Cycle injection schemes are often encountered in underground gas storage, and the involved hysteresis directly impacts storage and extraction efficiency. The geological formation generally has hierarchical features containing multiple-level pore sizes. Nevertheless, we still lack a comprehensive understanding of this phenomenon and the pore-scale mechanism behind the geometry affects saturation hysteresis and its cyclic responses. In this work, by 3D printing technology, we fabricate a hierarchically structured porous media chip with dual permeability and uniform one for comparison. Gas-liquid injection cycles are performed to investigate the impact of hierarchical structure on invasion behavior. The phase morphology shows the preferential invasion in 1st-order structure and the capillary trapping in 2nd-order structure, which are supported by the phase saturation at each level of the hierarchical structure. Furthermore, ganglion motion is suppressed in the hierarchical chip while they are significant in the uniform one. Through analysing local invasion behaviors, the connect-jump invasion mode is identified as the primary reason for this suppression. Then, the hysteresis effect is quantified based on the Land model, revealing a weaker saturation hysteresis effect in the hierarchical structure compared with the uniform structure. Finally, the upward trend of relative permeability with saturation is fitted by the van Genuchten model. The model parameter in the hierarchical structure is higher than that in the uniform structure, which is caused by extra pore space in 2nd-order structure. The findings improve the understanding of the hysteresis effect and can promote optimizing strategies for storage and extraction in underground hydrogen storage (UHS).

The stability of relaxation techniques has been studied for strongly coupled fluid-structure interaction (FSI) with application to a cantilever immersed in channel flow. The fluid is governed by Navier-Stokes equations for incompressible flow condition using turbulence modelling and the solid is governed by the equation of motion with compressible material modelling. The applied kinematic description is Lagrangian for the solid and Eulerian for the fluid. The coupling of the state solvers is achieved by the Arbitrary Lagrange-Euler procedure which involves a mesh motion solver and the FSI procedure is stabilised by relaxation. It is shown that the stability can be related to the frequency shift caused by FSI and they follow the same rate for the shape factor of the structure with an offset. This correlates well to theoretical results but also show that for given mesh resolution, all relaxations fail for sufficient high-frequency shift. We also propose a continuation technique to stabilise the solution near the instability region, which also improves the efficiency and can be integrated easily for the black-box FSI solution procedure.