Computational Modelling to Investigate the Sampling of Lead

8/18/2019 Computational Modelling to Investigate the Sampling of Lead

1/10

Computational modelling to investigate the sampling of lead

in drinking water

Colin R. Hayes*

School of Engineering, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, United Kingdom

a r t i c l e i n f o

Article history:Received 13 October 2008

Received in revised form

18 February 2009

Accepted 16 March 2009

Published online 24 March 2009

Keywords:

Lead

Drinking water

Plumbosolvency

Sampling

Computational modelling

a b s t r a c t

The monitoring of lead in drinking water is beset by difficulties relating to the inherenttemporal variation of lead emissions at individual premises. Such difficulties are com-

pounded by spatial variation when considering an entire water supply area (e.g., City or

Town), which is necessary to determine compliance with regulatory standards and to judge

the efficacy of corrective measures. A computational modelling system, that uses a Monte

Carlo probabilistic framework for simulating lead emissions within a water supply area,

has been successfully validated in a range of UK case studies and enabled corrective

treatment measures to be optimised for a range of water types. This modelling system

includes the simulation of a range of sampling methods, and has made it possible to

undertake an exhaustive comparison between daily average lead emissions (DAC – which

are equivalent to weekly average lead concentrations as a consequence of the modelling

system used), random daytime sampling (RDT), 30 min stagnation sampling (30MS) and 6 h

stagnation sampling (6HS). It is concluded that: (a) the stringency of UK and US compliance

assessment methods for lead in drinking water is fairly similar for waters of reducedplumbosolvency, despite different sampling approaches; (b) RDT sampling is equivalent to

random DAC for waters of moderate plumbosolvency; (c) RDT sampling is more stringent

than random DAC for waters of low plumbosolvency; (d) all random sampling methods

suffer from poor reproducibility, albeit less so for low plumbosolvency water; and (e) fixed

point stagnation sampling may not be representative.

ª 2009 Published by Elsevier Ltd.

1. Introduction

In the United Kingdom (UK) prior to the mid-1970s, lead indrinking water was not perceived to be a problem, except for

cities like Glasgow where extensive use of lead piping and lead

lined roof tanks were used to convey slightly acidic upland

water supplies. In consequence, few water authorities both-

ered to test for lead, and commonly, sampling at consumers’

taps was not practised. In this era, sampling problems with

lead in drinking water were not an issue.

Following a UK-wide survey (Department of Environment,

1977) for lead in drinking water in the mid-1970s, the more

widespread occurrence of ‘‘high’’ lead concentrations wasrealised, including high alkalinity groundwater supply areas (at

this time ‘‘high’’leadwastaken tomean>100 mg/l,following the

thenWorldHealthOrganizationguidelines). Three major leadin

drinking water assessment exercises then followed in the UK:

[1] In the late 1970s and early 1980s, water authorities were

required (Department of Environment, 1980) to undertake

* Tel.: þ44 (0)1792 602257.E-mail address: [email protected]

A v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m

j o u r n a l h o m e p a g e : w w w . e l s e v i er . c o m / l o c a t e / w a tr e s

0043-1354/$ – see front matter ª 2009 Published by Elsevier Ltd.

doi:10.1016/j.watres.2009.03.023

w a t e r r e s e a r c h 4 3 ( 2 0 0 9 ) 2 6 4 7 – 2 6 5 6

mailto:[email protected]://www.elsevier.com/locate/watreshttp://www.elsevier.com/locate/watresmailto:[email protected]


2/10

a representative numberof supply areaassessments,based

on random daytime sampling and the use of statistical

look-up tables fordeterminingprobabilityof compliance,to

identify which areas were in need of possible corrective

action. The monitoring protocol did not specify the period

of time over which the sampling was to be undertaken

and consequently many surveys were carried out during

the winter months. Also, some water authorities onlycarried out limited numbers of surveys, believing that

a small number of supply types would be representative

(such as ground and surface derived supply examples).

With hindsight, it is certainthat plumbosolvency problems

were under-estimated, and only limited corrective treat-

ment actions were taken (mostly pH elevation of low

alkalinity waters).

[2] In the late 1980s and early 1990s, water companies in

England and Wales were required (Department of Envi-

ronment, 1989) to undertake surveys of their water supply

areas, to determine compliance with the lead standard of

50 mg/l, that had been promulgated to implement the first

of the European drinking water directives (EuropeanCommission, 1980). Again, random daytime samples were

taken, but the definition of the word ‘‘random’’ was

ambiguous in the guidance. Most water companies

surveyed randomly throughout their water supply areas,

whereas a minority surveyed randomly but only from

houses believed to be supplied by lead pipe-work. The

latter had been intended, as confirmed by later Govern-

ment reports (Drinking Water Inspectorate, 1996). Not

surprisingly a much greater proportion of water supply

areas were found to be in need of corrective action by those

water companies who had adopted this approach, because

the former approach is less stringent as houses without

lead pipe-work are included. In overall consequence,dosing of ortho-phosphate corrosion inhibitor was initi-

ated for around 25% of UK water supplies.

[3] In 1998, the UK Government decided (Drinking Water

Inspectorate, 1998) to seek compliance with the updated

European lead standards of 25 mg/l and 10 mg/l (legal

requirements from December 2003 and December 2013,

respectively) by a treatment based strategy that would

minimise the replacement of lead pipe-work. Guidance

was circulated by the Drinking Water Inspectorate in

2000 and 2001 (Drinking Water Inspectorate, 2000, 2001)

in which water companies were required to develop

a strategy that included monitoring to demonstrate that

the treatment measures had been successful (or other-wise). This guidance made reference to both random

daytime sampling and to the use of fixed point sampling at

houses and/or lead pipe test rigs, but was not prescriptive.

In over-all consequence, over 95% of UK water supplies are

now dosed with ortho-phosphate, the remaining issue

being the extent to which such dosing has been optimised.

Looking more broadly at the rest of the European Union,

the second drinking water directive (European Commission,

1998) has an acknowledged problem (Hulsmann and Cortv-

riend, 2006) concerning the sampling of lead, copper and

nickel at points of consumer use. In Annex 1, Part B, Note 3,

this directive states that the parametric value for lead, copper

and nickel ‘‘applies to a sample of water intended for human

consumption obtained by an adequate sampling method at

the tap and taken so as to be representative of a weekly

average value ingested by consumers’’. It is not disputed that

the standards for these metals apply at points of consumer

use, but what is disputed is how the samples should be taken.

Where sampling for lead is being undertaken, it was clear

from a recent European Research Workshop (Cost Action 637,2007) that a wide range of approaches are in use, some

of which will either miss or underestimate the concentrations

of lead at the consumers’ taps.

In the United States (US), a more detailed prescriptive

approach (US Environmental Protection Agency, 1995) has

been in place since 1990, the Lead and Copper Rule (LCR). The

LCR requires prescribed numbers (dependent on the pop-

ulation involved) of fixed monitoring points to be selected and

their periodic survey. Compliance with the 15 mg/l standard for

lead is based on the 90th percentile concentration of the

samples taken in each survey. Where the standard is

breached, corrective measures are required. In Canada, the

Health Ministry has recently published (Health Canada, 2007)a consultation paper that proposes the implementation of

a more detailed regulatory regime for lead in drinking water,

largely based on the US LCR.

It can be readily concluded from the above that there is no

global consensus on how to monitor lead in drinking water,

and that the history of tackling the lead problem has been

hindered by sampling and surveying difficulties. A study in

Europe in the late 1990s (Van den Hoven et al., 1999) endeav-

oured to determine how best to sample for lead in drinking

water,but this wasnecessarily limitedto a fairlysmallnumber

of samples because of logistic and cost constraints. Since this

study was reported, a computational modelling system has

been developed (Van der Leer et al., 2002) for predicting theemissions of lead into drinking water across entire water

supply areas, and validated by numerous case studies, of

which several have been published (Hayes et al., 2006, 2008).

This modelling system includes the simulation of a range

of sampling methods, and has made it possible to undertake

an exhaustive comparison between composite sampling

(COMP) as used to determine weekly average lead emission

concentrations (in the model, COMP is equivalent to the

calculated daily average lead emission concentration – DAC),

random daytime sampling (RDT), 30 min stagnation sampling

(30MS) and 6 h stagnation sampling (6HS). The results provide

a deeper insight into the behavioural characteristics of the

sampling methods and are summarised in this paper.

2. The computational modelling procedure

The models, which are described in more detail elsewhere

(Van der Leer et al., 2002), enable the most relevant features of

a water supply zone to be incorporated in the prediction of

zonal compliance with lead standards, as a function of both

plumbosolvency (corrosivity of the water to lead) and the

zone’s physical characteristics. A zonal model simulates the

emissions of lead at individual simulated houses, through

time, across an entire water supply zone or area of supply. It

uses a single pipe model to determine the lead emission

w a t e r r e s e a r c h 4 3 ( 2 0 0 9 ) 2 6 4 7 – 2 6 5 62648


3/10

profile at each simulated house, the characteristics of each

simulated house being the outcome of the random ascription

of variables, which follows the Monte Carlo method for

establishing a probabilistic framework.

The single pipe model simulates the dissolution of lead

into the water flowing through or stagnating in a coupled lead

pipe and non-lead pipe, over a 24-hour period. The coupled

pipes are broken down into a series of elements and whenassuming simple plug flow, each element is treated as a stir-

red tank, flow being simulated by passing the contents of each

stirred tank to the next at a time interval of one second. The

rate of lead dissolution is determined by reference to an

exponential curve that declines towards equilibrium, as

illustrated in Fig. 1.

As M (the initial mass transfer rate which determines the

initial slope of the dissolution curve) and E (the equilibrium

concentration) reduce, the water is less plumbosolvent

(less lead dissolves: curves A–C) and these factors can be

determined by stagnation sampling at appropriate reference

housesor by laboratoryplumbosolvencytesting. CurvesA1 and

A2 in Fig. 1 relate to different dissolution characteristics. Theexponential curve and the assumption of plug flow are both

approximations, but they enable the computational demands

of the model to be greatly reduced. Extensive research (Hayes,

2002; Van der Leer et al., 2002) has demonstrated that these

approximations are adequate when compared to the more

scientifically exact diffusion model and the three dimensional

simulation of turbulent flow. The governing mathematical

equations, that under-pin these modelling options, are

described in Van der Leer et al., 2002.

As a guide, a moderately plumbosolvent water (e.g., a high

alkalinity groundwater that has not been phosphated, or a low

alkalinity water that has been pH adjusted to 8.0–8.5 but not

phosphate dosed) will often be described by M¼ 0.1 andE¼ 150. For 12 mm internal diameter lead pipes, the equilib-

rium concentration (E ) is predicted (Hayes, 2002) to occur after

about 8 h water stagnation, consistent with the observations

and predictions of others (Kuch and Wagner, 1983).

When the imaginary tap is closed (that is, zero flow), the

lead concentration increases over time as determined by M

and E. When the imaginary tap is open, the concentration of

lead in the emission from the pipe is either (i) a reflection of

the steady state flushed condition (with lead concentrations

normally below 1 mg/l unless the lead pipe is very long) or (ii) it

is determined by previous zero flow (stagnation) conditions,

as influenced by pipe geometry and the extent of the flow

event. It can be appreciated that the simulation of such events

in each stirred tank for every second of flow leads to millions

of calculations being performed for each simulated pipe.

Particulate lead is not simulated because the influencing

factors are highly variable and would be difficult to define.Such factors would include the physical condition of lead

corrosion deposits and their fragility, fluctuations in water

flow and scouring effects, and the extent of loose iron corro-

sion deposits at any time or location. In the UK context, it has

not been found necessary to include particulate lead, as

demonstrated by case studies (Hayes et al., 2006, 2008) and

this is probably a reflection of the major reductions in iron

discolouration problems since the early 1990s following

extensive replacement or refurbishment of old cast iron water

mains. In circumstances where iron discolouration is signifi-

cant, an adjustment would need to be made to the modelling

procedure reported here. This could be achieved empirically

by adjusting M and E.The zonal model is set up by the random ascription of

a series of zonal characteristics, as derived from sets of agreed

statistical distributions, and by the use of agreed variables and

constants. The statistical distributions used in this study are

shown in Fig. 2 and have been used successfully in many

zonal modelling studies on the basis of the validation ach-

ieved with field data (e.g. Hayes et al., 2008). Where pipe-work

and residency surveys have been undertaken (Hayes et al.,

2006) the observed departures from the standard statistical

distributions were only minor. The standard distributions

have the following features:

the length of lead and non-lead pipes have a log-normaldistribution, consistent with longer lengths occurring less

frequently;

for the lead pipes, 95% are assumed to have an internal

diameter of 12 mm and 5% 18 mm, as relates to UK

conditions;

the volume used per day relates to an individual simulated

house, the mean volume equating to the average water

consumption of a house in the UK and assumed to flow

through the simulated pipes;

pattern A describes water usage in a house in which there is

residency throughout the hours when water is consumed

(not during the night when residents are asleep);

pattern B describes water usage in a house in which allresidents are absent during ‘‘office hours’’ when no water is

used;

patterns A and B are applied for three and two water use

frequencies respectively, such that the weighting of A to B is

3 to 2, albeit with the water use frequencies within the two

categories having an equal weighting.

Changes in any of these assumptions can be readily made,

for example: in response to a reduction in water consumption

following a programme of compulsory metering, all that

would be necessary would be to amend the computer file that

holds the assumed distribution of water consumptions and is

used in establishing the probabilistic framework. However,

Fig. 1 – The dissolution of lead through time, under zero

flow conditions.

w a t e r r e s e a r c h 4 3 ( 2 0 0 9 ) 2 6 4 7 – 2 6 5 6 2649


4/10

the work of Hayes (2002) has shown that changes to all vari-

ables, other than plumbosolvency (M and E ) and the

percentage of houses with lead pipes, have to be substantial to

have an effect on the model’s results.

The aim of this probabilistic Monte Carlo framework is to

describe the huge variation that undoubtedly occurs in real

water supply zones. If we can mimic this real-world variationthen themodel canbe used for predictive purposes, as hasbeen

demonstratedby casestudies(Hayes et al., 2006, 2008). It should

be appreciated that the average lead concentrations predicted

by the model relate to a single plumbosolvency condition

occurring in time, whether it is appliedas a constantthroughout

an area or as a range. In consequence, the predicted results

relate to an averagecondition over time.This is reasonableif the

periods of time under consideration extend to multiples of

a year, such that seasonal variation is accommodated.

The zonal model calculates the daily average concentration

(DAC) of thelead emissions foreach simulated house andfrom

this can readily determine the percentage of simulated houses

that fail a series of specified standards (typically: 10, 25 and50 mg/l). As the zonal model uses a range of water use patterns

(Fig. 2) that also span week-day and week-end consumptions,

the DAC is taken to be equivalent to the weekly average

concentration, and is therefore also equivalent to composite

sampling over a weekly period (COMP) as was used by Van den

Hoven et al., 1999. This is of interest as the EU directive (Euro-

pean Commission, 1998) describes the lead standards in terms

of weekly average lead concentrations ingested.

It is of course not possible to validate these DAC outputs

directly without exhaustive composite sampling (which is not

logistically feasible) and so a sampling model is used, in order

to characterise the behaviour of the simulated zone in a way

that can be validated by the data collected by water

companies. Random daytime (RDT) sampling is of greatest

relevance in the UK, as it has been used for regulatory

purposes for many years (UK Government, 1989).

In order to simulate a RDT survey, the specified number of

simulated houses are selected at random and then a sampling

time is selected at random between the hours of 09-00 and

17-00. The RDT sample is simulated by a stirred tank of onelitre capacity as the outlet from the pipe. At the time of

simulated sampling, the pattern of water use that has been

applied to the simulated house is used to determine the

immediately previous water – pipe contact position. It is

routine to repeat the simulated survey, typically 100 times, in

order to be able to understand possible variation. The result

reported for the zone under investigation is the average

survey result from all the surveys simulated, although confi-

dence bands are also computed and can be used if required in

model validation. Examples of the validation of the zonal

modelling procedure are given in Table 1. It can also be noted

that the predicted zonal compliance for zones in Cambridge

and Wales (UK), following the optimisation of ortho-phos-phate dosing (Hayes et al., 2006) has been achieved in practice.

Therefore, the modelling procedure has been validated for

both pre- and post-ortho-phosphate dosing conditions.

Stagnation sampling is also used to characterise lead emis-

sions. In the UK, 30 min stagnation samples have been most

commonly used as a treatment benchmarking technique at

fixedpoints(Hayesetal.,1997)asopposedtosurveyingzonesfor

compliance.In theUS, 6 h stagnation sampling of selectedfixed

points is used for regulatory assessment. To simulate a stagna-

tion sample, theleadconcentration in thesimulated pipe is first

assumed to be zero and then follows the applied dissolution

curve (Fig.1) whereby the lead concentration after30 min or 6 h

stagnation is determined in a 1 l emission volume.

0

5

10

15

20

25

% % %

5 20 35 50 65 80 95

Length (m)

Length of lead pipe

0

5

10

15

20

25

0 10 20

Length (m)

Length of non-lead pipe

0

5

10

15

20

25

0 200 400 600 800

Volume (l)

Volume per day

0

2

4

6

8

10

12

14

16

%

1 4 7 10 13 16 19 22

hour

Water use pattern A

0

5

10

15

20

25

%

1 4 7 10 13 16 19 22

hour

Water use pattern B

¼ ½

Hour

Frequencies

¼

Hour

Frequencies

Fig. 2 – Statistical distributions used to set up the zonal model.

w a t e r r e s e a r c h 4 3 ( 2 0 0 9 ) 2 6 4 7 – 2 6 5 62650


5/10

The greatest uncertainty in the modelling procedure is the

estimate of the extent to which lead pipes are present in

a zone. In the UK Cambridge and Bristol studies (Hayes et al.,

2006) this was not a problem as the water companies had

inspected a large proportion of the houses in their area. In the

Wales study (Hayes et al., 2008) such survey data was notavailable; however, the extensive RDT data over a period of

around five years, prior to the commencement of ortho-

phosphate dosing, was assessed on the basis that if the

analytical result forlead was below the limit of detection, then

no lead pipe was present. This simple method was used for all

zones studied and enabled an estimate of the occurrence of

lead pipes to be gained; the fact that validation of the model,

calibrated in this way, was validated well by actual RDT

sample data indicates the adequacy of the approach.

3. Methodology for investigating sampling

There are two stages in the zonal-sampling modelling proce-

dure. Firstly, the zonal characteristics are assembled by

randomised ascription of the variables used. The statistical

distributions (Fig. 2) that control this process define percent-

ages of each value to be applied in the modelling framework.

The simplified description of each variable in a look-up table

format is very flexible and easy to amend, as opposed to

defining mathematically the shape of a curve (which in the

development of the model was found to give similar results).

In combination, the ranges in variables that are used give rise

to around 3000 permutations of pipe characteristics within

each zonal model. Each time the zonal model is executed,

a particular set of permutations is created, which differ

depending on the size of the zone being modelled. In this

study a zone size of 10,000 houses was used throughout and

the reproducibility of DAC simulations for all houses in the

zone, when looking at percentage failure to a range of lead

standards, was found to be better than 1%. However, in the

sampling simulations that followed, a single set of zonal

conditions was first established and then used repeatedly,

thereby removing this slight variation when comparing sampling methods.

The simulated sampling surveys were all based on taking

100 1 l samples, selected randomly from the simulated houses

within the zonal modelling framework and randomly in time

between 09-00 and 17-00 h, except for DAC which was calcu-

lated for the total period of water flow. For each condition

under investigation, thesurveys were repeated 100times,such

that results were in effect based on 10,000 simulated samples.

Four sampling methods were compared:

[1] daily composite to determine average concentration

(DAC), equivalent to (COMP);

[2] random daytime (RDT);[3] 30 min stagnation (30MS); and

[4] 6 h stagnation (6HS).

Samples types [1] to [3] were summarised to determine

percentage zonal failure rates against three lead standards

(10, 25 and 50 mg/l) whereas sample type [4] followed the US

LCR in which the 90th percentile concentration in a survey

was calculated and compared to the lead standard of 15 mg/l.

These methods were compared throughout for five zonal

conditions in which the percentage of houses with a lead pipe

was varied, between 10 and 90%, and for two plumbosolvency

conditions: [1] M ¼ 0.1 and E ¼ 150, equivalent to a moderately

plumbosolvent water, and [2] M ¼ 0.02 and E ¼ 30, equivalentto a phosphated water in which there has been an 80%

reduction in plumbosolvency (which Hayes et al., 2006, 2008

demonstrates is readily achievable in practice).

For a zone with 50% of houses with a lead pipe, a further

investigation examined the effect of varying the ratio between

the equilibrium and 30 min stagnation lead concentrations,

which relate to different shapes of the lead dissolution curve

through time. Laboratory plumbosolvency testing using the

method of Colling et al. (1987) has indicated (Hayes, 2007) that

this ratio can vary markedly, between 1.3 and 6.6 for phosph-

ated waters and more widely for non-phosphated waters.

4. Results

4.1. Comparison of DAC, RDT, 30MS and 6HS: moderate

plumbosolvency

The averaged results for five zones with varying percentages

of lead pipes and moderately plumbosolvent water conditions

are shown in Table 2. Percentage failure is clearly a function of

both the stringency of the lead standard and the percentage of

simulated houses which have a lead pipe (albeit of varying

length and diameter), for all four sampling methods. For the

lead standard of 10 mg/l, 30MS gives a slightly higher failure

rate than RDT and DAC. The range of zonal failure rates

Table 1 – Validation examples: predicted and observedzonal failure rates for RDT samples (from Hayes et al.,2006, 2008 ).

Study andbasis

Number of samples

% >10mg/l

% >25mg/l

% >50 mg/l

Bristol

Observed 259 46.9 27.3 9.7Predicted 35.0 22.9 9.6

Cambridge: zone

new 1

Observed 145 8.2 3.0 0.0

Predicted 7.4 2.0 0.2

Cambridge: zone

new 2

Observed 130 10.0 0.8 0.0


Cambridge: zone

old 1

Observed 525 32.4 15.0 4.5

Predicted 28.4 15.1 5.2

Cambridge: zone

old 2Observed 292 9.8 4.5 2.0


South East Wales

Observed 509 21.8 11.8 4.5

Predicted 18.4 11.3 4.8

w a t e r r e s e a r c h 4 3 ( 2 0 0 9 ) 2 6 4 7 – 2 6 5 6 2651


6/10

against 10 mg/l from DAC correlate very closely with RDT

(r2¼ 0.99) suggesting that the methods are equivalent for non-

phosphated waters, in general agreement with Van den

Hoven et al. (1999). Equivalence between DAC and RDT is less

for the 25 and 50 mg/l standards, due to the smoothing effect of

DAC that becomes more significant for the higher standards;

this indicates that RDT is the more stringent method forassessing regulatory compliance with 25 mg/l.

The UK Government required (Drinking Water Inspec-

torate, 2000, 2001) corrective treatment action to be taken and/

or optimised if more than 5% of RDT samples had exceeded

the future European standard for lead of 10 mg/l, and then

subsequently to achieve no more than 2% or better through

optimisation (there is a gap between the UK’s trigger and

subsequent target). It can be seen from Table 2 that zones in

which 10% of houses have a lead pipe were unlikely to require

such attention.

The relationship between DAC and 30MS is however

suspect as illustrated by Fig. 3 in which all 10,000 DAC and

30MS results have been compared for a selected condition.

Two trends are discernable for a zone in which 50% simulated

houses have a lead pipe:

[1] There is a declining relationship between DAC and the

number of simulated houses, which is a reflection of the

permutations of lead pipe and water flow characteristics

(the chart shows zero lead after 5000 houses because only

50% of houses were ascribed as having a lead pipe); and[2] the incremental behaviour of 30MS is due to dilution from

water in the non-lead pipe between the simulated lead

pipe and tap outlet (as dictated by the discretised distri-

bution of non-lead pipe length shown in Fig. 2) and to

dilution from incoming water prior to the lead pipe when

its length equates to less than 1 l in volume – for 12 mm

internal diameter lead piping greater than 8.8 m in length,

and assuming no non-lead pipe between the lead pipe and

the tap outlet, the 30MS results would be constant for any

given plumbosolvency condition.

The basis for assessing compliance with the LCR is

different. If the percentage of houses with a lead pipe is 10%,the 90th percentile concentration is generally very low and

only 1 in 100 surveys failed the 15 mg/l standard, a similar

result to that based on RDT sampling vs 10 mg/l and the UK’s

5% trigger for action. For higher percentages of lead (30% plus)

the 90th percentile increases in proportion to the percentage

of houses with lead pipes, but the LCR assessment is very

similar or the same.

4.2. Comparison of DAC, RDT, 30MS and 6HS: low plumbosolvency

The averaged results for five zones with varying percentages

of lead pipes and low plumbosolvent water conditions (80%reduction compared to moderate plumbosolvency) are shown

in Table 3. For DAC and RDT, similar trends are discernable to

those observed for moderately plumbosolvent water, with

both failure rates increasing with higher percentages of

houses with a lead pipe.

The RDT failureratesare noticeably higherthan those based

on DAC and this is of regulatory significance. In the current

debate in Europeon what samplingmethod to useto determine

compliance with the lead standards of 25 and 10 mg/l, if RDT

samplingwas adopted as the harmonised method, it would not

only be more feasible logistically (Van den Hoven et al., 1999)

but more stringent, providing no less public health protection

than the manner in which the standards are described in thedirective (European Commission, 1998).

The UK Government has indicated (Drinking Water

Inspectorate, 2000, 2001) that one measure of optimisation of

corrective treatment is that no more than 2% of RDT samples

should exceed 10 mg/l. This means that in zones with a higher

percentage of houses with a lead pipe the plumbosolvency of

the water must be reduced more than that in a zone with

a lower percentage of lead pipes, for water of similar plum-

bosolvency prior to corrective treatment. Table 3 also reveals

that 30MS fails to distinguish the influence of the percentage

of lead pipes.

With the US LCR and 6HS sampling, the influence of the

percentage of houses with a lead pipe is significant. Zones

Table 2 – A comparison between sampling methods formoderate plumbosolvency water and different extents of lead pipes.

(a) Predicted DAC, RDT and 30MS against European standards

Percentageof houses

with a leadpipe

Standardfor lead

(mg/l)

DAC RDT 30MS

Average %

samples>standard

Average %

samples>standard

Average %

samples>standard

10 10 3.71 3.94 4.53

25 1.13 1.56 2.22

50 0.18 0.43 0.00

30 10 12.35 12.28 14.23

25 2.91 5.18 7.09

50 0.69 1.37 0.00

50 10 20.41 20.23 24.27

25 4.66 8.02 11.63

50 1.00 1.91 0.00

70 10 28.65 27.33 33.89

25 7.38 11.60 16.80

50 1.62 2.76 0.00

90 10 37.85 36.39 43.38

25 9.50 15.28 21.33

50 1.85 3.69 0.00

(b) Predicted 6HS against the US standard of 15 mg/l

Percentage of houses witha lead pipe

Average %samples

>standard

Average 90thpercentile

concentration (mg/l)

% Surveysfailing thestandard

10 6.00 0.23 1

30 19.69 58.84 99

50 33.64 84.98 100

70 47.50 104.34 10090 60.95 115.94 100

The averaged results shown derive from 100 surveys each of

100 samples. All samples were selected randomly from the

zonal model. Moderate plumbosolvency was defined by M¼ 0.1

and E ¼ 150.

w a t e r r e s e a r c h 4 3 ( 2 0 0 9 ) 2 6 4 7 – 2 6 5 62652


7/10

with 10 or 30% lead mostly satisfy the LCR, zones with 70 or

90% lead substantially or completely fail the LCR, whereas

zones with 50% are border-line.

In Table 4, a direct comparison of DAC, RDT and 6HS

sampling has been made in relation to the 10 and 15 mg/l

standards (as far as was possible using the model as devel-oped) and it can be inferred that the UK optimisation target of

no more than 2% RDT samples exceeding 10 mg/l is broadly

equivalentto no more than 10% 6HS samples exceeding 15 mg/l

(assuming this equates to a 90th percentile concentration).

This suggests (at face value) that the UK and US approaches

provide a similar level of public health protection for

phosphated waters of low plumbosolvency.

4.3. Influence of the ratio between equilibrium ( E ) and

30MS lead concentrations

30MS samples have been considered (Lacey and Jolly, 1986) to

be a reasonable measure of the average lead concentrationemitted from a lead pipe, in consideration of the water

consumption patterns that are encountered in various types

of domestic household in the UK. It is also reasonable to

suppose the higher the equilibrium lead concentration (E ), the

greater will be the chance of obtaining a failure. This suppo-

sition is borne out in Tables 5 and 6 for both moderate and low

plumbosolvent water:

for a single pipe and moderate plumbosolvency water, with

M¼ 0.1 kept constant, the predicted 30MS lead concentra-

tion increases as the ratio of E/30MS increases; a similar

effect is observed with low plumbosolvency water with

M¼ 0.02;

for a zone in which 50% houses have a lead pipe, the

percentage of predicted compliance samples failing their

respective standards increases as the equilibrium concen-

tration increases when M is kept constant.

Differences between DAC and RDT are again of potentialregulatory significance for low plumbosolvent waters. The

influence on LCR compliance is also significant.

The phenomenon is illustrated in Fig. 1 by comparing curve

A1 with curve A2 and indicates that the relationship between

RDT and stagnation sampling can vary. That such variation in

E/30MS does occur has been shown by plumbosolvency

testing (Hayes, 2007). In consequence it is not possible to

utilise stagnation sampling to determine compliance with

lead standards unless the relationship with RDT sampling has

been characterised. In this context, RDT sampling is the only

method that can determine the spatial and temporal extent of

lead compliance across a zone (that is also logistically

feasible), given enough samples are taken.

4.4. RDT re-sampling

The RDT sampling model also determines the result of

a second RDT sample from each simulated house wherea RDT

sample in a survey exceeds specified standards for lead. The

second simulated sample is taken randomly in time within

the same time period (0900–1700 h) as for thefirstRDT sample,

at the same simulated house. For zoneswitha range of10–90%

houses with a lead pipe, the average re-sampling failure rates

vs 10 mg/l were found to be between 61.4 and 64.7% for

moderate plumbosolvency and between 38.9 and 51.3% for

0

20

40

60

80

100

120

140

1 812 1623 2434 3245 4056 4867 5678 6489 7300 8111 8922 9733

30ms

dac

Fig. 3 – A comparison of 30MS and DAC for a zone with 50% lead pipes and moderate plumbosolvency water ( M[0.1,

E[150). The Y -axis is the lead concentration in mg/l. The X-axis is the number of simulated houses in the zone that had the

particular lead concentration predicted, both on the basis of 30MS and DAC.

w a t e r r e s e a r c h 4 3 ( 2 0 0 9 ) 2 6 4 7 – 2 6 5 6 2653


8/10

low plumbosolvency conditions. It is clear that RDT re-

sampling is not able to reliably confirm an initial RDT failure.

4.5. Quantification of the variation inherent in sampling

In each simulated sampling survey, 100 samples were taken

randomly from throughout the zonal probabilistic frameworkand randomly in time between 09-00 and 17-00 h, for all

sampling methods investigated with the exception of DAC

which is calculated from the lead concentrations throughout

the daily pattern of use (Fig. 2). With approximately 3000

permutations across 10,000 simulated houses, it is not

surprising that each survey can give different results, purely

by chance. To illustrate: (a) for a zone in which 50% houses

had a lead pipe and with moderate plumbosolvency water

(M¼ 0.1 and E ¼ 150), the average percentage of RDT sample

exceeding 10 mg/l was 20.23% (Table 2) but with a minimum

of 12% and a maximum of 30% (standard deviation 3.81);

(b) for a zone in which 50% houses had a lead pipe and

with low plumbosolvency water (M¼ 0.02 and E¼ 30), the

average percentage of RDT sample exceeding 10 mg/l was

1.93% (Table 3) but with a minimum of 0% and a maximum of 7% (standard deviation 1.49).

With moderately plumbosolvent water(M¼ 0.1and E¼ 150)

the significance of the variation in survey results depends on

the numeric relationship between the lead emissions occur-

ring in the zone and the water quality standard that applies.

The UK trigger for action (Drinking Water Inspectorate, 2000,

2001)ofnomorethan5%ofRDTsamplesexceeding10 mg/lisso

stringent in relation to moderately plumbosolvent water that

the inherent variation in survey results has little practical

significance. However, the close numerical relationship

between the UK optimisation target (no more than 2% RDT

samples exceeding 10 mg/l) and the results predicted for low

plumbosolvency water (M¼ 0.02 and E¼ 150) could havepractical and regulatory significance. For the simulation

reported in (b) above 71% of surveys had either a 0, 1 or 2%

failure rate, whereas 29% had a failure rate of 3% or greater.

For random 6HS sampling a similar pattern of variation

was obtained (see Table 3) and for low plumbosolvency water

and a zone with 50% of houses with lead piping, 62% of

surveys failed the US LCR and 38% of surveys passed.

Table 3 – A comparison between sampling methods forlow plumbosolvency water and different extents of leadpipes.

(a) Predicted DAC, RDT and 30MS against European standards

Percentageof houses

with a leadpipe

Standardfor lead

(mg/l)

DAC RDT 30MS

Average %

samples>standard

Average %

samples>standard

Average %

samples>standard

10 10 0.18 0.41 0.00

25 0.00 0.02 0.00

50 0.00 0.00 0.00

30 10 0.75 1.34 0.00

25 0.00 0.01 0.00

50 0.00 0.00 0.00

50 10 0.86 1.93 0.00

25 0.01 0.04 0.00

50 0.00 0.00 0.00

70 10 1.54 2.96 0.00

25 0.01 0.04 0.00

50 0.00 0.00 0.00

90 10 1.79 3.47 0.00

25 0.00 0.01 0.00

50 0.00 0.00 0.00

(b) Predicted 6HS against the US standard of 15 mg/l

Percentageof houseswith a leadpipe

Average %samples

>standard

Average 90thpercentile

concentration(mg/l)

% Surveysfailing thestandard

10 2.80 0.53 0

30 6.41 11.83 5

50 11.76 17.08 6270 16.44 20.98 98

90 21.80 22.28 100

The averaged results shown derive from 100 surveys each of 100

samples. All samples were selected randomly from the zonal

model. Low plumbosolvency was defined by M ¼ 0.02 and E¼ 30.

Table 4 – Direct comparison of DAC and RDT with 6HSagainst standards of 10 and 15 mg/l for lowplumbosolvency water.

Sampling method Average % samples Average % samples

>10 mg/l >15 mg/l

DAC 0.84 0.30

RDT 1.91 0.516HS N/A 11.76

N/A¼notavailable from model.The averaged results shown derive

from 100 surveys each of 100 samples for a zone with 50% houses

with a lead pipe. All samples were selected randomly from the

zonal model (additional simulations to those summarised in Table

3). Low plumbosolvency was defined by M¼ 0.02 and E¼ 30. The UK

optimisation target for plumbosolvency control is that no more

than 2% RDT samples exceed 10 mg/l, whereas the US target for LCR

compliance is that no more than 10% 6HS samples exceed 15 mg/l

(assuming equivalence to the 90th percentile concentration).

Table 5 – Effect of equilibrium concentration on thepredicted 30MS result for a single lead pipe.

(a) Moderate plumbosolvency (M ¼ 0.1)Equilibrium (E ) leadconcentration (mg/l)

30MS leadconcentration (mg/l)

Ratio E /30MS

75 41.4 1.8

150 49.6 3.0

225 52.8 4.3

300 54.5 5.5

(b) Low plumbosolvency (M¼ 0.02)

15 8.3 1.8

30 9.9 3.0

45 10.6 4.2

60 10.9 5.5

Theresults were obtained with a singlelead pipe of 20 m lengthand

12 mm internal diameter, with no non-lead pipe.

w a t e r r e s e a r c h 4 3 ( 2 0 0 9 ) 2 6 4 7 – 2 6 5 62654


9/10

Although the real-world surveys undertaken to assess

compliance with the LCR are from selected properties that are

surveyed on a repeated basis, the simulations indicate the

sensitivity of property selection and the possibility for bias

which could in turn effect the extent of corrective action

perceived to be necessary.

Following optimisation of ortho-phosphate treatment to

reduceplumbosolvencyinCambridgeandinWales(Hayesetal.,

2006, 2008), the extent of real-world RDT samples complying

with thelead standard of10 mg/lwas99.5%(>1000 samples)and

99% (>5000 samples) respectively, based on field sampling over

severalyears.The generalconsistencyof thesefield datarelated

to percentage reductions in plumbosolvency that were better

than 80% in many cases, and suggests that potential sampling

error can be minimal when corrective treatment is optimised.

Forsuppliesinwhich80%reductionorlessisbeingachieved,the

practical significance of sampling error will be greater.

An additional simulation that assumed 50% of houses with

a lead pipe and a 90% reduction in plumbosolvency (M¼ 0.01

and E¼ 15)obtainedan average of 0.12% RDTsamples >10 mg/l,

with a range of 0–1% and a standard deviation of 0.32%. As this

entire rangeis well below the 2% target,the variation is shown

to have no bearing on the conclusion made, when such a high

plumbosolvency reduction has been achieved.

5. Conclusions

The successful validation of a modelling system that predicts

lead emissions across entire water supply zones enables

a searching examination of sampling methods to be under-

taken, far more exhaustively than could be achieved by field

sampling.

For water with moderate plumbosovency, DAC and RDT

sampling are equivalent methods for zonal assessment

against the standard of 10 mg/l. For water with low plumbo-

solvency, RDT sampling is more stringent than DAC for this

standard.

In consequence, RDT sampling could be used to determine

compliance with the regulatory lead standards in Europe,

without diminishing the level of public health protection that

would be afforded by DAC/COMP. The use of RDT sampling for

assessing compliance with lead standards in the UK since

1989 is clearly vindicated.

30MS sampling is not appropriate for zonal assessment as

a survey tool because it suffers from dilution artefacts.

All randomly based sampling methods produce inherently

variable results, albeit reproducibility is better for waters with

a low plumbosolvency.

For waters with a very low plumbosolvency (assuming that

corrective treatment has been optimised to achieve plumbo-

solvency reductions of 90%) the inherent variation in RDT

sampling results has been shown to be of little or no practical

significance in relation to demonstrating the achievement of

the UK target (that no more than 2% RDT samples should

exceed 10 mg/l).

Fixed point stagnation samplingto assess zonal compliance,

as practised in the US, is prone to bias, as demonstrated by the

range in results obtained between randomly selected sampling

points for certain zonal conditions.

Whereas the UK target for optimising plumbosolvency

control is that no more than 2% of RDT samples should exceed

10 mg/l and the US target for compliance is that no more than

10%of 6HSsamples should exceed 15 mg/l, the two approaches

have been shown to afford fairly similar levels of public health

protection, for phosphated waters achieving 80% lead

reductions.

Compliance with lead standards is influenced by the shape

of the lead dissolution curve, which is known to vary with

individual waters, such that a higher ratio of equilibrium

concentration to 30MS concentration will result in greater

extents of failure. Therefore, 30MS sampling at selected fixed

points alone may not be suitable for characterising zonal

compliance.

r e f e r e n c e s

Colling, J.H., Whincup, P.A.E., Hayes, C.R., December 1987. Themeasurement of plumbosolvency propensity to guide thecontrol of lead in tapwaters. Journal of the Institution of Water

and Environmental Management 1 (No. 3).

Table 6 – Effect of equilibrium lead concentration on predicted compliance with zonal targets.

(a) Moderate plumbosolvency (M¼ 0.1)

Equilibrium concentration(mg/l)

Average %DAC

Average %RDT

Average %6HS

Average 90th percentileconcentration

% 6HS surveysfailing

>10 mg/l >10 mg/l >15 mg/l

75 17.10 19.44 24.48 43.04 100150 20.41 20.23 33.64 84.98 100

225 21.94 20.48 34.75 129.90 100

300 24.20 21.07 33.94 158.70 100

(b) Low plumbosolvency (M ¼ 0.02)

15 0.14 0.79 0.00 8.87 0

30 0.86 1.93 11.76 17.08 62

45 1.19 2.60 23.70 25.67 100

60 1.48 3.07 23.63 30.94 100

The averaged results shown derive from a simulated zone in which 50% houses have a lead pipe and from 100 surveys each of 100 samples. All

samples were selected randomly from the zonal model.

w a t e r r e s e a r c h 4 3 ( 2 0 0 9 ) 2 6 4 7 – 2 6 5 6 2655


10/10

COST Action 637, 2007. Metals and related substances in drinking water. Research Seminars, 21–22 May 2007, Brussels, www.meteau.org .

Department of Environment, 1977. Lead in drinking water. DoEPollution Paper 12, London, HMSO.

Department of Environment, 1980. Report of the Expert Group onIdentification and Monitoring, Lead in Potable WaterTechnical Note No. 1.

Department of Environment, 1989. Guidance on safe-guarding thequality of public water supplies. HMSO.

Drinking Water Inspectorate, 1996. Nitrate, Pesticides and Lead,1991 to 1994. December 1996.

Drinking Water Inspectorate, 1998. The 1999 periodic review of prices and AMP3: further guidance. Information Letter 13/98.

Drinking Water Inspectorate, 2000. Determination of requirements to meet new lead standards. Information Letter12/2000.

Drinking Water Inspectorate, 2001. Further guidance onrequirements to meet new lead standards. Information Letter3/2001.

European Commission, 1980. Council Directive (80/778/EC) of 15th July 1980 relating to the quality of water intended forhuman consumption. Official Journal, L229/11-19, vol. 23,

30th August 1980.European Commission, 1998. Council Directive (98/83/EC) of 3rd

November 1998 on the quality of water intended for humanconsumption. Official Journal, L330/32, 5th December 1998.

Hayes, C.R., Bates, A.J., Goodman, A.H., Vinson, J.P., Sadler, T.P.,August 1997. Meeting standards for lead in drinking water.

Journal of the Chartered Institution of Water andEnvironmental Management 11.

Hayes, C.R., 2002. Ph.D. Thesis, Computational modelling of leadin drinking water, University of Wales.

Hayes, C.R., Bates, A.J., Jones, L., Cuthill, A.D., Van der Leer, D.,Weatherill, N.P., 2006. Optimisation of plumbosolvencycontrol using a computational model. Water and Environment

Journal 20, 256–264.Hayes, C.R., October 2007. Optimisation tools for achieving the

lead standard of 10 mg/l in drinking water. Proceedings of anInternational Conference on Metals and Related Substances inDrinking Water. Antalya, Turkey, 29–31. COST Action 637.

Hayes, C.R., Incledion, S., Balch, M., 2008. Experience in Wales(UK) of the optimisation of ortho-phosphate dosing forcontrolling lead in drinking water. Journal of Water andHealth 06.2, 177–185.

Health Canada, 2007. Consultation document on lead and copperin drinking water.

Hulsmann, A., Cortvriend, J., 2006. Water 21. Magazine of theInternational Water Association.

Kuch, A., Wagner, I., 1983. A mass transfer model to describe leadconcentrations in drinking water. Water Research 17 (No. 10),1303–1307.

Lacey, R.F., Jolly, P.K., 1986. Sampling for household lead, TR244.Water Research Centre.

US Environmental Protection Agency, 1995. Lead and copper rule.Fact Sheet EPA 570/9-91-400.

UK Government, 1989. The Water Supply (Water Quality)Regulations 1989. Statutory Instrument 1989, No. 1147, HMSO.

Van der Leer, D., Weatherill, N.P., Sharp, R.J., Hayes, C.R., 2002.Modelling the diffusion of lead into drinking water. AppliedMathematical Modelling 26 (6)), 681–699.

Van den Hoven, T.J.L., Buijs, P.J., Jackson, P.J., Gardner, M.,Leroy, P., Baron, J., Boireau, A., Cordonnier, J., Wagner, I., doMone, H.M., Benoliel, M.J., Papadopoulos, I., Quevauviller, P.,1999. Developing a New Protocol for the Monitoring of Lead inDrinking Water, EUR 19087 EN.

w a t e r r e s e a r c h 4 3 ( 2 0 0 9 ) 2 6 4 7 – 2 6 5 62656
http://www.meteau.org/http://www.meteau.org/http://www.meteau.org/http://www.meteau.org/

Computational Modelling to Investigate the Sampling of Lead

Documents

Transcript of Computational Modelling to Investigate the Sampling of Lead