Development of the mathematical model of the kinetics of the stationary process of bio-cleaning with substratic inhibition

Abstract

A scientifically sound method for calculating the parameters of bio-cleaning should contain as a basic a reliable mathematical description of the stationary process. The results of stationary laboratory experiments are presented in the coordinates “specific rate of destruction V – concentration ρ”. Statistical processing proves the presence of substrate inhibition for both gaseous and soluble and dissolved harmful substances in water. For an analytical description of the dependence of the biooxidation rate on the concentration of contaminants, a phenomenological approach is applied, taking into account in a simple form two obvious phenomena: the contact of a microorganism with a substrate molecule and the inhibitory effect of the medium on it. The numerical values of empirical dependency coefficients for the studied processes are calculated. A differential equation is proposed at the macro level that describes the kinetics of biochemical destruction. The concept of a macrokinetic mathematical model of bioremediation is defined as a system of two functions that quantitatively reflect the dependence of the specific oxidation rate of pollution on its concentration and concentration on time, as well as satisfying the relationship between the relationships of the same parameters in differential form. The dependence of concentration on time is defined both in the form of a numerical integration algorithm and in the form of an approximate formula. The adequacy and universality of the proposed model for the studied processes is proved. The advantage of the proposed model of substrate inhibition kinetics is the simplicity of the structure of the basic formula and the ease of determining empirical coefficients based on this. In addition to numerical integration for determining the time of destruction, an approximate analytical solution is found, which can be adequately used in the concentration range of the experimental study. Further research is aimed at developing methods for calculating non-stationary processes in biochemical purification plants of certain specific types.