Capillary filling and Haines jump dynamics using free energy Lattice Boltzmann simulations

Abstract

We investigate numerically the dynamics of capillary filling and Haines jump events using free energy Lattice Boltzmann (LB) simulations. Both processes are potentially important multi-phase pore-scale flow processes for geological CO 2 sequestration and oil recovery. We first focus on capillary filling and demonstrate that the numerical method can capture the correct dynamics in the limit of long times for both high and low viscosity ratios, i.e. the method gives the correct scaling for the length of the penetrating fluid column as a function of time.Examining further the early times of capillary filling, three consecutive length vs. time regimes have been observed, in agreement with available experimental work in the literature. In addition, we carry out simulations of Haines jump events in idealised and realistic rock pore geometries. We observe that the Haines jump events are cooperative, non-local and associated with both drainage and imbibition dynamics. Our observations show that the pore filling dynamics is controlled by the Ohnesorge number, associated with the balance between viscous forces and inertial / surface tension forces. Using this concept, we are able to identify the type of pore filling dynamics that will occur.

Pore-filling events in single junction micro-models with corresponding lattice Boltzmann simulations

“…An in-depth investigation of imbibition dynamics using lattice Boltzmann simulations was carried out in Zacharoudiou & Boek (2016). We emphasise here that matching the relevant dimensionless numbers is essential in correctly resolving the multiphase flow dynamics, as Ca itself is not sufficient to uniquely describe the flow.…”

“…Hence, we turn our attention to the imbibition dynamics. We recently (Zacharoudiou & Boek 2016) examined the dynamics of capillary filling in two-dimensional channels and covered both: (i) the limit of long times for both high and low viscosity ratios r η = η w /η nw and (ii) the limit of short times, demonstrating that the free energy LB method can capture the correct dynamics for the process. We recall that in the limit of high viscosity ratios and long times, when the total time is much larger than the viscous time scale t v ∼ ρL 2 s /η w (Quéré 1997;Stange, Dreyer & Rath 2003), the Lucas-Washburn regime (l ∼ sqrt(t)) (Lucas 1918;Washburn 1921) is expected.…”

Inertial Effects During the Process of Supercritical CO2 Displacing Brine in a Sandstone: Lattice Boltzmann Simulations Based on the Continuum‐Surface‐Force and Geometrical Wetting Models

“…When the inertial effects are no longer negligible, simulations must match viscosity and density ratio, the capillary number, , and the Reynolds number, , of the physical system to capture the full physics during the fluid displacement process, where μ nw and ρ nw are the dynamic viscosity and density of the nonwetting phase, respectively, σ is the surface tension, V is the average inlet velocity, and d is the characteristic length of the pore geometry which is chosen to be the average pore diameter in this work. In such case, the Ohnesorge number ( Oh ) which relates the viscous forces to inertial and surface tension forces can be introduced to better describe the flow (Chen et al, ; Zacharoudiou & Boek, ), where the velocity term vanishes and the dimensionless number is only related to fluid properties and geometry. For simplicity, assuming the density and the grid resolution are fixed in the simulation, then equation imposes a requirement on the ratio between viscosity and surface tension.…”

Validation of model predictions of pore-scale fluid distributions during two-phase flow

“…Systematic studies of whether an image-based model of a rock captures the appropriate physics or merely suffers from uncertainties on the experimental input properties are lacking, due to the complexity of extracting comprehensive information from such a comparison. Valuable progress has been made to provide pore-scale validation with micromodels [23,[28][29][30], yet these simple two-dimensional pore structures do not capture the three-dimensional structural complexity of natural rocks.…”