Analytical corrections to core relative permeability for low-flow-rate simulation

Relative permeability is one of the fundamental parameters controlling multiphase flow in reservoirs. Core samples recovered from subsurface formations are characterized in laboratory experiments to determine the core relative permeability curves. These curves represent the entire core sample and thus can be considered an effective property. Typically, coreflooding experiments are conducted at high injection rates so that the resulting flow is viscous-dominated. However, at lower rates, it has been shown that the effective curves may change as capillary heterogeneity effects become significant. Using relative permeability determined by conventional coreflooding in simulations with low-flow rates [e.g., to model gravity drainage or carbon dioxide (CO₂) storage] may incur significant error. A new method for calculating low-flow-rate relative permeability curves is presented. The method is based on approximate analytical solutions for effective relative permeability under steady-state and capillary-limit conditions. Derivation is performed using powerlaw averaging, assuming log normally distributed core permeability. We validate the analytical solution by comparing it with numerical solutions for a wide range of cases. An additional correction for the nonwetting-phase curves is shown to be necessary and derived by matching analytical and numerical results. Given a core that has been characterized by conventional high-rate coreflooding experiments, the current method gives a fast and efficient correction for low-flow-rate applications. It circumvents the need for additional experiments or computationally expensive coreflooding simulations.