About Numerical Modeling of Thermal Impact on the Bottomhole Zone of Layer

Abstract

The article considers a process of heat propagation from a heated gallery of production wells to an oil reservoir. A one-dimensional diffusion-convection equation for a region with an unknown moving boundary is proposed to describe this process. For the correct formulation of the problem, an auxiliary condition is set for the temperature at the gallery of wells. By changing variables, the problem is transformed into a coefficient inverse problem. Further, the time derivative is discretized and explicit-implicit schemes are used to approximate the operators of the problem. To solve the resulting differential-difference problem, a special representation is proposed. As a result, at each discrete value of the time variable, the differential-difference problem splits into two direct boundary-value problems and a linear algebraic equation with respect to the approximate value of the sought-for coefficient. The Thomas algorithm is used for the numerical solution of the obtained direct boundary value problems. Numerical experiments were performed on the basis of the proposed numerical algorithm.