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Flow and Solute Transport in Saturated Porous Media: 2. Violating the Continuum Hypothesis

Volume 11, Issue 5, 2008, pp. 421-441
DOI: 10.1615/JPorMedia.v11.i5.10
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ABSTRACT

Several reasons may be invoked that could result in the inappropriateness of assuming the continuum approach when dealing with transport phenomena in porous media. Probably the most serious of these may be the violation of the length scale constraints. In an attempt to explore this, experimental and numerical investigations were conducted to study the significance of violating the length scale constraints when modeling transport phenomena in porous media based on the continuum approach. Initially, a porous system was constructed that complied with all length scale constraints such that it may be safe to assume the medium as a continuum. Then, in successive experimental setups, the system was allowed to violate the length scale constraints in one of its regions, and the behavior of the system in each case was analyzed. It was found that in situations when the length scale constraints are violated, it may not generally be appropriate to model the system using the macroscopic properties. Moreover, the experiments showed that for the cases under study, when the length scale characterizing the domain was not very much larger than the size of the representative elementary volume, REV (i.e., violating the second length scale constraint), significant variations were observed between measurements and simulation, assuming the continuum approach. As the system's size continued to diminish to be in the order of the size of the REV (i.e., violating the first length scale constraint), a surprisingly better match was observed. It was concluded that the boundary effects become significant as the length scale characterizing the domain gets smaller. However, further decrease in length scale incorporates mixing processes that compensate for the effects of the boundary region.

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  2. Lange K., Van Geel P. J., Physical and numerical modelling of a dual-porosity fractured rock surrounding an in-pit uranium tailings management facility, Canadian Geotechnical Journal, 48, 3, 2011. Crossref

  3. salama Amgad, Abbas Ibrahim A., El-Amin M.F., Sun Shuyu, Comparison study between the effects of different terms contributing to viscous dissipation in saturated porous media, International Journal of Thermal Sciences, 64, 2013. Crossref

  4. Sun Shuyu, Salama Amgad, El-Amin M.F., An Equation-Type Approach for the Numerical Solution of the Partial Differential Equations Governing Transport Phenomena in Porous Media, Procedia Computer Science, 9, 2012. Crossref

  5. Bao Kai, Salama Amgad, Sun Shuyu, Upscaling of Permeability Field of Fractured Rock System: Numerical Examples, Journal of Applied Mathematics, 2012, 2012. Crossref

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  7. El-Amin M.F., Salama Amgad, Sun Shuyu, Numerical and dimensional investigation of two-phase countercurrent imbibition in porous media, Journal of Computational and Applied Mathematics, 242, 2013. Crossref

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  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

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

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

  26. 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

  27. 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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