Transitions of Fluid Invasion Patterns in Porous Media

Abstract

Fluid invasion into porous media to displace a more viscous fluid exhibits various displacement patterns. For such unfavorable displacements, previous works overlooked the dynamic effect of viscous force on pattern transitions at low flow rates. Consequently, the crossover from compact displacement to capillary fingering under various wetting conditions remains unclear. Here, we establish a theoretical model to capture pattern transitions affected by wettability and flow rate. We rigorously quantify the dynamic effect of viscous force and find that critical contact angles for the crossover from compact displacement to capillary fingering decrease with capillary number. Our model also well describes transitions from capillary fingering to the crossover to viscous fingering. The predicted phase diagram exhibits good agreement with our pore-scale simulations and microfluidic experiments and is highly consistent with existing experiments. This work extends the classic phase diagram under unfavorable conditions and is of practical significance in subsurface applications. Plain Language Summary Fluid invasion into porous media saturated with another more viscous, immiscible fluid exhibits various displacement patterns. The patterns are controlled by the competition between capillary and viscous forces and significantly affect oil recovery and CO 2 trapping efficiency. Although invasion patterns have been studied intensively, the dynamic effect of viscous force on pattern transitions is neglected. The crossovers from compact displacement to capillary fingering are not well understood. To explore pattern transitions affected by wettability and flow rate, we perform theoretical analysis of flow behavior at the pore scale, and then establish a model to describe pattern transitions as functions of contact angle and capillary number. We rigorously consider the dynamic effect of viscous force and find that the critical contact angles for the crossover from compact displacement to capillary fingering decrease with capillary number. The model also well describes the crossover from capillary to viscous fingering. We evaluate the phase diagram using pore-scale simulations, and microfluidic experiments performed in this and previous studies, justifying that the diagram can well capture the transitions under various wetting and flow-rate conditions. This work extends the classic phase diagram and is also of practical significance in predicting displacement patterns in subsurface applications.

Role of Pore‐Scale Disorder in Fluid Displacement: Experiments and Theoretical Model

“…Given the focus of this work is the drainage displacement with θ = 120°, the 3D nature of pore‐scale flow behaviors including wetting film (Levaché & Bartolo, 2014) and corner flow (Concus & Finn, 1969; Zhao et al., 2016) can be neglected. Thus, the overlap is controlled by the in‐plane curvature (Hu et al., 2018b; Lan et al., 2020). The occurrence of pore‐filling events was employed to predict the transition from capillary fingering to compact displacement in porous media with a fixed pore‐scale disorder λ .…”

“…As previously discussed in Figure 5, the underlying mechanism of this transition is that the overlap event dominates multiphase flow in the domain of compact displacement (Figure 5a). Note that even under such slow flow rate conditions (–7.4 ≤ log 10 Ca ≤ −6.9) in which the fluid displacement is capillary‐dominated, the transition from compact displacement to capillary fingering also depends on flow rate (Lan et al., 2020). It suggests that under such a range of capillary numbers, the viscous pressure cannot be neglected.…”

Wettability and Lenormand's diagram

“…This study was complemented by Lan et al. (2020), who used a dynamic pore-network model to explore the interplay between wettability and for which, like the model of Holtzman & Segre (2015), neglected corner flow and was therefore limited to . The phase diagrams produced in these studies correspond to a set of partial – slices of the –– diagram we present in our manuscript.…”

“…2016; Lan et al. 2020). We observe the same trend for all degrees of disorder: both the finger width and the fractal dimension are consistently higher in imbibition than in drainage (figure 16 b , c ).…”

Influence of Wetting on Viscous Fingering Via 2D Lattice Boltzmann Simulations

“…Zhao et al (2016) found in microfluidic experiments involving vertical posts representing a porous medium, that as wettability is increased, there is more efficient displacement and higher saturation up until a critical angle is reached, after which, the system undergoes a wetting transition and the trend is reversed. Other microfluidic research combined with theoretical analysis and pore-scale simulations (Hu et al 2019;Lan et al 2020) have studied the phase diagram capturing the viscous to capillary fingering transition to study the impact of medium disorder and wettability on this transition. Research using an invasion-percolation model by Primkulov et al (2018) extended the Cielpak and Robbins description of quasistatic fluid invasion reproducing the wetting transition in strong imbibition.…”