Pore Network Modeling of the Effects of Viscosity Ratio and Pressure Gradient on Steady-State Incompressible Two-Phase Flow in Porous Media

Abstract

We perform more than 6000 steady-state simulations with a dynamic pore network model, corresponding to a large span in viscosity ratios and capillary numbers. From these simulations, dimensionless quantities such as relative permeabilities, residual saturations, mobility ratios and fractional flows are computed. Relative permeabilities and residual saturations show many of the same qualitative features observed in other experimental and modeling studies. However, while other studies find that relative permeabilities converge to straight lines at high capillary numbers we find that this is not the case when viscosity ratios are different from 1. Our conclusion is that departure from straight lines occurs when fluids mix rather than form decoupled flow channels. Another consequence of the mixing is that computed fractional flow curves, plotted against saturation, lie closer to the diagonal than they would otherwise do. At lower capillary numbers, fractional flow curves have a classical S-shape. Ratios of average mobility to their high-capillary number limit values are also considered. These vary, roughly, between 0 and 1, although values larger than 1 are also observed. For a given saturation and viscosity ratio, the mobilities are not always monotonically increasing with the pressure gradient. While increasing the pressure gradient mobilizes more fluid and activates more flow paths, when the mobilized fluid is more viscous, a reduction in average mobility may occur.

A macroscopic model for immiscible two-phase flow in porous media

“…In conjunction, two-phase flow simulations at the pore scale have also been carried out extensively (Zhao et al 2019) with the aim of reproducing both microscopic and macroscopic observations. These have been performed using various representations of porous structures like pore networks (Gjennestad, Winkler & Hansen 2020;Maalal et al 2021), X-ray or scanning-electron-microscopy-based images (Aljasmi & Sahimi 2021;Shams et al 2021). Computations have been carried out in many different configurations using lattice-Boltzmann (Taghilou & Rahimian 2014;Shi & Tang 2018;Gu, Liu & Wu 2021) and other techniques, either based on two-fluid systems taking explicitly into account the interfaces with a volume of fluid method or continuous two-fluid approaches using level-set (Ambekar, Mondal & Buwa 2021;Jettestuen, Friis & Helland 2021) or Cahn-Hilliard models (Yang & Kim 2021) with improved algorithms making use of machine learning (see, for instance, Silva et al (2021)).…”

Quantification of Nonlinear Multiphase Flow in Porous Media

“…The flow of multiple fluids in porous materials occurs in a wide variety of important natural and engineered settings relevant for the understanding of geological CO 2 storage, geothermal energy extraction, magma flow, oil and gas recovery, contaminant transport, flow in fuel cells, microfluidics in drug delivery, and the effectiveness of respirators and surgical masks (see for instance, Blunt, 2017; Gjennestad et al., 2020; Iglauer et al., 2019; Pak et al., 2015; Reynolds & Krevor, 2015; Zhang et al., 2019; Zhao et al., 2018). It is assumed that the flow rate is proportional to the pressure gradient, governed by a Darcy‐type law (Blunt, 2017; Muskat, 1937; Muskat & Meres, 1936), where q p is the volume of phase p flowing per unit area per unit time, k rp is the relative permeability, K is the absolute permeability, μ p is the viscosity, ∇ P p is the pressure gradient, and ρ p g is the contribution of gravity.…”

Non-linear multiphase flow in hydrophobic porous media

“…Multiphase flow in porous media occurs in a wide variety of natural and engineered settings, including carbon geosequestration, geoenergy resources recovery, subsurface contaminant control, drug delivery and flow in fuel cells [1][2][3][4][5][6][7][8][9][10][11] . For the last 85 years multiphase flow has been quantified assuming that each fluid phase has its own pathway and the flow rate has linear relationship with pressure gradient, governed by an empirical extension of the Darcy law 2,12,13 ,…”