The theory of combined systems of extreme control, which is used in technical systems, was developed and adapted in socio-ecological-economic systems. For example, river basins are such systems. A combined extreme control system has been formalized to control the dilution of mineralized mine waters in river sections. A mathematical model of the distribution of water masses and pollution in river beds from point and diffuse sources is proposed on the basis of a system of difference balance equations under the influence of stochastic uncontrolled disturbances. With regard to such conditions as adequate instrumentation, a combined control system has been developed that uses decision-making according to environmental and economic criteria based on the analysis of input and output data simultaneously, identification and tracking of the optimum in conditions of displacement under the influence of the disturbances of extreme characteristics of the system. The structural and functional diagram is represented by the open-loop diagram, the identification of which is carried out on the basis of modeling the process of water dilution in various situations at a specific object. A closed part with a recognition system as a corrector provides feedback. Formalized mathematical models of the dynamics of water masses and pollution from point and diffuse sources are of a general nature and can be used for the basins of other rivers. The extreme control system can adapt to the hydrological conditions and water quality parameters of a particular river. A mathematical model has been formalized for the combined extreme control of mine water dilution in the section of the Ingulets river. The water for dilution comes from a storage pond in the Svystunov gully. Regulatory actions that maintain water quality without exceeding the normative values of maximum permissible discharge are determined. At the same time, water consumption for dilution is minimized. The scenario analysis of the options showed a saving of up to 30% of water resources, namely 17.5 million m3, compared to the dilution carried out in February-March 2021 according to the existing individual regulations.
The balance method of determining the share of Kryvyi Rig Basin enterprises by the accumulated volume of mine water in the storage pond was considered. The balance method of participation of mining enterprises by the shares of mineral substances was formalized. An integrated approach of the control of water removal into the storage pond when using linear convolution of two balance equations by both the share of water volumes and the mineralization rate in the water discharges of enterprises was developed. It takes into account the choice of equity participation in mine water removal by economic and environmental criteria. The algorithm of equity participation of mining enterprises of Kryvyi Rih Basin on the principles of equality of two criteria was substantiated. The calculations of the share of discharge water accumulation in the storage pond of the Svistunov gully were carried out. The estimated price for water removal of one cubic meter of water into the storage pond by two criteria was considered. The estimation criteria are the volumes of pumped water and mineralization rate. Graphical dependences of the estimated price on the ratio of discharges concentration of different enterprises to the mixture concentration were built. Different estimation coefficients were used: paid water removal by water volumes; assessment of water removal only by mineralization rate; equal approach by the volumes (50%) and mineralization rate (50%). The calculations showed the efficiency of the algorithm, the applicability of its use by enterprises for integrated control of mine water removal by the criteria of volume and mineralization rate. The proposed balance method can be easily generalized when using other indicators of water quality (chlorides, sulfates, etc.), which are considered to be the most relevant for determining the equity participation of enterprises. In the future it is necessary to develop a theory of paid water use and water removal in conditions of unsatisfactory water quality, taking into account the integrated approach by different indicators that means multi-criteria assessment of water removal and accumulation of mine water.
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