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This work considers the isothermal process of incompressible viscous fluid filtration in an oil-saturated, fractured-porous reservoir. A study of the pressure and water saturation distribution process is carried out for a case in which a production well is put into operation. For this problem, i.e., a mathematical model in a two-dimensional formulation, a numerical method and a parallel algorithm are proposed. The mathematical model of two-phase filtration is written in accordance with the classical laws of continuum mechanics and Darcy's law and also includes a function of fluid exchange between low-permeability pores and high-permeability natural fractures within the framework of the Warren–Root model. The numerical solution is based on the finite-difference method and a splitting scheme of physical processes and spatial coordinates. For a split system with respect to piezoconductivity, an implicit finite-difference scheme with fixed saturations is constructed, and with respect to saturation transfer, explicit and implicit difference schemes are constructed. For parallel implementation of the developed numerical approach, a method based on geometric parallelism is selected. Testing of the developed method is performed using the example of calculating liquid mass transfer for a wide range of parameters. To verify the model, the obtained calculated pressure curves are compared with field data recorded by a deep-well measuring device. The results allow for estimation of the distribution of reservoir pressure and water saturation depending on the permeability of the fracture set and the pore part. The obtained results allow for monitoring of well operations, reducing unexpected accident risks and optimizing the development system in order to increase oil production in fractured-porous reservoirs. Computational experiments confirm the efficiency of the developed numerical algorithm and its parallel implementation. [ABSTRACT FROM AUTHOR]

The utilization of lattice-based scaffolds emerging as an advance technique over conventional bio-implants in Bone Tissue Engineering. In this study, totally six lattice structures are considered for permeability and wall shear stress (WSS) investigation. Namely triply periodic minimal surfaces (TPMS)-based Gyroid, Schwarz-P, Schwarz-D, and two beam-based structure—Cubic and Fluorite are compared with the proposed new lattice structure at porosity level of 80%, 75%, and 70%. The proposed new lattice has combine characteristic of Gyroid and Schwarz-D TPMS lattice. The permeability is determined through Darcy's law, where the pressure drop across the lattice structure is calculated using a computational fluid dynamics (CFD) tool at flowrate between 0.2 and 10 ml/min. The Cubic and Schwarz-P lattice structures exhibited the highest permeability but at the cost of a lower active surface area for WSS, measuring below 155 mm², means least cell proliferation occurs while the permeability value in New Lattice structure is in the ideal range with the enhanced active surface area for WSS (514 mm²). The complex internal curvatures of New Lattice promote the cell proliferation while the through-pore holes allow the efficient cell seeding.The utilization of lattice-based scaffolds emerging as an advance technique over conventional bio-implants in Bone Tissue Engineering. In this study, totally six lattice structures are considered for permeability and wall shear stress (WSS) investigation. Namely triply periodic minimal surfaces (TPMS)-based Gyroid, Schwarz-P, Schwarz-D, and two beam-based structure—Cubic and Fluorite are compared with the proposed new lattice structure at porosity level of 80%, 75%, and 70%. The proposed new lattice has combine characteristic of Gyroid and Schwarz-D TPMS lattice. The permeability is determined through Darcy's law, where the pressure drop across the lattice structure is calculated using a computational fluid dynamics (CFD) tool at flowrate between 0.2 and 10 ml/min. The Cubic and Schwarz-P lattice structures exhibited the highest permeability but at the cost of a lower active surface area for WSS, measuring below 155 mm², means least cell proliferation occurs while the permeability value in New Lattice structure is in the ideal range with the enhanced active surface area for WSS (514 mm²). The complex internal curvatures of New Lattice promote the cell proliferation while the through-pore holes allow the efficient cell seeding. [ABSTRACT FROM AUTHOR]

The water table fluctuation (WTF) method is popular for groundwater recharge (GR) estimation, but its accuracy is challenged when applied in areas with thick vadose zones because of the signal lag and attenuation with depth and uncertainties from barometric pressure effect and lateral flow. Improvement of the WTF method used the linear regression method and Darcy's law, and has been assessed to give satisfactory results. In particular, the improved method presented lower GR (20–34%) relative to the conventional method. GR decreased from the centre to the edge of the tableland. The regional average GR was 63–81 mm year−1, equivalent to 11–14% of annual average rainfall. Lag times between recharge and rainfall ranged from 1 to 9 months. Rainfall and vegetation dominated the spatiotemporal variability of GR. Our study provides reference and technical support for GR estimation with the WTF method in regions with a thick vadose zone. [ABSTRACT FROM AUTHOR]

The aim of this study is to present forced convective nanofluid flow over a moving plate embedded in an absorbent medium. Following Darcy law's for porous medium, the flow analysis is explored in attendance of warmth basis/drop. The main objective of this study is to explore the effects of Brownian motion and thermophoresis. The plate is considered to move in both directions: in the way of movement of fluid and in the opposite route of fluid movement. Similarity alterations have been applied to alter the leading partial differential equations (PDEs) to ordinary differential equations (ODEs). Numerical solutions have been obtained with the help of MATHEMATICA software. Dual solutions have been obtained when the plate and liquid go in reverse ways. Wall shear stress, Nusselt and Sherwood numbers all are found to rise with the rising permeability parameter of absorbent medium. For Nusselt and Sherwood numbers, ranges of dual solutions diminish by the mounting values of permeability parameter K. The critical values for porosity parameter K = 0. 0 1 , 0.02, 0.03 are R c 1 = 1. 8 7 2 9 0 9 , R c 2 = 1. 9 2 7 2 1 1 , R c 3 = 1. 9 8 2 4 2 8 4 , respectively. For decreasing values of s, range of dual solutions decreases. For s = − 0. 4 5 , dual solutions exist in the range (1. 1 9 , 1. 2 0). [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]

The article "Closed equation model for cavity evolution in granular media" in the Journal of Fluid Mechanics presents a closed three-equation model for predicting cavity evolution in granular media, particularly in explosion-driven gas-particle flows. The study extends the classical Rayleigh-Plesset model to include gas expansion and non-Darcy gas-penetration effects, examining both symmetric and asymmetric gas injection scenarios. By non-dimensionalizing the equations, key dimensionless numbers are derived to characterize cavity expansion response time and non-Darcy effects intensity. The model's predictions were validated through refined numerical simulations, revealing discrepancies attributed to neglecting inertial effects and a buffer mechanism in the granular medium. The study further explores the impact of dimensionless numbers on cavity evolution processes and conducts additional tests to enhance the model's predictive accuracy. [Extracted from the article]

Magnesium phosphate cement (MPC) has a promising application in grouting. This study drew on the traditional cement-waterglass two-liquid grouting model. Creatively, the two main reaction components of MPC, dead-burned magnesium oxide and phosphate, were applied to the grouting field in a two-component liquid form. At the same time, through proportioning adjustment and experimental testing, we obtained A\B liquid components, which can be stabilized. In addition, MPC slurry was compared with the traditional grouting material, silicate cement slurry, to demonstrate its superiority. Finally, we simulated the grout diffusion process of the mixed slurry using the two-phase Darcy's law module of COMSOL Multiphysics subsurface fluids. The results show that the mixed slurry with a magnesium phosphate ratio of 1/3, a magnesium–boron ratio between 5% and 10%, and a water–cement ratio of 0.2–0.5 has better stability and mobility. Under the same fluidity, its strength is much higher than that of common silicate cement slurry and has good injectability. MPC was subjected to two-fluid grouting to take advantage of its fast-hardening and early-strengthening properties, while also improving its stability and fluidity. This study provided a theoretical foundation for the application of MPC. [ABSTRACT FROM AUTHOR]

The characteristics of gas seepage in broken coal and rock composed of different particle sizes and grades were investigated in this study. On the basis of Darcy's law and non‐Darcy seepage theory, equations of gas permeability in the nonlinear seepage of broken coal and rock, as well as the porosity of broken coal and rock, under triaxial compression were determined. The stress loading path of gas seepage in broken coal and rock was developed. The characteristics of gas seepage in broken coal and rock composed of different particle sizes and grades were analyzed, and the results showed that the gas permeability after compression was proportional to the particle size of the broken coal and rock. Under triaxial compression, the gas permeability of the broken coal and rock composed of graded‐particle sizes was lower than that of the broken coal and rock composed of different single‐particle sizes. The gas permeability of the broken coal was lower than that of the broken rock mass, and the gas permeability and porosity of the broken coal and rock can be described by the exponential decay function. At a constant porosity, the gas permeability of the broken coal and rock was proportional to the size grading index under triaxial compression. The coefficient of viscosity and gravity of the flow are key factors influencing the flow permeability in broken coal and rock. This study provides a reference for on‐site practice such as the efficient extraction of gas in goafs. [ABSTRACT FROM AUTHOR]

The paper presents a simulation-based approach for optimizing CO2 injection into depleted gas reservoirs, with the goal of enhancing underground CO2 storage. The research employs a two-dimensional dynamic reservoir model, developed using Darcy's law, to describe gas flow in a pressure-homogeneous porous medium, along with real gas equations. The model integrates the Du Fort–Frenkel and finite-difference methods to accurately simulate the behavior of CO2 during injection and storage. Real data from an operational gas storage facility were used to calibrate the model. CO2sim v1 software, specifically developed for this purpose, simulates CO2 injection cycles and quiescence phases, enabling the optimization of storage capacity and energy efficiency. The reservoir model, based on the engineering of the geological structure, is discretized into approximately 16,000 cells and solved using the finite-difference method, allowing for rapid simulation of CO2 injection and quiescence processes. The average computation time for a 150-day cycle is approximately 5 min. Simulation results indicate that increasing the number of injection wells and carefully controlling the injection rates significantly improves the distribution of CO2 within the reservoir, thereby enhancing storage efficiency. Additionally, appropriate well placement and prolonged quiescence periods lead to better CO2 dispersion, increasing the storage potential while reducing energy costs. The study concludes that further development of the software, along with comprehensive technical and economic assessments, is required to fully optimize CO2 storage on a commercial scale. [ABSTRACT FROM AUTHOR]

China's coal seam permeability is low, and the original coal seam gas extraction is difficult. CO2 displacement of coal seam CH4 technology is an effective gas extraction technology. CO2 is injected into the coal seam under pressure, and competitive adsorption occurs with CH4 in the pores. The gas composition is nonuniformly distributed, and its viscosity μ is the dynamic parameter. As the gas is compressible, the pressure drops, and migration distance does not satisfy a linear relationship. Therefore, the gas transport does not conform to Darcy's law. The mass transfer process and a multicomponent gas competitive adsorption were investigated theoretically and experimentally. The adsorption characteristics and gas compressibility determine the distribution of the gas components in pores and change the gas dynamic viscosity in different regions. The change in the gas dynamic viscosity in the channel is the direct reason for the nonlinear pressure gradient and gas flow curve. The permeability and gas component affect the degree of nonlinear deviation of the gas flow and pressure gradient curve. This affects the nonlinear deviation degree of the curve by changing the gas dynamic viscosity in the pore channel during displacement. The reasonable displacement pressure is the critical pressure (PO) through experimental and theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, the coupled linear theory of thermoelasticity for nanomaterials with triple porosity is considered in which the combination of Darcy's law and the volume fraction concept for three levels of pores (macro-, meso- and micropores) is provided. The 3D basic boundary value problems (BVPs) of steady vibrations of this theory are formulated and these BVPs are investigated using the potential method (boundary integral equation method) and the theory of singular integral equations. Namely, the formula of integral representation of regular vectors is obtained. The surface (single-layer and double-layer) and volume potentials are introduced and their basic properties are given. Some useful singular integral operators are defined for which Noether's theorems are valid. The symbolic determinants and indexes of these operators are calculated. The BVPs of steady vibrations are reduced to the equivalent singular integral equations. Finally, with the help of the potential method, we prove the existence theorems for classical solutions of the aforementioned BVPs. [ABSTRACT FROM AUTHOR]

Radiation of ocean water waves for (i) a system consisting of a hollow porous cylinder at the top, (ii) another system comprising a solid porous cylinder at the top; with a rigid solid cylinder considered at the bottom, is studied. Translational motions in the x-, and z-directions, surge and heave, are considered. Subsequently, the associated added mass and damping coefficients are investigated. The present configuration can be observed to be a wave energy device which taps ocean wave energy. Continuity conditions for pressure and velocity across the linear interfaces are used for setting up a system of linear equations. To validate the model, result of damping coefficients is compared with a result of Miloh [Wave loads on a floating solar pond. In: Proceedings of the international workshop on ship and platform motions. Berkeley: Department of Naval Architecture and Ocean Engineering; 1983] for the first case and with that of Yeung [Added mass and damping of a vertical cylinder in finite-depth waters. Appl Ocean Res. 1981;3(3):119–133] for the second case, both showing a good agreement. It is found that the variation of porous coefficient, radii, and depth has immense influence on the coefficients for such a cylindrical system. [ABSTRACT FROM AUTHOR]

We study surface gravity waves for viscous fluid flows governed by Darcy's law. The free boundary is acted upon by an external pressure posited to be in traveling wave form with a periodic profile. It has been proven that for any given speed, small external pressures generate small periodic traveling waves that are asymptotically stable. In this work, we construct a class of slowly traveling waves that are of arbitrary size and asymptotically stable. Our results are valid in all dimensions and for both the finite and infinite depth cases. [ABSTRACT FROM AUTHOR]

Most numerical simulations for modeling acid reactive fluid transport and wormhole propagation during matrix acidizing, waterflooding, and CO2 sequestration in carbonate formations are computationally expensive, limiting real-time reservoir management and deep learning training datasets generation for inverse modeling research. Therefore, there is a need for less computationally expensive acid-reactive fluid flow models with adequate accuracy. This study developed and validated a simplified acid reactive-transport model by integrating a simplified Stokes–Brinkman model (as opposed to Darcy's law), an averaged continuum model, and a pseudo-fracture model. Using FEniCS, the model effectively simulates acid-reactive fluid transport and wormhole propagation in carbonate rocks, achieving a high R-square value of about 0.97 based on a quantitative comparison of the breakthrough volume with other models. The simplified model can also simulate wormhole propagation for the reciprocal of the Damköhler number (1/Da) ranging from 0.001 to 1 with adequate accuracy. Sensitivity studies on the natural fracture parameters such as orientation, length, width, and density showed that higher fracture density, wider fracture aperture, longer fracture length, and orientation aligned with the direction of acid injection contribute to lower pore volume to breakthrough ratio but may not increase long-term acid stimulation efficiency. Also, the presence or absence of fractures in the matrix does not alter the dissolving patterns and optimum injection rate. This simple acid reactive-transport model can generate large training datasets for developing surrogate models in deep learning research. Finally, the FEniCS code in this paper is shared so future researchers can reproduce the results or extend the research work. [ABSTRACT FROM AUTHOR]

Shelterbelts provide essential protection against wind erosion and soil degradation, as well as protection for fruit-bearing plants and crops from strong winds. Enhancing their sheltering capabilities requires optimizing their pattern and orientation, as well as defining their height and desired canopy shape, according to the desired performance. In this work, Large Eddy Simulation is employed to investigate the flow field and windbreak effectiveness of single and double-arranged shelterbelts characterized by different geometry and resistance to the air passage for neutral atmospheric condition. In particular, the canopy of the shelterbelts is modeled as an isotropic porous medium immersed in atmospheric boundary layer flow using the Darcy–Forchheimer model. Results show that a shelterbelt with a rectangular-shaped cross-section and a large canopy height results in the most significant reduction in mean wind speed and TKE, thus providing a large wind-protection region. As the spacing distance of double-arranged shelterbelts increases, the protection zones formed by both shelterbelts are reduced. The systematic comparisons of flow patterns, drag force coefficients, and windbreak effectiveness indicators of a series of single and double-arranged shelterbelts are essential for optimizing the design and management of shelterbelts. [ABSTRACT FROM AUTHOR]

Saturated hydraulic conductivity (Ks) is a crucial parameter that influences water flow in saturated soils, with applications in various fields such as surface water runoff, soil erosion, drainage, and solute transport. However, accurate determination of Ks is challenging due to temporal and spatial uncertainties. This study addresses the knowledge gap regarding the long‐term behavior of Ks in sandy soils with less than 10% fine particles. The research investigates the changes in Ks over a long period of constant head tests and examines the factors influencing its variation. Two sandy samples were tested using a hydraulic conductivity cell, and the hydraulic head and discharge were recorded for over 50 days. The results show a general decline in Ks throughout the test, except for brief periods of increase. At the end of both tests, there are noticeable reductions in the saturated hydraulic conductivities of the samples, with one sample being 96% and the other sample 91% less than the maximum recorded saturated hydraulic conductivity during the tests. Furthermore, the relationship between flow rate and hydraulic head gradient does not follow the expected linear correlation from Darcy's law, highlighting the complex nature of sandy soil saturated hydraulic conductivity. The investigation of soil properties in three different sections of the samples before and after the tests revealed a decrease in the percentage of fine particles and a shift in specific gravity from the bottom to the top of the sample, suggesting particle migration along the flow direction. Factors such as clogging by fine particles and pore pressure variation contribute to the changes in Ks. The findings of this research show the importance of considering changes of saturated hydraulic conductivity during constant‐head laboratory tests. Therefore, this study provides evidence for the requirement to further assess the laboratory methods for measurement of the saturated hydraulic conductivity in sandy soil mixtures. Key Points: The estimation of saturated hydraulic conductivity through constant head tests demonstrates sensitivity to the duration of the testsObservations indicate an alteration in particle size distribution before and after testing within different sections of the samplesFlow rate and hydraulic gradient vary over the test duration, emphasizing the complex hydraulic system within the samples [ABSTRACT FROM AUTHOR]

The primary aim of this study was to examine the peristaltic flow of an unsteady non-Newtonian TiO2 nanofluid through a uniformly symmetric channel under the influence of electro-osmosis. The fluid behavior was modeled by the Sutterby model. Furthermore, the flow took place through a porous medium, following a modified form of Darcy's law. Additionally, the impacts of Dufour and Soret effects, chemical reaction, activation energy, viscous dissipation, heat generation, and thermal radiation were considered. A wave transformation was used to simplify the governing equations describing the velocity, temperature, and nanoparticle concentration. These simplified equations were then solved analytically using the homotopy perturbation method. Additionally, set figures were employed to illustrate and discuss the impact of the physical parameters involved in the problem on the obtained solutions. It is found that the presence of a modified Darcy's medium in the Navier–Stokes equation results in a porous term that is dependent on the index of the Sutterby model. Furthermore, it is found that as the thermophoresis parameter increases, the nanoparticles are more concentrated, and their flow from the hot region to the cold region is more effective. Additionally, it is observed that in the presence of thermal radiation, the activation energy and the Brownian motion parameter have similar effects on the concentration profile. [ABSTRACT FROM AUTHOR]

Porous ionic electrospray emitters have received significant interest for space propulsion due to their performance and operational simplicity. We have developed a diffusion equation for describing the transient flow response in a porous electrospray emitter, which allows for the prediction of the settling time for flow in the porous emitter. This equation accounts for both the change in liquid storage at exposed pores on the emitter with pressure and viscous diffusion through Darcy's law. Transient flow solutions are provided for the most common emitter topologies: pillar, cone, and wedge. Transient flow solutions describe the settling time and magnitude of current overshoot from porous electrosprays, while providing useful guidelines for reducing transient response time through emitter design. Comparing diffusion of pressure to the onset delay model for electrospray emission shows that diffusion is most relevant at higher voltages and when a porous reservoir is used. Accounting for multiple emission sites on the wedge geometry shows that emission sites settle in proportion to emission site spacing to the power − 1.74. Article Highlights: The transient response of porous electrosprays is affected by fluid storage in exposed pores. Pressure diffuses into a porous electrospray through depletion of fluid in exposed pores. Diffusion of pressure complements the existing onset delay model for porous electrosprays. [ABSTRACT FROM AUTHOR]

Natural gas hydrates (NGH) are considered a very promising source of clean energy due to their widespread distribution, high energy density, and pure combustion products. Currently, there are few studies on NGH reservoir well testing, and the models are often idealistic, lacking practical guidance for field application. In this paper, a well-testing model for partially perforated wells in the NGH reservoir is proposed, which takes into account the dynamic decomposition of hydrates. This model can simulate the performance of the perforated NGH well with a dynamic dissociation interface, which divides the reservoir into decomposed and undecomposed regions. Governing equations in cylindrical coordinates are formulated to depict fluid flow. Moving boundaries and dissociation coefficients are incorporated to describe the solid-to-gas transition within hydrates. Analytical solutions including the pressure transient behaviors of the NGH reservoir and the bottomhole pressure (BHP) of partially perforated wells are derived by utilizing the Laplace transform method of the separation of variables and the Stehfest numerical inversion algorithm. Sensitivity analysis is conducted using the parameters from partially perforated wells and NGH formation properties. We plot the pressure and pressure derivative curves in double logarithmic coordinates to study the pressure transient behaviors. There are seven flow regimes that are typical for partially perforated wells in the NGH reservoir, namely, pure wellbore storage, skin effect, spherical flow, pseudoradial flow, composite effect, improvement, and radial flow regimes. [ABSTRACT FROM AUTHOR]

Most of the implemented marine gas hydrate test exploitation in the world adopt the depressurization method to break down the hydrate in the reservoir into natural gas and then extract it, but because the gas production results are still a certain distance away from the commercial exploitation, and it mainly stays in the stage of theoretical research and trial exploitation. Based on two trial productions in the Shenhu area of the South China Sea, this study established a model for hydrate exploitation and investigated the impact of different well types on the recovery rates of hydrates and free gas in different development layers during depressurization. For the Class 1 hydrate reservoirs, horizontal wells are the optimal solution to extract hydrate and free gas simultaneously when exploiting the hydrate three-phase layer. Meanwhile, the effect of different well spacing in vertical wells on the recovery rate of hydrate and free gas was studied. It is found that the best recovery efficiency is achieved when the spacing between two wells is 80 m. The lower the bottom flow pressure of the well, the higher the production capacity, but its influence is limited. [ABSTRACT FROM AUTHOR]

In this article, a two-level overlapping domain decomposition preconditioner is developed for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite element method for discretizing the partial differential equation by Darcy's law with the no-flux boundary condition and is then followed by a velocity elimination technique to yield a linear algebraic system with only unknowns of pressure. Then, our main objective is to design a robust and efficient domain decomposition preconditioner for this system, which is accomplished by engineering a multiscale coarse space that is capable of characterizing high-contrast features of the permeability field. A generalized eigenvalue problem is solved in each nonoverlapping coarse element in a communication-free manner to form the global solver, which is accompanied by local solvers originated from additive Schwarz methods but with a non-Galerkin discretization to derive the two-level preconditioner. We provide a rigorous analysis that indicates that the condition number of the preconditioned system could be bounded above with several assumptions. Extensive numerical experiments with various types of three-dimensional high-contrast models are exhibited. In particular, we study the robustness against the contrast of the media as well as the influences of numbers of eigenfunctions, oversampling sizes, and subdomain partitions on the efficiency of the proposed preconditioner. Strong and weak scalability performances are also examined. [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]

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Evaluating groundwater inflow is greatly significant for ensuring the safety and economy during foundation pit dewatering with suspended waterproof curtains. However, there are limited applicable methods to predict the groundwater inflow of circle foundation pit with waterproof curtains in deep unconfined aquifers. In this study, based on Darcy's law and the continuity of water flow, the impact of suspended waterproof curtains on groundwater seepage was initially analyzed during circle foundation pit dewatering in deep unconfined aquifers. Furthermore, an analytical solution was proposed for groundwater inflow of circle foundation pit with suspended waterproof curtains in the unconfined aquifers. The effect of suspended waterproof curtains on seepage area, seepage direction, and seepage path were respectively considered by introducing the buried depth of waterproof curtain, the anisotropy coefficient, and the seepage path reduction coefficient. Finally, based on the self-conducted indoor seepage experiment and other cases (an indoor seepage experiment and two actual engineering projects), this proposed method was applied to conduct a comparative analysis with the existing methods. Results indicated that the proposed method can more reasonably evaluate the groundwater inflow of circle foundation pit with waterproof curtains in the unconfined aquifer, which can provide a better guidance for the groundwater inflow control in the practical dewatering projects. [ABSTRACT FROM AUTHOR]

Countries face challenges of excess, scarcity, pollution, and uneven water distribution. This study highlights the benefits of advances in groundwater engineering that improve the understanding of utilizing local geological characteristics due to their crucial role in resisting drought in southern Lebanon. The type of drought in the region was determined using the Standardized Precipitation Index (SPI), Standardized Vegetation Index (NDVI), Vegetation Condition Index (VCI), and Soil Moisture Anomaly Index (SM). The dry aquifer and its characteristics were analyzed using mathematical equations and established hydrogeological principles, including Darcy's law. Additionally, a morphometric assessment of the Litani River was performed to evaluate its suitability for artificial recharge, where the optimal placement of the water barrier and recharge tunnels was determined using Spearman's rank correlation coefficient. This analysis involved excluding certain parameters based on the Shapiro–Wilk test for normality. Accordingly, using the Geographic Information System (GIS), we modeled and simulated the potential water table. The results showed the importance and validity of linking groundwater engineering and morphometric characteristics in combating the drought of groundwater layers. The Eocene layer showed a clearer trend for the possibility of being artificially recharged from the Litani River than any other layer. The results showed that the proposed method can enhance artificial recharge, raise the groundwater level to four levels, and transform it into a large, saturated thickness. On the other hand, it was noted that the groundwater levels near the surface will cover most of the area of the studied region and could potentially store more than one billion cubic meters of water, mitigating the effects of climate change for decades. [ABSTRACT FROM AUTHOR]

A theoretical simulation is performed to evaluate how microcracks affect the flow resistance in tumors during the convection-enhanced delivery (CED) of nanofluids. Both Darcy's law and the theory of poroelasticity are used to understand fluid transport with or without microcrack introduction and/or enlargement. The results demonstrate significantly altered pressure and velocity fields in a spherical tumor with a radius of 10 mm due to the presence of a microcrack with a radius of 0.05 mm and length of 3 mm. The non-uniform fluid pressure field enlarges the original cylindrical microcrack to a frustum, with the crack volume more than doubled. Due to the larger permeability and porosity in the microcrack, flow in the tumor is much easier. One finds that the flow resistance with the enlarged microcrack is reduced by 14% from the control without a microcrack. Parametric studies are conducted to show that larger crack radii, longer crack lengths and higher infusing pressures result in further resistance reductions. The largest resistance reduction occurs when the infusing pressure is 4 × 105 Pa and the microcrack is 9 mm long, up to 18% from the control. We conclude that introducing a microcrack is an effective way to facilitate nanofluid delivery in porous tumors using CED. [ABSTRACT FROM AUTHOR]

Implementing rain garden (RG) designs is widespread worldwide to reduce peak flow rates, promote stormwater infiltration, and treat pollutants. However, inadequate RG design degrades its hydrological behaviour, requiring the development and validation of an appropriate hydrological model for the design and analysis of structures. This study aimed to improve a hydrological infiltration model based on Darcy's law by taking into account the height of the water column (HWC) at the surface of the RG and the filtration coefficients of soil materials. The model was tested by simulating the hydrological characteristics of a rain garden based on a single rain event of critical intensity (36 mm/h). Using the validated model, design curves were obtained that predict the performance of the RG as a function of the main design parameters of the structure: water column height, ratio of catchment area to structure area, layer thickness, and soil filtration coefficient. The hydrological efficiency of the RG was evaluated in terms of the time of complete saturation, filling of the structure with water, and determining the change in HWC caused by changes in the parameters. The filtration coefficient and thickness of the upper and intermediate infiltration layers of the RG are the main parameters that affect the depth of saturation of the layers of the structure and the HWC on the surface. The model is not very sensitive to the model parameters related to the lower gravel layer. If the top layer's thickness increases by 10 cm, it takes longer to fill the structure with water, and the HWC on the surface reaches 0.341 m. The rain garden's performance improves when the filtration coefficient of the top layer is 7.0 cm/h. Complete saturation and filling of the structure with rainwater do not occur within 7200 s, and the water column reaches a height of 0.342 m at this filtration coefficient. However, the rain garden's effectiveness decreases if the filtration coefficient of the upper and intermediate layers exceeds 15 cm/h and 25 cm/h, respectively, or if the catchment area to RG area ratio decreases to values below 15. The modelling results confirm that considering the HWC in RG hydrological models is essential for designing structures to minimise the risk of overflow during intense rainfall events. [ABSTRACT FROM AUTHOR]

An analytical framework is developed to analyze the interaction of oblique waves with multiple flexible porous breakwaters under the consideration of bottom undulation. The mathematical problem is tackled using the small amplitude water-wave theory, with Darcy's law being applied to account for wave interaction with porous media. The bottom topography is considered to have a finite length, flanked by two semi-infinite sections of uniform bottom. The solution to the boundary value problem is approached by employing the eigenfunction expansion method within the uniform bottom regions. For the varying bottom topography, a modified mild-slope equation (MMSE) is utilized. To address the solution at the slope discontinuity at the bottom, a mass-conserving jump condition is applied. By matching solutions at the interfaces, a set of equations is derived. This system of equations encapsulates the behavior of reflection and transmission coefficients, as well as the force exerted on the breakwaters. These parameters are then investigated across various factors such as the length of the varying bottom, depth ratio, angle of the mooring line, angle of incidence, and flexural rigidity. Graphical representations of the reflection and transmission coefficients, along with the breakwater force, provide insights into the system's behavior under different conditions. The water wave energy can be dissipated for the optimum values of flexural rigidity. The transmission coefficient is observed to be least for higher mooring angle. [ABSTRACT FROM AUTHOR]

Classical filtration equations incorporate microscopic parameters, which pose challenges when applied in industrial settings. Previous extensive research has established the impact of filter cake thickness and variations in filtration pressure on the filtration rate. Moreover, the thickness of the filter cake is influenced by various factors, such as the filtration chamber's design dimensions and the coal slurry's properties. Thus, by expressing the properties of the coal slurry at a macroscopic level, it becomes possible to achieve a macroscopic representation of the filtration rate. This study presents the derivation of a macroscopic filtration equation that relies on the viscosity of the filtrate. The derivation process is mainly based on Darcy's law, analyzing the relationship between the permeability of each layer and the permeability of cake under constant pressure and explaining and analyzing the method of determining the equation parameters. [ABSTRACT FROM AUTHOR]

The present research offers a physical explanation for the intricate movement in porous media. It details the electroosmotic factors that drive momentum transmission and regulate the mixing process, as well as the flow and thermal properties such as velocity, flow rate, streamlines, pressure, and temperature. This model is founded on an investigation of non-Newtonian fluid flow by electroosmosis in a tapering duct influenced by porosity. Modeling the momentum, continuity, and heat equations involves combining Gauss's law, the Poisson equation, Darcy's resistance, and the Jeffrey model equation. To recommend a physical interpretation, exact solutions are calculated for partial differential equations. Examining the controlling parameters enables the identification of the appropriate fluctuations in the temperature field, velocity field, and pressure gradient. The governing equations are solved using approximations for low Reynold number, long wavelength, and Debye–Huckel linearization. For the purpose of demonstrating thermal analysis, contours are utilized to discuss the entrapment process and temperature profile fluctuations caused by various factors. In addition, a comparison is made between electroosmotic flow in uniform and nonuniform channels for intrauterine fluid flow and other industrial applications, such as the transmission of industrial fluids under complex regimes for a variety of thermal systems. [ABSTRACT FROM AUTHOR]

The increasing appeal of artificial neural networks (ANNs) stems from their remarkable efficiency in dealing with complex and highly nonlinear mathematical concepts. In intricate domains like biological computation, fluid dynamics, and the field of biotechnology, ANNs offer a versatile computational framework that proves immensely valuable. Therefore, the current study employs machine learning techniques to investigate the bioconvective biological transport of Powell–Eyring nanofluid. Various influential factors, including temperature-dependent viscosity, thermal radiation, magnetic field, porous medium, mixed convection, and Ohmic heating, are considered in the analysis. By considering small Reynolds numbers and large wavelengths, the complexity of the system is reduced. A builtin NDSolve function in Mathematica is utilized to numerically address the system of differential equations at hand. Subsequently, the ANN-LMM technique is implemented, utilizing reference datasets for temperature, concentration, and motile microorganism profiles. The dataset is partitioned with 70% allocated for training, 15% for testing, and 15% for verification purposes. The reliability of the developed ANN-LMM is verified by evaluating precision, accuracy, and convergence. This validation is based on efficient fitness demonstrated in terms of mean-squared error (mse), thorough appropriate visualizations of error histograms and regression analysis. The study underscores the capability of ANNs in accurately predicting optimal heat and mass transfer, demonstrating their advantage in designing and improving engineering systems. [ABSTRACT FROM AUTHOR]

This article investigates the onset of convection in a bidispersive porous medium, considering the impact of viscous dissipation and throughflow using both linear and nonlinear theories. The flow is modeled using the Oberbeck–Boussinesq approximation and Darcy's law, with local thermal equilibrium between the fluid and solid phases. The temperature field depends solely on the vertical coordinate in the basic solution. The study employs a two-pronged approach to analyze the system's stability, utilizing the normal mode technique for linear analysis and the energy method for nonlinear analysis. The article confirms the validity of the principle of exchange of stabilities. The numerical solution of the eigenvalue problem for both linear and nonlinear theories is obtained using the bvp4c routine. The research explores the influence of various physical parameters on the system's stability. Viscous dissipation's effect on convection onset is noticeable only with significant throughflow. In the absence of viscous dissipation, the throughflow direction does not affect the system's stability. The effective permeability ratio stabilizes the system with upward throughflow and exhibits opposite behavior with downward throughflow. The sub-critical region remains unchanged for the Gebhart number range but increases with higher moment transfer coefficient and effective permeability ratio. Additionally, an analytical expression is derived for the small Peclet number regime of the Rayleigh number using asymptotic analysis. [ABSTRACT FROM AUTHOR]

The stability of thermally driven buoyant flow of a viscoelastic fluid saturating a vertical porous layer with viscosity depending linearly on temperature is investigated numerically. The rheological behavior of the fluid is described through the Oldroyd-B model, leading to a modified Darcy's law of momentum transfer in the porous medium. The study explores the linear stability of the base flow by analyzing the behavior of normal modes of perturbation. Neutral stability curves and the critical Darcy–Rayleigh number are determined for a wide range of viscoelastic and viscosity parameters. Transition curves from stability to instability in the viscoelastic parameters space are also provided for both constant and variable viscosity cases. Additionally, the results for Newtonian, Boger, and Maxwell fluids are delineated as particular cases from this study. [ABSTRACT FROM AUTHOR]

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 [ABSTRACT FROM AUTHOR]

The article focuses on using the MIKE SHE model to analyze the impact of land use and land cover (LULC) changes on streamflow in Ethiopia's upper Omo Gibe catchment. Topics include the effects of LULC changes on hydrological patterns, the application of statistical tests to identify trends and changes, and the implications for water management strategies in the region.

One effective technique for mitigating the earthquake-induced liquefaction potential is the installation of stone columns. The permeability coefficients of stone columns are high enough to cause a high seepage velocity or expedited drainage. Under such conditions, the fluid flow law in porous media is not linear. Nevertheless, this nonlinear behavior in stone columns has not been evaluated in dynamic numerical analyses. This study proposes a dynamic finite element method that integrates nonlinear fluid flow law to evaluate the response of liquefiable ground improved by stone columns during seismic events. The impact of non-Darcy flow on the excess pore pressure and stress path compared to conventional Darcy law has been investigated numerically in stone columns. Furthermore, the effects of different permeability coefficients and stone column depths have been studied under near and far field strong ground motions. The results indicate that the non-Darcy flow increases the excess pore water pressure as high as 100% in comparison to the Darcy flow. [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]

During tunnel development in metal mines, there are situations where a zone of contact between the ore and the surrounding rock is reached. Nevertheless, there is a notable disparity in the mechanical characteristics between the ore and the surrounding rock, leading to a specific response of grouting in the contact area between the ore and rock. This response differs from the typical diffusion and curtain formation effects observed when using grouting slurry. This study investigates the effects of grouting curtain creation when implementing highly advanced curtain grouting in a water-rich highway, utilizing the engineering conditions of Zhongjiu Iron Mine as a reference. At first, Darcy's law and the Navier-Stokes equation are used to control the flow of fluid in the area where the ore-rock meets the rock around it. COMSOL, a multi-physical field coupled analysis software, is employed for the numerical simulation of slurry plane diffusion, single-hole, and group-hole curtain grouting. Two optimization strategies for group-hole grouting parameters are subsequently suggested and proven using numerical simulation. Finally, the project implements the research to assess the influence of curtain grouting by employing the water influx of the exploratory apertures as the standard of comparison before and after grouting; the results demonstrate that the slurry forms a highly efficient grouting curtain, effectively impeding water infiltration. The findings indicate that slurry diffusion in the contact zone between the ore and rock follows a spherical motion pattern, resulting in a considerable decrease in the flow rate compared to the previous stage. The force of gravity visibly affects the spreading of the slurry in the area where the ore and rock come into contact, causing the slurry to mostly spread downwards. This inclination intensifies as the rate of grouting is elevated. To successfully address the inadequate distribution of the slurry, one can either increase the rate at which grouting is performed or decrease the distance between the grouting holes. [ABSTRACT FROM AUTHOR]

This work investigates a non-Newtonian MHD Carreau nanofluid over a stretched vertical cylinder of an incompressible boundary layer with mobile microorganisms. The flow exists in permeable media and follows the modified Darcy's law. An unchanged normal magnetic strength to the walls saturates the system. Ohmic dissipation, heat source, modified chemical reaction with activation energy properties, heat, volumetric nanoparticles fraction as well as microorganism profiles are covered. Thermal conductivity and mass diffusivity are taken as functions of heat and nanoparticle concentration, correspondingly. The fundamental governing system of nonlinear partial differential equations (PDEs) is converted into nonlinear ordinary differential equations (ODEs) by employing appropriate similarity transforms. The latter system is numerically analyzed through fourth-order Runge–Kutta (RK-4) simultaneously with the shooting process. The numerical outcomes showed that the curvature coefficient, magnetism and chemically activated energy perform a significant role in the velocity, heat, nanoparticle and chemical organism distributions. The impacts of several physical restrictions are tested and portrayed in a group of graphs. It is observed that the presence of microbes and nanoparticles, which are described in buoyancy terms, causes the flow to decay and slow down. By lowering the buoyancy and bio-convection characteristics, this infection can be prevented. With the development of all heat-related elements, heat transfer is enhanced, which is a significant feature associated with the current flow. These insights are important and useful in various physical and engineering fields. [ABSTRACT FROM AUTHOR]

We consider the homogenisation of the quasi-stationary Stokes equations in a porous medium that evolves over time. The evolution is a priori given. At the interface of the pore space and the solid part, we prescribe an inhomogeneous Dirichlet boundary condition, which enables a no-slip boundary condition at the evolving boundary. We pass rigorously to the homogenisation limit employing the two-scale transformation method. In order to derive uniform a priori estimates, we show a Korn-type inequality for the two-scale transformation method. The homogenisation result is a new version of Darcy's law. It features a time- and space-dependent permeability tensor, which accounts for the local pore structure, and a macroscopic inhomogeneous divergence condition, which induces a new source term for the pressure. In the case of a no-slip boundary condition at the interface, this source term relates to the change of the local pore volume. [ABSTRACT FROM AUTHOR]

AbstractA study is conducted on the unsteady motion of a free convective flow of second grade fluid, energy transfer, and Darcy’s law over an oscillatory smooth vertical plate. The study compares two different approaches in developing a fractional model: the Caputo-Fabrizio operator with nonsingular kernel and the constant proportional Caputo fractional operator with Fourier’s and Fick’s laws. By applying the Laplace method and transforming the provided set of equations into nondimensional form, we obtained semi-analytical results and presented these results through graphical analysis. The study examines how different flow parameters, including the fractional parameters, affect the velocity, mass, and heat profiles of the physical system. The results suggest that the physical model using constant proportional Caputo derivative leads to higher temperature, stronger concentration, and increased velocity compared to the Caputo-Fabrizio model. This highlights the importance of selecting an appropriate fractional model when studying complex physical systems. It is also depicted from the whole analysis that field variables with novel hybrid fractional derivative constant proportional Caputo exhibits a more effective and declining tendency than Caputo-Fabrizio. [ABSTRACT FROM AUTHOR]

Utilizing Besok-Karniadakist's motion equations for ultra-low permeability shale gas reservoirs, which accommodate four flow modes, and incorporating the Langmuir adsorption, transportdiffrential equations are derived. A pseudo-pressure formulation adhering to Darcy's law and a pseudo-time are introduced. By applying the mass conservation, a correspondence between nonlinear and linear equation parameters is established, merging both types of equations. Through examples, the production dynamics of nonlinear seepage, including fixed well-bottom pressure and production rates, and parameter sensitivity are analyzed, offering insights for enhancing shale gas productivity. [ABSTRACT FROM AUTHOR]

Tight glutenite reservoir structure is complex, mineral types are multi-seepage, and most of them are non-Darcy's law flows Based on the finite element COMSOL simulation of seepage flow in glutenite water flooding, this chapter mainly explores the influence of several related factors on displacement recovery. With the increase of wetting angle, the wettability makes the porous state of solids and fluids in glutenite stable, so that water can easily push oil out, which leads to the increase of water flooding recovery The higher the injection rate, the higher the water cut in a short time, which makes the oil-water two-phase displacement accelerate and the higher the displacement recovery With the increase of gravel diameter, the oil saturation decreases less and more crude oil is bound by the pore structure surrounded by large particles, which is not conducive to displacement Small gravel particles have little influence on the front of water drive, and there is no obvious dominant channel, which leads to the recovery effect. [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]

The landscape of computational modeling in cancer systems biology is diverse, offering a spectrum of models and frameworks, each with its own trade-offs and advantages. Ideally, models are meant to be useful in refining hypotheses, to sharpen experimental procedures and, in the longer run, even for applications in personalized medicine. One of the greatest challenges is to balance model realism and detail with experimental data to eventually produce useful data-driven models. We contribute to this quest by developing a transparent, highly parsimonious, first principle in silico model of a growing avascular tumor. We initially formulate the physiological considerations and the specific model within a stochastic cell-based framework. We next formulate a corresponding mean-field model using partial differential equations which is amenable to mathematical analysis. Despite a few notable differences between the two models, we are in this way able to successfully detail the impact of all parameters in the stability of the growth process and on the eventual tumor fate of the stochastic model. This facilitates the deduction of Bayesian priors for a given situation, but also provides important insights into the underlying mechanism of tumor growth and progression. Although the resulting model framework is relatively simple and transparent, it can still reproduce the full range of known emergent behavior. We identify a novel model instability arising from nutrient starvation and we also discuss additional insight concerning possible model additions and the effects of those. Thanks to the framework's flexibility, such additions can be readily included whenever the relevant data become available. [ABSTRACT FROM AUTHOR]

The 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. [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]

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]