Numerical model of non-isothermal pervaporation in a rectangular channel

A numerical model of non-isothermal pervaporation was developed to investigate the development of the velocity, concentration and temperature fields in rectangular membrane module geometry. The model consists of the coupled Navier-Stokes equations to describe the flow field, the energy equation for the temperature field, and the species convection-diffusion equations for the concentration fields of the solution species. The coupled nonlinear transport equations were solved simultaneously for the velocity, temperature and concentration fields via a finite element approach. Simulation test cases for trichloroethylene/water, ethanol/water and iso-propanol/water pervaporation, under laminar flow conditions, revealed temperature drop axially along the module and orthogonal to the membrane surface. The nonlinear character of the concentration and temperature boundary-layers are most significant near the membrane surface. Estimation of the mass transfer coefficient assuming isothermal assumption conditions can significantly deviate from the non-isothermal predictions. For laminar conditions, predictions of the feed-side mass transfer coefficient converged to predictions from the classical Lévêque solution as the feed temperature approached the permeate temperature.