Energy capillary number reveals regime transition of imbibition in porous media

Abstract

Imbibition, the process of a wetting fluid displacing a nonwetting one in porous media, occurs in many natural and industrial processes, such as enhanced oil recovery and geological carbon sequestration. The phenomenon of imbibition shifts from the capillary regime to the capillary–viscous regime as the externally imposed flow rate (viscous force) increases. In the capillary–viscous regime, there also exists a transition from the capillary-dominated regime to viscous-dominated regime, and the identification of this transition is fundamental to the description of forced imbibition. The main purpose of this work is to explore regime transition in imbibition. We first investigate forced imbibition in a heterogeneous porous media over a broad range of wettability conditions and flow rates. An energy capillary number is proposed to identify regime transitions based on the energy balance analysis of imbibition processes, especially the transition from a capillary-dominated regime to viscous-dominated regime. The energy capillary number is defined as the ratio of the reduced surface energy to the external work, measuring the relative total contribution of the capillary force vs the viscous force to the whole imbibition morphologies. We further present a phase diagram, which allows us to determine the imbibition regime directly from capillary numbers and wettability conditions. The energy capillary number and phase diagram are evidenced by a quantitative analysis of invasion morphologies.

Current advances in capillarity: Theories and applications

“…Guangpu Zhu, from the National University of Singapore, gave an online talk on "Energy capillary number reveals regime transition of imbibition in porous media". He investigated forced imbibition in a heterogeneous porous media over a broad range of wettability conditions and flow rates using the interface capturing method (Zhu et al, 2020;Zhu et al, 2021). An energy capillary number was proposed to identify regime transitions based on the energy balance analysis of imbibition processes, especially the transition from a capillarydominated regime to viscous-dominated regime.…”

Modeling swelling effects during coffee extraction with smoothed particle hydrodynamics

“…At the start of the filtration, the coffee grains are wetted rapidly by capillary action: micro-pores on the coffee grains and nano-pores on the cell walls imbibe the water by capillary force. This imbibition process can be approximately described by the classical Washburn equation 3 or by solving N-S equations numerically together with the volume of fluid method 36 . During the imbibition process, water molecules may also combine with the hydroxyl groups in the cellulose fibre, and cause the porous matrix to expand.…”

An Experimental Investigation on the Energy Signature Associated With Multiphase Flow in Porous Media Displacement Regimes

“…Previous studies have extensively examined displacement patterns and flow regimes under various wetting conditions through experimental investigations (Alzahid et al., 2019; Avraam & Payatakes, 1995; Herring et al., 2016; Hu et al., 2020; Jahanbakhsh et al., 2021; Lenormand et al., 1988; Primkulov et al., 2019, 2021; Yang et al., 2023; Zhang et al., 2011; Zhao et al., 2016; Zhu et al., 2021). However, the impact of these displacements on the work of displacement and interfacial surface area changes within porous media, as well as their influence on flow behavior, has received relatively little attention.…”