Identifying boundary conditions of an oil reservoir flow model from well pressure measurements. Part 1: Homogeneous reservoir - D. I. Usmanov; K. A. Potashev; D. R. Salimyanova (Учёные записки Казанского университета: Серия Физико-математические науки, 2024)
A method was outlined for determining the coefficient of third-kind boundary conditions of the piezoconductivity problem in an oil reservoir, particularly on its external contour, which has, as a rule, no specific hydrodynamic properties and is set to reduce computational costs. The coefficient was determined using an integral balance model of an interaction between the oil deposit and the outer region of the reservoir. The optimization problem of approximating the average reservoir pressure to the values obtained from the well pressure measurements was solved. Assuming the homogeneity of the reservoir, the applicability of the algorithm was assessed under various geometries of the external contour, well placements, and operating conditions. The stability of the algorithm for solving the inverse problem was analyzed against pressure measurement errors. The proposed approach offers a relatively simple algorithm for defining the boundary conditions of a reservoir flow model, which enables a good approximation of the hydrodynamic interaction of the reservoir with its outer region. However, due to uncertainties in the initial data for regions distant from the well-drilled area of the reservoir, significant difficulties remain in calibrating the model.