Mathematical model to simulate gas-oil gravity drainage in a naturally fractured oil-wet reservoir

To date, no numerical model mimicking gas-oil gravity drainage in a naturally fractured medium has been made commercial. In this study, a simulation code for gas free fall has been developed. Navier-stokes, Darcy, capillary pressure, and relative permeability constitutive equations have been used to simulate a two-phase gas-oil transport problem. Other constraint equations have also been used to model phase saturation change with respect to time. The momentum and continuity equations are then solved to calculate velocities, pressure, oil-gas distribution, and the recovery rate following free fall. The developed simulator model output is compared to the experimental results. The simulation results are found to be in accordance with the experimental observations. Inherent problems with convergence rate and model stabilization are dealt with and the developed software can now be used for prediction purposes. In this paper, the oil-bearing matrix is represented by a porous cylindrical core centered in the middle of a core holder with an annulus thickness of 0.43 cm, mimicking a natural fracture. As such, the problem is axisymmetric and reduces the study to simulation of multiphase flow in a two-dimensional cylindrical domain with only gas and oil (two-phase transport) considered present during flow.