New Method for Quaternary Systems LiquidâLiquid Extraction Tray to

Ind. Eng. Chem. Res. 1999, 38, 3083-3095

3083

New Method for Quaternary Systems Liquid-Liquid Extraction Tray to Tray Design A. Marcilla,* A. Go´ mez, J. A. Reyes, and M. M. Olaya Departamento Ingenierıá Quı´mica, Universidad de Alicante, Apartado 99, Alicante 03080, Spain

A new numerical method for the liquid-liquid extraction design has been developed and applied to quaternary systems. The method directly calculates the optimum number of equilibrium stages for a specified composition of the solutes in the product stream as well as the solvent flow rate, which satisfies the overall balance and the stage to stage calculations. The method is based on the geometrical concepts of the Ponchon and Savarit method for binary systems. A correlation of the solubility surface and the tie-line data is required in order to implement the calculation procedure. Different proposed methods with this objective are described in detail and applied to type 1 quaternary systems. Both experimental data and UNIQUAC-generated data have been used to illustrate the application which has been compared with the commercial design program ChemCad III, using the same thermodynamic model and the same binary parameters. The method has the advantage that it allows the direct design (determination of the number of stages for a given desired separation) and avoids the iterative calculations to solve the material balances and equilibrium conditions. 1. Introduction Generally speaking, the problems in separation processes can be divided into two categories: rating and design problems. At this point we would like to clarify the differences between a design method and a rating method which are relevant from the point of view of the present paper. In a rating method for extraction, the number of trays and the location of all of the feeds and side products are stated, and the flow and composition of the equilibrium phases in each stage are calculated. Such a method is actually a simulation method. On the other hand, a design method calculates the necessary number of stages and the solvent flow rate for a specified separation of components in products. The multistage liquid-liquid extraction, of partially miscible mixtures, with discontinuous flow is the extraction process most frequently used. For ternary mixtures the stage to stage calculations and the design of the equipment necessary can be achieved by a procedure similar to the Ponchon-Savarit method for the rectification of the binary mixtures, where the mass and energy balances (to relate the streams between stages) and equilibrium equations are solved alternatively in order to obtain the number of trays, the position of the feed stages, the composition, the temperature, and the flow of the phases that leave each stage. In the case of liquid-liquid extraction, if the enthalpy effects are neglected, only the mass balances are required to connect the streams which cross over between two consecutive stages (operating line), and the equilibrium relations, to connect the two equilibrium phases which leave each stage (tie lines). The plane where the equilibrium data are represented is defined by the mass or molar fraction of the solute and the mass or molar fraction of the solvent, and instead of using the enthalpy-composition curves, as in the Ponchon-Savarit * To whom all correspondence should be addressed. Tel: (34) 965 903 789. Fax: (34) 965 903 826. E-mail: antonio.marcilla@ ua.es.

Figure 1. Graphical representation of the Ponchon and Savarit method for a liquid-liquid ternary system with a pair of partially miscible components.

method for distillation, the solubility curve is considered. Figure 1 shows the graphical representation of the Ponchon and Savarit method for a liquid-liquid ternary system with a pair of partially miscible components. In this type of contact the extract and raffinate streams flow from one stage to another in countercurrent (Figure 2), the final products being those represented by R(n) and E(1). The trays are considered as ideal equilibrium stages, which means that the incoming currents are perfectly mixed and the outcoming currents are in equilibrium. Different arrangements can be used to perform these types of equilibrium tray operations, such as the single contact, repeated contact

10.1021/ie9900723 CCC: $18.00 © 1999 American Chemical Society Published on Web 07/13/1999

3084 Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999

Figure 2. Scheme of a countercurrent extractor.

with fresh solvent in each stage, countercurrent contact, and countercurrent contact with solvent reflux. The applications of multicomponent systems in liquidliquid equilibrium have received increased interest in chemical technology such as the salting-out effect (Olaya et al.1) or protein and polymer extraction (Pires and Cabral,2 Coen et al.,3 and Cheluget et al.4). The design of extractors becomes complex when more than three components are involved, such as, for example, when the feed is a mixture of three components, when the solvent is a mixture of two components, or when the salting-out effect is used to improve the separation conditions or selectivity (Olaya et al.5 and Marcilla et al.6). In these cases, the corresponding quaternary liquid-liquid equilibrium is to be considered. Another aspect that we would like to mention here, although it is not the scope of the present paper, is the relative lack of reliable experimental data on quaternary systems as well as the doubtful quality of several of the published data on this topic. Clear inconsistencies have been repeatedly detected in the literature published (Ruiz and Marcilla7). In a previous work (Ruiz et al.8) we suggested an interpolation method to run the equilibrium stage calculations for liquid-liquid extraction calculations for quaternary systems. The method was named as an iteration-free method and allowed the design of countercurrent cascades. Recently (Reyes Labarta9 and Marcilla et al.10), we suggested a method to perform the direct design of ternary distillation columns, which is based on different interpolation and correlation methods and is a direct extension of the Ponchon and Savarit method. This method allows the direct design and can also be classified as an iteration-free method in the same sense as the former; i.e., the equilibrium iterations are avoided. Nevertheless, iteration is still required in order to match the assumed residue with that calculated, solving in this manner the design problem (Yamada et al.11 and Ricker and Grens12). The objective of the present work is to combine the concepts of these two works and develop an improved method for the direct design (determination of the number of stages for a given desired separation) of quaternary extraction cascades. The results of this method will be compared with the ChemCad III13 commercial simulation program. 2. Design Method Proposed In this paper a method for the design of liquid-liquid extractors for the separation of the quaternary mixtures is proposed. The main objective of this method is to determine the optimum number of equilibrium stages in order to achieve a specified composition of the solutes in the product stream R(n) as well as the solvent flow rate E(0), which satisfies the overall mass balance and the stage to stage calculations, and the composition and flow of the phases that leave each stage. The design of the equipment or the simulation problems for the separation processes based on equilibrium

cascades are solved using the MESH (mass balance, equilibrium relations, sum, and heat balance) equations. The resulting equation system can be solved stage by stage or component by component (Kister14). Most of the simulation programs for the multicomponent extraction usually use component by component methods (ChemCad III13), and therefore the design problem cannot be directly solved. To directly solve the design problem, the stage by stage methods, such as the method presented in this paper, which combine the equilibrium data (tie lines) and the mass and energy balances (operating line) must be used. More details about these questions can be found elsewhere (King15 and Marcilla et al.10). When graphical stage by stage design methods, such as the Ponchon-Savarit method, are to be used in the extraction processes (see Figure 1), we should consider the following aspects: (a) The solubility curve data (solubility surfaces or hypersolubility surfaces for four or more components, respectively) must be available. If the experimental data are known, a graphical method or the fitting of the data to an adequate function can be used. (b) If a ternary system is considered, the method for the graphical solution of the problem is similar to the Ponchon-Savarit method (Treybal16). If a quaternary system is considered, the problem is much more complicated. In the bibliography some methods can be found, which use different projections of the solubility surfaces (Hunter,17 Smith,18 Powers,19 Cruickshank et al.,20 Treybal,16 Ruiz et al.,21,22 and Ruiz and Prats23). If the system contains more than four components, the graphical methods are not useful. Nevertheless, the same geometrical principles can be used to solve the problem, although in hyperspaces of more than three dimensions, and the calculations must obviously be implemented in a computer. (c) If a numerical or graphical method is to be used, the fitting of the data to solubility curves/surfaces has to be made. In addition, a method to interpolate or calculate tie-line data must be devised. (d) If the experimental equilibrium data are not known, the application of a thermodynamic model to predict the equilibrium data of the system considered will be necessary. Nevertheless, for systems whose behavior is very far from the ideal, such as those considered in extraction processes, the best thermodynamic models (NRTL, UNIQUAC, UNIFAC, etc.) do not yield results as good as would be desirable. (e) The development of a design method for liquidliquid extraction processes involves additional difficulties to that for conventional distillation (involving liquid-vapor equilibrium). The liquid-liquid equilibrium (at a given temperature and pressure, such as those normally used for design purposes) is restricted to a defined composition region that does not cover the complete range. Consider, for instance, the case presented in Figure 3, where two different types of quaternary systems are shown. Point M represents a heterogeneous mixture, and the E and F points repre-

Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 3085

Figure 3. Qualitative representation of the liquid-liquid equilibrium diagram for quaternary systems: type 1, only one partially miscible pair of components (1-3); type 2, two partially miscible pairs of components (1-3 and 3-4).

sent the compositions of the two-liquid conjugated phases (extremes of the corresponding tie line). The G point is the plait point for the 1-2-3 ternary system and the H point that for the 1-3-4 ternary system (type 1) or 2-3-4 ternary system (type 2). The GH curve separates the solubility surface in two regions: the aqueous and organic phases. In this paper the proposed design method is described in detail and applied to type 1 quaternary systems. The following steps constitute the procedure for the complete analysis of each system studied: 1. Localization of the experimental equilibrium data in the bibliography (case 1). 2. Correlation of the experimental equilibrium data using the UNIQUAC model and calculation of the corresponding binary parameters. 3. Generation of the set of equilibrium data homogeneously distributed on the solubility surface (case 2). 4. Correlation of the experimental or calculated tie lines corresponding to cases 1 and 2, to avoid iterations in the equilibrium calculations. 5. Fitting of the experimental or calculated solubility surface (cases 1 and 2 respectively), to be able to determine the intersection between the operative line and the equilibrium surface (to obtain the composition of the current entering the next stage). 6. Application of the proposed design method using the correlation parameters of both cases 1 and 2, to determine the number of equilibrium stages for a specified product separation as well as the solvent flow rate, which satisfies the overall balance and the stage to stage calculations. 7. Simulation of both extractors (cases 1 and 2) with a commercial program (ChemCad III13) using the results of the two previous designs (number of stages and solvent flow rate), the UNIQUAC model, and the binary parameters calculated in step 2. The extension to systems with more than four components or to another type of system is possible, with the same sequence of calculations, except changing the mathematical functions which describe the correlation of the tie-line data and the solubility surface. 2.1. Generation of Liquid-Liquid Equilibrium Data by the UNIQUAC Model. Because the results obtained will depend on the quality of the experimental data or the quality of the binary parameters used, the initial experimental equilibrium data (case 1) have been correlated using the UNIQUAC model. The binary parameters obtained have been used (a) to generate the

homogeneously distributed equilibrium points in all of the solubility surface (case 2) required to design the liquid-liquid extractor using the proposed method and (b) to solve the problem in the commercial simulator (ChemCad III13). 2.2. Tie-Line Correlation. The correlation of the ternary and quaternary tie lines proposed in this paper is very similar to that proposed by Marcilla et al.6 for quaternary systems involving an inorganic salt, which was based on the Eisen-Joffe24 equation for ternary systems including an inorganic salt. The Eisen-Joffe equation is an adaptation of the Hand25 correlation. All of these correlations are presented in Table 1. In this paper, a correlation very similar to that proposed by Marcilla et al.6 has been used, based on the similarity between the solubility surface for a type 1 quaternary system (without salt) and a quaternary system including an inorganic salt. The modifications introduced in this paper are as follows: (a) The composition of the aqueous phase (x(4)) on the right-hand side of the equation has been replaced by the ratio of compositions (x(4)/x(2)) to achieve a better fitting to the experimental points. (b) With the same objective, a square term of this ratio of compositions (x(4)/x(2))2 has also been introduced. (c) To allow the correlation of binary and ternary equilibrium data (concentrations with zero values would yield infinite ratios, not allowing the calculation of the fitting constants), a constant and positive value has been added up to all compositions in mass or molar fractions. (d) As Marcilla et al.6 proposed, three complementary equations have been used in order obtain the composition of the organic phase in equilibrium with an aqueous phase. Taking into account all of these considerations, the equations proposed in this paper are the following:

( ) [ ( ) ( )] [ ( ) ( )] ( ) [ ( ) ( ) ][ ( )] ( ) [ ( ) ( )] [ ( ) ( )] ( ) [ ( ) ( ) ][ ( )] ( ) [ ( ) ( )] [ ( ) ( )] ( ) [ ( ) ( ) ][ ( )]

y′(3) x′(4) x′(4) 2 ) a+b +c + y′(2) x′(2) x′(2) x′(4) x′(4) 2 x′(2) x′(4) d+e +f log + g+h + x′(2) x′(2) x′(1) x′(2) x′(4) 2 x′(2) 2 i log (1a) x′(2) x′(1)

log

log

log

y′(2) x′(4) x′(4) 2 ) a′ + b′ + c′ + y′(1) x′(2) x′(2) x′(4) x′(4) 2 x′(2) d′ + e′ + f′ log + x′(2) x′(2) x′(1) x′(4) x′(4) 2 x′(2) g′ + h′ + i′ log x′(2) x′(2) x′(1)

y′(4) x′(4) x′(4) 2 ) a′′ + b′′ + c′′ + y′(3) x′(2) x′(2) x′(4) x′(4) 2 x′(2) d′′ + e′′ + f′′ log + x′(2) x′(2) x′(1) x′(4) x′(4) 2 x′(2) g′′ + h′′ + i′′ log x′(2) x′(2) x′(1)

2

(1b)

2

(1c)

where x′(i) ) x(i) + C, molar or mass fraction corrected (adding the C constant) of the i component in the 4 aqueous phase, with ∑i)1 x′(i) ) 1 + 4C; y′(i) ) y(i) + C, molar or mass fraction corrected (adding the C constant) 4 y′(i) of the i component in the organic phase, with ∑i)1 ) 1 + 4C; a, b, c, d, ..., a′′, b′′, c′′, d′′, ..., fitting


polynomial degree in the previous equations in order to get a better reproduction of the solubility surface, for instance:

Table 1. Correlation Equations of the Liquid-Liquid Equilibrium Dataa Hand:25 Correlation for ternary systems

log

( )

( )

y(2) x(2) ) a + b log y(3) x(1)

x(2) + x(4) ) (AM2 + BM + C)(x(1) + x(4))3 + (DM2 + EM + F)(x(1) + x(4))2 + (GM2 + HM + I)(x(1) + x(4)) + (JM2 + KM + L) (3d)

Eisen-Joffe:24 Correlation for quaternary systems including an inorganic salt

( )

log

( )

y(2) x(2) ) (a + bX(4)) + (c + dX(4)) log y(3) x(1)

Modification proposed by Marcilla et al.:6 Correlation for quaternary systems including an inorganic salt

( )

( )

y(2) x(2) log ) (a + bx(4)) + (c + dx(4)) log + y(3) x(1)

[ ( )] x(2) x(1)

(e + fx(4)) log

2

a x(i) and y(i): molar or mass fractions of component i (1 ) water, 2 ) solute, 3 ) solvent, and 4 ) salt) in aqueous and organic phases, respectively. a, b, c, and d: parameters of the correlation which depend on the components and temperature but are independent of the composition. X(4): concentration of salt in the initial mixture.

parameters of the correlation which depend on the components and temperature but are independent of the composition; C, positive constant (C > 0), to allow the use of the binary and ternary equilibrium data in the proposed correlation. The fitting of the experimental data with the three equations is independent, obtaining a total of 18 parameters (6 for each equation), and all equilibrium data of the system are correlated simultaneously with each equation. The optimization method used to obtain the parameters of the correlation was the tool “Solver” included in the calculation sheet Excel 7.0 for Windows. The objective function used was the following: n

OF1 )

∑ k)1

[( ( ) ) ( ( ) ) ] y(i)

- log

log

y(j)

k exp

2

y(i) y(j)

(2)

k cal

where i and j are the components of the system (i * j), exp ) experimental, cal ) calculated, and n ) number of tie lines fitted. 2.3. Solubility Surface Fitting. The equations proposed for the solubility surface fitting, which contains the equilibrium data, are based on the Cruickshank20 projections. These projections are P1, projection onto a parallel plane to two nonconsecutive axes (1)(3) and (2)-(4) (x ) x(1) + x(4) and y ) x(3) + x(4)); and P2, projection onto a parallel plane to two nonconsecutive axes (1)-(2) and (3)-(4) (x′ ) x(1) + x(4) and y′ ) x(2) + x(4)). Then, the equations proposed for the fitting of the equilibrium data in both projections are

x(3) + x(4) ) (A′M + B′)(x(1) + x(4)) + (C′M + D′) (3a) x(2) + x(4) ) (AM2 + BM + C)(x(1) + x(4))2 + (DM2 + EM + F)(x(1) + x(4)) + (GM2 + HM + I) (3b) M)

x(4) x(2) + x(4)

(3c)

but in some cases it is necessary to increase the

where x(1), x(2), x(3), and x(4) are the composition of any point on the solubility surface and A, B, C, ... are the correlation parameters which have been calculated using the “Solver” tool included in the calculation sheet Excel 7.0. To minimize, the following objective function has been used: n

OF2 )

c

∑ ∑((x(i)k)exp - (x(i)k)cal)2) (

(4)

k)1 i)1

where the calculated points are obtained by fixing x(2) and x(4) and calculating x(1) and x(3) by means of the solubility surface equation. These equations will be used to obtain the intersections between the operating lines and the solubility surface to calculate the composition of the aqueous phase which crosses, between two stages, with an organic phase in the extraction cascade. The equilibrium points corresponding to both aqueous and organic phases have been fitted independently to obtain lower values of the objective function. Therefore, two sets of parameters will be obtained, Aa, Ba, Ca, ... for the correlation of the aqueous phases and Ao, Bo, Co, ... for the organic phases. 2.4. Liquid-Liquid Equilibrium Calculation Using the Proposed Correlation. From the composition of an aqueous phase and using the values for the parameters obtained in the correlation presented in the set of equations (1), the values of the constants C1, C2, and C3 (right-hand side of eq 1a-c, respectively) can be calculated. If the mass balance in the organic phase is also considered, the system of four equations obtained allows the calculation of the compositions in the organic phase in equilibrium with the aqueous phase considered.

100 + 4C -C 1 + C1C2 + C2 + C1C2C3 100 + 4C y(2)cal ) -C 1 + 1 + C1 + C1C3 C2 100 + 4C -C y(3)cal ) 1 1 + + 1 + C3 C1 C1C2 y(4)cal ) 1 - y(1)cal - y(2)cal - y(3)cal

y(1)cal )

(5)

2.5.a. Calculation of the Liquid-Liquid Extractor. According to all of the previous statements, a method for the calculation of a liquid-liquid extractor has been developed for the separation of quaternary mixtures. The calculation scheme is shown in Figure 4. (i) Mass Balances. Figure 2 shows a scheme of the extraction cascade to be calculated. This extractor has only one sector and the net mass flow between the two


x(2,0)R(0) + y(2,0)E(0) ) y(2,1)E(1) + x(2,n)R(n) (12) R(n) )

x(2,0)R(0) + y(2,0)E(0) - y(2,1)(E(0) + R(0)) x(2,n) - y(2,1) (13) E(1) ) R(0) + E(0) - R(n)

(14)

(iv) Equilibrium Calculation. From a known composition of an aqueous phase R(j), x(i,j), the composition of the organic phase in equilibrium E(j), y(i,j), is calculated using eqs 1 and 5 and the procedures explained previously in section 2.4. (v) Calculation of the Intersection between an Operating Line and the Solubility Surface. This intersection point is determined by solving the set of equations corresponding to the operating line (i.e., the line passing through the difference point and E(j)) and the solubility surface, using the Newton-Raphson method. If X(i) and Y(i) are two known points of the operating line (for example, x(i,j) and δ(i) points) and P(i) is the intersection point to be obtained (compositions in mass fractions of the stream from the next stage), the equations which have to be solved are

{

I. Mass balance and operating line equation P(1) - X(1)

Y(1) - X(1) P(1) - X(1) Y(1) - X(1)

Figure 4. Liquid-liquid extractor calculation scheme.

stages will be constant (there is only one difference point, ∆; Seader and Henley26):

E(0) + R(0) ) E(1) + R(n)

(6)

M ) E(0) + R(0)

(7)

zM(i) )

x(i,0)R(0) + y(i,0)E(0) R(0) + E(0)

(8)

R(0) + E(j+1) ) E(1) + R(j)

(9)

∆ ) R(k) - E(k+1) ) R(0) - E(1)

(10)

x(i,0)R(0) + y(i,1)E(1) δ(i) ) R(0) + E(1)

(11)

To locate the difference point ∆, which is necessary to calculate the operating lines, point E(1) has to be calculated. (ii) R(n) Calculation. x(2,n) and x(4,n) are known because they are specifications of the problem. Furthermore, R(n) is placed on the solubility surface and in the region corresponding to the aqueous phases. To calculate the composition of R(n), the equation of the line representing the intersection of the planes x(2,n) ) cte. and x(4,n) ) cte. must be obtained. Obviously, the intersection of this line with the solubility surface (eq 3) provides the R(n) composition searched. (iii) E(1) Calculation. The intersection point between the line which includes M (eq 7) and R(n) and the solubility surface (eq 3) corresponding to the organic phases provides the composition of E(1). Once the compositions of R(n) and E(1) are known, their corresponding flow rates can be defined as

{

-

P(2) - X(2) Y(2) - X(2) P(3) - X(3) Y(3) - X(3)

)0 )0

(15)

4

P(i) ) 1 ∑ i)1

II. Solubility surface equation R ) 100P(2) + 100P(4) + 200 Z ) (100P(4) + 100)/R β ) 100P(1) + 100P(4) + 200 (16) (AZ2 + BZ + C)β2 + (DZ2 + EZ + F)β + (GZ2 + HZ + I) - R ) 0

This equation system (eqs 15 and 16) is solved using the Newton-Raphson method for obtaining the value of the intersection point, P(i). The function f used in this method is the following:

f ) (AZ2 + BZ + C)β2 + (DZ2 + EZ + F)β + (GZ2 + HZ + I) - R (17) For the calculation of f and df/dP(1), P(2), P(3), and P(4) are calculated as a function of P(1) (eq 15). (vi) Continuation of the Procedure until the Composition of the E(1) Calculated from the Overall Mass Balance Is Reached or Exceeded (Figure 1). This procedure only allows the calculation of the different stages of an extractor where the compositions and the flow rates of feed and solvent streams are specified. Nevertheless, this is not the case of the design where the number of stages and the flow ratio are not known. A design procedure must be provided to solve this problem. 2.5.b. Design Method for the Liquid-Liquid Extractor. The application of the previous scheme


Next, when the initial estimation of the flow rate (mass) of the solvent stream E(0) is made and the composition of the last desired raffinate, x(i,n), is taken into account, the E(1) phase coherent with R(n) specified is calculated (section 2.5.a). The composition and the flow rate of E(1) depend on the assumed flow of E(0), and the objective function given by eq 18 must be minimized to calculate this flow rate. 3. Results

Figure 5. Liquid-liquid extractor design method scheme.

(Figure 4) provides the optimum number of stages corresponding to the specified compositions and flow rates, but it does not solve the design problem because the two phases R(n) and E(1) and their compositions are determined by the characteristics (composition and flow rate) of the feed streams R(0) and E(0) as well as the equilibrium trajectory along the extractor. Therefore, the composition of the product obtained by the stage by stage calculations does not probably satisfy exactly the mass balance with the initial specifications of the problem. In the present paper, the solvent flow rate (E(0)) is used as the variable to be optimized by an iterative procedure to achieve the condition where the composition of the last E(j) calculated by the stage by stage calculations (y(i,j)extractor) exactly matches the initial composition of E(1) obtained from the mass balance (y(i,1)mass balance). We have used the following objective function and the calculation scheme is shown in Figure 5: c

OF3 )

(ymass balance(i,1) - yextractor(i,j))2 ∑ i)1

(18)

Consequently, the initial specifications of the problem have to be considered: (a) Parameters obtained in the correlation of the tie lines and the solubility surfaces: a, b, c, ..., a′, b′, c′, ..., a′′, b′′, c′′, ..., A, B, C, ..., A′, B′, C′, ..., etc. (b) Composition and flow of the feed (mass): x(i,0) and R(0). (c) Composition of the solvent used: y(i,0). (d) Mass fraction of the two solutes in the end raffinate R(n): x(2,n) and x(4,n).

3.1. Liquid-Liquid Equilibrium Correlation Results. The proposed method for the prediction of liquidliquid equilibrium for designing extraction columns (stage by stage) has been applied to the next systems: system 1, water + acetone + 1-butanol + 1-propanol; system 2, water + acetone + 2-butanone + 1-propanol; system 3, water + acetone + chloroform + acetic acid. In these three quaternary systems there is a unique pair of partially miscible components: water + 1-butanol, water + 2-butanone, and water + chloroform. Therefore, these are type 1 systems. The experimental data used can be found elsewhere (Gomis Yaguës27 and Ruiz and Prats23). For system 1, the number of tie lines used was 41: 1 of these is the equilibrium data of the binary system water + 1-butanol, 5 correspond to the ternary system water + acetone + 1-butanol, 9 correspond to the water + 1-butanol + 1-propanol ternary system, and 26 are quaternary tie lines. For system 2, 29 tie lines were used, 7 of them corresponding to the ternary system water + acetone + 2-butanone, three tie lines to the ternary system water + 2-butanone + 1-propanol, and 19 to the quaternary region. For system 3, 48 tie lines were considered, 8 of them in the ternary system water + acetone + chloroform, another 8 in the water + chloroform + acetic acid ternary system, and 32 quaternary tie lines. In Tables 2-4, the values of the parameters obtained in the correlation of the equilibrium data of the studied systems are presented. A large number of decimals have been maintained in order to reproduce the equilibrium as precisely as possible. The comparison between the experimental equilibrium data and the results obtained using the correlation proposed is shown in Figures 6-9. In Tables 5 and 6, the deviations calculated using eq 19 are presented.

σ)

x

n

c

(∑((x(i)k)exp - (x(i)k)correl)2) ∑ k)1 i)1 4n

(19)

As can be observed, the results obtained using the suggested correlation are in very good agreement with the experimental data, especially taking into consideration the quality of the correlations and predictions provided by the thermodynamic and other existing models for the liquid-liquid equilibrium. Usually, the correlation of the equilibrium data has been achieved using a unique equation that relates the ratios between the mass fractions of solute and solvent in the organic phase and the mass fractions of solute and water in the aqueous phase (Table 1). The use of three equations, as proposed in this work (eq 1), allows the calculation of the composition of the organic phase in equilibrium with an aqueous phase considered. In liquid-liquid extraction calculations, it is necessary to

Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 3089 Table 2. Parameters of the Correlation (Eq 1) and Objective Function (Eq 2) Values of the Experimental Equilibrium Data (Case 1) for the Quaternary System Water + Acetone + 1-Butanol + 1-Propanol (Eq 1), Including Binary, Ternary, and Quaternary Equilibrium Data (C ) 100) eq 1a param a b c d e f g h i

eq 1b value

361.524 881 -749.989 588 389.378 215 2 801.499 42 -5 805.412 47 3 009.426 96 5 405.060 93 -11 205.814 7 5 805.687 77

OF1 (eq 2) 0.000 303 85

eq 1c

param

value

a′ b′ c′ d′ e′ f′ g′ h′ i′

-142.143 197 288.234 854 -147.604 579 -1 125.581 92 2 270.718 69 -1 155.350 31 -2 226.842 4 475.265 82 -2 266.645 42

param

value -328.092 406 675.691 116 -347.527 245 -2 615.969 85 5 386.279 95 -2 767.722 56 -5 122.437 79 10 580.959 -5 447.158 21

a′′ b′′ c′′ d′′ e′′ f ′′ g′′ h′′ i′′

OF1 (eq 2) 0.000 147 2

OF1 (eq 2) 0.000 322 81

Table 3. Parameters of the Correlation (Eq 1) and Objective Function (Eq 2) Values of the Experimental Equilibrium Data (Case 1) for the Quaternary System Water + Acetone + 2-Butanone + 1-Propanol (Eq 1), Including Binary, Ternary and Quaternary Equilibrium Data (C ) 100) eq 1a param a b c d e f g h i

eq 1b value

47.826 513 6 -99.708 990 8 51.699 981 438.572 315 -911.008 171 471.416 025 966.593 214 -2 014.742 41 1 042.349 55

OF1 (eq 2) 1.8659 × 10-5

param a′ b′ c′ d′ e′ f′ g′ h′ i′

eq 1c value

param

-44.374 603 6 96.630 791 5 -52.844 819 7 -365.618 38 794.089 004 -432.495 58 -702.432 457 1 541.790 24 -846.768 802

value -4.678 580 44 10.128 856 5 -5.171 723 69 -0.019 756 7 -1.002 583 39 2.970 898 76 185.237 512 -365.986 631 188.744 604

a′′ b′′ c′′ d′′ e′′ f ′′ g′′ h′′ i′′

OF1 (eq 2) 3.3685 × 10-5

OF1 (eq 2) 2.7643 × 10-5

Table 4. Parameters of the Correlation (Eq 1) and Objective Function (Eq 2) Values of the Experimental Equilibrium Data (Case 1) for the Quaternary System Water + Acetone + Chloroform + Acetic Acid (Eq 1), Including Binary, Ternary and Quaternary Equilibrium Data (C ) 100) eq 1a param a b c d e f g h i

eq 1b value

1.084 183 44 -1.696 708 41 0.549 181 14 10.619 118 5 -17.449 015 9 6.6495 420 7 24.810 838 -43.387 467 8 15.458 338 7

OF1 (eq 2) 7.9163 × 10-4

param a′ b′ c′ d′ e′ f′ g′ h′ i′

eq 1c value

param

0.976 978 05 -1.436 803 14 0.478 272 71 6.365 240 47 -11.682 048 2 4.311 609 26 12.773 781 6 -24.326 234 5 8.067 615 18

OF1 (eq 2) 1.8543 × 10-4

be able to calculate the composition of a phase in equilibrium with another one. If quaternary systems are considered, this calculation is iterative. Nevertheless, iterative calculation is not necessary with the correlation proposed in this work for quaternary systems. On the other hand, a constant and positive value (C) has been added to all compositions in mass or molar fractions to allow the use of the binary and ternary equilibrium data in the correlation. Two arbitrary values for the constant C were considered: C ) 1 and C ) 100, obtaining better results when C ) 100 was used. The C optimization (one more parameter in the correlation) was considered. However, the C values, which lead to the lower values of the objective function for the three correlation equations, do not lead to the lower values of the differences between experimental and calculated equilibrium data when the recalculation of the compositions of the organic phase is made using the parameters obtained in the correlation. This problem can be solved if the objective function were the standard deviation between experimental and calculated equilibrium data, but the time required for such

value

a′′ b′′ c′′ d′′ e′′ f ′′ g′′ h′′ i′′

0.315 395 57 -0.501 746 14 0.230 259 19 -1.263 802 34 -0.475 014 22 0.740 882 85 -5.005 086 51 3.584 361 22 0.923 882 34

OF1 (eq 2) 2.6877 × 10-4

Table 5. Deviation between the Experimental (Case 1) and Calculated Values, Using the Correlation Model Proposed in This Paper (Eq 1), for the Quaternary Systems Studieda C ) 100 system

component

σ (eq 19)

max deviation

1

water acetone 1-butanol 1-propanol

7.6 × 10-6 0.0165 0.0438 0.0341 0.0353

0.8085 0.6505 0.8893 0.7789 0.7818

2

water acetone 2-butanone 1-propanol

0.0988 0.0016 0.0839 0.0039 0.0471

1.2391 0.1187 1.0217 0.1844 0.6410

3

water acetone chloroform acetic acid

0.0034 0.0018 0.0073 0.0002 0.2053

0.9175 1.8774 2.2924 0.5825 1.4424

a Binary, ternary, and quaternary equilibrium data are included (C ) 100).


Figure 6. Comparison between the experimental (case 1) and calculated concentrations of component 1 in the organic phases (%, molar) using the equilibrium data correlation proposed, for the quaternary system water + acetone + chloroform + acetic acid.


calculation would be considerably increased. Since, the influence of the C parameter on the quality of the correlation is not great when the C value is in the same order of magnitude of the experimental data, and consequently the optimization of C has not been considered. 3.2. Solubility Surface Correlation Results. Table 6 shows the values of the parameters obtained in the correlation of the solubility surface, the objective function values (eq 4), and the deviation between experimental and calculated results (eq 19) for the three quaternary systems considered in this work.

In Figures 10 and 11 the Cruickshank20 projections of the experimental and calculated points on the solubility surface for the quaternary system water + acetone + chloroform + acetic acid are represented. As can be observed, a very good agreement between experimental and calculated results is obtained. Therefore, the equations proposed for fitting the points on the solubility surface are useful tools for the approximate calculation of liquid-liquid extractors. It is important to note that when only the points on the aqueous region of the solubility surface, or those on the organic region, are fitted separately, the quality of




the correlation is noticeably better than when they are fitted together. 3.3. Liquid-Liquid Extractor Design Results. When the equilibrium data have been correlated (eq 1), the aqueous and organic points on the solubility surface have been fitted to the equations proposed (eq 3), and the corresponding parameters have been obtained, the method for the design of the liquid-liquid extractor proposed in this work can be applied. The previous correlation steps might be considered as a disadvantage of this method compared to the

conventional simulation or design methods, where they are not necessary, because an additional time has to be used, though those parameters and correlation can be used for different design calculations involving the same system, pressure, and temperature. However, other previous steps are also required when a conventional thermodynamic method is used because binary parameters of the model have to be calculated to obtain the activity coefficients. However, as a clear advantage, the method suggested avoids the iteration in the equilibrium calculations and allows the direct design of the cascade.


Figure 10. Comparison between the experimental (case 1) and calculated solubility surfaces (aqueous region) using the correlation proposed and the Cruickshank projection P1, for the quaternary system water + acetone + chloroform + acetic acid. Table 6. Parameters (Eq 3), Objective Function (Eq 4), and Standard Deviation Values Obtained in the Correlation of the Experimental Solubility Surface (aqueous region) for the Quaternary Systems Studied (Case 1) projection 1 (eq 3a)

system 1

2

3

A′ B′ C′ D′

-0.492 499 032 -0.756 192 436 556.440 564 6 222.497 503

OF2 σ

0.031 7 0.001 1

A′ B′ C′ D′

-0.781 -0.609 51 617.677 4 191.163 1

OF2 σ

0.0028 0.0005

A′ B′ C′ D′

-0.561 666 92 -0.792 208 5 638.307 294 202.120 475

OF2 σ

5.022 4 0.026 2

projection 2 (eq 3b or d) A B C D

0.695 516 172 -0.448 661 596 -0.116 860 696 -241.887 425 9

E F G H I OF2 σ

197.478 232 3 57.092 186 84 -2 419.214 96 -4 983.664 097 -10 281.445 65 1.987 7 0.012 4

A B C D

-0.582 66 0.606 886 -0.177 21 143.833 5

E F G H I OF2 σ

-148.226 48.114 02 -202.068 -408.222 -814.864 0.403 4 0.005 5

A B C D E F

-0.000 217 9 -0.001 814 92 0.002 087 34 0.396 640 6 0.800 551 32 -1.492 266 64

G H I J K L OF2 σ

-100.019 097 -74.785 413 1 352.362 963 0.008 147 73 -0.036 656 72 -27 822.0805 3.215 8 0.016 7

To illustrate the method proposed for designing a liquid-liquid extractor to separate a quaternary mixture, the resolution of the next example is presented: “Calculation of the number of stages required and the quantity (kg/h) of chloroform necessary to obtain a raffinate with a mass fraction of acetone and acetic acid of 0.0009 and 0.11, respectively, from the feed of 350 kg/h of a mixture with the following composition (mass fraction): water, 0.75; acetone, 0.12; acetic acid, 0.13.” In Tables 7 and 8 the results obtained for this problem are shown. As can be observed, the extractor design procedure yields the compositions of the two phases which leave each stage, the solvent flow rate and the number of stages necessary. The objective function used is shown in eq 18.

3.4. Discussion of the Results. Different results are obtained when different sets of equilibrium data are considered (cases 1 and 2). These differences are inherent to the separation calculations based on cascades of equilibrium stages, where the results depend on the experimental data and on the model used to calculate the equilibrium in each stage. The results obtained using the experimental data (case 1) are not always the best, because sometimes these data are not homogeneously distributed over the solubility surface, and the interpolation/extrapolation may be somewhat risky. On the other hand and in many cases, the raw experimental data must be handled with special care because the interpolation/extrapolation may yield spurious results. In case 2 considered, the equilibrium points calculated


Figure 11. Comparison between the experimental (case 1) and calculated solubility surfaces (aqueous region) using the correlation proposed and the Cruickshank projection P2, for the quaternary system water + acetone + chloroform + acetic acid. Table 7. Liquid-Liquid Extractor Design Using the Method Proposed in This Paper and Experimental Equilibrium Data (Case 1) raffinate phase

extract phase

no. of trays

x(1)

x(2)

x(3)

x(4)

y(1)

y(2)

y(2)

y(4)

1 2 3 4

0.8814 0.8611 0.8352 0.7781

9.11 × 10-4 9.90 × 10-3 3.03 × 10-2 8.98 × 10-2

7.69 × 10-3 8.38 × 10-3 8.97 × 10-3 9.82 × 10-3

0.1100 0.1207 0.1227 0.1223

1.23 × 10-3 2.07 × 10-3 4.31 × 10-3 1.14 × 10-2

8.12 × 10-3 2.92 × 10-2 8.10 × 10-2 1.85 × 10-1

0.9786 0.9518 0.8913 0.7699

1.20 × 10-2 1.69 × 10-2 2.34 × 10-2 3.41 × 10-2

solvent flow E(0): 328.39 kg/h

OF3 (eq 18): 0.1106

Table 8. Liquid-Liquid Extractor Design Results Using the Method Proposed in This Papera raffinate phase no. of trays

x(1)

x(2) 10-4

1 0.8888 9.11 × 2 0.8539 4.78 × 10-3 3 0.8434 0.01156 4 0.8292 2.71 × 10-2 5 0.7982 6.25 × 10-2 solvent flow E(0): 379.57 kg/h a

extract phase

x(3) 10-4

3.17 × 1.01 × 10-3 1.03 × 10-3 8.27 × 10-4 9.38 × 10-4

x(4) 0.1100 0.1403 0.1440 0.1429 0.1383

y(1) 10-3

y(2) 10-3

9.51 × 3.06 × 9.92 × 10-3 8.39 × 10-3 -3 9.37 × 10 2.06 × 10-2 8.44 × 10-3 4.88 × 10-2 8.55 × 10-3 0.11093 OF3 (eq 18): 2.4229 × 10-2

y(2)

y(4)

0.9593 0.9495 0.9372 0.9130 0.8501

2.82 × 10-2 3.22 × 10-2 3.28 × 10-2 3.24 × 10-2 3.05 × 10-2

The equilibrium data were obtained using UNIQUAC (case 2).

using the UNIQUAC model are homogeneously distributed on the solubility surface, contrary to case 1 when using directly the raw experimental data where they are not homogeneously distributed on the corresponding solubility surface. Hunter,17 Smith,18 Powers,19 Cruickshank et al.,20 Treybal,16 Ruiz et al.,21,22 and Ruiz and Prats23 proposed graphical methods to interpolate equilibrium data not determined experimentally. Nevertheless, the method proposed in this work allows the easy resolution of the problem of direct design for mixtures with four or more components (no other methods in this line have been found in the literature). The computer program ChemCad III13 (using the UNIQUAC model) has been used to test the quality of the results obtained with the method proposed in this work. In the simulation, the feed streams have the same compositions as in the problem stated. The solvent flow rate and the number of stages are those obtained as

results using our design method. Because a deviation exists between experimental and equilibrium data obtained using a thermodynamic model and to prevent the effect of this deviation on the comparison made using ChemCad and the design model proposed in this work, the comparison has been carried out using both experimental data (case 1) and equilibrium points generated using the UNIQUAC model (case 2). The results obtained with ChemCad III are shown in Tables 9 and 10. Table 7 shows the results obtained using the model proposed in this paper and experimental data (case 1), obtaining the following results: solvent flow rate 328.39 kg/h and four stages. The results obtained for the same solvent flow rate and 4 stages using ChemCad III are presented in Table 9. As can be concluded, a good agreement exists between the results obtained by both methods. A similar conclusion can be drawn if the equilibrium data generated using the UNIQUAC model

3094 Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 Table 9. Liquid-Liquid Extractor Design Results Using ChemCad,13 Considering the Stage Number and the Feed Flow Presented in Table 7 (Case 1; Solvent Flow, 328.39 kg/h; Four Trays) raffinate phase

extract phase

no. of trays

x(1)

x(2)

x(3)

x(4)

y(1)

y(2)

y(2)

y(4)

1 2 3 4

0.8784 0.8480 0.8284 0.7977

2.84 × 10-3 9.55 × 10-3 2.46 × 10-2 5.69 × 10-2

6.67 × 10-3 7.77 × 10-3 8.42 × 10-3 9.35 × 10-3

0.1120 0.1346 0.1386 0.1361

3.36 × 10-3 4.21 × 10-3 5.34 × 10-3 7.85 × 10-3

6.16 × 10-3 1.99 × 10-2 4.94 × 10-2 1.07 × 10-1

0.9662 0.9456 0.9135 0.8523

2.43 × 10-2 3.03 × 10-2 3.18 × 10-2 3.24 × 10-2

Table 10. Liquid-Liquid Extractor Design Results Using ChemCad,13 Considering the Stage Number and the Feed Flow Presented in Table 8 (Case 2; Solvent Flow, 379.57 kg/h; Five Trays) raffinate phase no. of trays 1 2 3 4 5

x(1) 0.8858 0.8573 0.8454 0.8320 0.8036

x(2) 10-4

6.30 × 2.37 × 10-3 0.00705 1.94 × 10-2 5.01 × 10-2

extract phase

x(3) 10-3

6.44 × 7.52 × 10-3 7.95 × 10-3 8.35 × 10-3 9.19 × 10-3

x(4) 0.1071 0.1328 0.1396 0.1403 0.1371

(case 2) are used for the design of the extractor. The discrepancies increase when the number of stages increases, showing the effect of the error accumulation. The largest differences are observed for component 3 in the raffinate phase and component 1 in the extract phase. However, it has to be pointed out that both the latter are minor components with mass fractions of less than 0.1. 4. Conclusions A new method for extraction column design has been developed. This method is based on the geometrical concepts of the Ponchon and Savarit method for binary systems. The method proposed in this paper consists of the following global steps: (1) Generation of the equilibrium points using the UNIQUAC model, when the experimental equilibrium points are not available or they are not homogeneously distributed on the solubility surface. (2) Correlation of the tie lines, to calculate the equilibrium without iterations. (3) Fitting the solubility surface, to be able to determine the operative line-equilibrium surface intersection (to calculate the next stage). (4) Design of the extractor, to determine the optimum number of equilibrium stages for a specified product separation as well as the solvent flow rate, which satisfies the overall balance and the stage to stage calculations. The method which has been described in detail and applied to type 1 quaternary systems yields excellent results, which have been compared with the ChemCad III commercial simulator. The method suggested has the clear advantage that it allows the direct design of extraction cascades, avoids the iteration calculations involving the equilibrium, and involves very easy geometrical concepts that are direct extensions of those of the Ponchon and Savarit method. Notation a, b, c, d, ..., a′, b′, c′, d′, ...: equilibrium data correlation parameters which depend on the components and temperature but are independent of the composition A, ..., L, and A′, ..., D′: solubility surface correlation parameters using Cruickshank projections Aa, ..., La and A′a, ..., D′a: solubility surface (aqueous region) correlation parameters using Cruickshank projections

y(1) 10-3

3.15 × 3.71 × 10-3 4.14 × 10-3 4.99 × 10-3 7.30 × 10-3

y(2) 10-3

1.38 × 5.04 × 10-3 1.47 × 10-2 3.91 × 10-2 0.09572

y(2)

y(4)

0.9724 0.9616 0.9457 0.9237 0.8646

2.31 × 10-2 2.97 × 10-2 3.16 × 10-2 3.21 × 10-2 3.24 × 10-2

Ao, ..., Lo and A′o, ..., D′o: solubility surface (organic region) correlation parameters using Cruickshank projections C: positive constant (C > 0) C1, C2, and C3: constants defined in the resolution of the equation system (5) E(j): molar or mass flow of the extract phase which leaves stage j E(0): molar or mass flow of the solvent feed E(1): molar or mass flow of the end extract R(j): molar or mass flow of the raffinate phase which leaves stage j R(n): molar or mass flow of the end raffinate R(0): molar or mass flow of the feed introduced at the first stage x(i): molar or mass fractions of component i in the aqueous phase x(i,j): molar or mass fractions of component i, in the aqueous phase which leaves the stage j x′(i): corrected molar or mass fractions of component i in the aqueous phase (x′(i) ) x(i) + C) X(4): concentration of salt in the initial mixture y(i): molar or mass fractions of component i in the organic phase y(i,j): molar or mass fractions of component i, in the organic phase which leaves stage j y′(i): corrected molar or mass fractions of component i in the organic phase (y′(i) ) y(i) + C) zM(i): molar or mass fraction of component i in the fictitious current M Greek Characters δ(i): molar or mass fraction of component i in the fictitious difference current ∆ ∆: fictitious current difference point which represents the net mass flow in a stage

Literature Cited (1) Olaya, M. M.; Conesa, J. A.; Marcilla, A. Salt Effect in the Quaternary System Water + Ethanol + 1-Butanol + Potassium Chloride at 25 °C. J. Chem. Eng. Data 1997, 42, 858-864. (2) Pires, M. J.; Cabral, J. M. S. Liquid-Liquid Extraction of a Recombinant Protein with a Reverse Micelle Phase. Biotechnol. Prog. 1993, 9, 647-650. (3) Coen, C. J.; Blanch, H. W.; Prausnitz, J. M. Salting-out of Aqueous Proteins: Phase Equilibria and Intermolecular Potentials. AIChE J. 1995, 41 (4), 996-1004. (4) Cheluget, E. L.; Gelinas S.; Vera J. H.; Weber M. E. LiquidLiquid Equilibrium of Aqueous Mixtures of Poly(propyleneglycol) with NaCl. J. Chem. Eng. Data 1994, 39, 127-130. (5) Olaya, M. M.; Garcia, A. N.; Marcilla, A. Liquid-LiquidSolid Equilibria for the Quaternary System Water + Acetone +

Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 3095 1-Butanol + Sodium Chloride at 25 °C. J. Chem. Eng. Data 1996, 41, 910-917. (6) Marcilla, A.; Ruiz, F.; Olaya, M. M. Liquid-Liquid-Solid Equilibria of the Quaternary System Water-Ethanol-1-ButanolSodium Chloride at 25 °C. Fluid Phase Equilib. 1995, 105, 7191. (7) Ruiz, F.; Marcilla, A. Some Comments on the Study of the Salting out Effect in Liquid-Liquid Equilibrium. Fluid Phase Equilib. 1993, 89, 387-395. (8) Ruiz, F.; Marcilla, A.; Gomis, V. Method for EquilibriumStage Calculations in Liquid-Liquid Extraction. Application to Countercurrent Cascade Design for a Quaternary System. Ind. Eng. Chem. Process Des. Dev. 1986, 25 (3), 631-634. (9) Reyes Labarta, J. A. Disenõ de Columnas de Rectificacioń y Extraccioń Multicomponente. Ca´lculo del Reflujo Mıńimo. Ph.D. Dissertation, University of Alicante, Alicante, Spain, 1998. (10) Marcilla, A.; Go´mez, A.; Reyes, J. New Method for Designing Distillation Columns of Multicomponent Mixtures. Lat. Am. Appl. Res. 1997, 27 (1-2), 51-60. (11) Yamada, I.; Sawada, M.; Zhang, B. Q.; Haraoka, S. Radio Solution of Operation-Type Multicomponent Distillation Problems by the Ev-Matrix Method. Int. Chem. Eng. 1986, 26 (No. 3), 534539. (12) Ricker, N. L.; Grens, E. A. A Calculational Procedure for Design Problems in Multicomponent Distillation. AIChE J. 1974, 20 (No. 2), 238-244. (13) ChemCad III User Guide; Chemstations Inc.: 1993. (14) Kister, H. Z. Distillation Design; McGraw-Hill: New York, 1992. (15) King, C. J. Separation Processes, 2nd ed.; McGraw-Hill: New York, 1980. (16) Treybal, R. E. Extraccioń en fase lı´quida. Uteha: Me´xico, D. F., 1968.

(17) Hunter, T. G. Ind. Eng. Chem. 1942, 34, 963. (18) Smith, J. C. Ind. Eng. Chem. 1944, 36, 68. (19) Powers, J. E. Chem. Eng. Prog. 1954, 50, 291. (20) Cruickshank, A. J. B.; Haetsch, N.; Hunter, T. G. LiquidLiquid Equilibria of Four-Components System. Ind. Eng. Chem. 1958, 42, 2154-2158. (21) Ruiz, F.; Prats, D.; Marcilla, A. Liquid-Liquid Extraction: A Graphical Method for Equilibrium Stage Calculation for a Quaternary System. Fluid Phase Equilib. 1984. (22) Ruiz, F.; Prats, D.; Gomis, V. Evaluation of the Methods of Correlation and Interpolation of Quaternary Liquid-Liquid Equilibrium data. Fluid Phase Equilib. 1986. (23) Ruiz, F.; Prats D. Quaternary Liquid-Liquid Equilibria. Experimental determination and correlation of equilibrium data. Fluid Phase Equilib. 1983, 10, 79. (24) Eisen, E. O.; Joffe, J. Salt Effect in Liquid-liquid Equilibria. J. Chem. Eng. Data 1966, 11 (No. 4). (25) Hand, D. B. J. Phys. Chem. 1930, 34, 1961. (26) Seader, J. D.; Henley, E. J. Separation Process Principles; John Wiley & Sons, Inc.: New York, 1998. (27) Gomis Yaguës, V. Equilibrio Lı´quido-Lı´quido en Sistemas Cuaternarios con Dos Pares de Compuestos Parcialmente Miscibles. Ph.D. Dissertation, University of Alicante, Alicante, Spain, 1983.

Received for review January 28, 1999 Revised manuscript received April 29, 1999 Accepted May 19, 1999 IE9900723

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