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Journal articles on the topic 'Darcy flow model'

Author: Grafiati

Published: 2 December 2022

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1

Wang, Yuan, Yu-long Niu, and Qiang Feng. "Study on the REV Size of Fractured Rock in the Non-Darcy Flow Based on the Dual-Porosity Model." Geofluids 2018 (2018): 1–22. http://dx.doi.org/10.1155/2018/7535927.

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For the problem of whether the representative elementary volume (REV) obtained in the Darcy flow is also applicable to the case of the non-Darcy flow, the study on the REV size within the non-Darcy flow is proposed tentatively. The concept of the REV in the non-Darcy flow is based on the definition of the REV. According to the determination of the REV in the Darcy flow, the intrinsic permeability k and non-Darcy coefficient β are used simultaneously for the determination of the REV in the non-Darcy flow. The pore pressure cohesive element (PPCE) is developed with the subroutine in ABAQUS. Then

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2

Di Nucci, Carmine, and Daniele Celli. "From Darcy Equation to Darcy Paradox." Fluids 7, no. 4 (2022): 120. http://dx.doi.org/10.3390/fluids7040120.

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This theoretical paper focuses on the single-phase fluid flow through a granular porous medium. The emphasis is on the Darcy flow regime (without free boundary) of a linear viscous fluid in a saturated, deformable, homogeneous porous medium. The approach is developed at the Darcy scale (also referred to as macroscale or phenomenological scale). Within this framework, some discrete aspects of the flow model are highlighted, the governing equations are revisited, the thermodynamic state functions are reconsidered, and the Darcy paradox is presented. The Darcy paradox is illustrated for the isosh

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3

Yang, Bin, Tianhong Yang, Zenghe Xu, Honglei Liu, Wenhao Shi, and Xin Yang. "Numerical simulation of the free surface and water inflow of a slope, considering the nonlinear flow properties of gravel layers: a case study." Royal Society Open Science 5, no. 2 (2018): 172109. http://dx.doi.org/10.1098/rsos.172109.

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Groundwater is an important factor of slope stability, and 90% of slope failures are related to the influence of groundwater. In the past, free surface calculations and the prediction of water inflow were based on Darcy's law. However, Darcy's law for steady fluid flow is a special case of non-Darcy flow, and many types of non-Darcy flows occur in practical engineering applications. In this paper, based on the experimental results of laboratory water seepage tests, the seepage state of each soil layer in the open-pit slope of the Yanshan Iron Mine, China, were determined, and the seepage param

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4

Lai, Bitao, Jennifer L. Miskimins, and Yu-Shu Wu. "Non-Darcy Porous-Media Flow According to the Barree and Conway Model: Laboratory and Numerical-Modeling Studies." SPE Journal 17, no. 01 (2011): 70–79. http://dx.doi.org/10.2118/122611-pa.

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Summary This paper presents the results of our new experimental studies conducted for high flow rates through proppant packs, which show that the Barree and Conway (2004) flow model is capable of overcoming limitations of the Forchheimer non-Darcy equation at very high flow rates. To quantify the non-Darcy flow behavior using the Barree and Conway model, a numerical model is developed to simulate non-Darcy flow. In addition, an analytical solution is presented for steady-state linear non-Darcy flow and is used to verify the numerical-simulation results. The numerical model incorporates the Bar

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5

Sefidgar, Mostafa, M. Soltani, Kaamran Raahemifar, and Hossein Bazmara. "Effect of Fluid Friction on Interstitial Fluid Flow Coupled with Blood Flow through Solid Tumor Microvascular Network." Computational and Mathematical Methods in Medicine 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/673426.

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A solid tumor is investigated as porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multiscale mathematical method which calculates fluid flow to a solid tumor is used in this study to investigate how neglecting fluid friction affects the solid tumor simulation. The mathematical method involves processes such as blood flow through vessels and solute and fluid diffus

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6

Fu, Xiang, Xiang Fang Li, Shi Qing Cheng, Liang Huang, and Xiang Rong Nie. "Pressure Behavior of a Coupling Model with Variable Permeability Effect." Applied Mechanics and Materials 152-154 (January 2012): 364–68. http://dx.doi.org/10.4028/www.scientific.net/amm.152-154.364.

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It is indicated that the fluid flow does not abide by the Darcy law in certain low permeability reservoirs. The results of pressure date analysis in these low permeability reservoirs would be inaccurate when generalized using Darcy flow models. To improve analysis results, based on the concept of variable permeability effect, the dual non-Darcy coupling flow model is established in this paper. The iterative algorithm is adopted to solve the differential set of equations. This work also describes the pressure behaviors by pressure response curves.

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7

Fu, Xiang, Xiang Fang Li, Shi Qing Cheng, Liang Huang, and Xiang Rong Nie. "Pressure Behavior of a Coupling Model with Variable Permeability Effect." Applied Mechanics and Materials 152-154 (January 2012): 689–93. http://dx.doi.org/10.4028/www.scientific.net/amm.152-154.689.

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It is indicated that the fluid flow does not abide by the Darcy law in certain low permeability reservoirs. The results of pressure date analysis in these low permeability reservoirs would be inaccurate when generalized using Darcy flow models. To improve analysis results, based on the concept of variable permeability effect, the dual non-Darcy coupling flow model is established in this paper. The iterative algorithm is adopted to solve the differential set of equations. This work also describes the pressure behaviors by pressure response curves.

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8

Aryanti, N., Y. Bindar, and I. G. Wenten. "Two Dimentional Numerical Models Of Hollow Fiber Membrane Contactor." REAKTOR 6, no. 2 (2017): 77. http://dx.doi.org/10.14710/reaktor.6.2.77-84.

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Membrane contactor is separation processing unit using membrane as a contacting device. The major advantage of membrane contactor relies on its high contact area compared to conventional scrubber. One of the important applications of membrane contactor is to reduce emission of acid gases. In this work, modeling of membrane contactor is conductedto describe concentration distribution along fiber length used to predict effective fiber length by solving mass conservation equation. Solving of mass conservation equation required information of fluid flow distribution obtained by solving continuity

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9

Hdhiri, Najib, and Brahim Ben Beya. "Numerical study of laminar mixed convection flow in a lid-driven square cavity filled with porous media." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 4 (2018): 857–77. http://dx.doi.org/10.1108/hff-04-2016-0146.

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Purpose The purpose of this study is to produce a numerical model capable of predicting the mixed convection flows in a rectangular cavity filled with a porous medium and to analyze the effects of several parameters on convective flow in porous media in a differentially heated enclosure. Design/methodology/approach The authors used the finite volume method. Findings The authors predicted and analyzed the effects of Richardson number, Darcy number, porosity values and Prandtl number in heat transfer and fluid flow. On other hand, the porosity and Richardson number values lead to reducing the he

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10

Yan, Liang Dong, Zhi Juan Gao, and Feng Gang Dai. "Effective use Model of Low Permeability Oil Reservoir." Advanced Materials Research 753-755 (August 2013): 53–57. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.53.

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The throat of low permeability oil reservoir is narrow and small, the reservoir fluid flow resistance is big, and with the start-up pressure gradient, compare with medium and high permeability reservoir fluid flow, the characteristics are obviously different in performance for non-darcy flow at low speed. This kind of oil field reservoir started in the process of mining scope is small, the degree of use and the development effect is low. To solve these problems, this paper established considering start-up pressure gradient of the new unstable seepage flow mathematical model of non-darcy radial

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11

Zhang, Feng, and Daoyong Yang. "Determination of Fracture Conductivity in Tight Formations With Non-Darcy Flow Behavior." SPE Journal 19, no. 01 (2013): 34–44. http://dx.doi.org/10.2118/162548-pa.

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Summary In this paper, a mathematical model has been developed and successfully applied to accurately determine the fracture conductivity in tight formations with non-Darcy flow behavior. A new non-Darcy flow number is first defined to account for the effect of characteristic length in a hydraulic fracture. A semianalytical method is then applied to solve the newly formulated mathematical model by discretizing the fracture into small segments, assuming that there exists unsteady flow between the adjacent segments. The newly developed model has been validated by simplifying it to the traditiona

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12

Zhang, Longjun, Daolun Li, Lei Wang, and Detang Lu. "Simulation of Gas Transport in Tight/Shale Gas Reservoirs by a Multicomponent Model Based on PEBI Grid." Journal of Chemistry 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/572434.

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The ultra-low permeability and nanosize pores of tight/shale gas reservoir would lead to non-Darcy flow including slip flow, transition flow, and free molecular flow, which cannot be described by traditional Darcy’s law. The organic content often adsorbs some gas content, while the adsorbed amount for different gas species is different. Based on these facts, we develop a new compositional model based on unstructured PEBI (perpendicular bisection) grid, which is able to characterize non-Darcy flow including slip flow, transition flow, and free molecular flow and the multicomponent adsorption in

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13

Li, Juhua, and Chen Chen. "Numerical Simulation of the Non-Darcy Flow Based on Random Fractal Micronetwork Model for Low Permeability Sandstone Gas Reservoirs." Geofluids 2020 (October 9, 2020): 1–9. http://dx.doi.org/10.1155/2020/8884885.

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Darcy’s law is not suit for describing high velocity flow in the near wellbore region of gas reservoirs. The non-Darcy coefficient β of the Forchheimer’s equation is a main parameter for the evaluation of seepage capacity in gas reservoirs. The paper presented a new method to calculate β by performing gas and con-water flow simulations with random 3D micropore network model. Firstly, a network model is established by random fractal method. Secondly, based on the network simulation method of non-Darcy flow in the literature of Thauvin and Mohanty, a modified model is developed to describe gas n

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14

Xu, Hui, Nannan Liu, Yan Chen, et al. "A Novel Equivalent Numerical Simulation Method for Non-Darcy Seepage Flow in Low-Permeability Reservoirs." Energies 15, no. 22 (2022): 8505. http://dx.doi.org/10.3390/en15228505.

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The low permeability and submicron throats in most shale or tight sandstone reservoirs have a significant impact on microscale flow. The flow characteristics can be described with difficultly by the conventional Darcy flow in low-permeability reservoirs. In particular, the thickness of the boundary layer is an important factor affecting the formation permeability, and the relative permeability curve obtained under conventional conditions cannot accurately express the seepage characteristics of porous media. In this work, the apparent permeability and relative permeability were calculated by us

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15

Jiang, Liwu, Tongjing Liu, and Daoyong Yang. "A Semianalytical Model for Predicting Transient Pressure Behavior of a Hydraulically Fractured Horizontal Well in a Naturally Fractured Reservoir With Non-Darcy Flow and Stress-Sensitive Permeability Effects." SPE Journal 24, no. 03 (2019): 1322–41. http://dx.doi.org/10.2118/194501-pa.

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Summary Non-Darcy flow and the stress-sensitivity effect are two fundamental issues that have been widely investigated in transient pressure analysis for fractured wells. The main object of this work is to establish a semianalytical solution to quantify the combined effects of non-Darcy flow and stress sensitivity on the transient pressure behavior for a fractured horizontal well in a naturally fractured reservoir. More specifically, the Barree-Conway model is used to quantify the non-Darcy flow behavior in the hydraulic fractures (HFs), while the permeability modulus is incorporated into math

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16

Hagoort, Jacques. "An Improved Model for Estimating Flow Impairment by Perforation Damage." SPE Journal 12, no. 02 (2007): 235–44. http://dx.doi.org/10.2118/98137-pa.

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Summary In this work, we present two simple formulas for the skin of a perforated well caused by perforation damage: one for the reduction in permeability, and one for the increase in non-Darcy flow coefficient (beta factor). They are based on the inflow performance of a single perforation obtained by means of a prolate-spheroidal flow model. This model rigorously accounts for the flow convergence toward a perforation, especially near the tip of the perforation. It provides a more realistic description of the inflow than a radial flow model, the basis for the existing skin formulas proposed by

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17

Song, Hong Qing, Ming Yue, Wei Yao Zhu, Dong Bo He, and Huai Jian Yi. "Formation Pressure Analysis of Water-Bearing Tight Gas Reservoirs with Unsteady Low-Velocity Non-Darcy Flow." Advanced Materials Research 201-203 (February 2011): 399–403. http://dx.doi.org/10.4028/www.scientific.net/amr.201-203.399.

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Porous media containing water is the prerequisite of existence of threshold pressure gradient (TPG) for gas flow. Based on theory of fluid mechanics in porous medium considering TPG, the non-Darcy flow mathematical model is established for formation pressure analysis of water-bearing tight gas reservoirs. It could provide semi-analytic solution of unsteady radial non-Darcy flow. According to the solution of unsteady radial non-Darcy flow, an easy and accurate calculation method for formation pressure analysis is presented. It can provide theoretical foundation for development design of water-b

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18

Trilok, G., and N. Gnanasekaran. "Comparison of Numerical Models of Flow and Heat Transfer Through Porous Medium in a Vertical Channel." IOP Conference Series: Earth and Environmental Science 850, no. 1 (2021): 012023. http://dx.doi.org/10.1088/1755-1315/850/1/012023.

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Abstract Porous medium modelling technique has opened up ways for number of numerical studies to investigate the performance of many devices that involve heat exchanging process. Such modelling technique not only avoids huge cost and time as compared to experimental analysis but also makes computationally less time-consuming as in case of numerical simulation by exact geometry modelling of porous materials. In this regard the present paper analyses two different thermal models namely local thermal equilibrium model and local thermal non equilibrium model along with two different flow models na

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19

Chen, Jie, Shuyu Sun, and Zhangxin Chen. "Coupling Two-Phase Fluid Flow with Two-Phase Darcy Flow in Anisotropic Porous Media." Advances in Mechanical Engineering 6 (January 1, 2014): 871021. http://dx.doi.org/10.1155/2014/871021.

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This paper reports a numerical study of coupling two-phase fluid flow in a free fluid region with two-phase Darcy flow in a homogeneous and anisotropic porous medium region. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the anisotropic porous medium region. A Robin-Robin domain decomposition method is used for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Obtained results have shown the anisotro

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20

Akanni, Olatokunbo O., Hisham A. Nasr-El-Din, and Deepak Gusain. "A Computational Navier-Stokes Fluid-Dynamics-Simulation Study of Wormhole Propagation in Carbonate-Matrix Acidizing and Analysis of Factors Influencing the Dissolution Process." SPE Journal 22, no. 06 (2017): 2049–66. http://dx.doi.org/10.2118/187962-pa.

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Summary This study demonstrates the application of an alternative numerical-simulation approach to effectively describe the flow field in a two-scale carbonate-matrix-acidizing model. The modified model accurately captures the dissolution regimes that occur during carbonate-matrix acidizing. Sensitivity tests were performed on the model to compare the output with experimental observations and previous two-scale models in the literature. A nonlinear reaction-kinetics model for alternative acidizing fluids is also introduced. In this work, the fluid-field flow is described by the Navier-Stokes m

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21

Shao, Jianli, Qi Zhang, Wenbin Sun, Zaiyong Wang, and Xianxiang Zhu. "Numerical Simulation on Non-Darcy Flow in a Single Rock Fracture Domain Inverted by Digital Images." Geofluids 2020 (June 27, 2020): 1–13. http://dx.doi.org/10.1155/2020/8814327.

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The influence of rock seepage must be considered in geotechnical engineering, and understanding the fluid flow in rock fractures is of great concern in the seepage effect investigation. This study is aimed at developing a model for inversion of rock fracture domains based on digital images and further study of non-Darcy flow. The visualization model of single rock fracture domain is realized by digital images, which is further used in flow numerical simulation. We further discuss the influence of fracture domain geometry on non-Darcy flow. The results show that it is feasible to study non-Darc

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22

Deng, Jia, Wei Yao Zhu, Qian Ma, and Huai Jian Yi. "Study on the Unstable Seepage Flow Model and the Productivity Characteristics in Tight Gas Heterogeneity Reservoir." Advanced Materials Research 868 (December 2013): 465–72. http://dx.doi.org/10.4028/www.scientific.net/amr.868.465.

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In this paper, considering on the real threshold pressure gradient (TPG), the mathematical model for low velocity non-Darcy unstable gas flow was established for the tight gas reservoir. Based on the low velocity non-Darcy unstable gas flow model, the gas flow model in heterogeneity formation was developed, and the analytical solution was obtained on the condition of constant production for inner boundary. Then we calculated the model numerically by Matlab programming. Its analyzed that the pressure distribution and the influencing factors such as production rate, producing time, reservoir thi

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23

WANG, FUYONG, ZHICHAO LIU, JIANCHAO CAI, and JIAN GAO. "A FRACTAL MODEL FOR LOW-VELOCITY NON-DARCY FLOW IN TIGHT OIL RESERVOIRS CONSIDERING BOUNDARY-LAYER EFFECT." Fractals 26, no. 05 (2018): 1850077. http://dx.doi.org/10.1142/s0218348x18500779.

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Flow in nanoscale pore-throats of tight oil reservoirs is strongly affected by boundary-layers, and exhibits low-velocity non-Darcy flow phenomena. The relationship between flow velocity and pressure gradient is highly nonlinear and difficult to be modeled mathematically. This paper proposed a low-velocity non-Darcy flow model which can account for boundary-layer effect in tight oil reservoirs. First, a modified Hagen–Poiseuille equation coupled with boundary-layer effect in a single capillary tube was derived. Then, assuming pores in tight formations following fractal distribution, an analyti

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24

Lei, Xiao, Mu Wang Wu, Feng Bo Zhang, et al. "Variable-Permeability Well Test Model and Pressure Response of Non-Darcy Flow in Low-Permeability Reservoirs." Applied Mechanics and Materials 644-650 (September 2014): 5097–100. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.5097.

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Considering the variable-permeability effect of non-Darcy flow in low-permeability reservoirs, this work set up a two-dimensional model with boundaries. The implicit finite difference algorithm was employed to solve the well test model, and typical curves in log-log scale by considering the effects of variable-permeability and non-Darcy flow were obtained. The results show that, in reservoirs with impermeable boundary, the upturned part of the pressure derivative curve caused by boundary effect will be covered by that of non-Darcy effect, indicating boundary effect is postponed to appear. The

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25

Xue, Yi, Yang Liu, Faning Dang, et al. "Assessment of the Nonlinear Flow Characteristic of Water Inrush Based on the Brinkman and Forchheimer Seepage Model." Water 11, no. 4 (2019): 855. http://dx.doi.org/10.3390/w11040855.

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Underground fault water inrush is a hydrogeological disaster that frequently occurs in underground mining and tunnel construction projects. Groundwater may pour from an aquifer when disasters occur, and aquifers are typically associated with fractured rock formations. Water inrush accidents are likely to occur when fractured rock masses are encountered during excavation. In this study, Comsol Multiphysics, cross-platform multiphysics field coupling software, was used to simulate the evolution characteristics of water flow in different flow fields of faults and aquifers when water inrush from u

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26

Cui, Changzhi, and Kyosuke Ono. "Theoretical and Experimental Investigation of an Externally Pressurized Porous Annular Thrust Gas Bearing and Its Optimal Design." Journal of Tribology 119, no. 3 (1997): 486–92. http://dx.doi.org/10.1115/1.2833524.

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Static and dynamic characteristics of an externally pressurized porous annular thrust gas bearing (PATGB), which has a thin restricted surface layer, are investigated by numerical analysis and experiment. In the analysis, it is assumed that the fluid flow obeys Darcy’s law in the porous material, restricted with Darcy’s restrictor (Darcy-Darcy model) or orifice restrictor (Darcy-Orifice model) in the surface layer. From experimental investigation, it is found that the theoretical results calculated by the Darcy-Darcy model agree with the experimental data better than those of the Darcy-Orifice

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27

Skrzypacz, Piotr, and Dongming Wei. "Solvability of the Brinkman-Forchheimer-Darcy Equation." Journal of Applied Mathematics 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/7305230.

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The nonlinear Brinkman-Forchheimer-Darcy equation is used to model some porous medium flow in chemical reactors of packed bed type. The results concerning the existence and uniqueness of a weak solution are presented for nonlinear convective flows in medium with variable porosity and for small data. Furthermore, the finite element approximations to the flow profiles in the fixed bed reactor are presented for several Reynolds numbers at the non-Darcy’s range.

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Cui, Shuheng, Jie Kong, Hongwei Yu, Cheng Chen, and Junlei Wang. "Revising Transient-Pressure Solution for Vertical Well Intersected by a Partially Penetrating Fracture with Non-Darcy Flow Effect." Geofluids 2020 (November 26, 2020): 1–17. http://dx.doi.org/10.1155/2020/8884750.

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The principle purpose of this work is to formulate an accurate mathematical model to evaluate the transient pressure behavior of a well intercepted by a partially penetrating vertical fracture (PPVF) with non-Darcy flow effect. Fracture conductivity is taken into account by coupling the three-dimensional flow in reservoir and the two-dimensional flow within fracture; the Barree-Conway model is incorporated into the model to analyze non-Darcy flow behavior in fracture, which leads to the nonlinearity of the governing equations. A high-effective iterative algorithm using a combined technique of

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Ansari, Shahab U., Masroor Hussain, Sarvat M. Ahmad, Ahmar Rashid, and Suleman Mazhar. "STABILIZED MIXED FINITE ELEMENT METHOD FOR TRANSIENT DARCY FLOW." Transactions of the Canadian Society for Mechanical Engineering 41, no. 1 (2017): 85–97. http://dx.doi.org/10.1139/tcsme-2017-1006.

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Darcy flow is a steady-state model for laminar flow of a fluid through a porous medium. The present work proposes an extended model of laminar Darcy flow by introducing dynamic pressure and velocity to the classical formulation. The solution of the proposed time-space model is attained by discretizing the problem with a stabilized mixed Galerkin method in space and a forward Euler method in time. The resulting matrix equation is well-posed and is solved using the conjugate gradient (CG) method. The error analysis of the numerical solutions confirms convergence to the actual model.

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30

Lage, J. L., and B. V. Antohe. "Darcy’s Experiments and the Deviation to Nonlinear Flow Regime." Journal of Fluids Engineering 122, no. 3 (2000): 619–25. http://dx.doi.org/10.1115/1.1287722.

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Many important technological and natural processes involving flow through porous media are characterized by large filtration velocity. It is important to know when the transition from the linear flow regime to the quadratic flow regime actually occurs to obtain accurate models for these processes. By interpreting the quadratic extension of the original Darcy equation as a model of the macroscopic form drag, we suggest a physically consistent parameter to characterize the transition to quadratic flow regime in place of the Reynolds number, Re. We demonstrate that an additional data set obtained

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31

Wanjing, Luo, and Tang Changfu. "A Semianalytical Solution of a Vertical Fractured Well With Varying Conductivity Under Non-Darcy-Flow Condition." SPE Journal 20, no. 05 (2015): 1028–40. http://dx.doi.org/10.2118/178423-pa.

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Summary Fracture distributions (simple or complex fractures), fracture-conductivity heterogeneity (uniform or varying conductivity along the fracture), and flow regimes inside the fracture (Darcy or non-Darcy flow) are the three main issues that have been widely investigated for transient-pressure analysis of vertical fracture systems. In this study, we focus on the latter two issues by proposing a semianalytical solution to discuss the transient-pressure behaviors of a varying-conductivity fracture under non-Darcy-flow condition. First, a general fracture-flow equation is established for the

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32

Mustafa, Irfan, Abuzar Ghaffari, Tariq Javed, and Javeria Nawaz Abbasi. "Numerical Examination of Thermophysical Properties of Cobalt Ferroparticles over a Wavy Surface Saturated in Non-Darcian Porous Medium." Journal of Non-Equilibrium Thermodynamics 45, no. 2 (2020): 109–20. http://dx.doi.org/10.1515/jnet-2019-0019.

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AbstractIn this study, the effect of magnetic field on an incompressible ferrofluid flow along a vertical wavy surface saturated in a porous medium is investigated. Ferrofluid is made by incorporating magnetic particles, in this case cobalt, at the nanoscale level into a base fluid. For the study of porous medium two well-known models, namely, Darcy and non-Darcy, are used. The mathematical model in terms of governing partial differential equations which are based on conservation laws in mechanics according to the assumption is developed, and this model is converted into a dimensionless form b

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Juncu, Gheorghe. "Brinkman – Forchheimer – Darcy Flow Past an Impermeable Sphere Embedded in a Porous Medium." Analele Universitatii "Ovidius" Constanta - Seria Matematica 23, no. 3 (2015): 97–112. http://dx.doi.org/10.1515/auom-2015-0050.

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Abstract The flow past an impermeable sphere embedded in a fluid saturated porous medium was studied numerically considering valid the Brinkman-Forchheimer-Darcy (or Brinkman-Hazen-Dupuit-Darcy) model. The flow is viscous, laminar, axisymmetric, steady and incompressible. The porous medium is isotropic, rigid and homogeneous. The stream function - vorticity equations were solved numerically in spherical coordinates system by a multigrid method. The influence of the Darcy number and Forchheimer term on the velocities field was investigated for two boundary conditions on the surface of the spher

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Knabner, Peter, and Jean E. Roberts. "Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy–Forchheimer flow in the fracture." ESAIM: Mathematical Modelling and Numerical Analysis 48, no. 5 (2014): 1451–72. http://dx.doi.org/10.1051/m2an/2014003.

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XIAO, BOQI, YONGHUI LIU, HANXIN CHEN, XUBING CHEN, and GONGBO LONG. "A NOVEL FRACTAL SOLUTION FOR LAMINAR FLOW RESISTANCE IN ROUGHENED CYLINDRICAL MICROCHANNELS." Fractals 28, no. 06 (2020): 2050097. http://dx.doi.org/10.1142/s0218348x20500978.

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In this work, a novel fractal model for the laminar flow in roughened cylindrical microchannels is proposed. The average height of rough elements is derived using the fractal theory. The effects of relative roughness on the friction factor and the Poiseuille number are discussed. It is found that the Darcy friction factor and the Poiseuille number increase with the increase in the relative roughness in the cylindrical microchannel. Besides, it is observed that the Darcy friction factor decreases with the increase in the Reynolds number. Each parameter of the proposed model has a clear physical

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36

Sakamoto, H., and F. A. Kulacki. "Buoyancy Driven Flow in Saturated Porous Media." Journal of Heat Transfer 129, no. 6 (2006): 727–34. http://dx.doi.org/10.1115/1.2717937.

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Measurements are reported of heat transfer coefficients in steady natural convection on a vertical constant flux plate embedded in a saturated porous medium. Results show that heat transfer coefficients can be adequately determined via a Darcy-based model, and our results confirm a correlation proposed by Bejan [Int. J. Heat Mass Transfer. 26(9), 1339–1346 (1983)]. It is speculated that the reason that the Darcy model works well in the present case is that the porous medium has a lower effective Prandtl number near the wall than in the bulk medium. The factors that contribute to this effect in

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Ettefagh, J., K. Vafai, and S. J. Kim. "Non-Darcian Effects in Open-Ended Cavities Filled With a Porous Medium." Journal of Heat Transfer 113, no. 3 (1991): 747–56. http://dx.doi.org/10.1115/1.2910627.

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The importance and relevance of non-Darcian effects associated with the buoyancy driven convection in open-ended cavities filled with fluid-saturated porous medium is analyzed in this work. Several different flow models for porous media, such as Brinkman-extended Darcy, Forchheimer-extended Darcy, and generalized flow models, are considered. The significance of inertia and boundary effects, and their crucial influence on the prediction of buouancy-induced flow and heat transfer in open-ended cavities, are investigated. Analysis is made on the proper choice of parameters that can fully determin

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Liu, Piyang, Xiaoxia Ren, Liang Kong, and Jun Yao. "Three-dimensional simulation of acidizing process in carbonate rocks using the Darcy–Forchheimer framework." Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 75 (2020): 48. http://dx.doi.org/10.2516/ogst/2020035.

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Acidizing is an economical and effective practice to remove the near wellbore damage, which is performed by injecting acid into the formation through the wellbore. The injected acid dissolves the rock, by which the permeability nearby the wellbore can be improved. For a carbonate reservoir, the injected acid dissolves some of the minerals and some narrow and long channels, named wormholes, are formed then. These wormholes can bypass the damaged zone and hence improve the productivity of the well. The process for acid dissolving rocks involves complex physicochemical change, including the chemi

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Wu, Zhongwei, Chuanzhi Cui, Japan Trivedi, Ning Ai, and Wenhao Tang. "Pressure Analysis for Volume Fracturing Vertical Well considering Low-Velocity Non-Darcy Flow and Stress Sensitivity." Geofluids 2019 (November 20, 2019): 1–10. http://dx.doi.org/10.1155/2019/2046061.

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In general, there is stress sensitivity damage in tight reservoirs and fractures. Furthermore, the flow in tight reservoirs is the low-velocity non-Darcy flow. Currently, few researches of pressure analysis for volume fracturing vertical well are conducted simultaneously considering the low-velocity non-Darcy flow and stress sensitivity. In the paper, a novel flow model of a volume fractured vertical well is proposed and solved numerically. Firstly, the threshold pressure gradient, permeability modulus, and experimental data are, respectively, utilized to characterize the low-velocity non-Darc

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Tang, Yula, Turhan Yildiz, Erdal Ozkan, and Mohan G. Kelkar. "Effects of Formation Damage and High- Velocity Flow on the Productivity of Perforated Horizontal Wells." SPE Reservoir Evaluation & Engineering 8, no. 04 (2005): 315–24. http://dx.doi.org/10.2118/77534-pa.

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Summary A comprehensive semianalytical model has been built to investigate the effects of drilling and perforating damage and high-velocity flow on the performance of perforated horizontal wells. The model incorporates the additional pressure drop caused by formation damage and high-velocity flow into a semianalytical coupled wellbore/reservoir model. The reservoir model considers the details of flow in the vicinity of the wellbore, including 3Dconvergent flow into individual perforations, flow through the damaged zone around the wellbore and the crushed zone around the perforation tunnels, an

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Guo, Zhanwei, and Jincheng Shi. "Structural stability for the Darcy model in double diffusive convection flow with Magnetic field effect." AIMS Mathematics 7, no. 9 (2022): 16366–86. http://dx.doi.org/10.3934/math.2022894.

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

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Huang, Ting, Xiao Guo, and Kun Wang. "Nonlinear Seepage Model of Gas Transport in Multiscale Shale Gas Reservoirs and Productivity Analysis of Fractured Well." Journal of Chemistry 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/349507.

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Shale is abundant in nanoscale pores, so gas flow in shales cannot be simply represented by Darcy formula anymore. It is crucial to figure out the influence of gas flow in nano/micro pores on actual productivity, which can provide basic theories for optimizing parameters and improving the gas production from engineering perspective. This paper considers the effects of slippage and diffusion in nanoscale based on Beskok-Karniadakis (BK) equation, which can be applicable for different flow regimes including continuum flow, slip flow, transition flow, and free-molecule flow. A new non-Darcy equat

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Wang, Jingyu, Jian Yang, Long Li, Pei Qian, and Qiuwang Wang. "Numerical simulation and circuit network modelling of flow distributions in 2-D array configurations." Thermal Science 22, no. 5 (2018): 1987–98. http://dx.doi.org/10.2298/tsci171230256w.

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Packing configuration is widely used in chemical industries such as chemical re-action and chromatograph where the flow distribution has a significant effect on the performance of heat and mass transfer. In the present paper, numerical simulation is carried out to investigate the fluid-flow in three 2-D array configurations including in-line array, staggered array and hexagonal array. Meanwhile, a simplified equivalent circuit network model based on the Voronoi tessellation is proposed to simulate the flow models. It is found that firstly, the local Reynolds number could be used as a criterion

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Krotkiewski, Marcin, Ingeborg S. Ligaarden, Knut-Andreas Lie, and Daniel W. Schmid. "On the Importance of the Stokes-Brinkman Equations for Computing Effective Permeability in Karst Reservoirs." Communications in Computational Physics 10, no. 5 (2011): 1315–32. http://dx.doi.org/10.4208/cicp.290610.020211a.

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AbstractCavities and fractures significantly affect the flow paths in carbonate reservoirs and should be accurately accounted for in numerical models. Herein, we consider the problem of computing the effective permeability of rock samples based on high-resolution 3D CT scans containing millions of voxels. We use the Stokes-Brinkman equations in the entire domain, covering regions of free flow governed by the Stokes equations, porous Darcy flow, and transitions between them. The presence of different length scales and large (ten orders of magnitude) contrasts in permeability leads to highly ill

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Hamdan, Mohammad. "An empirical correlation for isothermal parallel plate channel completely filled with porous media." Thermal Science 17, no. 4 (2013): 1061–70. http://dx.doi.org/10.2298/tsci120419015h.

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This study reports a simple empirical correlation for friction factor and Nusselt number for laminar, steady state, hydraulically and thermally fully developed flow in isothermal parallel plate channel completely filled with porous media. The study is carried out using a finite difference numerical analysis. The Darcy-Brinkman-Forchheimer model is used to model the flow inside the porous media. The empirical correlations are developed to relate friction factor and Nusselt number to Darcy and Forchheimer coefficient.

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Gruais, Isabelle, and Dan Poliševski. "Thermal flows in fractured porous media." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 3 (2021): 789–805. http://dx.doi.org/10.1051/m2an/2020087.

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We consider the thermal flow problem occuring in a fractured porous medium. The incompressible filtration flow in the porous matrix and the viscous flow in the fractures obey the Boussinesq approximation of Darcy-Forchheimer law and respectively, the Stokes system. They are coupled by the Saffman’s variant of the Beavers–Joseph condition. Existence and uniqueness properties are presented. The use of the energy norm in describing the Darcy-Forchheimer law proves to be appropriate. In the ε-periodic framework, we find the two-scale homogenized system which governs their asymptotic behaviours whe

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Civan, F., C. S. S. Rai, and C. H. H. Sondergeld. "Determining Shale Permeability to Gas by Simultaneous Analysis of Various Pressure Tests." SPE Journal 17, no. 03 (2012): 717–26. http://dx.doi.org/10.2118/144253-pa.

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Summary A model-assisted analysis is presented of pressure-pulse-transmission data obtained under different pressure conditions with core plugs of shale-gas formations. Applications and validations for steady-state and transient-state laboratory tests are provided. Best-estimate values of the intrinsic permeability and tortuosity at a reference condition and the Langmuir volume and pressure are determined by matching the solution of a modified Darcy model to several pressure-pulse-transmission flow tests with core samples simultaneously. The data-interpretation model considers the prevailing c

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Eroglu, Fatma G., Songul Kaya, and Leo G. Rebholz. "POD-ROM for the Darcy–Brinkman equations with double-diffusive convection." Journal of Numerical Mathematics 27, no. 3 (2019): 123–39. http://dx.doi.org/10.1515/jnma-2017-0122.

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Abstract This paper extends proper orthogonal decomposition reduced order modeling to flows governed by double diffusive convection, which models flow driven by two potentials with different rates of diffusion. We propose a reduced model based on proper orthogonal decomposition, present a stability and convergence analyses for it, and give results for numerical tests on a benchmark problem which show it is an effective approach to model reduction in this setting.

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WU, JINSUI, DEZHI HU, WENJUN LI, and XIN CAI. "A REVIEW ON NON-DARCY FLOW — FORCHHEIMER EQUATION, HYDRAULIC RADIUS MODEL, FRACTAL MODEL AND EXPERIMENT." Fractals 24, no. 02 (2016): 1630001. http://dx.doi.org/10.1142/s0218348x16300014.

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In this paper, a brief summary of some of the relevant models for non-Darcy flow is reviewed, they mainly include seven models, among them three models are based on the average hydraulic radius, two are based on fractal geometry theory and technique, one is based on first principle, one is based on experimental measurement. Each model has its own advantages and disadvantages.

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Naderi, Masoud, Hossein Afzalimehr, Ayoub Dehghan, Nader Darban, Mohammad Nazari-Sharabian, and Moses Karakouzian. "Field Study of Three–Parameter Flow Resistance Model in Rivers with Vegetation Patch." Fluids 7, no. 8 (2022): 284. http://dx.doi.org/10.3390/fluids7080284.

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Bed shear stress in coarse–bed rivers with vegetation patches is one of the challenging parameters in hydraulic engineering, mechanical engineering, fluvial morphology, and environmental studies. Based on this necessity, in this study, the values of bed shear stress in four reaches of rivers in Iran were estimated and compared using the methods of boundary layer characteristics, logarithmic law, and Darcy–Weisbach. Data collection in this study started in February 2021 and ended in April 2021. Estimation of flow resistance is a key factor in many numerical and physical models. In order to obta

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