The Effect of Fracture Relative Permeabilities and Capillary Pressures on the Numerical Simulation of Naturally Fractured Reservoirs

Abstract

Abstract Engineers using numerical reservoir simulators to model fractured reservoirs typically have used straight-line (corner-to-corner) relative permeabilities and zero capillary pressure in the fractures, without a clear understanding of how these two parameters affect simulation accuracy and with no practical method for selecting alternate values.The present study uses the theoretical work of Rossen and Kumar (non-straight-line fracture relative permeabilities)[1,2] and of Firoozabadi and Haugh (non-zero capillary pressure in rough-walled fractures)[3] to quantify prediction errors and to demonstrate a method for selecting the correct set of relative-permeability and capillary curves for a particular simulation.Our results indicate that using straight-line relative permeabilities can lead to predicted oil-recovery errors as high as 70% in water-oil systems and to underestimating oil production times in some gas-oil systems by as much as a factor of three.In gas-oil systems where gas flows into the fractures, oil recovery from the matrix blocks could be underestimated by a factor of almost two when fracture capillary pressures are set at zero. Introduction Using straight-line fracture relative permeabilities and zero fracture capillary pressures, based on E. S. Romm's experiment[4,5] in 1966, may not always be appropriate, and could lead to large errors in reservoir definition and performance prediction. Recent experimental research, outlined below, clearly shows that relative permeabilities in a certain range of fractures are not straight lines, but implications for reservoir scale behavior have not yet been systematically examined.The present study focuses on quantifying prediction errors made in reservoir scale simulations by comparing results from straight-line fracture relative permeabilities and/or zero capillary pressures with results from non-straight-line fracture relative permeabilities and/or non-zero capillary pressures. A method for classifying a reservoir system to select the correct set of relative permeability and capillary pressure curves is given. The study investigated differences in behavior of two-phase (dead oil with water or gas injection) and three-phase systems, using straight-line fracture relative permeabilities and/or zero fracture capillary pressures (base case) and non-straight-line fracture relative permeabilities and non-zero fracture capillary pressures (sensitivity case). We used a homogeneous reservoir for most of the simulations, although a modified version of the reservoir model from the Sixth SPE Comparative Solution Project: Dual Porosity Simulators (Firoozabadi and Thomas[6]) was also used to assess the extent to which our results were influenced by heterogeneity. To determine sensitivities, we used different relative permeability and capillary pressure curves and a wide range of values for reservoir parameters, such as fracture spacing, fracture/matrix permeability ratio, and fluid properties. Background Conventional straight-line relative permeability curves originated with the 1966 publication by Romm.[4,5] His findings, based on experiments of flow between two parallel glass plates, showed a linear dependency between phase relative permeability and phase saturations, as well as zero capillary pressures. The experiments did not examine the effects of fracture aperture and roughness effects, or the implications for reservoir scale behavior. Firoozabadi and Thomas6 published the results on the Sixth SPE Comparative Solution Project: Dual Porosity Simulators (referred to hereafter as "SPE6"), which investigated aspects of the physics of multiphase flow in fractured reservoirs. The use of non-zero capillary pressures showed that predicted recoveries are affected dramatically by combinations of wettability and Enhanced Oil Recovery methods. In the same year, Firoozabadi and Hauge[3] published a phenomenological model for calculating the capillary pressures of a system based on fracture characteristics such as waviness, roughness, width, and interfacial tensions.