Engineering of pervaporation systems: Exact and approximate expressions for the average flux during alcohol dehydration by single-pass pervaporation

Assuming a concentration-independent flux with an Arrhenius dependence on temperature, and using temperature- and composition-averaged physical properties, an exact analytical expression is derived for the average flux in an adiabatic, single-pass pervaporation module. This expression incorporates the Exponential Integral, a special function known to arise in the analysis and design of ultrafiltration systems. The range of feasible activation energies of permeation is established for IPA-water and ethanol-water systems. Within this range, and over the range of typical operating conditions, a simple approximation to the exact analytical expression is derived, namely, Jav/Jf=(Jr/Jf)0.52 where Jf is the flux at the feed temperature and Jr is the flux at the retentate temperature. The 0.52 exponent is derived on the basis of minimising the maximum error over the range of conditions studied and the maximum error was found to be less than 1.2% in both systems. A value of n = 0.5 increases this maximum error to just under 2.5% for both systems but average errors in this instance remain below 0.5%. The approximate expression allows for the rapid estimation of pervaporation area for water-ethanol and water-IPA systems.