Numerical solution of an inverse problem of nonisothermal sorption dynamics

Abstract

We consider the inverse problem for a mathematical model of sorption dynamics that incorporates diffusion, intradiffusion kinetics, and the heat balance. Two numerical methods are proposed. Their efficiency is investigated in a computer experiment.Sorption processes in large-diameter columns are described by mathematical models that allow for heat release [1 -3]. The nonlinear dynamical parameters of these models (sorption isotherm, kinetic coefficient) are determined by solving inverse problems from experimental output concentration and heat curves. The solution method for some nonisothermal inverse problems for a mathematical model without diffusion has been proposed in [4]. Solution methods for isothermal inverse problems are discussed, e.g., in [5,6]; unique solvability of inverse problems is investigated, e.g., in [7 -8].In this article, we consider the inverse problem of determining the sorption isotherm for a mathematical model of sorption that incorporates diffusion, intradiffusion kinetics, and the heat balance [2,3]. Two numerical solutions are proposed.