| Khanlar Gamzaev, Sevinc Kerimova Computer Simulation of the Elastic Regime of the Development of a Single-Well Reservoir with an Unknown Initial State |
|---|
| Abstract. To describe the elastic regime of the development of a single-well oil reservoir, a model of a turbulent filtration flow of a single-phase liquid is proposed, presented in the form of a nonlinear parabolic equation with respect to the volume flow of the liquid. The laws of change in the time of the well flow rate and the pressure at the bottom of the well are considered to be set. The distribution of fluid flow in the reservoir at the initial moment of time, as well as the presence of a hydrodynamic connection between the reservoir and the external region, are considered unknown. Within the framework of the proposed model, the task is to determine the distribution of fluid flow in the reservoir, including the boundary. This problem belongs to the class of boundary value inverse problems without initial conditions. To numerically solve the inverse problem, a discrete analogue of the problem on a uniform difference grid is first constructed using the method of difference approximation. To solve the resulting system of linear equations, a computational algorithm is proposed that makes it possible to determine the flow rate of a liquid at all nodal points of the calculated part, with the exception of a certain triangular area. The calculated value of the fluid flow rate at the outer boundary of the formation determines the presence or absence of a hydrodynamic connection between the formation and the outer region. Numerical experiments for a model oil reservoir were carried out based on the proposed computational algorithm. |
| Keywords: single-well oil reservoir, elastic development mode, turbulent filtration law, boundary value inverse problem without initial conditions, difference approximation method |
 Download PDF |
| DOI: https://doi.org/10.54381/itta2026.1.06 |