Gas Mass Transfer for Environmental

Environ. Sci. Technol. 2001, 35, 149-156

Modeling of Solid/Liquid/Gas Mass Transfer for Environmental Evaluation of Cement-Based Solidified Waste LIGIA R. TIRUTA-BARNA,* RADU BARNA, AND PIERRE MOSZKOWICZ Laboratoire d’Analyse Environnementale des Proce´de´s et Syste`mes Industriels (LAEPSI), Institut National des Sciences Applique´es de Lyon, Baˆt. 404-69621 Villeurbanne, Cedex France

A physicochemical and transport model has been developed for the long term prediction of environmental leaching behavior of porous materials containing inorganic waste solidified with hydraulic binders and placed in a reuse scenario. The reuse scenario considered in the paper is a storage tank open to the atmosphere including material leaching with water and carbonation through the leachate contact with air. The model includes three levels: (i) the physicochemical pollution source term (chemical equilibria in the pore water and diffusion in the porous system); (ii) chemical equilibria and mass transfer in the tank; and (iii) gas/liquid transfer of carbon dioxide. The model was applied to the case of a material obtained through solidification of Air Pollution Control (APC) residues from Municipal Solid Waste Incinerator (MSWI). The simulation results are in good agreement with two scale experimental data: laboratory and field tests. Experimental data and simulations show the main trends for release of elements contained in the material: (i) the release of alkaline metals and chloride is not significantly influenced by carbonation and (ii) the release of Ca and Pb is governed by chemical equilibria in pore water and diffusion, while their speciation in the leachate is determined by pH and the presence of carbonate ions.

Introduction The environmental impact study of pollutants from the wastecontaining materials in contact with water requires characterization of the pollution source (defined as the source term) and the taking into account the specified reuse scenario conditions (1, 2). In this way, the main parameters influencing leaching release, e.g. the physicochemical characteristics of the material and the leachant composition, are identified and taken into account in the modeling of the pollutant flux transferred from the material (3-7). Models for long and very long term simulation of concrete materials degradation in a disposal scenario have been developed recently (8, 9). The problem of release modeling of mineral species contained in porous monolithic matrixes obtained from waste solidification/stabilization has been the object of much of our research for many years (10-13). Our studies underlined that, for very soluble species such as alkaline metals, the * Corresponding author phone: (33) 4 72 43 88 41; fax: (33) 4 72 43 87 17; e-mail: [email protected]. 10.1021/es000005w CCC: $20.00 Published on Web 11/17/2000

 2001 American Chemical Society

limiting release step is the diffusive transport, for the others, such as amphoteric metals, the transport/solubilization couple must be taken into account. Modeling leaching behavior of the pollution source term requires the taking into account of environmental factors e.g. material/leachant contact conditions (composition, solid/liquid, renewal, ...) in order to elaborate release estimations which are reliable in the long term. The model proposed here ensures a better taking into account of the following: (i) the physicochemical complexity of the mineral species, by considering the main dissolution/precipitation, complexing and acid/base reactions in the pores; (ii) the physicochemical evolution of the material and the leachate and in particular the progressive depletion of the acid/base capacity of the material; and (iii) the scenariosthe conditions of leachate renewal and the physicochemical processes due to contact with the reactive gas phases. The coupling of gas/liquid and liquid/solid mass transfer to describe a leaching process under natural conditions (atmospheric carbonation) is one of the contributions of our work. In parallel with the elaboration of the model, a set of characterization tests (“toolbox”) has been proposed. The experimental tool box described elsewhere (14) consists of two types of leaching tests: (i) equilibrium dissolution tests and (ii) dynamic leaching test. The equilibrium dissolution tests allow determination of main chemical parameters such as the pore water content, the available quantities for leaching of soluble elements, the basic character of materials, the pH-dependent solubility of weakly soluble elements and their availability under given pH conditions. The dynamic test is used for diffusion coefficient estimation and for the leaching model validation at laboratory scale. The experimental “tool box” supplies the input parameters of the behavioral model for the stabilized wastes leaching.

The Model Formalizing the Leaching Scenario. The reuse scenario of the porous material describes the leaching process conditions, such as the initial chemical composition and leachate renewal, the gas/liquid/solid interactions, the block size, etc. The porous material containing solidified waste is considered as being placed in a pool (Figure 1) and immersed in an aqueous solution, the leachant, which itself is in contact with a gaseous atmosphere. When immersed in water the dissolution/precipitation processes begin at the solid/pore water interface together with chemical reactions in the aqueous phase. At the same time, the soluble chemical species migrate in the pores from the core to the surface of the material and are found in the leachate. The leachant is complex from a chemical point of view; the contact time with the material is an important parameter for the system evolution. To formalize the scenario, it is necessary to identify the main chemical species, reactions and phase equilibria in the system as well as the main transport mechanisms involved. Modeling the pollutant flux of such a leaching system requires the use of simplifying hypotheses. In the cases studied we considered the following simplifications as satisfactory: (i) the porous matrix is chemically homogeneous; when placed in the pool, it is instantaneously water saturated; (ii) the same chemical species and the same chemical reactions occur in the porous matrix and the leachant; (iii) the transport of dissolved species in pore water is diffusional and the medium is isotropic; and (iv) the leachate is perfectly stirred (homogeneous composition) and changes with time; its transport is convective. VOL. 35, NO. 1, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Simplified scheme of the system: material-leaching scenario (see notation table for symbols used). The Chemical Species. For each application a limited base of chemical elements has been defined. This base consists of specific elements with regards to the porous matrix and the pollutants as well as the elements initially present in the leachate. Element speciation is determined by the set of chemical reactions occurring in the considered system. For the studied materials, prepared with hydraulic binders, the acid/base, complexing and precipitation reactions have been considered. For the considered chemical elements, the mobile (solubilized) and immobile (solid phase) chemical species were identified. The mass balance of the system was carried out for each element of the base. From a chemical point of view, the system was therefore composed of the following: (i) I elements whose total concentration in mobile species is ci, i ) 1,...,I; (ii) J mobile species of concentration qj, j ) 1,...,J [The mobile species diffuse in the pores under the effect of the concentration gradient. In the leachant, their transport is convective.]; and (iii) N solid phases of concentration sn, n ) 1,...,N. The concentrations in the porous matrix (c, q, s) are expressed in mol/m3 of porous volume. The concentrations in the leachate (solution outside the porous system), denoted as c′, q′, s', are expressed in mol/m3 of leachate. Taking the example of calcium leached from the material, we consider the calcium contained in the solid portlandite (concentration s) and solubilized calcium with concentration cCa (analyzed as the total Ca). In turn, the solubilized (mobile) calcium is mainly found as two species, Ca2+ and its complexed form Ca(OH)+ in concentrations qCa++ and qCa(OH)+. It naturally follows that cCa ) qCa++ + qCa(OH)+. If necessary, other species containing calcium can be taken into account. The reactions, taking place in a homogeneous liquid, respect the hypothesis of local equilibrium. They are reversible and much quicker than transport phenomena (the solution is considered to be in equilibrium at each point in space and time). The Debye-Hu ¨ ckel model was used to estimate the species activity in the pore water and in the leachate. The experimentally proven hypothesis of local solid/pore water equilibrium (15) is considered for dissolution/ precipitation reactions. We adopt a simple dissolution/ precipitation term

if (s > 0) or ((s ) 0) and (Π g Ks)) if (s ) 0) and (Π < Ks)

(

∂s Π -1 )k ∂t Ks ∂s )0 ∂t

) (1)

where Π is the product of the activities ai of solubilized species which precipitate J

Π)

∏

vH vOH (avj ) j aH aOH

(2)

j)1

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ν are the stoechiometric coefficients, Ks is the solubility product value and Π/Ks is the degree of saturation of the solution as regards a specific solid phase. According to the local equilibrium hypothesis, the kinetic constant k (mol/m3s) has a high value such that the dissolution/precipitation kinetics do not limit the evolution of concentrations in the pore water (rapid reactions) and such that mass flux is only determined by diffusion. Despite the rapid kinetics, eq 1 is necessary in the model to “pilot” the sense of reactions: if Π g Ks, the solution is supersaturated and precipitation occurs, if Π < Ks the solid dissolves (if present). The equilibrium and kinetic relations and the activity model apply in the same way for the leachate (superscript ′ for all parameters). Leachate/reactive atmosphere interactions have been integrated in the model in order to determine the role of carbonation on pollutant release following leachate/air contact. In fact, due to the chemical composition of the leachate, carbonation phenomena can appear: first the leachate carbonation followed probably in the long term by carbonation of the material which is protected from direct contact with the air. The carbonation process involves gas/ liquid CO2 transfer and its reactions in the leachant (acidbase and precipitation reactions). Modeling the gas/liquid transfer process represents a classical problem in chemical engineering, and we only present its application to the particular case studied. The theory of absorption with chemical reaction and the double film model (16, 17) allow calculation of the CO2 transferred from gas to liquid. Given the chemical nature of the studied materials, the leachate is most often basic. In a basic medium, CO2 reacts with OH- according to pseudo-first-order kinetics and moderately rapid reaction:

CO2(aq) + OH- ) HCO3-

(3)

In this case the CO2 absorption flux is given by

aGLF ) aGLkGLxq′OH-

(

PCO2 - q′CO2 KH

)

(4)

where F is the density of transfer flux (mol/m2s), aGL is the specific gas/liquid exchange surface (m2/m3 of liquid), q′CO2 is the CO2(aq) concentration in the liquid mass, PCO2 is the partial pressure of CO2 in the atmosphere, KH is Henry’s constant, and kGL is denoted as

kGL )

x

kCO2DCO2

(

1 +1 Ha2

)

(5)

where Ha is the adimensional Hatta number, defined as the ratio between (the maximal flux absorbed in the liquid interface layer with reaction) and (the maximal flux absorbed in the liquid interface layer without reaction). kCO2 is the kinetic constant for the reaction (m3/s mol), and DCO2 is the molecular diffusion coefficient of CO2 in water. The moderately rapid reaction rate satisfies the condition 0.3 < Ha < 3. Mass Balance Equations. In the porous matrix, the soluble species diffuse under the effect of a concentration gradient on the x axis (Figure 1) and participate in chemical equilibria in solution (pore water) and in precipitation/ dissolution reactions. For a given chemical element we have

∂c ∂t

) Do

∂2 c ∂x2

N

-

∂sn

∑ ∂t

n)1

(6)

TABLE 1. Input Model and Experimental Parameters of Assays 1 and 2 material parameters open porosity  height h (m) surface σ (m2) initial porewater c0,i (mol/m3) initial solid s0,i (mol/m3)

a

scenario parameters 0.45 0.32 assay 1 0.10 assay 2 40.1 assay 1 0.16 assay 2 Na+K: 1800 Cl: 4000 Ca, Pb: 0 Na+K and Cl: 0 Ca: 3820 Pb: 31

diffusion coefficientsa

Do (m2/s)

Na+K Ca Pb Ct

2.3 10-10 1.2 10-10 1.4 10-10 1.7 10-10

flow rate Q VL/σ (m) initial leachate composition c′e,i; c′0,I; s′0,i

0 0.5 demineralized water 0

kCO2 (m3/mol s) specific surface, aGL (m-1) partial pressure Pco2 (atm)

5 at 20 °C (8) 2 3.5 10-4

adjusted parameters Do for Cl- (m2/s) kGL (m2.5/s mol0.5)

1.5 10-10 3.0 10-4 assay 1 2.5 10-4 assay 2

Diffusion coefficients estimated by correlation (12).

where Do represents the observed diffusion coefficient of the considered element (Figure 1). The boundary conditions are as follows: (i) in the center of the material (x ) 0)

∂c | )0 ∂x x)0

∂c Do |x)h ) kSL(c′ - c|x)h) ∂x

(7)

where kSL (m/s) is the mass transfer coefficient between the leachate and the pore water at the surface of the material. The kinetic eqs 1 are added to the above equations that describe local precipitation phenomena. The behavior of H+ and OH- ions may be modeled in two manners: (i) their local concentration is determined by water hydrolysis and by the condition of electroneutrality [An apparent flux of H+ may be calculated.] and (ii) effective transport, i.e., diffusion, of H+ (or OH-) may be considered, but the condition of electroneutrality imposes that their fluxes are dependent on fluxes of all species. The two approaches are equivalent; the first was used in this study. In the leachate, the accumulation of an element is determined by the flux from the material, by transport through convection (with leachate flow rate Q), and by precipitation/dissolution reactions of N solid phases containing the element. Therefore we have

dt

) -aSLkSL(c′ - c|x)h) +

Q VL

N

(c′e - c) -

ds′n

∑ dt

(8)

n)1

with kinetic equations of type (1) in the leachate. The specific solid/liquid exchange surface aSL is defined by

aSL ) σ/VL

dt

) -aSLkSL(c′Ct - cCt|x)h) + N

ds′Ct,n

n)1

dt

∑

Q VL

(c′Ct,e - c′Ct) -

+ aGLkGLxq′OH-

(

PCO2 KH

- q′CO2

)

(10)

where Ct denotes the total inorganic carbon dissolved, and whose concentration is c′Ct and

and (ii) at the leachate/material interface (x ) h)

dc′

dc′Ct

(9)

where σ is the surface area of the material,  is its open porosity, and VL is the leachate volume. When taking carbonation into account, the balance equation of species coming from chemical transformations of CO2 contains the terms (from left to right in eq 10) flux entering/leaving the material, convective flux, the disappearance/creation by precipitation/dissolution of carbonates and the gas/liquid transfer term (eq 4)

c′Ct ) q′CO2 + q′HCO3- + q′CO3--

(11)

The dissolved CO2 is in equilibrium with HCO3-, CO32- and the precipitated carbonates if the solution is saturated. The mobile species diffuse in the matrix pores with an average diffusion coefficient Do,Ct. For the element Ct the diffusion/ chemical reaction balance eq 6 is applied with all the thermodynamic equilibrium relationships in the pore solution (CO2 acid/base and carbonates precipitation). Model Parameters. The model contains a certain number of known or experimentally accessible physicochemical parameters listed in Table 1. Other parameters, such as the kinetic constants of rapid reactions k and the material/ leachant transfer coefficients kSL, are unknown, but for reasons explained above (rapid reactions and rapid external mass transfer for the material/leachant interface), their values may be estimated. Values of k and kSL have been determined through simulations assuming that reaction kinetics and external transfer do not modify the evolution of the concentrations of species (k ) 1 mol/m3s and kSL) 1 m/s). Leachate concentrations of released elements, c′exp, were experimentally monitored versus time. Comparison of the calculated values of concentration c′ with available experimental data c′exp allowed adjustment of the unknown parameters, i.e., Do and kGL. The balance equations contain average diffusion coefficients for chemical elements. They can be determined by adjustment to the experimental data or evaluated by available correlations. Here we used a correlation (18) between the observed diffusion coefficient Do and the water porosity of the material 

Do ) 0.001 + 0.072 + H( - 0.18)1.8( - 0.18)2 (12) D where D is the water molecular diffusion coefficient of the considered species and H is the Heaviside’s function: H(0.18) ) 0 if  e 0.18 and H(-0.18) ) 1 if  > 0.18. VOL. 35, NO. 1, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 2. Elements Considered in the Example of Application of the Model: Molecular Diffusion Coefficients and Average Coefficients Used species

D (m2/s) × 109 (19)

element in the model

av D (m2/s) × 109

Na+ K+ Ca2+ Pb2+ ClCO2 HCO3CO32-

1.3 1.9 0.8 0.95 2.0 1.7 1.2 0.9

Na+Ka

1.6

Ca Pb Cl C tb

0.8 0.95 2 1.2

a By considering in the model the sum of Na+K (similar behavior of alkaline metals), an average D value was used in the calculations. b For dissolved carbon (Ct) an average D value was used obtained from the species CO2, HCO3- and CO32-.

The known molecular diffusion coefficients for the chemical species considered in the model are presented in Table 2. An average molecular diffusion coefficient D was used for the elements in order to calculate Do. For example, the molecular diffusion coefficient of carbon DCt is estimated as the average value of the molecular diffusion coefficients of the species CO2, HCO3- and CO32-. For certain chemical species such as Ca(OH)+, the D values are not known. In this case, the diffusion coefficient D of Ca was assimilated to the diffusion coefficient of the Ca2+ ion which is known. In Table 2 we have also indicated the average D values of the elements considered in the diffusion equations. The model was resolved using the finite differences method. An explicit formula was used for x-coordinate (δx ) h/100) and a numerical differentiation formula with variable step for time-coordinate.

Materials and Methods The model has been applied for leaching simulation of different materials obtained through solidification with hydraulic binders of inorganic wastes. It has been validated through experimental data obtained in the laboratory and pilot experiments and for periods of up to 5 months leaching (14). In this paper we present the results obtained for one of studied materials. The chosen reuse scenario is characterized by permanent contact of the material with a leachate in contact with the atmosphere. Laboratory and field scale experiments have supplied the data necessary to validate the model. The Porous Material. The material was obtained by solidification of Air Pollution Control residues (a semiwet process consisting on lime treatment of the gas) from a Municipal Solid Waste Incinerator and contained heavy metals as pollutants (20, 21). It was performed by mixing 59% (by mass) of APC residues, 12% water and 29% hydraulic binder and curing during 90 days. Physicochemical characterization tests (20) have shown that the solidified waste had a high acid neutralizing capacity. Leaching assays with water have shown that release of certain pollutants such as Cd, As, Zn and Pb was not detectable (respective detection limit: 0.001, 0.012, 0.001 and 0.010 mg/L) and that release of Na, K, Ca and Cl ions was very high. The behavior of Pb (amphoteric metal) strongly depends on the leachate pH. The chemical speciation of Pb in the solid phases of the material is very difficult to determine and even impossible when the Pb content is extremely low. The pH dependent solubilization of Pb was determined by a specific dissolution test: samples of fragmented material (e 1 mm) were put in contact with solutions containing different acid quantities, agitated during 7 days, filtered (0.45 µm) and 152

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analyzed for solutions pH and elements concentration. Lead solubilization was correlated to pH by an empirical relationship

log csat ) -0.00098pH4 + 0.0604pH3 - 0.9349pH2 + 4.6430pH - 8.0299 (13) The parameters characterizing the porous matrix which are necessary for simulation with the described model are presented in Table 1. The Scenario. The scenario studied in this case corresponds to a storage pool open to the atmosphere. The bottom was made of the experimental waste-containing material. The scheme of the pool corresponds in principle to the scheme in Figure 1. The nonrenewed leachate was in permanent contact with one side of the monolith. Two assays were carried out on two scales: a laboratory scale pool of about 0.08 m3 of water (Assay 1) and a field pilot with about 20 m3 of water (Assay 2). The experimental parameters of both assays are presented in Table 1. The physicochemical characteristics of the material, the leachate and the gas are the same in both assays, only the pool size differs. The aim of the experiment was to monitor pollutant release in the water. Samples were taken periodically from the pools. Na, K, Ca, Cl, and heavy metals including Pb were monitored as well as the evolution of pH. The metals were analyzed by Inductively Coupled Plasma-Atomic Emission Spectroscopy (ICP-AES); Cl was analyzed by ion chromatography. The field pilot was monitored for about 100 days and the laboratory pilot for a month. The experimental results for both assays are presented in Figures 2 and 3 (concentrations and pH versus time). The Model Application. The chemical elements considered in the model are Na, K, Ca, Pb and Cl plus inorganic carbon (denoted Ct) coming from atmospheric uptake. Alkaline metal salts (Na and K) are generally very soluble. The solubilization tests of the material under different pH conditions have shown that their solubility is very high and virtually independent of the chemical context. Consequently, we considered that Na and K are solubilized immediately on contact with water, that they do not react in the system and that they only participate in transport phenomena (diffusion in the matrix and convection with the leachant). Due to their physicochemical similarity, Na and K have been treated together as “alkaline species” in the model, using a single balance equation. We present the results of modeling as the sum of the release of the two elements. This approach is of interest as it reduces the calculation time. For the case studied, the Cl- ion is also considered as nonreactive, only participating in transport by diffusion or convection. The chemical equilibrium considered in the model and the values of equilibrium constants are presented in Table 3. The Ca present in the leachate mainly comes from dissolution of the portlandite generated in the material by the hydraulic binder’s hydration. Calcium silicate hydrates are not considered because they are less soluble than portlandite. Two species of soluble calcium are considered: Ca2+ (hydrated ion) and the complex CaOH+. The precipitated forms of calcium are portlandite Ca(OH)2 and calcium carbonate CaCO3. The CO2 participates in the gas/liquid equilibrium, the acid-base and precipitation equilibria. The chemical speciation of Pb in the solid phase in the material is unknown. The Pb solubilization versus pH is

FIGURE 2. Assay 1 (laboratory pilot). Concentrations of elements and leachate pH: ( experimental data, -- simulation with adjusted kGL, -x- CaCO3 formed (adjusted kGL). expressed by eq 13. The soluble species of Pb considered were Pb2+ and Pb(OH)3-, which predominates at alkaline pH. The input parameters of the model are presented in Table 1. The initial Na+K, Cl and Ca content in the pore water (c0) and in the solid phase (s0) were determined from acid neutralizing capacity test (20). The total content of Pb in the material was considered for s0,Pb. First, the effective diffusion coefficients of the elements taken into account in the model were estimated using the eq 12. With the correlated diffusion coefficient the concentration of Cl- in the pool was overestimated, and consequently the observed diffusion coefficient was adjusted to the experimental data cexp,Cl ) f(time). The nonreactive elements such as Na+K and Cl allow adjustment of the respective diffusion coefficients independently of the chemical context because their balance equation (eq 6) contains only a diffusion term and no dissolution/precipitation. The characteristic parameter of gas/liquid transfer kGL was determined by fitting to the experimental data for both assays.

Results and Discussion The estimated and adjusted parameters are presented in Table 1. Figures 2 and 3 show the experimental and calculated concentrations of the elements monitored as well as leachate pH. The points represent experimental data, and the lines represent simulations with adjusted kGL. The model parameters have the same values for both assays; there is a good similarity in behavior between laboratory and field scale experiments (fluxes (mol/m2s) of released elements are the same within experimental errors). Despite experimental uncertainties due to monitoring and analysis of a large scale pilot, good agreement between the calculations and field data in the case of Na, K, Ca, Cl and pH can be noted. The simulation results show that the leachates are saturated in Ca with regards to calcium carbonate: a certain quantity of precipitate is formed in the pool water (Figures3 and 4). However, the water is not saturated in dissolved carbon with regards to the atmospheric pressure of CO2; the

concentration of CO2 absorbed (CO2(aq)) is lower than the maximum concentration at gas/liquid equilibrium of CO2 (CO2sat) given by its partial pressure (CO2(aq)/CO2sat < 1 in Figure 4). The dissolved Ct content is not known experimentally. We have verified if the moderately rapid rate of reaction 3 is satisfied under the experimental conditions of the pilot and therefore if the absorption model of CO2 is validated by calculating the adimensional Hatta number from formula 5. With the adjusted value of kGL and with the values of DCO2 and kCO2 presented respectively in Tables 2 and 1, we obtain for the laboratory pilot Ha ) 0.32 and for the field pilot Ha ) 0.4. The condition of a moderately rapid reaction has been verified. The influence of CO2 on leachate composition can be shown by simulating different carbonation conditions. A quicker gas/liquid transfer process, for example aGLkGL) 1, leads to a decrease in pH (about 7.5) and to saturation of the leachate in CO2(aq); therefore CO2(aq)/CO2sat ) 1 (Figure 3). It must be noticed that the total quantity of Ca released by the material is the same in the two simulated cases. This quantity is found in the leachate, either dissolved or precipitated: total Ca ) Ca dissolved + Ca precipitated. In fact, Ca release is governed by its solubility in the material pore water and by interstitial diffusion. It is obvious that for sufficiently low leaching times the carbonation of the solid matrix does not start and that the Ca release is not influenced by the chemical reactions in the leachate. The process of leachate carbonation does not change the release of nonreactive elements such as Na, K, and Cl (transfer controlled by internal diffusion). In the paragraph entitled “The porous material” we mentioned that the water leaching tests of the material (without carbonation) showed an extremely low release of Pb (concentrations below the detectable limits of our analytical instruments). The analytical results of the two pilots also show an undetectable release of heavy metals including Pb (experimental detection limit of 0.01 mg Pb/L). The simulated Pb concentrations (not shown) are below the detection limit which is in agreement with experimental results. VOL. 35, NO. 1, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Assay 2: field pilot. Concentrations of elements and leachate pH: ( experimental data, -- simulation with adjusted kGL, -xCaCO3 formed (adjusted kGL), - - - simulation with aGLkGL ) 1.

TABLE 3. Chemical and Physical Equilibrium Constants (at 25 °C) Considered in the Model Applications log (K), concns in mol/L

equilibrium acid-base precipitation complexing gas-liquid

H2O ) H+ + OHCO2(aq)+H2O ) HCO3- + H+ HCO3- ) CO32- + H+ Ca(OH)2(s) ) Ca2+ + 2OHCaCO3(s) ) C2+ + CO3PbCO3(s) ) Pb2+ + CO3CaOH ) Ca2+ + OHPb(OH)3- ) Pb2+ + 3OHCO2(aq) T CO2(g)

-14 -6.36 -10.3 -5.33 -8.34 -12.83 -1.15 -13.91 KH ) 0.029 bar m3/mol (22)

Simulation of Reuse Scenarios. The modeling, which is validated by the experimental program, becomes a tool to predict the long term behavior of the system. For example, we have considered three storage scenarios of water in a pool with the same characteristics as the field pilot (Table 1): (i) Scenario 1: pool water without renewal and in contact with the air (“natural” carbonation); (ii) Scenario 2: pool water renewed every 3 months (periodic use) and in contact with the air (“natural” carbonation); and (iii) Scenario 3: pool water without renewal and protected from contact with the air (theoretical case). We present the leachate and pore water 154

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FIGURE 4. Concentration of elements in the matrix and leachate after 3 years without renewal and with carbonation (simulated scenario 1). compositions simulated for a period of three years and for all three scenarios. For the long-term contact of the leachate with the air, carbonation of the material is possible, due to diffusion in the pore water of species coming from atmospheric CO2. A

FIGURE 5. Simulation of Pb release for the field pilot in the 3 reuse scenarios: -- pool water, not renewed with carbonation (scenario 1), • poolwater renewed every 3 months with carbonation (scenario 2), ___ poolwater not renewed without carbonation (scenario 3), - - - experimental detection limit, _ _ _ maximum accepted by the standard. front of CaCO3 advances toward the core of the material and coexists with the portlandite. Figure 4 shows the simulation of the field pilot behavior in scenario 1, for three years leaching. The concentrations of the elements Ca, Na+K, Cl, and Pb and the pH in the pore water and leachate are shown. The high Ca solubility in porewater is due to the high chloride concentration and the high ionic strength. It can be noted that the solubility of Ca decreases in the porewater toward the surface of the monolith situated at h ) 32 cm. This is an unusual phenomenon, as we expect an increase in Ca solubility toward the material/leachate interface when a highly basic material undergoes leaching (case of matrixes with hydraulic binders). The explanation for the decreased Ca solubility resides in the chemical nature of the solidified waste. APC residues from MSW incineration solidified in the material have a high chloride content which induces a pH value less than 12 in the pore water. During leaching, Cl and alkaline metal concentrations decrease toward the surface of the monolith but not in the same way: the chlorides are more rapidly depleted than the alkaline metals, due to a higher concentration gradient between the monolith and the leachate. Consequently, in the region near the monolith surface, the anion/cation electroneutrality equilibrium in the pore water induces a slightly higher pH (over 12). Finally, depletion of the ions (Cl-, Na+, K+) reduces the ionic strength in the pore water and therefore increases the activity coefficient of Ca. The joint effect of pH and ionic strength determines the decrease in Ca solubility toward the surface of the material. Furthermore, carbonation of the

surface of the material acts in the same way (toward decreased Ca solubility) as the solubility of calcium carbonate is lower than that of portlandite. The model predicts the progressive formation in time of CaCO3 at the monolith surface and a slow advance of the front toward the core of the material. The Pb dissolved in the pore water is in equilibrium with the solid phase initially present in the material that we have denoted Pb(s). The model does not predict precipitation of PbCO3 in the material and in the leachate under the pH conditions and CO32- system concentration. The content and speciation of Pb in leachates have been simulated for the 3 scenarios and presented in Figure 5. The speciation of Pb (dissolved or precipitated) is determined by the pH which, in the case of scenarios with carbonation, is less than 9. The leachates in scenarios 1 and 2 (with carbonation) are saturated with regards to Pb oxide (hydroxide), and a fraction of total flux released is precipitated. Concentration of soluble Pb is about 10 times higher in scenario 3, and the leachate is not saturated. Under the considered scenario conditions no PbCO3 is formed, the calculated saturation index Π/Ps being < 1. It can be noticed that the dissolved Pb concentration is below the detection limit for the first 3 months of leaching. The French standard (23) concerning drinking water (not including natural mineral water) fixes the accepted limit of Pb concentration in water sources (to be treated by physicochemical processes to become drinking water) at 50 µg/L. The Pb concentration dissolved in the leachates is below this VOL. 35, NO. 1, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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limit in the scenarios with carbonation 1 and 2 (Figure 5); the concentration is above this limit in scenario 3. The total (dissolved and precipitated in the leachate) quantity of Pb released in 3 years is close for all 3 scenarios. It can be explained by the fact that the determining processes are dissolution and transport in the matrix. The exposed approach and model may be applied for simulation of other scenarios. The model takes into account the mainly physical and chemical phenomena taking place in the studied scenario. Nevertheless, the experimental validation of long-term simulation on field scale is desirable. The model may be improved in order to describe more accurately some phenomena. So, an improved activity model (a virial method) must be used to simulate the pore water composition at high ionic strength. Additional chemical species such as the metal-chloride complexes may be considered in order to better simulate metals behavior in the case of high chloride content of the material.

Acknowledgments The experimental database for the model validation is coming from the ADEME “Ecocompatibility” program on waste (1996-1999) and coordinated by POLDEN. We thank specially our colleagues Yves Perrodin (POLDEN), Zoltan Re´thy and Apichat Imyim (LAEPSI) et Lucie Lambolez-Michel (CERED) for their contribution in carrying out the experiments.

Nomenclature a

activity, mol/m3

aGL

specific surface area gas/liquid, m-1

aSL

specific surface area solid/liquid, m-1

c

element concentration, mol/m3

D

molecular diffusion coefficient, m2/s

Do

observed diffusion coefficient, m2/s

h

monolith height, m

Ha

Hatta adimensional number

k

kinetic constant, mol/m3s

kCO2

kinetic constant, m3/mol s

kGL

mass transfer parameter, m2.5/s mol0.5

kSL

solid-to-liquid mass transfer coefficient, m/s

KH

Henry's constant, bar m3/mol

Ks

solubility product

PCO2

carbon dioxide partial pressure, bar

q

species concentration, mol/m3

Q

leachate flow rate, m3/s

s

solid concentration, mol/m3

t

time, s

VL

leachate volume, m3

x

space coordinate, m

Greek letters water porosity



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ν

stoichiometric coefficient

σ

solid surface area, m

Π

activity product

Superscripts ′

related to the leachate

Subscripts 0

initial state

exp

experimental

i

element i

sat

saturation

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Received for review January 3, 2000. Revised manuscript received September 13, 2000. Accepted September 28, 2000. ES000005W