Homogeneous Porous Media Research Articles

Accounting for mesoscale geometry and intra-yarn fiber volume fraction distribution on 3D angle-interlock fabric permeability

Understanding resin flows within 3D interlock fabrics involves addressing a dual-scale flow problem. Indeed, the fluid can flow through inter-yarn channels, characterized by a unit cell mesoscale morphology, but also within yarns considered as homogeneous equivalent porous media. The former is assumed to follow the Stokes’ law while the latter be related to the Darcy’s law, directly linked to the microscopic intra-yarn fiber volume fraction (FVF) field. In this work, a coupled Stokes–Darcy steady-state flow within a 3D woven textile, modeled at mesoscale, is solved through a finite element monolithic approach with a mixed velocity-pressure formulation, stabilized by the Variational MultiScale Method (VMS) and implemented in the Z-set software. The fabric permeability tensor is then computed without any assumptions on its nature and analyzed both through its diagonal components, its eigenvectors and eigenvalues. The main contribution of this study lies in examining the influence of variations of the inter-yarn porous medium morphology, through textile compaction and geometrical reduction to prevent edge flows, and the intra-yarn permeability (from complete field to unique value) on the overall fabric permeability.

Adsorption of Pb(II) by UV-aged microplastics and cotransport in homogeneous and heterogeneous porous media

To investigate the adsorption effects of aged microplastics (MPs) on Pb(II) and their co-transport properties in homogeneous (quartz sand) and heterogeneous (quartz sand with apple branches biochar) porous media, we explored the co-transport of UV-irradiated aged MPs and coexisting Pb(II) along with their interaction mechanisms. The UV aging process increased the binding sites and electronegativity of the aged MPs' surface, enhancing its adsorption capacity for Pb(II). Aged MPs significantly improved Pb(II) transport through homogeneous media, while Pb(II) hindered the transport of aged MPs by reducing electrostatic repulsion between these particles and the quartz sand. When biochar, with its loose and porous structure, was used as a porous medium, it effectively inhibited the transport capacity of both contaminants. In addition, since the aged MPs cannot penetrate the column, a portion of Pb(II) adsorbed by the aged MPs will be co-deposited with the aged MPs, hindering Pb(II) transport to a greater extent. The transport experiments were simulated and interpreted using two-point kinetic modeling and the DLVO theory. The study results elucidate disparities in the capacity of MPs and aged MPs to transport Pb(II), underscoring the potential of biochar application as an effective strategy to impede the dispersion of composite environmental pollutants.

Real-time visualization of carbon quantum dot transport in homogeneous and heterogeneous porous media

The environmental behavior and mechanisms of CQDs in 2D homogeneous and heterogeneous porous media were revealed in real time by light transmission visualization.

Magnetohydrodynamic Flow of Immiscible Jeffrey Fluids Through a Horizontal Porous Cylinder

This paper investigates the steady and fully developed magnetohydrodynamic (MHD) flow of two nonmiscible Jeffrey fluids in a horizontal cylinder filled with a homogenous porous medium. A constant pressure gradient drives the flow in both regions, and a uniform magnetic field is applied transversely to the flow direction. Instead of the usual no‐slip condition, the linear Navier slip is used as a boundary condition on the cylinder’s surface, whereas the usual continuity conditions of velocity and shear stress are presumed at the fluid–fluid interface. The equations describing the problem under consideration are mathematically formulated and transformed into nondimensional forms with the proper choice of nondimensional variables. Analytical solutions have been obtained by solving the transformed equations of motion. The effects of different nondimensional parameters involved in the flow problem, including the magnetic number, Jeffrey parameter, Darcy number, ratio of viscosities, Reynolds number, slip parameter, and pressure gradient, on the velocity in each region are studied, and the results are exhibited graphically. In addition, numerical values for stress at the wall and volume flow rates are calculated for various fluid parameters and shown in tables. It is noticed that an increase in the values of the magnetic number and viscosity ratio reduces the velocity of the fluid, whereas increasing the Jeffrey parameters, Darcy number, Reynolds number, slip parameter, and pressure gradient enhances fluid velocity. Furthermore, the most favorable agreement was observed between the results of this study and the results of the previous studies.

Моделирование геомиграции радионуклидов с учетом цепочек радиоактивного распада в коде GeRa: верификация численной схемы и особенности расчетов

The paper describes a numerical scheme implemented in the GeRa code to solve the problem of radionuclide transport in porous medium taking into account radioactive decay chains. It is based on a scheme of splitting by physical processes and the use of separate modules for solving transport and radioactive decay chain problems. Verification of the numerical scheme was performed using an analytical solution for a specific case of the problem formulation in a homogeneous porous medium. The study explores the error introduced into the numerical solution by the use of the splitting scheme. The study provides recommendations regarding the selection of appropriate parameters for the numerical scheme to calculate the transport of nuclide chains with different sorption properties.

Modeling and semi-analytical solution for immiscible and miscible fingers formation during enhanced oil recovery

ABSTRACT The fingering phenomenon arises during the secondary and tertiary oil recovery processes when injected fluid (water, gases, nano/biomaterials, or polymer particles) shoots through a porous medium at a relative speed. Oil recovery is influenced by various factors including the fluid type, capillary pressure, permeability, and porous material structure. All these elements play crucial roles in determining the success and efficiency of the oil recovery process. Many scientists have debated the fingering phenomenon from different perspectives. Here, we developed mathematical models with and without considering mass flow rates of oil and water for an inclined oil layer flowing through a homogenous porous medium to generate immiscible fingers. Furthermore, a mathematical model of miscible viscous finger formation with carbonated water injection (flooding) during the enhanced oil recovery process (EOR) has been analyzed in this paper. To solve each of these mathematical models, we used the recently developed approach known as the Method of Directly Defining the inverse Mapping (MDDiM). We found approximate solutions to the nonlinear partial differential equations (PDEs), which describe each modeling of the fingering phenomenon in a homogeneous porous medium by incorporating gravitational effects for several types of flooding and discussed the effects of the saturation rate.

Investigation of the temperature field in gas condensate reservoirs taking into account thermodynamic effects

Based on modeling of non-isothermal filtration of a multiphase fluid, taking into account thermohydrodynamic effects and heat of condensation, the formation of a temperature field in a homogeneous porous medium at different pressures at the onset of condensation is studied. A numerical model of one-dimensional two-phase filtration taking into account the phase transition is obtained. Testing of the numerical solution was carried out on the basis of a well-known analytical solution for non-isothermal two-phase filtration in a reservoir taking into account mass transfer. The change in gas flow rate during condensate precipitation and the change in temperature over time on the well wall are considered. It is shown that, depending on the pressure of the onset of condensation (the radius of the onset of condensation in the formation), a different rate of formation of the temperature field in the formation is observed after the well is put into operation: the temperature anomaly can be positive, negative or inverse. The results of numerical experiments can be used when planning field studies in gas condensate wells.

Physics-Informed Neural Networks with Periodic Activation Functions for Solute Transport in Heterogeneous Porous Media

Simulating solute transport in heterogeneous porous media poses computational challenges due to the high-resolution meshing required for traditional solvers. To overcome these challenges, this study explores a mesh-free method based on deep learning to accelerate solute transport simulation. We employ Physics-informed Neural Networks (PiNN) with a periodic activation function to solve solute transport problems in both homogeneous and heterogeneous porous media governed by the advection-dispersion equation. Unlike traditional neural networks that rely on large training datasets, PiNNs use strong-form mathematical models to constrain the network in the training phase and simultaneously solve for multiple dependent or independent field variables, such as pressure and solute concentration fields. To demonstrate the effectiveness of using PiNNs with a periodic activation function to resolve solute transport in porous media, we construct PiNNs using two activation functions, sin and tanh, for seven case studies, including 1D and 2D scenarios. The accuracy of the PiNNs’ predictions is then evaluated using absolute point error and mean square error metrics and compared to the ground truth solutions obtained analytically or numerically. Our results demonstrate that the PiNN with sin activation function, compared to tanh activation function, is up to two orders of magnitude more accurate and up to two times faster to train, especially in heterogeneous porous media. Moreover, PiNN’s simultaneous predictions of pressure and concentration fields can reduce computational expenses in terms of inference time by three orders of magnitude compared to FEM simulations for two-dimensional cases.

Microscale Simulation of Carbon Support Structure Degradation in Polymer Electrolyte Fuel Cell

Understanding the mechanism of Polymer electrolyte fuel cell (PEFC) degradation plays an important role in improving fuel cell performance and durability. For the PEFC system, the structure of catalyst layers (CLs) is the critical component that determines cell performance. The PEFC degradation due to the reduction of carbon on the CLs has been investigated in previous studies [1]. In our past studies, we focused on the actual heterogeneous porous structure of catalyst layer. From these results, it was found that mass transport performance of oxygen and proton in heterogeneous porous catalyst layer, which consists of carbon support, ionomer and void space, is much lower than that of theoretical prediction in homogeneous porous media [2-5]. In addition, it depends on the structure of carbon black, the coating structure of ionomer and the local distribution of these materials. Thus, it is important to understand and to predict the carbon support structure change by degradation because this structural degradation strongly affect the mass transport performance. In this work, the effect of CLs porous carbon support degradation on cell performance is investigated by microscale simulation.The CLs structures, consisting of porous carbon, ionomer, and Pt, are created by our previous study multi-block method [2,6]. In our simulation, we focus on studying the effect of CLs' beginning-of-life (BOL) and end-of-life (EOL) structure in the degradation process. The CLs creation procedure is illustrated in Fig. 1. Firstly, CLs structure are created by packing CB and covered ionomer and Pt. The amount of ionomer and Pt are assumed as constant during the degradation process. Therefore, the amount of carbon is reduced in EOL structure. In this study, various CLs structures with decreasing of carbon volume are constructed. Furthermore, the mechanical stress distribution under compression condition was simulated in each structure to understand the effect of framework of carbon on local porosity in catalyst layer. The effect of carbon corrosion in CLs is investigated by calculating the cell performance of PEFC of each CLs structure by ORR mass transport and electrochemical reaction calculation with our previous method [6].The cell performance is significantly decreased by reducing carbon. The degradation mechanism of PFEC is explained by degradation of not only effective surface area but also the porous structure change which affect oxygen diffusion performance. Moreover, compared with BOL structure the apparant thickness of covered ionomer layer is higher in EOL structures because of carbon corrosion and constancy of ionomer. Hence, the higher oxygen diffusion resistance in secondary pore and ionomer layer occur in CLs degradation structures. The effect of this dynamic structure change on cell output performance will be reported in this presentation.Acknowledgements:This research was supported by the New Energy and Industrial Technology Development Organization (NEDO), Japan, grant number P20003-20001327-0.

Pore-scale natural convection in cavities filled with randomly distributed heat-conducting particles

Three-dimensional numerical simulations were carried out to analyze natural convection in a differentially heated cubic cavity filled with spherical particles. Three models were considered: a fluid-only case for reference, a homogeneous porous media approximation, and a heterogeneous model that considered the actual structure of the solid particles. DEM (discrete element method) simulations were used to generate a realistic particle distribution for the construction of volumetric meshes for the heterogeneous model. The impact of thermal conduction through the solid particles was evaluated by varying the solid to fluid ratio ( K * ) within the range 0.02 − 50 for Rayleigh numbers between 103 and 105. Additionally, different number and diameter of the particles inside the cavity were evaluated. The results of the homogeneous approximation indicate a continuous decrease in the Nusselt number (Nu) as K * increases, associated with a higher effective thermal conductivity and the pressure drop. However, the more realistic heterogeneous model predicted the opposite trend. For K * <1, solid particles acted as thermal insulators, impeding fluid flow, while for K * > 1 conduction heat transfer between the isothermal walls and the particles was highly efficient and the particles surface area acted like extensions of the isothermal walls, facilitating heat transfer to the fluid phase, especially at lower Rayleigh values.

Study of imbibition phenomenon in homogeneous porous medium model for oil recovery with temporal-fractional approach

In this article, the phenomenon of countercurrent imbibition in a specific displacement method occurs within a dipping homogeneous porous medium. This phenomenon plays a vital role in the process of oil recovery, which motivates our analysis. To overcome the difficulties associated with the nonlinear partial differential equation governing the countercurrent imbibition phenomenon, we have been using two distinct methods: the natural transform decomposition method and the variational iteration transform method with their convergence analysis for solutions. These techniques give different perspectives and enable us to obtain approximate solutions. Notably, both the proposed methods demonstrate the potential for substantial production of oil during the secondary oil recovery process in the petroleum industry. The obtained results by the proposed methods show the efficiency in optimizing the oil recovery rate.

CHARACTERISTIC METHOD FOR SOLVING FILTRATION PROBLEM

During construction, a liquid solution of a grout or waterproof filler is pumped into porous rock to improve its properties. The filtration of a suspension moving at a variable speed in a porous medium is simulated. A one-dimensional problem of filtration in a homogeneous porous medium with a curvilinear concentration front of suspended and retained particles is considered. For the numerical solution of the problem by the method of finite differences, the method of characteristics is used. The transition to characteristic variables allows one to straighten the front and construct a discrete grid with a constant step. When calculating the solution using an explicit difference scheme, additional points are used that do not coincide with the grid nodes. A detailed description of the algorithm for calculating a solution at the grid nodes and an example of a numerical solution of the problem are given.

Compositional Streamline-Based Modeling of Polymer Flooding Including Rheology, Retention, and Salinity Variation.

The chemical enhanced oil recovery (CEOR) technology that is most used worldwide is polymer flooding due to its proven commercial success at field scale, maturity, and versatility to combine with other technologies. So, there has been an increasing interest in expanding its applicability to more unfavorable mobility ratio conditions and adverse environments (such as high-temperature, high-salinity carbonate reservoirs, pH-sensitive polymers, and formations with active clays). Therefore, a requirement for successful field application is to find the design parameters of the process that balance material requirements and oil recovery benefits in a cost-effective manner, which is usually done through reservoir modeling. Polymer flooding predictive tools normally require detailed information and are based on time-consuming field reservoir simulations. Thus, for effective project management, a quick and sound tool is needed to screen for polymer flooding applications without giving up key physical-chemical phenomena that govern the oil recovery. In this research, we developed a two-dimensional polymer flooding model based on the streamlines approach. This is an alternative to having a multidimensional practical tool thoroughly representing the physical and chemical behavior of polymer flooding by considering key phenomena such as rheology behavior (shear thinning and shear thickening), salinity variations, permeability reduction, and polymer adsorption. Previously published streamline multidimensional models for polymer flooding lack the integrated modeling of the above-mentioned key phenomena. Additionally, the models to represent rheology and retention phenomena in the proposed tool consider a more complete description than the present streamline-based simulators. For the construction of streamlines, we considered a black oil formulation to estimate the pressure and saturation 2D distribution by applying the implicit in pressure and explicit in saturation method, coupled with an explicit formulation for the 2D composition computation. For saturation-composition along the streamlines, the 1D practical tool incorporated represents the polymer flooding key phenomena. The numerical algorithm used by the streamline-based tool is supported by laboratory experiments for waterflooding in homogenous porous media, analytical results for waterflooding in heterogeneous media, polymer flooding field scale simulation cases, and a CMG-STARS model built as a reference for waterflooding in both media (homogenous and heterogeneous) and for polymer flooding. The practical tool developed contributes to simplifying the upscaling from laboratory observations to field applications with better fitted numerical simulation models and to determining favorable scenarios; thus, it could assist in understanding how key parameters affect oil recovery without performing time-consuming CEOR simulations.

Macroscopic model for generalised Newtonian inertial two-phase flow in porous media

A closed macroscopic model for quasi-steady, inertial, incompressible, two-phase generalised Newtonian flow in rigid and homogeneous porous media is formally derived. The model consists of macroscopic equations for mass and momentum balance as well as an expression for the macroscopic pressure difference between the two fluid phases. The model is obtained by upscaling the pore-scale equations, employing a methodology based on volume averaging, the adjoint method and Green's formulation, only assuming the existence of a representative elementary volume and the separation of scales between the microscale and the macroscale. The average mass equations coincide with those for Newtonian flow. The macroscopic momentum balance equation in each phase expresses the seepage velocity in terms of a dominant and a coupling Darcy-like term, a contribution from interfacial tension effects and another one from interfacial inertia. Finally, the expression of the macroscopic pressure difference is obtained in terms of the macroscopic pressure gradient and body force in each phase, and interfacial terms that account for capillary effects and inertia, if present when the interface is not stationary. All terms involved in the macroscale equations are predicted from the solution of adjoint closure problems in periodic representative domains. Numerical predictions from the upscaled models are compared with direct numerical simulations for two-dimensional configurations, considering flow of a Newtonian non-wetting fluid and a Carreau wetting fluid. Excellent agreement between the two approaches confirms the pertinence of the macroscopic models derived here.

Characterizing the Transport and Surface Affinity of Extracellular Vesicles Isolated from Yeast and Bacteria in Well-Characterized Porous Media.

Extracellular vesicles (EVs) are membrane-bounded, nanosized particles, produced and secreted by all biological cell types. EVs are ubiquitous in the environment, operating in various roles including intercellular communication and plant immune modulation. Despite their ubiquity, the role of EV surface chemistry in determining transport has been minimally investigated. Using the zeta (ζ)-potential as a surrogate for surface charge, this work considers the deposition of EVs from the yeast, Saccharomyces cerevisiae, and two bacterial species, Staphylococcus aureus and Pseudomonas fluorescens, in well-characterized porous medium under various background conditions shown to influence the transport of other environmental colloidal particles: ionic strength and humic acid concentration. The affinity of S. cerevisiae EVs for the porous medium (glass beads) appeared to be sensitive to changes in ionic strength, as predicted by colloid stability (Derjaguin, Landau, Verwey, and Overbeek or DLVO) theory, and humic acid concentration, while P. fluorescens EVs deviated from DLVO predictions, suggesting that mechanisms other than charge stabilization may control the deposition of P. fluorescens. Calculations of attachment efficiency from these deposition studies were used to estimate EV transport using a clean-bed filtration model. Based on these calculations, EVs could be transported through such homogeneous porous media up to 15 m.

Nonlinear evolution dam problems in an unbounded domain

The aim of this paper is to give an existence theorem of a solution of the nonlinear evolution dam problem , associated with compressible or incompressible flows, in an unbounded domain of . We approximate by a sequence of bounded domains , and we consider a regularized problem on the bounded domain which has a unique solution. Now, we pass successively to the limit in , as and then as to get a solution to . Note that in a previos study of Gilardi and Kröner [7], an existence of a solution was given by using a different technique for the evolution dam problem related to an incompressible flow through a homogeneous porous medium.

Numerical study of liquid–liquid displacement in homogeneous and heterogeneous porous media

Immiscible liquid–liquid displacement is a fundamental problem in fluid mechanics and has many applications like, for instance, enhanced oil recovery. One of the most valuable methods to increase oil recovery is injecting a fluid into the reservoir to displace the oil, and the primary motivation of this work is to evaluate the liquid–liquid displacement in homogeneous and heterogeneous porous media. We carried out a direct numerical simulation of liquid–liquid displacement in three different porous media: medium I, II, and III. The medium I is homogeneous. Medium II is heterogeneous, in which the diameter of the spheres reduces from the bottom to the top boundary. Finally, in medium III, the diameter of the spheres is randomly distributed all over the domain. The three media were composed of spheres and had the same mean porosity. We tracked the liquid interface front over time until the breakthrough to compute the mass entrapped as a function of viscosity ratio and capillary number. The sweep efficiency increases when the displacing liquid viscosity also increases. The role played by the capillary number is more complex. In medias I and II, the entrapped mass rises with the capillary number. For a specific condition in medium III, when the displacing liquid is more viscous than the displaced one, the opposite can occur, i.e., the entrapped mass decreases with the capillary number. Beyond the capillary number and viscosity ratio, the sweep efficiency strongly depends on the kind of medium. Mainly, the entrapped liquid is smaller in the homogeneous medium.

Isothermal CO2 injection into water-saturated porous media: Lattice-Boltzmann modelling of pulsatile flow with porosity, tortuosity, and optimal frequency characterization

The Lattice Boltzmann Method (LBM) is used to simulate the isothermal injection of CO2 into a water-saturated, homogeneous porous medium. The complex multiphase flow is modeled using the 2D-pseudopotential Shan-Chen multiphase LBM. This work proposes a unique fluid-pulse technology similar to the one applied to enhance oil recovery with CO2 sequestration. This technology is different from classical CO2 sequestration in aquifers and, to our knowledge, has never been used before. The primary purpose is to investigate whether our LBM simulation allows the introduction of fluid-pulse CO2 injection patterns similar to those reported in the literature on hydrocarbon reservoirs and to evaluate the benefit of using such a technique compared to classical uniform injection. First, our simulations consider a transient homogeneous flow with uniform inlet velocity to determine the natural frequency of the instabilities triggered downstream of the interstitial pore array. Then, CO2 is injected at the inlet in a pulsating regime, varying the forcing frequency near and far from the natural frequency to determine its effect on CO2 penetration. Results demonstrate that a pulsatile injection effectively enhances CO2 sequestration in aquifers when forced with a characteristic frequency. However, this frequency resulting after CO2 is injected to displace the water differed from the natural frequency preliminarily obtained from the homogeneous water flow. Injecting at the characteristic frequency has proven an effective technique for boosting CO2 penetration into a water-saturated porous medium, with a significant enhancement estimated between 1.5% and 16% for a range of pulsatile amplitudes between 1% and 10%.

Numerical simulation of flow-diverting stent: comparison between branches in bifurcation brain aneurysm.

The usage of flow-diverting stents in the treatment of intracranial aneurysms is widespread due to their high success and low complication rates. However, their use is still not officially recommended for bifurcation aneurysms, as there is a risk of generating ischemic complications due to the reduced blood flow to the jailed branch. Many works utilize computational fluid dynamics (CFD) to study how hemodynamic variables respond to flow diverter placement, but few seem to use it to verify flow variation between branches of bifurcation aneurysms and to aid in the choice of the best ramification for device placement. This investigation was performed in the present work, by comparing wall shear stress (WSS) and flowrates for a patient-specific scenario of a middle cerebral artery (MCA) aneurysm, considering device placement on each branch. A secondary objective was to follow a methodology that provides fast results, envisioning application to daily medical practice. The device was simplified as a homogeneous porous medium, and extreme porosity values were simulated for comparison. Results suggest that stent placement on either branch is both safe and effective, significantly reducing WSS and flow into the aneurysm while maintaining flow to the different ramifications within acceptable thresholds.

Irregular and stepwise behaviour of hydraulic fracturing: insights from linear cohesive crack modelling with maximum stress criterion

There is growing evidence that fracture advancement in saturated and dry porous media may be smooth or stepwise. In the stepwise behaviour, there are also pressure oscillations in saturated porous materials, as predicted by Biot’s theory. The type of behavior depends on the specifications of the problem and material properties. Not all the adopted numerical models are capable of capturing stepwise behaviour. While non-local fracturing models are perfectly adapted to capture the stepwise behaviour, it is shown that cohesive models are also capable to model such a behaviour. In fact, it is necessary to satisfy a consistency condition for the numerical solution; in other words, the fracture advancement/time-stepping algorithm must not impose a constraint on the tip advancement speed. This is peculiar to cohesive models because there the unit of fracture advancement is specified beforehand, while in other models, such as peridynamics, it is an outcome of the analysis. In inhomogeneous media, it can be expected to capture irregular results from hydraulic fracturing (HF); however, homogeneous media can also show such behaviour as presented herein. In this study, the eXtended Finite Element Method (XFEM) is used in conjunction with a cohesive crack model to investigate the stepwise or irregular behaviour of HF in homogeneous saturated porous media both under quasistatic and dynamic conditions. The results clearly show that the extent of irregularity depends directly on the intensity of dynamic effects in the problem. Moreover, fracture forerunning is one of the reasons of the stepwise fracture growth in the solutions. Although the results are obtained by XFEM, the conclusions are not restricted to this particular numerical method, and the findings can provide useful insights into the necessary aspects of the numerical algorithms for dynamic HF modelling.