Environ. Sci. Technol. 1996, 30, 481-488
Predicting Multicomponent Adsorption and Transport of Fluoride at Variable pH in a Goethite-Silica Sand System J O H A N N E S C . L . M E E U S S E N , * ,†,‡ A N D R EÄ S C H E I D E G G E R , § , | TJISSE HIEMSTRA,‡ WILLEM H. VAN RIEMSDIJK,‡ AND MICHAL BORKOVEC§ Macaulay Land Use Research Institute, Craigiebuckler Aberdeen AB9 2QJ, Scotland, Department of Soil Science and Plant Nutrition, Wageningen Agricultural University, P.O.Box 8005, NL 6700 EC Wageningen, The Netherlands, and Institute of Terrestrial Ecology, Federal Institute of Technology (ETH), Grabenstrasse 3, CH-8952 Schlieren, Switzerland
Environmental impacts of soil pollution are greatly affected by the mobility and migration contaminants in soil. Multicomponent transport processes can play an important role in this migration. Therefore, modeling of transport processes and prediction of contaminant mobility as a function of soil properties can be a useful tool in risk evaluation. This work shows how a mechanistic model of ion adsorption on variable charged surfaces combined with a convective dispersive solute transport model was used to predict multicomponent transport of fluoride at variable pH in a goethite-silica sand column. In order to show the potential of this type of modeling, the chemical properties of the column material used in the transport calculations were not derived from measurements on the material itself, but predicted from independent data on synthetic goethite and silica. In this way the only parameters needed to predict the transport of fluoride and acidity were the chemical composition of the infiltrating solution, and the surface areas of goethite and silica present in the column. Although no chemical data of the actual column material were used, the agreement between predicted and experimental fluoride and pH breakthrough curves was very good. This shows that this type of modeling can be very useful for the understanding of multicomponent transport processes.
* Corresponding author e-mail address:
[email protected]. ac.uk. † Macaulay Land Use Research Institute. ‡ Wageningen Agricultural University. § Institute of Terrestrial Ecology. | Present address: Department of Plant and Soil Sciences, University of Delaware, Newark, DE 19717-1303.
0013-936X/96/0930-0481$12.00/0
1996 American Chemical Society
Introduction Transport behavior of reactive ions in natural porous systems is generally complex. The traditional approach to model monocomponent transport behavior of reactive species in columns is to calibrate an empirical sorption model with a sorption isotherm obtained from independent batch experiments with the column material. Such batch experiments have to be carried out under constant conditions with respect to salt concentration, pH, and the concentrations of competitive ions, as variation in these parameters may significantly affect the sorption behavior of the ions of interest. In natural systems, however, these parameters are far from constant as the chemical composition of the solid (soil) material as well the composition of soil solutions are highly variable. These types of situations can be handled effectively on the basis of existing mechanistic models. Such mechanistic models incorporate various multicomponent effects such as effect of ionic strength or pH on adsorption of inorganic micropollutants. One of the first things necessary for such a mechanistic approach is determination of the dominant sorption process and an estimation of the reactive surface area of the solid phase and its chemical properties. In case of oxy-anions and fluoride their behavior in natural porous systems might very well be dominated by multicomponent adsorption on variably charged metal (hydr)oxide surfaces. The aim of the work presented here is to test to what extent an independently calibrated mechanistic model for fluoride and proton adsorption by variable charge surfaces is able to predict the transport behavior of fluoride ions in a column composed of a mixture of two metal (hydr)oxides: goethite and silica. Fluoride has been chosen as an example because it is a potentially toxic element, with a narrow range of tolerable amounts taken up via food or drinking water (1). It is present in the waste material of several large scale chemical processes, such as aluminum smelting and production of phosphate fertilizer, and as a result contamination of soils with fluoride has occurred regularly (2-4). Risks for human health and the environment are largely determined by the concentrations of fluoride that occur in ground water and by the rate at which fluoride migrates through the soil. Both are strongly influenced by the interaction of dissolved fluoride with the soil solid phase via precipitation or adsorption. Precipitation will generally be more important at higher fluoride concentrations and in strongly acidic (AlF3) or alkaline calcareous soils (CaF2, Ca10[PO4]6F2), while adsorption will be more important at slightly acidic and neutral pH levels, or at low calcium concentrations (2). The most important solid surfaces for fluoride adsorption in soils are the surfaces of iron and aluminum (hydr)oxides, for example, goethite and gibbsite. The pH dependent charging behavior of these (hydr)oxides causes adsorption of ions on these surfaces to be strongly pH dependent. In turn, adsorption of ions on (hydr)oxide surfaces can affect the pH by influencing adsorption of protons. In case of fluoride, adsorption of the negative ion enhances proton adsorption and tends to increase the pH. However, unlike the case in ion exchange processes, the amount of adsorbing fluoride can be different from the amount of adsorbing protons. Electroneutrality of the overall adsorption process
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TABLE 1
Chemical Reactions Used in the Chemical Equilibrium Model Solution
(1) H+ + OH- S H2O (2) H+ + F- S HF
log K0 ) -14 log K0 ) 3.19
ref 18
Surface Reactions with Goethite o-plane: (3) S-OH-1/2 + H+ S S-OH2+1/2 (4) S-OH-1/2 + F- + H+ S S-F-1/2 + H2O d-plane: (5) S-OH-1/2 + Na+ S S-OHNa+1/2 (6) S-OH2+1/2 + NO3- S S-OH2NO3-1/2 (7) Si-O- + H+ S Si-OH
9
[this work] [this work]
log K0 ) -1.0 log K0 ) -1.0
[this work] [this work]
Surface Reaction with Silica (o-plane) log K0 ) 7.5
is maintained by simultaneous adsorption of background electrolyte ions in the diffuse double layer. Although the amount of background electrolyte ions involved in this adsoption is generally minimal relative to the amount present in the soil solution, this effectively uncouples the adsorption of protons and fluoride and makes the adsorption of fluoride at variable pH a multicomponent process. Multicomponent adsorption is characterized by the fact that at least two independent variables with accompanying mass balances are necessary to define an equilibrium situation. In case of fluoride adsorption on a charged surface, the two main independent variables are the concentration of dissolved fluoride and the pH, with accompanying mass balances for fluoride and the acidity. To enable modeling of mass transport of ions in such systems, it is necessary to describe the adsorption processes involved in terms of processes which correctly incorporate the effect of mass (and charge) exchange between the solution and the surface. To put this another way, the pH dependence of an adsorption process must be modeled taking into account the concomitant mass transfer of acidity. Only by doing so are feedback and competition mechanisms taken into account in a consistent way. Mechanistic adsorption models have these characteristics and are therefore suitable for multicomponent transport calculations. We will first discuss the migration of acidity through a column consisting of silica sand coated with goethite particles, using strong bases and strong acids. Subsequently we will discuss the transport of fluoride through the same column. The model parameters are derived from independent batch experiments using separate colloidal systems of silica (5, 6) and goethite. Numerical Modeling. To calculate the adsorption of protons and fluoride on goethite-silica sand, and subsequently the transport of these ions in an experimental column of this material, we used Ecosat, a computer program developed at the Wageningen Agricultural University (7). This program enables calculation of chemical equilibria, including different types of interaction of dissolved species with solid phases, in combination with onedimensional conservative convective dispersive mass transport. The mathematical solution of the convection dispersion equation in the program is achieved by a twostep method (8-10). In this method the nonlinear system of algebraic equations for the chemical equilibria and mass balances is solved separately from the set of ordinary partial differential equations which make up the convectivedispersive solute transport model. The chemical and the physical set of equations are solved numerically, and
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log K0 ) 9.5 log K0 ) 8.2
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ref 5
iteration between the chemical and the physical module takes place until convergence is reached at each time step. Adsorption Behavior of Goethite and Silica. Model Description. As mentioned, a first step in modeling multicomponent transport of protons and fluoride in a column is a quantitative description of the adsorption of protons on the relevant solid surfaces. In the experimental systems studied here, goethite-silica sand was used as the solid phase. In the adsorption model this material was assumed to consist of two independent surfaces: a goethite and a silica surface. Although fluoride supposedly only interacts with the goethite surface, the silica surface contributes significantly to the overall surface charging behavior of the solid phase. Therefore, the charging behavior of silica had to be included in the model representation. The charging behavior of metal (hydr)oxides is often described using a two-step protonation reaction:
S-O- + H+ S S-OH0 S-OH0 + H+ S S-OH2+
log KH1 log KH2
(1) (2)
However, if the groups that dominate the charging of iron and aluminum (hydr)oxides are oxygens that are only coordinated to one underlying metal ion, the charging behavior can be represented by just one reaction (reaction 3, see Table 1). In this reaction, the noninteger values for the charge of the surface group result from the mean charge attribution of half a unit per S bond and is related to structural considerations (5, 11). Thus only one proton affinity constant is required to describe the basic charging behavior of goethite. This approach, the so-called one-pK approach, was followed here. Also, it can be shown that one proton affinity constant is sufficient for the description of the charging behavior of the silica surface (reaction 7, Table 1) (11). In addition to the intrinsic binding of ions to the surfaces, a double layer model was used to calculate the effect of the surface potential on the ion binding. We used a combination of a Stern layer with a diffuse double layer, called the basic Stern approach, to describe the influence of the ionic strength on the charging behavior of both goethite and silica (5). Ion acivity coefficients for all dissolved ions were calculated according to the Davies equation.
Methods and Materials Preparation of Pure Goethite. The goethite used for the determination of the fluoride adsorption parameters was the same material as used for the determination of the
charging behavior of pure goethite (12). The material was prepared in three different batches according to the method described by Hiemstra et al. (11), which is based on the work of Atkinson et al. (13). In this method, a ferric nitrate solution is slowly neutralized with sodium hydroxide and aged at pH 12 at 60 °C for 48 h and subsequently dialyzed. All solutions used were prepared of bidistilled water. The individual batches, which reacted similarly in terms of charging behavior, were combined in one stock suspension. The point of zero charge (PZC) of this material is was 9.5, and the BET specific surface area was 105 m2 g-1. Determination of Fluoride Adsorption Isotherms on Pure Goethite. NaF stock solutions were prepared from NaF salt and standardized by measuring Na by flame atomic adsorption spectrophotometry. The concentration of F was determined with an ion selective solid state electrode (Orion 94-01) in combination with a calomel reference electrode. The electrode set was calibrated with the NaF solutions (ranging from 10-6 M to 10-2 M) of the appropriate pH and ionic strength, in a constant temperature (22.5 °C) cell. The stirring potential and suspension effect in this system were less than 1 mV. Fluoride adsorption was determined at three different pH levels (pH ) 4, 5, and 6) in 0.1 M NaNO3 using a successive addition/measurement method. A volume of 50 mL of a diluted suspension in 0.1 M NaNO3 was placed in a thermostated vessel (22.5 °C) and kept at constant pH using a pH-stat technique. A series of aliquots of NaF/0.1 M NaNO3 were added and after 0.5 h equilibration time for each, the F-electrode reading was recorded together with the added volumes of NaF/0.1 M NaNO3 and HNO3/0.1 M NaNO3. The amount adsorbed was calculated from these data as the difference between the amount added and that retained in solution (F + HF), assuming that no FeFx complexes were present in significant amounts at the fluoride levels applied. This assumption was checked by analyzing the suspension at the highest F level and the lowest pH (pH ) 4). After high speed centrifugation the total F concentration was measured using a TISAB buffer. Total F concentrations in the samples were measured after addition of a TISAB solution (mixture of 0.01 M Na citrate, 1 M NaCl and 1 M acetic acid which was adjusted with NaOH to pH 5.33) in a ratio of 10:1 (1:1 for low total F levels). These mixtures were left overnight before F was measured. Preparation of Goethite-Silica Sand. The goethitesilica sand used in the transport experiments was composed of calcined white silica sand (Seesand, Siegfried Handel Switzerland), sieved to a size fraction of 125-250 µm, washed with dilute HNO3, and brought to neutral pH. The prepared material had a solid phase density of 2.31 g/cm3 and a surface area of 0.08 m2/g. The goethite used to coat the sand was obtained commercially (Fe-52, Organic/ Inorganic Chemical Corp., CA) and freed from impurities by repeated centrifugation and redispersion in dilute HNO3, NaOH, 0.01 M NaNO3, and bidistilled water. The BET surface area this purified goethite is 24 m2/g, and its point of zero charge (PZC) was determined by potentiometric titrations at different NaNO3 concentrations in N2 atmosphere. The common intersection point of the titration curves lies at pH ) 7.9 (14). This low value in comparison with the PZC of the self-synthesized goethite described above may be caused by carbonate or silicate contamination (15). The goethite was coated irreversibly on the surface of the silica sand in a heterogeneous suspension reaction
as described by Scheidegger et al. (16) at a ratio of 6.5 mg of goethite/g of sand. The total BET surface area of the goethite-coated sand was 0.25 m2 g-1, which is close to the sum of both materials in pure form. This suggests that the interaction between goethite and silica does not affect their surface areas significantly. Column Experiments. The experiments were carried out with columns of 40 cm length and 10 mm inner diameter, filled with 2.58 ( 0.05 g of goethite-silica sand per mL pore volume. The feeding solutions were passed through a degasser (Erma) and pumped with an HPLCpump (Sykam) at flow rates of 0.2-3 mL min-1. In combination with the physical column dimensions and the porosity this resulted in flow velocities ranging from 8.9 × 10-5 to 1.3 × 10-3 m s-1. The column porosity and dispersivity were determined by pulse experiments with conservative tracers (NaBr, NaNO3) with on line UV/vis detection and derived from the average travel time and the pulse width. Observed dispersivities of 0.7 ( 0.1 mm were independent of flow rate and comparable to the particle size. The resulting hydrodynamic porosity of the columns was 0.49 ( 0.02. Column Pe´clet numbers Pe (defined as Pe ) L/DL where L is the column length, and DL is the dispersivity) were >500. For the step breakthrough experiments, pH was measured on-line with a flow-through electrode (Ingold) and the effluent was collected in a fraction collector. The solutions were mixed 1:1 with a buffer solution containing 57 mL of concentrated acetic acid (p.a., Merck), 58 g of NaCl (p.a., Merck), and 2 g of 1,2diaminocyclohexanetetraacetic acid (p.a., Riedel-deHaen) per liter, adjusted to pH 5.1 with NaOH (p.a., Merck), and analyzed for fluoride by flow-injection analysis using a fluoride sensitive electrode. The simulations of the transport experiments were carried out with the Ecosat program using the chemical equilibria listed in Table 1. Further input for the model was the amount of goethite-coated silica per pore volume, the composition of the solution initially present in the column, and the composition of the infiltrating solution. The calculations were performed by separating the spatial coordinate into 50 layers. This number is considerably smaller than needed to obtain a similar dispersivity in the calculations as in the experiments, which would take a number of layers greater than half the column Pe´clet number. However, using more layers in the calculations was not a practical option because this also requires the use of smaller time steps. These changes would increase total calculation times considerably. The higher dispersivity in the calculations limits the sharpness of the edges in the calculated breakthrough curves but does not influence their general features on which we focus in this paper. Typical calculation times for the fluoride transport calculations were about 2 min per pore volume on a 90 MHz Pentium PC.
Results and Discussion Adsorption Modeling. Proton Adsorption on Goethite and Silica. As explained in the introduction part of this paper, a first step in multicomponent transport modeling is a mechanistic model for the interaction of the substances of interest with the solid surface. Because the pH plays such an important role in the interaction of many solutes with solid surfaces, an adequate model for proton adsorption or charging behavior is especially important. The model description for the charging behavior of goehite used here is based on the work of Hiemstra and
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FIGURE 1. Surface charge of the synthesized pure goethite as measured by Hiemstra and Van Riemsdijk (1995) and as calculated with the adsorption model using a log K for the one pK model of 9.5, ion pair formation constants of 1.0 (Table 1), a site density of 6.0 sites/nm2, and a capacitance of 0.85 F/m2.
Van Riemsdijk (12). They interprete the charging behavior of goehite including heterogeneity caused by differences in reactivity of surface oxygen groups at the different crystal planes of the goethite crystals. However, the dominant plane with respect to relative surface area and the overall charging behavior is the 110 plane (17). We therefore use a simplified approach here in which we neglect the other planes and assume that the surface reactivity of the goethite is governed by the reactivity of the singly coordinated FeOH(H) groups at the 110 plane. The basic charging data of the goethite that is used to measure the fluoride adsorption isotherms could be described very well using a Stern layer capacitance of 0.85 F m-2 in combination with a site density of 6.0 sites nm-2 and adsorption of background electrolyte or ion pair formation positioned at the head end of the diffuse double layer (or d-plane, Table 1) (Figure 1). To describe the charging behavior of the silica surface we used a capacitance of 3.9 F m-2 in combination with a site density of 4.65 sites nm-2, data which were based on colloidal silica (5). To evaluate the performance of the combined proton adsorption model for goethite and silica (consisting of chemical reactions 1, 3, 5, 6, and 7 of Table 1) we used it to predict the total surface charge of the goethite-coated silica that was used in the transport experiments (Figure 2). The overall charging behavior of the goethite-coated silica sand was calculated as the sum of the contributions of the silica and the goethite surface present. The experimental results for the goethite-coated silica sand that are shown have been derived from a chromatographic experiment with this material (19). This type of experiment only gives information on the derivative of the charge to the pH (the slope of the curve) and not on the absolute value of the surface charge (height of the curve). The position of the dataset as a whole relative to the y-axis in Figure 2 is therefore arbitrary and was chosen such that it agreed with the absolute level of the predicted values. The slope of the measured charging curve is not arbitrary and, according to Figure 2, agrees very well with the predicted curve. Fluoride Adsorption on Goethite. Adsorption of fluoride on goethite is strongly pH dependent. As illustrated by the three fluoride adsorption isotherms as measured on the pure goethite at pH 4, 5, and 6 (Figure 3) adsorption is strongly enhanced by lower pH, which is typical for
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FIGURE 2. Surface charge of the goethite-coated silica as a function of pH at 0.01 M ionic strength. Data points refer to experimental data from Bu1 rgisser et al. on the same material (19); lines are predicted with the Ecosat program using the independent binding constants and the measured surface areas of the commercial goethite and silica. The dotted lines indicate the calculated contributions of the individual goethite and the silica surface to the total charge.
FIGURE 3. Fluoride adsorption isotherms for goethite at three different pH levels at 0.1 M ionic strength. Data points obtained from experiments with synthetic goethite; lines are calculated with the Ecosat program, using the binding constants for protons and fluoride of Table 1. adsorption of anions. In order to model the combined transport of acidity and fluoride ions it is necessary to describe the pH dependent adsorption of fluoride in a similar way as was done for the protons, i.e., in terms of chemical reactions and binding constants. In its simplest form such a model consists of just one chemical reaction between dissolved fluoride and the goethite surface, with an accompanying equilibrium constant (Table 1, reaction 4). In the reaction as proposed here, it is assumed that the fluoride ion effectively exchanges for an OH-surface group, with which it shares a similar size. By including fluoride adsorption in this way, the pH dependence of the adsorption is assumed to be caused by both the pH dependent surface charge of goethite and the pH dependent availability of adsorption sites. With this model we calculated fluoride adsorption isotherms at three pH levels and we fitted an equilibrium constant of 108.2 for the adsorption reaction. The resulting calculated curves are shown in Figure 3. Although the calculated adsorption isotherms do not match the data points perfectly, the model appeared adequate to describe the main features of the adsorption of fluoride at different pH levels.
a
FIGURE 4. pH breakthrough curve obtained from a goethite-coated silica sand column that was equilibrated at pH 9.6 at an ionic strength of 0.1 M, subsequently infiltrated with a solution at pH 3.6, and after 20 pore volumes again infiltrated with the solution at pH 9.6. Data points are obtained from Scheidegger et al. (16); the line is predicted with the Ecosat transport model. The arrow indicates the moment at which the input solution was changed.
Transport in Goethite-Silica Sand Column. pH Breakthrough. We used the model for the charging behavior of the goethite-silica sand as described above as a basis to predict the pH breakthrough in experiments that were partly reported by Scheidegger et al. (16). In the first experiment a column of goethite-coated silica was first equilibrated with an unbuffered 0.1 M NaNO3 solution at pH 9.6. Subsequently the column was infiltrated with 0.1 M NaNO3 at pH 3.6. After complete breakthrough of this acid solution, after 10 pore volumes, the initial solution of pH 9.6 was infiltrated again. In the column leachates the pH was measured to monitor acidity transport in the column (Figure 4). As discussed by Scheidegger et al. (16), the pH breakthrough curve in this experiment is a typical example of a front that exhibits a combination of a diffuse and a sharp subfront as a result of the S-shaped acidity adsorption isotherm. To calculate the pH breakthrough curves we used the modeled charging behavior of the goethite-coated silica in combination with the numerical transport module of the Ecosat program. As is shown in Figure 4, these predicted breakthrough curves agreed very well with the measurements. This is illustrated especially by the good prediction of the position of the final pH front, at about 24 pore volumes, which is very sensitive to differences between the slopes of the predicted and actual adsorption isotherms. Considering the difference between the PZC of the goethite on which the model description is based and the PZC of the commercial goethite that was used in the column experiments, this result might seem surprising. However, comparing data of Hoins et al. (14) and Hiemstra et al. (5), for both goethites it turns out that the slopes of the acidity adsorption isotherms, or charginge curves, as a function of pH are very similar. The model description seems adequate for the purpose of enhancing the understanding of transport of acidity in reactive porous systems. pH Breakthrough after a Change in Salt Concentration. After the monocomponent system as discussed above we shall now look at a multicomponent system. An example of such a system is the development and transport of a pH front that evolves in a goethite-coated sand column after a change in the salinity, or ionic strength, of the infiltrating solution. The two independent variables in such a system
b
FIGURE 5. Predicted pH (a) and salt (b) breakthrough curve obtained from a goethite-coated silica sand column that was equilibrated at pH 5.0 and at 0.01 M NaNO3 and subsequently leached with a 0.1 M solution at pH 5.0. After complete breakthrough of the pH, after 20 pore volumes, the initial solution was applied again. Data points refer to experimental data of Scheidegger et al. (16); the line is predicted. The arrow indicates the moment at which the input solution was changed.
are the acidity and the salt concentration. The multicomponent effect is demonstrated by an experiment of Scheidegger et al. (16), in which a goethite-coated sand column was first equilibrated with a 0.01 M NaNO3 solution at pH 5.0 and subsequently leached with a 0.1 M NaNO3 solution at pH 5.0 (Figure 5). Due to the effect of the salt concentration on the surface charge, the change to the higher salt level resulted in an increase in pH of the leaching solution to 5.6, which lasted for about 8 pore volumes. After equilibration with the 0.1 M solution and return of the pH to 5.0, the initial 0.01 M solution was infiltrated again. Now the opposite effect on the proton adsorption is illustrated by a decrease of the pH to 4.4. This pH slowly returned to its initial value by a diffuse front. The experiment described here shows that the adsorption of protons is a function of pH, but also of the salt concentration. This is caused by the combined effect that the salt concentration has on the activity of dissolved ions, on the extent and composition of the double layer, and on the surface potential. Because a description of these effects is present in the proton adsorption model it is possible to predict the adsorption of protons as a function of pH and ionic strength. Like the experimental results, the predictions show a temporary increase of the pH on infiltration of the lower salt concentration and a temporary pH decrease when the ionic strength increases again. Although the calculations
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a
b
FIGURE 6. Predicted pH (a) and fluoride (b) breakthrough as a function of leached pore volumes, in an experiment with a goethite-coated silica column that was equilibrated at pH 5.12, without fluoride, and subsequently infiltrated with a 2.5 × 10-4 M fluoride solution of the same pH. After equilibration with this solution the initial solution was infiltrated again. The data points represent the experimental results, while the line is predicted. The arrow indicates the moment at which the input solution was changed.
overestimate the extent of the pH increase and the amount of pore volumes that the pH remains high, the overall form of the predicted curves agrees well with the experimental observations. The same holds for the pH front that evolves upon switching back to the inital ionic strength again. The difference between the predicted and the experimental pH values is caused by an overestimation of the overall effect of the ionic strength on proton adsorption by the model. Breakthrough of Fluoride and pH. Our next objective was to use the model for fluoride and proton adsorption in combination with the numerical transport module to predict the breakthrough of fluoride and pH in a goethitecoated sand column. We conducted an experiment with an experimental system similar to the system described above. The column was now first equilibrated with an unbuffered 0.1 M NaNO3 solution at pH 5.12, without fluoride. Then the column was infiltrated with a solution of the same pH and ionic strength, but with 2.5 × 10-4 M fluoride added. After complete breakthrough of the fluoride and return of the pH to 5.12 the column was infiltrated with the initial solution without fluoride again. The conditions in this experiment were such that the adsorption of fluoride noticeably influenced the adsorption of protons, resulting in a measurable change of the pH in the effluent (Figure 6a).
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From the measured breakthrough curves, infiltration of the column with the fluoride solution results in breakthrough of fluoride after about 2.6 pore volumes. At the same time, as a result of the effect of the adsorbing fluoride, a pH front appears where the pH increases from 5.12 to 5.8. This increased pH level causes fluoride to adsorb less strongly as compared to the original pH of 5.12 (See also the fluoride adsorption isotherms in Figure 3). This results in a significantly lower retardation of fluoride in the column and thus in a more rapid initial breakthrough than would be the case if the pH of the column would have been fixed at pH 5.12. The pH breakthrough curve shows a second front after about 20 pore volumes where the pH of the effluent returns from pH 5.8 to pH 5.12. Because this pH difference affects the adsorption of fluoride, this implies that the amount of adsorbed fluoride will change at this front. Therefore there also has to be an accompanying fluoride front. At first sight such a second fluoride front is not apparent from the experimental results. Upon leaching of fluoride from the column after 62 pore volumes, again two fronts are visible. First a steep front at about 64 pore volumes where the fluoride concentration drops to virtually zero, accompanied by a pH front where the pH decreases from 5.12 to 4.4. This pH decrease hampers the desorption of fluoride and so slows down the leaching process. After this steep front a second diffuse front is visible, especially in the pH, where the pH returns to its original value of 5.12. As indicated above, this pH front implies that there also has to be an accompanying diffuse fluoride front. Turning to the prediction of these breakthrough curves. In this system, the pH and the fluoride concentration can vary independently. Therefore the system is not defined by either of these parameters individually. As illustrated by the fluoride adsorption experiments, a distinct fluoride adsorption isotherm exists at every pH level. Therefore, it is not possible to construct pH or fluoride breakthrough curves from a single one-component adsorption isotherm. In this case a multicomponent transport model is needed to predict breakthrough curves. The results of such predictions are shown in Figure 6a,b. If we compare the predicted and the measured breakthrough curves it appears that the position of the first front is predicted well. The increase in fluoride concentration is predicted accurately. The measured pH increase is slightly greater than predicted, which is partly due to differences between the actual and the predicted pH dependence of fluoride adsorption. The position of the second front, where the pH returns to the original value of 5.12, is predicted accurately. The calculations also show a small fluoride front here. With information on the size and position, this second fluoride front might also be present in the experimental curve. Although the concentration difference is small in comparison with the experimental error, the predicted concentration difference seems to be of the same magnitude as that measured. If we neglect the fact that the fluoride concentration changes slightly at this front, the position and shape of the pH breakthrough curve can be assumed to be determined by the slope of the acidity adsorption isotherm at a fluoride concentration of 2.5 × 10-4 M between pH 5.8 and 5.12. The shape of the pH front then is diffuse. The good prediction of the second pH front indicates that this slope of the charging curve is predicted well.
Upon leaching of the fluoride from the column the position and shape of the first sharp front in the pH and fluoride concentration is well predicted. The predicted decrease of the pH to 4.4 is very similar to the measurements. After this first front a short concentration plateau is predicted. Such a plateau is not visible in the measured results, which might be caused by effects of dispersion in the experimental system. After this plateau the second front starts at the point where the pH starts to rise again. Although the experimental pH front is somewhat more diffuse than the predicted curve, the predictions are very similar to the measurements. The results of these experiments are very much comparable to the results of the previous experiment (Figures 5 and 6). The overall form of the pH breakthrough is very similar in both cases. This similarity is caused by the fact that in both experimental systems the pH is dominated by the behavior of another component. In the first case this other component is the salt concentration; in the second case it is the fluoride concentration. In both experiments this other component has a comparable effect on the pH. Furthermore, in both cases the pH hardly or does not affect the behavior of the other component. Further Model Calculations. In the fluoride-pH system as discussed above, the separation of the infiltrating and the leaching fronts in two subfronts is easily seen in the pH breakthrough curve, but hardly distinguishable in the fluoride breakthrough curve. This is caused by the fact that at the chosen pH and fluoride concentration, the system is dominated by the behavior of fluoride. This is not always the case as we will show now with some predictions of pH and fluoride breakthrough under different conditions. In a first example we will change the conditions in such a way that the system becomes dominated by the acidity. This can be achieved by increasing the acidity of the system by choosing a lower pH or by decreasing the fluoride concentration. Combining the two conditions we have selected a fluoride concentration of 5 × 10-5 M and a pH of 3.5 for the infiltrating solution. Other input parameters were kept similar to those used in the preceding case. At this lower pH fluoride adsorbs well on the goethite surface, but the amount of protons involved in the adsorption process is small and thus fluoride adsorption affects the pH only very little (Figure 7a). Effectively the system has become more or less a constant pH system. Complete breakthrough of fluoride is predicted in a single steep front after about 14 pore volumes (Figure 7b). Because fluoride adsorption is predicted to be strongly nonlinear at this pH and fluoride concentration (see Figure 3), leaching of fluoride from the column occurs with a diffuse front and takes much longer to complete. In our next example we will choose the conditions such that both the fluoride concentration and the pH change noticeably during the transport process. We therefore applied a higher fluoride concentration of the infiltrating solution of 10-4 M, at the same acidity of the column and the infiltrating solution (pH 4.25). Under these conditions, the concentrations of fluoride and the acidity relative to their mass fluxes to and from the surface are of the same magnitude. So there is a maximum interaction between both adsorption processes during transport. The calculated breakthrough curves are shown in Figure 8. The curve of the pH as well as of the fluoride concentration now clearly show two separate fronts upon infiltrating the column with the fluoride solution. Upon leaching of the fluoride from
a
b
FIGURE 7. Predicted pH (a) and fluoride (b) breakthrough as a function of leached pore volumes in the goethite-coated silica column with an initial pH of 3.5, leached with a 1 × 10-6 M fluoride solution at pH 3.5. After 20 pore volumes the column was infiltrated with a solution at pH 3.5 without fluoride. The arrow indicates the moment at which the input solution was changed.
the column again two fronts are visible for both parameters To illustrate the effect of the variable pH, we also included predictions at constant pH (pH 4.25). Under these conditions both the infiltrating and the leaching front are split into two fronts. Although the mean retardation of fluoride remains the same, breakthrough of the first fluoride front at variable pH occurs considerably more rapidly than breakthrough at constant pH (2 pore volumes instead of 5 pore volumes). Complete fluoride breakthrough at variable pH takes longer (about 10 pore volumes) than it does at constant pH. Upon leaching of fluoride from the column the opposite is visible. Again the fluoride breakthrough curve is split in two fronts, one traveling faster and one traveling slower than the single front at constant pH.
Conclusions The work described here shows that the mechanistic model used for the adsorption behavior of goethite and silica is able to predict the charging behavior of a goethite-coated sand system from the surface areas of goethite and silica present quite well. The combination of this adsorption model with a multicomponent convective-dispersive transport model gave a good prediction of the transport of acidity and fluoride in a goethite-coated sand column. Good prediction of pH levels is essential for prediction of the transport of ions with pH dependent sorption behavior such as fluoride. Modeling of the fluoride adsorption on pure goethite shows that between pH 4 and pH 6 this adsorption can be
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behavior of fluoride demonstrates that for proper modeling it is essential to take into account its interaction with protons.
Acknowledgments The authors are grateful for the financial support for this research from the Scottish Office, Agriculture and Fisheries Department, the Dutch Ministry of Public Health, Spatial Planning and the Environment, the ETH Zurich, and the Swiss part of the COST D5 programme. Furthermore, the authors would like to thank Mr. Th. A. Vens and Mr. E. Kozak for their assistance in the experimental work.
Literature Cited b
FIGURE 8. Predicted pH (a) and fluoride (b) breakthrough curves as a function of leached pore volumes in the goethite-coated silica column equilibrated at pH 4.25 without fluoride, subsequently leached with a 1 × 10-4 M fluoride solution at pH 4.25. After 15 pore volumes the column was infiltrated with a solution at pH 4.25 without fluoride. The arrow indicates the moment at which the input solution was changed. The dotted lines indicate predictions at a constant pH 4.25.
described adequately using a single surface complexation reaction. This extension of the equilibrium model allowed prediction of the adsorption of fluoride at the goethitecoated sand and transport of fluoride in a goethite-coated sand column at variable pH. Results of these predictions were in close agreement with experimental results. The modeling approach allows for relatively simple addition of new substances of interest by adding their interaction with the goethite or silica surface. Interaction and competition between adsorbing ions is then taken into account via their individual interaction with the specific solid phases. The
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Received for review March 20, 1995. Revised manuscript received July 10, 1995. Accepted July 17, 1995.X ES950178Z X
Abstract published in Advance ACS Abstracts, December 1, 1995.
