Relative Permeability Variation Depending on Viscosity Ratio and Capillary Number

The relative roles of parameters governing relative permeability, a crucial property for two-phase fluid flows, are incompletely known. To characterize the influence of viscosity ratio (M) and capillary number (Ca), we calculated relative permeabilities of nonwetting fluids (k(nw)) and wetting fluids (k(w)) in a 3D model of Berea sandstone under steady state condition using the lattice-Boltzmann method. We show that k(nw) increases and k(w) decreases as M increases due to the lubricating effect, locally occurred pore-filling behavior, and instability at fluid interfaces. We also show that k(nw) decreases markedly at low Ca (log Ca < -1.25), whereas k(w) undergoes negligible change with changing Ca. An M-Ca-k(nw) correlation diagram, displaying the simultaneous effects of M and Ca, shows that they cause k(nw) to vary by an order of magnitude. The color map produced is useful to provide accurate estimates of k(nw) in reservoir-scale simulations and to help identify the optimum properties of the immiscible fluids to be used in a geologic reservoir.

Automated summary

This study investigates the relative roles of viscosity ratio and capillary number on relative permeability of nonwetting and wetting fluids in a Berea sandstone model. The results show that increasing viscosity ratio leads to an increase in nonwetting fluid relative permeability and a decrease in wetting fluid relative permeability. Additionally, low capillary number significantly reduces nonwetting fluid relative permeability while wetting fluid relative permeability remains relatively unchanged. The correlation between viscosity ratio, capillary number, and nonwetting fluid relative permeability provides important insights for reservoir-scale simulations.