A geometric method for the design of liquid extractors

A new design method for liquid extractors is developed using the geometric properties of the composition profiles in a multistage countercurrent arrangement. These profiles are found by solving the extractor model equations in the form of an initial value problem. An analysis of the fixed points or pinches in the profiles gives the minimum solvent flow requirement. Profiles at solvent flows above the minimum are guaranteed to be feasible and are to be used to find the equilibrium stage requirements and product distributions. The fixed points of the extractor model equations can be determined without performing stage-to-stage balances, and a comprehensive picture of the solutions and trade-offs in extractor design can thus be determined efficiently. This approach differs from the more classical techniques in that it is applicable to mixtures with mofe than three components, as illustrated in an example.