, and the second scenario was undertaken by reducing

pumping at 60 GL per year to better reflect total inputs to the aquifer. The model

was then run for a ten year period from 2000 to 2010 using climatic inputs from1990 to 2000. A comparison of these scenarios are included in figure 5 which

shows the change in net storage over time.

Calivil/Renmark net storage for 73 & 60 GL pumping till

2010

-300000

-200000

-100000

0

100000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Time (months)

N e t S t o r a g e ( M L )

pumping 73 GL/yr

pumping 60 GL/yr

Fig. 5: Comparison of the 73 GL and 60 GL pumping scenarios(73 GL – dark line, and 60 GL – light line)

The 60 GL scenario shows that the decrease in net storage over time reduces within10 years and the curve begins to flatten out. An analysis of the water balance shows

that total inputs are exceeding pumping by 12 GL/yr during the last two years. A

similar trend is noted for the 73 Gl scenario, however the flattening of the curve isnot as pronounced. Total inputs for the 73 Gl scenario are less than the pumping

rate by 5 Gl/year during the last two years of simulation, which indicates that

should the model be run for a longer period of time say 30 years the total inputs

should exceed pumping from the aquifer. As resource managers we need to decidehow best to use this information to manage the aquifer system. The key concerns

are at what level do we want to manage piezometric heads for the deeper aquifers

and what time frames should we allow for the piezometric surface to stabilize.




102

5. CONCLUSIONS

A groundwater model was developed for the Lower Murray region so that it could

be used to assist resource managers and the community to better manage thegroundwater resources of the region. The model comprises three layers each

representing an aquifer corresponding with the Shepparton, Calivil and Renmark

system. Layer water balances showed that the major increased groundwater

pumping during the calibration period has increased net leakage downward from the

shallow to the deeper system. The increase in pumping from the deeper aquifersfrom an average of 22 GL/yr to 73 GL/yr in 1998-2000 has resulted in a negative net

storage of –36 Gl/yr. This has also resulted in sharp declines in piezometric levels in

parts of the aquifer where pumping stresses are concentrated. Estimates ofsustainable yields based on the results of groundwater models will provide

information on managing groundwater resources on a long term sustainable basis.

In addition groundwater models will also provide information on the impact of shortterm extraction in excess of sustainable yields particularly in those periods whensurface water resources are fully committed. Based on the 2000-2010 scenarios an

initial sustainable yield estimate of 60 GL is proposed with 75 Gl as the 125 percent

limit of sustainable yield to meet short term groundwater supply requirements. In the

Lower Murray region deep groundwater pumping plays an important role ininducing net leakage downwards and also in reducing upward leakage to the shallow

Shepparton aquifer which is experiencing rising water levels due to irrigation

recharge, as such it has a positive environmental benefit.

REFERENCES:

Kulatunga N. (1999). "Groundwater resource status, Lower Murray alluvium GMA016". Groundwater status report No. 4. Land & Water Conservation, Murray

Region, 16 p.Punthakey JF, Prathapar, SA, Somaratne, NM, Merrick NP, Lawson S, and Williams

RM (1996). "Assessing impacts of basin management and environmental change in

the Eastern Murray Basin" . Journal of Environmental Software - Special Issue:MODSIM 95, Vol. 11. Nos 1-3, pp.135-142.

Ross J. (1999). "Sustainable yield estimates for high risk aquifers in NSW" . Land &

Water Conservation. Draft Report 16p.




Allied Publishers 2001,pp.103-114

113

Groundwater Modelling of Kallar

Watershed, Tamilnadu, India

M. Ramalingam

Abstract

The traditional management of land and water resources in a watershed should be reviewed periodically to keep pace with the modern methods ofresource management. In view of this an attempt has been made to develop a groundwater model for better utilisation of natural resources in a watershed.

In this study the Kallar Watershed has been chosen which lies in Tuticorindistrict, on the Southern part of Tamil Nadu. The above watershed has been

divided into grids of 1km X 1km in size and a distributed parameter(mathematical model) for the surface and subsurface systems have beendeveloped. The various inflow components and outflow components and netrecharge or discharge to the aquifer has been assessed. They were given as

input to the each grid of the groundwater model. The water requirements forthe various activities such as agricultural, human, animal population andindustrial requirements have been assessed. Similarly the total wateravailable in each micro watershed was assessed through the groundwatermodel. The analysis of data indicates that out of 81 microwatersheds 6

watersheds were assessed as surplus watersheds and the rest were deficit. From the above analysis it is possible to plan for suitable landuse accordingto the availability of water to get the maximum benefit.

Keywords : Mathematical modelling, Kallar watershed

1. INTRODUCTION

There is enormous pressure on the limited natural resources due to ever growing population thereby reducing the per capita availability of water resources. Thetraditional management of land and water Resources in a watershed should bereviewed periodically to keep pace with the modern methods of resourcemanagement. Hence there is an urgent need to adopt a holistic approach so as toensure maximum development of land and water Resources. In view of this an




104

attempt has been made to develop a groundwater model for better utilisation ofnatural resources in Kallar watershed located in Tuticorin district in the Southern part of Tamil Nadu. Thus the objective of this study to develop a model for thiswatershed to assesses the status of watershed by estimating the available surface andgroundwater resource by developing various sub models such as rainfall- runoff

models and distributed parameter model for the groundwater system. The modelformulation and the results obtained from this study are discussed in this paper.

2. FORMULATION OF THE MODEL

A distributed parameter model for the surface and the subsurface (groundwater)

systems has been developed. The various inflows such as (a) rainfall recharge, (b)river bed recharge, (c) return flow from irrigation and (d) subsurface inflow have been considered. Similarly the various outflows from the aquifer are (a) extractionfor irrigation from wells, (b) extraction of water to meet the requirements of human

and animal population, (c) loss due to evapotranspiration of natural vegetation and(d) subsurface outflow. A distributed mathematical model for the groundwater

system has been developed. The computations of various entities are brieflydiscussed below for both surface model and the subsurface model. The variousentities involves in the model are briefly discussed below.

2.1 Rainfall Recharge

Direct recharge by rainfall is one of the inputs to this aquifer and the magnitude of

the recharge depends on the intensity of rainfall over the aquifer and type of soilthrough which the rainwater infiltrates. The rainfall recharge is computed by

subtracting the runoff and evapotranspiration from the measured precipitation.

2.1.1 Surface Runoff

The surface runoff from the watershed is computed using the USDA (United StateDepartment Agriculture) SCS (Soil Conservation Service) curve number technique.

The SCS curve number (CN) assumes the following rainfall – runoff relation

(P-Ia)2

Q = 1(P-Ia+S)

where Q is the volume of runoff, P is the volume of precipitation, Ia is the initialabstraction which depends upon the type of landuse and the depression storageavailable in the watershed, S is the maximum potential retention which is computed

using the following relation

25400S = – 254 2

CN




105

where CN is the curve number and content 254 in the above equations for S in mmand P and Q are also expressed in mm. The CN is computed based on the landuse practice adopted, Hydrological soil groups and AMC (Antecedent MoistureCondition). In this study the runoff was computed using the above equation. Thelanduse map required for this study is prepared using IRS – 1C LISS-III Satellite

data.

2.1.2 Evapotranspiration

The potential evapotranspiration (ETo) was computed using the following modified penman equation

ETo = AHn + Ea! 3

(A+!)in which A is the slope of saturation vapor pressure curve at mean temperature inmm of mercury per °C, Hn is the net radiation in mm of evaporable water per day, ! is the psychrometric constant (ie) 0.49 mm of mercury per °C and Ea is estimated as

shown below

Ea = 0.35 1+ µ f(u) (ew – ea) 4160

where µ is the mean wind velocity in Km / day, f(u) is the weighting factor for day

and night wind velocity at different humidity levels (ie.,) 19.875 ew is the saturationvapour pressure at mean temperature in mm of mercury and ea is the actual vapour pressure in air in mm of mercury. The actual evapotranspiration was estimated bymultiplying the crop co-efficient. The type of crops are identified from the landuse

map prepared using the satellite data. The rainfall recharge for each grid wasestimated by subtracting the runoff and evapotranspiration from the precipitation.

2.2 River Bed Recharge

The recharge contribution by the river flowing in the watershed can be assessed

using the following equation

QR = K vwh 5

In which QR is the quantum of river bed recharge, K v is the vertical permeability, Wis the width of the river and h is the depth of water available in the river. Since,

sufficient data are not available it is approximated as 20% of the rainfall recharge.




106

2.3 Irrigation Return Flow

The area which are under cultivation are liable to be recharged by a considerablequantity of irrigated water by return flow. This flow is estimated as 25% of thewater extracted from the aquifer for agricultural activities from the field experiment.

2.4 Sub-surface Inflow

Across the western boundary of the aquifer, some quantity of subsurface inflow hasoccurred due to hydraulic gradient. The total subsurface flow across this boundaryis distributed along the boundary nodes. Subsurface flow has been estimated using

the following equation.

Q = T I B 6

when Q is the quantity of inflow, T is the Transimissivity, I is the hydraulic gradientand B is the width of the aquifer. The width of flow is taken as unit grid width for

each node.

2.5 Agricultural extraction

The major extraction taking place in the watershed is for various agricultural

activities. From the analysis of pre-monsoon and post monsoon satellite data, thecropped areas have been delineated. By using the cropping pattern statistics, the

types of crops grown in the watershed have been assessed. By applying crop waterrequirements for those crops, the quantum of water required in excess of rainfall

from the aquifer for cultivation is arrived at using the following equation

q1 = Ai [ETo x K c – (P-Pi)] 7

where q 1 is the abstraction of groundwater for irrigation during the month in

cubicmetre, Ai is the irrigated area in Sq.Km., ETo is the potential evapotranspirationin metre during the month, P is the rainfall during the month and Pi is the infiltratedrainfall during the month in metres and K c is the crop co-efficient.

2.6 Extraction for human and animal population

The volume of water extracted for human and animal population was assigned toeach node based on daily per capita consumption. The available village wise population was distributed to the nodes, which are falling in that village. All thestudy area consists of only rural settlements, the human daily per capitaconsumption is taken as 45 litters / day and per capita consumption for animal isconsidered at 25 litters per day as per IS 1172-1974.




107

The loss due to evapotranspiration of Natural vegetation was discussed in para 3.1.2and the subsurface outflow was computed by adopting the same procedure ofestimation of subsurface inflow as discussed in the para 3.4.

2.7 Computation of changes in storage

After computing all the inflows and outflows from the system the net recharge ordischarge to the aquifer was computed using the following relationship.

I ~ Q = + "Q 8

when I equal to total inflow and Q equal to the total outflow from the system and

"Q equal to net recharge or discharge or changes in storage to the system. Here allthe information were prepared spatially and stored in each layer. Using theARC/INFO GIS Software, all the layers are overlayed and finally the net recharge todischarge to each node has been computed. The above quantity was computed foreach node and given as input to the groundwater model.

3. DEVELOPMENT OF GROUNDWATER MODEL

Any artifact that can duplicate the working of a system is termed as a model. The behaviour of the physical system can be expressed in terms of algebraic ordifferential or integral equation in the mathematical formulation. The partial

differential equation (Bittinger et al) governing the non steady state three

dimensional flow of groundwater in a non homogenous and isotopic aquifer is∂

T∂h

+ ∂ T

∂h+

∂ T

∂h=

S

∂h +

Qw9

∂x ∂t ∂y ∂y ∂z ∂z T ∂ t T

where T is the transmissivity in sq.km/day, h is the head in m, t is the time in day, Sis the aquifer storage co-efficient, x, y are the rectangular co-efficients and Qw Netrecharge or discharge to the aquifer. Since there is no general solution for the aboveequation, however numerical solution has been obtained using the finite difference

approach. The differentials ∂x and ∂y are approximated by the finite lengths "x and"y respectively and they are small compared to the total area of the aquifer, thediscrete model is a reasonable representation of the continuous system. The above

model was applied to the study area.

4. APPLICATION OF THE MODEL

The study area lies between Kovilpatti in the north and Ottapidaram in the South of

Tuticorin District, Tamil Nadu. There is a small river called Kallar traversing the basin and the Kallar watershed is bounded by 8°55’00” to 9°10’00” North latitudeand 77°45’00” and 78°15’00” east longitude. The area of Kallar Watershed is 650Sq. Km. and the location is shown in Fig.1. The aquifer area is divided into 1Km X




108

1Km grids in both along x and y directions. There are 50 columns and 20 rows in thegrid. The aquifer is treated as non-homogenous and an isotropic. The finitedifference lattice adopted for the study area is shown in the Fig.2.

Fig. 2




109

4.1 Delineation of boundary conditions

It is well known that the specification of proper boundary conditions is animperative and important step in the application of numerical models. They clearlydistinguish between the two types of boundary conditions the drechetlary conditions

the function specified and noiman condition with the gradient of the functionspecified. For the groundwater flow problems, this corresponds to the specificationof the groundwater levels and flow rates. The boundary conditions are incorporatedexplicitly in the algebraic equation developed in the numerical model and thesolution of the same follows as the next step. In the aquifer under study the northern boundary is treated as no flow boundary based on the lithological characteristic of

the subsurface formation. The western boundary is considered as flow boundaryalong with the flow rates as specified. The eastern boundary is the sea throughwhich some meager subsurface underflow occurs. In the absence of satisfactorydata on the head or flow condition along the Southern boundary it is treated as flow

boundary with unknown head and unknown flows along the boundary.

4.2 Estimation of Aquifer parameters

Pump tests have been conducted in four wells spread over the entire area of aquifer by the State surface and Groundwater Data Centre, Water Resources Organization,(WRO), Govt. of Tamil Nadu. The data are analysed using the double porosity

techniques since most part of the aquifers are heterogeneous formation with twodifferent permeable media Barenblatt et al

(1960) assessed that any infinitely small volume of rock consists of a large number

of porous blocks as well as large number of randomly distributed sized and orientedfissures. Using his hypothesis an attempt has been made in this study and the aquifer

parameters were estimated.

Based on the pump test data the draw down function (W) and the dimension lesstime factor (#) are derived together with the aid of the established logarithmic plot

using the well function W=4π T1S1/ Q and the dimension less time factor # = 4Tt/S

1 r

2 in which T1 is the transmissivity, S1 is the draw down, Q is the discharge and

S1is the storage co-efficient, ‘r’ is the distance between the pumping well and

observation well.

The total aquifer area has been divided into four zones based on the field pump testresults. The zones have been divided taking into account the columns as divide.

The first zone is from column 1 to 15, the second zone is from column 15 to 22, thethird zone is from 22 to 40 and the last zone is from 40 to 50 columns. Thecomputed volume of Transmisivity were finally modified by running the PESTmodule of MODFLOW version 4.2 and the modified parameter values have been used in the model development and final values used in the model is given

below in the Table 1.




110

Table 1 Final value of Transmissivity used in the model

Zone Nodes Covering the zone Values of Transmissivity M2/sec.

I

IIIII

IV

01 – 15

15 – 2222 – 4040 – 50

5 X 10-3

2 X 10-4

2 X 10-3

1 X 10-1

4.3 Data input into the model

The various components of inflows such as (i) rainfall recharge, (ii) river bedrecharge, (iii) return flow from irrigation, (iv) sub surface inflow and the various

outflow quantities such as (i) agricultural extraction, (ii) extraction for population(iii) Evapotranspiration loss due to natural vegetation and (iv) sub surface outflowand also the total inflow and total outflow has been computed for each node and

given as input to the groundwater model.

4.4 Calibration of the groundwater model

The computed and observed value of the groundwater levels for the year 1983 to 1988 has been analysed for the well No.93016 which is situated nearer to the node 6, 47 which has been analysed in detail. A hydrograph has been plotted showing the observed andcomputed groundwater level for the above well and presented in Fig.3. Similarly the datafor the year 1989 to 1992 has been analysed for proving for the same well. The computedgroundwater level and the observed groundwater level during the proving phase was also

plotted and shown in Fig.4. To illustrate the longitudeal variation in the aquifer betweenthe higher and lower potential a longitutional section of the aquifer levels plotted along the4

th and 10th row of the finite difference lattice. Similarly transverse levels of the aquifer

was also plotted. The groundwater contour for the observed and computed groundwaterlevels for the entire aquifer for Dec 1992 is shown in Fig.5. All the hydrographs andgroundwater contour indicated the close agreement between the observed and computedgroundwater levels.

4.5 Computation of available water

The above watershed has been divided into 81 micro watersheds of having area rangingfrom 5 to 10 Sq.km. The total quantity of water available in each microwatershed has beenassessed by computing the surface runoff and groundwater. The surface water that can be

harnessed in each microwatershed by constructing water harvesting structures has beenassessed using USDA SCS curve number techniques as discussed in para 3.1.1. As regardsto groundwater after calibrating and proving the groundwater model, it is used for assessingthe quantity of groundwater available. The model is run for every fortnight and the waterlevel at each grid points are estimated. The microwatershed boundary is super imposedover the finite difference lattice and the spatial distribution of grid points for each

microwatershed is assessed. The computed groundwater level in the grid point has beentaken and the average groundwater level for the microwatershed is assessed. Knowing the




111

average groundwater level, porosity and area of the aquifer, the total quantity ofgroundwater available have been estimated.




112

4.6 Assessing the status of watershed

The total quantity of water required for each microwatershed for the variousactivities such as (i) Agricultural requirements, (ii) domestic requirements, (iii)cattle requirements and (iv) industrial requirements has been assessed. The available

water in each microwatershed also has been assessed and the status of watershedweather it is surplus or deficit has been assessed.

5. RESULTS

The following results were obtained form the study. The precipitation is the primary

input in the model. The analysis of rainfall-runoff data for ten years (1983 – 92)indicates that the minimum value of runoff is 18.6mm and the maximum value is139.56mm. The analysis of data indicates that 83% of the inflow to the aquifer isdue to rainfall recharge, 16% is due to irrigation return flow and the balance is

contributed by river bed recharge and subsurface inflow. As regards to outflow, theanalysis of data indicates that 75% of the extraction from the aquifer is for

agricultural activities 26% as loss due to evapotranspiration of natural vegetationand very little extraction for human & animal population. There is a continuousvariation in groundwater storage over the period of 1983 to 1992. The annualinflow, outflows and change in storage are presented in Table 2.

The surface water and groundwater available in the entire watershed has beenassessed. The min, max and the average quantity of water that can be extracted over

the period of ten years (1983 – 1992) are 2.00, 25.00 and 11.35 Mm

3

. The averagetotal quantity of water (both surface and subsurface available in the entire watershedwas assessed as 147.65 Mm

3. With regards to the status of the watershed, analysis

of data indicates that 6 Nos. of watershed are assessed as ‘surplus watershed’ andthe balance 75 microwatershed are considered as ‘deficit watershed’.

6. CONCLUSIONS

The analysis of data indicates that an average build up of 28 Mm3 per year is taking

place. The groundwater contour drawn form both computed and observed waterlevel shows a variation of about 20cm. The analysis of data indicates that theaverage annual groundwater that can be extracted is 136.30 Mm3 and the surfacewater harvested is 11.35 Mm3 and the total quantity of water hernessable is 147.65

Mm

3

, where as the required water is much more than this. From the above study it isassessed that 6 Nos. of microwatershed are found to surplus watershed. The analysisof data indicates that in the case of surplus watershed additional area can be broughtunder irrigation where as in the case of deficit watershed, the existing area underirrigation to be reduced to make the watershed self sufficient.



M o d e l l i n g i n H y d r o g e o l o g y

1 1 3

T a b l e - 2

:

A n n u a l i n f l o w s a n d o u t f l o w s f o r t h e a q u i f e r , M m

3

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r e c h a r g e

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r e c h a r g e

R e t u r n

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S u b

s u r f a c e

i n f l o w

A g r i c u l t u

r a l

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r

P o p u l a t i o n

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a n i m a l

e x t r a c t i o n

E v a p o

t r a n s p i r

a t i o n

S u b -

s u r f a c e

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T

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C h a r g e

i n

s t o r a g e

C u m u l a t i v

e c h a r g e i n

s t o r a g e

1 9 8 3 - 8 4

5 6 0 . 0

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7

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A v e r a g e





115

Numerical Simulation of Groundwater Flow

Regime in a Part of The Lower Palar River

Basin, Southern India

M. Senthil Kumar and L. Elango

Abstract

Numerical simulation of groundwater flow is an effective management tool to assess the

components of the hydrological processes, understand the hydrodynamics of a basin and provide a mechanistic description of the flow of water in an aquifer. Such a simulation study

was carried out in a part of lower Palar River basin, Tamil Nadu, India. The finite differencecomputer code MODFLOW with Groundwater Modelling System (GMS) as pre and post processor, was used to simulate the groundwater flow in this study. The groundwater flow

was simulated in transient state condition. Computed results of groundwater head mimicobserved field data. The model can be used as an effective management tool to understand

the behaviour of the aquifer system.

Keywords: Groundwater, flow modelling, Palar River basin.

1. INTRODUCTION

Groundwater is a major source of fresh water. Increasing population growth andconcentration in combination with socio-economic progress results in increasingdemand for groundwater. This necessitates proper and effective management ofavailable groundwater resources. Groundwater modelling is a powerful management

tool which can serve multiple purposes such as providing a framework fororganising hydrologic data, quantifying the properties and behaviour of the systems

and allowing quantitative prediction of the responses of those systems to externallyapplied stresses. No other numerical groundwater management tool is as effectiveas a 3-dimensional groundwater model. Groundwater modelling has been effectivelyused for management of aquifer systems (Ophori and Toth (1989); Corbet and

Bethke (1992); Gomboso et.al (1996); and Gnanasundar and Elango (2000)). Such astudy has been attempted here in the lower (eastern) part of the Palar River basin,Tamil Nadu, India. Gupta et.al (1994) have carried out a preliminary work in theupper (western) part of the Palar River basin to study the migration of the




116

contaminants let into the Palar River from the leather tanneries. However, theeastern part of the area is characterised by enormous amount of groundwaterabstraction for the Madras Atomic Power Station (MAPS), industrial, agriculturaland domestic purposes. Hence, the present study assumes significance, asgroundwater modelling in this part of the basin is necessary for effective

management of the system. Thus this study was carried out with the objective ofconstructing a numerical model and studying the hydrodynamics of the lower PalarRiver basin. Computer software Groundwater Modelling System (GMS) was usedsimulate the groundwater flow for this study. This paper describes the preliminaryresults obtained from an ongoing study.

2. DESCRIPTION OF THE STUDY AREA

The part of the lower Palar River basin, Tamil Nadu, India, considered for thisstudy, is located 75 km south of the Chennai city (formerly Madras) and it covers anarea of 392 Km

2 (Fig.1). This area is bisected into two halves by the Palar River.

This is a seasonal river flowing during the months of November, December andJanuary. Western side of this area is bounded by the Bay of Bengal. This area enjoyssub-tropical monsoon climate with January and February as the dry periods, March

to May as summer period, followed by the monsoon period. The southwest monsoon(June to September), the northeast monsoon (October to December) and thetransition period supply 40%, 51% and 9% respectively of the total rainfall (1266mm/year) in the study area.

2.1 Geology

The study area exhibits varied physiographic features and the elevation ranges from40 m in the west to sea level in the east. Numerous tanks are present in the depressed parts of the undulating topography of the study area. Geologically, the study area

has two district formations as crystalline rocks of Archean age and alluvium of therecent age. These alluvial deposits occur along the present and palaeo Palar Rivercourses. This alluvial is comprised of sand, clay, gravel and sandy clay. Thethickness of the alluvium along the sides of the Palar River ranges from 10 to 30 m.Crystalline rocks comprising of charnockites and gneiss form the basement and

some exposures are found in the southern part of this area.

2.2 Hydrogeology

The alluvium and weathered crystalline Charnockites function as an aquifer system.Groundwater occurs in unconfined condition in both the alluvial and the underlyingweathered rocks.




117

Figure 1: Part of Lower Palar River Basin, Southern India




118

Alluvium occurring as upper layer is characterised by sand, gravel and sandy clayand its thickness ranges from 1m at northern and southern boundaries to 30m alongthe river. The hydraulic conductivity value of this alluvium ranges from 20 – 50

(m/day). The transmissivity values range from 200 to 400 m2/day and specific yield

value ranges from 0.037 to 0.18(PWD 2000). The lower layer is characterised byweathered crystalline rocks. The thickness of the weathered layer varies from 0 to 7m. The hydraulic conductivity of this layer ranges from 0.5 to 8 m/day,transmissivity varies from 10 to 80 m2/day (PWD 2000). The pore spaces developedin the weathered rocks along with the overlying alluvium functions as the potentialwater bearing formations.

3. GROUNDWATER MODELLING

The groundwater flow in the aquifer of the study area was simulated using a finitedifference approximation of the three dimensional partial differential equation,(Rushton and Redshaw. (1979))

δ δh δ δh δ δh δh ___ K xx ___ + ___ K yy ___ + ___ K zz ___ - W = Ss ___

δx δ x δy δ y δz δz δt

Where,

K xx, K yy, K zz = components of the hydraulic conductivity tensor

h = potentiometric head

W = source or sink term,

Ss = specific storage

t = time

This equation describes the groundwater flow under non-equilibrium andanisotrophic medium, provided the principal axes of hydraulic conductivity arealigned with x-y Cartesian Coordinates axes. MODFLOW, a well established, three-

dimensional finite difference groundwater flow model was used to simulategroundwater flow of this study. The pre and post processor developed by the UnitedStates Department of Defence Groundwater Modelling System (GMS), was used togive input data and process the model output. Block-centered finite differenceapproach was used to solve groundwater flow equation in this model.




119

4. MODEL FORMULATION

A detailed study of geology, borehole lithology and water level fluctuations in wellshas helped to arrive at the conceptual model of the system. As the groundwaterlevels in the wells penetrating upto the alluvium and the hard rock formation bearthe same groundwater head this region was conceptualized as an unconfined aquifer.This unconfined aquifer is divided into two sublayers due to variations in lithologyand hydraulic characteristics. Upper layer being the alluvial (sand, sandy clay, clay)

and the lower layer being the weathered rocks. The model grid covering 392 km2 of

the study area was discretised into 2400 cells with 40 rows and 30 columns, and

vertically by 2 layers (Fig. 2). The length of model cells is 900 m along the east-westdirection and 500 m along the north- south direction of the study area.

4.1 Boundary Conditions

The alluvium thickness along the northern, southern and western part is less than

one metre. The flow into the system from these boundaries will be minimal andhence it is considered as no flow boundary (Figure.2). The eastern part of the studyarea was considered as constant head boundary as it is bounded by the Bay ofBengal. Numerous storage tanks are present in the study area. However, only theflux from Madurantakam tank was considered because it is the only perennial tank.

This storage tank is represented by specified variable flux boundary. The PalarRiver, which flows through the study area, and its contribution, were considered. A

flux boundary due to recharge from rainfall and irrigation return was considered atthe top of the surface.

4.2 Aquifer geometry

The aquifer geometry includes defining the aquifer top, bottom, hydraulicconductivity and specific yield for all the cells. They were mainly derived from theresults of pumping tests and borehole logs reported in the PWD (2000). These

values were extrapolated for the entire area considering the lithological variationsand field study of well sections. The upper alluvial layer reaches the maximum

thickness of 30m along the Palar River and a minimum thickness of 1m along thenorthern boundary of the study area. The thickness of the weathered charnorkitevaries from 0 to 7m. In the southern parts of the study area the thickness of the upper

alluvial layer vary 0-2m while the lower




120

Fig 2: Model grid pattern and Boundary conditions




121

weathered layer extends upto 5 to 7 m from the surface. Hydraulic conductivityvalues used range from 4 to 50 m/day and the specific yield values range from 0.02to 0.32 depending on the lithology of both the layers. The aquifer top and bottomconsidered for this study is given in Figure 3.

Top elevation

Bottom elevationFig. 3: Aquifer top and bottom

4.3 Groundwater abstraction

Groundwater is abstracted for irrigation, Madras Atomic Power Station (MAPS),industries and for domestic purposes. Abstraction for irrigation was estimated basedon the landuse pattern (Fig.4). Approximately 210 km2 of the study area is being

used for irrigational activity out of which 133 km2 area depends on groundwater.

The abstraction rate for this region is calculated by considering water requirement

for different kinds of crops. A pumping well located at Panakattuchery (Fig .1) is pumping at the rate of about 3.5 million gallons per day (MGD) for the MAPS(PWD 2000). Abstraction for supply to industries is carried out at Ayapakkam at the




122

rate of about 0.75 MGD (CGWB 1998). Another important pumping station locatedat Valipuram supplies 0.5MGD water to Chennai city outskirts (PWD 2000).Abstraction for domestic purposes in this area is arrived from population and it isabout 0.3 MGD.

Fig. 4: Landuse pattern in the study area.

4.4 Recharge

The recharge in this area varies considerably due to the differences in the landuse pattern, soil type, topography and relief. Rainfall is the principal source ofgroundwater recharge. A comparison between the monthly rainfall value and

consequent variation in groundwater level over a span of 30 years revealed that thegroundwater is replenished whenever the monthly rainfall exceeds 60 mm. Therecharge amounts derived are given in Table 1. The contribution from Palar River isconsidered by a constant riverhead of 3 m during the months of flow. The recharge

from Madurantakam tank was arrived at the model from the difference between thetank water head and the groundwater head.

Table 1 Recharge value incorporated in the model. Rainfall in

mm/month

Recharge in

%

60-100 25

100-200 30

200-300 35

300 and above 40




123


The calibration strategy was to initially vary the best known parameters as little as possible, and vary the poorly known or unknown values the most to achieve the best

overall agreement between simulate and observed. The calibration of deterministicgroundwater models is often accomplished through a trial and error adjustment ofthe model’s input data (aquifer properties, sources and sinks, and boundary andinitial conditions) to modify the model’s output. Steady state model calibration wascarried out to minimise the difference between the computed and field water level

condition. Hydraulic conductivity values is varied from 20 to 48 m/day for the uppersublayer and 0.5 to 17 m/day for the lower sublayer in order to get a good match of

the computed and observed heads (Fig.5). Table 2 shows the initial and calibratedhydraulic conductivity values of the simulated head. The figure indicates that there

is a very good match between the calculated and observed water head in most of thewells of the study area. RMS (Root Mean Square) error was minimised to 0.76 m

and the mean error was minimised to 0.12 m through numerous trial runs. Undertransient state condition the model was simulated for a period of 5 years (1994 to1998) with stress period of 30 days each. The trial and error process by whichcalibration of transient model was achieved required several trials until an

appropriate set of parameters was obtained which provided a good match betweenthe computed and observed heads over space and time. The hydraulic conductivityvalues incorporated in the transient model were then modified slightly from thosecalibrated by the steady state model. Based on the close agreement betweenmeasured and computed heads at 29 observation wells throughout the aquifer, the

transient models was considered to be calibrated satisfactorily. The sensitivity of themodel to an input parameter can be tested by varying only the parameter of interest

over a range of values and monitoring the response of the model by determining theroot mean square error of the esimulated heads compared to the measured heads.The model’s sensitivity to changes in transmissivity, pumpage, hydraulicconductivity, and recharge were tested by increasing and decreasing values by a

uniform factor.

Table 2. Initial and calibrated hydraulic conductivity

and specific yield of the simulated head.

Hydraulic conductivity(m/day)

Specific yieldGeology of

the area

Initial * Calibrated Initial* CalibratedSand 50 46 0.29 0.32

Sandy clay 37 32 0.18 0.22

WeatheredCharnockite

8 5 0.02 0.03

* PWD (2000)




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Fig. 5: Computed and observed head in steady state calibration

6. RESULTS OF THE SIMULATION

The calibrated model simulates the regional groundwater head, which is comparedwith the observed data from 29 wells. The predicted regional head distribution ingeneral follows closely, the observed regional groundwater head (Fig. 6). Thus a

reasonable match between the computed and observed heads values were obtained inmost of the wells. The result of the numerical simulations indicates that there a

gradual decline in the groundwater level in the some of the wells. A comparison between the observed and computed head values for the observation well no. 6 and19 is shown as an example in Figure 7. Mismatch (maximum of 1m) was observedin some observation wells.

Fig. 6: Computed regional groundwater head (October 1996)

Computed head




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well no:19

10

11

12

13

14

15

1994 1995 1996 1997 1998

years

g r o u n d w

a t e r h e a d

i n m ( w

. r . m . s . l )

computed

observed

Observed head

Fig. 7: Computed and observed water head in wells no. 6 & 19.

well no:6

0

1

2

3

4

5

6

1994 1995 1996 1997 1998

years

g r o u n d w a

t e r h e a d i n m

( w

. r . m . s . l )

computed

observed

Fig. 6: observed regional groundwater head (October 1996)




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7. CONCLUSION

Simulation of groundwater head was carried in a part of the lower Palar River basin,using a finite-difference flow model for better understanding of the aquifer system.The model formulated reasonably predicts groundwater heads similar to the

observed trends. Hence, the model can be used as an effective management tool tounderstand the behaviour of aquifer systems under various stress conditions.However, in order to do this further refinement of this model is necessary withrespect to lateral and vertical variations in lithology, which is currently beingundertaken.

ACKNOWLEDGEMENTS

The authors wish to thank the All India Council for Technical Education (AICTE), NewDelhi for Providing the financial assistance to carryout this work. The help rendered by

Prof. C. Mohana Doss, Director, Centre for Geoscience and Engineering, Anna Universityin providing necessary facilities is acknowledged. Water level data provided by the Public

Works Department, Tamilnadu is acknowledged.

REFERENCES:

Corbet, D and Bethke, W. E (1992), "Disequilibrium fluid pressures and groundwater flow

in western Canada sedimentary basin". J Geophys Res. 97(B5): 7203-7217.

Gnanasundar, D and Elango, L. (2000), "Groundwater flow modelling of a coastal

aquifer near Chennai city", India. Journal of Indian Water Resources Society Vol.20no.4 pp162-171

Gomboso, J. Ghassemi, F. and Jakeman, A.J (1996). "Modelling groundwater flowin the Northern Stirling land conservation district western Australia". EcologicalModelling vol.80 pp 169-175.

Gupta, C.P. Thangarajan, M and Gurunadha Rao, V.V.S (1994). "Preliminary study of groundwater pollution the upper Palar basin and feasibility of mass transport modellingto predict pollution and migration", NGRI. Tech Rep no. 94- GW-168. pp. 45.

Ophori.D.U and Toth.J (1989). "Characterisations of groundwater flow by fieldmapping and numerical simulation, Ross Creek Basin, Alberta, Canada”,Groundwater vol. 27 no.2. pp 183-196.

PWD (2000). "Groundwater Perspectives A profile of Kancheepuram district", Tamil Nadu. Public Works Department. June pp 1-220.

Rushton.K.R and Redshaw.S.C (1979). "Seepage and groundwater flow" . John

Wiley and Sons Ltd. NY 330 pp.

Thangarajan.M, Masie.M, Rana.T, Vincent Uhil, Bakaya.T.B and Gabaako, G.G(2000). "Simulation of arid multi-layered aquifer system to evolve optimalmanagement schemes. A case study in Shashe River valley, Okavango Delta,

Botswana". Journal Geological Society of India Vol .55 June 2000 pp.623-648.





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Preliminary Numerical Model of The Regional Guaraní

Aquifer System, South America and Information

Management Proposal

Luis Vives, Eduardo Usunoff,

Heraldo Campos and Carlos Fernández-Jáuregui

Abstract

This paper presents a groundwater modelling effort for the Guaraní Aquifer, in

which the numerical model is used at the early stages as a methodological toolaimed at testing the various hypotheses regarding the aquifer features andbehaviour. The results approximately matched existing data, although highlightingthe effect of scarce information and the low reliability on many available data.

Based on such shortcomings, a decision support system is proposed to

eventually benefit all organisms, agencies and individuals concerned with the sustainable management of the regional water resources. The system,efficient, powerful, and open, is made up of a database that can be remotelyinspected via Internet. It has downloading/uploading capabilities, advanced

mechanisms of data searching, filtering, and visualization, and includesdialogue/communication services for those visiting the site.

Keywords: regional aquifers, groundwater flow modelling, Guaraní Aquifer,information system management

1. INTRODUCTION

The Guaraní Aquifer (16º to 32º S latitude, 47º to 56º W longitude) coversapproximately 1.194.000 km2 within the Paraná Basin in SE Brazil (839.000 km2),and the eastern portion of the Chaco-Paraná Basin (355.000 km2) in Argentina,Paraguay, and Uruguay (Figure 1).




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International border

National border

Guaraní Aquifer System

10°

10°

30° 30°

10°

10°

80° 60° 40°

80° 60° 40°100°

500 km

Mato Grosso

Goiás

Minas GeraisMato Grossodo Sul

Sao Paulo

Paraná

Sta. Catarina

Rio Grandedo Sul

ER

CO

MI

Fig. 1: The Guaraní aquifer system (shaded) in South America (Kittl, 2000).

More than 15.000.000 people live in this area where the aquifer is increasinglyexploited and constitutes the main source of freshwater for urban supply as well asindustrial and agricultural uses.

Initially, the modelling objective was posed so as to numerically simulate the aquiferdynamics in order to develop a tool for the sustainable management of its waterresources. It soon became evident that the information available was scarce andsometimes unreliable as compared to the extension and complex nature of thehydrogeological system. Therefore, a decision was made to use groundwater flowmodelling as a way of integrating all available information and testing severalhypotheses concerning the aquifer hydraulic behavior. That is the reason why this presentation calls it a preliminary numerical model, although it will be referredhereto as the Guaraní Aquifer model out of simplicity.

The modelling exercise followed the conventional stages: conceptual modeldefinition to qualitatively describe the main features, numerical structure buildingup, assessment of the elements of the system to be reproduced, and calibration toselect the most appropriate conceptual model.

Based on the modelling results, in particular their uncertainties, a decision supportsystem is proposed in order to store and handle all information related to the Guaraní




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Aquifer. Such a database, that can be inspected and fed via Internet, is conceived asa tool for helping researchers and decision-makers involved in the sustainablemanagement of the Guaraní Aquifer. It houses numerical and non-numericalinformation (climatic variables, hydrological/hydrogeological data, hydrochemical/isotoperecords, images, texts, etc.), visualization tools (graphs, zooms), provided withdownloading/uploading features via Intermet.

The progressive enrichment of the database, aside from possessing an intrinsicstrategic regional value, may promote a new attitude towards the management oftransnational regional water resources. At least two major challenges are in order:(a) to overcome the value given to the information and the unwillingness to releaseit, and (b) to achieve the adequate level of commitment by all potential users(governments, agencies, research groups, stakeholders).

This paper starts by presenting a summary of the geology and hydrogeology settingof the Guaraní Aquifer, followed by the proposed conceptual behavioural model.The numerical model is then described, as well as the calibration strategy. Resultsare discussed, which gives rise to proposing an innovative information managementsystem.

It should be mentioned that this initiative matches the scope of the ISARM Program(Internationally Shared Aquifer Resources Management) established by IHP-UNESCO, FAO, IAH, and UN-ECE, in that it promotes multidisciplinary studiesand detailed knowledge of the scientific, socio-economical, legal, environmental,

and institutional aspects related to groundwater resources internationally owned andshared. In that sense, the data base/Internet proposed for the Guaraní Aquifer Systemcan easily be implemented for any hydrological basin not only touching upongroundwater issues but also incorporating the existing water surface network, beingtransnational or not.

1.1 Geographical setting, geology and hydrogeology

With a known extent close to 1.200.000 km2, the Guaraní Aquifer System (GAS) isone of the world´s largest freshwater subterranean reservoirs. It is located in SouthAmerica, covering part of the national territories of Argentina, Brazil, Paraguay, andUruguay (Figure 1).

The geological and hydrogeological characteristics of such a large groundwaterreservoir can be found in Almeida (1983), Araújo et al. (1995 and 1999), Kittl(2000), Lavina (1991), Rebouças (1976), and Vives et al. (2000), among others, andonly a brief summary is offered below.

The study area is within the South American Platform, a basin of tectonic origin thatmay reach a sedimentary thickness of about 5.000 m along the western Sao PauloState (Brazil). A massive tectonic activity at the end of the Jurassic, mainly along




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the NNE and the NW directions, produced numerous faults and folds. At the sametime, alkaline-type magmatic events gave rise to dikes and sills of relevantmagnitude (Almeida, 1983).

The aquifer is in Permian-Cretacic sandstones, covered on at least 90% of its knownsurface extent by Jurassic-Cretacic basalts of varying degrees of fracturing/fissuring.Such sandstones range in thickness from few meters to more than 800 meters (in RíoGrande Do Sul, Brazil), and can be found in the surface (outcrops) to a depth ofmore than 2.200 m in the center of the basin. It is basically a confined aquifer, andits main source of recharge is infiltrating rainfall in those places where the basalticcover is not present. The groundwater flow is from the North-East to the South-West, with waters that incorporate solutes along the flow direction. The aquifer ismade up of red , fine to medium quartz sandstones, with grains well selected whichincorporate progressive proportions of clay with depth (Lavina, 1991). Overlying theaquifer (Figure 2),

Fig. 2: Guaraní aquifer cross-sectional views (Araujo et al. ,1999).

the basalts of the Serra Geral Formation show variable degrees of fracturing, which

locally makes the system to behave as aquitard or aquiclude. These basalts areconfined to the north by the Bauru Formation. Finally, the Piramboia Formationconstitutes the base of the whole aquifer system.

In those areas where the system behaves as a water-table aquifer (direct recharge),waters have the following characteristics: temperature between 22 and 27 ºC, pH between 5,4 and 9,2, total dissolved solids less or around 50 mg/l (calcium- bicarbonate type, followed by calcium-magnesium bicarbonate waters). Where the




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aquifer is confined, water temperature varies between 22 and 58,7 ºC, pH between6,3 and 9,8, and the total dissolved solids between 50 and 500 mg/l (calcium bicarbonate and sodium bicarbonate types, followed by sodium sulfate-chloridewaters).

Due to the ample range in latitude and the various relief types, the regional climateis varied. According to 1931-1960 records, the mean annual rainfall is between1.000 and 2.400 mm, the mean annual temperature is around 20 °C, the mean annualevaporation is from 650 to 1.100 mm, and the evapotranspiration ranges from 882 to1.071 mm/year (Rebouças, 1976).

2. CONCEPTUAL MODEL

The area modelled covers 902.636 km2 in Brazil, Paraguay and Argentina, and belongsto the Paraná hydrological basin. Due to the low density of data and the scarceknowledge on their hydrogeological features, the south-western portion of the systemwas not taken into account. Thus, the model has the following boundaries: outcrops ofthe Guaraní sediments (S, E, and W), discharge area in the region close to Torres City(SE), the first Cenozoic outcrops (SW), and the region where the aquifer forms a wedge between the Serra Gearl aquifer and the Passa Dois aquitard (N).

The conceptual model was defined by extrapolating to a regional scale the preliminary hydraulic behavior proposed by Campos (1998) for the Sao Paulo State.It is conceived as a confined unit (mainly sandstones) with a hydraulic conductivity

ranging between 0,2 to 4,6 m/d, that decreases with depth because of the increasing proportion of clays in the sediments. The Bauru and Serra Geral Formationsconstitute the aquifer top, while its base is limited by the Passa Dois, Tubarao andPre-Cambric Formations.

There are structural alignments (aulacogens) that affect the groundwater flow: insome areas they behave as preferential flow paths (similar to fractures), whereas inothers the effect is that of permeability anisotropy (less dense fractures and unevenspatial distribution).

The main entrance of water to the aquifer is recharge by direct infiltration inBrazilian territory, spatially distributed along the outcrops in the States of Sao Paulo,Goias, Mato Grosso do Sul, Paraná, and Santa Catarina.

Natural discharge areas are the plain regions and wetlands between the Uruguay andParaná Rivers, the southern and eastern sectors of Porto Alegre, and along theParaná, Pelotas, and Tietê Rivers (related to structural alignments). Anotherdischarge area is the heavy pumping in the center-western region of Sao Paulo State,with evident signs of overexploitation around the Ribeirao Preto City.




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3. THE MODEL: NUMERICAL AND STRUCTURAL SCHEMES

The flow model addresses only the Guaraní Aquifer, without regarding the confiningFormations (Serra Geral and Bauru). The regime is steady state, and the grid is 2-Dfinite elements. The coordinates are UTM and the units are homogeneous allthrough (meters and days).

The code used is TRANSIN II (Medina et al., 1996), which is able to simulate waterflow and solute transport. A premier advantage of this code is that it allows theautomatic calibration of all flow and transport parameters, from measured values ofgroundwater levels and solute concentrations. The automatic calibration, based insolving what is known as the inverse problem, is achieved through statisticalmethods that maximize the likelyhood of the estimation errors (Carrera and Neuman, 1986). Data pre-processing and post-processing used the INTRANSIN-IIIcode (Vives, 1994).

The finite-elements grid was automatically generated. The discretization is larger(i.e., finer) in those areas where the hydraulic gradient is higher and/or where thedata density allows so (e.g., north-eastern portion of the model, see Figure 3). The basic grid has been modified along the structural alignments by superimposing 1-Delements to connect the nodes (edges of the triangular elements), so that the preferential flow paths can be explicitly modelled.

The study area was divide up into 14 zones of different transmissivity and 6 zones of

varying permeability (Figure 3). The transmissivity discretization allows thesimulation of the structural alignments (preferential flow paths), whereas the permeability zoning can simulate the effect of secondary (weak) fracturing. Theanisotropy tensor is oriented NNE-SSW and its components, according to the areatreated, were between 1 and 24 m/d. For the preferential flow regions, the width wastaken into account and its permeability estimated between 10 to 50 m/d.Permeability and transmissivity values are modified at each element by means of a

coefficient that considers the spatial variation of the aquifer thickness and thechanges in water viscosity due to varying temperatures at depth (Schneebeli, 1966).

The areal recharge, accounted for in the elements, considered 7 zones (Figure 3),and is defined as an amount of water entering or exiting the zone. Recharge, as

given by the model, is the difference between the water entering from rainfall orrecharge from the overlying aquifers and that extracted by well pumping. Theinfiltration from precipitations in the Guaraní Aquifer outcrops was estimated in10% of the rainfall (Rebouças, 1976), given that the mean annual precipitation in theregion varies between 1.300 and 1.800 mm.




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More than two decades ago an overexploitation area in the Ribeirao Preto (SaoPaulo, Brasil) has been identified, with discharges in the order of de 45 x 106m3/año (Gilboa et al., 1976). Chemical and isotope studies on the Guaraní andBauru Aquifers (Kimmelmann et al., 1996) have shown that the water pumped outdoes not belong to a single aquifer, most probably due to the heavy pumping rate.Some sparse data indicate that shallow waters migrate downwards and get mixedwith thermal waters. As for the rest of Sao Paulo State (Campos y Cerón-Garcia,1998) groundwater is extracted from about 1.000 wells reaching the aquifer wherethe basalt cover is thinner. Most discharges are in the range of 3 and 28 l/s, althoughthere are wells with depths close to 1.000 m and discharge rates between 80 and170 l/s.

The boundary conditions are shown in Figure 3, which basically considered thegroundwater contour map by Araújo et al. (1999):

• Fixed groundwater level at the west (Paraguay and outcrops of Cenozoicsediments in Argentina), south (Guaraní outcrops), and south-east (TorresCity zone).

• Fixed discharge to the east (outcrops of the Guaraní Aquifer in the MatoGrosso do Sul, Paraná, and Santa Catarina States, where the recharge byrainfall is simulated.

• Mixed conditions to the north, where the aquifer dissapears as a wedge.

The measured levels in 74 observation points (Figure 3) were used at the

calibration stage. Those points were selected so as to have a homogeneous spatialcoverage and to be compatible with the information provided by Araújo et. al(1999). Some of the measurements are not reliable: measuring dates do not match,the filtering section of wells is larger than the aquifer thickness (meaning that theoverlying basalt has no casing), partially penetrating wells (probably avoiding theclay-rich sediments), uncertainties on the static water level readings, etc.Therefore, weighting coefficients were used to value selectively the informationfor the wells.

4. CALIBRATION STRATEGY AND RESULTS

The calibration step consists of estimating the model parameters in such a way thatthe computed levels match the actual measurements. Aside from that, the calculated

parameters are to be coherent with their previous estimation and the conceptualmodel.

The first objective of the calibration phase was posed as to reproduce as closely as possible the existing groundwater contour levels. That allowed the modification ofthe conceptual model in order to minimize the effect of some initial uncertainties




136

and/or an underestimation of the water being pumped. Diminishing recharge rates inthe R4 zone is to be expected because the exploitation affects the overlyingformations, thereby making the Guaraní Aquifer to supply water from its storage.The overexploitation at Ribeirao Preto (R7 zone) seems to be larger that what had been previously thought and merits special treatment in future models.

It is important to highlight that the success of any modelling effort is strictly relatedto the quality, density and reliability of the available data. As applied to the GuaraníAquifer, then, the main limitations have been: uneven distribution and low reliabilityon data from observation points, incomplete knowledge of the groundwater pumpingvolumes, scarce information about the aquifer hydraulic properties, lack of detailedstudies on recharge from rainfall, disregard of the chemical information as related togroundwater flow, and the exclusion of the overlying aquifers (Bauru and SerraGeral).

According to what has been presented up to this point, any attempt to assess thewater resources potential of this giant aquifer may not have a good onset as long asthe shortcomings pointed out in the paragraph above remain. In essence, the problemhas been posed as to how effectively collect, store, and disseminate the informationrelevant to the Guaraní Aquifer System (GAS) knowledge in order to facerealistically its management. The IHP-UNESCO thought of some kind of decision-support system, driven by a large, well-structured database, and accessible in aremote way (via Internet), and decided to sponsor a pilot project with that objectivein mind. The partial results emerging from the initial one-year trial period will be

presented below.5. COMPREHENSIVE DATABASE, REMOTELY ACCESSED

It has been designed to be used as a decision support system, with capabilities ofstoring all data related to the GAS, accessible via Internet in a restricted or total way by all users in the system (Figure 5).

Fig. 5: Information management conceptual structure.

USUARIO

Base de Datos

USUARIO




137

The internal check distinguishes two types of users: member and public. Members, oncecleared up by the system, may enter new data and become owners of such information.Data owners assign the level of data availability, which may be “private”, “protected”, or“open”. In that way, the research groups will decide which information they want to sharewith other groups, keeping some data unavailable for their own purposes (processing,filtering), and let some other data be freely released. This scheme allows data loading inreal time and does not depend on the location of the eventual new data provider.

The database stores and organizes the information, and the web page allows its use by any person with Internet connection. In order to make easier and more efficientthe database exploitation, a set of visualization and consultation tools weredeveloped and embedded in the web page.

5.1 Database structure

The database contains different levels of information, from general to particularissues, including climatic, geologic, hydrologic, hydrogeology, water quality, etc.aspects. Its main features are:

• Stores all information related to the GAS, i.e., numerical data, pictures,satellite images, documents, contact names and addresses, links, etc.

• Incorporates engines for data consultation: images or documents finder,numerical data viewer and processing, data filtering.

• Clears the users status (member, public) and allows (user/password) thedistinction of the data availability level.

• Counts on a mechanism for massive data uploading from text format files(for normalizing the database internal structure).

5.2 Web site development

The main characteristics of the Web site are as follows:

• Easy and fluid navigation, oriented to non-experienced users.• Member and public users levels handling.• Interface between users and data, allowing information search, downloading

and filtering, as well as data presentation in various manners (raw data, 2Dand 3D graphs).

• Multilingual switchable presentation (initially in Spanish, Portuguese, and

English).• A critical factor is the communication speed, which is basically determined

by the delay time. The line delay is unavoidable because it depends on theInternet-connection providers and the bandwidth selected for the site server.The response time delay can be optimized using specific site architecturalfeatures, such as Enterprise Java Beans, and a DBMS (database managementsystem) of well-proven characteristics.




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5.3 Consultation and visualization session

Some basic data were predefined and data processors were made operative in orderto test the site behavior, although it should be said that many of them will have to bemodified and new possibilities will have to be considered. As an example,hydrochemical data were loaded and their processing will be shown below in theformat of an eventual consultation session:

• Selection of sites where the user wants to find out the information available (Figure 6).• Upload of new information (database enrichment): numerical data (through

windows or preset tables), images, texts, videos, etc.• Scatter X-Y graphs, provided with a simple toolbar.

• Two-dimensional graphs with zooming capabilities: maps, distribution ofmonitoring points, distribution of selected parameters, maps superposition(layering), with a simple toolbar. Isovalue maps drawing is an option notimplemented at this development phase.

Figure 6. Graphical selection of the domain from

which the information will be retrieved.




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• Images or pictures: visualization by means of a toolbar (zoom, cut and paste,etc. (Figure 7).

Figure 7. Screens of Images. With a click the user has the option of

downloading the file to his computer.

• Chemical analyses diagrams: column type or Collins , triangular or Piper,Schoeller-Berkaloff.

• Basic statistics on grouped data: mean, standard deviation, regressionindices, correlation, etc.

• Information retrieval: filters for selecting data, e.g., based on time span,location, etc.

• Bibliography: viewer, search within a text, authors, etc.




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• Users/institutions: list of individuals and involved organisms with contactinformation (address, email, etc).

• News: dedicated place for managers and users to transmit news, sendcomments/questions, etc.

5.4 Choice of technological framework

The selection of the development technology is a crucial step in the life of any project of this type. Many aspects depend on the decision, such as the applicationdesign, the working plan, the application portability, its futuremaintenance/updating, and the possibility of shortening the development phase.

For the GAS project, there was an initial, long stage in which decisions were madeon the basis of what was going to be used and what tools/technology were available.After laying out the objectives and the different alternatives, the followingtechnology was adopted: Oracle database; combination of FLASH, HTML andJavaScript for screens design, to facilitate the users navigation; the JSP technologyis of particular usefulness for keeping the dynamics required by the application; andServlets.

6. CONCLUSIONS

The preliminary numerical groundwater flow model proposed matches quiteapproximately the information available and reproduces qualitatively an existing

data-field drawn contour map. The methodology employed claims for the integrationof all available information keeping in mind that the final objective is to unravel theconceptual hydrogeological model. However, the model showed that somelimitations will have to be taken into account whenever the time comes to build up amore robust model aiming at reducing uncertainties.

In that sense, it seems reasonable to think of the GAS as a system to be modelled asa multi-layer or 3-D aquifer (that is, Bauru, Serra Geral, Guaraní Aquifers, andPassa Dois Aquitard), based on the existing hydrogeological cartography andincluding the structural alignments that affect the groundwater flow. Moreobservation points are clearly needed as well as updated data on water use (pumpingrates), direct infiltration rates, and aquifer hydraulic parameters from pumping tests.

A decision-support system is presented in order to integrate all availablehydrological information, for the benefit of agencies or organisms involved in thesustainable management of such a valuable regional water resource. This tool,efficient, powerful, and open for consultation, consists of a comprehensive databasethat can be inspected remotely via Internet. Data can be downloaded and, given proper authorization, the information can also be uploaded for sharing purposes. Itcounts with advanced mechanisms for information searching and filtering, as well asvisual applications for raw data and maps, and communication capabilities.




141

ACKNOWLEDGEMENTS

The authors wish to thank the following institutions: Programa HidrológicoInternacional (UNESCO, Montevideo), Universidad do Vale do Rio dos Sinos(UNISINOS, Brazil), Universidad Politécnica de Cataluña (UPC, Spain), Institutode Hidrología de Llanuras (Argentina), Instituto de Sistemas de Tandil (Argentina),Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil),Departamento de Águas e Energia Elétrica (DAEE , Brazil), and Servei Cartogràficde Catalunya (Spain).

REFERENCES:

Almeida, F. F .M. (1983). "Relaçoes tectônicas das rochas alcalinas Mesozóicas daregiao meridional da Plataforma" Sul-Americana. Rev. Brasileira Geociências,SBG, Vol.13, No.3, pp. 139-158.

Araújo, L. M.; França, A.B.; Potter, P.E. (1995). "Giant Mercosul aquifer of Brazil, Argentina, Uruguay and Paraguay: hydrogeologic maps of Botucatu, Pirambóia, Rosário do Sul, Buena Vista", Misiones and Tucuarembó Formations. Biblioteca deCiência e Tecnoligia, Centro Politénico, Curitiba, UFPR/PETROBRÁS.

Araújo, L. M.; França, A.B.; Potter, P. (1999). "Hydrogeology of the Mercosulaquifer system in the Paraná and Chaco-Paraná basins, South America, and comparisonwith the Navajo-Nugget aquifer system", USA. Hydrogeology Journal, Vol. 7, pp. 317-336

Carrera, J. and Neuman, S. (1986). "Estimation of aquifer parameters under

transient and steady state conditions, I, Maximum likelihood method incorporating prior information". Water Resouces Research, Vol. 22, No. 2, pp. 199-210.

Campos, H.C.N.S. y Cerón-Garcia, J.C. (1998). "Algunos aspectos de la hidroquímicadel sistema aqüífero Botucatu" (Cuenca del Paraná, Estado de Sao Paulo, Brasil).Revista Geogaceta. Sociedad Geológica de España, Vol. 23, pp. 23-25.

Campos, H.C.N.S. (1999). "Mapa Hidrogeológico do Aqüífero Guaraní, escala1:2.500.000 (inédito)". Editado por ISOMAPA – Consultoria e Projetos Ltda. (SaoPaulo, Brasil).

Campos, H. (2000). "Mapa hidrogeológico del Acuífero Guaraní. Proceedings of

the 1 st

Joint World Congress on Groundwater", Fortaleza, Brasil, 15 p. (in CDformat).

Gilboa, Y.; Mero, F.; Mariano, I.B. (1976). "The Botucatu aquifer of South America,

Model of an untapped continental aquifer". Journal of Hydrology, Vol. 29, pp. 165-179.Kimmelmann, A.; Foster, M.; Coelho, R. (1996). Environmental isotope andhydrogeochemical investigation of "Baurú and Botucatú aquifers, Paraná Basin, Brazil. Isotope Investigations in Latin America". IAEA, TECDOC 835, pp. 57-74.

Kittl, S., 2000. "Contributions to the knowledge on the stratigraphy andhydrochemical of the giant Guaraní Aquifer System", South America. Eberhard-Karls-Universität zu Tübingen, Alemania. Master Thesis.




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Lavina, E. L., (1991). "Geologia sedimentar e paleogeografia do Neopermiano e o Eotriássico (Intervalo Kazaniano – Scythiano) da Bacia do Paraná" . Porto Alegre,Curso de Pós-Graduação em Geociências, UFRGS, Tese de Doutorado.

Medina, A.; Galarza, G.; Carrera, J. (1996). TRANSIN II. "Fortran code for solving

the coupled flow and transport inverse problem in saturated conditions". ElBerrocal Project. Characterization and validation of natural radionuclide migration processes under real conditions on the fissured granitic environment. EuropeanCommission Contrac nº FI2W/CT91/0080. Topical Report 16. ENRESA.

Rebouças, A. C., (1976), "Recursos hídricos da Bacia do Paraná" . São Paulo, Tesede Livre Docência, IGc/USP, 143p.

Schneebeli, G. (1966). "Hidraulique souterraine" . Editors Eyrolles, París. 362 pp.

Vives, L. (1994). Manual del código INTRANSIN III Versión 2.0. "Barcelona, Escuela Técnica Superior de Caminos", Canales y Puertos de Barcelona,Universidad Politécnica de Cataluña. Informe interno.

Vives, L., Campos, H., Candela, L., and Guarracino, L. (2000). "Premodelo de flujodel Acuífero Guaraní" . Proceedings of the 1st Joint World Congress onGroundwater, Fortaleza, Brasil, 19 p. (in CD format).





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Sea Water Intrusion Vulnerability Mapping of

Aquifers Using Galdit Method

A.G. Chachadi and J.P. Lobo Ferreira

Abstract

The continued human interference into the coastal hydrologic system has led to the pollution of the coastal groundwater aquifers by salt water. The groundwater pollution incidents due to salt-water intrusions have increased many folds in thelast couple of decades. Generally one comes to know about the groundwater

pollution due to saltwater mixing only after the incident has occurred. Butexperience show that the remediation of the groundwater system, which hasundergone salt-water intrusion, is rather difficult and uneconomical in most of the

cases. Therefore it is required to develop a methodology to assess and map the probable potential areas of seawater intrusion by standard scientific method. A new

method of aquifer vulnerability mapping has been proposed to map and identify potential seawater intrusion areas along the coasts. The method has been derivedbased mainly on the intrinsic aquifer properties and hence provide timeindependent measure of aquifer vulnerability of an area to seawater intrusion problems. The proposed method has been validated using case studies in coastalGoa and East Godavari district.

Keywords : galdit, aquifer, Goa, vulnerability, pollution.

1. INTRODUCTION

Every year, 600 billion cubic metres of groundwater are pumped throughout the

world. In 1990, two countries extracted more than 40% of this - India with 150 billion cubic metres and USA with 100 billion cubic metres. Groundwater extractionaccounts for 32% of the total Indian water production, distributed for agriculture and

livestock (89%), drinking (9%), and industry (2%). The share of groundwater in netirrigated areas has risen from one third in 1965/66 to over half at present(Vaidyanathan 1996; Marothia 1997). This is mainly due to improvements in thedrilling technology, water lifting from deeper aquifers, and highly subsidised energy

supply and loans for minor irrigation works. Besides, the non-availability of




144

adequate supply of canal water during periods of high demand, long gestation periods of major irrigation projects have compelled the farmers to take upgroundwater development.

Indian coastal aquifers constitute the second richest groundwater reservoirs after the

Indo-Gangetic alluvial plain, which is one of the world's largest fresh groundwaterreservoirs. While aquifers along India's West Coast are predominantly of fractured porosity, one finds top alluvial aquifers followed by deeper fractured aquifers on theEast Coast. The topography of the East Coast is flat with vast spreads of more than50 km inland whereas the western coastal stretch is narrow, bounded by high risingmountains (Western Ghats). The East Coast gets about 10 months of rainfall both

from the North - East and South -West monsoons, receiving on an average about1500mm of rain annually. A major portion of the East Coast also experiences periodic cyclonic precipitation each year. The West Coast, on the other hand,receives more than 3000mm of annual rain from only Southwest monsoons from

June to September. No cyclonic precipitation is generally witnessed except atGujarat coast occasionally.

Stretching over a length of more than 7000km, the Indian coastline offers anexcellent opportunity for agriculture, particularly on the East Coast, which has vaststretches of fertile alluvial soils. The main urban centers and industrialestablishments are also crowded along the Indian coast. Coasts are stressed due to

industrial activity in Gujarat, Maharashtra, parts of Karnataka, and West Bengal.The coastal stretches of Goa, parts of Karnataka, Orissa, and Kerala are stressed due

to tourism activities. Coastal groundwater tracts are under stress due to agricultural/aquaculture activities and urbanization in Kerala, Tamil Nadu, Andhra Pradesh, and

parts of Orissa.

The overuse of groundwater along parts of the coastal belts of India for various purposes has affected groundwater quality and quantity. It has led to rapid decline ingroundwater levels leading to saltwater incursions and water quality deterioration particularly in parts of Gujarat, Tamil Nadu, Andhra Pradesh, Orissa, and West

Bengal. The nine maritime states include Gujarat, Maharastra, Goa, Karnataka,Kerala, Tamil Nadu, Andhra Pradesh, Orissa and West Bengal besides UnionTerritories of Diu, Daman, Lakshadweep, Pondicherry and Andaman and NicobarIslands. There are more than 156 districts in these States and Union Territories.

2. PROBLEM DEFINITION

The concentration of mega cities, industries, harbors, farm cultivation, aquacultureand tourist activities, clubbed with high population density has transformed resourcefull coastal belts into the resource scarce areas. Both the quality and the quantity ofall the natural resources are decreasing day by day along the coasts. The stress on

fresh water resources has indeed a matter of great concern. Though all the rivers endup with the sea in the coastal areas the major portion of the utilizable water




145

resources come from groundwater reservoirs. The continued and unconcerned use ofthe groundwater in the coastal belts has led to alarming situations in many parts ofour country.

The continued human interference into the coastal hydrologic system has led to the

pollution of the coastal groundwater aquifers by salt water. The groundwater pollution incidents due to salt-water intrusions have increased many folds in the lastcouple of decades. Generally one comes to know about the groundwater pollutiondue to saltwater mixing only after the incident has occurred. But experience showthat the remediation of the groundwater system, which has undergone salt-waterintrusion, is rather difficult and uneconomical in most of the cases. Therefore it is

required to develop a methodology to assess and map the probable potential areas ofseawater intrusion by standard scientific method.

In the present paper a new approach based on four intrinsic hydrogeological

parameters, one spatial parameter and one boundary parameter has been proposed tomap the potential coastal areas of seawater intrusion. The basic assumption made

here is that the seawater mixing into the fresh groundwater is essentially a pollution problem.

3. CONCEPT FOR THE DEFINITION OF GROUNDWATER

VULNERABILITY TO POLLUTION

Before considering the evaluation of groundwater vulnerability to pollution, it is

necessary to define the term vulnerability. The term vulnerability has been definedand used before in the area of water resources, but within the context of system

performance evaluation, e.g. the definition given by Hashimoto et al. [1982].

These authors present an analysis of system performance, which focuses on systemfailure. They define three concepts that provide useful measures of system performance: (1) how likely the system is to fail is measured by its reliability, (2)how quickly the system returns to a satisfactory state once a failure has occurred is

expressed by its resiliency, and (3) how severe the likely consequences of failuremay be is measured by its vulnerability. This concept of vulnerability defined in thecontext of system performance may also be used in the context of groundwater pollution due to seawater mixing by replacing "system failure" by "intensity ofgroundwater pumpage" due to which the seawater mixing takes place. The severity

of the consequences is measured in terms of water quality deterioration, regardlessof its value as a resource (for example, regardless of whether or not the aquifer is being used for public supply or is given any use at all).

It is believed that the most useful definition of vulnerability is one that refers to the

intrinsic characteristics of the aquifer, which are relatively static and mostly

beyond human control. It is proposed therefore that the groundwater vulnerability toseawater pollution be redefined, in agreement with the conclusions and




146

recommendations of the international conference on "Vulnerability of Soil andGroundwater to Pollutants", held in 1987 in The Netherlands, [Duijvenbooden et al,1987 and Anderson, et al. 1987], as

“ the sensitivity of groundwater quality to an imposed groundwater pumpage in

the coastal belt, which is determined by the intrinsic characteristics of the

aquifer.”

Thus defined, vulnerability is distinct from pollution risk . Pollution risk due toseawater mixing depends not only on vulnerability but also on the existence ofsignificant groundwater pumpage in the proximity of the coast. It is possible to have

high aquifer vulnerability but no risk of seawater intrusion, if there is no significantgroundwater pumpage in the proximity of the coast; and to have high pollution riskin spite of low vulnerability, if the groundwater pumpage is exceptional. It isimportant to make clear the distinction between vulnerability and risk. This is

because risk of seawater intrusion is determined not only by the intrinsiccharacteristics of the aquifer, which are relatively static and hardly changeable, but

also on the existence of intensive activities of groundwater pumpage along the coast,which are dynamic factors which can in principle be changed and controlled.

Considerations on whether a groundwater pollution episode due to seawater mixingwill result in a serious threat to groundwater quality and thus to its (already

developed, or designated) water supply are not included in the proposed definitionof vulnerability. The seriousness of the impact on water use will depend not only on

aquifer vulnerability to seawater intrusion but also on the magnitude of the seawaterintrusion episode, and the value of the groundwater resource.

4. METHODOLOGY

Hydrogeological conditions and human activities close to the coast mainly affectgroundwater pollution due to seawater mixing. There has been no methodology forevaluating the spatial distribution of the seawater intrusion potential, which

essentially take into account hydrogeological factors, and allows the seawaterintrusion of coastal hydrogeological setting to be systematically evaluated in anyselected coastal area where the hydrogeological information is available. Therefore,it is necessary to adopt a mapping system that is simple enough to apply using thedata generally available, and yet is capable of making best use of those data in a

technically valid and useful way.

Some of the systems for aquifer pollution vulnerability evaluation and rankinginclude a vulnerability index, which is computed from hydrogeological,morphological and other aquifer characteristics in some well-defined way. The

adoption of an index has the advantage of, in principle, eliminating or minimising

subjectivity in the ranking process. Given the multitude of authors and potentialusers of vulnerability maps in EEC countries, Lobo-Ferreira and Cabral, 1991




147

suggested that a vulnerability index be used in the vulnerability ranking performedfor European Community maps. Such a standardised index has been adopted in theU.S., Canada and South Africa, and is currently used in those countries. The

DRASTIC index, developed by Aller et al. 1987 for the U.S. EPA is one suchmethod. This index has the characteristics of simplicity and usefulness.

5. SUGGESTED SYSTEM OF VULNERABILITY EVALUATION AND

RANKING

Inherent in each hydrogeologic setting is the physical characteristics that affect theseawater intrusion potential. The most important mappable factors that control the

seawater intrusion are found to be;

1. Groundwater Occurrence (aquifer type; unconfined, confined and leaky confined).2. Aquifer Hydraulic Conductivity.3. Depth to Groundwater Level above Sea.4. Distance from the Shore (distance inland perpendicular from shoreline).5. Impact of existing status of seawater intrusion in the area.

6. Thickness of the aquifer which is being mapped.

The acronym GALDIT is formed from the highlighted and underlined letters of the parameters for ease of reference. These factors, in combination, are determined toinclude the basic requirements needed to assess the general seawater intrusion

potential of each hydrogeologic setting. GALDIT factors represent measurable

parameters for which data are generally available from a variety of sources withoutdetailed reconnaissance.

A numerical ranking system to assess seawater intrusion potential in hydrogeologicsettings has been devised using GALDIT factors. The system contains three

significant parts: weights, ranges and ratings. Each GALDIT factor has beenevaluated with respect to the other to determine the relative importance of eachfactor. Each GALDIT factor has been assigned a relative weight ranging from 1 to4. The most significant factors have weight of 4; the least significant, a weight of1as shown below:

Factors GALDIT weights

(i) 1. Groundwater Occurrence (Aquifer Type) 1(ii) 2. Aquifer Hydraulic Conductivity 3

(iii) 3. Depth to Groundwater Level above Sea 4

(iv) 4. Distance from the Shore 2 (v) 5. Impact of existing status of Seawater Intrusion 1

(vi) 6. Thickness of Aquifer being Mapped 2




148

The minimum value of the GALDIT index is therefore 13 and the maximum valueis 130. A rating value between 1 and 10 to each parameter are attributed, dependingon local conditions. High values correspond to high vulnerability. The attributedvalues are generally obtained from tables, which give the correspondence betweenlocal hydrogeologic characteristics and the parameter value. Next, the local index of

vulnerability is computed through multiplication of the value attributed to each parameter (rating) by its relative weight (GALDIT weight), and adding up all six products. The impact of each of the above six parameters on seawater intrusionepisode is described in the following paragraphs:

(i) Groundwater Occurrence (Aquifer Type) (G): In nature groundwater

generally occurs in the geological layers and these layers may be confined, unconfined orleaky confined in nature. This basic nature of groundwater occurrence has an influence onthe extent of seawater intrusion. For example an unconfined aquifer under naturalconditions would be more affected by seawater intrusion compared to confined aquifer as

the confined aquifer is under more than atmospheric pressure. Similarly a confined aquifermay be more prone to seawater intrusion compared to leaky confined aquifer as the leaky

confined aquifer maintains minimum hydraulic pressure by way of leakage from adjoiningaquifers. Therefore in assigning the relative weights to G one should carefully study thedisposition and type of the aquifers in the study area. The ratings generally are; unconfined(9), confined (10) and leaky confined (8). The confined aquifer is more vulnerable due tolarger cone of depression and instantaneous release of water to wells during pumping. In

case of multiple aquifer system in an area the highest rating may be adopted. For exampleif an area has all the three aquifers then the rating of 10 of an unconfined aquifer may be

chosen.

(ii) Aquifer Hydraulic Conductivity (A): The parameter aquifer hydraulicconductivity is used to measure the rate of flow of water in the aquifer. By definition

the aquifer hydraulic conductivity is the ability of the aquifer to transmit water. Thehydraulic conductivity is the result of the interconnected pores (effective porosity) inthe sediments and fractures in the consolidated rocks. The magnitude of seawaterfront movement is influenced by the hydraulic conductivity. Higher the conductivity

higher the inland movements of the seawater front. The high conductivity alsoresults in wider cone of depression during pumping. In this case the user should takeinto account the hydraulic barriers like clay layers, and impervious dykes parallel tothe coast, which may act as walls to seawater intrusion. The typical rating adoptedfrom Aller et. al 1987 are as under;

Rating Hydraulic conductivity range (m/day)

1 0 - 4.12 4.1 - 12.24 12.2 - 28.56 28.5 - 40.7

8 40.7 - 81.5

10 > 81.5




149

(iii) Depth to Groundwater Level above Sea (L): The level of groundwater withrespect to mean sea level is a very important factor in the evaluation of the seawaterintrusion in an area primarily because it determines the hydraulic pressureavailability to push the seawater front back. As seen from the Ghyben-Herzbergrelation, for every meter of fresh water stored above mean sea level, 40 meters of

freshwater are stored below it down to the interface. In assigning the ratings to L

one should look into the temporal long-term variation of the groundwater levels inthe area. Generally the values pertaining to minimum groundwater levels above sea(Premonsoon) may be considered, as this would provide the highest possiblevulnerability. The ratings adopted from Aller et. Al 1987 is as under;

Ratings Groundwater level above Sea (m)

10 < 1.59 1.5 - 4.67 4.6 - 9.1

5 9.1 - 15.23 15.2 - 22.9

2 22.9 - 30.51 > 30.5

(iv) Distance from the Shore (D): The impact of seawater intrusion generallydecreases as one moves inland at right angles to the shore. The following table gives

the general guidelines for rating assuming the aquifer is under undisturbedconditions;

Rating Distance from Shore Inland (m)

10 <1009 101 - 200

8 201 - 3007 301 - 4006 401 - 5005 501 - 600

4 601 - 7003 701 - 8002 801 - 1000

>1000

(v) Impact of Existing Status of Seawater Intrusion (I): The area under mappinginvariably is under stress and this stress has already modified the natural hydraulic balance between seawater and fresh groundwater. This fact should be consideredwhile mapping the aquifer vulnerability to seawater intrusion. The following ratingare given to take care of such field situations:




150

Ratings

10

Impact Status

Area already intruded by seawater in allseasons. Where epm value of the ratio of

Cl / (HCO3+CO3) is > 25 Area where seasonal seawater intrusion

prevails. Where epm value of the ratio ofCl /(HCO3+CO3) is between 1.5 - 2

0 Area where no seawater intrusion waswitnessed in the past. Where epm value

of the ratio of Cl /(HCO3+CO3) is < 1.5

The information for the above rating can be gathered from historical reports, inquiryfrom the local people, and chemical analysis data.

(vi) Thickness of the Aquifer being Mapped (T): Aquifer thickness or saturated

thickness of an unconfined aquifer plays an important role in determining the extentand magnitude of seawater intrusion in the coastal areas. It is well established thatlarger the aquifer thickness smaller the extent of seawater intrusion and vice versa.Keeping this as a guideline the following ratings are given for T:

Ratings Aquifer thickness (m) 10 < 19 1.1 - 2.08 2.1 - 3.0

7 3.1 - 4.06 4.1 - 5.0

5 5.1 - 6.04 6.1 - 7.03 7.1 - 8.02 8.1 - 10.01 > 10.0

7. MAPPING OF FINAL GALDIT INDEX

According to the GALDIT method, each of the six parameters has a pre-determinedfixed relative weight that reflects its relative importance to vulnerability. When the

GALDIT method is adopted, the aquifer vulnerability index to seawater intrusion is

obtained by the following expression:

GALDIT = 1*G + 3*A + 4*L + 2*D + 1*I + 2*T ….. (1)

Thus, the user can use hydrogeologic settings as a mappable unit, define the area of interest

by modifying to reflect specific conditions within an area, choose corresponding ratingsand calculate a seawater intrusion GALDIT index. This system allows the user todetermine a numerical value for any hydrogeological setting by using an additive model.




151

5 10 15

5

1 0

1 5

2 0

2 5

R.Chapor

Parra

Baga

River MandoviTaj Hotel

Watershed

44

1

3

2 4

5 6

7 8

9 5933

32 34 35

31 36

30 29 37

39

38

40

27 11

12 1413

1041

4643

4249

48 47

15 1816

26

50

52

53 54

55

58

56 57

2425

22

2821

45

19 2023

Chapora Assagao

Vagator

Anjuna

Arpora

Baga

Calangut

Fort

Saligao

Candolim

Fort

Fig. 1: AQUIFER VULNERABILITY MAP TO SEAWATER INTRUSION

GALDIT INDEX MAP

Once the GALDIT index has been computed, it is possible to identify areas, which aremore likely to be susceptible to seawater intrusion relative to one another. The higher theindex, the greater the seawater intrusion potential. The GALDIT index provides only arelative tool and is not designed to provide absolute answers. It is expected that as themodel is an open ended one the application and validation of GALDIT method to casestudies would help improve the rating values that are adopted in this paper.

8. APPLICATION OF THE GALDIT MAPPING – CASE STUDIES

The above method has been validated using case studies in the coastal areas of Goa andEast Godavari. The GALDIT scores at each of the 57-groundwater monitoring wells

were computed for the Goa study area in Bardez taluk (Table 1). These GALDIT values along with the x and y co-ordinates were used in the SURFER package to drawthe vulnerability score contour map. The map derived for this study area is given in Fig.

1. The geoelectrical profiles carried out in the study area to determine the seawater

intrusions are shown in Fig.2. From this figure and the GALDIT vulnerability map it isseen that the high scores of vulnerability coincides with the saltwater intruded areas,

which are indicated by the low electrical resistivity values on the profiles.




152

Fig. 2: Geoelectrical profiles along north Goa coast (a = 10m)

9. CONCLUSIONS

A new method of aquifer vulnerability mapping has been suggested. This method will provide a vulnerability map of coastal groundwater zone due to seawater intrusion.

These maps can be used as a tool for management of the coastal groundwater resources.Similar applications can be done on the island aquifers so that optimal management practices can be evolved for groundwater use. The maps can be prepared using GIS orif the area is small, point values of the vulnerability indices can be obtained from

equation (1) and then contoured using SURFER to get a vulnerability score map. The point values of index can be used in ascertaining the wellhead protection areas in the

coastal belts to prevent seawater pumping. For the cases where the aquifer bottom isabove the sea level all GALDIT parameters should be assigned zero values when usingthe SURFER for preparing the vulnerability maps. This can be taken care in GIS platform by defining the areas having such geological situations as a separate layer.

REFERENCES:

Andersen, L.J. and Gosk, E. (1987), Applicability of vulnerability maps, in W. vanDuijvanbooden and H.G. van Waegeningh (eds.), "Vulnerability of Soil andGroundwater to Pollution" , Proceedings and Information No. 38 of the InternationalConference held in the Netherlands, in 1987, TNO Committee on Hydrological

Research, Delft, The Netherlands.

0

200

400

600

800

1000

1200

0 100 200 300 400 500 600

Distance inland from the shore (m)

A p p

a r e n t r e s i s t i v i t y ( O h m - m

Sinquirim Beach

Calangute Beach

Candolim Beach

Baga Beach

Anjuna Beach

(a = 15m)




153

Aller, L., Bennett, T., Lehr, J.H. and Petty, R. J. (1987), DRASTIC: "a standardized system for evaluating groundwater pollution potential using hydrogeologic settings" , U.S. EPA Report 600/2-85/018.

Duijvenbooden, W. van and Waegeningh, H.G. van (1987), "Vulnerability of Soil

and Groundwater to Pollutants" , Proceedings and Information No. 38 of theInternational Conference held in the Netherlands, in 1987, TNO Committee onHydrological Research, Delft, The Netherlands.

Foster, S.S.D. (1987), Fundamental concepts in aquifer vulnerability, pollution riskand protection strategy, in W. van Duijvanbooden and H.G. van Waegeningh (eds.),"Vulnerability of Soil and Groundwater to Pollution" , Proceedings and Information No. 38 of the International Conference held in the Netherlands, in 1987, TNO

Committee on Hydrological Research, Delft, The Netherlands.

Hashimoto, T., Stedinger, J. R. and Loucks, D. P. (1982), Reliability, Resiliency,and Vulnerability Criteria for Water Resource System Performance Evaluation,"Water Resources Research" , 18(1), p14-20.

Lobo-Ferreira, J.P. and Cabral, M. (1991) Proposal for an Operational Definition of

Vulnerability for the European Community's Atlas of Groundwater Resources, in" Meeting of the European Institute for Water, Groundwater Work Group Brussels", Feb. 1991.

Marothia, D.K. 1997. Agricultural technology and environmental quality: aninstitutional perspective. "Indian Journal of Agricultural Economics" 52(3): 473-487.

TERI, 1999. Measuring, monitoring, and managing sustainability: the coastaldimension. "First year progress report of the INCO-DC" Project contract No. IC18-CT98-0296.

Vaidyanathan, A. 1996. Depletion of ground water: some issues. "Indian Journal of Agricultural Economics" 51(1-2): 184-192.




154

Table 1: Details of the Galdit Score Computation for Goa Case Study Area

Parameter G Parameter A Parameter L Parameter D Parameter I Parameter T Total ofWellno Aquifer Type Rating K (m/d) Rating GWL

(m)Rating Dist.

(m)Rating Initial

ConditionRating Aq. Th

(m)Rating GALDIT

score

1 unconfined 9 28.8 6 0.75 10 10 10 intruded 10 10 2 105

2 unconfined 9 28.8 6 0.7 10 250 8 not intruded 0 10 2 89



5 unconfined 9 4.3 2 14.4 5 2500 1 not intruded 0 12.5 1 46









14 unconfined 9 4.3 2 -1.55 10 2750 1 not intruded 0 15 1 58

15 unconfined 9 31.6 6 3 9 500 6 not intruded 0 12.5 1 77


18 unconfined 9 31.6 6 12.65 5 1900 1 not intruded 0 15 1 4619 unconfined 9 4.3 2 9.5 5 3150 1 not intruded 0 15 1 38





24 unconfined 9 4.3 2 15 5 3000 1 not intruded 0 19 1 38





29 unconfined 9 4.3 2 3.05 9 1250 1 not intruded 0 10.5 1 5430 unconfined 9 31.6 6 5.35 7 300 8 not intruded 0 5.5 5 83


32 unconfined 9 28.8 6 -0.86 10 350 7 not intruded 0 10 2 86







155











46 unconfined 9 4.3 2 3.55 9 3550 1 not intruded 0 15 1 5447 unconfined 9 31.6 6 5.5 7 1250 1 not intruded 0 12.5 1 54


49 unconfined 9 31.6 6 10 5 1050 1 not intruded 0 12.5 1 46








58 unconfined 9 31.6 6 2.55 9 450 6 not intruded 0 12 1 7759 unconfined 9 3.3 1 36.9 1 6600 1 not intruded 0 12.5 1 20

Legend:

GWL – Ground Water Level in metres above mean sea level

Aq. Th. – Aquifer thickness in metresDist. – Distance at right angles from the coast towards inland in metresK – hydraulic conductivity of the aquifer in metres per day





157

Density Dependent Groundwater Flow Modeling: An

Evaluation of Common Benchmark Problems

M.J. Simpson and T.P. Clement

Abstract

In the simulation of density dependent groundwater flow, an important partof the numerical code development is the validation of the solution againstother accepted solutions to standard problems. Making an assessment of thequality of the commonly used validation problems is useful so that thebenchmarking process can be focused upon the more thorough test cases.The Henry problem for salt-water intrusion and the Elder salt convection

problem are two standard benchmark scenarios analyzed here. These

problems are solved in a coupled and uncoupled mode to test theirapplicability for validation of density coupled codes. The difference in thecoupled and uncoupled solutions indicates that the Henry saltwater intrusion problem is a poor example for model evaluation because the dynamics of the flow are largely determined by the boundary forcing. Alternatively the Elder

convection problem is more suited to model validation because the flow patterns are completely determined by the internal balance of the pressureand gravity forces.

Keywords: groundwater-modelling, density dependent flow model verification

1. INTRODUCTION

Verification of a density dependent groundwater modeling code is necessary to

check the validity of the formulation before it can be applied to real problems. Sincethe availability of standard solutions for the verification of density dependentformulations is limited, it is important to verify the code with a flow scenario whichensures that the formulation is able to correctly simulate the balance of the pressureand gravity forces which determines density dependent flow.




158

2. MODELLING DENSITY DEPENDENT FLOW

2.1 Governing Equations for Density Dependent Groundwater Flow

The equations governing the movement of a fluid through a porous medium subject

to density gradients are obtained using mass conservation principles (Boufadel,1999a). In the present case, only two-dimensional (vertical) formulation isconsidered. The governing equations are cast as a set of two coupled non-linear partial differential equations in terms of the pressure of the fluid (written in terms ofthe fresh water pressure head) as well as the concentration of a dissolved solute. Forthe present model, the form of the equations used is,

( )z

K !

z!K

zx!K

xt

2

∂

∂−!

"

#$%

&

∂

ψ ∂

∂

∂+!

"

#$%

&

∂

ψ ∂

∂

∂=

∂

β∂θ

(1.0)

z

CV

x

CV

z

CD

z!

x

CD

x!

t

Czxzx∂

∂−

∂

∂−!

"

#$%

&

∂

∂

∂

∂+!

"

#$%

&

∂

∂

∂

∂=

∂

∂

(2.0)

Where θ is the porosity of the porous medium, is the ratio of the fluid density to areference freshwater density, K [LT

-1] is the hydraulic conductivity of the porous

medium, ψ [L] is the pressure head, C [ML -3] is the concentration of the dissolvedsolute, Di [L

2T

-1] is the dispersion coefficient in the i

th Cartesian direction and Vi

[LT-1] is the velocity of the fluid in the ith Cartesian direction.

These equations are coupled through the beta term, which represents the relative

difference of the density of the fluid to a reference fresh water fluid,

( *00 "C1#!## +== (3.0)

Where ρ [ML-3

] is the density of the fluid, ρo [ML-3

] is the density of freshwater, ε isa measure of the difference between the maximum density and freshwater density,and C

* is the non-dimensionalised concentration of the dissolved solute

2.2 Numerical Solution Strategy

The solution of the coupled equations is sought using the Galerkin finite elementtechnique where the domain is discretised into simple linear triangular elements.The coupling iterations are repeatedly performed within each time step until themaximum change in pressure and concentration converges to within some tolerancecriterion. The solution also encompasses the calculation of the transient velocity

field, which was achieved using the approach espoused by Yeh (1981) ensuring thatthe velocity is continuous along element boundaries. The discrete equations aresolved using a banded LU decomposition algorithm. Time weighting of the




159

0 20 40 60 80 100 120 140 160 180 2000

20

40

60

80

100

Length (cm)

E l e v a t i o n ( c m )

0.0=∂

∂

z

q z

0.0=∂

∂

z

q z

0.0

106.6 5

=

×= −

C

q x

0.0=∂

∂

z

C

0.0=∂

∂

z

C

0.0=∂

∂

x

C

( )( ) z H C −+= ε ψ 1

( )( ) z H C −+= ε ψ 1

0.10

=C

C

advection dispersion equation is allowed in the formulation, however for the presentwork a simple fully implicit weighting was used. The concept of mass lumping wasinvoked in the temporal discretization of both the flow and transport equations.Further details of the numerical solution are discussed in Simpson and Clement(2001).

3. COUPLED FLOW AND TRANSPORT

3.1 Henry's Saltwater Intrusion Problem

In general, variable density models are always verified by solving the well-known

Henry's saltwater intrusion problem (Henry, 1964). Henry's problem is unique because an analytical solution exists for the problem, however even after almost 40years no numerical model has been able to completely replicate the proposedanalytical solution. The historical analysis of Henry's problem is quite well studied,

and a comprehensive discussion of the developments, mistakes, and conceptionsabout the problem may be found in Croucher and O’Sullivan (1995). The problem

consists of a confined aquifer, which has fresh water discharging horizontally intoan open sea boundary. The boundary conditions for the flow and transport equationare shown in Figure 1.0.

Fig. 1: Domain and boundary conditions imposed for the Henry saltwater

intrusion problem.

The aquifer was regularly discretised into 231 nodes and 400 right-angled triangles.The aquifer properties are shown in Table 1.0




160

Table 1.0: Aquifer properties associated with Henry's saltwater intrusion problem.

SYMBOL QUANTITY VALUE UNIT

Dx, Dz Coefficient of moleculardiffusion

1.886×10-5

m2s

-1

G Vector of acceleration dueto gravity

9.80 ms-2

K Hydraulic Conductivity 1.0×10-2 ms-1

Q Fresh recharge rate 6.6×10-5 ms

-1

max Maximum density ratio 1.02499 -

Porosity 0.35 -

o Reference Density 1000.0 kgm-3

max Brine Density 1024.99 kgm-3

The time step for the simulation was gradually increased by a factor of 1.1 from 12seconds to 600 seconds and a constant diffusion coefficient was used for thetransport equation. The coupling between the flow and transport equation wasconsidered complete when the maximum change in pressure head was 0.005m

within each time step. For the most part of the simulation, this was achieved within2 iterations of the coupling loop. When the problem was resolved using a simpleupdating scheme without the coupling loop, the results were identical to thoseobtained using the coupling approach. The model was run for 280 minutes, afterwhich the density field was stationary and the position of the 0.5 isochlor was

obtained. The position of the 0.5 isochlor is shown in Figure 2.0. The comparison ofthe profile with that generated by Frind (1982) shows that the present model is

capable of describing the dynamics of the problem.

0 20 40 60 80 100 120 140 160 180 2000

20

40

60

80

100

Length (cm)

Elevation(cm)

Frind (1982)

0.5

0.25

0.75

Fig. 2: Position of the steady isochlors for the Henry saltwater intrusion problem.




161

0 1 0 0 2 0 0 3 0 0 40 0 5 0 0 6 0 00

5 0

1 0 0

1 5 0

0.0=∂

∂

z

q z

0.0=∂

∂

z

q z

0.0=∂

∂

x

q x0.0=∂

∂

x

q x

0.1=C 0.0=

∂

∂

z

C 0.0=

∂

∂

z

C

0.0=∂

∂

z

C 0.0=

∂

∂

x

C 0.0=

∂

∂

x

C

3.2 Elder's Salt Convection Problem

The original problem studied by Elder (1967) concerned a closed rectangular boxmodeled in cross section. The flow was initiated by a temperature gradient acrossthe box and thermally induced density gradients caused a complex pattern offingering of the denser water mixing in through the box. This problem was studied

both physically in the laboratory with the use of a Hele-Shaw cell as well as beingnumerically reproduced. A modified problem with parameters suited to porousmedia flow was also developed by Elder (1967) and is a commonly used test of theability to simulate larger scale bulk fluid flow driven purely from densitydifferences. The boundary conditions on the domain are shown in Figure 3.0. Table

2.0 defines the aquifer properties for the Elder problem,

Fig. 3: Domain and boundary conditions for the modified

Elder salt convection problem

Table 2.0: Aquifer and transport properties used for the Elder fingeringsimulation.

SYMBOL QUANTITY VALUE UNIT

Dm Coefficient of molecular diffusion 3.565×10-6 m2s-1

G Vector of acceleration due to gravity 9.80 ms-2

K Intrinsic permeability 4.845×10-13 m2

max Maximum density ratio 1.2 -

Porosity 0.2 -

Dynamic viscosity 1×10-3 kgm-1

s-1

o Reference Density 1000 kgm-3

max Brine Density 1200 kgm-3

The key difference between this problem and the Henry saltwater intrusion analysisis the magnitude of the density ratio. For the Elder problem the maximum value of

is 1.2, which has a significant impact upon the coupling. The discretization of the problem consists of a regular grid comprising 3000 nodes (100 horizontally, 30vertically) and 6000 right-angled triangular elements. The temporal discretizationused time steps of one month; the iterative coupling was conducted until themaximum pressure change observed in the entire domain between iterations is




162

0.005m. Typically, this convergence criterion required either 3 or 4 iterations for themost part of the simulation.

The distribution of the 0.2 and 0.6 isochlor after 1, 2, 4 and 10 years generated bythe present model are shown in Figure 4.0. These plots show the generation of a

complicated flow pattern with time. The flow field develops into a series of transientvortices, which spread the solute through both advection and diffusion. As wasexpected, the distribution of lobes of dense fluid is symmetric about the centerline ofthe box. Figure 5.0 shows a portion of the velocity field obtained after 10 hours ofsimulation, the velocity field clearly shows the swirling pattern of the fluid caused by the position of the solute. Similar to the Henry problem, there are several

published numerical results for the Elder salt convection problem, and the solutionsare dramatically different depending upon the numerical discretization and level ofmodeling sophistication chosen (Kolditz et al. 1998). The present model captures theessential features of the fluid flow and the predicted profiles are similar to those

reported in the literature (Boufadel et al. 1999b, Kolditz et al. 1998, Oldenburg andPruess 1995, Voss and Souza 1987)

0 100 200 300 400 500 6000

50

100

150

Length (m)

Elevation(m)

0 100 200 300 400 500 6000

50

100

150

Length (m)

Elevation(m)

0 100 200 300 400 500 6000

50

100

150

Length (m)

Elevation(m)

0 100 200 300 400 500 6000

50

100

150

Length (m)

Elevation(m)

Fig.4: Evolution of the fingering pattern shown by the 20% and 60%

concentration profiles for the modified Elder problem after 1, 2, 4 and 10 years.




163

0 50 100 150 200 250 3000

50

100

150

Length (m)

Elevation(m)

Fig. 5: Half of the concentration field superimposed upon the flow field for the

modified Elder problem after 10 hours.

The solution to Elder's problem may be hindered by the presence of someasymmetry in the results. This was explained by Boufadel et al. (1999b) whoencountered the same problem. The asymmetry is caused by the use of triangularelements. When the diagonal of the elements is aligned in the same direction causes

an asymmetrical grid which when coupled with the way the buoyancy force isrepresented causes the results to be skewed. The reason why Voss and Souza (1987)did not report this in their previous investigations because they used rectangularelements to discretize the domain, and of course this is a symmetrical discretization

and so the problem was not present. To achieve a good symmetrical result with thetriangular mesh, a fine level of discretisation is required to dampen the asymmetry.

4. UNCOUPLED FLOW AND TRANSPORT

In order to assess the quality of both the Henry and the Elder problems for theevaluation of the consistency of a density dependent algorithm, the numericalexperiments were repeated, but in this case the coupling of the flow and transport

equations was ignored. In effect, the same problem was resolved, but the value of in both the flow and transport equation was fixed at 1.0. The results from theanalysis of the solutions obtained from the uncoupling of the flow and transportequations enable the sensitivity to coupling to be analyzed.

4.1 Henry's Saltwater Intrusion Problem

To investigate the solution of Henry's problem without the coupling, the value of was fixed at a value of 1.0 for the solution of the fluid flow, fluid velocity and solute

transport formulations. Everything else in the analysis was left the same; thesimulation was performed for the same amount of time, after which the

concentration field was steady. The position of the 0.5 isochlor after this simulation




164

was measured and compared against that of the coupled solution in Figure 6.0. Thecomparison shows that the position of the intruded saline water was similar to thatobserved for the coupled solution.

0 20 40 60 80 100 120 140 160 180 2000

20

40

60

80

100

Length (cm)


Frind (1982)

0.5

Coupled SolutionUncoupled Solution

Fig. 6: Comparison of the coupled and uncoupled Henry solution.

Figures 7.0 and 8.0 show the velocity fields for the Henry problem under thecoupled and uncoupled conditions respectively. A comparison of the velocity fields

predicted with the coupled and uncoupled modes reveals some interesting results.The coupled velocity field shows that the horizontal velocities associated with theheavier saline water intrudes into the aquifer much further than for the uncoupledsituation. However, the two patterns are largely the same, with a constant inflowalong the freshwater side and a vertically distributed inflow along the base of the

seaward side. The inflow converges in the middle of the aquifer and rises and exits

above the seawater boundary. This similarity means that the actual component offlow, which is due to the interaction of the variably dense fluid and it’s mixing withthe lighter fluid is not completely responsible for this flow pattern.

0 50 100 150 2000

20

40

60

80

100

Length (cm)


Fig. 7: Velocity field for the Henry problem under coupled conditions.




165

0 50 100 150 200

0

20

40

60

80

100

Length (cm)


Fig. 8: Velocity field for the Henry problem under uncoupled conditions.

In fact the flow pattern is mostly determined by the imposed boundary conditions.

The implications of this observation are that if a variable density code is used tosimulate the Henry problem and there is some internal inconsistency in the couplingof the equations then the predicted distribution of the salt concentrations may stillappear similar to the true solution. This problem may also be compounded by theestablishment of a paradigm amongst the density dependent modelers in the way thatthe results are presented. Typically in the solution of the Henry problem, the analyst

presents the distribution of the isochlors, (for example Galeati et al. 1992, Kolditz et

al. 1998, Boufadel et al. 1999a). Obviously it is a necessary condition that for theinternal consistency of the model to be validated that the isochlors be comparable tothose from previous work, but it is not sufficient to claim that the problem has beensolved correctly simply because the isochlor positions are comparable. The analysis

of the internal velocity field for the problem as well as the position of the isochlorgives a higher degree of confidence as this provides a check against the intuitive physical processes occurring within the aquifer. This is particularly relevant to theHenry problem, as even after 40 years of analysis, there are several solutionsavailable, which are similar but are not completely uniform. Therefore it is probablethat an erroneous solution could appear to be similar to other solutions available in

the literature. Therefore the velocity field should also be used as a qualitative checkthat the correctness of the internal mixing environment within the aquifer before thesolution is deemed satisfactory.

4.2 Modified Elder Salt Convection Problem

The analysis of the uncoupled salt convection problem is quite straightforward.Since the boundary conditions for the flow equation describe a closed aquifer, thenthe only mechanism to initiate the flow is through the diffusion of the salt into the porous medium. The results for the modified Elder problem are shown in Figure9.0. The profiles show a simple diffusion pattern, which is expected since the fluid




166

is stationary. However, since the presence of the solute is assumed not to have anyimpact upon the flow, the fluid remains stationary for the entire simulation periodand there is absolutely no convection within the aquifer. This profile in comparisonto that obtained under full coupling show that the correct solution is completelydependent upon a correct numerical representation of the increased body force due

to the heavier fluid in the aquifer.

5. DISCUSSION

The results from this analysis show some clear points of distinction between theHenry saltwater intrusion problem and the modified Elder convection problem. The

comparison of the coupled and uncoupled results for the Henry problem generatesquantitatively similar profiles in both the flow field and the solute field.

This means that the patterns observed are largely due to the boundary forcing and

not because of the density coupling.

0 100 200 300 400 500 6000

50

100

150

Length (m)

Elevation(m)

0 100 200 300 400 500 6000

50

100

150

Length (m)

Elevation(m)

0 100 200 300 400 500 6000

50

100

150

Length (m)

Elevation

(m)

0 100 200 300 400 500 6000

50

100

150

Length (m)

Elevation(m)

Fig. 9: Evolution of the uncoupled solute distribution shown by the 20% and 60%

concentration profiles for the modified Elder problem after 1, 2, 4 and 10 years.

The comparison of the coupled and uncoupled Elder problem results show a totallydifferent flow scenario which indicates that the correct solution is completelydependent upon the correct numerical coupling of the equations. This means that in

the verification of a density dependent code, that the Elder problem should be thefocus of the verification study rather than the Henry problem.




167

Besides the relative importance of the boundary forcing, another difference betweenthe Henry and Elder problems is in the magnitude of the density difference. Sincethe Elder problem has a larger ratio of the fresh to the saline density difference, thenthe coupling between the equations for this problem is stronger than for the Henry problem. This weak dependence means that a simple updating scheme for the

coupling of the flow and transport equations is sufficient for the Henry problem.This simple updating scheme is only applicable because of the small value of $ %=0.00249). Conversely, the Elder convection problem is frequently termed a brine flow situation as the maximum fluid density is equivalent to that of a salt brine(Boufadel, 1999b). This means that the value of $ $is much larger %=0.2) and hencea simple updating scheme would be infeasible. Therefore, a successful simulation of

the Elder convection problem also necessitates the use of a coupling loop as well assome convergence criteria to exit the coupling when the solutions have convergedwithin each time step. For this reason it is clear that the Elder problem is bettersuited for the verification of coupled flow and transport models than the Henry

problem as the latter does not necessarily depend upon a consistent couplingscheme.

6. CONCLUSIONS

The worthiness of both the Henry saltwater intrusion problem and the Elderconvection problem were studied to assess their suitability to be used as a test case

for the verification of variable density groundwater flow models. The analysis ofthe Henry problem showed that the present model was able to reproduce typical

profiles for the distribution of the saline water observed by previous investigations.The quality of the solution was observed by resolving the problem in an uncoupled

mode where the transport equation was associated with a passive tracer. Theuncoupled results indicate that a similar pattern of fluid velocity and solute

distribution are observed. This means that if used alone for the verification of avariable density groundwater modeling code, it is feasible that the results mayappear to be capturing the physical processes without necessarily simulating thecorrect internal dynamics.

The Elder salt convection problem was also solved using the proposed algorithm tosimulate the dense fingering and complex velocity fields associated with this problem. The convection problem was also resolved using a completely uncoupledsolution. This resulted in a simple diffusion profile with no convection within the

aquifer. This has the advantage of illustrating the importance of the coupling between the equations in terms of correctly predicting the dynamics of coupledgroundwater flows. Since this dependence is not observed in the solution of Henry's problem, it is clear that the Henry saltwater intrusion problem should never be usedalone as it has in the past to verify density dependent groundwater flow codes.




168

REFERENCES

Boufadel, M.C., Suidan, M.T. and Venosa, A.D. (1999a) A Numerical model fordensity-and-viscosity- dependent flows in two-dimensional variably saturated porous media. "Journal of Contaminant Hydrology". 37, 1-20.

Boufadel, M.C., Suidan, M.T. and Venosa, A.D. (1999b) Numerical Modeling ofwater flow below dry salt lakes: effect of capillarity and viscosity. "Journal of Hydrology". 221, 55-74.

Croucher, A.E. and O'Sullivan, M.J. (1995) The Henry problem for saltwaterintrusion, "Water Resources Research" 31(7) 1809-1814

Elder, J.W., (1967) Transient convection in a porous medium. "Journal of Fluid

Mechanics". 27, 609-623

Frind, E.O. (1982) Simulation of long-term transient density-dependent transport ingroundwater. "Advances in Water Resources" , 5, 73-88

Galeati. G., Gambolati, G. and Neumann, SP. (1992) Coupled and Partially CoupledEularian-Lagrangian Model of Freshwater-Seawater mixing. "Water Resources Research". 28(1), 149-165

Henry, H.R. (1964) Effects of dispersion on salt encroachment in coastal aquifers,Sea water in coastal aquifers. "U.S. Geological Survey Water Supply Paper".,1613-C, 70-84

Herbert, A.W., Jackson, C.P. and Lever, D.A. (1988) Coupled Groundwater Flowand Solute Transport with Fluid Density Strongly Dependent upon Concentration.

"Water Resources Research" 24(10), 1781-1795

Kolditz, O., Ratke, R., Diersch H-J G. and Zielke, W. (1998) Coupled groundwater

flow and transport: 1. Verification of variable density flow and transport models."Advances in Water Resources", 21(1), 27-46

Oldenburg, C.M. and Pruess, K. (1995) Dispersive transport dynamics in a stronglycoupled groundwater-brine flow system. "Water Resources Research" . 31(2), 289-302

Simpson, M.J. and Clement, T.P. (2001) "Worthiness of the Henry and Elder problems for density dependent groundwater model evaluation" . (in preparation)

Voss , C.I. and Souza, W.R. (1987) Variable density flow and solute transport

simulation of regional aquifers containing a narrow freshwater saltwater transitionzone. "Water Resources Research". 23, 1851-1866

Yeh, G-T. (1981) On the computation of Darcian Velocity and Mass Balance in theFinite Element Modeling of Groundwater Flow. "Water Resources Research",17(5): 1529-1534





169

Modelling Advection-Dispersion Process for Dual

Radiotracer Dating of Groundwater with an Example of

Application to a14

C and36

Cl Data Set from

Central Australia

S.K. Gupta

Abstract

This paper investigates the applicability of the three commonly used models of

groundwater flow to a recent radiocarbon and chlorine-36 groundwater tracer data set from Central Australia (Cresswell et al., 1999 a, b). The models being considered

are (i) the Piston-Flow Model (PFM), (ii) the Well-Mixed Reservoir (WMR) Model,and the Dispersion-Advection (DA) Model. Any of the three flow models is able to

explain the available 14C and 36 Cl/Cl - data by invoking some addition of `dead'chloride during passage through the aquifer. The highest groundwater model ages are given by the DA model with D/u2 =106 a. Though, not unlikely, there is no real

justification for assuming such large value of D/u2. However, if lower values of D/u2 (~103 a), as are adequately able to explain the data points are accepted, the

groundwater model ages are highest for the WMR (~110ka) from the Amadeus Basin.The chloride/ sulphate data coupled with fracture type of secondary porosity for Ngalia, Arunta and Amedues formations suggest relatively local recharge of

groundwater with little dispersion between different flow streamlines. It also appearsthat the present data set does not permit calculating groundwater ages using PFM on36 Cl/Cl - measurements, ignoring 14C measurements and the drawing of palaeoclimaticinterpretations from the so calculated of very old ages

Keywords: Groundwater dating, radiotracers, flow models, radiocarbon,chlorine-36, dispersion-advection

1. INTRODUCTION

Radioisotopes of appropriate half-life are used for groundwater age determinationand in assessing the dynamics of flow within the aquifers. Typical groundwatervelocities in many large aquifers in arid and semi-arid zones range from <1 m.a

-1 to

>100 m.a-1. Radiotracers in the 103-106 a half-life range can be expected to showsignificant concentration change during groundwater flow over flow distances of 10to 1,000 km and are thus most useful. However, except for isotopes of oxygen and




170

hydrogen, all other tracers of groundwater movement can only be present in one orthe other dissolved forms, their concentrations may be affected by interactions withthe aquifer matrix. Presently, several models are available that attempt to quantify

the effect of non-radiogenic processes on tracer concentration variation duringgroundwater flow. Interpretation of radiotracer measurement data in terms of parameters of groundwater flow from a given region is; therefore, stronglydependent on the choice of flow model.

It is, therefore, important to understand the underlying assumptions and the

limitations of the various available flow models. This is expected to help in betterunderstanding of the dynamics of groundwater flow from the available data set. Inaddition, it should also help design better experiments while embarking on a programme of new investigations.

In this paper, three commonly used models of groundwater flow have been

investigated in respect of their applicability to a recent radiocarbon and chlorine-36groundwater tracer data set from central Australia (Cressel et al., 1999 a, b). Themodels being considered are (i) the Piston-Flow Model (PFM); (ii) the Well-MixedReservoir (WMR) Model; and (iii) the Dispersion-Advection (DA) Model. Anearlier work (Gupta et al., 1981) on dual radiotracer dating formed the basis of this

investigation.

2. BACKGROUND

Radiocarbon (

14

C) is cosmogenic in origin and has a half-life of 5730±

40 years. Thisisotope gets incorporated in groundwater by dissolution of soil CO2 at the plant rootlevel in unsaturated zone. The carbonic species formed are subject to interactionwith the matrix carbonate and this gives rise to number of problems in correct ageestimation (Wigley et al, 1978; Fontes, 1983, 1992; Geyh, 1992). Radiocarbonmeasurements in groundwater are generally reported in terms of Percent of Modern

Carbon (PMC) which indicates14C/C ratio in the dissolved carbon with reference to

modern wood standard.

36Cl has a half-life of 3.01x10

5 years and gets incorporated in groundwater along

with the anion chloride. Unlike radiocarbon, there can be significant in-situlithogenic production of 36Cl due to interaction of U and Th decay neutrons on 35Cl.The abundance of 36Cl is usually reported as atomic ratio of 36Cl to total chloride in

the sample. This ratio is always quite small in natural waters, typical value rangingfrom 10-15

to 10-11

. Over geologic time, equilibrium is established betweensubsurface in-situ production of 36Cl and its decay. The equilibrium 36Cl/Cl valuewill depend on the rate of production of 36Cl, which is a function of U and Thconcentration in the aquifer. The attractiveness of chlorine in hydrologic studies is

that it is highly soluble, exists in nature as a conservative non-sorbing anion anddoes not participate in redox reactions. However, in using 36Cl/Cl ratio an

assessment must be made of subsurface addition of stable Cl isotopes to the water by




171

either chemical reactions with rock, ion filtration or mixing with higher chloridewaters; such additions can substantially change 36Cl/Cl ratio. In common with 14C,age interpretation using 36Cl/Cl also require knowledge of initial (at t = 0) 36Cl/Clratio. In-situ production of 36Cl must also be taken into account through adequate

assessment of U and Th concentrations in the aquifer. Because at t = 0,36

Cl/Clvalues are in the 20-500x10

-15 range, in-situ production (~50x10

-15) can have

significant effect on the observed36

Cl/Cl ratios. At the other end, the presence ofeither thermonuclear 14C and 36Cl in groundwater clearly indicates a young age forwater or, in case of groundwater mixing, at least some significant portion of that

water.

3. GROUNDWATER FLOW MODELS

3.1 Piston Flow Model

The most commonly used groundwater flow model for interpretation of radiotracerdata assumes that as groundwater moves away from the recharge area, there are noflow lines of different velocities and that hydrodynamic dispersion as well asmolecular diffusion of the tracers are negligible. Thus, the tracer moves from therecharge area very much like a parcel pushed by a piston with the mean velocity ofgroundwater. This implies, that tracer which appears at a sampling point at any time

t entered the system at a time t -T , and from that moment its concentration hasdecreased by radioactive decay during the time span T. Therefore,

)exp()()( T T t C t C inout

λ −−= (1)

Equation 1 describes a dynamic system and is mathematically equivalent toEquation 2 describing the concentration of a radioisotope in a static water parcelseparated since the recharge time whereby

)exp()0()( t C t C λ −= (2a)

Where, t here is the radiometric age of water and corresponds to T of the dynamicsystem. If 'x' is the distance from the recharge boundary, T = x/u can be used toestimate the flow rate (u) of groundwater in the aquifer.

)/exp()0()( u xC t C λ −= (2b)

If two tracers '1' and '2' (e.g. 14C and 36Cl) are being measured one can write

)exp()0()( 111 t C t C λ −= (3)

)exp()0()( 222 t C t C λ −= (4)




172

Or

! " #

$% &

! " #

$% & =!

" #

$% &

)0()(

ln)0(

)(ln

2

2

2

1

1

1C

t C C

t C λ

λ (5)

This, on 'log-log' Dual Tracer plot gives a straight line with a slope λ1/λ2 (Fig.1).Thus, if the piston flow model is applicable, the samples must plot on the PFM linein the Dual Tracer 'log-log' plotting field. It is interesting to note that the distance ofa point on the PFM line from the recharge point C/C(0)=1 corresponds to T= x/u.

3.2 Well-Mixed Reservoir Model

Unlike in the PFM, if it is assumed that the recharge flux, with tracer concentrationC(0) completely mixes with the entire volume of the reservoir before outflow(concentration C(t)), we get another extreme case model known as Well-MixedReservoir (WMR) model. In application of this model to an aquifer system, it isassumed that the mixing reservoir comprises the entire volume between the recharge

area and the sampling point.

Under these conditions

)1(

)0()(

τ λ +=

C t C (6)

Where, λ is again the radioactive decay constant and τ, the ratio of reservoir volume

to the recharge volume flux, represents the estimated mixing time (or the meanresidence time) between the recharge area and the sampling location. It is seen that

!! "

#$$%

& −= 1

)(

)0(1

t C

C

λ τ (7)

estimated from tracer data actually represents a dynamic parameter-the mixing time.As before, if there are two tracers we get

! " #

$% &

! " #

$% &

++

=! " #

$% &

)0()(

ln)1(ln

)1(ln)0(

)(ln

2

2

2

1

1

1C

t C C

t C τ λ

τ λ (8)

On Dual Tracer 'log-log' plot, Equation 8 gives a curved line with slope changing

with changing value of 'τ' as shown in Fig.1.




173

Fig. 1

0.1

1

0.001 0.01 0.1 1

Tracer-1,14

C, C/C0

T r a c er -2 , 3 6 C l / C l - ,

C / C 0

Piston Flow Model (PFM)

Disp. Adv. Model (DA)

Well Mixed Res. Model (WMR)

t =x / u=1 0 5

t =x / u

=1 0 7

D / u2 =1 0 4 ; p=1 0 - 6

D / u2 =1 0 6 ; p=1 0 - 6

O A

B

C

D E F

G

t =x / u=1 0 6

DA ( D / u2 =

) 8

D / u2 =1 0 4 ; p= 0

D / u2 =1 0 6 ; p= 0

PFM

W M R




174

3.3 Dispersion-Advection Model

The phenomenon of mixing accompanying the movement of a chemical speciesthrough porous media can also be handled by a diffusion-advection equation in

which diffusion coefficient is replaced by a dispersion coefficient (Scheidegger,1961).

The one-dimensional continuity equation for a tracer in an isotropic dispersive

groundwater flow system, following Guymon (1972) may be written as

21 W W

x

uC x

C D

t

C −+

−=

δ

δ δ δ

δ

δ (9)

Where, ' D' is the diffusion coefficient of the tracer, and as in case of PFM, ' x' the

distance from the recharge boundary, 'u' the bulk flow velocity. W 1 and W 2, are therates of introduction and removal of the tracer.

With further assumption of u and D not being functions of x and in case of steady

state (i.e. 0=t C δ δ ), the equation reduces to

0212

2

=−+∂

∂−

∂

∂W W

x

C u

x

C D (10)

In case of radioactive tracers, the term W 2 will include in addition to radioactivedecay, loss of tracer due to non-radioactive processes. Dealing only with the case oftracer loss by radioactive decay alone and for W 1=0, Equation 10 can be re-writtenas

02

2

=−∂

∂−

∂

∂C

x

C u

x

C D λ (11)

This equation for the case D=0 and the boundary condition C = C 0 at x = 0 gives thesolution for an ideal piston flow

)/exp(0 u xC C λ −= (12)

In case of finite dispersion the solution of (11) for the boundary conditions C = C 0 at

x = 0 and C = 0 at x = ∞ is given by (Gupta et al., 1981).

''

(

)

**

+

,

-.

-/0

-1

-23

! "

#$%

& +−=

21

204

112

expu

D

D

xuC C

λ (13)




175

The tracer concentration decreases exponentially with distance; somewhat similar tothe case of the piston flow model. Therefore, a simplistic application of the pistonflow model would give an apparent velocity

In case of two radiotracers, we have from Equation 13

( ) ( )

( )

( )20212

2

2121

10 ln

411

411ln C C

u D

u DC C

λ

λ

+−

+−= (15)

Which is a straight line on Dual Tracer 'log-log' plot. The slope is function of D/u2

(Fig.1). The distance from the recharge boundary (characterised by C/C 0=1 for bothtracers to any point in the plotting field is a measure of the dimensionless parameter

xu/D (cf. Equation 13). Thus knowing x (i.e. distance of the sampling well from therecharge boundary in the field), both u and D can be estimated.

It is also seen from Equation 15 that as D→ ∞ , the slope term →√(λ1/λ2) indicatingthat different straight lines for different value of D/u2 will lie in the plotting field

between the slope of λ1/λ2 (PFM) and √(λ1/λ2) the limiting case of D→∞ (Fig. 1).

An interesting modification of the above DA model is the general case of semi-confined aquifer wherein some amount of young recharge is added due to leakage

influx from the overlying unconfined aquifer and there is also some leakage outfluxto the underlying aquifers. Following Gupta et al (1981) the continuity equation can be re-written as

( )002

2

=−−+∂

∂−

∂

∂qC C pC

x

uC

x

C D λ (16)

The term p represents the rate of leakage influx of relatively young water (activity~C 0) and q represents the rate of leakage outflux (activity = C ) from the aquifer.

In Equation 16, u, in general, is a function of x as governed by ∂ u/ ∂ x = p-q.

However, if both p and q are constant, ∂ u/ ∂ x = constant or zero. We further assume

that the activity of the tracer in the input flux is constant throughout the extent ofaquifer and is the same as that at the input boundary. In real aquifer systems it may

vary somewhat with `x’ .

Equation 16 was solved by Gupta et al (1981) for the case of ∂ C/ ∂ x = 0 at thedischarge boundary located at a distance L from the recharge boundary. Their

solution for the particular case of p = q and L→ ∞ is

-.

-/0

-1

-23

! "

#$%

& +−=

21

24

112 u

Duua

λ (14)




176

( ) ( ) ( )( )mx p pmxC C exp1)(exp0 −++= λ (17)

Where ( ) '(

)*+

,++−=

2124112

u D p D

um λ

It is easy to see for a non-zero p, the tracer concentration given by (17) will

approach an asymptotic value = (p/p+λ ) independent of eddy diffusivity (D). In factfor p=1 the asymptotic value is the same as that given by the Equation 6representing the Well-Mixed Reservoir model. So we visualise DA model as a more

general case of which special cases are: Piston Flow (for D = 0) and Well-MixedReservoir ( p = 1).

All the three models discussed above can incorporate a term for a finite loss of tracerfrom a confined aquifer owing to non-radioactive process. This can be done by

considering another rate constant E , similar to λ , the radioactive decay rate constant

and replacing λ by ( λ +E ) in the various solutions. In this way by studying theobserved deviations from any particular model curve in the 'log-log' Dual Tracer- plotting field, it is possible to estimate the magnitude of parameter E for the selectedflow model for one of the tracers. However, it is still required to assume that theother tracer did not undergo loss due to non-radioactive processes.

4. DISCUSSION: DUAL TRACER ‘LOG-LOG’ PLOT

In the light of the above discussion, it is now possible to subdivide the Dual

Radiotracer ''log-log'' plotting field into various sub-regions to get an idea about the parameters of the applicable flow model from a set of measurements. Table-1

summarises the applicability of different flow models as can be discerned from DualRadiotracer ''log-log'' Plot (Fig.1). The data points corresponding to Piston Flow andWell-Mixed Reservoir Models are expected to fall along lines marked PFM (straightline OB) and WMR (curve OGE) respectively. The various cases of the DiffusionAdvection (DA) model, for different values of D/u

2 and no leakage influx of

relatively young water (i.e. p = 0), plot as straight lines in the region lying between

the PFM and the limiting case for DA model as D/u2→ ∞. In Fig.1, two such curves

for D/u2 104a and 106a are shown. In all cases, the model groundwater age ( t = x/u)

increases as the data point moves away from the origin, O, along any particularcurve. In Fig. 1, lines joining the points with three values of model groundwater ages(10

5, 10

6and 10

7a) are shown across the straight lines for different values of D/u

2 for

p = 0. However, in case of leakage influx of relatively young water (i.e. p > 0), thecurve for any given value of D/u2 begins to deviate from the corresponding straightline and asymptotically meet the WMR curve asymptotically. It is seen that theRegion-OABO (Above the Piston Flow Line) is forbidden and no data point should

lie in this region, except in case of dissolution of radioactively dead Tracer-1 (in the present case

14C). Similarly, no data points can lie in the Region-OGE, i.e.




177

Table-1. Applicability of different flow models for points plotting in different regions of

Dual radiotracer 'log-log' plot (Fig.1). Note that Tracer-1 plotted on the Abscissa has

lower half-life compared to Tracer-2 plotted on the Ordinate.

Piston Flow Model Well-Mixed Reservoir Model Dispersion-Advection Model

Region of Plot p=0;E=0

P=0;

E≠0 p≠0;E=0

p≠0;

E≠0

p=0;E=0

P=0;

E≠0 p≠0;E=0

p≠0;

E≠0

p=0;E=0

P=0;

E≠0 p≠0;E=0

p≠0;

E≠0

Region-OABO:

Between Abscissa(Tracer 1 axis), PFM

and small part of thecurve of WMR close to

origin

! ! ! ! ! ! ! ! ! ! ! !

Region-OBCGO:

Between PFM, DA( D/u2

!) and part of

the curve of WMR between G and O

! " " " ! ! ! ! " " " "

Region-GCDEG:

Between DA ( D/u2!)

and WMR between E

and G

! " " " ! ! ! ! ! " " "

Region-OGO:Between DA ( D/u2

!)and WMR between G

and O

! " ! " ! " ! " " " " "

Region-OGEFO:Between Ordinate

(Tracer 2 axis), DA( D/u2

!) and WMR

between G and E

! " ! " ! " ! " ! " ! "

'p' is the fractional volume rate of leakage influx from the unconfined to confinedaquifer, with tracer concentration "C0 for both tracers.

'E' is the rate constant for loss of Tracer-2 due to non-radioactive processes. For

Tracer-1, it is assumed ≈ 0.

! Means 'Not possible'.

" Means 'Possible'.

'PFM’ means Piston Flow Model line. 'WMR' means 'Well-Mixed Reservoir' Model

line. ‘DA ( D/u2∞)' means 'Dispersion Advection' Model line for D/u

2approaching

infinity.




178

below WMR and DA limiting case for ( D/u2→ ∞ ), except in case of dissolution of

radioactively dead Tracer-2 (in the present case36

Cl), i.e. for E ≠ 0.

As an example of the applicability of the Dual Tracer ''log-log'' plot, we have plottedin Fig.2, data points taken from two recent papers (Cresswell et al, 1999a,b) fromCentral Australia. The relevant isotopic and other data are reproduced in Table-2. Itis interesting to note that there are no data points above the PFM line OB indicating

that dissolution of dead carbon may be negligible. But several points, belonging toall the three series of groundwater samples, lie below the section OGE, indicatingthat in the investigated regions a significant dissolution of dead chloride may betaking place as groundwater progressively moves within the aquifer.

The addition of dead chloride can be estimated using a model for chloride

dissolution in the aquifer. Several models of chloride increase with time, viz. Linear,exponential, logarithmic etc are possible. We will probably have no reasonable justification for choosing any particular model. Therefore, we choose one that ismathematically simple to handle and also does not appear unreasonable. One such

model could be that chloride addition is a first order process wherein the rate ofchloride increase at any given instant is proportional to its concentration (Cl

-) in

groundwater, i.e.

t E t eCl Cl or Cl E

t d

Cl d 0)()(. −−−

−

== (18)

It is implicitly assumes that the product ' E.t' is well below infinity.

Using this model for chloride addition, we can rewrite the equations for thethree flow models, viz. PFM, WMR and DA models.

For PFM,

t t eC C 14

01414 λ −=

t t eCl Cl 36

03636 λ −= (19)

Andt E

t eCl Cl 0−− =




179

Fig. 2:

0.1

1

0.01 0.1 1

14C, C/C0

3 6 C l / C l - , C / C 0

Piston Flow Model

Adv.-Disp. Limiting Model

Well Mixed Res. Model

Amadeus

Cainozoic

Ngalia

D = 23.37Ln(C/C0) - 25

D = 37.21Ln(C/C0) - 15

-140

-120

-100

-80

-60

-40

-20

0

0.10 1.0014

C, C/C0

D e p t h ( m )

A

B

C

D

E

F

PFM

WMR

G




180

Table-2. Groundwater isotopic tracer data from aquifers in Central Australia.

Source: Cresswell et al (1999a,b)

Stn No. Well Depth

(m)

Cl-

(mg/l)

36Cl - (C/C0)

+

14C - (C/C0)

+ 18

O

(‰)

D

(‰)

d=8x 18

O- D

(‰)

Ngalia Basin

14980* 31 22 1.05±0.08 1.10±0.13 -7.08 -53.5 -3.1

15472* 28 73 0.83±0.06 0.80±0.09 -8.35 -59.3 -7.5

15463* 28 54 0.86±0.07 0.35±0.04 -7.47 -54.1 -5.7

14055 23 595 0.82±0.06 0.82±0.10 -6.39 -51.0 -0.1

12910 72 270 0.85±0.07 0.30±0.04 -6.32 -49.0 -1.6

6165 34 953 1.02±0.07 0.59±0.07 -6.97 -50.0 -5.8

15477 45 336 0.85±0.07 0.26±0.03 -5.54 -45.0 0.7

12578 31 333 0.91±0.07 0.41±0.05 -6.52 -49.4 -2.8

10945 12 303 1.04±0.08 0.12±0.01 -8.42 -57.7 -9.7

Cainozoic Basin

13795 70 1560 0.51±0.04 0.93±0.11 -6.95 -51.6 -1.6

15740 55 110 1.04±0.08 0.42±0.05 -8.49 -58.0 -9.9

16694 75 786 0.29±0.03 0.10±0.01 -8.52 -59.5 -8.7

5754 48 129 0.98±0.07 0.95±0.11 -8.85 -60.3 -10.5Amadeus Basin

13669 - 312 0.79±0.06 0.46±0.05 - - -

13653 - 15 0.95±0.07 0.19±0.02 - - -

13652 - 212 0.79±0.07 0.21±0.02 - - -

11843 - 199 0.54±0.05 0.09±0.01 - - -

12681 - 215 0.83±0.07 0.08±0.01 - - -

14566 - 195 0.92±0.07 0.07±0.01 - - -

11396* 18 138 1.05±0.07 0.96±0.11 -9.52 -66.6 -9.56

*These samples were assigned by Cresswell et al (1999a) to Cainozoic Basin. Wehave reassigned them considering groundwater flow directions as shown in Fig. 2 ofCresswell et al (1999a).

+ C0, the average concentrations of radiotracers in the recharge areas of all the three

basins have been assumed as 85±10 percent modern carbon (pMC) for14

C and200±10 (x10

-15) for

36Cl/Cl

- ratio.




181

Therefore, ( )036

36

36

14

014

14

lnlnCl Cl

Cl Cl

E C

C t t −

!! "

#$$%

&

+=

!!

"

#

$$

%

&

λ

λ (20)

So that we get different straight lines for different values of E in the Dual Tracer'log-log' plot as shown in Fig.3.

0.1

1

0.01 0.1 1

14C, C/C 0

3 6 C l / C l - , C / C 0

Ngalia

Cainozoic

Amadeus

E=0

=10-6

=5X10-6

=10-5

=2X10-5

=5X10 -5

=10-4

t

f = 5 k a t

f =1 0 k a

t

f =2 0 k a

t

f = 3 0 k a

Piston Flow

Model

Fi . 3




182

Similarly for WMR,

WMRt

t

C C

14

014

1 λ +=

WMRt

t

Cl Cl

36

036

36

1 λ += (21)

And

WMRt E

Cl Cl

−

=−

−

1

0

Therefore,

( )

( )( )

( )( )036

36

36

14

014

14

ln

11

ln

11ln

ln−

−

''''

(

)

****

+

,

./0

123

+−

./0

123

+=

!!

"

#

$$

%

&

Cl Cl

Cl Cl

t t E

t

C

C t

WMR

WMR

WMRt

λ

λ (22)

In this case the Dual Tracer 'log-log' plots for different values of E are no morestraight lines as seen from Fig.4.

In case of DA model, the governing equations are:

( ) '(

)*+

,

./0

123

+−=212

1401414 411

2exp u D

D

u xC C t λ

( ) '(

)*+

,

./0

123

+−=212

3603636 411

2exp u D

D

u xC C t λ (23)

( ) '(

)*+

,

./0

123

−−= −− 2120 411

2exp u D E

D

u xCl Cl t

Therefore,

( ) ( ) ( )

( )( )036

36

21236

212

21214

014

14

ln

411411

411ln

−

−

''

(

)

**

+

,

+−−−−

+−=

!!

"

#

$$

%

&

Cl Cl

Cl Cl

u Du D E

u D

C

C t t

λ

λ (24)




183

Fig. 4

0.1

1

0.01 0.1 1

14C, C/C0

3 6 C l / C

l - , C / C 0

Ngalia

Cainozoic

Amadeus

Well-Mixed

Reservoir Model

=10-6

=5X10-6

=10-5

=10-4

t

= 5 k a

t wmr =2 0 k a

t

= 5 0 k a

t wmr =1 0 0 k a

=2X10-5

E=0




184

Which, as in case of Equation 15, is a straight line on Dual Tracer 'log-log' plot. Theslope, in addition to D/u2 is a function of E (Fig.5). Once again, the distance fromthe recharge boundary (characterised by C/C 0=1 for both tracers to any point in the plotting field is a measure of the dimensionless parameter xu/D (cf. Equation 23).

Fi . 5

0.1

1

0.01 0.1 1

14C, C/C 0

3

6 C l / C l - , C / C 0

Ngalia

Cainozoic

Amadeus

DA- Model

D/u2=1 0

6; E=0

D/u2=1 0

6; E=2.5x10

-7

D/u2=1 0

3; E=0

D/u2=1 0

4; E=0

D/u 2=1 04; E=2.5x10 -5

D/u2=10

3; E=2.5x10

-4




185

Radiocarbon model ages of groundwater for data points taken from (Cresswell et al, 1999a, b) are given in Table-3. It is seen that all flow models, except DA with D/u2 =106 a, givemodel groundwater ages that are significantly lower than obtainable by accounting 36Cl/Cl- changes due to radioactive decay of 36Cl only. Even for DA with D/u2 =106 a, the highest

model groundwater age is ~250ka (Amadeus Basin; Sample No. 14566). But, in this case,several data points give negative estimates of E '. This indicates that, in the Dual Tracer`log-log' Plot, the position of these samples is above the

36Cl/Cl

- value for the model curve

for D/u2 =106 a. Assuming a higher value of D/u2 would no doubt increase the modelgroundwater age estimates but, it is also seen from Fig. 2, that measurement errors do not

enable one to distinguish between the curves for D/u2 =105 a and D/u2 =∞. Even for D/u2 =

∞, it is still necessary to explain the plotting position of some data points by invoking

dissolution of `dead' chloride. In such a situation, it may not be logical to reject the same forother data points.

The estimated Cl- concentrations at time t = 0 obtained using Equations (19) - (23)

are given in (Table-3). These are plotted in Fig. 6 with data of δ18O (Cresswell et al,

1999a) on the ordinate. It is seen that the data points in the two enclosed areas (A &B) on Fig. 6, do not show much significant change from their measured Cl- concentrations for any of the flow models. Though most data points for Amadeus

Basin are not included in Fig. 6 (because δ18O values for these are not available),

Table-3 shows that these behave similarly except for DA with D/u2

=106a. The

geographical location of the sampling points in the two enclosed areas A & B in Fig.

6 can be seen in Fig. 2 of Cresswell et al (1999a). It is observed that the respectivesamples derive from two different groundwater flow regimes originating in the north(Ngalia Basin) and south (Arunta Block-Amadeus Basin) and draining towards the`in-between' depressed region containing playas/ saline lakes. It is only the samples

from this `in-between' region in the vicinity of the playas/ saline lakes that exhibitlarge differences in the measured Cl

- and its estimated value at t = 0. Hydrologically,

this is not unexpected, because the playas do contain lot of dead Cl- as exhibited by

the 36Cl/Cl- data of samples from the Playa Lake Ngalia (Cresswell et al, 1999a).

Central Australia

-1 0

-9

-8

-7

-6

-5

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Chloride (mg/l)

d e l t a 1 8 O ( p e r m i l )

-1 0

-9

-8

-7

-6

-5

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Ngalia-PFM

Cainozic-PF MAmadeus-PF MNgalia-WMR

Cainozic-WM RAmadeus-WM RNgalia-DA-D/u2=e3Cainozic-DA-D/u2=e3Amadeus-DA-D/u2=e3

Ngalia-DA-D/u2=e6Cainozic-DA-D/u2=e6Amadeus-DA-D/u2=e6Ngalia

Cainozic

Amadeus

137956166

14055

15477

12910

12578

14980

15463

13795

16694

15472

15740

5754

11396

A

B

Fig.6




1 8 6

T a b l e - 3 . M o d e l g r o u n d w a t e r a g e s a n d e s t i m a t e s o f c h l o r i d e c o n c e n t r a t i o n a t t h e t i m e o f r e c h a r g e f

o r d i f f e r e n t f l o w m o d e l s .

M o d e l A g e ( a ) b a s e d o n

1 4 C d a t a

M o d e l E s t i m a t e d E ( a - 1 )

M o d e l E s t i m a t e d C

l - 0 ( m g / l )

D A M o d e l

D A M o d e l

D A M o d e l

S

t n

N

o .

C l - t

( m g / l )

P F M

W M R

D / u 2

=

1 0 3 a

D / u 2 =

1 0 6 a

P F M

W M R

D / u 2

=

1 0 3 a

D / u 2 =

1 0 6 a

P F M

W M R

D / u

2 =

1 0 3 a

D / u 2 =

1 0 6 a

N g a l i a B a s i n

1 4

9 8 0 *

2 2

- 7 7 0 *

- 7 4 0 *

- 8 5 0 *

- 8 , 8 6 5 *

6 . 1 E - 0 5

6 . 6 E - 0 5

5 . 2 E - 0 5

- 1 . 5 E - 0 5 @

2 3

2 3

2 3

2 1

± 9 7 0

± 8 9 0

± 1 , 0 8 0

± 1 1 , 2 0 0

± 1 . 2 E - 0 4

± 1 . 3 E - 0 4

± 6 . 4 E - 0 5

± 5 . 4 E - 0 5

± 2

± 2

± 2

± 2

1 5

4 7 2 *

7 3

1 , 8 0 0

2 , 0 1 0

1 , 9 9 0

2 0 , 6 7 4

1 . 0 E - 0 4

8 . 5 E - 0 5

8 . 5 E - 0 5

- 5 . 9 E - 0 5 @

6 0

6 1

6 1

8 5 @

± 9 7 0

± 1 2 1 0

± 1 , 0 8 0

± 1 1 , 2 0 0

± 7 . 3 E - 0 5

± 6 . 2 E - 0 5

± 4 . 2 E - 0 5

± 7 . 8 E - 0 5

± 1 2

± 1 2

± 9

± 8

1 5

4 6 3 *

5 4

8 , 6 7 0

1 5 , 3 1 0

9 , 6 1 0

9 9 , 7 2 9

1 . 5 E - 0 5

7 . 2 E - 0 6

1 . 3 E - 0 5

2 . 4 E - 0 7

4 7

4 8

4 7

5 2

± 9 7 0

± 2 7 8 0

± 1 , 0 8 0

± 1 1 , 2 1 0

± 9 . 1 E - 0 6

± 4 . 8 E - 0 6

± 1 . 7 E - 0 6

± 2 . 9 E - 0 8

± 4

± 4

± 1

± 0

1

4 0 5 5

5 9 5

1 , 6 9 0

1 , 8 7 0

1 , 8 7 0

1 9 , 4 3 0

1 . 2 E - 0 4

9 . 4 E - 0 5

9 . 3 E - 0 5

- 7 . 4 E - 0 5 @

4 9 0

4 9 0

4 9 0

6 9 7 @

± 9 8 0

± 1 , 1 9 0

± 1 , 0 8 0

± 1 1 , 2 0 0

± 8 . 2 E - 0 5

± 7 . 0 E - 0 5

± 4 . 8 E - 0 5

± 1 . 0 E - 0 4

± 1 0 6

± 1 0 3

± 7 8

± 7 8

1

2 9 1 0

2 7 0

9 , 8 6 0

1 8 , 9 7 0

1 0 , 9 3 0

1 1 3 , 4 4 3

1 . 4 E - 0 5

6 . 0 E - 0 6

1 . 2 E - 0 5

2 . 2 E - 0 7

2 3 5

2 4 0

2 3 5

2 6 0

± 9 7 0

± 3 , 2 1 0

± 1 , 0 8 0

± 1 1 , 2 2 0

± 8 . 9 E - 0 6

± 4 . 3 E - 0 6

± 1 . 4 E - 0 6

± 4 . 7 E - 0 8

± 2 4

± 2 2

± 5

± 1

6 1 6 5

9 5 3

4 , 3 2 0

5 , 6 8 0

4 , 7 9 0

4 9 , 7 3 0

- 5 . 7 E - 0 6 @

- 5 . 0 E - 0 6 @

- 5 . 4 E - 0 6 @

- 3 . 3 E - 0 6 @

9 7 7 @

9 8 0 @

9 7 8 @

1 0 2 2 @

± 9 7 0

± 1 , 6 4 0

± 1 , 0 8 0

± 1 1 , 2 0 0

± 1 . 7 E - 0 5

± 1 . 3 E - 0 5

± 7 . 1 E - 0 7

± 2 . 6 E - 0 7

± 7 1

± 7 3

± 7

± 1 6

1

5 4 7 7

3 3 6

1 1 , 2 5 0

2 3 , 9 7 0

1 2 , 4 8 0

1 2 9 , 4 7 2

1 . 2 E - 0 5

4 . 3 E - 0 6

1 . 1 E - 0 5

1 . 3 E - 0 7

2 9 3

3 0 1

2 9 4

3 2 9

± 9 8 0

± 3 , 8 0 0

± 1 , 0 8 0

± 1 1 , 2 3 0

± 7 . 0 E - 0 6

± 3 . 1 E - 0 6

± 1 . 1 E - 0 6

± 7 . 5 E - 0 8

± 2 7

± 2 5

± 5

± 1

1

2 5 7 8

3 3 3

7 , 3 1 0

1 1 , 7 5 0

8 , 1 1 0

8 4 , 1 5 4

1 . 1 E - 0 5

6 . 0 E - 0 6

9 . 9 E - 0 6

8 . 1 E - 0 8

3 0 6

3 1 0

3 0 7

3 3 1

± 9 7 0

± 2 , 3 6 0

± 1 , 0 8 0

± 1 1 , 2 0 0

± 1 . 0 E - 0 5

± 6 . 1 E - 0 6

± 1 . 6 E - 0 6

± 1 . 3 E - 0 7

± 2 5

± 2 4

± 5

± 1

1

0 9 4 5

3 0 3

1 7 , 3 6 7

5 9 , 3 0 0

1 9 , 2 6 0

1 9 9 , 8 9 2

- 4 . 3 E - 0 6 @

- 3 . 0 E - 0 6 @

- 4 . 1 E - 0 6 @

- 2 . 9 E - 0 6 @

3 2 6 @

3 5 6 @

3 2 8 @

3 9 1 @

± 9 9 0

± 8 , 0 5 0

± 1 , 0 9 0

± 1 1 , 3 5 0

± 4 . 2 E - 0 6

± 1 . 4 E - 0 6

± 1 . 0 E - 0 7

± 3 . 5 E - 0 8

± 2 2

± 2 7

± 2

± 6

C a i n o z o i c B a s i n

1 3 7 9 5

1 , 5 6 0

6 4 0

6 6 2

7 1 0

7 , 3 2 7

1 . 1 E

- 0 3

7 . 5 E - 0 4

3 . 3 E - 0 5

- 8 . 4 E - 0 3

7 8 9

7 8 9

1

5 2 2

3 0 4 2 @

± 9 7 0

± 1 , 0 5 0

± 1 , 0 8 0

± 1 1 , 2 0 0

± 1 . 6 E

- 0 3

± 1 . 2 E - 0 3

± 1 . 4 E - 0 3

± 2 . 6 E - 0 2

± 2 3 0 5

± 1 7 3 4

± 1

5 9 0

± 5 7 6 1




1 8 7

1 5 7 4 0

1 1 0

7 , 2 0 0

1 1 , 4 7 0

7 , 9 8 0

8 2 , 8 0 8

- 7 . 8 E - 0 6 @

- 5 . 9 E - 0 6 @

- 7 . 3 E - 0 6 @ - 4 . 0 E - 0 6 @

1 1 6 @

1 1 7 @

1

1 7 @

1 2 5 @

± 9 7 0

± 2 , 3 3 0

± 1 , 0 8 0

± 1 1 , 2 0 0

± 1 . 0 E

- 0 5

± 6 . 8 E - 0 6

± 6 . 7 E - 0 7

± 2 . 7 E - 0 7

± 8

± 9

± 1

± 2

1 6 6 9 4

7 8 6

1 8 , 8 4 0

7 2 , 5 0 0

2 0 , 9 0 0

2 1 6 , 8 7 4

6 . 4 E

- 0 5

9 . 2 E - 0 6

5 . 4 E - 0 5

- 1 . 7 E - 0 5 @

2 3 4

2 6 1

2 3 5

1 7 5 0 @

± 9 9 0

± 9 , 6 8 0

± 1 , 1 0 0

± 1 1 , 4 0 0

± 6 . 4 E

- 0 6

± 1 . 4 E - 0 6

± 2 . 8 E - 0 6

± 2 . 6 E - 0 6

± 1 0 7

± 1 0 6

± 2 2

± 7 4

5 7 5 4

1 2 9

4 5 0

4 6 0

5 0 0

5 , 1 7 6

4 . 3 E

- 0 5

4 . 1 E - 0 5

3 . 7 E - 0 5

- 5 . 1 E - 0 6 @

1 2 7

1 2 7

1 2 7

1 3 0 @

± 9 7 0

± 1 , 0 3 0

± 1 , 0 8 0

± 1 1 , 2 0 0

± 1 . 9 E

- 0 4

± 1 . 8 E - 0 4

± 8 . 1 E - 0 5

± 3 . 9 E - 0 5

± 1 2

± 1 2

± 8

± 1 3

A m

a d e u s B a s i n

1 3 6 6 9

3 1 2

6 , 4 2 0

9 , 7 0 0

7 , 1 2 0

7 3 , 8 8 5

3 . 4 E

- 0 5

2 . 0 E - 0 5

3 . 0 E - 0 5

- 2 . 3 E - 0 6 @

2 5 0

2 5 2

2 5 1

3 3 8 @

± 9 8 0

± 2 1 2 0

± 1 , 0 8 0

± 1 1 , 2 0 0

± 1 . 4 E

- 0 5

± 8 . 2 E - 0 6

± 4 . 7 E - 0 6

± 1 . 5 E - 0 6

± 2 9

± 2 8

± 1 2

± 5

1 3 6 5 3

1 5

1 3 , 8 6 0

3 5 , 9 3 0

1 5 , 3 7 0

1 5 9 , 5 0 0

1 . 4 E

- 0 6

- 8 . 0 E - 0 7 @

1 . 0 E - 0 6

- 1 . 4 E - 0 6 @

1 5

1 5 @

1 5

1 7 @

± 9 8 0

± 5 , 2 3 0

± 1 , 0 8 0

± 1 1 , 3 1 0

± 5 . 2 E

- 0 6

± 2 . 1 E - 0 6

± 2 . 4 E - 0 7

± 5 . 8 E - 0 8

± 1

± 1

± 0

± 0

1 3 6 5 2

2 1 2

1 3 , 0 2 0

3 1 , 6 6 0

1 4 , 4 4 0

1 4 9 , 8 3 5

1 . 6 E

- 0 5

4 . 8 E - 0 6

1 . 4 E - 0 5

2 . 5 E - 0 7

1 7 3

1 8 0

1 7 3

1 9 7

± 9 8 0

± 4 , 7 5 0

± 1 , 0 9 0

± 1 1 , 2 0 0

± 6 . 7 E

- 0 6

± 2 . 5 E - 0 6

± 1 . 2 E - 0 6

± 5 . 8 E - 0 9

± 1 9

± 1 7

± 4

± 1

1 1 8 4 3

1 9 9

1 9 , 7 5 0

8 1 , 8 2 0

2 1 , 9 0 0

2 2 7 , 2 6 4

2 . 9 E

- 0 5

4 . 5 E - 0 6

2 . 6 E - 0 5

- 1 . 1 E - 0 6 @

1 1 1

1 2 7

1 1 2

2 3 1 @

± 1 , 0 0 0

± 1 0 , 8 5 0

± 1 , 1 0 0

± 1 1 , 4 6 0

± 5 . 2 E

- 0 6

± 1 . 1 E - 0 6

± 1 . 4 E - 0 6

± 3 . 2 E - 0 7

± 2 1

± 2 0

± 5

± 2

1 2 6 8 1

2 1 5

2 1 , 0 0 0

9 6 , 6 1 0

2 3 , 2 9 0

2 4 1 , 7 2 9

6 . 6 E

- 0 6

- 1 . 5 E - 0 7 @

5 . 7 E - 0 6

- 4 . 3 E - 0 7 @

1 8 7

2 1 8 @

1 8 8

2 3 3 @

± 1 , 0 0 0

± 1 2 7 3 0

± 1 , 1 1 0

± 1 1 , 5 5 0

± 4 . 0 E

- 0 6

± 9 . 0 E - 0 7

± 3 . 8 E - 0 7

± 6 . 1 E - 0 8

± 1 8

± 1 9

± 2

± 1

1 4 5 6 6

1 9 5

2 1 , 9 1 0

1 0 8 , 8 4 0

2 4 , 3 0 0

2 5 2 , 2 2 8

1 . 8 E

- 0 6

- 1 . 3 E - 0 6 @

1 . 4 E - 0 6

- 1 . 3 E - 0 6 @

1 8 8

2 2 3 @

1 8 9

2 3 5 @

± 9 9 0

± 1 3 , 9 2 0

± 1 , 0 9 0

± 1 1 , 3 1 0

± 3 . 4 E

- 0 6

± 7 . 9 E - 0 7

± 1 . 6 E - 0 7

± 3 . 9 E - 0 8

± 1 4

± 1 7

± 1

± 2

1 1 3 9 6 *

1 3 8

3 1 0

3 1 0

3 4 0

3 , 5 3 5

- 1 . 6 E - 0 4 @

- 1 . 6 E - 0 4 @

- 1 . 7 E - 0 4 @ - 2 . 4 E - 0 4 @

1 4 5 @

1 4 5 @

1 4 5 @

1 4 5 @

± 9 7 0

± 1 , 0 1 0

± 1 , 0 8 0

± 1 1 , 2 0 0

± 5 . 5 E

- 0 4

± 5 . 7 E - 0 4

± 5 . 9 E - 0 4

± 1 . 3 E - 0 3

± 3 2

± 3 3

± 3 2

± 7 5

* - v e m o d e l a g e m e a n s t h a t t h e m e a s u r e d 1 4 C a c t i v i t y i s > t h e a s s u m

e d 1 4 C a c t i v i t y o f g r o u n d w a t e r

i n r e c h a r g e a r e a i . e . > 8 5 ± 1 0 p M C .

@ -

v e e s t i m a t e o f E i n d i c a t e s t h a t t h e

s a m p l e p l o t s a b o v e t h e c u r v e f o r t h e p a r t i c u l a r m o d e l i n t h e D

u a l T r a c e r L o g - L o g P l o t . T h i s

i n d i c a t e s t h a t

t h e m e

a s u r e d 3 6 C l / C l - r a t i o , w h e n c o r

r e c t e d f o r t h e e s t i m a t e d m o d e l

a g e b a s e d o n

1 4 C d a t a , w o u l d g

i v e

3 6 C l / C l - i n r e c h a r g e a r e a > t h e a s s u m e d

i n i t i a l

v a l u e o f 2 0 0 ± 1 0 ( x 1 0 - 1 5 ) . A s a

r e s u l t t h e c o m p u t e d v a l u e o f C

l - 0 i s > C l - t ,

t h e m e a s u r e d v a l u e

o f C h l o r i d e .




188

The δ18O values for the samples originating in northern Ngalia basin (Fig. 6, Area

A) and the southern Arunta-Amedues basin (Fig. 6, Area B) average -7±1.5‰ and -

9±1‰ respectively. It is also noticed that even after correction for chloridedissolution, groundwater samples continue to fall in their original respective groupson the basis of chloride concentrations, namely those with Cl- #150mg/l and those

with Cl- $225 mg/l (Fig. 6). It is also observed that the samples belonging to the two

chloride groups are geographically distributed in both northern Nglia basin and thesouthern Arunta-Amedues basins, and within each basin their distribution shows no pattern. This, sort of random distribution of Cl- values, taken together with two

hydro-geologically coherent grouping based on δ18O data, suggest that different

groundwater in both hydro-geological regimes originated with different Cl-

concentrations in their recharge areas and that different streamlines did not undergomuch dispersion and mixing during subsurface flow. This may be an indication ofmore local origin of various groundwater masses as would be expected for the

fractured sandstone aquifer of Ngalia and Amadeus basins and the metamorphicrocks of Arunta complex.

5. CONCLUSIONS

It appears that the14C and 36Cl/Cl- data reported by Cresswell et al (1999 a, b) on

groundwater samples from central Australia can be explained by any of the threeflow models by invoking some addition of `dead' chloride during passage throughthe aquifer. The DA model with D/u

2= 10

6a gives the highest groundwater model

ages. Though not unlikely, there is no real justification for assuming such large

value of D/u2

. However, if lower value of D/u2

(~103

a), as is adequately able toexplain the data points is accepted, groundwater model ages are highest for the

WMR (~110ka) for sample No.14566 from the Amadeus Basin. The correspondingPFM age is only ~22ka. The groundwater model age for this sample for DA with D/u

2=10

3a is ~250ka. The present data set does not permit choosing any particular

value of D/u2, but D/u2 =106a would appear to be the highest permissible value because of four reasons. (i) The measurement errors do not permit distinguishing

between D/u2 =105a and D/u2 = ∞. (ii) Many samples give negative values of E - parameter that describes rate of chloride addition during subsurface flow for D/u2

=106a. (iii) The δ18O values for the samples originating from the two hydro-geologically coherent regions in northern Ngalia basin (Fig. 6, Area A) and the

southern Arunta-Amedues basin (Fig. 6, Area B) average -7±1.5‰ and -9±1‰respectively. (iv) The random distribution of chloride/ Sulphate between these

hydro-geologically coherent regions, coupled with fracture type of secondary porosity for Ngalia, Arunta and Amedues formations suggest more local recharge ofgroundwater with little dispersion between different flow streamlines. It is alsoshown that the flow models do not permit calculating groundwater ages using PFMon 36Cl/Cl- measurements, ignoring 14C measurements and the drawing of palaeoclimatic interpretations from the so calculated of very old ages.




189

ACKNOWLEDGEMENTS

Dr. Nipun Kapur was associated with this work in the initial stages. Mr. R.D.Deshpande has also participated in some discussions on interpretations andconclusions of this work. I sincerely thank both these colleagues. Gujarat Water

Resources Development Corporation Limited (GWRDC) provided part financialassistance for this work.

REFERENCES

Cresswell, R., Wischusen , J., Jacobson, G. and Fifield, K. (1999a): "Assessment of

Recharge to Groundwater Systems in the Arid Southwestern part of NorthernTerritory, Australia, Using Chlorine-36" . Hydrogeology Journal, Vol.7, pp393-404.

Cresswell, R.G., Jacobson, G., Wischusen, J. and Fifield, K.L. (1999b): "AncientGroundwaters in the Amadeus Basin, Central Australia: Evidence from the

Radioisotope36 Cl". Journal of Hydrology, Vol.233, pp.212-220.

Fontes, J.Ch. (1983): "Dating of Groundwater" . In: Guidebook on NuclearTechniques in Hydrology. IAEA, Vienna, pp.285-387.

Fontes, J.Ch. (1992): "Chemical and Isotopic Constraints on14C Dating of

Groundwater". In: R.E. Taylor, A. Long and R.S. Kra (Ed.) Radiocarbon After FourDecades. Springer-Verlag, New York. Pp.242-261.

Geyh, M.A. (1992): "The 14C Scale of Groundwater, Correction and Linearity". In:

Isotope Techniques in Water Resource Development 1991, IAEA, Vienna, pp.167-177.

Gupta, S.K.< Lal, D., Sharma, P. (1981): "An Approach to Determining Pathwaysand Residence Time of Groundwaters: Dual Radiotracer Dating". Jour. Geophys.Res., Vol.86(C6), pp.5292-5300.

Guymon, G.L. (1972): "Notes on the Finite Element Solution of Diffusion Advection Equation". Water Resour. Res., Vol.8, pp.1357-1360.

Lehmann, E.E. and Loosli, H.HY. (1991): Chapter 6. "Isotopes Formed byUnderground Production". In: F.J.Pearson et al. (Eds.), Applied IsotopeHydrogeology, A Case Study in Northern Switzerland. Studies in EnvironmentalScience 43. Elsevier, Amsterdam, 439p.

Phillips, F.M., Bentley, H.W., Davis, S.N., Elmore, D., Swanik, G. (1986):

Chlorine-36 "Dating of Very Old Groundwater" 2. Milk River Aquifer, AlbertaCanada. Water Resour. Res., Vol. 22, pp.2003-2016.

Scheidegger, A.E. (1961): "General Theory of Dispersion in Porous Media" .J. Geophys. Res. Vol.66, pp.3273-3278.

Wigley, T.M.L., Plummer, L.N., Pearson, Jr., F.J. (1978). "Mass Transfer andCarbon Isotope Evolution in Natural Water Systems" . Geochim. Cosmochim. Acta,

Vol.42, pp.1117-1139.




190

Fig. 1: Dual Tracer ‘log-log’ plot depicting expected variation in the concentrationof radiocarbon and chlorine-36 in a groundwater system for various models of flowand mixing conditions. The units are: C/C0, dimensionless; x = m; u = m.a

-1; D =

m2a-1; p = a-1. Note that curves for different values of D/u2 with no leakage influx ofrelatively young water (i.e. p = 0), plot as straight lines in the region lying between

the PFM and the limiting case for DA model for D/u2 → ∞. The model groundwaterage (t = x/u) increases as the data point moves away from the origin, O, along any

particular curve. As an aid to quick estimation DA model groundwater age, lines joining the points with three values of t = x/u (10

5, 10

6and 10

7a) across the straight

lines for different values of D/u2 are also shown.

Fig. 2: The

14

C and

36

Cl/Cl

-

data of (Cresswell et al., 1999a, b) from centralAustralia plotted on the Dual Tracer ‘log-log’ plot. The inset shows depth variation

of 14C for Ngalia and Cainozoic basin samples. C0 for 14C was assumed = 85±10

pMC and for 36Cl/Cl- = 200±10 (x10-15). Please note that no samples plot above thePFM line (Region-OABO) but several samples do plot outside the theoretical plotting area for any of the three flow models (Region-OGEFO) indicatingdissolution of `dead' chloride during flow through the aquifer (also refer to Table-1).

Fig. 3: Piston flow model for different values of the parameter E representing therate constant (a

-1) of chloride addition during passage of groundwater through the

aquifer. Lines joining equal PFM ages across lines for different values of E are parallel to the ordinate axis. Also plotted are the 14C and 36Cl/Cl- data points of(Cresswell et al., 19899a, b) from central Australia. This plot can be used to estimatethe model groundwater age (t pf ) and the value of E for any given data point under the

assumption that piston flow model is applicable.

Fig. 4: The same as in Fig. 3, but for the well-mixed reservoir (WMR) model.

Fig. 5: The same as in Fig. 3, but for the dispersion- advection (DA) model withdifferent values of D/u2 and E parameters.

Fig. 6: Variation of oxygen isotopic composition of groundwater samples with theirchloride concentration. Data from (Cresswell et al., 1999a). Also plotted on thisdiagram are the estimated initial (Cl-

0) values of chloride concentration forrespective samples at the time of recharge based on different flow models andaddition of chloride by interaction with aquifer material. Two enclosed areas A & B

contain samples that do not show much significant change from their measured Cl-

concentrations for any of the flow models. These also derive from two differentgroundwater flow regimes originating in the north (Ngalia Basin) and south (AruntaBlock-Amadeus Basin). See Fig.2 of (Cresswell et al., 1999a) for geographicallocations.





191

Physical Mechanisms Affecting Distribution of

Nutrients In Soils

F. Stagnitti and L. Elango

Abstract

Monitoring and modelling nutrient dynamics in cultivated soils is often

complicated by the non-random spatial and temporal variation in the

physical, chemical and biological properties. It is common practice to

measure soil properties in the laboratory using homogeneously mixed, air-

dried soils collected from just below the rooting zone of agricultural soils.

However, leaching experiments using repacked, sterile, homogenised soil

cores bear little resemblance to the physical reality since channels and paths

that normally transmit water and nutrients are destroyed. Recentexperiments illustrate how important soil structure is to understanding the

nature of nutrient transport. This paper discusses how soil structure plays an

important role in moisture and solute transport below the soil surface. The

paper also presents mathematical models for describing physical transport

and evaluates the performance of two solute transport models developed for

the purpose of describing small-scale nutrient dynamics. In conclusion, we

contend that a better knowledge of the factors causing preferential transport

of nutrients in cultivated field soils is required for sustainable agricultural

management.

Keywords : Modelling of nutrients, unsaturated zone, nutrients transport,

solute transport, field soils

1. INTRODUCTION

The movement of chemicals below the rooting zone in agricultural soils to the groundwater

or discharged to surface waters can pose a serious degradation of these resources. In many

countries, this form of pollution results in serious environmental and economic problems.

The chemicals of interest include nutrients, pesticides, salts and waste materials such as

heavy metals. In the case of nutrients, leaching losses also represent a decline in soil




192

fertility, and in the case of nitrate leaching, reduction of productivity due to soil

acidification, stream and lake eutrophication and domestic drinking water pollution.

Recent experiments have shown that current models and methods do not adequately

describe the leaching of nutrients through soil, often underestimating the rate of

transport through the vadose zone and overestimating the concentration of resident

solutes in the root zone (de Rooij and Stagnitti, 2000; Evans, et al. 1995; Evans, et

al. 1996; Stagnitti 1998; Stagnitti, et al. 1998; Stagnitti, et al., 1999, Stagnitti, et al.,

2001; Allinson, et al. 1999ab; Graymore, et al. 1999; Kelsall, et al. 1999; Ueoka, et

al. 1999; Allinson, et al. 2000ab). This inaccuracy results from ignoring soil

structure and non-equilibrium between soil constituents, water and nutrients.

2. EXPERIMENTAL METHODS

The use of undisturbed soil columns offer the best means of studying nutrient

transport under field conditions because they preserve the natural structure of the

soil (Stagnitti, et al. 1998). Large undisturbed soil cores (42.5 x 42.5 cm wide x 40

cm deep) were extracted from several sites in Australia. Multisegment percolation

systems (MSPS) were constructed to sample moisture and chemicals leaching from

these soil cores. The MSPS consists of a metal-alloy base-plate that is shaped into

25 equal sized collection wells (funnels) or mini-catchments. The dimension of each

well is 6 x 6 cm. Each well consists of a spring, a thin stainless steel plate and a

length of fibreglass wick. The purpose of the wick is to act as a hanging column,

providing a moderate capillary force in order to sample moisture and solutes during

unsaturated flow conditions. The MSPS was designed so that each well collects

moisture and solutes in the neighbourhood of the wick. Once mounted on theMSPS, the soil cores were irrigated with distilled water for several months prior to

the application of nutrient solutions. Further experimental details were presented in

(Stagnitti, et al. 1998; 1999).

3. MATHEMATICAL MODELLING OF SOLUTE BREAKTHROUGH

CURVES

The most challenging problem confronting mathematical modelling of solute transport in

soils is how to characterise and quantify the geometric, hydraulic, and chemical properties

of the porous media. To reduce the complexity involved in modelling the transport process,

many models are based on assumptions of homogeneous soil structure and instantaneous

sorption - sometimes referred to as the LEA (linear equilibrium adsorption) assumption.

The general equation governing contaminant transport under saturated, steady flow

conditions, and with chemical reaction, has the form of the classical advection-dispersion-

reaction equation:




193

2

2

C C CR D V C

t z z

∂ ∂ ∂= − − γ

∂ ∂ ∂ (1)

where R is the retardation factor (which is equal to 1 + ρk/θ ! !where ! !is the soil bulk density,

k is the distribution coefficient of absorption, and is the water content); γ is the reaction

rate coefficient, D is the dispersion coefficient and V is the pore water velocity.

The ADRE has a simple form because it describes an ideal process, that is

equilibrium transport. However, the LEA assumption is seldom valid in field soils.

Non-ideal transport (non-equilibrium transport), as observed in many experiments,

is more the norm than the exception. The causes of non-equilibrium transport insoils are soil heterogeneity and non-equilibrium chemical sorption. Non-equilibrium

transport is due to physical phenomena reflecting the heterogeneous properties of

soils. Here, we examine the non-equilibrium transport caused by possible

preferential flow through an undisturbed soil column. Considering the bicontinuum

conceptualisation, a two-region solute transport model (TRM) can be developed to

describe non-equilibrium solute transport in aggregated soils (van Genuchten and

Wierenga 1976; van Genuchten and Alves 1982; Li, Barry et al. 1994). The

governing equations are,

z

CV

z

CD

t

C1

t

CR m

m2

m

2

imm

∂

∂−

∂

∂=

∂

∂

β

β−+

∂

∂ (2a)

( )immim CCt

C1−ω=

∂

∂

β

β− (2b)

where subscripts m and im denote regions in which mobile and immobile solute

transport may occur; β is the ratio of the mobile region to the entire pore volume,

ie., β = θm/(θm+θim), θ is water content; Vm is the flow velocity in the mobile region

and the velocity in the immobile region is zero by definition (so the averaged flow

velocity is Vmβ ); ω is the rate coefficient (in the non-dimensional form, α = ωL/Vm,

L is the column length). The bicontinuum concept physically represents the soil

structure in aggregated soils. The region within the aggregates is the immobile

region where water and nutrients are stagnant except for lateral diffusion. The

region between the aggregates is the mobile region where water and nutrients move

due to advection and dispersion. The lateral diffusion has been simplified by using

the first-order equation (2b). Although this model was originally developed for

solute transport in aggregated soils, it is often used to model other non-equilibrium

transport processes.




194

Temporal moment analysis is a useful statistical technique for quantifying solute

transport properties independently from an underlying mathematical model such as

the ADR or TRM. The moment generating function for a continuous function, f(t) is

p

p0

M t f(t) dt∞

= ! (3)

where the subscript p = 0, 1, 2, 3 … represents the zeroth, first, second, third

moments, etc. The first moment is the expectation or mean, the second is the

variance and the third and fourth represent the skew and kurtosis of f(t) respectively.

In solute transport studies, the solute breakthrough curve (BTC) in dimensionless

form is represented by

f(t) = C(z,t) / Co (4)

where Co is the initial solution concentration at time t = 0. The zeroth order moment,

M o [T], represents the dimensionless mass.

0 00

M C(z, t) / C dT∞

= ! (5)

The mass balance ratio, r is given by

r = Mo / Mo<in>

(6)

where Mo

<in> [T] is the mass of the input pulse. The mass balance ratio, expressed as

a percentage, gives the percentage recovery of the solute at depth L; the difference

(1 - r) % is the percentage lost to adsorption, degradation, precipitation,

volatilisation and other processes.The normalised moment, µ p<n>, is defined by :

µ p<n> = M p / Mo

(7)

The first normalised moment is the mean concentration breakthrough time, τ ! [T] :

τ = µ1<n> = ! ! M1 / Mo

(8)Central moments, µ p, are defined as :

n p

p 1 o0

0

1(T ) C(z, t) / C dT

M

∞ < >µ = −µ! ; p = 0, 1, 2 … (9)

The second central moment µ2 [T2], quantifies the variance of the BTC, a measure

of the typical spread of the BTC in relation to the mean breakthrough time. The

standard deviation, σ [T], is given by the square root of the second central moment.




195

2σ = µ (10)

The dispersivity, λ [L], is given as,

λ = (L / 2) (µ2 / τ !2) (11)

The dispersivity, λ, can be related to the Advective-Dispersion equation (ADE) by

the following :

λ = D / V (12)

where D [L2T] is the dispersion coefficient and

T

0c

1V q(t) dt

T=

θ ! (13)

where q(t) [L T-1] is the Darcy flux and θc [L3 L-3] the calculated volumetric water

content. The third central moment characterises the asymmetry of the BTC and can

be used to calculate a non-dimensional skewness parameter, S, defined by

S = µ3 / µ2 !3/2 (14)

A positive value for S reflects a distribution with an asymmetrical tail extending to

the right of the peak concentration. A negative value indicates a distribution with a

long tail to the left of the peak concentration. Therefore, asymmetric BTC’s with

early peak concentrations and increased tailing to the right, ie. S > 0, qualitatively

reflect the existence of preferential flow. To calculate the temporal moments and

associated parameters in the equations above, previous studies have used cubic-

spline interpolation to first smooth the experimental BTCs before subjecting it to

numerical integration with either the trapezoidal or Simpson’s formulae. However,

we prefer to fit easily integrable analytical functions (e.g. polynomials) to the

experimental BTCs using an automated nonlinear least squares data fitting package,thus avoiding the usual problems associated with numerical integration techniques.

The procedure first determines a suitable analytical approximation to the

experimental BTC, then integrates this function analytically with the aid of a

ymbolic software package such as Mathematica. Herein we report the use of the

TMA to investigate solute transport parameters in the nutrient study and compare

and contrast these results with the ADR and TRM.




196

4. CONSTRUCTION OF A HETEROGENEITY INDEX

A heterogeneity index is invaluable in comparing and contrasting the behaviour of

soil-water and solute distributions in single soil column experiments or across

several experiments. The index of heterogeneity may also be used as a decision

support tool to assess the potential risk of groundwater contamination by surface-

applied chemicals. For example, low values for the heterogeneity index imply

uniformity in flow of soil-water and/or solutes and consequently the potential risk of

groundwater contamination by preferential flow is small. On the other hand, a high

value for the heterogeneity index may indicate significant preferential flow with the

consequent danger of groundwater contamination. The heterogeneity indexsuggested by (Stagnitti, et al. 1999) requires only a knowledge of the soil-water

percolation or solute elution curve as derived from in-situ field samplers or

laboratory tests on undisturbed soil cores. Thus it is easy to calculate. The

development of the heterogeneity index is restated here. We seek a continuous

probability distribution that has a random variable bounded by extreme values that

are both finite and positive. The distribution must be generally skewed to account

for the observed nature of the BTC and the amount of skew determined by

parameters of the distribution. The beta and triangular distribution fit these criteria.

The triangular distribution has all the desirable properties but is discontinuous.

Other continuous distributions such as gamma, exponential, Wiebull and Pearson

fail to meet one of more of the criteria. The standard beta function is defined as,

p(x;α, ζ) =Γ (α+ζ)

Γ (α)Γ (ζ)xα –1

(1–x)ζ –1

; for α≥0, ζ≥0, 0≤x≤1

(15)

where Γ is the gamma function (or Euler’s integral of the second kind) and α and ζ

are free parameters. Eq. (15) is often used in Statistics to model the variation in the

proportions of a quantity occurring in different samples. It also has the properties of

finite positive intercepts, bounded in the interval [0,1], in the x-axis and adjustable

skewness. These are the desired properties we seek. We now use properties of the

beta distribution to develop a heterogeneity index for water percolation and solute

elution in multi-sample percolation experiments. Note that if α•and ζ are both equal

to one, then Eq. (15) reduces to the uniform density function, p(x, 1, 1) = 1. The

expectation (or mean) and variance of Eq. (15) are respectively defined by

µx =α

(α + ζ)

and

σx2 =

α ζ

α + ζ2

(α + ζ + 1)

(16)

The cumulative density of Eq. (15) is defined by




197

c(x; α, ζ) = p(t; α, ζ) dt, for 0 ≤ x ≤ 10

x

(17)

where t is a variable of integration.

The standard deviation to mean ratio is often used as a measure to compare

dispersion between populations with different means. In a similar manner, we define

a (scaled) heterogeneity index (HI) as

HI(α, ζ) =3 σ x

µx

=3 ζ

α (α + ζ + 1)

(18)

where 3 is a factor that results from scaling HI to one when both α and ζ !equal

one. Thus a uniform distribution will result in HI = 1 and a non-uniform distribution

is indicated when HI > 1. For our purposes, Eq. (18) is valid for HI(α, "ζ) # 1. The

magnitude of HI greater than one indicates the magnitude of non-uniformity in the

distribution. The heterogeneity index (Eq. 18) may be used to quantify apparent

spatial or temporal heterogeneity in water and solute distribution patterns in

percolation experiments. This is illustrated in the next section.

5. RESULTS AND DISCUSSION

Actual and fitted solute breakthrough curves (BTCs) for each nutrient are presented

in Figures 1 to 3. The actual data are represented in each figure by diamonds andfitted analytical functions used to calculate the temporal moments are represented by

solid lines. Considerable asymmetry is exhibited for chloride and nitrate-nitrogen

leachate, with early peaks, long tails to the right and positive skew. The BTC for

phosphate-phosphorus exhibits a more symmetrical appearance. Table 1 presents a

summary of actual and fitted solute transport parameters for each model as well as

observed experimental values. The breakthrough curves for both chloride and

nitrate-nitrogen appear very similar, with time to peak concentrations occurring just

3 to 4 days after application. Phosphate-phosphorus on the other hand peaked at 11

days after application. The leached mass to applied mass ratios for Cl, NO3-N and

PO4-P were 129%, 68% and <1% respectively, indicating possible cation exchange

in the case of chloride, nitrification and mineralisation in the case of nitrate and

strong adsorption of phosphate. Stagnitti, et al., (1998) reported that most of the

phosphate was bound to the first 2 cm of the surface soil. The rate ofevapotranspiration was determined from a water budget over 18 days. The average

rate was approximately 25%. Using this value, the initial solute concentrations in

the applied irrigation were determined to be C0_Cl = 6186.10 mg/L, C0_NO3 = 273.65

mg/L and C0_PO4 = 4724.10 mg/L. The duration time (or input pulse) for irrigation of

the solutes was T = 0.484 days.




198

Optimal three-parameter analytical functions were fit to the experimental data using

an automatic least squares fitting procedure. These functions are shown in Figures 1

to 3 by the solid lines.

Fig. 1: The breakthrough curves for chloride. Experimental data are diamonds

and the fitted function used to calculate temporal moments is the solid line.

Fig. 2: The breakthrough curves for nitrogen-nitrate. Experimental data are

diamonds and the fitted function used to calculate

temporal moments is the solid line.

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 5 10 15 20

Time (days)

R e l a t i v e C o n c e n t r a t i o n ( C / C o

)

Actual

Fitted

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0 5 10 15 20

Time (days)

R e l a t i v e C o n c e n t r a t i o n ( C / C o )

Actual

Fitted




199

Fig. 3: The breakthrough curves for phosphorus-phosphate. Experimental data

are diamonds and the fitted function used to calculate

temporal moments is the solid line.

The fitted functions’ coefficients of determination were r 2 = 0.92, 0.96 and 0.86 for

Cl, NO3-N and PO4-P respectively. As the purpose of the fitting was to obtain easily

integrable analytical functions, the exact form of the function is irrelevant. The best

fitting 3-parameter functions as determined by the highest r 2 that also have the

correct characteristics, e.g. smooth first derivatives, finite ranges and asymptotesthat tend to zero as time tends to both zero and infinity, were selected for each

nutrient. The advantages of fitting analytical functions to the experimental data are

that they are easy to fit, tend to smooth out experimental noise and avoid the usual

problems associated numerical integration of data. Temporal moment analysis

(equations 3 to 14) was applied to each function to obtain the solute transport

parameters presented in Table 1. The predicted mass ratios, r = 117%, 76% and

0.6% were very close to the observed ratios. Also the predicted time to peak

concentrations and peak concentrations were also very close to the experimental

values. The mean travel time τ, represents an average breakthrough time. For

symmetrical distributions the mean travel time is equal to the time to peak

concentration. Thus differences between these two parameters reflect the degree of

asymmetry and possible preferential flow. For this reason, it is therefore important

to report both these statistics in solute transport studies. The mean travel time

represents a “bulk” breakthrough whilst the time to peak concentration represents

possible preferential flow in front of the “bulk” breakthrough. For both Cl and NO3-

N, the time to peak concentration was some 4 days prior to the mean travel time,

whilst for PO4-P, the mean travel time was almost identical to the peak

concentration time. These results are also confirmed by the values of the skew

coefficient. The values for both Cl and NO3-N are considerably greater than zero,

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

3.5E-04

0 5 10 15 20

Time (days)

R e l a t i v e C o n c e n t r a t i o n ( C / C o

)

Actual

Fitted




200

indicating significant positive skew and asymmetry, whilst the skew value for PO4-P

was close to zero, indicating symmetry. The predicted values for the dispersivity, α,

for Cl and NO3-N were between 11 and 12 cm, about ¼ of the length of the soil

column, and for PO4-P, 4.3 cm. These values appear to be quite consistent with

expectation.

Table 1. Summary of solute transport parameter values for each model.

Common Parameters (From

Experiment)

Chloride Nitrate Phosphate

Column Length, L (cm) 40 40 40Initial Concentration, Co (mg/L) 6186 274 4724

Time of Input Pulse, T (days)

0.484 0.484 0.484

Time to Peak Concentration (d)

4 3 11

Peak Relative Concentration (C/Co) 0.073 0.041 0.00032

Applied Mass (mg)

6987 404 6085

Leached Mass (mg) 9039 273 52

Mass Ratio, r (%) 129.4% 67.6% 0.9%

Temporal Moments Analysis (TMA)

Mass Ratio, r (%) 117.0% 76.0% 0.6%

Mean Time, τ ! !(d) 8.7 8.2 12.5


4 4 12


Standard Deviation (d) 6.6 6.6 5.8

Dispersivity, !λ (cm) 11.3 12.8 4.3

Skew 0.88 0.58 0.003

Advection-Dispersion-Reaction Model

(ADR)

Mass Ratio, r (%) 102.0% 71.4% 0.6%

Mean Time, τ ! !(d) 9.7 8.7 13.5


3 3 11


Standard Deviation (d) 7.4 6.7 5.1

Skew 0.65 0.54 0.003

Dispersivity, !λ (cm) 11.7 11.7 11.7

Retardation Factor, R 1 1.06 8.12

Reaction Rate, !γ (d-1) 0 0.035 1.78

Pore Water Velocity, V (m/d) 0.051 0.051 0.051




201

Dispersion Coefficient, D (m2/d) 0.006 0.006 0.006

Two-Region Model (TRM)

Mass Ratio, r (%) 118.0% 118.0%

Mean Time, τ ! !(d) 9.6 8.6


3 4

Peak Relative Concentration (C/Co) 0.071 0.059

Standard Deviation (d) 7.7 8.6

Skew 0.79 0.57

Dispersivity, !λ (cm) 3.7 3.7

Retardation Factor, R 1 1.27Mass Transfer Rate, !α 1.72 1.72

Mobile Water Fraction, !β 0.47 0.47

Pore Water Velocity, V=Vm !β, (m/d) 0.027 0.027

Dispersion Coefficient, D (m2/d) 0.001 0.001

Table 1 also presents predicted solute transport values from fitting the ADR and

TRM models to the experimental data. For each simulation, it was assumed that the

initial, resident concentrations of solutes in the soil prior to application of the

nutrient solution were negligible, ie. Ci = 0 mg/L. First, the ADR and TRM were

fitted to the Cl data assuming that Cl behaves as a conservative element, that is γ = 0

(no reaction) and R = 1 (no adsorption). The optimal values for the fitted parameters

in the ADR were V = 0.051 m/d and D = 0.006 m2

/d. Note that the model failed tomatch the data at the peak. The predicted peak relative concentration was 0.051 in

comparison to the observed value of 0.073. Also the ADR significantly

underestimated the mass ratio due to the under-prediction of the peak concentration.

The lack of agreement is due to the failure of the ADR to model the non-equilibrium

effects caused by the obvious heterogeneity in percolation rates reported by

Stagnitti, et al., (1999). The fitted velocity and dispersion coefficients, however, are

within the experimental constraints. The TRM was fitted to the Cl data and the

optimal values for the model parameters were Vm = 0.057 m/d, D = 0.001 m2/d, β =

0.47 and α = 1.72. The predicted time to peak and peak concentrations are in

excellent agreement with the experimental values, suggesting that non-equilibrium

transport of Cl has occurred. The results also confirm the veracity that little to no

retardation of chloride in the core occurred (ie. R = 1). The fitted parameter values

are also within experimental constraints and they have physical meaning. In particular, the averaged flow velocity, calculated according to Vmβ " is in accordance

with the experimental data. The fitted value for β is close to 0.5, which indicates

that nearly 50% of the pore volume is actively responsible for Cl transport. This too

is supported by experimental observations reported by Stagnitti, et al., (1998).




202

The BTC for NO3-N was fitted to both the ADR and TRM and the results are shown

in Table 1. In this case, knowledge gained from fitting the BTCs for Cl is used to fit

the BTC for NO3-N. The values for V and D determined from fitting the ADR to the

Cl data set are used for the NO3-N data set, as these in principle should not be

different. However, adsorption and reaction of NO3 is possible and therefore

permitted ie. R and γ should be “free” parameters and their values determined by

optimisation. The optimal values for R and γ were found to be 1.06 and 0.035 d -1

respectively, indicating a small adsorption and significant reaction rate. These

parameter values make sense physically and result from mineralisation and

denitrification in the soil. The fit is surprisingly good even though the ADR ignores

soil heterogeneity, e.g. accurate predictions for the mass ratio and travel times whencompared with the experimental observations. For similar reasons to before, the

values for the parameters Vm, D, β !and α in the TRM were fixed to be the same

values as those determined for the Cl BTC. In this case, however, the only free

parameter is R since we have no analytical solution for the TRM with reaction. The

optimal value for R was found to be 1.27, indicating considerably more adsorption

than the ADR. The TRM clearly over-predicted the concentration peak and mass

ratio. This is not a surprising result since the TRM in its present form does not

contain a reaction term. The better performance of ADR in this case most likely

results from the extra freedom of having two free parameters rather than one.

Indeed, if the TRM included reaction, then the performance for nitrate prediction

using this model will undoubtedly improve. The predicted value for the dispersivity

seems to be very large, particularly when compared with the value obtained using

the temporal moments method. The phosphate experimental data showed strong

adsorption and reaction (see Table 1). For this reason we did not fit the TRM to this

data set as the results would be meaningless if reaction is not considered. Table 1

presents the results for the predicted solute transport parameters using the ADR with

V and D fixed to the same values as determined for the Cl BTC and R and γ ! fitted

by optimisation. The optimal values for R and γ were 8.117 and γ = 1.781 d-1

respectively, indicating as expected, very strong adsorption and quick reaction. The

ADR predicted the solute transport parameters reasonably well. Again the good

performance of the ADR here does not necessarily imply that non-equilibrium

transport is negligible; rather it may be due to the extra freedom in the fitting

process. Also the reaction rate appears to be too fast to be physically realistic.Again, the predicted value for the dispersivity seems to be too large when compared

with the TMA.

The model for the heterogeneity index (equations 15 to 18) may be applied to any

experiment in which multiple samples of the solute and water flux are determined




203

within a defined spatial or temporal segment. The model is independent of the

Fig. 4: Fitted (solid lines) and actual (dashed lines) solute elution curves for

phosphate (A), chloride (B), nitrate (C), for a soil monolith collected from

Grassmere, Victoria, Australia and chloride (D) for a soil collected in a coastal

dune of South-West Holland.

Fig. 5: Fitted (solid lines) and actual (dashed lines) soil-water elution curves

for soil monoliths collected from five different sites in Australia : Tower Hill

(A), Rutherglen-2 (B), Grassmere (C), Redland Bay (D), and Rutherglen-1 (E).

Fraction of Area

F r a c t i o n o

f L e a c h e d S o l u t e

A

B

C

D

F r a c t i o n o f L e a c h e d W a t e r

Fraction of Area

A

B

C D

E




204

actual experimental technique used to determine the soil-water or solute elution.

Figures 4 and 5, present patterns of soil-water percolation and solute elution for a

series of experiments conducted in Australia and the Netherlands.

The experimental details are reported in Stagnitti, et al., (2000) and de Rooij and

Stagnitti, (2000). The heterogeneity indices and statistical results are presented in

Table 2.

Table 2. Heterogeneity indices calculated for a series

of experiments conducted in Australia and Holland.

Experiment Fig. α ζ µx σ2x

HI

Uniform 1 1 1/2 1/12 1

Solutes

Grassmere-P 4A

0.2411 2.034 0.1060 0.02892 2.78

Grassmere-Cl 4B

0.9199 1.935 0.3222 0.05665 1.28

Grassmere-N 4C

0.8755 1.524 0.3647 0.06817 1.24

SW Holland-Cl 4D

0.7499 1.353 0.3567 0.07396 1.32

Moisture

Tower Hill

5A 0.4527 1.699 0.2105 0.05275 1.89

Rutherglen-2 5B 0.8477 3.993 0.1865 0.03725 1.56

Grassmere 5C 0.7775 1.582 0.3295 0.06576 1.35

Redland Bay 5D 0.8651 1.842 0.3196 0.05867 1.31

Rutherglen-1 5E 0.8885 1.835 0.3262 0.05900 1.29

Figure 4 presents the results of solute leaching experiments conducted in Grassmere,

Australia (Stagnitti, et al., 1998) and in the south-west of Holland (deRooij and

Stagnitti, 2000). The observed fraction of total solutes (dots) eluted by the soil is

plotted with the fraction of total sampling area of the base of the collection

apparatus. These curves were constructed by calculating the fraction of the total

mass collected by each individual lysimeter in a multi-sample percolation system,

ranking these values in descending order and plotting them with the cumulative

cross-sectional sampling area. If the soil core was eluting solute mass at a uniform

rate, then there would be no spatial variation in the amount of solute collected by

each lysimeter, i.e. each collection lysimeter would contribute an equal mass of

solute to the total. In other words, if the soil leached solutes equally everywhere,then the fraction of the total mass plotted with the cumulative cross-sectional area of

the base would fall on a 1 to 1 line. Departures from a 1 to 1 line indicate

heterogeneity or potentially preferential flow. On each figure, the fitted cumulative

beta distribution c(x), given by Eq. (17), is also plotted. The fitted statistical

distribution is represented by a continuous (solid) line. For each solute, the

cumulative beta distribution fits the experimental data very well. The optimal values

for the fitted shape parameters, α and ζ are presented in Table 2 along with the




205

calculated descriptive statistics for the mean, variance and heterogeneity index, HI.

The optimisation of the free parameters was achieved very efficiently and simply

using the BetaDistribution, CDF and NonLinearRegress functions in Mathematica.

The calculated heterogeneity indices for phosphate, nitrate and chloride were 2.78,

1.24 and 1.28 respectively for the Australian site and 1.32 for chloride in the site in

Holland. All HI’s were larger than one, indicating heterogeneity in solute leaching

patterns. Phosphate exhibited the highest heterogeneity with just 20% of the soil

core leaching 80% of total leached phosphate, indicating that phosphate was very

strongly adsorbed to the soil.

Figure 5 illustrates the spatial variation in soil-water percolation patterns for all

Australian experiments. Like Fig. 4, the solid line represents the fitted cumulative

beta distribution. In all cases the beta distribution fit the experimental data verywell. The values for the free parameters and descriptive statistics are also presented

in Table 2. The Tower Hill site exhibited the strongest heterogeneity in soil-water

percolation with HI = 1.89. For this soil, about 60% of the drained soil-water was

collected from about 20% of the base area. The Rutherglen-2 experiment also

exhibited considerable heterogeneity, HI = 1.56. All other sites showed considerable

heterogeneity ranging from HI = 1.28 to 1.35. In the field prior to extraction, the

Rutherglen soil cores were separated by about 1 m. The HI’s for the two Rutherglen

cores differed considerably (HI = 1.29 and 1.56). This result suggests that

considerable heterogeneity was not only evident within the cores but also between

them, an important confirmation of the difficulty of scaling small-scale transport

phenomena to forecast field-scale effects.

6. CONCLUSIONS

Soil structure plays a very important role in influencing nutrient dynamics in

agricultural soils. An experimental framework for measuring the extent of soil

physical and chemical heterogeneity was developed. The experimental results

indicated strong preferential flow characteristics in both moisture and nutrient fluxes

over a small spatial scale. Consequently, accurate prediction of nutrient loading in

field soils is very difficult. Very few mathematical models adequately represent

spatial and temporal heterogeneity in soil physical and chemical properties. The

performance of two commonly used models in solute transport studies, the ADE and

TRM were contrasted and compared to simple statistical results obtained from

temporal moments analysis of the breakthrough curves from nutrient leaching

experiments. The ADE model performed reasonably well even though the

experimental data suggested considerable heterogeneity in percolation rates and

concentration. However, the comparative good fits for BTCs may be spurious,

resulting from the freedom of having two free parameters. At present, there are no

published analytical solutions for the TRM with a reaction term. Consequently, the

TRM in its present form can only be expected to perform well for solutes that have

negligible reaction times. A simple, efficient and effective method of quantifying

the level of heterogeneity in soil-water percolation and solute elution patterns




206

generated from multiple sample percolation experiments was also presented. The

method relies on calculating a heterogeneity index based on estimating two free

parameters of the beta-distribution. Using this index, the elution patterns for a

number of solute leaching experiments was compared and contrasted. The index

may be a valuable tool in estimating the potential risk of groundwater contamination

by the preferential transport of chemicals through the vadose zone.

REFERENCES:

Allinson, G. and Stagnitti, F. (2000), ' Behavior of 'Organic' and 'Synthetic'

Fertilizer Nutrients When Applied to Irrigated, Unsaturated Soil' . Bulletin of

Environmental Contamination & Toxicology. Vol. 64, No.5, pp. 644-650.Allinson, G., Stagnitti, F. (2000), "Comparison of behavior of natural and synthetic

phosphate fertilisers in a moderately water-repellent, sandy loam soil under winter

rainfall". Communications in Soil Science & Plant Analysis Vol. 31, No. 19&20,

pp. 3027-3035.

Allinson, M., Williams, B. (1999), "Environmental fate of pesticides used in

Australian viticulture". IV. Aqueous stability of dithianon. Toxological &

Environmental Chemistry, Vol. 70, pp. 401-414.

Allinson, M., Williams, B. (1999), ‘Environmental fate of pesticides used in

Australian viticulture. III. Fate of dithianon from vine to wine’. Toxicological &

Environmental Chemistry, Vol. 70, pp. 385-400.

de Rooij, G. H. and Stagnitti, F. (2000), "Spatial variability of solute leaching:

Experimental validation of a quantitative parameterization". Soil Science Society of

America Journal, Vol. 64, No. 2, pp.499-504.

Evans, L. and Sherwood, J. (1995), "Preferential flow of nutrients into groundwater

in Victoria's western district. Groundwater & The Community, Murray-Darling

1995 Workshop, Wagga", Environmental Geoscience & Groundwater Division,

AGSO, Canberra.

Evans, L. and Stagnitti, F. (1996), "Nutrient transport through basaltic agricultural

soils near Warrnambool: Evidence of preferential flow" . Australian and New

Zealand National Soils Conference: Soil Science - Raising The Profile, Volume 2,

Oral Papers, University of Melbourne.

Graymore, M. and Allinson, G. (1999), "Environmental fate of pesticides used in

Australian viticulture. V. Behaviour of atrazine in the soils of the South Australian Riverland" . Toxological & Environmental Chemistry, Vol. 70, pp. 427-439.

Kelsall, Y. and Allinson, M. (1999), "Leaching of Copper, Chromium and Arsenic

in a soil of the South West Victoria", Australia’. Toxological & Environmental

Chemistry, Vol. 70, pp. 375-384.

Li, L. and Barry, D. A. (1994), "Mass transfer in soils with local stratification of

hydraulic conductivity" . Water Resources Research , Vol. 30, pp. 2891-2900.




207

Stagnitti, F. (1998), "Modelling Preferential Transport of Soil Micro-Organisms :

Implications For Land Disposal of Sewage" . Canberra, Land & Water Resources

Research & Development Corporation: 7.

Stagnitti, F., Li, L., Allinson, G., Phillips, I., Lockington, D., Zeiliguer, A.,

Allinson, M., Lloyd-Smith, J. and Xie, M. (1999), "A mathematical model for

estimating the extent of solute- and water- flux heterogeneity in multiple sample

percolation experiments". Journal of Hydrology, Vol. 215, No. 1-4, pp. 59-69.

Stagnitti, F., Sherwood, J., Allinson, G., Evans, L., Allinson, M., Li, L. and Phillips,

I. (1998), "An investigation of localised soil heterogeneities on solute transport

using a multisegement percolation system". New Zealand Journal of Agricultural

Research, Vol. 41, pp. 603-612.

Stagnitti, F.and Allinson, G., Morita, M., Nishikawa, M., Ii, H., and Hirata, T.

(2000), "Temporal moments analysis of preferential solute transport in soils" .

Environmental Modelling & Assessment, Vol. 5, No. 4, pp. 229-236.

Stagnitti, F., Li, L., Barry, D. A., Allinson, G., Parlange, J.-Y.,Steenhuis, T., and

Elango, L. (2001), "Modelling solute transport in structured soils: Performance

evaluation of the ADR and TRM models". Mathematical and Computer Modelling,

Vol. 34, No. 3-4, pp. 433-440.

Ueoka, M. and Allinson, G. (1999), "Environmental fate of pesticides used in

Australian viticulture II. Behaviour of vinclozolin and dithianon in an acidic soil of

the Rutherglen region of Victoria, Australia" . Toxological & Environmental

Chemistry, Vol. 70, pp. 363-374.

van Genuchten, M. T. and Alves, W. J. (1982), "Analytical solutions to the one-dimensional convection-dispersion solute transport equation". USDA Tech. Bull.

1661.

van Genuchten, M. T. and Wierenga, P. J. (1976), "Mass transfer studies in sorbing

porous media I. Analytical solutions". Soil Science Society of America Journal, Vol

40, No.4, pp. 473-480.





209

Modelling the Movement of Chloride and Nitrogen

in the Unsaturated Zone

N. Rajmohan and L. Elango

Abstract

Study of the movement of water and solute within the soil profile is important forvarious reasons. Accumulation of prominent contaminants from agriculturalchemicals in the unsaturated zone over the years is the major cause for concern in

many parts of the world. As a result, the unsaturated zone has been a subject of studyduring the past decade. Such a study was carried out with the objective of

understanding the movement of chloride and nitrogen below an irrigated land nearChennai, India. Variation of chloride and nitrogen in the unsaturated zone below this

land were studied by systematic collection and analysis of soil core samples periodically during a cropping season. The field observation has lead toconceptualisation of the system, and then the movement of these ions in the

unsaturated zone was simulated using a solute transport model. The model

predictions were reasonably close to the observed trends. The model was used to study the impact of possible changes in the fertiliser usage in this area.

Keywords : Unsaturated zone, chloride, nitrogen, solute transport model,

field study.

1. INTRODUCTION

Application of agricultural chemicals, dumping industrial and domestic wastes at theland surface or within the unsaturated zone may have considerable impact on the

quality of groundwater. Among these, agricultural chemicals are the most significantanthropogenic source of groundwater contamination. Understanding the fate ofdissolved chemicals within the unsaturated zone can greatly aid in prediction of thechemistry of water that reaches the aquifers. Such an understanding would also

allow for evaluation of different preventive or remedial actions to protect thevaluable groundwater resources. Computer models of water and solute movement inthe unsaturated zone are useful tools for gaining insight into the processes that occurwithin the unsaturated zone. Tim and Mostaghimi (1989) developed a mathematicalmodel to predict the fate of pesticides and their metabolites in the unsaturated zone

of the soil, for a better understanding and estimation of different mechanismsaffecting their transport. Boateng and Cawlfield (1999) developed a two-




210

dimensional probabilistic transport model by coupling a reliability algorithm to atwo-dimensional unsaturated flow and transport model to determine the significanceof the uncertainty of each variable to the probability outcome. Present study wascarried out with the objective of understanding the movement of chloride andnitrogen below an intensively irrigated land, 70 km west of Chennai, India.

The most widely used fertilisers in this area contain chloride, nitrogen, phosphorusand potassium. As chloride and nitrate are the major pollutants that reach thegroundwater due to their high mobility, these two ions were considered for

modelling. The HYDRUS model (version 2.0) developed by the InternationalGroundwater Modelling Centre (Simunek et al 1999) was used in this study. This

model is capable of simulating water flow and solute transport in variably saturatedmedia.

2. FIELD STUDY

In an irrigated land identified for this study (Fig.1), soil core samples of 1m length,where collected at different days during cultivation of paddy. From each of the soilcore samples, sub samples were collected at an interval of 10 cm, and analysed for

the concentration of chloride and nitrogen. All these sub soil samples were subjectedto grain size analysis to determine the silt, clay and sand percentage. The amount ofapplication of fertiliser applied and the time of application were noted. Water levelin this irrigated land was also recorded every day. The soil core collected assisted inconceptualising the system and the results of chemical analyses were used to give

initial values and validate the solute transport model.

3. MODEL DESCRIPTION

HYDRUS model numerically solves the Richards’ equation for variably saturated

water flow and conversion - dispersion type equation for solute transport. TheGalerkins finite element method (Neuman 1975) with linear basis functions is usedto obtain a solution for the water flow equation. In this method, the solution isobtained by iterative process using Gaussian elimination. Similarly the sameGalerkin finite element method is also used to solve the solute transport equation. To

obtain numerical solution of the solute transport process, first, an iterative procedureis used to obtain the solution of the Richards’ equation. These methods of solutionare relatively standard and have been explained in detail by Simunek et al (1999). In

this study, modelling of solute transport for the study site (Fig.1) was carried out forthe unsaturated zone of 5 m thickness, as water table occurs at this depth. Solutetransport was considered to be one dimensional vertical flow in a column of unit

width and a length of 5 m. As irrigation return is the major source of flow in theunsaturated zone, one dimensional vertical flow was assumed.




211

Fig. 1 Field site description map

4. MODEL INPUT PARAMETERS

4.1 Finite Element Mesh

The finite element mesh is constructed for the 5m column (Fig. 2) by dividing theflow region into triangular elements whose shapes are defined by the co-ordinate

nodes that form the element corners. Transverse lines (Neuman 1974) formed byelement boundaries will transect the mesh along the general direction of its shortest

dimension. These transverse lines will be continuous and non-intersecting, but neednot be straight. Small finite element mesh size were given at and near the soil

surface, that is, upto 10 cm, as highly variable meteorological factors can cause fast




212

0 m

0.8 m

4.24 m

5 m

changes in the pressure head. Similarly, closer mesh intervals were given for thelower 10 cm of the column. In general, the size of the mesh along the X directionwas 0.04m and along Y direction it varied from 0.01 to 0.02m. Thus, the column of5m length was divided in to 250 nodes with 248 meshes.

4.2 Soil layers and properties

The number of soil materials andnumber of layers were decided basedon field data. The soil core collected

from the top one metre of theunsaturated zone and its grain sizeanalysis indicate that there are sevendifferent zones. As soil coring was

not carried out beyond one metre, thesame soil type was considered from 1

to 5 m of the column. Thus, sevenlayers (namely A – G) were consideredin the 5m column, based on thevariation in soil characteristics.

Analyses of the soil core for thecontents of sand, silt and clay (Fig. 3)

were used to input the soil hydraulic properties for modelling Theunsaturated soil hydraulic propertieswere determined by the percentage ofsand, silt and clay in different layers

by Genuchtan (1980) equation inHYDRUS model using neural

network predictions techniquedeveloped by US Salinity laboratory(Simunek 1999). The calculated soilhydraulic properties based on the

percentage of sand, silt and clay aregiven in Table 1.

Fig. 2 Finite element discretisationof the column for model simulation.




213

Fig. 3 Grain size analysis – sand, silt, clay percentages

Table 1 Soil hydraulic properties

Layers Depth

(cm)r s n Ks

m/day

l

A 0 – 10 0.035 0.385 2.8 1.81 1.20 0.5

B 10 – 20 0.036 0.391 2.1 1.73 1.10 0.5

C 20 – 30 0.032 0.385 1.6 1.62 1.03 0.5

D 30 – 60 0.031 0.389 2.7 1.73 1.31 0.5

E 60 – 80 0.030 0.395 2.3 1.82 1.02 0.5

F 80 – 90 0.038 0.385 2.6 1.73 1.11 0.5

G 90 - 500 0.030 0.391 2.4 1.62 0.91 0.5

θr = Residual water content, θs = Saturated water content, α = Inverse of air entryvalue (or bubbling pressure), n = Pore size distribution index, Ks = Saturatedhydraulic conductivity, l = Pore connective parameter

4.3 Solute properties

The dispersivity and diffusion co-efficient are important parameters in solutetransport process. The dispersivity of solutes in a particular soil will vary withrespect to the property of the soil. The dispersivity of chloride and nitrogen used inthe model is given in Table 2. The diffusion co-efficient for chloride in water is




214

assumed as 0.20 m2/day and N-NO3 is 0.016 m

2/day. These values were derived from the

soil characteristics of this area and from the literature. In the case of nitrate, plant uptakeand denitrification were considered with a degradation factor of 0.01 per day.

Table 2 Longitudinal dispersivity

Layers Longitudinal dispersivity (m)

A 0.009

B 0.008

C 0.007

D 0.010

E 0.008

F 0.007G 0.006

4.4 Boundary condition

Atmospheric boundary condition was assumed at the top of the column. The

atmospheric boundary condition varies depending up on the amount of rainfall,irrigation and evaporation. The actual variation in rainfall and water depth in theirrigation land was measured regularly in the field, which was used in the model.The evaporation is assumed as 60% of irrigation water. In addition to these, twolimiting values of surface pressure head are also provided. The maximum allowed

pressure head at the soil surface is zero and minimum allowed surface pressure head(defined from equilibrium condition between soil water and atmospheric vapour) is

assumed as 100m. Variable head was considered at the lower boundary.

4.5 Initial Condition

The initial condition to run the model was derived primarily from the field study.The initial conditions necessary for this model include pressure head and

concentration. The initial concentration values used for model simulation are givenin Table 3. These values were arrived form the analysis of soil core collected 3 days before transplantation during the field study.

Table 3 Initial condition for model simulation

Layers Cl (mg/kg) N-NO3 (mg/kg)

A 75 1.47B 65 0.97

C 55 0.85

D 70 1.2

E 61 0.99

F 62 1.1

G 60 1.0




215


The model was initially run with the above mentioned input parameters formodelling the movement of chloride in the column. The concentration computed by

the model was compared with field data. Then, the model was run by varying certaininput parameters such as evaporation, bulk density, co-efficient of diffusion anddispersivity. All these parameters were varied within the reasonable limit of 10 %and the sensitivity of these parameters on the model results was studied. The modelis sensitive to the variation in evaporation. When the evaporation rate was increased

by 10%, the concentration of chloride in the soil zone increases by about 17%. Themodel, however, is not very sensitive to the other parameters. Thus, by varying these

input parameters within the reasonable limit, concentration of chloride ion wassimulated and compared with observed field data. The model calibration was thus

carried out and the values actually used in the model arrived after calibration bysensitivity analysis is given in Table 4.

Table 4 Soil hydraulic parameters derived after calibration

Layers r s n Ks

(m/day)

l

A 0.030 0.391 2.4 2.10 1.20 0.5

B 0.030 0.397 1.9 1.60 0.90 0.5

C 0.029 0.399 1.3 1.46 0.78 0.5

D 0.027 0.393 2.5 1.59 0.92 0.5

E 0.025 0.396 2.0 1.47 0.76 0.5

F 0.031 0.395 2.3 1.50 0.85 0.5

G 0.029 0.399 2.1 1.43 0.73 0.5

The results of the model were more or less comparable with the observed data aftercalibration. The comparison was made up to a depth of one metre of the column asthe observed field data is available only for this depth. After the simulation ofchloride ion, the model was run to simulate the concentration of nitrate. It is

assumed that 6% of the applied fertiliser nitrogen becomes Nitrate-Nitrogen. Mostof the literature report that 4 to 10 % of applied nitrogen fertiliser becomes Nitrate- Nitrogen (Petrovic 1990). The model results obtained are comparable with observednitrate concentration. Initially, all these model runs were made for one irrigation

cycle. The model was run with time step of one day with time increment of aminute.

6. MODEL RESULTS

After calibration and testing, the model was used to simulate the concentration ofchloride and nitrate in the soil zone. The model results were initially obtained for thestudy period of 100 days after transplantation, that is, from 16th May 1999 to 23rd




216

August 1999. The simulation was carried out for a period of one year (three crops)(May 1999 to April 2000) to predict movement of the applied fertiliser towardsgroundwater.

6.1 Chloride

The simulation was carried out initially for one crop season and the computedresults were compared with the observed field data (Fig.4).

Fig. 4 Comparison of observed and simulated chloride

concentration in the unsaturated zone

0

100

200

300

C l ( m g / k g ) Observed

Simulated

0

50

100

150

C l ( m g / k g )

50

70

90

110

C l ( m g / k g )

50

75

100

C l ( m

g / k g )

50

75

100

C l ( m

g / k g )

40

60

80

100

C l ( m g / k g )

55

60

65

70

C

l ( m g / K g )

56

60

64

68

16 22 28 38 48 96

Days after T ransplantation

C l ( m g / K g )

50

70

90

110

C l ( m g / k g )

0

50

100

150

C

l ( m g / k g )

70 - 80 cm

90 - 100 cm

300 cm

500 cm

20 - 30 cm

30 - 40 cm

40 - 50 cm

60 - 70 cm

0 - 10 cm

10 - 20 cm




217

It clearly shows that there is a good agreement between the results of the model andthe observed field data. The chloride ion from the irrigated field reaches thegroundwater zone after about 45 days. Movement of mass of chloride in theunsaturated zone is given in Fig. 5.

Fig. 5 Movement of mass of chloride and

inflow solution in the unsaturated zone

Movement of mass through the unsaturated zone is controlled by the rechargingwater from the irrigated land. Hence, most of the fluctuation in chloride mass takes

place (i.e. from 0.00173 g/m3 to 0.274 g/m3 in the upper zone) during irrigation period, that is up 55 days. After about 55 days (i.e. after harvest) the mass ofchloride reaches the level measured before the commencement of irrigation. Thefluctuation in the mass of chloride with respect to time in the lower layers is not very

significant as inferred from the linear nature of the curve for mass in Fig.5.

-0.0001

0.0000

0.0001

0.0002

0.0003

I

n f l o w ( v

/ d )

0.00

0.10

0.20

0.30

M a s s ( g )

-0.0001

0.0000

0.0001

0.0001

I n f l o w ( v

/ d )

0.00

0.05

0.10

M a s s ( g )

0.0000

0.0001

0.0002

0.0003

0.0004

0 3 9 1 6

2 2

2 8

3 3

3 8

4 5

5 1

5 7

6 3

6 9

7 5

8 1

8 7

9 3

9 9

Days

I n f l o w ( v

/ d )

0.00

1.00

2.00

3.00

4.00

M a s s ( g )

60 - 80 cm

80 - 90 cm

90 - 500 cm

-0.0005

0.0005

0.0015

I n f l o w ( v

/ d )

0.00

1.00

2.00

3.00

4.00

M a s s ( g )

Inflow

Mass

-0.0002

0.0000

0.0002

0.0004

I n f l o w ( v

/ d )

0.00

0.05

0.10

M a s s ( g )

-0.0001

0.0000

0.0001

0.0002

0.0003

I n f l o w ( v

/ d )

0.00

0.05

0.10

0.15

M a s s ( g )

-0.0001

0.0000

0.0001

0.0002

0.0003

I n f l o w ( v

/ d )

0.00

0.05

0.10

0.15

M a s s ( g )

Total

0 - 10 cm

10 - 20 cm

20 - 30 cm

-0.0002

0.0000

0.0002

0.0004

I n f l o w ( v

/ d )

0.00

0.05

0.10

0.15

0.20

M a s s ( g )30 - 60 cm




218

6.2 Nitrogen

Similar to that of chloride, initially the model was simulated for one crop period andcompared with field data for nitrogen (Fig.6). The computed nitrogen trend in theunsaturated zone is in good agreement with field data. The nitrogen concentration in

the unsaturated zone varies significantly during irrigation period due to intenseagricultural activities. The temporal variation in mass of nitrogen is higher in theupper layers than in the lower layers (Fig.7). The mass of nitrogen varies from0.00034 g/m3 to 0.0154 g/m3 in the 80 - 90 cm layer. Further, after the completionof irrigation activity (i.e. after 55 days) the mass of nitrogen remains almostconstant. This is inferred from the linear nature of the curve for mass in Figure 7.

The model created with the field data, was used to predict the movement of chlorideand nitrogen in the unsaturated zone as described in the next section.

7. MODEL PREDICTION

After having been satisfied with the results of the model obtained for one crop period, the model was then used to predict the concentration of chloride and nitrogenin the unsaturated zone under different irrigation practices. The model was run for aone year and a five year period with the usual and increased application of fertiliser.

These model runs were made by assuming the same input concentration mentionedin the earlier section. The daily average rainfall and evaporation data calculated from past six years were used. The model run was made for the period starting from May

1999.

7.1 Three crops (one year)

The results of the model run for a three crop period show that the concentrationvaries significantly during the first and third cropping periods (Figs.8, 9). Thesecond crop period, however shows lower levels of variation in concentration, whichis attributed to monsoon. In groundwater zone, chloride varies from 60 to 65 mg/l

during this one year simulation. In the case of nitrate, the fluctuation was for 3.5 to3.6 mg/l in the groundwater zone. The overall fluctuation during the three crop period, is mainly due to variation in rainfall, fertiliser application and evaporation.The model predictions indicate that eventhough there is a variation in theconcentration of these ions, in general there is no upward or downward trend. In

general, the concentration of chloride and nitrate in the 40 to 50cm, vary from 55 to




219

Fig. 6 Comparison of observed and

simulated nitrogen (N-NO3) in the unsaturated zone

0

2

4

6

N

( m g / K g )

Observed

Simulated

0

2

4

6

N

( m g / K g )

0

2

4

6

8

N

( m

g / K g )

0

2

4

6

8

N

( m

g / K g )

0 - 10 cm

10 - 20 cm

20 - 30 cm

50 - 60 cm

0

5

10

15

N

( m g / K g )

0

5

10

15

N

( m

g / K g )

0

5

10

N

( m g / K

g )

0

2

4

6

8

N

( m g / K g )

0.8

1.0

1.2

1.4

N

( m g / K g )

70 - 80 cm

80 - 90 cm

90 - 100 cm

300 cm

1.00

1.00

1.00

1.00

16 22 28 38 48 96

Days after Transplantation

N

( m g / K g )

500 cm

60 - 70 cm




220

Fig.7 Variation in simulated mass of nitrogen (N-NO3)and inflow in the unsaturated zone




221

Fig.8 Simulated chloride at different depths for one year period

Fig. 9 Simulated nitrogen (N-NO3) at different depths for one year period

95 mg/kg and from 1.2 to 5.4 mg/kg respectively. Similarly, in groundwater,chloride varies from 60 to 66 mg/l and nitrate varies from 3.4 to 3.5 mg/l.

50

60

70

80

90

100

0 73 146 219 292 365

Days

1 m0.5 m

Groundwater

1

2

3

4

5

6

0 73 146 219 292 365

Days

0.5 m

1 m

Groundwater




222

7.2 Five year period

Assuming that the fertiliser application and other input parameters are similar, themodel was run for five years from May 1999, considering three paddy croppingseasons. The results indicate that the concentration of chloride and nitrogen

fluctuates significantly (Figs.10, 11).

Fig. 10 Simulation of chloride for five year period

Fig. 11 Simulation of nitrogen (N-NO3) for five year period

In general, the concentration of ions fluctuates in a cyclic trend during thesimulation period. This trend is mainly because of rainfall during monsoon and

summer period. The concentration of chloride varies significantly from 45 to 95mg/kg in 40 - 50 cm layer. But in the concentration of nitrate, it varies between 1.7to 5.3 mg/kg. In groundwater zone, the concentration of chloride fluctuates between60 to 68 mg/kg and nitrate from 3.5 to 3.6 mg/l.. Despite this cyclic trend, there is nosignificant overall upward or downward trend in the concentration of ions in the

4 5

5 5

6 5

7 5

8 5

9 5

0 3 6 5 7 3 0 1 0 9 5 1 4 6 0 1 8 2 5

Y ear

1 2 3 4 5

1 m

0.5m

Groundwater

1

2

3

4

5

6

0 3 6 5 7 3 0 1 0 9 5 1 4 6 0 1 8 2 5

Y ea r

31

1 m

0.5

2 54

Groundwater




223

unsaturated zone. It is further observed that these ions in the groundwater zone donot increase during the simulation period.

7.3 Application of excess fertiliser

The model was also used to predict the effect of excess fertiliser application onunsaturated zone and groundwater. During this simulation, application of fertiliserwas increased two fold and other model parameters were kept the same as in earlier predictions. The results of the five year run with increased fertiliser applicationindicate an increase in the concentration of chloride and nitrate in the unsaturatedzone and groundwater (Figs.12, 13).

Fig. 12 Simulated chloride concentration during excess

fertiliser application (2 fold) for five year period

A two fold increase in fertiliser usage results in an increase of 20 mg/kg of chloride

and 3 mg/kg of nitrogen in top one metre of the unsaturated zone. Similarly, theconcentration of chloride and nitrogen in the groundwater increase by 17 mg/l and2.3 mg/l respectively. Further, even this increase in the concentration of ions seemsto stabilise at the end of 5 years.

50

60

70

80

90

100

110

0 365 730 1095 1460 1825

Year

1 m

Groundwater

0 1 2 3 4 5




224

Fig. 13 Simulated nitrogen (N-NO3) concentration during

excess fertiliser (2 fold) application for five year period

8. CONCLUSION

Studies were carried out to find out the movement of chloride and nitrogen in theunsaturated zone through a field study and by simulation using solute transportmodel. Simulation was carried out initially for one crop season and shows that there

is a good agreement between the results of the model and the observed field trend.The model predicts that the chloride ion from the irrigated field reaches thegroundwater zone after about 45 days. The chloride and nitrogen concentration inthe unsaturated zone varies significantly during irrigation period due to intenseagricultural activities. The model simulation for a three crop period indicates that theoverall fluctuation during the three crop period, is mainly due to variation in rainfall,fertiliser application and evaporation. The concentration of ions fluctuates in a cyclic

trend during the simulation for five year period. There is no significant overallupward or downward trend in the concentration of ions in the unsaturated zone andin the groundwater zone. The results of the five year run with increased fertiliserapplication indicate an increase in the concentration of chloride and nitrate in the

unsaturated zone and groundwater. Further, even this increase in the concentrationof ions seems to stabilise at the end of 5 years. The model predicts that there is no

threat to the groundwater quality due to the present level of use of agrochemicals.Thus, the modelling exercise carried out may be used to compute the probableconcentration of chloride and nitrate in unsaturated zone and groundwater over atime period of a few years in the study area.

0

2

4

6

8

10

0 365 730 1095 1460 1825

Year

1 m

Groundwater

0 1 2 3 4 5




225

ACKNOWLEDGEMENTS

The authors acknowledge with thanks the financial assistance provided by theCouncil of Scientific and Industrial Research and Department of Science and

Technology. The authors also wish to thank Dr.Frank Stagnitti, School of Ecologyand Environment, Deakin University, Australia for providing the required facilities.

REFERENCES:

Boateng S. and Cawlfield J.D. (1999), "Two dimensional sensitivity analysis ofcontaminant transport in the unsaturated Zone", Groundwater, Vol.37, No.2, pp.185-193.

Genuchten V.M.Th (1980), "A closed form equation for predicting the hydraulicconductivity of unsaturated soils", Soil Sci. Soc. Am. J., pp.892-898.

Neuman S.P. (1975), "Galerkin approach to saturated – unsaturated flow in porous

media", John Wiley Sons, London, Vol.1, pp.205-217.

Neuman S.P., Feddes R.A. and Bresler E. (1974), "Finite element simulation of flowin saturated – unsaturated soils considering water uptake by plants", Third AnnualReport, Project No.A10-SWC-77, Hydraulic Engineering Lab, Technion, Haifa,

Israel.

Petrovic A.M. (1990), "The fate of nitrogenous fertilisers applied to turfgrass" ,J. Environ. Qual. Vol.19, pp.1 – 14.

Simunek J., Sejna M. and Genuchtan V.Th. (1999), Hydrus-2D/Meshgen-2D:

"Simulating water flow and solute transport in two-dimensional variably saturatedmedia", U.S. Salinity Laboratory, Agriculture research service, Riverside,California.

Tim V.S. and Mostaghimi S. (1989), "Modelling transport of a degradable chemicaland its metabolites in the unsaturated zone", Ground water, Vol. 27, No. 5, pp.672-681.





227

Modelling of NAPL Migration in the Porous Media

M. S. Mohan Kumar and Mini Mathew

Abstract

Modelling of NAPL migration in the saturated and the unsaturated porous medium is

discussed. A two dimensional cell centered finite difference model to predict NAPLmovement in a saturated porous media is developed and the model is verified using

the analytical and the experimental results. The modelling of multiphase flow iscarried out using different solution methodologies such as fully implicit simultaneousmethod and a two step fully implicit sequential method.

Keywords : Nonaqueous Phase Liquids; Saturated Medium; UnsaturatedMedium, Numerical Modelling

1. INTRODUCTION

Nonaqueous Phase Liquids (NAPLs) are hydrocarbons. They do not dissolve inwater and form a separate phase in the subsurface. NAPLs are either comprised of asingle or multiple component fluids. This study is carried out for single component NAPL migration in the subsurface. Groundwater contamination by NAPLs such aschlorinated solvents, TCE, PCB, and other liquids are widespread throughout theindustrialized area. Most of these chemicals are extremely toxic and insoluble in

water. To implement appropriate remedial schemes in the contaminated area, it isnecessary to evaluate the extent of the contaminated area. This information can beobtained by extensive field investigation, which generally is very expensive andtime consuming. Field investigation can be reduced or made more cost effective, if

the migration pattern of the NAPLs can be evaluated by using numerical modelsaccurately.

The movement of nonaqeous phase liquids (NAPLs) that are immiscible with waterthrough the porous media is an important part of contaminant hydrology and in petroleum engineering. NAPL migration in the subsurface is controlled by; (1)

Volume of NAPL released, (2) area of infiltration, (3) duration of NAPL release, (4) properties of the NAPL, (5) properties of the porous media and (6) subsurface flowconditions (Feenstra and Chezy; 1998). Fig.1 shows the typical movement of NAPLs in the porous media.




228

Fig. 1: General migration pattern of NAPLs in the subsurface

When NAPL is released into the subsurface, NAPL will migrate downward throughthe unsaturated zone by gravity. In addition to vertical migration, some extent oflateral spreading is also caused due to the effect of capillary forces (Schwille; 1988)

and also due to medium properties. As the NAPL progress its downward migration

through the unsaturated zone, it leaves behind residual saturation due to surfacetension and the vertical migration is governed by the properties of the NAPL and themedia. NAPL movement in the pore space will occur when enough pressure isavailable to overcome the displacement pressure. The amount of pressure requireddepends on the capillary forces acting on the fluids on either side of the pore throat.The capillary force between the fluids depends on the wettabiliy of fluids. NAPL

can be lighter than water (ie, density less than water), and the corresponding NAPLsare referred to as LNAPLs, and NAPL can also be heavier than water (ie, density isgreater than water), and such NAPLs are referred to as DNAPLs. If the quantity ofrelease is sufficiently large, some of the NAPLs will reach the saturated zone.

DNAPLs will displace water and continue its downward migration under pressureand gravity. LNAPLs are lighter than water, and hence they will float over the water

table. Hence in saturated porous medium, the movement of DNAPLs are considered

as a two phase system of water and DNAPL simultaneously in the porous medium.In unsaturated medium, the movement of both DNAPLs and LNAPLs areconsidered as a three phase system of water, NAPL, and air simultaneously in the

porous medium. NAPLs behavior in a small porous block is characterized as REVs,and in each REV physical properties such as permeability, porosity, relative permeability, and capillary pressure saturation relations remain constant with boththe fluids competing with each other to occupy the pore space.




229

2. GOVERNING EQUATIONS OF MULTIPHASE FLOW

Laboratory studies conducted in the oil industry, [Wyckoff and Botset; 1936], andLeverett; 1938], suggest that Darcy’s law can be extended to multiple fluid systemsin porous media. Darcy's law is extended to multiphase flow by postulating that the

phase pressures are involved in causing each fluid to flow. The governing equationsfor multiphase single component flow of immiscible fluids in the porous media isgiven by,

( ) ( )α α α α α

α

α

α ρ φ ρ ρ

µ

S

t

Q g

x

P k k

x j

r ij

i ∂

∂=±

!!

"

#+

∂

∂$$

%

&

∂

∂ (1)

where i and j are the direction indices, α is the phase, k ij is the intrinsic permeability

of the porous medium, k r α is the relative permeability, µ is the viscosity, ρ is thedensity, g is the acceleration due to gravity, and z is the elevation taken as positive

from bottom. Pα is the pressure, Sα is the saturation, Qα is the source sink term of

the phase α, and φ is the porosity of the medium.

α ∈w, nw in saturated porous medium and α ∈w, nw, g in unsaturated porousmedium. Here w is the wetting phase (water) and nw is the nonwetting phase(NAPL) in the saturated medium and w is the wetting phase (water), nw is theintermediate phase (NAPL), and g is the nonwetting phase (air) in the unsaturated

porous medium.

The governing equation ( Eqs.1) is subjected to the following constraints in the fulldomain.

where N is the number of phases. When the phases are immiscible, an interface willdevelop between the phases. The difference of phase pressures at the interface is thecapillary pressure between the phases and is given by,

Here α is the nonwetting phase having higher phase pressure and β is the wetting phase pressure for the two phases. The governing equations of multiphase flow ishighly nonlinear due to the dependency of relative permeabilities and capillary

)2(11

='= α

α S

N

( ) ( ) )3(,,,,,

)3(,,,,,,,bmedium saturated for nwwnww P P S P amediumd unsaturate for g nww g nww P P S P

C

C

β α α β β α α β

β α α αβ

β α α αβ

≠∈∈−=≠∈∈−=




230

pressures on the saturation of the respective phases and the governing equations alsohave to satisfy the following constraints.

3. CONSTITUTIVE RELATIONSHIPS

3.1 Capillary pressure saturation relation

In a two phase system, two fluids simultaneously exists in the porous medium, one

fluid will have more wettability for the solid phase and will occupy the smaller voidswhile the nonwetting fluid is consigned to larger voids. When two immiscible fluids

are in contact, a discontinuity in pressure exists at the interface between the fluids.The difference in pressure is expressed as the capillary pressure ( Eqs.3).Parameterizations of capillary pressure saturation relations widely used in theliterature are Brooks and Corey(1964) and Van Genuchten(1980). The Brooks and

Corey(BC) function is widely used in the petroleum engineering simulation and inthe contaminant hydrology problems and the capillary pressure saturation relation interms of wetting and nonwetting fluid saturation is given by,

PC = Pd Swe -1/λ

PC = Pd (1-Snwe)-1/λ

PC≤ Pd (5)

whereWr

nW nwe

Wr

Wr W we

S S S

S

S S S

−=

−

−=

1,

1 , Swr is the residual saturation of the

wetting fluid, λ is the pore size distribution index, and Pd is the displacement pressure of the medium. Similarly in the case of three phase flow equations,equations similar to Eqs. (5) are written for all combinations of the three phasesystem (Parker; 1989).

4. RELATIVE PERMEABILITY SATURATION RELATIONSHIPS

Following the concept of Burdine(1953) or Mualem(1976) for deriving the relative

permeability relationships from capillary pressure saturation relationships, therelative permeability relations in terms of wetting and nonwetting phase saturation

are given by,

Equations similar to Eqs.(6) are written for three phase system (Parker; 1989).

( ) )6(112

2! "

#$%

& −−=

+

λ

λ

eerNW S S k λ

λ 32+

= erW S k

( )

( ) )4(,,,

)4(,,,,

bmedium saturated for nwwS k k

amediumd unsaturate for g nwwS k k

r r

r r

∈=

∈=

α

α

α α α

α α α




231

5. BOUNDARY AND INITIAL CONDITIONS

The initial conditions of the primary variables have to be given for the full domainand the boundary conditions also to be specified on the boundaries in terms of the primary variables incorporating both Dirichlet and Neumann boundary conditions as

the case may be.

6. NUMERICAL MODELLING OF MULTIPHASE FLOW

A number of numerical models have been developed to simulate the migration ofnonaqueous phase liquids (NAPLs) in the subsurface. The majority of these models

are based on one or other type of formulation involving the primary variables of the phases. There are several ways to write the governing equations of multiphase fluidflow such as the two pressure approach and the fractional flow approach (Morel andSeytoux; 1973 ). The two pressure approach of the governing equations have been

widely used in the two phase unsaturated medium of air water system (Pinder andAbriola; 1986 ). The other approach to the numerical solution is the fractional flow

approach which include the work of Guarnaccia and Pinder(1997). The other possible approaches of numerical simulations involve all combinations of the primary variables such as the pressure and saturation of all the phases leading todifferent type of formulations. Here only the formulation involving the pressure andsaturation of the wetting phase in a saturated system is discussed in detail.

6.1 Saturated Porous Medium

The general equations of multiphase flow in the saturated medium for the two

dimensional vertical section is given by,

( ) )7(t

S g

z

P k k

z x

P k k

x

W W

W

W

rw z W

W

rw x

∂

∂=!!

"

#+

∂

∂$$%

&

∂

∂+!!

"

#

∂

∂$$%

&

∂

∂ φ ρ

µ µ

( ) )8(t

S g

z

P k k

z x

P k k

x

NW NW

NW

NW

rNW z NW

NW

rNW x

∂

∂=!!

"

#+

∂

∂$$%

&

∂

∂+!!

"

#

∂

∂$$%

&

∂

∂ φ ρ

µ µ

where the subscripts W and NW refer to the wetting and nonwetting fluids, µ is the

viscosity [M/LT], and ρ is the density [M/L3], z is the vertical distance taken as

positive from the bottom, SW and S NW are the wetting and nonwetting saturations, ϕ is the medium porosity, k x and k y [L

2] are the intrinsic permeabilities, k rW and k rNW are the relative permeabilities of the wetting and nonwetting fluids, g[L/T2] is the

acceleration due to gravity, and PW and P NW [M/LT2] are the wetting and nonwetting

pressures respectively.




232

1=+ NW W S S )( NW rNW rNW S k k =

The Eqs.(7) and (8) are coupled through the capillary pressure and is a function ofsaturation of wetting phase, and is given by,

And the governing equations are subjected to

The governing equations have strong nonlinearities such as the dependence of the

relative permeabilities k rW and k rNW on saturation and the dependence of PC on

saturation. In order to solve the governing equations numerically, constitutiverelations of the nonlinear terms have to be specified.

The coupled equations are highly nonlinear, Peaceman (1977) reported that explicitand alternating direction implicit methods are not stable for incompressible two

phase problems especially in heterogeneous media. In this study the coupledequations are solved numerically using a block centered fully implicit finitedifference scheme explained by Kueper and Frind (1991). The discretized equationsof wetting and nonwetting fluid (Eqs.(7 & 8)) in terms of wetting fluid pressure andwetting fluid saturation as the primary variable are given by,

The Coefficients B1, D1, E1, F1, H1, B2, D2, E2, F2, H2, B3, D3, E3, F3, and H3 arefuctions of relative permeabilities of phases and capillary pressure between the

phases. Hrere n+1 is the currenttime and n is the old time level.

7. TREATMENT OF NONLINEARITIES

The governing equations of multiphase flow are highly nonlinear due to the couplingof phases. The equations can be linearized using Picards method and Newton

Raphson method. The linearized form of the equations using Newton Raphsonmethod is given by ,

]

)11(0

[),(1

1

1

1

1

1

111111111

=∆+∆−∆

+

∆−++++=

++

+

++−−

z g H z g Bt

S

t

S P H P F P E P D P BS P F

W

n

W

nn

Wij

nWij

Wij jWiWij jWiWijW W

ρ ρ φ

φ

)10()( W rW rW S k k =

)9()( W NW W C P P S P −=

]

)12(0

[),(2

1

1

1

1

1

131331313

121221212

=∆+∆−∆

−

∆++++++

++++=

++

+

++−−

++−−

z g H z g Bt

S

t

S S H S F S E P DS B

P H P F P E P D P BS P F

W

n

W

n

n

Wij

nWij

Wij jWiWij jWiWij

Wij jWiWij jWiWijW W

ρ ρ φ

φ




233

where B’, D

’, E

’, F

’, H

’, B

’’, D

’’, E

’’, F

’’, H

’’, B

’’’, D

’’’, E

’’’, F

’’’, H

’’’, B

’’’’, D

’’’’, E

’’’’, F

’’’’,

and H’’’’ are the first partial derivatives with respect to corresponding primary

variables at those respective nodes. Similar approach can be used in formulating thenumerical equations for NAPL migration in unsaturated porous medium also. It

should be noted that one more phase equation corresponding to gas phase willappear in the formulation ( Parker; 1989).

8. SOLUTION METHODOLOGY

8.1 Simultaneous Method

Most of the modelling of multiphase flow in two phase system is carried out using

simultaneous method using ∆PW and ∆SW as unknowns. In this study forsimultaneous method, the primary variables are simulated simultaneously using thelinearized Eqs. (13) and (14) by taking PW and SW as unknowns. The Jacobianmatrix in simultaneous scheme is block pentadiagonal in nature with two degrees offreedom per node. The resulting matrix is in the form of,

where [A] is a 2N x 2N(N is the number of nodes) Jacobian matrix, [X] is a columnvector of 2N unknowns of PW and SW, [R] is the column vector of right hand side,(m+1) is the current iteration level and m is the previous iteration level. The explicit

method and the alternating direction implicit methods are not suitable for thesolution of multiphase flow simulation specially in immiscible type of fluids(Peaceman; 1977). In this paper for simultaneous method, block Incomplete

Cholesky Conjugate Gradient method is used as the matrix solver.

[

] [

] 1

)13(

,1

1

''

1

''''

1

''

1

''

1

'

1

'

'

1

'

1

'1,1

1

''

1

''''

1

''

1

''

1

'

1

''

1

'

1

'

F S H S F S E S DS B P H P F

P E P D P BS H S F S E

S DS B P H P F P E P D P B

mn

Wij jWiWij jWiWijWij jWi

Wij jWiWij

mn

Wij jWiWij

jWiWijWij jWiWij jWiWij

−++++++

+++=++

+++++++

+

++−−++

−−

++

++

−−++−−

[

] [

] 2

)14(

,1

1

''''

1

''''''''

1

''''

1

''''

1

'''

1

'''

'''

1

'''

1

'''1,1

1

''''

1

''''''''

1

''''

1

''''

1

'''

1

''''''

1

'''

1

'''

F S H S F S E S DS B P H P F

P E P D P BS H S F S E

S DS B P H P F P E P D P B

mn

Wij jWiWij jWiWijWij jWi

Wij jWiWij

mn

Wij jWiWij

jWiWijWij jWiWij jWiWij

−++++++

+++=++

+++++++

+

++−−++

−−

++

++

−−++−−

[ ] [ ] [ ] )15(1 mmm R X A =+




234

8.2 Sequential method

As discussed in the previous section normally simultaneous solution of governingEqs.(13) and (14) are obtained. The sequential method is a two step fully implicititerative method. In this method, the linearized equation of wetting fluid, Eqs.(13), is

used for the simulation of wetting fluid pressure by taking the primary variables ofsaturation of wetting fluid at the previous iteration on the right hand side. TheJacobian matrix of wetting fluid pressure is a five banded matrix and is given by

where [A1] is an N x N (N is the number of nodes) Jacobian matrix, PW is a columnof vector of N unknowns of PW, and [R 1] is the column vector consisting of right

hand side of Eqs.(13) and all the terms of SW.

In the second step, the primary variables of wetting fluid saturation is simulatedusing the linearized nonwetting phase equation, Eqs.(14), by taking the primaryvariables of wetting fluid pressure at (m+1/2) level. The Jacobian matrix of wettingfluid saturation is also a five banded matrix and is given by

where [A2] is an N x N (N is the number of nodes) Jacobian matrix, [SW] is acolumn vector of N unknowns of SW, and [R 2] is the column vector consisting ofEqs.(14), the coefficients of PW and SW at previous iteration level and thecoefficients of PW at (m+1/2) level. In this method, the global matrix Eqs.(16) and(17) are solved using Incomplete Cholesky Conjugate Gradient (ICCG) solver. FirstEq.(16) is solved for PW and then Eq.(17) is solved for SW and the iteration is donetill convergence is achieved.

9. RESULTS AND DISCUSSIONS

The analytical solution of the multiphase flow, incorporating fully the effect ofgravity and capillary pressure in transient multiphase flow through porous media is

not tractable. In this paper, model verification is carried out by comparison of

numerical results with analytical solutions reported in the literature (McWorter andSunada, 1990; Kueper, 1991.a). The analytical solution describes the displacementof water by nonaqueous phase liquid in a one dimensional horizontal column. Thecolumn is initially fully saturated by an incompressible wetting fluid. Anincompressible nonwetting fluid is continuously injected at the inflow end of the

column.. Fig. 2 shows a good agreement between analytical and numerical resultsobtained using both sequential and simultaneous methods.

[ ] [ ] [ ] )16(1

2/1

1

mm

W

m R P A =+

[ ] [ ] [ ] )17(2/1

2

12/1

2

+++ = mm

W

m RS A




235

For the case of multiphase flow through heterogeneous media, there are no analyticalsolutions available to test the accuracy of the model. Therefore, in order to examine the

accuracy of the model developed for the two phase flow in heterogeneous media, themodel is tested and compared with results for a laboratory experimental problem available




236

in the literature. This test problem is an experimental result reported in the literature(Helmig and Peter Bastian, 1998). Fig.3 shows the schematic diagram of the domain andthe boundary conditions. The domain is made up of two types of sand and the domain isfully saturated by water. The sand properties are reported in Table.1. The relative permeabilities and capillary pressures are defined using Brook's and Corey relations. This

problem is simulated for two cases, case 1 for a heterogeneous media of two types of sands,sand1 and sand2. The second case, case 2 is a homogeneous porous medium of sand 1through out the solution domain.

Table 1: Properties of sand 1 and sand 2

Sand φ k[L2] SWr λ Pd[pa]

1 0.4 6.64E-11 0.09 2.7 755

2 0.39 7.15E-12 0.12 2.0 2060

Fig.4a shows the distribution of nonwetting fluid using both sequential and simultaneousmethods at 2400sec in heterogeneous media (case 1) using wetting fluid pressure andsaturation model. Fig.4b shows the experimental result at 2400sec for the case 1(hetrogeneous media) of test problem. The results indicate that both simultaneous andsequential methods are simulating the same results and are matching well with the

experimental results. Fig.4c shows the distribution of nonwetting fluid using bothsequential and simultaneous method at 2400sec in homogeneous media (case 2) . Fig.4dshows the experimental result at 2400sec in homogeneous media (case 2). The resultsshow that both simultaneous and sequential method is simulating the same results and is

matching well with the experimental results. The results also show that the modeldeveloped is able to predict the NAPL migration in the subsurface accurately.




237

REFERENCES:

Aziz, K. and Settari, 1979. "Petroleum reservoir simulation", Applied Science,London.

Brooks, R.H. and Corey,A.T, 1964. "Hydraulic properties of porous media,hydrolo". Pap.3, Civ. Eng. Dep., Colo. State Univ., Fort Collins.

Bundine, N.T., 1953. "Relative permeability from pore size distribution data" ,

Trans, AIME, 198.

Guarnaaccia, J.F. and Pinder, G.F., 1997. NAPL: "A mathematical model for the study of NAPL contamination in granular soils, equation development and simulationdocumentation" . The university of Vermount, RCGED.

Helmig, R. and Huber, R., 1998. "Comparison of Galerkin type discretizationtechniques for two phase flow in heterogeneous porous media", Adv. Water Resour ., 21(8), 697-711.

Kueper, B.H., and Frind,E.O., 1991.a. "Two phase flow in heterogeneous porousmedia" 1. Model development, Water Resour. Res., 27(6), 1049-1057.

Kueper, B.H., and Frind,E.O., 1991.b. "Two phase flow in heterogeneous porous

media" 2. Model application, Water Resour. Res., 27(6), 1059-1070.

Leverett, M.C., 1938, "Flow of oil water mixtures through unconsolidated sands", Trans, Am. Min. Metall. Pet. Eng., 132, 149-191.

McWhorter,D.B., and Sunada D.K., 1990. "Exact integral solutions for two phase flow" , Water Resour. Res., 26(3), 399-414.

Peaceman,D.W., 1977. "Fundamentals of numerical reservoir simulation", Elsevier

New York.

Parker J. C., 1989, "Multiphase flow and transport in porous media" , Review ofgeophysics , 27,3,pp: 311-328.

Rainer, H., 1989, "Multiphase flow and transport processes in the subsurface", Springer New York.

Sleep, B.E. and Sykes, J.F., (1997) "Modelling the transport of volatile organic in

variably saturated media" . Water Resour. Res., 25, 81-92.

Sleep, B.E. and Sykes, J.F., 1993. "Compositional simulation of groundwatercontamination by organic compounds,2" . Model application. Water Resour. Res.,6(29), 1709-1718.

Spillette, A.G., Hillestad, J.G. and Stone, H.L., 1973. "A highly stable sequential solution approach to reservoir simulation". Soc.Pet. Eng. 48th Ann. Meet., SPE paper no. 4542.

Wyckoff, R.D., and Botset, H.G., "The flow of gas liquid mixtures throughunconsolidated sand" , Physics, 1936, 7, 325-345.





239

Review of Methods used for Modeling the Fate and

Transport of Hydrocarbon Plumes using RT3D

T. P. Clement

Abstract

Contamination of groundwater aquifers by petroleum hydrocarbon products

is a common environmental problem faced by both developed and developingcountries. Mathematical details of a public-domain reactive transport code

RT3D, which can be used for modelling the fate and transport of

hydrocarbon plumes under different types of aerobic and/or anaerobicconditions, are presented. Three types of conceptual models for representing

the hydrocarbon degradation reactions are discussed. The models, which

are listed in increasing levels of complexity, include the instantaneous

aerobic reaction model, the kinetic aerobic model, and the kinetic

aerobic/anaerobic model. Various levels of approximations made within

these three reaction models are discussed. The limits of these

approximations are analysed using test problems. Each of these models hasits own advantage and the choice would depend on the type of management

question one wants to address.

Keywords: hydrocarbon pollution, groundwater modelling, numerical model,

reactive transport

1 INTRODUCTION

Hazardous material released from leaking underground storage tanks and pipelineshave contaminated subsurface soil and groundwater at thousands of sites throughout

the world. Common urban groundwater contaminants include petroleum species

such as benzene, toluene, xylene, and ethylbenzene (collectively designated asBTEX species). Remediation of sites contaminated with these hazardous chemicals

is an expensive task. In the past, ineffective pump-and-treat methods that either

flush or remove contaminants from groundwater aquifers were employed as the

remedial option. Recent studies have identified that natural microbes present in the

aquifer have the potential for degrading several of these contaminants. These




240

findings have lead to the development of a cost-effective remediation technique broadly known as bioremediation. Application of bioremediation to field-scale

problems include two distinct approaches: active bioremediation and passive

bioremediation (also known as natural attenuation or monitored natural attenuation).

Active bioremediation is an accelerated cleanup technique, which is usually

accomplished by enhancing the activities of indigenous microbial population within

the contaminated region (Semprini et al., 1991). This can be done by actively

supplying required nutrients (primarily nitrogen or phosphorous), electron donors(acetate or lactate) and/or electron acceptors (oxygen or nitrate). Alternatively, the

remediation efficiency can be enhanced by introducing non-indigenous microbial

strains into the subsurface (Mayotte et al. 1996).

The natural attenuation approach is a passive remediation technique. This approach is a

plume-scale management strategy that relies on the natural assimilative capacity of thesystem to control contaminant migration rates and to provide site remediation. Theoverall attenuation potential would depend on the combined effects of naturally

occurring physical, chemical, and biological processes (Wiedemeier et al., 1998). The

processes include both biotic and abiotic degradation, volatilization, sorption, and

dispersion. When natural attenuation is adopted as remediation technique, it should beaccompanied with a long-term monitoring plan to quantify the rate of remediation.

Therefore, in the context of contaminated site management, natural attenuation is now

termed as monitored natural attenuation (MNA) (Wiedemeier et al., 1998).

Both the active and passive remediation approaches discussed above are now known

to work for a wide variety of contaminants including, petroleum compounds,

pesticide, phenolic compounds, nitrates, chlorinated compounds, explosives, andmetal wastes. Evaluation of active or passive bioremediation design requires a

thorough understanding of the biologically mediated reactive transport processes.Therefore, in recent years, several researchers have attempted to develop models for

predicting biologically mediated reactive processes occurring in subsurface

environments (Rifai et al., 1988; Clement, 1997; Waddill and Widdowson, 1998;Clement et al. 1998). Objective of this paper is to briefly review the capabilities of

a comprehensive three-dimensional reactive transport model, known as RT3D

(Clement, 1997), and to describe its use for modelling hydrocarbon contamination

problems using three different types of reaction modules.

2 DESCRIPTION OF THE RT3D CODE

2.1 Statement of Governing Equations

The general set of macroscopic equations describing the fate and transport of

aqueous- and solid-phase species, respectively, in multi-dimensional saturated porous media is written as:




241

( ) m...,2,1k ,where,r r r Cqs +Cvi

xi -

x j

CDij

xi =

t

Cdacsk

k k

k =+−+

φ∂

∂

!!

"

#

$$

%

&

∂

∂

∂

∂

∂

∂

(1)

)mn(...,2,1,=l where,,r -r +r ~ =dt

C~d

dacl −

(2)

where n is the total number of species, m is the total number of aqueous-phase(mobile) species (note, n-m is the total number of solid-phase or immobile species),

Ck is the aqueous-phase concentration of the k th species [ML

-3], lC

~ is the solid-

phase concentration of the lth species [MM

-1], Dij is the hydrodynamic dispersion

tensor, v is the pore water velocity [LT-1

], qs is the volumetric flux of water per unit

volume of aquifer representing sources and sinks [T-1

], Cs is the concentration ofsource/sink [ML

-3], r c is the reaction rate that describes the mass of the species

removed or produced per unit volume per unit time [ML3T-1], cr ~ is the reaction rate

at the solid phase [MM-1

T-1

], and r a and r d, respectively, are attachment (or

adsorption) and detachment (or desorption) rates that describe the kinetic exchangeof the transported species between aqueous and solid phases [ML

-3T

-1]. RT3D

software is a general-purpose reactive transport codes that numerically solves the

equations (1) and (2) for any arbitrary number mobile and immobile species

(Clement, 1997).

Saturated groundwater flow velocities vi are calculated by first computing thehydraulic heads by solving the three-dimensional groundwater flow equation; later,

transport velocities are calculated from the head values. The flow equations usedare:

si

iii

s qxhK

x =

thS +!!

" #$$

% &

∂∂

∂∂

∂∂ (3)

i

iii

x

h

K =v

∂

∂

φ−

(4)

where h is the hydraulic head [L], Ss is the specific storage coefficient [L-1

], and K ii

is principal components of the hydraulic conductivity tensor [LT-1

] (non-principal

components are assumed to be zero), and φ is the soil porosity. Solution to the flow

model, with appropriate boundary and initial conditions, are accomplished using the public-domain flow code MODFLOW.

2.2 Numerical Solution Procedure

RT3D utilizes a reaction Operator-Split (OS) numerical strategy to solve any

number of transport equations [in the form of (1) and

(2)], which may be coupled via nonlinear reaction expressions. The transport code




242

MT3D uses a similar operator-split approach to primarily solve the physicaltransport processes describe by equation (1); however, MT3D can be

used only to describe single-species transport (Zheng, 1990). In RT3D, the

contaminant transport part is solved using the original MT3D routines. The MT3D packages for solving advection, dispersion, and source-sink mixing are simply

invoked by RT3D multiple times to solve the transport of all mobile species.

However, a new reaction module, with provisions for incorporating problem-

specific reactions, was developed to solve the reaction problem. Use of this modular

OS approach for solving the reaction problem facilitates representation of differentcontaminant transport systems through a set of pre-programmed reaction packages

(Clement, 1997). Appropriate code modifications were also implemented to

facilitate the input of pertinent multi-species information, including the initial and boundary conditions for each species. Further details of the input and output data

structure and the numerical solution techniques used by the RT3D code are

described in Clement (1997) and Clement et al. (1998).

2.3 Code Testing and Verification

The RT3D software has been well tested against various numerical and analytical

solutions. In addition, different research groups have used RT3D for solving varioustypes of field-scale reactive transport problems. For example, Clement et al. (1998)

used the RT3D code to solve a variety of reactive transport problems. Sun and

Clement (1999) validated RT3D against a series of analytical solutions. Clement(2001) used RT3D to test a sequential analytical solution. Lu et al. (1999) applied

RT3D to model hydrocarbon bioremediation at a petroleum spill site in Utah, USA.

Johnson et al. (1998) used RT3D to design an active bioremediation system at a

chlorinated solvent site in California, USA. Clement et al. (2000) applied RT3D tomodel a chlorinated solvent site in Delaware, USA. Reed et al. (2000) employed

RT3D to evaluate monitoring requirements for a hydrocarbon plume. Panikumar etal. (2001) employed RT3D to design a denitrifying bioremediation system at a field

site in Michigan, USA. These studies have provided the necessary validation

datasets for the RT3D code.

3. MODELING HYDROCARBON CONTAMINATION

Prediction of the fate and transport of hydrocarbon plumes in groundwater aquifers

requires a detailed description of the kinetics of biological reactions of all BTEX

species (which serve as the electron donor), all the available electron acceptors (such

as oxygen, nitrogen, iron, manganese, sulphate, and the fermented substrate), andvarious microbial populations (such as aerobic microbes, denitrifiers,

iron/manganese reducers, sulphate reducers, and methanogens). Simulating thesimultaneous effects of all these reactions and microbial growth processes coupled

with advection and dispersion process is a difficult task and hence very limited workhas been done in this area. Most realistic field-scale models use a simpler

conceptual model to reduce this complex problem to a tractable system. In fact,




243

early modelling studies have completely ignored anaerobic degradation and solelyfocussed on aerobic degradation (Rifail et al., 1988). Even for the simple aerobic

system, two types of models have been employed. The first one simplifies the

kinetics by assuming that the aerobic biotransformation process as an instantaneousreaction; the model can track the concentrations of hydrocarbon and oxygen. This

method is designated as Model-1 in this work. The second approach uses a Monod-

type kinetic model and can track the concentrations of hydrocarbon, oxygen, and the

microbial population in different phases (liquid and solids). This method is

designated as Model-2 in this work.

Recent field studies have shown that natural anaerobic processes play a dominant

role in degrading hydrocarbon plumes (Wiedemeier et al., 1998). Attempts have been made to extend the simplified instantaneous reaction model to account for

coupled aerobic and anaerobic processes; however, these attempts have had limited

success. One the other hand, Waddill and Widdowson (1998) developed acomprehensive Monod-kinetics based model that can track all microbial

populations, electron donors, and various electron acceptors. However, the practical

value of these types of complex models is unclear because, using currently available

field sampling methods, it is impossible to characterize microbial populations and

other required parameters at a field scale. Therefore, Lu et al. (1999) used a simpleraerobic-anaerobic reaction model available in the RT3D code to simulate a

hydrocarbon plume at the Hill Air Force Base site in the USA. This simple, first-

order, aerobic-anaerobic kinetic model is designated as Model-3 in this work. Insections below we review the mathematical details of all three models and will also

illustrate their use by solving simple test problems.

3.1 odel-1: Instantaneous Model for Aerobic Degradation Reactions

In the instantaneous reaction modelling approach, two mobiles species representinghydrocarbon (electron donor) and oxygen (electron acceptor) are tracked using thefollowing two advection dispersion equations:

( ) Hq

+Hvx

-x

HD

x =

t

HR s

si

i jij

iH

φ∂

∂!!

"

#

$$

%

&

∂

∂

∂

∂

∂

∂

(5)

( ) Oq

+Ovx

-x

OD

x =

t

OR s

si

i jij

iO

φ∂

∂!!

"

#

$$

%

&

∂

∂

∂

∂

∂

∂

(6)

where H is the aqueous-phase hydrocarbon concentration, O is the aqueous-phase

oxygen concentration, Hs and Os are the source/sink concentrations, D is the

dispersion coefficient, and R is the retardation factor. At the end of each time step,

the hydrocarbon and oxygen plumes are mixed using the following instantaneousreaction algorithm (Rifai et al., 1988):




244

O(t)/F>H(t) when,0;=1)+O(tandO(t)/F,-H(t)=1)+H(t (7)

H(t)F>O(t) when,0;=1)+H(tandH(t)F,-O(t)=1)+O(t

(8)

where F is stoichiometric reaction ratio (average value is 3.0 for the aerobichydrocarbon decay reaction). The two-dimensional USEPA model BIOPLUME-II

(Rifai et al, 1988) and the USEPA screening tool BIOSCREEN (Newell et al., 1996)

use a similar instantaneous modelling approach.

The instantaneous reaction model is one of the pre-programmed reaction packagesavailable within RT3D. We used this RT3D package to simulate a test problem and

compared the results against BIOPLUME predictions. The problem domain

considered here has dimensions similar to an example problem discussed in the

MT3D user manual (Zheng, 1990, page 7-4). Here, in a similarly sized two-

dimensional domain, we studied the reactive transport between hydrocarbon andoxygen. The assumed two-dimensional confined aquifer is 500 m long (x-

direction), 300 m wide (y-direction), and 10 m thick. The domain was discretizedusing a numerical grid consisting of 50 nodes along the x-direction, 30 nodes along

the y-direction, and 1 layer. A continuous source introducing contaminated water at

the rate of 1 m3/day, at a concentration level of 1000 mg/L, is located at a grid cell

centered at x = 135 m and y = 135 m. The initial concentrations of hydrocarbon and

oxygen concentrations were assumed to be 0 mg/L and 9.0 mg/L, respectively.

These same concentration levels were used as constant contaminant concentration

boundary conditions at x = 0. Other boundary nodes were assumed to have free boundary conditions. The aquifer was assumed to be a homogeneous, isotropic

system with a constant transmissivity value. Steady-state flow conditions were

assumed. Other flow and transport parameters assumed in the simulation are: delx =dely = delz = 10 m; v = 0.33 m/day; porosity is 0.3; longitudinal dispersivity value

of 10 m; and the ratio of longitudinal to transverse dispersivity is 0.3.

The concentration contours of hydrocarbon and oxygen predicted by the two codes,

at the end of 2 years of simulation, are compared in Figure 1.

This figure reveals typical characteristics of the instantaneous reaction model. Note

the plumes are forced to have either zero hydrocarbon concentration in nodes where

oxygen is present, or zero oxygen concentrations where hydrocarbon is present.The oxygen plumes surrounds the contaminate region with the concentrations of

oxygen gradually decreasing as we move away from the plume centreline. The

instantaneous reaction model is a powerful tool for modelling field-scale problems(Rifai et al., 1988). Also the basic model description, as defined within RT3D, is

general enough to predict mixing of any two instantaneously reacting species by

using an appropriate stoichiometric factor F. Further, if multiple electron donors

and acceptors are present then the contributions from all donors and acceptors can beaveraged using an effective stoichiometry, which would describe the reaction

between an “effective” donor and an “effective” acceptor, to model the average




245

behaviour. For example, Wiedemeier et al. (1998) used a similar approximation toquantify combined oxygen and nitrate reactions with a hydrocarbon plume.

Fig. 1: Hydrocarbon and oxygen plumes predicted by the instantaneous aerobic

reaction model (contours are values in mg/L).

Data from Clement et al. (1998)

3.2 Model 2: Kinetic Model for Aerobic Degradation Reactions

The kinetic model considered here describes the transport and biodegradation ofhydrocarbon and oxygen, mediated by the aerobic bacteria that reside in both

aqueous and solid phases. Using the linear equilibrium model for sorption reactions

and the Monod model for aerobic reactions, the fate and transport of hydrocarbon

(electron donor) in a multi-dimensional saturated porous media can be written as

(Clement et al. 1996b):

( ) !! "

#$$%

& !! "

#$$%

& !! "

#$$%

&

φ

ρµ

φ∂

∂!!

"

#

$$

%

&

∂

∂

∂

∂

∂

∂

O+K

O

H+K

HX~

+X-Hq

+Hvx

-x

HD

x =

t

HR

OHms

si

i jij

iH

(9)

where H is the aqueous-phase hydrocarbon concentration [ML-3

], H~ is the solid-

phase hydrocarbon (mass of the contaminants per unit mass of porous media), [MM-




246

1]), Hs is the source/sink concentration [ML-3], X is the aqueous phase bacterial cell

concentration [ML-3

], X~

is the solid-phase cell concentration [MM-1

], O is the

aqueous-phase oxygen concentration [ML-3

], R H is the retardation coefficient of the

hydrocarbon, K H is the half saturation coefficient for hydrocarbon [ML-3

], K O is the

half saturation coefficient for oxygen [ML-3

], and µm is the contaminant utilizationrate [T

-1]. In this model, we assumed that the hydrocarbon degradation reactions

occur only in the aqueous phase.

The fate and transport of oxygen is modelled using the equation:

( ) !! "

#$$%

& !! "

#$$%

& !! "

#$$%

&

φ

ρµ

φ∂

∂!!

"

#

$$

%

&

∂

∂

∂

∂

∂

∂

O+K

O

H+K

HX~

+XY-Oq

+Ovx

-x

OD

x =

t

OR

OHmH/Os

si

i jij

iO

(10)

where YO/H is the stoichiometric yield coefficient for oxygen, and R o is the

retardation coefficient for oxygen, set at a value 1.0.

The fate and transport of bacteria in the aqueous phase can be described using theequation:

( ) XK -O+K

O

H+K

HXY+

X~

K +XK -X

q+Xv

x-

t

XD

x =

t

Xe

OHmH/X

detatts

si

iij

i!! "

#$$%

& !! "

#$$%

& µ

φ

ρ

φ∂

∂! "

#$%

&

∂

∂

∂

∂

∂

∂

(11)

where K att is the bacterial attachment coefficient [T-1

], K det is the bacterial

detachment coefficient [T-1

], and K e is the endogenous cell death or decay

coefficient [T-1

].

The growth of attached-phase bacteria can be described using an ordinarydifferential equation of the form:

X~

K e-O+K

O

H+K

HX~

mY+X~

K det-XK att =

dt

X~

d

OHH/X !

! "

#$$%

& !! "

#$$%

& µ

ρ

φ

(12)

Equations (11) and (12) assume first-order kinetic expressions for

representing the exchange of bacteria between aqueous and solid phases (Clement et

al., 1997). The conceptual modelling approach used for representing soil bacteria,implicitly assumed in this formulation, is similar to the macroscopic approach

described in Clement et al. (1996a). In this approach, no specific microscopic

biomass structure is assumed, and diffusional limitations across biofilm are also

neglected. Permeability and porosity changes caused by bacterial accumulation

were also ignored in this work. However, if required, the macroscopic-approach

models for biomass-affected porous-media properties, described in Clement et al.(1996a), may be integrated within the model. The complete mathematical

description for the aerobic, hydrocarbon bioremediation system is given by thecoupled set of partial/ordinary differential equations (9), (10), (11), and




247

(12). In RT3D, these equations are represented by three mobile species(hydrocarbon, oxygen, and aqueous-phase bacteria), and one immobile species (soil-

phase bacteria). After reaction-operator splitting, the reaction terms are assembled

together and coded into a pre-programmed reaction module (Clement, 1997).

The two-dimensional test problem considered here to test this reaction model is

identical to the one described in previous section. Except for reaction parameters,all transport and flow parameters were assumed to be the same as those previously

used. The reaction constants assumed are: K O = 0.1 mg/L, K H = 0.12 mg/L, YO/H =

3.0, YX/H = 0.05, K e = 0.001 day-1

, ρ = 1.6 x 106 mg/L, K det = 1.0 day

-1, and K att =

70.0 day-1

. The initial concentration of the hydrocarbon assumed is 0 mg/L, oxygen

is 9 mg/L, and solid-phase bacteria (X~

) is 3.0 x 10-9

mg dry wt/ mg of soil (which is

also equivalent to 0.016 mg/L of bacteria on liquid-volume basis computed from the

expression X

~

ρ/φ). Since, under natural conditions, most bacteria are expected liveon the solid-phase, a very low value of 2 × 10-17

mg/L bacteria was assumed for theinitial aqueous-phase bacterial concentration.

Simulation experiments were completed to study the system behaviour at four

reaction rates, µm = 0.05, 0.1, 0.125, and 0.2 day-1

. Other microbial growth andtransport parameters were not perturbed during these simulations. Figure 2 shows

the hydrocarbon and oxygen plumes predicted by the kinetic biodegradation model,

at the end of 2 years, for different µm values.

In this figure, hydrocarbon concentration contours at 1 mg/L and oxygen

concentration contours at 8.8 mg/L (a value close to the initial saturation value of

9.0 mg/L) are used to define the respective plume boundaries. For comparison

purposes, the figure also includes hydrocarbon and oxygen plumes predicted by the

instantaneous-reaction model (curve a), and the hydrocarbon plume predicted underno reaction (curve f is same as a tracer plume). It can be seen from these figures

that, as the value of µm is decreased, the shape of the hydrocarbon plume predicted

by RT3D tends to approach the tracer plume. On the contrary, as the value of µm

increases the size of the hydrocarbon plume decreases and tends to approach the plume predicted by the instantaneous-reaction model. A similar trend can also be

observed in the presented oxygen profiles where the oxygen plume is shown to relax

to the instantaneous model predictions at µm = 0.2 day-1

.

The solid-phase microbial concentration (in liquid volume basis) distributions

predicted using different µm values are given in Figure 3. These figures show thatthe pattern of bacterial growth and the accumulated concentration level of bacteria

clearly depend on the reaction rate, µm. At low reaction rates, bacterial concentration

contours nearly follow the shape of the hydrocarbon contours. But, at higher

reaction rates, bacterial distributions exhibit more complex patterns; this is because,at larger µm values, oxygen is immediately consumed near the hydrocarbon source.This produces rate-limiting conditions for microbial growth downstream of the




248

source according to the assumed Monod kinetics, and hence the biomassconcentration is low there. However, the oxygen depletion creates a large

Fig. 2: Comparison of hydrocarbon (1 mg/L contour) and oxygen (1 mg/L

contour) plumes predicted by the kinetic aerobic reaction model for variousutilization rates (a. instantaneous, b. m = 0.2 day-1, c. m = 0.125 day-1 d. m =

0.1 day-1

e. m = 0.05 day-1

f. tracer). Data from Clement et al. (1998)

concentration gradient in the transverse direction, and thus transverse dispersion promotes oxygen flow into the hydrocarbon plume; this phenomena stimulates

microbial growth near transverse distances of 100 m and 170 m resulting in the

horseshoe shaped high solid-phase biomass concentration zone. The aqueous-phase biomass also showed similar contour profiles (data not shown), but with biomass

concentration levels almost two orders of magnitude lower than those predicted for

the attached-phase biomass. It should be noted that the biomass growth patterns

would also be sensitive to the other microbial growth and other transport parameters.Sun et al. (1998) performed a detailed sensitivity study to quantify the variations in

biomass growth patterns.

This example demonstrates the importance of modeling microbial growth while

predicting bioreactive flow in subsurface aquifers. Models that ignore either the




249

presence of bacteria or their growth may not always be adequate for simulating bioremediation systems, particularly when aquifer clogging is an issue. Clement et

al. (1996a) and Clement et al. (1997) discuss issues related to effects of biological

clogging and the effects of bacterial attachment and detachment kinetics on porousmedia transport.

Fig. 3: Bacterial distributed predicted for various utilization rates (contours are mg/L of

equivalent liquid phase cell concentrations). Data from Clement et al. (1998).




250

3.3 Model 3: Kinetic Model for Aerobic and Anaerobic Degradation Reactions

In recent years, several laboratory and field studies have shown that microorganisms

indigenous to subsurface environments can degrade hydrocarbon contaminantsunder both aerobic and anaerobic conditions (Wiedemeier et al., 1998). The

microorganisms transform available carbon into forms useful for energy and cell

mass. This results in oxidation of the electron donor and reduction of electronacceptor (EA). The electron donors would include natural organic matter and

anthropogenically introduced carbon such as hydrocarbons. The EAs include

elements or compounds that occur in relatively oxidized states. The more commonEAs present in groundwater aquifers are: dissolved oxygen, nitrate, iron(III) or

Mn(III), and sulfate (Wiedemeier et al. 1998). In addition to these direct electronacceptor processes, the fermentative process methanogenesis would also contribute

to hydrocarbon removal.

For modelling purposes, the lumped BTEX concentration level is assumed to

represent the overall hydrocarbon contamination at a site. Previous field studieshave shown that the BTEX compounds, which are the most soluble contaminants,

correlate well with the overall hydrocarbon contamination at field sites (Wiedemeier

et al., 1998). BTEX biodegradation is essentially an oxidation-reduction processwhere the BTEX compounds, which act as electron donar, are oxidized and an EA

(e.g., O2, NO 3

1−, Fe

3+,or SO 4

2−) is reduced. The following conceptual biochemical

model can be used to represent the reaction:

BTEX (electron donor, ED) + electron acceptor (EA) + microorganisms + nutrients

→ carbon dioxide + water + microorganisms + "respiration" products

Field studies have shown that a complete sequence of microbially-mediated BTEX biodegradation processes can utilize the electron acceptors O2, NO 3

1−, Fe

3+or SO 4

2−,

and produce Fe(II) and methane. Using benzene as an example reactant, the

stoichiometry of different degradation processes can be described by the followingset of biochemical reactions (Wiedemeier et al., 1998):

OH3CO6O5.7HC 22266 +→+ (13)

222663 3NO6H6COHC6H6NO ++→++ +− (14)

++ ++→++ 222663 Fe30OH78CO6HCH60)OH(Fe30 (15)

S3.75HO3H6COHC7.5H3.75SO 2226624 ++→++ +− (16)

42266 CH75.3CO25.2OH5.4HC +→+ (17)

These reactions are listed here in the order in which they are expected to occur,

which can be deduced based on the Gibbs’ free energy of the redox reactions.




251

The overall fate and transport of BTEX and various EAs (or degradation products)observed at a field site can be modeled using the following set of reactive transport

equations:

( )BTEXs

s

i

i

jij

iBTEX r BTEX][

!

q+

x

[BTEX]v

x

[BTEX]D

x =

t

[BTEX]R +

∂

∂−

!!

"

#

$$

%

&

∂

∂

∂

∂

∂

∂ (18)

( )22 O2 s

s

i

2i

j

2ij

i

2O r ]O[

!

q+

x

][Ov

x

][OD

x =

t

][OR +

∂

∂−

!!

"

#

$$

%

&

∂

∂

∂

∂

∂

∂ (19)

( )-33 NO

-3 s

s

i

-3i

j

-3

iji

-3

NOr ] NO[

!

q+

x

][NOv

x

][NOD

x =

t

][NOR +

∂

∂−

!!

"

#

$$

%

&

∂

∂

∂

∂

∂

∂− (20)

( ) ++ +∂

∂−!!

"

#$$

%

& ∂

∂∂∂

∂∂ ++++

22 Fe2

s

s

i

2i

j

2ij

i

2

Fer ]Fe[

!

q+x

][Fev x

][FeD

x =

t

][FeR (21)

( )2-

42

4 SO2-

4 s

s

i

-24i

j

2-4

iji

2-4

SOr ]SO[

!

q+

x

][SOv

x

][SOD

x =

t

][SOR +

∂

∂−

!!

"

#

$$

%

&

∂

∂

∂

∂

∂

∂− (22)

( )44 CH4 s

s

i

4i

j

4ij

i

4CH r ]CH[

!

q+

x

][CHv

x

][CHD

x =

t

][CHR +

∂

∂−

!!

"

#

$$

%

&

∂

∂

∂

∂

∂

∂ (23)

Where R is the retardation coefficient for various species, r represent the biodegradation rate term, Dij is the dispersion tensor, vi is the transport velocity, qs is

the fluid sink/source term, and ϕ is effective porosity. The concentrations of

different species are represented by a square bracket around an appropriate notation

to represent the species.

A kinetic model is required to describe the reaction terms r listed in these transport

equations. Clement (1997) conceptualised the BTEX decay reactions that use fivedifferent EAs as first-order reactions. A Monod-type term was then used to account

for the presence (or the absence) of various EAs, and an inhibition model was used

to simulate inhibition due to the presence of any one of the earlier EA (i.e. an EAwith higher free energy). The kinetic equations are:

][OK

][O[BTEX]k r

2O

2OBTEX,O

2

22 +−= (24)

][OK

K

][NOK

][NO[BTEX]k r

2i,O

i,O

3 NO

3 NO NOBTEX,

2

2

3

33 ++−=

−

−

−

−− (25)




252

][NOK

K

][OK

K

][FeK

][Fe[BTEX]k r

3 NOi,

NOi,

2i,O

i,O

3

Fe

3

FeFeBTEX,

3

3

2

2

3

33−+

+

+++−=

−

−

+

++ (26)

][FeK

K

][NOK

K

][OK

K

][SOK

][SO[BTEX]k r

3

Fei,

Fei,

4 NOi,

NOi,

2i,O

i,O

24SO

24

SOSOBTEX,

3

3

4

4

2

2

24

24

24

+

−−

−

+

+++−=

+

+

−

−

−

−−

(27)

][SOK

K

][FeK

K

][NOK

K

][OK

K

][COK

][CO[BTEX]k r

24SOi,

SOi,

3Fei,

Fei,

3 NOi,

NOi,

2Oi,

Oi,

2CH

2MeMeBTEX,

24

24

3

3

3

3

2

2

4

−+

−

++

+++−=

−

−

+

+

−

−

(28)

where2O,BTEXr is the BTEX destruction rate utilizing oxygen, −

3 NOBTEX,r is the

destruction rate utilizing nitrate, +3Fe,BTEXr is the destruction rate utilizing Fe

3+ (or

producing Fe2+

), 24SOBTEX,

r − is the destruction rate utilizing sulfate, Me,BTEXr is the

destruction rate via methanogenesis, [O2] is oxygen concentration [ML-3],2Ok is the

first-order degradation rate constant for BTEX utilizing oxygen as the EA [T-1

],

2OK is the saturation constant for oxygen [ML-3

],2O,iK is the oxygen inhibition

constant [ML-3

]; similar nomenclature is used for subsequent reactions. Note that bysetting the half-saturation constants to small values, we can simulate zero-order

dependency with respect to the electron donor and thus a first-order degradation

model with respect to BTEX. The values of all the saturation constants were set at

0.01 mg/L.

Similarly, the inhibition constants can be set to small values to simulate pure

sequential EA process. The inhibition function is used to represent the concept thatthe availability of any one of the EAs may inhibit the utilization of other EAs that

provide less Gibbs-free energy to the system. However, if a K i is assigned a very

large value (much larger than the maximum value of the EA species) then the

inhibition function becomes one and the simultaneous use of EAs can be simulated.In our model all K i values, except K i,Fe3+, were set at 1.0 mg/L. The value of K i,Fe3+

was set 10 mg/L.

Since the concentrations of the two electron acceptors Fe3+

and CO2 cannot be

measured under field conditions and because they can change over time

(Wiedemeier et al., 1998), these terms were replaced in the model to predict the products of these EA reactions. The concentration levels of the products at every

node were limited by using two “capacity" terms defined by the equations:




253

]Fe[]Fe[]Fe[ 2max

23 +++ −= (29)

]CH[]CH[]CO[]Me[ 4max,42 −== (30)

where [Fe2+

max] and [CH4,max] are maximum measured levels of these species.Equations (17) and 18) are used to indirectly quantify the iron reducing and

methanogenic capacity of the node at a given time. Since methane production

reaction is a fermentation reaction, there is no external electron transfer process

involved in this reaction step. Therefore, the concentration term for CO2 used in

(28) should be considered as a hypothetical term that simply indicates the localmethanogenic capacity (Me) of the node. Similarly, the concentration term for Fe

3+

should also be considered as a hypothetical term that indicates the local iron

reduction capacity [bioavailable Fe(III)] of the node. The total rate of BTEXdestruction via destruction processes can be represented as:

42

42

32 CHBTEX,SOBTEX,FeBTEX, NOBTEX,OBTEX,BTEX r r r r r r ++++= −+− (31)

Rates of EA utilization or product formation are given by the corresponding rate ofBTEX destruction term multiplied by an appropriate yield stoichiometric coefficient

(Y):

222 O,BTEXBTEX/OO r Yr = (32)

−−− =333 NO,BTEXBTEX/ NO NO

r Yr (33)

+++ −= 322 Fe,BTEXBTEX/FeFer Yr (34)

24

24

24 SO,BTEXBTEX/SOSO

r Yr −−− = (35)

Me,BTEXBTEX/CHCH r Yr 44

−= (36)

For BTEX the stoichiometric yield values are: HC/O2Y is 3.14,

/HC NO3

Y − is 4.9,

HC/Fe2Y + is 21.8,/HCSO 2

4

Y − is 4.7, and HC/CH4Y is 0.78 (Wiedemeier et al., 1998).

It is important to note the kinetic model presented above is based on severalimportant assumptions. The model should be used with caution only at sites where

these assumptions are valid. The key assumptions used in the model are: (1) the

fuel chemical species benzene, toluene, ethylbenzene, and xylene species are

assumed to degrade at similar rates, and hence are combined and modelled as asingle electron donor species BTEX (2) production of Fe

2+ and methane are

restricted at a node at a "maximum-observed level"; however, the model assumes

that an infinite supply of electron acceptor will be available for iron-reduction and

methanogenic reactions; (3) more complex processes such as the rate-limitedinteraction of bioavailable, solid-phase Fe

3+ and aqueous-phase Fe

+2, interaction of

oxygen and Fe2+

, and/or variations in the spatial pattern of methanogenic activity




254

and CO2 availability are not considered; (4) growth and decay of various microbial populations and their interactions with contaminants and aquifer solids are assumed to be

negligible; (5) all BTEX decay reactions are approximated as first-order reactions and

hence the model ignores the Monod limitation due to the electron donor (BTEX)availability. Fortunately, these assumptions are expected to be reasonable

approximations for most field sites. However, there will always be some exceptions.

The multi-species reaction model discussed above was field tested to model a

hydrocarbon problem at the Hill Air Force Base (AFB) site in USA. The

hydrogeological details of the site are discussed in Lu et al. (1999). The unconfined

aquifer beneath the site is contaminated with BTEX dissolved from petroleum

products leaked from an underground storage tank. Based on site characterizationdata the distribution of BTEX, DO, nitrate, Fe(II), sulfate, and methane were

mapped in August 1993 and in July 1994. The August dataset was used as the initial

condition in this numerical experiment. Simulations were then completed for 365days and the model results were compared against the plume distribution observed

in July 1994. Figures 4a and 4b compare observed field data and model predictions

Fig. 4: Measured (in July 1994) and model-predicted plumes (concentration in

mg/L) a. BTEX, b. Oxygen. c. nitrate. Data from Lu et al. (1999)




255

at the end of the simulation period. The results show that the model has predictedthe overall plume patterns reasonably well. In addition, the model also closely

predicted the plume front locations. Mass balance analyses indicated that the

computed total mass of BTEX in the aquifer at the end of one-year simulation periodis close to the total mass estimated from field observations; the overall difference

was less than 10%. A detailed sensitivity analysis was completed to quantify the

uncertainly associated with various model parameters and these results are discussedin Lu et al. (1999).

4. SUMMARY AND CONCLUSIONS

Contamination of groundwater aquifers by petroleum hydrocarbons is a widespreadwater resource management problem currently faced by both developed and

developing countries. This paper reviews the mathematical details of a public-

domain numerical code, known as RT3D, that can be used for modelling the fate andtransport of hydrocarbon plumes in groundwater aquifers. Details of three types of

hydrocarbon biodegradation models (listed in increasing levels of complexity), the

instantaneous aerobic reaction model, the kinetic aerobic model, and the kinetic

aerobic/anaerobic model are reviewed. Of central importance to this paper are theunderlying approximations made within the three models. The example problems

solved in the paper demonstrate the limits of these approximations. Clearly, theinstantaneous reaction model is the simplest model and can be used to predict

natural degradation processes at most aerobic sites. Perhaps this method could also

be extended for anaerobic sites, by using an effective stoichiometric value, if large

amounts of electron acceptors are available. The kinetic aerobic model is the most

complex description for the aerobic problem and it can provide useful details aboutthe patterns of microbial growth which can used for quantifying hydraulic

conductivity reductions and associated bioclogging effects. The coupled aerobic-

anaerobic model discussed in this paper is a simple first-order description formodelling the coupled aerobic-anaerobic electron acceptors processes. It can be

used for predicting the natural attenuation patterns of large-scale hydrocarbon

plumes. However, it is important to note that the first-order rates assumed in the

aerobic-anaerobic model are bulk decay rates and they ignore the heterogeneousnature of the microbial growth and decay processes. Each of the three reaction

models has its own advantage, and the choice would depend on the type of

management question one wants to address. The example problems discussed inthis work also demonstrate how different types of reaction kinetic models can be

coupled and solved within the generalized RT3D reactive-transport-modelling

framework.

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256

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