Darcy's Law Research Articles

Electroosmotic effect on the flow of hybrid nanofluid containing para and ferri-magnetic nanoparticles through the micro-channel implementing Darcy law

This study investigates the flow of an incompressible electroosmotic hybrid nanofluid through a micro-channel. The hybrid nanofluid consists of paramagnetic (Ta) and ferrimagnetic (Fe3O4) nanoparticles suspended in ethylene glycol. The Darcy model is applied to the porous media in the momentum equation, and its effects are also considered in the temperature equation, accounting for frictional and Joule heating effects. The micro-channel is influenced by both pressure and magnetic flux. The study derives an exact solution for the proposed model and evaluates key engineering parameters, such as the heat transfer rate. The findings show that a higher particle volume fraction reduces the velocity distribution, while an increased Darcy parameter decreases the rate of heat transfer. Additionally, the heat transfer rate diminishes with increasing Darcy parameter and electric flux. Notably, the ferrimagnetic nanofluid exhibits better thermal conductivity than the paramagnetic nanofluid.

Design Constant Head Permeability Meter Digital: A Project-Based Learning Media

The permeability coefficient value is one of the most important parameters in soil mechanics. Quick, simple, and digital direct soil permeability tests in the field are needed to obtain data representing conditions. This research aims to create a portable soil permeability test tool based on microcontroller automation used as a project-based learning for Transportation Cadets peculiarly Palembang Aviation Polytechnic Cadets for new experiences of new learning circumstances. This research method based on the principle of permeability testing using the constant-head method by analyzing the requirements quantitatively. This principle uses water change level parameters, which are used to test the infiltration rate in sample soil. Furthermore, measurements of changes in water level are used by water leveling sensors and processed using Arduino Uno based on fuzzy logic with access to results via the web, tool design, and simulation using SIMULINK software. The results of designing a digital measuring instrument for permeability using the constant head method have been validated for its schematic circuit using SIMULINK and can work without error. In conclusion, a model based on Darcy's Law equation and constant head to find the permeability coefficient can be generated, which can then be a prototype of the tool. It concluded the design of constant head permeability meter digital is useful as project-based leaning media for the Palembang aviation polytechnic. Furthermore, the equipment design will be the first digital measuring tool for permeability coefficient using the constant head method. The design has advantage to measure the soil permeability coefficient at the airport in the fastest way.

Permeability of large‐scale fractures with ununiform proppant distributions in coalbed methane development

AbstractThe coalbed methane (CBM) productivity is directly determined by the fracture permeability during hydraulic fracturing, which is regulated by the distribution of proppants. The proppant may be unevenly distributed in the fracture because of variables like the architecture of the fracture and the characteristics of the sand‐carrying fluid. This study used two types of random functions to produce different ununiform distributions of proppant clusters in large‐scale fractures, with the aim of investigating the effect of these distributions on the overall permeability of the fracture. A model of fluid‐structure coupling is proposed. The closure of large‐scale fractures under in‐situ stress is analyzed using solid mechanics and the penalty function; the CBM flowing in proppant clusters and the high‐speed channel between them is simulated using Darcy's law and the Navier–Stokes equation, respectively; and the overall permeability of fractures is computed using the fluid pressure drop throughout the fracture and the fluid flowing velocity in the fracture's outlet. Since most CBM flows along high‐speed channels between the proppant clusters, the simulated findings show that the overall permeability of fractures with an uneven distribution of proppant clusters is significantly higher than that of the proppant cluster itself. As CBM becomes more discretely distributed, the proportion of CBM flowing within the proppant cluster continuously drops. As the permeability of the proppant cluster increases, the volume ratio of proppant clusters decreases, and the distribution of proppant clusters becomes more discrete, the overall permeability of the fracture continuously increases.

From Pre‐Darcy Flow to Darcy Flow in Porous Media: A Simple Unified Model

AbstractExtensive 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.

Profiles of suction stress of layered soils under infiltration conditions and its applications

Suction stress is critical for understanding the hydrological and mechanical behavior of unsaturated soils in construction and engineering. Many soils encountered in these fields exhibit layering due to geological sedimentation or artificial reinforcement. This study establishes the vertical distributions of matric suction and degree of saturation for layered soils under one-dimensional (1D) steady-state seepage, using the Darcy law and constitutive relationships of unsaturated soils. A closed-form suction stress is derived for an arbitrary number of layers and soil types. Hypothetical layered soils with varying hydraulic properties at four infiltration rates are assessed. Results show that soil stratification affects the suction stress profiles, with the impact depending on infiltration rates, soil configuration, and layer thickness. Abrupt variations in suction stress occur at most layered interfaces due to differences in permeability between adjacent layers. The suction stress profiles can be used to evaluate the earth pressure and stability of layered slopes under seepage conditions. Several case studies of multi-layered slope failures in Southern Italy are presented to demonstrate the suitability of the proposed framework for evaluating the stability of layered slopes under rainfall conditions.

Development and validation of an oil palm model for a wide range of planting densities and soil textures in Malaysian growing conditions

A semi-mechanistic oil palm growth and yield model called Sawit.jl was developed to account for a wide range of planting densities and soil textures under Malaysia's climate conditions. The model comprises components related to meteorology, photosynthesis, energy balance, soil water content, and crop growth. The model simulates instantaneous meteorological properties using daily weather data, calculates simultaneous evaporation from crop and soil with the Shuttleworth-Wallace model, determines soil water content through Darcy's law, and adapts a biochemical C3 model for photosynthesis. The model is also parameterized using updated measurements from the newer tenera oil palm, including temperature-dependent Rubisco kinetics, specific leaf area, and the partitioning of nutrients and dry matter between various tree parts. Sawit.jl was validated using historical field measurement data from seven Malaysian oil palm sites, encompassing palm ages spanning 1–23 years. These seven sites differed in soil type (Inceptisols and Ultisols), planting density (82–299 palms ha−1), soil texture (27–59 % clay and 7–67 % sand), and rainfall (1800–2800 mm yr−1). The model showed overall good accuracy in simulating oil palm parameters (except for trunk weight) across diverse conditions, with model agreement metrics ranging from 6 to 27 % for model absolute errors, −22 to +17 % for model bias, and 0.38 to 0.98 for the Kling-Gupta Efficiency index. The model also predicted the response of oil palm yield to abrupt rainfall changes, such as those during El Niño and La Niña events, while accounting for how soil texture, rainfall, and other meteorological factors influence water deficits and crop photosynthesis. However, model accuracy varied by site, planting density, and oil palm parameter. Model accuracy can be increased by more accurately representing the oil palm microclimate, incorporating fruiting activity, and refining the dry matter partitioning mechanism for the trunk.

Advancing Thrombosis Research: A Novel Device for Measuring Clot Permeability.

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.

Effects of fluid composition in fluid injection experiments in porous media

Experiments on fluid flow in porous media, using fluids loaded with solids of various grain sizes, have been conducted in a modified Hele-Shaw setup. This setup utilised weakly cemented porous media with specific hydraulic and mechanical properties. Fluid injection in coarse granular media with clean or low-concentration fine particles, results in infiltration only, with pressure close to the material tensile strength, while injection in finer granular material causes damage alongside infiltration, with the fluid pressure still close to the material tensile strength. When larger particle sizes or higher particle concentrations are used in the mixture, the fluid travels further within the porous medium, primarily influenced by the grain size of the granular medium. In the latter case, the Darcy flow equation with an effective permeability term can be employed to determine the pressure differential. For the largest particle sizes included in the fluid, the equation is still applicable, but the effective permeability requires adjustment for particle size within the fluid rather than the granular medium. This is crucial when the injection point is locally clogged. The experiments show that fracturing conditions are controlled by different mechanisms. Dimensional and statistical analysis was used to classify the injection pressures to regimes predicted by fracturing theory or by Darcy law with modified effective permeabilities. The findings show that both the material properties and fluid composition are important designing parameters.

Homogenization theory and nonlinearities in Darcy's law

The theory of homogenization of differential equations has become an open field of research in several areas of the exact sciences and has proved to be a powerful tool for understanding the global behavior of heterogeneous materials. Despite knowing that the deduction of Darcy’s law through the Navier-Stokes equations has been debated for decades, many questions remain open, mainly regarding more complex boundary conditions, cases involving multiphase flows and the numerical homogenization techniques. It is known today that Darcy’s law is presented in the form of a linear relationship only for a range of hydraulic gradient and that this range overlaps the range of laminar flow through soil voids. Therefore, it is proposed in this work to understand the loss of linearity in Darcy’s law, based on the theory of homogenization, modifying and exploring the limit results obtained by Allaire in 1991.

Thermally oscillatory flow inside an irregular channel through a porous medium with velocity and temperature slips

The purpose of this exploration is to scrutinize the heat transfer characteristics of oscillatory flow on the magnetized second-grade fluid within an asymmetric porous wavy channel with velocity slip and temperature jump conditions. Flow in porous space is characterized by modified Darcy's law. The use of a magnetized second-grade fluid in an asymmetric porous wavy channel could potentially enhance heat transfer within the fluid, leading to better control over drug release rates and spatial distribution. The fundamental flow equations are converted into ordinary differential equations (ODEs) utilizing suitable non-dimensional variables and then resolved analytically. The outcomes are graphically represented to illustrate the physical impacts of governing parameters on the temperature, and velocity profiles. Streamlines are also constructed for specific physical parameters to investigate trapping phenomena. In addition, variations on the coefficient of skin friction, mass flux, and heat transfer coefficients are illustrated with different values of pertinent parameters. The outcomes indicate that fluid velocity is enhanced by increasing the values of Darcy's number and Grashof's number. The fluid temperature decreases by increasing the values of the temperature jump parameter.

Evaporation of a heated saline marble: Interplay of interfacial and thermal effects

A multistage evaporation of continuously heated liquid marbles, coated with polytetrafluoroethylene colloidal particles was investigated experimentally and theoretically. Liquid marbles initially contained an almost saturated aqueous NaCl solution. Numerical heat transfer calculations and analytical evaluations of initial evaporation showed that the equilibrium marble temperature and saturated salt concentration are reached relatively rapidly compared to the “long” marble evaporation time. This means that a typical long period of marble evaporation is determined by the low permeability of the salt crust formed beneath the marble colloidal shell. A theoretical estimation of the total evaporation time of marble water based on Darcy's law for the porous crust and the marble shell is suggested. A comparison with experimental data allowed obtaining an approximate value of the very low permeability of this bilayer barrier to marble evaporation. The proposed phenomenological model of the saline marble evaporation provides insight into why marble evaporation is so slow.

Modeling heat and mass transfer in metal hydride hydrogen storage systems: Impact of operating parameters and reactor geometry

This work introduces a transient 2D axis-symmetrical model for hydrogen absorption in a cylindrical LaNi5 reactor employing finite volume method with a fully implicit Euler's time integration scheme, coupling equations for heat, mass, and momentum transport. The validated model is used to investigate the impacts of pressure, cooling fluid temperature, and variations in reactor geometry and size on temperature and reacted fraction profiles. The findings reveal that the charging pressure affects both peak temperature and reaction kinetics, whereas cooling fluid temperature predominantly impacts the absorption kinetics. A comparative analysis of two models, one incorporating Darcy's velocity and one without, demonstrates that while Darcy's law introduces numerical instability in the coupled equations, its impact on the model outcomes is negligible. The effect of changing the non-homogeneous Neumann to Dirichlet boundary condition is also demonstrated to anticipate the utilization of phase change materials (PCM) instead of the cooling fluid.

Effects of CO2 Geosequestration on Opalinus Clay

CO2 geosequestration is an important contributor to United Nations Sustainable Development Goal 13, i.e., Climate Action, which states a global Net-Zero CO2 emissions by 2050. A potential impact of CO2 geosequestration in depleted oil and gas reservoirs is the variations in induced pressure across the caprocks, which can lead to significant local variations in CO2 saturation. A detailed understanding of the relationship between the pressure gradient across the caprock and local CO2 concentration is of utmost importance for assessing the potential of CO2 geosequestration. Achieving this through experimental techniques is extremely difficult, and thus, we employ a coupled Computational Fluid Dynamics (CFD) and Finite Element Method (FEM) based solver to mimic sub-critical CO2 injection in Opalinus Clay under various pressure gradients across the sample. The geomechanical and multiphase flow modelling utilising Darcy Law helps evaluate local variations in CO2 concentration in Opalinus Clay. Well-validated numerical results indicate favourable sub-critical CO2 geosequestration under a positive pressure gradient across Opalinus Clay. In the absence of a positive pressure gradient, a peak CO2 concentration of 5% has been recorded, which increases substantially (above 90%) as the pressure gradient across the sample increases.

Analysis of the impact of uneven permeability of surrounding rock caused by the coupling effect of ground stresses and fault structure on sudden water inrush in tunnels

Affected by fault structure and in situ stress, the heterogeneity of the permeability of surrounding rock is universal. Treating it as a fixed value will reduce the prediction accuracy of water inflow and structural head. In view of this problem, considering the coupling effect of ground stress and fault structure, the permeability of surrounding rock is regarded as a spatially discrete type, a plane one-dimensional seepage calculation model in the vertical section is constructed, and the phreatic surface drop curve equation is established. Using Taylor's formula and series expansion theorem, the equation can be reduced to the expression of the falling curve when the permeability of the surrounding rock is homogeneous. Based on Darcy's law and the law of conservation of fluid mass, the calculation formula for tunnel water inflow and external water pressure of the structure was derived and verified through ongoing construction projects. Research shows that the calculation error of water inflow can be reduced from 23.1% to 7.5% when considering the influence of ground stress and fault structure on the permeability of surrounding rock, and the calculation error of water head borne by the supporting structure can be reduced from 43.8% to 30%, which improves the prediction accuracy. Thematic collection: This article is part of the Climate change and resilience in Engineering Geology and Hydrogeology collection available at: https://www.lyellcollection.org/topic/collections/climate-change-and-resilience-in-engineering-geology-and-hydrogeology

Numerical simulation of temperature field of a new type of freezing device under seepage effect.

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.

Aspects of conceptualization, development, and simulation of an extracellular vesicles' bulk isolation device for cosmetic and therapeutic applications

This paper discusses the concept and model to develop a prototype extracellular vesicle bulk-isolation device (EBID). It proposes an engineering design and potential ways to mitigate limitations in the currently available extracellular vesicle (EV) isolation techniques. A more convenient isolation technique is developed and presented to ensure production-scale isolation and purification of the specific size of EV (approximately 0.1 to 0.34 µm) from a large quantity of cell-culture media or biological fluid sources. A more appropriate design concept was established based on the chitosan-assisted precipitation of EV techniques and the membrane filtration technology-based prototype. After that, a novel theoretical model for bulk isolation of EVs was developed and presented using pressure-driven circulation and particulate flow in the EBID loop, where the EV production results from the biofluid flowing through the EBID membrane filter module (MFM). Governing equations are coupled with Darcy's law to investigate the biofluid flow behavior in the EBID MFM, therefore simulating the isolation process of EVs from their biofluids. The flow characteristics of the EV isolation process within the EBID MFM are theoretically simulated and discussed for improved isolation yield with a high degree of quality and purity.

Численно-аналитическая модель для интерпретации результатов индикаторных исследований нефтяных пластов: решение прямой задачи при наличии каналов низкого фильтрационного сопротивления

The article considers the problem of interpretation of tracer tests in oil reservoirs, into which a specific chemical substance - tracer - is injected via an injection well for flow monitoring and tracer concentration measurements in surrounding production wells. The testing data provide evidence of the existence of low resistance channels in the reservoirs, along which the tracer moves at velocities several orders of magnitude higher than in the reservoir. The nature and properties of these channels are unknown, and a semi-analytical model involving two small parameters is proposed to solve this problem. This makes it possible to construct two non-conjugate solutions: universal numerical and analytical. Such an approach allows us to solve both direct and inverse problems. The present article is devoted to solving the direct problem. The problem of pressure distribution in a rectangular reservoir pattern is solved in dimensionless coordinates and is universal, i.e., it does not depend on the size of the area and the pressure drop. This solution is approximated by power functions and is further used to determine the mass transfer between channel and reservoir. The problem of tracer slug propagation through the channel obeys the law of conservation of tracer mass and Darcy's law. Its solution is found by the methods of characteristics under the condition of smallness of the parameter reflecting the ratio of reservoir permeability to channel permeability. The results of the semi-analytical solution are compared with the numerical solutions previously obtained by other authors. The fundamental difference between these solutions is the presence of numerical diffusion when using the finite-difference method of solution, which leads to the «dissipation» of the trace slug edges.

Homogenization of non-Darcy flow in porous media containing spheroidal impervious inclusions

The aim of the present study is to determine the nonlinear filtration law of a porous medium containing spheroidal impervious inclusions through a homogenization framework. At the local scale, it is assumed that the fluid flow through the porous solid surrounding the inclusions obeys the Forchheimer equation. The macroscopic law is derived in the field of nonlinear variational approach applied to some representative cell, namely a porous spheroid containing a single centered spheroidal inclusion confocal to the outer. Both a static and kinematical approach are developed to bound the overall filtration properties of the heterogeneous solid. Appropriate trial fields are considered to determine closed-form estimates and are obtained from the solution of a linear problem replacing the Forchheimer law in the porous solid at the microscopic scale by the Darcy law. The analytic estimates are calculated through some approximations and lead to accurate solutions of the nonlinear problems. Finally, the analytic models are compared with FFT solutions in the case of a regular array of spheroidal impervious inclusions.

Legendre Galerkin spectral collocation least squares method for the Darcy flow in homogeneous medium and non-homogeneous medium

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.

Active Darcy's Law.

While bacterial swarms can exhibit active turbulence in vacant spaces, they naturally inhabit crowded environments. We numerically show that driving disorderly active fluids through porous media enhances Darcy's law. While purely active flows average to zero flux, hybrid active/driven flows display greater drift than purely pressure-driven flows. This enhancement is nonmonotonic with activity, leading to an optimal activity to maximize flow rate. We incorporate the active contribution into an active Darcy's law, which may serve to help understand anomalous transport of swarming in porous media.