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A theoretical and numerical study of complex sliding flows of yield-stress fluids is presented. Yield-stress fluids are known to slide over solid surfaces if the tangential stress exceeds the sliding yield stress . The sliding may occur due to various microscopic phenomena such as the formation of an infinitesimal lubrication layer of the solvent and/or elastic deformation of the suspended soft particles in the vicinity of the solid surfaces. This leads to a ‘stick–slip’ law which complicates the modelling and analysis of the hydrodynamic characteristics of the yield-stress fluid flow. In the present study, we formulate the problem of sliding flow beyond one-dimensional rheometric flows. Then, a numerical scheme based on the augmented Lagrangian method is presented to attack these kind of problems. Theoretical tools are developed for analysing the flow/no-flow limit. The whole framework is benchmarked in planar Poiseuille flow and validated against analytical solutions. Then two more complex physical problems are investigated: slippery particle sedimentation and pressure-driven sliding flow in porous media. The yield limit is addressed in detail for both flow cases. In the particle sedimentation problem, method of characteristics – slipline method – in the presence of slip is revisited from the perfectly plastic mechanics and used as a helpful tool in addressing the yield limit. Finally, flows through model and randomized porous media are studied. The randomized configuration is chosen to capture more sophisticated aspects of the yield-stress fluid flows in porous media at the yield limit – channelization.

We show that the return‐point memory of cyclic macroscopic trajectories enables the derivation of a thermodynamic framework for quasistatically driven dissipative systems with multiple metastable states. We use this framework to sort out and quantify the energy dissipated in quasistatic fluid‐fluid displacements in disordered media. Numerical computations of imbibition–drainage cycles in a quasi‐2D medium with gap thickness modulations (imperfect Hele‐Shaw cell) show that energy dissipation in quasistatic displacements is due to abrupt changes in the fluid‐fluid configuration between consecutive metastable states (Haines jumps), and its dependence on microstructure and gravity. The relative importance of viscous dissipation is deduced from comparison with quasistatic experiments. Plain Language Summary Fluid flow into a porous material filled with another is not only an everyday process (gardening, stains in fabrics, or printing) but is also a key process affecting the water cycle, contamination in soils and storage of energy or hazardous waste in the subsurface. These flows are controlled by the energy of the fluids, and its dissipation during their advancement, making the knowledge of energy dissipation crucial to our ability to predict these phenomena. However, to date there is no rigorous way to evaluate this energy. This paper describes a novel method that overcomes this challenge, explaining how the properties of the medium affect dissipation and showing why even for very slow flows the viscous energy (i.e., related to rapid fluid motion) still makes a difference. Key Points Rigorous account of the microscopic physics allows to compute the energy dissipated between consecutive two‐phase configurations We link the microscopic origins of hysteresis and dissipation to the macroscopic pressure‐saturation behavior Quasistatic pressure‐driven experiments point to a secondary contribution of viscous dissipation during Haines jumps

Visualising fluid flow in porous media using optical techniques is challenging due to the inability to see through the medium. Here, we present an experimental methodology based on shadowgraphy to investigate the dynamic spreading of convective plumes in saturated transparent porous media made of glass beads. The saturated porous medium can be tuned transparent by matching the refractive index of the solid glass beads to that of the saturating fluid mixture. The proposed technique allows to investigate the essential elements of convective mixing within a porous medium using miscible fluids. We also describe a method to determine the velocity of convective plumes as they propagate. Our experimental results show that the density difference achieved during convection significantly affects the convective front velocity of the plumes. This is significant because it allows to quantitatively predict the intensity of convective mixing in porous media from the speed of the convective front. Article Highlights Shadowgraphy has been successfully used to investigate fluid flow in transparent porous media. Convective front velocities are used to evaluate quantitatively convective mixing in porous media. In the fluid flow regime of our experiment, we observed a super-linear scaling of the convective front velocity and density difference.

Recent advances in deep neural networks have shed new light on physics, engineering, and scientific computing. Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots. The physics-informed neural network (PINN) is currently the most general framework, which is more popular due to the convenience of constructing NNs and excellent generalization ability. The automatic differentiation (AD)-based PINN model is suitable for the homogeneous scientific problem; however, it is unclear how AD can enforce flux continuity across boundaries between cells of different properties where spatial heterogeneity is represented by grid cells with different physical properties. In this work, we propose a criss-cross physics-informed convolutional neural network (CC-PINN) learning architecture, aiming to learn the solution of parametric PDEs with spatial heterogeneity of physical properties. To achieve the seamless enforcement of flux continuity and integration of physical meaning into CNN, a predefined 2D convolutional layer is proposed to accurately express transmissibility between adjacent cells. The efficacy of the proposed method was evaluated through predictions of several petroleum reservoir problems with spatial heterogeneity and compared against state-of-the-art (PINN) through numerical analysis as a benchmark, which demonstrated the superiority of the proposed method over the PINN.

With the rapid development of deep learning neural networks, new solutions have emerged for addressing fluid flow problems in porous media. Combining data-driven approaches with physical constraints has become a hot research direction, with physics-informed neural networks (PINNs) being the most popular hybrid model. PINNs have gained widespread attention in subsurface fluid flow simulations due to their low computational resource requirements, fast training speeds, strong generalization capabilities, and broad applicability. Despite success in homogeneous settings, standard PINNs face challenges in accurately calculating flux between irregular Eulerian cells with disparate properties and capturing global field influences on local cells. This limits their suitability for heterogeneous reservoirs and the irregular Eulerian grids frequently used in reservoir. To address these challenges, this study proposes a physics-informed graph neural network (PIGNN) model. The PIGNN model treats the entire field as a whole, integrating information from neighboring grids and physical laws into the solution for the target grid, thereby improving the accuracy of solving partial differential equations in heterogeneous and Eulerian irregular grids. The optimized model was applied to pressure field prediction in a spatially heterogeneous reservoir, achieving an average L2 error and R2 score of 6.710 × 10−4 and 0.998, respectively, which confirms the effectiveness of model. Compared to the conventional PINN model, the average L2 error was reduced by 76.93%, the average R2 score increased by 3.56%. Moreover, evaluating robustness, training the PIGNN model using only 54% and 76% of the original data yielded average relative L2 error reductions of 58.63% and 56.22%, respectively, compared to the PINN model. These results confirm the superior performance of this approach compared to PINN.

Geologic subsurface energy storage, such as porous-media compressed-air energy storage (PM-CAES) and underground hydrogen storage (UHS), involves the multi-phase fluid transport in structurally disordered or heterogeneous porous media (e.g., soils and rocks). Furthermore, such multi-phase fluid transport is likely to repeatedly occur due to successive fluid injections and extractions, thus, resulting in cyclic drainage–imbibition processes. To complement our preceding study, we conducted a follow-up study with microfluidic pore-network devices with a square solid shape (Type II) to further advance our understanding on the effect of the pore shape (aspect ratio, Type I: 5–6 > Type II: ~1), pore-space heterogeneity (coefficient of variation, COV = 0, 0.25, and 0.5), and flow rates (Q = 0.01 and 0.1 mL/min) on the repetitive two-phase fluid flow in general porous media. The influence of pore shape and pore-space heterogeneity were observed to be more prominent when the flow rate was low (e.g., Q = 0.01 mL/min in this study) on the examined outcomes, including the drainage and imbibition patterns, the similarity of those patterns between repeated steps, the sweep efficiency and residual saturation of the nonwetting fluid, and fluid pressure. On the other hand, a higher flow rate (e.g., Q = 0.1 mL/min in this study) appeared to outweigh those factors for the Type II structure, owing to the low aspect ratio (~1). It was also suggested that the flow morphology, sweep efficiency, residual saturation, and required pressure gradient may not severely fluctuate during the repeated drainage-–imbibition processes; instead, becoming stabilized after 4–5 cycles, regardless of the aspect ratio, COV, and Q. Implications of the study results for PM-CAES and UHS are discussed as a complementary analysis at the end of this manuscript.

Fluid injection in a porous medium is the underlying mechanism for many applications in the fields of groundwater hydraulics, hydrology and hydrogeology, and geo-environmental engineering and in the oil and gas industry. Fluid flow experiments in porous media with a viscous fluid at varying injection rates were conducted in a modified Hele-Shaw setup. The granular media were three-dimensional bio-cemented sands of various grain sizes across various cementation levels, generating a matrix of various hydraulic conductivities, porosities, and strengths. The fluid injection experiments showed that a cavity-like fracture developed, which transitioned to crack-like fractures at higher cementation levels (hence, higher strength). As the flow rate increased, less infiltration was evident and higher breakdown pressure was observed, with propagation pressure reducing to zero. It was harder to induce an opening in cemented specimens with higher hydraulic conductivity and a larger pore network despite their lower strength due to excessive infiltration dominance, which inhibited the build-up of pressure required to generate a fracture. The results of this study suggest that, when designing fluid injection programs, the combined effects of hydraulic conductivity and strength need to be carefully considered.

Compressed air energy storage (CAES) technology has been re-emerging as a viable energy storage option to address challenges coming from the mismatch between renewable energy sources and energy demands. Various geologic formations, such as hard rock caverns, depleted oil/gas reservoirs, and saline aquifers, have been considered as the alternative of salt dome caverns for CAES. Storing compressed air in either depleted oil/gas reservoirs or saline aquifers involves two-phase fluid flow in porous media. Moreover, the drainage-imbibition process is likely to be repeated numerous cycles during the CAES operation. In this regard, a thorough understanding of the two-phase fluid flow during the cyclic injection and withdrawal of compressed air is critical to predict the performance of CAES in porous media and to improve its efficiency. This study investigates the repetitive two-phase fluid (water/oil) flow using polydimethylsiloxane-based pore-network micromodels. Two different geometries, Type I with circular solids and Type II with square solids were prepared to represent an unconsolidated and/or partially consolidated sandstone and a fracture network of carbonate rock. During repetitive drainage-imbibition cycles, it was observed that the occupation efficiency of the non-wetting fluid (water) converged to a narrow range for Type I model, while it showed a pronounced fluctuation for Type II, which was partly due to the low residual saturation of the non-wetting fluid during the imbibition process. Besides, the prevalent displacement modes of wetting and non-wetting fluids at the pore-scale were noticeably different between the two pore structures, which were manifested in the unpredictable pattern of non-wetting fluid flow for Type II over the extended cycles. Sweep efficiency and residual saturation in Type I were greater than those in Type II; however, an analysis of effective sweep efficiency and effective residual saturation yielded an opposite result. It implies that the actual efficiency of non-wetting fluid invasion is higher in Type II, and the Type II geometry can accommodate more non-wetting fluid in a given reservoir volume during the charge period. Moreover, more non-wetting fluid can be discharged back for energy regeneration. In conclusion, the geometry of porous media has a great influence on the efficiency of repetitive drainage-imbibition cycles of two-phase fluid flow in porous media, and thus more elaborate study is needed to gain the confidence on the cyclic efficiency of CAES in porous media.

We study numerical methods for solving a non-stationary mixed Stokes-Darcy problem that models coupled fluid flow and porous media flow. A decoupling approach based on interface approximation via temporal extrapolation is proposed for devising decoupled marching algorithms for the mixed model. Error estimates are derived and numerical experiments are conducted to demonstrate the computational effectiveness of the decoupling approach.

We investigate viscous fluid flows and concurrent fluid-driven deformations in porous media. The hydro-mechanically (H-M) coupled pore-network model (PNM) is developed, which combines the two-dimensional square-lattice PNM and block-spring model. The single-/two-phase flows into saturated deformable porous media are simulated through iterative two-way coupling method in H-M coupled PNM. A comparison between simulations and laboratory observations on flow patterns, solid deformation behaviors, and pressure responses ensures the validity of our H-M coupled PNM in both single-/two-phase flows. Parametric studies using the validated model examine the effects of mechanical coupling, stiffness of solid particles, the viscosity of invading fluids, injection flow rate, and degree of disorder during immiscible viscous fluid injection. The viscous fluid-driven deformation increases the pore throat size and hence reduces the injection pressure. In particular, the viscosity of invading fluid significantly alters the patterns of fluid propagation and solid deformation, along with a transition from the viscous fingering to the stable displacement with increasing viscosity. Moreover, the structural disorder in porous networks magnifies the irregular flow pattern, the pressure fluctuation associated with Haines jumps, and the poromechanical deformation. The particle-level force analysis delineates two distinct regimes: fluid invasion with no deformation and drag-driven deformation, which depends on the balance between the seepage drag force and the skeletal force. The presented results contribute to a better understanding of the H-M coupled fluid flows during the injection of viscous fluids into disordered-deformable porous media.