Nonlinear Inverse Problem for an Ion-Exchange Filter Model: Numerical Recovery of Parameters

• Main Authors: Balgaisha Mukanova, Natalya Glazyrina
• Format: Article
• Language: English
• Published: Hindawi Limited 2015-01-01
• Series: Mathematical Problems in Engineering
• Online Access: http://dx.doi.org/10.1155/2015/357829

This paper considers the problem of identifying unknown parameters for a mathematical model of an ion-exchange filter via measurement at the outlet of the filter. The proposed mathematical model consists of a material balance equation, an equation describing the kinetics of ion-exchange for the nonequilibrium case, and an equation for the ion-exchange isotherm. The material balance equation includes a nonlinear term that depends on the kinetics of ion-exchange and several parameters. First, a numerical solution of the direct problem, the calculation of the impurities concentration at the outlet of the filter, is provided. Then, the inverse problem, finding the parameters of the ion-exchange process in nonequilibrium conditions, is formulated. A method for determining the approximate values of these parameters from the impurities concentration measured at the outlet of the filter is proposed.