# RESTORATION OF PRESSURE AT THE POOL BOUNDARY BASED ON THE SOLUTION OF INVERSE PROBLEM

Azerbaijan State \University of Oil and Industry
20 Azadlyg Ave., Baku, AZ 1010, Azerbaijan
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Èlektron. model. 2018, 40(4):19-28
https://doi.org/10.15407/emodel.40.04.019

### ABSTRACT

A numerical method has been proposed to solve the inverse problem of determining conditions on the outer pool boundary based on information obtained from the hole. The rectilinear-parallel flow of a single-phase fluid in a rectangular pool described by a linear parabolic equation is considered. The initial state of the pool, as well as the pressure and flow rate of liquid in the gallery of production wells are considered to be set, and the pressure on the outer boundary of the pool is unknown. This problem belongs to the class of boundary inverse problems. First, the nonlocal perturbation method of the boundary condition is applied. After that, the problem is discretized and a special representation is proposed to solve the resulting system of difference equations. As a re- sult, the problem is reduced to two difference problems and one linear equation with respect to the approximate value of pressure at the boundary of the pool. On the basis of the proposed computational algorithm, numerical calculations for model problems are carried out.

### KEYWORDS

oil pool, rectilinear-parallel flow, boundary inverse problem, nonlocal perturba- tion method, difference method.

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