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While experimental designs developed in recent decades have contributed to research on dynamic nonequilibrium effects in transient two-phase flow in porous media, this problem has been seldom investigated using direct numerical simulation (DNS). Only a few studies have sought to numerically solve Navier–Stokes equations with level-set (LS) or volume-of-fluid (VoF) methods, each of which has constraints in terms of meniscus dynamics for various flow velocities in the control volume (CV) domain. The Shan–Chen multiphase multicomponent lattice Boltzmann method (SC-LBM) has a fundamental mechanism to separate immiscible fluid phases in the density domain without these limitations. Therefore, this study applied it to explore two-phase displacement in a single representative elementary volume (REV) of two-dimensional (2D) porous media. As a continuation of a previous investigation into one-step inflow/outflow in 2D porous media, this work seeks to identify dynamic nonequilibrium effects on capillary pressure–saturation relationship (Pc–S) for quasi-steady-state flow and multistep inflow/outflow under various pressure boundary conditions. The simulation outcomes show that Pc, S and specific interfacial area (anw) had multistep-wise dynamic effects corresponding to the multistep-wise pressure boundary conditions. With finer adjustments to the increase in pressure over more steps, dynamic nonequilibrium effects were significantly alleviated and even finally disappeared to achieve quasi-steady-state inflow/outflow conditions. Furthermore, triangular wave-formed pressure boundary conditions were applied in different periods to investigate dynamic nonequilibrium effects for hysteretical Pc–S. The results showed overshoot and undershoot of Pc to S in loops of the nonequilibrium hysteresis. In addition, the flow regimes of multistep-wise dynamic effects were analyzed in terms of Reynolds and capillary numbers (Re and Ca). The analysis of REV-scale flow regimes showed higher Re (1 < Re < 10) for more significant dynamic nonequilibrium effects. This indicates that inertia is critical for transient two-phase flow in porous media under dynamic nonequilibrium conditions.

This work reviews the transient two-phase flow in porous media with engineering applications in Geotechnics. It initially overviews constitutive relationships, conventional theories, and experiments. Then, corresponding limitations are discussed according to conflicting observations and multiphase interfacial dynamics. Based on those findings, the dynamic nonequilibrium effects were so defined, which could also be abbreviated as dynamic/transient effects. Four advanced theories have already been developed to resolve these effects. This review collects them and discusses their pros and cons. In addition, this work further reviews the state-of-art in terms of experimental methods, influential factors in dynamic/transient effects, and modelling performance, as well as micromodel and numerical methods at pore-scale. Last, the corresponding geotechnical applications are reviewed, discussing their applicability in effective stress, shear strength, and deformation. Finally, the entire review is briefed to identify research gaps in Geotechnics.

The dynamic two-phase flow in porous media was theoretically developed based on mass, momentum conservation, and fundamental constitutive relationships for simulating immiscible fluid-fluid retention behavior and seepage in the natural geomaterial. The simulation of transient two-phase flow seepage is, therefore, dependent on both the hydraulic boundaries applied and the immiscible fluid-fluid retention behavior experimentally measured. Many previous studies manifested the velocity-dependent capillary pressure–saturation relationship (Pc-S) and relative permeability (Kr-S). However, those works were experimentally conducted on a continuum scale. To discover the dynamic effects from the microscale, the Computational Fluid Dynamic (CFD) is usually adopted as a novel method. Compared to the conventional CFD methods solving Naiver–Stokes (NS) equations incorporated with the fluid phase separation schemes, the two-phase Lattice Boltzmann Method (LBM) can generate the immiscible fluid-fluid interface using the fluid-fluid/solid interactions at a microscale. Therefore, the Shan–Chen multiphase multicomponent LBM was conducted in this study to simulate the transient two-phase flow in porous media. The simulation outputs demonstrate a preferential flow path in porous media after the non-wetting phase fluid is injected until, finally, the void space is fully occupied by the non-wetting phase fluid. In addition, the inter-relationships for each pair of continuum state variables for a Representative Elementary Volume (REV) of porous media were analyzed for further exploring the dynamic nonequilibrium effects. On one hand, the simulating outcomes reconfirmed previous findings that the dynamic effects are dependent on both the transient seepage velocity and interfacial area dynamics. Nevertheless, in comparison to many previous experimental studies showing the various distances between the parallelly dynamic and static Pc-S relationships by applying various constant flux boundary conditions, this study is the first contribution showing the Pc-S striking into the nonequilibrium condition to yield dynamic nonequilibrium effects and finally returning to the equilibrium static Pc-S by applying various pressure boundary conditions. On the other hand, the flow regimes and relative permeability were discussed with this simulating results in regards to the appropriateness of neglecting inertial effects (both accelerating and convective) in multiphase hydrodynamics for a highly pervious porous media. Based on those research findings, the two-phase LBM can be demonstrated to be a powerful tool for investigating dynamic nonequilibrium effects for transient multiphase flow in porous media from the microscale to the REV scale. Finally, future investigations were proposed with discussions on the limitations of this numerical modeling method.

Abstract We formulate a finite‐size scaling hypothesis to predict the global permeability of fracture networks. To validate the hypothesis, numerous discrete fracture networks are generated, and the permeability is numerically calculated. Results suggest that the dimensionless permeability, scaled by moments of local conductivity and fracture sizes and corrected by two stereological ratios, can capture variations in fracture attributes (orientations, sizes, and apertures). The universal form obtained in this study can also explain the contradictory observations where the permeability decreases or increases with the domain size of fracture networks. We show that how a clear transition point, where the permeability does not change with the domain size, is obtained from this universal form. This study provides a solid theoretical foundation to understand the connection between fracture attributes and field‐scale hydraulic properties.

Abstract Both intra-pore hydrate morphology and inter-pore hydrate distribution influence the physical properties of hydrate-bearing sediments, yet there has been no pore-scale observations of hydrate habit under pressure in preserved pressure core samples so far. We present for the first time a pore-scale micro-CT study of natural hydrate-bearing cores that were acquired from Green Canyon Block 955 in UT-GOM2-1 Expedition and preserved within hydrate pressure–temperature stability conditions throughout sub-sampling and imaging processes. Measured hydrate saturation in the sub-samples, taken from units expected to have in-situ saturation of 80% or more, ranges from 3 ± 1% to 56 ± 11% as interpreted from micro-CT images. Pore-scale observations of gas hydrate in the sub-samples suggest that hydrate in silty sediments at the Gulf of Mexico is pore-invasive rather than particle displacive, and hydrate particles in these natural water-saturated samples are pore-filling with no evidence of grain-coating. Hydrate can form a connected 3D network and provide mechanical support for the sediments even without cementation. The technical breakthrough to directly visualize particle-level hydrate pore habits in natural sediments reported here sheds light on future investigations of pressure- and temperature-sensitive processes including hydrate-bearing sediments, dissolved gases, and other biochemical processes in the deep-sea environment.