Geometric state function for two-fluid flow in porous media

Abstract

Models that describe two-fluid flow in porous media suffer from a widely-recognized problem that the constitutive relationships used to predict capillary pressure as a function of the fluid saturation are non-unique, thus requiring a hysteretic description. As an alternative to the traditional perspective, we consider a geometrical description of the capillary pressure, which relates the average mean curvature, the fluid saturation, the interfacial area between fluids, and the Euler characteristic. The state equation is formulated using notions from algebraic topology and cast in terms of measures of the macroscale state. Synchrotron-based X-ray micro-computed tomography (µCT) and highresolution pore-scale simulation is applied to examine the uniqueness of the proposed relationship for six different porous media. We show that the geometric state function is able to characterize the microscopic fluid configurations that result from a wide range of simulated flow conditions in an averaged sense. The geometric state function can serve as a closure relationship within macroscale models to effectively remove hysteretic behavior attributed to the arrangement of fluids within a porous medium. This provides a critical missing component needed to enable a new generation of higher fidelity models to describe two-fluid flow in porous media. PACS numbers: 92.40Cy, 92.40.Kf, 91.60.Tn, 91.60.Fe

High‐Speed Quantification of Pore‐Scale Multiphase Flow of Water and Supercritical CO2 in 2‐D Heterogeneous Porous Micromodels: Flow Regimes and Interface Dynamics

“…Moreover, it has been hypothesized that the inclusion of parameters representing the interfacial area in macroscale formulations of capillary pressure, P c , could account for hysteresis observed in the traditional capillary pressure-saturation (P c -S w ) relationship, enabling a unique relation between capillary pressure, saturation, and interfacial area (P c -S w -a nw ; Hassanizadeh & Gray, 1993;Joekar-Niasar & Hassanizadeh, 2012;Porter et al, 2010). In fact, recent theoretical studies have shown that hysteresis behavior can potentially be eliminated by accounting for the pore-scale topological features of the flow, such as interfacial area, interfacial curvature, and Euler characteristics (Armstrong et al, 2016;McClure et al, 2018;Picchi & Battiato, 2018). A number of studies have focused on characterizing the behavior of interfacial area in both 2-D and 3-D porous media (Cheng et al, 2004(Cheng et al, , 2007Hassanizadeh & Gray, 1993;Joekar-Niasar & Hassanizadeh, 2012;Karadimitriou et al, 2014;Porter et al, 2010).…”

Relative Permeability Scaling From Pore‐Scale Flow Regimes

“…Several approaches have been developed to incorporate the evolution of the fluid-fluid interface into macroscopic equations (e.g., Cueto-Felgueroso & Juanes, 2014;Gray & Miller, 2010;Gray et al, 2015;Hassanizadeh & Gray, 1990Hilfer, 1998;Jackson et al, 2009;McClure et al, 2016;Niessner & Hassanizadeh, 2008;Rybak et al, 2015), but additional complexity in the formulation of the closure problem and in the definition of state variables has been inevitably introduced. Only recently, Karadimitriou et al (2014) proposed a method to estimate such state variables from experimental measurements, while Schluter et al (2016) and McClure et al (2018) provided alternative approaches to identify the missing variables in terms of integral geometry (i.e., Euler characteristics). Over the years, more practical and ad hoc formulations of the relative permeabilities have been proposed (Chierici, 1984;Clavier et al, 2017;Dehghanpour et al, 2011;Gunstensen & Rothman, 1993;Li et al, 2018;Oliveira & Demond, 2003;Pasquier et al, 2017;Yiotis et al, 2007;Zhang et al, 2018), including the study of the impact of spatial heterogeneity on relative permeabilities (Jackson et al, 2018).…”

Description of Free Energy for Immiscible Two‐Fluid Flow in Porous Media by Integral Geometry and Thermodynamics

“…McClure et al () investigated which intrinsic volumes were required to describe the state of quasi‐static two‐phase flow in porous media. Further, they investigated constitutive relations among these parameters.…”

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In integral geometry, intrinsic volumes are a set of geometrical variables to characterize spatial structures, for example, distribution of fluids in two-fluid flow in porous media. McClure et al (2018, https:// doi.org/10.1103.084306) utilized this principle and proposed a geometric state function based on the intrinsic volumes. In a similar approach, we find a geometrical description for free energy of a porous system with two fluids.

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