Znd. E n g . C h e m . Res. 1987,26, 117-124
117
Analysis of Liquid Extraction for Hydrometallurgical Systems: Iron(II1) SulfateP-Alkenyl-8- hydroxyquinoline/Xylene System Cesar A. Savastano,?Pradeep M. Bapat,' Chun-Kuo Lee, and Lawrence L. Tavlarides* Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, N e w York 13244
The performance of a continuous-flow stirred tank hydrometallurgical extractor has been simulated. Two models are used for such simulations: a noninteraction model based on macroscopic material balances and an interaction model featuring a stochastic treatment of the microscopic hydrodynamics of the dispersion. The models incorporate equilibrium and intrinsic kinetic expressions pertaining to a chemical system of hydrometallurgical interest: iron(II1) sulfate-/3-alkenyl-8-hydroxyquinoline/xylene. Comparison between the model predictions and the experimental results indicates the interaction model to be more accurate than the noninteraction model. However, the computationally simple noninteraction model can be used to obtain first approximation to extractor performance, especially when interdrop mixing effects are not important. Liquid-liquid extraction is an important hydrometallurgical operation. Originally confined mainly to the processing of nuclear fuels, liquid extraction is now increasingly used for obtaining nonnuclear metals of industrial significance. The reasons for increased acceptance of liquid extraction as a commercially viable hydrometallurgical operation are poorer ore grades, stricter pollution control regulations, and higher costs of energy. These factors adversely affect the economy of traditionally practiced pyrometallurgy and favor the energy-efficient, moderately polluting hydrometallurgy. Large-scale hydrometallurgical operations involving liquid-liquid dispersions are usually carried out in mixersettler contactors. The aim of this work is to study the effect of varying operating conditions on the performance of a continuous-flow stirred tank reactor (CFSTR) commonly employed by the hydrometallurgical industry. To accomplish this objective, a chemical system of iron(II1) sulfate~-alkenyl-8-hydroxyquinoline (PA8HQ)/xylene was chosen. The incentive for studying the complex iron chemistry arises because of its ubiquitous presence as an impurity in ores of more valuable metals such as nickel and cobalt. The individual investigations on the hydrochemistries of the valuable metal and the undesired impurity are essential prerequisites for the investigation on the selective extraction of the valuable metal from the naturally occurring composite ores. Two reactor models were developed to predict the performance of a CFSTR as a liquid-liquid extractor. These models incorporate the reaction thermodynamics and kinetics of the Fe"' extraction by PA8HQ with the dispersion hydrodynamics. The models differ from each other in their treatment of the dispersion hydrodynamics. The total dispersion interfacial area and the interdrop mixing resulting from random drop processes of breakage and coalescence are important factors in the analysis of two-phase liquid-liquid dispersion reactions. The first model (noninteraction model) neglects the interactive droplet processes occurring in a mechanically agitated CFSTR. The interfacial area required to determine the interphase solute transfer is obtained by experimental measurements. The second model (interaction model) Present address: Imperial College of Science and Technology, London SW7 2AY, England. *Presentaddress: The Goodyear Tire and Rubber Company, Akron, OH 44316-0001. 0886-5885/87/2626-0117$01.50/0
employs a Monte Carlo algorithm to simulate the random droplet activities of coalescence and breakage. The interfacial area and the interdrop mixing are represented more realistically in this model and therefore the performance predictions by the interaction model agree better with the experimental results acquired from a laboratory-scale CFSTR system. The dual-model developmentwas intended to assess the efficacy of the sophisticated but computationally intensive stochastic simulation technique over the simple noninteractive model.
Theory The models on reaction chemistry (stoichiometry, thermodynamics, and kinetics) and dispersion hydrodynamics must be developed before a reactor model for two-phase liquid-liquid extraction can be synthesized. They are discussed below. Reaction Stoichiometry. In aqueous sulfate solution, iron is present in various ionic forms. The transfer of iron from the aqueous phase to the organic phase is likely to occur as a result of PA8HQ reacting with various iron species via a complex system of stoichiometric equations. However, out of the multiple ionic species of iron in the aqueous medium, only ferric iron (Fe3+)is extracted by PA8HQ. By use of the method of continuous variation, it has been shown (Agarwal and Tavlarides, 1986; Lee et al., 1983) that the extraction of iron in aqueous sulfate solution by PA8HQ can be represented by the stoichiometric equation (1). The overbar denotes an organic-phase species. Fe3+ + 3HR
E,+ 3H'
(1)
Reaction Equilibrium Thermodynamics. 1. Aqueous-Phase Equilibrium. The aqueous-phase chemistry of ferric iron in sulfate medium is very complicated due to the existence of numerous ionic species. Since the extraction stoichiometry involves only the ferric ion, its concentration in the aqueous phase has to be accurately known. The speciation of iron in the aqueous phase has been modeled by Lee and Tavlarides (1985). These authors found that the relationship among various ionic species in the aqueous phase is completely described by three nonlinear algebraic equations involving the species concentrations and the ionic strength. These equations result from substituting the expressions for equilibrium constants into the iron balance, sulfur balance, and the electroneutrality condition. The developed aqueous-phase 1987 American Chemical Society
118 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
equilibrium model predicts that under the range of experimental conditions investigated in this work, only 2-7 % of the total aqueous iron exists as ferric ion. The use of total iron concentration instead of ferric ion concentration in the kinetic modeling would obviously give erroneous results. 2. Two-Phase Equilibrium. A thermodynamic equilibrium model of the chelation reaction given by eq 1 was developed by Agarwal and Tavlarides (1986) over the following experimental range of conditions: [FeIfT= 0.01-0.2 g-mol dm-3, [PA8HQ] = 0.02-0.06 g-mol dm-3, pH 0.2-2.0, and temperature = 298-323 K. The reaction equilibrium constant was correlated to temperature and ionic strength as in eq 2 where T is in kelvin and I is in g-mol of ions/dm3.
= 8.79
(t
+ 2623
--
-
2k3)
+ 0.79P.5
(2)
Reaction Kinetics. Lee and Tavlarides (1986) studied the intrinsic kinetics of the iron(II1) sulfakPA8HQ/xylene system by using a liquid jet recycle reactor (LJRR). They proposed the mechanism of eq 3 for the chemical reaction 1 + HR, t+HR,
+ H+, F' H2R+, Fe3+ + H2R+, d FeR2+,+ 2H+, FeR2+,+ H2R+, FeR21s+ 2H+[+ 1 FeR2+, + m, FeR3,L+ H+, + E
rate expression unacceptably low. Therefore, the kinetic data were used to obtain the kinetic constants for the forward rate (cl, c3-c6) only. The constant c2 for the reverse reaction rate in eq 4 was obtained from the two-phase equilibrium data as shown in eq 5. = c,/K
cq
(5)
Dispersion Hydrodynamics. In a two-phase liquidliquid dispersion CFSTR, the drops undergo randomly occurring breakage and coalescence events. In addition, the dispersed phase is continually replenished by the entering feed drops and depleted by the exiting drops. The success of the simulation algorithm in predicting the extractor performance depends upon the accuracy of the frequency functions used to model these four droplet events. The droplet events frequency function used in this work as described below. 1. Feed Frequency. It is assumed that the feed drops are of constant volume, uf, and enter the CFSTR at a fixed deterministic interval set by the feed frequency function, eq 6.
ff
=
(Vd/T)/Uf
(6)
2. Exit Frequency. The exit frequency of a drop is assumed to be independent of its properties. The total exit frequency for a dispersion of N drops is given by eq 7. fe
HR,
= N/7
(7)
(3)
3. Breakage Frequency. The frequency function proposed by Coulaloglou and Tavlarides (1977) has been used in this work (eq 8). The total breakage frequency
where 1 is a vacant active site at the interface. The subscripts i and s refer to concentrations near and at the interface, respectively. Since the reaction is reversible, the rate expression must account for the reverse reaction. The intrinsic kinetic model used in this work is eq 4 (Bapat et al., 1984). R
of the dispersion is obtained by summing the individual drop frequencies (eq 9). Breakage is assumed to be binary. The daughter droplet probability volume distribution is given by the P distribution (eq 10).
C ~ [ F ~ ~ + ] [-HczR[ ]7~ ~ + 1 3 ) / ,&(Q~,u;) =
1 + c,[HR]
c1 =
1.08 X cq
+ c,[HR][H+] + c j
lo-,
= 119
[Fe3+][ m ] [H+l
+
3 0 ( ~ ~ / ~ ;-~ai3/aj3)' )~(1
(10)
4. Coalescence Frequency. The frequency of a drop of diameter ai merging with a drop of diameter aj is obtained as a product of collision frequency and coalescence efficiency (eq 11) (Coulaloglouand Tavlarides, 1977). The
cq = 1.14 X c3 = 29 = 8.2 CG = 1674 __
is the rate of ferric complex (FeR,) formation in g-mol cm-2 s-l. The formation of FeR2+sin the reaction mechanism (eq 3) is assumed to be the rate-determining step in the derivation of the rate equation (4). The kinetic data from the LJRR were used to obtain the constants in the kinetic expression. However, the data were primarily collected < for the low concentrations of the iron complex ([=,I 1.5 X g-mol dm-3). At higher iron complex concentrations, the dark outer organic liquid made it difficult to photograph the inner jet of the aqueous raffinate phase. Without the photograph, the jet interfacial area could not be estimated accurately. The low values of the iron complex concentrations rendered the confidence levels of the kinetic constants in the complete (forward and reverse)
coalescence frequency of a single drop of diameter ai is given by eq 12. The total coalescence frequency for an ensemble of N drops is obtained by the summation in eq 13. N
N
fc
=
72c
N
c
F(Ui,Qj)
(13)
1=1 J = ~ , J # I
Reactor Models. By use of the chelation stoichiometry, thermodynamics, and kinetics established in this work, two
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 119
c3
reactor models were developed to simulate a two-phase liquid-liquid CFSTR. The two models, the noninteraction model and the interaction model, differ in their treatment of the dispersed phase. The greater sophistication of the interaction model is representing the dispersed-phase droplet processes of breakage, and coalescence is achieved at the expense of larger computational effort. The synthesis of the two models is outlined below. 1. Noninteraction Model. This model is based on the macroscopic species balances over the entire CFSTR and does not consider the particulate nature of the dispersed phase. The balance equations are written for the total iron, the extractant anion, and the ferric complex (eq 14-16). total iron balance QPelfT = QJFelT + QdFR31
(14)
extractant anion balance
[E], = [E] + 3[=R3]
START
SIMULATION CLOCK M AN4GEMENT
INTERVAL OF OUIESCENCE
-
I
of REACTANTS
CONCENTRATIONS OF INDIVIDUAL DROPLETS IN THE DISPERSED PHASE
I
SYSTEM SPECIFIC EXTRACTION EOULlBRlUM AND KINETICS
I
EXTRACTION EWlLlBRlUM
(15)
IAOUEOUS PHASE I EOUlLlBRlUM CONCENTRATIONS OF SPECIES IN AOUEOUS PHASE
(16)
INTERFACIAL TENSION BETWEEN
ferric complex balance Qd[KR3] = a*V%!
The complexation reaction is assumed to be in the chemical regime, and therefore eq 16 does not contain any diffusion terms. The continuous and the dispersed phases are assumed to be well mixed. The two-phase hydrodynamics is completely characterized by the respective volumetric flow rates (8,and Qd) and the specific interfacial area (a*). Equations 14-16 together with those describing the aqueous-phase equilibrium are solved simultaneously by an iterative procedure (Savastano, 1984) to obtain the iron complex concentration in the organic extract phase. The extraction efficiency is obtained as eq 17.
E=
CONCENTRATION DEPENDENT E4CH DROP 4ND SURROUNDING
I
I
I
-1 ' i IEVENT SELECTION 4 N D E X E C U T I O N
NEW DROP EVENT F R E O U E N C I E S
NEW DISPERSED PHASE S T 4 T E
No
I
1 YES RESULTS
I
[HRIf- [HR]
H [RJ -W [FeR,I =IFeR3leq
l e q
Figure 1. Flow chart for simulation algorithm.
(17)
Themaximum concentration of the organic ferric complex (FeR3eq)obtained as a result of two-phase equilibration in the extractor is calculated by simultaneous solution of eq 2,14,15 and the aqueous-phase equilibrium. The density changes due to the interphase mass transfer in the CFSTR are assumed to be negligible. 2. Interaction Model. This model simulates the micromixing of the dispersed-phase mixing by considering the droplet coalescence and breakage. An event oriented Monte Carlo simulation algorithm based on the interval of quiescence was developed to assess the effect of dispersed-phase mixing on the extractor performance. The stochastic simulation is started by creating a sample of typically 500-600 drops, with sizes distributed according to the Chen and Middleman correlation (1967), and with zero iron complex concentration. The sample is subjected to the environment inside the CFSTR, which is considered homogeneous over the complete reactor volume. The drops undergo feed, exit, breakage, and coalescence events at frequencies given by eq 6,7,9, and 13, respectively. The random time intervals (intervals of quiescence) between two consecutive drop events are calculated by the Poisson formula (eq 18) where x is a uniform random number
between 0 and 1and fi is the long-rangeaverage frequency
of the ith event. The four constants used in the breakage and coalescence frequency functions are the same as used by Bapat et al. (1983). Their values are c1 = 4.81 X ~ m -c3 ~ =, 1 X ~ m - and ~ , c4 = 2 X ~ m -c2 ~ =, 8 X lo8 cm-2. By formulation of the frequency functions, these constants are universal. Due to both theoretical and experimental limitations, complete identification of the universal set of constants has not been possible (Cruz-Pinto and Korchinsky, 1981). However, on the basis of previous investigations (Coulaloglou, 1975; Ross et al., 1978; Hsia, 1981),a definite region of application has been established. This region has been discussed by Bapat and Tavlarides (1985). The simulation clock is advanced by the interval tIQ, during which no abrupt change due to drop birth or death takes place. Smooth changes do occur during tIQ, however, since the concentrations of species involved in the reaction change as a consequence of the interfacial flux. It is assumed that these changes in concentration have no effect on drop size. The simulation flow diagram is shown in the Figure 1. The extractant and the metal complex concentrations at the end of every interval of quiescence are calculated for each drop by solving the corresponding species material balance equations (eq 19). Here, Cij
represents the concentration of the jth species in the ith drop, and .Bij is the flux of species j across the boundary of drop i. The flux for the iron complex is given by eq 4.
120 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
The fluxes for other species can be computed from eq 4 and the stoichiometric equation (1). Applicetion of quasi-steady-state analysis (QSSA) makes possible the solution of this system of nonlinear ordinary differential equations by Euler’s method. The short intervals involved (tIQ 0.01-0.1 s) justify the assumption made in the QSSA of a constant concentration vector C, over the interval of quiescence. The extraction of iron(II1) by PA8HQ brings about a shift in the aqueous-phase equilibria. The simulation algorithm calculates the equilibrium concentrations of the aqueous-phase species involved in the interfacial reaction with each drop in the sample after each tq, using the thermodynamic model. The equilibrium shift is assumed to be infinitely fast. Due to the distribution of drop sizes, the concentrations of extractant and complex also distribute over the drop population. The drop property most affected by this concentration distribution is the interfacial tension. The changes in the dispersed-phase density and viscosity due to concentration variation are assumed negligible. The interfacial tension was found to correlate with the extractant and hydrogen ion concentrations as in eq 20 where u = -6.452 + 9.028pH - 10.582 log [HR] dyn/cm (20)
-
[m]
1.25 < pH < 2.0 and 3 X < < 4 X lo-’ g-mol/ dm3. The effect of metal complex concentration in the drop phase and ferric ion concentration in the continuous phase on the interfacial tension is found to be insignificant. The simulation algorithm accounts for the change in the concentration-dependent interfacial tension between the individual drop and the surrounding continuous phase by computing the drop event frequencies at the end of each interval of quiescence. The spread of the concentrations of the chemical species involved in the reaction depends upon the dispersed-phase mixing brought about by coalescence and breakage. The interaction model developed allows the simulation at varying degrees of dispersed-phase mixing. These simulations are started with the steady-state drop size distributions obtained from the simulation runs carried out for the actual experimental conditions (intermediate segregation). The initial concentration of the drops is the same as the dispersed-phase feed. To simulate complete segregation (zero mixing), the coalescence is completely suppressed ( f , = 0). However, because of the steady-state condition, the breakage cannot operate alone and has to be suppressed too. The drop activities allowed are drop entry and exit. The exited drop is replaced by a dispersed-phase feed drop of the same size. To simulate complete mixing, the same procedure is followed. However, as soon as the replacement for the exit drop is made, the dispersed-phase concentration is averaged out over its entire volume in the CFSTR. The drop exit frequency being sufficiently high, the mixing of the dispersed phase can be thought to be complete. The algorithm can be easily modified to increase or decrease the frequency of concentration averaging if needed.
Experimental System and Data Acquisition Chemicals. Kelex 100 (Trademark of Sherex Chemicals Co.) was used as the chelation reagent PA8HQ. Kelex 100 as supplied was washed first with 1.0 N sulfuric acid solution and then with distilled water. The active pA8HQ content of the washed Kelex 100 was determined by ultimate loading experiments (79.1‘70). Organic feed solutions of the desired concentration in PASHQ (0.04 g-mol dm-3) were obtained by diluting washed Kelex 100 with ACS grade xylene. All other chemicals were used as sup-
D
Figure 2. Experimental flow system.
plied. Two 50-L batches of 0.036 g-mol dm-3 Fe2(SO& solution were prepared with Fluka A.G. ferric sulfate dissolved in distilled water. Appropriate amounts of sulfuric acid were added to maintain the desired pH level. Chemical Analysis and Property Measurements. Atomic absorption spectroscopy was used to determine the concentration of total iron in aqueous-phase samples and the concentration of the iron-PA8HQ complex in the organic extract. A Fisher Accumet Model 630 was used to measure pH of aqueous samples. Buffers of pH 1.00 and 2.00 were used to calibrate this instrument. The pH of the samples stayed between 1.65 and 1.70 and showed negligible variation during an experiment and from run to run. A DuNouy ring tensiometer was used to measure the interfacial tension of dispersion samples taken from the reactor effluent toward the end of each experiment. The interfacial tension averaged to 22.0 dyn/cm under the experimental conditions studied. Experimental Apparatus. The extraction flow system is shown in Figure 2. The aqueous phase containing the metal and the organic phase containing the extractant are continually fed into a stirred tank reactor (SR) from their respective feed reservoirs (CR and DR) by peristaltic pumps (CP and DP). The cylindrical reactor (internal diameter 10 cm, height 10 cm) has a centrally located Rushton turbine (diameter 5 cm). Its speed is controlled by a speed controller SC. The reactor temperature is regulated by a circulating water thermostatic jacket (TJ). Only glass and inert fluoroelastomers are used in the construction of components wetted by the process liquids. Samples of aqueous and organic phases required to monitor iron extraction were obtained by the in situ dispersion separation (filtration) technique developed by Bapat and Tavlarides (1984). The dispersion drop diameter measurements were done photographically. The photomicrographic assembly used is similar to that described by Bapat (1982). The speed and ease of determining the drop size distributions were considerably enhanced by using a semiautomatic particle size analyzer (MOP-30, Carl Zeiss, Inc.) interfaced with a microprocessor (IBM PC). Under the assumption of perfect mixing (no slippage between the phases), volumetric flow rates of the two phases at the desired dispersed-phase holdup ( 4 ) and the resident time ( 7 ) were set as eq 2 1 and 22. The phase
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 121
samples and drop photomicrographs were taken after the extraction apparatus had attained steady state. The extractor was operated for 15 mean residence times to reach steady state. To effect economy and reduce waste disposal, the extractor effluents were recycled. The dispersion from the stirred tank was allowed to stand in a glass bottle. The settled aqueous phase was channeled back to the feed tank (CR): Under the experimental conditions studied, its composition underwent a very small change on its passage through the extractor. The organic phase was distilled to reclaim xylene. The purity of recycled xylene was checked by monitoring its refractive index. Most experiments were duplicated and some were repeated 3 or 4 times.
Results and Discussion The effect of operating conditions on the extractor performance was experimentally investigated. The operating conditions studied were specific power input, the residence time, and the dispersed-phase fraction. The extraction efficiencies were compared against the predictions made by the noninteraction model and the interaction model. Comparisons were also carried out between the experimental drop size distributions and the simulated distributions given by the stochastic interaction model. Marginal volume density concentration distributions were obtained from the interaction simulation model to gauge the effect of dispersed-phase mixing. Effect of Specific Power Input. The specific rate of energy input (E) into the reactor is a cubic function of the rotational speed of the agitator. Of the three operating variables studied, this produces the most pronounced effect. As shown in Figure 3, increasing N from 5.833 to 8.333 rps (E is increased from 0.620 to 1.806 m2/s3)causes the experimental Sauter mean diameter to decrease from 0.253 X lo-, to 0.190 X lo-, m. Predictions by the stochastic simulation for the intermediate segregation are also shown in Figure 3. The agreement between the two results is better at low specific power input. Figure 4 compares the predicted drop size distribution with the histogram obtained in a typical experiment. The crosshatched area represents the inherent oscillations in the steady-state simulation results due to the finite size of the sample. The oscillations can be reduced by increasing the sample size. The secondary peak at larger drop diameters corresponds to the feed drops. Both the distributions and the resulting values for a32 are in good agreement. Marginal drop size distributions predicted by the interactive simulation are shown as volume density functions in Figure 5 for the four stirring speeds used in this study. Figure 5 also shows that Sauter mean diameters decrease from 0.266 X m at 5.833 rps to 0.151 X lo-, m at 8.333 rps. The marginal volume density distribution of droplet sizes is shown to become narrower and to shift toward smaller size with increasing rotational speed. These predictions indicate that the simulation reflects the behavior of the dispersion. Marginal iron-PA8HQ complex concentration distributions are shown in Figure 5 for the simulated cases of intermediate and complete segregation. It can be noted that the average complex concentrations (and thus ex-
0.181
E
0.16
Q
v)
I
''I4[
0
6
0.620
8
7 I
0.925
I
N(rpr1
1
I
2
1.317
Figure 3. Effect of rotational speed on Sauter mean diameter. C#I = 0.10; T = 180 s; [ m ] r = 0.04 g-mol dm-3; = 0.0 g-mol dm-3; [Fe2(S04)&= 0.036 g-mol dm-3; (X) experimental; ( 0 )interaction model (intermediate segregation).
[m31f
OJI X l O %
A
EXPERIMENTAL SIMULATED
0 211
0 213
DROP DIAMETER, O X I O - 3 m
Figure 4. Experimental and simulated drop size distribution. N = 6.667 rps ( B = 0.932 m2s - ~ ) ;C#I = 0.10; 7 = 180 s. Feed concentrations same as noted in Figure 3.
traction efficiencies) increase as N is increased from 5.833 to 8.333 rps. Average complex concentrations for the completely segregated case = 0.00184-0.00249 mol/dm3) are higher than those corresponding to intermediate segregation ([=,] = 0.00171-0.00238 mol/dm3). For both segregation cases plotted, the marginal concentration distributions spread toward higher concentrations as N is increased. This is attributed to the higher rate at which drops mix their volumes and to the larger fraction of smaller drops generated at higher turbulence levels. It must be noted, however, that even if the number of tiny drops with high concentration is large, they account for a small fraction of the total volume. Figure 6 shows the effect of agitation on extraction efficiency. Experimental values rise linearly from 11.3% at 5.833 rps to 24.3% at 8.333 rps. The other three curves
([m,]
122 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
\
m!-
I
ov1 0
I 400
1 800
I
1200
I 1600
I 2000
SI
Figure 7. Effect of mean residence time on Sauter mean diameter. N = 7.500 rps; 9 = 0.10; (X) experimentah ( 0 )interaction model (intermediate segregation). Feed concentration same as noted in Figure 3.
xu 2%
2m SO
DO
2.PbzL0
02
04
0 0
06 0
2
4
6
0
2
4
6
Figure 5. Simulated marginal density distributions. Feed concentrations same as noted in Figure 3. 26
22
18
-
16
-
/r’ 6 41
55
I
6
I 7
I 8
I
85
N(rpsl
Figure 6. Effect of rotational speed on extraction efficiency. 6 = 0.10; T = 180 s. Feed concentrations same as noted in Figure 3. (X) experimentah ( 0 )interaction model, intermediate segregation, and complete mixing; (D) interaction model, complete segregation; (A) noninteraction model.
shown in Figure 6 represent the efficiencies predicted by the noninteraction model and by the stochastic simulation with the three different levels of interdrop mixing, namely complete segregation, intermediate mixing, and complete mixing. The noninteraction model predicts lower efficiencies than the interaction model. The former ignores the drop events of coalescence and redispersion, which are an essential parts of the interactive simulation technique.
The simulated case which assumes completely segregated droplets yields the highest predictions. It is apparent that the consideration of the microscopic phenomena of drop mixing and redispersion affects the efficiency predicted by the models. A general conclusion is that the efficiency decreases consistently as the drop mixing is increased. The kinetics described by eq 4 corresponds to a complex, multiple - reaction, whose order with respect to the reagent (HR) is not unique. This reaction order varies between 1.4 and 3.3 depending on the range of concentrations considered. The conclusion that the highest efficiency corresponds to complete segregation is to be expected for a reaction order larger than one (Levenspiel, 1972). For the condition given in Figure 6, the complete and intermediate mixing interaction models predict essentially the same efficiencies. This observation is explained in terms of the effect exerted by the drop mixing frequency factor. A sharp drop in the efficiency takes place as the volumetric mixing factor is increased from zero (complete segregation) to an intermediate value where E reaches a plateau. Further increase in the mixing factor toward complete mixing does not affect the predictions appreciably. Effect of Mean Residence Time. The effect of change in residence time on the Sauter mean diameter is shown in Figure 7. Experimental Sauter mean diameters decrease from 0.205 X to 0.162 X m as the residence time was increased from 180 to 1800 s at a constant dispersed-phase fraction of 0.10. Sauter mean diameters predicted by the stochastic simulation are also shown in Figure 7. They follow the same trend as the experimental results, decreasing from 0.175 X m at 180 s to 0.152 X m at 1800 s. The experimental extraction efficiencies are compared with those predicted by the noninteraction model and the interaction model in Figure 8. The experimental efficiencies increase from 20.1% to 55.6% as the residence time is increased from 180 to 1800 s. The corresponding interactive simulation predictions are 16.8-40.0%. The corresponding noninteractive predictions are still lower. The results of Figures 7 and 8 are indicative of a dispersion dominated by breakage. In a CFSTR, for a given set of dispersion physicochemical properties, the relative importance of breakage and coalescence is determined by the dispersed-phase feed drop size. In the present work, the feed drop size was larger than the maximum possible drop size expected in the extractor under the operating conditions studied. On entering the reactor, these drops were more likely to break than coalesce. Larger residence
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 123
12
’
0.05
I
I 0.10
I
PHASE FRACTION, 0
I
I
I
I
I
1
0.15
I
I
0.20
4
Figure ’9. Effect of Dhase fraction on extraction efficiency. N = 7.500 rps; T = 180 s; IX) experimental; (A)noninteraction-model. Feed concentrations same as noted in Figure 3.
with an increase in the dispersed-phase fraction can be rationalized.
time affords greater possibility of breakage with the result that the average drop size decreases as the residence time increases. The extraction efficiency increases with the residence time because of larger interfacial area available. The model predictions for extraction efficiency are considerably lower than the experimentally observed efficiencies (Figure 8). The kinetic rate expression (eq 4) used in this work was obtained from the initial rate data when the organic iron complex (product) concentration is low ( E < 5%). At the low product concentration, the forward reaction dominates over the reverse reaction. The model predictions, therefore, are in better agreement with the experimental efficiencies at low residence times when the reverse reaction rates are smaller compared to the forward rates. The disparity increases with increasing residence times as the reverse reaction rates became comparable to the forward reaction rates. The increasing failure of the model with increasing agitation level as seen in Figure 6 can be similarly explained. A more accurate rate expression obtained from the kinetic rate experimental data encompassing the complete range of conditions encountered in this investigation is needed. Effect of Organic-Phase Fraction. The influence of the dispersed-phase fraction on extraction performance was studied by varying it from 0.05 to 0.20. An increase in drop size from 0.184 to 0.222 mm was observed experimentally. The increase in Sauter mean diameter with the dispersed-phase fraction is attributed to the turbulence damping and the enhanced collision frequency (Bapat and Tavlarides, 1985). The variation in the extraction efficiency with the dispersed-phase holdup is shown in Figure 9. The experimental extraction efficiency decreased from 22.1% at 0.05 phase fraction to 19.1% at 0.20 phase fraction. The efficiencies predicted by the noninteraction model shown in Figure 9 also show a decreasing trend, though the predictions are lower by about 6%. The decrease in the extraction efficiency with an increase in the dispersed-phase fraction is caused by a decrease in the interfacial area of the dispersion per unit volume of the dispersed phase. Simple calculations show that although the interfacial area per unit volume of the dispersion increased from 16.3 to 54.1 cm2/cm3,the interfacial area per unit volume of the dispersed phase decreased from 326 to 271 cm2/cm3. Since the equilibrated complex concentration in eq 17 decreases only by 0.5% as the dispersed-phase fraction increased fourfold from 0.05 to 0.20, the efficiency is affected mainly by changes in the dispersed-phase iron complex concentration. With a decrease in the interfacial area available per unit volume of the dispersed phase, the decrease in extraction efficiency
Conclusions The comparison between the predictions made by the interaction model and noninteraction model with the experimental results indicates that the former is a more accurate description of the reactive dispersions. The drop size distributions generated by the interactive model simulation for iron(II1) sulfate-@A8HQ/xylene system closely resemble the experimental distributions and follow the same pattern as the latter change with the varying hydrodynamic conditions. The drop hydrodynamics in such homogeneous dispersions is faithfully represented by the breakage and coalescence rate functions of Coulaloglou and Tavlarides (1977). The constants in the drop rate functions used here were the same as those used earlier (Bapat, 1982) for the water-(iodine)-cyclohexane/carbon tetrachloride system. The application of the same constants for two systems of substantially different physicochemical properties attests to the possibility of an existence of the universal set of constants. Verification with a few more dispersion systems of different physicochemical characteristics is needed before a set of constants can be universally accepted. Also needed is the parametric sensitivity study of these constants. Such a study has not been possible so far because of the prohibitively large computer resource requirements. The interaction model extraction efficiencies, although in qualitative agreement with the experimentalefficiencies, are considerably underpredicted. The predictions made by the noninteraction model are still lower. The difference between the extraction efficiency predictions made by the two models is smaller at low extraction efficiencies. At higher extraction conditions, the spread in the droplet properties is larger, and therefore the error in the noninteraction model assumption of the well-mixed dispersed phase is larger as well. The metal extraction in the system studied was controlled by the slow interfacial reaction. Therefore, the effect of interdrop mixing was not large enough to warrant high computational effort required for the interaction model. Recourse to the computationally intensive interaction model may be required when the reaction is fast or where the diffusional resistances are important. In any case, it is recommended that a simple noniteractive model may be used first to obtain approximate results before employing the complex interaction model. The significant differences between the experimental and the interaction model extraction efficiencies are attributed to the deficiency in the chelation reaction kinetic rate expression. The attempt to extrapolate in the region of high conversion has resulted in an artificially high rate for the reverse reaction and therefore significant under-
124 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
predictions for operating conditions yielding higher extraction efficiencies. This deficiency not withstanding, this work has demonstrated the successful synthesis of a twophase reactor model from the essential component models of reaction thermodynamics and kinetics and the twophase liquid-liquid dispersion hydrodynamics. The reaction model synthesis technique can be a valuable tool in the design and development of two-phase liquid-liquid reactive processes. Acknowledgment We acknowledge support of this research by the Department of Energy through Contract DE-A-COB82ER13002 and thank R. Chiesa for experimental assistance. Nomenclature a = drop diameter a32= Sauter mean diameter a* = specific interfacial area c = concentration E = extraction efficiency f b = sample breakage frequency f, = sample coalescence frequency f, = sample exit frequency f f = sample feed frequency f, = volume density distribution F(a,,a,) = coalescence frequency between drops of diameter a, and a, FeR3 = organic ferric complex g(a) = breakage frequency of a drop of diameter a HR = extractant I = ionic strength K = two-phase equilibrium constant 1 = active site N = number of drops in the sample; stirrer speed Q = volumetric flow rate 3 = complex formation rate t = time T = temperature u = droplet volume V = stirred tank extractor volume Greek Symbols P(a,,a,) = probability density function of a drop of diameter
a, when a drop of diameter a, breaks
impeller power per unit mass = viscosity
e =
p
4 = dispersed-phase fraction = density u = interfacial tension 7 = residence time x = uniform random number between 0 and 1
p
Subscripts
c = continuous phase d = dispersed phase e = exit eq = equilibrium f = feed i = drop event I& = interval of quiescence Superscripts T = total
Registry No. Fe2(S04)3,10028-22-5.
Literature Cited Agarwal, R. K.; Tavlarides, L. L. Metall. Trans. B., in press. Bapat, P. M. Ph.D. Dissertation, Illinois Institute of Technology, Chicago, 1982. Bapat, P. M.; Tavlarides, L. L. Znd. Eng. Chem. Fund. 1984,23,120. Bapat, P. M.; Tavlarides, L. L. AIChE J. 1985, 31(4), 659. Bapat, P. M.; Tavlarides, L. L.; Smith, G. W. Chem. Eng. Sci. 1983, 38(12),2003. Bapat, P. M.; Savastano, C. A,; Lee, C. K.; Tavlarides, L. L. Eighth International Symposium on Chemical Reaction Engineering (ISCRE 8), Edinburgh, Scotland, Sept 10-13, 1984. Chen, H.T.; Middleman, S. AZChE J. 1967, I3(5), 989. Coulaloglou, C. A. Ph.D. Dissertation, Illinois Institute of Technology, Chicago, 1975. Coulaloglou, C. A.; Tavlarides, L. L. Chem. Eng. Sci. 1977,32, 1289. Cruz-Pinto, J. J. C.; Korchinsky, W. J. Chem. Eng. Sci. 1981,36,687. Hsia, M. A. Ph.D. Dissertation, Illinois Institute of Technology, Chicago, 1981. Lee, C. K.; Tavlarides, L. L. Polyhedron 1985, 4(1), 47. Lee, C. K.; Tavlarides, L. L. Znd. Eng. Chem. Fundam. 1986, 25(1), 96. Lee, C. K.; Agarwal, R. K.; Tavlarides, L. L. Paper presented at the ISEC Meeting, Denver, Aug 26-Sept 2, 1983. Levenspiel, 0. Chemical Reaction Engineering, 2nd ed.; Wiley: New York, 1972; Chapter 10. Ross, S. L.; Verhoff, F. H.;Curl, R. L. Znd. Eng. Chem. Fundam. 1978, 17, 101. Savastano, C. A. M.S. Thesis, Syracuse University, Syracuse, NY, 1984. Received for review May 20, 1985 Revised manuscript received May 6, 1986 Accepted June 12, 1986
