UNSTEADY-STATE MODELING AND ANALYSIS FOR LIQUID SURFACTANT MEMBRANE HYDROCARBON SEPARATION PROCESSES

The design of separation equipment using emulsion liquid membranes (ELM) requires independent predictive methods for the estimation of solute extraction rates. In this paper an analytical solution for the unsteady-state diffusion equations in a sphere with a time-dependent external-phase concentration as given by Vorstmann and Thijssen for liquid-liquid extraction has been adapted to model ELM hydrocarbon separations. This solution is based on approximating the concentration profile in the external phase by an asymptotic Sherwood number. It is seen that, at extraction factors and Biot numbers typical of hydrocarbon systems, the model gives a unique solution. This solution has been used to predict both batch and continuous countercurrent column ELM separation of benzene from mixtures with n-heptane. The model does not require any adjustable parameter, is easily programmable, and should be a useful tool in simulation/design calculations of ELM hydrocarbon separations.