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1
Patiño, I. D., J. D. Vanegas, and C. E. Correa. "State of the Art on Permeability Characterization of Fibrous Reinforcements used in Resin Transfer Molding Process." Advanced Composites Letters 20, no. 6 (2011): 096369351102000. http://dx.doi.org/10.1177/096369351102000604.
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The physical and mathematical fundamentals that are required for the measurement of permeability of fibrous reinforcement used in Resin Transfer Molding (RTM) and to interpret correctly the results of those experiments are considered in this article. The basic concepts of fluid dynamics through porous media applied to the analysis of the impregnation phenomena in fibre preforms are discussed. The principal assumptions to simplify the governing equations into the Darcy's law are summarized in order to give an idea of some typical features of the permeability tests regarding the injection parameters and types of fluids and preforms used. Three important concepts for determining permeability in any direction for anisotropic preforms are introduced: permeability tensor ( Kij), permeability ellipse and effective permeability ( Keff). This paper also deals with the deduction, from Darcy's law and Laplace Equation, of the basic equations used on the unidirectional and divergent radial permeability tests. The final conclusion remarks the importance of the concepts exposed in this work.
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Payne, L. E., J. F. Rodrigues, and B. Straughan. "Effect of anisotropic permeability on Darcy's law." Mathematical Methods in the Applied Sciences 24, no. 6 (2001): 427–38. http://dx.doi.org/10.1002/mma.228.
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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 parameters were obtained. The seepage behaviour in the silt layer, fine sand layer, silty clay layer and gravelly clay layer followed the traditional Darcy law, while the gravel layers showed clear nonlinear characteristics. The permeability increases exponentially and the non-Darcy coefficient decreases exponentially with an increase in porosity, and the relation among the permeability, the porosity and the non-Darcy coefficient is investigated. A coupled mathematical model is established for two flow fields, on the basis of Darcy flow in the low-permeability layers and Forchheimer flow in the high-permeability layers. In addition, the effect of the seepage in the slope on the transition from Darcy flow to Forchheimer flow was considered. Then, a numerical simulation was conducted by using finite-element software (FELAC 2.2). The results indicate that the free surface calculated by the Darcy–Forchheimer model is in good agreement with the in situ measurements; however, there is an evident deviation of the simulation results from the measured data when the Darcy model is used. Through a parameter sensitivity analysis of the gravel layers, it can be found that the height of the overflow point and the water inflow calculated by the Darcy–Forchheimer model are consistently less than those of the Darcy model, and the discrepancy between these two models increases as the permeability increases. The necessity of adopting the Darcy–Forchheimer model was explained. The Darcy–Forchheimer model would be applicable in slope engineering applications with highly permeable rock.
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Jiang, Shuai, Zheng Ming Yang, Xue Wei Liu, Meng Ting Wang, and Qian Zhang. "Study on the Nonlinear Flow Percolation Law in Low Permeability Carbonate Reservoir of HF Oilfield." Applied Mechanics and Materials 644-650 (September 2014): 5065–70. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.5065.
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With the development of the global oil industry,the production of the normal or high permeability reservoirs decline rapidly. Therefore, more and more low permeability reservoirs are used to the production stimulation. The oilfields overseas make great contribution to CNPC. The HF oilfield is one oilfield that the CNPC have in overseas. The HF oilfield is mainly the low permeability carbonate reservoirs which make it not easy to economically exploit. Due to the reason that the low permeability carbonate reservoirs present small porosity and the fluid’s flow situation in the low permeability carbonate reservoirs, the flow doesn't obey the Darcy's law. Thus it is greatly necessary to study the non-Darcy percolation characteristics. In this paper, the HF ‘s low permeability is tested and the threshold pressure gradient test is finished ,according to the experiment results, the nonlinear percolation ‘s law ,which is suited to HF-oil field , is illustrated and the reservoir classification is achieved.
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Yan, Shi Lin, Hang Lu, Hua Tan, and Zhong Qi Qiu. "Microscopic Analysis of Flow and Prediction of Effective Permeability for Dual-Scale Porous Fiber Fabrics." Advanced Materials Research 97-101 (March 2010): 1776–81. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.1776.
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In this paper, the permeability of fiber fabric used in liquid composite molding (LCM) is predicted by the method of numerical simulation. The three-dimensional finite element model of unit cell representing the periodic micro-structure of a plaid is established. In the process of numerical simulation, each fiber bundle in unit cell is treated as a porous medium. Stokes equation and Darcy's law are employed to model the saturated flow between the fiber bundles and the saturated flow in the fiber bundle, respectively. Steady state flow of the finite element model of unit cell is simulated. The effective permeability of the plaid is obtained from the postprocessing of the simulation results by using Darcy's law.
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Li, Huakang, Hongbo Liao, Qilin Yang, Kun Liu, and Dan Huang. "A Method for In-Situ Permeability Testing of Loose Porous Media Based on Vacuum Extraction." Advances in Engineering Technology Research 4, no. 1 (2023): 154. http://dx.doi.org/10.56028/aetr.4.1.154.2023.
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The permeability of loosely porous media is difficult to test. A vacuum extraction based in-situ permeability test for loose porous media has been proposed. The calculation follows from the typical Darcy's law. A mathematical computational model of in situ permeability testing based on pressure decay curves has been developed. The effect of the depth of the return packing on the permeability test is analysed and the permeability of the porous media is obtained to verify the validity of the calculated method.
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Xin, Xian Kang, Gao Ming Yu, and Zhuo Li. "Study on Application of Low Velocity Non-Darcy Flow." Advanced Materials Research 1078 (December 2014): 129–33. http://dx.doi.org/10.4028/www.scientific.net/amr.1078.129.
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The seepage underground is rather complicated in the low permeability reservoir and the heavy oil reservoir. One important point to note is that the seepage in these reservoirs does not follow Darcy's law, which brings difficulty to the development of oil field. Study on low velocity non-Darcy percolation theory, the impact on oil production index is analyzed. The key is the summary of the application in order to provide theoretical references for the rational exploitation of the relevant oil fields.
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Wang, HanYi, and Matteo Marongiu-Porcu. "Impact of Shale-Gas Apparent Permeability on Production: Combined Effects of Non-Darcy Flow/Gas Slippage, Desorption, and Geomechanics." SPE Reservoir Evaluation & Engineering 18, no. 04 (2015): 495–507. http://dx.doi.org/10.2118/173196-pa.
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Summary Permeability is one of the most fundamental reservoir-rock properties required for modeling hydrocarbon production. Many shale-gas and ultralow-permeability tight gas reservoirs can have matrix-permeability values in the range of tens to hundreds of nanodarcies. The ultrafine pore structure of these rocks can cause violation of the basic assumptions behind Darcy's law. Depending on a combination of pressure-temperature conditions, pore structure and gas properties, non-Darcy flow mechanisms such as Knudsen diffusion, and/or gas-slippage effects will affect the matrix apparent permeability. Even though numerous theoretical and empirical models were proposed to describe the increasing apparent permeability caused by non-Darcy flow/gas-slippage behavior in nanopore space, few literature sources have investigated the impact of formation compaction and the release of the adsorption gas layer upon shale-matrix apparent permeability during reservoir depletion. In this article, we first present a thorough review on gas flow in shale nanopore space and discuss the factors that can affect shale-matrix apparent permeability, besides the well-studied non-Darcy flow/gas-slippage behavior. Then, a unified shale-matrix apparent-permeability model is proposed to bridge the effects of non-Darcy flow/gas-slippage, geomechanics (formation compaction), and the release of the adsorption gas layer into a single, coherent equation. In addition, a mathematical framework for an unconventional reservoir simulator that was developed for this study is also presented. Different matrix apparent-permeability models are implemented in our numerical simulator to examine how the various factors affect matrix apparent permeability within the simulated reservoir volume. Finally, the impact of a natural-fracture network on matrix apparent-permeability evolution is investigated. The results indicate that, even though the conductive fracture network plays a vital role in shale-gas production, the matrix apparent-permeability evolution during pressure depletion cannot be neglected for accurate production modeling.
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Karmakar, Timir, Meraj Alam, and G. P. Raja Sekhar. "Analysis of Brinkman-Forchheimer extended Darcy's model in a fluid saturated anisotropic porous channel." Communications on Pure & Applied Analysis 21, no. 3 (2022): 845. http://dx.doi.org/10.3934/cpaa.2022001.
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<p style='text-indent:20px;'>We present asymptotic analysis of Couette flow through a channel packed with porous medium. We assume that the porous medium is anisotropic and the permeability varies along all the directions so that it appears as a positive semidefinite matrix in the momentum equation. We developed existence and uniqueness results corresponding to the anisotropic Brinkman-Forchheimer extended Darcy's equation in case of fully developed flow using the Browder-Minty theorem. Complemented with the existence and uniqueness analysis, we present an asymptotic solution by taking Darcy number as the perturbed parameter. For a high Darcy number, the corresponding problem is dealt with regular perturbation expansion. For low Darcy number, the problem of interest is a singular perturbation. We use matched asymptotic expansion to treat this case. More generally, we obtained an approximate solution for the nonlinear problem, which is uniformly valid irrespective of the porous medium parameter values. The analysis presented serves a dual purpose by providing the existence and uniqueness of the anisotropic nonlinear Brinkman-Forchheimer extended Darcy's equation and provide an approximate solution that shows good agreement with the numerical solution.</p>
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NGUYEN, H., B. CHOPARD, and S. STOLL. "HYDRODYNAMIC PROPERTIES AND PERMEABILITY OF FRACTAL OBJECTS." International Journal of Modern Physics C 18, no. 04 (2007): 732–38. http://dx.doi.org/10.1142/s0129183107010991.
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Using Lattice Boltzmann numerical simulations, we analyse the hydrodynamic properties of both fractal aggregates and artificial fractal objects. First we show that the hydrodynamic radius actually depends on three quantities: the fractal dimension, the so-called prefactor and the inside connectivity. Second, from the simulated velocity field inside the aggregate, we observe that Darcy's law describes the flow better than Brinkman equation. Finally we measure the permeability - porosity relation and observed that it departs from the prediction of Happel's model.
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Yang, Duanyang, Fengyuan Li, Yangyang Xia, Mingsheng Shi, Yanjie Hao, and Qi Liu. "Analysis of elastic viscoplastic consolidation of sand drain foundations with exponential seepages." E3S Web of Conferences 248 (2021): 01039. http://dx.doi.org/10.1051/e3sconf/202124801039.
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Studies have shown that the pore seepage in soft clay deviates from Darcy's law, with the compressibility and permeability of the soil demonstrating obvious nonlinear characteristics during the consolidation process. These factors will affect the sand drain foundation consolidation process. In order to explore the consolidation mechanism of sand drain foundation in saturated clay, this paper introduces the UH model considering the time effect to describe the nonlinear deformation relation of the soil skeleton under the Barron free strain assumption and introduces the exponential seepage equation as an alternative to Darcy's law. Additionally, the impact of the permeability coefficient and the smearing effect is considered which is used to re-derive the conventional sand drain consolidation equation, and then the finite difference method is adopted to give the implicit numerical solutions of the equation. By comparing with literature results, the validity of the method developed in this paper is verified. Then, the effects of the soil nonlinearity, construction disturbance, and external load on the sand drain foundation nonlinear consolidation process are studied as a function of time. The current results reveal that due to the viscous effect of soil, the pore pressure near the undrained boundary of the sand drain foundation during the pre-loading period increases. The above phenomenon is more evident when considering the non-Darcy seepage; meanwhile, the consolidation rate of the sand drain foundation also becomes increasingly slow. Moreover, the decrease of the permeability coefficient in the smear zone can significantly reduce the dissipation rate of the overall pore pressure of the sand drain foundation, while the increase of the external load accelerates foundation consolidation.
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Yang, Manzheng, Bingrui Li, and Shubo Li. "Calculation of permeability coefficient of coal seam under rapid measurement conditions." E3S Web of Conferences 136 (2019): 04004. http://dx.doi.org/10.1051/e3sconf/201913604004.
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In order to achieve rapid determination of coal seam permeability, the calculation method of coal seam permeability coefficient was studied. Based on the Darcy's law in the flow of gas in the coal seam, the relationship equation between the gas pressure of the borehole and the gas permeability coefficient of the coal seam is established under the radial unsteady flow state. The gas permeability coefficient of the coal seam is obtained by coordinate transformation and integral transformation. Solve the expression. The analysis and verification of the field measured data show that the expression of the analytical solution of the coal seam permeability coefficient is consistent with the variation of the borehole pressure-time curve, which can provide a theoretical basis for the rapid determination of coal seam permeability.
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Rosti, Marco Edoardo, Satyajit Pramanik, Luca Brandt, and Dhrubaditya Mitra. "The breakdown of Darcy's law in a soft porous material." Soft Matter 16, no. 4 (2020): 939–44. http://dx.doi.org/10.1039/c9sm01678c.
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We show that the flux through a poroelastic material is a super-linear function of the pressure-difference. The permeability is a universal function of the ratio of the pressure-difference over the shear modulus, proportional to the cube of porosity.
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Xinhua, Xue, Zhang Wohua, and Xingguo Yang. "Study on constitutive model of coupled damage-permeability of porous media." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 2 (2014): 359–75. http://dx.doi.org/10.1108/hff-04-2012-0086.
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Purpose – The paper aims to clarify the relationship between the micro-structures of porous media and the coefficient of permeability. Most materials involve different types of defects like caves, pores and cracks, which are important characters of porous media and have a great influence on the physical properties of materials. To study the seepage mechanical characteristics of damaged porous media, the constitutive model of porous media dealing with coupled modeling of pores damage and its impact on permeability property of a deforming media was studied in this paper. Design/methodology/approach – The paper opted for an exploratory study using the approach of continuum damage mechanics (CDM). Findings – The paper provides some new insights on the fluid dynamics of porous media. The dynamic evolution model of permeability coefficient established in this paper can be used to model the fluid flow problems in damaged porous media. Moreover, the modified Darcy's law developed in this paper is considered to be an extension of the Darcy's law for fluid flow and seepage in a porous medium. Research limitations/implications – Owing to the limitations of time, conditions, funds, etc., the research results should be subject to multifaceted experiments before their innovative significance can be fully verified. Practical implications – The paper includes implications for the development of fluid dynamics of porous media. Originality/value – This paper fulfils an identified need to study the relationship between the micro-structures of porous media and the coefficient of permeability.
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Kirby, JM, and DE Smiles. "Hydraulic conductivity of aqueous bentonite suspensions." Soil Research 26, no. 4 (1988): 561. http://dx.doi.org/10.1071/sr9880561.
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In many circumstances, filtration of two-phase, solid-liquid systems can be described by theory based on Darcy's Law and an appropriate continuity equation. The theory requires that relations between the water content and (a) the water potential, and (b) the permeability are well defined. This paper describes experiments which permit calculation of both these relations in a water-bentonite suspension. The permeability function calculated directly from steady state experiments compares with that calculated indirectly from transient experiments, thus confirming the basic assumptions of the theory. It is shown that both the water content-water potential, and the water content-permeability relations are sensitive to solution salt concentration. However, the water potential-permeability relation is nearly independent of salt concentration, thus allowing considerable simplification in the information sufficient and necessary to characterize this system.
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CAI, JIANCHAO, LIJUN YOU, XIANGYUN HU, JING WANG, and RONGHUA PENG. "PREDICTION OF EFFECTIVE PERMEABILITY IN POROUS MEDIA BASED ON SPONTANEOUS IMBIBITION EFFECT." International Journal of Modern Physics C 23, no. 07 (2012): 1250054. http://dx.doi.org/10.1142/s0129183112500544.
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Permeability is an important parameter for characterizing the transport properties (e.g. heat and mass transfer) of porous media. It is one of the crucial issues that the permeability of porous media is exactly and quickly decided in many fields such as reservoir engineering, groundwater engineering and composite material modeling. Spontaneous imbibition is a fundamental and ubiquitous natural phenomenon extensively existing in a variety of processes. In this paper, the relationships between the height and weight of imbibition versus the time are derived based on Darcy's law, and a simple method for predicting effective permeability of porous media using spontaneous imbibition effect is proposed, including expressions for permeabilities of artificial and natural porous media. The validity of the proposed models is analysed and tested by experimental data.
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HAYASHI, HIDEMITSU, SATORU YAMAMOTO, and SHI-AKI HYODO. "LATTICE-BOLTZMANN SIMULATIONS OF FLOW THROUGH NAFION POLYMER MEMBRANES." International Journal of Modern Physics B 17, no. 01n02 (2003): 135–38. http://dx.doi.org/10.1142/s0217979203017217.
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Simulations of flow through three-dimensional porous structures of NAFION polymer membranes are performed with a Lattice-Boltzmann method (LBM) for incompressible fluid. Geometry data of NAFION are constructed from a result of a dissipative particle dynamics simulation for three values of the water content, 10%, 20%, and 30%, and are used as the geometry input for the LBM. Permeability of the porous structure is extracted from results of the LBM simulation using Darcy's low. The permeability K is shown to be expressed as K = L2 × Ktpl with a characteristic length L and the dimensionless permeability Ktpl depending only on the topological structure of the porous media. Dependence of Ktpl is examined on the pressure gradient, the fluid viscosity, and the resolution of the computational grid.
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Zhao, Jinhu. "Natural convection flow and heat transfer of generalized Maxwell fluid with distributed order time fractional derivatives embedded in the porous medium." Networks and Heterogeneous Media 19, no. 2 (2024): 753–70. http://dx.doi.org/10.3934/nhm.2024034.
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<p>Numerical simulation was performed for unsteady natural convection flow and heat transfer in a porous medium using the generalized Maxwell model and fractional Darcy's law with distributed order time fractional derivatives. The finite volume method combined with the fractional <italic>L1</italic> scheme was used to solve strongly coupled governing equations with nonlinear fractional convection terms. Numerical solutions were validated via grid independence tests and comparisons with special exact solutions. The effects of porosity, Darcy number, and relaxation time parameters on transport fields are presented. The results illustrate that porosity and permeability have opposite influences on temperature and velocity profiles. Moreover, the relaxation time parameters have remarkable effects on velocity profiles, and the variations possess significant differences.</p>
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Singh, H., F. Javadpour, A. Ettehadtavakkol, and H. Darabi. "Nonempirical Apparent Permeability of Shale." SPE Reservoir Evaluation & Engineering 17, no. 03 (2014): 414–24. http://dx.doi.org/10.2118/170243-pa.
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Summary Physics of fluid flow in shale reservoirs cannot be predicted from standard flow or mass-transfer models because of the presence of nanopores, ranging in size from one to hundreds of nanometers, in shales. Conventional continuum-flow equations, such as Darcy's law, greatly underestimate the fluid-flow rate when applied to nanopore-bearing shale reservoirs. As a result of the existence of nanopores in shales, the molecular mean free path becomes comparable with the characteristic geometric scale, and we hypothesize that under this condition, Knudsen diffusion, in addition to correction for the slip boundary condition, becomes the dominant mechanism. Recently, a few models have been developed that use various empirical parameters to account for these modifications (Javadpour 2009; Civan 2010; Darabi et al. 2012). This paper aims to provide a different approach to modeling apparent permeability in shale reservoirs. The proposed model is analytical, free of any empirical coefficients, and has been derived without invoking the assumption of slip flow at the pore wall. Our model of apparent permeability represented by a single analytical equation, depends only on pore size, pore geometry, temperature, gas properties, and average reservoir pressure. The proposed model is valid for Knudsen numbers less than unity and it stands up under the complete operating conditions of a shale reservoir. Our model reasonably predicts results as reported by other models. Finally, the model shows that pore-surface roughness and mineralogy have a negligible influence on gas-flow rate, whereas pore geometry and pore size play a significant role in the proportion of diffusion in total flow rate. Our study shows that a combination of Darcy flow and Knudsen flow—ignoring the Klinkenberg effect—can describe gas flow for a range of Knudsen flow applicable to a shale-gas system.
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Landa-Marbán, David, Gunhild Bødtker, Bartek Florczyk Vik, et al. "Mathematical Modeling, Laboratory Experiments, and Sensitivity Analysis of Bioplug Technology at Darcy Scale." SPE Journal 25, no. 06 (2020): 3120–37. http://dx.doi.org/10.2118/201247-pa.
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Summary In this paper, we study a Darcy-scale mathematical model for biofilm formation in porous media. The pores in the core are divided into three phases: water, oil, and biofilm. The water and oil flow are modeled by a generalized version of Darcy's law, and the substrate is transported by mechanical dispersion, diffusion, and convection in the water phase. Initially, there is biofilm on the pore walls. The biofilm consumes substrate for production of biomass and modifies the pore space, which changes the rock permeability. The model includes detachment of biomass caused by water flux and death of bacteria, and it is implemented in the MATLAB Reservoir Simulation Toolbox (MRST). We discuss the capability of the numerical simulator to capture results from laboratory experiments. We perform a novel sensitivity analysis based on sparse-grid interpolation and multiwavelet expansion to identify the critical model parameters. Numerical experiments using diverse injection strategies are performed to study the impact of different porosity/permeability relationships in a core saturated with water and oil.
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Boloorian, Maryam, Mohammad Reza Rasaei, and Ali Nakhaee. "Modeling of Fluid Filtration around a Perforation and Wellbore and Investigating its Effect on Skin Factor." Journal of Petroleum & Environmental Biotechnology 14, no. 2 (2023): 4. https://doi.org/10.35248/2157-7463.23.14.526.
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In this paper, a mathematical model is presented for a water based mud filtration into a perforation and wellbore and its effect on reducing the relative permeability and damage of the formation. The proposed model includes fluid invasion, filter cake buildup, and relative permeability, formation damage model and skin factor. The penetration of solid particles into the formation was avoided. Filter cake and mud filtration models were developed based on a mass balance equation of cake deposition and erosion and Darcy's equation. The invasion flow of mud filtrate into the formation was considered radial. A convection dispersion equation was solved numerically to characterize filtrate invasion.
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van der Sluys, L., and W. Dierickx. "The applicability of Darcy's law in determining the water permeability of geotextiles." Geotextiles and Geomembranes 5, no. 4 (1987): 283–99. http://dx.doi.org/10.1016/0266-1144(87)90039-2.
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Civan, F. "Can Gas Permeability of Fractured Shale Be Determined Accurately by Testing Core Plugs, Drill Cuttings, and Crushed Samples?" SPE Journal 24, no. 02 (2019): 720–32. http://dx.doi.org/10.2118/194502-pa.
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Summary Determining the nanodarcy gas permeability and other parameters of naturally and hydraulically induced fractured shale formations by testing the pressure transmission of core plugs, drill cuttings, and crushed samples is discussed. The author reviewed and modified the available methods for interpreting pressure tests with an emphasis on the differences between intrinsic and apparent permeability, and the generally overlooked temperature effects. It is significant to note that the temperature of gas varies during transport through porous rock samples and various dead-volumes when testing equipment used for permeability measurement is involved; this is because of unavoidable viscous dissipation and Joule-Thomson effects. Improved formulations and analysis methods that honor the relevant physics of gas transport and interactions with shale are presented, for both the generally assumed isothermal conditions and the realistic case of nonisothermal conditions. These improved formulations provide valuable insights when comparing and evaluating the currently available equations used for permeability calculations with the experimental data obtained by various testing methods. Better design and analysis of experiments for simultaneously determining several unknown parameters that impact the transport calculations, including deformation, adsorption, diffusion, viscous dissipation, Joule-Thomson effect, and deviation from Darcy flow, are described. It is recommended that the permeability and other parameters of shale samples be determined by simultaneous analysis of multiple pressure tests conducted under different conditions to accommodate temporally and spatially variable conditions by consideration of the temperature effect. The inherent limitations of the methods that rely on analytical solutions of the diffusivity equation on the basis of Darcy's law are also explained.
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Montgomery, Susan M., Bernard Miller, and Ludwig Rebenfeld. "Spatial Distribution of Local Permeabilities in Fibrous Networks." Textile Research Journal 62, no. 3 (1992): 151–61. http://dx.doi.org/10.1177/004051759206200306.
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The shape of a developing radial fluid boundary in the plane of a fabric is a reflection of the structure of the fabric. Homogeneous fabrics, with permeabilities independent of position, yield circular or elliptical flow fronts, depending on the existence of a universally preferred flow direction. Heterogeneous networks yield flow fronts that deviate from this elliptical shape due to spatial variations in permeability. The time-dependent development of the fluid front that occurs when liquid flows radially in the plane of a fabric may be analyzed using Darcy's law to calculate local fabric permeabilities. The resulting spatial distribution of permeabilities is representative of the spatial heterogeneity of the fabric structure. Sample permeability distributions of geotextile fabrics are discussed.
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Khan, Muhammad Azhar Ali. "In-Plane Permeability Measurement of Biaxial Woven Fabrics by 2D-Radial Flow Method." Science and Engineering of Composite Materials 28, no. 1 (2021): 153–59. http://dx.doi.org/10.1515/secm-2021-0014.
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AbstractThe accurate characterization of fabrics used in vacuum assisted resin transfer molding (VARTM) is essential in order to model the flow through these porous preforms. A wide range of these fabrics are available for composite manufacturing through VARTM and thus brings about a need to opt a methodology which characterizes the in-plane permeability of these preforms. These permeability values can then be used in simulations that can track the flow front progression and mold filling time. This work identifies the permeability of an E-glass fabric based on Darcy's law. Woven fabric having areal weight of 200 grams per square meter (gsm) is under consideration. The experiments are conducted at constant pressure conditions using 2D Radial flow method. Stereo microscopy of the preform material is done for detailed study of the weaving pattern. It is concluded that plain woven fabric exhibits anisotropic behavior when tested for in-plane permeability. Permeability is found to be higher in a direction which offers more interspacing between adjacent fibers threads causing more resin to flow in this direction.
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Kong, F.-M., J. D. LeMay, S. S. Hulsey, C. T. Alviso, and R. W. Pekala. "Gas permeability of carbon aerogels." Journal of Materials Research 8, no. 12 (1993): 3100–3105. http://dx.doi.org/10.1557/jmr.1993.3100.
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Carbon aerogels are synthesized via the aqueous polycondensation of resorcinol with formaldehyde, followed by supercritical drying and subsequent pyrolysis at 1050 °C. As a result of their interconnected porosity, ultrafine cell/pore size, and high surface area, carbon aerogels have many potential applications such as supercapacitors, battery electrodes, catalyst supports, and gas filters. The performance of carbon aerogels in the latter two applications depends on the permeability or gas flow conductance in these materials. By measuring the pressure differential across a thin specimen and the nitrogen gas flow rate in the viscous regime, the permeability of carbon aerogels was calculated from equations based upon Darcy's law. Our measurements show that carbon aerogels have permeabilities on the order of 10−12 to 10−10 cm2 over the density range from 0.05–0.44 g/cm3. Like many other aerogel properties, the permeability of carbon aerogels follows a power law relationship with density, reflecting differences in the average mesopore size. Comparing the results from this study with the permeability of silica aerogels reported by other workers, we found that the permeability of aerogels is governed by a simple universal flow equation. This paper discusses the relationship among permeability, pore size, and density in carbon aerogels.
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Kačur, Jozef, and Hana Budáčová. "Determination of Pressure-Saturation-Permeability Relations by Centrifugation." Defect and Diffusion Forum 326-328 (April 2012): 261–66. http://dx.doi.org/10.4028/www.scientific.net/ddf.326-328.261.
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In this work we discuss the problem of coupled saturated and unsaturated flow in porous media under centrifugation. Our mathematical model is described by Darcy's equation in saturated region and Richard's nonlinear and degenerate equation in unsaturated region. We use Van Genuchten model with soil parameters and express the Richard's equation in both head and saturation. Our numerical method is based on space discretization. We reduce the problem to an ODE system with an algebraic condition to keep the water mass balance (DAE system). In our mathematical model we consider two interfaces separating fully saturated, partially saturated and dry subregions. Our goal is the determination of soil parameters. We control the input/output of infiltrated water in the sample. The only measurements concerning the sample require the measuring of the time moments in which the moving water achieves prescribed values of momentum. These data are sufficient to determine the soil parameters.
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Song, Y. S., K. Chung, T. J. Kang, and J. R. Youn. "Numerical Prediction of Permeability Tensor for Three Dimensional Circular Braided Preform by considering Intra-tow Flow." Polymers and Polymer Composites 13, no. 4 (2005): 323–34. http://dx.doi.org/10.1177/096739110501300401.
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Resin transfer moulding is characterized by the permeability tensor, which is a measure of the resistance to resin flow through the preform. Complete prediction of the second order permeability tensor for three dimensional circular braided preforms is critical to an understanding of the resin transfer moulding process. The permeability can be predicted by considering resin flow through the multi-axial fibre structure. In this study, the permeability tensor for a 3-D circular braided preform was calculated by solving a boundary problem of a periodic unit cell. The flow field through the unit cell was obtained by using a 3-D control volume finite element method (CVFEM) and Darcy's law was utilized to obtain the permeability tensor. The flow analyses were carried out for two cases, one in which the fibre tow was regarded as a permeable porous medium, and one in which it was regarded as an impermeable solid. It was found that the flow within the intra-tow region of the braided preform was negligible if the inter-tow porosity was relatively high, but flow through the tow, especially flow in the thickness direction must be considered when the porosity is low. The permeability of the braided preform was measured by a radial flow experiment and compared with the predicted permeability.
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Dixon, D. A., M. N. Gray, and D. Hnatiw. "Critical gradients and pressures in dense swelling clays." Canadian Geotechnical Journal 29, no. 6 (1992): 1113–19. http://dx.doi.org/10.1139/t92-129.
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Uncertainties exist with regard to the applicability of Darcy's law to dense swelling clays. These clays may not allow water to pass through them when the hydraulic gradient is below a critical value. Preliminary results are presented from a series of constant-head permeability tests on dry, confined, densely compacted bentonite clays. The tests are intended to clarify the applicability of Darcy's law to dense bentonites: these materials may be used for isolation of nuclear fuel wastes in deep geologic disposal vaults. On wetting and with increasing hydraulic gradient, the clays develop swelling pressures, and some specimens appear to exhibit a critical hydraulic gradient or pressure. Below these gradients and pressures, water does not appear to flow through the materials. Once the apparent critical gradient is exceeded, water flux through the materials increases linearly and directly with gradient. Water continues to flow if the gradient is subsequently decreased to values below the original critical value. The possible importance of this finding to effective stress testing of dense bentonite materials is briefly discussed. The hydraulic performance of dense bentonite clay barriers over the range of conditions anticipated in a nuclear-fuel-waste disposal vault remains uncertain. Studies of material behaviour within the anticipated constraints of emplacement state and hydraulic boundary conditions are required. Key words : clay, bentonite, Darcy's law, effective stress, compacted clay, swelling pressure.
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Liu, Wei, Chao He, Yueping Qin, and Peng Liu. "Inversion of gas permeability coefficient of coal particle based on Darcy's permeation model." Journal of Natural Gas Science and Engineering 50 (February 2018): 240–49. http://dx.doi.org/10.1016/j.jngse.2017.12.017.
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Pereira, G. S., C. P. Oliveira, and J. A. Souza. "INVESTIGATE OF INFLUENCE PERFORATED PLATE ON DETERMINATION OF TRANSVERSAL PERMEABILITY ON REINFORCED FIBER." Revista de Engenharia Térmica 22, no. 4 (2024): 22. http://dx.doi.org/10.5380/reterm.v22i4.95214.
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Polymeric composite materials can be build in different forms, resulting in different mechanical properties, with numerous industrial applications. Traditionally, they have been largely used in the automotive, naval and aerospace industries. A major concern in polymeric composites manufacture is related with the determination and control of the reinforcement and resin physical properties. They are responsible for the final composite mechanic properties and, if not correct defined, will result in defective composites. Reinforcement permeability is one of these physical properties that, in some cases, are difficult to be kept within the project specification. More specifically, for the case of the transverse permeability, its corrected determination is reported in literature as being considerably more difficult to experiment than the in-plane permeability. The most common experiment for transverse permeability determination is built with a cylindrical mold on which the reinforcement is positioned (and compressed) between two perforated plates. A fluid is forced transversely through the reinforcement, volumetric flow rate and pressure drop are measured, and the Darcy's Law is used to determine the permeability. In this experiment, flow is assumed rectilinear, and the holes of the perforated plates are ignored in the Darcy equation. It is known that size, number e position of these holes may influence the permeability determination, however this problem is not commonly discussed in literature. In this work it is presented a numerical study about the influence of the geometry of the perforated plates on the corrected determination of the reinforcement transverse permeability. The reinforcement region is molded as a porous medium and the two fluid flow (air + resin) is formulated with the Volume of Fluid (VoF) method. GMSH software was used to created and discretize the geometry and OpenFOAM software, more specifically using the interFoam solver, was used to solve the flow problem, determining pressure drop and flow rate inside the mold. Results have shown that correct determination of the transverse permeability is highly dependent on perforate plates geometry.
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Jusoh, Norhana, Muhammad Aqil Mustafa Kamal Arifin, Muhammad Hamizan Hilmi Sulaiman, et al. "Permeability of Bone Scaffold with Different Pore Geometries Based on CFD Simulation." Journal of Medical Device Technology 1, no. 1 (2022): 45–49. http://dx.doi.org/10.11113/jmeditec.v1n1.16.
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Scaffold plays a significant role in promoting cells proliferation and differentiation in bone regeneration. Permeability is one of the factors that affect the function as it is able to extract waste and supply nutrients or oxygen. The aim of this study was to design different pore shapes and to simulate its fluid model in order to predict permeability value of the scaffold. There were few steps in this project which were scaffold design, fluid simulation analysis and permeability calculation. Three different pore shapes were designed, which were circle, triangle, and hexagon by using the Solidworks software. Each scaffold was designed by the combination of three unit cells. Then, Computational Fluid Dynamics (CFD) simulation in the Ansys Fluent software was conducted to obtain the pressure drop from the pressure distribution within the pores. The permeability of scaffold was obtained by applying Darcy's permeability formula at inlet velocity of 0.001 m/s, 0.01 m/s and 0.1 m/s. Based on the calculation, the permeability for hexagon pore shape were 3.96691x10-07 m2, 3.52 x10- 07 and 1.92 x10-07 for 0.001 m/s, 0.01 m/s and 0.1 m/s inlet velocity, respectively. Therefore, by increasing the inlet velocities, permeability decreased for all types of scaffolds. Furthermore. hexagon pore shape showed the highest permeability value when compared with triangle and circle’s pore shape. Nevertheless, all pore shapes demonstrated permeability values that within the range of natural bone permeability.
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Ganapathy, R. "Thermal Convection in an Infinite Porous Medium Induced by a Heated Sphere." Journal of Heat Transfer 119, no. 3 (1997): 647–50. http://dx.doi.org/10.1115/1.2824158.
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This paper investigates the transient behavior of the free convection motion and heat transfer induced by a heated sphere with prescribed wall temperature embedded instantaneously in an infinite porous medium. Solutions for the velocity and temperature fields have been obtained in the form of series expansions in Rayleigh number which is based on the medium permeability and the temperature of the sphere. All discussions are based on the assumption that the flow is governed by Darcy's law and the thermal Rayleigh number is small.
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Rubinstein, Jacob, and S. Torquato. "Flow in random porous media: mathematical formulation, variational principles, and rigorous bounds." Journal of Fluid Mechanics 206 (September 1989): 25–46. http://dx.doi.org/10.1017/s0022112089002211.
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The problem of the slow viscous flow of a fluid through a random porous medium is considered. The macroscopic Darcy's law, which defines the fluid permeability k, is first derived in an ensemble-average formulation using the method of homogenization. The fluid permeability is given explicitly in terms of a random boundary-value problem. General variational principles, different to ones suggested earlier, are then formulated in order to obtain rigorous upper and lower bounds on k. These variational principles are applied by evaluating them for four different types of admissible fields. Each bound is generally given in terms of various kinds of correlation functions which statistically characterize the microstructure of the medium. The upper and lower bounds are computed for flow interior and exterior to distributions of spheres.
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Seong, D. G., K. Chung, T. J. Kang, and J. R. Youn. "A Study on Resin Flow through a Multi-layered Preform in Resin Transfer Molding." Polymers and Polymer Composites 10, no. 7 (2002): 493–510. http://dx.doi.org/10.1177/096739110201000702.
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In resin transfer molding, mold filling is governed by the flow of resin through a preform which is considered as an anisotropic porous media. The resin flow is usually described by Darcy's law and the permeability tensor must be obtained for filling analysis. When the preform is composed of more than two layers with different in-plane permeability, effective average permeability should be determined for the flow analysis in the mold. The most frequently used averaging scheme is the weighted averaging scheme, but it does not account for the transverse flow between adjacent layers. A new averaging scheme is suggested to predict the effective average permeability of the multi-layered preform, which accounts for the transverse flow effect. When the flow in the mold is unsaturated, the effective average permeability is predicted by using the predicted mold filling time and transverse permeability. The new scheme is verified by measuring the effective permeability of the multi-layered preforms which consist of glass fiber random mats, carbon fiber woven fabrics, aramid fiber woven fabrics. Fluid flow through the preform composed of more than two layers with different in-plane permeability shows different flow fronts between layers. The difference in the flow front advancement is observed with a digital camcorder. The predicted flow front is compared with the experimental results and shows a good agreement. It is expected that the effective average permeability can be used for modeling the resin flow through the multi-layered preform.
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Tanikawa, W., and T. Shimamoto. "Klinkenberg effect for gas permeability and its comparison to water permeability for porous sedimentary rocks." Hydrology and Earth System Sciences Discussions 3, no. 4 (2006): 1315–38. http://dx.doi.org/10.5194/hessd-3-1315-2006.
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Abstract. The difference between gas and water permeabilities is significant not only for solving gas-water two-phase flow problems, but also for quick measurements of permeability using gas as pore fluid. We have measured intrinsic permeability of sedimentary rocks from the Western Foothills of Taiwan, using nitrogen gas and distilled water as pore fluids, during several effective-pressure cycling tests at room temperature. The observed difference in gas and water permeabilities has been analyzed in view of the Klinkenberg effect. This effect is due to slip flow of gas at pore walls which enhances gas flow when pore sizes are very small. Experimental results show (1) that gas permeability is larger than water permeability by several times to one order of magnitude, (2) that gas permeability increases with increasing pore pressure, and (3) that water permeability slightly increases with increasing pore-pressure gradient across the specimen. The results (1) and (2) can be explained by Klinkenberg effect quantitatively with an empirical power law for Klinkenberg constant. Thus water permeability can be estimated from gas permeability. The Klinkenberg effect is important when permeability is lower than 10−18 m2 and at low differential pore pressures, and its correction is essential for estimating water permeability from the measurement of gas permeability. A simple Bingham-flow model of pore water can explain the overall trend of the result (3) above. More sophisticated models with a pore-size distribution and with realistic rheology of water film is needed to account for the observed deviation from Darcy's law.
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Newman, M. S. S., and X. Yin. "Lattice Boltzmann Simulation of Non-Darcy Flow In Stochastically Generated 2D Porous Media Geometries." SPE Journal 18, no. 01 (2013): 12–26. http://dx.doi.org/10.2118/146689-pa.
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Summary It is important to consider the additional pressure drops associated with non-Darcy flows in the near-wellbore region of conventional gas reservoirs and in propped hydraulic fractures. These pressure drops are usually described by the Forchheimer equation, in which the deviation from the Darcy's law is proportional to the inertial resistance factor (β-factor). While the β-factor is regarded as a property of porous media, detailed study on the effect of pore geometry has not been performed. This study characterized the effect of geometry on the flow transition and the β-factor using lattice Boltzmann simulations and stochastically constructed 2D porous media models. The effect of geometry was identified from a large set of data within a porosity range of 8–35%. It was observed that the contrast between pore throat and pore body triggers an early transition to non-Darcy flows. Following a quick transition where the correction to the Darcy's law was cubic in velocity, the flows entered the Forchheimer regime. The β-factor increased with decreasing porosity or an increasing level of heterogeneity. Inspection of flow patterns revealed both steady vortices and onset of unsteady motions in the Forchheimer regime. The latter correlated well with published points-of-transition. In developing a dimensionally consistent correlation for the β-factor, we show that it is necessary to include two distinctive characteristic lengths to account for the effect of pore-scale heterogeneity. This finding reflects the fact that it is the contrast between pore bodies and throats that dictates the flow properties of many porous media. In this study, we used the square root of the permeability and the fluid-solid contact length as the two characteristic lengths.
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Septiani, Virma, Direstu Amalia, Viktor Suryan, Siti Salbiah Ristumanda, and Suci Ryski Nur Afriyani. "Design Constant Head Permeability Meter Digital: A Project-Based Learning Media." JMKSP (Jurnal Manajemen, Kepemimpinan, dan Supervisi Pendidikan) 9, no. 2 (2024): 856–68. http://dx.doi.org/10.31851/jmksp.v9i2.15191.
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The permeability coefficient value is one of the most important parameters in soil mechanics. Quick, simple, and digital direct soil permeability tests in the field are needed to obtain data representing conditions. This research aims to create a portable soil permeability test tool based on microcontroller automation used as a project-based learning for Transportation Cadets peculiarly Palembang Aviation Polytechnic Cadets for new experiences of new learning circumstances. This research method based on the principle of permeability testing using the constant-head method by analyzing the requirements quantitatively. This principle uses water change level parameters, which are used to test the infiltration rate in sample soil. Furthermore, measurements of changes in water level are used by water leveling sensors and processed using Arduino Uno based on fuzzy logic with access to results via the web, tool design, and simulation using SIMULINK software. The results of designing a digital measuring instrument for permeability using the constant head method have been validated for its schematic circuit using SIMULINK and can work without error. In conclusion, a model based on Darcy's Law equation and constant head to find the permeability coefficient can be generated, which can then be a prototype of the tool. It concluded the design of constant head permeability meter digital is useful as project-based leaning media for the Palembang aviation polytechnic. Furthermore, the equipment design will be the first digital measuring tool for permeability coefficient using the constant head method. The design has advantage to measure the soil permeability coefficient at the airport in the fastest way.
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Deng, Jia, Jiujiang Li, Lan Zhang, Fuquan Song, Dong Wang, and Hongjian Wang. "CH4 transport in micro–nano porous media associated with supercritical CO2 flooding." Physics of Fluids 34, no. 7 (2022): 076112. http://dx.doi.org/10.1063/5.0100762.
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Injecting supercritical CO2 into tight gas reservoirs to displace CH4 is an extremely promising technology of unconventional gas exploitation. However, Darcy's law cannot describe the gas flow due to ultra-low permeability and micro–nano porosity of tight rock. The present work is an analytical approach to investigating the nonlinear seepage characteristics of CH4 displacement by supercritical CO2. Moreover, considering the steady and unsteady state conditions, mathematical models for planar linear flooding, planar radial flooding, and single well and one-well injection/one-well production types are presented, computed, and verified. Their equipotential and streamline charts are first determined by implementing the model. Additionally, by investigating variables such as formation pressure, producing pressure drop, permeability, temperature, well spacing, and mass flow, their contributions to gas production rate are determined. Finally, an approach for improving the gas recovery efficiency is obtained based on the obtained results.
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Secerov-Sokolovic, Radmila, Olja Stanimirovic, and Slobodan Sokolovic. "The influence of fibrous bed bulk density on the bed properties." Chemical Industry 57, no. 7-8 (2003): 335–40. http://dx.doi.org/10.2298/hemind0308335s.
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The mean properties of seven different fibrous materials and the properties of their different bed bulk densities were investigated. The morphology of the surface, size and geometry were measured by optical microscopy. The bed porosity was measured by the weighing method. The experimental bed permeability, in a high range of bulk density, was calculated from the values of the sanitary water pressure drop at a constant temperature of 15?C, since the data followed Darcy's law. The Reynolds number for a fibrous bed was calculated using a relation from the literature. The Reynolds number was less than 1 for all ranges of fluid velocity. Three empirical relations for fibrous bed permeability were used and compared with the experimental data. It was determined that the empirical data depended on the fiber diameter and fraction of solid in the bed. The relative error linearly increased with increasing fiber diameter.
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Pour Mahmoud, N., and A. Zabihi. "Numerical Simulation of a Single-Phase Flow Through Fractures with Permeable, Porous and Non-Ductile Walls." Engineering, Technology & Applied Science Research 7, no. 5 (2017): 2041–46. http://dx.doi.org/10.48084/etasr.1448.
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This paper attempts to study flows within fractures through a set of numerical simulations. In addition, a special care is given to hydraulic features and characteristics of fractures. The research is performed through the application of calculative fluid dynamics and a finite volume discrete schema. The investigated flows are laminar, single-phase and stable flows of water and air through fractures with penetrable walls. The selected fracture geometry is inspired from the tomographic scan of a stone fracture. Water and air are modeled in fractures with permeable walls and different permeability levels. It has been observed that in case of permeable matrixes, the friction coefficient is lower compared to impermeable matrixes. In fact permeability reduced friction. In addition, highest pressure drops were observed in areas with smaller fracture diaphragms. Nonetheless, the surrounding area of the fracture is analyzed with the consideration of Darcy's rule.
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Pour, Mahmoud N., and A. Zabihi. "Numerical Simulation of a Single-Phase Flow Through Fractures with Permeable, Porous and Non-Ductile Walls." Engineering, Technology & Applied Science Research 7, no. 5 (2017): 2041–46. https://doi.org/10.5281/zenodo.1037234.
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This paper attempts to study flows within fractures through a set of numerical simulations. In addition, a special care is given to hydraulic features and characteristics of fractures. The research is performed through the application of calculative fluid dynamics and a finite volume discrete schema. The investigated flows are laminar, single-phase and stable flows of water and air through fractures with penetrable walls. The selected fracture geometry is inspired from the tomographic scan of a stone fracture. Water and air are modeled in fractures with permeable walls and different permeability levels. It has been observed that in case of permeable matrixes, the friction coefficient is lower compared to impermeable matrixes. In fact permeability reduced friction. In addition, highest pressure drops were observed in areas with smaller fracture diaphragms. Nonetheless, the surrounding area of the fracture is analyzed with the consideration of Darcy's rule.
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Noh, Myeong H., and Abbas Firoozabadi. "Effect of Wettability on High-Velocity Coefficient in Two-Phase Gas/Liquid Flow." SPE Journal 13, no. 03 (2008): 298–304. http://dx.doi.org/10.2118/102773-pa.
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Summary Gas-well productivity is affected by two distinct mechanisms: liquid blocking and high-velocity flow in two-phase flow. The former has been studied extensively recently, but the understanding of the latter is limited. High-velocity gas flow in single phase has been studied thoroughly by a large number of authors. Despite the fact that high-velocity coefficient in the presence of an immobile and a mobile liquid phase is much higher than that in single phase, only a handful of studies have been made on the subject. In this work, we have measured the high-velocity coefficient, ß in steady-state two-phase gas/liquid flow. The results are presented as a function of liquid relative permeability and liquid saturation. In our measurements, the wetting state is varied by the treatment with a fluorochemical compound. Then, the effect of wettability on the high-velocity coefficient in two-phase flow is investigated. Results show that when the liquid is strongly wetting, the high-velocity coefficient increases approximately 270-fold in water/gas two-phase flow. However, our data show a systematic reduction of high-velocity coefficients for the altered wetting state in two-phase flow. We present measurements of the velocity coefficients in single-phase flow and two-phase flow, for both oil/gas and water/gas flow and strong liquid-wetting and altered-wetting states. On the basis of our measurements, we conclude that the treatment of the wellbore region can result in significant improvement in well deliverability from the large reduction of high-velocity coefficients. Introduction Gas deliverability in gas-condensate reservoirs can be significantly affected by liquid blocking, either from condensate accumulation or water blocking, and high-velocity flows in the near-wellbore. Hydrocarbon blocking in gas-condensate reservoirs results in a significant loss of well productivity; water blocking from hydraulic-fracturing operation often limits the advantage of fractures. In addition to liquid blocking, the increased pressure drop, caused by inertial effects at high gas velocity in both low-permeability and hydraulically fractured reservoirs, can also result in low productivity. The focus of this work is on the high-velocity gas flow in two-phase gas/liquid flow in gas reservoirs. Darcy's law is inadequate to describe high-velocity gas flow in porous media. Through the high-velocity coefficient, ß, Darcy's law is modified, and the additional pressure drop from high-velocity flow can be expressed as the Forchheimer equation (1901). The general understanding is that the high-velocity coefficient in two-phase flow is higher than in single-phase gas flow in a dry rock. However, very few attempts have been made for conclusive experiments in determining the high-velocity coefficient in two-phase gas/liquid flow because of experimental difficulties in maintaining a constant liquid saturation for different pressure drops. Gas flow at low velocity is governed by Darcy's law, which describes a linear relationship between pressure gradient and volumetric flux. At high gas velocity, the pressure gradient required to maintain a certain flow rate through porous media is higher than that predicted by Darcy's law. The effect of inertia has to be added. The result is the Forchheimer equation expressed by[Equation 1] where µg is gas viscosity, kg is the effective gas permeability, ug is the gas volumetric flux, ß is a high-velocity coefficient, and ??g is gas density. Eq. 1 is valid both for single-phase gas flow and for two-phase gas/liquid flow provided, that the capillary effect is negligible. In 1D, one may integrate Eq. 1 to obtain [Equation 2] Here, p1 and p2 are the inlet and outlet pressure; M and jg are molecular weight and mass flux of gas, respectively; R and Z are the gas constant and the gas deviation factor, respectively; T is temperature; and L is the length. Effective gas permeability and high-velocity coefficient are determined by plotting M?p2 / 2µgZRTLjg vs. jg / µg, provided that the saturation is constant. Fig. 1 shows a schematic of determining the effective gas permeability and the high-velocity coefficient. Note that the effective permeability in Eq. 2 becomes the absolute permeability when the rock is dry (Sg = 100%, krg = 1.0). There has been much work in the literature on high gas velocity in single-phase flow in dry rocks. There has also been a fair amount of work in single-phase gas flow with immobile liquid saturation. Very little work, however, has been done in two-phase gas/liquid flow at high gas velocity. In the following, we will briefly review the literature in experimental studies and set the stage for our work in two-phase gas/liquid flow at high gas velocity.
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Chen, Zeliang, Xinglin Wang, Guoqing Jian, et al. "Fast Permeability Estimation of an Unconventional Formation Core by Transient-Pressure History Matching." SPE Journal 25, no. 06 (2020): 2881–97. http://dx.doi.org/10.2118/201107-pa.
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Summary Unconventional resources are of great importance in the global energy supply. However, the ultralow permeability, which is an indicator of the producibility, makes the unconventional production challenging. Therefore, the permeability is one of the critical petrophysical properties for formation evaluation. There are many existing approaches to determine permeability in the laboratory using core analysis. The methods can be divided into two categories: steady-state and unsteady-state approaches. The steady-state approach is a direct measurement using Darcy's law. This approach has disadvantages because of the accuracy in the measurement of low flow rate and the long run time. The unsteady-state approach includes pulse decay, oscillating pressure, and Gas Research Institute methods. These approaches are complicated in terms of setups and interpretations. Both steady-state and unsteady-state approaches typically have a constraint on the maximum differential pressure. We propose a novel unsteady-state method to determine the permeability by transient-pressure history matching. This approach involves simulation and experiments. On the experiment side, the ultralow-permeability core undergoes 1D CO2-flooding experiments, during which the transient pressure is monitored for history matching. On the simulation side, the transient-pressure history is simulated using the finite-volume method incorporating real-gas pseudopressure and table lookup to deal with the nonlinearity in fluid properties and singularity during phase transition. The free parameter permeability in the simulation is adjusted for history matching to determine the rock permeability. Our new unsteady-state approach is developed for fast and convenient permeability estimation for unconventional formation cores. This approach is a valuable addition to existing permeability measurement methods.
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Fanchi, John R. "Directional Permeability." SPE Reservoir Evaluation & Engineering 11, no. 03 (2008): 565–68. http://dx.doi.org/10.2118/102343-pa.
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Summary A relationship between permeability tensor and coordinate orientation is used to estimate the error that occurs when some of the terms in the permeability tensor are neglected. The formula for calculating the errors that appear in the magnitude and direction of flow rate are presented. The results are applicable to any reservoir system that is influenced by directional permeability. Introduction Reservoir management experience has demonstrated that anisotropic permeability is needed to correctly solve fluid-flow problems in a variety of realistic settings. Permeability anisotropy in a plane is usually represented using two directions: the direction of maximum permeability, and the direction that is transverse to the direction of maximum permeability. This procedure establishes a natural coordinate system for describing directional permeability. The coordinate system is considered the diagonalized coordinate system. If flow-rate calculations are not aligned with the diagonalized coordinate system, then additional terms should be included in the form of Darcy's law, which is used in flow calculations. All of the permeability terms are considered the elements of the permeability tensor. Most commercial reservoir simulators solve fluid-flow equations that have been formulated on the basis of the assumption that the permeability tensor has been diagonalized (Fanchi 2006b; Ertekin et al. 2001). As a rule, the off-diagonal permeability terms are not included in flow calculations, and an error occurs. Engineers usually assume without justification that the error can be neglected. Research in naturally fractured reservoir modeling (Gupta et al. 2001), geomechanics (Settari et al. 2001), and upscaling (Young 1999) has demonstrated that the full permeability tensor is needed to correctly solve fluid-flow problems in a variety of realistic settings. The purpose of this paper is to show how to assess the magnitude of the error that occurs when the off-diagonal terms are not included in reservoir flow calculations. The directional dependence of permeability and the permeability tensor are introduced in the section titled "Directional Dependence of Permeability." A relationship between the diagonalized-permeability-tensor assumption and coordinate orientation is discussed in the section titled "Permeability Tensor and Coordinate Orientation." This relationship is used in the section titled "Error Analysis" to estimate the error that occurs when some of the terms in the permeability tensor are neglected. We show that the error depends on orientation of the coordinate system, the permeability aspect ratio, and the pressure gradient. The formulas for calculating the errors that appear in the magnitude and direction of the flow rate are presented. Concluding remarks are then presented.
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Rahatekar, S. S., J. A. Roux, E. Lackey, and J. G. Vaughan. "Multiple Injection Port Simulation for Resin Injection Pultrusion." Polymers and Polymer Composites 13, no. 6 (2005): 559–70. http://dx.doi.org/10.1177/096739110501300602.
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Resin injection pultrusion is a continuous process for manufacturing composite materials. Complete wet-out of the reinforcement fibres in the resin injection chamber is essential for producing good quality pultruded parts. The magnitude of the injection pressure is extremely important to achieve good wet-out of the reinforcement fibres. At high pull speeds, high viscosity, or high fibre volume fractions, the injection pressures required to achieve complete wet-out are very high and are practically very difficult to achieve. This work focuses on reducing the injection pressure needed to achieve complete wet-out by using a multiple injection port system for epoxy/glass rovings and polyester/glass rovings composites. The recommended injection pressures for complete wet-out are predicted for a variety of processing parameters. Darcy's law for flow through porous media is employed for modelling the fibre/resin system of injection pultrusion. The governing equations are solved via the finite volume method to predict the resin pressure field, the resin velocity field, and the location and shape of the resin flow front. Different permeability models1,2 are used to determine the transverse permeability and the longitudinal permeability.
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Abouorm, Lara, Maxime Blais, Nicolas Moulin, Julien Bruchon, and Sylvain Drapier. "A Robust Monolithic Approach for Resin Infusion Based Process Modelling." Key Engineering Materials 611-612 (May 2014): 306–15. http://dx.doi.org/10.4028/www.scientific.net/kem.611-612.306.
Full textAbstract:
The aim of this work is to focus on the Stokes-Darcy coupled problem in order to propose a robust monolithic approach to simulate composite manufacturing process based on liquid resin infusion. The computational domain can be divided into two non-miscible sub-domains: a purely fluid domain and a porous medium. In the purely fluid domain, the fluid flows according to the Stokes' equations, while the fluid flows into the preforms according to the Darcy's equations. Specific conditions have to be considered on the fluid/porous medium interface. Under the effect of a mechanical pressure applied on the high deformable preform/resin stacking, the resin flows and infuses through the preform which permeability is very low, down to 10-15 m2. Flows are solved using finite element method stabilized with a sub-grid scale stabilization technique (ASGS). A special attention is paid to the interface conditions, namely normal stress and velocity continuity and tangential velocity constraint similar to a Beaver-Joseph-Saffman’s condition. The originality of the model consists in using one single mesh to represents the Stokes and the Darcy sub-domains (monolithic approach). A level set context is used to represent Stokes-Darcy interface and to capture the moving flow front. This monolithic approach is now perfectly robust and leads to perform complex shapes for manufacturing process by resin infusion.
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Borge, Hans, and Øyvind Sylta. "3D Modelling of Fault Bounded Pressure Compartments in the North Viking Graben." Energy Exploration & Exploitation 16, no. 4 (1998): 301–23. http://dx.doi.org/10.1177/014459879801600402.
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The work presented in this paper involves modelling of the overpressure distribution in Jurassic reservoir and carrier rocks in the North Viking Graben. The main concept used in this study is that faults may form low-permeability barriers to fluid flow in compacting basins, and may thus influence overpressure distribution. The mapped faults in the study area are linked together so that they divide the area into 225 compartments. A model based on Darcy's law and information about offset and burial depth describes the flow conditions across the faults and between the compartments. This model describes a regional fault permeability architecture. A commercial reservoir simulator is used to calculate the fluid flow and the pressure development in all the compartments. The model was calibrated to pressures measured in 16 released exploration wells. The best match to these wells was obtained with a mean deviation of 9.5 bars and a standard deviation of 18.5 bars between the observed and predicted overpressures for the Brent Group. The results from this pressure modelling can be used to simulate secondary migration of oil and gas.
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Pereira, G. S., C. P. Oliveira, and J. A. Souza. "COMPARISON BETWEEN TWO WAYS OF MODELING THE FLOW RESISTANCE IN A POROUS MEDIUM." Revista de Engenharia Térmica 22, no. 1 (2023): 40. http://dx.doi.org/10.5380/reterm.v22i1.90974.
Full textAbstract:
Pieces manufactured from polymeric composites are known for their good mechanical properties and low specific weight. However, controlling their fabrication process requires precise knowledge of the reinforcement and resin physical properties. This is needed to ensure that defective composites are not manufactured. Investigations into these materials physical properties are generally carried out experimentally, which makes it difficult to observe what happens on microscale level. Present work aims to analyze, and compare, flow behavior in a porous medium using two approaches: a) flow resistance is modeled with Darcy's Law, and b) fluid flow is solved through the reinforcement fibers in a micro-sample level. Medium permeability determination was used in results comparison. A good quantitative agreement in predictions obtained with both methods was observed.
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Minh, Chanh Cao, and Padmanabhan Sundararaman. "Nuclear-Magnetic-Resonance Petrophysics in Thin Sand/Shale Laminations." SPE Journal 16, no. 02 (2010): 223–38. http://dx.doi.org/10.2118/102435-pa.
Full textAbstract:
Summary We discuss the use of nuclear-magnetic-resonance (NMR) logging in the petrophysical evaluation of thin sand/shale laminations. NMR helps detect thin beds, determine fluid type, establish the hydrocarbon type and volume if hydrocarbon is present, and, finally, determine the permeability of the sand layers (as opposed to that of the sand/shale system). Experiments were conducted on samples of 100% sand, 100% clay, and sand/clay layers with an NMR-logging tool at surface to verify the characteristic T2 bimodal relaxation distribution often observed in NMR logs that are acquired in thin beds. From the bimodal distribution, it is often possible to determine a cutoff to separate the productive sand layers from the shale layers and, with it, the porosity fraction of each component. Subsequently, the sand fraction, or net/gross ratio, can be estimated assuming that the 100%-sand porosity is known. Because gas, oil, and water have different NMR properties, fluid-typing techniques such as 2D NMR offer useful insights into the fluid type and properties in thin-layer sands. Because the laminations thickness is often less than the antenna aperture, the estimated permeability of the sand/ shale system will undercall the true permeability of the sand layers only. In this case, their permeability can be estimated quickly from Darcy's fluid-flow model. We show examples of thin sand/shale laminations that are oil-bearing and gas-bearing. In each case, the NMR detection was verified against borehole-imaging logs, and the fluid type in the sands was determined from multidimensional NMR analysis. The derived hydrocarbon volume was then compared with the results estimated from a triaxial induction tool. Permeability of the sand layers was also computed and compared to that of nearby thick sands. Core data in one well was used to validate NMR detection, porosity, permeability, and net sand thickness.