A Mechanistic Approach for Calculating Oil-Gas Relative Permeability Curves in Unconventional Reservoirs

A mechanistic approach for calculation of oil-gas capillary pressure curves and relative permeabilities in unconventional reservoirs is presented. The approach accounts for reservoir fluid composition, contact angle wettability and pore size distribution of each specific reservoir and generates a unique set of relative permeability curves based on those inputs. This allows calculation of curves in reservoirs where historical production data is limited. Phase behavior calculations are computed by coupling the Peng-Robinson equation of state and the Young-Laplace capillary pressure model. This coupling allows for inclusion of the effect of confinement of reservoir fluids on volumetric and transport properties. The reservoir is modeled as a bundle of tubes with diameters representative of the pore size distribution found in the reservoir. A multi-step depletion is modeled followed by gas injection and a secondary depletion. Separate capillary pressure results are obtained for each part of the process. After the capillary pressure curves are generated, an integration is performed on the capillary results to generate a set of relative permeability curves following the Nakornthap and Evans method (1986). The multi-step process is used to allow recalculation of the relative permeability curves as the reservoir fluid composition changes due to the initial depletion and then secondary gas injection.The approach yields a unique set of relative permeability results for each set of input parameters.The mechanistic approach is demonstrated on two different oil compositions, a black oil sample and a volatile oil. For each of the oil compositions, two different injection gasses are evaluated (methane and carbon dioxide). The intermediate calculations are summarized and the final permeability results are included in the paper. The results show that for both oil samples evaluated, the gas injection results in an increase in oil relative permeability. Carbon dioxide is more effective at increasing the oil relative permeability than methane for both oil samples. This suggests that carbon dioxide could be an effective option for enhanced oil recovery operations in unconventional reservoirs. A unique element of the approach presented is that the calculation of relative permeability curves for the initial reservoir depletion is immediately followed by the calculation of new relative permeability curves as the reservoir composition changes due to gas injection. This allows prediction of relative permeability results in an unconventional reservoir for both the initial reservoir depletion and also for hypothetical enhanced oil recovery operations. Since the model can be run quickly and repeatedly, sensitivity analyses can be performed on the permeability curves as a function of initial reservoir conditions and injection gas compositions and amounts.