Abstract
Imbibition is an important process encountered in many porous media applications. At the pore scale, pore network models (PNM) are computationally efficient and can model drainage accurately. However, using PNM to model imbibition still remains a challenge due to the complexities encountered in understanding pore-scale flow phenomena related to pore body filling (PBF) and snap-off along with the relative competition between these events. In this work, we use direct numerical simulations (DNS) to revisit the basic principles of PBF in a two-dimensional synthetic pore geometry. We notice that PBF during spontaneous imbibition is dependent on several parameters such as shape of the transition zone, contact angle and the fluid properties like density. The interactions between these parameters are investigated in a quantitative manner. We demonstrate the existence of a critical contact angle \U0001d703c and a barrier contact angle \U0001d703b. \U0001d703c depends on the shape of the pore geometry, whereas \U0001d703b depends on the pore geometry, contact angle and fluid properties. For a system comprising of light fluids, \U0001d703b is only slightly larger than \U0001d703c; whereas for a system occupied by dense fluids, \U0001d703b is notably larger than \U0001d703c. The contact angle of the wetting phase \U0001d703 in relation to \U0001d703c and \U0001d703b decides if the wetting phase can imbibe a pore body. Imbibition always occurs if \U0001d703 < \U0001d703c. For \U0001d703 > \U0001d703c, we observe capillary barrier zones in which capillary forces accompany viscous forces to resist spontaneous imbibition. For this case, we observe smooth transition of the meniscus curvature while the meniscus enters and exits capillary barrier zones. For \U0001d703c ≤ \U0001d703 ≤ \U0001d703b, inertia assists the wetting phase to overcome resisting forces and imbibe the pore space. For \U0001d703 > \U0001d703b, the resisting forces dominate over inertia so that the wetting phase cannot imbibe the pore space. For the synthetic pore geometries investigated, we provide analytical and semi-analytical expressions to determine \U0001d703c and the position of capillary barrier zones respectively. The barrier contact angle \U0001d703b is computed numerically for several inertial systems and for various shapes of the synthetic pore geometry. The results of this quantitative analysis can be utilised to improve the existing pore filling rules and predictive capabilities of PNM used for two-phase flows.
Highlights
Multiphase flows occur in a wide range of industrial and engineering applications such as in the recovery of hydrocarbons, carbon capture and sequestration, fuel cells and Electronic supplementary material The online version of this article contains supplementary material, which is available to authorised users.Extended author information available on the last page of the article.lab-on-a-chip devices
The pore geometry along with the fluid properties and contact angle govern the magnitude of inertial, viscous and capillary forces acting within the system [8, 16] which in turn govern the displacement pattern of the fluids
We systematically investigate the principles of pore body filling under different inertial conditions and extend the study to a simple pore network model comprising of two pores having different size and shape
Summary
Focussing exclusively on PBF, Ferrari and Lunati [8] have shown the occurrence of meniscus reconfigurations at the corners of a square and circular pore during forced imbibition and used the principles of energy balance to study meniscus reconfigurations analytically They notice that the meniscus reconfigurations have their own time scales and velocities. We revisit the concept of PBF in this paper by investigating meniscus dynamics that occur at the transition zone (pore space that connects a pore throat and pore body) having different shapes. We quantitatively analyse PBF using DNS for different scenarios by tuning the following dependent parameters: pore geometry (transition zone shape, aspect ratio), contact angle and the fluid properties. To showcase the importance of acknowledging capillary barriers, we investigate spontaneous imbibition at different contact angles in a pore doublet comprising of two pores having different size and transition zone shape.
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