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.
0169-7722/89/$03 50
© 1989 E l s e v i e r S c i e n c e P u b l i s h e r s B V
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.
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