Geometric, topological and petrophysical measurements of hysteresis in water-wet and mixed-wet Bentheimer sandstones

Cyclic drainage and imbibition processes in porous media are characterized by the saturation state, flow pathway, and hysteresis. These processes play a crucial role in applications such as geological storage of carbon dioxide and hydrogen. While classical empirical hysteresis models have been shown to adequately describe bounding behaviour (primary drainage and imbibition), their accuracy in capturing the scanning and intermediate saturation regions (where most field processes occur) is not well understood. In this work, we investigate the impact of hysteresis and trapping at intermediate saturations during multiple cycles of drainage and imbibition in a water-wet and mixed-wet Bentheimer sandstone. Using fast 4D micro-CT imaging, we characterise the dynamic evolution of topological (Euler characteristics), geometric (interfacial area) and petrophysical (relative permeability) measurements. For both wetting conditions, across all measures, we find that hysteresis is present in the primary bounding cycle, but subsequent cycles are fully reversible along the same hysteretic pathway. Yet, we see clear differences in the trapping extent in the water-wet and mixed-wet samples, indicating that if the primary hysteresis behaviour is well characterised, subsequent cyclic behaviour is predictable. Finally, we show that the relative permeability hysteresis extent is well predicted by changes in the specific interfacial area, highlighting the key role of geometric hysteresis in multiphase flow.