Environ. Sci. Technol. 1992, 26, 1417- 1427
Gerba, C. P.; Bitton, G. In Groundwater Pollution Microbiology; Bitton, G., Gerba, C. P., W.;Wdey-Interscience: New York, 1984; pp 67-70. Matthess, G.; Pekdeger, A.; Schroeter,J. J. Contam. Hydrol. 1988,2, 171-188. Lawrence, J. R.; Delaquis, P. J.; Korber, D. R.; Caldwell, D. E. Microb. Ecol. 1987, 14, 1-14. Bales, R. C.; Hinkle, S. R.; Kroeger, T. W.; Stocking, K.;
Gerba, C. P. Environ. Sci. Technol. 1991,25, 2088-2096.
Received for review November 11, 1991. Revised manuscript received March 25, 1992. Accepted March 27, 1992. Any use of trade, product, or firm names is for identification purposes only and does not constitute endorsement by the US.Geological Survey.
Use of a Reactive Surface-Diffusion Model To Describe Apparent Sorption-Desorption Hysteresis and Abiotic Degradation of Lindane in a Subsurface Material Cass T. Mlller' and Joseph A. Pedlt
Department of Environmental Sciences and Engineering, CB 7400, 106 Rosenau Hall, University of North Carolina, Chapel Hill, North Carolina 27599-7400 Desorption hysteresis has been reported frequently in the literature, with several theories advanced to explain the cause of this phenomenon. Several of these theories hypothesize that desorption hysteresis is an experimental artifact. Batch experiments were performed to observe sorption-desorption and transformation of the solute lindane in systems that included a subsurface sand material. Results of these experiments were interpreted with a diffusion and reaction model. Methods were developed to isolate and determine model parameters from experimental data. Rates of dehydrochlorination were determined for lindane in solution and solid phases. A pseudo sorption-desorption equilibrium experiment was performed by allowing 720 h for attainment of sorption equilibrium and 384 h for attainment of equilibrium for each of three desorption steps-longer than most experiments of a similar nature have been allowed to equilibrate. The pseudoequilibrium data showed marked hysteresis. A surface-diffusion model, which accounted for solute degradation from the solution and solid phases, was calibrated with sorption rate data. The model was verified with desorption rate data. Model predictions of the pseudo sorption-desorption experiment showed that slow sorption-desorption rates explained most of the apparent hysteresis.
Introduction Many common subsurface contaminants undergo multiple reactions, such as sorption, desorption, volatilization, biological degradation, and abiotic degradation, in addition to the normal transport processes of advection and hydrodynamic dispersion (1-6). Accurate description of solute concentration distributions in the solution, solid, and vapor phases of a subsurface environment as a function of time is a desirable goal, but accurately making such predictions-even in laboratory systems-has proven difficult. Uncertainty exists in the fundamental understanding of each of the above-noted processes, and the common existence of subsurface heterogeneity contributes further difficulties with the construction of models for predicting contaminant fate and transport in the subsurface environment. This paper describes experimental results, mathematical model development, and model predictions of experimental data for multiple reaction systems comprised of a subsurface material and the solute 7-hexachlorocyclohexane 0013-936X/92/0926-1417$03.00/0
(lindane). This work examines the level of prediction possible for describing the rate of solute desorption and the extent to which slow rates of desorption may contribute to the often-observed desorption hysteresis phenomenon.
Background A substantial literature has developed on fluid flow and contaminant transport in groundwater systems; comprehensive reviews have been published annually (7-11). Of the significant body of literature that exists, sorption processes, desorption processes, and lindane behavior in the environment are areas most applicable to the investigation summarized herein. Sorption. Considerable advancements have been made in the understanding of sorption processes over the last decade. Primary areas of advances have been in understanding fluid, solute, and solvent properties that affect sorption equilibrium; in understanding rates at which sorption occurs and factors that affect such rates; in development of models to simulate sorption processes; and in theoretical and simulation results that have elucidated conditions under which various transport and sorption characteristics are important. While a linear sorption equilibrium relationship is a common assumption in the literature, a significant body of evidence has been accumulated that shows that nonlinear sorption equilibrium is a common occurrence for a variety of solutes in natural systems (5,12-17). This nonlinear equilibrium has been described frequently using the Freundlich equilibrium model, for which even small deviations from linearity (e.g., a Freundlich exponent of 0.8) can lead to significant variations in the predicted transport of a contaminant in the environment when compared to linear equilibrium models (18,19).However, most modeling approaches continue to rely on linear descriptions of equilibrium (2&28), sometimes by restricting experimental and modeling investigations to low solute concentrations (17,29). For many environmental systems, the assumption of linear local equilibrium for solute distribution between the solid and solution phases has been common practice within the last decade (2,30-33).This approach has been based upon the assumption that time scales for advective and dispersive transport in natural systems are much larger than time scales over which sorption and desorption occur. However, significant evidence has been accumulated which
0 1992 American Chemical Society
Environ. Sci. Technol., Vol. 26, No. 7, 1992
1417
shows that sorption occurs at rates that are sufficiently slow to render the local equilibrium assumption inappropriate for many systems (13, 14, 17, 18, 29, 34-39). Most sorption rate models developed and applied to date can be divided into several categories: first-order rate models and two-site rate models (18, 28, 39-43); pore; models diffusion models ( 17 , 2 0 , 2 1 , 2 9 ) surface-diffusion (44-46); or combined pore and surface-diffusion models (47-50). The various classes of diffusive transport models differ in the controlling mechanism for solute movement within a solid particle or aggregate of solid particles. Ball and Roberts (51) provide a good review of diffusive transport processes in natural solids and polymers. While the current consensus in the literature is that slow rates of sorption are a result of a diffusive process (13-15, 18, 36, 37, 511, considerable uncertainty exists as to the dominant mechanism for sorption and the appropriate form of the model to describe this process. Recent fundamental work has shown that both intraparticle diffusion ( 17, 29, 52) and intraorganic matter diffusion (26) are important mechanisms. More mechanistic work is needed in this regard. Desorption. Investigators have observed for nearly 2 decades that desorption of organic solutes from natural solids frequently display a hysteretic or history-dependent path (53). That is, sorption and desorption equilibrium relationships depicted as solid-phase concentrations as a function of solution-phase concentrations are nonsingular, and desorption equilibrium relationships are dependent upon the maximum concentration achieved during the sorption process. Several theories have emerged as potential explanations for nonsingular desorption: (1)solute degradation or loss during the course of an experiment; (2) slow rates of desorption; (3) sorption to nonsettling particles; (4) presence of competing solutes; (5) change in sorbent characteristics as a function of time; and (6) formation of site-specific solute-solid bonds (54,55). A popular explanation for desorption hysteresis is that the rate of desorption is sufficiently slow such that equilibrium does not exist between the solution and solid phases after a desorption step. An apparent hysteresis would be observed, assuming equilibrium is achieved during the sorption phase of an experiment, but equilibrium is not achieved during desorption steps. Several studies have suggested this explanation of nonsingular sorption-desorption (55-61),but a detailed, systematic study of this explanation for a degrading solute has not been reported in the literature. Lindane Behavior. A significant literature on the behavior of lindane in the natural environment has been developed over the past 4 decades, with much of this literature summarized in a thorough recent review (62). Lindane has been shown to sorb to natural solids, degrade abiotically, biodegrade aerobically, and biodegrade anaerobically. Factors affecting the sorption and desorption of lindane in solution-solid systems have been investigated for more than 30 years (63-68),and vapor-phase diffusion and sorption of lindane to natural solid materials have been investigated far more than 20 years (69-72). Results show that the organic carbon content of the solid phase is an important factor affecting the extent of sorption (14,64, 65,67),and system pH and cation-exchangecapacity have little affect on the extent of sorption to the solid phase (63, 67, 68). The thermodynamics of the sorption-desorption process have been investigated by varying system temperature (66, 68, 70, 72) with results that depend upon the solid phase investigated. Sorption of lindane to natural solid materials 1418
Environ. Sci. Technol., Vol. 26, No. 7, 1992
Table I. Lindane Properties source molecular formula molecular mass, g/mol density, g/cm3 melting point, "C boiling point, "C aqueous solubility, mg/L vapor pressure, atm H,,atmm3/mol 1% KO,
Eastman Kodak Co. C6H6Cb 290.83 1.87 112.5
323.4 7.3 7.33 x 10-8 2.92 X lo* 3.61
has been found to be nonlinear at equilibrium and describable with the Freundlich model (36, 65, 66, 68, 73). Sorption rate investigations have shown a direct relationship between the fraction of organic carbon and the time required to approach equilibrium (36, 64), and lindane sorption has been found to persist for more than 100 h (14, 68). The abiotic dehydrochlorination of lindane, an E2 reaction, has been known to occur for more than 40 years (74,75). The dehydrochlorination rate is first order with respect to the hydroxide ion concentration and first order with respect to the lindane concentration, or second-order overall. These early studies showed that lindane is converted first to y-pentachlorocyclohexene (y-PCCH) and ultimately to primarily 1,2,4-trichlorobenzene. The ratelimiting step in the sequential elimination reactions has been assumed to be the first step: the conversion of yhexachlorocyclohexaneto r-PCCH (74). It has also been found, using a polarographic method, that the rate constant for conversion of yPCCH to y-tetrachlorocyclohexene (yTCCH) is approximately the same as the rate constant of the first elimination step-the conversion of y-hexachlorocyclohexane to yPCCH (75). Biodegradation of lindane has also been documented in the literature. Aerobic degradation using lindane as a sole carbon source was found to occur readily in the individual presence of eight bacteria and three fungi species (76). Anaerobic and faculative microorganisms were found to readily degrade lindane (77). The primary degradation product found under anaerobic conditions was y-TCCH. A similar rapid degradation of lindane to yTCCH was observed under anaerobic incubation with Clostridium sphenoides (78),although under alkaline conditions dehydrochlorination of lindane to y-PCCH was also observed. Methods Materials. Water used throughout the experiments was distilled and deionized by a Corning AG-11 still and Corning Mega-Pure System D1 deionizer. Chemicals added to distilled and deionized water to make a buffered solution for the experiments included sodium azide (0.005 M), sodium tetraborate (0.005 M), and calcium chloride (0.005 M). Azide was added to inhibit biological activity, thus reducing the potential for biodegradation of the target compound. The lack of biodegradation was noted in a confirmatory study by substituting 100 mg/L of mercuric chloride in the buffer solution in place of sodium azide, performing a sorption rate study, and observing nearly identical resulta for solution-phase lindane concentrations as a function of time. Hydrochloric acid was used to adjust the borate buffer to a pH of 8.4 f 0.02; buffering was employed to maintain constant abiotic degradation rates. Calcium aided in the separation of particles from solution during centrifugation. The organic solute y-1,2,3,4,5,6-hexachlorocyclohexane was used for all studies. The physical and chemical properties of lindane are summarized in Table I (62,791.
Lindane is characterized as moderately lipophilic, based upon the octanol-water partition coefficient (KDw); nonvolatile, based upon the Henry's constants (Hc);and slightly polar. Lindane was introduced into the buffer solution using a methanol carrier solvent. Methanol solutions of lindane ranged in concentration from 40 to 100 g/L, thus methanol concentrations in the buffer solution were below M. Methanol has been found to have no measurable effect on sorption at such low concentrations (80). A single subsurface material (Wagner) was used for all studies. The Wagner material was collected from a gravel pit, at a depth of about 25-m below ground surface. The collected material was air dried and then sieved to remove grains 1 2 mm in diameter. The solid material was characterized by grain-size distribution (median grain size 0.43 mm), uniformity (uniformity coefficient 2.71), pH (8.13), and density (2.68 g/ cm3) (81). The total organic carbon content of the Wagner material was 0.08% (standard deviation of 0.01% for 10 samples) when analyzed by using a persulfate oxidation technique (82) and an 0.1.Corporation Model 700 TOC analyzer. The results of these analyses show that the Wagner material is a uniform fine sand with a low organic carbon content. Rate Studies. The following procedure was used for preparation of the bottle-point rate studies: 1. Predetermined masses of subsurface material were placed into 40-mL Kimax glass centrifuge bottles, correct to f10 mg. 2. The solid material in the bottles was prewetted with the buffer solution (pH 8.4) and allowed to hydrate overnight. The volume of prewetting solution depended on the solid quantity and the solid to solution ratio for the experiment. The actual volume of prewetting solution was determined by measuring mass and converting to volume, assuming the density of water to be 0.9976 g/cm3 at 23 "C. 3. Buffer solution spiked with lindane was added to the bottles the following day. The spiked buffer was delivered in a volume that gave the target solids ratio and in a concentration that gave the desired initial solute concentration. Bottles were sealed with Teflon-lined caps. A control study performed in similar bottles, with no solids present and at pH 6.9, showed that no detectable loss of lindane occurred in bottles sealed with Teflon-lined caps over a 2018-h period. 4. The initial solute concentration in the bottle readors (C,) was found by measuring concentration of the spiked buffer and correcting for dilution by the prewetting. A known volume of the spiked solution was extracted with hexane, which contained heptachlor as an internal standard. Gas chromatographic analysis was used to determine the analyte concentration. Because quantifying the initial solute concentration was important to the studies, at least six samples were collected and analyzed to determine C, for each bottle-point rate study. 5. The bottle-point reactors were constantly mixed at 23 f 2 "C on a tumbler and removed in duplicate for times of equilibration that ranged from about 1 to 2115 h. 6. Bottles removed were centrifuged for 0.5 h at 1500g to separate the solution and solid phases. A small volume of the supernatant was pipetted from each sample and extracted with hexane, which contained heptachlor as an internal standard. Equilibrium Studies. The procedure for preparing equilibrium studies was nearly identical to that for rate studies. Solids were weighed into centrifuge bottles, hydrated with buffer overnight, and filled with the appro-
priate volume of spiked solution the following day. Bottles were sealed and tumbled constantly at 23 f 2 "C; all bottles were removed simultaneously for analysis. Equilibrium studies covered an initial concentration range of more than 2 orders of magnitude with at least two replicate bottles at each concentration. The range was chosen such that the equilibrium concentrations covered the range of concentrations expected in the rate studies. Desorption Studies. Desorption studies were performed using similar procedures as detailed for the bottle-point rate and equilibrium studies in the previous two subsections. For desorption equilibrium studies (1)sorption was allowed to proceed for a time believed to be sufficient to approach equilibrium conditions; (2) phase separation was performed by centrifugation; (3) 25 mL of the solution phase was removed and replaced with solute-free solution; (4) the solute concentration in the solution phase removed was measured; (5) the bottles were allowed to reequilibrate, which resulted in solute desorbing from the solid phase; and (6) steps 2-5 were repeated two additional times. Desorption rate studies were performed using a procedure similar to the procedure used to perform desorption equilibrium experiments. The main differences were that identical initial solids and solute concentrations were used for all bottles and that following the sorption equilibration step, seta of bottles (two replicate samples) were removed after varying lengths of desorption time. Sorbent Extraction. Extraction of the sorbent was performed periodically during rate and equilibrium studies to investigate mass balance in the systems. After the solution-phase sample was removed from the centrifuge bottle, additional solution phase was quantitatively removed, leaving a known, small volume (-10 mL) of solution in the bottle with the solid material. One drop of hydrochloric acid was added to the bottle to reduce pH, thereby minimizing further degradation by dehydrochlorination. An equal volume fraction mixture of acetone and hexane (20 mL total) was then added to reduce partitioning to the solid phase for the system relative to the pure water system. It has been shown that use of acetone as a cosolvent can reduce partitioning to the solid phase (80). The slurry was tumbled typically for 48 h and centrifuged, and 10 mL of the hexane phase was removed and replaced with 10 mL of hexane. Six additional, similar phaseseparation and extraction steps were performed over a period of about 216 h. The removed hexane fractions were combined and brought to a known volume. A portion of the hexane was analyzed for solute concentration. Analytical Methods. Gas chromatographic (GC) analysis was performed on a portion of the hexane fraction using a Hewlett-Packard 5890A GC equipped with an electron capture detector, a HP 3396A integrator, and an automatic injector. A 10-m HP-1 column (Hewlett-Packard, Avondale, PA) was used, which had a 0.53-mm4.d. and a 2.65-pm cross-linked methyl silicone gum phase. The packed column injector temperature was 250 "C; analysis was isothermal with an oven temperature of 225 "C and a detector temperature of 300 "C. Makeup gas flow was approximately 60 mL/min, and carrier gas flow was 5 mL/min. Individual sample runs were about 3-min each. Each sample and standard were injected twice, and the ratio of analyte peak area to internal standard peak area was calculated. A multipoint calibration was used, which was fit with a second-order polynomial. Modeling Methods. For the general case of a batch reactor, a material balance expression may be expressed as Environ. Sci. Technol., Vol. 26, No. 7, 1992
1419
_dt where C is the solution-phasesolute concentration (Mc/L3), t is time (T), M, is the mass of the solid phase in the batch reactor, V is the volume of the solution phase (L3),q is the solid-phase mass-averaged solute concentration (MJM,), the subscript srp indicates sorption and rxn indicates solute reaction in the solution phase, and r(C) is a general solute source function. For the case of a pseudo-first-order degradation reaction in the solution phase and no solute source other than the initial condition, eq 1 becomes
_"---( ) v M, dq
dt
-k,C
srp
C(t=O) = c, (3) where k, is a pseudo-first-order solute degradation rate for solute loss in the solution phase (l/T). Sorption rates are often considered to be a result of a diffusive transport process (13,14,44,83, 84). Several types of diffusive transport processes are possible. One common type of diffusive model is a dual-resistance surin which sorption rates face-diffusion model (14,36,37,44) are represented as the result of a resistance due to diffusion through a boundary layer and diffusion radially along the solid surfaces within a spherical particle. Another potential diffusive transport resistance is pore diffusion, where the mechanism for transport is assumed to be diffusion within a liquid phase contained within the solid particle or aggregate of particles. Surface-diffusion models usually assume equilibrium between the sorbent and solution at the exterior portion of a particle, whereas pore-diffusion models usually assume equilibrium between the solid and solution phases at all locations within a particle. Combined pore and surface-diffusion models also exist (47). The appropriate diffusion model for sorption to natural solids has not been resolved. A general dual-resistance surface-diffusion model was used in this work, which may be incorporated with eq 2 to give (4)
and the companion solid-phase equation is
subject to kb
= -(C
- C,)
centration (MJM,) as a function of radial position r ( L ) , D, is a surface-diffusion coefficient ( L 2 / T ) k, , is a pseudo-firsborder solute decay coefficient for solute in the solid phase ( l / T ) , Kfis a Freundlich equilibrium model capacity constant [ ( M c / M , ) ( L 3 / M c ) band f ] , nf is a Freundlich equilibrium model intensity constant. A method of lines solution was used to solve the surface-diffusion model in a batch reactor by first converting eqs 5-9 to a set of ordinary differential equations in time using the Galerkin finite element method (46).The resulting set of ordinary differential equations was solved using an algorithm for stiff equations (85). Results Overview. The investigation of the long-term sorption-desorption phenomena of lindane to the Wagner material was complicated by the slow nature of the sorption and desorption process and by the degradation of lindane that occurred from the solution and solid phases at different rates. With respect to the surface-diffusion modeling framework previously presented, the behavior of lindane in batch reactor systems is a function of six unknown model parameters for a singular sorption-desorption relationship and eight unknown model parameters for a hysteretic sorption-desorption relationship (86).The unknown parameters for the singular equilibrium case are k,, k,, Kf, nf, kb, and D,. These parameters correspond to solute degradation parameters, sorption equilibrium parameters, and sorption rate parameters. For hysteretic desorption, two additional desorption parameters are needed. Only the singular case was considered in this work. The approach isolated subsets of these parameters in single types of experiments and tested the adequacy of the independently-determined parameters through the prediction of results from desorption rate experiments. Finally, after calibration and experimental validation, the model was used to evaluate the central issue: the importance of sorption nonequilibrium as a cause of apparent desorption hysteresis. Solution-Phase Degradation. Conventional bottlepoint methods were used to quantify the rate of abiotic degradation in the solution phase. This was accomplished by observing the disappearance of lindane as a function of time in a buffered solution that was devoid of solids. For this system, the general second-order relationship reduces to a pseudo-first-order model, described by eq 2 without sorption. Figure 1 shows the experimental data for the dehydrochlorination of lindane in a buffered system (pH 8.4) as a function of time and the pseudo-first-order model fit for k,. Experiments were performed for initial concentrations that ranged from 102 to 5048 pg/L. The model was fit by nd
min (7) qr(O Ir IR,t = 0 ) = 0
(8)
where kb is a boundary-layer mass-transfer coefficient (LIT), R is the radius of the spherical solid particlesassumed constant (L),p is the macroscopic particle density of the solid phase (M,/L3),C, is the solution-phase solute concentration corresponding to an equilibrium with the solid-phase solute concentrtaion at the exterior of particle [i.e., qr(r=R)]( M c / L 3 )qr , is the solid-phase solute con1420
Environ. Sci. Technol., Vol. 26, No. 7, 1992
k,
n=l
[(cd,n - ~ r n , n ) / ~ m , n l z
(10)
where Cd,,is the experimental solute concentration (Mc/L3),C,,n is the model solute concentration (M,/L3) corresponding to data point n, and nd is the number of experimental points. The minimization process resulted l/h. in the estimate: k, = 1.23 X An solution-phase sample that showed marked solute degradation based upon GC screening was used to perform gas chromatograph/mass spectrometer (GC/MS) analysis. GC/MS analysis was performed using a VG 70-250 SEQ using both electron impact (30 eV) and negative ion chemical ionization methods. Results achieved with these analyses were consistent with results expected from sequential dehydrochlorination reactions. The main deg-
Table 11. Experimental Conditions
expt
tYPe
iso89-01 kin88-04 kin89-01 kin89-04 kin89-05 lindane6
equilibrium rate rate rate rate degradation
mass of solids, g
solution vol, mL
initial concn, wg/L
sorption time, h
desorption time, h
1-3 6 3 3 3
30.0 30.1 29.8 29.6 29.6 30.0
25-4542 1012 2333 2553 2553 102-5048
732 2115 1679
384/ea 813 1487
50
723
Table 111. Parameter Estimates
parameter
value
95% confidence interval
k* k, nr Kf Kf
1.23 x 10-4 7.48 x 10-5 7.42 X lo-' 4.23 X 10-1 5.65 X lo-'
kb
m
D,
5.29 X
lo-'
1.15 X 4.78 X 7.19 X 3.31 X 5.16 X
10-4-1.30 X 10-6-1.03 X lod 10-l-7.64 X lo-' 10-'-5.42 X lo-' 10-'-6.14 X lo-'
4.21
10-'-6.38
X
X
units
from expt
l/h l/h (g/g)(cm3/gY"' (g/g)(cm3/gY"' cm/h cm2/h
lo-'
lindane6 kin88-04 iso89-01 iso89-01 kin88-04, kin89-01 kin88-04, kin89-01
1 .oo ~
~
0
~
D0a t a0 Model
0.80
v)
0.60
I
' t1 o"o.90
.-+a,>
0
0.85
0.80
0.75
9,
1
0
S 0.40 a,
111:
0.20
'
I
I
I
I
I
400
800
1200
1600
2000
Time (hr)
0
400
800
1200
1600
2000
2400
Time (hr)
Figure 1. Solution-phase llndane dehydrohalogenation as a function of time.
Figure 2. Solute mass normalized by initial solute system mass as a functlon of time and phase for experiment kln88-04.
radation peak was consistent with T-PCCH,while positive confirmation of 1,2,4-trichlorobenzenewas achieved for a secondary degradation peak. Solid-Phase Degradation. It is well-known that the rate of abiotic degradation may vary as a function of whether a solute is present in the solution phase or sorbed to the solid phase. Experimental determination of the solid-phase solute degradation rate is complicated because sorption, solution-phase degradation, and solid-phase degradation occur simultaneously. While it is possible to fit a model simultaneously for several parameters, the significance of the resultant parameter values is difficult to assess. For this reason, a method was devised to estimate the solid-phase degradation rate independently of all other parameters in the reactive surface-diffusion model, except the previously determined solution-phase degradation rate. The solid-phase degradation rate, k,, was determined using data from a bottle-point rate study, which was performed over a period of 2115 h (kin88-04). Extraction measurements of the mass of solute on the solid phase as a function of time were made during this experiment. The experimental data allowed calculation of the solution-phase solute mass, the solid-phase solute mass, and the total
system solute mass as a function of time. These data are shown in Figure 2 for experimental conditions that are summarized in Table 11. Model parameters are summarized in Table 111. The procedure used to determine k, was (1)fit an empirical model to the solution-phase solute concentration data as a function of time; (2) derive an expression for total system solute mass as a function of time using the empirical model from step 1; and (3) estimate k, by using the solid-phase solute extractions and the results from step 2. The sole purpose of this exercise was to determine the rate of solid-phase degradation. The empirical model used to accomplish this purpose is incidental and should not be confused with or linked to the mechanistic surface-diffusion model described previously and used later in this work. The empirical model used to describe the solution-phase solute concentration as a function of time was
C , = a. + alexp(-plt) + a2 exp(-p2t) (11) which was restricted to require a match of the initial starting concentration by
Envlron. Scl. Technoi., Vol. 26, No. 7, 1992
1421
r
where C, is the model-predicted solute concentration (M,/L3),and (YO, a1 and a 2 (Mc/L3)and P1 and P2 (1/T) are empirical constants. A four-parameter fit was accomplished for the objective function
noom0 A
(Cm,n - Cd,n)'
~
.
~
* + i t
nd
C
min
Subset 1 Subset 2 Subset A 3 + Sorption Data
0 0 0 0 0
A
(13)
~1,a2,Pl,P2 n = l
0
n
where Cm,nis the solute concentration in the solution phase predicted by the empirical model (M,/L3),cd,n the solute concentration in the solution phase calculated from the experimental data (M,/L3),and C, is the initial solute concentration in the system (M,/L3). As may be noted from Figure 2, an accurate description of the solutionphase solute concentration data was obtained by using this method, while the values of the coefficients used to fit the solution-phase data were a. = 127 pg/L, a1 = 425 pg/L, a2= 460 pg/L, P1 = 1.17 X 10-1 l/h, and PZ= 6.09 X low3 l/h. An analytical solution for the total mass of solute in the system as a function of time may be derived by first noting M , = VC M,q (14) where M, is the mass of solute in the system (MJ. If solute mass is lost from the system as a result of pseudo-firstorder degradation from both the solution and solid phases, the system solute mass loss rate may be expressed as dM,/dt = -k,VC - k,M,q (15)
+
Combining eqs 14 and 15 yields dM,/dt = (k, - k,)VC - k&fc
(16)
Combining eqs 11 and 16 by substituting the expression for C, in place of C gives dM,/dt = (k, - ka)V[ao + a1 exp(-Plt) + a2 exp(-Pd)l - k,M, (17) which may be solved, giving M , = M, exp(-k,t) + V(k, - k,) ([l - exp(-b,t)] X (adk,) + [exp(-Plt) - exp(-k,t)l (al/(k, - PI)) + texp(-P~t) - exp(-k,t)l (a2/(k, - Pz))) (18) where M , is the total solute mass predicted by the model (M,), and M, is the initial solute mass in the system (M,). Experimental data on total solute mass, Md, were used along with the empirical model given by eq 18 to satisfy the objlective function nd
min C k, n=2
Wm,n
- Md,n)'
(19)
where Mm,nand Md,n are the solute mass predicted by the model, eq 18, and calculated from the experimental data for data point n, respectively (A&). The minimization l/h, procedure yielded a best-fit value for k, = 7.48 X which is about 613' % of the solution-phase degradation rate. This estimate of k, is an upper limit, since an extraction efficiency of 100% was assumed. A slower rate of abiotic degradation for solute on the solid phase compared with solute in solution is consistent with previous experimental results for base-catalyzed reactions (87). This result follows from the negative charge associated with natural solids, in the near neutral pH range in which this experimental work was performed, and the corresponding lower hydroxide ion concentration near the surface and within the solid phase. Pseudo Sorption-Desorption Equilibrium. A pseudo sorption-desorption equilibrium experiment was performed by using methods previously described. The 1422
Envlron. Sci. Technol., Vol. 26,
No. 7, 1992
5- Y
t I
A
4
P
-
I
Figure 3. Pseudo sorptlon-desorption equilibrium data for experiment iso89-0 1.
sorption step was performed for 720 h, followed by three consecutive desorption steps in which 384 h was allowed for equilibration during each step. Consecutive desorption data was collected on three subsets of data, each subset consisting of eight replicates having similar initial conditions. The data collected from this experiment are shown in Figure 3. These data are called pseudoequilibrium data since the change in solution-phase solute concentration with respect to time at 720 h was greater than could be explained based upon solute degradation alone (Figure 2). The sorption-desorption data shown in Figure 3 are markedly hysteretic. Data shown in Figure 3 were corrected for solute transformations that occurred in both phases during the course of the experiment. The correction was performed by (1)analyzing the data assuming that the independently measured solution-phase degradation rate was an upper bound and the independently measured solid-phase degradation rate was a lower bound; (2) estimating the time-averaged fraction of the solute in the solution and solid phases over the course of the pseudoequilibrium experiment as a function of the solids concentration, for a mean initial concentration; (3) computing a weighted degradation rate based upon the results from step 2; and (4) correcting all data based upon a mass of solute computed to remain in the system after accounting for decay. The overall system degradation rate used to correct the l / h for a solids concentration of 1g/30 data was 1.1 X mL and 1.0 X lo4 l / h for a solids concentration of 3 g/30 mL. The total amount of solute degraded during the sorption-desorption pseudoequilibrium experiment of 1872 h was approximately 18% of the initial solute mass. If the overall rate of transformatian in the system was the same as the solution-phase degradation rate, 79% of the solute mass would have remained in the system at the end of the experiment. If the overall rate of transformation in the system was the same as the solid-phase degradation rate, 87% of the solute mass would have remained in the system at the end of the experiment. Because the fraction of mass lost was small, the approximate correction procedure was concluded to be adequate. Equilibrium parameters Kf and nf cannot be determined from the sorption data shown in Figure 3, because these data are known not to be at equilibrium. However, preliminary numerical experiments with the reactive sur-
1
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i
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0.20
0.00
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800
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1600
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Time (hr) Figure 4. Experimentaldata and model fR for sorption rate experiment kin88-04.
facediffusion model indicated that an estimate of Kf would be much more sensitive to nonequilibrium conditions than nf. Therefore, the Kf estimated from the data in Figure 3 should be viewed as a lower limit of the true equilibrium value of Kf, and the estimated nf is similar to that which would be estimated for a system at equilibrium. This assumption will be evaluated in the discussion that follows. Least-squares regression in log-log space was performed to estimate nf (0.742). Sorption Rates. The previously described steps yielded independent estimates for three of the six parameters needed in the reactive surface-diffusion model: k,, k,, and nf. The remaining model parameters are K,, kb, and D,-the sorption capacity constant, and both sorption rate parameters. Recall that no physical or mechanistic significance was ascribed to the empirical fits of the sorption rate data used to determine the solid-phase degradation rate. Previous experimental work with similar materials (36, 37) found that boundary-layer mass-transfer resistance was an unimportant factor in determining the rate of sorption. That is, D, was sufficiently small that internal particle diffusion was the rate-determining step. Based upon this evidence, boundary-layer mass-transfer resistance was assumed negligible for the Wagner-lindane solid-solute pair. All simulations were performed by setting k b = lo3 cm/ h, which yielded simulation results indicative of the sorption process being rate limited only by surface diffusion. The remaining two parameters needed to specify the reactive surface-diffusion model, Kf and Os, were estimated simulataneously using two experimental sorption rate data sets (kin88-04 and kin89-01). The kin88-04 data set was used previously to determine the solid-phase decay rate. The parameter estimation performed can be summarized by
where ne is the number of the experiment, nne is the number of data points in experiment number ne, Cd,ne,n is the experimental solution-phase solute concentration corresponding to the ne experiment and the n point (Mc/L3),and is the modeled solution-phase solute
0.00
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'
400
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I
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Time (hr) Flgure 5. Experimentaldata and model fit for sorption rate experiment kin89-01.
concentration corresponding to the ne experiment and the n point ( M c / L 3 ) . Model predictions based upon results from the twoparameter minimization are shown along with the experimental data in Figures 4 and 5, where experimental conditions are summarized in Table I1 and model parameter values in Table 111. Examination of Figures 4 and 5 shows excellent agreement between model predictions and experimental data. Two features of the parameter estimates were noted: the derivative of the sum of squares for error, eq 20, was small with respect to the model parameters fit near the optimal parameter values; and the optimal parameter values were highly correlated. These features of the parameter estimation procedure suggest that model fits of a similar quality could be achieved with different sets of parameters. While a global minimum cannot be guaranteed, an exhaustive grid search in addition to the normal parameter estimation did not reveal any superior fit to the one reported. Desorption Rate Validation. The previous sections described a systematic experimental and modeling procedure used to establish estimates of unknown parameters present in the reactive surface-diffusion model. These estimates yielded accurate descriptions of the data sets used to estimate the parameters. This is a necessary but not a sufficient condition for model accuracy. To assess the adequacy of the model and the reasonableness of the parameters, desorption rate experiments were performed and model predictions were made based upon the independently-determined parameters in the reactive surface-diffusion model. The results of two desorption rate experiments and simulation predictions are shown by Figures 6 and 7, for experimental conditions that are summarized by Table 11. The difference between the two desorption simulations is that kin89-04 was allowed to sorb for 50 h before desorption was initiated and kin89-05 was allowed to sorb for 723 h before desorption was initiated. Review of Figures 6 and 7 shows a rapid decline in C/Co at the end of the respective sorption periods-a result of initiating the desorption phase as detailed in the Methods section. The hump in the desorption portion of Figure 6 is predicted accurately by the model. This hump is the result of the small amount of time allowed for sorption to occur before initiating desorption; which resulted in a large concentration gradient within the solid phase. When the Environ. Sci. Technol., Vol. 26, No. 7, 1992
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__ Fluid Phase
.............. Solid Phase Fluid o n d Solid Phases
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Time (hr) Flgure 8. Simulation prediction for long-term sorption-desorption and degradation dynamics using input parameters consistent with kin88-04.
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1
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Time (hr) Flgure 7. Experimentaldata and model prediction for desorption rate experiment kin89-05.
solution-phase concentration is lowered to initiate desorption, a negative concentration gradient forms near the outer edge of the particle. After a short period of desorption, the concentration gradient is again positive throughout the particle and sorption resumes. Results from the prediction of both desorption experiments were similar: simulated normalized solution-phase solute concentrations were typically within 2 % of the experimental data, with predicted solution-phase concentrations slightly higher than observed concentrations. The accuracy of these simulations suggests that the reactive surface-diffusion model was a reasonable predictor of the dynamics of solute reaction, sorption and desorption for the system investigated.
Discussion For a degrading solute in a batch reactor, a nonzero solute concentration equilibrium condition is never achieved. To demonstrate the predicted dynamics of the system, a long-term simulation was performed by using input conditions consistent with rate experiment kin88-04 1424
Environ. Sci. Technol., Vol. 26, No. 7, 1992
and the model parameters estimated and previously described. The results of this simulation, shown in Figure 8, are a prediction of a monotonic decrease with time in the total system mass and solution-phase solute mass. The solid-phase solute mass is predicted to increase rapidly initially, to reach a maximum value after about 1000 h, and to decrease with time thereafter. Although not shown, the model predicts that all solute would decay from the solution and solid phases as time tends to infinity. An important assumption made in estimating the reactive surface-diffusion model parameters was than nf could be determined accurately from a pseudoequilibrium experimental data set that was only allowed to sorb for 732 h. To test this assumption, simulations were performed by using initial conditions identical to those that existed in the pseudoequilibrium experiment (iso89-01). Model parameters used in the simulations were the final set of estimated reaction and surface-diffusionmodel parameters. The procedure used involved (1)performing sorption rate simulations for each of the initial conditions used in iso89-01; (2) using rate model simulation results at varying times as input to a least-squares regression in log-log space to estimate Kf and nf; and (3) noting the trends in predicted values of Kf and nf relative to the assumed true values as a function of time. The results of this procedure are shown by Figure 9. Three interesting features are evident from this analysis. First, the assumptions of nf being insensitive and Kf being relatively sensitive to time was accurate. Second, the use of pseudoequilibrium data collected after 732 h was adequate to predict accurately the value of nf. Third, Kf increases as a function of time up to about 6000 h, at which time the regressed value exceeds the true value of Kp This is so because solute degradation from the solution phase is faster than solute degradation from the solid phase and at long times desorption is occurring from the solid phase because of the difference in degradation rates between the solution and solid phases. The final test of the model, and the major objective of this investigation, was to evaluate the effect of slow sorption rates as an explanation for apparent desorption hysteresis. To accomplish this objective, rate model simulations were performed, using conditions that mimicked the experimental conditions of the pseudoequilibrium sorption-desorption experiment (iso89-01). Results of
translate to a slower rate of desorption as the solutionphase solute concentration decreases, thus more apparent desorption hysteresis. Future work should compare results from pore- and surface-diffusion models and perform experiments to discriminate between the two mechanisms. Another possibility is that due to correlation in the joint K f D , parameter estimates, an alternative set of parameters (a higher Kf and a lower D,)would give similar fits to the sorption rate data and would predict greater hysteresis. Methods for providing better estimates of these parameters are not readily apparent at present. Conclusions
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Time (hr) Flgure 9. Freundlich equilibrium model parameters from repeated regression of rate model predictions as a function of time. ,
, ,,,,,,,
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A systematic approach was developed to determine independently parameters needed to describe solute sorption and degradation in batch reactor systems, within the structure of a reactive surface-diffusion model. The formulated model was challenged for validation by predicting experimental results in which sorption, desorption, and solution- and solid-phase decay were operative using the independently-determined parameters. Good agreement was attained for these validation experiments, however slightly less desorption occurred than was predicted. The model was then used to analyze a set of pseudoequilibrium data in which 732 h was allowed for equilibration of a sorption step and 384 h was allowed for each of three desorption steps. The model explained most of the observed desorption hysteresis. Errors between experimental data and model predictions were consistent for the desorption rate validation and the sorption-desorption pseudoequilibrium studies. These results suggest that either a systematic error existed in the model used for these studies-an error that is consistent with a porediffusion mechanism-or a parameter correlation prevented optimal estimation of model parameters for predicting apparent desorption hysteresis.
10000
(PLg/l)
Figure 10. Rate model simulation of pseudoequllibrium sorption-desorption data from experiment iso89-01.
these simulations are compared to the experimental data from iso89-01, corrected to eliminate the effects of solute degradation using the independently-determined degradation parameters. Figure 10 shows that most of the apparent desorption hysteresis is explained by the rate model. Therefore, rate effects are an important contributor to apparent desorption hysteresis for the lindane-Wagner system investigated in this work. Even accounting for rate effects, some apparent desorption hysteresis remains. This observation is also consistent with the desorption rate experiments and simulations in which a lower solution-phase solute concentration was observed than predicted. Many possible explanations for this observation are possible. One notion is that the reactive surface-diffusion model is not the appropriate rate model. A reactive pore-diffusion model may be a more appropriate choice. A reactive pore-diffusion model is typically formulated, assuming an equilibrium condition at all locations of contact between the solution and solid phases within a particle. Due to the favorable nature (nf < 1) of the equilibrium model, this would
We are indebted to Angela Levert, formerly a student at the University of North Carolina and presently with ERM,Southwest in Houston, TX, for her assistance with the experimental work, and to Dean Marbury for his assistance with the GC/MS analysis. Registry No. y-1,2,3,4,5,6-Hexachlorocyclohexane,58-89-9. Literature Cited (1) McCarty, P.L.;Reinhard, M.; Rittman, B. E. Enuiron. Sci. Technol. 1981,15, 40. (2) Roberts, P.V.; Reinhard, M.; Valocchi, A. J. J. Am. Water Works Assoc. 1982,74, 408. (3) Mackay, D.M.; Roberts, P. V.; Cherry, J. A. Enuiron. Sci. Technol. 1985,19,384. (4) Sawhney, B. L.;Brown, K. Reactions and Mouement of Organic Chemicals in Soib; Soil Science Society of America, Inc., and American Society of Agronomy, Inc.: Madison, WI, 1989. (5) Weber, J. B.;Miller, C. T. In Reactions and Mouement of Organic Chemicals in Soils; Sawhney, B. L., Brown, K., Eds.; Soil Science Society of America, Inc. and American Society of Agronomy, Inc.: Madison, WI, 1989;pp 305-334. (6) Cheng, H.H.Pesticides in the Soil Environment; Soil Science Society of America, Inc.: Madison, WI, 1990. (7) Miller, C. T. J . Water Pollut. Control Fed. 1987,59,513. (8) Miller, C. T; Comalander, D. R. J. Water Pollut. Control Fed. 1988,60, 961. (9) Miller, C. T.;Mayer, A. S. J . Water Pollut. Control Fed. 1989,61, 954. (10) Miller, C. T.; Mayer, A. S. Res. J . Water Pollut. Control Fed. 1990,62, 700. (11) Miller, C. T.; Rabideau, A. J.; Mayer, A. S. Res. J . Water Pollut. Control Fed. 1991,63, 552. Environ. Sci. Technol., Vol. 26, No. 7, 1992
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(12) Rao, P. S. C.; Davidson, J. M. Water Res. 1979, 13, 375. (13) Karickhoff, S. W. J. Hydraul. Eng. 1984, 110, 707. (14) Miller, C. T.; Weber, W. J., Jr. J. Contam. Hydrol. 1986, 1, 243. (15) Bouchard, D. C.; Wood, A. L.; Campbell, M. L.; NkediKizza, P.; Rao, P. S. C. J. Contam. Hydrol. 1988,2, 209. (16) Piwoni, M. D.; Banerjee, P. J. Contam. Hydrol. 1989,4,163. (17) Ball, W. P.; Roberts, P. V. Enuiron. Sci. Technol. 1991,25, 1223. (18) Brusseau, M. L.; Rao, P. S. C. Crit. Rev. Environ. Control 1989, 19, 33. (19) Miller, C. T.; Pedit, J. A.; Staes, E. G.; Gilbertsen, R. H. Modeling Organic Contaminant Sorption Impacts on Aquifer Restoration. Report Number 246, Water Resources Research Institute: Raleigh, NC, 1989. (20) Wu, S.-C.; Gschwend, P. M. Environ. Sci. Technol. 1986, 20, 717. (21) Wu, S.-C.; Gschwend, P. M. Water Resour. Res. 1988,24, 1373. (22) Brusseau, M. L.; Jessup, R. E.; Rao, P. S. C. Water Resour. Res. 1989, 25, 1971. (23) Brusseau, M. L.; Jessup, R. E.; Rao, P. S. C. Water Resour. Res. 1990, 26, 165. (24) Ball, W. P.; Goltz, M. N.; Roberts,P. V. Water Resour. Res. 1991, 27, 653. (25) Brusseau, M. L.; Jessup, R. E.; Rao, P. S. C. Water Resour. Res. 1991, 27, 657. (26) Brusseau, M. L.; Jessup, R. E.; Rao, P. S. C. Environ. Sci. Technol. 1991,25, 134. (27) Brusseau, M. L. Water Resour. Res. 1991,27, 589. (28) Brusseau, M. L.; Larsen, T.; Christensen, T. H. Water Resour. Res. 1991, 27, 1137. (29) Ball, W. P.; Roberts, P. V. Enuiron. Sci. Technol. 1991,25, 1237. (30) Curtis, G. P.; Roberts, P. V.; Reinhard, M. Water Resour. Res. 1986,22, 2059. (31) de Marsily, G. Quantitative Hydrogeology: Groundwater Hydrology for Engineers; Academic Press: Orlando, FL, 1986. (32) Roberts, P. V.; Goltz, M. N.; Mackay, D. M. Water Resour. Res. 1986, 22, 2047. (33) Fetter, C. W. Applied Hydrogeology, 2nd ed.; Merrill Publishing Co.: Columbus, OH, 1988. (34) Karickhoff, S. W.; Morris, K. R. Enuiron. Toxicol. Chem. 1985, 4, 469. (35) Coates, J. T.; Elzerman, A. W. J. Contam. Hydrol. 1986, 1, 191. (36) Weber, W. J., Jr.; Miller, C. T. Water Res. 1988,22, 457. (37) Miller, C. T.; Weber, W. J., Jr. Water Res. 1988,22, 465. (38) Witkowski, P. J.; Jaff6, P. R.; Ferrara, R. A. J. Contam. Hydrol. 1988, 2, 249. (39) Weber, W. J., Jr.; McGinley, P. M.; Katz, L. E. Water Res. 1991, 25, 499. (40) Cameron, D. R.; Klute, A. Water Resour. Res. 1977,13,183. (41) Rao, P. S. C.; Davidson, J. M.; Jessup, R. E.; Selim, H. M. Soil Sci. SOC.Am. J . 1979, 43, 22. (42) N k e d i - k , P.; Biggar, J. W.; Selim, H. M.; van Genuchten, M. T.; Wierenga, P. J.; Davidson, J. M.; Nielsen, D. R. Water Resour. Res. 1984,20, 1123. (43) Lee, L. S.; Rao, P. S. C.; Brusseau, M. L. Enuiron. Sci. Technol. 1991, 25, 722. (44) Miller, C. T.; Weber, W. J., Jr. Ground Water 1984,22,584. (45) Jaff6, P. R.; Tuck, D. M. In Proceedings of the Ground Water Geochemistry Conference; National Water Well Association: Dublin, OH,1988; pp 429-444. (46) Pedit, J. A.; Miller, C. T. In Proceedings of the VII International Conference,Computational Methods in Water Resources; Volume 2, Numerical Methods for Transport and Hydrologic Processes; Celia, M. A., Ferrand, L. A., Brebbia, C. A., Gray, W. G., Pinder, G. F., Eds.; Computational Mechanics Publications: Southampton, U.K., 1988; Vol. 2, pp 293-298. (47) Crittenden, J. C.; Hutzler, N. J.; Geyer, D. G.; Oravitz, J. L.; Friedman, G. Water Resour. Res. 1986, 22, 271. (48) Hutzler, N. J.; Crittenden, J. C.; Gierke, J. S.;Johnson, A. S. Water Resour. Res. 1986, 22, 285. 1426
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(49) Fong, F. K.; Mulkey, L. A. Water Resour. Res. 1990, 26, 843. (50) Fong, F. K.; Mulkey, L. A. Water Resour. Res. 1990,26, 1291. (51) Ball, W. P.; Roberts, P. V. In Organic Substances and Sediments in Water: Volume 2, Processes and Analytical; Baker, R. A., Ed.; Lewis Publishers: Chelsea, MI, 1991;Vol. 2, pp 273-310. (52) Wood, W. W.; Kraemer, T. F.; Hearn, P. P., Jr. Science 1990,247, 1569. (53) Swanson, R. A.; Dutt, G. R. Soil Sci. SOC. Am. Proc. 1973, 37, 872. (54) Chang, S.-L. Sorption-Desorption of Diuron in Subsurface Systems: An Investigation of Desorption Hysteresis. M.S. TechnicalReport; University of North Carolina, Chapel Hilk 1989. (55) Pignatello, J. J. In Reactions and Movement of Organic Chemicals in Soils; Sawhney, B. L., Brown, K., Eds.; Soil Science Society of America, Inc. and American Society of Agronomy, Inc.: Madison, WI, 1989; pp 45-80. (56) Huang, J. C. J. Water Pollut. Control Fed. 1971,43,1739. (57) Corwin, D. L.; Farmer, W. J. Enuiron. Sci. Technol. 1984, 18, 507. (58) Isaacson, P. J.; Frink, C. R. Enuiron. Sci. Technol. 1984, 18, 43. (59) Jaff6, P. R. J . Enuiron. Sci. Health 1986, A21, 55. (60) Bouchard, D. C.; Lavy, T. L. J. Environ. Qual. 1985, 14, 181. (61) McCloskey, W. B.; Bayer, D. E. Soil Sci. SOC. Am. J. 1987, 51, 605. (62) Howard, P. H. Handbook of Environmental Fate and Exposure Data f o r Organic Chemicals, Volume 111, Pesticides; Lewis Publishers: Chelsea, MI, 1991. (63) Swanson, C. L. W.; Thorp, F. C.; Friend, R. B. Soil Sci. 1954, 78, 379. (64) Kay, B. D.; Elrick, D. E. Soil Sci. 1967, 104, 314. (65) Lotse, E. G.; Graetz, D. A.; Chesters, G.; Lee, G. B.; Newland, L. W. Environ. Sci. Technol. 1968, 2, 353. (66) Mills, A. C.; Biggar, J. W. Soil Sci. SOC.Am. Proc. 1969, 33, 210. (67) Adams, R. S., Jr.; Li, P. Soil Sci. SOC.Am. Proc. 1971,35, 78. (68) Boucher, F. R.; Lee, G. F. Environ. Sci. Technol. 1972,6, 538. (69) Ehlers, W.; Letey, J.; Spencer, W. F.; Farmer, W. J. Soil Sci. SOC.Am. Proc. 1969, 33, 501. (70) Ehlers, W.; Farmer, W. J.; Spencer, W. F.; Letey, J. Soil Sci. SOC.Am. Proc. 1969, 33, 505. (71) Guenzi, W. D.; Beard, W. E. Soil Sci. SOC.Am. Proc. 1970, 34, 443. (72) Spencer, W. F.; Cliath, M. M. Soil Sci. SOC.Am. Proc. 1970, 34, 574. (73) Miller, C. T.; Weber, W. J., Jr. In Proceedings 2nd International Conference on Ground Water Quality Research; University Center for Water Research, Oklahoma State University: Stillwater, OK, 1984; pp 47-49. (74) Cristol, S. J. J. Am. Chem. SOC.1947, 69, 338-342. (75) Nakazima, M.; Okubo, T.; Katumura, Y. Botyu-Kagahu 1949, 14, 10. (76) Tu, C. M. Arch. Microbiol. 1976, 108, 259. (77) Jagnow, 0.;Haider, K.; Ellwardt, P.-C. Arch. Microbiol. 1977,115, 285. (78) Heritage, A. D.; MacRae, I. C. Aust. J. Biol. Sci. 1979,32, 493. (79) Verschueren, K. Handbook of Environmental Data on Organic Chemicals, 2nd ed.; Van Nostrand Reinhold Co.: New York, 1983. (80) Nkedi-Kizza, P.; Rao, P. S. C.; Hornsby, A. G. Enuiron. Sci. Technol. 1985, 19, 975. (81) Black, C. A. Methods of Soil Analysis-Part I ; American Society of Agronomy: Madison, WI, 1965. (82) Ball, W. P.; Buehler, C.; Harmon, T. C.; Mackay, D. M.; Roberts, P. V. J.Contam. Hydrol. 1990,5, 253. (83) Wu, S.-C.; Gschwend, P. M. Environ. Sci. Technol. 1986, 20, 717.
Environ. Sci. Technol. 1992, 26, 1427-1433
Brusseau, M. L.; Rao, P. S. C. Chemosphere 1989,18,1691. Gear, C . W. Numerical Initial Value Problems in Ordinary Differential Equations; Prentice-Hall: Englewood Cliffs, NJ, 1971. Miller, C . T. Ph.D. Dissertation, University of Michigan, Ann Arbor, MI, 1984. Macalady, D. L.; Wolfe, N. L. Abiotic Hydrolysis of Sorbed
Pesticides. EPA-600/D-84-240;U.S. EnvironmentalPro-
tection Agency: Athens, GA, 1984. Received for review September 16, 1991. Revised manuscript received March 6,1992. Accepted March 26,1992. The research described in this paper was supported by Grant 14-08-0001G1484 from the Department of the Interior, U.S. Geological Survey, and the Water Resources Research Institute of North Carolina.
Fuel Rich Sulfur Capture in a Combustion Environment Erlc R. Lindgren and David W. Pershlng'
Chemical Engineering Department, University of Utah, Salt Lake City, Utah 841 12 D. A. Klrchgessner and D. C. Drehmel
U.S. Environmental Protection Agency, Research Triangle Park, North Carolina 27709
rn A refractory-lined, natural gas furnace was used to study fuel rich sulfur capture reactions of calcium sorbents under typical combustion conditions. The fuel rich sulfur species H2Sand COS were monitored in a near-continuous fashion using a gas chromatograph equipped with a flame photometric detector and an automatic sampling system which sampled every 30 s. Below the fuel rich zone, 25% excess air was added and the ultimate fuel lean capture was simultaneously measured using a continuous SO2 monitor. Under fuel rich conditions high levels of sulfur capture were obtained, and calcium utilization increased with sulfur concentration. The ultimate lean capture was found to be weakly dependent on sulfur concentration and independent of the sulfur capture level obtained in the fuel rich zone. Thus, for the sorbents used in this study, the high captures realized in the rich zone were lost in the lean zone. Introduction A major concern associated with the combustion of coal for heat and electricity is the emission of acid rain precursors, NO, and SO2. Dry, calcium-based sorbent injection is a potential method for reducing SO2emissions from existing coal-fired boilers. The calcium sorbents most frequently considered are calcium carbonate and calcium hydroxide, which upon injection into a furnace environment rapidly decompose to highly reactive calcium oxide. Ca(OH&) + heat CaO(s) + H 2 0 (1) CaC03(s) + heat CaO(s) + C02 (2)
--
It is generally assumed that the above calcination reactions occur with little change in the particle dimensions (2). Since the molar volume of CaO (16.9 cm3/mol) is less than the molar volume of CaC03 (36.9 cm3/mol) or Ca(OH)2 (33.1 cm3/mol), the CaO formed is greater than 50% porous and surface areas of 90 m2/g have been reported (3). Considerable study has been devoted to the fuel-lean SO2 reaction (1, 4, 5): CaO + SO2 + Y202 CaS04 (3) Since the molar volume of CaS04(52.2 cm3/mol) is greater than that of either parent material, the pore volume of the CaO will theoretically be filled before complete conversion to CaS04is reached. Thus, there is a theoretical basis for an upper limit on the fuel lean SO2capture, assuming no particle expansion during the short reaction times. Borgwardt et al. ( 2 , 4 )have shown that the important fuel rich sulfur capture reactions to be considered are
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0013-936X/92/0926-1427$03.00/0
--
CaO(s) + H2S CaS(s) + H 2 0 (4) CaO(s) + COS CaS(s) + COz (5) Cas is thermodynamically more stable at higher temperatures than is CaS04and Borgwardt et al. have shown the fuel rich reactions are kinetically faster than the fuel lean. Also, the fuel rich reactions should be less limited by intraparticle resistances because the molar volume of Cas (28.9 cm3/mol) allows for complete conversion of CaO to CaS before the initial void space is filled. Background The fuel rich reactions have not been as extensively studied as the fuel lean reaction, especially under combustion conditions. Most early kinetic studies of reactions 4 and 5 utilized microbalance techniques (6-9) where milligram quantities of relatively large particles were reacted in a bed. These studies indicated activation energies of 3-5 kcal/mol, which are typical of gas diffusion control and do not reflect the true chemical kinetics. The large particles that were typically used resulted in substantial intraparticle diffusion resistance, and even with small particles (8),agglomeration increases the effective particle size. Also, interparticle effects are not easily eliminated in a bed of solids because of the close proximity of adjacent particles. Borgwardt (2) used milligram quantities of well-dispersed, 2-pm CaO particles to study the kinetics of reactions 4 and 5 as a function of the CaO surface area. He found the activation energy of both reactions to be 31 kcal/mol. Attar and Dupuis (10) used a pulsed differential reactor and measured an activation energy of 37 kcal/mol for reaction 4. Extrapolating the results of these studies to higher temperatures indicates that high levels of sulfur capture may be obtainable in the fuel rich zone of a multistage pulverized coal burner provided the sulfur capture is not lost during the transition to fuel lean conditions. However, high-temperature study is required to verify this extrapolation. Zallen et al. (11)burned pulverized coal premixed with limestone and found staging increased sulfur capture with Utah coal, but the effect was less with western Kentucky coal. Freund and Lyon (12)found that mixing sorbent and coal produced poor results but that ion-exchangeable calcium in coal was much more effective in fuel rich sulfur capture. Freund (13)reacted dispersed 69-pm limestone and dolomite particles with H2S (1250 and 2600 ppm) in a tubular reactor at 1065 and 1320 "C and various levels of calcium availability (Ca/S = 1-4). The sulfur reductions
0 1992 American Chemical Society
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