Signatures of fluid–fluid displacement in porous media: wettability, patterns and pressures

Abstract

We develop a novel "moving capacitor" dynamic network model to simulate immiscible fluid-fluid displacement in porous media. Traditional network models approximate the pore geometry as a network of fixed resistors, directly analogous to an electrical circuit. Our model additionally captures the motion of individual fluid-fluid interfaces through the pore geometry by completing this analogy, representing interfaces as a set of moving capacitors. By incorporating pore-scale invasion events, the model reproduces, for the first time, both the displacement pattern and the injection pressure signal under a wide range of capillary numbers and substrate wettabilities. We show that at high capillary numbers the invading patterns advance symmetrically through viscous fingers. In contrast, at low capillary numbers the flow is governed by the wettability-dependent fluid-fluid interactions with the pore structure. The signature of the transition between the two regimes manifests itself in the fluctuations of the injection pressure signal.

Jamming transition and emergence of fracturing in wet granular media

“…As a result, the injection pressure shows fluctuations in a stick-slip manner for all θ and φ 0 , as has been documented in slow drainage experiments [53][54][55] and simulations [44]. As θ decreases, indicating that the substrate becomes more wetting to the invading fluid, the fluid-fluid displacement is controlled by cooperative pore-filling events (touch and overlap) with smaller P cap compared with burst events [35,36,43,44]. This explains the general decreasing trend of injection pressure as θ decreases [ Fig.…”

“…These events determine how the interface advances, enlisting one or more new particles when a node on the interface reaches its filling capacity and becomes unstable. This model reproduces both the displacement pattern and the injection pressure signal under a wide range of capillary numbers and substrate wettabilities [43,44,50]. and initial packing densities φ 0 .…”

“…In a drainage displacement, instead of fluctuating around a mean value [44], the injection pressure exhibits a surprising convex shape as a function of time, first decreasing and then increasing with time. This is a signature of the fluid-solid coupling: The particles around the cavity are separated (opening up the throats and decreasing P cap ) during the initial stages of expansion, and then brought closer together (narrowing the throats and increasing P cap ), as the granular pack is being compacted during the late stages [ Fig.…”

“…As one of the factors that influences multiphase flow in porous media, wettability (the relative affinity of the substrate to each of the fluids, and measured by the contact angle θ ) has been studied for decades. While much is now known about the role of wettability on multiphase displacements in porous media [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47], fundamental gaps remain in the context of grain-scale mechanisms and their macroscale consequences. Given the importance of capillarity on the fracture of granular packs [10,14,21,22,24], here we focus on the impact of wetting properties on the emergence of such fracture patterns.…”

“…We adopt a recently developed "moving capacitor" dynamic network model to simulate fluid-fluid displacement at the pore level [44] (see Supplemental Material [49]). The model employs an analog of the pore network geometry, where resistors, batteries, and capacitors are responsible for viscous, out-of-plane, and in-plane Laplace pressure drops, respectively.…”