Chapter 41
Microscale Processes in Porous Media
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Transport of Chlorinated Benzenes in Porous Aggregates 1
Roger C. Bales and James E. Szecsody
Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721
Sorption and desorption of chlorinated benzenes were investigated in a series of column experiments using surface-modified silica of known chemical composition. The resulting breakthrough curves were fit to equilibrium (two-parameter), first -order (three-parameter), and mobile-immobile region (four parameter) one -dimensional advection, dispersion and retardation mathematical models. Slow sorp tion and desorption, evidenced by tailing of the breakthrough curves, was attributed primarily to slow binding and release rather than diffusion through immobile liquid or diffusion through an organic phase. An equilibrium model could be used to fit breakthrough curves with slow sorption/desorption, but the magnitude of the result ing dispersion coefficient includes effects of both media-specific intra-agregate transfer and sorbate/sorbent-specific binding/release processes. Using the first-order model with independently determined dispersion coefficients gave afittedfirst-order rate coefficient for media- and sorbate/sorbent-specific processes. Comparison of first-order model results from particles with different geometries and experiments at different temperatures suggested that release of sorbates from strong binding sites was the rate-limiting desorption step. The binding involved strong van der Waals interactions, as would be found in many natural waters. The additional parameter provided by the mobile-immobile model could not be physically defined in the experimental system studied, and provides no additional insight for interpreting microscale sorption-desorption processes. The same lack of physical definition for additional parameters should apply to many similiar solute-transport situations.
The rates of microscale processes involved in sorption and desorption of organic solutes in subsurface media, together with time scales for advection and dispersion, determine whether equilibrium or nonequilibrium descriptions can be used for transport modeling. Diffusion through immobile fluid (i.e. intra-aggregate diffusion), transport through a bound organic phase, or binding/release (Figure 1) can contribute to slow sorption and desorption. Resistances to sorption in both subsurface and chromato graphic media have also been described in terms of film resistance, intraparticle diffusion, and physi cal or chemical adsorption (1,2). The governing equation for one-dimensional solute transport in a porous media with both mobile and immobile regions and reversible sorption in both regions is (3) : Current address: Battelle, Pacific Northwest Laboratories, P.O. Box 999, Richland, W A 99352 0097-6156/90/0416-0526$06.00/0 © 1990 American Chemical Society
Melchior and Bassett; Chemical Modeling of Aqueous Systems II ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
41.
BALES & SZECSODY
ac
Microscale Processes in Porous Media
dC:
e
ds
2
dS:
e
ac
527
dc
e
e
-3
where C and C are the solute concentrations (pg cm ) in the mobile and immobile regions respec tively; S and S- are the respective bound concentrations (pgg ); 0 and 0 are the volume fractions of the mobile and immobile liquid regions, p is the dry bulk density (g cm ) of the porous media, / is the fraction of sorbent in the mobile region; D is the longitudinal hydrodynamic dispersion coefficient (cm s ); and u is the average interstitial velocity (cms ). Diffusion through the immobile region is described as slow mass transfer between mobile and immobile water. The solute concentrations in the two regions are related by: e
t
-1
e
t
e
t
-3
b
2
-1
-1
e
dC: dS: e +p (l-/)-^- =a (C -C ) L
i
s
6
e
e
(2)
i
-1
where a , the mass transfer coefficient (s ), depends on both the solute diffusion coefficient and sor bent geometry (4). The relation can also be formulated with a diffusion model for planar, rectangular, spherical or cylindrical geometries {5}. At equilibrium, the sorbed and aqueous concentrations in each region are related by: e
S=K C
(3)
p
3
_1
where K is the equilibrium partition coefficient (cm g ). Transport through a bound organic phase can be formulated in a similar manner: p
p - ^ • = a .(A C -S ) b
|
p
i
(4)
i
where α,· is the mass transfer coefficient between water and the bound organic layer. For kinetically limited binding and release the governing equation is:
_1
where kf and k are thefirst-orderforward and reverse rate coefficients (s ), respectively. In terms of the dimensionless variables and parameters of Table I, equation (1) becomes: b
ac,
ac
ι
2
2
a c\
ac,
where the dimensionless parameters are retardation factor (/?), Peclet number (P) and mobileimmobile fraction parameter (β). For the equilibrium model C - C > Considering a single step of Figure 1 to be rate limiting, equations (2), (4) and (5) can each become, in dimensionless form: x
ac (l-β)*
2
2
= a>(C -C ) 1
2
(7)
where ω is the dimensionless mass-transfer coefficient. Analytical and numerical solutions for various boundary conditions can be found in the literature. The purpose of the work reported in this paper is to investigate sorption/desorption rates in well-characterized model systems and distinguish physical versus chemical processes that determine the degree of equilibrium versus non-equilibrium behavior. METHODS Column experiments consisted of feeding a KC1 solution containing an organic contaminant into a 1.0 cm by 14 cm column packed with silica or bonded silica until breakthrough occurred, then feeding a lower conductivity, contaminant-free solution until all of the contaminant was removed from the column. The organic solutes used were chlorobenzene (CLB), 1,4-dichlorobenzene (DCB), 1,2,4trichlorobenzene (TCB), 1,2,4,5-tetrachlorobenzene (TeCB) and pentachlorobenzene (PeCB). A l l experiments were done under saturated conditions. The resulting breakthrough curves were then
Melchior and Bassett; Chemical Modeling of Aqueous Systems II ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
528
CHEMICAL MODELING OF AQUEOUS SYSTEMS II
evaluated using the above models and sorption parameters (R, Ρ, ω, β) estimated. Sorbents were porous aggregates of silica, which in most cases had been partially coated with an aliphatic ( C C , or C ) or aromatic (phenyl) organic group. Organic modifiers were chosen to simulate portions of natural organic matter that are important in the sorption of the hydrophobic compounds. The experi mental procedure has been described previously (6). lt
8
18
Table I. Model parameters and dimensionless variables Model
Ζ
Ρ
tu
X
uL
L
L
D
