Modeling of spiral wound pervaporation modules with application to the separation of styrene/ethylbenzene mixtures

Abstract

A mathematical model is derived to simulate the performance of spiral wound membrane modules for the pervaporative separation of binary liquid mixtures. Permeation through the polymer membrane is described by a detailed solution–diffusion model. Flory–Huggins theory is used to predict solubility of the penetrants, while the composition and temperature dependence of the diffusion coefficients are described by phenomenological relations. Unknown parameters of the solution–diffusion model are determined from sorption and flux data using nonlinear least-squares estimation. Standard correlations are used to estimate the mass transfer resistance due to the liquid boundary layer on the feed side of the module. The solution–diffusion model is coupled to differential mass, momentum and energy balances on the feed and permeate sides of the module to predict separation performance. The resulting model is two-dimensional as the feed-side and permeate-side stream properties vary in both the feed and permeate flow directions. Required input data to the model includes the feed flow rate, composition and temperature, the outlet permeate pressure, the membrane properties and the module dimensions. A numerical solution technique based on the use of the shooting method in the permeate flow direction and numerical integration in the feed flow direction is proposed. The model yields predictions of the feed-side and permeate-side stream properties as a function of both spatial coordinates. The separation of styrene and ethylbenzene with a polyurethane membrane is used to illustrate the modeling approach. A single module and a 10-module system with interstage heating are simulated to demonstrate potential uses of the pervaporation model.