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Flow and Solute Transport in Saturated Porous Media: 1. The Continuum Hypothesis

卷 11, 册 4, 2008, pp. 403-413
DOI: 10.1615/JPorMedia.v11.i4.60
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摘要

The continuum hypothesis provides one alternative to dealing with transport phenomena in porous media. If adapted correctly, the continuum approach may be easier than dealing with the system at the microscopic level. However, to adopt the continuum approach to phenomena occurring in porous media, certain conditions and length scale constraints need to be satisfied. Failing to satisfy these conditions may restrict the use of this approach, and other sophisticated methods need to be devised. This article provides an overview of the conditions and length scale constraints needed to be able to adopt the continuum hypothesis. Two types of length scale constraints may be identified. The first type arises when establishing the conditions and requirements for proper upscaling; they are thus essential and hence have to be completely satisfied. They have been collected in four constraints. The second type represents those derived during mathematical manipulations and order of magnitude analysis to neglect higher-order terms. It will be shown that most of the second type of length scale constraints are automatically satisfied once the essential constraints are satisfied.

对本文的引用
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  2. Salama Amgad, El-Amin M. F., Abbas Ibrahim, Sun Shuyu, On the viscous dissipation modeling of thermal fluid flow in a porous medium, Archive of Applied Mechanics, 81, 12, 2011. Crossref

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  19. Bao Kai, Salama Amgad, Sun Shuyu, Numerical Investigation on the Effects of a Precursor Wetting Film on the Displacement of Two Immiscible Phases Along a Channel, Flow, Turbulence and Combustion, 96, 3, 2016. Crossref

  20. Ferrage Eric, Hubert Fabien, Tertre Emmanuel, Delville Alfred, Michot Laurent J., Levitz Pierre, Modeling the arrangement of particles in natural swelling-clay porous media using three-dimensional packing of elliptic disks, Physical Review E, 91, 6, 2015. Crossref

  21. Perović Nevena, Frisch Jérôme, Salama Amgad, Sun Shuyu, Rank Ernst, Mundani Ralf-Peter, Multi-scale high-performance fluid flow: Simulations through porous media, Advances in Engineering Software, 103, 2017. Crossref

  22. Salama Amgad, Amin Mohamed F. El, Kumar Kundan, Sun Shuyu, Flow and Transport in Tight and Shale Formations: A Review, Geofluids, 2017, 2017. Crossref

  23. Salama Amgad, Zoubeik Mohamed, Henni Amr, A multicontinuum approach for the problem of filtration of oily water systems across thin flat membranes: I. The framework, AIChE Journal, 63, 10, 2017. Crossref

  24. Salama Amgad, Zoubeik Mohamed, Henni Amr, A multicontinuum approach for the problem of filtration of oily-water systems across thin flat membranes: II. Validation and examples, AIChE Journal, 64, 3, 2018. Crossref

  25. Bao Kai, Salama Amgad, Sun Shuyu, Flow split characterization of two immiscible phases with different wettability scenarios: A numerical investigation using a coupled Cahn–Hilliard and Navier–Stokes system, International Journal of Multiphase Flow, 100, 2018. Crossref

  26. Zoubeik Mohamed, Ismail Mohamed, Salama Amgad, Henni Amr, New Developments in Membrane Technologies Used in the Treatment of Produced Water: A Review, Arabian Journal for Science and Engineering, 43, 5, 2018. Crossref

  27. Roubtsova Varvara, Chekired Mohamed, 3D Numerical Simulations of Particle–Water Interaction Using a Virtual Approach, in Advances in Hydroinformatics, 2016. Crossref

  28. Fan Xiaolin, Salama Amgad, Sun Shuyu, A locally and globally phase-wise mass conservative numerical algorithm for the two-phase immiscible flow problems in porous media, Computers and Geotechnics, 119, 2020. Crossref

  29. Khuzhayorov Bakhtiyor, Mustofoqulov Jabbor, Ibragimov Gafurjan, Md Ali Fadzilah, Fayziev Bekzodjon, Solute Transport in the Element of Fractured Porous Medium with an Inhomogeneous Porous Block, Symmetry, 12, 6, 2020. Crossref

  30. Negara Ardiansyah , Salama Amgad , Sun Shuyu , Density-Driven Flow Simulation in Anisotropic Porous Media: Application to CO2 Geological Sequestration, All Days, 2014. Crossref

  31. Salama Amgad, Velocity Profile Representation for Fully Developed Turbulent Flows in Pipes: A Modified Power Law, Fluids, 6, 10, 2021. Crossref

  32. Negara Ardiansyah , Salama Amgad , Sun Shuyu , 3-D Numerical Investigation of Subsurface Flow in Anisotropic Porous Media using Multipoint Flux Approximation Method, All Days, 2013. Crossref

  33. Zoubeik Mohamed, Salama Amgad, Henni Amr, Table Optimization of Operating Conditions for a Superwetting Ultrafiltration ZrO2 Ceramic Membrane, Journal of Environmental Engineering, 146, 4, 2020. Crossref

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