Abstract
Drainage is typically understood as a process where the pore space is invaded by a nonwetting phase pore-by-pore, the controlling parameters of which are represented by capillary number and mobility ratio. However, what is less understood and where experimental data are lacking is direct knowledge of the dynamics of pore drainage and the associated intrinsic time scales since the rate dependencies often observed with displacement processes are potentially dependent on these time scales. Herein, we study pore drainage events with a high speed camera in a micromodel system and analyze the dependency of interfacial velocity on bulk flow rate and spatial fluid configurations. We find that pore drainage events are cooperative, meaning that capillary pressure differences which extend over multiple pores directly affect fluid topology and menisci dynamics. Results suggest that not only viscous forces but also capillarity acts in a nonlocal way. Lastly, the existence of a pore morphological parameter where pore drainage transitions from capillary to inertial and/or viscous dominated is discussed followed by a discussion on capillary dispersion and time scale dependencies. We show that the displacement front is disperse when volumetric flow rate is less than the intrinsic time scale for a pore drainage event and becomes sharp when the flow rate is greater than the intrinsic time scale (i.e., overruns the pore drainage event), which clearly shows how pore-scale parameters influence macroscale flow behavior.
Highlights
The physics of drainage is commonly regarded as well understood and many multiphase flow macroscopic properties are explained by invasion percolation theory [1]
Potential energy is stored in liquidliquid menisci to a given threshold, at which point energy is released resulting in irreversible fluid rearrangement until a new local energy minimum is obtained
The dynamics of pore drainage events were studied in a two-dimensional micromodel at low and intermediate capillary numbers using a high speed camera which explicitly resolves meniscus propagation
Summary
The physics of drainage is commonly regarded as well understood and many multiphase flow macroscopic properties are explained by invasion percolation theory [1]. A cascade of pore drainage events is possible if sequentially available pores have entry pressures lower than the initial energy barrier (Pore 1 and Pore 2 drain once Pentry 1 is exceeded). Potential energy is stored in liquidliquid menisci to a given threshold (i.e., during reversible displacement), at which point energy is released resulting in irreversible fluid rearrangement until a new local energy minimum is obtained (as seen, a stable meniscus exists at Pentry 1 until the applied pressure is greater than Pentry 1 at which point energy is released and both Pore 1 and Pore 2 drain). With this geometrical model pore space is artificially subdivided (e.g., Pore 1 and Pore 2 in Fig. 1) which due to accessibility can drain in cascadelike events (Region 1). The geometrical model, often used in percolation theory, essentially falls short in the description of pore drainage because the dynamics are not considered and capillarity is assumed to be strictly local (i.e., only the capillary entry pressures of localized individual pores are considered)
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