Modeling the process of biological deferrization of underground waters in contact loading of bioreactor

The conducted analysis of modern biotechnologies in the field of groundwater treatment showed that one of the development trends is the direction of biological iron removal, which has not only a long history and fundamentality of research into the physiology, ultrastructure and life mechanisms of ferrobacteria, but also a wide implementation of the method at water treatment plants in Europе, Australia, Canada, USA, Japan. The introduction of modern technological equipment at such stations calls for the need to forecast their work using methods of mathematical modeling of processes with their subsequent computer implementation. The work provides a brief analysis of existing mathematical models, most of which are based on the kinetics of enzymatic reactions and are presented as modifications of the Michaelis-Menten and Monod equations. 
Despite the large number of studies on this topic, until now there is no comprehensive model that would take into account all the processes that take place in the contact loading of bioreactors, in contrast to the physicochemical mechanisms in the filtering process, for which modern multicomponent mathematical models have been developed. 
The aim of the work is to development of a mathematical model of the kinetics of the process of biological iron removal groundwater in bioreactors and verification of its computer implementation with the data of experimental studies. The mathematical model is represented by the Cauchy problem for a nonlinear system of differential equations in partial derivatives of the first order. The system of the Cauchy problem consists of five equations with five unknown functions, which describe the distribution the concentration of ferrum cations, bacteria and the matrix structures in two phases (movable and immobilized) both in space and time The inverse influence of the characteristics of the process, in particular, the concentration of matrix structures in the inter-pore space, as well as characteristics of the medium with the help of coefficients of mass exchange and porosity, were taken into account. The model makes it possible to predict changes in cleaning efficiency depending on the duration of the filter cycle, filtration speed, Fe2+ concentration, the content of iron bacteria and their matrix structures in the interpore space, and to determine the optimal time of operation of the bioreactor between washings 
 