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In this paper, the linear coupled theory of thermoelasticity for nanoporous materials with a triple porosity structure based on Darcy's law and the volume fraction concept is considered. The fundamental solution of the system of steady vibration equations is constructed by means of elementary functions. Finally, some basic properties of this solution are established. [ABSTRACT FROM AUTHOR]

This article theoretically investigates the diffraction and radiation of an array of coaxial double-layer porous cylindrical structures placed on a porous seabed. The array of the structures is considered a bottom-mounted cylindrical structure with vanishing thickness. Under the assumption of a small amplitude wave theory, the hydrodynamic characteristics of an array of coaxial double-layer porous cylindrical structures are investigated. The diffraction and the radiation of the structure array are investigated using the eigenfunction expansion method, Bessel function addition theory, and Darcy's law. Analytical expressions for the velocity potentials and free-surface elevations for the diffraction and radiation of the structural array are derived. Finally, the unknown coefficients of the velocity potential are determined using the matching feature function method. After completing the validation, a detailed parameter study is conducted on the structural array, and the hydrodynamic characteristics of the structure array under the influence of different parameters are discussed and explained. Taking the horizontal layout as an example, the results show that in addition to the influence of structure parameters such as porosity, the radius ratio, and the cylinder distance on the hydrodynamic presence of the array of porous structures, the number of cylinders has a greater influence on the hydrodynamic characteristics of the array of porous structures. The calculation results of the diffraction and radiation of an array of porous structures placed on a porous seabed are closer to the actual situation, which can better understand the interaction between waves and porous structure and provide effective theoretical reference for engineers to design ocean structures. [ABSTRACT FROM AUTHOR]

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Subsurface processes are important in solving many of the grand challenges facing our society today, including the sustainable extraction of hydrocarbons, the permanent geological sequestration of carbon dioxide, and the seasonal storage of renewable energy underground. Permeability characterization of underground rocks is the critical first step in understanding and engineering these processes. While recent advances in machine learning methods have enabled fast and efficient permeability prediction of digital rock samples, their practical use remains limited since they can only accommodate subsections of the digital rock samples, which is often not representative of properties at the core‐scale. Here, we derive a novel analytical solution that approximates the effective permeability of a three‐dimensional (3D) digital rock consisting of 2 × 2 × 2 anisotropic cells based on the physical analogy between Darcy's law and Ohm's law. We further develop physics‐informed neural network (PINN) models that incorporate the analytical solution and subsequently demonstrate that the PINN equipped with the physics‐informed module achieves excellent accuracy, even when used to upscale previously unseen samples over multiple levels of upscaling. Our work elevates the potential of machine learning models such as 3D convolutional neural network for rapid, end‐to‐end digital rock analysis at the core‐scale. Key Points: We derive a novel analytical solution that approximates the permeability of a three‐dimensional (3D) digital rock consisting of 2 × 2 × 2 anisotropic cellsWe develop physics‐informed neural network (PINN) models that incorporate the analytical solution for accurate permeability upscalingThe PINN model, when applied in concert with a 3D convolutional neural network model, achieves rapid, accurate permeability prediction of large digital rock samples [ABSTRACT FROM AUTHOR]

The flow of Newtonian incompressible fluid inside a two-dimensional lid-driven cavity with two non-adherent porous square blocks was numerically studied. The non-linear governing equations, Darcy-Forchheimer-Brinkman for the porous medium and Navier-Stokes for the free fluid region, were solved using the finite element method. The streamlines and velocity profile of the fluid inside the cavity, as well as the maximum value of the stream function and the coordinates of the main vortex created, are investigated to determine the effect of the Reynolds number, the different combinations of Darcy number and the different placements of the porous squares, on the behaviour of the fluid flow. [ABSTRACT FROM AUTHOR]

This paper presents a method based on Darcy's law to determine the pressure drop between the dendrite tip and root during the formation of porosity. After verification by the measurement result of the porosity region in 30Cr15Mo1N ingot, this method is employed to investigate the change in the pressure drop with solidification pressure, considering various factors such as the second dendrite arm spacing, solid fraction, cooling rate, temperature gradient, density, liquidus temperature, and solidus temperature. The relationship between the pressure drop and solidification pressure determines the formation of porosity. The results demonstrate that as the solidification pressure increases from 0.3 to 0.7 MPa, the pressure drop decreases from 1.572 to 0.676 MPa. When the solidification pressure is below 0.6 MPa, the pressure drop consistently exceeds the solidification pressure, leading to inadequate interdendritic feeding of the molten steel and subsequent porosity formation. Conversely, when the solidification pressure ranges between 0.6 and 0.7 MPa, the pressure drop undergoes minimal change and is approximately equal to the solidification pressure, which leads to sufficient interdendritic feeding. Consequently, increasing the solidification pressure effectively suppresses the formation of porosity by reducing the hindrance to molten steel feeding and enhancing its feeding capacity. Furthermore, a more accurate determination of the constant kC was obtained to calculate the pressure drop in 30Cr15Mo1N ingot, within the range of 2.77 to 3.11. [ABSTRACT FROM AUTHOR]

Continuous semigroup theory is applied to proof the existence and uniqueness of a solution to a fluid-structure interaction (FSI) problem of non-stationary Stokes flow in two bulk domains, separated by a 2D elastic, permeable plate. The plate's curvature is proportional to the jump of fluid stresses across the plate and the flow resistance is modeled by Darcy's law. In the weak formulation of the considered physical problem, a linear operator in space is associated with a sum of two bilinear forms on the fluid and the interface domains, respectively. One attains a system of equations in operator form, corresponding to the weak problem formulation. Utilizing the sufficient conditions in the Lumer-Phillips theorem, we show that the linear operator is a generator of a contraction semigroup, and give the existence proof to the FSI problem. [ABSTRACT FROM AUTHOR]

In this paper, the coupled linear quasi-static theory of elasticity for materials with double porosity is considered in which the concepts of Darcy's law and volume fractions are proposed. The system of general governing equations is expressed in terms of the displacement vector field, the changes of the volume fractions of pores and fissures, and the changes of the fluid pressures in pores and fissures networks. By virtue of Green's identity, the uniqueness theorems of the basic internal and external boundary value problems (BVPs) are proved. The fundamental solution of the system of steady vibration equations in the theory under consideration is constructed. Then, the surface and volume potentials are constructed and their basic properties are given. Some useful singular integral operators are studied. Finally, on the basis of these results the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations. [ABSTRACT FROM AUTHOR]

Soil deformation is prone to occur in the process of the foundation pit dewatering. A large number of metro existing tunnels are located in soft soil layers. The compression of soft soil poses a threat to metro existing tunnels. Previously, plenty of research on foundation pit dewatering is focused on the hydraulic head and deformation characteristics of the aquifer. However, the law of water releasing and compression deformation of overlying soft soil has not been taken seriously. In order to study the artificial recharge groundwater effect on overlying soft clay, a three-dimensional seepage–soil deformation coupling numerical model was established. The theoretical basis of the model is Darcy's law and the principle of effective stress. A foundation pit located in Nanjing, China was selected as an example. The numerical model was used to simulate the hydraulic head and soil deformation caused by foundation pit dewatering and artificial recharge groundwater outside. The result shows that, due to the difference of hydraulic head between the aquifer and the aquitard reducing, it also has a good control effect on the deformation of the soft soil by recharging water into the aquifer. The location of recharge wells around the metro existing tunnel can control the soil deformation effectively, which could help to reduce the impact on the metro existing tunnel. [ABSTRACT FROM AUTHOR]

In order to study the influence of structural parameters of porous gas bearing and operating parameters of linear compressor on the static and dynamic performance of porous gas bearing, based on gas lubrication theory, Darcy's law and Reynolds equation, the mathematical model and simulation model of porous gas bearing of linear compressor are derived and established. The static and dynamic characteristics of the porous gas bearing of the linear compressor are studied by using Fluent software simulation. According to the simulation results, the effects of inlet pressure, porous material thickness and gas gap on the gas consumption and bearing capacity of the porous gas bearing under different eccentricities are analyzed. The results show that the higher the inlet pressure is, the larger the gas consumption and bearing capacity; the thicker the porous material is, the smaller the gas consumption and the larger the bearing capacity, the thicker the gas gap is, the larger the gas consumption and the smaller the bearing capacity. On the basis of simulation research, considering the difficulties of processing and assembly, multi-objective optimization of porous gas bearings is carried out based on response surface methodology. Taking the bearing capacity and gas consumption as the objective functions, the intake pressure is set between 0.3 and 0.5 MPa, the thickness of porous materials is set between 3 and 5 mm, and the thickness of gas gaps is set between 10 and 20 μm. While ensuring the stable operation of the linear compressor, the optimal combination of design parameters is provided for the optimal design of gas bearings used in linear compressors. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the forced convective heat transfer of power-law fluid flow through porous annular sector duct by applying the Brinkman-extended Darcy flow model. A strongly implicit procedure (SIP) is utilized to solve the algebraic momentum and energy equations which was discretized by using the finite volume method (FVM). The effects of permeability factor and power-law index corresponding to the Brinkman-extended Darcy flow model and power-law fluid, respectively, on flow and heat transfer rate are carried out numerically and graphically against different values of parameters corresponding to geometrical configuration. In the pseudo-plastic fluids, a maximum decrease of more than 1 0 0 % has been observed in f Re , whereas maximum decrease in dilatant fluid is around 3 0 % , when we increase the values of k. A decrease of 16.02% in Nu has been carried out in pseudo-plastic fluid, whereas unforeseen decrease in Nu has been observed in both Newtonian and dilatant fluids comparably pseudo-plastic fluid for particular values of k. [ABSTRACT FROM AUTHOR]

Perforating well is one of the main production wells in reservoir development. Perforating effect directly affects well production, so the optimization of perforating parameters has attracted wide attention. Because pressure difference serves as the driving force for fluid flowing from formation to wellbore, it is important to understand the composition of production pressure difference in perforating well, which can guide the optimization of perforating parameters and the evaluation of perforating effect. In order to clarify the composition of production pressure difference during the production process of perforated wells, a pressure drop model pressure drop model is established based on fluid mechanics theory, which includes a pressure drop model of formation and a pressure drop model of perforation hole. The pressure drop model of formation is firstly constructed based on the Darcy's law and the equivalent resistance method, and the pressure drop model of perforation hole is built by the fluid tube-flow theory. Secondly, the numerical calculation method is adopted to realize the coupling solution of models, and the accuracy of this model is verified by comparison of the Karakas-Tariq model. Finally, the effects of formation physical properties and perforating parameters on flow pressure drop are discussed. The results show that there is a difference of more than 2 orders of magnitude between the pressure drop generated in perforation hole and flow pressure difference, and pressure drop of perforation hole can be neglected in practical applications. Comparing with medium–high permeability reservoirs, optimizing perforation parameters in low permeability reservoirs has a more significant impact on flow pressure drop. Among perforating parameters, perforation length and perforation density have great influence on flow pressure difference, while perforation diameter and phase angle have relatively little influence. These results have certain guiding significance for optimizing perforating parameters in different permeability reservoirs. [ABSTRACT FROM AUTHOR]

Aortic dissection (AD) has a high mortality rate. About 40% of the people with type B AD do not live for more than a month. The prognosis of AD is quite challenging. Hence, we present a triphasic model for the formation and growth of thrombi using the theory of porous media (TPM). The whole aggregate is divided into solid, liquid and nutrient constituents. The constituents are assumed to be materially incompressible and isothermal, and the whole aggregate is assumed to be fully saturated. Darcy's law describes the flow of fluid in the porous media. The regions with thrombi formation are determined using the solid volume fraction. The velocity- and nutrient concentration-induced mass exchange is defined between the nutrient and solid phases. We introduce the set of equations and a numerical example for thrombosis in type B AD. Here we study the effects of different material parameters and boundary conditions. We choose the values that give meaningful results and present the model's features in agreement with the Virchow triad. The simulations show that the thrombus grows in the low-velocity regions of the blood. We use a realistic 2-d geometry of the false lumen and present the model's usefulness in actual cases. The proposed model provides a reasonable approach for the numerical simulation of thrombosis. [ABSTRACT FROM AUTHOR]

A mathematical model is presented for the process of separating air into nitrogen and oxygen in a membrane installation, in which separation occurs in dynamics on the inside and outside of a tubular porous membrane. Using numerical modeling of the said process, a distribution has been obtained for nitrogen concentration after passage through the membrane. It has been established that the permeability of the membrane tubes has a significant effect on the quality of the bleed gas and the installation ramp-up time. [ABSTRACT FROM AUTHOR]

Based on the finite-discrete element method (FDEM), this paper proposes a continuous-discrete mixed seepage model that considers the fluid exchange and the pore pressure discontinuity across the fracture. The continuous-discrete seepage model uses the cubic law to express the fluid flow in the fracture and Darcy's law to describe the pore seepage in the rock matrix. Combining the continuous-discrete mixed seepage model with the FDEM, a hydro-mechanical coupling model is constructed to solve fluid-driven fracturing of a rock mass. The continuous-discrete seepage model and hydro-mechanical coupling model update the node sharing relationship of triangular elements on two sides of the fracture during fracture propagation which sufficiently consider the influence of the fracture propagation on the pore seepage. In this paper, the analytical solutions are used to verify the model's accuracy with the help of four examples. In addition, the hydro-mechanical coupling model is used to simulate a hydraulic fracturing problem for rock mass involving a complex fracture network. According to the simulation results, this hydro-mechanical coupling model can catch fracture initiation, propagation, the interaction between hydraulic fractures and discrete fracture, as well as the evolution of pore pressure and fracture pressure. [ABSTRACT FROM AUTHOR]

Centrifugal dewatering is a common process used for solid-liquid separation in chemical industry. This process involves the intricate interaction between particles and liquid under centrifugal pressure. Accurate modeling and simulation of the kinetic process are key to optimizing the dewatering parameters. However, the feeding stage is often disregarded in most of the simulation studies, leading to obvious differences from the actual conditions in the dewatering behavior and initial solid concentration. In this study, a 1D-axisymmetric model is established to simulate the feeding and pre-dewatering stages of an inverting filter centrifuge. The simulation results at different rotating speeds agree with the experimental observations and show a significant difference compared to the model that ignores the feeding stage. Both phenomena demonstrate the method in this study is accurate and reliable. Furthermore, the effects of feeding parameters are investigated using the Sobol global sensitivity analysis method. This study provides crucial assistance for the parameters' optimization and prediction of centrifugal dewatering. [ABSTRACT FROM AUTHOR]

The linear two-dimensional problem of flexural-gravity waves generated by an oscillating rigid plate build-in a floating poroelastic plate is studied. The problem is coupled. The plate deflections and the hydrodynamics loads are determined at the same time. The liquid under the poroelastic plate is inviscid and incompressible. Dynamics of the floating plate is described by a thin elastic plate equation. Porosity of the floating plate is taken into account only through the liquid flux into the plate. The velocity of the inflow is assumed to be governed by Darcy's law being proportional to the hydrodynamic pressure at the plate/liquid interface. Two cases of the oscillating rigid plate with and without its part in the liquid are considered. The problems are solved by the Fourier transform method for non-zero porosity and by the vertical mode method for elastic plates with zero porosity. The deflection and strain distributions are analyzed depending on the excitation frequency and the porosity. Two models of floating plate porosity, where the hydrostatic pressure is included into Darcy's law (Zavyalova's model) and excluded (Meylan's model), are compared. Plate porosity induces damping to the system. It is shown that the damping rate is non-monotonic with respect to the plate porosity. [ABSTRACT FROM AUTHOR]

This article, published in Acta Polytecnica: Journal of Advanced Engineering, examines the effects of porosity and surface roughness on annular discs under squeeze film lubrication. The study uses a semi-analytical approach and the Rabinowitsch fluid model to analyze the characteristics of the discs. The findings show that the performance of annular discs is significantly influenced by porous material and radial roughness patterns. The research aims to optimize the design of these discs for specific applications, such as heat exchangers and filtration systems. The text also provides equations and mathematical formulations to understand the behavior of fluid flow within these discs. The study concludes that further research should focus on advanced materials, optimization of porous structures, and numerical modeling. The provided list of references includes research papers that cover various aspects of lubrication in different systems and materials, providing valuable insights for researchers studying tribology and engineering. [Extracted from the article]

In container production, the key issue is proper irrigation and fertilization. Typically, the water required for plant growth is supplied through an irrigation ramp system, which can also perform fertilization. The frequency of irrigation and the amount of water supplied by the ramp depends on several factors, such as the species of plants grown, the container used, the substrate, and atmospheric factors accompanying production. For effective irrigation, the substrate in the container cell must retain the supplied water long enough for plant absorption. However, any excess water should drain from the container. To optimize irrigation, it is important to determine the parameter of the water outflow speed from the container cell, which is difficult to determine. This work proposes a new solution for a station that can measure the water outflow speed from various container cells (patent application P.443675 2022). In tests, the water outflow speed was assessed for two Styrofoam container types (V150—650/312/150 mm, 74 cells, and 0.145 dm3 cell volume; and V300—650/312/180 mm, 53 cells, and 0.275 dm3 cell volume). Both were filled with a peat and perlite substrate (95/5%) using the Urbinati Ypsilon line (V150 substrate moisture 75.7 ± 1.1%, and V300 75.9 ± 2.1%, efficiency of the line 400 containers∙h−1, vibration intensity of the vibrating table—maximum acceleration 12 G). The results indicated that the water outflow speed varied between container types. The V300 container had a higher outflow speed (0.0344 cm·s−1) compared to the V150 (0.0252 cm·s−1). This discrepancy may be due to differences in dry bulk density, with a correlation of r = −0.523. The V300 had a lower actual and dry bulk density (0.418 g·cm−3; 0.079 g·cm−3) compared to V150 (0.322 g·cm−3; 0.103 g·cm−3). This highlights the need for individual selection of parameters on the backfilling line for different container types when filling. Using identical parameters for diverse containers can lead to varying substrate volume densities, impacting water outflow rates. [ABSTRACT FROM AUTHOR]

In this paper, firstly, the in situ leaching process of ionic rare earths and the mechanism of transforming effect of in situ leaching on the material composition and structure of the soil body of the slope were studied. Then, using ammonium sulfate as a leaching agent, the distribution law of rare piles of earth in minerals, water-leaching filtrate and acid-leaching filtrate in different leaching columns was analyzed, and the equilibrium relationship of each main substance in the process of elemental migration was calculated. At the same time, based on Darcy’s law to study the change rule of the permeability and strength parameters of rare earth ore bodies in the process of leaching liquid leaching. Finally, based on the results of the study, a program for managing slopes for ionic rare earth ore is proposed. It is analyzed that the total amount of ionic rare earths in the minerals and the total amount of rare earths in the water-leaching filtrate and acid-leaching filtrate after five stages of leaching are 5.5 g, 3.25 g and 5.39 g. When the leaching solution is water, 2% ammonium sulfate and 5% ammonium sulfate, the permeability coefficients of the ore body are increased to 4.12×10−3, 5.02×10−3 and 6.56×10−3, respectively.

This paper aims to analyze the problem with the study of thermal and momentum transport with entropy generation in view of the second law of thermodynamics in Magneto hydrodynamics (MHD) micropolar fluid through porous medium under the consideration of the non-Darcy model, temperature-dependent viscosity and thermal conductivity. In practical situations at higher temperatures and high speed fluid flow, it becomes reasonable to consider variable fluid flow parameters. The governing boundary layer flow equations are first converted into a coupled system of the ordinary differential equations (ODE) under the assumption of differing plate temperatures by applying appropriate similarity transformations. A shooting method has been applied to solve ordinary differential equations numerically. The last effect of microrotation, magnetic field, variable viscosity coefficient, variable thermal conductivity, etc. on momentum and thermal transport has been depicted through various graphs. The table for skin friction coefficient and Nusselt number for ideal cases has been shown to validate the model by previous findings. It is seen that K and m enhance the velocity profile on their increment opposite to this M, δ , F and Da have been found to reduce the velocity profile. Table 3 is constructed for numerical values of skin friction coefficient and Nusselt number for different values of parameters where it can be concluded that magnetic parameter M has a tendency to enhance the skin friction and heat transfer, while variable viscosity parameters have a tendency to decline the skin friction and heat transfer. [ABSTRACT FROM AUTHOR]

A mathematical model is developed for incompressible steady-state dissipative CNT-aqueous nanofluid boundary layer flow from a stretching sheet to a saturated isotropic porous medium. Three different CNT shapes (spheres, blades and platelets) are considered. Both single-walled (SWCNT) and multi-walled (MWCNT) carbon nanotubes are examined. A Darcy-Brinkman model is adopted for the porous medium and a modified viscous dissipation formulation is considered which features porous media influence in the energy conservation equation. Appropriate expressions are deployed for the CNT-modified nanofluid viscosity, density, specific heat capacity, thermal conductivity and CNT shape factor. Via similarity transformations, the governing conservation equations for mass, momentum and energy with associated boundary conditions are normalized to generate a coupled nonlinear ordinary differential boundary value problem. A numerical solution is presented with the robust MATLAB-based bvp4c method and 4th order Runge-Kutta shooting scheme. Validation with previous studies is included. Velocity, temperature, skin friction and Nusselt number are computed for a range of selected parameters. The computations show that elevation in CNT volume fraction parameter accelerates the boundary layer flow whereas increment in the Darcian (inverse permeability) parameter induces strong deceleration. MWCNTs produce higher velocities than SWCNTs. Temperature and thermal boundary layer thickness are found to be enhanced with increasing Eckert number, Darcian (inverse permeability) parameter, CNT volume fraction and CNT shape factor. Significantly greater temperatures are computed for MWCNTs. • CNT-aqueous nanofluid boundary layer flow from a stretching sheet to a saturated isotropic porous medium is modeled. • Three different CNT shapes (spheres, blades and platelets) are considered. • Single and multi-walled carbon nanotubes are accounted. • Non-linear problems are tackled analytically through bvp4c scheme. [ABSTRACT FROM AUTHOR]

The object of this study is underground gas storage facilities (UGSF). The main problem being solved is to ensure effective management of the operation process of underground gas storage facilities (UGSF) at operational and forecast time intervals. One of the main factors that affect the operating modes of UGSF is significantly non-stationary filtration processes that take place in the bottomhole zones of wells. The complexity of assessing the multifactorial impact on depression/repression around the wells affects both the speed and accuracy of calculating the mode parameters of UGSF operation. Analysis of the results of well studies revealed a significant area of uncertainty in the calculation of the filtration resistance coefficients of their bottomhole zones. A satisfactory accuracy of the result in the expected time was achieved by building a model of integrated consideration of the influence of the parameters of all the bottomhole zones of the wells on the mode of UGSF operation. It turned out that the integrated consideration of the impact on the parameters of the bottomhole zones of the wells neutralized the effect of significant changes in the filtration resistance coefficients of the wells and ensured a sufficient speed of calculation of UGSF operation modes. Simultaneous simulation of ten operating UGSFs under the peak mode of withdrawal the entire available volume of active gas takes no more than six minutes. The speed of simulation of filtration processes in the bottomhole zones of wells ensured finding the best of them according to one or another criterion of operation mode quality. As a result of the research, a model was built and implemented by software, which was tested under real operating conditions and provides optimal planning of UGSF operating modes for given time intervals. Its use is an effective tool for the operational calculation of current modes and technical capacity of UGSF for a given pressure distribution in the system of main gas pipelines. The performance of the constructed mathematical methods has been confirmed by the results of numerical experiments. [ABSTRACT FROM AUTHOR]

The permeability of mesh wicks is important for various applications, including two‐phase heat transfer. However, the understanding of the permeability of single‐layer, free‐standing mesh wicks, with liquid–gas interfaces on both sides, is limited. A novel and simpler method is presented to determine the permeability of a free‐standing wick and apply it to a representative mesh. This method involves modifying the capillary pressure via elevation and simultaneously measuring the permeability to determine the permeability‐capillary pressure relationship. When applied to a copper mesh with plain weave having undergone surface cleaning, the permeability is found to decrease as capillary pressure for deionized water increases. A dimensional analysis is presented to generalize this data for other mesh sizes with similar weaves and fluids. The behavior of mesh in application is modeled, based on the integration of Darcy's law with an analytic function fit to measured data, and parametric studies are conducted to investigate the superficial velocity of liquids through the mesh under varying driving pressures, transport lengths, and liquid viscosity, based on the obtained capillary pressure–permeability relationship. This study provides valuable insights into the transport properties of mesh wicks, with potential applications in fields such as electronics cooling, electrochemical devices, and fluid purification technologies. [ABSTRACT FROM AUTHOR]

Determination of relevant model parameters is crucial for accurate mathematical modelling and efficient numerical simulation of a wide spectrum of applications in geosciences. The conventional method of choice is the global sensitivity analysis (GSA). Unfortunately, at least the classical Monte-Carlo based GSA requires a high number of model runs. Response surfaces based techniques, e.g. arbitrary Polynomial Chaos (aPC) expansion, can reduce computational effort, however, they suffer from the Gibbs phenomena and high hardware requirements for higher accuracy. We introduce GSA for arbitrary Multi-Resolution Polynomial Chaos (aMR-PC) which is a localized aPC based data-driven polynomial discretization. The aMR-PC allows to reduce the Gibbs phenomena by construction and to achieve higher accuracy by means of localization also for lower polynomial degrees. We apply these techniques to perform the sensitivity analysis for the Stokes–Darcy problem which describes fluid flow in coupled free-flow and porous-medium systems. We consider the Stokes equations in the free-flow region, Darcy's law in the porous-medium domain and the classical interface conditions across the fluid–porous interface including the conservation of mass, the balance of normal forces and the Beavers–Joseph condition for the tangential velocity. This coupled problem formulation contains four uncertain parameters: the exact location of the interface, the permeability, the Beavers–Joseph slip coefficient and the uncertainty in the boundary conditions. We carry out the sensitivity analysis of the coupled model with respect to these parameters using the Sobol indices on the aMR-PC expansion and conduct the corresponding numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a general power form of head-loss (pressure-drop) equation and the concept of shear velocity were used to study non-Darcy filtration through coarse granular materials. Using new laboratory data, the validity of four widely-used power form pressure-drop equations were evaluated. The results indicated that for the lower size of grain diameter (d ≤ 8.7 mm) the Wilkins (in: Proceedings of the 2nd Australia-New Zealand Conference on Soil Mechanics and Foundation Engineering, Christchurch, 1956) method has predicted satisfactorily the hydraulic gradient, while for the higher size of grain diameter (d ≥ 15.6 mm), the Stephenson (Rockfill in Hydraulic Engineering, Elsevier Science Publishers B.V., Amsterdam, 1979) method predicted acceptably the pressure gradient. The results also indicated that the best estimation for the Izbash coefficient a is the Wilkins method. Finally, new correlations for friction factor, shear velocity and Reynolds number as well as new threshold limits for Darcy, partially-turbulent, and fully-turbulent flow regimes are presented and discussed. [ABSTRACT FROM AUTHOR]

Present work demonstrates the complete numerical modeling and experimental validation of transient incompressible two-phase flow during vacuum infusion (VI) in the presence and absence of high permeability media (HPM) considering gravity effects. Coupled flow modeling based on continuity equations, Darcy's law for porous media flow, including gravity effects with level set front tracking algorithm, has been developed on the multiblock-structured grid with higher-order finite-difference framework to predict the spatio-temporal preform saturation during infusion with/without HPM on the complex mold configurations. The model-predicted instantaneous change in pressure, thickness elevation, fill time, flow front positions, and influence of gravity have been validated with experiments for horizontal and vertical flat plates using pressure sensors and digital cameras. For the first time, the complete modeling and experimentation of transient VI in the presence or absence of HPM, including gravity, shows the ability to predict realistic preform saturation during VI in different mold geometry. [ABSTRACT FROM AUTHOR]

It is often highly difficult to predict the main flow path of reactive fluids in porous media with complexly distributed fractures and/or caves. Based on Darcy's law, this research defines the control domain of fractures/caves that represents the interference range of fractures/caves. This control domain can be used to identify the connectivity possibility between fractures/caves and predict the flow paths of reactive fluids at the optimal flow rate. Furthermore, after simplifying the geometry of fractures/caves, a threshold geometric aspect ratio of 20 is set to distinguish fractures and caves, concerning the flow mechanisms, by clarifying the ranges of control domains. Moreover, the control domain theory is combined with the two-scale continuum model for acidizing carbonate rocks to estimate the flow paths of acid in fractured-vuggy carbonate rocks at an optimal flow rate, thereby validating the accuracy of the reactive fluid main flow path estimation based on the control domain theory. The primary criterion to determine the reactive transport in porous media with complex fracture/cave distribution is the overlap degrees of control domains of adjacent isobaric bodies along their width and length directions, while the directions of isobaric bodies offer supplementary material. If the control domains of two isobaric bodies overlap with each other perpendicular to the flow direction, these isobaric bodies have higher odds of connected fluid flow. [ABSTRACT FROM AUTHOR]

The analysis of the Rayleigh–Bénard instability due to the mass diffusion in a fluid-saturated horizontal porous layer is reconsidered. The standard diffusion theory based on the variance of the molecular position growing linearly in time is generalized to anomalous diffusion, where the variance is modeled as a power-law function of time. A model of anomalous diffusion based on a time-dependent mass diffusion coefficient is adopted, together with Darcy's law, for momentum transfer, and the Boussinesq approximation, for the description of the buoyant flow. A linear stability analysis is carried out for a basic state where the solute has a potentially unstable concentration distribution varying linearly in the vertical direction, and the fluid is at rest. It is shown that any, even slight, departure from the standard diffusion process has a dramatic effect on the onset conditions of the instability. This circumstance reveals a strong sensitivity to the anomalous diffusion index. It is shown that subdiffusion yields instability for every positive mass diffusion Rayleigh number, while superdiffusion brings stabilization no matter how large is the Rayleigh number. A discussion of the linear stability analysis based on the Galilei-variant fractional-derivative model of subdiffusion is eventually carried out. [ABSTRACT FROM AUTHOR]

We perform three-dimensional numerical simulations to understand the role of viscous fingering in sweeping a high-viscous fluid (HVF). These fingers form due to the injection of a low-viscous fluid (LVF) into a porous media containing the high-viscous fluid. We find that the sweeping of HVF depends on different parameters such as the injection velocity (U0) of the LVF, ease of diffusion of the fluid (D), and the logarithmic viscosity ratio of HVF and LVF ℜ. The two-phase Darcy's law module of COMSOL Multiphysics is used to simulate different cases with varying parameters. At high values of U0 and ℜ and lower values of D, the fingers grow non-linearly, resulting in earlier tip splitting of the fingers and breakthrough, further leading to poor sweeping of the HVF. In contrast, the fingers evolve uniformly at low values of U0 and ℜ , resulting in an efficient sweeping of the HVF, while a higher diffusion coefficient leads to a smooth flow with fewer fingers. We also estimate the sweep efficiency and conclude that the parameters U0, D, and ℜ be chosen optimally to minimize the non-linear growth of the fingers to achieve an efficient sweeping of the HVF. [ABSTRACT FROM AUTHOR]

The clogging problem caused by the migration of suspended particles in in situ leaching of uranium has become an important factor restricting production efficiency. However, research on the laws and mechanisms related to physical clogging in this field has not yet been reported. This study established a simulation experimental system for the migration and clogging of suspended particles in porous media, and studied the clogging laws of suspended particles with different particle sizes and the ratio of pore diameter to suspended particle size o/d in porous media. The results show that under the conditions of a suspended particles concentration of 200 mg/L and a suspension flow velocity of 9 mL/min, when o/d ≥ 11.4, only a small amount of internal deposition of suspended particles occurs in porous media; When 2.8 < o/d < 11.4, the suspended particles in the porous medium are mainly characterized by internal deposition and internal pore clogging; When o/d ≤ 2.8, surface clogging will occur in the porous medium, and in severe cases, "mud cake" phenomenon will occur. The dimensionless parameter Reynolds number is introduced to identify the critical state of clogging by correlating the ratio of pore diameter to suspended particle size suspension velocity and suspended particle concentration through an exponential law model. The research results have laid the foundation for further research on alleviating the clogging problem caused by suspended particles in the in situ leaching process of uranium. [ABSTRACT FROM AUTHOR]

The technology of composite ground has been widely adopted in various engineering projects, and it presents the trend from a single column type to the combined use of multiple types. The combined use of long prefabricated vertical drains (PVDs) and short soil–cement columns (impervious columns) has been proposed and utilized in several ground improvement projects. The research for the consolidation behavior of combined composite ground could facilitate the design and calculation of it in practice. Nevertheless, almost no analytical theories for consolidating such a technique are available in the literature. To fill this gap, an analytical model including multiple long PVDs and short impervious columns is proposed to predict the coupled radial–vertical consolidation of the combined composite ground. The analytical solutions under instantaneously and multistage loading are obtained based on the assumption of equal strain and Darcy's law. The average degree of consolidation calculated by the current study is then compared with several existing analytical models of composite ground. Furthermore, a parametric study is carried out to investigate the impacts of various factors on consolidation behavior. The results show that the increasing penetration ratio of the short impervious columns can accelerate the consolidation rate. Moreover, the distribution patterns of the construction site, the compression modulus ratio of impervious columns and soil, and the well resistance and smear effect of PVDs can also influence the consolidation behavior of the combined composite ground. Finally, the reasonability of the proposed analytical model is verified by comparing it with the measured test data reported in the literature. [ABSTRACT FROM AUTHOR]

Infrastructure development over quaternary unlithified, unconsolidated sediments is quite critical and poses geo-hydro-engineering challenges. The challenges are more perceptible near high groundwater table areas and increase with the depth of construction. In this study, long-duration (t ≤ 40 h) permeability experimentation on fine-grained soil sample is conducted under varying confining stress (σ3) and fluid flow pressure (fp) employing a flexible wall permeameter to simulate the behavior of fluid flow under the stress conditions equivalent to a depth of approximately 40 m below the earth's crust. The obtained result indicates a nonlinear relationship between discharge, q (m3/s), and time, t (s), there is a rapid reduction in q up to t (≤16 h), which becomes almost constant after attaining steady-state flow and complete saturation. The q linearly increases with an increase in fp and follows Darcy's law; however, q significantly decreases with an incremental change in σ3. Further, a nonlinear relationship exists between k and σeff. The percentage variation in qavg with changes in fp (=40–80 kPa and 80–120 kPa) corresponding to σ3 (=200 kPa) is about 50% and 70%. respectively. There is less change (5%) in qavg, corresponding to incremental change in σ3 from 100 to 200 kPa; however, the change is quite significant and rapid (about 28%) on an increase in σ3 from 200 to 300 kPa. Further, slow or negligible change can be observed beyond σ3 (=300 kPa). This research highlights the significance of σ3 over fp on the behavior of fluid flow through fine-grained soil and demarcates the flow boundaries, namely unsteady-state, critical-state, and steady-state flows, specific to unsaturated or partially saturated clayey–sandy–silty soil. The research provides quantitative assessment of the behavior of fluid flow through fine-grained soil under varying confining stress and fluid flow pressure conditions, which may be valuable in optimizing the design and construction of any civil or geoengineering projects especially where the depth of construction has significance. The research clearly highlights the flow boundaries, namely unsteady-state, critical-state, and steady-state flow boundaries, specific to unsaturated or partially saturated clayey–sandy–silty soil and provides the relationship among discharge, time, confining stress, and fluid flow pressure, which may assist in developing accurate predictive models to investigate fluid flow through fine-grained soil. [ABSTRACT FROM AUTHOR]

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Based on the assumption of linear potential flow theory, the scattering problem of a composite breakwater placed in front of an impermeable back wall is theoretically investigated. The velocity potential in each subregion is found using the eigenfunction expansion method. The boundary conditions of the porous region are treated using Darcy's law. The semi-analytical solution of a composite breakwater placed in front of an impermeable back wall is then obtained based on the matching conditions of the boundaries of the different regions. The effects of different parameters on the wave loads and wave amplitudes are investigated. In addition, to better understand the performance of the composite breakwater, the scattering problem of the composite breakwater without considering an impermeable back wall is also investigated. The correctness of this theoretical model is verified by comparing the results with previous work. Based on the results of hydrodynamic calculations and analysis of various aspects of a composite breakwater placed in front of an impermeable back wall, the study of the effect of a composite breakwater placed in front of an impermeable back wall allows us to propose a long-term and cost-effective solution for the protection of various marine facilities from wave attacks. [ABSTRACT FROM AUTHOR]

This study compares biochar (BCW) systems' pollutant removal effectiveness to conventional subsurface flow (CCW) in constructed wetland systems to treat textile wastewater. The two systems were identical in construction, but the biochar was 0.1 m thick over gravel and sand (maximum flow rate of 0.021 m3 h−1) as the primary medium over CCW (flow rate of 0.02 m3 h−1). The results revealed that the BCW approach was more efficient than the CCW system (pebble over sand and gravels) in removing and lowering heavy metals below thresh hold limits such as Cr, Cd, Cu, Pb, Ni, and Zn. The alkaline nature of textile water achieves neutrality in both CCW and BCW. However, BCW is more efficient due to a larger active surface area and the ability to filter out more metal and organic ions. TDS reduction efficiency in BCW was 53.07%, compared to 40.04% in CCW. Heavy metal removal was 100% in BCW at 3 to 12 h, whereas it takes 6 to 24 h in CCW (82% for Cr to 93% for Cu). The quick removal of Na from textile wastewater by BCW was reversed and achieved equilibrium in 24 h in contrast to the CCW system (> 24 h). The findings obtained at the lab scale level demonstrated that the BCW system was more effective in reducing TDS, neutralizing the alkalinity of textile wastewater, and removing heavy metals. This study strongly supports the potential application of biochar-constructed wetlands for textile wastewater treatment. [ABSTRACT FROM AUTHOR]

Using the temperature and seepage field-coupling module within COMSOL Multiphysics software, we examined freezing behavior and its evolving patterns in curved underground freezing pipes. This study employed transient states, with the Darcy's law and porous-media heat-transfer options activated in the Physical Field Interface of the Physical Field and Variable Selection column. The models were created to establish numerical models of freezing reinforcement for both single and multiple pipes with various curvatures. These models were designed to simulate the evolving temperature and seepage fields of soil under diverse freezing conditions. Subsequently, this research utilized the models to simulate the freezing and consolidation conditions of a shallowly buried tunnel within the context of shallow tunnel conditions. The study reveals that after freezing a single pipe using water flow, the change in thickness of the frozen wall in curved pipes is notably smaller than that in straight pipes. This difference is particularly pronounced in the upstream section. Specifically, at a distance of −2000 mm from the main surface, the change in thickness of the frozen wall in straight pipes exceeds that in s = 7 curved pipes by approximately 350 mm. The smaller the long arc ratio s, the greater the arc of the freezing tube and the better the water-blocking effect. In the multi-pipe freezing model, the s = 7 curved pipes exhibit a frozen-wall thickness approximately 120 mm greater than that of straight pipes at a distance of −2000 mm from the main surface. Under the condition of a shallow buried concealed excavation with surging water, a pipe with a long arc ratio s = 7 arc freezing at 46 d attains a permafrost curtain thickness that is equivalent to that achieved by the straight pipe freezing at 58 d. This reduction in thickness shortens the working period by 12 days, resulting in a more efficient process. The successful application of the freezing method in the water-rich aquifer is expected to be a valuable reference for similar projects in the future. [ABSTRACT FROM AUTHOR]

In this article, the onset of double-diffusive convection with the effect of viscous dissipation in a horizontal fluid-saturated porous layer is examined. Two impermeable isothermal and isosolutal walls bound the porous layer, and Darcy's law models the flow. The onset of convective instability is studied by two approaches: the linear stability analysis and the nonlinear stability analysis. The nonlinear stability analysis is performed by utilizing the energy method. The literature on the nonlinear stability analysis of onset of convective instability with the viscous dissipation effect is limited. The present article aims to fill this gap. It is observed that, when the fluid is at rest, the effect of viscous dissipation does not influence the critical thermal Rayleigh number corresponding to both the linear and nonlinear stability analyses. Moreover, sub-critical instabilities do not occur when R a S > 0 . But in contrast, the region of sub-critical instabilities increases along the negative R a S direction. [ABSTRACT FROM AUTHOR]

In this work, a previously published model for the water up take of stormwater in sponge-like porous bodies by the group is further developed. This is done by investigating the highest-performing model and considering the water uptake from the surroundings of a pond and rain-infiltrated soil. This implies that water uptake from impermeable to partially permeable surfaces is examined. Hence, the following cases are considered: (1) impervious bottom surface and no precipitation, (2) impervious bottom surface with precipitation, (3) permeable soil with no precipitation, and (4) permeable soil with precipitation. A mathematical model covering all these cases is presented, where the governing equations are the mass conservation and Darcy's law together with an assumption of a sharp wetting front being a first-order approximation of the complete Richard's equation. Results for the water uptake height, pond depth, and wetting front are computed numerically and plotted against time. Analytical solutions are also presented in certain cases, and critical values are obtained. The parametric study includes variations in the ratio of the model- to the surrounding ground surface area, initial pond depth, precipitation, and soil characteristics. To exemplify, the time it takes to absorb the water from the pond after a precipitation period is presented. The results are related to the Swedish rainfall data of 1 h duration with a return period of 10 years. When evaluating efficiency, the focus is on the absorption time. Results vary considerably, demonstrating a general trend that with soil infiltration, the water absorption rate is higher. For most cases, the considered water amount is absorbed completely, although depending on the parameters and conditions. These results serve to optimize the model for each of the cases. The main focus of the research lies in the theoretical aspect. [ABSTRACT FROM AUTHOR]

Traditionally, steady-state relative permeability is calculated from measurements on small rock samples using Darcy's law and assuming a homogenous saturation profile and constant capillary pressure. However, these assumptions are rarely correct as local inhomogeneities exist; furthermore, the wetting phase tends to be retained at the outlet–the so-called capillary end effect. We have introduced a new method that corrects the relative permeabilities, analytically, for an inhomogeneous saturation profile along the flow direction. The only data required are the measured pressure drops for different fractional flow values, an estimate of capillary pressure, and the saturation profiles. An optimization routine is applied to find the range of relative permeability values consistent with the uncertainty in the measured pressure. Assuming a homogenous saturation profile systematically underestimates the relative permeability and this effect is most marked for media where one of the phases is strongly wetting with a noticeable capillary end effect. Relative permeabilities from seven two-phase flow experiments in centimetre-scale samples with different wettability were corrected while reconciling some hitherto apparently contradictory results. We reproduce relative permeabilities of water-wet Bentheimer sandstone that are closer to other measurements in the literature on larger samples than the original analysis. Furthermore, we find that the water relative permeability during waterflooding a carbonate sample with a wide range of pore sizes can be high, due to good connectivity through the microporosity. For mixed-wet media with lower capillary pressure and less variable saturation profiles, the corrections are less significant. [ABSTRACT FROM AUTHOR]

The effect of permeable pavement in reducing stormwater runoff is dependent on its infiltration performance. The monitoring and modeling methods were adopted to analyze infiltration performance of permeable pavement and was primarily based on Darcy's law in previous studies. But Darcy's law disregards the changing infiltration rate with the change of water content in permeable pavement medias. Neglecting the infiltration rate change frequently resulted in significant deviation between the monitoring and modeling results. To address these issues, the accuracy of two modeling methods for the infiltration performance of permeable brick pavement system (PBPs) was evaluated. The first is the low impact development (LID) module of the stormwater management model (SWMM), and the second is a new equivalent modeling approach based on the Horton model for PBPs. According to the results, the Horton model accurately described the infiltration performance of PBPs in SWMM. Under high return periods situation, the coefficients of determination (R2) and Nash-Sutcliffe efficiency coefficients (Ens) reach 0.82 and 0.88, respectively, and the simulation error ranges from 6.57% to 8.75%. The experimental and simulation results of the LID module in SWMM were compared in greater detail. The result demonstrated that the LID module of SWMM underestimated the infiltration capacity of PBPs because it ignored the fluctuating infiltration rate throughout the whole PBPs infiltration process. Therefore, the proposed equivalent modeling method is superior to simulating the infiltration performance of PBPs in SWMM , and the Horton model improved the simulation accuracy of PBPs infiltration. [ABSTRACT FROM AUTHOR]

We consider the interaction between a free flowing fluid and a porous medium flow, where the free flowing fluid is described using the time dependent Stokes equations, and the porous medium flow is described using Darcy's law in the primal formulation. To solve this problem numerically, we use a diffuse interface approach, where the weak form of the coupled problem is written on an extended domain which contains both Stokes and Darcy regions. This is achieved using a phase-field function which equals one in the Stokes region and zero in the Darcy region, and smoothly transitions between these two values on a diffuse region of width (ϵ) around the Stokes-Darcy interface. We prove convergence of the diffuse interface formulation to the standard, sharp interface formulation, and derive rates of convergence. This is performed by deriving a priori error estimates for discretizations of the diffuse interface method, and by analyzing the modeling error of the diffuse interface approach at the continuous level. The convergence rates are also shown computationally in a numerical example. [ABSTRACT FROM AUTHOR]

The main goal of this manuscript is to generalize Darcy's law from conventional calculus to fractal calculus in order to quantify the fluid flow in subterranean heterogeneous reservoirs. For this purpose, the inherent features of fractal sets are scrutinized. A set of fractal dimensions is incorporated to describe the geometry, morphology, and fractal topology of the domain under study. These characteristics are known through their Hausdorff, chemical, shortest path, and elastic backbone dimensions. Afterward, fractal continuum Darcy's law is suggested based on the mapping of the fractal reservoir domain given in Cartesian coordinates x i into the corresponding fractal continuum domain expressed in fractal coordinates ξ i by applying the relationship ξ i = ϵ 0 (x i / ϵ 0) α i − 1 , which possesses local fractional differential operators used in the fractal continuum calculus framework. This generalized version of Darcy's law describes the relationship between the hydraulic gradient and flow velocity in fractal porous media at any scale including their geometry and fractal topology using the α i -parameter as the Hausdorff dimension in the fractal directions ξ i , so the model captures the fractal heterogeneity and anisotropy. The equation can easily collapse to the classical Darcy's law once we select the value of 1 for the alpha parameter. Several flow velocities are plotted to show the nonlinearity of the flow when the generalized Darcy's law is used. These results are compared with the experimental data documented in the literature that show a good agreement in both high-velocity and low-velocity fractal Darcian flow with values of alpha equal to 0 < α 1 < 1 and 1 < α 1 < 2 , respectively, whereas α 1 = 1 represents the standard Darcy's law. In that way, the alpha parameter describes the expected flow behavior which depends on two fractal dimensions: the Hausdorff dimension of a porous matrix and the fractal dimension of a cross-section area given by the intersection between the fractal matrix and a two-dimensional Cartesian plane. Also, some physical implications are discussed. [ABSTRACT FROM AUTHOR]

This article explores the possibility of using samples with embedded glass capillaries of various diameters as rock-mimicking samples with a-priori known values of the absolute gas permeability coefficients. The measured values of the absolute gas permeability coefficient were compared with those obtained by theoretical calculation. The results of measuring the absolute gas permeability coefficient were obtained using the State primary standard of units of specific gas adsorption, specific surface area, specific pore volume, pore size, open porosity, and gas permeability coefficient of solid substances and materials (GET 210-2019). The theoretical values of the permeability coefficient were obtained by measuring the diameters of the capillaries using an optical microscope. Based on the values of these diameters, the permeability coefficients of the samples with capillaries were calculated according to the combined Poiseuille and Darcy equation. It was proved that the measurement results obtained with the use of GET 210-2019 are consistent with the theoretically calculated values of the permeability coefficient within the uncertainty limits. In accordance with the obtained data, the possibility of utilizing cylindrical samples with embedded glass capillaries for measuring gas permeability coefficients of solid substances and materials has been confirmed. The results of this research will be useful for oil and gas professionals, for example, when performing petrophysical studies and geological exploration. [ABSTRACT FROM AUTHOR]

In this paper, the Biot's consolidation model is considered, and Darcy‐Forchheimer equation is used to describe the relationship between the fluid velocity and pressure. The model is nonlinear and the unknown variables are the solid displacement, the fluid velocity and pressure. The Bernardi‐Raugel element is used for displacement and the RT mixed element is used for the fluid velocity and pressure. The parameter‐robust BR‐RT0‐P0 method presented here is uniformly stable not only with respect to the Lamé constant λ$$ \lambda $$, but also with respect to the constrained specific storage coefficient c0$$ {c}_0 $$. We demonstrate the well‐posedness of the BR‐RT0‐P0 finite element solutions, and give the error estimates of the finite element approximations using the monotonicity of the nonlinear Forchheimer term. The error estimates are divided into two cases, that is, c0$$ {c}_0 $$ is positive and c0$$ {c}_0 $$ is nonnegative. Numerical experiments are presented to verify theoretical analysis. Moreover we focus on the variation of pressure by several poroelasticity problems. [ABSTRACT FROM AUTHOR]