Transport in chemically and mechanically heterogeneous porous media IV: large-scale mass equilibrium for solute transport with adsorption |
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| Institution: | 1. L.E.P.T.—ENSAM (UA CNRS), Esplanade des Arts et Métiers, 33405 Talence Cedex, France;2. Department of Chemical Engineering and Material Science, University of California at Davis, Davis, CA 95616, USA;1. Department of Civil Engineering, University of Bechar, Bechar 08000, Algeria;2. Laboratory of Materials and Hydrology (LMH), University of Sidi Bel Abbes, Sidi Bel Abbes 2200, Algeria;3. Department of Mechanical Engineering, University of Bechar, Bechar 08000, Algeria;4. Mechanics Laboratory of Lille, CNRS UMR 8107, University of Lille 1, 59655 Villeneuve d’Ascq, France;1. Applied Mechanical Dept., Universidad Nacional del Nordeste, Las Heras 727, Resistencia, Chaco, Argentina;2. Applied and Computational Mechanical Center (CEMACOM), Federal University of Rio Grande do Sul., Av Osvaldo Aranha 99, 3° Andar, Porto Alegre (RS), Brazil;3. CONICET, Argentine Council for Science and Technology, Argentina |
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| Abstract: | In this article we consider the transport of an adsorbing solute in a two-region model of a chemically and mechanically heterogeneous porous medium when the condition of large-scale mechanical equilibrium is valid. Under these circumstances, a one-equation model can be used to predict the large-scale averaged velocity, but a two-equation model may be required to predict the regional velocities that are needed to accurately describe the solute transport process. If the condition of large-scale mass equilibrium is valid, the solute transport process can be represented in terms of a one-equation model and the analysis is simplified greatly. The constraints associated with the condition of large-scale mass equilibrium are developed, and when these constraints are satisfied the mass transport process can be described in terms of the large-scale average velocity, an average adsorption isotherm, and a single large-scale dispersion tensor. When the condition of large-scale mass equilibrium is not valid, two equations are required to describe the mass transfer process, and these two equations contain two adsorption isotherms, two dispersion tensors, and an exchange coefficient. The extension of the analysis to multi-region models is straight forward but tedious. |
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