Numerical solution of an inverse problem for a two-dimensional mathematical model of sorption dynamics

Abstract

We consider a two-dimensional mathematical model of sorption that allows for inner-diffusion kinetics as well as longitudinal and transverse diffusion. The inverse problem of determining the sorption isotherm from an experimental dynamic output curve is investigated for this model and stable solution methods are proposed for the inverse and the direct problem. The efficiency of the solution methods is explored in computer experiments.Keywords: mathematical sorption model, inverse problem, numerical methods.Large-diameter sorption columns are common in gas chromatography. Modeling of sorption processes in such columns requires two-and three-dimensional mathematical models. Mathematical modeling of pollutant propagation in groundwater also requires two-and three-dimensional mathematical models of sorption and diffusion. In this article we consider a mathematical model of sorption that allows for inner-diffusion kinetics as well as longitudinal and transverse diffusion [1,2]. For this mathematical model we investigate the inverse problem of determining the sorption isotherm from an experimental dynamic output curve and propose stable solution methods for the inverse and the direct problem. Inverse problems for one-dimensional mathematical models of sorption dynamics have been considered, e.g., in [3-5]. Two-Dimensional Sorption ModelWe consider a mathematical model of sorption that allows for inner-diffusion kinetics as well as longitudinal and transverse diffusion:D T u y (x, 0, t) = 0, D T u y (x, B, t) = 0, 0 < x < L, 0 < t ≤ T ,u(x, y, 0) = 0, a(x, y, 0) = 0, 0 ≤ x ≤ L, 0 ≤ y ≤ B.

Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm

“…A modern technique for obtaining sorption isotherms involves solving an inverse problem so that the simulated dynamic quantity coincides with the actual experimental results. During the last decades, certain inverse problems in estimating sorption isotherms and other parameters in some dynamic PDE models have been intensively studied, for example, [3,5,10,14,20,22,23,[25][26][27][29][30][31]. We also refer to [1,2,7,8,12,[15][16][17][18][19]28] for more related inverse problem studies.…”