Analytical corrections to CO₂-brine Core Relative permeability for low rate flow modeling

Relative permeability of CO₂ and brine is one of the fundamental parameters controlling flow related to carbon storage in saline aquifers. Core samples recovered from subsurface formations are characterized in laboratory experiments to determine effective core relative permeability curves. 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 CO₂ migration in aquifers, 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 flow conditions. Derivation is carried out using power law averaging, assuming log normally distributed core permeability. We validate the analytical solution by comparison to numerical solutions for a wide range of cases. An additional correction for the CO₂ curves is shown to be necessary and derived by matching analytical and numerical results. Given a core which 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.