Transition From Viscous Fingering to Capillary Fingering: Application of GPU‐Based Fully Implicit Dynamic Pore Network Modeling

Abstract

Immiscible two-phase flow through porous materials exhibits different invasion patterns controlled by dynamic conditions, competition between the viscous and capillary forces, and the contrast between the fluids viscosities. Two distinct invasion patterns are viscous and capillary fingering. While the first one happens under unfavorable viscosity ratios at high injection rates, the second one happens when the viscous forces are very small compared to the capillary forces. Depending on whether the invasion is under the capillary fingering or viscous fingering regime, the remaining oil saturation and the effective permeability of the fluids can significantly change. The contribution of the present work has two key aspects: (a) It addresses how the remaining saturation changes at different flow rates (i.e., capillary numbers) for different unfavorable viscosity ratios in a three-dimensional system; (b) it presents a new dynamic pore network model using the fully implicit scheme which has been enhanced by the graphic processing unit (GPU) parallel computing. Additionally, the model has been carefully validated against micromodel experiments in both time and space, which to our best knowledge has not been reported in such detail in the literature. The results of the validated 3-D dynamic pore network model demonstrate the remaining saturation at the breakthrough time as a nonmonotonic trend with the imposed capillary number.

A Brief Review of Capillary Number and its Use in Capillary Desaturation Curves

“…9). Other factors for the nonmonotonicity in micromodels may be associated with the flow regime crossover from capillary fingering to viscous fingering (An et al 2020;Khosravian et al 2015;Chen et al 2017;Wang et al 2013;Ferer et al 2004), model inhomogeneity (Wang et al 2013), solid surface wettability (Zhao et al 2016), flow history (Krummel et al 2013;Khosravian et al 2015), and rock surface roughness (Glass et al 2003;Chen et al 2017). predict recovery to be independent of viscosity and to decrease with length scale because the pressure drops and hence the velocity decreases.…”

Impact of Displacement Direction Relative to Heterogeneity on Averaged Capillary Pressure‐Saturation Curves

“…The non‐monotonicity was reported in several previous studies; the trade‐off between capillary and viscous forces was recognized as the underlying mechanism for this behavior (An, Erfani, et al., 2020; An, Hasan, et al., 2020; Dias & Payatakes, 1986; Joekar‐Niasar & Hassanizadeh, 2012; Rodriguez de Castro et al., 2015; Singh & Mohanty, 2003). The reason is that by increasing the capillary number (ratio of the viscous to capillary forces), the viscous forces become more important and the displacement behavior changes from capillary fingering to viscous fingering, if the injected fluid has a smaller viscosity compared to the receding fluid (An, Erfani, et al., 2020; An, Hasan, et al., 2020; Singh & Mohanty, 2003), following the classical phase diagram proposed by Lenormand (1986) for immiscible displacement. Depending on the capillary number and the viscosity ratio, stable displacement, viscous fingering, or capillary fingering may take place.…”

“…The procedure for manufacturing a PDMS micromodel is explained in detail elsewhere (Auset & Keller, 2004; Karadimitriou & Hassanizadeh, 2012; Karadimitriou et al., 2013; Quake & Scherer, 2000; Xia & Whitesides, 1998). After fabrication, the micromodel was treated with a mixture of 2.5 μL trichloro(1H, 1H, 2H, 2H‐perfluorooctyl) silane to 1 mL ethanol to make the micromodel uniformly and stably hydrophobic (An, Erfani, et al., 2020; An, Hasan, et al., 2020; Zhou et al., 2010). The overall dimensions of the micromodel were 6 × 30 mm 2 , with a uniform internal depth of 60 μm.…”

Fluid-Driven Instabilities in Granular Media: From Viscous Fingering and Dissolution Wormholes to Desiccation Cracks and Ice Lenses

“…The Rayleigh-Taylor instability, observed when a lighter fluid ascends through a heavier fluid, develops at large Bond numbers. Different invasion modes lead to distinct fluid pressure fields: the pressure drop occurs mainly in the more viscous phase, i.e., the invading phase in stable displacement or the defending phase in viscous fingering; on the other hand, the viscous pressure drop is negligible compared to the capillary pressure difference between the fluids in the capillary fingering regime (An et al, 2020).…”