1618
Ind. Eng. Chem. Res. 1999, 38, 1618-1624
Intensive Periodic Liquid-Liquid Extraction in a Thin Extractant Layer Alon Dolev, Ephraim Kehat, and Ram Lavie* Department of Chemical Engineering, TechnionsIsrael Institute of Technology, Haifa, Israel 32000
The periodic extraction of a solute from an aqueous solution into a thin layer of an organic solvent (extractant) and its back extraction into a second aqueous solution have been studied experimentally. An aqueous solution of citric acid, whose temperature was cycled as a square wave, was circulated through a bed of polypropylene pellets that were coated with a thin layer of an organic solvent containing Alamine 336. The results indicate the following: (a) Periodic extraction by means of a minute amount of extractant, spread on a suitable support material, is feasible. (b) Frequent shallow penetration of the solute into the extractant layer is both feasible and useful as it will intensify the overall average mass transport. (c) The penetration by diffusion of the solute into deep layers of the extractant is too slow to affect the average overall mass transfer. The results of this study should be applicable to liquid-liquid extraction systems using a driving force other than thermal. Introduction Stagewise separation processes rely on the intimate mixing of two phases for equilibration followed necessarily by the reconstitution of the mixture into two distinct and contiguous phases. The intimate contact is favored by the fine dispersion of one of the phases into the other in the form of drops or bubbles. The smaller the drops or bubbles, the tougher is the phase’s reconstitution. Separation processes suffer therefore from an inherent contradiction: on the one hand, intimate mixing is essential to mass transfer; on the other hand, this imposes a high toll on the reconstitution of the phases. Nowhere is this contradiction more disturbing than in liquid-liquid extraction (LLE), which is at the focus of this study. In a recent work,1 an attempt was made at changing the geometry of (thermally driven) LLE to that of a continuous mass transfer across an organic supported liquid membrane (SLM) separating two aqueous phases. It was observed that a thin stable supported liquid membrane already constitutes a formidable resistance to mass transfer because of diffusion limitations. This observation led us to speculate that it may perhaps be possible to reduce the length of the diffusion path by limiting the depth of penetration, such as by frequently alternating the contact of each of the two aqueous phases with a single side of the organic liquid membrane. Once willing to accept this inconvenient mode of operation, one need not be constrained to a flat liquid membrane. Obviously, a dense pack of immobilized bubbles of extractant should provide a much larger surface density than would a flat SLM. One may impart stability to the bubbles by “filling” them with some support. The bubbles will then be represented by a thin film of the organic phase, spread on pellets of a suitable solid support material that will bond the organic layer * To whom correspondence should be addressed. Telephone: 972 4 829 2934. Fax: 972 4 823 0476. E-mail:
[email protected].
with sufficient stability. Configurationwise, we are essentially reformulating the LLE task to the form of an equivalent “rapid-swing sorption process”, reminiscent of the heat mass exchange (HME) adsorption configuration.2 True, in view of its limited surface, the “adsorption” capacity of such a bed cannot be expected to be very large, but this can hopefully be compensated for by frequent reutilization of this smaller capacity. An important additional advantage of such a configuration could be the maintenance of a LLE process using a scarce or expensive extractant, where conventional LLE would otherwise require a costly inventory of the extractant. A possible drawback of the method proposed is possible contamination of the extract with the raffinate, as both periodically occupy the same space. Looking up other related previous work in the field, one will observe that immobilizing the extractant onto solid pellets is not new. The use of SIR (solventimpregnated resin), where the extractant is dispersed homogeneously within a polymeric matrix, has been studied.3 Unless it is chemically bonded, the extractant within the SIR is expected to behave as in the liquid phase. SIRs have been mostly applied to the recovery of divalent metal ions.4,5 Most of these studies deal with the equilibrium distribution of the separated species between the aqueous and the SIR phase reached after several hours. Others have investigated the kinetics of extraction and observed that the process is often controlled by the rate of diffusion in the SIR phase.6 The extraction of citric acid and metals using impregnated resins has been investigated,7-10 with the conclusion that sorption is controlled by the diffusion within the resin. Our present work considers the thermally driven extraction of aqueous citric acid using an amine-based extractant. Related previous work on liquid-liquid extraction of carboxylic acids using amine extractants includes many studies.11-17 The equilibrium between the phases is modeled by assuming a set of reactions between i nondissociated acid molecules in the aqueous phase and j amine molecules, thus forming a complex
10.1021/ie980502+ CCC: $18.00 © 1999 American Chemical Society Published on Web 03/13/1999
Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1619
in the organic phase:
(
)
-∆Hij ∆Sij + RT R
βij ) exp
(1)
For the sake of simplicity,18 we assume that the only citric acid-amine complex that is formed is the 1:1 complex, matching one molecule of acid to one molecule of amine. With the assumption of activities equaling concentrations, the reaction equilibrium is modeled by Figure 1. Experimental apparatus.
β11Caq,undissCBT Corg ) 1 + β11Caq,undiss
(2)
where Corg represents the concentration of the total acid in the organic phase, Caq,undiss, represents the concentration of the nondissociated acid in the aqueous phase, and CBT represents the total amine concentration in the organic phase. β11, the equilibrium constant, is a function of temperature as
(
β11 ) exp
)
-∆H11 ∆S11 + RT R
(3)
where ∆H11 and ∆S11 are respectively the enthalpy and entropy of the exothermic complexation reaction. Increasing the temperature will tend to increase the acid concentration in the aqueous phase. To establish our expectation concerning the irrelevance of the extractant layer thickness as long as we consider only shallow penetration, two alternative mathematical models of the system are developed and confronted with experimental data. Physical Model. Because our interest lies primarily in shallow penetration, we could focus exclusively on extractant coated pellets (ECP) in which the extractant does not penetrate the impermeable pellets. However, stability considerations lead us to prefer a somewhat porous pellet which can impart more stability, as indeed was observed by adding a dye to the extractant and studying the dissected pellets under the microscope. As eventually established further down, those impregnated pellets still deserve being named ECP, as most of their surface was indeed coated with the extractant. In any case, the penetration depth can be reduced by frequent switching of the contacted aqueous phases. As will be evident soon, when switching frequently, the thickness of the extractant layer plays no role other than affecting the physical properties of the supporting pellets. Experimental Section The task and the reactants used in this study are identical to those of Rockman,1 i.e., to extract citric acid from a cold dilute aqueous solution, into an organic phase, and its backextraction to a second hot concentrated aqueous solution. The polypropylene pellets (size 2-4 mm) were impregnated with the organic phase which consisted of a solution of Alamine 336 (the complexing reagent), tetradecane (a diluent), and n-octanol (a modifier). Alamine 336 (technical grade), a tertiary amine with C8-C10 aliphatic chains, was first washed twice with distilled water and then dissolved in the other pure constituents of the organic phase to a composition of 50:45:5 % v/v Alamine 336/tetradecane/n-octanol. The
aqueous phase was prepared by dissolving citric acid in distilled water and saturating it with n-octanol. A solution of citric acid brought in contact with the original nonimpregnated pellets for several hours showed no change in conductivity. Hence, it was deduced that the pellets do not adsorb the acid. The ECPs were prepared by immersing the raw pellets in the extractant solution for 1 min, filtering, and then blowing away any excess of extractant with air at room temperature. The ECPs were then immersed in distilled water at a temperature of 80-90 °C for 15 min and filtered, and the excess of water was blown away with air at room temperature. Typically the ECPs would add 16-20%, in weight, as compared to the original PP pellets. The void fraction was ) 0.45. Experimental Apparatus. The experimental apparatus is depicted in Figure 1. It consists of the following: (1) a feed tank; (2) a 52 cm3 extraction chamber; (3) a heat exchanger at the entrance to the extraction chamber, alternatingly heating and cooling the feed to the chamber, by changing the heating/cooling medium in steps; (4) a recycle pump; (5) a wellcalibrated, thermally compensated, electrical conductivity cell (the feed to the cell was constantly cooled to reduce measurement noise); (6) data logging and processing of the essential data. The total internal volume of the apparatus was 92 mL, 28 mL of which was occupied by the ECPs and the balance of 64 mL being the aqueous phase. The feed to the extraction chamber was well dispersed. The aqueous phase was recirculated at a rate of 214 mL/min in most of the runs. Because of the dispersion in the extraction chamber and the relatively fast recycle, the aqueous phase was considered as well mixed. Experimental Runs. Each experimental run followed the subsequent procedure: (1) The extraction chamber was filled with fresh ECPs. (2) A citric acid solution with an initial concentration of 0.009 M was fed from the feed tank to fill the experimental apparatus. (3) The aqueous phase was then recirculated at constant temperature for 15-45 min for initial stabilization. (4) The temperature of the feed to the extraction chamber was then switched between two temperatures, at a prescribed frequency. The list of runs is detailed in Table 1. Mathematical Model. We need first to establish which of the following two descriptions fit the experimental data: (a) homogeneous dispersion of the extractant in the pellet or (b) heterogeneous dispersion in (or coating with partial penetration of) the pellet. Consider first the homogeneous dispersion of the extractant in a spherical pellet. A similar problem was solved for the
1620 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 Table 1. List of Experimental Runsa run
pellets extraction back extraction period, batch temp, °C temp, °C min
1
4
15.5
29.5
12
2
4
15.5
30
12
3 5 6 7 8 9
3 1 1 1 2 2
27 15.5 24 26 16.5 15.5
26 35 71 27 27
6 6 4 3 6
2
15.5
27
12
10 a
remarks initial stabilization 45 min at 15.5 °C; five periods at a recycle flow of 214 mL/min + five periods at a recycle flow of 110 mL/min initial stabilization 45 min at 15.5 °C; five periods at a recycle flow of 110 mL/min + five periods at a recycle flow of 214 mL/min constant temperature 7.7 h initial stabilization 30 min at 16 °C initial stabilization 30 min at 24 °C initial stabilization 15 min at 25 °C + 4 min at 70 °C initial stabilization 45 min at 15.5 °C six feeds; initial stabilization 45 min at 16 °C; seven washes between feeds with distilled water at 65-70 °C initial stabilization 45 min at 15.5 °C
Unless stated otherwise, all runs were conducted at a recirculation flow rate of 214 mL/min.
diffusion of a gas in a catalyst pellet19 and for the extraction of copper ions in extractant impregnated resins9 (EIRs). The following assumptions are used: (1) Internal diffusion is the rate determining step. (2) The citric acid is not adsorbed by the polymer matrix. (3) There is a uniform temperature in the pellets. (4) The diffusion coefficient depends on the temperature only. (5) It is a perfectly mixed aqueous phase. (6) The only complex in the organic phase is the complex 1:1. (7) Equilibrium prevails at the ECP-aqueous interface. (8) Pellets are uniform spheres of 1.5 mm radius. (9) There is radial diffusion only. A mass balance within the pellet yields
(
)
∂Corg Deff ∂ 2 ∂Corg r ) 2 ∂t ∂r r ∂r
(4)
with initial condition
Corg(r,0) ) 0
Figure 2. Heterogeneous dispersion of the extractant in the pellets.
The concentration of the nondissociated acid in the water needed for eq 8 is calculated from the total concentration of the aqueous phase using the dissociation constants of the acid as found in the literature.20 Consider now the simplified heterogeneous dispersion model, as typified in Figure 2. Here, the pellet is coated with a uniform layer of extractant, of thickness L, over a 3 fraction of its surface, while the rest of the surface (a fraction 2 of the surface) of the pellet has been penetrated by the extractant. This is equivalent to stating that a fraction 2 of the volume of the pellet has been penetrated by the extractant and 3 is the fraction of the pellet that is only coated.
(5) 2 + 3 ) 1
and boundary conditions
At r ) 0,
∂Corg/∂r ) 0 (symmetry)
At r ) Rad,
Corg ) f(Caq,T)
(6) (7)
f represents the equilibrium concentration of the organic phase as a function of temperature and concentration in the aqueous phase. When eq 2 is inserted, boundary condition (7) can be rewritten as
At r ) Rad,
Corg )
β11Caq,undissCBT 1 + β11Caq,undiss
|
∂Caq ∂Corg ) -1ADeff ∂t ∂r
r)Rad
(9)
In eq 9 Vaq is the aqueous phase volume, 1 is the total volume fraction of the ECPs occupied by the extractant, and A is the total external surface area of the ECPs. The initial condition for eq 9 is the aqueous feed concentration:
At t ) 0,
Caq ) Caq,feed
With 1 defined as for the homogeneous model, it can be shown by a material balance on the extractant that for L , Rad
4Π × Rad3 1 - L × 4Π × Rad2 3 2 ) 4Π × Rad3 - L × 4Π × Rad2 3
(12)
(8)
The mass balance in the aqueous phase is given by
Vaq
(11)
(10)
Using the same assumptions as above, the mass balance within the internal extractant (Corg,int) as well as in the external extractant layer (Corg,ext), yields equations identical to eq 4-8, with the exception that the boundary condition (6) must be replaced by
∂Corg,ext )0 ∂r (the polymer matrix does not adsorb acid) (6a)
At r ) Rad - L,
The mass balance in the aqueous phase, assuming the same effective diffusion coefficient in the coating and
Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1621
Figure 3. Concentration in the aqueous phase vs time at two different recycle flow rates: solid line, run 1; dashed line, run 2. Table 2. Equilibrium Experiments
interior extractant, becomes
|
∂Caq ∂Corg,int Vaq ) -2ADeff ∂t ∂r
-
|
r)Rad
∂Corg,ext 3ADeff ∂r
r)Rad
(9a)
with unchanged initial condition (10). In the two descriptions above, we presumed that the distribution of the resistance to mass transfer in and around a pellet is such that diffusion within the organic phase constitutes most of the resistance. This turns out to be supported by experimental evidence on two counts: (1) Figure 3 represents the results of two runs, at conditions that are equal in every respect, except for the circulation of the aqueous phase through the chamber being twice as big in one than in the other. Little change is apparent between the outcome of the two runs in Figure 3, even though the resistance to mass transfer between the aqueous phase and the pellet must be significantly different. (2) Suppose the resistance to mass transfer by diffusion within the organic layer was negligible, and the only resistance was that between the aqueous phase and the pellet. Then, one would expect a uniform concentration distribution within the organic layer at any depth, leading to a unique rate of mass transfer corresponding to a given aqueous phase concentration. This is evidently contradicted by comparing times t2 - t1 to t4 t3 in Figure 3. We conclude that the presumption claiming that the diffusion within the organic phase constitutes most of the resistance is plausible. Parameter Fitting and Discussion. The unknown parameters in the homogeneous model are Deff and its temperature dependence, β11 and its temperature dependence (∆H11, ∆S11), and 1. In the heterogeneous model, L is also unknown. Hence, in order to deduce the validity of either description, it is necessary to determine the parameters through separate unrelated experiments. 1. Temperature Dependence of Deff. Deff can be evaluated by18
T/Tref Deff(T) ) Dref 1 1 exp B T Tref
[(
)]
(13)
In eq 13 Dref is the effective diffusion coefficient at a
temp, °C
Caq, M × 103
Corg, M × 103
Caq,undiss, M × 103
β11 exp
16.5 26.5 39
2.9 4.8 6.0
93 65 46
1.8 3.2 4.2
58 22 11
reference temperature Tref (taken as 20 °C). Using data from Rockman,21 who has evaluated the value of B for extractants of similar compositions, the B parameter was extrapolated as B ) 2500 K. Dref cannot be taken from the same reference because it depends on the particular composition of extractant. 2. Determination of the Temperature Dependence of β11 (through ∆H11 and ∆S11). ∆H11 and ∆S11 were evaluated, in a separate set of tests, carried out at the temperatures of interest, by equilibrating at different constant temperatures 10 mL of extractant (of composition 50:45:5, v/v) with 154 mL of a 0.009 M aqueous citric acid solution. The volume ratio of extractant/aqueous phase was chosen to approximate the relative calculated amount of extractant attached to the pellets relative to the amount of aqueous phase in the periodic runs. The equilibrium concentration of the aqueous phase was determined by electrical conductivity measurement. The composition of the organic phase, at equilibrium, was evaluated by carrying a mass balance on all of the citric acid. β11 was calculated from eq 2. The results of these runs are delineated in Table 2. β11 fits eq 3 in the temperature range of 16.5-39 °C. Equilibrium was measured with the purpose of determining a boundary condition in the kinetic models. It was found convenient to divide the temperature range into two subranges, 16.5-26.5 and 26.5-39 °C, to improve the accuracy of the model description. The best fits for ∆H11 and ∆S11 were found to be
For the temperature range of 16.5-26.5 °C: ∆H11 ) -70576 [J/mol]; ∆S11 ) -210 [J/(mol‚K)] For the temperature range of 26.5-39 °C: ∆H11 ) -40582 [J/mol]; ∆S11 ) -109.9 [J/(mol‚K)] 3. Determination of E1. The total volume fraction of the ECPs occupied by the extractant 1 was determined by weighing the pellets before and after the coating. The average weight gain was 17%. The measured density of the PP pellets was measured as 0.75 g/mL; which is about the density of the extractant; hence
1622 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999
1 )
0.17 ) 0.145 1 + 0.17
4. Fitting of Dref and L. Dref for the homogeneous extractant dispersion model or Dref and L for the heterogeneous dispersion model were evaluated through a best fit of the data:
Min ERR )
∑λ(t) (Cexp(t) - Ccalc(t))2
(14)
where Ccalc(t) are calculated values obtained by numerical integration (eqs 4-12) and the weighing function λ(t) stresses the periodic part of the experimental data. No reasonable fit through eq 14 was obtained for the homogeneous description. On the other hand, the fit for both Dref and L in the heterogeneous extractant dispersion model, as repeated with different batches of pellets and evaluated for a number of runs all conducted with the same batch of pellets, did provide trustful results. The best fits found by eq 14 were
Figure 4. Concentration in the aqueous phase vs time. Fitting the heterogeneous dispersion model to the experimental data: solid line, simulation; dashed line, run 10.
In batch 1: L ) 2.4 × 10-5 [m], Dref ) 6.5 × 10-13 [m2/s] In batch 2: L ) 2.4 × 10-5 [m], Dref ) 2.5 × 10-13 [m2/s] A typical comparison of model to experimental data is presented in Figure 4. The effective diffusion coefficient of citric acid in a supported liquid membrane containing 30% Alamine 336 was found to be1 1.64 × 10-12 [m2/s] at 20 °C. Considering the different support and organic phase used in ref 1, this value is deemed reasonable. We conclude the following: (1) The heterogeneous extractant dispersion model fits the experimental results satisfactorily. (2) The thickness of the external shell of extractant coating the pellets is of order 24 µm. (3) The effective diffusion coefficient into the extractant coating and interior at 20 °C is of order 5 × 10-13 [m2/s]. (4) The extractant occupies 10% of the pellet’s interior (2 ≈ 0.1); i.e., 90% of the pellet’s surface functions as an ECP.
Figure 5. Concentration in the aqueous phase vs time over a long time span (data from run 3).
Experimental Results and Discussion As is apparent in Figures 3 and 4, a sharp drop in the aqueous phase concentration is observed in all of the runs, during the first minutes of the initial stabilization stage, leveling off with time. This is attributed to the saturation of the external layer extractant followed by slow gradual penetration into internal layers. In a separate run, covering stabilization only (Figure 5), diffusion to the interior of the pellets is observed to continue for hours. In run 5, it was found that the total amount of acid extracted by the pellets (norg) at a temperature of 15.5 °C, after a stabilization time of 30 min, was 2.5 × 10-4 g‚mol. Simulation of the same run with L ) 24 µm and Dref ) 6.5 × 10-13 m2/s, indicates that the total amount of acid extracted in the external shell (norg,ext) is 2.4 × 10-4 g‚mol. It follows that, within 30 min, 96% percent of the extracted acid has only penetrated the external shell of extractant coating the pellets. Furthermore, complementing the experiments by a calculated space distribution of the complex within the external shell
Figure 6. Concentration profile in the extractant layer, at the limit cycle. Simulation run 10. Symbols: *, end of the extraction stage; +, end of the backextraction stage. Location index: 0, pellet surface; 15, external surface of the extractant layer.
(Figure 6), it is observed that the concentration Co at the original pellet surface remains roughly constant throughout the extraction and backextraction steps, for all runs (which covered a 4-fold range of frequencies). It may then be concluded that, at the switching frequencies applied in our experiments, penetration of the complex into internal layers of the pellet is of little significance. Furthermore, because our objective is shallow penetration into a thin coat of extractant, we conclude that, for a sufficiently frequent switching, this is achievable irrespective of the thickness of the extractant layer.
Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1623 Table 3. Effect of Temperature Level TL on the Concentration Span ∆Caq run
period time, min
TEX, extraction temp, °C
TBX, back extraction temp, °C
∆T, temp span, °C
∆Caq, conc span, M × 103
TL, (TEX + TBX)/2, °C
5 6
6 6
15.5 24
26 35
10.5 11
0.8 0.55
20.75 29.5
range. This conclusion is in line with data published by Bizek.14 In that study a decrease in the equilibrium concentration sensitivity to temperature with increasing temperature level was reported for a similar extraction system using a similar volume ratio of the phases. 2. Even though frequent shallow extraction need not necessarily be implemented using a thermally driven process, it is of interest to consider the implications of such. The amount of heat transferred at each cycle from one solution to the next may affect the economy of a thermally driven process. Assuming that each of the aqueous phases is well mixed, the heat transfer is22
Qt Q∞
)1-
6
∞
∑ 2 n)1
Π
1 2
exp(-Rn2Π2t/Rad2)
(15)
n
where R ) k/FCp, Qt is the amount of heat transferred to the pellets at time, and Q∞ is the heat transferred to the pellet at infinite time. Using typical values of
k ) 0.15 w/(m‚K), F ) 800 kg/m3, Cp ) 2000 J/(kg‚K) Figure 7. Average flux and concentration amplitudes as a function of switching frequency.
Switching Frequency Considerations A primary premise of this work is the assumption that, up to a practical limit, it should be possible to increase the productivity of the “packed-bed extraction” process by increasing the frequency of alternating the contact of the two aqueous phases with the bed. Thus, one will compensate for the limited amount of active extractant participating in the process. Figure 7 depicts the results of a set of identical runs carried at different switching frequencies over a 4-fold range. It plots the resulting amplitude of the aqueous acid concentration periodic response as well as a representative average flux calculated as ∆Caq/∆t. We have here a clear indication that indeed one can intensify the process by switching at intervals on the order of minutes. Considerations Specific to the Thermally Driven Process. 1. The temperature level, TL (taken as an average of extraction and backextraction temperatures), can be expected to affect the outcome of the process in two ways: (1) the effect of temperature on transport rates and (2) the effect of temperature on complexation equilibrium. A lower temperature is expected to disfavor transport rates by virtue of its effect on viscosity. Table 3 summarizes runs carried out at the same conditions except for the temperature level TL. It is apparent that, within the considered range of conditions, the average mass flux decreases with higher temperature level. This is contrary to the expectation for the process to slow when lowering the temperature level. It follows that this trend is due to the equilibrium being more sensitive to temperature, at least within this lower temperature
for respectively the thermal conductivity, the density, and the specific heat in an ECP, it follows (as expected) that the heat transfer to/from the pellet is much faster (99% completion within 10 s) than the mass transfer. Hence, the amount of heat transferred at each cycle is proportional to the heat capacity of the ECP, indicating a preference for pellets of low heat capacity. Stability Considerations. The stability of the extractant shell on the ECP is obviously important. This consideration includes two components: (a) Physical stabilitysis the extractant layer eroded or dissolved with time and how fast? (b) Chemical stabilitysdoes the layer lose some or all of its activity with time and how fast? Both considerations cannot be generalized at this stage because they depend on many factors that were not at the focus of this limited study. Still, a series of tests, in which the same batch of ECP was repeatedly washed, with hot distilled water, and reused, were carried out (run 9). An overall loss of activity of 14% during the initial 21 washing cycles and little observable change afterward was observed. This cannot be considered a comprehensive test of stability and certainly cannot serve to predict how some other similar system will behave. It does, however, indicate that this should not constitute a formidable obstacle. Conclusions Periodic, liquid-liquid extraction of citric acid on a bed of extractant-coated polymer pellets appears to be feasible. Diffusion of the formed complex within the extractant is slow. Frequent, shallow penetration into the extractant layer at each cycle intensifies the masstransfer rate.
1624 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999
Acknowledgment This work was supported by a grant from the fund for promotion of research at the Technion. Nomenclature A: total external surface area of ECPs, m2 B: parameter of viscosity sensitivity to temperature, K C: concentration, g‚mol/m3 Cp: specific heat, J/(kg‚K) Deff: effective diffusion coefficient, m2/s ERR′: sum of squares of deviations, (g‚mol/m3)2 ∆H: enthalpy of reaction, J/g‚mol k: thermal conductivity coefficient, J/(s‚m‚K) L: thickness of external coating, m r: radial coordinate, m R: gas constant, J/(g‚mol‚K) Rad: radius of pellets, m ∆S: entropy, J/(g‚mol‚K) t: time, s T: temperature, K V: volume, m3 Greek Symbols β: equilibrium constant λ: weight function : overall void fraction 1: total volume fraction of the ECPs occupied by the extractant 2, 3: fractions of pellet surface or volume, defined in eqs 11 and 12 F: density, kg/m3 Subscripts Aq: aqueous phase aq,undiss: undissociated acid in the aqueous phase avg: average BT: total amine in the organic phase BX: back extraction calc: simulations data EX: extraction exp: experimental data L: level o: original pellet surface org: organic phase ref: reference temperature 11: 1:1 complexation
Literature Cited (1) Rockman, J. T.; Kehat, E.; Lavie, R. Thermally Enhanced Extraction of Citric Acid Through Supported Liquid Membrane. AIChE J. 1997, 43 (9), 2376-2380. (2) Lavie, R. An Optimal Interaction of Heat and Mass Exchange for the Improvement of Separation Efficiency. Chem. Eng. Sci. 1985, 40, 2019-2025. (3) Warshawsky, A. Extraction with Solvent Impregnated Resins. Ion Exchange and Solvent Extraction; Marcel Dekker: New York, 1981. (4) Cortina, J. L.; Miralles, N.; Aguilar, M.; Warshawsky, A. Solid Liquid Distribution of Divalent Metals from Nitrate Media Using Impregnated Resins Containing a Bifunctional Organophosphorous Extractant (O-methyl-dihexyl-phosphine-oxide O′hexyl-2-ethyl phosphoric acid). React. Funct. Polym. 1995, 27, 6173.
(5) Akita, S.; Takeuchi, H. Sorption and Separation of Metals from Aqueous solution by a Macromolecular Resin Containing Trin-octylamine. J. Chem. Eng. Jpn. 1990, 23 (4), 439-443. (6) Cortina, J. L.; Miralles, N. Kinetic Studies on Heavy Metal Ions Removal by Impregnated Resins Containing Di-(2,4,4-trymethylpentyl) Phosphinic Acid. Solvent Extr. Ion Exch. 1997, 15 (6), 1067-1083. (7) Juang, R. S.; Chou, T. C. Sorption Kinetics of Citric Acid from Aqueous Solutions by Macroporous Resins Containing a Tertiary Amine. J. Chem. Eng. Jpn. 1996, 29 (1), 146-151. (8) Juang, R. S.; Chou, T. C. Sorption of Citric Acid from from Aqueous Solutions by Macroporous Resins Containing a Tertiary Amine Equilibria. Sep. Sci. Technol. 1996, 31 (10), 1409-1425. (9) Juang, R. S.; Lin, H. C. Metal Sorption with ExtractantImpregnated Macroporous Resins. 1. Particle Diffusion Kinetics. J. Chem. Technol. Biotechnol. 1995, 62, 132-140. (10) Juang, R. S.; Lin, H. C. Metal Sorption with ExtractantImpregnated Macroporous Resins. 2. Chemical Reaction and Particle Diffusion Kinetics. J. Chem. Technol. Biotechnol. 1995, 62, 141-147. (11) Tamada, J. A.; Kertes, A. S.; King, C. J. Extraction of Carboxylic Acids with Amine Extractants. 1. Equilibria and Law of Mass Action Modeling. Ind. Eng. Chem. Res. 1990, 29, 13161327. (12) Tamada, J. A.; Kertes, A. S.; King, C. J. Extraction of Carboxylic Acids with Amine Extractants. 2. Chemical Interactions and Interpretation of Data. Ind. Eng. Chem. Res. 1990, 29, 13271333. (13) Tamada, J. A.; Kertes, A. S.; King, C. J. Extraction of Carboxylic Acids with Amine Extractants. 3. Effect of Temperature, Water Coextraction, and Process Considerations. Ind. Eng. Chem. Res. 1990, 29, 1333-1338. (14) Bizek, V.; Horacek, J.; Rericha, R.; Kousova, M. Amine Extraction of Hydrocarboxylic Acids. 1. Extraction of Citric Acid with 1-Octanol/n-Heptane solutions of Trialkylamine. Ind. Eng. Chem. Res. 1992, 31, 1554-1562. (15) Bizek, V.; Horacek, J.; Rericha, R.; Kousova, M. Amine Extraction of Citric Acid: Effect of Diluent. Chem. Eng. Sci. 1993, 48, 1447-1457. (16) Eyal, A. M.; Canari, R. pH Dependence of Carboxylic and Mineral Acid Extraction by Amine-Based Extractants: Effects of pKa, Amine Basicity, and Diluent Properties. Ind. Eng. Chem. Res. 1995, 34, 1789-1798. (17) Prochazka, J.; Heyberger, A.; Volaufova, E. Amine Extraction of Hydrocarboxylic Acids. 3. Effect of Modifiers on Citric Acid Extraction. Ind. Eng. Chem. Res. 1997, 36, 2799-2807. (18) Rockman, J. T.; Kehat, E.; Lavie, R. Mathematical Model for Thermally Enhanced Facilitated Transport. Ind. Eng. Chem. Res. 1995, 34, 2455-2463. (19) Cussler, E. L. Diffusion Mass Transfer in Fluid Systems, 2nd ed.; Cambridge University Press: Cambridge, U.K., 1997; pp 76-78. (20) Dissociation Constants of Acids in Water at various Temperatures. In CRC Handbook of Chemistry and Physics, 67th ed.; Weast, R. C., Astle, M. J., Beyer, W. H., Eds.; CRC Press: Boca Raton, FL, 1986-1987. (21) Rockman, J. T. Thermally Driven Liquid Liquid Extraction. Ph.D. Dissertation, TechnionsIsrael Institute of Technology, Haifa, Israel, 1995. (22) Carslaw, H. S.; Jaeger, J. C. Conduction of Heat in Solids, 2nd ed.; Oxford University Press: Oxford, U.K., 1959.
Received for review August 3, 1998 Revised manuscript received January 5, 1999 Accepted January 15, 1999
IE980502+
