Scaling Parameters for Characterizing Waterflood Recovery From Anisotropic Matrix Blocks in Naturally Fractured Reservoirs

The characteristic complexities of naturally fractured reservoirs have forced numerical models to be based on conceptual approximations that simplify the problem. These models are the so-called dual porosity and dual permeability models. The complexity of the processes that control the exchange of fluids between matrix blocks and fractures in both dual porosity and dual permeability models results in a large number of spatially distributed parameters, most of which cannot be determined with even a small degree of accuracy. The purpose of this study was to attempt to determine the characteristic scaling parameters that control countercurrent imbibition in anisotropic matrix blocks in waterflooded naturally fractured reservoirs in order to establish the minimum number of parameters necessary. In the first part of this study, the imbibition process with constant capillary diffusion coefficient in anisotropic rectangular matrix blocks is investigated. This approach allowed an analytical solution from which an appropriate set of dimensionless variables and characteristic parameters were obtained. These characteristic parameters basically describe the overall capability of matrix blocks to interchange fluids with the fracture system, as well as characterize anisotropy and shape effects. In the second part, results are extended to the variable capillary diffusion coefficient case by using detailed single matrix block simulations. In this case a new parameter had to be included to characterize the late-flow period (pseudosteady state flow). A brief numerical study on gravity effects was also conducted. Results suggest that the Bond number, which represents the ratio of capillary to gravitational forces, should be included as a characteristic parameter when gravity effects are important. Finally, the proposed parameters were successfully tested at the reservoir scale by waterflooding a hypothetical naturally fractured reservoir using a typical five-spot pattern. This test was carried out with the VIP commercial reservoir simulator. The characteristic parameters found to control the imbibition process when gravity effects are considered are 1) the effective diffusion time, 2) the mobile oil volume in the matrix blocks, 3) the dimensionless water saturation where the maximum variable capillary diffusion coefficient occurs, and 4) the Bond number.Petroleum and Geosystems Engineerin