Exploring global and local minima for fluid distributions within porous media: more robust and faster computations...

Simulation of equilibrium fluid distribution within porous media is a long-standing problem required in multitude of applications. For example, the pore-network modelling is currently hampered by inability to robustly predict menisci in heterogeneously wet pores and throats. Existing analytical and semi-analytical solutions are predictive for simple pore shapes such as triangular, and do not account for varying wettability. Existing simulation methods based on energy minimization are either do not reproduce the fluid interfaces correctly - something specific to simulated annealing (SA) approach, or do not explore the energy landscape and usually stuck in local minima - something that, as we show in this paper, is a usual problem with direct flow solvers. In this work, we hypothesized that combination of simulated annealing and direct simulations using phase-field model (PFM) can address aforementioned issues. Simulations.In this work, we combine two energy minimization solutions into a single one. We first prepare a rough interface solution by minimizing surface energy with the help of SA. The results of SA and transferred into phase-field Navier-Stokes two-phase flow model with density gradient theory for interface treatment. This polishing step allows for smoothing out the interfaces and additional energy minimization. We first consider numerous simple pore shapes and then verify our approach against published experimental results. Moreover, we analyze input image effects and execution times, next we discuss possible modification of our methodology to improve it in the future.

We show that combination of SA+PFM model works much better in almost all cases compared to each vanilla model. This highlights the problem with spinodal decomposition approach which is routine used for equilibrium fluid distribution modelling. Introduction of simulated annealing not only significantly improves resulting energy due to better exploration of the energy landscape, but also quite often results in very different phase distribution patterns. In addition, the fast initial computation by SA algorithm significantly speeds up the overall procedure making it much faster than spinodal decomposition alone. We believe that our novel approach can be used to solve numerous applied problems, such as computing entry pressures under non-uniform wettability conditions, parameterization of pore-network models, simulation of CO₂ distributions after geological time passed (as based on our finding regular flow models are unable to do) since injection, and many more.