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.

During imbibition, initially connected oil is displaced until it is trapped as immobile clusters. While initial and final states have been well described before, here we image the dynamic transient process in a sandstone rock using fast synchrotron‐based X‐ray computed microtomography. Wetting film swelling and subsequent snap off, at unusually high saturation, decreases nonwetting phase connectivity, which leads to nonwetting phase fragmentation into mobile ganglia, i.e., ganglion dynamics regime. We find that in addition to pressure‐driven connected pathway flow, mass transfer in the oil phase also occurs by a sequence of correlated breakup and coalescence processes. For example, meniscus oscillations caused by snap‐off events trigger coalescence of adjacent clusters. The ganglion dynamics occurs at the length scale of oil clusters and thus represents an intermediate flow regime between pore and Darcy scale that is so far dismissed in most upscaling attempts.

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In multiphase flow in porous media the consistent pore to Darcy scale description of two-fluid flow processes has been a long-standing challenge. Immiscible displacement processes occur at the scale of individual pores. However, the larger scale behavior is described by phenomenological relationships such as relative permeability, which typically uses only fluid saturation as a state variable. As a consequence pore scale properties such as contact angle cannot be directly related to Darcy scale flow parameters. Advanced imaging and computational technologies are closing the gap between the pore and Darcy scale, supporting the development of new theory. We utilize fast x-ray microtomography to observe pore-scale two-fluid configurations during immiscible flow and initialize lattice Boltzmann simulations that demonstrate that the mobilization of disconnected nonwetting phase clusters can account for a significant fraction of the total flux. We show that fluid topology can undergo substantial changes during flow at constant saturation, which is one of the underlying causes of hysteretic behavior. Traditional assumptions about fluid configurations are therefore an oversimplification. Our results suggest that the role of fluid connectivity cannot be ignored for multiphase flow. On the Darcy scale, fluid topology and phase connectivity are accounted for by interfacial area and Euler characteristic as parameters that are missing from our current models.

The macroscopic description of the hysteretic behavior of two-phase flow in porous media remains a challenge. It is not obvious how to represent the underlying pore-scale processes at the Darcy-scale in a consistent way. Darcy-scale thermodynamic models do not completely eliminate hysteresis and our findings indicate that the shape of displacement fronts is an additional source of hysteresis that has not been considered before. This is a shortcoming because effective process behavior such as trapping efficiency of CO 2 or oil production during water flooding are directly linked to pore-scale displacement mechanisms with very different front shape such as capillary fingering, flat frontal displacement, or cluster growth. Here we introduce fluid topology, expressed by the Euler characteristic of the nonwetting phase (v n ), as a shape measure of displacement fronts. Using two high-quality data sets obtained by fast X-ray tomography, we show that v n is hysteretic between drainage and imbibition and characteristic for the underlying displacement pattern. In a more physical sense, the Euler characteristic can be interpreted as a parameter describing local fluid connectedness. It may provide the closing link between a topological characterization and macroscopic formulations of two-phase immiscible displacement in porous rock. Since fast X-ray tomography is currently becoming a mature technique, we expect a significant growth in high-quality data sets of real time fluid displacement processes in the future. The novel measures of fluid topology presented here have the potential to become standard metrics needed to fully explore them.

[1] For subsurface flow, the correct definition for the balance of viscous and capillary forces, the so-called capillary number (Ca), which predicts the mobilization of nonwetting phase, has been a long-standing controversy. The most common microscopic definition results in nonwetting phase mobilization at Ca~10 À5, which is counterintuitive. Rather, mobilization should occur at Ca ≥ 1. As demonstrated herein, by using fast synchrotronbased X-ray computed microtomography and averaging of thereby accessible pore-scale parameters to macroscale values, a macroscale Ca definition is validated and shown to correctly describe mobilization at Ca~1. The presented methodology provides a connection between desaturation and pore-scale fluid topology and gives insight into when and how Ca changes with system size. The broader implication implies that it makes a difference whether desaturation is driven by an increase in flow rate or viscosity or decrease in interfacial tension since Ca incorporates nonwetting phase cluster length, which is process-dependent.

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a b s t r a c tWhen nonwetting fluid displaces wetting fluid in a porous rock many rapid pore-scale displacement events occur. These events are often referred to as Haines jumps and any drainage process in porous media is an ensemble of such events. However, the relevance of Haines jumps for larger scale models is often questioned. A common counter argument is that the high fluid velocities caused by a Haines jump would average-out when a bulk representative volume is considered. In this work, we examine this counter argument in detail and investigate the transient dynamics that occur during a Haines jump. In order to obtain fluid-fluid displacement data in a porous geometry, we use a micromodel system equipped with a high speed camera and couple the results to a pore-scale modeling tool called the Direct HydroDynamic (DHD) simulator. We measure the duration of a Haines jump and the distance over which fluid velocities are influenced because this sets characteristic time and length scales for fluid-fluid displacement. The simulation results are validated against experimental data and then used to explore the influence of interfacial tension and nonwetting phase viscosity on the speed of a Haines jump. We find that the speed decreases with increasing nonwetting phase viscosity or decreasing interfacial tension; however, for the same capillary number the reduction in speed can differ by an order of magnitude or more depending on whether viscosity is increased or interfacial tension is reduced. Therefore, the results suggest that capillary number alone cannot explain pore-scale displacement. One reason for this is that the interfacial and viscous forces associated with fluid-fluid displacement act over different length scales, which are not accounted for in the pore-scale definition of capillary number. We also find by analyzing different pore morphologies that the characteristic time scale of a Haines jump is dependent on the spatial configuration of fluid prior to an event. Simulation results are then used to measure the velocity field surrounding a Haines jump and thus, measure the zone of influence, which extends over a distance greater than a single pore. Overall, we find that the time and length scales of a Haines jump are inversely proportional, which is important to consider when calculating the spatial and temporal averages of pore-scale parameters during fluid-fluid displacement.