Diffusion of inorganic chemical species in compacted clay soil

Journal of Contaminant Hydrology, 4 (1989) 241 273

241

E l s e v i e r Science P u b l i s h e r s B V., A m s t e r d a m - - P r i n t e d in T h e N e t h e r l a n d s

D I F F U S I O N OF INORGANIC CHEMICAL S P E C I E S IN COMPACTED CLAY SOIL

C H A R L E S D S H A C K E L F O R D 1, D A V I D E D A N I E L 2 a n d H O W A R D M L I L J E S T R A N D 2

1Department of Ctwl Engzneenng, Colorado State University, Fort Colhns, CO 80523, U S A 2Department of Cw~l Eng~neenng, Unwers~ty of Texas, Austin, TX 78712, U S A (Received J u n e 13, 1988, r e v i s e d a n d a c c e p t e d S e p t e m b e r 26, 1988)

ABSTRACT Shackelford, C D_, Daniel, D E a n d Lll]estrand, H M , 1989 Diffusion of i n o r g a n i c c h e m i c a l species in c o m p a c t e d clay soil. J Contain. Hydrol., 4 241-273 T h i s r e s e a r c h was c o n d u c t e d to s t u d y t h e diffusion of i n o r g a n i c c h e m i c a l s m c o m p a c t e d clay soil for t h e d e s i g n of w a s t e c o n t a i n m e n t b a r r i e r s T h e effective diffusion coefficients (D*) of a m o n l c (C1 , Br , a n d I ) a n d c a t i o n i c (K ~, Cd 2+, a n d Zn 2÷) species in a s y n t h e t i c l e a c h a t e were m e a s u r e d Two clay soils were u s e d in t h e study. T h e soils were c o m p a c t e d a n d pre-soaked to m l m m l z e m a s s t r a n s p o r t d u e to s u c t i o n in the soil T h e r e s u l t s of t h e diffusion t e s t s were a n a l y z e d u s i n g two a n a l y t i c a l s o l u t i o n s to F l c k ' s s e c o n d law a n d a c o m m e r c i a l l y a v a i l a b l e s e m l - a n a l y h c a l s o l u t i o n , P O L L U T E 3.3 M a s s b a l a n c e c a l c u l a t i o n s were p e r f o r m e d to i n d i c a t e possible s i n k s / s o u r c e s in t h e diffusion s y s t e m E r r o r s in m a s s b a l a n c e were a t t r i b u t e d to p r o b l e m s w i t h t h e c h e m i c a l a n a l y s i s ( I ) , t h e inefficiency of t h e e x t r a c t i o n p r o c e d u r e (K ÷), p r e c i p i t a t i o n (Cd 2. a n d Zn 2÷ ), a n d c h e m i c a l comp l e x a t l o n (C1- a n d B r - ) T h e D* v a l u e s for C1 r e p o r t e d in this s t u d y are in e x c e l l e n t a g r e e m e n t with p r e v i o u s findings for o t h e r t y p e s of soil T h e D* v a l u e s for the m e t a l s (K + , Cd 2÷ , a n d Zn 2~ ) are t h o u g h t to be h i g h ( c o n s e r v a t i v e ) d u e to (1) Ca 2÷ s a t u r a t i o n of t h e e x c h a n g e c o m p l e x of t h e clays, (2) p r e c l p i t a t m n of Cd 2÷ a n d Zn 2÷ , a n d (3) n o n l i n e a r a d s o r p t m n b e h a v i o r I n general, h i g h D* v a l u e s a n d conserv a t i v e d e s i g n s of w a s t e c o n t a i n m e n t b a r r i e r s will r e s u l t if t h e p r o c e d u r e s described in t h i s s t u d y a r e u s e d to d e t e r m i n e D* a n d t h e a d s o r p t i o n b e h a v i o r of t h e s o l u t e s is s i m i l a r to t h a t described in this s t u d y

INTRODUCTION

Recent field studies indicate that molecular diffusion controls solute transport in fine-grained soils when the advective component of flow is low (Goodall and Quigley, 1977; Desaulniers et al., 1981, 1982, 1984, 1986; Crooks and Qulgley, 1984; Quigley et al., 1984; Johnson et al., 1989). These findings are slgmficant with respect to waste disposal because the design of earthen barriers for waste containment traditionally has been based on the assumption that advectlon dominates pollutant mass transport. In reality, both diffusion and advection may be required to be considered when designing earthen barriers.

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242 Most studms of diffusion of chemicals in soils have been performed by soil scmntmts and geologists. The soil science research has centered around studies of the movement of nutrmnts through unsaturated soil to plant roots (e.g., Olsen and Kemper, 1968; Nye, 1979) The geologic research has focused on the movement of m o r g a m c species in hydrogeologlc and sediment-water systems (Duursma, 1966, Manheim, 1970; Lerman and Tamguchi, 1972; Li and Gregory, 1974; Domemco, 1977, Lerman, 1978, 1979, Desaulnlers et al., 1981, 1982, 1984, 1986; Drever, 1982) No systematic study of diffusion of chemmals in compacted clay soil has been performed This paper describes the procedures and results of laboratory experiments designed to measure the diffusion coefficients of several inorganic chemical species in compacted clay soil. The specific objectives of this study were: (1) to measure the effective diffusion coefficients (D*) of inorganic chemicals diffusing m compacted clay soil; (2) to develop improved laboratory procedures to measure the diffusion coefficmnts; and (3) to draw conclusions that will aid in the selection of D* values for use in the design of earthen barriers for waste containment BACKGROUND Transport of a nonreactive solute

The differential equation describing one-dimensional, transmnt transport of a nonreactive solute in a saturated soil may be wmtten as: ~c ~--7 =

D ~2C ~x 2 -

~c vs ~

(1)

where c is the concentration of the solute in the hquid (ML 3), t is time (T), D is the coefficmnt of hydrodynamm dispersion in the direction of transport (L2T 1); vs is the average linear groundwater, or seepage, velocity (LT 1); and x is the space coordinate (L). The hydrodynamic dispersion coefficient accounts for the spreading of the solute front during transport and consists of mechanical dispersion and diffusion, or: D = D m + D*

(2)

where Dm is the mechanical dispersion coefficient (L2T 1) and D* is the effective diffusion coefficmnt (L2T 1). The effective diffusion coefficient is assumed to be directly proportional to the free-solution diffusion coefficient, Do, of a solute in an aqueous solution. In contaminant transport, the effective diffusion coefficmnt is defined as follows (e.g, Freeze and Cherry, 1979; Glllham et al., 1984, Rowe et al., 1985b; Shackelford, 1988) D* = DoT

(3)

where r is a tortuoslty factor. The tortuosity factor accounts for the tortuous

243

pathways experienced by solutes diffusing through soil (Porter et al., 1960; Olsen and Kemper, 1968; Bear, 1972). Bear (1972) recommends a tortuoslty factor of 0 67 for unconsolidated medm, and Perkins and Johnston (1963) found that ~ ranged between about 0.5 and 0.8 for granular material Transport of a reactive solute subject to sorptmn

For a reactive solute subject to reversible sorptlon reactmns, the one-dlmensmnal form of the solute transport equation for saturated soft must be modffied as follows' ~C ~t

D t~2c R ~x 2

Vst~C R Ox

(4)

where the retardation factor, R, is given by the following equation R = 1 + p~ Kp n

(5)

where Pb is the dry (bulk) density of the soil (ML 3); n is the total porosity of the soil (volume of voids per unit volume of soil), and Kp (L3M 1) is the "partition coefficient". The partition coefficient relates the mass of solute sorbed per mass of soil, S, to the concentration of the solute in solution, c, at equlhbrmm When the S versus c relationship is hnear, Kp is termed the distribution coefficient, Kd. Otherwise the partition coefficient is dependent upon the eqmhbrium concentration in soil [1.e., Kp = f(c)]. Since the seepage velocity and hydrodynamic dispersion coefficient are divided by the retardation factor, the rate of transport of a chemmal species undergoing adsorption reactions is inversely proportional to the value of the partition coefficient, i e., the greater the degree of adsorption, the slower the rate of transport. Advective versus diffusive transport

Equations (1) and (4) account for both advectlve and diffusive transport of solutes. At the velocities which commonly occur in coarse-grained soils (sands, gravels), advection dominates the mass transport and diffusion is negligible. However, as the advective velocity is lowered, diffusion becomes more significant. In the limit (1.e., v~ --* 0), eqns. (1) and (4) reduce to Fick's second law, or 0c _ D* ~2-~c ~t ~x2

(6)

and ~c

D* ~2c

~t

R~x 2

(7)

which describe pure diffusive transport of nonreactive and reactive solutes, respectively. Glllham et al. (1984) indicate that molecular diffusion is the

244 d o m i n a n t t r a n s p o r t m e c h a n i s m w h e n v~ is on the o r d e r of 1.6 × 10-1°ms 1, which is the seepage velocity in a clay liner if the h y d r a u l i c g r a d i e n t is one, the porosity is 0.5, and the h y d r a u l i c c o n d u c t i v i t y is 8.0 × 10-11ms 1. Since c u r r e n t U.S. r e g u l a t i o n s r e q u i r e the h y d r a u l i c c o n d u c t i w t y of clay liners to be ~< 1 0 × 10 9m s-l, diffusmn is expected to be a significant, if not dominant, m e c h a n i s m for the t r a n s p o r t of solutes t h r o u g h clay liners. The coefficients D* and R in eqn. (7) can be combined into a single p a r a m e t e r as follows: Ds = D * / R

(8)

w h e r e Ds is the "effective diffusion coefficient of the r e a c t i v e solute" (Glllham et a l , 1984, Qulgley et al., 1987, M y r a n d et al., in prep.). However, Rowe et al. (1985b) and Rowe (1987) c a u t i o n against the use of a single p a r a m e t e r m eqn (7) w h e n the b o u n d a r y conditions are flux-controlled. W h e n only Ds is used m an analysis with flux-controlled b o u n d a r y conditions, the r e s u l t i n g analyses are b o t h i n c o r r e c t and u n c o n s e r v a t l v e . As a result, the effective diffusion coefficients for the reactive, as well as the n o n r e a c t i v e solutes, in this study are defined with respect to eqn. (3), not eqn. (8).

MATERIALS AND METHODS Soils

K a o h n l t e , a c o m m e r c i a l l y processed clay, and L u f k m clay, a n a t u r a l l y o c c u r r i n g smectitic soil were used in this study. The p r o p e r t m s of the two soils are p r e s e n t e d in Table 1. The sum of the e x c h a n g e a b l e cations listed in Table 1 for e a c h of the soils is g r e a t e r t h a n each of the r e s p e c t i v e CEC's. The s h g h t differences ( < 18%) can be a t t r i b u t e d to dissolution of c a r b o n a t e minerals (e.g., CaCO3) m the soils d u r i n g the m e a s u r e m e n t . This results m elevated c a l c m m c o n c e n t r a t i o n s , especially for the L u f k m clay. As indicated in Table 1, the e x c h a n g e complex of the L u f k i n clay is d o m i n a t e d by Ca 2÷ whereas t h a t of k a o h n i t e is d o m i n a t e d by Na ÷ . Leachate

A s y n t h e t i c waste l e a c h a t e was used m this study. The a m o n s chloride ( C 1 ) , bromide ( B r - ) , and iodide ( I ) were chosen as c o n s e r v a t i v e tracers. Chloride and bromide c o m m o n l y are used as c o n s e r v a t i v e t r a c e r s and iodide is a useful t r a c e r due to its similarity to C1 and Br and its r e l a t i v e l y low b a c k g r o u n d c o n c e n t r a t i o n s ( < 0 . 0 1 m g L 1) m soil (Davis et al., 1980). B o w m a n (1984) c o n c l u d e d t h a t I m a y be useful as a t r a c e r u n d e r a n a e r o b i c l a b o r a t o r y c o n d i t i o n s Since I is a l a r g e r ion t h a n C1- and Br , it should not compete as effectively as a ligand as e i t h e r C1 or B r - in the c o m p l e x a t i o n of metal cations. As a result, I should exist p r i m a r i l y in its free form and, therefore, form a basis

245 TABLE 1

Physlcal and chemlcal properties of soils Property

Dominant clay mineral Specffic gravity of sohds Optimum water content (g g 1) Max dry density ( g c m -~) L l q m d h m l t ( g g 1) P l a s t i c i t y i n d e x (g g- 1) Particle size distribution silt a n d clay ( < 0075 mm) sand (0 075~475 mm) Soil pH at 1 1 soil s o l u t i o n Catmn exchange capacity (meq/100 g) Exchangeable cartons (meq/100 g)Na K+ C a 24

M g ~+ Cd2+ in 2 +

Background ion concentrations (mg L 1) ClBr I K~ Cd 2~ Zn 2+

Method of measurement .1

X-ray diffraction A S T M D854 A S T M D698 A S T M D698 A S T M D4318

Value of property

kaohnlte

L u f k l nclay

kaohnlte 2 64 32% 1 331 54%

smectlte 2 69 20% 1 635 56%

ASTM D4318

23%

42°,0

ASTM DII40 ASTM D422 *~ .2

100% 0% 3 65 5

82% 18% 6 93 25

.2

38 08 10 <01 <01 <01

64 27 191 <01 <01 <01

71 4_7 <01 32 <01 <01

179 56 <01 47 <01 <01

*' A S T M r e p r e s e n t s 1986 A n n u a l B o o k of A S T M Standards by the American Society for Testing and Materials .2 P a g e et a l , 1982

for the a s s e s s m e n t of the effects of c h e m m a l s p e c l a t i o n on the m e a s u r e d effective diffusion coefficients. C a d m i u m (Cd 2+) and zinc (Zn 2+) w e r e c h o s e n as i n o r g a n i c c a t i o n s for t w o reasons: (1) both are listed in the U.S. d r i n k i n g w a t e r standards as toxic elements; and (2) both are a m o n g t h e m o r e m o b i l e h e a v y m e t a l s in soils and clay s y s t e m s (Farrah and P i c k e r i n g , 1977, 1978; T n e g e l , 1980) For c o n v e m e n c e of c o m p a r i s o n , 0 . 0 1 N s o l u t i o n s of e a c h o f the ions were used The s y n t h e t i c l e a c h a t e w a s m a d e by d i s s o l v i n g 0.01 N c o n c e n t r a t i o n s of CdI2, ZnC12, and K B r salts in "standard" w a t e r (0.01 N CaSO4). Therefore, the total c o n c e n t r a t i o n of the s y n t h e t i c l e a c h a t e w a s 0.04 N. As a result of c o m p l e x f o r m a t i o n , the initial e q u i h b r i u m s p e c i a t i o n is expected to i n c l u d e < 13% of t h e Ca 2÷ as c o m p l e x e d , < 2% of t h e K ÷ as complexed, ~ 45% of the c a d m m m as free Cd 2÷ , ~ 80% if the zinc as free Zn ~÷ , and a b o u t 68% of the sulfate, 83%

246 TABLE 2 Compamson of selected charactemstlcs of the synthetic leachate with representative values for leachates taken from sanitary, mumclpal, and m d u s t r m l landfills and lagoons Parameter

Synthetic leachate (mgL -1)

Actual m o r g a m c leachates 1 ( m g L 1) representative range

probable extremes

Metals cadmium calcmm potassmm zmc

562 200 391 327

0-2 100-3000 200-2000 0-100

0-17 ~4800 3 3770 0-1000

Nonmetals. bromide chloride iodide sulfate

799 355 1269 480

30-2800 0-1280

0-3000

Other charactermtlcs: electmcal conductivity (pmhos cm 1 at 25°C) pH

Synthetic leachate 3090-3950 40~37

0-1826 Representative range 300~17000 4 9

1Compilation based on data presented by Griffin et al_ (1976), Freeze and Cherry (1979, p 435), and Darnel and L d j e s t r a n d (1984, pp 17 and 18)

of the C1 , 87% of the Br , and 100% of the I- as free ions. A c o m p a r i s o n of the c o n c e n t r a t i o n s in the s y n t h e t i c l e a c h a t e with those in a c t u a l l e a c h a t e s from municipal, s a n i t a r y , and i n d u s t r i a l landfills and lagoons is p r e s e n t e d in Table 2. The pH of the s y n t h e t i c l e a c h a t e was adjusted to t h a t of the soft solution before the s t a r t of the diffusion test m o r d e r to minimize the effects of pH on the a d s o r p t m n c h a r a c t e r i s t i c s of the softs (Frost and Griffin, 1977, U.S. Enw r o n m e n t a l P r o t e c t i o n Agency, 1987). As a result, the pH of the s y n t h e t i c l e a c h a t e is r e p o r t e d as a r a n g e of values m Table 2. Batch equthbrium tests Batch equilibrium tests were performed to determine the adsorption characteristics of the soils with respect to the specified ions Competition between the ions for the exchange sites on the softs was accounted for indirectly by using the synthetic leachate instead of solutions containing individual ionic specms. A 1:4 soil. soluUon ratio (by weight), which is the highest recommended ratio (U.S. Environmental Protection Agency, 1987), was used in the batch equihbrmm tests to approximate the conditions in the diffusion cell. The concen-

247 t r a t i o n s of the specffied ions in e a c h flask were v a r m d by serial d i l u t i o n of the 0 . 0 4 N s y n t h e t i c l e a c h a t e w i t h a n e l e c t r o l y t e s o l u t i o n (0.01N CaSO4) s o m e t i m e s r e f e r r e d to as " s t a n d a r d w a t e r " . As a result, the r e d u c e d concent r a t i o n s of the ions in the flasks w e r e w i t h r e s p e c t to a c o n s t a n t 0 01 N CaSO4 solution. A flask c o n t a i n i n g 200 ml of 0.04 N l e a c h a t e soil was used as a control. All flasks were stoppered, placed in an end-over-end, r o t a r y mixer, a n d m i x e d for 48 h at a t e m p e r a t u r e of 23 ° + 2°C. A t the end of the m i x i n g period, samples of the soil-solution s l u r r i e s from the flasks were p o u r e d into 50-ml c e n t m f u g e tubes, sealed, a n d c e n t r i f u g e d for 30 m m . at 3000-4000 r p m (1980-3520 g). T h e s u p e r n a t a n t f r o m e a c h t u b e was t h e n p i p e t t e d to s a m p l e bottles and the equlhb r m m c o n c e n t r a t i o n s of the ions in the s o l u t i o n were d e t e r m i n e d by a n i o n c h r o m a t o g r a p h y or flame a t o m i c a b s o r p t i o n s p e c t r o s c o p y . T h e r e s u l t s of t h e c h e m i c a l a n a l y s e s were p l o t t e d m the form of a d s o r p t i o n i s o t h e r m s , or s o r b e d c o n c e n t r a t i o n , S, v e r s u s dissolved e q u i h b r i u m c o n c e n t r a tion, c of solute for e a c h 1on. T h e sorbed c o n c e n t r a t i o n s were d e t e r m i n e d by m a s s b a l a n c e u s i n g the following equation" {Co -

S=\M

(9)

"

w h e r e Co is the initial c o n c e n t r a t i o n of the specffied ion in the flask; VSOLlS the v o l u m e of the s o l u t i o n (200 ml); a n d M s is the soil m a s s (50 g).

Diffusion tests Sample preparation T h e t e s t s p e c i m e n s of soil were p r e p a r e d by m i x i n g alr-drmd soil w i t h s t a n d a r d w a t e r (0.01N C a S O , ) u n t i l a w a t e r c o n t e n t a b o u t 1-2% wet of

Burel

3oaklng _lne

Fig 1 D]ffuslon apparatus

248

optimum water c ont e nt was obtained. After hydration, the soil was compacted into 102-ram-diameter molds in accordance with American Society for Testing and Materials (ASTM) method D698, also known as the "standard Proct or method". The standard P r o c t o r method consists of compacting soil in three layers at 25 blows per layer using a 2.5-kg hammer falling 30.48cm per blow. Based on the standard 944-cm3 compaction mold, this procedure results m 592.7 k J m 3 of compactmn energy The standard Pr oct or compaction procedure was followed for both kaolinite and Lufkin clay except t hat some of the soil samples were compacted into molds with volumes of 472cm 3, 1 e., one-half that of the standard mold. The same compactive effort was used for the soils compacted into the smaller molds by reducing the total number of blows. The smaller molds were used pr,marily to reduce the time required for soaking the samples prmr to dlffusmn testing. After compaction, the test specimens were assembled Into the fixed-wall diffusmn cells shown schematmally in Figure 1. The sample port was used to fill and drain the dlffusmn apparatus as well as to draw leachate samples from the reservoir during the diffusion test An mr pressure/vacuum system consisting of a panel board and an acrylic accumulator connected by flemble Teflon tube was used to fill and w~thdraw soaking solutmn and leachate from the reservoir The buret was used to provide volume change readings during both soaking and diffusion periods. The entire diffusion apparatus was supported by a stand as depicted m Figure 1, further details of the diffusion system are prowded by Shackelford (1988)

Soaking stage The soil samples were saturated with standard water (0.01 N CaSOt) prior to the start of the dlffumon tests to minimize mass transport due to suction m the soil Three soaking procedures were used The first procedure consisted of exposing the soil sample to the soaking solution from both the top, via the reservoir, and the bottom, via the soaking line, of the sample and perlodmally recording volume readings from the buret (Fig. 1). A separate buret filled with soaking solution was set-up In order to account for evaporation during the soaking pemod. After equilibrium was established, the soaking solution was withdrawn from the system, the cell was disassembled, and the soil, which had swelled, was trimmed flush with the top of the mold. After trimming, the cell was re-assembled and the soaking solution re-introduced into the system so that equllibrmm could be estabhshed again A second soaking procedure was used with the Lufkln clay samples to reduce the soaking period. With this procedure, the samples were immersed completely m soaking solution in separate containers. After an initial soaking period, the samples were removed from the containers, trimmed, and set-up in the diffusion cells. Soaking solution was re-introduced into the reservoir, and volume readings were recorded until equilibrium was re-estabhshed. This procedure, along with the use of the smaller compaction molds, reduced the overall soaking pemod from 160 to 70 days.

249

The third soaking procedure was the same as the second procedure except only the bottom of the sample was exposed to the soaking solution. This modffication was made because of concern t hat the initial soaking of the samples from the top can cause more disturbance to the soil structure than if they were soaked only from the bottom (Hillel, 1980, pp. 102-103; Shackelford, 1988). The total soaking permd for these samples was reduced to 17 days.

Diffuszon stage The diffusion stage of the tests was initiated by draining the soaking solution, and measuring and recording the pH, electrical conductivity (EC), and temperature of the solution. Next, the pH of the leachate was adjusted to approximately th at of the soaking solution by tltrating the leachate with 0.1 MH2SO4 The volume of sulfuric acid added to the leachate for adjustment of the pH was usually < 0.5ml and never > 2.0ml. Finally, samples of the synthetic leachate were taken for chemmal analysis of the specified ions as well as EC and temperature determinatmns, and leachate was introduced into the diffusion apparatus. The time reqmred to fill the apparatus with the leachate varied, but was never greater than four minutes. An elapsed time of four minutes is negligible with respect to the diffusion test periods, which ranged between one and three months. Two layers of 10 16-cm-wide parafilm were stretched over the buret to minimize evaporation losses. A separate buret filled with leachate and covered with two layers of parafilm also was assembled. The volume changes m the separate buret were neghglble ( < 0 I cm 3) t h r o u g h o u t the entire period of the diffusion test, indicating that the parafilm acted as an effective barrier to evaporation After the diffusion test was set up, the leachate concentration was monitored periodically by withdrawing samples from the reservom The leachate samples were analyzed for the specified ions to determine how the reservoir c o n c e n t r a t m n varied with time. The diffusion tests were performed at ambmnt laboratory temperatures which ranged between 21 and 25°C. This variation m temperature should not affect significantly the measured effective diffusion coefficients Upon completion of the diffusion stage of the test, whmh lasted from 30 to 109 days, the last reservoir samples were taken, and the pH, electrical conductivity, and temp er at ur e of the leachate were recorded and the diffusion cell was disassembled. The final weight of the compaction mold plus the sod was measured. The soil was extruded and sectioned to provide (1) a dlstmbutlon of the water contents existing m the sample, and (2) a concentration profile of the specified runs for use m determinatmns of mass balances and effective dlffusmn ecoefficients. The soil was sectmned at regular intervals into slices approximately 0.254cm m thickness. The water content of each shce of soil was determined by oven drying at 110 + 5°C for a period of 18h_ In order to determine the ion c onc e nt r at m ns m the soil, the ions were extracted from the oven-drmd soil. Based on the results of a study by Farrah and Pickerlng (1978), a solutmn containing H4EDTA was chosen to extract

250 c a d m i u m a n d zinc from the soil. Since t r a n s i t i o n m e t a l c a t i o n s (including Zn ~ and Cd 2+) c o m p e t e m o r e effectively t h a n m o n o v a l e n t c a t i o n s at e q u a l conc e n t r a t i o n s of E D T A 4- (Bohn et al., 1979, p 36), it was not k n o w n if all of the p o t a s s m m ions sorbed to the clay soil could be e x t r a c t e d w i t h the H4EDTA s o l u t i o n Since the p m m a r y e m p h a s i s of the s t u d y was to m e a s u r e the effective diffusion coefficmnts of the h e a v y m e t a l s cations, the e x t r a c t i o n of the p o t a s s m m ions was of s e c o n d a r y i m p o r t a n c e A one m l l h m o l a r ( l m M ) c o n c e n t r a t i o n of H4EDTA was used as the c a t i o n e x t r a c t i n g s o l u t i o n for the first two k a o l i m t e s a m p l e s (S-1 and S-2). The p H of the s o l u t i o n was a r o u n d 2 8 P r e h m m a r y m a s s b a l a n c e c a l c u l a t i o n s f r o m the r e s u l t s of t h e s e tests m d m a t e d p o o r efficiencies with r e s p e c t to e x t r a c t i o n of the c a t i o n s (Cd 2~, Zn 2 +, and K - ). Thus, the c o n c e n t r a t i o n of the H 4 E D T A s o l u t i o n was i n c r e a s e d for the r e m a i n i n g tests to 5 m M and the p H was adjusted to 7.0 with 1.0 M N a O H to i m p r o v e the c a t i o n e x t r a c t i o n efficmncms. I m t l a l l y , it was t h o u g h t t h a t the H4EDTA s o l u t i o n e x t r a c t s could be used to d e t e r m i n e the a m o n c o n c e n t r a t m n s as well as the c a t m n c o n c e n t r a t m n s . H o w e v e r , the H 4E D T A s o l u t i o n was found to i n t e r f e r e w i t h the ion c h r o m a t o g r a p h i c d e t e r m i n a t i o n of the chloride a n d b r o m i d e c o n c e n t r a t i o n s for the first two k a o h m t e tests T h e r e f o r e , a s e p a r a t e a n a l y s i s for a m o n c o n c e n t r a t m n s was m a d e for all of the r e m a i n i n g d i f f u s m n tests The s e p a r a t e a n a l y s i s for a n i o n s r e q m r e d t h a t two c e n t r i f u g e tubes be used per slice - - one for a m o n s and one for c a t m n s The a d s o r p t m n test results i n d i c a t e d t h a t the specified a m o n s (C1 , Br , and I ) were not a d s o r b e d to the soils; therefore, d e - m m z e d , distilled w a t e r (DDW) was used as the e x t r a c t i n g s o l u t m n for the a m o n analysis. This n o r m a l l y is not the case since d l l u t m n with D D W c h a n g e s the e q u f l i b r m m c h e m i s t r y b e t w e e n the sorbed and free c o n c e n t r a t i o n s of the runs e x i s t i n g in the soft at the t i m e of b r e a k d o w n . Soft f r o m e a c h s h c e f r o m the s e c t i o n i n g s t a g e was placed into a 50-ml c e n t m f u g e t u b e a n d the a p p r o p r i a t e e x t r a c t i n g s o l u t m n w a s added 0.e-, D D W was added to one c e n t r i f u g e t u b e for a m o n a n a l y s i s a n d H 4 E D T A was added to the o t h e r c e n t r i f u g e t u b e for c a t m n analysis). The c e n t r i f u g e tubes filled with the m i x t u r e of soil a n d e x t r a c t i n g s o l u t m n were sealed, p l a c e d m a r o t a r y , end-over-end m i x e r a n d mixed at 30 r p m for at l e a s t 48 h. T h e tubes were t h e n r e m o v e d f r o m the m i x e r and c e n t r i f u g e d for 3 0 m m . at 3000-4000rpm (19803520 g) T h e s u p e r n a t a n t f r o m the c e n t m f u g e tubes was p l p e t t e d to a p p r o p r i a t e c o n t a i n e r s for c h e m m a l a n a l y s i s The l a b o r a t o r y - m e a s u r e d m n c o n c e n t r a t m n s of the s a m p l e s from the c e n t r i f u g e t u b e s a r e less t h a n those e x i s t i n g m the soft due to the d i l u t i o n of the c o n c e n t r a t i o n s by the e x t r a c t i n g s o l u t m n . In o r d e r to e s t i m a t e the t o t a l c o n c e n t r a t m n of e a c h c h e m i c a l species e x i s t i n g in the soft, c', at the time the diffusion cell was disassembled, t h e m e a s u r e d c o n c e n t r a t m n , c~, was m u l t i p l i e d by the i n v e r s e of the d i l u t i o n f a c t o r as follows.

/ WsoL

c, : cm -W- w )

251 w h e r e WsoL is the w e i g h t of the e x t r a c t i n g s o l u t i o n m the c e n t r i f u g e tube, and Ww is the w e i g h t of the w a t e r in the soil at the time of soil s e c t i o n i n g . E q u a t i o n (10) assumes t h a t the densities of the e x t r a c t i n g solution and the w a t e r are equal. The c o n c e n t r a t i o n , c', r e p r e s e n t s the t o t a l c o n c e n t r a t m n of the chemical species m the soil a s s u m i n g the e x t r a c t i n g s o l u t i o n is 100% efficient The soluble or mobile c o n c e n t r a t i o n of the chemical species, c, m the pore space of the soil can be estimated by d i w d m g the total c o n c e n t r a t m n by the r e t a r d a t m n factor, R, or c

=

(11)

c'/R

In the case of n o n a d s o r b i n g tracers, the r e t a r d a t m n factor is 1.0. DATA ANALYSIS Two different a n a l y s e s were used to determine the D* values. The first analysis utilized the r e s e r v o i r c o n c e n t r a t i o n s in c o n j u n c t i o n with two closedform s o l u t i o n s to eqn. (7). The second analysis utilized the c o n c e n t r a t i o n s d e t e r m i n e d from the soil s e c t i o n i n g and e x t r a c t i o n p r o c e d u r e with a contamin a n t t r a n s p o r t model, POLLUTE 3.3., developed by Rowe et al. (1985a) Closed-form

solutions

After the I n t r o d u c t i o n of the l e a c h a t e into the reservoir at time zero (t = 0), mass t r a n s p o r t of the chemical c o n s t i t u e n t s m the l e a c h a t e o c c u r r e d via m o l e c u l a r diffusion from the reservoir into the soil The diffusive mass t r a n s p o r t r e s u l t e d in a decrease m the c o n s t i t u e n t c o n c e n t r a t i o n s m the r e s e r v o i r as a f u n c t i o n of time. Since the bottom of the cell (x = 0) was closed d u r i n g the diffusion stage of the test, none of the mass of the diffusing cons t l t u e n t s e n t e r i n g the soil at the soil-reservoir interface (x = a) could exit the soil at the b o t t o m of the cell. Based on these conmderations, the initial and b o u n d a r y c o n d i t i o n s for the diffusion cell are: c -

0

at

0 <~x

c -

Co

at

?c ?x

-

0

at

+

n

~x

t

=

0

a <. x <~ a + l,

t

=

0

x

t

>

=

~

a,

O,

0

and Ry

=

lco

at

x = a,

t

> 0

w h e r e a is the l e n g t h of the diffusion cell (L), l is the effective length of the r e s e r v o i r (L), and y is defined as the a m o u n t of the free solute per unit of soil c o n t a i n e d b e t w e e n the planes at x = 0 (Le., base of the soil) and at a n y distance w i t h i n the soil, or"

252

y(x, t) = n | c(x, t)dx o

E x c e p t for the constant, lco, the second b o u n d a r y c o n d i t i o n is of the SturmLlouville type (Wilson, 1948). The effective l e n g t h of the r e s e r v o i r was d e t e r m i n e d by dividing the total v o l u m e of l e a c h a t e i n t r o d u c e d into the a p p a r a t u s (reservoir, top cap, PVC tube, and buret) by the cross-sectional area, A, which was constant. One solution to Flck's second law for s i m u l t a n e o u s diffusion and a d s o r p t i o n m sod with the above initial and b o u n d a r y conditions (Wilson, 1948, Crank, 1975, p. 57), is" M~ . M~

1 .

.

~, 2a(1 + ~) (-D*q~t~ . 2 : exp m=ll + ~ + ~ q ~ ~ )

(12)

w h e r e Mt ~s the total mass of a given solute in the soil at any time t after the s t a r t of diffusion and M~ is the c o r r e s p o n d i n g mass at infinite time. The qm's m eqn. (12) are the non-zero positive roots given by: tan qm aqm (13) w h e r e :t is a coeiticmnt given by the following relation: l u

-

(14)

nRa

The e q m l i b r i u m mass of the solute in the soil at infinite t~me is given by. M~

(1)

=

~

Mo

(15)

where/14o is the initial mass of the solute m the reservoir, w h m h is equal to the product, Alco. The complete d e r i v a t i o n for eqn (12) for a s a t u r a t e d sod as well as the roots to eqn. (13) are given by S h a c k e l f o r d (1988). A second a n a l y t i c a l solution c o n s i d e r e d in this study is g~ven by Carslaw and J a e g e r (1959, p 306) and C r a n k (1975, p. 58), or c~ Co

1

Me M~(1 + ~)

exp (z 2) erfc (z)

(16)

where n

z = 7 Rx//R-D-~

(17)

erfc( ) is the c o m p l e m e n t a r y e r r o r function, and ct is the c o n c e n t r a t i o n of solute m the r e s e r v o i r at an elapsed time t. Tables of values of erfc() are provided by Carslaw and J a e g e r (1959), C r a n k (1975), Freeze and C h e r r y (1979), and others. B o t h eqns. (12) and (16) were used to d e t e r m i n e the D* v a l u e s r e p o r t e d in this study. The assumptions i n h e r e n t in the use of eqns. (12) and (16) are' (1) D* is c o n s t a n t , (2) the r a t e of a d s o r p t i o n is v e r y fast c o m p a r e d with the r a t e of

253 diffusion; (3) s o r p t i o n is r e v e r s i b l e ; a n d (4) t h e soil p r o p e r t i e s (n a n d Pb) a r e constant. POLLUTE33 P O L L U T E 3 3 (Rowe et al., 1985a) w a s u s e d to a n a l y z e t h e m e a s u r e d c o n c e n t r a t i o n profiles. T h e p u r p o s e for u s i n g POLLUTE 3 3 to c a l c u l a t e e f f e c t i v e d i f f u s i o n coefficients w a s to p r o v i d e (1) a n i n d e p e n d e n t c h e c k on t h e c a l c u l a t e d D* v a l u e s from t h e c l o s e d - f o r m s o l u t i o n s a n d (2) a n a s s e s s m e n t of t h e r e l a t i v e m e r i t s of t h e use of r e s e r v o i r c o n c e n t r a t i o n d a t a v e r s u s c o n c e n t r a t i o n d a t a from soil e x t r a c t i o n s . POLLUTE 3 3 r e p r e s e n t s a " s e m i - a n a l y t i c a l " s o l u t i o n to eqn. (10) for s o l u t e m i g r a t i o n in a n o n - h o m o g e n e o u s soil d e p o m t T h e t h e o r y for t h e d e r i v a t i o n of t h e s e m i - a n a l y t i c a l s o l u t i o n i m p l e m e n t e d by t h e c o m p u t e r p r o g r a m POLLUTE 3 3 IS d e s c r i b e d by R o w e a n d B o o k e r (1984, 1985). T h e use of t h e t h e o r y to d e t e r m i n e D* v a l u e s in t h e l a b o r a t o r y is d e s c r i b e d by R o w e et al (1985b).

RESULTS AND DISCUSSION

F~nal physLcal properties of soils T h e final p r o p e r t i e s of t h e soil s a m p l e s (i.e. a f t e r s o a k i n g a n d t r i m m i n g t h e soil) u s e d in t h e d a t a a n a l y s i s for t h e e f f e c t i v e d i f f u s i o n coefficients a r e p r e s e n t e d in T a b l e 3. T h e w a t e r c o n t e n t s for t h e c l a y s a m p l e s p r e s e n t e d in T a b l e 3 r e p r e s e n t w e i g h t e d a v e r a g e s of t h e w a t e r c o n t e n t s d e t e r m i n e d from e a c h soil slice. T h e w a t e r c o n t e n t s of t h e soil s a m p l e s v a r i e d c o n s i d e r a b l y . The n o n u n i f o r m i t y in t h e w a t e r c o n t e n t d i s t r i b u t i o n of t h e soil s a m p l e s r e f l e c t s n o n u n i f o r m i t y in t h e o t h e r soil p r o p e r t i e s (e.g., n a n d Pb)- S i n c e t h e d i f f u s i o n TABLE 3 Final soil properties used for effective diffusion coefficient analyses Soil

Soil sample

Water content w(%)1

Total porosity n

Degree of saturation, St(%)2

Volumetric water content 03

Bulk (dry) density Pb(g cm ~)

Kaohnlte

S-1 S-2 K-4

43 1 41 7 39 9

0 54 0.54 0 52

96 2 95.15 97 9

0 52 0 51 0 51

1 210 1 225 1 272

Lufkln clay

L-1 L-2

28 8 27 8

0 47 0 45

86 2 90 7

0 41 0 41

1 417 1 474

1Weighted averages from soil slices 2Percent of void space filled with water

~0

=

nS~/lO0

254

of the chemical constituents is assumed to occur only in the liquid phase, the volumetric soil-water contents (0) were used m place of the total porosities (n) in the analysis for effective diffusion coefficmnts. As a result of the relatively high degrees of saturation, the volumetric soil-water contents presented in Table 3 are only slightly less than the total porosities.

Soaktng solutton and characteristics of synthetic leachate The electrical conductivity and pH of the soaking solution and the synthetic leachate used for each soil sample are presented in Table 4. The electrical conductivity (EC) of the soaking solution and leachate can be related directly to the ionic strength of the solution (e.g., Griffin and Jurinak, 1973) The changes in EC are evidence that the ionic strength of the synthetm leachate is significantly greater than that of the soaking solution. The higher ionic strength directly indicates a higher ionic concentration In the leachate, due to the presence of the metal and tracer ions, relative to that of the background (0.01 N CaSO4) solution. The somewhat reduced EC values of the final leachate solution relative to the initial leachate solution reflect the diffusive mass transport of the ions, initially present in the leachate, from the reservoir into the soil. The presence of soluble salts in the soil is reflected by the EC measurement of the soaking solutions. The EC values for the soaking solutions of all the soil samples are greater than the EC of the 0.01N CaSO4 solution, which was 960~mhos cm 1 at 25°C. These higher values reflect diffusion of soluble salts from the soil into the reservoir during the soaking stage of the test. The relatively higher EC values for the soaking solutions of kaolinite samples S-1 and S-2 reflect the longer soaking periods associated with these tests. The adjustment of the pH of the initial leachate, as previously described, IS reflected by the similarity of the pH values reported In Table 4. In general, the pH of the final leachate solution is only slightly less than that of the initial leachate solutmn. This slightly lower pH may reflect "counter diffusion" of TABLE 4 Characteristics of final soaking solution and synthetic leachate Soil sample

S-1 S-2 K-4 L-1 L-2

Final s o a k i n g solution

Initial leachate

EC at 25°C (#mhos c m - ' )

pH

EC at 25°C ( g m h o s c m 1)

pH

EC at 25°C (gmhoscm-')

pH

1520 1480 1040 1030 1030

4 03 4 01 4_15 6 78 6 87

3950 3950 3120 3090 3090

4 00 4.01 4.07 6.67 6 67

2600 2600 3820 2810 2600

3 90 3 57 3 67 5 65 5 85

EC = electmcal conductivity

Final leachate

255 p r o t o n s (H ÷) from the soil into the r e s e r v o i r after d i s p l a c e m e n t from the soil by i n v a d i n g cations (Cd 2÷ , Zn 2÷ , and K ÷ ). The r e l a t i v e l y acidic n a t u r e of the k a o h n i t e is i l l u s t r a t e d by the pH values b e t w e e n a b o u t 4 0 and 4.1 for the s o a k i n g s o l u t m n s of samples S-l, S-2, and K-4 The pH v a l u e s of the s o a k i n g s o l u t m n s for the L u f k m clay are a r o u n d 6.8. In summary, the d a t a p r e s e n t e d m T a b l e 4 i n d i c a t e t h a t the effects on the a d s o r p t i o n c a p a c i t y of softs associated with changes in pH should h a v e been minimal, and q u a h t a t i v e i n f o r m a t i o n r e g a r d i n g l a b o r a t o r y test c o n d l t m n s can be a s c e r t a i n e d from e l e c t r i c a l c o n d u c t i v i t y and pH m e a s u r e m e n t s of soft solutions and leachates. Therefore, pH and EC m e a s u r e m e n t s should be i n c l u d e d m the q u a l i t y a s s u r a n c e p r o c e d u r e s for the l a b o r a t o r y tests.

Batch-equlltbrtum test results T h e results of the b a t c h - e q u i l i b r i u m tests for the k a o l i m t e and the L u f k i n clay are p r e s e n t e d as a d s o r p t i o n isotherms for cations m F i g u r e 2. Imtially, it was e x p e c t e d t h a t a m o n a d s o r p t i o n (especially C1 and SO~- ), as well as c a t i o n adsorption, would be o p e r a t i v e m the clays, especially for the k a o l i n i t e w h m h has a p H - d e p e n d e n t a d s o r p t i o n c a p a c i t y (Bohn et al., 1979, p. 174) However, it was found from the results of the b a t c h - e q u i l i b r i u m tests t h a t a n i o n a d s o r p t i o n of C1 , Br , and I did n o t o c c u r m e i t h e r of the soils. B o h n et al. (1979, p. 174) state t h a t at all pH values, the d i v a l e n t SO~ ion is adsorbed to a g r e a t e r e x t e n t t h a n the m o n o v a l e n t C1- ion, as is expected on the basis of e l e c t r o s t a t i c c o n s i d e r a t i o n s Also, since s t a n d a r d w a t e r (0 0 1 N CaSO4) was used as the d i l u t i o n w a t e r for the b a t c h - e q u i h b r m m samples, the SO~ c o n c e n t r a t i o n r e m a i n e d r e l a t i v e l y high as the o t h e r a n i o n c o n c e n t r a t i o n s ( C l - , Br , I ) were diluted. On the basis of c h a r g e and c o n c e n t r a t i o n effects, it would be expected t h a t SO42- would compete m u c h more f a v o r a b l y for the positive a d s o r p t i o n rotes t h a n would C1 , Br , or I . Since the clays were p r e - e q u i h b r a t e d with 0 . 0 1 N CaSO4 and the SO~ c o n c e n t r a t i o n r e m a i n e d c o n s t a n t t h r o u g h o u t all tests, the soil should h a v e been m e q u i h b r l u m with 0.01 N SO~-, and no f u r t h e r SO42a d s o r p t i o n was expected. Finally, C1 is not adsorbed at all in the slightly acid to n e u t r a l pH r a n g e for m o n t m o r i l l o m t l c soils (e.g, L u f k i n clay), where pHd e p e n d e n t c h a r g e is of m i n o r i m p o r t a n c e (Bohn et al., 1979, p. 174). Since Br and I a n i o n s are l a r g e r t h a n the C1- a m o n and, therefore, h a v e smaller c h a r g e d e n s m e s , Br and I- should not be expected to be adsorbed to montmorxllonitm soils either. On the basis of these considerations, it was expected t h a t m e a s u r a b l e a d s o r p t i o n of the C l - , Br , and I- a m o n s would not o c c u r u n d e r the c o n d i t i o n s imposed in this study. Based on s e c a n t lines d r a w n to the curves in F i g u r e 2, the r e l a t i v e m o b l h t m s of e a c h of the cations with e a c h of the soils was found to be: Cd 2.

> Zn 2+ > K ÷

Cd 2÷ >

K ÷ > Zn 2÷

(for k a o l l m t e ) (for L u f k i n c l a y )

256 300 K

0~

o I-

z Lg (3 Z O (J a Lg a2 nO ¢D

200

A E

Cd

B _o P

100

1:4

Sod:SoluUon

Ratio

i

i

i

i

i

100

200

300

400

500

600

EQUILIBRIUM CONC., c (rng/L)

(a)

1200 1000 1

Zn

K

¢/;

z 2

800

6OO z O o (J ,,,-, .o uJ E

4OO

m

0(D

200

0

:

0

50

~

100

150

200

250

EQUILIBRIUMC O N C , C (rag/L)

300

350

(b)

Fig 2 Adsorption isotherms for (a) kaohmte and (b) Lufkln clay Because the adsorption isotherms are nonlinear, the associated retardation f a c t o r is a f u n c t i o n o f t h e e q u i l i b r i u m c o n c e n t r a t i o n . T h i s r e p r e s e n t s a deviation from the constant retardation factor assumed in the dervlation of the a n a l y t i c a l s o l u t i o n s a s w e l l a s i n POLLUTE 3 3. A s a r e s u l t , s e c a n t l i n e s w e r e u s e d to estimate the retardation factors, R However, there are an infinite number o f s e c a n t l i n e s w h i c h c o u l d b e u s e d T h e c o n t r o l l i n g p a r t i t i o n c o e f f i c i e n t is s e t b y t h e s t e p f r o m t h e c = 0 to c = co c o n c e n t r a t i o n . T h i s m e a n s t h a t gp

-

S[co Co

SIc=o --

0

AS Ac

gleN co

Co

g ~ c N-1

(18)

257 TABLE 5

Freundhch isotherm parameters for kaohnlte and Lufkm clay Ion

Soft

Kaohmte

potassmm cadmmm zinc

L u f k m clay

potassium cadmium zinc

Freundhch isotherm parameters

Correlatmn coefficmnt

g~

Y

r

0 8929 0 5270 0 6925

0 98 0 98 0_99

0 7999 0 3987 0 4747

0 98 1 00 1 00

2_237 8 564 5 078 20_59 121.5 123 7

where Co is the initial concentration of the solute under consideration and Kf and N are the Freundhch isotherm parameters given by: S

=

(19)

K~c N

The same conclusion has been reached by Rao (1974, Appendix 6) who presented the above deravation in terms of a '~weighted-mean distribution coefficient". Based on eqns. (5) and (18), the controlling retardation factor, R, is defined as: R =

fib .~- N-1

1 + -0-~fe°

(20)

where the total porosity, n, in eqn (5) has been replaced by the volumetme soil-water content, 0. Equations (18) and (20) provide a eonvement means for obtaining an overall, albeit conservative, estimate of a constant retardation factor for use with analytical solutmns describing solute transport wxth adsorption. The parameters which resulted from fitting Freundlich xsotherms to the adsorption data are provided m Table 5. The correlation coeffiemnts (r) from the hnear (log-log) regression analysis of the data also are provided m Table TABLE 6

Retardation factors for effective dlffumon coefficient determinations Soal

Retardation factor, R

sample

S-1 S-2 K-4 L-1 L-2

potassium

cadmium

zinc

3 75 3 83 3 95 22_7 23 5

2 00 2 03 2 04 10_35 10 8

2 98 2 97 3 15 21 9 22 8

258

5. T h e r e t a r d a t i o n f a c t o r s used to c a l c u l a t e the effective diffusion coefficients for e a c h of the c a t i o n s of i n t e r e s t in e a c h of the tests are p r o v i d e d in T a b l e 6. T h e v a l u e s r e p o r t e d in T a b l e 6 w e r e d e t e r m i n e d w i t h eqn. (20) u s i n g the d a t a p r o v i d e d in T a b l e s 3 a n d 5 w i t h the initial c o n c e n t r a t m n of the c a t i o n in the test.

Mass balance considerations M a s s b a l a n c e s for e a c h of the ions a n d e a c h of the tests w i t h clay w e r e c a l c u l a t e d to assess the possibility of e x p e r i m e n t a l e r r o r as well as u n k n o w n c o n c e n t r a t i o n s o u r c e s a n d / o r sinks T h e m a s s b a l a n c e s were c a l c u l a t e d by c o m p a r i n g t h e m a s s of an ion w h i c h diffused from the r e s e r v o i r o v e r the diffusion period (MR) to the m a s s of the ion in the soil at the end of the diffusion t e s t period (Ms). T h e m a s s of the ion in the soil was c a l c u l a t e d from the d i s t r i b u t i o n of t o t a l (as opposed to free) c o n c e n t r a t i o n s of the ion in the soil as d e t e r m i n e d by the soil s e c t i o n i n g a n d e x t r a c t i o n p r o c e d u r e . A l i n e a r distrib u t i o n was a s s u m e d to exist b e t w e e n the c o n c e n t r a t i o n s at e a c h section. The r e s u l t s of the m a s s b a l a n c e c a l c u l a t i o n s are p r e s e n t e d as the p e r c e n t difference b e t w e e n the diffused m a s s (MR) and the m a s s in the soil M~ r e l a t i v e to the diffused mass, as s h o w n in T a b l e 7. T h e p e r c e n t differences in m a s s are s o m e w h a t h i g h a n d the possible c a u s e s of t h e d i s c r e p a n c i e s s h o u l d be noted. T w o c o n t r o l tests (i.e., w i t h o u t soil) did n o t r e v e a l a n y s i g n i f i c a n t s o u r c e s a n d / o r s i n k s a s s o c i a t e d w i t h the diffusion a p p a r a t u s . Aside f r o m e x p e r i m e n t a l e r r o r in the a n a l y s i s of the c o n c e n t r a t i o n s a n d n a t u r a l s c a t t e r in the data, t h e r e are s e v e r a l o t h e r logical e x p l a n a t i o n s . T h e differences In m a s s for the c a t i o n s (K + , Cd 2÷ , Zn 2. ) c a n be a t t r i b u t e d to two causes. First, it IS h k e l y t h a t the E D T A e x t r a c t i n g s o l u t i o n r e s u l t e d in p o o r r e m o v a l efficiencies of the p o t a s s i u m . As m e n t i o n e d p r e v i o u s l y , t h a t E D T A w o r k s well as an e x t r a c t a n t for d i v a l e n t cations, s u c h as c a d m i u m a n d zinc, b u t n o t as well for m o n o v a l e n t c a t i o n s E v e n t h o u g h the c o n c e n t r a t i o n of the TABLE

7

Mass balance errors Soil sample

Percent differences in mass 1 C1

S-1 S-2 K-4 L-1 L-2

15 - 39 23 45 47

3 2 8 8 9

Br-

I

47 2 ND 16 0 78 4 78_1

44 5 - 255 72 84

1Percent difference - (M a Ms)lMa M s ~ mass m soil at end of test ND = no data or msufficmnt data

4 2 2 9

× 100%, where

K+

C d 2+

Z n "~+

44 43 66 86 85

39 35 26 35 48

46 52 21 43 52

2 4 4 4 9

4 5 3 3 4

M a = mass diffused from reservoir,

0 0 7 6 2

and

259 EDTA solution was five times greater for sample K-4 t han it was for samples S-1 and S-2 (5mM vs lmM), the percent difference in potassium mass for sample K-4 is greater, indicating t h a t the increased strength of the extracting solution had no effect on potassium extraction. The higher values for the Lufkin clay samples L-1 and L-2 also may reflect potassium fixation, possibly between layers of montmorillonite clay minerals (Grim, 1953, p. 153) The use of the stronger, 5 mM EDTA extracting solution for kaolinite sample K-4 is reflected in lower mass balance errors of cadmium and zinc relative to those of the initial kaolinite samples (S-1 and S-2). However, the mass balances for Cd 2÷ and Zn 2+ for the initial kaolinite samples are not lower than those for the Lufkin clay samples (L-1 and L-2) The higher values with the Lufkln clay may reflect the greater adsorptive capacity of the Lufkin clay. The second cause of the mass balance discrepancies for cadmium and zinc can be related to precipitation. In the presence of anaerobic bacteria, the sulfur In sulfate (SO 2 ) is reduced to sulfide (S 2-) which precipitates metal species. The pertinent reactions are descmbed by Middleton and Lawrence (1977), Sawyer and McCarty (1978, p. 476), Freeze and Cherry (1979, p 118), and Klm and Amodeo (1983)' CaSO4

--+ Ca2+ + SO42

2CH20 + SO42

--+ H S - + 2HCOf + H +

HS

--+ H + + S 2

HS

+ H + --'H2S --+ H2S(~)

M 2+ + S 2

---+ MS(~)

HCO3 + H + --+ H2CO3 --+ H20 + CO2(g) where CH20 represents organic matter, M 2+ represents a divalent metal cation, and (s) and (g) represent solid and gas, respectively. From the series of reactions shown above, it is seen t hat C d 2+ and Z n 2+ could precipitate as their sulfides under the appropriate conditions It was evident from visual observations th at biological activity occurred in the reservoir of all of the tests, especially the first two kaolinite samples (S-1 and S-2) A gaseous odor, probably hydrogen sulfide (H2S(s)), was detected upon disassembling the diffusion cells. Therefore, it seems t hat conditions were appropriate for heavy metal precipitation in the reservoirs of the diffusion cells, and that the mass balance errors for cadmium and zinc can be attributed, in part, to precipitation With respect to the anions, the mass balance errors for Iodide can be attributed to the problems associated with chemical analysis for iodide These problems included (1) broad-based peaks requiring long periods (>/40 min) for complete ion chromatographic analysis, (2) baseline fluctuations; and (3) severe tailing of the iodide peaks The most likely cause for the mass balance discrepancies associated with the chloride and bromide is chemical complexation or speciation. Some of the

260

c a t i o n s p r e s e n t in the diffuse ( e l e c t r o s t a t i c ) double l a y e r a s s o c i a t e d w i t h c l a y p a r t m l e s i n c l u d e c o m p l e x e d species of b o t h chloride a n d b r o m i d e (e g., CdC1 ÷ , CdBr + , ZnC1 ÷ , and Z n B r ÷). S i n c e t h e s e species would n o t be e x p e c t e d to be e x t r a c t e d w i t h DDW, the t o t a l m a s s of chloride a n d b r o m i d e w h i c h h a d diffused into the soil w o u l d be u n d e r e s t i m a t e d . In addition, a n y u n c o m p l e x e d , free C1a n d / o r B r - a n i o n s a s s o c i a t e d w i t h the diffuse double l a y e r would be "left b e h i n d " d u r i n g the e x t r a c t i o n s t a g e of the e x p e r i m e n t . In o r d e r to e s t i m a t e the significance of c h e m i c a l s p e c i a t l o n on the m a s s b a l a n c e d e t e r m i n a t i o n s , REDEQL2 ( M c D u f f and Morel, 1973) was used to p e r f o r m e q u i l i b r i u m c h e m i c a l c a l c u l a t i o n s for the c o n d i t i o n s a s s o c i a t e d w i t h the initial (aqueous) l e a c h a t e T h e r e s u l t s i n d i c a t e d t h a t r o u g h l y 17% of the C1 a n d 12.5% of t h e B r - are a s s o c i a t e d w i t h Cd 2÷ a n d Zn 2+ as the c o m p l e x e d c a t i o n s CdC1 ÷ , CdBr ÷, ZnC1 ÷ , a n d Z n B r ÷ . W h i l e t h e s e p e r c e n t a g e s c a n n o t a c c o u n t t o t a l l y for t h e m a s s b a l a n c e d l s c r e p a n c m s r e p o r t e d in T a b l e 7, t h e y a r e significant, e s p e c i a l l y w i t h r e s p e c t to s a m p l e K-4. T h e c a l c u l a t i o n s also i n d i c a t e d t h a t iodide ( I ) exists e n t i r e l y as a n u n c o m p l e x e d , free anion.

Effectwe diffusion coefficients determined from reservoir concentrations T h e effective diffusion coefficients (D*) w e r e c a l c u l a t e d for e a c h 1on u s i n g the c o n c e n t r a t i o n s d e t e r m i n e d f r o m the r e s e r v o i r s a m p l e s In all cases except for s a m p l e K-4, s e v e r a l D* v a l u e s w e r e c a l c u l a t e d for e a c h ion since s e v e r a l TABLE 8 A v e r a g e D* values for soil samples based on reservoir c o n c e n t r a t i o n s Soil

Sod sample

D* × 10 l°m2s-1 C1-

Kaohmte

L u f k m clay

Br-

I-

K*

Cd 2~

Zn 2+

S-1

80 (2 7)

87 (26)

17.6 (0 2)

145 (4A)

49 (0 6)

85 (1_1)

S-2

61 (3.5)

53 (2.7)

42 (1 2)

136 (2 1)

44 (0 7)

105 (2 7)

K-4

8.7

83

0_15

12 9

58

59

averages

72 (1 0)

72 (1 0)

75 (1 6)

13 9 (0 6)

48 (0 4)

91 (1 5)

L-1

47 (2 1)

21_9 (9 0)

5_8 (4 6)

19 6 (4_3)

104 (0 6)

25 8 (2_1)

L-2

47 (2_5)

15 5 (10_7)

47 (2,2)

19 5 (2 2)

96 (0 5)

25 1 (0 8)

averages

47 (0 03)

18 2 (3 2)

53 (0 5)

19 6 (0 1)

10 0 (O 04)

25 4 (0 3)

Values m p a r e n t h e s e s are s t a n d a r d deviations

261 E500j 400 ~

~600 [

CHLORIDE D" = 8.0X10(-10)SO M/S

E

CADMIUM

r~

D- = 4 9x10(.10) s o M/S

t\ •

uO 200

150

~ 300

U

0

50 100 TIME(days)

TIME(days)

1000 #

S' 900

BROMIDE D" = 8 7X10(-10)SQ M/S

150

i 400 [ ZINC 300.~ D*--'= SXl 0(-1O)SO M/S

800

ioo

1\

7O0

O

500

0

50 100 TIME(days)

-150

~ 1400~ IODIDE 1300"~ D* = 17 6X10(-10)SQ U/S

!

o

1100 1000 900 800 700 I o 0

O

0

50 100 TiME(days)

150

400 i ~ m POTASSIUM 1~ D" = 14.5X10(-10)SQ M/S 3O0

200 ] ""' 50 100 TIME(days) .

.

.

.

"

•

"

"

150

100

0

.

.

.

.

.

50 100 TIME(clays)

150

Fig 3 Concentration-time profiles for kaohmte sample S-1 r e s e r v o i r s a m p l e s w e r e t a k e n d u r i n g the c o u r s e of e a c h test. T h e a v e r a g e D* v a l u e s a n d t h e s t a n d a r d d e v i a t i o n s are r e p o r t e d in T a b l e 8. T h e D* v a l u e s r e p o r t e d for s a m p l e K-4 are b a s e d on the c o n c e n t r a t i o n s f r o m only one r e s e r v o i r s a m p l e since the r e s e r v o i r was s a m p l e d o n l y at the end of the test. T h e a v e r a g e D* v a l u e s b a s e d on the r e s u l t s of all tests are also s h o w n in T a b l e 8. In d e t e r m i n i n g the a v e r a g e values, the effective diffusion coefficients w e r e w e ] g h t e d w i t h r e s p e c t to t h e n u m b e r of r e s e r v o i r s a m p l e s used in t h e i r determination. V o l u m e r e a d i n g s w e r e t a k e n w i t h the b u r e t d u r i n g the diffusion t e s t to d e t e r m i n e if s i g n i f i c a n t v o l u m e c h a n g e s , w i t h a s s o c i a t e d m a s s flow, h a d occurred. In all cases, the v o l u m e c h a n g e s w e r e small (~< 1.1%) r e l a t i v e to the initial v o l u m e in t h e r e s e r v o i r i n d i c a t i n g t h a t dlffumon was the sole m e c h a m s m of t r a n s p o r t . No a t t e m p t w a s m a d e to c o r r e c t the r e s e r v o i r c o n c e n t r a t m n s for the b a c k g r o u n d ion c o n c e n t r a t i o n s m e a s u r e d m the soil. T h e b a c k g r o u n d ion c o n c e n t r a t i o n s w e r e m e a s u r e d on s a t u r a t e d soil e x t r a c t s t h a t do not r e p r e s e n t the c o n d i t i o n s in t h e soil m the diffusion tests. S o m e of the b a c k g r o u n d ions in the soil u n d o u b t e d l y diffused into the r e s e r v o i r d u r i n g the s o a k i n g s t a g e of the

262 ~" 400 ~

i 200

k CHLORIDE l~xD" = 6-1X10('10)SQM/S

0

1000~ 900~

.=, zo oo

50 100 TIME(days)

~1200~

150 TIME(days)

400 ~ ZINC 300 ~ D" = 10 5X10(.10)SQ U/S

. . . ..... 50 100 150 TIME(days)

IODIDE

• •

t.)

i

~) 1000 900

D" = 4.4X10(-10)SO M/S

150

BROMIDE D* = § 3X10(-10)SQ M/S

. 0

iill C 500 ~

0

50 100 TIME(days)

400 ~

POTASSIUM

300 1 ~

= 13"6X10('10)SO M/S

150

•

w 800 700 0

50 100 TIME(days)

150

0

50 100 TIME(days)

150

Fig 4_ Concentration-time profiles for kaohmte sample S-2

tests and subsequently were removed when the soaking solution was replaced by the synthetic leachate. Therefore, the background concentrations of the ions in the soil samples are unknown. Plots of reservoir concentration versus time are presented in Figures 3 ~ I n c l u d e d m e a c h of the c o n c e n t r a t i o n - t i m e profiles ]s the t h e o r e t i c a l l y predmted profile using the values hsted in Table 8. In general, the results for the kaolimte samples range from good to poor for chloride, bromide, iodide, and potassium, and from good to e x c e l l e n t for cadmium and zinc. The results for L u f k m clay samples are fair for the a m o n s and e x c e l l e n t for the cations The order of the D* values for the cations m the tests is as follows. D~ > D~, > D~d (for kaohmte) D~,, D~ > D~d (for Lufkin clay) This series is almost e x a c t l y opposite to the o r d e r predicted by the results of the b a t c h - e q u i h b r l u m tests. The d i s c r e p a n c y is a t t r i b u t e d to the different c o n d i t i o n s set-up m the diffusion tests r e l a t i v e to the b a t c h - e q u i h b r m m tests The soils in the diffusion tests were soaked with a 0 01 N CaSO4 s o l u t i o n over periods of weeks w h i c h were m u c h g r e a t e r t h a n the 48 h for the batch-equ]li-

A ~

380~ 360 ~ D "

34°1

~°kc,~DM,u!

CHLORIDE : 4 7X10(-10) SO M/S

4OO 3O0 200

300 280 ] . . . . . . . . . . 0 20 40 60 TIME(days)

~ 900~

=

800 ] ~ ' =

i i

5 0 0 1 \ D" = 10 4X10(-10) SQ M/$ I k

320

(J

263

" . 80

100

•

100

"100 liME(days}

'°°]

BROMIDE 21 9X10(-10) SO M/S

3O0

700

2O0

100

°°

o

2o,o

.o

8o loo

liME(days)

Ol

0

.

.

,

20

.

.

,

.

.

'

40 60 TIME(days)

= . .

80

100

A

1600~

(J

1200

1 0

POTASSIUM

s: x10(.10) SO M/S

I5°° ~ . ~ i4oo

,,=,

4OO

IODIDE

200

100

20

40

60

TIME(days)

80

100

0 , - - , - - , - - , - . ,

0

20

40

60

•

80

100

liME(days)

Fig. 5 Concentratzon-tzme profiles for Lufkm clay sample L-1 b r m m tests. T h e r e f o r e , the soils in t h e diffusion t e s t s w e r e e s s e n t i a l l y calciums a t u r a t e d before t h e c a t i o n s f r o m the l e a c h a t e diffused into them. I f the soils w e r e c a l c m m - s a t u r a t e d , or n e a r l y so, m the diffusion test, the m o b i h t y s e r m s w o u l d be e x p e c t e d to be a l t e r e d since c a l c i u m w o u l d be e x p e c t e d to be p r e f e r e n t i a l l y a d s o r b e d in the c o m p e t i t i o n for the soil e x c h a n g e sites Thin is n o t t h e case m t h e b a t c h - e q u i l i b r i u m tests, w h e r e more-or-less e q u a l comp e t i t i o n b e t w e e n all of the c a t i o n species is e x p e c t e d U n d e r t h e c o n d i t i o n of c a l c m m s a t u r a t i o n of the soil, p o t a s s i u m (K+), a m o n o v a l e n t cation, is e x p e c t e d to c o m p e t e m u c h less f a v o r a b l y t h a n the d i v a l e n t c a t i o n s (e.g., Cd 2÷, Zn 2÷) for the e x c h a n g e sites; therefore, the D* v a l u e s for K ÷ s h o u l d be r e l a t i v e l y g r e a t e r t h a n one or m o r e of the o t h e r c a t i o n s S u c h is the case for all of the tests. T h e t h e o r e t i c a l free-solution diffusion coefficmnts (Do) at infinite d i l u t i o n forC1 , B r , a n d I are on the o r d e r of 2 0 - 2 1 × 10 9m 2s l ( R o b i n s o n a n d Stokes, 1959) N o n e of the a m o n D* v a l u e s listed in T a b l e 8 exceed this u p p e r limit. T h e effects of the m a s s b a l a n c e e r r o r s on the c a l c u l a t e d D* v a l u e s were a c c o u n t e d for by a d j u s t i n g the l a s t r e s e r v o i r c o n c e n t r a t i o n for e a c h ion to

264 ~

380~

CHLORIDE

3601~=4 340

.7)(10(.10) SO M/S

1

300 O

280

0

900 ~

600 ~ 500 I \

CADMIUM D" : 9.8XI0(-I0) SO M/S

I ~,

2OO , 20

•

800 t ~

80

46 60 TIME(days)

100

1000 " 20

40" "6'0

~0

100

TIME(days)

BROMIDE

400 I

: 15 qXl0('lO) SO M/S

300

ZINC

, 2OO 100

600

o 8 ~oo~

0

2o , ' o 6'o 6'o loo

0

TIME(days)

1600

- • , - - , - • . - - , - 20 40 60 80 100 TiME(days)

,OD,DE

300 t ~ D" = 19 5 X 10(-10) SO M/S 1200

2OO

1000

100

LI

0

20

40 60 TIME(days)

80

0

100

0

20

40 60 TIME(days)

80

100

Fig 6 C o n c e n t r a t i o n - t i m e profiles for L u f k m clay sample L-2 TABLE 9 D* values for soil samples based on reservozr c o n c e n t r a t i o n s modzfied for m a s s balance e r r o r s Soil

Sozl sample

D* × 10-10 m 2s - 1 C1-

Kaohnlte

K+

Cd 2÷

Zn 2+

S-1

34

46

15

1_1

11

0.47

ND

42

1.5

0 95

1_9

44 28 (1_7)

54 28 (2_6)

22 37 (1 0)

068 12 (0 4)

27 16 (0 8)

31 20 (0_8)

L-1

15

0 70

0 65

0.011

4_1

22

L.2

1_4

0 63

0 43

0.0074

18

12

1 45 (0 05)

0 67 (0 35)

0 54 (0 11)

29 (1_1)

17 (0 5)

averages

0 19

I

S-2 K-4 averages

L u f k m clay

Br

0.0092 (0_0018)

ND = no d a t a or insufficient d a t a Values in p a r e n t h e s e s r e p r e s e n t s t a n d a r d devlat]on for three values for k a o h n l t e and variability b e t w e e n two v a l u e s for L u f k m clay

265 CONCENTRATION 100

(rag/L)

150

200

250

i

i

i•

0

CONCENTRATION 300

200 300 . . . . . . .

0 '

1 •

2

'-

•

(rag/L) 400 ~:

100

500

•

2 CHLORIDE

3

3 '

4

CADMIUM

4'

5'

•

D* = 4.5X10(-10) S Q M / S

D* = 3 5 X I 0 ( - 1 0 ) S Q M / S 6'

CONCENTRATION 0

300

350 i

400 i

450 i

500 •1

550 t

2

3

~

4

600

0

ot

100

(mg/L)

200

300

, ..y.

:t/

1

'-

CONCENTRATION

(rag/L)

MIDE

5 D* = 6 0 X 10(-10) S Q M / S

D* =.3 5X10(-10) S Q M / S 6

Fig 7 Concentrahon.depth profiles for kaohnlte sample K-4 a c c o u n t for the mass balance differences reported in Table 7. This modified c o n c e n t r a t i o n was used with the original c o n c e n t r a t i o n (Co) to recalculate a single D* v a l u e for each ion and the results are presented in Table 9. The average D* v a l u e s based on the results of all tests are also presented m Table 9 V a l u e s of D* corrected for mass balance are, in m a n y cases, m u c h less than the original (unmodified) D* values. However, except for Cd 2÷ and Zn 2÷ , the mass b a l a n c e errors probably are associated with causes w h i c h should not be reflected in a modfficatlon to the reservoir c o n c e n t r a t i o n For the h e a v y metal ions, a portion of the mass b a l a n c e error m a y be associated with precipitation, in w h m h case an adjustment in the reservoir c o n c e n t r a t i o n m a y be appropriate. The D* v a l u e s for Cd 2÷ and Zn 2÷ for sample K-4 are s o m e w h a t different than the c o r r e s p o n d i n g v a l u e s for the S-designated samples. Since the extracting s o l u t i o n for sample K-4 was 5 times greater m c o n c e n t r a t i o n than that of the other k a o h n i t e samples, it seems likely that a portion of the difference in D* v a l u e s can be attributed to the inefficiency of the extraction procedure

266 C O N C E N T R A T I O N (mg/L) 0

100

150 i

1

200 i

•

250 300 i _-,

350 .

CONCENTRATION (rag/L) 400 0

,

100 r

200 , i

]

300 ,

i

400 ,

•

2

" ¢.

3

r.

4

CHLORIDE

3

CAD\IIITM

5 D* = 1 8X10(-10) SQ M/S

|

D* = 4 0Xl0(-10)

SQ M/S

6 C O N C E N T R A T I O N (mg/L) 200

300

400

500

600

700

CONCENTRATION (rag/L) 800 0

1

•

50

100

150

Ii

~

i

200

•

2

2" ZINC

~

3

BROMIDE

3-

4" 5

5" D* = 2 8X10(-10) SQ M/S

D* = 1 1Xl0(-10) SQ ~US 6

6"

Fig 8 Concentration-depth profiles for Lufkm clay sample L-1 Therefore, it is likely that t h e Cd 2+ and Zn 2÷ D* v a l u e s reported for K-4 represent the more accurate values POLLUTE 3.3 analysis

Effective diffusion coefficients (D*) w e r e d e t e r m i n e d for C l - , B r - , Cd 2÷ , and Zn 2 ~ u s i n g POLLUTE 3 3 and the m e a s u r e d profiles of c o n c e n t r a t i o n versus depth for soil s a m p l e s K-4, L-l, and L-2 POLLUTE 3 3 a n a l y s e s for I and K ÷ w e r e n o t m a d e due to the v a r l a b l h t y a s s o c i a t e d w i t h the c h e m m a l a n a l y s m for I and the poor e x t r a c t i o n efficiency a s s o c i a t e d w i t h the K + c o n c e n t r a t i o n determanations. T h e o r e t i c a l c o n c e n t r a t i o n - v e r s u s - d e p t h profiles d e t e r m i n e d u s i n g POLLUTE 3_3 were fit "by eye" to t h e m e a s u r e d c o n c e n t r a t i o n - v e r s u s - d e p t h profiles. The "best-fit" t h e o r e t i c a l profiles are provided in Figures 7, 8, and 9. The results vary from g o o d to poor T h e scatter in the catxon distributions m a y be a s s o c i a t e d w i t h the use of a c o n s t a n t r e t a r d a t i o n coefficmnt to d e t e r m i n e the

CONCENTRATION 100 0

150 i

200 i••

250 i

•

(rag/L)

300 i

350 i

0 0

1-

2

2"

! •

."

CONCENTRATION

400

1

3

267

100

,

i

200

.

= i

(rag/L) 300

,

i

400

,

CHLORIDE

4

5

5" D* = I 5X10(-10) S Q M / S

6 CONCENTRATION

1

2

0

,

50

Tm

,

100 i

,

(mg]L) 150 i

200 ,

1-

•

•

2-

3-

F- 3 e-,

CONCENTRATION

(rag/L)

200 300 400 500 600 700 800 0 ' " ' • ' " i = , , i . i

~.

D* = 3_0X10(-10) S Q M / S 6

4

5 D* = 1 0 X l 0 ( - 1 0 ) S Q M / S

D* = 1 5X10(-10) S Q M / S

6

Fig 9 Concentration-depth profiles for Lufkm clay sample L-2 free c a t i o n d i s t r i b u t i o n in the sod. The s c a t t e r in the a m o n d i s t r i b u t i o n is p r o b a b l y a s s o c i a t e d with the c o m p l e x a t i o n effect p r e v i o u s l y described. A c o m p a r i s o n of the D* v a l u e s d e t e r m i n e d from the P O L L U T E 3 3 analysis and the D* values based on modffied and unmodified r e s e r v o i r c o n c e n t r a t m n s is p r e s e n t e d in Table 10. In general, the a g r e e m e n t b e t w e e n the modified and the POLLUTE 3 3 D* v a l u e s tends to be slightly b e t t e r t h a n the a g r e e m e n t b e t w e e n the unmodified D* values a n d the P O L L U T E 3_3 D* v a l u e The d i s a g r e e m e n t b e t w e e n the a n a l y t i c a l D* values and the P O L L U T E 3 3 D* values is r e l a t i v e l y m i n o r in m o s t cases, and the use of the unmodffied D* v a l u e s would tend to be conservative.

Effect of soil mineralogy on D* Based on the o r i g i n a l (unmodified) r e s e r v o i r c o n c e n t r a t i o n s (Table 8), the a v e r a g e D* v a l u e s for Br , K ÷ , Cd 2÷ , and Zn 2÷ are g r e a t e r with the L u f k i n clay t h a n t h e y are with k a o h n i t e , whale the D* v a l u e for C1 is less for the L u f k l n

268 TABLE 10 Analytmal versus POLLUTE 3 3 effective dlffusmn coetficmnts (D*) Soil sample

Analysis method

D* × 10 ~°m2s 1 Cl

Br

Cd2+

Zn2+

K-4

POLLUTE 3.3 analytmal (M)~ analytmal (UM)2

45 4.4 87

61 5,4 83

35 27 58

35 31 59

L-1

POLLUTE 3.3 analytical (M) analytical (UM)

18 15 47

11 07 21 9

40 41 10 4

28 22 25 8

L-2

POLLUTE 3.3 analytmal (M) analytmal (UM)

15 1.4 47

10 0 63 15 5

3.0 18 96

15 12 25 1

1M = reservoir concentratmns modified for mass balance errors 2UM = original (unmodified) reservoir concentrations

clay. T h e r e is t o o m u c h v a r i a b i l i t y i n t h e i o d i d e r e s u l t s to d r a w a r e l e v a n t c o n c l u s i o n . T h e r e s u l t s a r e s u r p r i s i n g i n t h a t i t w o u l d be e x p e c t e d t h a t t h e D* v a l u e s w i t h t h e L u f k l n c l a y w o u l d be less t h a n t h o s e for t h e k a o l i n i t e , e s p e c i a l l y for t h e c a t i o n s , s i n c e a g r e a t e r a d s o r p t i o n c a p a c i t y is a s s o c i a t e d w i t h t h e L u f k i n c l a y H o w e v e r , c a l c i u m m a y b e h e l d m o r e s t r o n g l y to t h e s m e c t i t i c m i n e r a l s t h a n i t is to t h e k a o l i n i t e . I f t h i s is t r u e , t h e o t h e r c a t i o n s ( e . g , K ÷ , Cd 2+ , Z n 2÷ ) w o u l d be m u c h m o r e m o b i l e i n t h e L u f k l n clay, s i n c e t h e n u m b e r of i n t e r a c t i o n s w i t h t h e c l a y m i n e r a l s u r f a c e s w o u l d be r e d u c e d for t h e o t h e r c a t i o n s . I n a d d i t i o n , t h e r e t a r d a t i o n f a c t o r for t h e c a t i o n s w i t h L u f k l n c l a y m a y be u n d e r e s t i m a t e d b e c a u s e of t h e g r e a t e r s o l l ' s o l u t i o n r a t m i n t h e d i f f u s i o n tests. A n u n d e r e s t i m a t i o n o f t h e r e t a r d a t i o n f a c t o r r e s u l t s i n a n o v e r e s t i m a t i o n of D*.

Tortuostty factors T o r t u o s i t y f a c t o r s (z) u s u a l l y a r e b a s e d o n C I - e f f e c t i v e d i f f u s i o n c o e f f i c m n t s u s i n g eqn. (3). B a s e d o n t h e D* v a l u e s for C1- r e p o r t e d m T a b l e 8 a n d t h e p r e v i o u s l y m e n t i o n e d Do v a l u e for C1- of 2.0 × 1 0 - g m 2 s -1 t h e r v a l u e s a r e 0.24 for L u f k m c l a y a n d r a n g e f r o m 0.31 to 0.40 for k a o h n i t e . T h e s e z v a l u e s a r e s i g n i f i c a n t l y l o w e r t h a n t h o s e r e p o r t e d b y B e a r (1972) for u n c o n s o l i d a t e d m e d i a a n d b y P e r k i n s a n d J o h n s t o n (1963) for g r a n u l a r m a t e r i a l .

Comparison of D* values wtth previous results T h e D* v a l u e s for C1 r e p o r t e d i n T a b l e 8 for t h e k a o l i n i t e s a m p l e s r a n g e f r o m 6 I 8.0 × 10-1°m2s 1. T h e D* v a l u e for C1 m L u f k i n c l a y w a s c o n s i s t e n t

269 at 4.7 × 10 l°m2s 1. T y p m a l l y , a r a n g e of from 2.0 to 6.0 × 10 l°m2s 1 is a s s u m e d to a p p l y to C1- diffusion m c l a y e y soils ( J o h n s o n et a l , 1989), and D* v a l u e s r e p o r t e d in the l i t e r a t u r e t e n d to lie b e t w e e n 2.0 × 10-1°m2s 1 and 1.0 × 10-gm2s 1 w h e n CI- is diffusing m s a t u r a t e d clays, silty clays, and s a n d : b e n t o m t e m i x t u r e s (e.g, C l a r k e a n d G r a h a m , 1968, B a r r a c l o u g h and T i n k e r , 1981; D e s a u l n i e r s et al., 1981; C r o o k s and Q m g l e y , 1984; Q u i g l e y et a l , 1984; G i l l h a m et ah, 1984) T h e r e f o r e the D* v a l u e s r e p o r t e d m this s t u d y are in e x c e l l e n t a g r e e m e n t w i t h p r e v i o u s findings B a r r a c l o u g h and T i n k e r (1981, 1982) found t h a t the e f f e c n v e diffusion coefficmnt for Br fell w i t h i n a fairly n a r r o w r a n g e of 3 7 7 0 × 10 l°m'~s 1 T h e i r v a l u e s w e r e d e t e r m i n e d from l a b o r a t o r y tests u s i n g s a t u r a t e d soil s a m p l e s e i t h e r p r e p a r e d in the l a b o r a t o r y or r e c o v e r e d from the field m a r e l a t i v e l y u n d i s t u r b e d state. T h e D* v a l u e s for Br for the k a o h m t e samples in this s t u d y are m good a g r e e m e n t w i t h the p r e v i o u s findings, f a l h n g w i t h i n the r a n g e of 5 3-8 7 × 10-l°m2s 1 H o w e v e r , the b r o m i d e D* values for the L u f k i n clay s a m p l e s are m u c h higher. T h e diffusion coefficmnts b a s e d on the o m g m a l (unmodified) r e s e r v o i r conc e n t r a t i o n s for all of the m e t a l species g e n e r a l l y are g r e a t e r in L u f k m clay t h a n t h e y a r e in k a o h m t e . This c a n be a t t m b u t e d to the e x c h a n g e complex of the L u f k i n c l a y b e i n g d o m i n a t e d by c a l c m m w h e r e a s t h a t of k a o h m t e is d o m i n a t e d by s o d i u m (see T a b l e 1). T h e p o t a s s i u m D* v a l u e s r e p o r t e d in T a b l e 8 a p p e a r to be q m t e high, from 1.3 to 1.5 × 10 9m2s ~ for k a o h m t e a n d a r o u n d 2 0 × 10 9m2s-~ for L u f k m clay T h e r a t e of p o t a s s m m diffusion m a y be e n h a n c e d for t h r e e reasons. (1) m l t m l l y , the clay e x c h a n g e sites are p m m a r i l y filled with Ca -~ ions, (2) the m o n o v a l e n t p o t a s s i u m i~ns m u s t c o m p e t e w i t h m u l t i p l e d~valent c a t m n s (Ca ''~ , Cd 2÷, a n d Zn 2÷) for the c l a y e x c h a n g e sites, and (3) the K + is diffusing m a s o l u t m n c o n t a i n i n g n u m e r o u s a m o n specms w h i c h m a y effectively " h o l d " the K + runs and lessen t h e i r a t t r a c t i o n for the e x c h a n g e sites. T h e zinc D* v a l u e for s a m p l e K-4 was 5.9 × 10 mm2s ~w h i c h c o m p a r e s well w i t h the v a l u e of 5.1 × 10-~°m2s ~ r e p o r t e d by Ellis et al (1970) for a l a b o r a t o r y d l f f u s m n test p e r f o r m e d w i t h s a t u r a t e d k a o h m t e . The zinc D* v a l u e s for L u f k m clay are s h g h t l y l o w e r if modified r e s e r v o i r c o n c e n t r a t i o n s are used m the c a l c u l a t m n of D*, b u t m u c h h i g h e r if the original r e s e r v o i r c o n c e n t r a t m n s are used T h e difference m the zinc D* v a l u e s m a y be due to the use of a n overly c o n s e r v a t i v e r e t a r d a t m n f a c t o r m the a n a l y s e s a n d / o r to the longer test p e r m d s a s s o c m t e d w i t h the L u f k m clay tests versus t h a t of sample K-4 (76 v e r s u s 30 days). F o r n o n l i n e a r i s o t h e r m s s u c h as the ones s h o w n in Fig_ 2, a s e c a n t v a l u e for Kp will be less t h a n a h n e a r coefficmnt, Kd, d e t e r m i n e d from a t a n g e n t line d r a w n to the m i t m l p o r t m n of the i s o t h e r m As a result, the r e t a r d a t m n f a c t o r b a s e d on the s e c a n t v a l u e for Kp will u n d e r e s t i m a t e the r e t a r d a t m n of a solute species at low c o n c e n t r a t m n s . In a d d l t m n , the a d s o r p t m n i s o t h e r m s (Fig. 2) w e r e d e t e r m i n e d from the r e s u l t s of b a t c h - e q m h b r m m tests p e r f o r m e d at a s o H : s o l u t m n r a t i o w h m h r e p r e s e n t s t h a t of a

270 suspension (1 e , 1:4), whereas the soil:solution ratio of the column tests was much d~fferent. If the batch-equilibrium results underestimate the adsorptive capacity of the soils, a greater underestlmatmn of the r e t a r d a t m n factor for L u f k m clay is expected since Lufkin clay has a much greater adsorptive capacity Therefore, much higher D* values for Zn 2÷ should be expected with Lufkln clay. Also, ff the microbiological a c t i w t y occurring m the dlffusmn cells is a function of time, the longer dlffusmn times associated with the Lufkin clay samples would have resulted in greater precipitation of the metal specms and, therefore, higher estimates of the D* values for the metal specms. Since the mobflltms and precipitation chemlstmes of Cd 2+ and Zn 2÷ are similar, the above arguments should apply equally well to the cadmium results. CONCLUSIONS Measurement of effective diffumon coefficmnts (D*) for inorganic chemicals diffusing into compacted clay soil is difficult; numerous interferences and problems were identified m this study. Soaking the compacted soils with water prior to the start of a dlffumon test was effective m saturating the soils sufficiently to mimmlze mass flow from gradients other than those imposed by concentration differences However, the soaking procedures resulted m nonuniform water contents within the soils. As a result, the analyses for the determination of D* values assuming uniform (constant) soil propertms were m error. Nonetheless, the magnitude of the error is thought to be insignificant from an engineering perspective, and similar variations would be expected m reahstlc field problems Mobility seines based on batch-equdlbrium tests performed in the laboratory were very different from those determined from the diffusion tests on soil columns The cause for the difference is thought to be associated with the different soft:solution ratios used m the batch-equlhbrmm and column tests Since a soil column more correctly simulates field conditions, the usefulness of batch adsorption tests to determine r e t a r d a t i o n factors for analysis of contaminant transport in sods is questioned Effective diffusion coefficients (D*) of reactive solutes measured with t r an s mn t systems like the one in this study are sensitive to inaccuracies m the r e t a r d a t m n coefficient Relatively accurate values of D* will be determined when the soft-solute interactions are characterized by linear adsorptive behawor. However, many realistm situatmns will be described by n o n h n e a r adsorptive b e h a w o r Under the conditions imposed m this study, conservative (high) values of D* resulted when the nonlinear adsorptmn behavior of the reactive solutes was approximated by a constant ret ardat i on factor based on a secant line described by eqn. (20). In most cases, conservative estimates of D* result from the use of reservoir c o n c e n t r a t m n s to calculate effective diffusion coefficmnts. However, relatively good matches between theoretmally and experimentally determined plots of c o n c e n t r a t i o n versus time do not necessarily mean that accurate effective

271 dlffusmn coefficmnts have been determined Other processes which are not a c c o u n t e d f o r d i r e c t l y m t h e a n a l y s i s , s u c h as p r e c i p i t a t m n , m a y be o p e r a t i v e a n d b i a s t h e r e s u l t s . M a s s b a l a n c e s h e l p to i n d i c a t e p o s s i b l e s i n k s / s o u r c e s m t h e d i f f u s i o n s y s t e m , b u t r e s u l t s a r e s e n s i t i v e to t h e e f f i c i e n c y o f t h e e x t r a c t m n procedure T h e r e w e r e no m a j o r differences m the effective diffusmn coefficmnts of a g i v e n s o l u t e f o r k a o h n i t e a n d t h e s m e c t l t i c soft, L u f k m c l a y T h u s , s o i l m i n e r a l o g y h a d little i n f l u e n c e on the results of the tests, and the small d i f f e r e n c e s t h a t w e r e o b s e r v e d w e r e o n t h e s a m e o r d e r as t h e e x p e r i m e n t a l errors. Based on the c h l o r i d e diffusion results in this study, the c a l c u l a t e d v a l u e s f or t h e t o r t u o s l t y f a c t o r (3) fell m t h e r a n g e 0.24~).40 Thin r a n g e o f r v a l u e s g e n e r a l l y is l o w e r t h a n o t h e r v a l u e s r e p o r t e d f o r t h e t o r t u o s l t y f a c t o r m u n c o n s o h d a t e d o r g r a n u l a r softs. ACKNOWLEDGEMENTS T h i s r e s e a r c h w a s s p o n s o r e d by t h e U.S. E n v i r o n m e n t a l P r o t e c t i o n A g e n c y u n d e r c o o p e r a t i v e a g r e e m e n t CR812630-01 T h e c o n t e n t s o f t h i s a r t i c l e do n o t n e c e s s a r i l y reflect the views of the Agency, nor does m e n t m n of trade n a m e s or c o m m e r c i a l p r o d u c t s c o n s t i t u t e an e n d o r s e m e n t or r e c o m m e n d a t m n for use T h e s e m o r a u t h o r e x t e n d s h~s s i n c e r e a p p r e c m t i o n t o t h e E a r t h T e c h n o l o g y C o r p o r a t m n o f L o n g B e a c h , C a l i f o r n i a , f o r a f e l l o w s h i p i n 1985 1987 w h m h helped to s u p p o r t this w o r k In p a r t i c u l a r , the efforts of Mssrs. F r e d D o n a t h , Geoff Martin, and Hudson Matlock are apprecmted. REFERENCES Barraclough, P B and Tinker, P.B, 1981 The determination of lomc diffusion coefficmnts m field soils_ I Diffusion coefficmnts m staved soils m relation to water content and bulk density J Soll Scl, 32 225~236_ Barraclough, P B. and Tinker, P.B_. 1982 The determination of lomc diffusion coetficmnts m field soils II Diffusion of bromide ions m undisturbed soil cores J Soil Scl. 33 13 24 Bear, J , 1972 Dynamics of Flmds m Porous Media Elsevmr, New York, NY, 764 pp Bohn, H L, McNeal, B L and O'Connor, G A, 1979 Soil Chemmtry John Wiley and Sons, New York. NY, 329 pp Bowman, R S , 1984 Evaluation of some new tracers for soil water studies J Soil Scl Soc Am , 48 987 993 Carslaw, H S and Jaeger, J C , 1959 Conduction of Heat m Sohds. Oxford Umv Press. Oxford, 2nd ed, 510pp Clarke, A L and Graham, E R, 1968 Zinc diffusion and distribution coefficients m soil as affected by soil texture, zinc concentration and pH Soil ScL, 10 409~118_ Crank, J , 1975 The Mathematics of Diffusmn Clarendon Press, Oxford, 2nd ed, 414 pp Crooks. V E and Qmgley, R M, 1984 Saline leachate migration through clay A comparative laboratory and field mvestlgatmn Can Geotech J , 21 349 362 Darnel, D E and Lfljestrand. H M, 1984 Effects of landfill leachates on natural hner systems Chem Manuf Assoc Rep, Umv Texas, Geotech Eng Center, Austin, TX, 86pp Davis, S N, Thompson, G M, Bentley, H W and Stiles, G, 1980 Groundwater tracer A short revmw Ground Water, 18 14-23

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