Using extensive numerical simulation of the Navier–Stokes equations, we study the transition from the Darcy’s law for slow flow of fluids through a disordered porous medium to the nonlinear flow regime in which the effect of inertia cannot be neglected. The porous medium is represented by two-dimensional slices of a three-dimensional image of a sandstone. We study the problem over wide ranges of porosity and the Reynolds number, as well as two types of boundary conditions, and compute essential features of fluid flow, namely, the strength of the vorticity, the effective permeability of the pore space, the frictional drag, and the relationship between the macroscopic pressure gradient
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
- Award ID(s):
- 1918126
- NSF-PAR ID:
- 10234482
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Transport in Porous Media
- Volume:
- 138
- Issue:
- 3
- ISSN:
- 0169-3913
- Format(s):
- Medium: X Size: p. 511-538
- Size(s):
- ["p. 511-538"]
- Sponsoring Org:
- National Science Foundation
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