Beyond Darcy's law: The role of phase topology and ganglion dynamics for two-fluid flow

Abstract

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.

X‐ray Microtomography of Intermittency in Multiphase Flow at Steady State Using a Differential Imaging Method

“…The Euler characteristic is also computed to indicate the connectivity of the nonwetting phase (Armstrong et al, 2016; Herring et al, 2013; Liu et al, 2017), and was calculated using the image analysis Avizo software. A large negative value indicates that the oil is well connected.…”

“…The relative permeability could also be computed from the measured pore‐scale configurations of fluid and compared to the experimental measurements (Armstrong et al, 2016). In addition, the technique could be applied to a wide range of rock types and wettabilities.…”

Ensemble distribution for immiscible two-phase flow in porous media

“…A recent review summarizes the status of this class of models, see [31]. A very different approach is the Lattice Boltzmann method [32,33], see also [34,35]. Whereas the network models are ideal for large network without detailed knowledge of the presice shape of each pore, the Lattice Boltzmann method has the opposite strength.…”

Oil Fragmentation, Interfacial Surface Transport and Flow Structure Maps for Two-Phase Flow in Model Pore Networks. Predictions Based on Extensive, DeProF Model Simulations

“…With recent advances in imaging technology, these flows are observed in real porous media as well (Georgiadis et al, 2013;Oughanem et al, 2015;Rücker et al, 2015). The observed flow structures show a significant and À presumably À systematic mutation ranging from practically no oil-flow, to large and small oil ganglion dynamics, to drop traffic and connected pathway flow mixtures, depending À primary À on the flow conditions and À secondary À on the physicochemical, size and network configuration of the oil-water-p.m. system Payatakes, 1995 and1999;Krummel et al, 2013;Armstrong et al, 2016). These studies show that during simultaneous flow of oil and water, the disconnected phase (oil) contributes significantly to the total flow and, in certain cases even exclusively, e.g.…”

“…The latter are described as oil Ganglion Dynamics (GD) and Drop Traffic Flow (DTF), modes that have been systematically observed during flow within model pore networks (Avraam and Payatakes, 1995;Tzimas et al, 1997;Tallakstad et al, 2009;Krummel et al, 2013;Datta et al, 2014;Armstrong et al, 2016). Apart from laboratory studies, virtual studies, implementing dynamic pore network simulations Payatakes, 1996 andAlGharbi and Blunt, 2005;Nguyen et al, 2006), or lattice Boltzmann methods (Pan et al, 2004;Ghassemi and Pak, 2011;Ramstad et al, 2012;Armstrong et al, 2016), have also addressed disconnected-oil flow modes. With recent advances in imaging technology, these flows are observed in real porous media as well (Georgiadis et al, 2013;Oughanem et al, 2015;Rücker et al, 2015).…”