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

Abstract EN

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.