We develop a novel "moving capacitor" dynamic network model to simulate immiscible fluid-fluid displacement in porous media. Traditional network models approximate the pore geometry as a network of fixed resistors, directly analogous to an electrical circuit. Our model additionally captures the motion of individual fluid-fluid interfaces through the pore geometry by completing this analogy, representing interfaces as a set of moving capacitors. By incorporating pore-scale invasion events, the model reproduces, for the first time, both the displacement pattern and the injection pressure signal under a wide range of capillary numbers and substrate wettabilities. We show that at high capillary numbers the invading patterns advance symmetrically through viscous fingers. In contrast, at low capillary numbers the flow is governed by the wettability-dependent fluid-fluid interactions with the pore structure. The signature of the transition between the two regimes manifests itself in the fluctuations of the injection pressure signal.

Abstract

Geological carbon dioxide (CO 2 ) sequestration entails capturing and injecting CO 2 into deep saline aquifers for long-term storage. The injected CO 2 partially dissolves in groundwater to form a mixture that is denser than the initial groundwater. The local increase in density triggers a gravitational instability at the boundary layer that further develops into columnar plumes of CO 2 -rich brine, a process that greatly accelerates solubility trapping of the CO 2 . Here, we investigate the pattern-formation aspects of convective mixing during geological CO 2 sequestration by means of high-resolution three-dimensional simulation. We find that the CO 2 concentration field self-organizes as a cellular network structure in the diffusive boundary layer at the top boundary. By studying the statistics of the cellular network, we identify various regimes of finger coarsening over time, the existence of a non-equilibrium stationary state, and a universal scaling of three-dimensional convective mixing.

Motivated by the process of CO 2 convective mixing in porous media, here we study the formation of rock-dissolution patterns that arise from geochemical reactions during Rayleigh-Bénard-Darcy convection. Under the assumption of instantaneous chemical equilibrium, we adopt a formulation of the local reaction rate as a function of scalar dissipation rate, a measure that depends solely on flow and transport, and chemical speciation, which is a measure that depends only on the equilibrium thermodynamics of the chemical system. We use high-resolution simulations to examine the interplay between the density-driven hydrodynamic instability and the rock dissolution reactions, and analyse the impact of geochemical reactions on the macroscopic mass exchange rate. We find that dissolution of carbonate rock initiates in regions of locally high mixing, but that the geochemical reaction shuts down significantly earlier than shutdown of convective mixing. This early shutdown feature reflects the important role that chemical speciation plays in this hydrodynamics-reaction coupled process. Finally, we extend our analysis to three dimensions and explore the morphology of dissolution patterns in three dimensions.

We develop a continuum-scale phase-field model to study gas-liquid-hydrate systems far from thermodynamic equilibrium. We design a Gibbs free energy functional for methane-water mixtures that recovers the isobaric temperature-composition phase diagram under thermodynamic equilibrium conditions. The proposed free energy is incorporated into a phase-field model to study the dynamics of hydrate formation on a gas-liquid interface. We elucidate the role of initial aqueous concentration in determining the direction of hydrate growth at the interface, in agreement with experimental observations. Our model also reveals two stages of hydrate growth at an interface-controlled by a crossover in how methane is supplied from the gas and liquid phases-which could explain the persistence of gas conduits in hydrate-bearing sediments and other nonequilibrium phenomena commonly observed in natural methane hydrate systems.