Porous media transport descriptions — non-local, linear and non-linear against effective thermal/fluid properties

Abstract

The momentum and scalar transport equations obtained using volume-averaging theory (VAT) involve additional terms which quantify the influence of the medium morphology. There are many mathematical models currently in use which are actually competing without comparison or analysis. The few most common and the VAT-based models are analyzed along with effective coefficients conventional equations. The random morphology fluctuations are incorporated into the VAT-based transport equations by means of randomly varying morpho-convective and morpho-diffusive terms. Methods for closure of the morpho-fluctuation terms in the governing transport equations are outlined. Statistical and numerical techniques were applied to classical irregular morphologies to treat the morpho-diffusive and morpho-convective terms along with integral terms. At present there are few well-developed closure expressions for the VAT-based transport equations in porous media. Some of them exploit the properties of available solutions to transport problems for individual morphological elements (F. Zanotti, R.G. Carbonell, Chem. Eng. Sci. 39 (1984) 263; C.T. Hsu, P. Cheng, Int. Comm. Heat Mass Transfer 15 (1988) 689; M. Quintard, S. Whitaker, Advances in Heat Transfer, vol. 23, Academic Press, 1993) and others are based on the natural morphological data of porous media (V.S. Travkin, I. Catton, Proceedings of the 28th National Heat Transfer Conference, San Diego, CA, August 1992, ASME HTD, vol. 193, 1992; L. Gratton, V.S. Travkin, I. Catton, Heat Transfer in Porous Media, ASME HTD, vol. 240, 1993; H. Ma, D.W. Ruth, Trans. Porous Media 13 (1993) 139). The challenging problem in irregular and random morphologies is to produce an analytical or numerical evaluation of the deviations in scalar or vector fields. In previous work, the authors have presented a few exact closures for predetermined regular and random porous medium morphologies. The questions related to effective coefficient dependencies, boundary conditions and porous media experiment analysis are discussed. A few issues particularly related to mass transport in different scale adsorbing media analysed with VAT techniques.