Adaptive mesh refinement in locally conservative level set methods for multiphase fluid displacements in porous media

Abstract

Multiphase flow in porous media often occurs with the formation and coalescence of fluid ganglia. Accurate predictions of such mechanisms in complex pore geometries require simulation models with local mass conservation and with the option to improve resolution in areas of interest. In this work, we incorporate patch-based, structured adaptive mesh refinement capabilities into a method for local volume conservation that describes the behaviour of disconnected fluid ganglia during level set simulations of capillary-controlled displacement in porous media. We validate the model against analytical solutions for three-phase fluid configurations in idealized pores containing gas, oil, and water, by modelling the intermediate-wet oil layers as separate domains with their volumes preserved. Both the pressures and volumes of disconnected ganglia converge to analytical values with increased refinement levels of the adaptive mesh. Favourable results from strong and weak scaling tests emphasize that the number of patches per processor and the total number of patches are important parameters for efficient parallel simulations with adaptive mesh refinement. Simulations of two-phase imbibition and three-phase gas invasion on segmented 3D images of water-wet sandstone show that adaptive mesh refinement has the highest impact on three-phase displacements, especially concerning the behaviour of the conserved, intermediate-wet phase.

Ripening of Capillary-Trapped CO2 Ganglia Surrounded by Oil and Water at the Pore Scale: Impact of Reservoir Pressure and Wettability

“…We solve eq by explicit numerical schemes in both space and iteration time using finite differences. , The numerical implementation also includes reinitializing the level-set functions ϕ α to signed distances at fixed iteration intervals. For the stationary states (∂ϕ α /∂τ = 0, α = g , o , w ), we declare convergence when max α { ∑ Ω H ϵ false( ψ + ϵ false) H ϵ false( ϕ α n + λ false) H ϵ false( prefix− ϕ α n + λ false) false| ϕ α n − ϕ α m false| ∑ Ω H ϵ false( ψ + ϵ false) H ϵ false( ϕ α n + λ false) H ϵ false( prefix− ϕ α n + λ false) } < c normalΔ x , goodbreak0em1em⁣ where α = g , o , w ...…”

“…We solve eq by explicit numerical schemes in both space and iteration time using finite differences. , The numerical implementation also includes reinitializing the level-set functions ϕ α to signed distances at fixed iteration intervals. For the stationary states (∂ϕ α /∂τ = 0, α = g , o , w ), we declare convergence when Here, ϕ α n – ϕ α m is the difference between the level-set functions after the two last reinitializations (denoted n and m ), while λ = b × ϵ is the width of the band around ϕ α = 0 in the pore space where this difference is evaluated. Further, c specifies the error tolerance.…”

“…This is particularly important in three-phase scenarios where the mass transfer of the gas component through oil and water can occur at different orders in time and at time scales that differ by several orders of magnitude . The local-volume-conserving level-set model has shown good computational performance , in three-phase systems; thus, it provides a good option for determining bubble pressures. Finally, versatile computational fluid dynamics methods that solve an advection–diffusion equation numerically on a grid present another simulation approach. , However, for ripening, these methods would suffer from high computational costs due to the large difference in time scales for diffusion and interface dynamics.…”