Non-equilibrium effects in the CD equation

In many miscible flood experiments. Equation 7.15 does not fit the observed tailing in the effluent frontal breakthrough profiles. One proposed cause of 

When the adsorption isotherm in Equations 7.18 and 7.19 is non-linear, these equations have no analytical solution. However, analytical solutions have been found (Van Geneuchten and Wierenga, 1976 De Smedt and Wierenga, 1979 Van Geneuchten, 1981) for the case of a linear reversible adsorption isotherm. Such solutions are now characterised by four quantities— D, Fr,/pv and a (and additionally, if it is a slug-type experiment, the pulse or slug size)—which are contained in the analytical solution. The dimensionless mass transfer coefficient, co, and Peclet number are defined in this case 

an effluent profile may be fitted to this analytic form by a non-linear least-squares procedure on these four quantities (and the pulse size). The actual form of this analytic result is rather lengthy and is given elsewhere (De Smedt and Wierenga, 1979 Van Geneuchten, 1981). 

In the following sections, the experimental results which have been found in various studies of single-phase polymer flow in 1-D porous media will be discussed. Results will be referred to the convection-dispersion equation outlined above as a model for the flow. However, when there are deviations from this, the appropriate equations/models will be developed. In addition to discussing the macroscopic fit of the generalised convection-dispersion model for polymer transport in porous media, some aspects of the microscopic or physical basis of the phenomena under consideration will also be discussed. 

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