Influence of Wetting on Viscous Fingering Via 2D Lattice Boltzmann Simulations

Peter Mora,Dave A Yuen,Ruben Juanes,Gabriele Morra

doi:10.1007/s11242-021-01629-8

Abstract

We present simulations of two-phase flow using the Rothman and Keller colour gradient Lattice Boltzmann method to study viscous fingering when a “red fluid” invades a porous model initially filled with a “blue” fluid with different viscosity. We conducted eleven suites of 81 numerical experiments totalling 891 simulations, where each suite had a different random realization of the porous model and spanned viscosity ratios in the range Min [0.01,100] and wetting angles in the range theta _win [180^circ ,0^circ ] to allow us to study the effect of these parameters on the fluid-displacement morphology and saturation at breakthrough (sweep). Although sweep often increased with wettability, this was not always so and the sweep phase space landscape, defined as the difference in saturation at a given wetting angle relative to saturation for the non-wetting case, had hills, ridges and valleys. At low viscosity ratios, flow at breakthrough is localized through narrow fingers that span the model. After breakthrough, the flow field continues to evolve and the saturation continues to increase albeit at a reduced rate, and eventually exceeds 90% for both non-wetting and wetting cases. The existence of a complicated sweep phase space at breakthrough, and continued post-breakthrough evolution suggests the hydrodynamics and sweep is a complicated function of wetting angle, viscosity ratio and time, which has major potential implications to Enhanced Oil Recovery by water flooding, and hence, on estimates of global oil reserves. Validation of these results via experiments is required to ensure they translate to field studies.

Highlights

In this paper, we study the physics and morphology of immiscible two-phase fluid flow in a 2D model of a porous medium with the aim of increasing understanding of patterns fluid–fluid displacement and their effect on the fluid saturation, and in particular, the effect of wettability, a measure of the degree to which a fluid is attracted to the solid.Extended author information available on the last page of the article1 3 Vol.:(0123456789)We will make use of the Lattice Boltzmann Method (LBM), a well-known method to simulate fluid flow, which is capable of modelling flow of immiscible fluids at the pore scale
A major goal is to study the effect of the wetting angle on the flow regimes from viscous fingering when the invading fluid has a lower viscosity than the second fluid, to stable displacement when the invading fluid has higher viscosity
We present 2D simulations of immiscible two-phase fluid flow in a porous medium to study the effect of the wetting angle on the morphology of flow and the evolution of saturation

Summary

Introduction

We will make use of the Lattice Boltzmann Method (LBM), a well-known method to simulate fluid flow, which is capable of modelling flow of immiscible fluids at the pore scale. Lattice Boltzmann Methods have their origins in Lattice Gas Automata (LGA) in which particles move and collide on a discrete lattice representing a simplified discrete version of molecules moving and colliding in a gas. The LGA lead to socalled Lattice Boltzmann Methods where one is solving the classical Boltzmann equation on a discrete lattice involving number densities moving and colliding on a discrete lattice. Since an efficient method via relaxation to calculate the collision term due to Bhatnagar, Gross and Krook—the BGK method (Bhatnagar et al 1954)—was developed (Qian et al 1992; Chen and Doolen 1998), research and applications of the Lattice Boltzmann Method have undergone an explosion (see Succi 2001, 2018)

Results

Discussion

Conclusion