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We derive linear instability and nonlinear stability thresholds for a problem of thermal convection in a bidispersive porous medium with a single temperature when Darcy theory is employed in the micropores whereas Brinkman theory is utilized in the macropores. It is important to note that we show that the linear instability threshold is the same as the nonlinear stability one. This means that the linear theory is capturing completely the physics of the onset of thermal convection. The coincidence of the linear and nonlinear stability boundaries is established under general thermal boundary conditions.

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.

Finger-like protrusions that form along fluid–fluid displacement fronts in porous media are often excited by hydrodynamic instability when low-viscosity fluids displace high-viscosity resident fluids. Such interfacial instabilities are undesirable in many natural and engineered displacement processes. We report a phenomenon whereby gradual and monotonic variation of pore sizes along the front path suppresses viscous fingering during immiscible displacement, that seemingly contradicts conventional expectation of enhanced instability with pore size variability. Experiments and porescale numerical simulations were combined with an analytical model for the characteristics of displacement front morphology as a function of the pore size gradient. Our results suggest that the gradual reduction of pore sizes act to restrain viscous fingering for a predictable range of flow conditions (as anticipated by gradient percolation theory). The study provides insights into ways for suppressing unwanted interfacial instabilities in porous media, and provides design principles for new engineered porous media such as exchange columns, fabric, paper, and membranes with respect to their desired immiscible displacement behavior.

A quantitative in situ characterization of the impact of surface roughness on wettability in porous media is currently lacking. We use reservoir condition micrometer-resolution X-ray tomography combined with automated methods for the measurement of contact angle, interfacial curvature, and surface roughness to examine fluid/fluid and fluid/solid interfaces inside a porous material. We study oil and water in the pore space of limestone from a giant producing oilfield, acquiring millions of measurements of curvature and contact angle on three millimeter-sized samples. We identify a distinct wetting state with a broad distribution of contact angle at the submillimeter scale with a mix of water-wet and water-repellent regions. Importantly, this state allows both fluid phases to flow simultaneously over a wide range of saturation. We establish that, in media that are largely water wet, the interfacial curvature does not depend on solid surface roughness, quantified as the local deviation from a plane. However, where there has been a significant wettability alteration, rougher surfaces are associated with lower contact angles and higher interfacial curvature. The variation of both contact angle and interfacial curvature increases with the local degree of roughness. We hypothesize that this mixed wettability may also be seen in biological systems to facilitate the simultaneous flow of water and gases; furthermore, wettability-altering agents could be used in both geological systems and material science to design a mixed-wetting state with optimal process performance.

Bacteria in porous media, such as soils, aquifers, and filters, often form surface-attached communities known as biofilms. Biofilms are affected by fluid flow through the porous medium, for example, for nutrient supply, and they, in turn, affect the flow. A striking example of this interplay is the strong intermittency in flow that can occur when biofilms nearly clog the porous medium. Intermittency manifests itself as the rapid opening and slow closing of individual preferential flow paths (PFPs) through the biofilm–porous medium structure, leading to continual spatiotemporal rearrangement. The drastic changes to the flow and mass transport induced by intermittency can affect the functioning and efficiency of natural and industrial systems. Yet, the mechanistic origin of intermittency remains unexplained. Here, we show that the mechanism driving PFP intermittency is the competition between microbial growth and shear stress. We combined microfluidic experiments quantifying Bacillus subtilis biofilm formation and behavior in synthetic porous media for different pore sizes and flow rates with a mathematical model accounting for flow through the biofilm and biofilm poroelasticity to reveal the underlying mechanisms. We show that the closing of PFPs is driven by microbial growth, controlled by nutrient mass flow. Opposing this, we find that the opening of PFPs is driven by flow-induced shear stress, which increases as a PFP becomes narrower due to microbial growth, causing biofilm compression and rupture. Our results demonstrate that microbial growth and its competition with shear stresses can lead to strong temporal variability in flow and transport conditions in bioclogged porous media.

We numerically characterize the temporal regimes for solutal convection from almost first contact to high dissolved solute concentration in a two-dimensional ideal porous layer for Rayleigh numbers $\\mathcal{R}$ between $100$ and $5\\times 10^4$. The lower boundary is impenetrable. The upper boundary is saturated with dissolved solute and either impermeable or partially permeable to fluid flow. In the impermeable case, initially there is pure diffusion of solute away from the upper boundary, followed by the birth and growth of convective fingers. Eventually fingers interact and merge, generating complex downwelling plumes. Once the inter-plume spacing is sufficient, small protoplumes reinitiate on the boundary layer and are swept into the primary plumes. The flow is now in a universal regime characterized by a constant (dimensionless) dissolution flux $F=0.017$ (the rate at which solute dissolves from the upper boundary). The horizontally averaged concentration profile stretches as a simple self-similar wedge beneath a diffusive horizontal boundary layer. Throughout, the plume width broadens proportionally to $\\sqrt{t}$, where $t$ is (dimensionless) time. The above behaviour is parameter independent; the Rayleigh number only controls when transition occurs to a final $\\mathcal{R}$-dependent shut-down regime. For the constant-flux and shut-down regimes, we rigourously derive upscaled equations connecting the horizontally averaged concentration, vertical advective flux and plume widths. These are partially complete; a universal expression for the plume width remains elusive. We complement these governing equations with phenomenological boundary conditions based on a marginally stable diffusive boundary layer at the top and zero advective flux at the bottom. Making appropriate approximations in each regime, we find good agreement between predictions from this model and simulated results for both solutal and thermal convection. In the partially permeable upper boundary case, fluid from the convecting layer can penetrate an overlying separate-phase-solute bearing layer where it immediately saturates. The regime diagram remains almost the same as for the impermeable case, but the dissolution flux is significantly augmented. Our work is motivated by dissolution of carbon dioxide relevant to geological storage, and we conclude with a simple flux parameterization for inclusion in gravity current models and suggest that the upscaled equations could lay the foundation for accurate inclusion of dissolution in reservoir simulators.

Modeling of fluid flow in porous media is a pillar in geoscience applications. Previous studies have revealed that heterogeneity and fracture distribution have considerable influence on fluid flow. In this work, a numerical investigation of two-phase flow in heterogeneous fractured reservoir is presented. First, the discrete fracture model is implemented based on a hybrid-dimensional modeling approach, and an equivalent continuum approach is integrated in the model to reduce computational cost. A multilevel adaptive strategy is devised to improve the numerical robustness and efficiency. It allows up to 4-levels adaption, where the adaptive factors can be modified flexibly. Then, numerical tests are conducted to verify the the proposed method and to evaluate its performance. Different adaptive strategies with 3-levels, 4-levels and fixed time schemes are analyzed to evaluate the computational cost and convergence history. These evaluations demonstrate the merits of this method compared to the classical method. Later, the heterogeneity in permeability field, as well as initial saturation, is modeled in a layer model, where the effect of layer angle and permeability on fluid flow is investigated. A porous medium containing multiple length fractures with different distributions is simulated. The fine-scale fractures are upscaled based on the equivalent approach, while the large-scale fractures are retained. The conductivity of the rock matrix is enhanced by the upscaled fine-scale fractures. The difference of hydraulic property between homogeneous and heterogeneous situations is analyzed. It reveals that the heterogeneity may influence fluid flow and production, while these impacts are also related to fracture distribution and permeability. Article highlights A multilevel adaptive implicit scheme up to 4-levels adaption is presented for two-phase ow in heterogeneous fractured reservoir. Discrete fracture model is combined with an equivalent continuum approach to reduce the complexity of fracture networks. The effects of permeability, orientation, size and number of fractures on hydraulic properties are studied. A comparison study of fluid flow and numerical performance between homogeneous and heterogeneous media is conducted.

Fluid flow in porous media drives the transport, mixing, and reaction of molecules, particles, and microorganisms across a wide spectrum of natural and industrial processes. Current macroscopic models that average pore-scale fluctuations into an effective dispersion coefficient have shown significant limitations in the prediction of many important chemical and biological processes. Yet, it is unclear how three-dimensional flow in porous structures govern the microscale chemical gradients controlling these processes. Here, we obtain high-resolution experimental images of microscale mixing patterns in three-dimensional porous media and uncover an unexpected and general mixing mechanism that strongly enhances concentration gradients at pore-scale. Our experiments reveal that systematic stretching and folding of fluid elements are produced in the pore space by grain contacts, through a mechanism that leads to efficient microscale chaotic mixing. These insights form the basis for a general kinematic model linking chaotic-mixing rates in the fluid phase to the generic structural properties of granular matter. The model successfully predicts the resulting enhancement of pore-scale chemical gradients, which appear to be orders of magnitude larger than predicted by dispersive approaches. These findings offer perspectives for predicting and controlling the vast diversity of reactive transport processes in natural and synthetic porous materials, beyond the current dispersion paradigm.

This study investigates the impact of pore network characteristics on fluid flow through complex and heterogeneous porous media, providing insights into the factors affecting fluid propagation in such systems. Specifically, high-resolution or micro X-ray computed tomography (CT) imaging techniques were utilized to examine outcrop stromatolite samples of the Lagoa Salgada, considered flow analogous to the Brazilian Pre-salt carbonate reservoirs. The petrophysical results comprised two distinct stromatolite depositional facies, the columnar and the fine-grained facies. By generating pore network model (PNM), the study quantified the relationship between key features of the porous system, including pore and throat radius, throat length, coordination number, shape factor, and pore volume. The study found that the less dense pore network of the columnar sample is typically characterized by larger pores and wider and longer throats but with a weaker connection of throats to pores. Both facies exhibited less variability in the radius of the pores and throats in comparison to throat length. Additionally, a series of core flooding experiments coupled with medical CT scanning was designed and conducted in the plug samples to assess flow propagation and saturation fields. The study revealed that the heterogeneity and presence of disconnected or dead-end pores significantly impacted the flow patterns and saturation. Two-phase flow patterns and oil saturation distribution reveal a preferential and heterogeneous displacement that mainly swept displaced fluid in some regions of plugs and bypassed it in others. The relation between saturation profiles, porosity profiles, and the number of fluid flow patterns for the samples was evident. Only for the columnar plug sample was the enhancement in recovery factor after shifting to lower salinity water injection (SB) observed. •Investigating the impact of pore network characteristics on flow through heterogeneous porous media•Generating Pore Network Model (PNM) and quantifying the relationship between key features of the porous system using high-resolution CT scanning•Quantifiying the relationship between key features of the pore network for the complex porous system•Core flooding experiments coupled with medical CT scanning to assess flow patterns and oil saturation distribution

In hydromechanical applications, Darcy, Brinkman, Forchheimer and Richards equations play a central role when porous media flow under saturated and unsaturated conditions has to be investigated. While Darcy, Brinkman, Forchheimer and Richards found their equations mainly on the basis of flow observations in field and laboratory experiments, the modern Theory of Porous Media allows for a scientific view at these equations on the basis of precise continuum mechanical and thermodynamical investigations. The present article aims at commenting the classical equations and at deriving their counterparts by the use of the thermodynamical consistent Theory of Porous Media. This procedure will prove that the classical equations are valid under certain restrictions and that extended equations exist valid for arbitrary cases in their field.