2025 , Volume 30, № 1, p.89-103

The paper proposes an approach to finite element calculation of the pressure field in oil producti on problems, which, without an iterative process, ensures correspondence of pressure distribution along the wellbore to hydrostatic head in the case mixture productions or agent injection, are specified at the wells. To do this, special boundary conditions, which ensure the appropriate distribution of production or injection along the wells, are proposed. We obtain relations for calculating the components of the matrix and the vector of the finite element system of equations, along with the special boundary conditions, which lead to additional relationships between the components of the weight vector for mesh nodes at the boundaries approximating well perforation zones. Computational experiments, which are carried out for a highly heterogeneous model of an oil reservoir, show that the proposed mathematical model allows obtaining both distribution of productions or injections at wells and pressure field that varies along each well in accordance with the hydrostatic head without iterative process. The results of computational experiments show that without using the proposed procedure for “equalizing” the pressure along a well in accordance with the hydrostatic head, the calculated production indicators, including oil production and water cut, are incorrect.