Evaluating hysteresis mechanisms through pore networks simulations

Hysteresis in capillary pressure and relative permeability relationships with saturation degree, is an important phenomenon essential for accurately predicting multiphase retention and flow in porous media, relevant for hydrological applications such as groundwater management and soil water dynamics. The observed hysteretic loops reflect complex, history-dependent interactions between fluids and pore structures.

We used three-dimensional (3D) pore network models to systematically investigate how media properties (pore size distribution, correlation, and connectivity) and different imbibition and drainage modes determine the combined and decoupled quasi-static mechanisms of hysteresis: geometric ink bottle effects, non-wetting fluid trapping, and network-dependent effects arising from complex pore accessibility. We decoupled these mechanisms by leveraging controlled, simulated drainage and imbibition scenarios (e.g., invasion vs random percolation, bond vs site-governed displacement, and with vs without trapping).

The different mechanisms present distinct effects on the hysteretic loops, where trapping primarily affects retention curves at high wetting saturation (S_w) and dramatically reduces wetting phase relative permeability (k^W_r). Ink bottle hysteresis, driven by pore geometry, is visible across the entire capillary head (h_c) range. In contrast, network hysteresis significantly shapes the retention (S_w(h_c)) loop and drives k_r(S_w) hysteresis at low S_w.

Furthermore, the impact of these mechanisms is highly dependent on media structure. Increasing pore size distribution variability enhances non-wetting phase trapping volume while mitigating ink bottle effects. Correlation between pore bodies' and throats' radii strongly increases the impact of trapping on k^W_r. Conversely, increasing connectivity (i.e., higher coordination number) reduces the trapped fluid fraction, and generally mitigates ink bottle and network hysteresis effects in the two-phase retention.

These results provide necessary mechanistic understanding, supporting the inverse interpretation of measured hysteretic loops to deduce the underlying topological structure of porous media.