Fluid-saturated Porous Medium Research Articles

MHD Mixed Convection Flow Over a Permeable Vertical Flat Plate Embedded in a Darcy–Forchheimer Porous Medium

AbstractThe purpose of this paper is to describe the stead MHD mixed convection flow over a permeable vertical flat plate embedded in a Darcy–Forchheimer porous medium. Using appropriate similarity variables, the partial differential equations are transformed into ordinary (similar) differential equations, which are numerically solved using the bvp4c function in MATLAB. The numerical results are used to present graphically and in tables, illustrations of the reduced skin friction, reduced Nusselt number, velocity, and temperature profiles. Dual (upper and lower branch) solutions are discovered in this exciting analysis. Although numerous studies on the mixed convection past a vertical plate embedded in a fluid-saturated porous medium exist, none of the researchers have focused on the Darcy–Forchheimer flow with asymptotic solutions. The behavior of the flow and heat transfer has been thoroughly analyzed with the variations in governing parameters, such as Darcy–Forchheimer $$G,$$ G , suction/injection $$S$$ S , MHD $$M,$$ M , and mixed convection $$\lambda$$ λ parameters.

Comparative analysis of double and single porosity effects on SH-wave induced vibrations in periodic porous lattices

The manuscript presents a novel study comparing the impact of single and double porosity on horizontally polarized shear wave (SH-wave) propagation in corrugated elastic void materials. The considered mathematical model comprises two cases; the first one depicts SH-wave propagation through a void porous layer having creased boundaries and resting over a heterogeneous anisotropic fluid-saturated fractured porous half-space, whereas according to the second case, heterogeneous anisotropic fluid-saturated porous semi-infinite medium without fractures has been considered. In both cases, rigidity and density of the half-space vary quadratically with depth. The separable variable method is used to attain the complex frequency equation for each case that leads to two different dispersion relations associated with two distinct wave fronts. The first wave front depends on the void parameters, whereas the second wave front defines the propagation of SH-waves in an elastic layer without void pores. In each case, the complex dispersion relation has been separated into two equations that illustrate the dispersion and attenuation properties of SH-waves. Using the variations in the inhomogeneity, position, fluctuation, flatness, total porosity, and anisotropy parameters, case I and case II have been compared in each graphical execution. In addition, the surface response of shear stress and displacement have been implemented graphically.

Physics-informed neural network for turbulent flow reconstruction in composite porous-fluid systems

This study explores the implementation of physics-informed neural networks (PINNs) to analyze turbulent flow in composite porous-fluid systems. These systems are composed of a fluid-saturated porous medium and an adjacent fluid, where the flow properties are exchanged across the porous-fluid interface. The segregated PINN model employs a novel approach combining supervised learning and enforces fidelity to flow physics through penalization by the Reynolds-averaged Navier-Stokes (RANS) equations. Two cases were simulated for this purpose: solid block, i.e. porous media with zero porosity, and porous block with a defined porosity. The effect of providing internal training data on the accuracy of the PINN predictions for prominent flow features, including flow leakage, channeling effect and wake recirculation was investigated. Additionally, L2 norm error, which evaluates the prediction accuracy for flow variables was studied. Furthermore, PINN training time in both cases with internal training data was considered in this study. Results showed that the PINN model predictions with second-order internal training data achieved high accuracy for the prominent flow features compared to the RANS data, within a 20% L2 norm error of second-order statistics in the solid block case. In addition, for the porous block case, providing training data at the porous-fluid interface showed errors of 18.04% and 19.94% for second-order statistics, representing an increase in prediction accuracy by 7% compared to without interface training data. The study elucidates the impact of the internal training data distribution on the PINN training in complex turbulent flow dynamics, underscoring the necessity of turbulent second-order statistics variables in PINN training and an additional velocity gradient treatment to enhance PINN prediction.

Nanoparticle shape factor impact on double diffusive convection of Cu-water nanofluid in trapezoidal porous enclosures: A numerical study

Enclosures that contain both fluid and porous regions are utilized in various industries and geophysical processes to enhance heat and mass transfer. These enclosures find applications in fields such as geothermal engineering, drying of porous solids, cooling of electronics, metal solidification, and many others. In line with the motivation behind these applications, the present study explores double diffusion in the naturally convective flow of water-based nano fluid saturated in the trapezoidal porous enclosure and containing Copper (Cu) nano particles. The impact of uniformly applied radiative heat flux and nano particle shape factor is also accounted. A numerical investigation was carried out using a finite difference methodology integrated into a computational MATLAB code for numerical simulation. The simulation aimed to study the effect of nanoparticle shape factor on the effectiveness of a porous medium, which is exposed to two distinct objectives: enhancing heat transfer and optimizing mass transfer within a fluid-saturated porous medium. This research conducts a meticulous parametric exploration, underscoring the pivotal roles played by Darcy number (Da), nanofluid shape factor (m), Rayleigh number (Ra), thermal radiation (Rd), buoyancy ratio (Nr), and Lewis number (Le) in shaping the dynamics of flow, heat, and concentration transfer. The analysis of Nusselt and Sherwood numbers reveals that changing the shape of nano-particles from spheres to bricks increases the heat flux and mass flux coefficients by approximately 0.33% and 1.37% respectively. The results show a significant increase in Nusselt and Sherwood numbers, with blade-shaped nanoparticles demonstrating approximately a 2.97% and 10.82% improvement, respectively, compared to sphere-shaped nanoparticles. The outcome of this analysis yields an exhaustive dataset encompassing Nusselt and Sherwood numbers can be written as mathematical functions based on the parameters we talked about earlier.

Natural Convection in a Spherical Porous Annulus with Diathermal Partition Wall

The influence of the diathermal partition wall on natural convection in a fluid-saturated porous medium has been numerically studied in the present paper. A concentric diathermal wall of infinitesimal thickness is inserted in the fluid-saturated spherical porous annulus. Due to the flow symmetry along the vertical axis, only half of the sphere is considered for simulation. A Successive Accelerated Replacement Scheme has been used to solve the Darcy flow model using the finite difference method. The average Nusselt number value decreases with the presence of a partition wall within the fluid-saturated spherical porous annulus. The percentage decrease in average Nusselt number value depends upon the position of the diathermal wall within the width of the spherical annulus. There is about a 50% reduction in the average Nusselt number with a diathermal partition wall for the cases considered in this work. The results of the present investigation will help in the proper design of porous insulation in spherical porous containers for the storage of thermal energy.

Influence of periodicity on natural convection in a square porous cavity due to non-uniform heat under LTNE state

In this article, the influence of the local thermal non-equilibrium (LTNE) state on free convection in a square cavity filled with fluid-saturated porous medium is investigated numerically. The steady-state flow is induced due to sinusoidal heat distributed on the side walls of the cavity and insulated of the horizontal walls. The coupled flow governing equations are solved numerically by using the finite volume method (FVM) consisting of the SIMPLER (Semi-Implicit Method for Pressure Linked Equation Revised) Algorithm. The numerical simulations of temperature and stream-function contours are carried out for the non-Darcy model. The developed code is validated with existing numerical and present computed results for the case of a square enclosure associated with non-uniform heat source. Then, the present numerical results are analyzed over a range of physical parameters, like periodicity parameter ( N ≥ 1 ), interface heat transfer coefficient ( 10 − 2 ≤ H ≤ 10 2 ), porosity scaled thermal conductivity ratio ( 10 − 2 ≤ γ ≤ 10 2 ), with a fixed Rayleigh number ( Ra = 10 6 ), Darcy number ( Da = 10 − 4 ), Prandtl number (Pr = 0.71), and porosity ( ε = 0.8 ). To study the impacts of these key parameters on the fluid flow behavior and isotherm patterns of fluid as well as solid phase in the porous-square enclosure. From present numerical experiments that the structure of flow is controlled by multicellular structure with rotating clockwise and anticlockwise directions in the entire results. The flow dynamics are highly affected by the periodicity parameter (N) under LTNE circumstances. The characteristics of the local Nusselt number have the point of inflection and the maximum magnitude of it increases with N. The significant effect of H is found on the heat transfer rate of fluid phase but it is negligible on the heat transfer rate of solid phase. However, the influence of γ is found reverse in nature on the heat transfer rate of fluid as well as solid phase when as compared to the effect of H.

Pressure Effects on Plane Wave Reflection and Transmission in Fluid-Saturated Porous Media

Pressure Effects on Plane Wave Reflection and Transmission in Fluid-Saturated Porous Media

Frequency-dependent elastic properties of fracture-induced VTI rocks in a fluid-saturated porous and microcracked background

Fractures are widely distributed underground. The stiffness matrix of fractured rocks has been extensively investigated in a fluid-saturated porous background medium. However, the existing stiffness models only incorporate the attenuation mechanism of wave-induced fluid flow (WIFF). For macroscopic fractures, the elastic scattering (ES) of fractures cannot be ignored. To alleviate this issue, a frequency-dependent stiffness matrix model is developed, including the mesoscopic WIFF between fractures and background (FB-WIFF), the microscopic squirt flow, and the macroscopic ES from the fractures. By combining the far-field scattered wavefields of normal incident P and SV waves with the linear slip theory, the dynamic full-stiffness matrices for fracture-induced effective vertically transversely isotropic rocks in a fluid-saturated porous and microcracked background are derived. Then, the P, SV, and SH-wave velocities and attenuation can be obtained through the Kelvin-Christoffel equation. The results indicate that the FB-WIFF mechanism significantly affects the velocities and attenuation of the P and SV waves but has almost no effect on the SH wave, whereas the squirt flow and ES mechanisms affect the velocities and attenuation of all the P, SV, and SH waves. For validation, the model is compared with existing models and previous experimental ultrasonic data.

The influence of slip boundary effect on the propagation of shear horizontal guided waves in a fluid-saturated porous medium

The influence of slip boundary effect on the propagation of shear horizontal guided waves in a fluid-saturated porous medium

Lattice Boltzmann Simulations of Non-Homogeneous Li–O2 Battery Cathode: The Effect of Spatial and Temporal Porosity Variations

Abstract The porosity of the cathode in a lithium–oxygen battery is a crucial parameter that influences oxygen transport and active surface area availability. This study explores various cathode models with different initial porosity distributions and analyzes the porosity evolution during discharge. The objective is to maximize the active surface area utilization of the cathode and increase the battery’s discharge capacity. The simulations employ a recently developed lattice Boltzmann method (LBM) model proposed by Chen et al. (2017, “Simulation of Double Diffusive Convection in Fluid-Saturated Porous Media by Lattice Boltzmann Method,” Int. J. Heat Mass Transfer, 108, pp. 1501–1510), which is capable of handling spatial and temporal variations in diffusion coefficient values. The results demonstrate that a hierarchical porous cathode provides a better specific capacity than a uniform porous cathode with the same average initial porosity. The specific capacity increases as the magnitude of initial porosity variation in the domain increases. Furthermore, incorporating oxygen channels improves oxygen transport in the cathode and offers a better specific capacity than the hierarchical porous cathode. A combination of hierarchical porous media and oxygen channels delivers the best specific capacity among all the other cathode models, as it efficiently balances oxygen transport and active surface area.

Characteristics of poroelastic deformation and dissipation of heat and pore pressure in fluid-saturated porous strata

Although there has been extensive research on the coupling process, some unexplored issues still deserve deeper exploration. In this study, our focus is on analysing the characteristics of poroelastic deformation and dissipation in thermal-hydraulic-mechanical (THM) coupling in fluid-saturated porous media. First, a coupled THM model is established as an extension of our previous study, where a solution strategy is presented based on the finite Fourier transform. The formulation is a unified framework that is compatible with the existing methods, and can be naturally decoupled into the simpler HM or TM version. Then, it is verified by benchmark study. The coupling behaviours of four different geomaterials (clay, salt rock, granite and marble) are analysed and compared in detail. We focus on several aspects: (1) dominance of hydraulic and thermal effects in different geomaterials; (2) evolution of pore pressure and heat dissipation; (3) effect of geomaterial properties on poroelastic deformation; (4) characteristics of drainage effect, cooling effect and expansion relaxation. It demonstrates that the proposed model is competent to capturing the essentials in coupling process. The insights gained from the simulations are intuitive and consistent with the existing knowledge. Further study and dimensional analysis reveal that the mechanisms in the coupling process are attributed to the combined effects of the temporal evolution in poroelastic deformation and dissipation.

The influence of thermal dispersion on the initiation of convective instability in Prats flow through a low permeability porous medium

This study investigates the effect of thermal dispersion on the onset of convective thermal instability in a fluid-saturated porous medium. A horizontal throughflow is considered along the layer, which is bounded by two uniformly heated horizontal rigid impermeable walls from above and below. The two walls are maintained at a constant temperature gradient, which is responsible for the buoyancy to occur and thus making the convection happen. Considering thermal dispersion, we have examined how it affects the natural convective instability occurring due to the thermal buoyancy. This paper proposes an entirely new perspective on the accountability of thermal dispersion in the convective instability. The consideration of Prats flow causes the instability in monotonic and oscillatory modes, where in some of the cases, the convection initiates in the oscillatory modes.

Effect of Temperature Gradients and DC Electric Field on Electrothermal Convection in a Rotating Layer of Walter's-B Fluid Saturated Porous Media

Thermal convection in fluid-saturated porous media has diverse applications across geothermal energy utilisation, thermal insulation engineering, grain storage and understanding geodynamic processes. The thermal convection's physics is crucial for optimising the thermofluid system, improving energy efficiency, and enhancing our understanding of natural phenomena. The study examines how the initiation of electrothermal convection in a rotating viscoelastic fluid layer (Walter's B) is influenced by basic temperature gradients and a uniform vertical DC electric field, considering three different types of velocity boundary conditions: free-free, rigid-rigid, and lower rigid and upper free. By applying an electric field to a fluid, studying electrothermal convection helps engineers design effective cooling systems for electronics. The eigenvalue problem is solved by using the Galerkin technique. The Galerkin method is a widely used numerical technique for solving eigenvalue problems. The DC electric field effect exhibits a more stabilising effect for free-free boundaries than rigid and rigid-rigid boundaries. Moreover, the linear temperature profile exhibits a more stabilising effect than the parabolic temperature profile. The control of electrothermal convection on the system with the impact of other physical parameters is also discussed.

On Poro-hyperelastic Torsion

The paper examines the torsion of a solid cylinder composed of a fluid-saturated porous medium with a hyperelastic porous skeleton. The general formulation of the problem is followed with applications to special cases where the strain energy function for the skeletal behavior is described by either a neoHookean or an Ogden-type hyperelastic behavior. The analytical developments involve the numerical solution of the governing equations followed by a computational treatment of the problems using the ABAQUS™ finite element code. The time-dependent mechanics of the twisted cylinder is examined for the instantaneous short-term behavior as well as the long-term behavior when the excess fluid pressures generated during the application of a finite twist have dissipated.

Inferring rock strength and fault activation from high-resolution in situ Vp/Vs estimates surrounding induced earthquake clusters

Fluid injection/extraction activity related to hydraulic fracturing can induce earthquakes. Common mechanisms attributed to induced earthquakes include elevated pore pressure, poroelastic stress change, and fault loading through aseismic slip. However, their relative influence is still an open question. Estimating subsurface rock properties, such as pore pressure distribution, crack density, and fracture geometry can help quantify the causal relationship between fluid-rock interaction and fault activation. Inferring rock properties by means of indirect measurement may be a viable strategy to help identify weak structures susceptible to failure in regions where increased seismicity correlates with industrial activity, such as the Western Canada Sedimentary Basin. Here we present in situ estimates of Vp/Vs for 34 induced earthquake clusters in the Kiskatinaw area in northeast British Columbia. We estimate significant changes of up to ±4.5% for nine clusters generally associated with areas of high injection volume. Predominantly small spatiotemporal Vp/Vs variations suggest pore pressure increase plays a secondary role in initiating earthquakes. In contrast, computational rock mechanical models that invoke a decreasing fracture aspect ratio and increasing fluid content in a fluid-saturated porous medium that are consistent with the treatment pressure history better explain the observations.

The Elder Problem with Reactive Infiltration Effects

The occurrence of buoyancy-driven flow and reactive solute transport in a fluid-saturated porous medium can be induced by either natural processes or human activities. Typical examples include the groundwater salinization in carbonate-rock aquifers and the acid treatment of oil wells in petroleum drilling industry. In this paper, the classical Elder problem of buoyancy-driven convection in two-dimensional porous media is extended to include the local chemical interactions between the solute in the pore liquid (e.g. salt such as NaCl or acids such as HCl and HCl/HF mixtures) and the solid space of the porous medium (e.g. minerals such as calcite and dolomite). Effects of the geochemical processes on the flow and mass transport are investigated. For the reactive, strongly solute-driven case in the regime dominated by the diffusive mass transport, a decrease in the net solute concentration is found as compared to the non-reactive case. This decrease is pronounced at higher values of the Damköhler number when the solute reaction rate becomes larger than the solute diffusion rate. Furthermore, the flow structure is affected by products generated by the chemical reaction when the Rayleigh number for the products is sufficiently high. In that case, numerical simulations show the formation of diluted fluid tongues exhibiting damped periodic oscillations about a nonzero mean. The results are obtained using the pseudospectral numerical method, verified against the analytical solution for the non-reactive, purely diffusive case.

Effect models for the stationary Navier–Stokes fluid in a porous medium with different scales

In this paper, we investigate an incompressible flow through a thin corrugated domain fill with fluid saturated porous medium. The porous medium flow is governed by Navier–Stokes model. The thickness of the domain is assumed to be aɛ and the solid part is supposed to be periodical cylinders of size ɛ. We rigorously derive different asymptotic models by comparing the relation between ɛ and aɛ. To prove the main results, we employ the homogenization technique based on the generalized Poincaré inequality.

Biot's theory-based dynamic equation modeling using a machine learning auxiliary approach

Abstract Characterizing seismic wave propagation in a fluid-saturated porous media well enhances the precision of interpreting seismic data, bringing benefits to understanding reservoir properties better. Some important indicators, including wave dispersion and attenuation, along with the wavefield, are widely used for interpreting the reservoir, and they can be obtained from a rock physics model. In existing models, some of them are limited in scope due to their complexity, for example, numerical solutions are difficult or costly. In view of this, this study proposes an approach of establishing equivalent dynamic equations of existing models. First, the framework of the equivalent model is derived based on Biot's theory, while the elastic coefficients are set as unknown factors. The next step is to use deep neural networks (DNNs) to predict these coefficients, and surrogate models of unknowns are established after training DNNs. The training data is naturally generated from the original model. The simplicity of the equation forms, compared to the original complex model and some other equivalents such as the viscoelastic model, enables the framework to perform wavefield simulation easier. Numerical examples show that the established equivalent model can not only predict similar dispersion and attenuation, but also obtain wavefields with small differences. This also indicates that it may be sufficient to establish an equivalent model only according to dispersion and attenuation, and the cost of generating such data is very small compared to simulating the wavefield. Therefore, the proposed approach is expected to effectively improve the computational difficulty of some existing models.

Effects of confining pressure and pore pressure on multipole borehole acoustic field in fluid-saturated porous media

In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated porous media under stress. Based on the acoustoelastic theory of fluid-saturated porous media, the field equation of fluid-saturated porous media under the conditions of confining pressure and pore pressure and the acoustic field formula of multipole source excitation in open hole are given. The influences of pore pressure and confining pressure on guided waves of multipole borehole acoustic field in fluid-saturated porous media are investigated. The numerical results show that the phase velocity and excitation intensity of guided wave increase significantly under the confining pressure. For a given confining pressure, the phase velocity of the guided wave decreases with pore pressure increasing. The excitation intensity of guided wave increases at low frequency and then decreases at high frequency with pore pressure increasing, except for that of Stoneley wave which decreases in the whole frequency range. These results will help us get an insight into the influences of confining pressure and pore pressure on the acoustic field of multipole source in borehole around fluid-saturated porous media.

Near-field seismoacoustic wave scattering due to an irregular interface: a unified framework

SUMMARY Near-field seismoacoustic scattering must be considered across various domains, including marine seismic exploration, ocean acoustics and marine seismic engineering. This is a complex process due to the fluid–solid interaction between seawater and the seabed, particularly when the seabed is saturated with fluid. The interaction between sea fluid, saturated porous seabed and solid bedrock must also be considered. In this study, seawater and dry bedrock are treated as generalized saturated porous media with porosity of one and zero, respectively. The coupling between seawater, saturated seabed and dry bedrock can be analysed within a unified framework of generalized saturated porous media. Therefore, we proposed an efficient, unified method to address the challenges posed by near-field seismoacoustic scattering. This method comprises free field wave motion computation, which is used to provide input for scattering analysis. It also introduces a unified computational framework for modelling the wave propagation in the water-saturated seabed-bedrock system, and local transmitting boundary are used to account for the effect of an infinite domain. First, the differential equation of the generalized saturated porous media is discretized using lumped mass-based FEM, and the ordinary differential equation is integrated in time using an explicit scheme. Then, the equations for the motion of the nodes on the interface between two generalized saturated porous media with various porosity are derived. These equations are suitable for special cases such as fluid–solid interface, fluid-saturated porous media interface and saturated porous media-solid interface. To demonstrate the validity and feasibility of the proposed approach, a 1-D problem is considered, and the obtained response is verified using an analytical solution. Then, we compute the cases of a vertically incident plane P wave onto a 2-D basin-like fluid–solid structure, and compared the synthetic seismograms with results reported by other researchers. In this study, the findings of our proposed approach satisfy the continuity requirements at the interface and are consistent with those obtained using the reflection/transmission matrix method. Additionally, a 3-D site with basin-like terrain was analysed. The proposed approach treats the fluid, saturated porous media and solid in a unified framework, and has high efficiency due to lumped mass matrix-based explicit finite element and local transmitting artificial boundary. Furthermore, our approach can be easily implemented in parallel, making it suitable for solving large-scale seismoacoustic scattering problems.