Numerical Solution to a Problem of Optimizing Placement and Flow Rates of Wells

Abstract

The paper proposes an approach to the numerical solution of the problem of optimizing wells’ placement and the values of their flow rates. The selection of rational placement of wells is the first and extremely important task that oil and gas companies face when designing the development of hydrocarbon fields. Typically, standard patterns are used for well placement, in which wells are located at the nodal points of various regular grids. The method proposed in this paper for determining the optimal placement of wells and their flow rates is based on considering an oil reservoir as a dynamic system with distributed parameters and on application of the methods for optimal control of such systems. The optimization goal is to achieve a uniform distribution of reservoir pressure over the area of the oil deposit after withdrawing the planned volume of oil from it. Fulfillment of this criterion ensures, in particular, a uniform rise of bottom water and prevents early water flooding of production wells. The state of the reservoir is described by the equation of non-stationary two-dimensional filtration of weakly compressible oil. Thus, the problem under consideration is a problem of optimal control of distributed systems, the solution of which is carried out by reducing the original problem to a discrete problem for which the gradient of the objective functional is determined, which allows to use standard first-order optimization methods. The paper presents the results of numerical experiments and their analysis.