Algorithm for modeling two-component sorption dynamics in the case of mixed diffusion kinetics

Abstract

In 1981, Mark Moiseevich Senyavin tasked with determining the ion-exchange equilibrium and kinetic coefficients of strontium and ammonium ions from low-mineralized waters on clinoptilolite-containing tuffs of various deposits in Russia. As a result, a group of employees of the laboratory of sorption methods of GEOKHI created an experimental stand to calculate the output curves of sorption, as well as software for determining the coefficients of internal and external diffusion and the constants of constant exchange of sorbents.

The disadvantage of the work carried out is that the calculations were carried out using simplified formulas, either for external or internal diffusion, while should be considered the possibility of mixed diffusion should be taken into account. The time has passed for which the power of computing devices has multiplied. Now the problem of sorption can be solved directly, with the help of a numerical calculation. The advantage of this approach is that there is no need to impose any additional conditions on the task. For example, there is no need to consider a column completely washed before the start of the experiment, if desired, you can specify a column filling and, optionally, this filling should be uniform along the length of the column.

In this paper, we describe an algorithm for the two-component sorption dynamics in the case of mixed diffusion kinetics. Previously, we created the "CreateScheme" program, which is capable of calculating a multicomponent sorption process. However, the program does not allow us to investigate the subtleties of the sorption dynamics, since it uses rather large time steps to calculate the diffusion process according to equilibrium formulas. This article describes an algorithm that describes the process of mixed diffusion with smaller steps in time. The main difficulty was the docking of the first-order external diffusion equation with the second-order internal diffusion equation. This coupling was achieved with the help of the original method of replacing the second-order internal diffusion equation near the grain surface of the sorbent by an equation of the first order. The algorithm is implemented as a "DifFind" program, which is currently in the process of debugging.