Journal of Contaminant Hydrology, 4 (1989) 241 273 241 Elsev ie 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 in t ed in The N e t h e r l a n d s

DIFFUSION OF INORGANIC CHEMICAL SPECIES IN COMPACTED CLAY SOIL

C H A R L E S D S H A C K E L F O R D 1, DAVID E D A N I E L 2 and 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, rev i sed and accepted Sep tember 26, 1988)

A B S T R A C T

Shackel ford , C D_, Daniel , D E and Ll l ]es t rand, H M , 1989 Dif fus ion of i no rgan i c chemica l species in compac ted clay soil. J Contain. Hydrol., 4 241-273

This r e s e a r c h was conduc t ed to s t udy the di f fus ion of i no rgan i c chemica l s m compac ted clay soil for the des ign of was te c o n t a i n m e n t bar r ie rs The effective diffusion coefficients (D*) of a m o n l c (C1 , Br , and I ) and ca t ion ic (K ~, Cd 2+, and Zn 2÷) species in a syn the t i c l eacha te were m e a s u r e d Two c lay soils were used in the s tudy. The soils were compac ted and pre-soaked to m l m m l z e m a s s t r an spo r t due to suc t i on in the soil The r e su l t s of the di f fus ion t es t s were ana lyzed u s i n g two ana ly t i ca l so lu t ions to F lck ' s second law and a commerc ia l ly ava i lab le s e m l - a n a l y h c a l so lu t ion , P O L L U T E 3.3

M a s s ba l ance ca l cu l a t i ons were per formed to ind ica te possible s i nks / sou rce s in the di f fus ion sys t em Er ro rs in m a s s ba l ance were a t t r i bu t ed to problems wi th the chemica l ana lys i s ( I ) , the inefficiency of t he ex t r ac t i on p rocedure (K ÷), p rec ip i t a t ion (Cd 2. and Zn 2÷ ), and chemica l com- p l exa t lon (C1- and B r - )

The D* va lue s for C1 repor ted in th is s t udy are in exce l len t a g r e e m e n t wi th p rev ious f indings for o the r types of soil The D* va lues for the me t a l s (K + , Cd 2÷ , and Zn 2~ ) are t h o u g h t to be h i g h (conserva t ive) due to (1) Ca 2÷ s a t u r a t i o n of the e x c h a n g e complex of the clays, (2) p r e c l p i t a t m n of Cd 2÷ and Zn 2÷ , and (3) n o n l i n e a r a d s o r p t m n behav io r In general , h i gh D* va lues and conser- va t ive des igns of was te c o n t a i n m e n t ba r r i e r s will r e su l t if t he p rocedures descr ibed in th i s s t udy are used to de t e rmine D* and the adso rp t ion behav io r of t he so lu tes is s imi la r to t h a t descr ibed in this s t udy

I N T R O D U C T I O N

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.

0169-7722/89/$03 50 © 1989 Elsev ie r Sc ience P u b l i s h e r s B V

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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 morgamc 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, t ransmnt transport of a nonreactive solute in a saturated soil may be wmtten as:

~c D ~2 C ~c ~--7 = ~ x 2 - 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; Shackel- ford, 1988)

D* = DoT (3)

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

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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-dlmen- smnal form of the solute transport equation for saturated soft must be modffied as follows'

~C D t~2 c Vst~C

~t R ~x 2 R Ox (4)

where the retardation factor, R, is given by the following equation

R = 1 + p~ Kp (5) n

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 "parti t ion 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 signifi- cant. In the limit (1.e., v~ --* 0), eqns. (1) and (4) reduce to Fick's second law, or

0c _ D* ~2-~c (6) ~t ~x 2

and

~c D* ~2 c

~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

dominan t t r anspo r t mechan ism when v~ is on the order of 1.6 × 10-1°ms 1, which is the seepage veloci ty in a clay l iner if the hydrau l ic gradient is one, the poros i ty is 0.5, and the hydrau l ic conduc t iv i ty is 8.0 × 10-11ms 1. Since cu r r en t U.S. regu la t ions requi re the hydrau l ic c o n d u c t i w t y of c lay l iners to be ~< 1 0 × 10 9m s- l , d i f fusmn is expected to be a significant, if not dominant , mechan ism for the t r anspo r t of solutes t h ro u g h clay liners.

The coefficients D* and R in eqn. (7) can be combined into a single pa rame te r as follows:

Ds = D*/R (8)

where Ds is the "effect ive diffusion coefficient of the reac t ive solu te" (Gll lham et a l , 1984, Qulgley et al., 1987, Myrand et al., in prep.). However , Rowe et al. (1985b) and Rowe (1987) cau t ion agains t the use of a single pa rame te r m eqn (7) when the bounda ry condi t ions are f lux-controlled. When only Ds is used m an analysis with f lux-control led boundary condit ions, the resul t ing analyses are bo th incor rec t and unconserva t lve . As a result , the effective diffusion coefficients for the react ive , as well as the nonreac t ive solutes, in this s tudy are defined wi th respect to eqn. (3), not eqn. (8).

MATERIALS AND METHODS

Soils

Kaohn l t e , a commerc ia l ly processed clay, and L u f k m clay, a na tu ra l ly occur r ing smect i t ic soil were used in this study. The proper tms of the two soils are p resen ted in Table 1. The sum of the exchangeab le cat ions l isted in Table 1 for each of the soils is g rea te r t han each of the respect ive CEC's. The shgh t differences ( < 18%) can be a t t r ibu ted to d issolut ion of ca rbona te minera ls (e.g., CaCO3) m the soils dur ing the measurement . This resul ts m elevated ca lcmm concen t ra t ions , especial ly for the L u f k m clay. As indicated in Table 1, the exchange complex of the Lufk in clay is domina ted by Ca 2÷ whereas tha t of k a o h n i t e is domina ted by Na ÷ .

Leachate

A syn the t i c waste leacha te was used m this study. The amons chlor ide (C1 ) , bromide (Br - ) , and iodide ( I ) were chosen as conserva t ive t racers . Chlor ide and bromide commonly are used as conserva t ive t racers and iodide is a useful t r ace r due to its s imi lar i ty to C1 and Br and its re la t ive ly low background concen t r a t i ons ( < 0 . 0 1 m g L 1) m soil (Davis et al., 1980). Bowman (1984) concluded t ha t I may be useful as a t r ace r under anaerobic l abo ra to ry condi t ions Since I is a la rger ion than C1- and Br , it should not compete as effect ively as a l igand as e i ther C1 or Br - in the complexat ion of meta l cat ions. As a result , I should exist pr imar i ly in its free form and, therefore , form a basis

TABLE 1

Physlcal and chemlcal properties of soils

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Property Method of measurement .1

Value of property

kaohnlte Lufkln clay

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 la s t i c i ty index (g g- 1 ) Particle size distribution

si l t and c lay ( < 0075 mm) sand (0 075~475 mm)

Soil pH at 1 1 soil so lu t ion Catmn exchange capacity (meq/100 g) Exchangeable cartons (meq/100 g)-

Na K + C a 24

Mg ~+ Cd 2+ i n 2 +

Background ion concentrations (mg L 1) Cl - Br I K ~ Cd 2~ Z n 2 +

X-ray diffraction kaohnlte smectlte AS T M D854 2 64 2 69 AS T M D698 32% 20% AS T M D698 1 331 1 635 A S T M D4318 54% 56% ASTM D4318 23% 42°,0

ASTM DII40 100% 82% ASTM D422 0% 18%

*~ 3 65 6 93 .2 5 25 . 2

3 8 6 4 08 27 10 191

< 0 1 < 0 1 < 0 1 < 0 1 < 0 1 < 0 1

71 179 4_7 5 6

< 0 1 < 0 1 32 47

< 0 1 < 0 1 < 0 1 < 0 1

*' ASTM rep re sen t s 1986 A n n u a l Book of ASTM Standards by the American Society for Testing and Materials .2 Page 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 spec la t ion on the measured ef fect ive di f fus ion coefficients.

Cadmium (Cd 2+) and z inc (Zn 2+) were c h o s e n as inorgan ic ca t ions for two reasons: (1) both are l isted in the U.S. dr inking water s tandards as tox ic e lements; and (2) both are a m o n g the more mobi l e h e a v y meta l s in soi ls and clay sys tems (Farrah and Picker ing , 1977, 1978; T n e g e l , 1980)

For c o n v e m e n c e of compar i son , 0 . 0 1 N s o l u t i o n s of each o f the ions were used The s y n t h e t i c l e a c h a t e was made by d i s so lv ing 0.01 N c o n c e n t r a t i o n s of CdI2, ZnC12, and KBr salts in "standard" water (0.01 N CaSO4). Therefore, the tota l c o n c e n t r a t i o n of the synthe t i c l e a c h a t e was 0.04 N. As a result o f complex format ion , the in i t ia l e q u i h b r i u m spec ia t ion is expected to inc lude < 13% of the Ca 2÷ as complexed , < 2% of the K ÷ as complexed, ~ 45% of the c a d m m m as free Cd 2÷ , ~ 80% if the z inc as free Zn ~÷ , and about 68% of the sulfate , 83%

246

TABLE 2

Compamson of selected charactemstlcs of the synthet ic leachate with representat ive values for leachates taken from sanitary, mumclpal , and mdus t rml landfills and lagoons

Parameter Synthetic Actual morga mc leachates 1 leachate (mgL 1) (mgL -1)

representat ive probable range extremes

Metals cadmium 562 0-2 0-17 calcmm 200 100-3000 ~4800 po tassmm 391 200-2000 3 3770 zmc 327 0-100 0-1000

Nonmetals. bromide 799 chloride 355 30-2800 iodide 1269 - sulfate 480 0-1280

0-3000

0-1826

Other charactermtlcs:

electmcal conductivity (pmhos cm 1 at 25°C)

pH

Synthetic Representative leachate range 3090-3950 300~17000

40~37 4 9

1 Compilation based on data presented by Griffin et al_ (1976), Freeze and Cherry (1979, p 435), and Darnel and Ldjes t rand (1984, pp 17 and 18)

of the C1 , 87% of the Br , and 100% of the I- as free ions. A compar ison of the concen t ra t ions in the syn the t ic l eacha te with those in ac tua l l eacha tes from municipal , sani ta ry , and indus t r ia l landfills and lagoons is presented in Table 2.

The pH of the syn the t i c l eacha te was adjusted to tha t of the soft so lut ion before the s ta r t of the diffusion tes t m order to minimize the effects of pH on the adso rp tmn charac te r i s t i c s of the softs (Frost and Griffin, 1977, U.S. En- w r o n m e n t a l P ro t ec t i on Agency, 1987). As a result , the pH of the syn the t ic l eacha te is repor ted as a range of values m Table 2.

Batch equthbrium tests

Batch equilibrium tests were performed to determine the adsorption charac- teristics 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 equih- brmm tests to approximate the conditions in the diffusion cell. The concen-

247

t r a t i ons of the specffied ions in each f lask were v a r m d by ser ia l d i lu t ion of the 0 .04N syn the t i c l e acha t e wi th an e lec t ro ly te so lu t ion (0.01N CaSO4) somet imes re fe r red to as " s t a n d a r d wa te r " . As a resul t , the reduced concen- t r a t i ons of the ions in the f lasks were wi th respec t to a cons t an t 0 01 N CaSO4 solut ion. A f lask con ta in ing 200 ml of 0.04 N l eacha te soil was used as a control . All f lasks were s toppered, p laced in an end-over-end, r o t a r y mixer, and mixed for 48 h a t a t e m p e r a t u r e of 23 ° + 2°C. At the end of the mix ing period, samples of the soi l -solut ion s lur r ies f rom the flasks were poured into 50-ml centmfuge tubes, sealed, and cen t r i fuged for 30 mm. a t 3000-4000 rpm (1980-3520 g). The s u p e r n a t a n t f rom each tube was then p ipe t ted to sample bot t les and the equlh- b r m m c o n c e n t r a t i o n s of the ions in the so lu t ion were de te rmined by an ion c h r o m a t o g r a p h y or f lame a tomic absorp t ion spect roscopy.

The resu l t s of the chemica l ana lyses were p lo t ted m the form of adsorp t ion i so therms, or sorbed concen t r a t i on , S, versus dissolved e q u i h b r i u m concent ra - t ion, c of so lu te for each 1on. The sorbed concen t r a t i ons were de te rmined by mass ba l ance us ing the fol lowing equation"

{ C o - (9) S = \ M "

where Co is the in i t ia l c o n c e n t r a t i o n of the specffied ion in the flask; VSOL lS the vo lume of the so lu t ion (200 ml); and M s is the soil mass (50 g).

Diffusion tests

Sample preparation The tes t spec imens of soil were p repa red by mix ing a l r -drmd soil wi th

s t anda rd w a t e r (0 .01N CaSO,) unt i l a wa t e r con ten t abou t 1-2% wet of

Burel

3oaklng _lne

Fig 1 D]ffuslon apparatus

248

optimum water content 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 Proctor method".

The standard Proctor 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-cm 3 compaction mold, this procedure results m 592.7 k J m 3 of compactmn energy The standard Proctor compaction procedure was followed for both kaolinite and Lufkin clay except that 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 t ransport 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 that the initial soaking of the samples from the top can cause more disturbance to the soil s t ructure 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 that of the soaking solution by t l t rat ing 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) throughout the entire period of the diffusion test, indicating that the parafilm acted as an effective barrier to evaporat ion

After the diffusion test was set up, the leachate concentrat ion was monitored periodically by withdrawing samples from the reservom The leachate samples were analyzed for the specified ions to determine how the reservoir concent ra tmn varied with time.

The diffusion tests were performed at ambmnt laboratory temperatures which ranged between 21 and 25°C. This variat ion 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 conduc- tivity, and temperature 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 concentrat ion 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 approxi- mately 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 concentratmns 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

cadmium and zinc f rom the soil. Since t r ans i t i on me ta l ca t ions ( including Zn ~ and Cd 2+) compete more effect ively t h a n m o n o v a l e n t ca t ions at equal con- cen t r a t i ons of EDTA 4- (Bohn et al., 1979, p 36), i t was not k n o w n if all of the p o t a s s m m ions sorbed to the c lay soil could be ex t rac ted wi th the H4EDTA solu t ion Since the p m m a r y emphas i s of the s tudy was to measu re the effect ive diffusion coefficmnts of the h e a v y meta l s cat ions, the ex t r ac t i on of the p o t a s s m m ions was of s econda ry 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 ca t ion e x t r a c t i n g so lu t ion for the first two k a o l i m t e samples (S-1 and S-2). The pH of the so lu t ion was a round 2 8 P r e h m m a r y mass ba l ance ca lcu la t ions f rom the resu l t s of these tests m d m a t e d poor efficiencies wi th respec t to ex t r ac t ion of the ca t ions (Cd 2 ~, Zn 2 +, and K - ). Thus, the c o n c e n t r a t i o n of the H4EDTA solu t ion was inc reased for the r e m a i n i n g tests to 5 mM and the pH was adjus ted to 7.0 wi th 1.0 M N a O H to improve the ca t ion ex t r ac t ion efficmncms.

Imt l a l ly , it was t h o u g h t t h a t the H4EDTA solu t ion ex t rac t s could be used to de t e rmine 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 . However , the H 4 EDTA so lu t ion was found to in te r fe re wi th the ion chromato- g raphic d e t e r m i n a t i o n of the chlor ide and bromide concen t r a t i ons for the first two k a o h m t e tes ts Therefore , a s epa ra t e ana lys i s for a m o n c o n c e n t r a t m n s was made for all of the r e m a i n i n g d i f fusmn tests The s epa ra t e ana lys i s for an ions r e q m r e d t h a t two cen t r i fuge 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 resul ts ind ica ted t ha t the specified a m o n s (C1 , Br , and I ) were not adsorbed to the soils; therefore , de-mmzed, dist i l led w a t e r (DDW) was used as the ex t r ac t i ng s o l u t m n for the a m o n analys is . This n o r m a l l y is not the case since d l lu tmn with DDW changes the e q u f l i b r m m chemis t ry be tween the sorbed and free concen t r a t i ons of the runs exis t ing in the soft a t the t ime of b reakdown.

Soft f rom each shce f rom the sec t ion ing s tage was p laced into a 50-ml cen tmfuge tube and the a p p r o p r i a t e e x t r a c t i n g so lu tmn was added 0.e-, DDW was added to one cen t r i fuge tube for a m o n ana lys i s and H4EDTA was added to the o the r cen t r i fuge tube for c a t m n analysis) . The cen t r i fuge tubes filled wi th the mix tu r e of soil and ex t r ac t i ng s o l u t m n were sealed, p laced m a ro ta ry , end-over-end mixe r and mixed at 30 rpm for at leas t 48 h. The tubes were then r emoved f rom the mixer and cen t r i fuged for 30mm. at 3000-4000rpm (1980- 3520 g) The s u p e r n a t a n t f rom the centmfuge tubes was p lpe t ted to app rop r i a t e con ta ine r s for c h e m m a l ana lys 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 samples f rom the cen t r i fuge tubes a re less t h a n those exis t ing m the soft due to the d i lu t ion 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 so lu tmn. In order to e s t ima te the to ta l c o n c e n t r a t m n of each chemica l species exis t ing in the soft, c', a t the t ime the diffusion cell was disassembled, the m e asu red c o n c e n t r a t m n , c~, was mul t ip l ied by the inverse of the d i lu t ion fac to r as follows.

/ WsoL c, : cm -W- w )

251

where Wso L is the weight of the ex t rac t ing solut ion m the centr i fuge tube, and Ww is the weight of the water in the soil at the time of soil sec t ion ing .Equat ion (10) assumes tha t the densit ies of the ex t rac t ing solut ion and the water are equal. The concen t ra t ion , c', represents the tota l c o n c e n t r a t m n of the chemical species m the soil assuming the ex t rac t ing solut ion is 100% efficient

The soluble or mobile concen t r a t ion of the chemical species, c, m the pore space of the soil can be est imated 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 = c ' / R (11)

In the case of nonadsorb ing tracers, the r e t a rda tmn factor is 1.0.

DATA ANALYSIS

Two different analyses were used to determine the D* values. The first analysis util ized the reservoir concen t ra t ions in con junc t ion with two closed- form solut ions to eqn. (7). The second analysis utilized the concen t ra t ions determined from the soil sec t ioning and ext rac t ion procedure with a contami- nan t t r anspor t model, POLLUTE 3.3., developed by Rowe et al. (1985a)

C l o s e d - f o r m s o l u t i o n s

After the In t roduc t ion of the leachate into the reservoir at time zero (t = 0), mass t r anspor t of the chemical cons t i tuents m the leachate occurred via molecu la r diffusion from the reservoir into the soil The diffusive mass t r anspor t resul ted in a decrease m the cons t i tuen t concen t ra t ions m the reservoir as a func t ion of time. Since the bot tom of the cell (x = 0) was closed dur ing the diffusion stage of the test, none of the mass of the diffusing con- s t l tuents en te r ing the soil at the soil-reservoir interface (x = a) could exit the soil at the bot tom of the cell. Based on these conmderat ions, the initial and boundary condi t ions for the diffusion cell are:

c - 0 at 0 < ~ x ~ a, t = 0

c - Co at a <. x <~ a + l, t = 0

?c - 0 a t x = O, t > 0

?x

and

R y + n ~ x = lco at x = a , t > 0

where a is the length of the diffusion cell (L), l is the effective length of the reservoir (L), and y is defined as the amount of the free solute per uni t of soil con ta ined between the planes at x = 0 (Le., base of the soil) and at any dis tance wi th in the soil, or"

252

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

Except for the constant , lco, the second boundary condi t ion is of the Sturm- Llouvi l le type (Wilson, 1948). The effective length of the rese rvo i r was de te rmined by dividing the to ta l volume of l eacha te in t roduced into the appara tus (reservoir , top cap, PVC tube, and buret) by the cross-sect ional area, A, which was constant .

One solut ion to Flck 's second law for s imul taneous diffusion and adsorp t ion m sod with the above ini t ia l and boundary condi t ions (Wilson, 1948, Crank, 1975, p. 57), is"

M~ 1 ~, 2a(1 + ~) ( - D * q ~ t ~ . . . . 2 : exp (12)

M~ m=ll + ~ + ~q~ ~ )

where Mt ~s the to ta l mass of a given solute in the soil at any t ime t af ter the s ta r t of diffusion and M~ is the cor responding mass at infinite time. The qm's m eqn. (12) are the non-zero posi t ive roots given by: tan qm - aqm (13)

where :t is a coeiticmnt given by the fol lowing relat ion:

l u - ( 1 4 )

nRa

The eqml ibr ium mass of the solute in the soil at infinite t~me is given by.

(1) M~ = ~ Mo (15)

where/14o is the ini t ia l mass of the solute m the reservoir , whmh is equal to the product , Alco. The complete de r iva t ion for eqn (12) for a sa tu ra ted sod as well as the roots to eqn. (13) are given by Shackel ford (1988).

A second ana ly t ica l so lut ion cons idered in this s tudy is g~ven by Carslaw and J a e g e r (1959, p 306) and Crank (1975, p. 58), or

c~ 1 Me - exp (z 2) erfc (z) (16) Co M~(1 + ~)

where

n z = 7 Rx//R-D-~ (17)

erfc( ) is the complemen ta ry e r ro r funct ion, and ct is the concen t r a t i on of solute m the rese rvo i r at an elapsed t ime t. Tables of values of erfc() are provided by Cars law and J a e g e r (1959), Crank (1975), Freeze and Cherry (1979), and others.

Both eqns. (12) and (16) were used to de te rmine the D* values repor ted in this study. The assumptions i nhe ren t in the use of eqns. (12) and (16) are ' (1) D* is cons tant , (2) the ra te of adsorp t ion is ve ry fast compared wi th the ra te of

253

diffusion; (3) s o r p t i o n is r evers ib le ; and (4) the soi l p r ope r t i e s (n and Pb) a re cons t an t .

POLLUTE33

POLLUTE 3 3 (Rowe et al., 1985a) was used to ana lyze the m e a s u r e d concen- t r a t i o n profi les. The pu rpose for us ing POLLUTE 3 3 to c a l c u l a t e effect ive d i f fus ion coefficients was to p rov ide (1) an i n d e p e n d e n t check on the c a l c u l a t e d D* va lues from the c losed-form so lu t ions and (2) an a s se s smen t of the r e l a t i v e mer i t s of the 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 ve r sus c o n c e n t r a t i o n d a t a from soi l ex t r ac t i ons . 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 " so lu t i on to eqn. (10) for so lu te m i g r a t i o n in a non -homoge ne ous soil depomt The t h e o r y for the d e r i v a t i o n of the s e m i - a n a l y t i c a l so lu t i on i m p l e m e n t e d by the c o m p u t e r p r o g r a m POLLUTE 3 3 IS desc r ibed by Rowe and B o o k e r (1984, 1985). The use of the t h e o r y to d e t e r m i n e D* va lues in the l a b o r a t o r y is desc r ibed by Rowe et al (1985b).

RESULTS AND DISCUSSION

F~nal physLcal properties of soils

The final p r o p e r t i e s of the soi l samples (i.e. a f te r s o a k i n g and t r i m m i n g the soil) used in the d a t a a n a l y s i s for the effect ive d i f fus ion coefficients a re p r e s e n t e d in Tab le 3. The w a t e r c o n t e n t s for the c l ay samples p r e sen t ed in Tab le 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 the w a t e r c o n t e n t s d e t e r m i n e d from each soi l sl ice. The w a t e r c o n t e n t s of the soi l samples v a r i e d cons ide rab ly . The n o n u n i f o r m i t y in the 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 the soi l samples ref lec ts n o n u n i f o r m i t y in the o t h e r soi l p rope r t i e s (e.g., n and Pb)- S ince the d i f fus ion

TABLE 3

Final soil properties used for effective diffusion coefficient analyses

Soil Soil Water Total Degree of Volumetric Bulk (dry) sample content porosity saturation, water density

w(%) 1 n St(%) 2 content Pb(g cm ~) 0 3

Kaohnlte S-1 43 1 0 54 96 2 0 52 1 210 S-2 41 7 0.54 95.15 0 51 1 225 K-4 39 9 0 52 97 9 0 51 1 272

Lufkln clay L-1 28 8 0 47 86 2 0 41 1 417 L-2 27 8 0 45 90 7 0 41 1 474

1Weighted averages from soil slices 2 Percent 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

Character is t ics of final soaking solution and synthet ic leachate

Soil Final soaking solution Initial leachate Final leachate sample

EC at 25°C pH EC at 25°C pH EC at 25°C pH (#mhos c m - ' ) (gmhoscm 1) ( g m h o s c m - ' )

S-1 1520 4 03 3950 4 00 2600 3 90 S-2 1480 4 01 3950 4.01 2600 3 57 K-4 1040 4_15 3120 4.07 3820 3 67 L-1 1030 6 78 3090 6.67 2810 5 65 L-2 1030 6 87 3090 6 67 2600 5 85

EC = electmcal conductivity

255

pro tons (H ÷) from the soil into the rese rvo i r af ter d i sp lacement from the soil by invad ing ca t ions (Cd 2÷ , Zn 2÷ , and K ÷ ).

The re la t ive ly acidic na tu r e of the k a o h n i t e is i l lus t ra ted by the pH values be tween about 4 0 and 4.1 for the soaking so lu tmns of samples S-l, S-2, and K-4 The pH values of the soaking so lu tmns for the L u f k m clay are a round 6.8.

In summary, the da ta presented m Table 4 indica te tha t the effects on the adsorp t ion capac i ty of softs associa ted wi th changes in pH should have been minimal, and q u a h t a t i v e in fo rmat ion regard ing l abo ra to ry test condl tmns can be asce r ta ined from e lec t r ica l conduc t iv i ty and pH measurement s of soft so lut ions and leachates . Therefore , pH and EC measurement s should be inc luded m the qual i ty assurance procedures for the l abo ra to ry tests.

Batch-equlltbrtum test results

The resul ts of the ba tch-equi l ibr ium tests for the kao l imte and the Lufkin clay are p resen ted as adsorp t ion isotherms for cat ions m Figure 2. Imt ia l ly , it was expected tha t a m o n adsorp t ion (especial ly C1 and SO~- ), as well as ca t ion adsorpt ion, would be opera t ive m the clays, especial ly for the kaol in i te whmh has a pH-dependent adsorp t ion capac i ty (Bohn et al., 1979, p. 174) However , it was found from the resul ts of the ba tch-equi l ibr ium tests t ha t an ion adsorp t ion of C1 , Br , and I did no t occur m e i the r of the soils. Bohn et al. (1979, p. 174) s ta te tha t at all pH values, the d iva lent SO~ ion is adsorbed to a g rea te r ex ten t t han the monova l en t C1- ion, as is expected on the basis of e lec t ros ta t ic cons idera t ions Also, since s t andard wa te r (0 0 1 N CaSO4) was used as the d i lu t ion wa te r for the ba t ch -equ ihb rmm samples, the SO~ co n cen t r a t i o n remained re la t ive ly h igh as the o the r an ion concen t ra t ions (Cl- , Br , I ) were diluted. On the basis of charge and concen t r a t i o n effects, it would be expected tha t SO42- would compete much more favorably for the posi t ive adsorp t ion rotes t han would C1 , Br , or I . Since the clays were pre -equihbra ted wi th 0 .01N CaSO4 and the SO~ concen t r a t i on remained cons tan t t h r o u g h o u t all tests, the soil should have been m equ ihbr lum with 0.01 N SO~-, and no fu r the r SO42- adsorp t ion was expected. Final ly , C1 is not adsorbed at all in the s l ight ly acid to neu t ra l pH range for mon tmor i l l omt l c soils (e .g, Lufk in clay), where pH- dependent charge is of minor impor tance (Bohn et al., 1979, p. 174). Since Br and I an ions are l a rger t han the C1- a m o n and, therefore , have smal ler charge densmes , Br and I- should not be expected to be adsorbed to montmorxl loni tm soils ei ther. On the basis of these considera t ions , it was expected tha t measurab le adsorp t ion of the Cl - , Br , and I- am o n s would not occur under the condi t ions imposed in this study.

Based on secant l ines d rawn to the curves in Figure 2, the re la t ive moblh tms of each of the cat ions with each of the soils was found to be:

Cd 2. > Zn 2+ > K ÷ (for kao l lmte )

Cd 2÷ > K ÷ > Zn 2÷ (for L u f k i n c l a y )

256

0~

o I -

z Lg (3 Z O (J a Lg a2 n- O ¢D

A E

B

_o P

300

200

100

K

1:4 S o d : S o l u U o n R a t i o

C d

i i i i i

100 200 300 400 500 600

EQUILIBRIUM CONC., c (rng/L) (a)

¢/;

z 2

z O (J ,,,-, uJ m

0 (D

1200

o .o E

1000 1 Zn K

800

6OO

4OO

200 : ~

0 0 50 100 150 200 250 300 350

EQUILIBRIUM CONC, C (rag/L) (b )

Fig 2 Adsorption isotherms for (a) kaohmte and (b) Lufkln clay

B e c a u s e t h e a d s o r p t i o n i s o t h e r m s a r e n o n l i n e a r , t h e a s s o c i a t e d r e t a r d a t i o n 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 d e v i a t i o n f rom t h e c o n s t a n t r e t a r d a t i o n f a c t o r a s s u m e d in t h e d e r v l a t i o n o f t he a n a l y t i c a l s o l u t i o n s as w e l l as in 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 sed to e s t i m a t e t h e r e t a r d a t i o n f a c t o r s , R H o w e v e r , t h e r e a r e a n i n f i n i t e n u m b e r o f s e c a n t l i n e s w h i c h c o u l d be 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 coe f f i c i en t is se t by t h e s t e p f rom t h e c = 0 to c = co c o n c e n t r a t i o n . Th i s m e a n s t h a t

g p - S[co - SIc=o A S g l e N g ~ c N-1 (18)

C o - - 0 A c co Co

TABLE 5

Freundhch isotherm parameters for kaohnlte and Lufkm clay

257

Soft Ion Freundhch isotherm parameters

g~ Y

Correlatmn coefficmnt r

Kaohmte

L u f k m clay

potassmm 2_237 0 8929 0 98

c a d m m m 8 564 0 5270 0 98

zinc 5 078 0 6925 0_99

potassium 20_59 0 7999 0 98

cadmium 121.5 0 3987 1 00

zinc 123 7 0 4747 1 00

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

S = K~c N (19)

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:

fib .~- N-1 R = 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

potassium cadmium zinc

S-1 3 75 2 00 2 98 S-2 3 83 2 03 2 97

K-4 3 95 2 04 3 15 L-1 22_7 10_35 21 9 L-2 23 5 10 8 22 8

258

5. The r e t a r d a t i o n fac to r s used to ca l cu la t e the effect ive diffusion coefficients for each of the ca t ions of in te res t in each of the tes ts are provided in Table 6. The va lues r epor t ed in Tab le 6 were de t e rmined wi th eqn. (20) us ing the da ta provided in Tab les 3 and 5 wi th the in i t ia l c o n c e n t r a t m n of the ca t ion in the test.

Mass balance considerations

Mass ba lances for each of the ions and each of the tests wi th c lay were ca l cu la t ed to assess the poss ibi l i ty of expe r imen ta l e r ro r as well as u n k n o w n c o n c e n t r a t i o n sources and /o r s inks The mass ba lances were ca lcu la ted by c o m p a r i n g the mass of an ion which diffused f rom the r e se rvo i r over the diffusion per iod (MR) to the mass of the ion in the soil a t the end of the diffusion tes t per iod (Ms). The mass of the ion in the soil was ca lcu la ted f rom the d i s t r ibu t ion of to ta l (as opposed to free) conce n t r a t i ons of the ion in the soil as de te rmined by the soil sec t ion ing and ex t r ac t i on procedure . A l inear distri- bu t ion was assumed to exis t be tween the con cen t r a t i ons at each sect ion. The resu l t s of the mass ba l ance ca lcu la t ions are p resen ted as the pe rcen t d i f ference be tween the diffused mass (MR) and the mass in the soil M~ re la t ive to the diffused mass, as shown in Tab le 7.

The pe rcen t d i f ferences in mass are s o m e w h a t h igh and the possible causes of the d i sc repanc ies should be noted. Two cont ro l tests (i.e., w i thou t soil) did not revea l any s igni f icant sources and /or s inks assoc ia ted wi th the diffusion appa ra tus . Aside f rom expe r imen ta l e r ro r in the ana lys i s of the c o n c e n t r a t i o n s and n a t u r a l s c a t t e r in the data , the re are severa l o the r logical exp lana t ions .

The di f ferences In mass for the ca t ions (K + , Cd 2÷ , Zn 2. ) can be a t t r i bu ted to two causes. First , i t IS h k e l y t ha t the E D T A ex t r ac t i ng so lu t ion resu l ted in poor r emova l efficiencies of the po tass ium. As men t ioned previous ly , t ha t EDTA works well as an e x t r a c t a n t for d iva len t cat ions , such as cadmium and zinc, but not as well for m o n o v a l e n t ca t ions Even t hough the c o n c e n t r a t i o n of the

T A B L E 7

M a s s b a l a n c e e r r o r s

So i l P e r c e n t d i f f e r e n c e s i n m a s s 1

s a m p l e C1 B r - I K + C d 2+ Z n "~+

S-1 15 3 47 2 44 4 44 2 39 4 46 0

S-2 - 39 2 N D 5 2 43 4 35 5 52 0

K-4 23 8 16 0 - 255 66 4 26 3 21 7

L-1 45 8 78 4 72 2 86 4 35 3 43 6

L-2 47 9 78_1 84 9 85 9 48 4 52 2

1 P e r c e n t d i f f e r e n c e - ( M a M s ) l M a × 1 0 0 % , w h e r e M a = m a s s d i f f u s e d f r o m r e s e r v o i r , a n d

M s ~ m a s s m so i l a t e n d o f t e s t

N D = n o d a t a o r m s u f f i c m n t d a t a

259

EDTA solution was five times greater for sample K-4 than 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 that the increased strength of the extract ing 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 montmoril lonite 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 pert inent 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 --+ HS- + 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 that C d 2+ and Z n 2+ could precipitate as their sulfides under the appropriate conditions It was evident from visual obser- vations that 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 that conditions were appropriate for heavy metal precipi tat ion 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 at tr ibuted 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 tail ing 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

ca t ions p re sen t in the diffuse (e lec t ros ta t ic ) double l aye r a s soc ia ted wi th c lay pa r tmles inc lude complexed species of bo th chlor ide and bromide (e g., CdC1 ÷ , CdBr + , ZnC1 ÷ , and ZnBr ÷). S ince these species would not be expec ted to be ex t r ac t ed wi th DDW, the to ta l mass of chlor ide and b romide which had diffused into the soil would be underes t ima ted . In addi t ion, any uncomplexed , free C1- and /or B r - an ions assoc ia ted wi th the diffuse double layer would be " lef t beh ind" dur ing the e x t r a c t i o n s tage of the exper iment .

In order to e s t ima te the s ignif icance of chemica l spec ia t lon on the mass ba l ance de te rmina t ions , REDEQL2 (McDuff and Morel , 1973) was used to pe r fo rm equi l ib r ium chemica l ca l cu la t ions for the condi t ions assoc ia ted wi th the in i t ia l (aqueous) l e acha t e The resu l t s ind ica ted t h a t r ough ly 17% of the C1 and 12.5% of the B r - are a s soc ia ted wi th Cd 2÷ and Zn 2+ as the complexed ca t ions CdC1 ÷ , CdBr ÷, ZnC1 ÷ , and ZnBr ÷ . Whi le these pe rcen tages can not a c c o u n t to ta l ly for the mass ba l ance d l sc repancms repor t ed in Tab le 7, they are s ignif icant , espec ia l ly wi th respec t to sample K-4. The ca l cu la t ions also ind ica ted t h a t iodide ( I ) exists en t i re ly as an uncomplexed , free anion.

Effectwe diffusion coefficients determined from reservoir concentrations

The effect ive diffusion coefficients (D*) were ca lcu la ted for each 1on us ing the c o n c e n t r a t i o n s de t e rmined f rom the r e se rvo i r samples In all cases except for sample K-4, severa l D* va lues were ca lcu la t ed for each ion since severa l

TABLE 8

Average D* values for soil samples based on reservoi r concen t ra t ions

Soil Sod D* × 10 l°m2s-1 sample

C1- Br - I - K * Cd 2~ Zn 2+

K a o h m t e S-1 80 87 17.6 145 49 85 (2 7) (26) (0 2) (4A) (0 6) (1_1)

S-2 61 53 42 136 44 105 (3.5) (2.7) (1 2) (2 1) (0 7) (2 7)

K-4 8.7 8 3 0_15 12 9 5 8 5 9

averages 7 2 7 2 7 5 13 9 4 8 9 1 (1 0) (1 0) (1 6) (0 6) (0 4) (1 5)

Lufkm clay L-1 4 7 21_9 5_8 19 6 104 25 8 (2 1) (9 0) (4 6) (4_3) (0 6) (2_1)

L-2 4 7 15 5 4 7 19 5 9 6 25 1 (2_5) (10_7) (2,2) (2 2) (0 5) (0 8)

averages 4 7 18 2 5 3 19 6 10 0 25 4 (0 03) (3 2) (0 5) (0 1) (O 04) (0 3)

Values m paren theses are s t andard devia t ions

E500 j CHLORIDE 400 ~ D" = 8.0X10(-10) SO M/S

t \

uO 200

TIME(days) 150

~600 [ CADMIUM E r~ D- = 4 9x10(.10) s o M/S

•

~ 300 U 0 50 100 150

TIME(days)

261

1000 # BROMIDE S' 900 D" = 8 7X10(-10) SQ M/S

800

ioo 7O0

500 - - O 0 50 100 150

TIME(days)

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

1 \

O 0 50 100 150 TiME(days)

~ 1400 ~ IODIDE ! 400 i ~ m POTASSIUM 1300 "~ D* = 17 6X10(-10) SQ U/S 1~ D" = 14.5X10(-10) SQ M/S

o 3O0 1100 1000

200 ] 900 800 700 I " " ' . . . . " • " " 100 . . . . .

o 0 50 100 150 0 50 100 150 TIME(days) TIME(clays)

Fig 3 Concentration-time profiles for kaohmte sample S-1

r e se rvo i r samples were t a k e n dur ing the course of each test. The a v e r a g e D* va lues and the s t a n d a r d dev ia t ions are r epor t ed in Tab le 8. The D* va lues r epor t ed for sample K-4 are based on the c o n c e n t r a t i o n s f rom only one r e se rvo i r sample s ince the r e se rvo i r was sampled only a t the end of the test. The a v e r a g e D* va lues based on the resu l t s of all tes ts are also shown in Table 8. In de t e rmin ing the a v e r a g e values , the effect ive diffusion coefficients were we]ghted wi th r e spec t to the n u m b e r of r e se rvo i r samples used in the i r deter- mina t ion .

Vo lume read ings were t a k e n wi th the bu re t du r ing the diffusion tes t to de t e rmine if s igni f icant vo lume changes , wi th assoc ia ted mass flow, had occurred. In all cases, the vo lume changes were smal l (~< 1.1%) re la t ive to the in i t ia l vo lume in the r e se rvo i r ind ica t ing tha t dlffumon was the sole m e c h a m s m of t r anspor t .

No a t t e m p t was made to co r rec t the r e se rvo 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. 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 were m eas u red on s a t u r a t e d soil ex t r ac t s t h a t do not r ep re sen t the condi t ions in the soil m the diffusion tests. Some 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 se rvo i r du r ing the soak ing s tage of the

262

~" 400 k CHLORIDE

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

i 200 0 50 100 150

TIME(days)

iill C 500 ~ D" = 4.4X10(-10) SO M/S

150 TIME(days)

1000~ BROMIDE 900 ~ D* = § 3X10(-10) SQ M/S

.=, zo . . . . . . . . . oo 0 50 100 150

TIME(days)

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

t.) 0 50 100 150 TIME(days)

~1200~ IODIDE

~) 1000

900 • • •

w 800

700 0 50 100 150 TIME(days)

i 400 ~ POTASSIUM

300 1 ~ = 13"6X10('10) SO M/S

0 50 100 150 TIME(days)

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 ~ Inc luded m each of the concen t ra t ion- t ime profiles ]s the theore t i ca l ly 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 exce l len t for cadmium and zinc. The resul ts for L u f k m clay samples are fair for the amons and excel lent for the cat ions

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 a lmost exac t ly opposi te to the order predicted by the resul ts of the ba tch -equ ihbr lum tests. The d iscrepancy is a t t r ibu ted to the different condi t ions set-up m the diffusion tests re la t ive to the ba t ch -equ ihb rmm tests The soils in the diffusion tests were soaked with a 0 01 N CaSO4 solu t ion over periods of weeks which were much g rea te r t han the 48 h for the batch-equ]li-

A ~ 380~ CHLORIDE

360 ~ D " : 4 7X10(-10) SO M/S

34° 1 3 2 0

300

280 ] . . . . . . . . . . " . (J 0 20 40 60 80 100

TIME(days)

~ 900~ = BROMIDE

800 ] ~ ' = 21 9X10(-10) SO M/S

700

°° o 2 o , o .o 8o loo liME(days)

i ~° k c,DM,u! ~ 5001\ D" = 10 4X10(-10) SQ M/$

I k 4OO

3O0

200 •

100 "100

liME(days}

i '°°] 3O0

2O0

100

O l . . , . . , . . ' = . . 0 20 40 60 80 100

TIME(days)

263

1600~ IODIDE

i4oo I5°° ~ . ~ s: x 10(.10) SO M/S

1 1200 ,,=,

(J 0 20 40 60 80 100

TIME(days)

A 4OO

POTASSIUM

2 0 0

1 0 0

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. Therefore , the soils in the diffusion tes ts were essen t ia l ly calc ium- s a t u r a t e d before the ca t ions f rom the l eacha t e diffused into them. I f the soils were c a l c m m - s a t u r a t e d , or nea r l y so, m the diffusion test, the m o b i h t y serms would be expec ted to be a l t e red s ince ca lc ium would be expected to be p re fe ren t i a l l y adsorbed in the compe t i t i on for the soil exchange si tes Thin is not the case m the ba tch -equ i l ib r ium tests, where more-or- less equal com- pe t i t ion be tween all of the ca t ion species is expec ted

U n d e r the condi t ion of c a l c m m s a t u r a t i o n of the soil, po t a s s ium (K+), a m o n o v a l e n t ca t ion , is expec ted to compete m u c h less f avo rab ly t h a n the d iva len t ca t ions (e.g., Cd 2÷, Zn 2÷) for the exchange sites; therefore , the D* va lues for K ÷ should be r e l a t ive ly g rea t e r t han one or more of the o the r ca t ions Such is the case for all of the tests.

The theo re t i ca l f ree-solut ion diffusion coefficmnts (Do) a t infini te d i lu t ion forC1 , B r , a n d I are on the order of 2 0 - 21 × 10 9m 2s l ( R o b i n s o n a n d Stokes, 1959) None of the a m o n D* va lues l isted in Table 8 exceed this upper limit.

The effects of the mass ba l ance e r rors on the ca lcu la ted D* va lues were accoun ted for by ad jus t ing the las t r e se rvo i r c o n c e n t r a t i o n for each ion to

264

~ 3 8 0 ~ CHLORIDE

3 6 0 1 ~ = 4 .7)(10(.10) SO M/S 340

1 300

O 280 , 0 20 46 60 80 100

TIME(days)

600 ~ CADMIUM 500 I \ D" : 9.8XI0(-I0) SO M/S

I ~,

2OO

1000 " 20 40" "6'0 ~ 0 100 TIME(days)

900 ~ • BROMIDE

800 t ~ : 15 qXl0(' lO) SO M/S

,

600 o 8 ~oo~ 2o , ' o 6'o 6'o loo

TIME(days)

400 I ZINC

300

2OO

100

0 - • , - - , - • . - - , - - 0 20 40 60 80 100

TiME(days)

1600 ,OD,DE

1200

1000

LI 0 20 40 60 80 100

TIME(days)

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

2OO

100

0 0 20 40 60 80 100

TIME(days)

Fig 6 Concentra t ion- t ime profiles for Lufkm clay sample L-2

TABLE 9

D* values for soil samples based on reservozr concent ra t ions modzfied for mass balance errors

Soil Sozl D* × 10-10 m 2 s - 1

sample C1- Br I K + Cd 2 ÷ Zn 2 +

Kaohn l t e S-1 3 4 0 19 4 6 1 5 1_1 1 1

S-2 0.47 ND 4 2 1.5 0 95 1_9

K-4 44 54 22 068 27 31 averages 2 8 2 8 3 7 1 2 1 6 2 0

(1_7) (2_6) (1 0) (0 4) (0 8) (0_8)

Lufkm clay L-1 1 5 0 70 0 65 0.011 4_1 2 2

L.2 1_4 0 63 0 43 0.0074 1 8 1 2

averages 1 45 0 67 0 54 0.0092 2 9 1 7 (0 05) (0 35) (0 11) (0_0018) (1_1) (0 5)

ND = no data or insufficient data

Values in pa ren theses represent s tandard devlat]on for three values for kaohnl te and variabil i ty between two values for Lufkm clay

265

100 0

2

' - 3

4

C O N C E N T R A T I O N (rag/L)

150 200 250 300 i i i •

C H L O R I D E

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

C O N C E N T R A T I O N (rag/L)

1 0 0 200 300 400 500 0 ' . . . . . . . ~ :

1 • • •

2

3 ' C A D M I U M

4 '

5 ' •

D* = 3 5XI0 ( -10 )SQ M/S

6 '

C O N C E N T R A T I O N (rag/L)

300 350 400 450 500 550 600 0 i i i •1 t

1

M I D E

5

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

2

' - 3

~ 4

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

0 100 200

o t , . . y . : t /

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

6

300

Fig 7 Concentrahon.depth profiles for kaohnlte sample K-4

account for the mass balance differences reported in Table 7. This modified concentrat ion was used with the original concentrat ion (Co) to recalculate a s ingle D* va lue for each ion and the results are presented in Table 9. The average D* va lues based on the results of all tests are also presented m Table 9 Values of D* corrected for mass balance are, in many cases, much less than the original (unmodified) D* values. However, except for Cd 2÷ and Zn 2÷ , the mass balance errors probably are associated with causes which should not be reflected in a modfficatlon to the reservoir concentrat ion For the heavy metal ions, a port ion of the mass balance error may be associated with precipitation, in whmh case an adjustment in the reservoir concentrat ion may be appro- priate.

The D* va lues for Cd 2÷ and Zn 2÷ for sample K-4 are somewhat different than the corresponding va lues for the S-designated samples. Since the extract ing so lut ion for sample K-4 was 5 t imes greater m concentrat ion than that of the other k a o h n i t e samples, it seems l ikely that a portion of the difference in D* va lues can be attributed to the inefficiency of the extract ion procedure

266

2

" 3 ¢.

r. 4

CONCENTRATION (mg/L)

1 0 0 150 200 250 300 350 400 0 i i i _-, .

1 • •

CHLORIDE

5

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

CONCENTRATION (mg/L)

200 300 400 500 600 700 800

1 • •

2

~ 3 BROMIDE

5

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

CONCENTRATION (rag/L)

1 0 0 200 300 0 , r , i ] , i ,

3 CAD\IIITM

| D * = 4 0 X l 0 ( - 1 0 ) SQ M/S 6

CONCENTRATION (rag/L)

50 100 150 0 I i ~ i

2"

ZINC 3 -

4 "

5"

6 "

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

400

200

Fig 8 Concentration-depth profiles for Lufkm clay sample L-1

Therefore , it is l ike ly that the Cd 2+ and Zn 2÷ D* va lues reported for K-4 represent the more accura te va lues

POLLUTE 3.3 analys is

Effect ive di f fus ion coeff ic ients (D*) were determined for C l - , B r - , Cd 2÷ , and Zn 2 ~ us ing 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 soi l samples K-4, L-l, and L-2 POLLUTE 3 3 ana lyses for I and K ÷ were no t made due to the v a r l a b l h t y a s soc ia t ed wi th the c h e m m a l ana lysm for I and the poor e x t r a c t i o n eff iciency a s soc ia t ed wi th the K + c o n c e n t r a t i o n determa- nat ions .

T h e o r e t i c a l concentra t ion -versus -depth profiles determined us ing POLLUTE 3_3 were fit "by eye" to the measured concentra t ion -versus -depth profiles. The "best-fit" theore t i ca l profi les are provided in Figures 7, 8, and 9. The resul ts vary from good to poor The scat ter in the catxon d is tr ibut ions m a y be as soc ia ted wi th the use of a c o n s t a n t re tardat ion coeff icmnt to determine the

267

100 0

1

2

3

4

5

6

C O N C E N T R A T I O N (rag/L)

150 200 250 300 350 400 i i • • i • i i

• C H L O R I D E

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

C O N C E N T R A T I O N (rag/L)

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

1

~. 2 • •

F- 3

e-, 4

5

D* = 1 0Xl0 ( -10 ) SQ M/S

6

0 0

1 -

2 " !

5 "

6

0

1 -

2 -

3 -

C O N C E N T R A T I O N (rag/L)

100 200 300 , i . = i , i , ."

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

C O N C E N T R A T I O N (mg]L)

50 100 150 , T m , i , i ,

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

400

200

Fig 9 Concentration-depth profiles for Lufkm clay sample L-2

free ca t ion d is t r ibut ion in the sod. The sca t te r in the a m o n dis t r ibut ion is probably associa ted with the complexat ion effect previously described.

A compar i son of the D* values determined from the P O L L U T E 3 3 analysis and the D* values based on modffied and unmodified reservoir c o n c e n t r a t m n s is presented in Table 10. In general, the agreement between the modified and the P O L L U T E 3 3 D* values tends to be s l ight ly bet ter t han the agreement between the unmodified D* values and the P O L L U T E 3_3 D* value The d isagreement between the ana ly t ica l D* values and the P O L L U T E 3 3 D* values is re la t ively minor in most cases, and the use of the unmodffied D* values would tend to be

conservat ive .

Effect of soil mineralogy on D*

Based on the or ig inal (unmodified) reservoir concen t ra t ions (Table 8), the average D* values for Br , K ÷ , Cd 2÷ , and Zn 2÷ are greater with the Lufkin clay than they are with kaohni te , whale the D* value for C1 is less for the Lufkln

268

TABLE 10

Analytmal versus POLLUTE 3 3 effective dlffusmn coetficmnts (D*)

Soil Analysis D* × 10 ~°m2s 1 sample method

Cl Br Cd 2+ Zn 2+

K-4 POLLUTE 3.3 4 5 6 1 3 5 3 5 analytmal (M) ~ 4.4 5,4 2 7 3 1 analytmal (UM) 2 8 7 8 3 5 8 5 9

L-1 POLLUTE 3.3 1 8 1 1 4 0 2 8 analytical (M) 1 5 0 7 4 1 2 2 analytical (UM) 4 7 21 9 10 4 25 8

L-2 POLLUTE 3.3 1 5 1 0 3.0 1 5 analytmal (M) 1.4 0 63 1 8 1 2 analytmal (UM) 4 7 15 5 9 6 25 1

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

clay. T h e r e is too m u c h v a r i a b i l i t y i n the iod ide 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 . The r e s u l t s a re s u r p r i s i n g i n t h a t i t w o u l d be expec ted t h a t the D*

v a l u e s w i t h the L u f k l n c lay w o u l d be less t h a n those for the k a o l i n i t e , e s p e c i a l l y for the c a t i o n s , s i nce 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 th the L u f k i n c lay Howeve r , c a l c i u m m a y be h e l d m o r e s t r o n g l y to the

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 the k a o l i n i t e . I f th i s is t rue , t he o t h e r c a t i o n s (e .g , K ÷ , Cd 2+ , Zn 2÷ ) w o u l d be m u c h m o r e m o b i l e i n t he L u f k l n clay, s i nc e the

n u m b e r of i n t e r a c t i o n s w i t h t he c l ay m i n e r a l su r f ace s w ou l d be r e d u c e d for the

o t h e r c a t i ons . I n a d d i t i o n , the r e t a r d a t i o n f ac to r for the c a t i o n s w i th L u f k l n c lay 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 the g r e a t e r s o l l ' s o l u t i o n r a t m in the d i f fu s ion tes ts . A n u n d e r e s t i m a t i o n of the r e t a r d a t i o n f ac to 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 ac to r s (z) u s u a l l y a re based on CI- ef fec t ive d i f fu s ion coeff icmnts u s i n g eqn. (3). Based on the 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 the

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 × 10-gm2s -1 the r v a l u e s a re 0.24 for L u f k m c l ay a n d r a n g e f rom 0.31 to 0.40 for k a o h n i t e . These z v a l u e s a re s i g n i f i c a n t l y l ower t h a n those r e p o r t e d by 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 by 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

The D* v a l u e s for C1 r e p o r t e d in T a b l e 8 for the k a o l i n i t e s a mp l e s r a n g e f rom 6 I 8.0 × 10-1°m2s 1. The D* v a l u e for C1 m L u f k i n c l ay was c o n s i s t e n t

269

at 4.7 × 10 l°m2s 1. Typmal ly , a r a n g e of f rom 2.0 to 6.0 × 10 l°m2s 1 is a ssumed to apply to C1- diffusion m c layey soils ( Johnson et a l , 1989), and D* va lues r epor t ed in the l i t e r a tu r e t end to lie be tween 2.0 × 10-1°m2s 1 and 1.0 × 10-gm2s 1 when CI- is dif fusing m s a t u r a t e d clays, si l ty clays, and s a n d : b e n t o m t e mix tu re s (e .g , C la rke and Graham, 1968, B a r r a c l o u g h and Tinker , 1981; Desau ln i e r s et al., 1981; Crooks and Qmgley , 1984; Quig ley et a l , 1984; Gi l lham et ah, 1984) There fo re the D* va lues r epor ted m this s tudy are in exce l len t a g r e e m e n t wi th p rev ious findings

B a r r a c l o u g h and T i n k e r (1981, 1982) found tha t the e f fecnve diffusion coef- f icmnt for Br fell wi th in a fa i r ly n a r r o w r ange of 3 7 7 0 × 10 l°m'~s 1 The i r va lues were de te rmined from l a b o r a t o r y tes ts us ing s a t u r a t e d soil samples e i ther p r epa red in the l a b o r a t o r y or r ecove red f rom the field m a re la t ive ly und i s tu rbed state. The D* va lues for Br for the k a o h m t e samples in this s tudy are m good a g r e e m e n t wi th the previous findings, f a lhng wi th in the r ange of 5 3-8 7 × 10-l°m2s 1 However , the bromide D* values for the Lufk in clay samples are m u c h higher .

The diffusion coefficmnts based on the o m g m a l (unmodified) rese rvo i r con- cen t r a t i ons for all of the meta l species genera l ly are g rea t e r in L u f k m clay t h a n they are in k a o h m t e . This can be a t tmbu ted to the exchange complex of the Lufk in c lay be ing domina ted by c a l c m m whereas tha t of k a o h m t e is domina ted by sodium (see Table 1).

The po t a s s ium D* va lues r epor ted in Table 8 a p p e a r to be q m t e high, f rom 1.3 to 1.5 × 10 9m2s ~ for k a o h m t e and a round 2 0 × 10 9m2s-~ for L u f k m clay The r a t e of p o t a s s m m diffusion m a y be enhanced for th ree reasons . (1) ml tml ly , the clay exchange sites are pmmar i ly filled with Ca -~ ions, (2) the m o n o v a l e n t po t a s s ium i~ns mus t compete wi th mul t ip le d~valent c a t m n s (Ca ''~ , Cd 2÷, and Zn 2÷) for the c lay exchange sites, and (3) the K + is diffusing m a s o l u t m n con t a in ing n u m e r o u s a m o n specms which may effect ively "ho ld" the K + runs and lessen the i r a t t r a c t i o n for the exchange sites.

The zinc D* va lue for sample K-4 was 5.9 × 10 mm2s ~ which compares well wi th the va lue of 5.1 × 10-~°m2s ~ repor ted by Ellis et al (1970) for a l a b o r a t o r y d l f fusmn tes t pe r fo rmed wi th s a t u r a t e d k a o h m t e . The zinc D* va lues for L u f k m clay are s hgh t l y lower if modified r e se rvo i r concen t r a t i ons are used m the c a l c u l a t m n of D*, but much h igher if the or ig inal r e se rvo i r c o n c e n t r a t m n s are used

The di f ference m the zinc D* va lues m a y be due to the use of an over ly c o n s e r v a t i v e r e t a r d a t m n fac tor m the ana lyses and /or to the longer tes t pe rmds a s socmted wi th the L u f k m clay tests versus t ha t of sample K-4 (76 versus 30 days). For n o n l i n e a r i so the rms such as the ones shown in Fig_ 2, a s ecan t va lue for Kp will be less t h a n a h n e a r coefficmnt, Kd, de te rmined from a t angen t l ine d r awn to the m i t m l p o r t m n of the i so the rm As a resul t , the r e t a r d a t m n fac to r based on the secan t va lue 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 so lu te species a t low c o n c e n t r a t m n s . In addl tmn, the a d s o r p t m n i so the rms (Fig. 2) were de te rmined f rom the resu l t s of ba t ch -eqmh- b r m m tes ts pe r fo rmed at a soH:so lu tmn ra t io whmh represen t s tha 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 underest lmatmn of the re tarda tmn factor for Lufkm 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 act iwty 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 saturat ing the soils sufficiently to mimmlze mass flow from gradients other than those imposed by concentrat ion 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 reahst lc 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 re tardat ion factors for analysis of contami- nant t ransport in sods is questioned

Effective diffusion coefficients (D*) of reactive solutes measured with t ransmnt systems like the one in this study are sensitive to inaccuracies m the re tarda tmn 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 nonhnear adsorptive behawor 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 re tardat ion factor based on a secant line described by eqn. (20).

In most cases, conservative estimates of D* result from the use of reservoir concentra tmns to calculate effective diffusion coefficmnts. However, relatively good matches between theoretmally and experimentally determined plots of concentra t ion versus time do not necessarily mean that accurate effective

271

d l f f u s m n coe f f i cmnt s h a v e b e e n d e t e r m i n e d O t h e r p r o c e s s e s w h i c h a re n o t

a c c o u n t e d fo r d i r e c t l y m the 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

and b ias t h e r e su 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 poss ib l e s i n k s / s o u r c e s m

the d i f f u s i o n sys tem, b u t r e s u l t s a re s e n s i t i v e to t he e f f ic iency of t he e x t r a c t m n

p r o c e d u r e

T h e r e w e r e no m a j o r d i f f e r e n c e s m the e f f e c t i v e d i f f u s m n coef f i cmnts of a

g i v e n s o l u t e fo r k a o h n i t e and t h e s m e c t l t i c soft, L u f k m c lay Thus , soi l

m i n e r a l o g y h a d l i t t l e i n f l u e n c e on t h e r e s u l t s of the tes ts , and t h e sma l l

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 on the 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

e r ro r s .

B a s e d on t h e c h l o r i d e d i f fu s ion r e s u l t s in t h i s s tudy , t he c a l c u l a t e d v a l u e s

for t he t o r t u o s l t y f a c t o r (3) fel l m the r a n g e 0.24~).40 Thin r a n g e of 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 for t he 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 or g r a n u l a r softs.

ACKNOWLEDGEMENTS

T h i s r e s e a r c h was s p o n s o r e d by the 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 of th i s a r t i c l e do n o t

n e c e s s a r i l y r e f l e c t t h e v i e w s of t h e A g e n c y , n o r does m e n t m n of t r a d e 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 to 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 of L o n g B e a c h , C a l i f o r n i a , for a f e l l o w s h i p in 1985 1987 w h m h

h e l p e d to s u p p o r t t h i s w o r k In p a r t i c u l a r , t he e f for t s of Mssrs . F r e d D o n a t h ,

G e o f f M a r t i n , and H u d s o n M a t l o c k a re a p p r e c m t e d .

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

272

Desaulmers, D E, Cherry, J A and Fritz, P , 1981 Origin, age and movement of pore water m argillaceous Quaternary deposits at four sites m southwestern Ontario J Hydrol, 50 231-257

Desaulnlers, D E , Cherry, J A and Fritz, P , 1982_ Origin. age and movement of pore water m clayey Pleistocene deposits in south-central Canada In E C Perry and C W Montgomery (Editors), Isotope Studies m Hydrogeologlc Processes Northern Ilhnols Unlv Press, Dekalb, I1, pp 45 55

Desaulmers, D E , Cherry, J A and Glllham, R W, 1984 Hydrogeologlc analysis of long term solute migration m thick clayey Quaternary deposits Proc Int Symp Groundwater Resources Utlhzatlon and Contaminant Hydrogeology, Montreal, Quebec, May 1984, Int Assoc Hydrogeol, 2 349 356

Desaulmers D E, Kaufman. R S, Cherry, J A and Bentley, H W, 1986 ~7C1 35C1 variations in a diffusion-controlled groundwater system Geochlm Cosmochlm Acta, 50 1757-1764

Domenico P A, 1977 Transport phenomena in chemical rate processes in sediments Annu Rev Earth Planet Scl, 5 287 317

Drever, J I , 1982 The Geochemistry of Natural Waters Prentice-Hall, Englewood Cliffs, NJ , 388 pp

Duursma, E K , 1966 Molecular diffusion of radioisotopes m lnterstltml water of sediments Proc Symp Disposal of Radioactive Wastes into Seas, Oceans, and Surface Waters Vienna, 16 20 May, IAEA, Vienna, pp 355 371

Ellis, J H, Barnhlsel, R I and Phdhps, R E , 1970 The diffusion of copper, manganese, and zinc as affected by concentration, clay mineralogy, and associated anions Proc Soil Soc Am, 34 866-870

Farrah, H and Plckermg, W F , 1977 Influence of clay-solute mteractmns on aqueous heavy metal ion levels Water, Air Sod Pollut , 8 189-197.

Farrah, H and Pmkermg, W F, 1978 Extraction of heavy metal ions sorbed on clay Water, Air Soft Pollut , 9 491 498

Freeze, R A and Cherry, J_A, 1979 Groundwater Prentice-Hall, Englewood ChiTs, NJ, 604pp_ Frost, R R and Griffin, R A, 1977 Effect of pH on adsorptmn of copper, zinc, and cadmium from

landfill leachate by clay minerals J Environ Scl Health, A12(4, 5) 139-156 Glllham, R W, Robin, M L J , Dytynyshyn, D J and Johnston, H M, 1984 Diffusion of nonreactive

and reactive solutes through fine-grimed barrier matermls Can Geotech J , 21 541 550 Goodall, D C and Qmgley, R M, 1977 Pollutant migration from two samtary landfill sites near

Sarnla. Ontario Can Geotech J , 14:223-236 Griffin, R A and Jurmak, J J , 1973 Estimation of actlwty coefficients from the electrical conduc-

tlvlty of natural aquatic systems and soil extracts Soil So_, 116 26-30 Griffin, R A, Cartwrlght, K , Shlmp, N F , Steele, J D, Ruch, R R., White, W A, Hughes, G_M and

Gdkeson, R H, 1976 Attenuation of pollutants in mumclpal landfill leachate by clay minerals, Part 1 Column leaching and field verification Ill Geol Surv, Enwron_ Geol Notes, 78, 34 pp

Grim, R E, 1953 Clay Mineralogy_ McGraw-Hill, New York, NY, 384 pp Hlllel, D, 1980 Fundamentals of Soil Physics Academic Press, New York, NY, 413 pp_ Johnson, R L, Cherry, J A and Pankow, J F , 1988 Diffusive contaminant transport in natural

clay a field example and lmpllcatmns for clay-hned waste disposal sites Environ Scl Technol, 23 34(~349

Klm, B M and Amodeo, P A, 1983. Calcmm sulfide process for treatment of metal-containing wastes Environ Progr , 2- 17~180

Lerman, A, 1978 Chemical exchange across sediment-water interface Annu Rev Earth Planet S c l , 6 281 303

Lerman. A, 1979 Geochemical Processes Water and Sediment Environments John Wiley and Sons, New York, NY, 119pp

Lerman, A and Tamguchh H, 1972 Strontmm-90-- dlffusmnal transport m sediments of the Great Lakes J Geophys Res, 77 474-481

LL Y -H and Gregory, S, 1974 Dlffusmn of runs m sea water and in deep-sea sediments Geochlm Cosmochlm Acta, 38:703 714

Manheml, F T, 1970 The diffusion of runs m unconsohdated sediments Earth Planet_ Scl Let t ,

273

9:307-309 McDuff, R E and Morel, F M , 1973 Descmptlon and use of the chemical eqmhbrmm program

REDEQL2 (updated July, 1975). W_M. Keck Laboratory of Environmental Engineering Science, Cahfornla Inst i tute of Technology, Pasadena, CA, Tech Rep EQ-73-02_

Mlddleton, A C and Lawrence, A W, 1977 Kinetics of microbial sulfate reduction J , Water Pollut Control Fed, 49 165~1670

Myrand, D., Glllham, R W_, Cherry, J A and Johnson, R , 1989 Diffusion of volatile orgamc compounds m na tura l clay deposits Dep Ear th Scl, Umv Waterloo, Waterloo, Ont , Canada (m prep_)

Nye, P .H, 1979 Dlffumon of ions and uncharged solutes m soils and soil clays Adv. Agron, 31 225-272_

Olsen, S_R and Kemper, W D. 1968 Movement of nut r ients to plant roots Adv Agron, 20 91 151 Page, A L , Miller, R H and Keeney, D R (Editors), 1982 Methods of Soil Analyms, Par t 2-

Chemical and Microbiological Properties Am Soc_ Agron and Soil Scl Soc Am, Madison, WL 2nd ed, l159pp

Perkins, T K and Johnston, O C 1963 A revmw of diffusion and dispersion m porous media Petrol_ Eng J , 3 70-84

Porter, L K, Kemper, W D, Jackson, R D and Stewart, B A, 1960 Chloride dlffumon m soils as influenced by moisture content Proc , Soil Scl Soc Am, 24 400~403

Qmgley, R M , Crooks, V E and Fernandez, F , 1984 Engineered clay hners (an overvmw report) Preprmts of papers presented at the Seminar on the Demgn and Constructmn of Mumclpal and Industrml Waste Disposal Facilities, June 6-7, Toronto, On t , pp 115-134

Qmgley, R M, Yanful, E K and Fernandez, F_, 1987 Ion transfer by diffusion through clayey barriers In R D Woods (Editor), Geotechmcal Practice for Waste Disposal ASCE Spec Publ , 13 137 158

Rao, P S C, 1974 Pore geometry effects on solute dispersion m aggregated soils and evaluation of a predmtlve model Ph D Thems, Umv Hawan, Honolulu, HI, 195pp

Roblson, R A and Stokes, R H, 1959 Electrolyte Solutions, Butterworths, London, 2nd ed, 559pp Rowe, R K, 1987 Pol lu tant t ranspor t through barriers In_ R D Woods (Editor), Geotechmcal

Practice for Waste Disposal, ASCE Spec Publ , 13 15~181 Rowe, R K and Booker, J R, 1984 The analyms of pol lutant migrat ion m a non-homogeneous soil

Geotechmque, 34' 601-612 Rowe, R K and Booker, J R , 1985 1-D pol lutant m~gratmn m soils off imte depth J Geotech Eng ,

ASCE, 111 479~499_ Rowe, R K . Caers, C_J and Crooks, V E , 1985a POLLUTE 3 3, 1-D pol lutant mlgratmn through

a non-homogeneous soft Univ Western Ontario, London, Ont , Rep SACDA 84-13, July Rowe, R K, Caers, C J and Crooks, V E , !985b Pol lu tant mlgra tmn through clay soils Proc , l l t h

Int Conf on Soil Mechamcs and Foundat ion Engineering, San Francisco, Cahf , pp 1293-1298 Sawyer, C N and McCarty, P L , 1978 Chemistry for Environmental Engineering McGraw-Hill,

New York, N Y, 532 pp Shackelford, C D, 1988 Dlffusmn of lnorgamc chemical wastes in compacted clay Ph D Thesm,

Umv Texas, Austin, TX, 449pp Trmgel, E K, 1980 At tenua tmn by softs of selected potential contaminants from coal conversmn

facflitms A h te ra ture revmw Oak Ridge National Laboratory, Oak Ridge, TN, ORNL/TM-7249, 48 pp,

U S Environmenta l Protect ion Agency, 1987 Batch-type adsorptmn procedures for estimating sml a t tenua t ion of chemmals Draft Technmal Resource Document for Pubhc Comment, EPA/530- SW-006 (NTIS PB87-146-155), Cincinnati , OH, 179pp

Wilson, A H., 1948 A dlffusmn problem m whmh the amount of diffusing substance is fimte - - I PhHos Mag . Ser 7, 39 4~58