Development of an easy to solve phenomenological model including pore and surface diffusions applied to batch adsorption

Abstract

This work introduces the Quadratic Pore Volume and Surface Diffusional Model (QPVSDM), which incorporates quadratic functions to approximate the average intraparticle concentration profiles of adsorption processes. It was developed to batch adsorption operations assuming instantaneous reaction (local equilibrium given by the Langmuir isotherm), external mass transfer, and intraparticle pore and surface diffusions. It consists of an ordinary differential equation that is simple to solve numerically. Experimental data from distinct real systems reported in the literature were reproduced by the QPVSDM (R2 > 0.92), which was compared with the Pore Volume and Surface Diffusional Model (PVSDM) consisting of a partial differential equation system. Both models reached the exact same equilibrium condition successfully. To encourage the testing and application of the QPVSDM, as well as to compare it with the PVSDM, an easy-to-use executable program written in python is available at GitHub platform.