Simulating water injection into an oil reservoir using the Buckley-Lorette equation for oil extraction

Given the importance of two- and multi-phase flows and achieving the lowest error in simulating porous media, in this study, the analytical simulation and solution of oil displacement by water was performed using the Buckley-Leverett equation and compared and validated with its numerical solution. The Buckley-Leverett equation is a conservation equation used to model two-phase flow in porous media, and this equation describes a one-dimensional or quasi-one-dimensional immiscible displacement process. Also, this equation obtains incompressible and immiscible phases in one-dimensional and horizontal flow conditions, regardless of capillarity and gravity. In this study, the reservoir, which is initially filled with oil, is driven out by water and finally the entire reservoir is filled with water. This technique is used for oil extraction in the oil industry. The water inlet velocity in this study is assumed to be ۰.۰۰۱ m/s, and the phase is incompressible and immiscible, and capillarity and gravity are ignored. The results of this study showed that the simulation and analytical solution had a significant overlap with the numerical solution of the Buckley-Lourdes equation and only at the points where the fluid was shocked, a series of numerical fluctuations were created. The results also showed that the pressure difference between oil and water changes linearly, so that the slope of this line shows the amount of surface tension, and it can also be seen that with increasing viscosity, the Reynolds number decreases, and when the surface tension increases, the Weber number also decreases.

کلیدواژه ها:

Two-phase flow ، oil ، water ، Buckley-Leverett ، analytical solution