Environ. Sci. Technol. 1991, 25, 1237- 1249
(93) Mingelgrin, U.; Gerstl, Z. J.Environ. Qual. 1983, I , 1-11.
Received for review August 14,1990. Revised manuscript received February 22,1991. Accepted March 14,1991. This research was funded by the U S . Environmental Protection Agency's Office
of Exploratory Research through Grant R813844. T h e manuscript has not been subjected to E P A review and therefore does not necessarily reflect their views. Additional funding from the American Water Works Association (Abel Wolman Fellowship Fund) and the ARCS Foundation of Northern California is also gratefully acknowledged.
Long-Term Sorption of Halogenated Organic Chemicals by Aquifer Material. 2. Intraparticle Diffusion William P. Bail"
Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina 27706 Paul V. Roberts
Department of Civil Engineering, Stanford University, Stanford, California 94305 The rate of sorptive uptake of tetrachloroethene (PCE) and 1,2,4,5-tetrachlorobenzene(TeCB) was studied on sandy aquifer material from Borden, ON, by use of a batch methodology designed to accurately measure sorption over long equilibration periods. Measured rates of uptake were interpreted with an intraparticle diffusion model and diffusive rate constants were determined for different size fractions of the Borden solids as well as with pulverized material. In general, measured rates were quite slow in comparison with previously reported results in other systems. The rate constants for TeCB were consistently lower than for PCE, with inverse correlation between observed rate constants and equilibrium distribution coefficients, consistent with a concept of retarded intraparticle diffusion. Good model fits with the coarsest size fractions and dramatic increases in rate with particle pulverization suggest that sorption occurs throughout the grain volume and that particle radius may be the appropriate length scale for diffusion. Based on measured particle size and independent estimates of porosity and internal retardation, effective pore diffusion coefficients are estimated to be roughly 2-3 orders of magnitude lower than bulk aqueous diffusivities, consistent with the low porosity of the calcareous rock fragments studied and an additional 3- to 20-fold rate reduction due to constrictive effects of pore size. Interpretations of results assuming intraorganic matter diffusion are also presented and discussed. Introduction
The fate of organic contaminants in groundwater and surface water is directly affected by sorptive interactions with soils, sediments, and aquifer solids. Most current transport and degradation models account for sorption by assuming an equilibrium distribution of contaminant, but there is a growing body of evidence that sorption and desorption may not reach equilibrium within time scales characteristic of solute transport or degradation. Such rate limitations can influence contaminant transport in the subsurface and may potentially hinder remediation efforts, whether such remediation is attempted through vapor extraction, groundwater extraction and treatment ( I ) , or in situ biological degradation (2, 3). For better understanding and prediction of organic chemical fate and transport, accurate models are required not only for estimating the extent of sorption at equilibrium, but also for estimating the rate at which contaminants sorb to and desorb from the solid matrix. Evidence for nonequilibrium transport of contaminants has been documented in a number of field-scale ground0013-936X/91/0925-1237$02.50/0
water systems (4-7). For example, field results from a major transport experiment in Borden, ON, have suggested that sorption/desorption rate limitations may have played an important role in organic solute transport at that site ( 4 , 8, 9). Although field results alone do not provide sufficient information to separate potential effects of grain-scale rate processes from those that might result from field-scale heterogeneities (9, IO), recent laboratory research has shown significantly slow rates of sorption and desorption at the particle scale. This research is briefly cited under Background and has been more extensively reviewed elsewhere (11-14). Long-term sorption experiments have been conducted with two halogenated organic chemicals and aquifer solids from the Borden field site. As discussed in the first paper of this two-part series (15),equilibrium sorption of tetrachloroethene (PCE) and 1,2,4,5-tetrachlorobenzene(TeCB) required contact times that were significantly longer than is usually allowed in batch and column studies. Accurate quantification of sorption with the Borden material therefore required long periods of solid/solute contact and careful attention to experimental technique. Paper 1 described the equilibrium distribution of solutes and the experimental methods used. In this paper, we describe experiments specifically designed to evaluate the rate at which the sorption equilibrium was approached. The rate data are analyzed by use of an intraparticle diffusion model, and the modeling results are interpreted in the context of alternative mechanisms for slow diffusive uptake. Background
Sorption of dissolved solute by a solid matrix, whether as adsorption to mineral surfaces or partitioning with nonaqueous organic phases, requires the transfer of solute from bulk solution to sites of immobilization. Regarding suspended particles in a batch reactor, resistance to such mass transfer may stem from transport across a fluid boundary layer external to the particle (external mass transfer), from diffusion to internal sites of the immobile phase (intrasorbent diffusion), or from rate limitations of the sorption process itself (chemical kinetics). For porous or solid sorbents, these processes are generally perceived as occurring in series, although the order of the last two processes will depend upon the nature of the diffusive process-Le., aqueous- or sorbed-phase diffusion. For slow rates of observed uptake in batch systems, appropriate sample mixing will ensure that external mass transfer is rapid relative to the overall rate of uptake, except at very
@ 1991 American Chemical Society
Environ. Sci. Technol., Vol. 25, No. 7, 1991 1237
early times (when the driving force for intrasorbent diffusion is exceptionally high). For nonpolar organic chemicals, physical adsorption and partitioning to organic phases are the dominant processes and are believed to be rapid in comparison with time scales of solute transport. First-order rate models have been frequently used to describe sorption rate processes in transport experiments, but usually with the understanding that the first-order coefficients are approximations for physical diffusion into often undefined regions of solute immobilization. A number of investigators have invoked physical models of sorption nonequilibrium to interpret soil column studies, as reviewed elsewhere (12,16). One difficulty with such models has been an inability to describe the relevant length scale for diffusion. First-order rate models avoid the question entirely, whereas diffusive interpretations often assume flow channeling around undefined zones of aggregated material, with diffusive length scale as a model-fitting parameter. An additional difficulty arises if the time scale of sorption is much greater than that of column transport, since high rates of fluid flow in laboratory columns may preclude accurate measurement of sorption uptake rate (17). In batch systems, first-order models have also been used to describe sorption or desorption rates of organic chemicals, again with the explicitly stated understanding that intrasorbent diffusion was the most likely source of rate limitation (18-25). However, there have been relatively few batch soil sorption studies in which data have been directly interpreted by diffusion rate models. Spherical diffusion into soil particles has been assumed in some studies (26,27),and particle size was considered to be the relevant length scale for diffusion. Although the particle size distribution was explicitly considered in at least one study (26), particle size classes were not individually characterized or studied with respect to rate of uptake. In the present work, data were obtained for the sorptive uptake of halogenated organic chemicals (PCE and TeCB) by sandy aquifer material from the Borden site. Careful characterization of the well-defined size fractions allowed a more thorough consideration of potential diffusive mechanisms than in prior work, and the long-term nature of the studies made it possible to accurately quantify rates of uptake, even in certain sorbent/solute systems that were extremely slow to equilibrate. To our knowledge, batch measurement of diffusive rate parameters for such slowly equilibrating soil/water systems has not been previously reported. Theory The driving force for diffusion may be either the concentration gradient of solute in the porewater (pore diffusion), the concentration of sorbed solute on the pore walls (surface diffusion),or, for nonaqueous sorbing phases, the concentration of chemical in that phase. For transient conditions of uptake into a sorbent, mass balance considerations over a volume element of the porous sorbent can be combined with Fick's first law of diffusion to obtain p,(dq/dt) + ~i(dc/st)= c~D,V'(C)+ PaD,V2(q) (1) where D, is the effective pore diffusion coefficient and D, is the effective surface (or sorbed-phase) diffusion coefficient. Other abbreviations and symbols are given at the end of this paper. For the case of linear partitioning, reversible equilibrium within the pores, and spherical geometry, eq 1 can be rewritten as
dC/dt = (D,/r2) d / d r [ r z ( d C / d r ) ] 1238 Envlron. Scl. Technol., Vol. 25, No. 7, 1991
(2)
where the apparent diffusion coefficient is defined as Da
=
ciDp/(ci
+ PaKdi) + PaKdiDs/(Ci + PaKdi) (3)
where Kdi is the internal distribution coefficient, considering only the diffusively limited sorbed phase (i.e., solute mass sorbed to diffusively limited sites per unit mass of solids per unit intraparticle aqueous concentration). Solution of eq 2 for the boundary conditions appropriate to a batch reactor is described subsequently, under Model Simulation. Where diffusion of sorbed species is not believed to play an important role in the overall rate of uptake, a pore diffusion interpretation may be appropriate (26,28,29). With diffusion only in the aqueous phase, eq 3 simplifies to Da = Dp/[1 + (Pa/ci)Kdil (4a) where the denominator on the right-hand side can be equated to an internal retardation factor for intraparticle diffusion, Rint. That is Da = Dp/Rint (4b) On the other hand, one may assume that diffusion occurs predominantly in the sorbed phase (e.g., refs 27 and 30). In this case, and with linear partitioning and pa& >> ci, D, will be mathematically equivalent to D,. In the more specific case where diffusion is envisioned to occur through organic matter, the apparent (sorbed-phase)diffusivity will be related to an intraorganic matter diffusivity (e.g., refs 11, 12, and 31). In such a case, the relation between D, and & is less straightforward to predict (see Discussion). With the pore diffusion model (eq 4), it is important to recognize that Dp will be less than the bulk aqueous diffusivity in water (Db),since the diffusion model assumes simple geometries and straight diffusion paths, whereas real systems involve more tortuous pathways, dead-end pores and variability in pore diameter. In addition, for very small pore diameters, pore constrictivity will also play an important role (32,33).Following Satterfield et al. (32), we write the following expression for D,: Dp = (D,K,)/x (5) where K, is a constrictivity factor (51) and x is the tortuosity factor (21). Several theoretical models for determining the tortuosity factor have been proposed (34-36); van Brake1 and Heertjes (37) provided a good review of the theoretical prediction of tortuosity. Theoretically and experimentally proposed values in unconsolidated material generally range between 1.3 and 3. However, consideration of interconnectivity between random pores suggests a direct inverse relation between tortuosity and porosity (36),such that much higher values are predicted for systems with very low porosities (e.g., x = 100 for porosity of 0.01). In addition, dead-end pores and networking of nonuniform pore sizes can also reduce the measured value of effective diffusivity (38, 39). In practice, it is often impractical to separate the effects of K, and x in eq 5. Because of this, it is sometimes useful to define an effective tortuosity factor, xe, which also incorporates steric effects. Thus Dp = Db/Xe (64 Xe
=
x/K
(6b)
With respect to estimation of K,, Chantong and Massoth (33)have presented an empirical correlation, based upon measured diffusion of polyaromatic compounds in aluminas of known pore size. This correlation, developed for
solute/pore size ratios between 0.04 and 0.4, is in agreement with prior results (32,40) and is reproduced below: K , = 1.03 exp(-4.5 A) (7) where X is the ratio of critical molecular diameter (32) to pore diameter. The pore diffusion model (eq 4), if applicable, allows some degree of a priori prediction, based on solute diffusivity and hydrophobicity, combined with the measured sorbent characteristics of particle size and intraparticle porosity. For the aquifer solids used in this work, extensive mineralogical characterization has been conducted, and intraparticle porosities and surface areas have been directly measured by use of mercury porosimetry and nitrogen adsorption (41). Thus, relationships between xe and porosity could be explored. For the Borden solids, very high values of xe were anticipated, due to low intraparticle porosity and possible steric hindrance in microporous regions. However, independent estimation of K , was not possible-the location of sorption capacity as a function of pore size is unknown and measured pore sizes [on dried and evacuated samples (41)Jmay not accurately reflect the aqueous pore volume, as potentially affected by watersolvated organic matter in pore spaces. If intraorganic matter diffusion is believed to be the rate-controlling mechanism, independent estimation of rate parameters is still more difficult. As reviewed elsewhere (11, 42), rates of solute diffusion in organic polymers can vary over several orders of magnitude and will be a function of the nature and extent of polymer cross-linking, as well as the concentration, molecular size, and chemical interaction of the diffusing molecule. Since very little is known about the nature of solute diffusion in natural organic matter, a priori estimation of intraorganic matter diffusivity is quite difficult. Moreover, available methods do not allow a determination of the precise size and location of the organic phases in natural solids ( 4 0 , and with the Borden material, partitioning to organic phases may not account for all of the observed sorption (15). Nonetheless, it is useful to consider the observed rate data in the context of an intraorganic diffusion mechanism. In particular, the relative effects of solute size and hydrophobicity can help reveal the nature of the diffusive process, and particle size effects can provide information about the relevant length scale for diffusion.
Experimental Materials and Methods Sorbates and Sorbents. Selection of sorbates was described in paper 1(15). Briefly, tetrachloroethene (PCE) was selected because of its relevance to the Borden field experiment and its demonstrated resistance to transformation over long time periods in soil/water systems. 1,2,4,5-Tetrachlorobenzene(TeCB) is similarly resistant to degradation and was selected for study in order to evaluate the effect of sorption strength on rate of uptake. TeCB has an octanol/water partition coefficient roughly 100 times higher than that of PCE, and TeCB’s equilibrium distribution coefficient (Kd)with fractions of Borden aquifer material is roughly 40 times higher (15). Sorbents used in this work were size fractions of sandy aquifer material, as described in ref 15. As described there and elsewhere (13,41,43), the solids were obtained from the Borden, ON, field site and carefully size fractionated and divided into subsamples by sequential riffle splitting, thus minimizing variability in solid composition among experimental samples (13). Pulverized Borden material was obtained by grinding aliquots of a given size fraction of solids for 1min in a tungsten/carbide shatterbox (13, 41).
Analytical Methods. 14C-Labeledsolute was used for all studies, with liquid scintillation counting of aqueous samples. Scintillation counting times were adjusted to ensure that counting error (2a) was less than 2% of the total count whenever concentrations of radiolabeled solute were determined. Extensive measures were taken to ensure radiochemical purity of the PCE and TeCB spike solutions. These measures, and the methods used for the analysis of solute concentration and radiochemical activity, have been described in ref 15. Batch Sorption Methodology. The objective of the sorption experiments was to determine the relative distribution of solute between the aqueous and sorbed phases, both at equilibrium and as a function of time. Samples used for the rate interpretations described here were treated identically with the longer term samples used for evaluation of equilibrium sorption (15). Briefly, a bottle-point sorption measurement was made using flamesealed ampules. Sorbed-phase concentrations were determined by difference, based on sampling of the aqueous phase and calculation of mass lost to headspace or glass surfaces. The latter were found to be proportional to aqueous concentration and were determined directly from blank samples (containing no soil). Samples were continuously mixed for the first 3 days and intermittently mixed thereafter. Continuous mixing was initially at 12 rpm and was reduced to 2 rpm after the first day. Intermittent mixing consisted of 5 min of 2 rpm rotation, with increasingly longer periods between mixing (13). External mass-transfer rates under the intermittently mixed conditions were shown to be sufficiently rapid as to not affect observed uptake rates (13). Spiking and sampling of the shorter term samples was identical with that described for the long-term samples (15), with the exception that samples taken within less than 8 h of spiking were filtered rather than centrifuged, since centrifuged samples experienced an approximate 45-min time delay between cessation of mixing and sampling of the aqueous phase. Filtering of samples involved withdrawing an aqueous aliquot (containing small amounts of suspended fines) into a 5-mL glass syringe, attaching a 25-mm stainless filter assembly with an 0.45-pm silver membrane filter (Millipore Corp., Bedford, MA), expeling air and the first 2 mL of filtered water to waste, and expressing the remaining 1-1.5 mL of filtered water directly into scintillation fluid for subsequent determination of 14C activity. This process took 1-3 min, such that uncertainty with regard to the time of solid/water contact was at most 20% (15-min samples), and generally much less. Recoveries with filtration were 93.2 f 1.5% and PCE losses to the headspace and apparatus (X in ref 15) averaged 1.01 f 0.24 g/(g/mL) for the filtered samples, vs 0.77 f 0.16 g/(g/mL) for centrifuged samples (13). Table I shows the sorbent/sorbate systems and the range of solid/liquid ratios (m8/ V,) used in the rate work, as well as the equilibrium distribution coefficients, Kd (13, 15). The solid/liquid ratio did not affect the observed Kd in these studies (13). Also shown in Table I is the particle size range of each sorbent, and the range of ultimate fractional uptakes, F, that would be observed in the samples if all had been allowed to proceed to equilibrium. These parameters are important to rate modeling and their independent estimation is addressed further in the sections that follow.
Data Analysis and Model Simulation Data Analysis. Sorbed-phase concentrations (9) and apparent distribution coefficients (KdaPP)were determined for all samples, as already described for equilibrium samEnviron. Sci. Technol., Vol. 25, No. 7, 1991 1238
Table I. Sorbent/Solute Systems Studied size fractiona
size range,* mm
solute
A. bulk solids B. -12+20 C. -20+40
