1696
Ind. Eng. Chem. Res. 1988,27, 1696-1701
Maiorella, B. Ph.D. Thesis, University of California, Berkeley, 1983. Mannfeld, R. L. US.Patent 4 308 106, 1981. Otsuki, H.; Williams, F. C. Chem. Eng. Prog. Symp. Ser. 1953, 49(55), 55-68. Pemberton, R. C.; Mash, C. J. J. Chem. Thermodyn. 1978,10,867. Peters, M.; Timmerhaus, K. Plant Design and Economics For Chemical Engineers, 3rd ed.; McGraw-Hill: New York, 1979. Petterson, W. C.; Wells, T. A. Chem. Eng. 1977, 84(19), 1. Raphael Katzen Associates "Grain Motor Fuel Alcohol Technical and Economic Assessment". US DOE HCP/J6639-01, June 1978.
Standiford, F. C.; Weimer, L. D. Chem. Eng. Prog. 1983, 79(1), 1. Stephenson, R. M.; Anderson, T. F. Chem. Eng. Prog. 1980, 76(8), 1.
Tyreus, B. D.; Luyben, W. L. Hydrocarbon Processing, 1975, 93. Zurawski, D A.P.V. Equipment Inc., Tonawanda, NY, personal communication, 1984. Received for review August 6, 1986 Revised manuscript received April 18, 1988 Accepted May 5, 1988
A Systematic Method for the Study of the Rate-Controlling Mechanisms in Liquid Membrane Permeation Processes. Extraction of Zinc by Bis(2-ethylhexy1)phosphoricAcid Inmaculada Ortiz Uribe,' Supriya Wongswan, and E. Susana Perez de Ortiz* Department of Chemical Engineering, Imperial College of Science and Technology, London SW7 2BY, England
A new systematic method based on a mathematical model of metal ion extraction with interfacial reaction is described and applied to the study of the rate-controlling mechanisms in liquid membrane permeation. Four different controlling regimes are predicted by the model depending on the range of concentrations of the species involved and the hydrodynamic conditions of the contactor. Experimental results on the extraction of zinc by bis(2-ethylhexyl)phosphoric acid obtained in a spray column and a stirred tank under a wide range of concentrations are analyzed using the proposed method and are found to cover three of these regimes. Following the pioneering work of Li in 1971, there has been an increasing interest in the study of the kinetics and mechanisms of liquid membrane permeation. The process seems particularly attractive when very dilute solutions are involved since the volume ratio between the stripping phase and the feed can be reduced drastically. The process is also capable of giving a higher degree of concentration of solute in the extract in fewer stages while maintaining the high selectivity of conventional solvent extraction. Substantial savings can also be made in the organic solvent inventory. Two forms of membrane geometry are commonly used, the liquid surfactant membranes or emulsion-type liquid membranes (Biehl et al., 1982; Bock and Valint, 1982; Boyadzhiev and Kyvchoukov, 1980; Cahn et al., 1981; Casamatta et al., 1978; Frankenfeld and Li, 1977; Frankenfeld et al., 1981; Hochhauser and Cussler, 1975; Kitagawa et al., 1977; Kondo et al., 1979,1981; Kremesec, 1981; Lee et al., 1978; Marr et al., 1981; Martin and Davies, 1976/ 1977; Melling, 1979; Nakashio and Kondo, 1980; Reddy and Doraiswamy, 1971; Reusch and Cussler, 1973; Schiffer et al., 1974; Schlosser and Kossaczky, 1980; Strzelbicki, 1978; Strzelbicki and Charewicz, 1978; Strzelbicki and Charewicz, 1980; Volkel et al., 1980) and the supported liquid membranes (Barker et al., 1977; Carraciolo et al., 1975; Chiarizia et al., 1983; Choy et al., 1974; Cussler, 1971; Danesi et al., 1981,1983; Imato et al., 1981; Komasawa et al., 1983). The surfactant liquid membrane is the continuous phase of an emulsion dispersed into a third phase. Usually, phases separated by a membrane are completely miscible. The emulsion is stabilized by surfactants. In general, the solute transfers through the membrane from the external Permanent address: Departamento de Ingenieria Quimica, Facultad d e Ciencias, Universidad del Pais Vasco, Apdo. 644, Bilbao 48080, Spain. 0888-5885/88/2627-1696$01.50/0
phase into the emulsion droplets (or internal phase). There are two types of facilitation methods used to increase the mass-transfer rate across the membrane. In one case a reactant is added into the internal phase so that the solute concentration at the membrane-internal phase interface is effectively zero, thus maximizing the concentration gradients through the membrane. Chan and Lee (1984) present a review of the various models which are commonly used to describe this type of facilitated mass-transfer phenomena. In the other type of facilitated transport, a reactant is added to the membrane which reacts with the solute at the external phase-membrane interface, as schematically shown in Figure 1for the transfer of zinc ion. The complex formed diffuses across the membrane, and on reaching the other side of the membrane, the reverse reaction takes place, regenerating the extractant and liberating the solute into the internal phase. This mechanism of transfer is usually called carrier-mediated transport. In both types of facilitated transport, the reactions taking place at the internal side of the membrane can be very fast, so they are not expected to be rate controlling. Then the possible rate-controlling steps are diffusion in the continuous and membrane phases and chemical reaction at the external interface for the carrier-mediated type of transport. Most theoretical treatments of membrane kinetic behavior developed during the last decade, however, have assumed extreme conditions in which negligible contributions due to chemical reaction and aqueous-phase diffusional process are assumed, as Komasawa et al. (1983) and Danesi et al. (1981) point out in their respective works. Thus, only the diffusional process in the membrane has been considered as a possible resistance to the permeation process. The reason for this is most likely due to the lack of available information on the kinetic behavior of the chemical reaction occurring at the aqueous-organic in0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 9, 1988 1697
0
M b4
P
n Y
I
I I FEED 91.
MEHBRME
2
Figure 2. Graphical representation of the model for P = 1.5.
Although the intrinsic diffusivities of Zn2+and H+ are different, electric neutrality in the aqueous film must be maintained so that KH = K D Elimination of the interfacial concentrations from eq 2 gives the following quadratic expression (Wongswan et al., 1981):
STRPpllli 911.
Figure 1. Schematic representation of concentration profiles.
terface (Komasawa et al., 1983). In the present work, a model for carrier-mediated transport that includes the interfacial chemical reaction and the membrane and continuous phase diffusional resistances has been applied to the interpretation of experimental results obtained in a spray column and a stirred tank. The model (Wongswan et al., 1981) is based on the mechanism of interfacial reaction between zinc and bis(2-ethylhexy1)phosphoric acid (HDEHP) in n-heptane (Ajawin et al., 1980,1983,1984) and includes the effect of the emulsifying agent SPAN 80 on the kinetic rate (Breysse and PBrez de Ortiz, 1981). The influence of the reactant concentrations as well as the mass-transfer parameters on the rate-controlling mechanisms of extraction has been analyzed by using the discrimination method developed by the authors (PBrez de Ortiz and Ortiz Uribe, 1987). Mathematical Model The processes controlling the membrane permeability are schematically shown in Figure 1. The membrane permeation equation is derived taking into account such processes as aqueous film diffusion, interfacial chemical reaction, and membrane diffusion. The decomposition rate of the complex at the stripping solution side may reasonably be assumed to be very fast when a strong acid is employed (Chan and Lee, 1984). The resistance to hydrogen and zinc ion diffusion in the stripping solution is also assumed to be negligible. Ajawin et al. (1980) found that, in a surfactant-free system, the extraction of zinc by HDEHP takes place according to the following overall stoichoimetry:
Zn2++
Y2m*
+ 2H+
D
h 2
(1)
where the bars indicate species in the organic phase, RH denotes the dimeric form of HDEHP, and H X is the metal complex. They also reported (Ajawin et al., 1983) that the rate-controlling reaction is interfacial. It is further assumed that the presence of the surfactant affects the interfacial rate of reaction but leaves the stoichoimetry of the overall reaction unchanged. In the mixed regime, the reaction rate equation must be combined with the equations of mass transfer of reactants and products to and from the continuous-disperse interface with the stoichiometry given above. Applying the film theory, the following equations are obtained:
where RZis the rate of extraction of zinc per unit interfacial area. In order to apply the method for the interpretation of experimental results reported elsewhere (PBrez de Ortiz, and Ortiz Uribe 1987), it is convenient to express eq 3 in a dimensionless form. By introducing the dimensionless groups
kI -CZ Da, = kICZCO/CH -_ KOcO
Da, =
KOCH
kIcZcO/cH = -kIKZCZ
CO
KZ CH
eq 3 becomes 2pDa2(2P - 3Dal) + (1 + 2Da2 + 3Dal) = l / p (4) Since the stripping rate has been assumed to be very fast, this equation represents the membrane permeation model at short contact times. Results of computations using eq 4 are shown graphically as log p vs log Da, for P = 1.5 in Figure 2. Four different regions can be seen in this graph which correspond to four different types of rate control represented by the variation of p with Da, and Da,. Region I is the line p = 1.0, which at the conditions of Figure 2 is obtained for Da, < and Da, < 7 X This is the region of maximum efficiency where diffusional resistances are negligible and the extraction flux is equal to the rate of interfacial reaction (chemical regime). In region 11, p varies with Da, but is independent of Da,; this indicates a dependence of the interfacial flux on mass-transfer resistances in the membrane, while in region IV the reverse situation is observed: p varies with Da2 but is fairly independent of Da,; i.e. the extraction rate is affected by mass-transfer resistances in the continuous phase. In region 111, p depends on diffusional resistances in both the continuous and membrane phases. The fact that the proposed model assumes a thin film configuration for the membrane limits the application of eq 4 to short contact times and/or to well-mixed emulsion globules where emulsion droplets are renewed by internal circulation. Ho
1698 Ind. Eng. Chem. Res., Vol. 27, No. 9, 1988
et al. (1982) have proposed a model for unsteady transport in noncirculating spherical emulsion globules which takes into consideration solute accumulation in the emulsion droplets. However, the use of this model for short contact times, Le., when the membrane resistance to complex transfer is low, is expected to yield the same control regimes as discussed before. Theoretically, either of these four types of rate control could take place in a liquid membrane contactor. In this work, the rate-controlling steps of experimental results obtained in both a spray column and a stirred tank are discussed.
Table I. ExDerimental Conditions in the SDrav Column Co, kmol P m-3 run Cz, kmol m-3 CH,kmol m-3 C0/CH 1 2.04 x 10-3 0.075 48.3 1.31 2 1.78 x 10-3 1.17 X 63.83 1.517 0.075 3 1.64 x 10-3 1.526 i.07 x 10-3 140.0 0.15 1.584 4 70.0 1.70 x 10-3 0.075 1.07 X 4.74 x 10-3 5 1.1 X 45.60 0.05 4.32 6 4.62 x 10-3 1.12 X 66.84 0.10 4.12 7 4.77 x 10-3 1.12 X 89.12 4.25 0.10
20
Experimental Section Experiments were performed in a spray column, 1 m long and 0.05 m internal diameter, with sampling points a t 0.20-m intervals along the height. Full details of the setup and procedures are given elsewhere (Wongswan et al., 1981). The membrane phase consisted of HDEHP in n-heptane with 3 vol % SPAN 80 (Honeywell-Atlas) as surfactant, and the internal aqueous phase was a 1.5 M solution of sulfuric acid. The aqueous-oil emulsion with a phase ratio of 1:l was prepared just before each run with a Silverson high-shear homogenizer a t a stirring speed of 1500 rpm running for 30 min. The continuous phase had an ionic strength of 0.3 kmol m-3, and its initial pH value was adjusted by addition of small amounts of sulfuric acid. HDEHP was purified by the method of Partridge and Jensen (1969), n-heptane was knock-testing quality, and the rest of the reagents were AnalaR grade. The column was operated under semibatch conditions. The column was first filled with the continuous phase which remained stagnant throughout the run. Fresh disperse phase was continuously introduced through four nozzles at a flow rate of 13 cm3 min-l per nozzle. The coalesced phase was continuously drawn from the top of the column. Pictures of the disperse phase were taken with a Bolex high-speed camera running at 64 fps. Analysis of the fiim gave globule size distribution, specific interfacial area, holdup, and average velocity of the disperse phase. In some runs, the emulsion was separated immediately after contact with the continuous phase. Analysis of the phases showed that the zinc concentration in the organic membrane was less than 3% of that in the stripping phase. Results and Interpretation Spray Column. For any increment of height, bh, in the column where the continuous phase remains stagnant, the mass balance on zinc gives dC,/dt (1- t)A,Gh = -Rza,(l - t)A,Gh + NZlh- Nzlh-ah(l - t)A,bh ( 5 ) Analysis of the samples of the continuous phase taken at different points showed no variations of Cz with height. For this case, eq 5 reduces to dC,/dt = -Rza, = -rz
(6)
The rising emulsion globules were oscillating and had an average equivalent diameter of 0.003 m. Under these conditions, good mixing inside the globules was assumed. In addition, the globule average residence time was 12 s. Thus, either eq 3 or eq 4 can be used as a design equation for the column provided that the mass-transfer coefficients and the kinetic constant are known. Wongswan et al. (1981) estimated the value of the rate constant of chemical reaction from previous experiments conducted in the spray
-
18
m
#E
E
16
Y m
p
14
X N U
12
0
10
20
30
LO
50
Time [ minl Figure 3. Changes in zinc concentration with time for runs 1-4.
I .
:c cc’
P
12
Oa2
Figure 4. Graphical representation of the model for P = 1.4 and experimental results obtained in the spray column.
column. The reported value, k , = 2 X lo-’ ms-l, is in good agreement with that obtained by Breysse and Perez de Ortiz (1981) for the extraction of zinc by HDEHP in the presence of the same surfactant (SPAN 80) in a nondispersive stirred cell. In order to establish the values of mass-transfer coefficients, a set of four experiments was performed, keeping the ratio Cz/CH constant at an average value of 1.4. Table I gives the experimental conditions (runs 1-4), and Figure 3 shows some typical changes in zinc concentration in the continuous phase with time. The initial slopes were calculated from quadratic curves fitted to the data points. The graphic representation of the model for P = 1.4 is shown in Figure 4. The values of p were calculated by dividing the experimental initial fluxes by the maximum values, that is, the values corresponding to the rate of chemical reaction for the bulk concentrations, taking kI =2X ms-’. The experimental results lie on a region where the sensitivity of p to Da, is low, and curves for Da, 55X fit them within an estimated experimental error of 5 5%. However the variation of p with Daz for the same
Ind. Eng. Chem. Res., Vol. 27, No. 9, 1988 1699
I
P.4 2
I
‘0 39 08
07 06
p
a5 QL 03
02
01
Figure 5. Graphical representation of the model for P = 4.2 and experimental results obtained in the spray column.
points is substantial. Since Da, and Da2 contain KO and
Kz,respectively, it can be concluded that at the conditions of this set of experiments the rate-controlling step is the diffusional resistance in the continuous phase. An average value of Kz = 2 x m/s is calculated from the four values of Da2,while for the mass-transfer coefficient in the organic phase, KO,any value of KO1 6 X lo4 ms-’ satisfies the rate equation. A second set of experiments was designed to move the system to the region of membrane diffusional control. Figure 4 shows that this can be achieved at greater values of Da,. Since the hydrodynamic conditions of the column cannot be substantially changed, the variation of Da, was achieved by selecting a value of Cz/CH 3 times greater than the previous one; Le., P = 4.2. The new experimental conditions are given in Table I, runs 5-7, and Figure 5 shows the representation of the model for P = 4.2. From this figure, it can be seen that the best fitting of the results is given by the curve Da, = 9 X which leads to a calculated value of KO = 9 X lo4 ms-l. These values are in good agreement with those predicted from correlations (Skelland, 1974; Wongswan et al., 1981). In addition this figure shows the increasing importance of the diffusional control of the membrane, represented by well-separated Da, curves, as the value of P increases for the hydrodynamic conditions of this study. The value of Dal is now of the same order of magnitude as Da2,thus indicating that the deviation from the chemical regime is due to diffusional control shared by the continuous and membrane phases. Stirred Tank. Results obtained by Amin (1983) with the same system in a stirred tank under batch conditions were also interpreted following the same discrimination method. In this case, the hydrodynamic conditions of the globules were unknown, so only initial rates were considered. The experimental conditions, listed in Table 11, cover a range of values of P from 0.15 to 2.30 and CO/CHfrom 5 to 15. In these experiments, neither the interfacial area per unit volume of dispersion nor the rate constant of chemical reaction is known. But since all of them were performed at the same stirring speed and disperse-phase holdup, a, was assumed constant. Values of p K I a , could then be calculated from the experimental rates of extraction and are shown in Table 11. It can be observed that the variations of pkIa, do not follow any particular trend and oscillate around an average value of 1 X lo4 s-l. These variations can be attributed to the experimental errors, which for the stirred tank were estimated at 115%. Results are then considered to be independent of P and Co/CH. Since the hydrodynamic conditions were kept constant in all experiments,these calculations indicate that p is independent of Da, and Da2. A change in Da, by a factor of 15 and of Da, by a factor of 3 are not followed
Table 11. Values of the Product pk,a, in the Stirred Tank P CnICw okra,, s-l 0.15 1.2 x 10” 5.0 0.15 1.7 X 10“ 7.5 0.15 1.1 x 10” 10.0 0.15 1.0 x 10-6 15.0 0.411 1.0 x 10-6 5.0 1.2 x 10” 0.38 7.5 1.1 x 10” 0.38 10.0 1.0 x 10“ 0.38 15.0 1.1 X 15+ 0.77 5.0 0.9 x 1 0 4 0.77 7.5 1.2 x 10” 0.77 10.0 1.0 x 10-6 0.77 15.0 1.58 5.0 0.61 X lo4 0.9 x 10” 1.53 7.5 1.0 x 10” 1.53 10.0 1.1 x 10“ 1.53 15.0 0.9 x 10-6 2.31 5.0 0.9 x 10-6 2.31 7.5 1.0 x 10-6 2.30 10.0 1.1 x 10“ 2.30 15.0
by changes in p , only when the process is in the chemical regime. It is therefore concluded that at the experimental conditions investigated the extraction in the stirred tank was controlled by the interfacial reaction. Assuming that the value of the rate constant of chemical reaction is of the same order of magnitude as for the conditions in the spray column (the concentration of SPAN 80 used in the stirred tank experiments was not the same as in the spray column), the values of the mass-transfer coefficients for the continuous phase and the membrane calculated from ms-’ and K Z 1 4 X Da, and Da2 are KO 1 3 X ms-l. These values are in good agreement with those reported by Chan and Lee (1984).
Discussion Danesi et al. (1981) and Komasawa et al. (1983) pointed out the relative importance of the chemical reaction control and diffusion through the continuous-phase control in the extraction rate of a carrier-facilitated liquid membrane permeation process, specially in those cases where the interfacial chemical reaction is not very fast. Danesi et al. (1981) also showed the importance of the aqueous-phase film diffusional resistance in the extraction of copper with a supported liquid membrane impregnated with LIX 64. By means of their simulated curves, they managed to fit the results of Barker et al. (1977), who on the other hand had proposed a membrane-controlled model for the same system. Working with the extraction of copper with a membrane impregnated with LIX 65N in dioctyl phthalate, Imato et al. (1981) analyzed their results assuming that membrane diffusion control conditions applied. Although the observed flux agreed with their prediction at extremely low concentrations of hydrogen ions, the observed flux became systematically lower than the prediction in the range of CH 3 1 X kmol m-3. They also observed that as the hydrogen ion concentration was increased and copper concentration decreased, discrimination between chemical and membrane diffusion control became difficult. This situation may have arisen from their use of asymptotic approximations of the model in the interpretation of results. The effect of concentrations on the rate-controlling mechanisms has not been thoroughly investigated in these studies, and thus significant deviations may occur when extrapolating outside the experimental range of conditions, as shown in Figure 2.
1700 Ind. Eng. Chem. Res., Vol. 27, No. 9, 1988
The hydrodynamic conditions of the investigations reported in the literature are also narrow. Continuous-phase control is found to occur when supported liquid membranes are used (Danesi et al., 1981), i.e., for laminar flow in the continuous phase, while for surfactant liquid membranes in stirred tanks the assumed rate-controlling step is diffusion in the membrane (Martin and Davies, 19761 1977). At intermediate conditions of turbulence for both continuous and disperse phases (Komasawa et al., 19831, interfacial chemical control is observed. These findings are coherent with the effect of turbulence on transfer rate, but when a chemical reaction is present, a high transfer rate may still be low as compared to the possible rate of reaction. Therefore, mass-transfer parameters and concentrations are coupled in their effect on the rate-controlling steps, and experimental designs should be based on Damkohler numbers and concentration ratios rather than individual variables. This approach was followed in this work by using eq 4 for the design of experiments and interpretation of experimental results conducted under a wide range of concentrations and hydrodynamic conditions. Experiments in the spray column were conducted at two values of the ratio Cz/CH: 1.4 and 4.2 for Daz varying from 0.05 to 0.15. At the lower value of P, the extraction was found to be controlled by diffusional resistances in the continuous phase, while at P = 4.2 diffusional control was shared by the membrane and the continuous phase. Although the points obtained at P = 1.4 are closer to the chemical regime, both sets of experiments have an efficiency p lower than 0.75, thus indicating that a faster rate of extraction would be possible at higher values of the mass-transfer coefficients. Since the two sets of experiments were conducted at the same hydrodynamic conditions, the change in the extraction rate control can only be due to the changes in concentrations. It can be seen from Table I that the ratio of the concentration of reactants Co/Cz is substantially higher for the set of experiments at P = 1.4 than for P = 4.2. This means that in the runs at P = 1.4 the relative potential driving force of HDEHP with respect to zinc is high enough not to be rate controlling, while in the second case it is not. Obviously if the mass-transfer coefficients were changed, the control regimes would also be likely to change. Results obtained in the stirred tank in the interval 0.15 5 P I 2.30 and wide range of values of C o / C ~were fitted with the same model and found to be controlled by the interfacial chemical reaction. It can therefore be concluded that the proposed mathematical model describes the mechanism of extraction of the surfactant liquid membrane process at initial times for the system investigated and that the rate-controlling steps may be the diffusional resistances in the continuous phase, the continuous and the membrane phases, or purely chemical depending on the concentrations of the species involved and the hydrodynamic conditions of the system. The mass-transfer coefficients calculated with the model for the spray column are in good agreement with reported data.
Conclusions A liquid membrane process has been applied to the separation of zinc from sulfate solutions with the purpose of studying the effect of concentrations and hydrodynamic conditions on the rate-controlling resistances. The organic membrane phase was a solution of the extractant bis(2ethylhexy1)phosphoric acid in n-heptane containing SPAN 80 as the emulsifying agent.
By means of the discrimination method developed for the study of liquid-liquid systems with interfacial chemical reactions, the validity of a simplified model that takes into consideration the influence of the interfacial chemical reaction and of the membrane and aqueous-phase diffusion in the process rate control has been investigated. Three different types of rate-controlling regimes predicted by the model were confirmed experimentally by results obtained in a spray column and a stirred tank. By varying the range of concentrations, the controlling regime was changed from diffusion in the continuous phase to a combined diffusional control of this phase and the membrane. In the stirred tank the extraction rate was found to be controlled by the interfacial chemical reaction. The mass-transfer coefficients in the spray column calculated with the model, KO = 9 X ms-' and K z = 2 x lo" ms-l, are in good agreement with values predicted from correlations (Wongswan et al., 1981). In the chemical regime, there is no sensitivity to the mass-transfer coefficients; therefore, in the stirred tank, only the range of values KO 1 3 X ms-' and K Z 1 4 X ms-' could be determined. The validity of the model is restricted to initial rate values. For longer contact times, accumulation of solute in the membrane and the composite nature of the disperse phase may change the distribution of mass-transfer resistances. However, even under these conditions, the possibility of continous-phase diffusional control should not be ruled out in low-turbulence contactors.
Nomenclature a, = interfacial area per unit volume of dispersion A , = cross-sectional area of the spray column C = molar concentration Da, = membrane Damkohler number Daz = continuous-phaseDamkohler number h = spray column height kI = surface-based rate constant of interfacial chemical reaction K = mass-transfer coefficient N = molar interfacial flux P = ratio cz/cH RZ = rate of reaction per unit interfacial area rz = volumetric rate of reaction t = time Greek Symbols t
= disperse-phase fraction
p
= extraction ratelmaximum possible extraction rate
Subscripts
H = hydrogen ion i = value at the interface 0 = HDEHP Z = zinc Registry No. Zn, 7440-66-6; bis(2-ethylhexy1)phosphoric acid, 298-07-7.
Literature Cited Ajawin, L. A.; Demetriou, J.; Perez de Ortiz, E. S.; Sawistowski, H. Inst. Chem. Eng. Symp. Ser. 1984,88,183. Ajawin, L. A.; Perez de Ortiz, E. S.; Sawistowski, H. Proc. ISEC'80, Liege, Belgium, 1980. Ajawin, L. A,; Perez de Ortiz,E. S.; Sawistowski, H. Chem. Eng. Res. Des. 1983, 61, 67. Amin, S. M.Sc. Thesis, University of London, 1983. Barker, R. W.; Tuttle, M. E.; Kelly, D. F.; Lonsdale, H. K. J.Membrane Sei. 1977, 2, 213. Biehl, M. P.; Izatt, R. M.; Lamb, J. D.; Christensen, J. J. Sep. Sci. Technol. 1982, 17, 289. Bock, J.; Valint, P. L. Ind. Eng. Chem. Fundam. 1982, 21, 417. Boyadzhiev, L.; Kyvchoukov, G. J. Membrane Sci. 1980, 6, 107.
Ind. Eng. Chem. Res. 1988,27, 1701-1707 Breysse, J.; PBrez de Ortiz, E. S. CHISA 81,1981,Prague. Cahn, R. P.; Frankenfeld, J. W.; Li, N. N.; Naden, D.; Subramanian, K. N. Recent Dev. Sep. Sci. 1981,4,51. Carraciolo, F.; Evans, D. F.; Cussler, E. L. AZChE J. 1975,21,160. Casamatta, G.;Chavarie, C.; Angelino, H. AZChE J. 1978,24,945. Chan, Ch. Ch; Lee, Ch. J. J. Membrane Sci. 1984,20, 1. Chiarizia, R.; Castagnola, A.; Danesi, P. R.; Horwitz, E. P. J.Membrane Sci. 1983,14, 1. Choy, E. M.; Evans, D. F.; Cussler, E. L. J. Am. Chem. SOC. 1974, 96,7085. Cussler, E. L. AIChE J. 1971,17,1300. Danesi, P. R.; Clanetti, C.; Violante, V. J. Membrane Sci. 1983,14, 175. Danesi, P. R.;Horwitz, E. P.; Vandegriff, G. F. Sep. Sci. Technol. 1981,16,201. Frankenfeld, J. W.; Li, N. N. Recent Dev. Sep. Sci. 1977,3, 285. Frankenfeld, J. W.; Cahn, R. P.; Li, N. N. Sep. Sci. Technol. 1981, 16,385. Ho, W. S.;Hatton, T. A.; Lightfoot, E. N.; Li, N. N. AZChE J. 1982, 28,662. Hochhauser, A. M.; Cussler, E. L. AZChE Symp. Ser. 1975,71,136. Imato, T.; Oeawa, H.: Morooka. S.: Kato. Y. J. Chem. Enp. - JDn. . 1981,14,289. Kitagawa, T.; Nishikawa, Y.; Frankenfeld, J. W.; Li, N. N. Environ. Sci. Technol. 1977,11. 602. Kondo, K.; Kita, K.; Koide, I.; hie, J.; Nakashio, F. J. Chem. Eng. Jpn. 1979,12,203. Kondo, K.; Kita, K.; Nakashio, F. J. Chem. Eng. Jpn. 1981,14,20. Komasawa, I.; Otake, T.; Yamashita, T. Znd. Eng. Chem. Fundam. 1983,22,127.
1701
Kremesec, V. J. Sep. Purif. Methods 1981,10, 117. Lee, K. H.; Evans, D. F.; Cussler, E. L. AZChE J. 1978,24, 860. Li, N. N. Ind. Eng. Chem. Process Des. Dev. 1971,10,215. Marr, R.; Bart, H. J.; Bouvier, A. Ger. Chem. Eng. 1981,4, 209. Martin, T.P.; Davies, G. A. Hydrometallurgy 197611977,2, 315. Melling, J. "Liquid Membrane Processes in Hydrometallurgy: A Review". Warren Spring Laboratory, LR 330 (ME), 1979;Stevenage. Nakashio, F.; Kondo, K. Sep. Sci. Technol. 1980,15,1171. Partridge, J. A.; Jensen, R. C. J. Znorg. Nucl. Chem. 1969,31,2587. PBrez de Ortiz, E. S.; Ortiz Uribe, I. In Separation Processes in Hydrometallurgy; Davies, G. A., Ed.; Ellis Horwood Ltd.: New York, 1987. Reddy, K. A.; Doraiswamy, K. K. Ind. Eng. Chem. Fundam. 1971, 6,424. Reusch, C. F.; Cussler, E. L. AZChE J. 1973,19,736. Schiffer, D. K.; Hochhauser, A.; Evans, D. F.; Cussler, E. L. Nature (London) 1974,250,484. Schlosser, S.; Kossaczky, E. J. Membrane Sci. 1980,6,83. Skelland, T.Diffusional Mass Transfer; Wiley: New York, 1974. Strzelbicki, J. Sep. Sci. Technol. 1978,13,141. Strzelbicki, J.; Charewicz, W. J. Znorg. Nucl. Chem. 1978,40,1415. Strzelbicki, J.; Charewicz, W. Hydrometallurgy 1980,5,243. Volkel, W.; Halwachs, W.; Schugerl, K. J. Membrane Sci. 1980,6, 19. Wongswan, S.;PBrez de Ortiz, E. S.; Sawistowski, H. Proc. Hydrometallurgy 81,Society of Chemical Engineers, 1981. Received for review June 2, 1986 Accepted September 25, 1987
GENERAL RESEARCH Improved Mathematical Model for a Falling Film Sulfonation Reactor J. Guti&rez-GonzBlez,* C. Mans-Teixidb, and J. Costa-Lbpez Department of Chemical Engineering, Faculty of Chemistry, University of Barcelona, Mart; i Franquss I, 08028 Barcelona, Spain
A mathematical model of a process in which an exothermic, second-order reaction takes place in a falling film reactor was developed. This model is applicable to a process in which any step, liquid mass transfer, reaction rate, or gas mass transfer, can affect the process rate. The model includes a turbulent diffusivity term for the liquid mass transfer, valid through the entire liquid film. The mathematical model predicts conversions and interfacial temperatures as the most important variables for product yields and product quality. Its validity was proved by means of experimental sulfonation of dodecylbenzene. This model could be applicable to any process that takes place in a falling film reactor. The sulfonation or sulfation reaction is generally utilized for the production of detergents. By means of this reaction, hydrophilic groups-CS0,- or COSOs--are introduced in organic compounds with hydrophobic chains. The sulfonation agent SO3 is one of the most utilized because it has some advantages with regard to other agents: sulfuric acid or oleum. Two of these advantages are that it reacts stoichiometrically and without secondary products. However, SO3 reaction with organic compounds is very exothermic, -1.68 X lo5J/mol of SO3, for the sulfonation of dodecylbenzene and requires good refrigeration to avoid the degradation of the products. A frequently utilized apparatus for the sulfonation or sulfation of organic compounds is the falling film reactor. Other types of reactors are the stirred tank, the Votator, and the spray reactor. 0888-5885/88/2627-1701$01.50/0
In the falling film reactor, a liquid film of the organic reactant falls by gravity, completely wetting the solid wall and contacting the SO3 vapor which is diluted in an inert gas, generally air. The solid surface is refrigerated by externally circulating water. Due to the high surface to volume ratio of liquid in the column, efficient heat elimination takes place. In the process of sulfonation/sulfation, the liquid normally circulates in a laminar flow, and the gas, cocurrently with the liquid, circulates in a turbulent flow. The simple geometry of the system and the laminar circulation of the liquid enables us to describe the fluid dynamics, the mass transfer, and the heat transfer through equations that can be analytically or numerically integrated. Different models are proposed in the bibliography. 0 1988 American Chemical Society
