Mathematical modeling of macrohomogeneous transport phenomena in ion-exchange membranes.

摘要

The ionic transport phenomena occurring in perfluorinated ionomer membranes were investigated by the construction of several mathematical models. A model of a single-layer ion-exchange membrane was developed and used to simulate a separator in a chlorine-caustic electrolysis cell. The macrohomogeneous transport of multiple ions through the membrane was considered in this model, and equations describing a water dissociation reaction were included. Fixed parameters were used to generate concentration, potential, and pressure profiles inside the membrane. Several case studies using different model parameters were performed, and the obtained data were used to predict the membrane's responses under a variety of operating conditions. A maximum in the pressure distribution within the membrane was also predicted.; In order to investigate the utility of process modeling software packages that solve complex coupled equations, the SPEEDUP process simulation software was also used to model this monolayer membrane separator. A comparison of the results obtained from this model to those obtained from the FORTRAN program was conducted. It was found that the SPEEDUP software could generate results that were identical to the FORTRAN code but only when the governing equations were written in a specific form. Therefore, the utility of this software is uncertain.; The complex transport phenomena occurring in multiple-layer ion-exchange membranes have been discussed and modeled by a limited number of researchers, and their models often contain restrictive assumptions in order to simulate the specific system being modeled. Several approaches to the modeling of the ionic transport phenomena in multiple-layer membranes were reviewed, and the macrohomogeneous transport phenomena in a bilayer membrane separator used in a chlorine-caustic cell were modeled. This model contained the characteristic features of the monolayer membrane model described previously. Specific interface conditions at the boundary between the perfluorosulfonic and perfluorocarboxylic acid layers were also derived. The results obtained by the use of this model for two sample case studies are discussed. It was determined that the primary driving force for ionic transport, the potential gradient, is the dominant term in the velocity expression, thereby allowing the pressure in the membrane to vary more freely than expected qualitatively.