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This paper establishes the concept of elastic wave propagation in a multi-porous medium with different permeabilities by assuming there are n distinct pore fluid phases. The dynamic equation of motion of elastic wave propagation through this multi-porous medium is derived based on Lagrangian mechanics. In this regard, the generalized form of mass coefficients and then the energy loss due to the fluid phases in terms of dissipation coefficients are presented for low-frequency limits with the help of Darcy's Law of multi-phases system. The elastic coefficients of the constitutive equation in terms of compliance matrix are identified using a series of Gedanken experiments. Some significant results regarding the compressional and rotational waves in a multi-porosity medium are derived. The validation of the theory has been shown by comparing it with the existing theory of single and double porosity. It is observed that there are (n+1) compressional waves corresponding to solid and fluid phases, whereas only one rotational wave is associated with the solid phase. The concept of multi-porosity theory can contribute to a deeper understanding of wave behaviour in a porous medium. [ABSTRACT FROM AUTHOR]

In order to investigate the development of the temperature field of a new type of freezing reinforcement under seepage conditions, in this paper, COMSOL finite element software was used to simplify the model and simulate the effect of groundwater seepage on the development of the temperature field of frozen pipes by coupling the Darcy's law module and the heat transfer module for porous media. The heads of water were also varied to simulate the change in seepage velocity to further investigate the effect of seepage velocity on the temperature field. The results of the study show that the freezing wall formed in the high head region was thinner than that in the low head region due to the effect of seepage, and this phenomenon was aggravated with the increase of seepage rate; The effect of seepage action on the temperature field had a hysteresis along the seepage direction; When the seepage rate was greater than 1.65 m/d, the soil in the center of the device feezed better and could form a tight and dense freezing wall comparable to the size of the freezing device; When the seepage rate was greater than 5.78 m/d, the temperature of the center soil body gradually increased, and eventually the freezing curtain cannot be formed. [ABSTRACT FROM AUTHOR]

This work introduces a novel isogeometric method for addressing steady, saturated groundwater flow as a free-boundary problem. The innovation lies in adopting a double spline parameterization technique for accurately representing both the porous medium and the fully saturated zone. To linearise the governing equation, we differentiate them with respect to the coefficients of the geometric parameterization. This process results in a quasi-Newton method. Several benchmark numerical tests demonstrate the applicability and effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

The present article highlights a few fundamental aspects that need to be considered while characterizing fluid flow through a petroleum reservoir. Darcy’s law, as applied in describing fluid flow through pipes or saturated groundwater aquifers, cannot be directly applied under all circumstances. Darcy’s original version of Darcy’s law carries a simple algebraic equation relating linear Darcy flux with the hydraulic gradient. Steady-state Darcy’s law is being applied with lots of assumptions, even when describing saturated groundwater fluid flow. However, fluid flow through a petroleum reservoir involves multi-dimensional, multi-phase and multi-component, compressible fluid flow with inertial effects under non-isothermal conditions. This article highlights first why already established Navier–Stokes Equation cannot be applied to characterize fluid flow through a petroleum reservoir; and then shows why the fundamental principle associated, even with fluid flow through a saturated groundwater aquifer, cannot be applied directly to characterize the flow through a petroleum reservoir. Finally, the article presents critical limitations associated with mass conservation equation, momentum conservation equation and fluid flow equation used to characterize flow through petroleum reservoirs. [ABSTRACT FROM AUTHOR]

Porous ceramics for aerostatic bearing restrictors were fabricated using carboxymethyl cellulose and polystyrene microspheres as pore formers. The three‐dimensional morphology of the porous ceramics was nondestructively obtained using laser scanning confocal microscopy, and the processing information was eliminated by fitting the pore area fractal dimensions at different heights. A mathematical model was developed based on the assumption of elliptical tortuous capillaries to relate microstructural pore parameters to permeability by combining fractal theory, Darcy's law, and the gas conservation equation. The calculated permeability closely matched the experimental results, with an error of less than 3.5%. This method has promising potential as an alternative to pressure drop experiments. Moreover, the capacity of the fractal calculation model to establish a correlation between microstructural parameters and permeability paves a new way to design future porous aerostatic bearings. [ABSTRACT FROM AUTHOR]

In thermal protection systems (TPS), Darcy's law or Darcy-Forchheimer's law is employed to model the pyrolysis gas flow within the anisotropic porous ablator depending on the flow regime considered. A key challenge with using these laws is first, the knowledge of the validity domain of each flow regime in terms of a critical Reynolds number (R e c ). Secondly, the lack of data on macroscopic properties, namely, the permeability and Forchheimer tensors is particularly challenging for the relevance of the models. The objective of this work is to contribute to overcoming these challenges by performing experimental and X-ray tomographic image-based characterization of Calcarb, a commercial carbon preform used for manufacturing TPS. For this purpose, fluid flow within Calcarb was studied experimentally in the Through-Thickness (TT) and the In-Plane (IP) directions for Reynolds numbers of 0.05 to 10.46 -representative of the TPS application. Tomography image-based micro-scale simulations, involving the direct resolution of the Navier–Stokes equations under both flow regimes, were also performed. Experimental results exhibit the anisotropic nature of Calcarb, namely through R e c values, corresponding to the Darcy flow regime limit, slightly different in the two directions (R e c of 0.31 and 0.43) with measured permeability values of 1. 248 × 1 0 − 10 m 2 and 1. 615 × 1 0 − 10 m 2 for TT and IP directions respectively. In the Forchheimer regime, experimental Forchheimer coefficients β were 2. 0010 × 1 0 5 m−1 (TT) and 1. 4948 × 1 0 5 m−1 (IP). During the simulation process, a numerical strategy was defined to obtain the permeability tensor yielding values within 8% of the experimental ones. The comparison of experimental results vs simulation results in the Forchheimer regime was performed through the analysis of the pressure gradients as functions of R e in the x , y , and z directions. The numerical estimations were compared successfully with experimental measurements, with a discrepancy of 5.2%, for R e values up to 2.4. [Display omitted] • Experimental investigation and tomography analysis of the parameters of a carbon preform. • It is applied in Darcy-Forchheimer flows in thermal protection systems. • The permeability is calculated via direct resolution of the Navier–Stokes equations. • The Darcy flow regime limit in Calcarb is observed at a Reynolds number of 0.43. [ABSTRACT FROM AUTHOR]

We study cut finite element discretizations of a Darcy interface problem based on the mixed finite element pairs RTk x Qk, k ≥ 0. Here Qk is the space of discontinuous polynomial functions of degree less than or equal to k and RT is the Raviart--Thomas space. We show that the standard ghost penalty stabilization, often added in the weak forms of cut finite element methods for stability and control of the condition number of the resulting linear system matrix, destroys the divergence-free property of the considered element pairs. Therefore, we propose new stabilization terms for the pressure and show that we recover the optimal approximation of the divergence without losing control of the condition number of the linear system matrix. We prove that with the new stabilization term the proposed cut finite element discretization results in pointwise divergence-free approximations of solenoidal velocity fields. We derive a priori error estimates for the proposed unfitted finite element discretization based on RTk X Qk, k ≥ 0. In addition, by decomposing the computational mesh into macroelements and applying ghost penalty terms only on interior edges of macroelements, stabilization is applied very restrictively and active only where needed. Numerical experiments with element pairs RT0 x Q0, RT1 x Q1, and BDM1 x Q0 (where BDM is the Brezzi--Douglas--Marini space) indicate that with the new method we have (1) optimal rates of convergence of the approximate velocity and pressure; (2) well-posed linear systems where the condition number of the system matrix scales as it does for fitted finite element discretizations; (3) optimal rates of convergence of the approximate divergence with pointwise divergence-free approximations of solenoidal velocity fields. All three properties hold independently of how the interface is positioned relative to the computational mesh. [ABSTRACT FROM AUTHOR]

Incorporating the nuclear magnetic resonance (NMR) technique, a newly developed infiltration instrument constructed from polytetrafluoroethylene is designed for the rapid determination of unsaturated hydraulic conductivity of bentonite materials. The proposed approach is founded on measuring the variation of the NMR signal in numerous cross sections of the specimen during the infiltration test, enabling the determination of water content distribution. Through integration with the instantaneous profile method, unsaturated hydraulic conductivity can be obtained using Darcy's law. The mechanism underlying the observed U-shaped trend of unsaturated hydraulic coefficient with decreasing suction can be attributed to the relatively high value controlled by water vapor diffusion at higher suction stages, as well as the hydraulic conductivity increasing near saturation, similar to the behavior of most unsaturated soils. The consistency of test results with those acquired from conventional measurements, regarding amplitude level and evolutionary pattern, provides evidence of the reliability of the proposed method. The primary improvement lies in the real-time acquisition of the water content profile using the spatial encoding technique in the NMR in the infiltration test. Simultaneously, the approach substantially reduces the test duration from thousands of hours to dozens of hours while maintaining measurement accuracy. [ABSTRACT FROM AUTHOR]

The paper investigates the effects of the Forchheimer term (form drag) and vertical pressure gradient on the buoyancy‐induced instability of power‐law saturating fluid in a porous plane medium. Two isobaric permeable layers are assumed to sandwich the horizontal porous plane. In the meantime, Dirichlet and Neumann equations are the thermal boundary conditions considered for the lower and upper layers. A base flow developed analytically via the governing equations is just in function of the Péclet number P $P$, with no dependence on the characteristic parameter of the power law fluid. A linear stability analysis consists of substituting a base flow with a small perturbation into the governing equations leads to a four‐order eigenvalue problem. An analytical solution is performed for the asymptotic cases of an infinite wavelength. The Runge–Kutta solver is applied together with the shooting technique to evaluate numerical solutions for the general case of nonnegligible wave numbers. Among the findings is the contribution of the Forchheimer term in the variation of the threshold Péclet number whose value can switch the wave numbers from zero to nonzero and increase the stability of the system. [ABSTRACT FROM AUTHOR]

Estimating the flow rate accurately through a single rough fracture poses a fundamental challenge. This study presents an analytical model for single-phase saturated nonuniform laminar flow through rough fractures. The flow analytical model of the fractures is constructed using homotopy thinning methods, average inertia approaches, and shortest path techniques, thereby simplifying the nonuniform flow problem to solving the integral of the incircle aperture function, from which the modified average Darcy velocity considering inertial effects is expressed. The flow equations in the global coordinates are then derived. The validity of the proposed model is verified by comparing it with flow simulations with the Navier–Stokes equations, perturbation solutions, previously corrected Reynolds equations, and experimental flow tests. The results obtained from the proposed model agree very well with those from simulations and experiments. The effective errors Di range within ±4.0% of the simulation results with an arithmetic mean of |Di| equal to 1.03%. As surface roughness increases, the proposed model can effectively capture the inertial behaviors arising from the nonuniform flow field. Compared to the previous corrected Reynolds equations and perturbation solutions, the proposed model demonstrates enhanced accuracy and applicability, introducing a new approach to address nonuniform flow problems in rough fractures with more complex geometries. [ABSTRACT FROM AUTHOR]

Precipitation is one of the most important factors inducing shallow slope failures, and the shallow slope covering bedrocks is prone to instability after heavy rainfall. In one-dimensional (1D) seepage–deformation coupling issues, permeability coefficient and moisture vary with matric suction in unsaturated soil. Combining mass conservation, Darcy's law, and elastic theory, an analytical solution for coupled seepage–deformation in unsaturated soil slopes during rainfall infiltration is derived using the Fourier integral transformation method. The analytical solution can be applied to a 1D seepage problem in a soil slope with flux at the top and impervious bedrock in the base under heavy precipitation, and is conducive to study infiltration into the slope under rainfall conditions. To validate the accuracy of the proposed analytical solution in this study, it is compared with monitored pore-water pressure data from the Gufenping Landslide in the red-bed region located in Nanjiang, Sichuan, China. The compared result shows a good consistency between the analytical solution and the measured results, with a minor relative error. Investigation of the parameters demonstrates that the water-level rise is closely related to the coupling, which is influenced by precipitation duration, precipitation intensity, soil properties, and slope angle. The bottom boundary of the slope is considered to be impermeable in this study, which leads to rainfall accumulation at the base over time, and the coupled effect becomes more pronounced at the bottom boundary. [ABSTRACT FROM AUTHOR]

After the mines closed, the groundwater level quickly rises, and pollutants in the underground space will migrate outward along the flow channel, causing pollution to the surrounding environment. The different morphologies of interlayer fractures in the goaf fracture zone are one of the main flow channels, including interlayer expansion fracture. Fracture expansion can impact a local flow field, which, in turn can affect solute transport characteristics. The microscale flow field and solute transport behavior in fracture with different expansion characteristics were investigated by a microscale visualization experiment. The experimental results indicate that there is a significant difference in the pressure gradient between different expansion regions. When nonlinear flow characteristics (reflux or eddy) begin to occur within the expansion region, the pressure gradient value also begins to deviate from Darcy's law under the same Re. The maximum velocity position changes from the centerline to the upper and lower surfaces of the expansion region, a low velocity region is generated in the main flow channel, which moves to the outlet as Re increase, and the cross-section velocity curve also transforms into a bullet shape as Re increase. By developing a set of programs to establish a relationship between the average image luminance and the tracer particles concentration, the solute concentration variation curve in the expansion region was obtained. The process of solute invasion into fractures is divided into four stages. The change in the local flow field caused by the different expansion characteristics directly affects the duration of these four stages. As the area of the region increases, the proportion of the main channel area decreases relatively, the difference between the solute concentration curve of the whole fracture and the expansion region gradually decreases. [ABSTRACT FROM AUTHOR]

Bentonite slurry is frequently used to temporarily stabilize the excavation for slurry tunnel boring machines (TBMs) driving in permeable soils, such as sand and gravel. In this study, two types of bentonite slurries (BS1 and BS2) were subjected to a series of infiltration column tests and modified fluid-loss tests under various pressure levels. Monitoring of water discharge and pore pressures at different depths of the sand bed enabled the identification of two effective sealing patterns during infiltration: the formation of a filter cake and rheological blocking. BS1 exhibited a tendency to form a filter cake, which played a vital role in effectively transferring the applied pressure to the underlying soil skeleton. The application of higher pressure facilitated the rapid formation of a filter cake, resulting in a shorter time span for slurry invasion and minimizing fluid loss. On the other hand, rheological blocking was dominant when using BS2, and the maximum infiltration distance was found to linearly increase with the applied pressure. A comparison between the measurement and a simple prediction model derived from Darcy's law revealed an overestimation of the infiltration distance during slurry invasion. Furthermore, based on the modified fluid-loss test, higher pressure was found to densify the filter cake and result in lower hydraulic conductivity. [ABSTRACT FROM AUTHOR]

The Phase-Change Heat Exchanger Unit in Layered Porous Media (PCEU-LPM) is obtained through frozen pouring processing, and exhibits characteristics such as high thermal conductivity, high latent heat, and high permeability, making it suitable for dissipating heat in airborne electronic devices. This study numerically investigates the impact of aircraft speed acceleration conditions, which lead to weightlessness or overload, on the performance of the PCHEU-LPM, with a particular focus on the influence of natural convection in the liquid-phase region. Initially, a microscale thermal analysis model is established based on the Navier–Stokes equation scanning electron micrograph to calculate the effective thermal conductivity and permeability of the PCHEU-LPM under different porosities. Subsequently, these parameters are incorporated into a macroscale thermal analysis model based on Darcy's law, employing an average parameter approach. Using the macroscale thermal analysis model, temperature and velocity fields are computed under various porosities, acceleration magnitudes, and directions. The calculation results indicate that as the acceleration increases from α = 0 to α = 10 g, the interface temperature of the PCHTU-LPM decreases by approximately 5.2 K, and the temperature fluctuation decreases by 2.4 K. If the porosity of the PCHTU-LPM is increased from ε = 70% to ε = 85%, the influence of acceleration change on natural convection will be further amplified, resulting in a decrease in the interface temperature of the PCHTU-LPM by approximately 10.2 K and a decrease in temperature fluctuation by 5.8 K. When the acceleration direction is +z, the interface temperature of the PCHTU-LPM is at its lowest, while it is highest when the acceleration direction is −z, with a maximum difference of 15.4 K between the two. When the acceleration direction is ±x and ±y, the interface temperature lies between the former two cases, with the interface temperature slightly higher for ±y compared to ±x, with a maximum difference of 3.9 K between them. [ABSTRACT FROM AUTHOR]

Relevance. The necessity to calculate the changes in filtration properties during injection of suspensions for subsequent forecasting of technological parameters of wells. This calculation is complicated by the presence of different-scale effects, since the penetration depth of dispersed particles is orders of magnitude smaller than the characteristic dimensions of the formation. These effects have not been studied in detail before. Aim. To analyze the effect of a small parameter on the behavior of flow characteristics using a mathematical model of suspension filtration in a porous medium. Objects. Colmatation coefficient, filtration coefficient, distribution of concentration of dispersed particles in the formation, porosity, mathematical model of deep-bed suspension migration into a porous medium. Methods. Numerical modeling, explicit finite-difference scheme, solution of a problem with a small parameter, introduction of dimensionless parameters, method of characteristics. Results and conclusions. It is shown that the processes of conformance control and colmatation of a porous medium are described within the framework of a unified system of equations of deep-bed suspension migration into a porous medium. It is identified that the concentration of retained particles is a small parameter that allows reducing the complete system of equations of deep-bed suspension migration into a porous medium to a simplified form, in which the solution can be obtained analytically using the method of characteristics. The authors compared the solutions of the complete and simplified systems of equations of deep-bed suspension migration into a porous medium, indicating their compliance with an error of less than 4 %. They obtained the distributions of the concentration of dispersed particles and porosity in the reservoir during colmatation, showing that over time the colmatation front propagates at a constant rate. It is shown that the colmatation coefficient is a small parameter that significantly determines the nature of oil displacement by water, and a decrease in the colmatation coefficient leads to a decrease in the rate of colmatation and the appearance and growth of the size of the stabilized zone near the displacement front.

The permeability coefficient of coal seams is a key parameter that judges the difficulty of gas flow in coal seams. In the current calculation formula for the permeability coefficient of coal seams, the coefficient of the nonlinear partial differential equation with variable pressure is assumed to be a constant, which leads to significant errors in the theoretical derivation results and results in significant deviations in the permeability coefficient measured on site. To solve the inaccurate determination problem of the coal seam permeability coefficient, this paper derived the process of using the radial flow rate method to test the coal seam permeability coefficient, and pointed out the problems of this method during the derivation process. Based on the Langmuir's gas content and Darcy's law, a dimensionless model was established, and the model solution results were inverted and fitted. A new calculation formula for the coal seam permeability coefficient was obtained, which was verified by on-site drilling data. The current testing method for coal seam permeability coefficient was revised, and an accurate and reliable new method for calculating the coal seam permeability coefficient was proposed. The results indicate that using a parabolic equation to represent the coal seam gas content and treating variable p1.5 as a constant to derive the coal seam permeability coefficient calculation formula is equivalent to fitting the gas content into a proportional relationship with the square of pressure. There are theoretical problems and significant errors in actual calculations. Using the Langmuir dimensionless model to calculate Y' for inversion fitting can solve the shortcomings of current calculation methods. When the product of the adsorption constant b and the original gas pressure p0 (the dimensionless original gas pressure) is different, the function curve of the dimensionless gas emission velocity Y' and the dimensionless time Fo' is significantly different. Therefore, the permeability coefficient calculation formula containing the dimensionless original gas pressure was obtained. When the coal seam and drilling conditions are constant, the values of the coal seam permeability coefficient λ calculated from the gas emission volume at different times have a good reproducibility. The new on-site measurement method for the permeability coefficient of coal seams is completely the same as the current method without adding additional workload. However, the new calculating method is more accurate and reliable.

The responses of gel electrolytes to stimuli make them useful in applications such as sensors and actuators. However, few studies have explored their transport properties from a molecular viewpoint. We studied the transport coefficients of gel electrolytes based on perfluorinated sulfonic acid using molecular dynamics simulations. The transport coefficients for electric and pressure fields, namely, the ionic conductivity, Darcy permeability, and cross coupling constant, were calculated based on Kubo's linear response theory from the corresponding velocity correlation functions and mean square displacements. The effects of the water content of the gel electrolyte and those of the monovalent cationic species were also analyzed. The calculated transport coefficients qualitatively agree with the reported experimental results. The role of the cross coupling constants in determining the functional efficiency of gel electrolytes as pressure sensors or electroactive actuators is discussed. [ABSTRACT FROM AUTHOR]

This study looks at the Darcy–Brinkman flow across a stretched sheet of porous dissipation and frictional heating. The geometry of a steady flow of dust particles fluid through a porous material in the existence of slip effect and porous dissipation is the subject of this study. The equations that govern the system are shown and summarized as boundary layer assumptions, and then modified into framework of first-order DEs using the similarity approach. By using similarity transformation, a two-dimensional nonlinear partial differential equation is decreased to a sequence of nonlinear ordinary differential equations (ODEs). Then, by employing numerical techniques such as Maple packages, the solution of system of nonlinear equations is represented using the RK4 method. The numerical findings are derived under specific unique situations. The Nusselt number and coefficient of skin-friction are also given numerically. The increase in Brinkman number γ raises the temperature profile for both the dusty and the fluid phases. The results also demonstrate that rise in the suction number S falls the temperature distribution within the boundary layer for the dusty phase and fluid phase. For a variety of flow quantities of attention, the variation of parameters is studied, and the outcomes are reported in the shape of graphs and tables. Several industrial processes make advantage of boundary layer flow and heat transfer over such a stretched surface in porous materials. [ABSTRACT FROM AUTHOR]

Predicting the production amounts has great significance for exploitation of oil and gas resources. The flow-geomechanical coupling effect plays an important role in predicting production. Shale rocks and the stress-dependent permeability model are critical for representing this coupling effect. The pore network of shale rock is not abundant like that of coal rock, and the matrix blocks of shale rock are not completely separated by the pore network. There is stress concentration around the pores when shale rock is deformed. Based on previous studies, the stress-dependent permeability model considering the impact of stress concentration is used in this study to build a numerical simulation model for flow-geomechanical coupling in a shale gas reservoir and validation using field data. Sensitivity studies are conducted to discuss the difference in production prediction between the new and common models. The main conclusions of this study are as follows: 1) The new model can fit both the field and experimental data well; the average error in daily production rate between the numerical solution and field data is 8%, which indicates that the new model can be used to predict shale gas production. 2) Under the geomechanical condition of a real reservoir, the difference in predicted production between models with and without stress concentration can be large and increase with the ratio of a to b. If this ratio is less than 50, the impact of stress concentration is not significant. Otherwise, the impact of stress concentration on production increases sharply and can exceed 20%. 3) The adsorption-induced strain enhances the impact of stress concentration on production. When the Langmuir pressure exceeds 1 MPa and Langmuir strain exceeds 0.01, the impact magnitude of stress concentration can exceed 10%. [ABSTRACT FROM AUTHOR]

This study observes the numerical analysis of Powell-Eyring hybrid nanofluid along a stretching sheet. The movement of sheet in x-direction is taken to be the source of motion in the fluid. Nanoparticles are considered as agents for increasing thermal properties of fluids. This research emphasizes the amalgamation of copper oxide and carbon nanotubes with engine oil as a base fluid. A significant increase is observed by adding these agents. Porous medium is considered using Darcy law. Magnetics field is also taken for studying mass transfer analysis. For heat transfer mechanisms, thermophoresis and Brownian diffusions are taken into account. The whole procedure is shown through nonlinear differential equations. Appropriate transformations are used for simplification purposes. After transformations, partial differential equations are converted into ordinary differential equations and handled through numerical technique. Shooting numerical technique has been used to solve the governing system of equations, and the obtained results are thoroughly examined and discussed graphically. The thermal characteristics of the hybrid nanofluid are analyzed, in the presence of thermal radiation and thermophoresis effects. To validate our results, a comparison analysis is drawn with existing literature in some specific scenarios. [ABSTRACT FROM AUTHOR]

This computational study was designed to examine the effect of alumina and copper on the flow of a nanofluid based on engine oil through a Darcy–Forchheimer porous media. The flow model incorporates the generalized radiative heat and mass transport rules. The Darcy–Forchheimer terms in the momentum equation and radiation term in the energy equation are integral parts of the governing nonlinear Navier–Stokes equations, which are two-dimensional partial differential equations. Under the constraint of the convective boundary, the stated PDEs are transformed into highly nonlinear versions of the ordinary differential equations. In order to solve the final ODEs, the numerical RK-45 approach is combined with the shooting methodology. Important aspects of the governing model include porosity, magnetohydrodynamics (MHD), a convective boundary, thermal radiation, and viscous dissipation. The final findings show that when the Forchheimer number increases, the velocity decreases because of the inertial effect included in the flow model. In addition, the velocity profile is improved due to the increased volume percentage of both kinds of nanoparticles. The temperature varies greatly depending on the volume fraction. A higher Biot number and the resulting convective border cause a greater heat flow than a non-convective barrier. For two particular examples, with and without MHD influence, interesting streamlines and contour graphs are produced. [ABSTRACT FROM AUTHOR]

In the process of coalbed methane development, drilling fluid and fracturing fluid cannot achieve absolute compatibility with formation. The incompatibility between the working fluid and reservoir will lead to the intrusion of working fluid into the reservoir and cause reservoir pollution. This is a very common phenomenon. There is a large amount of pulverized coal in the coal seam, and the intrusion of working liquid will be combined with the pulverized coal to form cement to block the seepage space in the reservoir. Since pressure relief and fracturing fluid backflow will be performed at the first time after fracturing, the intrusion range of the working fluid is small, generally reaching 10 m to 50 m. Compared with a conventional gas reservoir or shale gas reservoir, the working fluid loss during CBM development will seriously affect the subsequent production project and even make the gas well lose production capacity. On the other hand, in order to avoid this phenomenon, measures such as acidification or volumetric fracturing are sometimes used to improve the seepage environment near the well and near the fracture. The purpose of this study is to quantitatively evaluate the impacts of working fluid filtration and reservoir reconstruction on production. In this study, a single well productivity evaluation model and sensitivity analysis method considering drilling fluid filtration loss, fracturing fluid filtration loss, reservoir reconstruction and other processes is proposed. The formation mechanism of fluid loss during drilling and fracturing is described, and the productivity evaluation model considering fluid loss is combined with the Langmuir isothermal adsorption equation, steady-state diffusion law, Darcy's seepage law and Duhamel convolution formation. Combined with the distribution of actual gas reservoir flow characteristics, the sensitivity of single well productivity to gas reservoir porosity, gas reservoir permeability, coal seam adsorption coefficient, working fluid filtration loss and reservoir reconstruction measures are analyzed. Through the analysis and fitting of the actual production data on site, the relationship curve can better fit the field production data, and the evaluation results are in line with the drilling and fracturing conditions at that time and the subsequent production conditions, with small errors. The obtained method is suitable for predicting the productivity of fractured vertical wells in different working conditions and provides a basis for the development and productivity prediction of CBM reservoirs in China and in international cooperation. [ABSTRACT FROM AUTHOR]

Drainage capacity of pervious pavement mixtures is commonly measured using a falling head permeameter at hydraulic heads much higher than expected in the field. Recent advancements in computational fluid dynamics (CFD)– and X-ray computed tomography (XRCT)–based modeling eliminates the laboratory challenges of maintaining lower hydraulic heads. However, improper characterization in digital image processing (DIP) and finite-volume simulations resulted in significant errors in permeability measurements and fluid flow behavior. In addition, past studies have identified non-Darcy fluid flow characteristics in pervious pavement mixtures following the Izbash and Forchheimer laws. This paper attempts to bridge this research gap by comparing the Darcy and non-Darcy permeability parameters at different laboratory and field hydraulic heads using advanced XRCT-based modeling. It was found from the analyses that the use of laboratory hydraulic head could result in significant underestimation of permeability parameters compared with the field hydraulic heads for Darcy and Izbash equations (by up to 73%), and overestimation for Forchheimer equations (by up to 216%). Fluid flow behavior in pervious mixtures was found to be in transition flow regime (neither laminar nor turbulent) at both laboratory and field hydraulic gradients. Overall, this study can help in a better fundamental understanding of the current limitations of laboratory measurements and the need for XRCT-based numerical modeling to bridge field and laboratory permeabilities of pervious pavement mixtures. [ABSTRACT FROM AUTHOR]

A new microporous ceramic emitter (MCE) was recently developed to reduce the investment cost of subsurface irrigation systems. Nevertheless, a dynamic mechanism in the flow rate uncertainty of MCE was still unclear, which caused difficulty in making a water usage schedule for farmers. To address this issue, a simplified model was developed based on Darcy's law to quantify the emitter flow rate uncertainty. The model revealed that soil temperature indirectly caused the emitter flow rate uncertainty through its effect on the water viscosity inside the micropores of the ceramic material. • Microporous ceramic emitters present variable flow rate during entire tomato growth period. • Soil temperature highly affects flow rate variability. • A simplified model is developed to quantify the flow rate uncertainty of MCE. [ABSTRACT FROM AUTHOR]

Motivated by biological applications on tumour invasion through thin membranes, we study a porous medium type equation where the density of the cell population evolves under Darcy's law, assuming continuity of both the density and flux velocity on the thin membrane which separates two domains. The drastically different scales and mobility rates between the membrane and the adjacent tissues lead to consider the limit as the thickness of the membrane approaches zero. We are interested in recovering the effective interface problem and the transmission conditions on the limiting zero-thickness surface, formally derived by Chaplain et al. (2019), which are compatible with nonlinear generalized Kedem-Katchalsky ones. Our analysis relies on a priori estimates and compactness arguments as well as on the construction of a suitable extension operator, which allows us to deal with the degeneracy of the mobility rate in the membrane, as its thickness tends to zero. [ABSTRACT FROM AUTHOR]

It is widely known that a low Mach number gas flow can be approximated as incompressible at the leading order in a small Mach number expansion of the full solution. However, it has been shown recently that such an incompressible approximation becomes invalid for a semi-sealed system with no inlets and no boundary movements. Studies based on linearized compressible Navier–Stokes equations for such a system made of small capillary tubes have revealed some counter-intuitive flow characteristics such as no-slip flow with a slip-like mass flow rate. Here, we extend these works to gas drainage from a semi-sealed porous system. It is shown that gas drainage is solely driven by its volumetric expansion, and it cannot be approximated as an incompressible flow modulated by a small compressible effect. At the pore-scale, gas motion is governed by a damped rarefaction wave, and multiple scattering of the wave leads to an effective diffusion of the gas at the macroscopic scale. A large number of pore-scale simulations are performed for various pore structures, and the results are used to extract the macroscopic wave-mediated effective diffusion coefficient. Experiments are carried out to validate the wave-mediated effective diffusion model. The flow rates predicted by the effective diffusion model agree well with the experiments while results based on Darcy's law severely underestimate the flow rate. It is established that Darcy's law cannot be applied to a semi-sealed system, and no-slip flow with a slip-like flow rate is inherently embedded in the compressible Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

There are limited comparative studies on modeling fluid transport in fractured porous media. Hence, this paper systematically compares the steady-state creeping flow Stokes–Brinkman and Darcy–Darcy models for computational efficiency and accuracy. Sensitivity analyses were also conducted on the effect of fracture orientations, fracture sizes, mesh resolution, and fractures with Local Grid Refinement (LGR) under the FEniCS computational framework. Both models were validated numerically, and the accuracy of their solution is compared using the R-squared metric and L2 norm estimates. Key results showed that both models have similar pressure and velocity field solutions for a given fracture orientation. The computational time required for solving the Stokes–Brinkman models for a single fracture case was unusually lower than that of the Darcy–Darcy model when the pressure and velocity terms in the Darcy–Darcy model were solved simultaneously using two equations, contrary to where only one equation solves for the pressure and the velocity is obtained by projecting the gradient of pressure onto a vector space. The Stokes–Brinkman model is more sensitive to mesh resolution, and as a result, the Darcy–Darcy model tends to be more accurate than the Stokes–Brinkman model at low resolutions. Local Grid Refinement (LGR) can improve the Stokes–Brinkman model's accuracy at low mesh resolution. Furthermore, both models showed similar results when compared for complex fracture systems such as multiple fracture cases: interconnecting and isolated fractured porous media systems under low-velocity and steady-state creeping flow conditions. The FEniCS code in this paper is shared for future researchers to reproduce results or extend the research work. [ABSTRACT FROM AUTHOR]

This study envisions the hydrothermal characteristics of a viscous fluid in a homogenously permeable hexagonal enclosure. Permeability aspects in the flow domain are described by employing the Brinkman-extended Darcy law. A corrugated hexagonal enclosure along with the placement of a star-shaped fin is taken into account. Heated rectangular blocks at horizontal extremities are installed and sliding sides of the enclosure are considered to be cold to provide convegtive potential to the flow. In addition, adjoining portions of the heated rectangular blocks are supposed to be adiabatic. The dimensionless governing .quations of the resultant problem are derived initially and then solved numerically by implementing the Galerkin finite element approach, and COMSOL is obliged. For this purpose, first, domain discretization is demonstrated in view of 2D elements by performing hybridized meshing. Then, the system of non-linear equations is resolved by a non-linear solver (PARADISO). The grid convergence test is performed to confirm the credibility of the carried out simulations by calculating the average Nusselt number at different refinement levels. A change in associated distributions against the involved physical parameters (Darcy number (Da), Rayleigh number (Ra), and Prandtl number (Pr)) for a wide range is revealed through graphs and tables. Quantities like kinetic energy and heat flux (local and average) are also evaluated through concerned parameters. The results clearly demonstrate that the Darcy number tends to reduce the heat transfer rate. In particular, it is depicted that by increasing the Rayleigh number (Ra), strengthening in the temperature potential arises in the system, thereby magnifying the heat transfer rate. Moreover, it is disclosed that by reducing the Darcy number, kinetic energy shows a decreasing trend. [ABSTRACT FROM AUTHOR]

We employ the Baker–Campbell–Hausdorff formula to derive closed-form expressions for the effective properties, including emergent Willis coupling, of a one-dimensional heterogeneous poroelastic medium consisting of a periodically repeating two-layer unit-cell. In contrast to the elastic and fluidic analogs, the Willis coupling of this periodic poroelastic medium does not vanish in the low-frequency limit. However, the effective wavenumber and impedance of this asymmetric lamellar material demonstrate symmetric reflection and absorption behavior that is indicative of symmetric structures in the low-frequency limit due to the effect of Darcy's law on the dynamic effective density, which is inversely proportional to frequency. These closed-form expressions are validated against results obtained by direct numerical evaluation. The scattering coefficients, particularly the two reflection coefficients for incidence from either side of a finite length asymmetric structure, are different at non-zero frequencies but still in the metamaterial limit and are correct when the Willis coupling is included. The results show that asymmetry in poroelastic layers results in direction-dependent absorption coefficients, one of which could be optimized based on layer properties and asymmetry factors. As a consequence, the frequency range of validity of these scattering coefficients is wider when the Willis coupling matrix is accounted for than in its absence. This work paves the way for better control of elastic and acoustic waves in multiphase materials by considering poroelastic behavior. [ABSTRACT FROM AUTHOR]

This work investigates the scattering of oblique incident waves by two floating horizontal porous plates over a trench-type sea bed to study the role of different pairs of barriers in dissipating the incident wave energy. This problem is modelled based on Darcy's law for flow past a porous structure. Havelock's expansions of water wave potentials, suitable matching conditions, and the algebraic least-square method handle the boundary value problem. The role of the horizontal porous plates is studied by analysing the scattering coefficients, energy loss, hydrodynamic wave force and free surface elevation through graphs which show a periodic oscillatory pattern as a function of gap length. The study reveals that if the porous effect parameter of plates or the length of plates is increased, more energy is dissipated and the plates experience less wave force, and the free surface elevation on the lee side is decreased. The present results also signify that as compared to rigid plates, significant changes are found in wave scattering coefficients, hydrodynamic force and free surface elevation due to the consideration of one porous plate along with one rigid plate and also two porous plates, where a pair of porous plates are more effective as compared to one porous plate. The present study reveals that the scattering of water waves by two floating horizontal porous plates over uneven bottom topography plays a vital role in constructing floating structures having more staying power in harsh wave environments. [ABSTRACT FROM AUTHOR]

As more and more promising applications of magnetic nanoparticles in complicated environments are explored, their flow properties in porous media are of increasing interest. We here propose a hybrid approach based on the multiparticle collision dynamics method extended to porous media via friction forces and coupled with Brownian dynamics simulations of the rotational motion of magnetic nanoparticles' magnetic moment. We simulate flow in planar channels homogeneously filled with a porous medium and verify our implementation by reproducing the analytical velocity profile of the Darcy–Brinkman model in the non-magnetic case. In the presence of an externally applied magnetic field, the non-equilibrium magnetization and friction forces lead to field-dependent velocity profiles that result in effective, field-dependent permeabilities. We provide a theoretical expression for this magneto-permeability effect in analogy with the magneto-viscous effect. Finally, we study the flow through planar channels, where only the walls are covered with a porous medium. We find a smooth crossover from the Poiseuille profile in the center of the channel to Brinkman–Darcy flow in the porous layers. We propose a simple estimate of the thickness of the porous layer based on the flow rate and maximum flow velocity. [ABSTRACT FROM AUTHOR]

The basis for ensuring the safe operation of hydraulic structures is facility monitoring systems. The introduction of software tools for diagnostic modelling of filtration flows into the software of such systems is an objective step caused by recent real-life events. The aim of this study is to improve the accuracy of existing methods for numerical modelling of two-dimensional stationary filtration flows using the mesh method in the software of the facility monitoring system. The methods used in the study included the mesh method, the finite difference method, as well as approximation methods and numerical algorithms. As a result of the study, it was found that the proposed method of organizing the iterative computing process was effective and useful. Its application can significantly reduce the complexity of software development, as it is based on the formalization and standardization of operations, which simplifies the programming process. In addition, the use of conventional loop statements makes the process of writing programmes more understandable and accessible to developers. The additional array used in the algorithm allows easily changing the configuration of the grid boundaries and the order of operations for each node, which makes the method flexible and suitable for various challenges. A special advantage of the algorithm is its logical simplicity, which contributes to successful adaptation in the case of using multiprocessor systems. Thus, the results of the study confirm the high efficiency and potential of the proposed method for use in practical computing tasks. The proposed method of iterative computation is of considerable practical importance in the field of software development for numerical modelling, since its use simplifies the programming process and provides flexibility in working with different problem conditions, which makes it an important tool for a wide range of research and practical applications in hydraulic engineering and related fields.. [ABSTRACT FROM AUTHOR]

Numerical simulation was performed for unsteady natural convection flow and heat transfer in a porous medium using the generalized Maxwell model and fractional Darcy's law with distributed order time fractional derivatives. The finite volume method combined with the fractional L1 scheme was used to solve strongly coupled governing equations with nonlinear fractional convection terms. Numerical solutions were validated via grid independence tests and comparisons with special exact solutions. The effects of porosity, Darcy number, and relaxation time parameters on transport fields are presented. The results illustrate that porosity and permeability have opposite influences on temperature and velocity profiles. Moreover, the relaxation time parameters have remarkable effects on velocity profiles, and the variations possess significant differences. [ABSTRACT FROM AUTHOR]

This study numerically examines the fluid flow in porous media used in desalination. This topic is of significant current interest in the fields of science, engineering and technology, particularly in the process of water filtration. Moreover, in this work, we are attracted to correlation and diffusion process of the porous medium below the effect of permeability, dynamic pressure and friction coefficient. These parameters characterized the fluid flow in porous medium. To study numerically this phenomenon, many models have been proposed. However, we developed our investigation by using the Langevin dynamics model. Furthermore, this dynamic framework is based on Newton's second law and Darcy's law. Hence, we modeled the medium as a set of random diameters pores, which are dispersed randomly. The obtained results indicate that the average velocity time evolution presents an exponential profile with two different states: the first is transient and the second is permanent. The two regimes are separated by a cross-over time. Furthermore, time evolution exhibits an increasing profile versus the permeability, then it presents a decreasing profile versus the friction coefficient. Likewise, the diffusion process and correlation are tested for different parameters, especially the permeability and the dynamic pressure. We remark that the effective diffusion coefficient decreases exponentially with permeability and increases linearly with dynamic pressure. Hence, the fluid flow correlation in porous media presents a Gaussian function profile, with standard deviation function which increases exponentially with permeability. [ABSTRACT FROM AUTHOR]

Clay is widely encountered in nature and directly influences seepage behaviors, exerting a crucial impact on engineering applications. Under low hydraulic gradients, seepage behaviors have been observed to deviate from Darcy's law, displaying a non-linear trend. However, the impacts of clay content on non-linear seepage behavior and its pore-scale mechanisms to date remain unclear. In this study, constant-head seepage experiments were conducted in sand–clay porous media under various hydraulic gradients. Low-field nuclear magnetic resonance (LF-NMR) technology was utilized to monitor the bound-water and free-water contents of sand–clay porous media under different seepage states. The results show a threshold hydraulic gradient (i0) below which there is no flow, and a critical hydraulic gradient (icr) below which the relationship between the hydraulic gradient (i) and seepage velocity (v) is non-linear. Both hydraulic gradients increased with clay content. Moreover, the transformation between bound water and free water was observed during the seepage-state evolution (no flow to pre-Darcy or pre-Darcy to Darcy). As the hydraulic gradient reached the i0, the pore water pressure gradually overcame the adsorption force of the bound-water film, reducing the thickness of the bound-water film, and causing non-linear seepage behavior. When i0 < i < icr, the enlarging hydraulic gradient triggers the thinning of bound water and enhances the fluidity of pore water. Moreover, the increasing clay content augments the bound-water content required for the seepage state's change. [ABSTRACT FROM AUTHOR]

[Display omitted] • Estimated amount of ∑ 26 PFAS released from landfills (M ̇ SW) was 36.8 g/ha-yr. • 97% and 3% of M ̇ SW was found in leachate and stormwater, respectively. • Less than 1% of M ̇ SW was found in gas condensate and groundwater. • ∑ 8 PFAA-precursors/∑ 26 PFAS was consistent in the leachate released. • PFAS from landfills will be released for an estimated period of over 40 years. Per- and polyfluoroalkyl substances (PFAS) have been found at high levels within landfill environments. To assess PFAS distributions, this study aimed to evaluate PFAS mass flux leached from disposed solid waste and within landfill reservoirs by mass balance analyses for two full-scale operational Florida landfills. PFAS mass flux in different aqueous components within landfills were estimated based on PFAS concentrations and water flow rates. For PFAS concentration, 26 PFAS, including 18 perfluoroalkyl acids (PFAAs) and 8 PFAA-precursors, were measured in samples collected from the landfills or estimated based on previous studies. Flow rates of aqueous components (rainfall, evapotranspiration, runoff, stormwater, groundwater, leakage, gas condensate, and leachate) were evaluated through the Hydrologic Evaluation of Landfill Performance model, water balance, and Darcy's Law. Results showed that the average PFAS mass flux leached from the solid waste standardized by area was estimated as 36.8 g/ha-yr, which was approximately 1 % to 3 % of the total amount of PFAS within the solid waste. The majority of PFAS leached from the solid waste (95 % to 97 %) is captured by the leachate collection system, with other aqueous components representing much smaller fractions (stormwater system at 3 % to 5 %, and gas condensate and groundwater at < 1 %). Also, based on the results, we estimate that PFAS releases will likely occur at least over 40 years. Overall, these results can help prioritize components for waste management and PFAS treatment during the anticipated landfill release periods. [ABSTRACT FROM AUTHOR]

In this paper, based on the experimental parameters of polar permafrost formation, the mathematical module, solid mechanics module, and Darcy's law module of COMSOL Multiphysics software are used to realize the coupled solution of PDE of temperature field, moisture field, and stress field considering the ice-water phase transition and moisture convection, and the relationship between the permafrost moisture convection and temperature change is analyzed by using the heat-flowsolid-moisture mutual coupling, which reveals that the law of action of low temperature intrusion into rock formation by polar drilling. [ABSTRACT FROM AUTHOR]

The measurement of groundwater exchange between neighboring regions is a critical topic in water resource management and can usually be achieved through a combination of field investigations and the use of groundwater flow models. In this study, we employed the water balance and Darcy's law methods, utilizing downscaled Gravity Recovery and Climate Experiment (GRACE) and GRACE-Follow On (GRACE-FO) data to assess groundwater exchange patterns in the Beijing-Tianjin-Hebei (BTH) region of China. Additionally, we determined the contributions of human activities and climate factors to the observed variations via residual analysis. The results revealed a consistent decrease in groundwater storage in the study area since 2008, especially in the spring and summer months. The groundwater exchange rates calculated by 1° and 0.05° groundwater storage anomalies (GWSAs) were basically consistent, and the downscaled GWSAs could better reflect the small-scale groundwater exchange characteristics. The groundwater exchange rate showed a decreasing trend from the Piedmont plain to the coastal areas. A notable trend of declining groundwater exchange between the Taihang Mountains and Piedmont plains was observed, and the downward trend gradually intensified from north to south between 2003 and 2007. After 2008, there was an increasing trend, and coastal areas exhibited the smallest amount of groundwater exchange. Human activities emerged as the predominant factor accounting for more than 90.9% of the overall reduction in groundwater storage, while climate change imposed a minimal influence on groundwater storage variations. The insights obtained in this study hold significant implications for groundwater resource planning and management in the region. [ABSTRACT FROM AUTHOR]

In recent years, there has been a spike in interest in multiphase tissue growth models. Depending on the type of tissue, the velocity is linked to the pressure through Stoke's law, Brinkman's law, or Darcy's law. While each of these velocity-pressure relations has been studied in the literature, little emphasis has been placed on the fine relationship between them. In this paper, we want to address this dearth of results in the literature, providing a rigorous argument that bridges the gap between a viscoelastic tumor model (of Brinkman type) and an inviscid tumor model (of Darcy type). Specifically, we prove the convergence of solutions of the Brinkman nonlocal transport system toward a weak solution of the Darcy nonlinear parabolic system in the limit of vanishing viscosity. [ABSTRACT FROM AUTHOR]

Flow fluctuations that are commonly associated with multiphase flow in porous media are studied using concepts from non-equilibrium thermodynamic and statistical mechanics. We investigate how the Green–Kubo formulation of the fluctuation dissipation theorem can be used to predict the transport coefficient from the two-phase extension of Darcy's law. Flow rate-time series data are recorded at the millisecond timescale using a novel experimental setup that allows for the determination of flow fluctuation statistics. By using Green–Kubo relations, a transport coefficient is predicted based on the integrated autocorrelation function. Notably, this coefficient aligned closely with the total effective phase mobility computed using Darcy's equation for multiphase flow, particularly in scenarios where a linear relationship between flow rate and pressure gradient was observed. Our results open a new field of coefficient explorations where microscale fluctuations during multiphase flow are directly linked to macroscale parameters. [ABSTRACT FROM AUTHOR]

Copyright of Hydrogeology Journal is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Hydrogeology Journal is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copper powder and copper wire mesh were used as raw materials, and porous copper powder/mesh plates were prepared by pressing, rolling, and vacuum sintering. The plate morphology was observed by scanning electron microscopy. The air permeability of the porous plates was tested according to Darcy's law, and uniaxial tensile tests were carried out on the porous plates to determine the influence of raw material mesh number and powder content on the porous plates' permeability and tensile mechanical properties. The porous plate was fabricated into a restrictor of an aerostatic thrust bearing, and the static bearing performance of the bearing was tested on a bearing capacity testing platform. The results showed that the copper powder/mesh porous plate had a uniform pore distribution and a porosity range of 10% to 30%; the higher the porosity and lower the powder concentration, the better the performance was in terms of gas permeability. Tensile mechanical properties improved with decreasing porosity and increasing powder content. At a gas film thickness of 10 μm, the prepared gas hydrostatic thrust bearing could support a maximum load of 381.1 N. [ABSTRACT FROM AUTHOR]

In complex marine environments, the wave-induced instantaneous liquefaction of the seabed is a key issue for the long-term safety control of marine structures. Existing computational frameworks for instantaneous liquefaction result in unreasonable tensile stresses in a non-cohesive seabed. To address this issue, a liquefaction-associated non-Darcy flow model has been proposed, but it has only been applied to the scenario of a pure seabed without a structure. In this study, we applied the previously proposed non-Darcy flow model to investigate the mechanism of wave–seabed–structure interactions under extreme wave loading considering a pipeline fully buried in a non-cohesive seabed. By comparing the liquefaction depths in the presence and absence of structures, it was found that the existence of structures weakens the attenuation of the pore pressure amplitude and influences the overall pore pressure distribution. Parametric studies were conducted. It was found that the liquefaction depth from the non-Darcy model is approximately 0.73 times that from the traditional Darcy model, regardless of whether or not a pipeline is involved. A quantitative relationship between the wave loading and structural size was established. The liquefied zone above the buried pipeline was found to be smaller than that in a pure seabed without a structure. A tentative explanation is provided for this phenomenon. [ABSTRACT FROM AUTHOR]

Non-Newtonian nanofluids are widely utilized in medical and engineering fields, such as in cooling of microchips, lubrications, cancer therapy, drug delivery etc. In the present article, we focused on the electro-osmotic effect on the peristaltic transport of a non-Newtonian nanofluid inside a horizontal micro-channel. The fluid obeys Williamson model, flowing through a porous medium with modified Darcy's law. In addition, the effects of a chemical reaction with the contribution of activation energy are taken in consideration. Furthermore, in the case of modified Darcy's law, the apparent viscosity of the fluid is used in the governing equations. Furthermore, when temperature of the hot wall tube is less than three times that of the cold wall, the term of the activation energy is simplified by using Taylor expansion.The governing equations that illustrate the velocity, temperature, and concentration of nanoparticles distributions are considered and simplified under the assumptions of a long wavelength and low Reynolds number. The homotopy perturbation method is used as semi-analytical solution for the governing equations. Moreover, some figures are used to illustrate and discuss the role of physical parameters entering the problem on the obtained solutions. Since, most of non-Newtonian fluids are viscoelastic materials, it is important to discuss the effect of Weissenberg number that represents product of strain rate and relaxation time. It is found that Weissenberg number has dual effects on the axial velocity as well as the temperature and the concentration distributions. In addition, according to Fick's law of diffusion; the temperature and concentration distributions should have opposite effects, however, it is found that the increases in the thermophoresis parameter increases both temperature and concentration distributions. This means the nanoparticles are more concentrated when migrates from one side of the tube to the other side. Furthermore, the graphs illustrate the dissimilar effect of the activation energy and the rate of the chemical reaction on the concentration of nanoparticles. [ABSTRACT FROM AUTHOR]

Using extensive numerical simulation of the Navier–Stokes equations, we study the transition from the Darcy's law for slow flow of fluids through a disordered porous medium to the nonlinear flow regime in which the effect of inertia cannot be neglected. The porous medium is represented by two-dimensional slices of a three-dimensional image of a sandstone. We study the problem over wide ranges of porosity and the Reynolds number, as well as two types of boundary conditions, and compute essential features of fluid flow, namely, the strength of the vorticity, the effective permeability of the pore space, the frictional drag, and the relationship between the macroscopic pressure gradient ∇ P and the fluid velocity v. The results indicate that when the Reynolds number Re is low enough that the Darcy's law holds, the magnitude ω z of the vorticity is nearly zero. As Re increases, however, so also does ω z , and its rise from nearly zero begins at the same Re at which the Darcy's law breaks down. We also show that a nonlinear relation between the macroscopic pressure gradient and the fluid velocity v, given by, - ∇ P = (μ / K e) v + β n ρ | v | 2 v , provides accurate representation of the numerical data, where μ and ρ are the fluid's viscosity and density, K e is the effective Darcy permeability in the linear regime, and β n is a generalized nonlinear resistance. Theoretical justification for the relation is presented, and its predictions are also compared with those of the Forchheimer's equation. [ABSTRACT FROM AUTHOR]

Purpose. Investigation of the velocity fields of non-equilibrium fluid filtration in a layer under harmonic action on it and assessment of the influence of relaxation effects on the attenuation of the amplitude of initial disturbances within the framework of mathematical modeling of non-equilibrium plane-radial filtration. Methodology. A mathematical model of non-equilibrium plane-radial filtration with a generalized dynamic Darcy law in the form of a boundary value problem in a half-space with a harmonic excitation law at its boundary is considered. Based on the exact solutions of the boundary value problem, the attenuation of the amplitude of initial disturbances under the model’s parameters varying and influence of parameters on the size of the disturbed region are investigated. Findings. A differential equation modeling non-equilibrium filtration processes in the massif in the cylindrical reference frame was obtained. Using the method of separation of variables, a solution was constructed, bounded at infinity, to the model differential equation subjected to harmonic action at the layer boundary. The solution’s asymptotic approximation was constructed for large values of the argument. Using the asymptotic solution of the boundary value problem, the damping of velocity field during non-equilibrium filtration was analyzed depending on the frequency of the harmonic action, the ratio of the piezoconductivity coefficients of the layer, and the relaxation time. Profiles of the dependences of the size of the influence zone on the model parameters were plotted and the choice of parameters for optimal influence on the bottom-hole zone of the well was analyzed. Originality. On the basis of the non-equilibrium filtration model, it is shown that harmonic disturbances applied to the boundary of a semi-infinite layer can penetrate the reservoir over a greater distance under the conditions of manifestation of the relaxation mechanism of the fluid-skeleton interaction, compared to the equilibrium filtration process. Such an effect is observed at a finite interval of disturbance frequencies, while at high frequencies relaxation contributes to a more significant damping of disturbances. In the parametric space of excitation frequency – relaxation time, there is a locus of points that corresponds to the maximum size of influence zone of disturbances. Practical value. The obtained results are relevant for research on the impact of wave disturbances on the layer with the aim of intensifying filtration processes, as well as for creation of new wave technologies to increase the extraction of mineral resources from productive layers. [ABSTRACT FROM AUTHOR]

The space of production well plays a crucial role in the heat extraction performance of the Enhanced Geothermal System (EGS), which have the potential to meet the growing global energy demand as a reliable energy source. Nonetheless, there has been insufficient research and attention focused on comprehending the impact of the space of production well on the efficiency and effectiveness of EGS. In this work, a series of numerical simulations were conducted to assess the impact of the space of production well on heat extraction efficiency in EGS. Three different cases were considered: Case 50 with 50mproduction well spacing, Case 100 with 100mproduction well spacing, and Case 150 with 150m production well spacing. At the X-Y plane and Y-Z plane, the simulation results indicated that there were slight differences in temperature variation among the Case 50, Case 100 and Case 150. And the cooling area decreasing as the spacing of production wells decreased. Moreover, the delivery of cooling water via the injection well and its subsequent distribution to various reference points lead to a decline in temperature at each point, albeit with varying degrees of variation. Besides, the established efficiency (ef) for Case 50 is smaller than the Case 100 and Case 150 during the last 15 years. These findings contribute valuable insights to the exploration and exploitation of EGS systems and can serve as a guide for further research in this field. [ABSTRACT FROM AUTHOR]