Environ. Sci. Technol. 1998, 32, 1721-1726
Leach Models for Contaminants Immobilized by pH-Dependent Mechanisms BILL BATCHELOR* Civil Engineering, Texas A&M University, College Station, Texas 77843
A component-based leach model for describing leaching of hazardous contaminants that are immobilized by pH-dependent reactions is presented, and applications to environmental problems are described. The model describes simple chemical systems in which a solid phase provides acid-neutralizing capacity, and the contaminants are immobilized by precipitation or sorption reactions that are dependent on pH. Results of model simulations are related to predictions based on simple analytical leach models. Internal concentration gradients within the solid are predicted by the model, and their forms are used to explain how contaminants are immobilized and re-immobilization within the solid and how the concentration of acid in the leaching solution affects leaching of contaminants. Simulations show that the concentration of acid in the leaching solution affects leaching of contaminants in a complex manner that cannot be simply related to leaching of acid-neutralizing capacity. Even with these complex chemical interactions, the simulation results show that simple half-order models can be used to describe leaching if the observed diffusivity can be measured accurately. However, simulations show that conventional leaching tests such as the ANS 16.1 procedure are not likely to measure accurately the observed diffusivity when applied to contaminants that are effectively immobilized.
The assumptions made in developing leach models are critical to their validity and usefulness. The most common assumption in leach modeling is that transport is due to Fickian diffusion. A material balance for a mobile compound diffusing in one direction is
∂C ∂2C ) De 2 + R ∂t ∂x
Leaching models are important tools in evaluating the efficiency of immobilization by solidification/stabilization (s/s) treatment technologies. They can help identify leaching mechanisms by predicting behavior under different conditions such as found in various leach tests. They can provide methods for correlating leach data. They can support risk assessments for the disposal of treated wastes by estimating leaching of contaminants over long periods of time and under different environmental conditions. They may also be useful in helping to develop improved binder/additive formulations for s/s. The purpose of this paper is to present several leach models and to apply the models to investigate interactions among immobilization reactions and transport mechanisms that affect overall leaching of contaminants. The models that will be presented describe leaching of hazardous contaminants from materials treated by conventional s/s when the contaminants are immobilized by pH-dependent precipitation or sorption reactions. * Phone: 409-845-1304; fax: 409-862-1542; e-mail: bill-batchelor@ tamu.edu. 1998 American Chemical Society
(1)
where C is the concentration of mobile phase within solid (M/L3), De is the effective diffusivity (L2/T), R is the rate of transfer of compound from immobile to mobile phase, (M/L3 - T), t is time (T), and x is the distance into solid (L). Solution of this equation requires assumptions about boundary and initial conditions as well as the possible reactions. Simple assumptions for the boundary and initial conditions are an infinite bath (bath is large relative to solid so that concentration in bath does not change), an infinite solid (concentration in interior of solid does not change), and a homogeneous distribution of contaminant. Using these assumptions and the assumption that the contaminant does not react, eq 1 can be solved for the concentration gradient within the solid. The concentration gradient can be integrated to give the fraction of contaminant leached at any time (1):
( )
Mt 4Det ) M0 πLva2
0.5
(2)
where Mt is mass of contaminant leached at time t, (M), M0 is the mass of contaminant initially in solid (M), and Lva is the ratio of solid volume to external surface area exposed to bath (L). The assumption of no reaction is normally not valid. However, some analytical leach models can be developed to describe systems with simple reactions such as linear equilibrium sorption, precipitation/dissolution, and instantaneous reaction with a component leaching into the solid from the bath (2). They take the following form:
( ) (
Mt 4Dobst ) M0 πLva2
Introduction
S0013-936X(97)00747-5 CCC: $15.00 Published on Web 04/18/1998
Background
0.5
)
)
4(Dobs/De)th π
0.5
(3)
where Dobs is the observed diffusivity (L2/T) and ht is dimensionless time ) Det/Lva2 ( ). The observed diffusivity (Dobs) in eq 3 represents both chemical and physical factors that affect leaching, while the effective diffusivity (De) in eq 2 represents only physical effects such as the tortuosity of pores on diffusive transport. For the simple case of linear sorption, the observed diffusivity is equal to the effective diffusivity divided by a retardation factor that depends on the equilibrium coefficient for sorption. Similar proportionalities exist between Dobs and De for other types of immobilization reactions (3). Although simple analytical models can provide some useful information, they are not able to predict leaching in complex systems in which several components can determine porewater pH, which in turn affects contaminant mobility. Multicomponent leach models can be developed by solving a set of material balance equations for each chemical species. They can be simplified by adopting the concept of chemical components, such as used by chemical equilibrium programs such as MINTEQA2 (4). With these assumptions, a material balance on the system total concentration (solution phase VOL. 32, NO. 11, 1998 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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and solid phase) of a component can be expressed as follows (2):
∂Tss,i ∂2Ci ) De 2 ∂t ∂x
(4)
where Tss,i is the system total concentration of the ith component in solid and solution phases (mol/L3) and Ci is the concentration of the ith component in solution phase (mol/L3). The effect of components in the bath surrounding the solid is described by choice of boundary conditions. If an infinite bath is assumed, the concentrations in the bath and at the boundary of the solid are assumed to not change over time. If the bath is assumed to be finite, a differential boundary condition is specified to ensure that the increase in the amount of component in the bath is equal to the decrease in amount of component in the solid. The flux from the solid is described by Fick’s law:
Vbath
( )
∂Tss,i,bath ∂Ci ) ADe ∂t ∂x
x)0
(5)
where Vbath is the volume of bath surrounding solid (L3) and A is the external area of solid exposed to bath (L2). Note that there is no reaction term in eq 4, although reactions can occur. This is because the total concentration of the component is conserved by reactions. Note also that a component-based model does not require simulation of all chemical species that are present. Components such as sodium can be excluded when they do not significantly affect the components of interest. Therefore, the model will not maintain electroneutrality, because some compounds are not modeled. The problem is also simplified by assuming local chemical equilibrium, which will be valid for most materials treated by s/s under most circumstances. This assumption will be valid when reactions in the solid occur on time scales that are shorter than the time scale for diffusive transport out of the solid. The relative importance of these processes is described by the second Damko¨hler number. Appendix A (in Supporting Information) shows that the second Damko¨hler number for this system is equal to the ratio of the square of the pore length to the square of the pore radius. Reactions will usually occur at pore lengths substantially larger than the pore radius, resulting in Damko¨hler numbers much greater than 1.0. This means that the system is controlled by diffusion of the component out of the solid rather than reactions within the solid. However, this will not be true when leaching first begins and reactions occur very near the solid surface. Other reactions can occur over long time scales that can affect leaching behavior, such as those reactions that change the form of a solid phase to a less soluble type. If such changes can be predicted, they can be incorporated into the model by changing value of equilibrium coefficients over time. Models that describe leaching from wastes treated by s/s are examples of the general class of reactive transport models. A review of this type of simulation model has classified them in terms of the way the transport and reaction equations are solved (5). Some models solve the equations that describe chemical reaction and then solve the transport equations (6-15). Other models solve the equations for transport and reaction in one single step (16-22). Bishop and co-workers have developed and tested an analytical leach model that describes the effect of time-varying acid concentration on leaching (23-29).
Leach Models for PH-Dependent Immobilization Precipitation-Dissolution. A component-based numerical leach model has been developed to describe leaching when 1722
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FIGURE 1. Numerical simulations of ratio of observed diffusivity to effective diffusivity as function of concentration of acid in bath as compared to predictions by analytical models. contaminants are immobilized by pH-dependent reactions. The model solves eq 4 with a modified Crank-Nicholson algorithm (2) as described in Appendix B (Supporting Information). Concentrations of mobile components (Ci in eq 4) are calculated using simple chemical equilibrium models. These models consist of a set of nonlinear, algebraic equations that represent molar balance equations for each component and definitions of equilibrium coefficients. Details are given in Appendix C (Supporting Information). A simple model with three components (Ca2+, H+, Ac-) and six species (H+, OH-, Ac-, HAc, Ca2+, Ca(OH)2(s)) was used to investigate leaching of acid-neutralizing capacity (ANC). Substantially all ANC was supplied by calcium hydroxide, which served as a surrogate for calcium silicate hydratesthe major source of ANC in cementitious waste forms. The bath was assumed to contain different initial concentrations of acetic acid (HAc), and the solid was assumed to contain different initial concentrations of calcium hydroxide. No activity corrections were made. Initial and boundary conditions were taken to be the same as used for the model in eq 2, i.e., infinite bath and infinite and homogeneous solid. Effective diffusivities were considered constant for all components. Although there are variations in diffusivities among chemical species, the variation in effective diffusivities is small (factor of 2 or 3) as compared to the variation in observed diffusivities (orders of magnitude). The main limitations of this model are (a) simplified description of ANC of solid as single compound; (b) simple description of contaminant chemistry (only precipitation/ dissolution as hydroxide, no sorption, no complex formation, no activity corrections); (c) assumption of local equilibrium; (d) description of transport as total component rather than individual compounds. The simple descriptions of contaminant chemistry limit the ability of the model to predict leaching of specific chemical compounds, but they do not limit the ability of the model to describe the general behavior of chemical compounds during leaching. Figure 1 shows the results of applying this model to evaluate the effect of the concentration of acid in the bath on the observed diffusivity of ANC, represented by the calcium component. Results are presented in terms of observed diffusivities, because leaching of ANC was found to agree with eq 3; i.e., the fraction leached was proportional to the square root of time.
FIGURE 2. Dimensionless concentration profiles in solid for calcium and three target metals. Figure 1 shows that the numerical model agrees well with the two applicable analytical models. At high acid concentrations, the numerical model agrees with analytical models that assume leaching is controlled by the reaction of ANC with acetic acid that has leached in from the bath (3, 28). At low acid concentrations, the numerical model agrees with an analytical model that assumes that leaching is controlled by dissolution of a solid without reaction with other compounds (3). Figure 1 demonstrates the potential problem of extrapolating results of leaching tests conducted at high acid concentrations to predict leaching at low acid concentrations. It also indicates that leaching models based on reaction of ANC with acid (3, 28) will not be applicable to conditions at neutral to high pH where acid concentrations are low. The model was also applied to predict leaching of contaminants that could exist in a mobile form (M2+) and in an immobile form (M(OH)2(s)). Metals with different solubilities were simulated by assuming solid formation coefficients that ranged from 10-20 to 10-2. These metals were identified by the negative logarithm of their formation coefficient (e.g., MK20 for formation coefficient ) 10-20). The system total concentrations of the contaminant metals were set at 1 mM so that the assumption could be made that dissolution/precipitation reactions of the metal would not affect pH, which was controlled by calcium hydroxide (0.55.5 M). Figure 2 shows that sharp leaching fronts are predicted not only for the component that represents ANC (Ca) but also for the metals (MK2, MK8, and MK14). The dimensionless concentrations used in Figure 2 are the simulated concentrations divided by their initial concentrations. Such behavior has been described previously (30), and experimental verification of sharp pH gradients has been made (25, 26). The position of these secondary leaching fronts is determined by the solubility of the metal. Metals that are less soluble leach more slowly, so their secondary leach fronts are closer to the bath where the pH is lower. In Figure 2, two metals (MK8, MK14) have leach fronts that coincide. Note that the total concentration of the contaminants exceeds their initial concentrations (dimensionless concentrations greater than 1.0) at the leach front. The reason for this can be seen in Figure 3, which shows the simulated profiles for pH and concentrations (total and soluble) of one contaminant.
FIGURE 3. Concentration profiles for pH, soluble and total dimensionless concentration of a metal with formation coefficient of 10-14 (MK14). Figure 3 shows that the concentrations of the soluble contaminant metal are predicted to decrease in both directions from the maximum value observed at the secondary leaching front. This will cause the soluble metal to diffuse in both directions. The diffusion toward the interior of the solid leads to precipitation, which increases the concentrations of metal above initial values. Despite the complexity of contaminant behavior predicted to occur at the secondary leach front, leaching simulated by the numerical model always agreed with predictions of the simple half-order leach model (eq 3). This allowed characterization of leachabilty with the observed diffusivity. Substantial amounts of material can be leached as matrix species dissolve. This could lead to leached and unleached zones with different physical characteristics such as porosity. However, experimental results indicate that sharp differences in properties exist between leached and unleached zones (25, 26). This means that compounds that leach from the solid will be transported through a leached zone with relatively constant properties. The simulated effect of acid concentration on leaching of contaminant metals with different formation coefficients is shown in Figure 4. It shows that higher acid concentrations and smaller formation coefficients generally are predicted to result in more rapid leaching (higher observed diffusivities). However, the observed diffusivity of a metal is not simply related to its formation coefficient. For each acid concentration, there is a range of formation coefficients over which the observed diffusivity is independent of formation coefficient. Such behavior was seen in Figure 2 when two metals had simulated secondary leach fronts at the same location. An explanation for this behavior can be seen in Figure 5, which shows pH profiles for two different concentrations of acid in the bath. A relative distance of 1.0 in Figure 5 represents the location of the primary leach front predicted by the model. This is the point at which the compound that provides ANC (Ca(OH)2(s)) reacts. As the primary leach front moves toward the interior, the pH profiles will also move inward, resulting in movement of the secondary leach fronts. The location of the secondary leach fronts depends on the solubility of the metals, with relatively insoluble metals (large formation coefficients) having secondary leach fronts at low pH values nearer the bath. When the pH gradient is very sharp, a wide range of pH values will be observed over a small distance, resulting in secondary VOL. 32, NO. 11, 1998 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. Effect of log of formation coefficient on ratio of observed to effective diffusivity for various concentrations of acid in bath.
FIGURE 5. Profiles of pH in solid for two concentrations of acid in bath. leach fronts being close together and observed diffusivities being similar. One way to try to correlate the effect of acid concentration on leaching of metals is to assume that the observed diffusivity of the metal is proportional to that of ANC (28). Figure 6 shows simulation results that predict that this assumption is valid only at high acid concentrations. These results are consistent with those shown in Figure 1 for leaching of ANC that showed a shift in leaching mechanism between high and low acid concentrations. Experimental data support the simulation results shown in Figure 6. Hinsenveld and Bishop (28) presented data that showed no effect of acetic acid concentration in the range 0.2-0.5 M on the fraction leached of lead. Baker and Bishop (29) showed that the pH of the leaching solution near pH 3 affected leaching of zinc. The concentration of acid was not given, but it would be in the range below 0.1 M. This is a range where Figure 6 predicts that acid concentration will have an effect on observed diffusivities of metals relative to ANC. The numerical leaching model was also applied to evaluate the appropriateness of the ANS 16.1 dynamic leaching test (31). The procedure calls for reporting results as a leaching 1724
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FIGURE 6. Effect of acid concentration in bath on ratio of observed diffusivities of contaminant metals (MK2, MK8, MK14) to acidneutralizing capacity component (Ca).
FIGURE 7. Fraction leached for metal with formation coefficient of 10-16 (MK16) for infinite bath assumption and for simulated ANS 16.1 test. index (LI), which is the negative logarithm of the observed diffusivity. Simulations were conducted with an ANC of 20 equiv/L (total volume basis), effective diffusivity of 5 × 10-10 m2/s, and volume to surface area ratio of 0.01 m. Simulation of the ANS 16.1 test was accomplished by using the sampling times specified in the ANS 16.1 test methodology (2, 7, 24, 48, 72, 96, 120, 456, 1128, and 2160 h) and setting concentrations of all components in the bath to zero after every simulated sampling time to simulate replenishment of the leaching solution. Figure 7 shows results of simulating leaching of metal MK16 under the infinite bath assumption and under conditions of the ANS 16.1 test. The simulated ANS 16.1 test results for MK16 do not agree well with results of simulations using the infinite bath assumption. Metals that are less soluble than MK16 showed poorer agreement. Data obtained in the simulated ANS 16.1 test after 120 h showed poorer agreement with infinite bath simulations than did data obtained before 120 h. This is the time when the interval between sampling times specified by the ANS 16.1 procedure changes significantly. These simulations indicate that the ANS 16.1 test may not accurately determine observed diffusivities under some conditions.
M (both based on porewater volume); and ANC ) 22 equiv/ L. It was assumed that the sorption reaction had negligible effect on pH and was not included in the component balance for hydrogen ion. The severity of leaching conditions was varied by assuming different concentrations of acetic acid in the leaching solution (0.0008, 0.0040, 0.020, 0.10, and 0.50 M). The simulations showed again that the leach rate for the metal is predicted to follow a half-order rate expression (eq 3). Simulated internal concentration distributions were found to be similar to those predicted for immobilization by precipitation. Figure 8 shows model predictions for the effects of the affinity of the metal for the solid (Ks) and acid concentration in the leaching solution on the observed diffusivity of the metals that are similar to those found when immobilization occurred by precipitation (Figure 4). These results indicate that the leaching behavior for contaminants is not determined by the specific type of immobilization reaction, as long as it is dependent on pH.
Acknowledgments FIGURE 8. Effect of sorption formation coefficient and concentration of acid in bath on observed diffusivities of metals immobilized by sorption. Slower leaching in the ANS 16.1 simulations as compared to that in infinite bath simulations is due to accumulation of higher concentrations of contaminants in the bath. The difference between ANS 16.1 simulations and infinite bath simulations is more pronounced for contaminants that have lower solubility and, hence, lower concentrations in the porewater of the solid. This effect could be reduced by using shorter intervals between sampling. However, this could result in problems associated with lower concentrations in the leaching solution such as a greater fraction of contaminant sorbed on container surfaces and higher relative errors in measurement. These results indicate that it will be difficult to develop protocols for measuring observed diffusivities of a broad range of contaminants if fixed time intervals for leachant replenishment are specified. Sorption-Desorption. Sorption-desorption was investigated with the numerical leaching model as another pHdependent immobilization mechanism. A simple adsorption model was used in which a metal was assumed to react with a surface site as follows:
tSOH + M2+ f tSOM+ + H+
(6)
where tSOH is the surface adsorption site and tSOM+ is the adsorbed metal. By assuming homogeneous surface sites of fixed total concentration, the concentration of sorbed metal can be determined:
Ks St + [M2+] [H ] [tSOM+] ) Ks 1 + + [M2+] [H ]
(7)
where St is the total concentration of surface adsorption sites (mol/L3) and Ks is the equilibrium formation coefficient for sorption. Metal adsorption was included in a simple chemical equilibrium model consisting of five components (H+, Ca2+, Ac-, M2+, tSOH) and nine species (H+, OH-, Ca2+, Ca(OH)2, Ac-, HAc, M2+, tSOH, tSOM+). Metals were simulated with 10 different values of the adsorption formation coefficient (102-10-7). Other assumptions were total concentration of surface sites ) 0.012 M; total metal concentration ) 0.006
This paper is the result of research conducted with federal funds as part of the program of the Gulf Coast Hazardous Substance Research Center, which is supported under Cooperative Agreement R815197 with the United States Environmental Protection Agency. The contents of this paper do not necessarily reflect the views and policies of the U.S. EPA, nor does the mention of trade names or commercial products constitute endorsement or recommendation for use.
Supporting Information Available Three appendices giving the derivation of the second Damko¨hler number, the modified Crank-Nicholson method, and the simple chemical equilibrium model (7 pp) will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the Supporting Information from this paper or microfiche (105 × 148 mm, 24× reduction, negatives) may be obtained from Microforms Office, American Chemical Society, 1155 16th St. NW, Washington, DC 20036. Full bibliographic citation (journal, title of article, names of authors, inclusive pagination, volume number, and issue number) and prepayment, check or money order for $18.00 for photocopy ($20.00 foreign) or $12.00 for microfiche ($13.00 foreign), are required. Canadian residents should add 7% GST. Supporting Information is also available via the World Wide Web at URL http://www.chemcenter.org. Users should select Electronic Publications and then Environmental Science and Technology under Electronic Editions. Detailed instructions for using this service, along with a description of the file formats, are available at this site. To download the Supporting Information, enter the journal subscription number from your mailing label. For additional information on electronic access, send electronic mail to
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(9) Hostetler, C. J.; Erikson, R. L. In Metals in Groundwater; Allen, H. E., Perdue, E. M., Brown, D. S., Eds.; Lewis Publishers: Chelsea, MI, 1993; p 173. (10) Kirkner, D. J.; Jennings, A. A.; Theis, T. L. J. Hydrol. 1985, 90, 81-115. (11) Liu, C. W.; Narasimhan, T. N. Water Resour. Res. 1989, 25, 869882. (12) Narasimhan, T. N.; White, A. F.; Tokunaga, T. Water Resour. Res. 1986, 22, 1820-1834. (13) Schulz, H. D.; Reardon, E. J. Water Resour. Res. 1983, 19, 493502. (14) Walsh, M. P.; Bryan, S. L.; Schechter, R. S.; Lake, L. W. AIChE J. 1984, 30, 317-328. (15) Yeh, G. T.; Tripathi, V. S. Water Resour. Res. 1991, 27, 30753094. (16) Engel, D. W.; Chen, Y.; Fort, J. A.; McGrail, B. P.: Steefel, C. I. Report CONF-9504179-2. Pacific Northwest Laboratory, Richland, WA, 1995. (17) Jennings, A. A.; Kirkner, D. J.; Theis, T. L. Multicomponent Equilibrium Chemistry in Groundwater Quality Models. Water Resour. Res. 1982, 18, 1089-1096. (18) Lewis, F. M.; Voss, C. L.; Rubin, J. J. Hydrol. 1987, 90, 81-115. (19) Lichtner, C. P. Geochim. Cosmochim. Acta 1985, 49, 779-800. (20) Miller, C. W.; Benson, L. V. Water Resour. Res. 1983, 19, 381391. (21) Steefel, C. I.; Lichtner, P. C. Geochim. Cosmochim. Acta 1994, 58, 3595-3612. (22) Steefel, C. L.; Lasaga, A. C. Am. J. Sci. 1994, 294, 529-592. (23) Cheng, K. Y.; Bishop, P. L. J. Hazard. Mater. 1990, 24, 213-224.
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(24) Cheng, K. Y.; Bishop, P. L. J. Air Waste Manage. Assoc. 1992, 42, 164-168. (25) Cheng, K. Y.; Bishop, P. L.; Isenburg, J. J. Hazard. Mater. 1992, 30, 285-295. (26) Cheng, K. Y. In Stabilization/Solidification of Hazardous, Radioactive and Mixed Wastes: 3rd Volume; Gilliam, T. M., Wiles, C. C., Eds.; ASTM STP 1240; ASTM: West Conshohocken, PA, 1996; pp 73-79. (27) Cheng, K. Y. In Stabilization/Solidification of Hazardous, Radioactive and Mixed Wastes: 3rd Volume; Gilliam, T. M., Wiles, C. C., Eds.; ASTM STP 1240; ASTM: West Conshohocken, PA, 1996; pp 375-387. (28) Hinsenveld, H.; Bishop, P. L. In Stabilization/Solidification of Hazardous, Radioactive and Mixed Wastes: 3rd Volume; Gilliam, T. M., Wiles, C. C., Eds.; ASTM STP 1240; ASTM: West Conshohocken, PA, 1996. (29) Baker, P. G.; Bishop, P. L. J. Hazard. Mater., 1997, 52, 311-333. (30) Cote, P. Ph.D. Dissertation, McMaster University, Hamilton, Ontario, Canada, 1986. (31) Measurement of the Leachability of Solidified Low-level Radioactive Wastes by a Short-term Test Procedure; American Nuclear Society Standards Committee Working Group ANS-16.1 Standard ANSI/ANS-16.1-1986; American Nuclear Society: LaGrange Park, IL, 1986.
Received for review August 25, 1997. Revised manuscript received March 2, 1998. Accepted March 9, 1998. ES970747Y
