application of a geochemical transport model to predict

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Application of a geochemical transport model to predict

heavy metal retention (Pb) by clay liners

Ray E. Ferrell a,*, Per Aagaardb, Johan Forsman a, Lea Greenwood a, Zuoping Zhengb

aDepartment of Geology and Geophysics, Louisiana State University, Baton Rouge, LA 70803, USAbDepartment of Geology, University of Oslo, Oslo, Norway

Received 25 October 2000; received in revised form 2 February 2001; accepted 16 July 2001

Abstract

PHREEQC, a geochemical transport model, is used to simulate diffusive transport of Pb through a 10-cm-thick clay liner.

The results are compared to those of Roehl and Czurda [Applied Clay Science 12 (1998) 387] who studied Pb migration by

diffusion in a carefully monitored laboratory experiment. The computer simulation accounts for effects due to adsorption by ion

exchange, changes in CEC, variable ion selectivity, and porosity or compacted density. It facilitates evaluation of changes in the

diffusion coefficient and solution input parameters. The effective Pb diffusion coefficient determined for the simulation is

3 10 10 m2 s 1 and for the 520-day experiment of Roehl and Czurda it is 2.3 10 10 m2 s 1. Differences in theretardation factors (23.6 and 503, respectively) indicate that the model does not account for all of the adsorption mechanisms

suggested by the experimental investigation. Thus, less Pb is retained and the liner is predicted to fail more rapidly than theactual results indicate. Models have great flexibility, but need to be verified by field data before they can be applied to specific

waste site conditions. D 2002 Elsevier Science B.V. All rights reserved.

Keywords: Transport; Lead; Clay liner; Diffusion

1. Introduction

Geochemical transport models have great utility in

assessing the retention of potential heavy metal con-taminants by clay liners. Natural and compacted clay-

rich materials and geosynthetic textiles containing

clay minerals are among the most commonly em-

ployed methods to isolate landfill wastes from the

environment. Clay liners are particularly important

with respect to the role that they may play in the

isolation of high-level nuclear wastes (Madsen, 1998).

Computer models incorporating the results of modern

studies of reaction mechanisms provide the opportu-

nity to examine factors affecting waste retention andoffer the potential to identify those factors that are

most likely to influence the integrity of natural and

engineered clay barriers. Several models (Selim, 1992)

based on the assumption of local equilibrium are

available to assess processes such as ion exchange,

complexation, and competitive adsorption. Others

have developed multireaction multisite models incor-

porating varying kinetic effects and irreversible reac-

tions (Selim, 1992; Hinz et al., 1992). One of the most

thorough laboratory and field studies of Cd, Pb, Zn

0169-1317/02/$ - see front matterD 2002 Elsevier Science B.V. All rights reserved.P I I : S 0 1 6 9 - 1 3 1 7 ( 0 1 ) 0 0 0 9 2 - 8

* Corresponding author. Fax: +1-225-578-2302.

E-mail address: [email protected] (R.E. Ferrell).

www.elsevier.com/locate/clay

Applied Clay Science 21 (2002) 5966


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and Cr diffusion and sorption by clay minerals is that

reported by Wagner (1992).

PHREEQC (Parkhurst, 1995) is one of the com-

puter programs for geochemical reaction modelling incommon use. Based on an ion-association aqueous

model, it can perform speciation and saturation index

calculations; simulate reaction-paths and 1D-transport

involving reversible reactions, and inverse modelling

of reactions to account for differences in composition

between waters. Reactions considered include those

involving aqueous, mineral, and gaseous phases;

solid-solution, surface complexation and ion-ex-

change equilibria; and irreversible reactions involving

specified mole transfers of reactants, kinetically con-

trolled reactions, mixing of solutions, and temperature

changes. The latest version of PHREEQC (Parkhurst

and Appelo, 1999) includes capabilities to simulate

dispersion or diffusion in 1D-transport calculations,

with or without advective transport. A WINDOWS

version of PHREEQC prepared by Vincent Post may

be obtained free of charge from the website, http://

www.geo.vu.nl/users/posv/phreeqc.html.

The purpose of this paper is to illustrate the use of

PHREEQC to simulate changes in clay content, cation

exchange capacity, metal concentration, ion exchange

and other factors on the diffusive transport of Pb

through a 10-cm barrier. Diffusion may be the mostimportant transport processes when the permeability is

about 110 9 m s 1 (Shackelford, 1991). Allcalculations were performed without advective trans-

port, thus focusing on reactions within the liner. The

results represent the best-case situation when com-

pared to actual waste repositories, as some advective

transport is often observed (Johnson et al., 1989).

Computed results are compared with the experimental

results of Roehl and Czurda (1998) for Pb in order to

assess the validity of the model assumptions.

2. Methods

2.1. Simulation conditions

PHREEQC commands for simulation of Pb trans-

port by diffusion are presented in Table 1. The major

command blocks are identified with all upper case

letters. SOLUTION is used to define the temperature

and composition of up to 20 initial solutions. In this

example, a low ionic strength calciumsodium bicar-

bonatechloride solution has been used to represent

the initial composition of the pore water in the barrier.

The solution contained 0.9 mmol/kgw Ca, 0.1 mmol/

kgw Na, 0.2 mmol/kgw Cl and alkalinity of 1.7 mmol/

kgw expressed as HCO3. The amounts and types of

exchangers are defined in the EXCHANGE block. X

equals the CEC (equivalents per l i ter) of the

Table 1

Typical input for simulation of diffusive flux through a clay barrier

(Pb) with ion exchange

SOLUTION 1 20

-units mmol/kgw

Ca 0.9

Na 0.1

Alkalinity 1.7 as HCO3

Cl 0.2

EXCHANGE 1 20

X 1.0

-equil 120

EXCHANGE_SPECIES

P b + 2 + 2 X = PbX2log_k 1.05

END

SOLUTION 0

-units mmol/kgwpH 6

Pb 1

Cl 2

END

TRANSPORT

-cells 10 #number of cells

-length 0.01 #length (m) of cells

-flow_direction diffusion_only

-shifts 1 #value times time_st is total time for

diffusion calculation

-diffc 3.0e 10 # diffusion coefficient = 3.0e 10 m2/s-bcon constant flux

-time_st 3.15e7 #1 year

USER_GRAPH-heading Distance/m Cl Cd CdX2 CaX2 NaX

-axis_scale x_axis 0 1

-axis_scale y_axis 0 1

-axis_titles Distance/m mol/l

-chart_title

-initial_solutions false

-start

10 graph_x Dist

20 graph_y tot(Cl) * 1e6, tot(Pb) * 1e6,

mol(PbX2) * 1e6, mol(CaX2) * 1e6, mol(NaX) * 1e6

-end

END

R.E. Ferrell et al. / Applied Clay Science 21 (2002) 596660


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exchanger utilised in these simulations and CaExchinitially occupies more than 99% of the exchange

sites. Half reactions and relative log k values for

exchange reactions are defined next. This block(EXCHANGE_SPECIES) is ordinarily left blank

and values in the database file are used automatically.

Alternatively, the user can identify new half reactions

or modify the relative log k. SOLUTION 0 establishes

the composition of the input fluid. In this case, it is a

pH 6.0 PbCl2 solution containing 1 mmol/l of the

metal. Conditions for the TRANSPORT calculations

are established next. The cell was divided into 10

segments 0.01 m in length, the effective diffusion

coefficient (Deff) was 3 10 10 m2 s 1 and the

experiment was conducted for 3.15 108 s, or 10years. Deff is often used to represent the diffusion

coefficient derived from laboratory or field determi-

nations of element profiles. It is equal to the product

(Roehl and Czurda, 1998) of the free solution diffu-

sion coefficient (D0) and the tortuosity factor (s)

divided by the retardation factor (R). Graphing and

output conditions are established in the last block.

END statements throughout signify the end of each

input block.

2.2. Variable clay properties

The influence of changes in clay type on the metal

diffusion profile can be simulated in three ways.

Variations in the total quantity of clay and the type

of clay can be used to modify the total sample CEC.

Ten weight percent clay with a CEC of 100 meq/100 g

is equivalent to 50 wt.% clay with a CEC of 20 meq/

100 g. Porosity (e) and bulk density (qb) also influ-

ence the available cation exchange capacity. CEC in

meq/l can be obtained by multiplying the value

measured as meq/100 g by 10qb/e (Appelo and

Postma, 1994). A sample with a CEC of 18.5 meq/100g with a bulk density (qb) of 1.68 g/cm3 and a porosity

(e) of 35% will have a CEC of 885 meq/l. Increasing

this value increases the quantity of an element

adsorbed by the solids and thus increases the effective

retardation. Converting CEC to a constant volume

facilitates comparison with the quantities of elements

in the pore solution and mass transfer associated with

reaction and transport through the clay. In most of the

simulations described below, the exchange capacity

was either 1.0 or 1.1 mol of a univalent exchanger/l.

A third effect attributable to changes in the char-

acter of the clay or clay minerals can be simulated by

changing the apparent exchange constant for the

metal/exchanger half-cell with regard to the Na/exchanger half-cell used as the reference reaction

(log k= 0.0). For example, changing the log k for Pb

exchange from 1.05 to 0.0 will eliminate the specific-

ity of the exchanger for the Pb ion and Na and Pb

exchange will proceed as a linear reaction.

2.3. Initial concentration of metal

The effects of initial metal concentration in the

input solution on values associated with a given depth

in a penetration profile can be determined from Ficks

second law of diffusion. The partial differential equa-

tion can be integrated to obtain a solution (Appelo and

Postma, 1994) for the concentration of a mobile

component at a given point and time that can be

expressed in terms of the initial or boundary condi-

tions. Increasing the input concentration increases the

concentration or apparent rate of penetration at a

given point.

3. Results

3.1. Ion exchange capacity

Increasing clay content or the CEC of the clay

produces the changes in the apparent penetration

profile of a metal illustrated in Fig. 1. In this diagram,

results for 10 years of diffusion are compared for

initial exchange capacities varying from 0.5 to 2.0

equivalents/l. The highest value is equivalent to a

sample with a CEC of 41 meq/100 g with 35%

porosity and a density of 1.7 g/cm3. This represents

a solid with 100 wt.% of a high CEC illite orvermiculite, or 41 wt.% smectite with a CEC of 100

meq/100 g mixed with a material with no ion

exchange capacity. Profiles shown depict changes in

exchangeable Ca and Pb plus Cl and Pb in the pore

fluid. Exchangeable Na is not illustrated because the

values are smaller than 0.0001 mol/l. After 10 years,

Pb occupies 50% of the exchange sites (0.5 mol PbX2)

at a depth of 1.0 cm when the CEC is 2 equivalents/l

(Fig. 1A). The depth to 50% exchangeable Pb

increases to 1.4 and 2.0 cm, respectively, when the

R.E. Ferrell et al. / Applied Clay Science 21 (2002) 5966 61


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exchange reservoir is reduced to 1.0 and 0.5 equiv-

alents/l. Cl in solution (Fig. 1B) has reached a steadystate equal to the input value in all cells because it is a

conservative element and is not involved in the

simulated reactions. The diamond-shaped data points

for ExcPb in the 0.5 equivalents/l simulation illustrate

how much more Pb is held in exchange positions than

in pore fluids. Depth of penetration for Pb in the pore

fluid (SolPB) varies inversely with the CEC of the

liner material. The depth to C/Co of 0.1 is 4.3, 2.7, and

2.0 cm when the CEC is 0.5, 1.0, and 2.0 equivalents/

l, respectively.

3.2. Ion exchange selectivity

Ion exchange selectivity can be modelled by mod-

ifying the log k of the element with regard to thereference half-cell. Changes in the relative ion

exchange constant for Pb produce the effects shown

in Fig. 2. After 10 years of diffusion, there is less ion

exchange when the relative ion exchange constant for

the Pb half cell (log k= 0.1) is close to that for Na. The

system retains a strong selectivity for Ca. The depth to

50% Pb exchanged decreases from 1.4 to 0.9 and 0.3

cm as the relative log k changes from 1.05 to 0.53 to

0.1 (Fig. 2A). The change in adsorption is accompa-

nied by a change in the depth to the Pb C/Co of 0.1

Fig. 2. Changes in Pb penetration profiles associated with variable

log k for Pb exchange in the simulated liner. (a) Exchangeable Ca

and Pb by clays with relative log kof 0.1, 0.53 and 1.05 with respect

to Na. (b) Pb and Cl in solution with one of the exchangeable Pb

values reproduced for comparison with a.


total cation exchange capacity (CEC) of the simulated liner. (a)

Exchangeable Ca and Pb at total exchange capacities of 0.5, 1.0 and

2.0 mol/l. (b) Pb and Cl in solution with one of the exchangeable Pb

values reproduced for comparison with a.



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(Fig. 2B). Decreasing the relative log k decreases the

adsorbed Pb, so the apparent migration takes place

more rapidly. Depths to C/Co of 0.1 are 2.7, 4.5, and

7.5 cm, respectively. Exchangeable Pb is still signifi-cantly higher than the quantity in solution. When the

barrier material has a stronger preference for the

naturally occurring elements in the pore fluid, the

metal contaminant will migrate more rapidly than

when there is a strong ion exchange preference for

the metal.

3.3. Effective diffusion coefficient

Changes in the effective diffusion coefficient uti-

lised in the simulation produce the changes in the

penetration profiles illustrated in Fig. 3 after 10 years

of transport. As the coefficient increases from 1.5 to

3.0, and 6.0 10 10 m2 s 1, the depth to 50%exchangeable Pb increases to 1.5, 1.9, and 2.4 cm,

respectively (Fig. 3A). The depth to C/Co of 0.1 for Pb

in the pore fluid also increases from 1.8, 2.4, and 3.8

cm (Fig. 3B) A 4 increase in the diffusion coef-ficient increases the rate of Pb penetration about 2 .

3.4. Input fluid composition

Increasing the concentration of Pb in the input fluidincreases the depth of Pb penetration as shown in Fig.

4. When Pb is 0.1 mmol/l and the ion exchange

capacity is 1.0 equivalent/l, exchangeable Pb is only

detectable in the first centimeter of the cell. When Pb

in the input solution is 10.0 mmol/l, the depth to the

50% exchangeable level increases to 3.7 cm (Fig. 4A).

At this high concentration level, Pb is no longer

confined to the simulated liner and C/Co in the last

cell of the barrier is 0.3 (Fig. 4B). Increases in the Pb

concentration in the input solution satisfy the demands

for ion exchange more rapidly. Subsequently, the build up and transport through the pore network is

more rapid.

3.5. Ionic strength of pore fluid

The chief consequence of increasing the ionic

strength of the pore fluid is a decrease in the apparent

selectivity of the ion exchanger for the ions that are

more strongly attracted to the exchanger at low con-

centrations. The exchange relative to Na becomes

more linear and effects similar to those illustrated in

Fig. 2 are observed. A 10 increase in millimoles ofNa and Ca in the pore fluid increases the mole fraction

of Na in the exchanger from < 0.01 to almost 0.04, sothe magnitude of the expected change in Pb retention

is small.

3.6. Summary of modelling results

The results of the transport simulations described

above illustrate several of the basic principles govern-

ing the retention of metal wastes by clay liners. The

magnitude and selectivity of the ion exchanger has a

major effect on the retardation of diffusing wastes.


effective diffusion coefficients (m2 s 1). (a) Exchangeable Ca and

Pb with coefficients of 1.5e 10, 3.0e 10, and 6.0e 10 m2 s 1.(b) Pb and Cl in solution with one of the exchangeable Pb values

reproduced for comparison with a.



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Important relationships controlling diffusive transport

include:

Increased CEC of the barrier materials retards

metal movement. Increased clay content increases the effective

CEC and thus promotes retardation. When the clay has a strong exchange preference

for an ion in the waste fluid compared to those

naturally present in the pore fluids of the barrier,

the input ion movement will be strongly retarded. Increasing the effective diffusion coefficient

increases the rate of penetration.

Rate of metal penetration is directly related to

increases in its concentration in the input

solution.

Large changes in the composition of the porefluid produce minor changes in the mole

fraction of weakly adsorbed ions, thus creating

the potential for minor increases in metal

penetration rate.

3.7. Comparison with experimental results

The experimental results obtained by Roehl and

Czurda (1998) for Pb provide an excellent basis for

comparison with PHREEQC simulations. The authors

assessed the retardation and solid speciation of Pb(also Cd) migrating into an illitic/smectitic loess loam

during experiments lasting from 43 to 520 days. The

loam had a CEC of 18.5 meq/100 g and experiments

were performed at a Proctor density of 1.68 g/cm3 at

moisture content of 17.5 wt.%. Calculated apparent

diffusion coefficients for input solutions containing

0.001 M Pb or Cd chloride were in the range of 3.6

7.4 10 9 cm2 s 1 for Pb and 4.9 6.7 10 8

cm2 s 1 for Cd, with a slight tendency to decrease

with the length of the experiment. The bulk of the

adsorbed metal was in the fraction defined as ex-

changeable (6080%) by selective sequential extrac-

tion procedures. The operationally defined carbonate

fraction (representing specific fixation on pH-depend-

ent sites) was next most abundant.

Fig. 5. Comparison of simulated Pb penetration profiles with data

(open circles and triangles) from the 520-day experiment of Roehl

and Czurda (1998).


Pb content and ionic strength of the simulated waste. (a)

Exchangeable Ca and Pb at total Pb concentrations of 0.1, 1.0,

and 10.0 mol/l. (b) Pb and Cl in solution with one of the

exchangeable Pb values reproduced for comparison with a.



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A comparison of the Roehl and Czurda (1998) data

for the 520-day experiment with PHREEQC-simu-

lated Pb pore fluid profiles is presented in Fig. 5. The

simulations were conducted with a CEC of 18.5 meq/

100 g, bulk density of 1.68, porosity of 36% and the

other input parameters identified in Table 1. Pb input

was constant and the bottom of the column was open.

Pb concentrations were modified by ion exchange

with a relative log k of 1.05. Effective diffusion

coefficients (Def f) were 1.0, 3.0, 4.0, 5.0 and

6.0 10 10. The best visual fit to the experimentaldata was obtained with Deff=3.0 10

10 m2 s 1.

Deff reported by Roehl and Czurda (1998) from other

laboratory experiments was 2.3 10 10 m2 s 1.The two values are essentially equal.

Retardation (R) in the simulation was evaluated at

several values of C/Co by dividing the depth of Cl

penetration by the corresponding depth for Pb. Results

are presented in Table 2. The simulated R is 23.6

when C/Co is equal to 0.5 and 22.3 for C/Co of 0.1.Simulated retardation decreases to about one-half

these values when C/Co is 0.01, presumably due to

dispersion introduced by the choice of cell size for the

model and other factors increasing the apparent dis-

persion of the advancing pore fluid front. Simulated

retardation values near 23 are 22 smaller than thevalue (503) reported by Roehl and Czurda (1998).

Differences in R are reflected in differences in the

apparent diffusion coefficients (Dapp), 4.7 10 13

and 1.3 10 11 m2 s 1, respectively. These coef-

ficients suggest slower rates of Pb transport in theexperimental situation because more Pb is retained by

reaction with the soil.

4. Discussion

The experiment and the simulation produced

nearly identical results for Deff, the diffusion coeffi-

cient that accounts for the influence of tortuosity on

the free-solution aqueous diffusion coefficient. The

differences between the simulated and experimental

results are most obvious with respect to R and Dapp. R

is a dimensionless retardation factor reflecting the

relative rate of transport of a non-reactive solute to areactive one. The apparent diffusion coefficient (Dapp)

is the parameter that most closely approximates the

movement of a reactive solute through a particular

soil. Dapp is the value that is often used to compare

element behaviour in different samples, but is mean-

ingless without an estimate of the retardation factor.

The factors are related by:

Dapp Deff=Retardation R

Differences in the estimate of the retardation factor

account for the large differences in the apparent dif-

fusion coefficient derived from the experiment and the

simulation. A good estimate of this R is critical when

attempting to evaluate the retention of Pb by clay liners.

R is different in the two instances described above

because it is calculated differently. Roehl and Czurda

(1998) used actual determinations of Pb in the soil and

an independent experimental determination of Deff to

calculate retardation. The PHREEQC simulation used

input values of Deff to match the Pb in the pore fluid

of the 520-day experiment and only precipitated the

amount of Pb required to satisfy a simple linear ionexchange process. Retardation was calculated by com-

parison with the hypothetical penetration profile of a

non-reactive solute. Actual measurements indicate

that the clay materials are retaining more Pb than

the simulation predicts.

The differences in retained Pb are apparent in Fig.

6, which compares the total quantity of Pb adsorbed by

ion exchange under the simulated transport conditions

with the actual measurements of Roehl and Czurda

(1998) after 121 and 520 days. The simulated values

are always lower than the measured ones but are veryclose to the quantities attributed to the exchangeable

fraction by Roehl and Czurda (1998). Comparing the

solid circles that represent measured values to the

curve drawn through the open circles (Fig. 6) illus-

trates that the simulated values are within 7080% of

the measured total after 520 days of reaction. The data

for 121 days provide a similar comparison. The

simulations fail to account for (up to 30%) the Pb

contained in the carbonatic fraction. Other sorption

mechanisms should be used to account for all the

Table 2

Calculated retardation factors (R)

C/Co Cl distance (cm) Pb distance (cm) R (Pb)

0.01 50.0 3.65 13.70.1 31.2 1.4 22.3

0.5 13.7 0.58 23.6



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reactions retarding the transport of Pb. In essence, the

PHREEQC model is 7080% effective in simulating

the adsorption observed in laboratory studies, and thus

predicts a more rapid failure of the clay liner.

The demonstration of the relative importance of

factors related to specific liner characteristics is one of

the most useful products of transport simulation.

PHREEQC provides a way to compare clays with

differing CECs, mineral content, ion exchange selec-tivity, and compacted density or porosity. Apparent

diffusion coefficients and the effects of different reac-

tion mechanisms can also be considered. The model

may also utilise variable input such as the composition

of the initial pore fluid or the metal-containing solution.

The chief limitations of the model are ones that

affect all models; they are only as good as the input

data and their ability to reproduce natural conditions.

It is best to use a model to extend interpretations based

on solid laboratory and field investigations. The model

can be used as a sensitivity tool to determine howchanges in field conditions such as porosity might

affect the integrity of clay liners or chemical conditions

that might accelerate transport by diffusion.

5. Conclusions

Simulated transport modelling provides an excellent

means to evaluate the relative influence of the variables

affecting Pb migration through a clay liner. The uncer-

tainties associated with the natural environment can

be modelled to evaluate their relative importance.

PHREEQC is a flexible routine that provides ways to

assess the roles of changing clay content, particularlyCEC and exchange ion specificity, on the calculated

element profiles produced by diffusive transport. Spe-

cific adsorption reactions can be included in the model

to account for the retardation of reactive elements.

Modelling is a useful approach for the study of metal

retention by clay liners. However, it must not be used

as a complete substitute for field and laboratory inves-

tigations. PHREEQC results are in generally good

agreement with Deffdetermined in the laboratory study

of Roehl and Czurda (1998) but differences in the

observed and predicted retardation factors result in the

more rapid transport of Pb in the model clay liner.

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Fig. 6. Total quantity of adsorbed Pb predicted by simulations based

on ion exchange (curves) compared with the data from 121- (open

squares) and 520-day (open circles) experiments of Roehl andCzurda (1998).


application of a geochemical transport model to predict

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