Pore-scale mechanisms for hysteresis in capillary-dominated drainage and imbibition (Invited)

Understanding the flow of two immiscible fluid phases through the pore space of rocks and soils is a complex problem involving fluid dynamics, surface science and geometry. Invariably one fluid, usually water, preferentially coats the solid surface. Of major interest, and a significant challenge for multiphase fluid modelling, is the fact that the flow displays hysteresis: the measured difference in pressure between fluids (the capillary pressure) is higher when the water is draining out than when it is imbibing back in. One consequence of this hysteresis include capillary trapping, of relevance to waterflooding oil recovery and geosequestration of CO¬2. While several models have attempted with mixed success to capture this hysteresis at the macro-scale, no consensus yet exists on its pore-scale causes. The current work makes use of X-ray micro-tomography (MCT) data to help identify resolve this question. We first enumerate the different mechanisms that have been proposed in the literature for this hysteresis. We break these mechanisms into two categories: local mechanisms that may occur inside a single geometric feature (such as a pore or throat) and those that may only be observed within some sort of labyrinth. Local mechanisms include contact angle hysteresis (induced by surface, chemistry surface roughness and/or interface pinning), the ink-bottle effect and geometric bistability associated with the stability of both main terminal menisci and arc menisci in a constrictive pore space element. The nonlocal mechanisms are fluid trapping (possible for both wetting and nonwetting fluids) and structure hysteresis arising from heterogeneity in the pore system. Our results arise from the analysis of imaging experiments in which water was successively imbibed into and drained from small samples of Bentheimer sandstone and unconsolidated grain packs. The experiment were conducted at both synchrotron and laboratory X-ray MCT facilities, with both imaging setups having sufficient resolution to show the distribution of the two fluid phases throughout the material while also capturing fluid menisci in individual pores. We apply a range of topological and geometric analyses to these images, most notably the calculation of Betti numbers, interfacial area and interfacial curvature, to quantify the differences in fluid configurations during imbibition and drainage. While our results suggest that geometric bistability may be the primary cause for hysteresis in these particular experiments, we discuss the significance of our results and suggest that far more work is needed before definitive conclusions can be drawn.