A unified grayscale lattice Boltzmann model for multiphase fluid flow in vuggy carbonates

Abstract

In addition to intrinsic matrix pores, ranging in size from submicrons to microns, vuggy carbonates often contain significantly larger vug spaces. Immiscible multiphase fluids flowing through this type of microporous systems exhibit complicated flow mechanisms that are involved in the interactions between multiphase fluids and different types of pore spaces. Modeling multiphase fluid flows requires using the appropriate governing equations for different porosity systems. More specifically, while multiphase Darcy's equations might hold for a matrix system, they are not applicable for a vug system. To improve understanding this difficult multiphase flow problem in vuggy carbonates, we developed a unified grayscale lattice Boltzmann (LB) model for multiphase flows. The proposed model combines the generalized LB model in porous media with the pseudo-potential multiphase approach by adding the fluid-fluid interaction force, the fluid-solid interaction force, and the linear and nonlinear drag forces induced by the porous matrix. The model is still within the framework of the generalized LB model, and it switches freely from the Darcy's regime to the free-flow regime via rock property (i.e., porosity). It can also extend to a wide range of porosity systems because we incorporated both the linear and nonlinear drag effects. A continuous flow interface between the porous matrix and the vug region is captured by simulation without incorporating complex interface boundary conditions between the two porosity systems. The current model is validated and calibrated with theory, and then it is applied to a number of test cases. The test cases include the simulations of two-phase displacement in non-vuggy porous media, isolated vuggy porous media, and connected vuggy (fractured) porous media. Moreover, the effect of vug spaces on the interface-front speed and the breakthrough time is investigated. In addition, we simulated water displacing oil in two real vuggy carbonate cores imaged using low-resolution and high-resolution X-ray computed microtomography, and we investigated the effects of matrix heterogeneity, vug connectivity, and matrix wetting preference.