Mathematical modeling of stationary thermopervaporation through hydrophobic membrane

Abstract

The paper proposes a one-dimensional mathematical model of stationary thermopervaporation of water-organic mixture through a non-porous hydrophobic membrane. The driving force of the process is the difference in the temperature and concentration of the mixture components on both sides of the membrane. The model takes into account the difference in interaction between molecules of the liquid and vapor phases of the mixture components with the membrane matrix (equilibrium distribution coefficients), as well as the difference in the diffusion coefficients of the components in all areas. The problem of heat transfer is solved independently. The temperature distribution in layers of the membrane system (diffusion boundary layer, membrane and permeate) is determined. It is assumed that the evaporation front coincides with the working side of the membrane. In the general case, the boundary value problem is solved numerically by the shooting method. As a result, the distribution of the mass fraction of the organic component over the membrane cell is obtained. The dependences of the separation factor and the pervaporation separation index (PSI) on the main parameters of the problem are determined. It is demonstrated that the dependence of the PSI on the separation factor has extremal character. This allows to select optimal conditions for thermopervaporation for the given parameters of the membrane system. In the limiting case when the fluxes of the mixture components are equal to zero, the solution is obtained analytically. The maximum possible separation factor can be determined using an analytical solution. The present model was successfully verified using the literature experimental data on the thermopervaporation separation of butanol and ethanol aqueous solutions through the membranes of various types.