laboratory determination of diffusion and distribution coefficients of contaminants using...

Laboratory determination of diffusion and distribution coefficients of contaminants using undisturbed clayey soil

R. KERRY ROWE Faculty of Engineering Science, The University of Western Ontario, London, Ont., Canada N6A 5B9

CHRIS J. CAERS Proctor & Redfern, 379 Dundas Street, London, Ont., Canada N6B IV5

AND

FRANK BARONE Faculty of Engineering Science, The University of Western Ontario, London, Ont., Canada N6A 5B9

Received May 20, 1987

Accepted September 29, 1987

This paper describes a technique for determining the diffusion coefficient and the distribution coefficient for contaminants using saturated, intact (undisturbed) clayey soil samples. The technique is illustrated with reference to a number of laboratory tests involving advective-diffusive migration of potential contaminants through an intact clayey soil from Samia, Ontario. An important aspect of the proposed technique is that the mass of contaminant in the system is kept constant and so significant decrease in source leachate concentration occurs during each test. A simple theoretical model is used to analyze this case and it is shown that this phenomenon can be used to deduce both the diffusion coefficient and the distributionlpartitioning coefficient from a single test. Parameters are deduced for a number of salt solutions passing through the clay from the Samia area. On the basis of these tests it is suggested that for the Samia soil and advective velocities up to the maximum examined (0.035 mla), mechanical dispersion does not measurably affect the magnitude of the "coefficient of hydrodynamic dispersion" (i.e., there is no significant dispersion). It is also suggested that the effective porosity corresponds to that deduced from the water content of the soil.

Key words: contaminant migration, soil, laboratory study, experimental, analysis, diffusion, advection, clays, groundwater.

Cet article dCcrit une technique pour la dktemination des coefficients de diffusion et de distribution pour les contaminants en utilisant des Cchantillons intacts de sol argileux. Cette technique est illustrke au moyen d'un certain nombre d'essais de laboratoire impliquant une migration advective-diffusive des contaminants potentiels 2 travers un sol argileux de Samia (Ontario). Un aspect important de la technique suggCrCe est que la masse de contaminant dans le systkme est gardCe constante, et ainsi, une diminution significative dans la concentration du filtrant se produit au cours de chaque essai. Un modkle thCorique simple est utilisC pour analyser ce cas et l'on dCmontre que ce phCnomkne peut Etre utilisC pour dCduire en partant d'un seul essai les coefficients de diffusion et de distributionlsCparation. Les paramktres sont dCduits pour un certain nombre de solutions de sels filtrant 21 travers l'argile de la rCgion de Sarnia. Sur la base de ces essais, il est suggCrC que, pour le sol de Samia, et pour des vitesses d'advection allant jusqu'au maximum Ctudit (0,035 mla), la dispersion mCcanique n'affecte pas de f a ~ o n mesurable la grandeur du "coefficient de dispersion hydrodynamique" (i.e., il n'y a pas de dispersion significative). I1 est Cgalement suggCrC que la porositC effective correspond ?i celle dCduite de la teneur en eau du sol.

Mots clks : migration de contaminant, sol, Ctude en laboratoire, expkrimental, analyse, diffusion, advection, argiles, eau souterraine.

[Traduit par la revue]

Can. Geotech. J. 25, 108-118 (1988)

Introduction

Contaminant migration through the pores of clayey soils is a well-established phenomenon (e.g., Goodall and Quigley 1977; Crooks and Quigley 1984; Quigley et al. 1986; Desaul- niers et al. 1981). Recognizing the practical impossibility of ensuring indefinite containment of waste leachate, the process of controlled contaminant migration through a liner may provide a useful means of attenuation. However, safe design of these clay barriers will usually require both experimentai and theoretical consideration of clay-leachate interaction and migration rates through the clay.

Recent semianalytic techniques for modelling contaminant migration through clay liners and into the surrounding groundwater provide the designer with a relatively simple means of evaluating different liner designs. For example, these a~~roaches allow convenient assessment of the effect of factors s k h as liner thickness and multiple soil layers on the quality of the groundwater outside the landfill-lining system (see, e.g., Rowe and Booker 1985a, b, 1986a, 1988). However, appro-

priate soil -1eachate parameters are required before any mean- ingful calculation can be performed.

The objective of this paper is to describe a technique for determining some of the key parameters for saturated natural clay liners by means of a modified column test. The application of the technique will then be demonstrated with regard to the migration of various salt solutions through undisturbed samples of a clayey till from Sarnia, Ontario.

Basic concepts and assumptions

Experimental evidence would suggest (Crooks and Quigley 1984; Desaulniers et al. 1981) that the transport of contaminants through saturated clay can be approximated by a law having the form

ac [ I ] f = ncv - nD-

az

where f is the contaminant flux (mass of contaminant transported per unit area per unit time) at a point at depth z at time t;

Printed in Canada 1 lmprimt au Canada

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y U

nive

rsité

Lav

al B

iblio

theq

ue o

n 07

/14/

14Fo

r pe

rson

al u

se o

nly.

ROWE ET AL. 109

n is the soil porosity; c is the concentration of the contaminant being considered; v is the average linearized pore-water velocity (seepage velocity); and D is commonly referred to as the coefficient of hydrodynamic dispersion.

The coefficient of hydrodynamic dispersion D is defined I (see, e.g., Gillham and Cherry 1982) as the sum of the coeffi-

cient of mechanical dispersion, Dm, and effective diffusion coefficient in the porous medium, D,, viz.,

However, it is also commonly assumed (Bear 1979; Freeze and Cheny 1979) that the mechanical dispersion is propor- tional to the average linearized pore-water velocity v and the dispersivity a , viz.,

[2b] Dm = av

while the effective diffusion coefficient is related to the diffusion coefficient in free solution Do by an empirical parameter T, referred to as the "tortuosity," i.e.,

[2c] D, = 7D0

The test described herein can be performed for seepage conditions similar to those expected in the field, and consequently the parameter D determined from the test may potentially include a component due to mechanical dispersion as well as diffusion. Nevertheless, the available evidence (e.g., Gillham and Cherry 1982; Rowe 1987) would suggest that at typical seepage velocities through clay liners it is, in fact, diffusion rather that dispersion that controls the coefficient D. Thus, the coefficient D might more appropriately be referred to as the diffusion-dispersion coefficient or more simply the diffusion coefficient, since, as will be demonstrated, the contribution of dispersion may be negligible even though there is seepage through the soil. Thus, for the remainder of this paper, the so called "coefficient of hydrodynamic dispersion" will be referred to as the "diffusion coefficient" to more clearly reflect the fact that diffusion is the dominant mechanism.

Assuming the chemical processes (such as adsorption) that influence the transport of contaminant through the soil can be reasonably approximated by an "instantaneous" linear sorption isotherm, then the equation governing one-dimensional contaminant transport (see Freeze and Cherry 1979, p. 402) can be written:

which may be written as

where D* = Dl(l + p Kln); v* = vl(1 + p Kln); p is the bulk density of the dry soil; K is the distribution or partitioning coefficient for linear adsorption; and all other terms are as defined above.

In [I] and [3], it is assumed that porosity n is totally available for flow and diffusion and that n is a soil property inde- pendent of the species of contaminant being considered. Normally, this porosity is taken to be the porosity of the soil determined from the water content in accordance with usual geotechnical practice. It may be argued, however, that the ''effective porosity" available for contaminant transport is less than that determined from the water content, since some pores

may not be accessible. Furthermore, processes such as anion exclusion from the vicinity of the negatively charged clay surface may also reduce the "effective porosity." The validity of this argument may be assessed using the technique proposed herein, and at least for the soil considered in this paper the porosity n determined from the water content of the soil does appear to provide a good indicator of the effective porosity.

The calculation of contaminant concentrations and fluxes for the assumed conditions requires a knowledge of the parameters n, p, v, D, and K. As noted above, the porosity n and bulk density P may be determined using conventional geotechnical methods. The seepage velocity v will, of course, depend on the hydraulic conductivity, k, which may in turn be a function of both the type of clay and the leachate. The determination of this parameter has been discussed in some detail by Fernandez and Quigley (1985) and Quigley et al. (1986). The diffusion- dispersion coefficient D and the distribution (partitioning) coefficient K can be determined for a given clay and contaminant using a modified column test as described in the following paragraphs.

Laboratory models may take many forms (see, e.g., van Genuchten 1978). In most column tests a source leachate of interest is maintained at a constant concentration co above a column of (usually remoulded) soil (see Fig. I). After allowing a period of time for diffusive transport to occur, the test is terminated, the sample is sectioned, and the concentration profile through the sample is determined. By adjusting an apparent diffusion coefficient, D* = Dl(l + pKln), an analytic solution (e.g., Lapidus and Amundson 1952) may be matched to the observed concentration profile to give an inferred value of D*.

For situations where contaminant transport is solely by diffusion and where the concentration is specified at the boundaries, a knowledge of D* may be all that is needed. However, if flux is to be calculated, then a knowledge of D* alone is not sufficient, since the flux depends on D and not D* (see [ I ] ) . Fur- thermore, in a great many practical situations either the boundary conditions are flux controlled (e.g., if one considers a finite mass of contaminant in a landfill, as discussed by Rowe and Brooker 1985a, b) or the soil deposit consists of more than one layer and continuity of flux must be maintained between the layers (e.g., if there are sand layers beneath the liner). In either case, the use of the parameter D* (and the corresponding apparent velocity v*) would give rise to incorrect predictions of contaminant transport because of the depen- dency of flux on D rather than D*. The errors associated with incorrect use of D* (and v*) may be substantial and unconser- vative, as demonstrated by Rowe et al. (1985). Thus, in the majority of cases it is necessary to know both the diffusion- dispersion coefficient D and the distributionlpartitioning coefficient K.

It may be argued that the distribution coefficient K can be estimated from separate batch tests (Hajek and Ames 1968; Schwanzenbach and Westall 1981), and hence the diffusion coefficient can be inferred from the knowledge of D*, K, n , and p. However, the batch tests are often performed at low solids-to-water ratios, and K values developed this way are not necessarily appropriate at solids-to-water ratios typical of field situations (Voice et al. 1983). Thus it would be desirable to have a test that allows the determination of both D and K from the one test on undisturbed samples of the liner material under consideration. It may still be appropriate to perform batch tests and the results of the two tests may provide greater insight regarding the mechanisms involved.

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y U

nive

rsité

Lav

al B

iblio

theq

ue o

n 07

/14/

14Fo

r pe

rson

al u

se o

nly.

110 CAN. GEOTECH. J. VOL. 25, 1988

Source Leachate changed regularly to maintain constant surface concentration

L zero ou t t~ow

FIG. 1. Schematic of a concentration-controlled column test.

Formulation of the test An examination of [I] and [3] suggests that it may be pos-

sible to distinguish the different effects of diffusion (i.e., D) and the retardation due to sorption (i.e., K ) from a single test by modifying the column test such that the surface boundary condition is flux controlled (i.e., depends on [I] directly) instead of being a specified constant concentration as is usually the case. This objective can be achieved very simply by intro- ducing the source solution (leachate) above the clay column at a known concentration co but then allowing this concentration to change (decrease) as contaminant is transported in the soil. Suppose that the volume of source solution (leachate) is equal to AHf where A is the plan area of the column and H f is the "height of the leachate" in the column (see Fig. 2). Then at any time ti, the mass of any contaminant species of interest in the source solution is equal to the concentration c,(ti) in the solution multiplied by the volume of solution (assuming here that the solution is stirred so that c,(ti) is uniform throughout the solution). The principle of conservation of mass then requires that at this time ti, the mass of contaminant in the source solution is equal to the initial mass of the contaminant minus the mass that has been transported into the soil up to this time ti. This can be written algebraically as

ti

[4a] c, (ti) AHf = co AHf - A 1 (t)d t

where c,(ti) is the concentration in the source solution at time ti; co is the initial concentration in the source solution (t=O); A is the plan area of the column; Hf is the height of leachate (i.e., the volume of leachate per unit area); and$(t) is the mass flux of this contaminant into the soil at time t.

Dividing [4a] throughout by the volume AHf then gives

As noted earlier, the movement of contaminant through the soil itself depends on the quantity D* = Dl(l + pKln) ([3b]). However, in contrast, Booker and Rowe (1987) have proven analytically that the variation in source concentration with time is related to the quantity D** = D(l + pKln) (i.e., D** = D*(1 + p Kl r~ )~ . Consequently, there is a unique combination of the parameters D andp K that will provide a good match to both the surface concentration variation with time and the concentration profile with depth. Thus, provided there is not significant scattering of the data points, a single test provides sufficient information to determine both parameters without ambiguity.

In the proposed test, an undisturbed sample of soil is placed

Source Ledchote has initial concentration Co Concentrotion will decrease as contaminant moves into the soil Distilled water may be added as needed to maintain the height Ht

Effluent Collected Porous and Monitored Collection Plote

FIG. 2. Schematic of the proposed test. Flux-controlled boundary conditions at top and bottom of soil sample.

in a column and the leachate of interest is placed above the soil. Contaminant is then permitted to migrate through the specimen under the prescribed head (which may be zero). The volume of leachate above the soil will normally be selected to be sufficiently small to allow a significant drop in concentration of contaminant within the source solution (typically the height of leachate in the column above the clay will range from 0.05 to 0.3 m). This drop in concentration with time should be monitored. If necessary, additional reference fluid (which does not contain the contaminant species of interest) can be added to the reservoir to maintain a constant volume of leachate and any dilution resulting from this is automatically taken into consideration by the theory used for the back-analysis of parameters.

A number of possible boundary conditions at the base of the sample may be considered. If the test is to be conducted with advective transport through the specimen, then a porous collection plate can be placed beneath the sample, as shown in Fig. 2, and the effluent collected and monitored. Considera- tion of conservation of mass for this case gives the concentration in the collector ch(ti) at any time ti as

where& is the flux into the collector plate at time t; nh is the porosity of the collector plate; h is the thickness of the collector plate; and v, is the advective (Darcy) velocity of flow through the sample.

If there is no advective flow, then two other base boundary conditions may be considered. Firstly, the base could be an impermeable plate (see Fig. 3a). In this case, the base boundary condition is given by

[5b] fb(t)=O for t r O

The second alternative is to have a closed cgllection chamber (reservoir) similar to that for the leachate but initially having only a background concentration of the contaminant of interest (see Fig. 36). Thus, as contaminant passes through the soil, it accumulates (and can be monitored) in this collection chamber. The increase in concentration ch(ti) with time ti in this collection chamber is given by

I 1;

t5cI ~b(ti) = Cbr + - 1, fh(t)dt Hr

where chr is the initial background concentration (which may

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y U

nive

rsité

Lav

al B

iblio

theq

ue o

n 07

/14/

14Fo

r pe

rson

al u

se o

nly.

ROWE ET AL

Height of I Source leochate has initial

Leachate H f concentrotion Co \ Concentration will decrease as contaminant moves into the soil

Zero Outfiow

Col lection chamber Concentration will increase as contaminant moves through the soi l Concentration variation w i t h time can be monitored

Zero outflow

FIG. 3. Schematic of pure diffusion tests: (a) zero flux at base of the soil; (b) migration into a collection chamber.

be zero); H, is the volume of fluid in the reservoir per unit area; f,(t) is the flux into the reservoir from the soil at time t.

The migration of contaminant through the soil is governed by [3] -151. These equations could be solved numerically using standard finite difference or finite element techniques. Nevertheless, a more efficient and convenient approach is to take the Laplace transform of equations [3a], [4b], and [5] and then find an analytic solution in transform space. For any given set of parameters, the concentration and flux at any specified times can then be obtained by numerically inverting the Laplace transform. This theoretical analysis has been described in detail by Rowe and Booker (1985a, 1987) and has been implemented in the computer program POLLUTE (Rowe et al. 1983). This approach permits very accurate calculation of concentration in only a few seconds on a microcomputer and hence is well suited for use in interpretation of the results of the column tests.

When the test is terminated at some time t, the sample is sectioned and the concentration profile with depth is determined. By adjusting the diffusion coefficient D and the distribution coefficient K, the semianalytic solution outlined above may be matched to the observed concentration profile to give inferred values of both D and K . The values of D and K deduced in this way can be checked by comparing the calculated and observed variations of contaminant concentration with time in the source leachate. When adopting this procedure, an initial estimate of D can be obtained by first experimentally determining the tortuosity, 7, for a nonreactive reference species (e.g., for chloride, 7 = D(C1-)/(Do(C1-)) and then multiplying the diffusion coefficient of the species of interest in free water Do by this tortuosity (i.e., D = ?Do) It should be noted that this is only an approximation, sincethe "tortuosity" is not a true soil constant and can be expected to vary somewhat from one contaminant to another (see Quigley et al. 1987).

The sensitivity of this approach for the determination of D and p K can be illustrated by considering the migration of a contaminant through a 10 cm thick sample given a soil porosity of 0.4, an advective velocity (v, = nv) of 0.033 m/a, and a height of leachate (volume of leachate + plan area of specimen) Hf = 0.1 m, as indicated in the insert to Fig. 4. Taking a typical diffusion coefficient D (e.g., for Na+) of 0.015 m2/a, Fig. 4a shows the theoretical concentration profile at 0.25 a for values of R K = 0.0.2. and 0.4. It can be seen that

TABLE 1. Soil description (after Crooks and Quigley 1984)

Property Below landfill waste

Liquid limit (%) Plastic limit (%) Specific gravity Moisture content (%) Mineralogy ( < 74 pm) (%)

Carbonates Quartz and feldspars Illite Chlorite Smectite

Cation exchange capacity ( < 2 pm) (meq/ 100 g)

combinations of parameters (D, pK), viz., (0.01 m2/a, 0) and (0.015 m2/a, 0.2). These two combinations of the parameters correspond to the same value of D* (i.e., 0.01 m2/a) and in tests where the leachate concentration was held constant (c,(t) = co) these two sets of parameters would give identical concentration profiles at any time. However, as is clearly evident from Fig. 4b, in the proposed test where the source concentration is allowed to drop with time, these two sets of parameters give rise to different concentration profiles illus- trating the different effects of D and pK. It is for this reason that both parameters can be determined. The effect is even more pronounced for lower values of leachate height Hf.

Laboratorv column tests on a Sarnia till The migration of contaminant through the clay till beneath

the Confederation Road landfill (located approximately 6.4 km southeast of Samia, Ontario) has been carefully monitored over a 12 year period by researchers at The University of West- em Ontario (e.g., Goodall and Quigley 1977; Crooks and Quigley 1984; Quigley and Rowe 1986). To obtain soil- leachate parameters for the analysis of this case, a series of column tests was performed by the present authors on "undisturbed" tube samples of the unweathered grey clay till found beneath this landfill. The basic geotechnical properties and mineralogy of this till are summarized in Table 1.

, ,

even this relatively &all difference in sorption results in a sig- Experimental procedures nificant difference in the concentration profiles. Figure 4b A schematic diagram of the apparatus used in the investiga- shows the theoretical concentration profile at 0.25 a, for two tion is shown in Fig. 5. Each column consisted of a 7.50 cm

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y U

nive

rsité

Lav

al B

iblio

theq

ue o

n 07

/14/

14Fo

r pe

rson

al u

se o

nly.

CAN. GEOTECH. J. VOL. 25, 1988

Pore-Water Concentration (rng/L 1 Pore-Water Concentration ( mg/ L 1

Depth (crn 1

0 - 0 200 400 600 800 1000

n = 0.4 2 - Va = 0.033 m /a

4 - Time = 0.25 a

6 -

8 -

Plate 10

0 200 400 600 800 1000

-- - 0.01 0 0.01

- 0.015 0.2 0.01

Va = 0.033 m?'a

Time = 0.25 a

( b )

FIG. 4. Concentration profiles with depth in a hypothetical test at 0.25 a showing sensitivity of concentration profiles: (a) to small change in pK, (b) to different combinations of D and pK giving the same value of D*.

outside diameter, hollow Plexiglas cylinder with an inside diameter of 6.731 cm. A cutting shoe with an inside diameter of 6.770 cm was fitted to the end of the Plexiglas cylinder. Using a triaxial compression machine, an undisturbed 7 cm diameter soil sample of approximately 10 cm in length was pressed into the Plexiglas cylinder. Once the soil sample was in place, porous polyethylene plates (porosity nb = 0.43) of 0.3 cm thickness were placed at the top and bottom of the sample. The porous plate at the top was used to ensure that the permeating solution entered the soil surface evenly and provided a uniform concentration. The porous plate at the base of

ing from the addition of distilled water is automatically considered by [4] and hence does not need to be explicitly considered when using the analysis program POLLUTE.

At specified times, the models were taken apart, the soil samples sectioned, and the clay analyzed to determine the ver- tical distribution of the chemical constituents. The pore fluid of each of these subsections was obtained using a pneumatic pore- water squeeze apparatus by squeezing at a pressure of 13 MPa for approximately 4 h.

Cation and chloride ion analyses were performed in The University of Western Ontario Soils Laboratory. Calcium,

the soil sample was completely saturated and was used to col- magnesium, sodium, and potassium were analyzed for each lect and channel the effluent from the soil to the drainage test using an atomic absorption spectrophotometer. Chloride point. Once the soil sample was in place, a Plexiglas base plate ion concentrations were determined using a specific ion elec- was fixed to the Plexiglas cylinder using an ethylene dichloride trode attached to a multipurpose meter. Dilutions were required resin bond. A plastic fitting was attached to the base plate to bring the concentrations into range. through which the effluent could be drained. A mass balance was performed for each test to provide a

Once the base plate and polyethylene effluent collector were check that there had not been unintended loss of contaminant attached to the Plexiglas column, the model was moved to a wooden frame where it remained for the duration of the test. A hanger weight system was set up and a pressure of 87 kPa was initially applied to the soil sample for 2 days. This pressure was considered to be large enough to provide good seating of the sample in the Plexiglas column while being well below the preconsolidation pressure of 172 kPa (Ogunbadejo 1973; Quigley, personal communication, 1985). After the first 2 days, the soil sample was allowed to reconsolidate for two more days at an applied pressure of 30 kPa. To prevent drying of the clay surface, a small quantity of distilled water was maintained above and below the sample (zero hydraulic gradient) during the consolidation period. After consolidation, the distilled water was replaced by salt solution above the soil and drainage into a small polyethylene collection bottle was permitted at the bottom of the column. The source salt solution was mixed periodically to maintain a relatively uniform concentration throughout the reservoir depth. The models were maintained at a laboratory temperature of 22 k 1 "C .

The total fluid flow through the soil and into the collection bottle was monitored. To prevent a drop in height of solution in the reservoir due to seepage into the soil, a volume of distilled water equal to volume of effluent collected was added

(e.g. due to sorption onto the Plexiglas or squeeze equipment). For both cations and anions, the mass balance at the end of the test was to better than 99% of the original mass in four out of five cases. In the fifth and worst case (i.e., C1- in model C and Ca+ + in model B) the mass balance was 98.8 % and 95.8% of the original mass respectively. The fact that models B and C were duplicate tests provides confirmation of the results in these two worst cases. It is concluded that there were no significant losses of contaminant from the system in these tests.

Tests conducted Six tests (referred to as models A-F) were conducted as

described above. Each model was permeated with specified salt solution (calcium chloride, sodium chloride, or potassium chloride) under a controlled total head for a predetermined period as indicated in Table 2. Models A - E involved a single cation source solution. Model F involved a source solution of both potassium and calcium chloride and will be discussed in detail in a subsequent publication.

All soil samples were obtained from borehole 83-1. Table 3 gives the sample number used for each model and the corresponding depth below ground surface where the silty clay soil was obtained. It also lists the samples used to obtain the back-

after each monitoring period. Thus, the height of leachate in ground pore-water concentrations-of the ions of interest. the reservoir remained relatively constant. The dilution result- The soil samples used in tests A-F were selected after full-

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y U

nive

rsité

Lav

al B

iblio

theq

ue o

n 07

/14/

14Fo

r pe

rson

al u

se o

nly.

ROWE ET AL

TABLE 2. Model test details

Initial concentrations Advective Hydraulic Testing in source loading ( m g / ~ ) Height of (superficial) Hydraulic conductivity?

Leaching period leachate* velocity gradient k Model solution (days) Cation Anion Cl- H, (m) (m/a) I (cmls) x

A NaCl 86 975 1501 0.3 0.034 4 2.7 B CaCI, 84 975 1725 0.3 0.033 4.16 2.4 C CaCl, 141 975 1725 0.3 0.030 4.16 2.2 D KC1 105 975 885 0.3 0.035 4.0 2.7 E KC1 97 975 885 0.1 0.025 2.0 3.9 F KC1 108 975 2609 0.3 0.035 4.0 2.7

CaCl, 975

*Height of leachate H, = volume of leachate + internal cross-sectional area of the column. +Calculated for n = 0.39 and average cross-sectional area 35.2 cm'.

PLEXIGLAS TOF \

PERFORATED PLEXIGLAS DISTRIBUTION PLATE

POROUS POLYETHYLEN PLATE

PLEXIGLAS BASE PLATE

PLASTIC TUBING-

WOODEN SUPPORT

PLEXIGLAS CYLINDER

STAINLESS STEEL ROO

THREADED STEEL ROD

LEACHATE

SOIL SAMPLE

1.7 cm THICK PLYWOOD EFFLUENT COLLECTOR

SCALE LLI n R

crn WEIGHTS

ALUMINUM CIRCULAR PLATE

FIG. 5. Schematic diagram of Plexiglas models.

size radiographic examination to ensure that the samples did not contain any significant stones or pebbles that would influence the contaminant migration through the soil. The water content of the various samples was 22 1 % .

Experimental results and interpretation The effluent discharge volume was found to be linear with

time over the entire test period for each of the six tests. Based on these discharge rates, the advective velocity and hydraulic conductivity were deduced as shown in Table 2. The calculated hydraulic conductivities of between 2 x lo-* and 4 x

cmls are only marginally higher than a field value of 1.5 x cmls reported by Goodall and Quigley (1977), which was obtained from falling head tests on piezometers installed in the clay below the landfill at Sarnia. This suggests that there was no significant channelling of flow along the sample - Plexiglas interface and that the apparatus performed as expected.

- 1200 _I \ c3 w 5 @

[L 800 z 2 g 6

400 z W U z S

Theory 400 I-- =0.05 rn2/a, p K = 0.18

- MODEL A (NaCI) Co= 1 5 0 0 m g / L

0 Observed

- Theory 0. - D = 0.018 m2/a 0 f

END OF TEST

- v, = 0 . 0 3 3 rn/a -

Cb no = 0 .39

Hf = 3 0 c m

I I

[L

TIME ( a )

( b )

FIG. 6. Source and base concentration changes over time in model A: (a) for chloride; (b) for sodium.

As indicated previously, the design of this experiment involves a decrease in contaminant concentration in the source solution. This concentration drop was monitored in each test. The rate of concentration decrease depends on the volume of leachate, the diffusion coefficient, and the distribution coefficient. All other things being equal, the higher the distribution coefficient, the larger will be the rate of contaminant decrease with time. The computer program POLLUTE permits direct modelling of this test. Thus by adjusting the diffusion (D) and distribution ( K ) coefficients and matching the resulting theoretical curve to the observed drop of concentration with time it is possible to obtain an estimate of these parameters as previously described.

Figures 6-8 show the observed and typical best-fit theoretical matching curves for source concentration (c,) of sodium chloride (NaCl), calcium chloride (CaCl*), and potassium chloride (KCI) solutions respectively.

The results presented in Figs. 6 -8 were all obtained for the same volume of source leachate (Hf = 0.3 m) and it can be seen that the decrease in chloride concentration with time is

'OoO * -+ -7 - -+L -,- -+-+-- L-+-+ W + 800-Ct B f

- co = 9 7 5 rng/L + Observed

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y U

nive

rsité

Lav

al B

iblio

theq

ue o

n 07

/14/

14Fo

r pe

rson

al u

se o

nly.


TABLE 3. Summary of the sample depth and their use and background pore-water conditions (all samples

obtained at BH83-1 from Samia, Ontario)

Sample depth (m) Sample number Sample use

6.64-6.79 3-4 Background 6.79-6.95 3-3 Model A 6.95-7.10 3-2 Model B 7.10-7.25 3- 1 Model F 7.28-7.44 4-4 Background 7.59-7.74 4-2 Model E 7.74-7.86 4- 1 Model C 7.86-8.02 5-4 Background 8.02-8.17 5-3 Model D

Background concentrations* (mg/L)

Sample C1- Ca++ Mg++ Na+ Kf

\ MODEL B ( C a C I 2 )

co = 1725 rng/L - w 0 Observed :-.Theory ; =,O~I;~/O , T:iT

END OF

va = 0 . 0 3 4 m/a

C b . no= 0 . 3 9 tif = 3 0 c m

0:

A Observed c0 : 9 7 5 rng / L

' U Theory

$ 4 0 0 D = O 0 1 2 m2/a, pK= 2 . 0 0 U a

A

FIG. 7. Source and base concentration changes over time in model B: (a) for chloride; (b) for calcium.

*At a water content of 21 %.

fairly similar (minor differences reflect small differences in advective velocity). However, comparing the rate of change in cation concentrations with time for three cations (Naf, Ca++, Kf), it is apparent that there is a significant difference in diffusion coefficient (D) and distribution coefficient (K) for the three cations. The values of the parameters D and p K deduced by fitting the theoretical curve to the observed change in concentration are summarized in Table 4.

For a given soil, the rate of concentration drop with time depends on the contaminant being considered, as shown above. It also depends on the volume of source solution (i.e., on H,). Figures 8 and 9 illustrate this effect for the migration of potassium chloride with the same initial concentration but different volumes of leachate (Hf = 0.3 m for model D and 0.1 m for model E). Comparing the two sets of results, it is apparent that the rate of concentration decrease is substantially faster for model E with the lower leachate volume. This faster decrease makes it a little easier to obtain good parameters, since the theoretical curve is more sensitive to the values of D and pK. Nevertheless, the parameters D and K deduced from the two tests are very similar, as indicated in Figs. 8 and 9 and Table 4.

Figures 6-8 also show the variation in the effluent concentration (cb) with time. As might be expected, the concentration of ions in the effluent starts at zero and increases with subsequent time. This trend is most noticeable for the anion (Cl-) and is less apparent for the cations. The rate of increase in effluent cation concentration is greatest for sodium (which has a low distribution coefficient, p K - 0. IS), is less for calcium (pK = 2.0), and is negligible for potassium (pK = 7).

In principle, it should be possible to match calculated and observed base concentrations; however, dilution of effluent occurred in the porous plate at the bottom of the models (which was initially saturated with distilled water). The effect of dilution varied with time (being greatest at low times) and so the "observed" effluent concentrations do not represent the true outflow concentration from the soil but, rather, represent a lower bound to these concentrations. In addition, "averaging7' of concentration occurred in the collection bottle during the periods between sampling. Thus, although the base concentra-

_I I I O O ~ ; * ' : m E

co = 885 rng/L

- w 800 MODEL D ( K C 1 ) m Q z [T

Observed - .

Theory

400 D - 0 . 0 2 0 m'/a va = 5 . 0 3 m/a END OF

TEST no = 0 . 3 9

W

z 8 co = 9 7 5 rng /L

2 800 "' -'- --.-1 0: I> - - - _ _ _

Observed - - - _ _ p Gi rn

a m --- Theory

3 2 400 D = 0.022 rn2/a . OK = 7

TIME ( a )

FIG. 8. Source and base concentration changes over time in model D: (a) for chloride; (b) for potassium.

tion trends are qualitatively correct, the values do not warrant analysis. This shortcoming of the test has been eliminated in subsequent application of this general procedure by modifying the collection system.

The variation in source concentration (c,) with time provides an initial means of estimating the parameters D and pK, however, the variation in the concentration throughout the sample at the termination of the test provides the primary data for determining (or checking) these parameters. Figures 10 - 14 show the observed anion (Cl-) and cation concentrations with depth for models A-E respectively. Also shown are the theoretical curves through the data obtained using the deduced values of D and pK, given in Table 4.

Allowing for some small experimental scatter of data points, inspection of Figs. 6-9 and 10- 14 indicates that in each case the theoretical curves provide a very good fit to both the decrease in the source fluids concentration with time and the variation in concentration with depth in the soil at the end of each test. The consistency of results demonstrates the power of the analytical model (and program POLLUTE) and provides

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y U

nive

rsité

Lav

al B

iblio

theq

ue o

n 07

/14/

14Fo

r pe

rson

al u

se o

nly.

ROWE ET AL.

TABLE 4. Summary of solute diffusion-dispersion coefficients and distribution coefficients deduced from these tests

D (m2/a), p K

Model:

A B C D E

Ion \ velocity Advective (mla) 0.034 0.033 0.030 0.035 0.025

1200 I I ( a )

MODEL E ( K C ! ) END OF * co = 885 mg/L 800 - -

Observed

eTEsi -

- Theory 4 0 0 - D = 0.020 mZ/o vo = 0.025 m/o

no = 0 3 9

c b . * * , Hf = lOcm 0 I

= Observed co = 975 mg/L Theory D = 0.020 rn2/o , pK = 7 .. - - - - - - - L - - ~ - - & -

TIME ( a )

FIG. 9. Source and base concentration changes over time in model E: (a) for chloride; (b) for potassium.

some confidence in the parameters D and p K. To provide an indication of parameter variation that might be

expected for a given soil, a number of tests were duplicated. The diffusion coefficient, D, for chloride was deduced for each model and ranged between 0.018 and 0.02 m2/a with an average value of 0.019 m2/a. This small variation in D does not appear to be related to small differences in advective velocity, nor does it appear to be particularly related to the nature of the associated cation (see Table 4). Rather, the variability from 0.018 to 0.02 m2/a is seen as an indication of the level of repeatability that may be achieved for this type of test.

The influence of dispersion

The advective velocity of between 0.025 and 0.035 m/a used in these experiments exceeds that expected in most practical field applications involving clayey liners. As noted in the pre- vious section, the change in velocity from 0.025 to 0.035 did not give rise to a discernible difference in the coefficient D and this raises the question as to whether any dispersion is evident in these tests. To provide some indication regarding the effect of the advective velocity on the coefficient D, a pure diffusion test was conducted for chloride allowing for a concentration drop in the source leachate but zero flux at the base of the soil (i.e., migration was governed by [3a], [4b], and [5b] with v = 0). Tests at this scale can be performed very quickly and the concentration profile through the sample after 4 days is

PORE-WATER CONCENTRATION ( rng / L )

0 2 0 0 400 6 0 0 8 0 0 1000 1200 1400 I I I -/ I I

C I- I NO+ v c o ( m g / L ) 1500 9 7 5 D (rn2/ol 0.018 0.015 A

0 .0 0.1 8 ( N a C I ) Observed . + + ' i 1 Theory - - -- /

/+ /

/*Vo = 0.033 rn/o 0.3 crn Porous *' no = 0.39 + f plate ( nb=0.43) / H f . 3 o c m

t/ Time = 86 days

FIG. 10. Chloride and sodium concentration vs. depth of sample for model A.

shown in Fig. 15. Also shown is the predicted concentration profile using the average value of D = 0.019 m2/a obtained from the advective-dispersive tests A-E. It is seen that the prediction is in excellent agreement with the observed profile and this suggests that the contribution of mechanical dispersion to the coefficient D at velocities of 0.035 m/a or less is negligible for this clay and hence it is appropriate here to refer to it as the diffusion coefficient.

Effective porosity and tortuosity To this point, it has been assumed that the porosity n calcu-

lated on the basis of the water content of the soil is fully available for contaminant transport. A value of 0.39 has been adopted in these calculations, although some variability in water content was observed corresponding to a porosity rang- ing from 0.37 to 0.39. The calculated concentration profile using D = 0.02 m2/a and both n = 0.39 and 0.37 are shown in Fig. 14 for model E. For potassium, the difference in the curves is not plottable. For chloride, the difference is plottable but not significant. A similar conclusion is reached if the other model tests are reinterpreted using n = 0.37. Thus the uncertainty as to the precise value of porosity n (due to the small variation in water content) does not significantly influence the magnitude of the parameters D and p K deduced using n = 0.39.

It could be argued that the effective porosity might be significantly less than the values calculated based on water content (i.e., 0.37 I n 5 0.39) owing to the presence of immobile pore fluid. To examine this possibility, an attempt was made to

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y U

nive

rsité

Lav

al B

iblio

theq

ue o

n 07

/14/

14Fo

r pe

rson

al u

se o

nly.

116 CAN. GEOTECH. J . VOL. 25, 1988

PORE-WATER CONCENTRATION ( rnq / L )

0 2 0 0 4 0 0 6 0 0 8 0 0 1000 1200 1400 1600

I I I f/ I I

MODEL @ A/ /

( Ca C12 )

1 0 3 Porous f 4 Plate

( n = 0.43) A,

/

A,'

w<,,~mg/~ 0 (m2/a

P K /+/ Observed

Theory

FIG. 11. Chloride and calcium concentration vs. depth of sample for model B.

PORE-WATER CONCENTRATION ( r n q / L )

0 2 0 0 4 0 0 6 0 0 8 0 0 1000 1200 1400 1600 0 1 1 I 7 I ,

A ' MODEL C /

(CaCI2) A ,' /

/ C O I ~ ~ / L I

A ~ ( m ~ / a l

PK Observed Theory

va ' 0035 rn/a

no = 0.39

t i t = 3 0 c m TlME = 141 days

FIG. 12. Chloride and calcium concentration vs. depth of sample for model C.

reinterpret the chloride tests using lower porosities (i.e., n I 0.35); however, it was not possible to obtain a good match to the experimental data for these parameters. The discrepancies between the observed and calculated profiles increased with decreasing assumed porosity. Thus it would appear that the effective porosity of the soil is not significantly less than that deduced from the water content.

The migration of different species of contaminant through the clay may be affected by factors such as the ionic radius and the charge of the species (Quigley et al. 1987). With this proposed technique, these factors are incorporated in the effective diffusion coefficient and will be manifested in terms of differences in the "tortuosity" (i.e., the ratio of the effective diffusion coefficient deduced from these tests for a given species to the diffusion coefficient of that species in aqueous solution). For the nonreactive tracer chloride the tortuosity determined from these tests is 0.32. For sodium and potassium, quite similar values of 0.38 and 0.36 were obtained. However, calcium was found to have a "tortuosity" of 0.52. Thus, the movement of calcium through this calcium-rich clay is much faster than would be expected based on geometrical consideration (i.e., the tortuosity deduced for a nonreactive species) and the diffusion coefficient in aqueous solution. It may be speculated that this is the result of physical -chemical interaction between the Caf + ions in the solution and the clay, although additional research is required to fully understand the behaviour of

PORE-WATER CONCENTRATION ( mg/ L ) 0 2 0 0 4 0 0 6 0 0 8 0 0 1000 I I I Y I

7' MODEL D ( K C I ) s,'

- ' TlME = 105 days ' H f = 3Ocm /.

- / va = 0.03 m/a

CI- K + '' co(rnq/L) 8 8 5 9 7 5

1 . ~ ( r n ' / a ) 0.020 0.022

-r, P K 0 7 Observed e . ! T h e y - - - -

FIG. 13. Chloride and potassium concentration vs. depth of sample for model D.

PORE-WATER CONCENTRATION ( rng / L )

0 2 0 0 4 0 0 6 0 0 8 0 0 1000 I

MODEL E / I

? n = 0.39

n = 0.37 Ei 0.39 4 )

,! Theory & TlME = 9 7 days I. - CI-

t I --- K + -

r 1)

& I I L I I -

FIG. 14. Chloride and potassium concentration vs. depth of sample for model E.

calcium. It is worth noting that it was not possible to get a reasonable fit to the observed migration profile for tortuosities of less than 0.52 for calcium.

Distribution coefficients and nonlinearity The proposed approach is based on the assumption that the

adsorption isotherm is linear and reversible. The species most affected by sorption is potassium. The tests involving potassium were performed at a concentration which could be expected to fully occupy the exchange sites on the clay. This represents the upper limit to which linearity of sorption could possibly occur and greatly exceeds concentrations found in many landfill leachates in southern Ontario.

A series of batch tests were performed using this Samia clay and distilled water spiked with KC1 (i.e., the same leachate as used in tests D and E). The isotherm shown in Fig. 16 is linear (with p K = 7.1) up to a concentration of approximately 900 mg/L. This confirms that the assumption of linearity adopted in the interpretation of the model tests is reasonable. The value of p K deduced from this batch test is in excellent agreement with the value back-figured from tests D and E. The model test was also analyzed using the finite element program

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y U

nive

rsité

Lav

al B

iblio

theq

ue o

n 07

/14/

14Fo

r pe

rson

al u

se o

nly.

ROWE ET AL. 117

PORE-WATER CONCENTRATION ( mg / L ) 0 2 0 0 4 0 0 600 800 I000 1200 I400

01 , , I 1 I I I

BASE

OBSERVED CI- CONCN. - THEORY D = 0019 rnZ/o

FIG. 15. Chloride concentration vs. depth of sample for pure diffusion model.

SFIN (Rowe and Booker 1983), which allows direct modelling of the isotherm obtained from the batch tests (assuming that the process is either reversible or irreversible). The results from the nonlinear analysis are not substantially different from those obtained using a linear (reversible) isotherm for this case, since the initial concentration in the leachate is only marginally greater than the concentration at which nonlinearity occurs. Clearly, for problems where the concentration of contaminant is very high and where nonlinearity becomes important, then parameters back-figured using the proposed procedure may not be appropriate.

Discussion

The proposed technique provides a relatively simple means of estimating the coefficient of hydrodynamic dispersion (or diffusion coefficient) and distribution coefficient for leachate passing through undisturbed clayey soil. The interpretation of the test assumes that the sorption process can be reasonably approximated as being a linear isotherm over the concentration range of interest. The validity of this assumption can be checked in one of two ways.

When dealing with inorganic contaminants, batch tests can be conducted to determine the range of linearity. The proposed column test described in this paper could then be performed within this range to provide values of both D and pK for undisturbed soil.

The alternative to performing batch tests in conjunction with a column test is to perform at least two column tests at different concentrations within the range of interest. If the linearity assumption is valid then the values of D and p K deduced from both tests will be the same. If the assumption is not reasonable, then markedly different values of pK will be back-calculated for the different concentrations and, furthermore, it will be dif- ficult to obtain a good fit to both the variation in leachate concentration with time and the variation in concentration with depth within the sample (at the end of the test).

The application of an effective stress to the soil sample adopted in these tests is not an essential part of the proposed technique for determining the parameters D and K. The authors have also performed tests without the applied stress, and for the particular combination of clay and permeants considered herein, similar results were obtained both with and without the application of the effective stress. However, for some combinations of clay and permeant, shrinkage of the clay may occur in the absence of a confining stress and this can give quite mis-

4 - A - 109 Wet Soil in 100 rnL

Distil led Woter Spiked With KC1

-

-

FIG. 16. Potassium batch test for spiked distilled water.

leading results (see, e.g., Fernandez and Quigley 1987). For these clays, tests should be performed at an effective stress similar to that anticipated in the field.

It is noted that the parameters deduced from the tests reported in this paper are generally consistent with those back- figured from field observations beneath the Confederation Road landfill (Quigley et al. 1987).

The results reported in this paper were obtained using a source solution consisting of distilled water spiked with a single salt solution. The same procedure may be adopted for deducing the diffusion and distribution coefficients obtained with more complex source solutions involving many salts (Caers 1985; Barone et al. 1988). It is noted in passing that the parameters obtained for a given soil may depend on the chemical composition of the source solution. This will be discussed in detail in a subsequent paper (Barone et al. 1988).

Conclusions The prediction of contaminant migration through saturated

clayey soil involves the use of appropriate theoretical models and soil-leachate parameters. This paper has described a number of laboratory tests involving the migration of potential contaminants through an intact clayey soil from Sarnia, Ontario. A theoretical model was used to interpret the experimental results and to deduce appropriate soil-leachate parameters. Based on this study, the following conclusions were made: (1) Diffusion was the dominant mechanism for contaminant transport through the intact Sarnia clay in these tests with seepage velocities of between 0.064 and 0.09 mla. (2) Significant decrease in source leachate concentration occurred during each test owing to contaminant transport into the soil and it was shown that this phenomenon could be used to deduce both the diffusion coefficient and the distribution1 partitioning coefficient from a single test. (3) The tests were shown to be repeatable and parameters determined from a number of different tests involving different salt solutions and volumes of leachate were found to be quite consistent. (4) For the conditions examined in these tests, the diffusion coefficients were, for chloride, 0.019 m2/a; sodium, 0.015 m2/a; calcium, 0.012 m2/a; potassium, 0.02 m2/a. The dimen- sionless products p K, which measure the "sorption" of a particular contaminant species in the Sarnia clay, were, for

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y U

nive

rsité

Lav

al B

iblio

theq

ue o

n 07

/14/

14Fo

r pe

rson

al u

se o

nly.


chloride, 0 ; sodium, 0.18; calcium, 2.0; potassium, 7.0. (5) The migration of calcium through the clay was much faster than would be expected based on geometrical considerations (i.e., the tortuosity deduced for a nonreactive species) and the diffusion coefficient in aqueous solution. Additional research is required to fully understand the migration of C a + + ions. (6) The assumption of linear sorption appears to be valid for the range of conditions examined in these tests. (7) For this clay and the range of velocities considered, mechanical dispersion was not apparent and the "coefficient of hydrodynamic dispersion" for C1- was the same as the diffusion coefficient in the absence of advection. (8) The porosity of the soil calculated on the basis of the water content appeared t o give a very reasonable indication of the effective porosity.

Acknowledgements

tion in bes IV-The effect of longitudinal diffusion in ion exchange and chromographic columns. Journal of Physical Chemistry, 56: 984-988.

OGUNBADEJO, T. A. 1973. Physico-chemistry of weathered clay crust formation. Ph.D. thesis, University of Western Ontario, London, Ont.

QUIGLEY, R. M., and ROWE, R. K. 1986. Leachate migration through clay below a domestic waste landfill, Sarnia, Ontario, Canada: chemical interpretation and modelling philosophies. In Hazardous and industrial solid waste testing and disposal: sixth volume. American Society for Testing and Materials, Special Technical Publication 933, pp. 93 - 103.

QUIGLEY, R. M., ROWE, R. K., and FERNANDEZ, F. 1986. Engi- neered clayey barriers to control groundwater contamination. Geo- technical Research Report GEOT-6-86, The University of Western Ontario, London, Ont.

QUIGLEY, R. M., YANFUL, E. K., and FERNANDEZ, F. 1987. Ion transfer by diffusion through clayey barriers. Proceedings of ASCE Specialty Conference on Geotechnical Aspects of Waste Disposal, Ann Arbor, pp. 137- 158. The work described in this paper was by grant No' Rowa, R. K. 1987. Pollutant transport through barriers. Proceedings

from the Sciences and Engineering Research of ASCE Specialty Conference on Geotechnical Aspects of Waste Council of Canada (NSERC). Additional funding was pro- Disposal, A*or, pp. 159 - vided by NSERC Strategic Grant GO921 and by The University ROWE, R. K., and BOOKER, J. R. 1983. SFIN-a finite element of Western Ontario Inc. The authors gratefully acknowledge analysis program for single contaminant migration under 1D condi- the value of discussions with Dr. R. M. Quigley. tions. Geotechnical Research Centre, University of Western

BARONE, F., YANFUL, E. K., QUIGLEY, R. M., and ROWE, R. K. 1988. Effect of multiple contaminant migration on diffusion and adsorption of some domestic waste contaminants in a natural clayey soil. Geotechnical Research Report GEOT-5-88, Geotechnical Research Centre, The University of Western Ontario, London, Ont.

BEAR, J. 1979. Hydraulics of groundwater. McGraw Hill. BOOKER, J. R., and ROWE, R. K. 1987. One dimensional advective-

dispersive transport into a deep layer having a variable surface concentration. International Journal for Numerical and Analytical Methods in Geomechanics, l l(2): 131 - 142.

CAERS, C. J. 1985. Some theoretical and experimental aspects of pollutant migration. M.E.Sc. thesis, University of Western Ontario, London, Ont.

CROOKS, V. E., and QUIGLEY, R. M. 1984. Saline leachate migration through clay: a comparative laboratory and field investigation. Canadian Geotechnical Journal, 21: 349 - 362.

DESAULNIERS, D. D., CHERRY, J. A., and FRITZ, P. 1981. Origin, age and movement of pore water in argillaceous quaternary deposits at four sites in Southwesten Ontario. Journal of Hydrology, 50: 23 1 -257.

FERNANDEZ, F., and QUIGLEY, R. M. 1985. Hydraulic conductivity of natural clays permeated with simple liquid hydrocarbon. Cana- dian Geotechnical Journal, 22: 205-214.

1987. Effect of viscosity on the hydraulic conductivity of clayey soils permeated with water-soluble organics. Preprint, 40th Canadian Geotechnical Conference, Regina, Sask., pp. 3 13 -320.

FREEZE, R. A., and CHERRY, J. A. 1979. Groundwater. Prentice- Hall, Englewood Cliffs, NJ.

GILLHAM, R., and CHERRY, J. A. 1982. Contaminant migration in saturated unconsolidated geologic deposits. In Recent trends in hydrogeology. Edited by T. N. Narasimhan. Geological Society of America, Special Paper 189, pp. 3 1-62.

GOODALL, D. C., and QUIGLEY, R. M. 1977. Pollutant migration from two sanitary landfill sites near Sarnia, Ontario. Canadian Geotechnical Journal, 14: 223-236.

HAJEK, B. F. , and AMES, L. L. 1968. Trace strontium and cesium equilibrium distribution coefficients: Batch and column determina- tions. Battelle Pacific Northwest Laboratories, Richland, WA.

LAPIDUS, L., and AMUNDSON, N. R. 1952. Mathematics of adsorp-

Ontario, London, Ont. 1984. The analysis of pollutant migration in a nonhomogen-

eous soil. Gtotechnique, 34: 601 -612. 1 9 8 5 ~ . 1-D pollutant migration in soils of finite depth. ASCE

Journal of Geotechnical Engineering, ll l(GT4): 479 -499. 1985b. Two-dimensional pollutant migration in soils of finite

depth. Canadian Geotechnical Journal, 22: 429-436. 198%. The analysis of multiple-contaminant migration

through clayey soils. Proceedings of 5th International Conference on Numerical Methods in Geomechanics, Nagoya, Vol. 1, pp. 581 -588.

1986a. A finite layer technique for calculating 3D pollutant migration in soil. Gtotechnique, 36: 205-226.

1987. An efficient analysis of pollutant migration through soil. In Numerical methods for transient and coupled problems. John Wiley and Sons, pp. 13 -42.

1988. Prediction of diffusion-controlled contaminant transport in landfill - clay liner systems. In Computer and physical modelling. Edited by A. S. Balasubramanian. Balkema, Rotter- dam, The Netherlands. In press.

ROWE, R. K., BOOKER, J. R., and CAERS, C. J. 1983. POLLUTE- 1D pollutant migration through a non-homogeneous soil: Users manual. Report No. SACDA 84-13, The University of Western Ontario, London, Ont.

ROWE, R. K., CAERS, C. J., BOOKER, J. R., and CROOKS, V. E. 1985. Pollutant migration through clayey soils. Proceedings of XIth International Conference on Soil Mechanics and Foundation Engineering, San Francisco, Vol. 3, pp. 1293-1298.

SCHWARZENBACH, R. P., and WESTALL, J . 1981. Transport of non- polar organic compounds from surface water to groundwater. Lab- oratory sorption studies. Environmental Science and Technology, 15: 1360-1367.

VAN GENUCHTEN, M. T. 1978. Simulation models and their application to landfill disposal siting: A review of current technology. Land disposal of hazardous wastes in Proceedings of the 4th Annual Research Symposium, EPA-60019-78-016, pp. 191 -214.

VOICE, T. C., RICE, C. P., and WEBER, W. 0 . 1983. Effect of solids concentration on the sorptive partitioning of hydrophobic pollutants in aquatic systems. Environmental Science and Technology, 17: 513-518.

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y U

nive

rsité

Lav

al B

iblio

theq

ue o

n 07

/14/

14Fo

r pe

rson

al u

se o

nly.

laboratory determination of diffusion and distribution coefficients of contaminants using...

Documents