Non-linear flow simulations with corrected Peaceman formula for well pressure calculation

• Main Authors: Anikeev, Daniil P., Ibragimov, Akif I., Indrupskiy, Ilya M., Zakirov, Ernest S.
• Format: Conference Proceeding
• Language: English
• Subjects: Darcys law; Flow simulation; Gas flow; Inflow; Reservoirs; Simulation
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0164189

A problem of well inflow calculations for non-linear flows is considered. In numerical simulations of petroleum reservoirs wells are treated as sources or sinks, and well pressure is related to the pressure in a grid block containing the well. This is done by means of the so-called inflow formula. Peaceman’s approach is universally accepted to match the analytical inflow relation to the numerical solution on the grid. It includes the formula for so-called equivalent radius R0 which was derived for linear flows under Darcy law. For high-velocity near-wellbore flows of gas, two-term nonlinear Forchheimer law is generally used. For this case the inflow formula derived by Dake is adopted in reservoir simulations, but no correction is made for R0 computed with Peaceman’s formula. In this paper we address calculation of R0 for non-linear Forchheimer flows. For large grid blocks, the corresponding correction to Dake’s formula can be neglected. But for finer grids and high velocities it becomes significant. The effect of the introduced correction to inflow formula is demonstrated by means of comparative gas flow simulations with typical reservoir parameters.