Simulation of Viscous Fingering in Rectangular Porous Media with Lateral Injection and Two- and Three-Phase Flows

Abstract

Understanding multiphase flow in porous media is of tremendous importance for many industrial and environmental applications at various spatial and temporal scales. The present study consequently focuses on modeling multiphase flows by the Volume-of-Fluid method (sharp interface) in porous media with a simplified Darcy-scale approach and shows simulations of Saffman-Taylor fingering. The simplification of the Darcy scale approach is performed by assuming sharp interfaces between pure phases. The Volume-of-Fluid method with octree mesh refinement is used. It is implemented in the Gerris code which allows efficient parallel computations. We measure the scaling properties of the fractal viscousfingering patterns that appear in the numerical simulations. One of these properties is the fractal or Hausdorff dimension D F. The other is the variation of the area A of the viscousfingering cluster with the length L of its perimeter, which varies as a simple power law A ∼ L α. The injection of an intermediate-viscosity Newtonian fluid as a second step is also simulated. We are thus able to observe an increase of recovery of the high-viscosity fluid behind the fingering front, due to the reduction of the viscosity contrast. Some of these results are compared to waterflooding experiments of extra-heavy oils in quasi-2D square slab geometries of Bentheimer sandstone.

Immiscible Viscous Fingering: The Simulation of Tertiary Polymer Displacements of Viscous Oils in 2D Slab Floods

“…These results were generated using a standard commercial numerical simulator (CMG STARS v2021.1) [ 27 ]. This represents a significant advance in terms of the simulation of unstable immiscible displacement, as these particular experiments have received much attention in the literature and other attempts have been made to directly match the oil recovery, water cut, pressure drop and finger patterns with mixed levels of success [ 28 , 29 , 30 ].…”

Viscous Fingering and Preferential Flow Paths in Heterogeneous Porous Media

“…Interestingly, the streamtube method is inaccurate in the case of favorable viscosity ratios when quasi-uniform displacements occur (Martin et al, 1973). Also note that Lagrée et al (2016) found that viscous fingers simulated using a continuum Darcy-type method with an enforced sharp fluid interface, indeed corresponded to high-fluid velocity channels (see Figures 8 and 9).…”

“…Interestingly, the streamtube method is inaccurate in the case of favorable viscosity ratios when quasi-uniform displacements occur (Martin et al, 1973). Also note that Lagrée et al (2016) found that viscous fingers simulated using a continuum Darcy-type method with an enforced sharp fluid interface, indeed corresponded to high-fluid velocity channels (see Figures 8 and 9). Thus, the treatment of reservoir-scale heterogeneity in the streamtube method relies on a conceptual link between preferential single-phase flow paths and two-phase flow viscous fingers.…”

Experimental and computational advances on the study of Viscous Fingering: An umbrella review

“…Displacements considering three-phase flow were studied by Lagreé [ 97 ]. Numerical simulations using the software GERRIS were conducted to study the displacement of two subsequent injections with different fluids.…”