Scaling of Multiphase Flow in Simple Heterogeneous Porous Media

The nature of flow in porous media is determined by the interaction of the physical properties of the medium and fluids, and by the interplay of various forces involved in the displacement process. Identifying flow regions at a given reservoir operating condition is a key issue in forecasting reservoir performance and hence of optimizing operations. This work identifies dominant flow regions at various conditions. Three dimensionless groups, NgvM/(1 + M) (gravity/viscous ratio), NcvM/(1 + M) (capillary/viscous ratio) and Ri2 (shape factor), are defined and used to resolve flow regions. The analysis shows that the relative magnitudes of forces involved in the system combined with the reservoir properties determine the flow region and fluid distribution in the medium. By choosing appropriate ranges for the dimensionless numbers, recovery processes can be specified from the general theory, and the boundaries to flow regions confirmed by comparison with existing experimental and simulation results. Three commonly studied flow systems have been investigated, which are miscible displacements without dispersion (Ncv ≈ 0) in layered reservoirs, immiscible displacements (Ngv ≈ 0) in layered and homogeneous media, and flow in highly fractured reservoirs.