Чувствительность функционала эффективности процесса биологической очистки сточных вод к параметрам модели динамики концентраций биогенов

Abstract

Introduction. The analysis of the water quality functional sensitivity to the parameters of the multiparametric model of the artificial water ecosystem of the biological sewage treatment, which is formulated as an initial-boundary value problem for the system of reaction-convection-diffusion equations describing the biogen dynamics, is discussed. The use of the multidimensional non-stationary models of aquatic ecosystems with a detailed description of biochemical reactions is complicated by a large number of parameters, the importance of which must be obtained experimentally. To simplify the providing data process, the sensitivity of the water quality functional to the model parameters is evaluated. Materials and Methods. A brief review of the existing estimation techniques is carried out. And further on, an algorithm for studying the functional sensitivity characterizing the water quality to the parameters of the water ecosystem model is formulated using methods of the theory of small perturbations and conjugate equations. Research Results. The analysis algorithm of the functional sensitivity to the parameters of the aquatic ecosystem model is obtained. A practical example of the method application for the optimal control problem for an aeration tank (an element of the sewage treatment plant for the biological sewage treatment) is considered. Discussion and Conclusions. On the basis of the analysis, the most and the least significant parameters of the mathematical model of the artificial aquatic ecosystem of the aeration tank, which is included as an integral part of the problem of optimal aeration control, are revealed. The sensitivity estimation algorithm given in the paper can be applied to other processes related to the mass transfer of reacting substances, such as the solution to inverse source problems of dynamics and kinetics of gaseous impurities and aerosols in the atmosphere, modeling of biological processes in living organisms, control of the mass transfer in devices of the chemical technologies, and others.