Viscous Fingering and Preferential Flow Paths in Heterogeneous Porous Media

Abstract

Preferential flow channeling and viscous fingering are widely observed phenomena in heterogeneous porous media from the pore scale to the core and reservoir scales. The transition from capillary to viscous fingering with increasing injection rate is also a well‐known phenomenon. Based on the previously observed visual similarity of viscous fingers and preferential single‐phase flow paths in 2‐D simulations, we postulate that these single‐ and two‐phase flow patterns should also be interrelated in 3‐D porous media. Capillary fingering is a manifestation of invasion percolation, a process restricted to the subnetwork of pores obtained from the critical path analysis. We investigated single‐phase flow channeling by applying a method similar to critical path analysis to the flow rate field and compared the subnetwork thus determined to the set of invaded pipes in drainage simulations. Our aim is to quantify the relation between preferential flow paths and viscous fingering, its dependence on pore‐scale heterogeneity and pore connectivity, and ultimately to upscale the network observations to the field scale appropriate for the engineering applications involving drainage in heterogeneous media.

Numerical Analysis of Invasion Patterns During Drainage Process in a Simplified Pore Network Model

“…Observing the state at breakthrough (Fig. 6d), the seemingly preferential path to the upper pores is evident, which is not by the capillarity but rather by the channeling effect [13,14]. In the viscous fingering pattern, since bulk pressure difference is much larger than the local capillary pressure difference, the pore selection of invasion does not occur pore by pore unlike the capillary fingering pattern.…”

Fluid Flow Concentration on Preferential Paths in Heterogeneous Porous Media: Application of Graph Theory

“…where n is the total number of pores. A perfectly uniform flow field is indicated by θ ≈ 1 while θ = n p /n << 1 corresponds to a complete concentration of the flow on a single path containing n p << n pores (see Tang et al, 2020).…”

“…The significance of the associated subnetwork {Q c } is that the through-going paths contained in it have average flow rates larger than Q c , identifying them as potential preferential paths. Determination of {Q c } is done by means of a dichotomy technique using Dijkstra's shortest path algorithm (Dijkstra, 1959) to test the connectivity of {Q} (see Tang et al [2020] for details). The output parameters of this method are the critical flow rate Q c and the relative size S c of the critical subnetwork (i.e., the ratio of the number of pores in {Q c } to the total number of bonds, occupied or not, in the network).…”

“…It is also interesting to characterize the percolation properties of the flow field. Tang et al (2020) developed a method inspired from the critical path analysis (CPA), which was introduced decades ago for modeling permeability in heterogeneous rocks (Charlaix et al, 1987;Friedman & Seaton, 1998;Katz & Thompson, 1986) and has often been applied to various flow and transport problems (Hunt, 2001;Hunt et al, 2014;Hunt & Sahimi, 2017;Hunt & Skinner, 2008;Sahimi, 1998Sahimi, , 2011Sahimi & Knackstedt, 1994). For a given network realization, the method consists in considering the subnetwork {Q} that includes the pores i having |Q i | greater than or equal to a given positive value Q.…”

“…; see also Didari et al, 2020, in the case of non-Newtonian fluid flow). As in reservoir-scale flow, a greater non-uniformity of the pore-scale flow field is associated with enhanced dispersion of solute transport Bernabé, Wang, et al, 2015;Bijeljic & Blunt, 2006;Kang et al, 2015;Li et al, 2018;Sahimi et al, 1986) and multi-phase flow fingering (Blunt et al, 1992;Holtzman, 2016;Tang et al, 2020).…”