Pore-Scale Simulation of Relative Permeability Hysteresis from a Workflow of Level-Set and Lattice-Boltzmann Methods: The Case of Consolidated Media with Low Pore-to-Throat Aspect Ratio

Abstract We present a workflow, based on level-set and lattice-Boltzmann methods, for numerical estimation of relative permeability and capillary pressure curves with hysteresis in capillary-dominated flow on segmented 3D rock images. Calculation of relative permeability from rock images has commonly been limited to studies of the bounding hysteresis loop and conventional porous media. Here, we demonstrate the workflow on an almost unexplored case, a consolidated sandstone with low pore-to-throat aspect ratio, and obtain a complex relative permeability hysteresis behavior, consistent with the few studies available for such media. The pore-scale simulations include primary drainage, followed by the main bounding hysteresis loop and scanning curves for secondary drainage and secondary imbibition. We also explore the impact of initial saturation after primary drainage on hysteresis and phase trapping. The relative permeability hysteresis is larger for the non-wetting phase than for the wetting phase, yet the extent of both decreases with increasing initial wetting-phase saturation. For the non-wetting-phase relative permeability, imbibition and drainage curves may cross, while scanning curves cross each other and exhibit a more significant hysteresis than the bounding loop. The role of trapped ganglia makes secondary processes different from primary. The behavior complies with hysteresis in phase connectivity, in which snap-off/coalescence breaks/recovers pathways. The results deviate significantly from the nested hysteresis loops seen for unconsolidated media and show that hysteresis in scanning curves cannot be neglected, indicating that flexible machine learning methods are better suited approaches than standard hysteresis models to implement this complex relative permeability behavior in reservoir simulators.