Mathematical model of variable volume diafiltration with time dependent water adding

Abstract

Purpose The purpose of this paper is to introduce a mathematical model, an algorithm and numerical procedure for determining the duration of a diafiltration process with variable volume. This model should decrease diafiltration time and water usage. Design/methodology/approach A mathematical model of a diafiltration process, with constant water adding is considered, as well as the relationships between macro‐ and micro‐solute and the equation for process duration. By introducing α ( t )= Q D / Q F , i.e. time dependent ratio of diafiltration water flow and filtrate flow rate, a mathematical model of diafiltration process with time dependent water adding is proposed. In order to solve this model, an algorithm is suggested, based on the simulation of single time dependent water adding process with a sequence of constant water adding processes. The algorithm is applied for developing both a numerical procedure and simple QBASIC‐program that are tested on one illustrative example. Findings The results obtained by the algorithm improve the diafiltration process time around 10 percent and are a step towards finding an optimal dependence function α ( t ). Research limitations/implications Further on, the analysis of water usage in variable volume diafiltration needs to be done. Also, the problem of finding the optimal α ( t ) is still open. Practical implications The suggested algorithm is applicable to various membrane filtration processes and can be applied with little modification of the existing filtration equitment. Originality/value This paper is the first to view ALFA as a continuous function of time. Previous authors have considered step functions but never used this general approach.