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Ind. Eng. Chem. Res. 2001, 40, 892-897
Purification of Phosphoric Acid by Extraction with 2-Ethyl-1-Hexanol: Equilibrium Data and Mass Transfer Coefficients A. Go´ mez-Siurana,* F. Ruiz-Bevia´ , J. Ferna´ ndez-Sempere, and E. Torregrosa-Fuerte Departamento Ingenierı´a Quı´mica, Universidad de Alicante, Apartado 99, 03080 Alicante, Spain
Solubility and liquid-liquid phase equilibrium data for the ternary system water-phosphoric acid-2-ethyl-1-hexanol at 25 °C have been determined. Hand’s method and the UNIQUAC equation have been used to correlate the experimental tie lines. On the other hand, a horizontal liquid-liquid contactor with constant interfacial area has been developed in order to obtain mass transfer coefficient values. Experimental results show that the equipment is useful for mass transfer coefficient determination. Introduction The necessity of very pure phosphoric acid has increased in recent years because of its increased use in foodstuffs, animal feed additives, and liquid fertilizers. Solvent extraction processes have attracted great attention for wet process phosphoric acid purification, and a considerable number of solvents have been studied as extractants, including alcohols,1-5 ketones,4-8 long-chain tertiary amines,9,10 and ethers.11-14 Some patented processes are described in the literature by authors related to the R&D departments of commercial firms involved with either phosphoric acid processing or the associated equipment.1,2,15 The design of the equipment for these separation operations requires the knowledge of the mass transfer coefficients. The main characteristics of the different systems described in the bibliography for the determination of the mass transfer coefficients and for the study of the interfacial stability are the following: no possibility of accumulation of impurities at the interface, simple and reproducible flow pattern, relatively short contact times, possibility of visual inspection, and known interfacial area. With this in mind, different types of apparatuses are described in the bibliography, with different hydrodynamic characteristics and with different procedures to permit the contact between the phases. Some authors use equipment that permits the formation and withdrawal of drops16-22,; in other cases, stirred transfer cells,23 horizontal cylindrical flow channels,24,25 horizontal co-current contactors,26 or wet-wall columns26 have been used. Much research has been devoted to the study of liquid-liquid equilibrium involving phosphoric acid1-15 and the study of the mass transfer processes, interfacial phenomena, and mass transfer coefficient measurement.16-24 To our knowledge, however, few authors have studied mass transfer coefficients in liquid-liquid systems containing phosphoric acid. Park et al.27 studied the mass transfer inside droplets in the ternary phosphoric acid-n-octanol-water system and developed a dimensionless correlation between the Sherwood number (including the mass transfer coefficient) and the Pe´clet number and the viscosity of the two phases. The aim of this paper is to present the results obtained for the ternary equilibrium system water (W)* Author to whom correspondence should be addressed. E-mail:
[email protected] phosphoric acid (PA)-2-ethyl-1-hexanol (EH) at 25 °C and to develop an apparatus for the mass transfer coefficient determination. The main characteristics of the liquid-liquid contactor designed are a constant interfacial area, to show a reproducible flow pattern, and the possibility of visual inspection. Details about the contactor, as well as the values obtained for the mass transfer coefficients, are provided in the next sections. Experimental Section Equilibrium Data Determination. For the study of the equilibrium data, 2-ethyl-1-hexanol supplied by Merck-Schuchardt (with more than 99% purity and less than 0.2% water), phosphoric acid (with more than 99% purity; Panreac) within a 85% (by weight) solution in water, and bidistilled water were used. Data for the ternary tie lines were determined by an intensive stirring of known amounts of the constituents, followed by a period during which the phases were allowed to settle (for at least a day at 25.0 ( 0.1 °C) and separate. The PA content was analyzed by potentiometric NaOH titration in both the organic and the aqueous phases, and the water content of the organic phase was determined by titration with a Karl Fisher apparatus (DL18 by Mettler). The relative accuracy of the measurements had an error of less than 1% in all cases. In accordance with the literature,3 the second inflection point of the phosphoric acid titration curve was used to determine the PA concentration. For the complete determination of the equilibrium data, the following variables were experimentally measured: (1) mass of the three components in the initial heterogeneous mixtures, (2) mass of PA in the aqueous phase, (3) mass of PA in the organic phase, and (4) mass of W in the organic phase. The other three unknown variables (mass of W in the aqueous phase and moles of EH in the aqueous and in the organic phases) were obtained from the corresponding mass balances (threecomponent mass balances or two-component mass balances plus the overall mass balance). Mass Transfer Coefficient Determination. Figure 1i shows the designed horizontal contactor. The cell was constructed of stainless steel with dimensions 0.12 m × 0.13 m × 0.52 m and an interfacial area of 0.0347 m2 (0.386 m × 0.090 m). One lateral side was provided with a glass window in order to observe the flow of the two phases. The contactor has five orifices (inner diameter,
10.1021/ie000065a CCC: $20.00 © 2001 American Chemical Society Published on Web 01/06/2001
Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 893
Figure 1. (i) Frontal view of horizontal contactor with known constant interfacial area constructed for the experimental determination of mass transfer coefficients: (a) glass window, (b) wedge, (c) interfacial area, (d) input of organic phase, (e) output of organic phase, (f) input of aqueous phase, (g) output of aqueous phase, and (h) air input/output. (ii) Circulation of the phases: La and Lb represent the flow rates of the aqueous and the organic phase, respectively; Cb,1 and Cb,2 represent the concentrations of the organic phase at the entrance and at the exit of the apparatus, respectively; and Ca,1 and Ca,2 represent the concentrations of the aqueous phase at the entrance and at the exit of the apparatus, respectively. It can be assumed that, during the runs, Ca,1 ) Ca,2 ) Ca.
0.008 m): two for the input, another two for the output of the phases, and the fifth to keep the interior of the apparatus at atmospheric pressure. A wedge was placed at the entrance of the phases in order to prevent their mixing and minimize the turbulence. Another wedge placed at the end of the contactor facilitates the separation of the phases. Pure 2-ethyl-1-hexanol and an aqueous solution of phosphoric acid (of about 40% by weight) were used as the organic and aqueous phases, respectively, and the two phases flowed in parallel (Figure 1ii). Figure 2i shows the experimental equipment used for the determination of the mass transfer coefficients. Level tanks of variable height were used to regulate the interface position and to guarantee constant flows (Figure 2ii). Maroudas and Sawistowski26 studied the hydrodynamics of the horizontal contactor. The two phases flow co-currently in parallel streams having a parabolic velocity profile with a maximum at the interface. Bulk mixing of the phases at the entrance of the equipment is avoided. Once the steady state was reached, the flow and the composition of the two phases, at the entrance and at the exit of the apparatus, were measured by potentiometric NaOH titration, and the mass transfer coefficients were determined by means of the following equation:
N Kb ) / (Cb - Cb)ml
(1)
where Kb is the global mass transfer coefficient referred to the organic phase, N is the phosphoric mass transfer through the interface, Cb is the phosphoric acid concentration in the organic phase [at different locations, depending on the numerical subindex (Figure 1ii)], and C/b is the phosphoric acid concentration in the organic phase in equilibrium with the aqueous phase. The rate
Figure 2. (i) Experimental setup for the global mass transfer coefficient determination; (a) extraction cell; (b) storage tank for the organic feed; (c) storage tank for the aqueous feed; (d1), (d2), and (d3) storage tanks for the aqueous phase; (e) storage tank for the organic phase for recirculation; (f), (g1), and (g2) level tanks; (h) and (i) pumps; and (j), (k1), (k2), (k3), (k4), and (k5) keys with several uses. (ii) Level tanks of variable height to regulate the interphase position and guarantee constant flows: (a) upper exit orifice to ensure constant level, (b) lower exit orifice, (c) pierced cover (the phase input by the hole), (d) system of height regulation, and (e) maximum level in the tank.
of mass transfer for the PA from the aqueous phase to the organic phase is calculated from
N)
(Cb,2 - Cb,1)Lb a
(2)
and the driving force for the mass transfer was calculated using
(C/b - Cb)ml )
(C/b - Cb,1) - (C/b - Cb,2) ln
(
)
C/b - Cb,1
C/b - Cb,2
(3)
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Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001
Table 1. Composition of the Initial Mixtures for the Determination of the Tie Lines for the System W-PA-EH, at 25 ×bcC (weight percentages) initial mixtures xW
xPA
xEH
45.0 39.9 35.0 29.9 27.3 25.0 22.5 20.0 15.0
10.0 20.3 30.1 40.2 44.9 50.0 55.0 60.0 70.0
45.0 39.8 35.0 29.8 27.8 25.0 22.5 20.0 15.0
Table 2. Tie Lines Obtained for the System W-PA-EH at 25 ×bcC (weight percentages) aqueous phase
organic phase
xW
xPA
xEH
xW
xPA
xEH
81.1 66.4 53.1 43.1 38.5 34.1 29.9 25.1 19.9
18.8 33.5 46.8 56.9 61.4 65.9 70.0 74.9 80.0
0.14 0.12 0.07 0.03 0.12 0.08 0.02 0.04 0.10
3.4 3.6 5.3 5.7 5.3 6.8 6.9 7.1 7.2
0.19 0.63 2.95 9.29 12.3 18.1 23.6 30.3 44.6
96.4 95.8 91.8 85.0 82.4 75.1 69.5 62.6 48.2
/ / Strictly speaking, Cb,1 and Cb,2 (phosphoric acid concentration in equilibrium with the aqueous phase at the entrance and at the exit of the contactor) should appear in eq 3. However, as the aqueous phase composition was practically constant during the runs, only a value of C/b has been considered.
Figure 3. Experimental tie lines for the system W-PA-EH at 25 °C (weight percentage). Table 3. Results of the Correlation of the Experimental Equilibrium Data for the W-PA-EH System Using UNIQUAC pure-component molecular structure UNIQUAC constant component W (Chemcad V Database32) PA (arbitary values) EH (Chemcad V Database32)
log(xPA/xEH)org ) -1.337 + 2.258 log(xPA/xW)aq
(4)
with a determining coefficient r2 ) 0.9884. As is well-known, it is difficult to apply thermodynamic activity coefficient models for the correlation of equilibrium data from systems containing electrolytic substances29,30 such as the PA. Nevertheless, this can be done if some arbitrary values are assigned to several physical and structural parameters, such as the purecomponent molecular structure UNIQUAC constants, r and q. Thus, the thermodynamic model is applied as an empirical model, which is valuable for the prediction of new equilibrium data. In this work, the correlation
q 1.4 4 6.1511
UNIQUAC interaction parameters (K) obtained by fitting the nine tie lines for the W-PA-EH system
Results and Discussions Equilibrium Data. Equilibrium between the liquid phases was studied at 25 °C. Nine tie lines were studied in the heterogeneous region of the system. Initial mixtures used in the determination of the tie lines were all prepared in the straight line from the PA vertex to the binary mixture 50/50 (by weight) W/EH (Table 1). The compositions of equilibrium phases are presented in Table 2. All concentrations are expressed as weight percentages. As previously stated, knowledge of the composition of the initial mixtures showed in Table 1 is necessary for the complete determination of the equilibrium data using the overall mass balance. Figure 3 represents the ternary diagram obtained for the system W-PA-EH at 25 °C, showing the existence of an extensive heterogeneity region. The following equation shows the result for the tie lines correlation by Hand’s method:28
r 0.92 3 5.208
W PA EH
W
PA
EH
0.0 -341.1 249.6
431.8 0.0 -169.7
457.8 400.8 0.0
of the ternary liquid-liquid equilibrium data has been made using the arbitrary values of r ) 3 and q ) 4 for the volume and area structural parameters of PA, respectively. The simplex flexible method31 was used for the optimization of the UNIQUAC interaction parameters, with an objective function that minimizes the distances between the experimental and calculated mole fractions. Table 3 shows the results obtained from this correlation. Figure 4 shows the distribution curve obtained for the phosphoric acid in the system W-PA-EH. Marcilla et al.7 performed a comparative study of the extractive capability of different solvents and found that the compatibility, on the basis of the percentage of PA extracted, between solvent and phosphoric acid is better for alcohols, followed by ketones, esters, and ethers. An increase in the chain length results in a wider heterogeneous zone. Thus, as can be inferred from the shape of the distribution curve (Figure 4) and from the wide heterogeneous zone in Figure 3, it is possible to extract phosphoric acid from very concentrated aqueous solutions, although the organic solutions obtained will be very diluted in phosphoric acid. Thus, we can expect that 2-ethyl-1-hexanol was an acceptable solvent for the phosphoric acid and at least comparable with other solvents studied in the literature,1-15,27,33 As an example, Figure 5 shows a comparison between the coefficient of distribution of PA in several W-PA-
Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 895 Table 4. Results of the Experiments for the Determination of the Mean Global Mass Transfer Coefficients Kb exp La × 106 Ca × 10-3 Lb × 108 Cb,1 Cb,2 C/b × 10-2 N × 107 (C/b - Cb)ml × 10-2 Kb × 109 no. (m3/s) (mol of PA/m3) (m3/s) (mol of PA/m3) (mol of PA/m3) (mol of PA/m3) (mol of PA/s/m2) (mol of PA/m3) (m/s) 1 2 3 4 5 6 7 8 9 10
1.14 1.31 1.39 1.42 1.35 1.07 1.07 1.38 1.27 0.73
5.4 5.4 5.5 5.5 5.3 5.5 5.5 5.3 5.4 5.4
1.45 1.73 2.13 2.53 3.86 5.95 8.17 9.57 13.1 18.7
0 0 0 0 0 0 0 0 0 0
1.27 1.27 1.02 0.94 0.68 0.51 0.51 0.43 0.43 0.43
Figure 4. Distribution curve for the phosphoric acid in the W-PA-EH system at 25 °C.
alcohol systems.7 Furthermore, 2-ethyl-1-hexanol is an aliphatic alcohol with a high molecular weight, which is readily available at a very low price. In fact, according with the Kirk-Othmer Encyclopedia,34 44% of the U.S. production of alcohols used as plasticizers was 2-ethyl1-hexanol, with a price of 0.93 U.S. $/kg. This value is about 47% lower than the price of hexanol and 54% lower than the price of n-octanol. One of the aims of this paper is to present the equilibrium data corresponding to the W-PA-EH system, which do not exist in the literature. Mass Transfer Coefficient Data. Table 4 shows the results obtained for 10 experiments carried out with the previously described equipment. For each experiment, the global mass transfer coefficients for the organic phase have been calculated using eqs 1-3. Table 4 shows the values for the organic phase flow and phosphoric acid concentration of the organic phase at the entrance and at the exit of the cell, as well as the concentration of the organic phase in equilibrium with the aqueous phase. This concentration at equilibrium, C/b, was calculated by interpolation of the distribution curve obtained from the experimental data. Finally, the resulting N, (C/b - Cb)ml, and Kb values are presented. For these experiments, the aqueous phase flow ranged between 0.73 × 10-6 and 1.42 × 10-6 m3/s and the concentration between 5.34 × 103 and 5.53 × 103 mol of PA/m3. The flow of the organic phase ranged between 1.45 × 10-8 and 18.7 × 10-8 m3/s. As can be seen in Table 4, the values for the global mass transfer coefficients of phosphoric acid for the organic phase ranged between 3.00 × 10-9 and 1.35 × 10-8 m/s. The relative error in the K measurement is related to the errors in the determination of N and (C/b - Cb)ml
1.78 1.78 1.87 1.87 1.70 1.87 1.87 1.70 1.78 1.70
5.33 6.36 6.25 6.83 7.58 8.76 12.0 11.7 16.1 22.9
1.78 1.78 1.86 1.86 1.70 1.87 1.87 1.70 1.78 1.70
3.00 3.58 3.35 3.66 4.47 4.69 6.44 6.91 9.02 13.5
Figure 5. PA distribution coefficient in several W-PA-solvent systems.
and is dominated by the C/b and Cb,2 measurement errors. In a typical experiment, the relative error calculated for the Kb value is around 10%. In all of the experiments, the resistance to mass transfer of the aqueous phase can be assumed negligible because the equilibrium distribution coefficients (ratio of solute concentration in the organic phase to solute concentration in the aqueous phase) were found to be very low. Thus, the mass transfer is controlled by the organic phase, and for this phase, the global mass transfer coefficients can be considered equal to the individual mass transfer coefficients. Several authors17,20,27,35 have used empirical expressions such as eq 5 to correlate experimental data.
Sh ) cte Rem Scn
(5)
where
Sh ) Sherwood number )
(Kb,medxt) DPA,EH
(6)
Re ) Reynolds number )
LbFbdeq,b Sµb
(7)
Sc ) Schmidt number )
µb FbDPA,EH
(8)
A similar correlation has been used with the experimental data obtained in the present work. The geometrical information and the data required to apply eq 4 are listed in Table 5.
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Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001
Table 5. Geometrical Information and Required Data for Application of Eq 4 xt Fb deq,b Sb µb deq,a Sa µa
interfacial area length organic phase density equivalent diameter for the organic phase cross-sectional area for the organic phase flow organic phase viscosity equivalent diameter for the aqueous phase cross-sectional area for the aqueous phase flow aqueous phase viscosity
0.385 m 832.8 kg/m3 0.018 m 0.0009 m2 0.01 kg m-1 s-1 0.064 m 0.0045 m2 0.0039 kg m-1 s-1
as 2.3 × 10-10 m2/s, and t can be calculated from the equivalent diameter of the organic phase (Table 5) and the volumetric flow rate. Introducing these values into the model of Potter, Kd can be obtained. The values of Kd predicted by the model of Potter38 range from 5.38 × 10-8 to 1.62 × 10-7 m/s, about 20 times greater than the experimental values obtained in this work (Table 4). This discrepancy can be explained because the viscosity of the aqueous phase is 3 times greater that the viscosity of water, as the aqueous phase is very concentrated and the viscosity of the solute (PA) is very high. Furthermore, the model of Potter assumed that the solutions are identical in density and viscosity with the pure liquids, so it is not really applicable in our case. Moreover, the low Reynolds number used in this work also reduces considerably the applicability of this theory. Nomenclature Figure 6. Fit of the function Sh vs 1.263 straight line y ) x. r2 ) 0.9338.
Re0.662
Sc0.327
to a
The diffusion coefficient of phosphoric acid in 2-ethyl1-hexanol was estimated by means of the Wilke and Chang equation36 to be DPA,EH ) 2.3 × 10-10 m2/s. Values for the constant and the exponents, m and n, in eq 5 were obtained by applying the solver method of Microsoft Excel 7.0 to search for the values that best fit a straight line y ) x, with y ) Sh and x ) cte Rem Scn. The results are shown in Figure 6, and as can be seen, the correlation found in present work is
Sh ) 1.263 Re0.662 Sc0.327
(9)
The correlation is valid for the following conditions: (1) mass transfer is from the aqueous phase to the organic phase, (2) the two phases flow in parallel (3) the Reynolds number for the organic phase is between 0.02 and 0.31, and (4) he Reynolds number for the aqueous phase is between 3.4 and 6.6. The type of correlation between the Sc, Re, and Sh numbers as well as the order of the exponents are similar to those presented by other authors.16,17,20,27,29,37 Potter38 applied approximate laminar boundary layer solutions for mass transfer across plane interfaces between two co-current parallel fluid streams, obtaining the following correlation:
Kb ) 0.548
( ) DAB t
0.5
(10)
where DAB is the diffusion coefficient and t is the contact time. According to Potter,38 this model assumes that the solutions are dilute and identical in density and viscosity with the pure liquids, and modifications must be made to the theory if the concentrations at the interface and in the stream are widely different. In our system, the diffusion coefficient of PA in EH was estimated36
a ) interfacial area (m2) Ca,1 ) molar concentration of phosphoric acid in the aqueous phase at the entrance of the extraction cell (mol PA/m3) Ca,2 ) molar concentration of phosphoric acid in the aqueous phase at the exit of the extraction cell (mol PA/ m3) Ca ) molar concentration of phosphoric acid in the aqueous phase (mol PA/m3), constant during the runs. Cb,1 ) molar concentration of phosphoric acid in the organic phase at the entrance of the extraction cell (mol PA/m3) Cb,2 ) molar concentration of phosphoric acid in the organic phase at the exit of the extraction cell (mol PA/m3) / Cb ) molar concentration of phosphoric acid in equilibrium with the aqueous phase (mol PA/m3) Cb ) molar concentration of phosphoric acid in the organic phase (mol PA/m3) / (Cb - Cb)ml ) driving force logarithmic-mean (mol PA/m3) DAB ) diffusion coefficient of A in B (m2/s) deq,a ) equivalent diameter for the aqueous phase deq,b ) equivalent diameter for the organic phase EH ) component 2-ethyl-1-hexanol Kb ) global mass transfer coefficiente for the organic phase (m/s) La ) flow of aqueous phase (m3/s) Lb ) flow of organic phase (m3/s) N ) phosphoric mass transfer through the interphase (mol PA/(s‚m2)) PA ) component phosphoric acid q ) molecular area UNIQUAC constant r ) molecular volume UNIQUAC constant r2 ) determining coefficient Sa ) cross-sectional area for the aqueous phase flow Sb ) cross-sectional area for the organic phase flow t ) mass transfer time xEH ) mass percent of 2-Ethyl-1-hexanol xPA ) mass percent of phosphoric acid xW ) mass percent of water xt ) interfacial area length (m) W ) component water
Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 897 µa ) organic phase viscosity (kg/m/s) µb ) organic phase viscosity (kg/m/s) Fb ) density of the organic phase (kg/m3)
Acknowledgment Financial support for this investigation from the Spanish “Comisio´n de Investigacio´n Cientı´fica y Tecnolo´gica” de la Secretarı´a de Estado de Educacio´n, Universidades, Investigacio´n y Desarrollo (CICYT PB960338) is gratefully acknowledged. Literature Cited (1) Bergdorf, J.; Fischer R. Extractive Phosphoric Acid Purification. Chem. Eng. Prog. 1978, 74 (11), 41. (2) Ruiz, F.; Marcilla, A.; Ancheta, A. M.; Caro, J. A. Purification of Wet Process Phosphoric Acid by Solvent Extraction with Isoamyl Alcohol. Part I. Liquid-Liquid Equilibrium of the WaterPhosphoric Acid-Isoamyl Alcohol at 25 °C. Solvent. Extr. Ion Exch. 1985, 3 (3), 331. (3) Ruiz, F.; Marcilla, A.; Ancheta, A. M.; Caro, J. A., Purification of Wet Process Phosphoric Acid by Solvent Extraction with Isoamyl Alcohol. Part II. Study of the Impurities Distribution. Solvent Extr. Ion Exch. 1985, 3 (3), 345. (4) Marco, J. M.; Gala´n. M. I.; Costa, J. Liquid-Liquid Equilibria for the Quaternary System Water-Phosphoric Acid-1Hexanol-Cyclohexanone at 25 °C. J. Chem. Eng. Data 1988, 33 (2), 211. (5) Ruiz, F.; Gala´n, M. I.; Boluda, N. Quaternary Liquid-Liquid Equilibrium: Water-Phosphoric Acid-1-Butanol-2-Butanone at 25 °C. Fluid Phase Equilib. 1998, 146, 175. (6) Marcilla, A.; Ruiz, F.; Martinez-Pons, D. Purification of Wet Process Phosporic Acid by Extraction with 3-Pentanone. Study of the Impurities Distribution. Comments on the Purification Behavior of Different Solvents. Solvent Extr. Ion Exch. 1993, 11 (3), 445. (7) Marcilla, A.; Ruiz, F.; Martinez-Pons, D. Liquid-Liquid Equilibrium of the Water-Phosphoric Acid-3-Pentanone System at 25 °C. A Comparative Study of the Extraction Power of Different Solvents. Solvent Extr. Ion Exch. 1993, 11 (3), 469. (8) Feki, M.; Fourati, M.; Chaabouni, M. M.; Ayedi, H. F. Purification of Wet Process Phosphoric Acid by Solvent Extraction Liquid-Liquid Equilibrium at 25 °C and 40 °C of the System Water-Phosphoric Acid-Methylisobutylketone. Can. J. Chem. Eng. 1994, 72, 939. (9) Stenstro¨m, S.; Wingefors, S.; Gharib, A. Solvent Extraction of Phosphoric Acid with Long Chain Tertiary Amines. Solvent Extr. Ion Exch. 1986, 4 (5), 883. (10) Stenstro¨m, S.; Wingefors, S. On the Modelling of Multicomponent Acid Extraction with Long-chain Aliphatic Amines. Can. J. Chem. Eng. 1988, 66, 248. (11) Ruiz, F.; Marcilla, A.; Ancheta, A. M.; Rico, C. LiquidLiquid Equilibrium of the System Water-Phosphoric Acid-di-nPropyl Ether at 25 and 40 °C. Influence of the Isomer Propylisopropyl Ether on the Appearance of Three Liquid Phases at Equilibrium. Solvent Extr. Ion Exch. 1986, 4 (4), 771. (12) Ruiz, F.; Marcilla, A.; Ancheta, A. M.; Rico, C. LiquidLiquid Equilibrium of the Three Phases at Equilibrium System Water-Phosphoric Acid-di-n-Propyl Ether at 25 and 40 °C. Solvent Extr. Ion Exch. 1986, 4 (4), 789. (13) Ruiz, F.; Marcilla, A.; Ancheta, A. Purification of Wet Process Phosphoric Acid by Solvent Extraction with Propyl Ethers. Solvent Extr. Ion Exch. 1987, 5 (6), 1141. (14) Marcilla, A.; Ruiz, F.; Campos, J.; Asensio, M. Purification of Wet Process Phosphoric Acid by Solvent Extraction with Dibutyl Ether. Part I. Liquid-Liquid Equilibrium of the System WaterPhosphoric Acid-Dibuthyl Ether at 25 °C. Solvent Extr. Ion Exch. 1989, 7 (2), 201. (15) McCullough, J. F.; Frederick, L. L. Purification of phosphoric acid with methanol and ammonia. J. Agric. Food Chem. 1976, 24 (1), 180.
(16) Heertjes, P. M.; De Nie, L. H. Mass transfer to drops. In Recent Advances in Liquid-Liquid Extraction; Hanson, C., Ed.; Pergamon Press: Oxford, U.K., 1971. (17) Sawistowski, H.; Goltz, G. E. The Effect of Interface Phenomena on Mass-transfer Rates in Liquid-Liquid Extraction. Trans. Inst. Chem. Eng. 1963, 41, 174. (18) Schu¨gerl, K.; Dimian, A. The Influence of the Interfacial Resistance on the Liquid-Liquid Mass Transfer of Carboxilic Acids. Chem. Eng. Sci. 1980, 35, 963. (19) Lo, T. C.; Baird, M. H. I.; Hanson, C. Handbook of Solvent Extraction; John Wiley & Sons: New York, 1983. (20) Nahringbauer, I.; Larson, B.; Mass Transfer across LiquidLiquid Interfaces. Part 1. A Computer-controlled Apparatus Based on the Free-falling Droplet Technique. Anal. Chim. Acta 1983, 151, 153. (21) Hillgren, U.; Nahringbauer, I. Mass Transfer across Liquid-Liquid Interfaces. III. The Accuracy and Precision of the Measurements of Mass-transfer Coefficients Obtained by an Automatic Falling-drop Apparatus. Acta Pharm. Suec. 1985, 22, 17. (22) Nahringbauer, I.; Larson, B. Mass Transfer across LiquidLiquid Interfaces. Part 2. Calculation of Mass Transfer Coefficientes from Experiments with an Automated Falling-drop Apparatus. Anal. Chim. Acta 1985, 151, 171. (23) McManamey, W. J.; Multani, S. K. S.; Davies, J. T. Molecular Diffusion and Liquid-Liquid Mass Transfer in Stirred Transfer Cells. Chem. Eng. Sci. 1975, 30, 1536. (24) Shah, A. K.; Sharme, M. M. Mass Transfer in LiquidLiquid (Horizontal) Pipeline Contactors. Can. J. Chem. Eng. 1971, 49, 9 (5), 596. (25) Voigtla¨nder, R.; Blaschke, H. G.; Halwachs, W.; Schu¨gerl, K. Investigation of the Mass Transfer of Two Countercourrent Laminar Flowing Liquids in a Horizontal Cylindrical Channel-I. Chem. Eng. Sci. 1980, 35, 1211. (26) Maroudas, N. G.; Sawistowski, H. Simultaneous Transfer of Two Solutes Across Liquid-Liquid Interfaces. Chem. Eng. Sci. 1964, 19, 919. (27) Park, J. S.; Choi, C. K.; Kim. L. H. Mass Trasfer inside the Droplets in the Ternary Phosphoric Acid-n-Octanol-Water System. Int. Chem. Eng. 1986, 26 (3), 540. (28) Hand, D. B. Dineric Distribution. J. Phys. Chem. 1930, 34, 1961. (29) Sørensen, J. M.; Arlt, W. Liquid-Liquid Equilibrium Data Collection, Ternary Systems; DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, Germany, 1980. (30) Prausnitz, J. M.; Lichtenthaler, R. N.; Gomes de Azevedo, E. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd Ed.; Prentice Hall: New York, 1999. (31) Himmelblau, D. M. Process Analysis Statistical Method; John Wiley & Sons: New York, 1968. (32) CHEMCAD 5.0, Chemstations Inc., Houston, TX, 1999. (33) Kim, L. H.; Choi, C. K. Hwahak Kong-hak 1981, 19, 159. (34) Kirk-Othmer. Encyclopedia of Chemical Tecnology, 4th ed.; John Wiley & Sons: New York, 1991; Vol. 1, p 872. (35) Sherwood, T. K.; Pigford, R. L.; Wilke, C. R. Mass Transfer; McGraw-Hill Kogakusha, Ltd.: Tokyo, Japan, 1975 (international student edition). (36) Wilke, C. R.; Chang, P. C. Correlation of Diffusion Coefficients in Dilute Solutions. AIChE J. 1955, 1, 264. (37) von Berg, R. Simultaneous Heat and Mass Transfer. In Recent Advances in Liquid-Liquid Extraction; Hanson, C., Ed.; Pergamon Press: Oxford, 1971. (38) Potter, O. E. Mass Transfer between co-current fluid streams and boundary layer solutions. Chem. Eng. Sci. 1957, 6, 170.
Received for review January 19, 2000 Revised manuscript received October 30, 2000 Accepted November 1, 2000 IE000065A
