Multistage multicomponent extraction

Multicomponent systems containing four or more components become difficult to display graphically. However, process-design calculations can often be made for the extraction of the component with the lowest partition ratio K and treated as a ternaiy system. The components with higher K values may be extracted more thoroughly from the raffinate than the solute chosen for design. Or computer calculations can be used to reduce the tedium of multicomponent, multistage calculations. 

Smith and Brinkley developed a method for determining the distribution of components in multicomponent separation processes. Their method is based on the solution of the finite-difference equations that can be written for multistage separation processes, and can be used for extraction and absorption processes, as well as distillation. Only the equations for distillation will be given here. The derivation of the equations is given by Smith and Brinkley (1960) and Smith (1963). For any component i (suffix i omitted in the equation for clarity)... 

Assuming the liquid phases remain immiscible, the modelling approach for multicomponent systems remains the same, except that it is now necessary to write additional component balance equations for each of the solutes present, as for the multistage extraction cascade with backmixing in Section 3.2.2. Thus for component j, the component balance equations become... 

E. C. Roche and H. K. Staffin Rigorous Solution of Multicomponent Multistage Liquid-Liquid Extraction Problems, 61st Annual AIChE Meeting, Los Angeles, California, December 1968. 

Rigorous Solution of Multicomponent, Multistage Liquid-Liquid Extraction Problems,... 

The BP and SR methods for vapor-liquid contacting converge only with difficulty or not at all for separations involving very nonideal liquid mixtures (e.g., in extractive distillation) or for cases where the separator is like an absorber or stripper in one section and a fractionator in another section (e.g., a reboiled absorber). Furthermore, BP and SR methods are generally restricted to the very limited specifications stated above. More general procedures capable of solving ail types of multicomponent, multistage separation problems are based on the solution of all the MESH equations, or combinations thereof, by simultaneous correction (SC) techniques. 

Extraction Calculations by Triangular Diagrams Approximate Methods for Multicomponent, Multistage Separations... 

Then they simulated the extraction and scmbbing behavior from the leaching solution of phosphor waste shown in Table 8 by the equilibrium model for the multicomponent and multistage system. Using simulations, yttrium, europium, and terbium were found to be obtained with the efficiencies and purities shown in Table 9. As such, the simulation based on the equilibrium constant of each element is thought to be useful as a predictive tool and would considerably save the experimental effort to conduct multistage extraction operations. 

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