Intermittent Dynamics of Slow Drainage Experiments in Porous Media: Characterization Under Different Boundary Conditions

Abstract

The intermittent dynamics of slow drainage flows in a porous medium is studied experimentally. This kind of two-phase flow is characterized by a rich burst activity and our setup allows us to characterize those bursts directly via images of the flow and pressure measurements. Two different boundary conditions were analyzed: controlled withdrawal rate (CWR) and controlled imposed pressure (CIP). We have characterized geometrical and statistical properties of the bursts from images and pressure measurements. We have shown that in spite of leading to similar final invasion patterns, some dynamical features of the invasion differ considerably between the CWR and CIP boundary conditions. In particular, their pressure signatures are very distinct, which then translates into very distinct features on the power spectrum density of the pressure signals. A fully integrable analytical framework is presented which successfully describes the scaling features of the power spectrum for the CIP case.

Effect of Grain Shape on Quasi‐Static Fluid‐Fluid Displacement in Porous Media

“…Figure 3b(iii) shows * c P signal for the whole simulation. Similar pressure signal signatures in a stick-slip manner have been observed in experiments at quasi-static condition (Furuberg et al, 1996;Måløy et al, 1992;Moura et al, 2020).…”

“…The distribution of , the avalanches starting pressure, can also be directly obtained from the simulation (Figure 5b), where is the capillary pressure at pressure‐driven event (red circle in Figure 3b(i)). For experiments conducted using spherical glass beads in drainage, is found to distribute within a relatively narrow region (Furuberg et al., 1996; Måløy et al., 1992; Moura et al., 2020). The distribution is linked to the total volume capacitance stored in all active menisci (Furuberg et al., 1996), which reflects the characteristics of pore geometry.…”

Gravitational and Finite‐Size Effects On Pressure Saturation Curves During Drainage

“…If, by contrast, the outlet pressure is allowed to decrease to have a hydrostatic pressure in the defending fluid during this series of numerical invasion events, a Haines jump corresponds to a set of successive invasion events during an avalanche, defined by the outlet pressure series: An avalanche starts when the outlet pressure starts to decrease and finishes when it rises again above the value it had prior to this decrease. Such avalanches in experimental systems have been studied, for example, by Måløy et al (1992) and Moura et al (2020). Figure 2 shows a selected set of snapshots captured for different Bond numbers, displaying the growth of the displacement structure from the start of the invasion up to the end of the experiments, when all the pores bordering the outlet channel have been invaded and the final saturation S F nw is reached.…”

“…If, by contrast, the outlet pressure is allowed to decrease to have a hydrostatic pressure in the defending fluid during this series of numerical invasion events, a Haines jump corresponds to a set of successive invasion events during an avalanche, defined by the outlet pressure series: An avalanche starts when the outlet pressure starts to decrease and finishes when it rises again above the value it had prior to this decrease. Such avalanches in experimental systems have been studied, for example, by Måløy et al (1992) and Moura et al (2020).…”

“…Furthermore, it has revealed a variety of pattern-forming processes emerging from the pore scale up to the system scale (Lenormand et al, 1983;Måløy et al, 1985;Méheust et al, 2002;Løvoll et al, 2004;Toussaint et al, 2005), typically governed by the interplay between viscous, capillary, and gravitational forces. The structures have shown to exhibit a complex behavior, characterized by its rich intermittent dynamics (Clotet et al, 2016;Furuberg et al, 1988;Måløy et al, 1992;Moura et al, 2020;Moura, Måløy, Flekkøy, et al, 2017;Planet et al, 2009). We study two phase flow in a quasi two-dimensional (2-D) porous confinement and look at the simple case of drainage at pore scale, where a nonwetting phase displaces a wetting one.…”