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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]

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]

Extensive experiments have demonstrated that fluid flow in low‐permeability media deviates from Darcy's law at low pressure gradients, which is called pre‐Darcy flow. Although numerous pre‐Darcy flow models have been proposed, these models generally contain one or more empirical parameters with no clear physical meaning. In this paper, we present a simple unified model to describe pre‐Darcy flow in porous media by introducing the concept of loss permeability. The physical meaning of the loss permeability parameter and its relationship to permeability are analyzed. Based on the statistics of the loss permeability parameter results of 24 core samples, we found that there is a good positive correlation between the loss permeability parameter and the absolute permeability. A smaller loss permeability indicates a stronger fluid‐solid interaction and a stronger nonlinearity between the flow velocity and the pressure gradient. Taking a one‐dimensional linear unsteady flow of a slightly compressible fluid in a homogeneous porous medium as an example, we solve the pressure diffusion equation based on the proposed model using a finite difference method. Our results demonstrate that the rate of pressure propagation for pre‐Darcy flow is slower than that for Darcy flow for the entire observation period, which corrects previous conclusions. This study is highly important for improving the understanding of fluid flow in low‐permeability media. Plain Language Summary: Pre‐Darcy flow usually occurs in low‐permeability media when the pressure gradient is very low. As the pressure gradient increases, the flow gradually transitions from the pre‐Darcy flow to Darcy flow. For a long time, pre‐Darcy flow and Darcy flow were described using two relatively independent equations, which is highly inconvenient. Because it is very difficult to accurately determine the critical pressure gradient between the pre‐Darcy flow and the Darcy flow, especially for the fluid flow in natural low‐permeability reservoirs. How to perfectly unify the pre‐Darcy flow and the Darcy flow in a simple and easy‐to‐use model is a scientific problem that has been researched for decades. Although several unified models have been proposed in recent years, they all contain one or more empirical parameters with no clear physical meaning. In this study, we propose a simple unified model to describe the flow from the pre‐Darcy flow to the Darcy flow in a porous medium by introducing the concept of loss permeability. Then, we discuss the relationship between the loss permeability parameter and permeability based on a series of experimental data from published papers. Finally, we analyzed the pressure propagation feature for a one‐dimensional linear unsteady flow of a slightly compressible fluid in a homogeneous porous medium. Key Points: A simple unified model is proposed to describe the flow from pre‐Darcy flow to Darcy flow by introducing the concept of loss permeabilityThe physical meaning of the loss permeability parameter and its relationship to permeability are analyzedThe pressure propagation characteristics of pre‐Darcy flow and Darcy flow at the field scale are analyzed [ABSTRACT FROM AUTHOR]

This document is an editorial for a special issue on recent advances in hydrological modeling. It provides an introduction to hydrological models and their role in water resources operations and management. The editorial discusses the historical development of hydrological modeling, from empirical equations to sophisticated numerical models, and highlights the advancements in computing technology and data assimilation techniques that have improved the predictive capabilities of these models. It also summarizes the papers featured in the special issue, which cover topics such as machine learning in assessing the performance of hydrological models, improved estimation of extremes using adaptive filtering methods, and the impact of climate change on snow seasonality and water supply. The editorial concludes by emphasizing the importance of continued application and validation of novel techniques, particularly those involving machine learning and data assimilation, in hydrological modeling. [Extracted from the article]

To avoid or mitigate the unwanted water and gas content, inflow control devices (ICDs) are designed and installed in the well to disturb the water and gas breakthrough which are trying to overtake the oil inflow, water and gas coning and sand production. Smart wells with permanent downhole valves such as ICDs are used to balance production and injection in wells. A paramount issue regarding using downhole control devices is determining the required cross-sectional area of them for control of the imposed pressure drop across the device to stabilize the fluid flow. Current methods for calculating the opening size of the ICDs are mainly based on sensitivity analysis of the ICD flow area or optimization algorithms coupled with simulation models. Although these approaches are quite effective in oil field cases, they tend to be time-consuming and require demanding system models. This paper presents a fast analytical method to determine the ICD flow area validated by a genetic algorithm (GA). Analytically, a closed-form expression is introduced by manipulating Darcy's law applicable to multi-layer injection wells with different layer properties to balance the injection profile in the reservoir pay zone, based on equalizing injected front velocity in layers with different permeability. Considering various scenarios of analytical technique, GA optimization, and sensitivity analysis scenarios for ICD cross-sectional area determination, results for oil recovery, water production, water breakthrough time, and net present value (NPV) are discussed and compared. NPV values obtained by both analytical and GA approaches are virtually identical and greater than those of other scenarios. Compared to the base field case, the analytical method improved the oil recovery by almost 1%, reduced water production by almost 91%, and synchronized the water breakthrough time of high- and low-permeability layers (from a ratio of 1.76–1.06). The proposed analytical solution proved to be capable of providing desirable results with only one reservoir simulation run in contrast to GA and sensitivity analysis scenarios which require iterative simulation runs. The proposed analytical solution outperformed the GA as it is less computationally demanding in addition to its success in case of lowering water production for the field data. The findings of this study can help for a better understanding of the situation where water injection into the oil reservoir is problematic as the layers present different permeabilities which can induce problems such as early water breakthrough from the more permeable layer and hinder the success of the water injection process. Using ICDs and a faster and more accurate approach to calculate its cross-sectional area such as the analytical method that was used in this study can greatly increase the success rate of water injection in case of oil recovery and lower the amount of the produced water. [ABSTRACT FROM AUTHOR]

Backward erosion piping, a soil erosion phenomenon induced by seepage, compromises the stability of water-retaining structures such as dikes. During floods, the seepage in the dike body increases due to high water levels, which directly affects the progression of the piping channel. The formation of the piping channel then impacts the stability of the dike. In this paper, an improved piping model that considers the impact of seepage in the dike body is proposed based on Wewer's model. Specifically, we added a seepage field of the dike body to the original model to account for the impact of dike-body seepage on the evolution of piping. The seepage field of the dike body is solved using Darcy's law and the continuity equation for unsaturated porous media. In addition, this approach also incorporates the coupling effect of seepage stress. The accuracy of the model was verified through comparing the calculated results with the IJkdijk experiment and Wewer's results. The effects of BEP on dike stability were investigated using the proposed improved piping model. The two major conclusions of the study are that (1) the incorporation of unsaturated seepage enhanced the performance of the piping model, allowing it to more accurately simulate the development of pipe length and the changing of pore pressure; and (2) the formation of the pipe impacted dike stability, leading to a substantial reduction in the safety factor of the dike slope. [ABSTRACT FROM AUTHOR]

Thromboembolism, a global leading cause of mortality, needs accurate risk assessment for effective prophylaxis and treatment. Current stratification methods fall short in predicting thrombotic events, emphasizing the need for a deeper understanding of clot properties. Fibrin clot permeability, a crucial parameter in hypercoagulable states, impacts clot structure and resistance to lysis. Current clot permeability measurement limitations propel the need for standardized methods. Prior findings underscore the importance of clot permeability in various thrombotic conditions but call for improvements and more precise, repeatable, and standardized methods. Addressing these challenges, our study presents an upgraded, portable, and cost-effective system for measuring blood clot permeability, which utilizes a pressure-based approach that adheres to Darcy's law. By enhancing precision and sensitivity in discerning clot characteristics, this innovation provides a valuable tool for assessing thrombotic risk and associated pathological conditions. In this paper, the authors present a device that is able to automatically perform the permeability measurements on plasma or fibrinogen in vitro-induced clots on specific holders (filters). The proposed device has been tailored to distinguish clot permeability, with high precision and sensitivity, between healthy subjects and high cardiovascular-risk patients. The precise measure of clot permeability represents an excellent indicator of thrombotic risk, thus allowing the clinician, also on the basis of other anamnestic and laboratory data, to attribute a risk score to the subject. The proposed instrument was characterized by performing permeability measurements in plasma and purified fibrinogen clots derived from 17 Behcet patients and 15 sex- and age-matched controls. As expected, our results clearly indicate a significant difference in plasma clot permeability in Behcet patients with respect to controls (0.0533 ± 0.0199 d vs. 0.0976 ± 0.0160 d, p < 0.001). This difference was confirmed in the patient's vs. control fibrin clots (0.0487 ± 0.0170 d vs. 0.1167 ± 0.0487 d, p < 0.001). In conclusion, our study demonstrates the feasibility, efficacy, portability, and cost-effectiveness of a novel device for measuring clot permeability, allowing healthcare providers to better stratify thrombotic risk and tailor interventions, thereby improving patient outcomes and reducing healthcare costs, which could significantly improve the management of thromboembolic diseases. [ABSTRACT FROM AUTHOR]

The paper considers a mathematical model of the filtration of two immiscible incompressible fluids in deformable porous media. This model is a generalization of the Musket–Leverett model, in which porosity is a function of the space coordinates. The model under study is based on the equations of conservation of mass of liquids and porous skeleton, Darcy's law for liquids, accounting for the motion of the porous skeleton, Laplace's formula for capillary pressure, and a Maxwell-type rheological equation for porosity and the equilibrium condition of the "system as a whole." In the thin layer approximation, the original problem is reduced to the successive determination of the porosity of the solid skeleton and its speed, and then the elliptic-parabolic system for the "reduced" pressure and saturation of the fluid phase is derived. In view of the degeneracy of equations on the solution, the solution is understood in a weak sense. The proofs of the results are carried out in four stages: regularization of the problem, proof of the maximum principle, construction of Galerkin approximations, and passage to the limit in terms of the regularization parameters based on the compensated compactness principle. [ABSTRACT FROM AUTHOR]

This paper takes the freezing project of the North Arch Tunnel of the Hong Kong–Zhuhai–Macao Bridge as an example. Based on Darcy's law and the theory of heat transfer in porous media, using the coupled module of the temperature field and seepage field in the COMSOL Multiphysics software, numerical simulations of the freezing reinforcement of the new pipe curtain freezing method are conducted to study the influence of different factors on this method under seepage conditions. The research shows that an increase in the groundwater flow velocity will affect the development of frozen soil curtains, prolonging the formation time of frozen soil curtains. A rise in the initial ground temperature will increase the time required for the formation of frozen soil curtains during the freezing process, resulting in a slight increase in the temperature of the final frozen soil curtains. With an increase in the salinity of the groundwater, the temperature at the temperature measurement point upstream of the freezing pipe increases, while the temperature at the temperature measurement point downstream of the freezing pipe decreases. The average temperature of the frozen soil curtain also increases with an increase in the salinity of the groundwater. This study is expected to provide a valuable reference for similar projects in the future. [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]

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]

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Thermal ablation plays an important role in the aerospace field. In this paper, to study the chemical kinetics effects on heat transfer and surface ablation of the charring ablative material during aerodynamic heating, a charring ablation model was established using the finite element method. The AVCOAT 5026-39H/CG material, one typical thermal protection material used in thermal protection system, was employed as the ablative material and heated by aerodynamic heating condition experienced by Apollo 4. The finite element model considers the decomposition of the resin within the charring material and the removal of the surface material, and uses Darcy's law to simulate the fluid-flow in the porous char. Results showed that the model can be used for the ablation analysis of charring materials. Then effects of chemical kinetics on ablation were discussed in terms of four aspects, including temperature, surface recession, density distribution, and mass flux of pyrolysis gas. The pre-exponential factor and activation energy have different effects on ablation, while the effect of the reaction order is little. This paper is helpful to understand the heating and ablation process of charring ablative materials and to provide technical references for the selection and design of thermal protection materials. [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]

The uneven pore water distribution in unsaturated soil will cause water movement, change the hydraulic and mechanical characteristics of soil, and then cause soil damage. Therefore, it is important to study the hydraulic characteristics of unsaturated soil. In this paper, the law of conservation of mass and Darcy's law were used to analyze the unit soil after seepage to obtain a continuous equation. Combined with the soil-water characteristic curve (SWCC), the effect of matric suction and permeability coefficient of unsaturated soil on infiltration rate is substituted into the equation. Through the analysis of pore water stress of the unit soil, the function of the unsaturated permeability coefficient with the effective saturation degree is obtained, and the theoretical formula of the one-dimensional infiltration rate of unsaturated soil is derived. Compared with other models, this formula has fewer parameters and is easy to use. [ABSTRACT FROM AUTHOR]

This paper introduces a hybrid approach, merging the two-grid and domain decomposition strategies, to address the coupled Navier-Stokes-Darcy challenge, which is then elaborated and examined. First, the current Robin boundary condition-based domain decomposition technique is used to get the approximate solution on the coarse grid. Following the substitution of certain interface elements with coarse meshbased functions, an improved fine grid problem is obtained. [ABSTRACT FROM AUTHOR]

The Darcy's equation consists of the mass conservation equation and the Darcy's law that involves the hydraulic potential (or called pressure) and the fluid velocity, which governs the flow of an incompressible fluid through a porous medium. In this paper, we investigate the Legendre Galerkin spectral collocation least squares method for approximating the problem of Darcy flow in homogeneous medium and non-homogeneous medium, respectively. The proposed scheme can be solved the approximate solutions of the hydraulic potential and the average velocity of the fluid simultaneously. A symmetric positive definite coefficient matrix of the corresponding linear algebra equation is obtained by applying our scheme. Numerical examples are presented to validate the efficiency and accuracy of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, the coupled linear theory of thermoviscoelasticity for porous materials is considered in which the coupled phenomenon of the following four mechanical principles is proposed: the deformation of the skeleton of a porous solid, the volume fraction concept of the pore network, Darcy's law for the flow of a fluid through a porous medium, and Fourier's law of thermal conduction. The governing systems of equations of motion and steady vibrations are proposed. The fundamental solution of the system of steady vibration equations is presented explicitly by means of elementary functions, and its basic properties are established. By virtue of Green's identity the uniqueness theorems for the classical solutions of the basic internal and external boundary value problems (BVPs) of steady vibrations are proved. Then, the surface and volume potentials are presented and their basic properties are given. Finally, the existence theorems for classical solutions of the above-mentioned BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations. [ABSTRACT FROM AUTHOR]

A change in temperature induces thermo-osmosis (T-O) and thermofiltration (T-F) effects in soils, which can influence consolidation under certain conditions. Whether such conditions are met is not always known a priori. Therefore, this paper first develops a coupled model to assess these effects on the thermohydromechanical coupled behavior of saturated soils. The proposed model, which incorporates the extended Darcy's law and Fourier's law, is implemented in the finite-element method (FEM) solver OpenGeoSys version 6.3.3. To determine when T-O/T-F effects become relevant in an analysis, two characteristic numbers are then derived from the extended governing equations, which can be directly expressed by readily available soil and water parameters. Both theoretical and numerical analyses were conducted, and the results indicate that the T-F effect has little influence on heat transfer in typical soils, while the T-O effect appears to be significant for both sandy and clayey soils, provided the T-O coefficient exceeds 4.3 × 10-12 m²=ðs · KÞ. The T-O effect could even lead to the development of negative excess pore water pressure (PWP) and, consequently, soil compression, with relevance for the stability of geotechnical facilities subjected to temperature gradients. It is thus inferred that the T-O coefficient should be measured in conjunction with related necessary experimental work, in addition to soil permeability, to determine whether the T-O effect should be treated with caution. [ABSTRACT FROM AUTHOR]

In this paper, two different approaches for tumor growth modeling are presented and implemented. In the first part of the paper, a macroscopic approach using a PDE model, where the tumor is viewed as a cell mass, is implemented using the level-set method to track the tumor moving boundary in one hand by using Darcy's law to compute the normal velocity of the free boundary and on the other hand using the shape optimization to draw the normal velocity. In the second part of the paper, a microscopic approach, which focuses on the cellular scale, is presented. A hybrid model using agent-based modeling for the cell behavior and a PDE for the description of the tumor environment is presented. A sensitivity analysis is performed on the hybrid model for a better understanding of its impact on the tumor growth. Numerical experiments are provided for the proposed approaches. [ABSTRACT FROM AUTHOR]

When conducting numerical upscaling, either for a fractured or a porous medium, it is important to account for anisotropy because in general, the resulting upscaled conductivity is anisotropic. Measurements made at different scales also demonstrate the existence of anisotropy of hydraulic conductivity. At the "microscopic" scale, the anisotropy results from the preferential flatness of grains, presence of shale, or variation of grain size in successive laminations. At a larger scale, the anisotropy results from preferential orientation of highly conductive geological features (channels, fracture families) or alternations of high and low conductive features (stratification, bedding, crossbedding). Previous surveys of homogenization techniques demonstrate that a wide variety of approaches exists to define and calculate the equivalent conductivity tensor. Consequently, the resulting equivalent conductivities obtained by these different methods are not necessarily equal, and they do not have the same mathematical properties (some are symmetric, others are not, for example). We present an overview of different techniques allowing a quantitative evaluation of the anisotropic equivalent conductivity for heterogeneous porous media, via numerical simulations and, in some cases, analytical approaches. New approaches to equivalent permeability are proposed for heterogeneous media, as well as discontinuous (composite) media, and also some extensions to 2D fractured networks. One of the main focuses of the paper is to explore the relations between these various definitions and the resulting properties of the anisotropic equivalent conductivity, such as tensorial or non-tensorial behavior of the anisotropic conductivity; symmetry and positiveness of the conductivity tensor (or not); dual conductivity/resistivity tensors; continuity and robustness of equivalent conductivity with respect to domain geometry and boundary conditions. In this paper, we emphasize some of the implications of the different approaches for the resulting equivalent permeabilities. [ABSTRACT FROM AUTHOR]

A popular equation that is often employed to represent the relationship between the pressure loss and the fluid flow in fluidized or packed granular beds is the Ergun equation, which is an extension of Darcy's law. In this paper, the method of Smoothed Particle Hydrodynamics (SPH) is used to numerically study the flow field across a rectangular channel partially filled with a porous layer both at the Representative Elementary Volume (REV) scale using the Ergun equation and at the pore scale. Since the flow field can be estimated at the REV scale with a much lower cost compared to the pore scale, it is important to evaluate how accurately the pore-scale results can be reproduced at the REV scale. The comparison between both scales is made in terms of the velocity profiles at the outlet of the rectangular channel and the pressure losses across the clear and porous zones for three different arrays of solid grains at the pore scale. The results show that minimum differences in the flow structure and velocity profiles between the REV and the pore scale always occur at intermediate values of the porosity ( ϕ = 0.44 and 0.55). As the porosity increases, the differences between the REV and the pore scale also increase. The details of the pressure losses are affected by the geometry of the porous medium. In particular, we find that the pressure profiles at the REV scale match those at the pore scale almost independently of the porosity only when the grains are uniformly distributed in a non-staggered square array. [ABSTRACT FROM AUTHOR]

Controlling the microclimate condition inside a greenhouse is very important to ensure the best indoor conditions for both crop growth and crop production. To this regard, this paper provides the results of a novel approach to study a greenhouse, aiming to define a porous media model simulating the crop presence. As first, an experimental campaign has been carried out to evaluate air temperature and air velocity distributions in a naturally ventilated greenhouse with sweet pepper plants cultivated in pots. Then, the main aspects of energy balance, in terms of mass transfer and heat exchange, and both indoor and outdoor climate conditions have been combined to set up a computational fluid dynamics model. In the model, in order to simulate the crop presence and its effects, an isotropic porous medium following Darcy's law has been defined based on the physical characteristics of the crops. The results show that the porous medium model could accurately simulate the heat and mass transfer between crops, air, and soil. Moreover, the adoption of this model helps to clarify the mechanism of thermal exchanges between crop and indoor microclimate and allows to assess in more realistic ways the microclimate conditions close to the crops. [ABSTRACT FROM AUTHOR]

In this paper, we consider a vertically positioned cylindrical filtering element. Filtering occurs in the radial direction, therefore, the direction of the velocities of the liquid and suspended particles coincide with this radial direction. The flow can be considered to be one-dimensional and radially axisymmetric. To describe such a filtering process, the axisymmetric Stefan problem will be formulated. The radial mass balance formalism and Darcy's law are utilized to obtain a basic equation for cake filtration. The boundary condition at the moving surface is derived and the cake filtration is formulated in a Stefan problem. Equations are derived that describe the dynamics of cake growth in the cake filtration, and they are numerically solved. The influence of different model parameters on the compression and fluid pressure across the cake and the growth of its thickness are studied. [ABSTRACT FROM AUTHOR]

China is a country with the most widely distributed karst, and the karst is extensively developed in its southwesten part where 2,836 underground rivers are distributed with about 1,847.8 x 108 m³⋅a-1 of karst groundwater resources and a total discharge of 479.7 x 8 m³⋅a-1 in the dry season. These underground rivers become the main water source for people's life as well as the development of industry and agriculture in Southwest China. However, water shortage has often occurred in recent years, due to the unreasonable development and utilization of karst water resources. How to make scientific, reasonable and effective use of karst water resources has become a difficult problem in tackling water resource crisis. In this paper, we have studied the hydrological process and numerical simulation of groundwater in karst areas from the perspective of groundwater science, which is of great significance to the accurate evaluation, and rational development and utilzation of karst water resources. In this study, we take Dajing basin, a typical karst peak-cluster depression area in southern Guizhou Province, as the study area. Water-bearing media in karst areas often include karst pipelines with high permeability and dissolved gaps with low permeability. The flow mechanism of groundwater in these two media is quite different. The groundwater in the gap mainly accords with Darcy's law and the laminar flow mechanism, while the groundwater in the karst pipeline is mostly in the turbulent state due to the large flow rate. In the actual situation, the two media are independent of each other, but there is an interrelated process of hydraulic exchange on the boundary. Based on this, we adopt MODFLOW-CFP coupling model to carry out a numerical simulation of Dajing basin. MODFLOW-CFP is a dual-system coupling model based on dual structure theory. MODFLOW-CFP model contains three groundwater flow simulation methods. In this study, CFPM1, the most basic model, is adopted. In this pattern, the traditional groundwater flowing model is coupled with a specific pipeline model. The main purpose is to depict caves, cracks in interstitial space and basaltic aquifer pipes in karst aquifers, where groundwater can be fully or partially filled and flow patterns can be laminar or turbulent. Therefore, a complete simulation of the hydrological process of karst groundwater may help us to grasp the law of groundwater movement in Dajing basin, accurately evaluate karst water resources, and thus promote the rational development and utilization of the resources. The process of using MODFLOW-CFP to establish a mathematical model of groundwater in Dajing basin includes the establishment of porous media model in MODFLOW and pipeline model in CFP. Subsequently, the two models are combined together to identify the model and analyze the water balance, based on the coupling model. Finally, the water resources are evaluated and the mechanism of groundwater migration is studied. In this study, it is found that Dajing basin is a groundwater system with complete recharge, runoff and drainage conditions, and the North-South and the Northeast-Southwest trending structures control the distribution of regional karst aquifers and the development of karst. According to the buried conditions of groundwater and the practical significance of water supply, the main source of recharge in this area is atmospheric rainfall, and the main discharge is the outflow from the southern Dajing basin. Meanwhile, the simulation results show that the exchange capacity between pipes and porous media is 6,719.1 m³⋅a-1, mainly in the upper and middle reaches of Dajing basin. The total recharge water in the study area is 10,977.3 x 104 m³⋅a-1, and the recharge module is 133.495 m³⋅km-2⋅a-1. The rainfall inflow and infiltration accounts for 81.35% of the total recharge, and the total discharge is 10,813.47 x 104 m³⋅a-1, mainly from the outlet of the underground river. Based on the research findings, the migration mechanism of groundwater in Dajing basin is clarified, and new development and utilization of water resources are put forward to address the shortage of local water resources. [ABSTRACT FROM AUTHOR]

Reservoir simulation is to solve a set of fluid flow equations through porous media, which are partial differential equations from the petroleum engineering industry and described by Darcy's law. This paper introduces the model, numerical methods, algorithms and parallel implementation of a thermal reservoir simulator that is designed for numerical simulations of a thermal reservoir with multiple components in three-dimensional domain using distributed-memory parallel computers. Its full mathematical model is introduced with correlations for important properties and well modeling. Efficient numerical methods (discretization scheme, matrix decoupling methods, and preconditioners), parallel computing technologies, and implementation details are presented. The numerical methods applied in this paper are suitable for large-scale thermal reservoir simulations with dozens of thousands of CPU cores (MPI processes), which are efficient and scalable. The simulator is designed for giant models with billions or even trillions of grid blocks using hundreds of thousands of CPUs, which is our main focus. The validation part is compared with CMG STARS, which is one of the most popular and mature commercial thermal simulators. Numerical experiments show that our results match commercial simulators, which confirms the correctness of our methods and implementations. SAGD simulation with 7406 well pairs is also presented to study the effectiveness of our numerical methods. Scalability testings demonstrate that our simulator can handle giant models with billions of grid blocks using 100,800 CPU cores and the simulator has good scalability. [ABSTRACT FROM AUTHOR]

This paper presents an analytical model to describe the transient fluid flow to a horizontal fracture in frac‐packed vertical wells. A physical model is first established where a horizontal frac‐packed fracture is located in the middle of a cylindrical reservoir. The pressure distribution in the fracture is then derived concerning time and the distance to the wellbore. The analytical model assumes a homogeneous and isotropic reservoir where Darcy's law applies to a single‐phase fluid flow, a radial fracture with a radius much greater than pay zone thickness, and a constant fracture width. For ease of application, a Type Curve Matching approach is introduced which features the matching of a defined dimensionless pressure between field pressure data and model data, and some exemplar curves are illustrated in this paper. The principle of applying curve matching here is to tune model parameters to match the measured pressure/rate data. Once the curves are matched, the model parameters, that is, fracture permeability, etc, are naturally obtained. The validity of the derived model is informed in two ways. The results show that the model will degenerate to the classic radial flow equation for practical values of certain model parameters and upon reasonable simplification. Model validity is further verified by applying the type curve matching technique using field data. This model can be used as a quick and reasonable method to analyze the transient pressure/rate test data to reveal fundamental fracture and reservoir properties for a frac‐packed horizontal fracture at shallow depths where the vertical formation stress is the least in situ stress. [ABSTRACT FROM AUTHOR]

The fault water inrush is a key factor which leads to tunnel construction in karst regions. Based on the fluid mechanics principles, the paper addresses a numerical coupled model for karst fault tunnel with COMSOL Multiphysics software. Besides, the Darcy law equation, Brinkman equation, and Navier-Stokes equation are inserted to stimulate the steady flow of aquifer, the non-linear seepage of fault and the free flow in tunnel excavating area in software, respectively. Then, the pressure and flow velocity in three flow fields are analyzed under different permeability ratios in numerical model. It is shown that the fault permeability is the key factor affecting water inrush, and that the pressure and flow velocity change visibly in adjacent domains between two flow fields. [ABSTRACT FROM AUTHOR]

In this paper, a two-dimensional, steady, laminar boundary layer analysis is presented to analyze numerically the internal heat generation and Soret–Dufour effects on mixed convection flows of power-law fluids adjacent to a vertical flat plate maintained at variable heat flux and variable mass flux conditions in a Darcy porous medium. The Ostwald–de Waele power-law model is utilized here. The transformed governing equations are solved by the Keller box method. After performing comparisons with previously published results, good agreement is obtained. [ABSTRACT FROM AUTHOR]

There are many nanoscale pores in deep low permeability coal seams. The flow of coalbed methane (gas) in nanoscale pores belongs to the gas flow in porous media with medium and high Knudsen numbers. Its flow mechanism is one of the key unsolved scientific problems. In order to explore the gas transport law in nanopores of coal, a gas transport model based on microscopic boundary restriction was adopted to describe the gas flow law, and its rationality was verified by experimental data. The Field Emission Scanning Electron Microscope was used to scan the nanopores of customized anodized aluminum membrane. Then, the Maximally Stable Extremal Regions (MSER) algorithm of MATLAB and binarization algorithm were employed to quantify the pore structure parameters (equivalent pore size and porosity) of the membrane nanoscale pores. Finally, PMI micro-flow permeability tester was used to carry out different rarefied degree gas penetration experiments through anodized aluminum membranes, and the adopted gas transport model was verified. The results show that the binarization method is more accurate to characterize sample whose theoretical pore sizes are 20–35 nm, while MSER characterizes samples whose theoretical pore sizes are 110–150 nm and 200–300 nm more accurately. In other words, binarization method is more accurate for characterizing mesopores, while MSER algorithm is more accurate for macropores. The results have important reference value for more accurate extraction of nanopore parameters of porous media. Compared with traditional gas transport model, the adopted model considering the microscopic boundary restriction in this paper is closer to the experimental results. Moreover, it is suitable for describing the gas flow law in multiscale nanopores. The study provided important guiding significance for ascertaining the gas migration law in low permeability coal seam, improving the prediction accuracy of gas extraction and taking effective measures to increase production. The research results can further enrich the theoretical system of gas transport in coal, which is conducive to the efficient gas extraction, and is of great significance to promote the realization of carbon peak and carbon neutrality. [ABSTRACT FROM AUTHOR]

Nicotine is harmful to the health of smokers and the inhalation of second-hand smoke is more harmful. A high efficiency of nicotine filtration for a cigarette filter is much needed. This paper suggests a formulation to predict filtration efficiency of a filter with X- or Y-shaped fibers. Main effects affecting the efficiency are elucidated using a fractal modification of the Darcy's law. [ABSTRACT FROM AUTHOR]

Predicted evolution of the liquid height with an ideal falling-head setup (no outlet pressure drop and zero pressure at the sample bottom) for different permeability values. First, the mentioned limiting permeability value of HT ht is again chosen arbitrarily by the discussers (see previous point). Indeed, the proposed value of HT ht is solely based on the discussers' naked eye perception. [Extracted from the article]

Field tests indicate that temporary well shut-ins may enhance oil recovery from a shale reservoir; however, there is currently no systematic research to specifically guide such detailed operations in the field, especially for the design of the shut-in scheme and multiple rounds of shut-ins. In this study, the applicability of well shut-in operations for shale oil reservoirs is studied, and a numerical model is built using the finite element method. In order to simulate the production in a shale oil reservoir, two separate modules (i.e., Darcy's law and phase transport) were two-way coupled together. The established model was validated by comparing its results with the analytical Buckley–Leverett equation. In this paper, the geological background and parameters of a shale oil reservoir in Chang-7 Member (Chenghao, China) were used for the analyses. The simulation results show that temporary well shut-in during production can significantly affect well performance. Implementing well shut-in could decrease the initial oil rate while decreasing the oil decline rate, which is conducive to long-term production. After continuous production for 1000 days, the oil rate with 120 days shut-in was 9.85% larger than the case with no shut-in. Besides, an optimal shut-in time has been identified as 60 days under our modeling conditions. In addition, the potential of several rounds of well shut-in operations was also tested in this study; it is recommended that one or two rounds of shut-ins be performed during development. When two rounds of shut-ins are implemented, it is recommended that the second round shut-in be performed after 300 days of production. In summary, this study reveals the feasibility of temporary well shut-in operations in the development of a shale oil reservoir and provides quantitative guidance to optimize these development scenarios. [ABSTRACT FROM AUTHOR]

This paper puts forward a perspective or opinion that we can demonstrate Darcy's law is valid at any scale where fluid can be modeled/analyzed as a continuum. Darcy's law describes the flow of a fluid through a porous medium by a linear relationship between the flow rate and the pore pressure gradient through the permeability tensor. We show that such a linear relationship can be established at any scale, so long as the permeability tensor is expressed as a function of adequate parameters that describe the pore space geometry, fluid properties, and physical phenomena. Analytical models at pore scale provide essential information on the key variables that permeability depends on under different flow regimes. Upscaling techniques based on the Lippman-Schwinger equation, pore network models, or Eshelby's homogenization theory make it possible to predict fluid flow beyond the pore scale. One of the key challenges to validate these techniques is to characterize microstructure and measure transport properties at multiple scales. Recent developments in imaging, multiscale modeling, and advanced computing offer new possibilities to address some of these challenges. [ABSTRACT FROM AUTHOR]

Darcy's law has long been used to describe the flow in porous media. Despite the progress that took place in oil production industry research, it became clear that there is a loss of pressure, especially in the area near the wellbore region, where Darcy's law is not applicable. For this reason, Forchheimer presented his equation in 1910, where he added a new term to Darcy's law dealing with pressure loss due to inertial forces by introducing a new term, the β coefficient, into the equation. This paper presents a study of fluid flow through porous media, where water was used as a working fluid. Furthermore, the characteristics of the non-Darcy flow were analyzed by presenting the corresponding pressure and velocity gradient curves for each pressure. Extensive analysis indicates that many of the correlations available in the literature either have defective units or are the product of a small number of experiments. In this study, we benefit from relatively large samples, the radial flow, and the perforation in the middle of the samples. The properties of the samples were measured using mercury intrusion porosimetry. It was found that there is a direct relationship between the porosity and the grain's size; the greater the size of the grains, the greater the porosity, and vice versa. The non-Darcy coefficient term, β, is found to be inversely proportional to the porosity and permeability. In a previous study, the β was investigated for compressible flow scenarios; however, this study calculated it for an incompressible flow. Finally, by analyzing the β values of both studies, we could deduce new novelty correlations for the β coefficient term, where the permeability, porosity, and tortuosity are included. [ABSTRACT FROM AUTHOR]

Copyright of Canadian Journal of Chemical Engineering is the property of Wiley-Blackwell 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.)

The development of new scaling criteria for steam flooding process is presented in this paper. The mathematical development is done by using modified Darcy's law, constitutive relationships, constraints, and the initial and boundary conditions. Dimensional and inspectional analyses are used to develop sets of dimensionless groups by incorporating rock and fluid memory concept. The variety of scaling criteria and their comparative advantages and limitations are discussed. Currently available scaling criteria development for steam flooding processes used the same fluid, same porous media in model and prototype. However, it requires a high-pressure model with different porous media, which causes difficulties in scaling properties, and therefore, largely depends on pressure and the porous media itself. In this paper, different methods are presented which permit scaling of all properties dependent on pressure or temperature by relaxing the requirements of geometric similarity. A set of relaxed scaling criteria is determined to satisfy a major mechanism. A comparative study of different approaches and their relative merits and demerits are discussed. Approach 2 (same fluids, same pressure drop, same porous medium, and geometric similarity) seems to be the most appropriate for the steam flooding process; however, gravitational forces cannot be scaled properly with this approach. Approach 3 (same fluids, same pressure drop, same porous media, and relaxed geometric similarity) is suitable for this process if the effect of transverse dispersion is considered negligible. Finally, a table is developed which can act as a guideline to select an appropriate approach that best scales a major mechanism for a specific steam flooding recovery process. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Darcy model with magnetic field affect which is used to describe the double diffusive flow of a fluid containing a solute. Using the energy estimate methods, we derive the prior bounds of the solutions. By using these a prior bounds, the continuous dependence of the solutions to Darcy model on the magnetic coefficient and the boundary parameter is established. [ABSTRACT FROM AUTHOR]

Seepage-induced failure may disable the bearing capacity of foundations in dams and embankments. However, the evolution mechanism of the seepage failure process in granular soils is not well understood. In this paper, a series of laboratory hydraulic tests were performed to investigate the seepage failure process in sandy gravels and fine-grained sands. Seepage behaviors of the hydraulic gradient, seepage flow velocity, and permeability coefficient were observed, and then, the Reynolds number was obtained to describe the seepage regime. By linking the hydraulic gradients with the Reynolds number, the seepage failure process was quantitatively divided into four phases: (i) incubation (Re < 0.85), (ii) formation (0.85 ≤ Re ≤ 5), (iii) evolution (5 < Re ≤ 50), and (iv) destruction (50 < Re). The findings of the study identified an approximately linear relationship between the hydraulic gradient and the seepage velocity in the phases of incubation and formation in which the viscous drag effects are not negligible, corroborating Darcy's view. However, in the phases of evolution and destruction, the hydraulic gradient and the seepage velocity are nonlinearly related, indicating that the inertial force plays a leading role, and the quadratic equation is relevant for the regime transition from laminar flow to turbulent flow. Finally, the mechanism of each phase in the seepage failure process was clarified. Fine content and uniformity coefficient are internal factors that affect the potential of seepage failure, while the seepage force that drives the transport of fine particles is an underlying cause that promotes the development of seepage failure. This study will be quite useful in identifying the limits of applicability of the well-known "Darcy's law," in further improving the physical modelling associated with fluid flow through granular soils. [ABSTRACT FROM AUTHOR]

Copyright of Archives of Mining Sciences is the property of Polish Academy of Sciences 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.)

This paper investigates, with the help of micromechanics, the overall nonlinear filtration law of a porous solid containing impervious inclusions. At the microscopic scale, we assume that the fluid flow in the porous region is described by the Forchheimer law. More specifically, the nonlinear variational homogenization approach is considered to derive closed-form bounds for the macroscopic filtration law, which is based on velocity or pressure gradient-dependent potentials applied to a unit cell with uniform boundary conditions. The approach is developed in the case of a porous solid with impervious cylinders or spheres, for which we derive explicit analytic upper and lower bounds, considering appropriate simple trial fields. The closed-form expressions of the non-linear bounds are provided and compared to FFT solutions for various microstructures. [ABSTRACT FROM AUTHOR]

The paper considers an axisymmetric problem of filtering suspensions with the formation of a cake on the filter surface. It is supposed that the cake has elastic–plastic properties. Using the mass conservation equation and Darcy's law, the suspension filtration equations at the elastic–plastic regime are derived, which characterize the partial irreversibility of the filtration characteristics when the system is unloaded after loading. An equation is also derived that describes the increase in the thickness of the cake. Problems of suspension filtering for the derived equations are posed and numerically solved. The role of partial irreversibility of deformation on the filtration characteristics is estimated. Distributions of compression pressure, the concentration of solid particles in the cake, relative permeability in the mode of primary and secondary loading of the system, as well as in the mode of unloading after the first loading are obtained. The growth dynamics of the cake thickness are also established. The parameters of plasticity in terms of particle concentration and permeability mainly affect the corresponding indicators, i.e., on the particle concentration distribution and on the relative permeability of the cake. It is shown, that depending on the change in the model parameters characterizing the elastic–plastic properties of the cake, the filtration characteristics change significantly. This indicates a significant effect of the elastic–plastic deformation of the cake on the suspension filtration characteristics. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the asymptotic behavior of solutions of M 1 model proposed in the radiative transfer fields. Starting from this model, combined with the compressible Euler equation with damping, we introduce a more general system. We rigorously prove that the solutions to the Cauchy problem of this system globally exist and time-asymptotically converge to the shifted nonlinear diffusion waves whose profile is self-similar solution to the corresponding parabolic equation governed by the classical Darcy's law. Moreover, the optimal convergence rates are also obtained. Compared with previous results obtained by Nishihara, Wang and Yang in [29] , we have a weaker and more general condition on the initial data, and the conclusions are more sharper. The approach adopted in the paper is the technical time-weighted energy estimates with the Green function method together. [ABSTRACT FROM AUTHOR]

Since the wide applicability of axisymmetric consolidation model, the axisymmetric consolidation problem of unsaturated soils has gradually become a hot issue. However, the mixed boundary conditions of axisymmetric free strain consolidation of unsaturated soils have not been fully considered. The boundary condition is the main factor affecting the consolidation process with the determined consolidation model and related parameters. In this paper, the governing equations of water and air in the polar coordinate were given according to two stress state variables theory of unsaturated soils, Darcy's law, and Fick's law under the axisymmetric condition. Based on the free strain hypothesis, a series of semianalytical solutions of the axisymmetric consolidation for unsaturated soil grounds under four different boundary conditions are proposed by using the Laplace transform and the finite Hankel transform. After the correctness of the proposed governing equations and semianalytical solutions is verified by degeneration verification, the parametric consolidation characteristics of unsaturated soils under different parameters through numerical examples and parametric studies are analyzed. Combining the four boundary conditions, the entire consolidation process under homogeneous boundary will be overestimated compared to that under the mixed boundary. In other words, the time required to complete consolidation will be extended accordingly if the boundary condition is not homogeneous. It is clear that the study on the axisymmetric consolidation of unsaturated soils considering multiple boundary conditions is conducive to a more comprehensive understanding of unsaturated soils and provides strong theoretical support for engineering practice. [ABSTRACT FROM AUTHOR]