A simple predictive treatment of the permeation process in pervaporation

Abstract

In pervaporation, a liquid feed contacts one side of a membrane and a vacuum is drawn on the other side of the membrane, producing a permeate vapor. Conventional transport models describe pervaporation in terms of sorption equilibrium between the liquid feed and the membrane material, diffusion through the membrane driven by a chemical potential gradient, and desorption into a vapor phase on the permeate side of the membrane. This is called the solution-diffusion model. The treatment presented in this paper is based on the same model but the driving force for permeation is expressed as a vapor pressure difference rather than a concentration difference. To simplify the mathematical treatment of pervaporation, the initial sorption step between the liquid feed solution and the membrane is separated into two sequential steps that together are thermodynamically equivalent to sorption from the liquid. These steps are: (1) evaporation of the feed liquid to produce a saturated vapor phase, and (2) permeation of the vapor through the membrane, driven by a partial pressure gradient. It is important to note that step (1) is conceptual only; in pervaporation, no vapor is actually present on the feed side of the membrane. This simple modification to the model leads to an equation for the pervaporation separation factor, β pervap, which contains a term β pervap, defined by the vapor-liquid equilibrium of the feed mixture, and a term α mem, the membrane selectivity, which is identical to the parameter used in gas and vapor separation. The resulting pervaporation transport equation contains the feed-side and permeate-side partial vapor pressures and the membrane normalized permeation flux, as commonly defined in gas and vapor separation. An advantage of our approach is that the role of the operating conditions of pervaporation (feed temperature and permeate pressure) becomes clear. Membrane performance can be separated from the operating conditions, so that comparison of pervaporation separation data from various sources can be made, even if the operating conditions are not identical. Another advantage is that the contributions of the vapor-liquid equlibirium and the membrane selectivity to the overall pervaporation separation factor are recognized. Experimental data taken from our own work and from the literature are analyzed using the proposed model. The analysis confirms the usefulness of our approach.