Numerical Calculation of Multicomponent Extraction

Extraction calculations involving more than three components cannot be done graphically but must be done by numerical solution of equations representing the phase equilibria and material balances over all the stages. Since extraction processes usually are adiabatic and nearly isothermal, enthalpy balances need not be made. The solution of the resulting set of equations and of the prior determination of the parameters of activity coefficient correlations requires computer implementation. Once such programs have been developed, they also may be advantageous for ternary extractions. 

For each component, the condition of equilibrium is that its activity is the same in every phase in contact. In terms of activity coefficients and concentrations, this condition on stage k is written  

The most useful relations of this type are the NRTL and UNIQUAC which are shown in Table 14.1. 

When combined with Eq. (14.19), the material balance becomes 

The overall balance from stage 1 through stage k is 

The operating point P is at the intersection of lines FE, and SR,. The triangular diagram construction shows that six stages are needed. 

The equilibrium line of the rectangular diagram is constructed with the preceding tabulation. Points on the material balance line 

The McCabe-Thiele construction also shows that six stages are needed. 

These calculations are of equilibrium stages. The assumption is made that the oil retained by the solids appears only as entrained solution of the same composition as the bulk of the liquid phase. In some cases the solute may be adsorbed or retained within the interstices of the solid as solution of different concentrations. Such deviations from the kind of equilibrium assumed will result in stage efficiencies less than 100% and must be found experimentally. 

Point P is at the intersection of lines EtF and SRN. Equilibrium compositions are related on lines through the origin, point A. 

Material balance compositions are related on lines through the 

The feed F, extract E, and raffinate are located on the triangular diagram. The ratio of solvent/feed is specified by the location of the point M on line SF. 

Other nomenclature is identified on the flowsketch. The solvent-free reflux point Rq is located on the extension of line SEi. Operating point Q is located at the intersection of lines SRq and RnM. Lines through Q intersect the binodal curve in compositions of raffinate and reflux related by material balance for instance, R and En+. When the line QF is crossed, further constructions are 

In this example, only one stage is needed above the feed F and five to six stages below the feed. The ratio of solvent to feed is 

Flowsketch and triangular diagram construction with extract reflux. 

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