Nonlinear parameter estimation for solution-diffusion models of membrane pervaporation.

An optimization-based procedure for estimating unknown parameters in solution-diffusion models of membrane pervaporation is presented. Permeation of two components through a polymer membrane is described by distinct solution and diffusion models. The solution model is based on a modified form of Flory-Huggins theory that accounts for interactions between the two penetrants. The diffusion model is derived from Fick's law, where the diffusion coefficients are allowed to depend on the local concentration of each component in the membrane. A phenomenologic relation is used to account for the effect of temperature on the component fluxes. The solution and diffusion models, as well as the temperature-flux relation, contain parameters that are not directly measurable. It is shown that these parameters can be estimated effectively from sorption and flux data by the solution of suitably formulated nonlinear optimization problems. The separation of styrene and ethylbenzene with a polyurethane membrane is used to illustrate the parameter estimation procedure.