Relative Permeability Variation Depending on Viscosity Ratio and Capillary Number

Abstract

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.

Key Points

• Relative permeability in two-phase flow is calculated in a three-dimensional digital Berea rock using lattice-Boltzmann Method

• Relative permeability varies due to lubrication effect, shear force, and capillary force, and is related to fluid droplet fragmentation

• Relative permeability on viscosity ratio-capillary number map is created to predict spatiotemporal variation of reservoir permeability

Plain Language Summary

The relative permeability is a crucial parameter in a system where two fluid phases exist simultaneously. For example, in carbon capture and storage, relative permeability is important to assess the replacement mechanism of the existing fluid in the reservoir (wetting fluid) by the injected CO₂ (nonwetting fluid). It is also an important parameter in enhanced oil recovery fields, as high relative permeability of oil indicates that the oil in the reservoir can be extracted quickly. The relative permeability is temporally and spatially varied by reservoir conditions (e.g., temperature). But currently, in reservoir-scale fluid flow simulation, relative permeability is assumed to be constant regardless of the different conditions. In this study, we conducted simulations to calculate relative permeability in various viscosity ratio (M) and capillary number (Ca) conditions. We found that relative permeability changes dramatically in different M and Ca conditions, and we further mapped relative permeability on the diagram between M and Ca to predict relative permeability accurately in various reservoir conditions. Our findings can be useful to determine the suitable fluid properties to be used in reservoir management and to accurately estimate fluid behavior based on reservoir-scale simulation with variant relative permeability.