Darcy's law governs most flow patterns in petroleum recovery processes. However, when fluid flow velocity is very high, for example, near the wellbore, Darcy's law may be inadequate to simulate the fluid flow.
The non-Darcy effect has been incorporated into the Department of Energy (DOE) reservoir simulator MASTER (Miscible Applied Simulation Techniques for Energy Recovery). Based on the simulator BOAST (Black-Oil Applied Simulation Tool), MASTER was developed by DOE mainly to solve gas injection problems. However, only Darcy's flow was considered in these simulators. In this study, Forchheimer's non-Darcy flow equation has been incorporated into the simulator code and an iterative method has been used to solve for pressures.
The modeling of non-Darcy flow proved successful and enabled the simulator to match high-velocity gas flow more accurately. Based on a number of non-Darcy flow coefficient equations found in the literature, a general correlation was proposed. The appropriate constants in the proposed correlation were found by running simulations with the modified simulator for the non-Darcy flow experiments.
The model has been verified using laboratory high flow data obtained using single-phase nitrogen gas. The data comprised a wide range of flow rates collected using a heterogeneous Berea sandstone wafer. The gas flowed into and out of a hockey puck-shaped wafer via 0.125-in. diameter ports. Thus the flow rate varied within the wafer, simulating near-wellbore flow conditions. It was found that the differential pressures from simulations were in good agreements with their counterparts from experiments.