Documentation and Applications of the Reactive Geochemical ... · reactive transport simulations in...
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NUREG/CR-6871 I I i i Documentation and Applications of the Reactive Geochemical Transport Model RATEQ Draft Report for Comment U.S. Geological Survey U.S. Nuclear Regulatory Commission Office of Nuclear Regulatory Research Washington, DC 20555-0001
Transcript of Documentation and Applications of the Reactive Geochemical ... · reactive transport simulations in...
NUREG/CR-6871
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iDocumentation and Applicationsof the Reactive GeochemicalTransport Model RATEQ
Draft Report for Comment
U.S. Geological Survey
U.S. Nuclear Regulatory CommissionOffice of Nuclear Regulatory ResearchWashington, DC 20555-0001
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NUREG/CR-6871
Documentation and Applicationsof the Reactive GeochemicalTransport Model RATEQ
Draft Report for CommentManuscript Completed: March 2005 -
Datc Published: June 2005
Prepared byG.P. Curtis
U.S. Geological SurveyMenlo Park, CA 94025
J.D. Randall, NRC Project Manager
: DPrepared forDivision of Systems Analysis and Regulatory EffectivenessOffice of Nuclear Regulatory ResearchU.S. Nuclear Regulatory CommissionWashington, DC 20555-0001NRC Job Code Y6462
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COMMENTS ON DRAFT REPORT
Any interested party may submit comments on this report for consideration by the NRC staff.Comments may be accompanied by additional relevant information or supporting data. Please - --
specify the report number NUREG/CR-6871, in your comments, and send them by September30, 2005, to the following address:
Chief, Rules Review and Directives BranchU.S. Nuclear Regulatory Commission iMail Stop T6-D59Washington, DC 20555-0001
An electronic version of the report is available in Adobe Portable Document Format athttp://www.nrc.gov/reading-rm/doc-collections/nuregs/contract/cr6871.pdf and can be read withAdobe Acrobat Reader software, available at no cost from http://www.adobe.com. The reportand the computer files for the test cases discussed therein are available athttp://wwwrcamnl.wr.usgs.gov/rtm.
Electronic comments may be submitted to [email protected].
For any questions about the material in this report, please contact:
John D. RandallMS T9C34 aU.S. Nuclear Regulatory CommissionWashington, DC 20555-0001Phone: 301-415-6192E-mail: jdrenrc.gov
ABSTRACT
The computer program RATEQ implements a numerical method for simulating reactive transport inporous media. For RATEQ simulations, groundwater flow is simulated using MODFLOW-2000. Thereactive transport simulations in RATEQ are built on MT3DMS. RATEQ is intended for a wide range ofapplications involving biogeochemical reactions governed by rate- or equilibrium-controlled reactions.This report documents the input requirements and the output capabilities of RATEQ. The report alsopresents a number of example simulations illustrating the capabilities of RATEQ. The examplesimulations include five benchmark simulations that compare results obtained with RATEQ with resultsobtained independently. Simulations of U(VI) transport at the UMTRA site near Naturita, CO, are alsodescribed. Finally, several addition simulations are included that illustrate the application of RATEQ toproblems with immobile zones, redox-controlled reactive transport, and biogeochemical transport.
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Foreword
The U.S. Nuclear Regulatory Commission (NRC) uses environmental models to evaluatethe potential release of radionuclides from NRC-licensed sites. In doing so, the NRC recognizesthat, at many sites, groundwater-related pathways could contribute significantly to the potential dosereceived by members of the public. Consequently, consistent with its mission to protectthe health and safety of the public and the environment, the NRC and others have developedcontaminant transport models to predict the locations and concentrations of radionuclides in soilas a function of time.
Because many radionuclides temporarily attach, or adsorb, to the surfaces of soil particles,their mobility is reduced compared to that of compounds that move with the groundwaterwithout interacting with solid surfaces. As a result, most subsurface-transport models usedby the NRC and its licensees estimate the effects of the anticipated interactions betweenradionuclides and solids in the ground. Toward that end, these subsurface-transport modelsuse a "distribution coefficient," which is assumed to be constant and reflects the proportion ofradionuclide in the groundwater compared to the radionuclide associated with the solids in theground. These distribution coefficients are widely used by licensees and, consequently, therelevant literature documents ranges of their values for various soil types and radionuclides.However, the documented ranges can be very large because the chemical reactions that causeradionuclides to attach to solids are very sensitive to water chemistry and soil mineralogy.As a result, uncertainties in the parameters used to characterize the adsorption of radionuclidesin soils have been identified as a major source of uncertainty in decommissioning, uranium recovery,and radioactive waste disposal cases evaluated by the NRC.
Surface-complexation and ion-exchange models offer a more realistic approach to consideringsoil-radionuclide interactions in performance-assessment models. These models can alsoaccount for variable chemical environments that might affect such interactions. This reportdescribes the theory, implementation, and examples of use of the RATEQ computer code,which simulates radionuclide transport in soil and allows the use of surface-complexationand ion-exchange models to calculate distribution coefficients based on actual site chemistry.
The RATEQ code will help the NRC staff define realistic site-specific ranges of the distributioncoefficient values used to evaluate NRC-licensed sites. In site-remediation cases, such asrestoration of the groundwater aquifer in and around uranium in-situ leach mining facilities,the RATEQ code can aid in the estimation of restoration costs by estimating the volume of treatmentwater needed to restore sites to acceptable environmental conditions.
(dart J. Paperiello, DirectorOffice of Nuclear Regulatory Research
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CONTENTS
ABSTRACT ........................... iii
FOREWORD ............- v
FIGURES............................................. .......... ix
TABLES .............. ; ; xi
1. INTRODUCTION .................................. I1.1 MODEL OVERVIEW ........................ I
1.1.1 Model Input .............. 2 -; ; .;.21.1.2 Model Output .............. 21.1.3 Model Applicability and Limitations .................................. 2
1.2 PURPOSE AND SCOPE..2....................;. ; 2
2. MODEL EQUATIONS AND ASSUMPTIONS 5...............................................2.1 INTRODUCTION ............................................... 52.2 REACTION STOICHIOMETERY ............................................... 52.3 TRANSPORT EQUATION ............................................... 62.4 MULTICOMPONENT TRANSPORT ............................................... 82.5 EQUILIBRIUM EQUATIONS . .............................................. 8
2.5.1 Dissolved Species and Precipitated Phases ............................................ 92.5.2 Surface Complexation .102.5.3 Ion Exchange .12
2.6 RATE EXPRESSIONS .122.7 GROUNDWATER FLOW EQUATION . 142.8 DARCY'S LAW ............. ; 152.9 OVERVIEW OF NUMERICAL SOLUTION ......................................... 15
3. COMPUTER PROGRAM STRUCTURE AND INPUT . . ....................................... 173.1 INTRODUCTION ......................................... 173.2 GROUNDWATER FLOW ......................................... 173.3 RATEQ MODEL INPUT ......................................... 19
3.3.1I Name File .193.3.2 Array Reader .213.3.3 Transport and Reaction .23
3.3.3.1 Basic Transport File .233.3.3.2 Advection .293.3.3.3 Dispersion .293.3.3.4 Source/Sink .303.3.3.5 Generalized Conjugate Gradient Package .33
3.3.4 Reaction Database file .333.3.4.1 Description of Rate Laws Implemented in RATEQ .38
3.3.5 Geochemical Solver File .413.3.5.1 Setup Data Block .413.3.5.2 Reactions Data Block .433.3.5.3 Calculations Data Block .453.3.5.4 Output Data Block .47
3.3.5.5 Initial Conditions Data Block .................................................. 493.3.5.6 Timed Events Data Block ...................................................... 50
4. BENCHMARK SIMULATIONS ............................................................... 514.1 INTRODUCTION ............................................................... 514.2 BATCH CALCULATIONS ............................................................... 51
4.2.1 Naturita Groundwater Speciation ....................................................... 514.2.2 Simulation of Rate-Controlled Reactions in Batch .................................... 524.2.3 Adsorption of Cd+2 by Ferrihydrite ...................................................... 54
4.3 ONE DIMENSIONAL REACTIVE TRANSPORT SIMULATIONS . . 604.3.1 Rate-Limited Sorption, Aqueous Speciation and Biodegradation .................. 604.3.2 Equilibrium-Controlled Heterovalent Ion Exchange ................................. 64
5. REACTIVE TRANSPORT SIMULATIONS RELATED TO THENATURITA SITE ............................................................... 705.1 INTRODUCTION ............................................................... 705.2 TRANSPORT IN LABORATORY COLUMNS WITH KINETICALLY
CONTROLLED SORPTION REACTIONS ................................................... 705.3 TWO-DIMENSIONAL REACTIVE TRANSPORT AT THE NATURITA
FIELD SITE ............................................................... 705.3.1 Domain ............................................................... 705.3.2 Recharge ............................................................... 755.3.3 San Miguel River ............................................................... 755.3.4 Simulation Results ............................................................... 75
5.4 EFFECT OF HETEROGENEITY ON TRANSPORT AT THE NATURITASITE ............................................................... 76
6. EXAMPLE SIMULATIONS ............................................................... 816.1 INTRODUCTION ............................................................... 816.2 TRANSPORT WITH IMMOBILE ZONES ......................................................... 816.3 TRANSPORT WITH REDOX REACTIONS ....................................................... 836.4 SIMULATIONS OF BIOGEOCHEMICAL TRANSPORT ...................................... 84
APPENDIX 1: TRANSFORMATION OF REACTIVE TRANSPORT EQUATIONS ...................... 94
REFERENCES ............................................................... 95
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FIGURES
4.1 Comparison of simulated concentrations computed using RATEQ and FITEQL .................... 53
4.2 Comparison of simulated concentrations computed using RATEQ and MATLAB ................. 58
4.3 Comparison of simulated percent of Cd2 adsbrbed computed using RATEQand FITEQL and the diffuse layer model ............................... ; .; 58
4.4 Comparison of RATEQ and PHREEQC simulation results for the Tebes-Stevensand Valocchi (1997) benchmark problem.'.' ............................. 64
4.5 Comparison of RATEQ and PHREEQC simulation results for the heterovalention exchange benchmark problem .68
4.6 Comparison of RATEQ and PHREEQC simulation results for the heterovalention exchange benchmark problem for the case where Ho exchange wasnot included .69
5.1 Simulated rate-controlled transport of U(VI) in laboratory columns using theflow interruption technique .74
5.2 Location of groundwater wells and contoured elevations of the bottom ofalluvial aquifer .75
5.3 Predicted temporal evolution of U(VI) concentrations in the alluvial aquiferof the Naturita UMTRA site, Colorado .76
5.4 Summary of measured specific surface area and hydraulic conductivitymeasured at the Naturita field site .77
5.5 Ten realizations of the spatial distribution of specific surface area (m2/g)generated by sequential Gaussian simulation .79
5.6 Ten realizations of the spatial distribution of log KH (mis) generated bysequential Gaussian simulation .79
5.7 Ten simulations of U(VI) transport that used a fixed KH and spatiallyvariable Asp.................................8.......................................................80
5.8 Ten simulations of U(VI) transport that used spatially variable KH and afixed Asp .80
6.1 Comparison of U(VI) transport simulations assuming immobile zones (x)and no immobile porosity (-) .83
6.2 Simulated concentration profiles after 3 pore volumes of an oxidizing solutionhaving entered a reducing zone containing pyrite and uraninite .86
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6.3 Two-dimensional cross section used for biogeochemical transport simulations .87
6.4 Two-dimensional biogeochemical simulations results for oxidation of lactateby multiple terminal electron acceptors at pH 6.5 .91
6.5 Two-dimensional biogeochemical simulations results for oxidation of lactateby multiple terminal electron acceptors at pH 7.5 .92
6.6 Two-dimensional biogeochemical simulations results for oxidation of lactateby multiple terminal electron acceptors, including U(VI), at pH 7.5 .93
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TABLES
3.1 MODFLOW Packages and Support Status by Link-MT3DMS and RATEQ ........................... 18
3.2 Format LMT Input File ............................................................................. 18
3.3 Summary of Input Files Required for a RATEQ Simulation .......................................... 20
3.4 Example of the Namefile .......................................... 20
3.5 Alternative Input Formats of Array Reader .......................................... 22
3.6 Printing Formats Corresponding to the IPRN Code ..................................................... 23
3.7 Summary of Input Required for the BTN Package ..................................................... 25
3.8 Summary of Input Required for the ADV Package ..................................................... 29
3.9 Summary of Input Required for the DSP Package ..................................................... 30
3.10 Summary of Input Required for the Source-Sink Package ............................................... 30
3.11 Summary of Input Required for the GCG Package ..................................................... 33
3.12 Summary of Input Information in the Reaction Database file .......................................... 34
3.13 Summary of Reaction Options for Geochemical Reactions in RATEQ ............................... 38
3.14 Summary of Reactions Options in Benchmark and Example Simulations ........................... 41
3.15 Summary of Input in the Setup Data Block ..................................................... 42
3.16 Summary of Input in the Reactions Data Block ..................................................... 43
3.17 Summary of Input in the Calculations Data Block ..................................................... 46
3.18 Summary of Input in the Output Data Block ..................................................... 48
3.19 Summary of Input in the Initial Conditions Data Block ................................................. 49
3.20 Summary of Input in the Timed Events Data Block ..................................................... 50
4.1 Composition of Groundwater at Well NAT26 at the Naturita UMTRA Site ......................... 51
4.2 RATEQ Input File for NAT26 Groundwater Speciation Calculation ................................. 52
4.3 Summary of Parameter Values in the Batch Kinetic Simulation ....................................... 54
4.4 RATEQ Input File for Batch Kinetic Rate Law ..................................................... 55
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4.5 Summary of Predominant Reactions for Adsorption of Cd+2 by Ferrihydrite ........................ 57
4.6 RATEQ Input File for Batch Adsorption of Cd 2 by Ferrihydrite Usingthe Diffuse Double layer Model ........................................................ 59
4.7 Model Parameters for the Tebes-Stevens Benchmark Simulation ..................................... 61
4.8 RATEQ Input File for the Tebes-Stevens Benchmark Simulation ..................................... 61
4.9 Assumed Groundwater Composition for Ion Exchange Benchmark Simulation ..................... 65
4.10 Ion Exchange Reactions and Equilibrium Constants ..................................................... 65
4.11 RATEQ Input File for the Ion Exchange Benchmark Simulation ...................................... 65
5.1 Input File for Flow Interruption Simulations ........................................................ 71
5.2 Basic Transport File for Spatially Variable Surface Site Concentrations .............................. 78
6.1 Input for Simulating Transport with Immobile Zones ................................................... 81
6.2 Input File for Uranium Roll Front Simulation ........................................................ 84
6.3 Input File for Biogeochemical Transport Simulation ................................................... 88
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1. INTRODUCTION
The fate and transport of chemicals such asradionuclides in groundwater aquifers isaffected by both the flow of ground water,and by geochemical reactions. Computermodels are often used to simulate thereactive transport of radionuclides ingroundwater in order to predict futureconcentrations and subsequently the dose.These computer models therefore mustsimulate the groundwater flow whichaccounts for fluid sources and sinks and''changes of storage within the aquifer. Inaddition, the models must simulate theeffects of advection, dispersion, diffusion -and geochemical reactions on radionuclidetransport.
MODFLOW-2000 (Harbaugh et al., 2000)is one of the most widely used models for ;simulating groundwater flow. This model iscapable of simulating transient or steadystate flow in three dimensional confined orunconfined aquifers. MODFLOW-2000(Harbaugh et al., 2000) is applicable tomany near-surface groundwaterenvironments that have constant temperatureand fluid density. MODFLOW-2000,however, does not have the capability tosimulate solute transport, but the modelMT3DMS (Zheng and Wang, 1999)provides an approach for using thegroundwater flow simulation resultsobtained using MODFLOW-2000 tosimulate transport of multiple species thatcan participate in simple rate or equilibrium.controlled adsorption reactions.
The computer program RATEQ,-which is . ;described in this report, extends thecapability of MT3DMS to simulate multi-component, reactive solute transport inthree-dimensional ground-water flow ,systems. A wide variety of geochemicalreactions can be simulated using RATEQincluding aqueous complexation,precipitation-dissolution, surfacecomplexation, ion exchange,oxidation/reduction and formation of
separate gas phases. Any of the reactionscan be specified as either rate or equilibriumcontrolled. The reaction rates can berepresented by a wide array of reaction ratelaws including variable order kinetics, mass'action or 'Transition State Theory' kinetics,Monod kinetics, and user defined rate laws.Thus, RATEQ replaces the simple reactionpackage available in MT3DMS with a fairlygeneral geochemical reactions package. Akey advantage of RATEQ is thatmulticomponent geochemical reactions canby added to a groundwater flow modelimplemented using MODFLOW-2000.Simple one dimensional simulations canalso be conducted independently ofMODFLOW-2000.
1.1 Model Overview
This section briefly summarizes the input tothe model, options for producing modeloutput, and describes the applicability andlimitations of the model.
In two- and three- dimensional simulations,RATEQ is intended to be used withMODFLOW 2000 which is used to simulategroundwater flow. After MODFLOW-2000is run, RATEQ is used to simulate reactivetransport. Because RATEQ is an extensionof MT3DMS, all of the major processes thatcan be simulated with MT3DMS can besimulated using RATEQ. These processesinclude advection, dispersion, and exchangebetween mobile and immobile zones.
RATEQ is written in Fortran-90. All arrays'are allocated dynamically and allcalculations are conducted using doubleprecision. Computational requirements forsimulations conducted with RATEQ varysignificantly with the dimensionality of thedomain and with the number of chemicalcomponents. Simple one dimensionalsimulations with a few components mayrequire substantially less than a minutewhereas multidimensional simulations
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involving 105 to 106 nodes and 10 or morecomponents could require hundreds of hoursor more to complete.
1.1.1 Alodel InputThe majority of the model input for areactive transport simulation using RATEQconsists of multiple files that specify themodel input for MODFLOW-2000 andMT3DMS. The files that are commonbetween MT3DMS and RATEQ includethose that describe, (1) the generalproperties of the domain and the initialconditions, (2) the input to the advection,dispersion and diffusion, and source-sinkpackages, and (3) the input for thegeneralized conjugate gradient solver. Twoadditional files are required for RATEQ.The first file contains a list of geochemicalreactions which describes the reactionstoichiometry, the associatedthermodynamic data and a description ofany kinetic rate laws. This file is looselybased on the PHREEQC thermodynamicdatafile format. The second additional filespecies the composition of each of varioussolutions that are used to represent the initialconditions and the composition of each ofthe various fluid sources and associatedmineral phases and reactive surfaces.Finally, the last new input file specifies thethree dimensional spatial distribution ofeach of the solutions in the initial conditions.
1.1.2 Model OutputThe most important model output fromRATEQ consists of (I) the results ofspeciation calculations that are conducted sothat the concentrations in the reactivedomain and in the fluid sources can beinitialized, (2) concentration histories at agiven location, (breakthrough curves) and(3) concentrations distributions at a giventime (concentration snapshots). For theselatter two output files, the output can becustomized so that the output file is createdat specific times and can contain theconcentration of selected species or selectedcomponent concentrations.
The breakthrough curves and concentrationsnapshots can be written using a userspecified format, or they can be writtenusing the MT3DMS list directed format. Inthis latter case, the simulated concentrationscan be visualized using Model Viewer(Hsieh and Winston, 2002). Alternatively,on the windows platform, simulation resultscan be visualized using compiled Matlab®scripts provided with RATEQ.
1.1.3 Model Applicability andLimitationsRATEQ can simulate reactive geochemicaltransport in fully saturated confined orunconfined aquifers and in laboratorycolumn studies. It is assumed that the flow isnot impacted by variable temperature orvariable fluid density. Changes in fluid flowbecause of variable porosity that resultsfrom the formation or dissolution of newsolid or gaseous phases are not considered.Geochemical activity coefficients arecomputed using either the Davies equationor the extended Debye-Huckel equation andtherefore the model is not appropriate forionic strengths exceeding approximately0.1M.
1.2 Purpose and Scope
This report first documents the RATEQcode which is derived from the MT3DMSmodel (Zheng and Wang (1999). MT3DMSand therefore RATEQ have been created towork with MODFLOW-2000 (Harbaugh etal., 2000). This report is intended only toserve as documentation of RATEQ and doesnot fully document MODFLOW-2000 orMT3DMS. The users are referred toHlarbaugh et al. (2000) and Hill et al (2000)for more information on MODFLOW-2000,and to Zheng and Wang (1999) for moreinformation on MT3DMS. However, thisreport does contain documentation for theMT3DMS packages used in RATEQ.Specifically, this report describes the inputrequired for the basic transport, advection,dispersion, source-sink, and generalizedconjugate gradient packages available in
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both MT3DMS and RATEQ. The user isreferred to Zheng and Wang (1999) for adescription of the MT3DMS reactionspackage.
This report first describes the simulationsetup and operational procedures forconducting reactive transport simulationsusing RATEQ. The report then presentsresults of several benchmark test problemswhere simulation results obtained withRATEQ are compared directly with resultsobtained with other geochemical or reactivetransport codes. The remainder of the reportpresents simulation results for a wide varietyof reactive transport scenarios.
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2. MODEL EQUATIONS AND ASSUMPTIONS
2.1 Introduction
The first section of this chapter describes theapproach used to simulate transport influencedby multiple interacting geochemical reactions.This is presented together with a descriptionchemical equilibrium equations, surfacecomplexation equations, ion exchangeequations, and the rate laws applicable to thegeochemical reactions. Subsequently, therelation between the a'dvection,' dispersion,reaction equation and the groundwater flow -
equation is described. Finally, the generalprincipals of the numerical solution areoutlined.
2.2 Reaction Stoichiometry
The transport of multiple reacting species in,porous media is intricately related to thereaction stoichiometry." Chemical reactions'can be written using several differentapproaches. In some approaches, a set ofprimary or master species is defined and allother species, termed the secondary species,are formed from the primary species. Theapproach used in RATEQ is simply to definestoichiometrically balanced reactions fromwhich the required mass balance constraintsare derived. This second approach has the-advantage that primary species that havenegligible concentrations over a wide range ofchemical conditions can be ignored in somesimulations. This can yield a slightimprovement in numerical performance whichcould become significant if many simulationsare conducted as in a Monte Carlo analysis.
In this report, the reactions are expressed inmatrix form since this approach is quite ,general and yields equations that can bemanipulated using linear algebra. Allreactions treated here are written with allspecies on one side of the equatioin using theconvention that products have positivestoichiometric coefficients. In the general
case, the set of NR interacting reactionsinvolving NT species can be written as
[vcIA]= o (2-1)
where v, is a matrix of stoichiometriccoefficients containing NR rows and NTcolumns and A is a column vector containingNT chemical symbols [Smith and Missen,1982]. The system of NR reactions canconsist of NR. aqueous reactions, Np_ surfacereactions and NRp precipitation-dissolutionreactions. Similarly, the NTspecies consists ofN, aqueous species, N, surface species and NPsolid species. Writing the reactions in thisform has several advantages: (1) the approachcan be applied to all stoichiometricallybalanced reactions; (2) the mass balanceequations can be derived from v, as describedbelow; (3) the mass action expressions aredirectly related to v.; and (4) the approacheliminates the need to express all reactions interms of a primary species.
For example, the formation of UO 2(CO3)3'2-from U02
12 and C032 is
U02*2 + 3Co32 -= UO 2 (CO 3 )3 4 (2-2)
This reaction can also be writte'n''in the~standard form of equation 2-1:
UO22 - 3C0 32 - + UO2 (CO3 )3 4 =0 (2-3)
where the convention that the stoichiometriccoefficients of reactants are negative and thestoichiometric coefficients of products arepositive is used. In matrix form, Equation 2-3is
[-I -3 = 0 (2-4)
5..
where the elements of the row vector [ -1 -3 1] are the stoichiometric coefficients of thereactants and the column vector contains thesymbols of the chemical species considered.The approach can be readily extended toconsider pultple species. For example, thereactions for the formation of U0 2(C0 3)3 ,U0 2(CO3 )j2 , U0 2CO3 and are
Xci N R-t = Zvi~
Otj=I(2-6)
where Rj is the rate of reaction j and NR is thetotal number of reactions. Thus, for a systemof reactions, the change in concentration in aclosed system is given by
[i 1II
- 3-2
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I
0
0
0
1
0
0
0
iJ
UO+22
CO- 23
U0 2 (CO3 )34
U02 (CO3 ) 22
U02 C03
=0
,IC-= [VIT(2-7)at
where C is a vector of concentrations, [kyr isthe transpose of the reaction stoichiometrymatrix defined in equation 2-1 and R is avector of reactions rates.
2.3 Transport Equation
The mass balance equation for each reactingspecies in a groundwater flow system is theadvection-dispersion-reaction equation. Thisis a partial differential equation which can bewritten as follows for the fate and transport ofspecies k in 3-D groundwater flow systems:
(2-5)
The purpose of the remaining part of thissection is to illustrate the relation betweenstoichiometry matrix, v, and the reaction rates.The change in concentration of species iresulting from all reactions
+ m_ (= (0D1j M s + E Vk,rRrat at a aJ ) )x r=1(2-8)
where the Einstein summation convention onthe repeated indices i and j applies, and
Crk - dissolved concentration of species k inthe mobile zone, (ML-3)
ckm = dissolved concentration of species k inthe immobile zone, (ML- 3)
Omr= porosity of the mobile zone in thesubsurface medium, (dimensionless)
0im= porosity of the immobile zone in thesubsurface medium, (dimensionless)
xi = distance along the respective Cartesiancoordinate axis, (L)
-k = equals I if species k is mobile and 0otherwise (dimensionless)
D 1j = hydrodynamic dispersion coefficienttensor, as described below (L2T')
qs= volumetric flow rate per unit volume ofaquifer representing fluid sources(positive) and sinks (negative), (T'l)
NR = the number of reactions in thegeochemical network, (dimensionless)
Rrk = the rate of production of the k'th species
by the rth reaction (ML 3 T').
t= time, (T)
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When the solute transport is simulated usingthe dual porosity domain approach, Equation2-8 must be coupled with an equation thatfthatdescribes the rate of mass transfer into theimmobile zone:
8(0 k (2-9)=kla (Cm im
where
kia = first-order mass transfer rate between themobile and immobile domains (T').' Equation'2-9 applies to the diffusive exchange of asolute between two fluid compartments andtherefore only applies to dissolved species.-.
Vk= groundwater velocity in the k"h direction(k-ij) (LT'), and
vi = the magnitude of the velocity (LT').
It is has been observed in several field studiesthat 'transverse spreading in the verticaldirection is much smaller that transversespreading in the horizontal direction. 'Tosimulate this effect, Burnett and Frind (1987)made an ad hoc modification to equation 2-10to allow different dispersivities in thehorizontal and vertical directions. These
,modifications are included in MT3DMS andtherefore RATEQ and can be writtenexplicitly as
Hydrodynamic dispersion in porous media,which is included in Equation 2-10, refers Ithe spreading of contaminants that resultsfrom deviations of actual velocity on amicroscale from the average groundwatervelocity, and from molecular diffusion dri%by concentration gradients. Molecular --diffusion is often negligible compared witheffects of mechanical dispersion, and is onlimportant when groundwater velocity is vesmall.
The hydrodynamic dispersion tensor, Dij, ftan isotropic porous medium, is defined as(Bear, 1979)
Dij (Dm + aTivl}ij + T(aL (
where
2 2
to' DXX =aL l +a lI
(2-11)
ren Dv 2 2'D aL+aTHI +aTV v +Dm
the = I lV I Ivi(2-12)
ry2 22
Dlvia lvii.(2-.13)
xy =Dyx =(aL - ) vxvl . vi
(2-14)
(2-15)L DxzD=(aL'-aTV)vxvz-vi
Dj = a component of the dispersion tensor.L ) ' ; I . ' . ": : !.-' 4lrl), -
D.= molecular diffusion coefficienit (LT): "1 :
DYZ = DZY = (aL-caTV) vyvyNV
- (2-16)
aL = the longitudinal dispersivity (L),: .... . _: ,
aT= the transverse dispersivity (L),
I... . ..
.;q ,....~
j _.
where a-n, is the transverse dispersivity in thehorizontal direction and arv is the transversedispersivity in the vertical direction.Equations 2-12 through 2-16 reduce toequation 2-11 for the case where aTH equalsaTv.
Oj = Kronecker delta' that equals I if i j, and -zero othervise (dimensionless),
7
2.4 Multicomponent Transport IN R = a NR X NR identity matrix .
Equations 2-8 describes the transport of asingle species in a porous medium. Thepurpose of this section is to consider all of thespecies in the reacting system and thendevelop the set of transport equations solvedin RATEQ. First, it is useful to rewriteequation 2-8 for the complete set of species as
et (Qmrm + OimCim)L (C)+ vR (2-17)
where
L t- Dij c3km - a (Ovicm +Scs
as described in equation 2-8 if species m is
mobile and L = 0 if species m is immobile.
Equation 2-17 is a system of equationsrepresenting the transport and reaction of eachspecies. This system of equations is nottypically solved in a reactive transportsimulation because, in part, the reaction ratesare not known for each of the reactions; manyreactions are assumed to proceed sufficientlyfast that the reactions can be approximated asan equilibrium process.
Equation 2-17 can be transformed using linearalgebraic methods to yield a new set ofequations that isolate reaction rates intoseparate equations. Approaches foraccomplishing this transformation aredescribed in Appendix 1. The result of thesetransformations is a set of equations with thefollowing form:
a(Onm, + OimVim) L(V)+[INR ]R(2-18)
where
V a vector of primary dependent variablesfor the transport PDEs, and
Because linear transformations are used indeveloping equation 2-18, the primarydependent variables are linear combinations ofthe species concenctrations:
V = [S]C (2-19)
where
S = a matrix resulting from the lineartransformations and
C = of the concentration of each of thespecies. A key assumption made informulation equation 2-19 is that a singledispersion coefficient applies to all dissolvedspecies. If species-dependent diffusion mustbe considered, then the fIll set of equations in2-18 needs to be retained.
Equation 2-18 is a set of equations thatconsists of NR equations that each containingone reaction rate term in each equation andNT-NR equations that do not contain anyreaction rates. These latter equations that donot contain rate terms can be interpreted asmass balance equations for a set of primary orbasis species.
Equation 2-18 consists of NT equations for theNT unknown concentrations. In RATEQ, if arate law is specified in the input as describedin chapter 3, then the corresponding equationin 2-18 is retained and used in the numericalsolution. Conversely, if the rate law is notspecified, then the transport equation for thereaction in 2-18 is replaced by thecorresponding equilibrium expression.
2.5 Equilibrium Equations
The mass action expressions for theequilibrium controlled reactions depend on thetype of reaction because chemical activitiesare treated differently depending on whether aspecies is dissolved in an electrolyte, presentas a separate phase, or adsorbed to a surface.
8
111
This section summarizes the kinds of massaction expressions used in RATEQ for the -
different types of reactions.
2.5.1 Dissolved species andprecipitated phases.
1n = a' III + ai°Bj
(2-22)
where,
ys = the activity coefficient of the ith species,
For dissolved species the mass actionexpression is
A,-B = Debye-Htickel parameters,
-4 !;- a,'= the hydrated ionic radius, and
Ki = flai Y('.D* j=1,
- (2-20) b = ion pair interaction parameter.
where
N. = the number of aqueous species,
K; = the equilibrium constant of the i6'reaction,
aj = the activity of species j and
VM(i,j)= the stoichiometric coefficient of
species j in reaction i. VM is a subset vc thatrepresents the equilibrium controlled aqueousspeciation reactions.
In RATEQ, the activities of solid phases are'assumed to equal unity. The activities ofsolution species are related to theconcentrations by
ai =yiCi (2-21)
where
'y is the activity coefficient [Stummm andMorgan, 1996].
The activity coefficient can be computed fromone of several approaches available inRATEQ. In the first approach, the activitycoefficients of species in electrolyte solutionscan be represented by the Debye-Hickelrelation
The variable I in equation 2-22 is the ionicstrength defined by
I =-Yz iCi2 H
(2-23)
where zi is the charge of the iih species.
In addition to the Debye-HIickel relation, othermethods for computing activity coefficientsinclude the Davies equation defined as
Inyi =- __ 0-21i +i 0.21
(2-24)
and the extended Debye-Htckel
Z.n. 1- -+a.lny;l=- I'
+ I + a13-/1(2-25)
where a and B are extended- Debye-Huckelparameters. -
RATEQ only simulates isothermal conditions,but the temperature the fixed temperature canbe set in the input file.' When a'simulation isconducted at temperatures other than 25C, theequilibrium constant can be computed usingone of two approaches. In the first approach,
9..
the equilibrium constant at a giventemperature can be computed from
InlKT =lIn K29 8 'H (I-I (2-26)R (298 T)
where
KT is the equilibrium constant at temperatureT,
AMI = the standard enthalpy of reaction,
T is the temperature in Kelvin, and
Alternatively, the equilibrium constant can becomputed from
logKT = Al + A2T + A3 + A4 logT +A2T2
2-27
surface charge and potential, all approachesshare two common attributes; (1) the Gibbsfree energy of adsorption is partitioned intochemical and electrostatic components and (2)and the properties of electrical double layer(EDL) adjacent to the surface are described bya model that relates surface potential andsurface charge.
Although many models have been proposed tosimulate the EDL, the only EDL modelsupported by RATEQ is the diffuse layermodel (DLM). In the diffuse layer model,mass action expressions for the adsorption ofan ion are modified by an electrostaticpotential term as described by
Kj =1 [a ij exp( RT (2-28)
where
where in
KT is the equilibrium constant at temperatureT,
A, to A5 are empirical coefficients,
T is the temperature in Kelvin, and
Log refers to base 10 logarithms
2.5.2 Surface complexationThe surface complexation modeling approachfor simulating the adsorption of ions is basedon the premise that adsorbed ions formcoordinative bonds with specific functionalgroups present on the adsorbing surface. Insurface complexation models, the surfacecharge varies as a result of both theaccumulation of ions at the surface and thedissociation of surface functional groups. Inaddition, the surface ions alter the electricalpotential at the adsorbing surface.
Although several approaches have beendescribed to account for the relation between
Az2 is the change in the change of the surfaceresulting from the jth reaction,
F is Faraday's constant,
Ps is the surface potential,
R is the gas constant, and
T is the absolute temperature
The relation between Ts and a, the surfacecharge resulting from the charged surfacespecies, also varies for different EDL models.In the DLM, the Ps and C are related by
a =-8xl03RTeco cl 1 2 sinh(ZVOF/RT)
(2-29)
where
R = gas constant,
10
'il
T = absolute temperature, This surface charge balance can be expressedas
E = the dielectric constant of water,
go = the permittivity of free space
c = the molar electrolyte concentration,
Z = the ionic charge for the symmetricalelectrolyte,
Ns NA.zs,+ .z CF =0j=1 i=1
(2-30)
where
Ns is the number of surface species,
T, = the surface potential, and
F Faraday's constant.
Although adsorption reactions generally result,in the accumulation of charge at mineral/waterinterfaces (Davis and Kent, 1990), quantifyingthe effects of this surface charge is oftendifficult for sediments and aquifer materialsbecause the surfaces of these materials areinherently complex. The non-electrostatic, - -
semi-empirical surface complexation model(SCM) neglects that actual accumulatedsurface charge should be balanced by acounter ion in the diffuse layer to maintain -
electroneutrality at the surface.
If the surface charge that forms because of theadsorption reaction is large enough, errors in 'major ion chemistry could result because the-surface cation is immobile while the counterions that actually balance the surface chargethat are present in the diffuse layer are mobile.For example, the surface charge resulting from'the formation of a surface cation could bebalanced by accumulation anions such asHC03- and C03
2 anions in the diffuse layer.'This could cause calcite to dissolve if presentand possibly change the solution pH..
zJ is the charge of the jh surface species,
Sj is the concentration of the jth surfacespecies,
NA is the number of the aqueous species,
z1 is the charge of the ih species, and
CF is the surface excess concentration of the
iVh species. The excess concentration of eachion is assumed to be given by
cF = fizil8ici (2-31)
where
f is a proportionality constant that applies toall ions,
zi is the charge of ih ion,
Bi is I if the charge z1 is opposite that of thesurface charge and is 0 otherwise, and
C1 is the concentration of the ion in bulkaqueous solution.
A direct approach of simulating counter ionsin the diffuse layer by integrating the charge--potential versus distance equations, [Parkhurstand Appelo, 1999] is not possible in the'semi-empirical approach because the electricaldouble layer is not included. Alternatively,adsorbed surface charge can be balancedempirically by removing ions from bulksolution to exactly balance the surface charge.
The approach of using the charge to weightthe immobilized concentrations is empirical inthis instance but is analogous to ionassociation models for dilute solutions.Equations 2-30 and 2-31 can be combined togive
11-
Ns
f = j=1NA 2
, 5i~zj-Ci=I
KNa\M = XNa{M}AY.{Na}
(2-34)(2-32)
Given this definition of f, the immobilizedsurface concentrations (Ci') can be calculatedfrom Equation 2-31. The combination ofequations 2-30 to 2-32 together with massbalance equations modified to account forimmobilized counter ions can be usedapproximate the sensitivity of modelsimulations to the development of surfacecharge.
2.5.3 Ion ErchanigeIon exchange reactions are similar to anonelectrostatic SCM in that the electricalfield at the mineral water interface is notexplicitly considered. The two primarydifferences between the nonelectrostatic SCMand the ion-exchange approach are; (I)reactive site in the ion exchange model isalways assumed to be occupied by an ionwhereas in the SCM approach the surfacecomplex can dissociate to yield a surface ionand (2) there are several commonly usedconventions for approximating the activities ofexchanged species in an ion exchange modelwhereas in the nonelectrostatic and DLMSCM the activity coefficients of the surfacespecies are assumed to equal unity.
where ,3 is the equivalent fraction which isassumed to represent the activity of theexchanged ion on the exchanger. RATEQconverts equivalent fractions to concentrationsand used the modified equilibrium constants inthe nonelectrostatic SCM
zNa+ + MXZ = Mz+ + zNaX (2-35)
and the corresponding equililbrium constant is
KNa\M = ( za Y (M}
PM {Na}(2-36)
where the symbols are as described above.
2.6 Rate Expressions
Three types of rate laws are available include:(I) simple stoichiometric rates laws, (2) massaction kinetics, and (3) multiple Monodkinetics.
The first option in RATEQ for simulating areaction rate considers separate terms for theforward and backward rates of reaction asillustrated by
In RATEQ, ion exchange simulations aresolved using the same computational routinesas used for the surface complexation reactions.Two approaches for approximating theactivities of exchanged complexes in RATEQare the Gapon convention and the Gaines-Thomas convention. In the Gapon approach,ion exchange reactions are written as
NT UrNT UrkRk = kf(k) HCIi -kb(k) ICi Flk (2-37)
i=l i=1
where
Rk is the rate of the kth reaction,
kfck) is the forward rate constant of the k"hreaction,
Na+ +)ZMXz =,ZMz+ +NaX (2-33)
The equilibrium constant for this reaction is
C; is the concentration of the ith species,
jzk is the coefficient for the ith species in
forward rate term,
12
4l
krk) is the backward rate constant of the k"hreaction, -' K= kf
kb(2-38)
Ik is the coefficient for the ith species inU..
backward rate term.
The coefficients of k and uik in 2-37 are notrequired to equal the stoichiometriccoefficients of the reaction. However, the thecoefficients equal the stoichiometric values'and if the values of kr and kb are related to thethermodynamic equilibrium constant by.
then this approach can be used to approximatetransport controlled by the local equilibriumapproximation which can be achieved if thevalue of kf is sufficiently large.
An alternative rate law usually applied to theprecipitation and dissolution of mineral phasesthat is supported in RATEQ is
NT UDk (I-Q(k /K(k)) mrk = Asp(k)kf(k) 11fi 1+ a"frak) (k) IK(k) a(k)
i=1 k(2-39)
where
A3pok) is the specific surface area of thereacting phase,
kf(k) is a forward rate constant,
Qk) is the ion activity product,
K(k) is the equilibrium constant,
m is an empirical coefficient,
fm is an empirical coefficient that limits thereaction rate for reactions that are far from
equilibrium and thus empirically accounts forthe fact that reaction rates are inherentlylimited by pore scale diffusion (Lichtner andFelmy, 2003).
6(k) is unity if the solid is present and zerootherwise and is used to assure that a phasecan not dissolve if it is not present.
The final rate law embedded in RATEQallows the rate of reaction to be simulatedusing the so-called Multiple Monod Kineticsand this approach is commonly used tosimulate microbially mediated reactions(Kindred and Celia, 1988; Essaid et al., 1995).In this model, the rate of reaction is given by
NT U Nm) Vmax(kCk ) Kl(,p) + Ckp
i=l j=k M(Mk,j) + Ckj) p= KI(k,p)+(2-40)
where .. ..
kf is a forward rate constant,
13
NT U0Hla. ik is a term that permits the specifici=I
catalysis by one or more species,
N,,Xk) is the number of Monod terms included inthe kt rate law,
Vmx(kj) is the maximum rate of substrateutilization,
Cki is the concentration of the substrateconsidered in the Monod rate law,
KM(ki) is the Monod half velocity coefficient,
Np~k) is the number of inhibition terms includedin the kit rate law,
Ck.p is the concentration of the p' inhibitingspecies,
spatially and be anisotropic (restricted to havingthe principal directions aligned with the gridaxes), and the storage coefficient may beheterogeneous. Specified head and specified fluxboundaries can be simulated as can a head-dependent flux across the outer boundary of thesystem being modeled. Such head-dependentfluxes allow water to be supplied to a boundaryblock in the modeled area at a rate proportionalto the head difference between a "source" ofwater outside the modeled region and theboundary block.
MODFLOW 2000 simulates constant densitygroundwater flow in aquifers under theassumption that the principal components of thehydraulic conductivity tensor are aligned withcoordinate axes of the model grid so that all ofthe nonprincipal components equal zero. Underthese assumptions, the groundwater flow partial-differential equation used in MODFLOW is(McDonald and Harbaugh,1988)
KI(kJ) is the inhibition constant of the pLh
inhibiting substance in the jth rate, and
f(AGtxN) is a function of the Gibbs free thatinsures that the rate of irreversible reactionsimulated by the Monod rate law equals zerowhen the reaction is energetically unfavored:
a Ki Oh )+qs =Ss hOxi ( xi cat
(241)
{ 1 if AGRXN<AGTHRf(AG ) -_ 0O if AGRXN 2AGTHR
where AGRXN is the Gibbs free energy ofreaction and AG-nR is at threshold free energy ofreaction and must be less than or equal to zero(Curtis, 2003).
2.7 Ground Water Flow Equation
MODFLOW-2000 simulates steady andnonsteady flow in an irregularly shaped flowsystem in which aquifer layers can be confined,unconfined, or a combination of confined andunconfined. Flow from external stresses, such asflow to wells, areal recharge, evapotranspiration,flow to drains, and flow through river beds, canbe simulated. Hydraulic conductivities ortransmissivities for any layer may differ
where
K; = the principal component of the hydraulicconductivity tensor, (L17');
h = the potentiometric head (L);
qs = the volumetric flux per unit volumerepresenting sources and/or sinks ofwater, with qs <0.0 for flow out of thegroundwater system, and qs >0.0 forflow into the groundwater system (T');
Ss= the specific storage of the porous material(L.a); and
t= time (T)
and it is assumed that the Einstein summationconvention applies in Equation 241.
The groundwater flow equation is solved inMODFLOW-2000 using the block-centeredfinite-difference approximation. The flow regionis subdivided into blocks in which the mediumproperties are assumed to be uniform. In planview the blocks are made from a grid of
14
:11
mutually perpendicular lines that rmay bevariably spaced. Model layers can have varyingthickness. A flow equation is written for eachblock, called a cell. Several solvers are provided.for solving the resulting matrix problem; theuser can choose the best solver for the particularproblem being simulated. Flow-rate andcumulative-volume balances from each type ofinflow and outflow are computed for each timestep.
The MODFLOW-2000 software includes thecapability to simulate several kinds of fluid - -sources and sinks including flow to and fromwells, recharge, evapotranspiration, rivers,streams, constant-head boundaries, drains, andlakes. However, as described below, not all ofthese fluid sources can be simulated usingMT3DMS and therefore they cannot besimulated using RATEQ.
0 = porosity of the subsurface mediumcontaining flowing groundwater,dimensionless
K; = principal component of the hydraulicconductivity tensor along Cartesian axis i,LT'
h = hydraulic head, L
x; distance along the respective Cartesiancoordinate axis, L
The linear groundwater velocities are computedin RATEQ using Darcy's Law and thevolumetric fluxes that are computed inMODFLOW-2000.
2.9 Overview of the NumericalSolution
Equation 242, when combined with boundaryand initial conditions, describes transient three-dimensional ground-water flow in aheterogeneous and anisotropic medium,provided that the principal axes of hydraulicconductivity are aligned with the coordinatedirections. Solution of this equation gives thegroundwater head and water fluxes for each ofthe fluid sources but the solution does notdirectly yield groundwater velocities.
2.8 Darcy's Law
The groundwater velocity is related to the flowequation through Darcy's Law
MT3DMS is designed to be independent ofMODFLOW-2000 and although MT3DMS ismost often used with MODFLOW, it can beused with any flow code that stores flow relatedoutput as defined by the LINK-MT3DMSpackage for MODFLOW-2000. MT3DMSindependently reads the unformatted filescreated by the LINK-MT3DMS package. Theunformatted file contains the MODFLOW-2000output required for conducting a transportsimulation. This output consists of modelgeometry, groundwater fluxes, the magnitude ofall fluid sources and other miscellaneousinformation as described elsewhere (Zhang etal., 2002). By using an unformatted file to savethe intermediate results the MODFLOW-2000results are stored without loss of accuracy.However, because different compilers usedifferent formats for the creating unformattedfiles, it is usually necessary that bothMODFLOW-2000 and MT3DMS or RATEQ becompiled using the same Fortran-90 compiler.MT3DMS supports many, but not all of thepackages that have been developed forMODFLOW-2000.
vi =qi =_ Ki OhOm OM Ax;
(243)
where
v; = seepage or linear pore water velocity, (LT),
qi ,groundwater flux (flow rate per unit area) ofaquifer representing fluid; (LT'), The set of transport (mass balance) equations
and mass action equations can be solved usingthe method of operator splitting. In the operatorsplitting method, the temporal derivatives are
15 -
split so that different processes are solvedseparately. MT3DMS uses operator splitting toseparately solve for the processes of advectionand dispersion. For example, for the i' transportequation, first advection is simulated by solving
Finally, the
Om At -Ri=O
and
NR p
n(yiCi)t = Kji=1
(245)
V;A - V9
At(2-43)
(246)and then dispersion simulated by solving
Om ¾i ,S +V*(-DVV 1)=OAt
(2-44) are solved simultaneously.
16
II
3 COMPUTER PROGRAM STRUCTURE AND INPUTI: .- . .
3.1 IntroductionThis section describes the model input that isrequired to conduct a reactive transportsimulation using RATEQ. Following theapproach used in MODFLOW-2000, input for 7
individual processes is supplied in separate files.-This approach is used in RATEQ.
- which activates the LMT package (version 6) inI MODFLOW-2000, attaches unit 66 to the LMT
input, and defines 'filename.lmt'tas the existinginput file containing the user-specified optionsfor controlling how to save the flow-transportlink file from MODFLOW-2000.
3.2 Groundwater Flow -Input to the Link-MT3DMS Package is readfrom the file that has the file type "LMT6" in the
MODFLOW-2000 is a comprehensive model for' _ name file. The LMT input file has the formatflow subject to illustrated in Table 3-2. All input records aresimulating groundwater IO Ugttomany .(fluid sources and sinks). preceded by a case-insensitive keyword. The
kIndsv of str eskes a t d .. _ underscore character must not be skipped. TheIndividualfollowing paragraphs describe the input recordseach kind of stress. Table 3-1 lists the packages - fleo.2i more detai.that are available in MODFLOW-2000 andwhether or not that inrticulnr nncrris -k - -
supported in MT3DMS, and therefore whetheror not the package is supported in RATEQ.
Each of the packages listed in Table 3-1 requires,a separate input file. In addition, input files arealso required to define the computational grid,specify what simulation results to save to output,and to control numerical methods used in the-simulation. A full description of all of thisoutput is beyond the scope of this report and hasbeen presented elsewhere (Harbaugh et al.,2000; see also citations listed in Table 3-1).
In addition to the packages listed in Table'3.1,;MODFLOW-2000 can be used with the 'LinkMT3DMS' (LMT) package. This packagecauses the MODFLOW-2000 code to save flow'--related simulation results in an unformatted--Fortran file. This file contains disciitization:-information, fluxes between cells; and source.and sink fluxes. The LMT package is described tin detail in Zheng et al., (2001).
The LMT package is activated by including anentry in the MODFLOW-2000 name file..Specifically, the name file must contain the line:
1mt6 66 filename.lmt
Record 1. FNAME is the name of the flow-transport link file produced by MODFLOW-2000 through the LMT6 Package for use by theMT3DMS transport model. Directory pathnames may be specified as part of Fname as in .-D:\ MF2K\ DATA\ TWRI\ TWRI . Theconvention for the file extension of the LMT6Package produced output file is designated as'FTL' for 'Flow-Transport Link'. If Fname isnot specified (left blank) after the keyword'OUTPUTFILENAME', or if the entirerecord including the keyword is missing, theoutput file is assigned the default name,"RootName.FTL", where "RootName" iswhatever file name is ass igned to the LMT6
-Package input file. For example, if the input file:to the LMT6 Package is named "TESTI. LMT",then the name for the LMT6 Package producedoutput file is "TESTI. FTL" by default.
Record 2. INFTL is the unit number on whichthe LMT6 Package produced output file will besaved. A positive, unique integer must be usedthat has not been associated with any other file.If an invalid input is entered, an error message iswritten to the MODFLOW-2000 LIST outputfile, and the program execution is terminated. IfINFTL is not specified by the user, or if the
Table 3-1. MODFLOW Packages and Support Status by Link-MlT3DMS and RATEQMODFLOW package name (Harbaugh et al., 2000; NIT3DNIS RATEQor as noted) Support Example'
Block-Centered Flow Yes 5.3, 5.4, 6.2Layer Property Flow Yes NT2
Horizontal Flow Barrier Yes NT'
River Yes 5.3, 5.4Recharge Yes 52,5.4Well YesDrain Yes 5.3Evapotranspiration Yes NTGeneral-Head Boundary Yes 6.2, 6.3
Time-Variant Constant [ead Boundary YesHydrogeologic Unit Flow (Anderman and Hill, Yes NT2000)Streamflow-Routing Yes NTReservoir Yes NTSpecified Flow and Head Boundary Yes NAvInterbed Storage No NATransient Leakage No NALake (Merritt and Konikow, 2000) No NADrain with Return Flow (Banta, 2000) No NA
Evapotranspiration with a Segmented Function No NA(Banta, 2000) No NA' Numbers refer to sections in this report2Flow package not tested with RATEQ3Flow package not available in RATEQ
Table 3.2 Format of LMIT Input FileRecord Keyword DescriptionI OUTPUT FILE NAME FNAME2 OUTPUT FILE UNIT INFTL3 OUTPUT FILE HEADER FHEADER4 OUTPUT FILE FORMAT FFORMAT
entire record including the keyword is missing,the output file will be saved on the default unitnumber of 333.
Record 3. FHEADER is a string that specifiesthe header structure of the LMT6 Packageproduced flov-transport link file. In MT3DMS,FHEADER can be either STANDARD orEXTENDED and the default value isSTANDARD.
For the STANDARD option, the Well, Drain,River, General Head Boundary, Recharge,Evapotranspiration packages are supported. Notethat the Time-Variant Specified Head (CHD)Package (Leake and Prudic, 1991) isautomatically supported since its functionality isimplemented through an internal flow package,such as the Block-Centered Flow (BCF)Package. In addition, the Stream-Routing (STR)Package (Prudic, 1989) is supported if it is not
18
*II
used concurrently with the River Package in the.',same simulation. -
For the EXTENDED-option, the flow-transport,link file supports most of the sink/sourcepackages that have been added to MODFLOW-96 and MODFLOW-2000, such as the SpecifiedFlow and Head Boundary (FHB) Package(Leake and Lilly, 1997) and the Reservoir (RES)Package (Fenske et al., 1996). In addition, theStream-Routing (STR) Package can besupported along with the River Package in thesame simulation. However, these packages havenot been tested with RATEQ.
Record 4. FFORMAT can be either formattedby UNFORMAlTED or FORMATTED. Theunformatted file is preferable because it is muchsmaller in size than an equivalent ASCII textfile. The FORMATTED file should be used onlywhen the user needs to check the contents of thefile or when MODFLOW-2000 and MT3DMSuse different unformatted file formats. '
3.3 RATEQ model input
RATEQ is capable of conducting a several typesof geochemical calculations including simplebatch speciation calculations, batch kineticcalculations, simple one dimensional (ID)transport simulations that have no external fluidor solute sources and relatively complexsimulations in that can external sources of soluteand possibly multiple dimensions. The number.of input files required for a RATEQ sirmulation'varies with the complexity of the problem beingsimulated. In addition, because RATEQ is"closely related to MT3DMS, several RATEQinput files are identical to those used byMT3DMS or have very small differences.'
Table 3.3 summarizes the input files that mayberequired for a RATEQ simulation. The first six-files in the'table are identical orlvery closely ''related to files used by MT3DMS. Specifically, 'these files provide input for the basic transport, 2"advection, dispersion, generalized conjugategradient and source sink packages in MT3DMSand therefore also RATEQ. The input requiredin these files is described below and the
descriptions inciude a discussion of the minordifference between the RATEQ and M3DMSinput files. RATEQ also requires thegeochemical solver (GSR) file. This file is usedto specify the input required to setup and solvethe geochemical calculations. The geochemical:solver file provides the option of specifying thegeochemical reactions. While it is possible tospecifying all of the geochemical reactions in thegeochemical solver input file, this is notrecommended because this list of reaction isusually very long. Instead, the recommendedpractice is to include all or most of thegeochemical reactions in the geochemicalreaction database file. Reactions that areincluded in the geochemical solver file are theused to add reactions that are not contained inthe database, or are used to override reactionparameters contained in the database file.
For batch and simple ID calculations, RATEQcan be executed using only the geochemicalsolver file and, in most instances, the reactiondatabase file. For these simple ID calculations,the following conditions must be met: (1) thereare no fluid sources along the ID domain exceptfor the fluid that enters at the end of the column,'(2) the computational grid must be uniform, and(3) the flow is a steady state. Conversely, flowand transport in complex geometries andpossibly involving 2 or 3 spatial dimension andmultiple fluid source
3.3.1 Name FileRATEQ reads a Name File when execution isstarted. The Name file is nearly identical to thatused by MT3DMS and an example is shown inTable 3.4.; The Name file contains a list of thepackages that will be used in a simulation andthe name of the input file for each package. The.input for each package is contained on a singleline, and each line contains the package name,the unit used for input, and the name of the inputfile. The package name can be LIST, BTN, -ADV, SSM, GCG, RCT, FTL, RDB, and GSR.These abbreviations correspond to.MT3DMS/RATEQ packages as follows: LISTfor the standard MT3DMS output file, BTN forthe MT3DMS Basic Transport Package, ADV
19
Table 3.3 Summary of Input files Required for a RtTEQ Simulation
INPUT Description of File Batch/ Simple Complex NIT3DMIS -ID ID/2D/3D RATEQSimulations Differences
Name File Lists the names of the Optional Yes Yes (seeinput files and the basic section 3.3.1)output file
Basic Sets problem dimensions, No Yes Minor (seeTransport spatially distributed section 3.3.2)
concentrations, output,and discretization
Advection Sets the advection No Yes Nonepackage options
Dispersion Input for dispersivities No Yes Noneand molecular diffusioncoefficient
Generalized Sets options for the No Yes NoneConjugate generalized conjugateGradient gradient solverSource Sink Describes the location and No Yes Minor (see
composition of fluid section 3.3.6)sources
Geochemical Sets up geochemical Yes Yes RATEQ GSRSolver reactions; can be used to replaces
set up ID transport NIT3DMISsimulations RCT
Reactions A database of reactions Recommended Recommended Not Used inDatabase including thermodynamic T3DNIS
and kinetic properties
for the MT3DMS Advection Package, DSP forthe MT3DMS Dispersion Package, SSM for theMT3DMS Sink-Source Mixing Package, RCTfor the MT3DMS Reaction Package, GCG forthe MT3DMS Generalized Conjugate-GradientSolver Package, FTL for the flow modelproduced flow-transport link file, RDB for thereaction database file name, and GSR for theGeochemical Reaction package. Unit numberscan be specified after the package name, but it isrecommended that the default units be used forinput. The default units are selected when theunit number is zero in the Name File.Comments are indicated by the # character incolumn I and can be located anywhere in thefile. Any text characters can follow the #character. All comment records after the firstitem-I record are written in the listing file.
The following list is an example Name Filerequired to start a RATEQ simulation.
Table 3.4 Example of the Namefile# Standardoutput fileList 0 naturita.lst
U In put filesBTN 0 naturita.btnADV 0 1naturita.advDSP 0 naturita.dspGCG 0 naturita.gcgGSR 0 naturita.gsrRDB 0 reactions.dat
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3.3.2 A rray Reader . A - - r Re rIREAD determines how array values are read.
MODFLOW-2000 and MT3DMS both use anarray reader package to read input for spatially _ ' If eal t th ve eleTntidependent properties, such as hydraulicconductivity, porosity, recharge rates or -
concentrationsi.The array'reader reads'data files' -s If IREAD = 100, an array of input valueswhich either specifies constant or cell associated -. follows the control record. The array values arevalues. -However, the array reader does not--- -- read in the format specified in the third field ofallow for the spatially dependent properties to be - the array-control record (FMTIN) from the samedependent on the physical dimensions of the .. unit used for reading the array-control record.problem; instead the array reader reads values 'for individual finite difference cells. This _ If IREAD 101, an array of values organized inlimitation can be a great disadvantage if the "block" format follows the array-control record.model discretization is changed because all of The block format consists of a record specifyingthe input files containing spatially variable data the number of blocks; NBLOCK, followed bywould need to be redefined. This can be time NBLOCK records of input values (all in freeconsuming if a pre-processeor or a graphical format), specifying the first row (11),' last rowuser interface in not available. Consequenily a ' (12), first column (J 1),and last column (J2) ofnew routine was developed for the array'readeF,---- each block as well as the value for each cellsupplied with MT3DMS that allows spatial data'- -- within the block. If a subsequent block overlapsto be dependent on the physical dimensions of --- any preceding blocks, the subsequent blockthe problem and therefore be completely - overrides the preceding blocks. It isindependent of the finite difference -. - --recommended that the first block cover thediscretization. Property values for the finite entire grid to insure that each cell is initialized.difference cells are determined from the physical --dimensions for each layer using bilinear -"' If IREAD = 102, an array of values organized ininterpolation if the real values are being read and -"zonal" format follows the array-control record.by using the nearest neighbor if integer values Each zone represents one value of the inputare being read. To use this new addition to the variable, and each zone is identified by a zonearray reader, the variable IREAD should be set number - an integer which may actually beto either 170 or 180 as described below. thought of as a code for the corresponding value
of the input variable. The zonal format consistsThe general format of the data read by the array of a record specifying the number of zones,reader is listed in Table 3.5. The first variable NZONE, followed by an array of values for theread, IREAD, determines how the spatial data is input variables, ZV(NZONE) which are listed inread. The first record must have one of the sequence according to zone numbers (1, 2, 3,.following 3 formats: . - etc.); Following ZV-is the zone indicator array
A(NCOL,NROW)IIA(NCOLNROW)Record 1: IREAD CNSTNT FMTIN IPRN specifying the zone number assigned to each
. .node (cell) in a given layer of the model. [heinput vales are read using free format.
or
Record 1: 170Species type
input option Species name.Species-value or filenamne - '
If IREAD = 103, an array of values follows thearray-control record. The array values are readusing list-directed or free format.
Or
Record 1: 180 input-option Value.
If IREAD = any value other than 0, 100, 101,102, 103, 170 and 180 array values are readfrom a separate file. I .
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Table 3.5 Alternative Input Formats for the Array Reader
Record1 0 CNSTNT FMITIN IPRN
1 100 CNSTNT FMITIN IPRN2 Table of values read with format FMTIN
1 101 CNSTNT FAITIN IPRN2 NBLOCK3 11 12 J1 J2 Value (Repeated NBLOCK Times)
1 102 CNSTNT FMTIN IPRN2 NZONE3 ZONE VALUES(NZONE)4 ZONE INDEX(NCOL,NROW)
1 103 CNSTNT FMTIN IPRN2 Table of values read with using free format
1 170 input option Species name Speciestype Species value or filename2 xmin:dx:xmax ymin:dy:ymax3 Table of values
1 180 input option value or filename2 xmin:dx:xmax ymin:dy:ymax3 Table of values
_ _ _ I I
If IREAD = 103, an array of values follows thearray-control record. The array values are readusing list-directed or free format.
If IREAD = any value other than 0, 100, 101,102, 103, and 170, array values are read from aseparate file.
If IREAD > 0, it is the unit number on which theexternal file is read using the format specified inFMTIN.
If IREAD < 0, the absolute value of IREADgives the unit number on which the array valuesare read from an external unformatted file. Theunformnatted file contains one record of header,followed by an unformatted record ofNCOL*NROW values.
b. CNSTNT is a constant. Its use depends on thevalue of IREAD and can be either a real value oran integer value, depending on the array beingread.
If IREAD = 0, every element in the array is setequal to CNSTNT/ICONST.
If IREAD • 0, and CNSTNT/ICONST °0,
elements in the array are multiplied byCNSTNT/ICONST.
FMTIN is the user-specified format to read arrayvalues or the zonal indicator array. The formatmust be enclosed in parentheses; for example,(I5F5.0) for real values and (1515) for integerinput values.
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IPRN is a flag indicating whether or not the'array being read should be printed out forchecking, and it also serves as a code indicatingthe format that should be used in printing.' It is§. iused only if IREAD is not equal to zero. IPRN isset to zero if the specified value exceeds thosedefined in Table 3.6 If IPRN is less than zero,the array will not be printed.
Table 3.6 Printing Formats Corresponding tothe IPRN Code (after McDonald andHarbaugh 1988)PRN RARRAY |ARRAY0 10G11.4 10]1111 11 G10.3 60112 9G 13.6 40123 * 15F7.1 30134 15F7.2 25145 15F7.3 20156 15F7.47 20F5.0 -
8 20F5.19 20F5.210 20F5.311 20F5.412 10G11.4
dx is the distance between values in the xdirection, and xmax is the maximum distance inthe x direction. Ymin, dy and ymax have similarmeanings for the y direction. The values ofxmin, xmax, ymin and ymax define physicaldimensions characterized by a possibly spatiallyvariable physical property. The value of theproperty is contained in record 3 as definedbelow.
Record 3: Record 3 contains the input data infree format.
If IREAD = 170, then record 1 has the format
IREAD'input option Species_nameSpeciestype Value.
If the array reader is used to set the initialgeochemical conditions in the simulations ind'ifthe initial conditions are specified as species 'concentrations instead of solution numbers asdescribed in the input for the geochemicalreactions package, then the values ofSpeciesname Species type Species value'are optional character strings that are'required in'some uses of the array reader The'variables -'
Species name and Species type are described in"secation 3.3.5.
Record 2: xmin:dx:xmax ymin:dy:ymax. Theseentries are used to define the x and y dimensionsfor the spatial array of data read in Record 3. IfXmin is the minimum distance in the x direction,
If inputoption is 'file', then the string containsthe name of the file and the file must have thesame structure as defined by Records'2 and 3.
Input option is a case insensitive string and canequal either 'const', 'file' or 'next'
If input-option is 'const', the Value contains anumerical value and each cell in the array is setequal to that value.
If IREAD = 180 then the input is structure of theremaining input is the same as when IREAD =170 except that the variables Speciesname andSpecies type are not read.
3.3.3 Transport andReactionMT3DMS requires input for 6 differentpackages; for RATEQ, the input for the ADV,DSP, and GCG packages are identical to that forMT3DMS. However, the input for theADVECTION package is restricted to the thirdorder TVD package. The CHEMICALREACTION PACKAGE, which was designedfor simulating simple reactions such as firstorder reactions and nonlinear isotherms, isreplaced by a new GEOCHEMICAL SOLVER(GSR) PACKAGE.' The input in the BTN andSSM packages were slightly modified, toinclude capabilities to provide input forsimulating geochemical reactions.
3.3.3.1 Basic Transporit File
Table 3.7 summarizes the information format ofthe basic transport file. This file consist of 23
23
records that mainly control the modeldiscretization, set the initial conditions in themodel, control selected model output, and definethe time steps used in the model. Table 3.7 alsoindicates whether the input records werechanged relative to the initial MT3DMS code.When the input is changed, the changes arelimited to the meaning of the input rather thanthe number of variables. The changes in themeaning of the input only activate new options;in this way traditional MT3DMS input files canstill be used in RATEQ. However, thesimulations cannot be conducted simultaneously,because the MT3DMS Reaction package cannotbe used in the same simulation as theGeochemical Reaction Package. One otherimportant change is that the input for RATEQwas converted to free format. This changesacrifices backward compatibility becauseMT3DMS requires formatted input, but the freeformatted input greatly simplifies input andreduces the chances for input errors.
Record I is the first line of any title or headingfor the simulation run. The line should not belonger than 80 characters.
Record 2: Heading(2) is the second line of anytitle or heading for the simulation run. The lineshould not be longer than 80 characters.
Record 3: NLAY, NROW, NCOL, NPER,NCOMP, MCOMP
NLAY is the total number of layers,
NROW is the total number of rows,
NCOL is the total number of columns,
NPER is the total number of stress periods, andNCOMP determines how the initial conditionswill be input.
MCOMP is read for consistency withMT3DMS, but it is not used in RATEQ.
TUNIT is the name of unit for time, such asDAY or HOUR,
LUNIT is the name of unit for length, such asFT or M, and,
MUNIT is the name of unit for mass, such as LBor KG.
Note that these names are used for identificationpurposes only and do not affect the modeloutcome.
Record 5: TRNOP(10)
Each value in TRNOP is a logical flags formajor transport and solution options. TRNOP(I) through (6) correspond to Advection,Dispersion, Sink & Source Mixing, ChemicalReaction, and Generalized Conjugate GradientSolver packages and Geochemical Reactions,respectively. If any of these options is used,enter its corresponding TRNOP element as T,otherwise as F. TRNOP (7) through (10) arereserved for add-on packages.
Record 6: LAYCON(NLAY)
LAYCON is a l-D integer array indicating thetype of model layers. Each value in the arraycorresponds to one model layer. Enter LAYCONin as many lines as necessary if NLAY > 40.
If LAYCON = 0, the model layer is confined.The layer thickness, DZ, to be entered in asubsequent record will be used as the saturatedthickness of the layer.
If LAYCON X0, the model layer is eitherunconfined or convertible between confined andunconfined. The saturated thickness, ascalculated by the flow model and saved in theflow-transport link file, will be read and used bythe transport model.
Record 4: TUNIT, LUNIT, MUNIT
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Table 3.7 Summary of Input Required for the BTN PackageRecord Modified Array Input Description1 N N HEADINGI Descriptive title2 N N HEADING2; Descriptive title3 V N -NLAY, NROW, NCOL, NPER, Problem dimensions
. NCOMP, MCOMP -_-4 N N - TUNIT, LUNIT, MUNIT Units labels
5 N N TRNOP Packages6 N N LAYCON(NLAY) Layer type7 N Y DELR(NCOL) Row-wise grid8 N Y DELC(NROW) Column-wise grid9 N Y HTOP(NCOL,NROW) Top of aquifer10 N Y DZ(NCOLNROW) Layer11 N Y PRSITY(NCOLNROW) Porosity12 N y ICBUND(NCOLNROW) Ibound array13 Y Y SCONC(NCOL,NROW) Initial concentration or
solution number used to. _ . . give initial concentration
14 N N CINACT, THKMIN15 N N IFMTCN, IFMTNP, IFMTRF,
._ _ IFMTDP, SAVUCN16 N N NPRS - ;. Number of periods
17 N-t . N- TIMPRS(NPRS)18 N N NOBS, NPROBS19 N N KOBS, IOBS, JOBS20 N N CHKMAS, NPRMAS21 N N PERLEN, NSTP, TSMULT -22 N N TSLNGH(NSTP)23 N N DTO, MXSTRN, TTSMULT,
. TTSMAX
25'.
__ _aL
Record 7: DELR(NCOL)
DELR is a 1 -D real array of the cell width alongrows (x) in the direction of increasing columnindices (j). Specify one value for each column ofthe grid.
Record 8: DELC(NROW)
DELC is a 1-D real array representing the cellwidth along columns (-y) in the direction ofincreasing row indices (i).
Record 9: HTOP(NCOL,NROW)
HTOP is a 2-D array defining the top elevationof all cells in the first (top) model layer, relativeto the same datum as the hydraulic heads.
If the first model layer is unconfined, HTOP canbe set most conveniently to a uniform elevationabove the water table. Note that the differencebetween 1ITOP and the bottom elevation of thefirst layer must be equal to the layer thickness,DZ, to be defined in the next record.
If the first model layer is confined, HTOP isequal to the bottom elevation of the confiningunit overlying the first model layer.
Record 10: DZ(NCOL,NROW) (one array foreach layer in the grid)
DZ is the thickness of all cells in each modellayer. DZ is a 3-D array. The input to 3-D arraysis handled as a series of 2-D arrays with onearray for each layer, entered in the sequence oflayer 1, 2, ..., NLAY. The thickness of the firstlayer must be equal to the difference betweenHITOP and its bottom elevation. When the grid isdiscretized into horizontal layers, HTOP for thefirst layer and DZ within each layer are uniform.However, if a vertically distorted grid is used,both -ITOP and DZ may be variable for cellswithin the same layer.
Record 11: PRSITY(NCOL,NROW) (onearray for each layer)
PRSITY is the effective porosity of the porousmedium in a single porosity system and it equalsthe mobile porosity as described in Section 2.2when a dual porosity simulation is conducted.Note that if a dual-porosity system is simulated,PRSITY should be specified as the "mobile"porosity (i.e., the ratio of interconnected porespaces filled with mobile water over the bulkvolume of the porous medium); the "immobile"porosity is defined through the ChemicalReaction Package.
Record 12: ICBUND(NCOL,NROW) (oneinteger array for each layer)
ICBUND is an integer array specifying theboundary condition type (inactive, constant-concentration, or active) for every model cell.
If ICBUND = 0, the cell is an inactiveconcentration cell for all species. Note that no-flow or "dry" cells are automatically convertedinto inactive concentration cells. Furthermore,active cells in terms of flow can be treated asinactive concentration cells to minimize the areaneeded for transport simulations, as long as thesolute transport is insignificant near those cells.
If ICBUND > 0, the cell is an active (variable)concentration cell where the concentration valuewill be calculated.
ICBUND values less than 0, which indicatesconstant concentration cells in MT3DMS, arenot allowed with geochemical reactions.
Record 13: Array: SCONC(NCOL,NROW)(one array for each layer)
SCONC is the initial concentration for thesimulation (unit, ML 3). For RATEQ, ifNCOMP equals one, then SRCONC equals thesolution number specified in the GeochemicalReaction package. If SRCONC is greater thanone, then NCOMP must equal then number ofcomponents, and SCONC must be specified
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NCOMP times for each layer. In~ addition, theSCONC array must be entered using the arrayreader using the options described forIREAD= 170 as described in 'Section 3.3.2)
Record 14: CINACT, THKMIN
CINACT is the value for indicating an inactiveconcentration cell (ICBUND = 0). Even ifinactive cells are not anticipated in the model, avalue for CINACT still must be submitted.THKMIN is the minimum saturated thickness ina cell, expressed as the decimal fraction of themodel layer thickness, DZ, below which the cellis considered inactive. The default value is 0.01(i.e., 1 percent of the-model layer thickness).
Record 15: IFMTCN, IFMTNP, IEFMTRF,IFMTDP, SAVUCN Format: 4I10, LI O
IFMTCN is a flag indicating whether thecalculated concentration should be printed to the*'standard output text file and also serves as aprinting-format code if it is printed. The codes "f"
for print-formats are the same as those listed inTable 3.7.
If IFMTCN > 0, concentration is printed in thewrap form (80 columns of output) or ifIFMTCN< 0, concentration is printed with anunlimited number of columns.
If IFMTCN = 0, concentration is not printed.
IFMTNP, IFMTRF, and IFMTDP are not usedin RATEQ but these input variables are retainedfor compatibility with MT3DMS, and thereforevalues must beiprovided.
SAVUCN is a logical flag indicating whetherthe concentration solution should be-saved in a' ldefault unformatted file named MT3Dnnn.UCN, 'where nnn is the species index number, for post- 'processing purposes or for use as the initial ' '
condition in a continuation run. -
If SAVUCN = T, the concentration of each'species will be saved in the default fileMT3Dnnn.UCN. In addition,ithe model spatial:discretization information will be saved in
another default file named MT3D.CNF to beused in conjunction with MT3Dnnn.UCN forpostprocessing purposes.
If SAVUCN = F, neither MT3Dnnn.UCN norMT3D.CNF is created.
The concentrations saved in these files willequal the total dissolved concentration of theprimary dependent variables (PDVs) that wereused in solving the partial differential equations(transport equations). In some instances, thePDVs equal easily recognized values, such astotal dissolved concentrations, but this is alwaystrue. The Geochemical Reaction package hasadditional options-for creating output files withspecific species concentrations or functions ofthe species concentrations, such as pH, total 7
dissolved concentrations, total adsorbed '' 'concentrations, reaction rates, and free energiesof reaction for rate controlled reactions.
Record 16: NPRS
NPRS is a flag indicating the' frequency of theoutput and also indicating whether the outputfrequency is specified in terms of total elapsedsimulation time or the transport step number.Note that what is actually printed or saved iscontrolled by the input values entered in thepreceding record (Record 15).
If NPRS > 0, simulation results will be printedto the standard output text file or saved to theunformatted concentration file at times asspecified in record TIMPRS(NPRS), to beentered in the next record.
If NPRS = 0, simulation results will not beprinted or saved except at the end of thesimulation.
If NPRS < 0, simulation results will be printedor saved whenever the number of transport stepsis an even multiple of NPRS.
Record 17: TIMPRS(NPRS)
TIMPRS is only entered if NPRS>0 and equalsthe total elapsed time at which the simulation
27
results are printed to the standard output text fileor saved in the default unformatted (binary)concentration file MT3Dnnn.UCN. Note that ifNPRS > 8, enter TIMPRS in as many lines asnecessary.
Record 18: NOBS, NPROBS,LOCATIONTYPE
NOBS is the number of observation points atwhich the concentration of each species will besaved at the specified frequency in the defaultfile, MT3Dnnn.OBS, where nnn is the speciesindex number.
NPROBS is an integer indicating how frequentlythe concentration at the specified observationpoints should be saved in the observation file,MT3Dnnn.OBS. Concentrations are saved everyNPROBS step.
LOCATIONTYPE is optional input that affectshow the values in record 19 are read. IfLOCATIONTYPE is omitted or is a text string'kij', then the input in record 19 is interpreted ascell indices. Alternatively, ifLOCATIONTYPE is 'xyz' or 'zyx', then theinput in record 19 is interpreted as cell distances.
Record 19: KOBS, IOBS, JOBS (Enter NOBStimes if NOBS > 0)
KOBS, IOBS, and JOBS are the cell indices(layer, row, column) or cell distances (z, x, y), asdetermined in record 18, in which theobservation point or monitoring well is located,and for which the concentration is to be printedat every transport step in file MT3Dnnn.OBS.Enter one set of KOBS, IOBS, and JOBS foreach observation point.
Record 20: CHKMAS, NPRMvAS
CHKMAS is a logical flag indicating whether aone-line summary of mass balance informationshould be printed, for checking and post-processing purposes, in the default fileMT3Dnnn.MAS, where nnn is the species indexnumber.
If CHKMAS = T, the mass balance informationfor each transport step will be saved in fileMT3Dnnn.MAS.
If CIHKMAS = F, file MT3Dnnn.MAS is notcreated.
NPRMAS is an integer indicating howfrequently the mass budget information shouldbe saved in the mass balance summary fileMT3Dnnn.MAS. Mass budget information issaved every NPRMAS step.
Record 21: PERLEN, NSTP, TSMULT
Record 21 is entered once for each stress period.
PERLEN is the length of the current stressperiod. If the flow solution is transient, PERLENspecified here must be equal to that specified forthe flow model. If the flow solution is steady-state, PERLEN can be set to any desired length.
NSTP is the number of time-steps for thetransient flow solution in the current stressperiod. If the flow solution is steady-state, NSTP= 1.
TSMULT is the multiplier for the length ofsuccessive time steps used in the transient flowsolution; it is used only if NSTP > 1.
If TSMULT > 0, the value of each flow time-step within the current stress period is calculatedusing the geometric progression as inMODFLOW. Note that both NSTP andTSMULT specified here must be identical tothose specified in the flow model if the flowmodel is transient.
If TSMULT it 0, the value of each flow time-step within the current stress period is read fromthe record TSLNGH (see record 22). This optionis needed in case the value of time steps for theflow solution is not based on a geometricprogression in a flow model, unlikeMODFLOW.
Record 22: TSLNGII(NSTP) (Enter ifTSMULT • 0)
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TSLNGH provides the length of time steps for;- -'' TTSMULT is the multiplier for successivethe flow solution in the current stress period. transport steps within a flow time step if theThis record is needed only if the value of time _-: GCG solver is used and the solution option forsteps for the flow solution is not based on a the advection term is the standard finite-geometric progression. Enter TSLNGH in asmany lines as necessary
Record 23: DTO, MXSTRN, TTSMULT,TTSMAX
DTO is the user-specified transport step sizewithin each time step of the flow solution. DTOis interpreted differently depending on whetherthe solution option chosen is explicit or implicit.
For explicit solutions (i.e., the GCG solver is notused), the program will always calculate amaximum transport step size that meets thevarious stability criteria. Setting DTO to zerocauses the model-calculated transport step sizeto be used in the simulation. However, themodel-calculated DTO may not always beoptimal. In this situation, DTO should beadjusted to find a value that leads to the bestresults. If DTO is given a value greater than themodel-calculated step size, the model-calculatedstep size will be used in the simulation instead of'the user-specified value.
For implicit solutions (i.e., the GCG solver isused), DTO is the initial transport step size. If it'is specified as zero, the model-calculated valueof DTO, based on the user specified Courantnumber in the Advection Package, will be used.''The subsequent transport step size may increaseor remain constant depending on the user-specified transport step size multiplier,TTSMULT, and the solution scheme for theadvection term.
MXSTRN is the maximum number of transportsteps allowed within one time step of the flowsolution. If the number of transport steps withina flow time step exceeds MXSTRN, thesimulation is terminated.
Ldifference method. TTSMULT is not used whenthe third order TVD method is used andtherefore TTSMULT is not applicable toRATEQ. It is listed for compatibility withMT3DMS.
3.3.3.2 Advection
The advection package simulates advection asdescribed in section 2.3. The input to theadvection package is relatively simple forRATEQ because only the third order TVDmethod is supported. Aside from this limitation,no changes were made. The input is summarizedin Table 3.8.
Record 1: MIXELM, PERCEL
MIXELM must equal -I for RATEQ, indicatingthat the TVD solver will be used,
PERCEL is the grid Peclet number that is usedto limit the maximum time step used in thesimulations. PERCEL must be greater than 0and less than or equal to 1.
3.3.3.3 Dispersion
Table 3.9 summarizes the input required for the---dispersion package which simulates dispersion
and molecular diffusi6n as described in Section' 2.3. The dispersion package is used to define
the dispersivities and the molecular diffusioncoefficients. The dispersion equations aresolved numerically, either explicitly or.implicitly, depending on whether or not the
-GCG package is used. The GCG package alsoprovides the option of including all of the cross
__terms of the dispersion tensor The input to thedispersion package was not changed for RATEQ
Table 3.8 Summary of Input Required for the ADV PackageI Record I Modified I Arrav I input ' -
I 1 - N N -MIXELM, PERCEL
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Table 3.9 Summary of Input Required for the DSP PackageRecord Modified Array Input Description1 N Y AL Longitudinal dispersivity2 N Y TRPT Ratio of transverse to longitudinal dispersivity3 N Y TRPV Ratio of vertical to longitudinal dispersivity4 N Y DMCOEF Molecular diffusion coefficient
implicitly, depending on whether or not the TRPV is the ratio of the vertical transverseGCG package is used. The GCG package also dispersivity, -TV , to the longitudinalprovides the option of including all of the cross dispersivity, -AL . Each value in the arrayterms of the dispersion tensor The input to the corresponds to one model layer. Some recentdispersion package was not changed for RATEQ field studies suggest that TRPT is generally not
greater than 0.01.Record 1: AL(NCOL,NROW) (one array foreach layer) Set TRPV equal to TRPT to use the standard
isotropic dispersion model.AL is the longitudinal dispersivity, -L , forevery cell of the model grid (unit, L). Record 4: DMCOEF(NLAY)
Record 2: Array: TRPT(NLAY) MCOEF is the effective molecular diffusioncoefficient (unit, L2 r'). Set DMCOEF = 0 if the
TRPT is a l-D real array defining the ratio of the effect of molecular diffusion is consideredhorizontal transverse dispersivity, -TH , to the unimportant. Each value in the arraylongitudinal dispersivity, -AL. Each value in corresponds to all species in one model layer.the array corresponds to one model layer. Somerecent field studies suggest that TRPT is 3.3.3.4 Source/Sinkgenerally not greater than 0. 1;
The source-sink package is used to define theRecord 3: TRPV(NLAY) chemical composition of all fluid sources or
sinks.
Table 3.10 Summary of Input Required for the Source-Sink Packa eRecord Modified Array Input DescriptionI N N FWEL, FDRN, FRCH, Logical Flags indicating source
FEWT, FRIV, FGIIB type2 N N rVLXSS Maximum number of point
_____ ____sources
3 N N INCRCH Flag indicating recharge4 N Y CRCH Solution numbers for recharge5 N N INCEVT Flag indicating
evapotranspiration6 N Y CEVT Solution numbers for
evapotranspiration7 N N NSS, LOCATIONTYPE Total number of source/sink
terms, location type8 N N KSS, ISS, JSS, CSS, Location, type and solution
I ITYPE, SOLN number of sources
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all ..-
The input for this package is summarized inTable 3.10. The source sink package in RATEQis identical to that in MT3DMS, excepthat thelocations 'of the point sources can be specified aseither cell indices as in MT3DMS, or also as celllocation (x, y, z) values. This latter optiongreatly simplifies the process of solving asimulation on a finer or coarser numerical grid.:As with other packages, all input is free format.:One limitation of the source-sink package whenused with the Geochemical Reaction package isthat the composition of sources and sinks mustbe specified as solutions and not specified ascomponent concentrations.
Record 1: FWEL, FDRN, FRCH, FEVT,.FRIV, FGHB, (FNEW(n), n=1,4)FWEL is alogical flag for the Well option,
FDRN is a logical flag for the Drain option,
FRCH is a logical flag for the Recharge option,
FEVT is a logical flag for the Evapotranspirationoption,
FRIV is a logical flag for the River option, and,
FGHB is a logical flag for General-Head-Dependent Boundary option.
FNEW are logical flags reserved for additionalsink/source options. If any of these options isused in the flow model, its respective flag mustbe set to T (True), otherwise, set to F (False).
Note that when MODFLOW is used to obtainiflow solutions for MT3DMS, the LKMT -
package (Version 2 and later) of MODFLOWwill store appropriate values for these flags in-the unformatted flow-transport link file. If these -
flags are not specified correctly here, MT3DMS 'will issue a waming, reset the flags to correct -values, and proceed with the simulation. Alsonote that a commonly used add-on package toMODFLOW, the Streamflow-Routing (STR)package is supported through the River option.This is done by associating the River option inMT3DMS with the STR package instead of theRIV package in MODFLOW. For this reason,
the RIV and STR packages cannot be usedconcurrently in the same MODFLOWsimulation.
Record 2: MXSS is the maximum number ofall point sinks and sources included in the flow,model. Point sinks and sources include constant-head cells, wells, drains, rivers, and general-head-dependent boundary cells. Recharge andevapotranspiration are treated as areallydistributed sinks and sources; thus, they shouldnot be counted as point sinks and sources.MXSS should be set close to the actual numberof total point sinks and sources in the flowmodel to minimize computer memory allocatedto store sinks and sources.
Records 3 through 8 are entered once for eachstress period.
Record 3: INCRCH is a flag indicating whetheran array containing the concentration ofrecharge flux for each species will be read forthe current stress period.
If INCRCH - 0, an array containing theconcentration of recharge flux for each specieswill be read.
If INCRCH < 0, the concentration of rechargeflux will be reused from the last stress period. IfINCRCH < 0 is specified for the first stressperiod, then by default, the concentration ofpositive recharge flux (source) is set equal tozero and that of negative recharge flux (sink) is'set equal to the aquifer concentration.
Record 4: CRCH(NCOLNROW) (EnterRecord 4 for each species if FRCH = T andINCRCH - 0)
CRCH is the solution number of recharge fluxfor a particular species. If the recharge flux ispositive, it acts as a source whose concentrationcan be specified as desired. If the recharge fluxis negative, it acts as a sink (discharge) whoseconcentration is always set equal to the - -concentration of groundwater at the cell wheredischarge occurs. Note that the location and flowrate of recharge/discharge are obtained from the
31.
.Al
flow model directly through the unformattedflow-transport link file.
Record: 5: INCEVT (Enter only if FEVT = T)
HNCEVT is a flag indicating whether an arraycontaining the solution number ofevapotranspiration flux for each species will beread for the current stress period.
If INCEVT - 0, an array containing theconcentration of evapotranspiration flux for eachspecies will be read. If INCEVT< 0, theconcentration of evapotranspiration flux for eachspecies will be reused from the last stress period.If INCEVT < 0 is specified for the first stressperiod, then by default, the concentration ofnegative evapotranspiration flux (sink) is set tothe aquifer concentration, while theconcentration of positive evapotranspiration flux(source) is set to zero.
Record 6: CEVT(NCOL,NROW) (Enter foreach species if FEVT = T and INCEVT - 0)
CEVT is the solution number ofevapotranspiration flux for a particular species.Evapotranspiration is the only type of sinkwhose concentration may be specifiedexternally. Note that the concentration of a sinkcannot be greater than that of the aquifer at thesink cell. Thus, if the sink concentration isspecified greater than that of the aquifer, it isautomatically set equal to the concentration ofthe aquifer. Also note that the location and flowrate of evapotranspiration are obtained from theflow model directly through the unformattedflow-transport link file.
Record 7: NSS, LOCATIONTYPE
NSS is the number of point sources whoseconcentrations need to be specified. By default,unspecified point sources are assumed to havezero concentration. (The concentration of pointsinks is always set equal to the concentration ofgroundwater at the sink location.)
with a flow rate in the flow model, but also thoseindependent of the flow solution. This type of"mass-loading" source may be used to includecontaminant sources that have minimal effectson the hydraulics of the flow field.
LOCATION TYPE is optional input that affectshow the values in record 8 are read. IfLOCATION TYPE is omitted or is a text string'kij', then the input in record 8 is interpreted ascell indices. Alternatively, ifLOCATION TYPE is 'xyz', 'zyx', or 'zxy',then the input in record 8 is interpreted as celldistances.
Record 8: KSS, ISS, JSS, CSS, ITYPE, SOLN(Enter NSS times if NSS > 0)
KSS, ISS, JSS are the cell indices (layer, row,column) of the point source for which aconcentration needs to be specified for eachspecies.
CSS is not used, but a dummy value still needsto be entered here for compatibility withMT3DMS.
ITYPE is an integer indicating the type of thepoint source as listed below:
ITYPE = 1, constant-head cell;
= 2, well;= 3, drain (note that in MODFLOWconventions, a drain is always a sink, thus, theconcentration for drains cannot be specified ifthe flow solution is from MODFLOW);= 4, river (or stream);= 5, general-head-dependent boundary cell;= 15, mass-loading source;= -1, constant-concentration cell.SOLN defines the solution number for a pointsource for multispecies simulation.
Several important notes on assigningconcentration for the constant-concentrationcondition (ITYPE = -1) are listed below:
Note that in MT3DMS, point sources aregeneralized to include not only those associated
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1) The constant-concentration condition definedin this input file takes precedence to that definedin the Basic Transport Package input file.-
2) In a multiple stress period simulation, aconstant concentration cell, once 'defined, willremain a constant concentration cell in theduration of the simulation, but its concentrationvalue can be specified to vary in different stress-periods.
3) In a multispecies simulation, if it is onlynecessary to define different constant-concentration conditions for selected species at.vthe same cell location, to specify the desiredconcentrations for those species, and to assign a:negative value for all other species. The negativevalue is a flag used by MT3DMS to skipassigning the constant-concentration conditionfor the designated species.
3.3.3.5 Generalized Conjugate GradientPackage
No changes were made the to GeneralizedConjugate Gradient (GCG) Package. Input forthe GCG package consists of two lines as shown '-in Table 3.11 and described below.
Input to the GCG package is read on unitINGCG = 9, which is preset in the mainprogram. The input file is needed only if theGCG solver is used for implicit solutionschemes. This package is a new addition in 'MT3DMS.
isotherm is included in the simulation. ITERI isthe maximum number of inner iterations; a valueof 30-50 should be adequate for most problems.ISOLVE is the type of preconditioners to beused with the Lanczos/ORTHOMINacceleration scheme:
= 1, Jacobi=2, SSOR= 3, Modified Incomplete Cholesky (MIC)
MIC usually converges faster, but it needssignificantly more memory.NCRS is an integer flag for treatment ofdispersion tensor cross terms:
= 0, lump all dispersion cross terms to theright hand-side (approximate but highlyefficient).
= 1, include full dispersion tensor (memoryintensive).Record 2: ACCL, CCLOSE, IPRGCG
ACCL is the relaxation factor for the SSORoption; a value of 1.0 is generally adequate.
.CCLOSE is the convergence criterion in termsof relative concentration;'a real value between1 04 and 1 04 is generally adequate. IPRGCG isthe interval for printing the maximumconcentration changes of each iteration. SetIPRGCG to zero as default for printing at theend of each stress period.
- 3? 7?d ROprY~hji 7lnfnhiTVp fljp1d
Record 1: MXITER, ITERi, ISOLVE, NCRS - The reaction database file is based on the formatof the thermodynamic datafile used in the
MXITER is the maximum number of outer p - - -iterations; it should be set to an integer greater -
than one only when a nonlinear sorption - --
Table 3.11 Summary of Input Required for the GCG Package -
Record Modified Array Input -- Description1 N--- N MXITER, ITERI, ISOLVE, Longitudinal dispersivity
NCRS- _'--_-_";
2 N N TRPT Ratio of transverse to longitudinaldispersivity
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PHREEQC (Parkhurst and Appelo, 1999).Although RATEQ can directly use a PHREEQCthermodynamic input file, there are additionaloptions that can be included in the RATEQreaction input file.
The most significant difference for the RATEQinput file is that the rate law associated witheach geochemical reaction must be included inthe reaction input file.
The general format of the reaction database fileis illustrated in Table 312. The reactiondatabase file specifies master species that areused to both formulate association reactions andto set up the reactive transport equations. Thereare three possible kinds of master species:solution master species, surface master species,and exchange master species. These masterspecies are used in formulating reactions insolution, on an adsorbing surface, and on an ionexchanger.
Record 1: SOLUTIONMASTERSPECIES isa keyword indicating that the following linesdefine the correspondence between elementnames and aqueous primary and secondarymaster species. As a keyword,SOLUTIONMASTERSPECIES is the onlyentry read from the reaction database file.
Record 2: ELEMENT NAME, MASTERSPECIES, ALKALINITY, FORMULAWEIGHT or FORMULA, FORMULAWEIGHT OF ELEMENT
ELEMENT NAME is an element name or anelement name followed by a valence state inparentheses. The element name must begin witha capital letter, followed by zero or more lowercase letters or underscores ("").
Record 2 is repeated once for each masterspecies in the reaction database file.
Table 3.12 Summary of Input Information in the Reaction Database file1 SOLUTION NIASTER SPECIES2 Element Element master alkalinity gram formula formula gram formula
name species weight weight for__ element
3 SOLUTION SPECIES4a Solution Reaction4b Reaction Properties5 PHASES6a Phase Name6b Phase Dissolution Reaction6c Reaction Properties7 SURFACE MASTER SPECIES8 |Surface Name, Surface Master Species9 SURFACE SPECIES10a Surface Reactions10b Reaction Pro erties11 EXCHANGE MASTER SPECIES12 |Exchange Master Species List13 EXCHANGE REACTION14a Surface Reactions14b Reaction Properties
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MASTER SPECIES is the formula for the master.species, including its charge. The term MASTERSPECIES is taken from PHREEQC ahd is aspecies used to formulate other or secondaryspecies. If the ELEMENT NAME does notcontain a valence state in parentheses, thecorresponding master species is a primary master.species. If the ELEMENT NAME does contain avalence state in parentheses, the master species. -
is a secondary master species. The MASTER-SPECIES must be defined in theSOLUTIONSPECIES datablock.
ALKALINITY is the alkalinity contribution ofthe master species. The alkalinity contribution ofaqueous non-master species will be calculatedfrom the alkalinities assigned to the master -,
species.
FORMULA WEIGHT is used to convert inputdata in mass units to mole units for the element orelement valence. For alkalinity, the gramequivalent weight is entered. Either FORMULAWEIGHT or FORMULA is required, but onlyone of them can be specified.
FORMULA is the chemical formula used tocalculate gram formula weight, which is used toconvert input data from mass units to mole units.for the element or element valence. Foralkalinity, the formula for the gram equivalentweight is entered. Either FORMULA WEIGHTor FORMULA is required.
ExamplesCa Ca+2 0.0 Ca 40.08 -
Fe(+2) Fe+2 0.0 Fe
Record 3: SOLUTION-SPECIES is akeyword indicating that the following linesdefine the species that occur in solution.Solution species are usually defined viaformation reactions involving master species,although this is not required in RATEQ.
Record 4: This entry is used to define asolution species by a chemical reaction thatshould be balanced with respect to both massand charge. Note that unlike PHREEQC,RATEQ does not require that identity reactions
(e.g. H+ = H+) be defined for each 'masterspecies. Identity reactions are ignored inRATEQ.
Record 4a: These entries define specificproperties that apply to the reaction listed inRecord 4. These properties include thethermodynamic equilibrium constant and theenthalpy of reaction, among other reactionproperties. A complete list of reactionproperties is discussed below.
Example: (4 and 4a)C03-2 + H+ = HCO3-
LogK 10.329
Record 5: PHASES is a keyword indicatingthat the following lines define separate phasesthat can be included in a simulation.
Records 6a-6c: Generally, a minimum of 3 linesis required to define a geochemical phase. Thefirst line defines the name of phase, which canbe a common mineral name, the second linedefines the dissociation reaction for the phase,and the last line defines the reaction properties.
Example:Calcite
CaCO3 = C03-2 + Ca+2log_k -8.480
Record 7: SURFACEMASTERSPECIESThis keyword data block is used to define thecorrespondence between surface binding-sitenames and surface master species. The defaultdatabases contain master species for Hfos andHfo_w, which represent the weak and strongbinding sites of hydrous ferric oxides (Dzombakand Morel, 1990).
Record 8: This record defines: (1) the name'ofthe surface binding site, and (2) the master 'species for the surface species. The name of asurface binding site must begin with'a capitalletter or a '>'j followed by zero or more lowercase letters. Multiple binding sites can be definedfor each surface. -
Example:
35 -
Mu1
Surf] >WOHSurfI >SOH
In this example data block, a surface named"Surfl" has a strong (>SOH) and a weak bindingsite (>WOH). In setting up the equations for asimulation that includes multiple binding sites, amole-balance equation is created for both the>WOH site and the >SOH site, and one charge-balance equation is created for surface SURF .
Record 9: SURFACE SPECIES is a keywordindicating that the following lines define surfacespecies that can be included in a simulation.This is a keyword and no other input is readfrom this line.
Records IOa-IOb: A minimum of 2 lines isrequired to define an adsorption reaction. Thefirst line defines a chemical balanced adsorptionreaction, and the second or more defines thereaction properties.
Example:K+ + X- = KX
logK 0.7
Example:>SOH + U02+2 = >SOU02+ + H+
log_K= 1.234
Each of the reactions that define solutionspecies, phases, surface species and exchangespecies can have supplemental informationwhich defines important reaction propertiesincluding the thermodynamic equilibriumconstant, the enthalpy or reaction, activitycoefficient parameters and rate law information.
Table 3-13 gives a summary of all of thepossible reaction information that can beincluded for each reaction.
logK option. Logio K at 25TC for the reactionis given.
Examples:log~k 10.LogK 1.0LogK = 2.0
delta h option. Enthalpy of reaction at 25TC isgiven. The enthalpy of reaction is used in thevan't Hoff equation to determine thetemperature dependence of the equilibriumconstant. The default units are kilojoules permole. Units may be calories, kilocalories, joules,or kilojoules per mole. Only the energy unit isneeded (per mole is assumed) and abbreviationsof these units are acceptable. Explicit definitionof units for all enthalpy values is recommended.
Examples:delta h 10.0 kj/moledelta h 3.0 kcal/molDelta h= 12.1
gamma option, aobo. This option specifies thatthe Debye-Huckel 'Bdot' method will be used tocalculate the activity coefficient for the speciesdefined by the association reaction.
Record 11:EXCHANGEMASTERSPECIES
This is a keyword for the data block and noother data are read from line.
Record 12: The exchanger name is a name forthe exchange site. The exchanger masterexchange species is a species used in writing ionexchange reactions.
Example:X X-
where X is the name of the exchanger and X- isthe master species.
Record 13a,b: Exchange species are written ashalf-reactions for the master exchange species(e.g., X- ) and an ion to form the exchangedcomplex. Each exchange half-reaction must bemass and charge balanced. Multiple halfreactions are combined internally to give a'typical' ion exchange reaction.
Example:gamma 5.000 0.1650
analytical expression option, A1, /12, A3, 314,
Af. Identifier for coefficients for an analyticalexpression for the temperature dependence of log
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K A,, A2, A3, A4, A5 are five values defining logK as a function of temperature in equation 2-27.
Example:analytical 107.8871-5151.79 -38.92561
I _.
be different in the mass balance equations andthe mass action expressions. This approach is anempirical approach that is sometimes used tosimulate adsorption of species that formbidentate surface species, but where it isbelieved that the mass action expression shouldnot depend on the square of the siteconcentration (see Waite et al., 1994).
0.03252849563713.9
nocheck option. Indicates the reactionequation should not be checked for chargebalance. Default is to always check chargebalance
Example:No check
is ignored option. Toggle to ignore a reactionfor a simulation. Default is to always includeeach reaction if all of the components arepresent in a solution. This option is useful foreasily turning off or on a reaction whenconducting iterative modeling studies.
Example:Is ignored
force eq option. Toggle to force the reaction tobe equilibrium controlled even if a rate law isgiven. Default behavior is to use the rate law ifone is provided and the equilibrium expression ifno rate law is provided. This option is useful foreasily converting a rate-controlled reaction to anequilibrium-c6ntrolled reaction when conductingiterative modeling studies.
Examples:Forceeq - -
force equilibrium ''. '
. . .Examples:
K_stoic >SOH 1.0K stoic >WOH 1.0
Convention option. Defines the conventionused for simulating ion exchange equilibria.Methods for computing ion exchange equilibriavary in the approach used to approximate theactivity of the exchanged species. Ion exchangereactions in RATEQ can be simulated using the
- Gapon or Gaines-Thomas conventions asdescribed in section 2.5.3. All reactionsinvolving a particular exchanger use the sameconvention and the default is the Gaines Thomasconvention.
Examples:Convention Gaponconvention gaines
' rate law option. Defines the rate law for eachrate-controlled reaction. This can be any'number of lines and must end with the phrase"Endratelaw". There methods for describingrate laws are described in greater detail below.
. .; . .
! ._ _ _
molardens option. Molar density of mineralphase (molesAL) is given. This option is usedwhen changes in mineral concentration areprinted as a volume fraction. Alternatively, the''-keyword density can be by given.
Examples: -
Molardens 44.167molardensity 50.'density 62.5 ' -
K_stoic option. Sets an option so that thestoichiometric coefficient for surface species can
37 I
-- Ma
Table 3.13 Summary of Reaction Options for Geochemical Reactions in RATEQSpecies Type
Solution Surface Solid Exchange Option' DescriptionPhase
x x x x log k Logio of the thermodynamicequilibrium constant
x x x x delta h Enthalpy of reactionsX x x X delta h units Units of enthalpy of reactionX Gamma Debye-Iluckel activity coefficient
parameters.X x x x analytical Coefficients of an analytical expression
used in adjusting the temperaturedependence of the log K.
X x x x no-check Toggle to suppress checking thereaction for charge balance
X x x x is ignored2 Toggle to ignore a reaction for asimulation
X x x x force eq2 Toggle to force the reaction to beequilibrium controlled even if a ratelaw is given
x min dens2 molar density of mineral phase_(moles/L)
x x K-stoic Sets an option so that thestoichiometric coefficient for surfacespecies can be different in the massbalance equations and the mass actionexpressions
x convention 2 Defines the convention used forcompute ion exchange equilibria
X x x x ratelaw2 Defines the rate law for each ratecontrolled reaction. This can bemultiple lines long and must end withthe phrase "End rate law"
' Each option can be specified by any mixture of upper and lower case letters. In addition, eachoption can be written with a leading hyphen (e.g. -logK) 2 Indicates an option in RATEQ but notPIIREEQC
Example:ratelawsimpleforward 0.01 (OH-)A2 (Fe+2) (02)
endratelaw
There are two options for including rate laws fora given reaction in the reaction file. These twooptions are referred to as the simple and generalmethods, and both of these approaches aredescribed below. These different approaches arespecified by including the name simple orgeneral on the line immediately following therate-law identifier.
3.3.4.1 Description of Rate LawsImplemented in RATEQ
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Time units To guard against errors the couldresult from inconsistent units, the variable unitst_units can be specified in the rate law. This is'a*case insensitive variable that is compared withthe units given in the'BTN file and if the units'.do not match, the simulation is stopped
The simple rate law. The format of the simplerate law is described in Section 2.6 (equation 2-37). The simple rate law includes a line for theforward reaction rate, the backward reactionrate, and an option to compute the backward rateconstant from the log K.
Forward: The first line of the simple rate law.specifies the forward reaction rate. The linecontains the forward rate constant followed by alist of species that are included in the forwardrate term. No units are specified with the ratelaw, and it is assumed that the units areconsistent with the time units used in thereactive transport model.
entered multiple times in the forward orbackward reactions.
Additional Examples. The following rate lawdescribes the irreversible oxidation of acetate byoxygen:
ratelawt_units secondssimpleforward l.Oe-O Ac- 02
endratelaw
The rate law below describes the reversible rateof an adsorption reaction, where the backwardrate constant is calculated from the equilibriumconstant and the specified forward rate constant.
ratelawsimpleforward l.Oe-Ol >SOH U02+2backward 2 >SOU02+2 H+adjustkb
end ratelaw
Finally, the following example specifies theirreversible oxidation of Fe 2 by 02:
Exampleratelaw
simpleforward l.Oe-Ol Fe+2 02 OH- OH-
endrate law
Example:forward 2.2 U02+2 C03-2
Backward: The second line, which is optional ''specifies the backward rate constant followed by'a list of species that are included in thebackward rate term.
Example:backward 1.3 U02C03
Adjustkb: The third line, which is also'optional, contains the phrase 'adjust kb', whichindicates that the backward rate constant read onthe second line will be replaced by a rateconstant calculated from the forward rateconstant and the equilibrium constant (kb=kfK).
Examples:Adjust kbadjust-kb
The simple rate law'does' not allow for species ; -raised to non-integer powers, but these can be iconsidered by using the general rate law. If a' -
species concentration occurs in the rate lawraised to an integer power, that species must be
The general rate law. The general rate lawincludes the ability to simulate rate- controlledreactions that are governed by both equation 2-39 and 240. These rate laws are rather generalrate laws that include Monod kinetics, massaction kinetics and other nonlinear processes.The general rate law is selected by including aline containing the word, general, on the lineafter rate law.- After this specifier,' the followinglines can be included in specifying a general ratelaw.
k forward K FORW: This is the forward rateconstant for the reaction:.No units are specifiedwith the rate law and it is assumed that the units
39 -
---
are consistent with the time units used in thereactive transport model.
Example:K forward 1.3e-2
thermodynamic equilibrium constant, and Q isthe ion activity quotient. The Q value iscomputed using activities, except as notedbelow, so that the term (I-Q/K) equals zero atequilibrium. If the variable P is included, thenthe rate thermodynamic driving term is raised tothe P power, e.g., (I -Q/K)pk backward KBACK: This is the backward
rate constant for the reaction. No units arespecified with the rate law and it is assumed thatthe units are consistent with the time units usedin the reactive transport model.
Example:K_backward 1.3e-2
forward-stoic SPECIES COEFF: Thisoption specifies the species to be included in aforward rate law and a coefficient for thatspecies. The coefficient is a positive real valuethat is used as an exponent in the forward ratelaw. Forward-stoic may be repeated as manytimes as is necessary, and multiple species andcoefficients may be specified on the same line.
Example:Mass action kinetics 2.0
Monod Km SPECIES: This option specifiesC
that a monod term of the form isKm+C
included in the forward rate term. Km is the halfvelocity coefficient of the Monod equation, andC is the concentration of the indicated species.
Example:Monod Ac- 1.0e-03
Example:Forward-stoic I[+ 0.5
Inhibition: This option specifies that a Monod
term of the form i is included in theKi
forward rate term. Ki is the inhibition constanthalf velocity coefficient of the Monod equation,and C is the concentration of (he indicatedspecies.
backward stoic SPECIES COEFF: Thisoption specifies the species to be included in abackward rate law and a coefficient for thatspecies. The coefficient is a positive real valuethat is used as an exponent in the backward ratelaw. Backward stoic may be repeated as manytimes as is necessary, and multiple species andcoefficients may be specified on the same line
Example:Inhibition N03- 1.OE-05
Example:backwardstoic U020H 0.5
vmax: vmax: This is maximum rate ofsubstrate utilization used in a Monod Rate law.No units are specified with the rate law and it isassumed that the units are consistent with thetime units used in the reactive transport model.
Gibbs: Specifying this option limits irreversiblereactions to proceed only when the Gibbs freeenergy of reaction is less than a threshold value.If the Gibbs free energy of reaction is greaterthan the threshold, then the reaction rate is set tozero.
Example:Gibbs
Threshold AGIXN: This specifies AGRXN, thethreshold free energy of a reaction in units ofkJ/mol. This option is included because, in someinstances, biologically mediated reactions arebelieved to require a minimum free energy ofreaction in order to sustain metabolism. Units
Example:vmax 1.3e-2
Massaction kinetics P: This option adds theterms (I -Q/K) to the rate law where K is the
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can be written after the threshold value, but they' -- -' OUTPUT blocks are not required if only a batchare not read. speciation calculation is conducted.
Example:Threshold -2.0
3.3.5.1 SETUP DATA BLOCK
activation energy EA: This option species theactivation energy (EA) of a rate- controlledreaction. The units must be in W/mol. Theactivation energy is used in the Arrheniusequation to adjust the reaction rate fortemperatures other than 250C. Units can bewritten after the value of EA, but they are notread.
Example:activationenergy 45 kJ/mol
rate-variable OPTION: By default, the ratelaw is computed using concentrations, except forthe thermodynamic driving term (e.g., (1-QIK)).If OPTION is 'conc', then concentrations are.used in all calculations, and if OPTION is'activity' then activities are used in allcalculations.
Example:Ratevariable activityrate-variable conc
Each of the options available for describing the,,geochemical reactions is illustrated in asimulation presented in the following sections.Table 3.14 presents a list that identifies whichsimulation illustrates a particular geochemical .reaction option.
3.3.5 Geochemical Solver File - .The input file for the geochemical conditionsconsists of 6 data blocks, 'which are- labeledSETUP, REACTIONS, CALCULATION, -
OUTPUT, INITIAL CONDITIONS, andTIMED EVENTS. The SETUP data block is'optional. The INITIAL CONDITIONS andTIMED EVENTS blocks are only'used when:one-dimensional simulations-are conductedwithout using MODFLOW-2000 to compiute the'flow field. Finally, the CALCULATION and
Including the Setup data block in thegeochemical reactions file is optional. All of theinput in this data block are either not required, orhave default values. The data that can be inputinto the setup block are summarized in Table3.15
Record 1: SETUP is a keyword that indicatesthat this is the setup data block.
Example:Setup
Record 2: TITLES is a keyword indicating thatthe following lines are titles that will be printedat the top of most output files.
Table 3.14 Summary of Reactions Options inBenchmark and Examnle Simulations
No Option Ex' -
I log k - - ' All2 delta h 6.13 delta h units 6.14 Gamma All6 no check 4.37 is ignored8 force eq 6.310 min dens NS211 K- stoic NS 2
12 Convention 4.3313 rate law - simple - 4.2--14 Rate law-monod 4.2'15 Rate law general 5.2,6.316 T unit 6.3' Numbers refer to sections in this report; 2
Not shown in an example, see database; 3 Seedatabase
41:
-- .JI
Table 3.15 Summary of Input in the Setup Data BlockI SETUP
2 TITLES3 Title lines
4 ACTIVITY5 Activity Model6 = Ionic strength
7 NUMERICS8 j ITMINAX, DTSTEPS, DT_FACTOR TOLNONLIN
9 END SETUP
Example:TITLESTitles
Record 3: Title lines Each title line at most,200 characters long. Titles are printed at thebeginning of each output file. Up to 20 title linescan be input.
Example:Simulation of U(VI) transportusing the Waite et al surfacecomplexation model
Record 4: ACTIVITY is a keyword indicatingthat the next line establishes the method forcomputing activity coefficients. The defaultmethod is the use the Davies equation.
Record 5: Activity method, A parameter, Bparameter Three methods for computingactivity coefficients are available are the Daviesequation, the Debye-Huckel equation and theextended Debye-Huckel model, also known asthe 'B-dot' model. The default is the extendedDavies. The a and b values for each method canalso be included.
Record 6: FIXEDIONICSTRENGTH, Iindicates that the value entered as I will be useda constant ionic strength for computing activitycoefficients regardless of what thesimulated ionic strength is in any given iterationor location. If this line is omitted, the defaultbehavior is to use the computed ionic strength inthe simulations.
Examples:FixedIonic Strgth .01
Fixed-I 0.02
Record 7: NUMERICS is keyword thatindicates that the next input are parameters usedin controlling the numerical solution of thegeochemical calculations.
Example:NUMERICS
Record 8: ITMAX, TOLNONLIN,DT STEPS, DT_FACTOR ITANIX is themaximum number of iterations that thenonlinear solver will attempt. The default is200. TOLNONLIN is the tolerance to be usedin solving the nonlinear system of equations.The default value is 1.0E-09. DT STEPS is thenumber of chemistry time steps that will beattempted if the solver does not solve a set ofrate-controlled equations in one step. Thedefault is 100. DTFACTOR is the factor bywhich the time step will be reduced if the solverfails and attempts to restart itself.
Example:Debye l luckel 0.51 0.33B_dot 3.5 0.0150
42
11
Example:20 1.0e-06 500
3.3.5.2 REA CTIONS DA TABLOCK -
methods. For example, the electrical doublelayer parameters are included in this data block.Table 3.16 summarizes the data that can' beincluded in the REACTIONS data block.
Record l: REACTIONS is a keyword thatindicates the beginning of the REACTIONS datablock
The purpose ox the reactions data block Is todefine the solutions that are used to initialize the Exam]reactive transport model and to set the boundaryconditions. This data block is also used toidentify certain reaction-specific calculationTable 3.16. Summary of Input in the Reactions Data Block
ple:REACTIONS
I REACTIONS
2 File3* Database
4 Ignore5 Ignored Species
6 EDL7 EDL Method8 = EDL Surface Master Species
9 Diffuse10 Diffuse Species
11 Reaction set No.12 Reaction Input
13 Solution No.14 Species Type Conc Guess M2/g | G
15 End Solution No.
16 Reaction set No.17 | Reaction input
18 Solution No.'19 - Species | Type; Conc Guess M2/g G
20 End Solution No.
21 END REACTIONS
Record 2: File This specifies the reactiondatabase file that will be used for batch and I -D
calculations when MODFLOW-2000 is not usedto compute the flow field.Example:
43 '
-. �.Il
File
Record 3: Filename. This specifies the name ofthe reaction database file that will be used forbatch and l-D calculations.
Example:C:\RATEQ\DATA\RXNS.DAT
Record 4: Ignore This record indicates that thenext line or lines contain a list of species thatwill not be included in the simulation.
Example:Ignore
Record 5: Ignored species is list of species thatwill be excluded from the simulations.
Example:DIFFUSE
Record 10: Diffuse species This is a list of thenames of species that are included in the diffuselayer calculations. If 'All' is entered, then everycharged species in solution will be included inthe calculations.
Examples:Ca+2 Mg+2 Na+
All
Record 11: Reaction set No This keyword isused to identify that the following lines identifynew master species, new reactions, or newreaction properties. The numerical value No isused to identify the reaction set. Multiplereaction sets (with related solutions) can bedefined possibly containing a unique phaseassemblage.
Example:Aragonite Chalcedony e-
Record 6: EDL This keyword is used toidentify the following lines as EDL properties.
Example:EDL
Record 7: EDL METHOD Defines themethod for computing electrical double layerproperties. Currently, only the diffuse layermodel is supported.
Example:diffuse
Record 8: EDL surface master species This isa list of the names of surfaces as defined in theSURFAEMASTERSPECIES block that areincluded in the electrical double layercalculations.
Example:Reactionset I
Record 12: Reaction Input New reactions canbe specified using the format described insection 3.3.4.
Example:SOLUTIONSSPECIESAc- + H+ = C114 + C02Rate-law
GeneralVmax 12.0Monod Ac- 0.01
Endratelaw
Record 13: Solution N This keyword is toindicate that the following lines identify the Nthsolution. All solutions must be number so thatthey can be referenced in defining the initial andboundary conditions and source concentrations.
Example:>SOII
Record 9: Diffuse This keyword is used toidentify the selected species will be removedfrom solution and accumulated in the diffuselayer to maintain electroneutrality The defaultis to not remove any species from solution.
Example:Solution I
Record 12: Species, Type, Conc, Guess,m2/g, g/l This input is defined as follows.
44
Species is the name of a master species, a. - . I -
surface master species, an exchange masterspecies, a kinetically controlled species,-amineral phase, a gas phase or it may be'alkalinity'. Type can be fixed, aqueous, total, 7>pH if the species is H+, or gas if the species is a,gas. If the species is fixed, the concentration of lthe given species will equal the specified Kconcentration. If type is aqueous, then theconcentration refers to total dissolvedconcentration and if the species type is total theconcentration refers to the total aqueous, surfaceand exchanged concentration. Theconcentration is the pH value if the type ofspecies is pH, the alkalinity if the species is :'alkalinity', the log of the partial pressure if thespecies is a gas, or the concentration in moles/L.Guess is an optional value that is used as aninitial guess of the species concentration. M2/g isthe specific surface area and only applies tosurface site. Similarly, g/l is the concentration'of the adsorbing phase. Both m2/g and g/1l musthave units after the value.
Records 18-20: Solution Input These recordsare optional and if included are identical toRecords 16-17. Each new solution should havea unique solution number.
Record 21: ENDREACTIONS is a keywordthat indicates the end of the REACTIONS datablock.
Example:ENDREACTIONS
3.3.5.3 Calculations Data BlockThe calculations data block determines the typeof calculation that is being conducted and certainspecies controls for each calculation type. Thereare four types of calculations that can beconducted, including batch kinetic simulations,batch range simulations (where theconcentration of one variable is varied in a batchcalculation), I -D transport calculations, andMT3DMS calculations. The input for each ofthese calculation options varies as shown inTable 3.17.
Example: -'Solution 1H20 total cU02+2 totalH+ pHC02(g) gasNa+ aqueous>FeOHs total>FeOHw total 1.end-solution I
55.I.Oe-06I n
Record 1: CALCULATION is a keyword that- . indicates the beginning of the CALCULATION
data block.o.u
-2.0I.Oe-21.Oe-5
Oe-3 600 m2/g 2 g/L _
Records 16-17: Reaction_set and inputThese records are optional and if included are .identical to Records 11 and 12. This is usefulfor defining a new set of reactions that will beused to compute the initial solutions that areused for initial and boundary conditions andsource waters. Alternatively, new reactions canbe defined that apply to the transportcalculations. For example, it is possible toconvert a reaction from being equilibriuimL 'controlled for the purposes of computing theinitial solution composition to a rate-controiedreaction for the purposes of transportsimulations.
Example:CALCULATION
Record 2: Calculation type defines the type ofcalculation to be conducted. Calculation typecan be either kinetic, range, I -D or MT3DMS.
Example:kinetic
Records for kinetic calculationsOnly one record is read for kinetic calculations
Record 3: tmax TIME This record is used tospecify the maximum time of the batchcalculation.
Example:
45
TMAX 10. Table 3.17. Summary of Input in theCalculations Data Block
Records for range calculationsOnly one record is read for range calculations
Record 3: Species Cmin:Cstep:Cmax TypeSpecies is the species whose concentration willbe varied in the range calculations, Cmin is theminimum concentration of the species, Cstep isthe change in concentration from one calculationto the next, Cmax is the maximumconcentration of the species. Type is optionalinput that indicates that the input concentrationsare logs of concentrations and Cstep is the logunits.
Examples:pH 5:.2:8Fe+2 I E-04: I E-05: I E-06Hg+2 -9:.1:- 6 log
Records for IMT3DNIS or l-D calculationsOnly two records are read for MT3DMScalculations, and both are optional.
Record 3: Ignore This record indicates that thenext line or lines contain a list of species thatwill not be included in the simulation
Example:Ignore
Record 4: Ignored species is list of species thatwill be excluded from the simulations.
I CALCULATION
2 Calculation Type
RECORDS FOR KINETICCALCULATIONS
3 tmax
RECORDS FOR RANGE CALCULA TIONS
3 Cmin:Cstep:Cmax type
RECORDS FOR M MT3DS or l-DCALCULA TIONS
3 Ignore4 Ignored species
5 Reaction Set, No.
RECORDS ONL Y FOR I-DCALCULATIONS
6 Domain7 Value input type
8 ID Transport9 Value input type
10 Discretization11 Value input type
12 END CALCULATIONExample:Aragonite Dolomite e-
Record 5: Reaction set, No, Although multiplereaction sets can be used to define the solutions,only one reaction set can be used in the transportsimulation. This record selects the desiredreaction set. The default is to use reaction set l.
Records only for i-D transport calculationsSeveral records are required to conduct l-Dtransport simulations. These records arerequired to create the LMT file used in thesimulations. All of these records are optional.These records are in addition to the optionalinput in Records 3-5.
Example:Reaction-set 2 Record 6: Domain This entry is used to
indicate that the default values for the length ofthe I- dimensional column and the total time for
46
11
the simulation will be changed. The; default ' 'length is I and the default time is 2.
Example:Domain
velocity,' porosity, dispersivity, molecular'diffusion coefficient, immobile'porosity andmass transfer coefficient will be changed. *Thedefault velocity is 1, the default dispersivity is0.01, the default porosity is 1, the defaultmolecular diffusion coefficient, immobileporosity and mass transfer coefficient are all 0.
Record 7: Value, Input Type This record carbe used to override the default values for thedomain. The input type can be either 'xmax' or'tmax' to override the total length of the colufior the length of the simulation. Either one orboth default values can be overridden
I
, 1
11nI
i
Example:I-D Transport
Example:10 tmax
Record 8: Discretization This entry is used toindicate that the default values for the number ofgrid cells in the one-dimensional column and thelength of the time step. The default number ofgrid cells is 10 and the default time is computedfrom a Courant number (V*At/Ax) equal to 0.5.
Example:discretization .
Record 9: Value, Input Type This record canbe used to override the default values for thediscretization. To change the grid spacing theinput type can be either ndx for the number ofgrid cells, dx for the length of grid cells, orPegrid to compute Ax from the grid Pecletnumber (Ax2/(DAt). To change the time step theinput type can be either dt for the length of steps,or Courant to compute At from the Courant -number (V*At/Ax). When either Ax or the'grid-Peclet number is specified, the Ax may bedecreased slightly to give a uniform gridthroughout the column.
Record 11: Value, Input Type This record canbe used to override the default values for the I -Dtransport properties. The input type must be --either the initial velocity, dispersivity, diffusion,porosity, im_porosity or masstransfer. Record11 may be repeated as necessary. Units may besupplied and if they are present, they will becompared with the units given in the BTN file tocheck for consistency.
Examples:velocity0.3 porosity0.02 im porosity0.2 mass-trans
Record 12: ENDCALCULATION is akeyword that indicates the end of the'CALCULATION data block.
Example:ENDCALCULATION -
3.3.5.4 Output Data Block
The output DATABLOCK controls how thegeochemical concentrations will be written toselected output files and the options for this datablock are summarized in Table 3.18.'
Examples:- ndx
0.8 Pegrid0.02 dt0.9 courant
Record 1: OUTPUT is a keyword that indicatesthat this is the output data block.
Example:OUTPUT
Record 10: 1-D Transport This entry is usedto indicate that the default values for the
47
_ _ _ .au
Record 2: Output Type indicates the type ofoutput to be printed. The type can be'breakthrough' for concentration histories,'profile' or 'snapshot' for concentrationdistributions at all nodes at a selected time,'kinetic' for batch kinetic simulations, or 'range'for range calculations.
Examples:Breakthroughsnapshot
Record 3: file indicates that the next name willspecify the file name
Example:FILEfile
Record 4: filename indicates the name of theoutput file including the extension. Specifyingthe filename is optional. If the filename is notspecified, then the output file will be createdfrom the name of the geochemical reactionsfilename. The root of that filename (thecharacters up to the first dot) will be used and anextension of .brk, will be added to the name ofbreakthrough files, .prf will will be added to thename of profile files, .kin will be added to thename of kinetic output files, and .mg will beadded to the name of range output files. Inaddition, if breakthrough curves are printed atmore than one location, then a number will beappended to the filename root.
Table 3.18 Summary of Input in the OutputData Block
I OUTPUT
2 Out ut Type
3 file4 File name
5 format6 Format description
7 = PV
8 species9 Species list
10 = locations11 Location list
12 time13 Time values
14 END OUTPOUT
Record 5: format description indicates theformat of the output. The file format can beeither MT3 for a binary file in MT3DMS outputformat, or a legal fortran format string enclosedin parentheses.
Examples:MT3(lx,i5,3(2x,el2.4))
Example:background.brk
Record 7: PV indicates that the pore volumeswill be included in the output file. This is onlyuseful for 1-dimensional transport simulations
Record 5: format indicates that the next recordwill specify the output format Example:
PV
Example:Format
Record 8: species indicates that the next recordwill specify a list of species.
Example:species
48
11
Record 9: Species list is a list of species thatwill be written to the'output file. The speciescan contain the names of individual species, pH'or alkalinity. In addition, if a master species isimmediately followed by (aqu) then the total --:concentration of that master species in solution'will be printed. Similarly, if the master speciesis followed by (ads) the total adsorbedconcentration is printed, and if the totalconcentration is followed by(s) the total solidphase concentration is printed.
Examples:Ca+2(aqu) pHU02+2(aqu) U02+2(ads)'Alkalinity, U(+4)(s)
Example:0.1 1251020
3.3.5.5 INITIAL CONDITIONSDATA BLOCKThe initial coinditions block identifies the initialconditions for simple l-D transport where flowvelocities are specified in the GeochemicalSolver filer rather than read from the LMT filecreated by MODFLOW-2000. Table 3.19summarizes the input that can be included in theinitial conditions data block.
Record 1: INITIALCONDITIONS is akeyword that indicates that this is the initialconditions data block.
Example:INITIALCONDITIONS
Table 3.19. Summary of Input in the InitialConditions Data Block
I INITIAL CONDITIONS
TYPE XMIN XMAX SOLUTION
8 END INITIAL CONDITIONS
Record 10: locations indicates that the nextlines will specify the output locations. Thisoption only applies to breakthrough curves
Example:Locations
Record 11: location list indicates locations in -'the model domain where the breakthroughcurves will be recorded and then printed. Thelocations are specified in physical dimensions ashx,y,z values, and the concentration at the cellcontaining that location will be printed.
Example:10 2 Record 2: TYPE refers to the type of initial22 6.7 condition and is used to distinguish simulations
' - that have immobile zones from those that do notRecord 12: time indicates that the'next record have immobile zones. If type is l-D, then thewill specify the when the output will be printed. initial conditions defined on this line applies toThis option only applies to breakthrough curves all nodes. If TYPE is IMMOB, the initialand concentration snapshots. In addition, conditions apply to only the immobile zones,specifying the time is optional. The default is to and if TYPE is MOB, then the initial conditionsprint 10 evenly spaced concentration snapshots .x apply to only the mobile zone. XMIN is theand approximately 100 evenly distributed -- minimum distance along the column where thebreakthrough values. initial conditions will be defined, XMAX, is the
maximum distance along the column where theExample: initial conditions will be defined, and
Time SOLUTION is the solution number used toidentify the initial conditions. The following
Record 13: time list is a list of times when the example defines a column that has solution 2output will be printed. The list of values must be throughout the column, except in the immobilein ascending order. zone between distances of 2 and 3. If XMAX
49 '
-- 1I
exceeds the length of the column, the XMAX ismaximum length of the column is used. Table 3.20. Summary of Input in the Timed
Event Data Block
Example:ID 0 10 2IMMOB 2 3 1
Record 3: ENDINITIALCONDITIONS is akeyword indicating the end of the initialconditions data block.
I TIMED EVENTS
2 BOUNDARY CONDITIONS3 __Location, Solution 2
4 VELOCITY5 J Flow velocity
6 DURATION7 J TIME
8 END TIMED EVENTS
Example:ENDINITIALCONDITIONS
3.3.5.6 TIMED EVENTS DATABLOCKThe timed events data block contains input thatchanges the boundary conditions or flowvelocity at selected times. Table 3.17 contains asummary of the information that can be includedin this data block. This data block is only usedfor simple ID calculations. The parametervalues are set and held constant until thesimulation time reaches the value in Record 7.
Record 1: TIMED EVENTS is a keyword thatindicates that this is the timed events data block.
Example:TIMEDEVENTS
the velocity is optional and is useful forsimulating flow interruption experiments.
Example:Velocity
Record 5: This specifies the velocity in thecolumn.
Example:I .OE-09
Record 6: Duration is a keyword indicating thenext input will specify the duration of theboundary conditions or flow velocity.
Record 2: BOUNDARYCONDITIONS is akeyword that the next input will change theboundary conditions.
Example:Duration
Example:Boundary conditions
Record 3: This option specifies the location ofthe boundary and the solution number for theboundary. The location is either left for x=0 orright for x=L
Record 7: This specifies the time the velocity orboundary condition are held constant.
Example:2.9
Record 8: END TIMED EVENTS is akeyword indicating the end of the timed eventsdata block.
ExampleLeft 3 Example:
ENDTIMEDEVENTSRecord 4: Velocity is a keyword indicating thenext input will change the velocity. Changing
50
11
4 BENCHMARK SIMULATIONS
4.1 INTRODUCTION
Benchmark simulations were performed to testthe RATEQ code- produces results that agreewith other geochemical and reactive transportsimulators that have been independentlydeveloped. It should be noted that thesebenchmark studies do not 'verify' a particular
as IM. Both water and calcite are listed as fixedspecies, which indicates that each species will
' - - have the specified concentration -afer theif speciation is completed. Calcium is not
included in the input file, but the calciumconcentration was computed from calcitesolubility. Similarly, the OH- concentration wascomputed from the equilibrium with water.
code for a particular appucation. I nesebenchmark simulations also illustrate many ofthe features of RATEQ.
4.2 BATCH CALCULATIONS
In using RATEQ for a reactive transportsimulation, it is first necessary to complete a.speciation calculation so that the initialconditions in the transport domain can bedefined. These speciation calculations areidentical to the calculations conducted by many --
speciation codes, including PHREEQC,HYDRAQL (Papelis et al., 1988); MINTEQA2; - -and FITEQL. Two simulations are presented to -demonstrate that batch calculations performedwith RATEQ agree with other geochemicalmodels. These simulations consider: (1) thespeciation of U(VI) in Naturita groundwater, and(2) the sorption envelope for As(III) sorbed byferrihydrite. A third simulation compares batch-kinetic simulations conducted with RATEQ with..results obtained with a commercially available_numerical package.
4.2.1 Naturita Groundwater Speciation
In September 1999, well NAT26 at the Naturita -
Mill Tailings site (Davis and Curtis, 2003) wassampled, and the measured composition is listedin Table 4.1 The correspondin'g RATEQ input-:'file is listed in Table 4.2. Table 4.2 lists the 'RATEQ input of each of the species in Table ;4.1. The units for the dissolved species aremoles/L (M) with the exception of pH. TheRATEQ input file also contains an entry forwater that must be explicitly stated in the inputfile. An initial concentration'of calcite is given
The RATEQ input file also contains entries forthe surface sites >WOH, 0>SOH, and >ZOH.These sites can react with dissolved U(VI) to
-'form adsorbed U(VI) complexes. However,~because the concentration of UO2 ' 2 is specifiedas an 'aqueous' variable, the adsorptionreactions do not reduce the total dissolved UO2+2
concentration. Instead, the calculation computesthe surface U(VI) species that are in equilibriumwith the measured groundwater concentration.
-The adsorption reactions used in these'simulations were taken from Davis et al. (2004a)and were included in the thermodynamicdatafile.
Speciation calculations were also conductedwith the geochemical equilibrium model.FITEQL (Herbelin and Westall, 1999). Theresults'obtained using the two models are shownin Figure 4.1, which illustrates the speciesconcentration computed with each of the two'models. The figure includes all of the U(VI)species as well as the concentrations of majorions. The results show an excellent agreement
Table 4.1 Composition of Groundwater atwell NAT26 at the Naturita UMTRA Site
Species 1 Concentration (M)
-- .Ij
Table 4.2 RATEQ Input File for NAT26 Groundwater Speciation CalculationSetup
TitlesSpeciation Calculation for Naturita well NAT26Sampled on: 21-Sep-1999Assume equilibrium with calcite
End Setup
Reaction Set I ! define geochemical reactions and solution compositionsfile
..\reaction file\PHIREEQC nat.dat
ignore ! define species not considered in the solutionsJarosite-K S-2 [IS- CH4 C114(g)
solution 1! SPECIES TYPE CONCENTRATION !Molar concentrationsH120 fixed 55.Calcite fixed 1.U02+2 aqueous 1.0042e-005H1+ plI 7.15Alkalinity aqueous 1.1260e-002Kit aqueous 1.4937e-004INMg+2 aqueous 3.1845e-003Na+ aqueous 4.4367e-002S04-2 aqueous 1.5833e-002Cl- aqueous 1.6360e-002>WOH total 1.711E-05>SOIl total 2.079e-07>ZOII total 1.732e-08
end solution I
end of solutionsEnd of reactions
between the two models for aqueous processes that occur on different time scales,concentrations that vary over 20 orders of which results in computed profiles that changemagnitude. abruptly with time. For this example, a complex
organic was assumed to be transformed to a4.2.2 Simulation of Rate-Controlled simple organic acid, acetate (Ac-). Then theReactions in Batch acetate reacts with two terminal electron
acceptors in tile system, namely 02 and SO42.The purpose of this benchmark calculation was Acetate also formed C114 and CO2 in theto demonstrate the ability of RATEQ to solve simulations. The initial degradation of therate-controlled reactions in a batch system complex organic was described by:characterized by a stiff set of equations. Stiffdifferential equations are characterized by Complex Organic = Ac- + H4 + CO2
52
11
100
C;
4
|a Simulated Conceintration I- 1:1 Line .. I
E 1
° 10*c
.0,a)
10
C)
w
.-.us
W . _-;
j
10
15
2M-20
I1 I I1 -20 10 10
FITEQL: Species Concentration (M)10-5 100
Figure 4.1. Comparison of simulated concentrations computed using RATEQ and FITEQL.
which was simulated using a simple first orderdecay rate law:
ri= -klComplexOrganic
The oxidation of acetate by 02 is described by:
Ac +O 2 +H+=2CO2 + H2O
The rate for this reaction was assumed to begoverned by Monod kinetics:
Acr2=-VMA X2 2 (C 'C0 2 -
Ac
where where vmAx2 is the maximum rate ofsubstrate utilization, K2 is the Monod halfvelocity constants, The intermediate Ac- wasalso oxidized by S04 '2 in the simulations by thefollowing reaction:
Ac + 2H+ + S0 42 2CO2 + 2H20 + HS
This rate was also modeled by the Monodmodel, but this time a dual Monod formulationwas used, and it was assumed that S04 2.reduction was inhibited by the presence of 02-This gives a rate law: -
r3 = -VMAX3 =a C K C.
53
-- -JI
where VMAX3 is the maximum rate of substrateuitilization, Ks3 and Ka3 are Monod half velocityconstants, K13 is an inhibition constant, and thelast term in brackets inhibits the reaction ratewhen C02 >> K13. Finally, the cleavage ofacetate,
Ac-+l- = CH4+ CO2
was modeled using a Monod model that wasinhibited by the presence of SO4 2.
r4 = VMAX4 [ Ac ]tic K14+CS 4 )
VMAX4 is the maximum rate of C1 4 formation,KS4 is the Monod half velocity constant formethanogenesis and K14 causes the reaction to beinhibited by SO4, The inhibition terms in theabove rate laws are one of the reasons that theresulting set of equations becomes stiff.Table 4.3 contains a list of all of the parametersused in the simulation. These parameters havelittle physical or experimental basis but wereselected to make the equations relatively stiff.
The RATEQ input file is listed in Table 4.4.This input file illustrates that the degradationreactions are listed in the RATEQ input filerather than in the thermodynamic datafile. Thisapproach is often most convenient whenconducting iterative modeling studies. The inputfile also illustrates how the Monod rate laws aredescribed in the input file. Note that the speciesH12S was ignored in the simulation so that
Table 43 Summary of Parameter Values inthe Batch Kinetic Simulation
Parameter Valuek, I .Ox I 4 (d-82
Vmaxi 1.0 xlO (d- )Vms1 2 1.0 x104 (d-l)Vmax3 1.0 xI l dI)KrI 1.0 xl02 (,,V)
KS2 2.0 xlO-3 (X 1)KS3 2.0 xlO-3 (M)
K 2 1.0 x-10'3 (M)
K13 1.0 x10-8 (m)
comparisons could be easily made as describedbelow. Finally, the CALCULATION blockdefines the time at which the output will bestored in the output file.
Comparisons were made with results obtainedusing MATLAB® to integrate the set of rateequations. The solution obtained usingMATLAB® considered only the reactantsincluded in the four degradation reactions listedabove. Thus, the approach cannot easilyconsider other species, such as H2S or H20.Nevertheless, MATLAB® includes several verystable numerical routines that can be used forsolving stiff sets of differential equations, andtherefore provides a good tool for conductingcomparisons between two numerical approaches.
The simulated concentration histories obtainedusing RATEQ and MATLABO are compared inFigure 4.2. The simulations show that 02 isgradually consumed and once the 02 is nearlycompletely consumed, then S04 2 is very rapidlyconsumed, followed immediately by theconversion of Ac- to CE14 and CO2. For each ofthe six species considered, there is an excellentagreement between the two very differentnumerical approaches.
4.23 Adsorption of Cd+2 by Ferrihydrite
The purpose of this benchmark simulation is toillustrate how to set up electrical double layercalculations and to demonstrate that adsorptioncalculations performed with RATEQ using thediffuse double layer model agree withcalculations obtained using a different numericalmodel. In addition, this simulation demonstrateshow to conduct batch simulations where theconcentration of one species is varied (in thiscase, p1l) over a range of values, while keepingall other values constant.
The dominant reactions, which were included inthe reaction file, consist of the adsorption ofCd 2 on ferrihydrite, and in one instance,complexation of Cd2 ' by relatively highconcentrations of Cl- (Table 4.5).
54
11
:;I
Table 4.4 RATEQ Input File for Batch Kinetic Rate LawSetup
TitlesBenchmark Simulation 2Demonstration of integration kinetics in RATEQ for areaction set with a stiff set of equations
Activity ! fixed to zeroFixed I 0.
End Setup
Reaction Set 1 ! define geochemical reactions and solution compositionsfile
..\reaction file\PHREEQC nat.dat
ignore ! define species not considered in the solutionse- H2S CH4(g) 02(g) H2(g) Hac
Reaction ! define new reactions not I the database
SOLUTION SPECIES
Complex = Ac- + H+ + C02log K 1rate law
generalkf 1.OeO4linear Complex
end rate law
Ac-+02+H+ 2C02+H20log K 1.0
rate lawgeneralvmax 1.Oe+05monod Ac- 1.Oe-02linear 02
end rate law
Ac-+ 2H++ S04-2= 2C02+ 2H20+ HS-log K 6.0rate law
55
Table 4.4 RATEQ Input File for Batch Kinetic Rate Law (continued)
generalvmax 1.0e04monod Ac- 2.0e-03monod S041-2 2.0e-03inhib 02 1.0e-10
end rate law
Ac- + I+ = C114 + C02logK 6.0rate lawgeneraevmax 1.0eO3monod Ac- I.Oe-04inhib S04-2 1.0e-10
end rate lawv
end
end_
solution ISPECIES TYPE CONCENTRATION
1120 fixed 55.11+ pH1 7.02 fixed 2.0e-04Alkalinity aqueous _.Oe-03Complex fixed 8.0e-03Ac- fixed 1.0e-10S04-2 fixed 1.le-03HS- fixed 1.0e-50C114 fixed 1.0e-50
end solution 1
end solutionsend of reactions
Calculationkinetic
tmax 10.01End Calculation
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Table 4.4 RATEO Innut File for Batch Kinetic Rate Law (continued)Output
kinetictime
le-10 le-09 le-08le-07 2e-07 4e-07 6e-07 8e-07le-06 2e-06 4e-06 6e-06 8e-06le-05 2e-05 4e-05 6e-05 8e-05le-04 2e-04 4e-04 6e-04 8e-04le-03 2e-03 4e-03 6e-03 8e-03le-02 2e-02 4e-02 6e-02 8e-02le-01 2e-01 4e-01 6e-01 8e-01le-00 2e-00 4e-00 6e-00 8e-00
SpeciesComplex Ac- 02 S04-2 HS- CH4 -
End
End
le 4.5 Summary of Predominant Reacti6nsf6r Adsorption of Cd'2 by FerrihydriteReaction - LogKHfo sOH + Cd 2 = Hfo sOCd+ + H 0.47Hfo wOH + Cd 2 = Ho wOCd+ + H+ -2.91Cd 2 + Cl- = CdCI+ 1.98CdI2 + 2 Cl = CdC12 2.60Cd' + 3 cr = CdCI3 2.40
Tab!
The percent of Cd'2 that was adsorbed byferrihydrite was computed over the pH 'rangefrom 5.5 to 8.0 for a batch system that contained0.1 g/L of ferrihydrite.'- The calculations wererepeated three times for the cases of total Cd2
concentration 10-7M, 10'5M, and 10-5M with10-2M Cl- as the electrolyte anion, instead ofNo3-.
(m2/L), and this value is computed from thesupplemental information provided on the linespecifying the total HfowOH concentration.Finally, the CALCULATION block uses theRANGE option to vary the pH in thecalculations from 5.5 to 8.0. The output fromthe RANGE calculation gives a simple tablecontaining pH and total adsorbed Cd.
Table 4.6 lists the RATEQ input file for this Simulations conducted with RATEQ aresimulation. First, this file illustrates the 'edl' --compared with results obtained with FITEQL inoption in the REACTION data block. The Figure 4.3.- The simulations show that thefollowing lines indicate that the diffuse double percent of Cd adsorbed decreases withlayer model will be used and the names of the '; increasing Cd concentration and in the presencesurface master species included in the EDL of Cl. For all 3 scenarios, the two models givecalculations. The diffuse double layer model an excellent agreement for the simulated percentrequires a value of the surface area concentration of Cd adsorbed by the ferrihydrite.
57.
-.- IV
CuM-.0 5Ma
14
E 0.2
N0 .10o
gE
a)
69
1
E
0ejn _------
0 -10 - -2 10°10 -6 10 -4 10 2 100
E2
i 05I
E:I
Time (d) Time (d)Figure 4.2.
pH
Figure 4.3. Comparison of simulated percent of Cd2 - adsorbed computed using RATEQ andFITEQL and the diffuse layer model.
58
11
Table 4.6 RATEQ Input File for Batch Adsorption of Cd+2 by Fcrrihydrite Using the DiffuseDouble Layer Model.
Setup
TitlesBenchmark Simulation 3Diffuse double layer model of Cd+2 adsorption on ferrihydrite
End Setup
Reaction Set I ! define geochemical reactions and solution compositionsfile
.Areaction file\PHREEQC nat.dat
edl ! use the diffuse layer modelDiffuse
Hfo s Hifo w
end -
solution 1SPECIES TYPE CONCENTRATION
H20 fixed 55.H+ pH 5.5Cd+2 total 1.Oe-07Na+ aqueous 1.0e-01N03- aqueous 1.0e-01iHfo sOH total 5.0e-06iHfo wOH total 2.0e-04 600. mA2/g 0.1 g/L
end solution 1
end solutionsend of reactions
CalculationRange-
H+ fix 5.5:0.1:8.01 ! Step pH from 5.5 to 8 in 0.1 pH units
End CalculationOutput
RangeSpecies
pH Cd+2(ads)
End
End
59 -
- - -Al
4.3 ONE DIMENSIONALREACTIVE TRANSPORTSIMULATIONS
Benchmark calculations using one dimensionalreactive transport scenarios were conducted totest the model in applications that coupletransport and geochemical reactions. Twobenchmark calculations were considered thatincluded: (I) rate-limited sorption, aqueousspeciation and biodegradation, and (2)equilibrium controlled transport withheterovalent ion exchange.
4.3.1 Rate-Limited Sorption, AqueousSpeciation and Biodegradation
This benchmark problem was originallyproposed by Tebes-Stevens and Valocchi(1997). This simulation involves a reactionnetwork that comprises: (I) complexation ofCo+2 by various forms of NTA, (2) microbialoxidation of HNTA 2 by oxygen, and (3) rate-limited sorption of Co+2 and CoNTA7. Thisproblem is also included as an examplesimulation in the PHREEQC documentation.The key reactions that dominate the reactivetransport in this system are listed below.For the conditions of the simulation, thedominant species of NTA in solution areHNTK 2 and CoNTA'. The dominant species ofCo in solution are Co+2 and CoNTA-. Thesespecies were related by the followingequilibrium controlled reactions:
NTA-3 + II+ = HNTA-2Co+2 + NTA-3 = CoNTAN
Several other reactions involving NTA and Cowere considered, and these reactions are listed inthe reaction file 'tebes-stevens.dat'. Theadsorption of Co+2 was described by a simplelinear isotherm. In addition, the sorption wasassumed to be kinetically slow and the rate lawwas described by:
Co+2 = >CO' 2
r1 =-k(Cc +2 - Kdl
where k, is a first order sorption rate constant,and Kdj is the sorption Kd value for the Co+2species. CoNTA- was assumed to sorb in similarfashion as Co+2. The adsorption reaction wasrepresented by:
CoNTA- = >CoNTA-
and the rate of sorption was represented by
r2 =-k2ICCoNTA. - C T Jwhere k2 is the first order sorption rate constantand Kd2 is the sorption Kd value for the CoNTA-species.
IINTA-2* was assumed to be biodegraded asdescribed by:
IINTA-2 + 1.62 02 + 1.272 1120 + 2.42H1+ =
0.576Biomass + 3.12CO2 + 0.424NI-14+
where the term, Biomass, is used to representactive microbial cells in the simulation. The rateof the biodegradation reaction was representedby the multiple Monod approach:
r3 =-VMAXXBI K + C T )(Ka+ )
where VMAx, K, and Ka are Monod parametersand Xrno is the biomass concentration. Finally,biomass produced by the IINTA-2 oxidation wasassumed to decay by a first order process:
r4 = -bXBIo
The specific values for the model parametersdeveloped by Tebes-Stevens andValocchi(1997) are listed in Table 4.7.Often in modeling microbial systems, anequation for the growth and decay of thebiomass is included in the set of equations, suchas:
60
iI
173O = YVMAXXBIOK HTA-J Kae+-J -bXBIO
where Y is the cell yield (g cells/mol HNTA 2).It is not necessary to include this equation inRATEQ because it is done implicitly by thestoichiometry of the HNTA2 oxidation reaction.
The benchmark simulation also specified a totaldistance of 10 m, a linear velocity of I mlhr, asolids concentration of 3750 g/L, a dispersivityof 0.5 m, and a total simulation time of 75 hr.Table 4-8 contains the RATEQ input file for'the'nTebes-Stevens benchmark problem. ' '
Simulation results are presented in Figure-4-4,which shows the simulated pH value andconcentrations of CoNTA-, HNTA2, Co+2,Biomass, and adsorbed CoW2. The RATEQsimulations are compared with simulationsobtained using the input file from thePHREEQC documentation (Parkhurst and
Appelo, 1999) in Figure 4.4. For each speciesshown in the figure, there is an excellentagreement between the two model simulations.
Table 4.7 Model Parameters for the Tebes-Stevens Benchmark Simulation
Parameter ValueLog K1 10.3Log K2 - 11.7
k 1 hr'k2 hr'''Kd, 5.07x104 g
Kd2 - 5.33x10 4 L/ZgVMAX 0.1604 mol/hr -
Ks 7.64x107 MKa 6.25x104 Mb - 0.00208 hr'
Table 4.8 RATEQ Input File for the Tebes-Stevens Benchmark SimulationSetup
ActivityDavies Equation .2 ! activity coeff method, b valueFixed I 0.00 ! fixed ionic strength
Ignore - !define species not considered in the solutionsC02(g) e-
!-DEFINE SOLUTIONsolution I1 Background concentration
120 fixed: 55HC03- fixed 1.513e-07 ...
61
--- JII
Table 4.8 RATEQ Input File for the Tebes-Stevens Benchmark Simulation (continued)NH41+ fixed 1.Oe-2002 fixed 3.125e-05NTA-3 aqueous 1.Oe-56Co+2 aqueous 1.Oe-56Na+ aqueous I.Oe-03Cl- aqueous I.E-03II+ p1i 6.0
Biomass fixed 1.2035e-06Dead Biomass fixed 1.Oe-20>WOH total 1.Oe-02>WOHCo+2 fixed 8.46e-26>WOHCoNTA- fixed 8.46e-26
end solution I
solution 2 ! Background concentration1120 fixed 5511C03- fixed 1.513e-07N114+ fixed 1.Oe-2002 fixed 3.125e-05HNTA-2 fixed 0.4366e-06CoNTA- fixed 4.793e-06Na+ aqueous 1.Oe-02Cl- aqueous I.E-021X+ pil 6.0Biomass fixed 1.Oe-20Dead Biomass fixed 1.Oe-20
end solution 2
End of solutions
End of reactions
CalculationTransport ! Options: Batch, Range, Transport, Mix
ignore ! define species not considered in the solutionsC02(g) e-
Domain10. xmax (meters)75.01 tmax (hours)
Discretization80 ndx Pegrid Number.25 Courant Number8 PDE method
62
11
Table 4.8 RATEQ Input File for the Tebes-Stevens Benchmark Simulation (continued)
1D-Flow1.0 velocity (mfyear) .0.05 dispersivity
End Calculation
Output
! define the species for the breakthrough curvesbreakthru
speciesCl- pH Co+2 CoNTA- HNTA-2 >WOH >WOHCo+2 >WOHCoNTA-Biomass Dead Biomass 02 NH4+ H2 Na+
End output
Initial Conditions ! Set the initial conditions on the grid
ID 0.0 I.e19 1 !dummy, xmin, xmax, soln number
End Initial Conditions
Timed Events
Boundary conditionsleft 0 10 2 ! location, ymin, ymax, soln num
Duration20
Boundary conditionsleft 0 10 1 ! location, ymin, ymax, soln num
Duration . .100000
End Timed Events -
63
- l
M0L
zM
2
1
00
0.2
Time (hr) Time (hr)
0.4
0.3I
0.21
0.15
N 0.1
0.050.1
U- Lup20 40
Time (hr)60 80 o 20 40
Time (hr)60 80
-J
v72E0
40 60 80 0 20 40Time (hr) Time (hr)
80
Figure 4.4. Comparison of RATEQ and PHREEQC simulationValocchi (1997) benchmark problem.
4.3.2 Equilibrium-Controlled assumed ciHeterovalent Ion Exchange shown in 1
media hadThis simulation is based loosely on the chemical capacity ofconditions in the Cape Cod aquifer and simulationexamines the effect of injecting a 5 mM KBr to the watetracer into a one-dimensional flow system. The and then in
results for the Tebes-Stevens and
:omposition of the initial water is'able 4.9. In addition, the porousan assumed total ion exchangeF2.1 meq/L of groundwater. Thewas conducted by adding 5 mM KBrr (composition shown in Table 4.9),ijecting 1.8 pore volumes into a
64
Il
hypothetical column. No dispersion was transport of the major ions, Ca, Mg, K and Na.included in the model simulations. The increase, Conversely, when H' ion exchange is included,in K concentration in the influe nt water caused the mtajor ions Ca, Mg, K and Na have a largerelease of Ca, Mg, Na and H from the exchanger ' - effect on the exchanged H'. In systems withsurface. The ion exchange reactions considered negligible pH buffering, such as in thein the simulation are listed in Table 4.10. Table simulation considered here, the changes in4.11 contains the RATEQ input file for the -- exchanged He cause large transients in pH inHeterovalent ion exchange benchmark problem. -- - solution. This could be important for the
--.---- transport scenarios that also include ions the
Figure 4.5 illustrates the simulation results - - exhibit strongly pH dependent adsorption.obtained using both RATEQ and PHREEQC. - -
The agreement between the two simulations isvery good. The results illustrate that therelatively high K concentrations displaced all ofthe other cations from the exchanger to varyingextents. The increase in K concentration causesan initial sharp decrease in pH, because'H'bound to the exchangers is released to solution.Subsequently, the pH increases because H+ is-readsorbed by the exchanger as the K - -
concentration retums to the initial concentration.--Similarly, Na, Ca, and Mg all show initialincreases in aqueous concentration, followed bya decrease below the initial concentration as the -- - -V innk rphime tn the initia1 gnntntrntrnn
Table 4.9 Assumed GroundwaterComposition for Ion Exchange BenchmarkSimulation
Species ConcentrationpH ' 5.2
- 1.5e-04Na l 1.5e-03Ca+2 3.0e-05Cl 2A41e-03KC 0.2e-03Br - 0.2e-03
Table 4.10 Ion Exchange Reactions and
The second example calculation repeated the Equilibrium Constants'first simulation except that ion exchange of H4 Exchange Reaction Liwas not included in the simulation. Again, the _ E
comparison between RATEQ and PHREEQC is CK* + >XNa - >XK + Na4' 0.excellent as shown in Figure 4.6. In addition, Ca42 + 2 >XNa = >X2Ca7+2 Nat 0.eliminating the He exchiangeireactionfrom the' ' ''Mg42 +2 >XNa = >X2Mg +2 Na+ 0.reaction network has a negligible effect on the ' - ' r + >XNa = >XH + Na ' 1.transport of K,'Na, Ca, and Mg -but there was a-'---significant effect on the simulated pH values. -.- .
This small effect results because the IT . .--concentration at pH values near 5 isapproximately 100 times smaller than the -concentration of the other ions. Thus, the protonconcentration has a negligible effect on the
C7 .7.86.0H
Table 4.11 RATEQ Input File for the Ion Exchange Benchmark SimulationSetup
TitlesBenchmark 5: Heterovalent ion exchange
End Setup
Geochemical Conditions
65:-
-- -I
Table 4.11 RATEQ Input File for the Ion Exchange Benchmark Simulation (continued)Reaction Set I ! define geochemical reactions and solution compositions
FilebenchS database.dat ! thermodynamic data file to use
!-DEFINE SOLUTIONsolution I -The background solution
1120 fixed 55II+ p'I 5.2E+00
Mg+2 aqueous 1.5e-04Na+ aqueous 1.5e-03Ca+2 aqueous 3.0e-05Cl- aqueous 1.95e-03K+ aqueous 0.2c-03Br- aqueous 0.2e-03>X total 2.1e-02
end solution
solution 2- The injectate1120 fixed 55II+ p1i 5.2E+00NMg+2 aqueous 1.5e-04Na+ aqueous 1.5e-03Ca+2 aqueous 3.0e-03Cl- aqueous 1.95e-03K+ aqueous 5.0e-03Br- aqueous 5.2e-03>X total 2.1e-02
end solution
End of solutions
End of reactionsCalculation
Transport
reactions I
I)omainI xmax13 tmax
Discretization100 ndx.75 Courant Number ! Cr =v*dt/dx
66
Table 4.11 RATEQ Input File for the Ion Exchange Benchmark Simulation (continued)1D-Flow
1 velocity0.0 dispersivity -
End Calculation
Output
breakthrough..species
pH Cl- K+ Na+ Ca+2 Mg+2
End output
Initial Conditions ! Set the-initial conditions on the grid
ID 0.0 1.eI9 1 Itype, xmin, xmax, soln number
End Initial Conditions - -
Timed Events
Boundary conditions -
left 0 10 2
Duration1.8
Boundary conditionsleft 0 10 I
Duration100000
End Timed Events
67
-- IL
.-- I
2E
IL-M
Pore Volumes
M
CLz
Pore Volumes
+
Pore Volumes Pore Volumes
1 6
E+ U.5
co
+
cm0)
41
21Io
C1I 5 10
Pore Volumes15
Pore Volumes
Figure 41.5. Comparison Of RATEQ and PIIREEQC simulation results for the heterovalent ionexchange benchmark problem.
68
11
I
4E.
0
6
+Ne.2
Pore Volumes - - Pore Volumes
6
2 4
z 2
I
lf I
0Pore Volumes
5 - 10Pore Volumes
15
EC4d - . .
- .c)
M
0)
5 10 .:15 0 5 10 15Pore Volumes -Pore Volumes
Figure 4.6. Comparison of RATEQ and PHREEQC simulation results for the heterovalent ionexchange benchmark problem 'for the case where H+ exchange was not included.'.
69
_-__JI
5. REACTIVE TRANSPORT SIMULATIONS RELATED TO THENATURITA UMTRA FIELD SITE
5.1 Introduction
Reactive transport simulations related to theNaturita field site were performed with theRATEQ code to simulate reactive transport inlaboratory columns, at the field scale withuniform properties, and at the field scale withnon-uniform properties. This section presents adiscussion of these simulations, and in so doing,illustrates additional features of RATEQ.
5.2 Transport in LaboratoryColumns with KineticallyControlled Sorption Reactions
The first example related to the Naturita fieldstudy simulates uranium transport in laboratorycolumns. These simulations were based onexperiments that were described previously(Davis and Curtis, 2003). The experiments usedthe flow interruption technique to evaluate theimportance of possibly slow sorption anddesorption kinetic effects. In this method, flowin the column is stopped for a period of time andthen the original flow rate is resumed. If kineticeffects are important, the concentrationmeasured in the column effluent changes duringthe flow interruption, because of slow sorptionor desorption that continues even in the absenceof flow. In the RATEQ simulations, the velocitycan be set to zero at specific time intervals, andthis causes the advection and mechanicaldispersion to stop. Molecular diffusion can besimulated if a non-zero molecular diffusioncoefficient is specified in either the DSP inputfile for in the l-D calculation data block.
The input file for these example simulations isshown in Table 5.1. The rate laws included inthe simulation were fit to batch data (Davis andCurtis, 2003). Two simulations were conducted.One simulation used rate constants derived fromthe batch data, and the second simulation usedthe same kinetic model except that the rateconstants were all decreased by a factor of 2.For these simulations, it is convenient to print
pore volumes instead of time, as shown in Table5.1. Simulation results are shown in Figure 5.1.For the slow kinetics simulations, there weresignificant changes in the U(VI) concentrationafter 19, 28 and 38 pore volumes, when the flowin the column was interrupted for approximately4 days. The changes are slightly smaller whenthe rates constants were not changed.
5.3 Two-Dimensional ReactiveTransport at the Naturita Field Site
This section describes some of the assumptionsmade in constructing the flow and transportmodel, but for brevity, does not reproduce eachof the input files required for the simulation.
The flow model was created using the ArgusMODFLOW graphical user interface (Winston,2000). All of the input files required forsimulating 2-dimensional reactive transport atthe Naturita site are available at the web site(http://wwwrcamnl.wr.usgs.gov/rtm). The sitecontains both the Argus 1 input file and all of theMODFLOW-2000 input files that are created bythe graphical user interface. Some of the detailsof the model construction are described below.
5.3.1 DomainThe spatial extent of the aquifer was taken fromaerial surveys of the site. The western boundaryof the aquifer was taken as the toe of the slope ofthe surrounding canyon walls. The easternborder of the site was taken as the eastern borderof the San Miguel River. This assumption wasbased on the fact that there is a sandstoneoutcrop along the eastern edge of the river. Thewidth of the alluvial aquifer becomes negligiblein both the upstream and downstream locationsand therefore the western and eastern boundarieseffectively define the boundary of the aquifer.
70
11
Table 5.1 Input File For Flow Interruption SimulationsGeochemical Conditions
Reaction Set 1 ! define geochemical reactions and solution compositionsFile
phreega no ads.dat ! thermodynamic data file to use
Ignore ! define species not considered in the solutionsC02(g) U03(C) Gummite B -UO2(0H)2 Schoepite Rutherfordine
ReactionSURFACE SPECIES
>SOH2 + U02+2 = >SOH2U02+ + H+log K 1.817name S prate law
Generalmass action kineticskfor 2.0e-06
end rate law
>WOH2 + U02+2 = >WOH2UO2+ + H1+log K 2.570name Wrate law
Generalmass action kineticskfor2.0el9rate variable activity
end rate law
>ZOH2 + U02+2 + H20= >ZOH2U020H + 2H+log K -0.671name SS n - -,rate law
Generalmass action kineticskfor 5.0e24rate variable activity
end rate law
>SOH2 + U02+2 + H20= >SOH2U020H + 2H+logK -2.082name S n -- -'rate law - --
General
71
- l
Table 5.1 Input File For Flow Interruption Simulations (continued)mass action kineticskfor 2.0e19rate variable activity
end rate lawforce rate
>WOH12 + U02+2 + 1120= >WO112UO20H + 211+log K -5318name W nrate law
General!gibbsmass action kineticskfor 2.0eI9rate variable activity
end rate lawEnd
End
!-DEFINE SOLUTIONsolution I ! average conditions at NAT-20
1120 fixed 55Alkalinity fixed 1.51E-03 2.0e-03 guessU02+2 aqueous I.OE-08 I.Oe-24 guessII+ pf1 7.46>SOH2 total 0.248E-04>SO112UO2+ fixed 0.19275E-04>SO12UO201[ fixed 0.16019E-05
end solution Isolution 2 ! composition of contaminated water
1120 fixed 55Alkalinity fixed 1.51E-03 2.0e-03 guessU02+2 aqueous I.OE-05 1.Oe-24 guess11+ p1l 7.46
end solution 2End of solutions
End of reactions
CalculationTransportreactions I
Ignore ! define species not considered in the solutionsC02(g) U03(C) Gummite B UO2(01)2 Schoepite Rutherfordine
72
Table 5.1 Input File For Flow Interruption Simulations (continued)Domain
6.4 xmax (cm)6.5 tmax (d)
Discretization60 ndx Pegrid Number ! alt:. 5 Pegrid Number.2 Courant Number ! Cr=- v*dt/dx4 PDE method
1D-Flow15.7248 velocity (m/year)6.10E-02 dispersivity1.Oe-9 molecular diffusion
End Calculation -- -Output
BreakthroughPore volumes
SpeciespH H+ U02+2 >SOH2 U02(C03)3-4 U02+2(aqu) HC03->SOH2U02+ >SOH2UQ20H
End
End outputInitial Conditions ! Set the initial conditions on the grid* ID 0.0 1.e19 1
End Initial ConditionsTimed Events
Boundary conditions ! event 1 Start pulseleftO10 2
Duration6.02 !13.69
Boundary conditions ! event 2 Resume Clean waterleft 01 1 ,
Duration1.90
Velocity ! event 3 Interupt flow~.1.Oe-10-- ; <,,,.
Duration,4.17
Velocity ! event 4 Resume flow15.7248
73
- it
Table 5.1 Input File For Flow Interruption Simulations (continued)Duration
3.75Velocity ! event 5 Interupt flow
L.Oe-10Duration
4.17Velocity ! event 6 Resume flow
15.7248Duration
500End Timed Events
6
5
-4
_ 3
D 2
0 20 40 60 80Pore Volumes
100
Figure 5.1. Simulated rate-controlled transport of U(VI) in laboratory columns packed withNaturita aquifer background sediments (NABS) using the flow interruption technique. Flow wasinterrupted for 4.17 hours after 19, 29 and 39 pore volumes. The two simulations used the samerate model but with rate constants that differed by a factor of 2.
The bottom of the aquifer was based on theelevation of the top of the fine-grained shale thatunderlies the alluvial aquifer. This elevationwas taken from drilling logs obtained whenground water monitoring wells were installed in1998 and 1999 by USGS, and in some cases inthe 1980s by DOE (Davis and Curtis, 2003).Figure 5.2 illustrates the locations of where thewells were installed and contoured elevations ofthe bottom of the alluvial aquifer.
A uniform finite difference grid with nearlyequal grid spacing was used. The grid consistedof 69 rows, each with a width of 25.12 feet(7.83m) and 263 columns with a width of 25.01feet (7.80 m). The grid was rotated 30°counterclockwise to minimize inactive cells.
74
11
composition of the recharge was estimatedduring the calibration simulations (Davis andCurtis, 2003). The extent of the contamination
* was estimated from aerial photographs of thesite taken in 1974, prior to when the tailingswere removed from the site.
5.3.3 San Miguel RiverThe San Miguel River was simulated using theMODFLOW-2000 river package. The river wasrepresented in the Argus graphical interface by
- approximately 1000 quadrilateral cells that werefitted to the shape of the river. The riverelevations used in the simulations were based onriver stage measurements taken during low flowconditions in the aquifer. The top of the riverbed was assumed to be I foot below the watersurface. The vertical conductivity of the riverbed was assumed to equal 20 ftfd.
Figure 5.2. Location of groundwater wellsand contoured elevations of the bottom of thealluvial aquifer.
5.3.2 RechargeThe simulations assumed a temporally andspatially uniform recharge rate equal to 1% ofthe average annual rainfall. The chemicalcomposition of the recharge water was assumedto equal that of the average conditions of theupgradient wells where no contamination hadbeen observed. However, below the formertailings pile and the former mill yard, the
5.3.4 Simulation ResultsSimulation results for U(VI) transport, as well asseveral other species have been presentedpreviously (Davis and Curtis, 2003). Most ofthose simulations focused on the spatialdistribution of U(VI), alkalinity, and pH after 62years of transport. Little attention was given tothe temporal behavior of any of the solutes.Figure 5.3 illustrates the temporal evolution ofthe simulated U(VI) plume. This figureillustrates the complex mixing that occursbetween the San Miguel River and the alluvialaquifer, and that high concentrations of U(VI)exist near the bend on the western edge of theaquifer. The plume moves very slowly as shownby the simulation results for 40, 51 and 62 years.
75
- - II
1 1Years 23Years
4'~29Years x,
10
8":r
l16
4
2
4OYears 51 Years 62Years
-6
x10
10
8
6
4
2
Figure 5.3 Predicted temporal evolution of U(VI) concentrations in the alluvial aquifer of theNaturita UNITRA site, Colorado.
5.4 Effect of Heterogeneity onTransport at the Naturita Field Site
Transport simulations were conducted to extendthe reactive transport modeling discussed aboveto include the effects of spatially variableparameters. The specific
surface area (Asp) of the Naturita sediments isknown to vary spatially in the aquifer, based onspecific surface area measurements made oncontaminated sediments (Kohler et al., 2004).Similarly, slug test results also demonstrated thathydraulic conductivity (KH) is also variable atthe site. Figure 5.4 shows that the Aspmeasurements varied by approximately a factorof 4, whereas the slug test results varied by a
76
ii
factor of nearly 30. Although the slug testresults were biased upward relative to the KHestimated from model calibration to chloridetransport (Davis and Curtis, 2003), it wasassumed that the variance from the slug testresults was applicable to the calibrated KHvalues. Using these results and assumptions,variograms were constructed for Asp and KH,and 10 realizations of the spatial distribution ofAsp and KH were generated using sequential
simulations. When spatially variable Asp wasconsidered, the total weak, strong and very
- strong surface site concentrations werecomputed from the Asp value for each modelcell. These three site concentration's were inputinto RATEQ using separate two-dimensionalarrays for each site concentration. The names ofthe files were entered into the BTN file as shownin Table 5.2.
Gaussian simulation. -These distributions are ---- - - The simulation results for the case of constantillustrated in Figures 5.5 and 5.6, respectively -. KH and variable Asp are shown in Figure 5.7.
-- -- -' - There is essentially no difference between any of25 the ten simulations, presumably because of
- '~ averaging that occurs for the reacting water20 which encounters cells with higher and lower
M- site concentrations. Simulation results for theX5 -- variable KH and constant specific surface area
show a very strong effect of hydraulic -10 'conductivity on the simulated U(VI)
7 concentration. 'The relatively large effect occurss- -; because the measured KH values varied by a
factor of 30, whereas the ASP values varied by5 10 15 o----- only a factor of 4. This causes the groundwater
-- - to have spatially variable velocity.
WI
.2C
The simulations with variable KH also had-maximum concentrations that varied among the10 realizations. In some cases, the.-concentrations were lower because more U(VI)
-; was flushed into the river by a preferential flow-path. Different concentrations can also resultfrom differences in groundwater velocity. Thevelocity in each cell varied spatially, therecha rga,.- iF. themarie in each ce*ITherefore, recharge water that mixed withgroundwater that had a low velocity would yield
-- -------a higher U(VI) concentration, because there'would be a smaller amount of groundwater
ecific available for dilution. Conversely recharge-ity derived U(VI) that mixed with a groundwater
that had higher velocity would yield a smallerdissolved U(VI) concentration.
Figure 5.4. Summary of measured spisurface area and hydraulic conductivimeasured at the Naturita field site.
Model simulations were conducted thatconsidered: (1) spatially variable Asp andconstant KH, (2) constant Asp and spatiallyvariable KH, and (3) spatially variable Asp andspatially variable KH. For simulations withvariable Kto, only the two-dimensional hydraulicconductivity input array for the MODFLOWBCF file was changed for each of the 10
77 ''
I
Table 5.2 Basic Transport File For Spatially Variable Surface Site ConcentrationsReactive Transport in the Naturita Alluvial AquiferInitial concs determined from spatial input files - free format
1 263 69 2 10 7 !NLAYNROW,NCOL,NPER,NCOMP,MCOrviPDAY MI KG !TUNIT,LUNIT,NMUNITT T T F T T F F FF !TRINOP: ADV,DSP,SSNI,RCT,GCCG,RATEQ00 !LAYCON
0 25. !DELR0 25. !DELC0 6080. !ITOP0 6. !DZ0 .20 !PRSITY-LAYER I0 1 !ICBUND-LAYER I
170 const [120 fixed 55. !1120 LAYER I170 const Calcite total 1.0170 const Alkalinity fixed 4.87E-03170 const Cl- aqueous 0.008902170 const Na+ aqueous 0.008902170 const U02+2 aqueous 6.05E-08170 const II+ p11 7.1170 file >WOH112 total WOE! l.dat170 file >SO11112 total SOII l.dat170 file >SSOIIH2 total SSOH l.dat
999.99 0 !CINACT,THKINIIN1 2 0 0 T !OUTPUT CONTROL0 MNPRSI I !NOBS,NPROBS1 8 3 !KOBSIOBSJOBST 1 !CHKMAS,NPRMIAS
20819 1 1. !PERLENNSTP,TSMIULT7. 40000 1. 0 !DTO,N1XSTRN,TTSMULTTTSMAX
1826 1 1. !PERLEN,NSTPTSMULT7. 40000 1. 0 !DTO,M.XSTRNTTSMULT,TTSMAX
78
11
4 it ¢20
* -10
20
V 1 5
510
Figure 5.5. Ten realizations of the spatial distribution of specific surface area (m2Ig) generated bysequential Gaussian simulation. ,. -
4 4.3'1f -35
Figure 5.6. Ten realizations of the spatial distribution of log K11 (mis) generated by sequentialGaussian simulation.'--
79
'4
I
II1 (AA
.1
;15
.1 10
j15
10
. 5
Figure 5.7. Ten simulations of U(VI) transport that used a fixed Ki, and spatiallyPlumes are shown after 62 years of transport.
variable Asp.
dIAI'
4. AA
Al Aii
t : A 15
10
5
15
iv 10
j ' 5
Figure 5.8. Ten simulations of U(VI) transport that used spatially variable Kt, and a fixed Asp.Plumes are shown after 62 years of transport.
80
6 EXAMPLE SIMULATIONS
6.1 Introduction Reactive transport in groundwater is oftenaffected by the heterogeneous nature of the
This section presents additional example porous medium, which can cause thesimulations of reactive transport. The examples groundwater velocity to vary significantly ininclude transport with immobile zones, transport space. One simple approach to address thiscontrolled with equilibrium-controlled redox heterogeneity is to assume that this'-reactions and simulations of biogeochemical heterogeneity can be simulated by assuming thattransport. -The parameter values (especially the the velocity in some of the porous medium israte param eter values) used in the simulations zero. Transport of U(VI) was simulated for awere selected for illustrative purposes only and one-dimensional porous medium where 25% ofnew approaches are needed for determining- - the porosity was assumed to be immobile. Thereactions and parameter values for the purpose - - simulations are loosely based on conditionsof reactive transport modeling.(Davis'et al., : -. - - - observed at the Naturita UMTRA field site2004b). - -(Davis and Curtis, 2003). This simulations
illustrate the effect of a transient pulse of low
6.2 Transport with immobile zones - alkalinity water on U(VI) concentrations. The*-- input file for this simulation is listed in Table 6.1
and the results are shown in Figure 6.1.
Table 6.1 Input File for Simulating Transport with Immobile ZonesREACTIONS
Reaction Set 1 ! define geochemical reactions and solution compositionsfile -
PHREEQA nat.datignore ! define species not considered in the solutionsDolomite -
temperature15
solution 1 ! average conditions at NAT-251H20 fixed 55Mg+2 total 1.65e-03 -Calcite total 1.0Alkalinity aqueous 9.0e-03 2.0e-03 guessCl- aqueous 3.44E-03 - '2.0e-03 guess -
Br- aqueous 1.OE-05 2.0e-03 guessK+ aqueous 2.51e-04Na+ aqueous 1.99E-02 2.0e-03 guessU02+2 aqueous 4.OE-06 1.Oe-24 guessS04-2 aqueous 9.03E-03H+ pH 7.06>WOH2 total 3.79E-02>SOH2 total 3.795E-05>ZOH2 total 3.795E-06
end solution 1solution 2 ! DOE 547
81-s
-I
1120 fixed 55iNlg+2 total 1.65e-03Calcite total 1.0Alkalinity aqueous 3.0e-03 2.0e-03 guessCl- aqueous 3.44E-03 2.0e-03 guessBr- aqueous L.OE-05 2.0e-03 guessK+ aqueous 2.5 1c-04Na+ aqueous 1.99E-02 2.0e-03 guessU02+2 aqueous 4.OE-06 I.Oe-24 guessS04-2 aqueous 9.03E-03I1+ pH 7.06
end solution 2End of solutions
End of reactionsCalculation
IDignore ! define species not considered in the solutions
DolomiteDomain
2. xmax (meters)20 tmax (days)
Discretization50 ndx0.6 Courant Number
ID-Flow0.75 velocity (mi/days)0.005 dispersivity !0.00304891590.15 porosity0.05 kla 0.0030528140.1 immobile-theta
End CalculationOutput
breakthruspeciespit Alkalinity U02+2(aqu) U02+2(ads)
End outputInitial Conditions ' Set the initial conditions on the grid
ID 0.0 1.el91End Initial ConditionsTimed Events
Boundary conditionsleft O 10 2
Duration2.5 !13.69
Boundary conditionsleftO 10 I
Duration1000000
End Tinted Events
82
X i3-
7.2 8
7.1
.7I0r._
6
46.91
6.8-2
O*,
0 10Time
20 10Time
20
x 10l K 10_-
1.5
+ e'00o
10CVco-.I. cm
0
1
0.5
rk II-
0 10Time
20 0 10Time
20
Figure 6.1. Comparison of U(VI) transport simulations assuming immobile zones (x) and noimmobile porosity (-).
The results show that the pulse of low alkalinity 6.3 Transport with oxidation-water decreases the U(VI) concentration, eventhough the U(VI) in the boundary conditions reduction reactionswas not changed. This was caused by anincrease in adsorption, resulting from decreased reaction is-o-teaqueous complexation by carbonate. After the Transpoi with redoxalkalinity peak elutes, the U(VI) held back by - L numerically difficult to solve, becausethe increased adsorption is desorbed by native -- concentrations of many species can varygroundwater, which had the initial concentration- significantly over very small spatial scales.of 4 pM. The desorption creates U(VI) - example presents a RATEQ simulation of iconcentrations that exceed that of the influent -basic processes that lead to a uranium roll Iwater. In the presence of a significant fraction deposit. In this scenario, oxidizing water eof immobile porosity, the increase in dissolved _ a porous medium that contains reduced phzU(VI) after 8 days is small, but in the absence of such as pyrite and uraninite. The oxidizingimmobile porosity, the U(VI) concentrations are - _ solution oxidizes U(IV) in uraninite to relaiapproximately 25 percent larger than the initial s - nobile U(VI) species, which are transporteconcentration. -; - downgradient. This process creates a front
Thishefrontntersises
LivelydofA.-Iefu
-... U- UhA iL.. UlaauIULIuUL. A 11, %L I V sJ IL1I 13 jIUVUUA-U
j by uraninite oxidation migrates faster than the
83
- it
mineral dissolution front. Therefore, the U(VI)encounters reduced phases, including pyrite,which reduces U(VI) back to U(IV), whichforms uraninite. The input file for thissimulation is shown in Table 6.2 and thesimulated output is shown in Figure 6.2.
The simulations illustrate the numerical stabilityof RATEQ. In addition, the simulations alsoillustrate expected results, including the decreasein pH resulting from the pyrite oxidation, theincrease in U(VI) concentration at thedissolution front, and the increase in uraninite atthe roll front.
6.4 Simulations of biogeochemicaltransport
In many environments, microbial processes canhave a significant effect on local geochemicalconditions. These effects result in large partbecause of the changes in chemical propertiesthat result when the valence state of an elementchanges. Conceptual models for simulatingbiogeochemical reactions vary widely and rangefrom simple first order degradation kinetics tocomplex, multiple Monod formulations that
include growth and decay of microorganisms(see section 4.3.1). With multiple electronacceptors, the number of parameters required forsimulations using the Monod approach can bevery large. An alternative is to use the partialequilibrium approach, which assumes thatorganic substrate is slowly converted tointermediates that react with the terminalelectron acceptor via an equilibrium-controlledreaction.
This section presents simulations of theoxidation of an organic substrate by multipleterminal electron acceptors using the partialequilibrium approach. In the simulations, theorganic substrate was represented by lactate (2-hydroxypropanoic acid) that slowly degrades,releasing H2(g):
1/6 Lactate+ +1120 = 1/311H + 1/2H1C0 3 - + H2
The 112 then reacts with the terminal electronacceptor via an equilibrium-controlled reaction.This is a simple approach that honors thereaction stoichiometry and thermodynamics. Inaddition, the approach can be expanded toinclude multiple sources of 1-12, intermediatesother than 112 such as acetate, and rate-controlledterminal electron accepting reactions.
Table 6.2. Input File for Uranium Roll Front Simulation! Geochemical ConditionsReaction Set I ! define geochemical reactions and solution compositions
filephreega nat6.dat
ignore ! define species not considered in the solutionsU409(C) U02(am) U409(C) U308(C)
!-DEFINE SOLUTIONsolution 1
1120 fixed 55Calcite total 1.0Pyrite total 0.0011Uraninite total 0.0001Goethite total 0.01U02+2 total l.e-30Alkalinity fixed 1.51E-03 2.0e-03 guessI1+ pH 7.46>WVO112 total 2.26E-02 !2.026E-02>S0112 total 2.27E-05 !1.223E-04
84
11
>ZOH2 total 2.27E-06 !1.223E-06end solution 1
solution 2 ! composition of contaminated waterH20 fixed 55Fe+2 aqueous 1.0e-40HS- aqueous 1.Oe40Calcite total 1.0Alkalinity fixed 1.51E-02 2.0e-03 guessH+ pH 7.4602 aqueous 1.Oe-03
end solution 2End of solutions
End of reactionsCalculation
Transportreactions 1 ! Solution 1 is used as the defaultignore ! define species not considered in the solutions
U03(C) Gummite B U02(OH)2 SchoepiteRutherfordine U409(C) U02(am) U409(C) U308(C)
Domain20 tmax PV
Discretization60 ndx-
End CalculationOutput
breakthruspecies
pH HC03- Fe+3 Pyrite 02 U02+2(aqu) U02+2(ads) UraniniteEnd outputInitial Conditions !Set the initial conditions on the grid
iD 0.0 l.el9 1End Initial Conditions iTimed Events :
event 1 Start pulseBoun-dary conditions
left 0 10 2Duration
20.02 !13.69
event 2 Resume Clean water ......Boundary conditions
leftOl0 1Duration
500End Timed Events
85'
- -
1i 1
7.4
0.57.2
0M 0
7-0
O0_00.5
Distance1 0.5
Distance1
0.0'I
o 0.00t
00
NI
+ c4 %J1o 0
I -
5
0 0.5Distance
xI0-10
4L-'
a-
Cu
w.
0.5Distance
x lo'
I'JO- 0.5Distance
10 L
0.5Distance
1
Figure 6.2. Simulated concentration profiles after 3 pore volumes of an oxidizing solution havingentered a reducing zone containing pyrite and uraninite.
86
8m
4,14,Recharge (7cm/y)
.... , . 4, 4, 4,organic
.oure .
Costn
4-ConstantHead=10 m
- Constant-Head=9 m _
No Flow-I4.(
400 m
Figure 63. Two-dimensional cross section used for biogeochemical transport simulations.
The simulation examples were conducted for atwo-dimensional domain illustrated in Figure6.3. The system is driven by recharge thatpasses through an organic source, whichtransports lactate into an aquifer.
The electron acceptors in the simulation were250 p.M 02, 1.5 mM FeOOH, 250 A.M SO4 andCO2. The FeOOH was used to represent ironoxide coatings, and it was assumed to have anintermediate stability between that for freshly _7precipitated ferrihydrite and goethite. The-inputfile is listed in Table 6.3.
water was assumed to have very small.concentrations for each of these species. Thereactions of 02 and S04 were primarily confinedto the boundaries of the plume. -For theimmobile FeOOH, the decrease in concentrationresults only from reaction. The FeOOH iscompletely exhausted immediately below theorganic source, and a long area depleted in
7 FeOOH extends downgradient.- Immediatelybelow the source area, a CH4 plume develops atthe end of the simulation, and some of the Fe+2
forms a precipitated FeS phase.
Simulation results are shown after 10 years of -
transport in Figure 6.3. The results show thatthe electron acceptors 02, FeOOH and S04 aresignificantly decreased below and downgradientof the waste source. For the mobile electronacceptors O2 and SO4, most of the decrease in .concentration results because the contaminated-
87..
EL2
Table 6.3 Input File for Biogeochemical Transport SimulationReaction Set 1 ! define geochemical reactions and solution compositions
filec:\rateq\data\phreega.dat
ignore ! define species not considered in the solutionse-
temperature25 C ! degrees C
ReactionSolution Species02 +2H2 =2H20log K 83.11
Fe+2 + .2502 + 2.5H20 = FeOOH + 2H+rate law
generalkfor l.Oe20 ! time units in dayslinear Fe+2linear 02 -linear OH-linear OH-
end rate law
H20 + 0.16667 Lactate- = 0.3333H+ + 0.50 HC03- + 112log K -8.33rate law
generalkf 5.0e-04linear Lactate-
end rate lawforce rate
0.25 S04-2 + H2 + .2511+ = 0.25 HS- + H20log K 11.50
.25 HC03- + H2 +.25H+ = .25 CH4 + .375 H20log K 10.08
PHASESFeOOHFeOOH + 2 H+ + 0.500 H2 = Fe+2 + 2 1120
!log K 15.6 ! least stable lepidocrocitelog K 13.8 ! most stable lepidocrociteRate law
GeneralKfor 1.OeO2
Mfass action kineticsLinear FeOOII
88
if
End rate lawForce eq
FeSFeS + H+ = Fe+2 + HS-
log k -4.648name Mackrate lawgeneral-mass action kineticsvmax 1.Oe-3
end rate law
solution 1 ! initial conditionAlkalinity fix 2.5e-03H+ pH 6.501Lactate- fix 1.De-05FeOOH fix 1.5e-03
_04-2 total 1._e-04H20 fix 55.0100 ! conc (M)02 fix 2.5e-04FeS fix 0.0e-95
end solution 1solution 2 ! boundary conditionH20 fix 55.0100 ! conc (M)H+ pH 6.501!CH4 fix 1.0e-50H2(g) gas -16.8Lactate- fix 0.005Alkalinity fix 2.5e-03Buf- total 1.0e-2S04-2 fix 1.Oe-04
end solution 2End of solutions
End of reactionsCalculation
MT3reactions 1ignore ! define species not considered in the solutions
Siderite FeSppt MackinawiteC02(g) 02(g) H2(g) H2S(g) CH4(g) C02(g) 02(g) _2(g) CH4(g)Melanterite Hematite Goethite Fe(OH)3(a) Fe203 Hematite Goethite
End CalculationOutput
profilcspecies
02 Lactate- pH HICO3- Fe+2 FeOOH CH4 112 S04-2 HS- FeSEnd output
89
Figure 6.5 shows the results from a similarsimulation, except in this simulation the initialpH was 7.5 instead of 6.5. Comparison ofFigures 6.4 and 6.5 shows that significantly lessFeOOH is reduced at the higher pH. Thisdecrease in the amount of FeOOH reducedoccurs because the FeOOH reduction reaction isless favorable at higher pH values. As aconsequence of the smaller extent of FeOOHconsumption, less FeS forms and more CH4forms.
The final simulation is a slight modification ofthe previous case. Sulfate was removed fromthe system and was replaced by U02 '2. Inaddition, it was assumed that U02'2 was sorbedto the sediment, although only a 1-siteadsorption model was used. Finally, it wasassumed that excess calcite was present in thesimulations. The simulation results are shown inFigure 6.6. The results are generally comparableto Figure 6.5 for 02, FeOOH, pH, and CH4.
Figure 6.6 also illustrates that the some of theU(VI) that was present in solution and adsorbedon the sediment was reduced to U(IV) andprecipitated as uraninite. The extent of thisreduction was strongly impacted by adsorption.When no adsorption was considered, very smallamounts of uraninite were formed, because mostof the dissolved U(VI) was displaced byadvection, and there was minimal mixing andreaction between the reduced and oxidizedwater.
The results presented in this section as well as inSections 4 and 5 demonstrate that RATEQ is avery useful tool for simulating complexgeochemical systems. RATEQ is based on thewidely used groundwater flow modelMODFLOW-2000 and on the numerically stableTVD algorithm in MT3DMS. Thus, RATEQshould have applicability to many geochemicalscenarios in the groundwater environment.
90
11
....
Lactate- I
I
-3x103
9 2
1 .
°2I
I
Ix4
x1O
I*0
-3x10
13HCU3 I
I
pHIi
SO4~iI
I
2- -
I
10x1010
-5
x102.521.5 c1 -
0.5 -
II..II
FeOOH (s) II1
I'
2
i1 .5
1
0.5
6.7
6.6
6.5.3
x10
4
2
0.4
x10
86
...4-
20
O4
x10
I
- 0.5
0
HS- I
I
Fe+2wI
I.
CH4
x10
8,6
4
02 --*0
FeS(S) I
IFigure 6.4. Two-dimensional biogeochemical simulation results for oxidation of lactate by multipleterminal electron acceptors at p'1 6.5. The concentrations in each plot are given in units of Mexcept pH. -
91
-3x 10'3
-4x10
MLactate-
II;31'1
IR'
02
2
I
tI
I-3
I
HCO3I
I
x1O3
2
.I
pH Ii
;21.5
1I0.5
7.6
7.55
7.5
7.45-3
x10
3
2
.1
1
,so42I
i
O0x1010
5
.5
FeOOH(. )
LL1 I
I
II. *00-5
xio-4
XlO
HS' I Fe+22t: I
II
I
M
CH.4.
I
I-
*0
x10
86
4
2
0
.5
FeS(a)
1
0.5
0-5
x15
10
5
I..
5
Figure 6.5. Two-dimensional biogeochemical simulation results for oxidation of lactate by multipleterminal electron acceptors at pH 7.5. The concentrations in each plot are given in units of NIexcept pH.
92
Lactate- II;
HC03- I
I
x103
2
2-
''1
x10
4
X0
2.52
0.5
02 I
I
21.5
I0.5
7.55
7.5
7.45
pH
-4x10
Ie.I.
U02+2(aqu) II
FeOOH
e -I:eJ_ jt'v'w 77
I
I
*7.4
x104
3
- 2
I
'3
Uraninfte
IFe+2
I
I
x10xl
I.I
0.5
0-4
X1O
CH4 II1
1.5
1
0.5
0
Figure 6.6. Two-dimensional biogeochemical simulation results for oxidation of lactate by multipleterminal electron acceptors, including U(VI), at pH 7.5. The concentrations in each plot are given inunits of M except pH.
93
:I
Appendix 1. Transformation of the Reactive Transport Equations
The reactive transport equations for all of thespecies in geochemical system can berepresented as
NTOT is the total number of species,
NM is the number of mobile species, and
at (OmI~r + Oirnlim)= L (C)+ Vc (2-17)
where
L (ax ~i ( j Ix-d _~ ax (OvC )+ 'Ck}
as described in equation 2-8. This equation canalso be written as
[IkI(OmIm +OimCim)= [ 0](c)+VCR
where,
I is the identity matrix of size NTOT,
Im is the identity matrix of size NM,
v is matrix of stoichiometric coefficients of sizeNTOT x NR,
R is a vector of chemical reaction rates (MT') ofsize NR,
NR is the number of geochemical reactions.
In RATEQ, the equations are transformed byperforming a gauss Jordan elimination of thematrix of stoichiometric coefficients, v.Because the equation above is actually a set ofequations, the same operations applied to v must
also be applied to[I] and [I 01]. The
transformations are not unique and depend onthe order of variables in the v matrix. InRATEQ, the master species are used as basisspecies. This produces mass balance constraintsfor the master species. As a result of the lineartransformation, the coefficients for the reaction
rate R has the form INr where Nr is theI 0 J
number of reactions and I is the identity matrix.This approach is quite general and applies to alltypes of reactions. In addition, it is notnecessary to strictly write all reactions in termsof the master species, and redox reactions do notnecessarily need to be written in terms of theelectron
!1
94
1I
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NRCFORM 335 U.S. NUCLEAR REGULATORY COUMISSION 1. REPCRT NUERv3(249) (AssIgned by NRC. Add Vol, Supp, Rev,NRCM 1102. BIBLIOGRAPHIC DATA SHEET and Addendum Numbers. It nv.1
(See Instructions on Uhe reverse) NUREG/CR-68712. TITLE AND SUBTITLE
Documentation and Applications of the Reactive Geochemical Transport Model RATEQ3. [CATE fiOXT R2JSEttD
Draft Report for Comment MONTH YEARJune 2005
4. RN OR GRANT M1U9E3
Y64625. AUTHORS) & ETYIWF RI703T
Gary P. Curtis Technical
7. RIO (inclusive Dates)
1/04- 10/04
S. PRFOWRMING ORGANIZTAMN . NAME AM ADD S (hifNRC. provide Division. office or Region. U.S. Nuclear Regutatory Commission, and mailing address; i contractorprovide name and maiing address.)
U. S. Geological SurveyMenlo Park, CA 94025
9. SPONSORING oRGANZATION - NRUE AND AORESS (ffNRC, tpe Same as above if contractor. provide NRC Division, Office or Region. U.S. Nuclear Regulatory Commission,and mailing addressj
Division of Systems Analysis and Regulatory EffectivenessOffice of Nuclear Regulatory ResearchU.S. Nuclear Regulatory CommissionWashington, DC 20555-0001
10. SUPPLENTARY NOTE1SJ. Randall, NRC Project Manager
11. ABSTRACT (200 words or less)
The computer program RATEQ implements a numerical method for simulating reactive transport in porous media. For RATEQsimulations, groundwater flow Is simulated using MODFLOW-2000. The reactive transport simulations In RATEQ are built onMT3DMS. RATEQ is intended for a wide range of applications Involving biogeochemical reactions governed by rate- orequilibrium-controlled reactions. This report documents the Input requirements and the output capabilities of RATEQ. The reportalso presents a number of example simulations Illustrating the capabilities of RATEQ. The example simulations include fivebenchmark simulations that compare results obtained with RATEQ with results obtained independently. Simulations of U(VI)transport at the UMTRA site near Naturita, CO, are also described. Finally, several addition simulations are included thatillustrate the application of RATEO to problems with Immobile zones, redox-controlled reactive transport, and biogeochemicaltransport.
12 KEY .CESR R (Lst words or phrass that wilt ass)stresearrhers In locating the report. 13. AVAILABILITY STATEMENT
Uranium, subsurface transport, sorption, Ion exchange, surface complexation, mathematical modeling unlmited14. SECURITY CLASSIFICATION(This Page)
unclassified(This Report)
unclassified.. '15.NL EROFPAGES
16.PRIE
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NUREGICR-6871 DOCUMENTATION AND APPLICATIONS OF TIlE REACTIVE GEOCHEMICAL JUNE 2005DRAFT TRANSPORT MODEL RATEQ
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