Sensitivity of Large-Scale Water/Oil Displacement Behavior to Fine-Scale Permeability Heterogeneity and Relative Permeabilities

Abstract Waterflood simulations in two-dimensional cross-sections are used to investigate the effects of fine-scale relative permeabilities and permeability heterogeneity on displacement permeabilities and permeability heterogeneity on displacement performance. Heterogeneity is found to be most significant performance. Heterogeneity is found to be most significant when deviations from the mean are highly correlated in the direction of flow, i.e., a layered reservoir. As spatial correlation decreases, the production behavior approaches that of a homogeneous medium. The critical features of the fine-scale relative permeabilities are the end-point relative permeability to water at residual oil saturation and the approach of the oil relative permeability curve to residual oil saturation. Relative permeability variations are found to be less important, but not necessarily negligible, when permeability heterogeneity is large and highly correlated in the displacement direction. Under most circumstances, the minimum relative permeability data required to avoid gross errors in simulation predictions are the end-point effective permeabilities to predictions are the end-point effective permeabilities to each phase and the fractional flow curve approaching residual oil saturation. Waterflood simulations using exact relative permeability data are compared with simulations where permeability data are compared with simulations where complete relative permeability information is not available. Cases are considered where relative permeabilities are estimated by straight lines between known end points and relative permeabilities derived from end point measurements and fractional flow data for high water cuts. An approximate method is proposed to derive relative permeability information from limited production history data. permeability information from limited production history data. The importance of production behavior at low fractional flow of oil also suggests the use of centrifuge measurements to help define the oil relative permeability curve approaching residual oil saturation. Introduction Reservoir simulation is currently limited by the number of grid blocks that can be used for practical simulation calculations. Grid block dimensions of hundreds of feet areally and tens of feet vertically are often required to describe an entire reservoir or even a portion of a reservoir. Individual grid blocks are assigned uniform properties for porosity, permeability, relative permeability and other properties. permeability, relative permeability and other properties. Frequently, however, rock properties are not uniform within a grid block. Properties assigned to grid blocks that differ from values Properties assigned to grid blocks that differ from values measured on smaller core samples are referred to as effective properties. Effective properties are usually necessary when phase distributions or rock properties or both are nonuniform within a grid block. Several investigators have proposed methods to determine effective rock properties that incorporate effects of sub-grid scale properties that incorporate effects of sub-grid scale heterogenity on single-phase flow. However, there are no general, theoretical methods available to evaluate effective multiphase flow properties for grid blocks containing permeability heterogeneity. permeability heterogeneity. P. 25