Energy Conversion Reveals Regime Transition of Imbibition in a Rough Fracture

As externally imposed flow rate increases during imbibition, viscous force increasingly dominates displacement over capillarity and imbibition shifts from capillary to capillary-viscous regimes. Previous studies focused on capillary regime, lacking a fundamental understanding of regime transition. Here we study the imbibition transition via flow rate-controlled experiments in a rough fracture. By analyzing energy balance in multiphase flow system, we find a fundamental link between regime transition and energy conversion. In capillary regime, surface energy is partially transformed into external work and an amount of 51-58% is dissipated via local rapid, irreversible events; while in capillary-viscous regime, surface energy together with external work is transformed into kinetic and dissipated energies. This transition, corresponding to critical capillary number, is evidenced by quantitative analysis of invasion morphologies. Our work bridges the gap between energy conversion/dissipation and multiphase flow and has important implications for identifying imbibition regimes in enhanced oil recovery and geological CO2 sequestration. Plain Language Summary The displacement of nonwetting phase by wetting phase in permeable media, known as imbibition, is central to diverse processes including enhanced oil recovery and geological carbon sequestration. As externally imposed flow rate increases during imbibition, viscous force increasingly dominates the imbibition over the capillary force, leading to the transition of imbibition from capillary to capillary-viscous regimes. Since imbibition involves energy conversion among surface energy, dissipated energy, external work, and kinetic energy, is there a fundamental link between energy conversion and regime transition? To explore this issue, we perform imbibition experiments in a rough fracture and analyzed energy balance enabled by real-time imaging. We find that regime transition is intrinsically linked with energy conversion. In capillary regime, surface energy is partially transformed into external work, and 51-58% of the total surface energy is dissipated. In capillary-viscous regime, surface energy together with external work is transformed into kinetic and dissipated energies. Such transition is evidenced by quantitative analysis of invasion morphologies. Our findings bridge the gap between energy conversion/dissipation and multiphase flow and have important implications for identifying imbibition regimes in enhanced oil recovery and geological CO2 sequestration.