On the problem of spacing of oil wells and control of their production rates

Abstract

A statement and a numerical solution of the optimization problem for sites of spacing of wells (well clusters) and modes of their operation in an oil field are presented. The mathematical problem represents a parametric problem of optimal control of the distributed system with concentrated sources, which is described by partial differential equations. Similar problems arise in the development and control of technological processes of various assignments and the design of control systems of technical objects. For its numerical solution, the initial problem is reduced to a finite-dimensional optimization problem with constraints of special features. Formulas of a gradient of the functional of the reduced problem are derived. Results of the solution of control problems are given.