Book of Abstract : “ Flow and transport in porous media with applications ”

Abstract

Flow, heat, and mass transfer in porous media are encountered in a great many fields of engineering: civil, chemical, mechanical and petroleum, to name a few. A wide variety of flow patterns can be realized in the porous medium. These are controlled by the flow regime-for example, steady or unsteady, laminar or turbulent, fluid interfaces in multi-phase flow, non-equilibrium phenomena in the transported variables such as pressure, temperature and concentration, chemical reactions, and phase change. Additionally, it is well-established that flow patterns and transport depend intricately on the variability of the pore space and the solid matrix. Strategies employed for studying transport phenomena in a non-uniform porous medium include the following: 1. Formulate the governing equations for an inhomogeneous, anisotropic region. Properties such as permeability and dispersion are interpreted here as second order tensors that have built-in dependence on spatial location. 2. Permeability and dispersion are treated as random variables with a well-defined average that can be a function of space. These are associated with appropriate statistics that account for fluctuations in the physical properties and possible spatial correlation, apart from correlations among the properties themselves. While approach 1 leads to a deterministic model that can be solved by a numerical technique, approach 2 leads to a stochastic model that must be solved several times to generate realizations of the resulting flow and scalar fields. One of the major difficulties encountered in the two approaches referred above pertains to the sensitivity of the predicted variables on the specification of pore-scale variation (deterministic or statistical). For example, a refinement of the computational grid will permit greater details of the pore structure to be prescribed and yield a completely new solution. Yet another difficulty is experienced when the model parameters have to be determined from laboratory or field-scale experiments. The scale of measurements may be such that variations on a smaller scale are completely masked. The difficulties become compounded when transport occurs over a wide range of length scales or over an extremity of pore scales. The best one can accomplish is to determine parameters in such a way that a few limited goals of the mathematical model are fulfilled, though the estimations may not strictly conform to every possible variation in the pore geometry. The subject of hierarchical modeling of transport in porous media is in its infancy. The present talk is introductory and deterministic modeling of flow and transport in …

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