Stochastic Model and Method of Optimization of Operation Modes of a Group of Artesian Wells in Water Supply Systems

Groups of spatially distributed wells interconnected by sections of pipelines (a common collector) supplying water to a clean water reservoir are used in water supply systems in order to provide drinking water to settlements. A group of wells together with a clean water reservoir is called a water intake facility of the water supply system. Further, water is supplied from the clean water reservoir to consumers in settlements by means of second stage pumping stations. In terms of each well the operating mode of the submersible pumping unit, i.e. the position of its operating point at a fixed moment in time, depends on the actual values ​​of many internal and external factors: dynamic water level in the well; the actual characteristics of the pumping unit; the position of the final control elements (drive speed, opening degree of the regulating valve); hydraulic resistances of pipeline sections of the water intake facility; the water level in the clean water reservoir; the number and operating modes of pumping units in other wells of the water intake facility. The paper describes a deterministic model of a water intake well. At the same time, the processes of water consumption are random processes, since they depend on many uncontrolled and unmanageable factors. The parameters of the technological equipment of the water intake facility are also random values, since they are estimated from experimental data of finite length. Therefore, a stochastic model of a water intake well is also proposed. A model of a quasi-stationary operation mode of a water intake facility, which is used to optimize the operation of a group of artesian wells operating on a common collector, is considered.