MODIFIED SERIES RESISTANCE MODEL - DETERMINATION OF MEAN CONCENTRATION BY INTEGRAL TRANSFORMATION

Abstract

There are several mathematical models that describe permeate flow in membrane separation processes. Among these, the series resistance model plays a prominent role. It takes into account membrane strength, concentration polarization, polarized layer and fouling to describe the permeate flow over time. In this work, an analysis of the modified series resistance model was performed, in which the resistance by polarization of the concentration is defined as being directly proportional to the transmembrane pressure. The proportionality constant is given by the product of a specific coefficient of resistance – which is determined by means of experimental data – the thickness of the boundary layer of concentration and the mean concentration. Due to the inability to obtain experimentally the value of the average concentration within the boundary layer of concentration, its simulation is carried out from the conservation equation of the chemical species. Thus, the objective of the present work was to solve the equation of the conservation of chemical species using GITT (Generalized Integral Transform Technique) and apply the modified series resistance model to describe the permeate flow of a solution of dextran through a permeable tube under laminar flow. GITT provided satisfactory results for the mean concentration, verified by comparison with the permeate flow obtained by the series resistance model with experimental results reported in the literature.