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Transport in Porous Media, Vol.59, No.3, 357-372, 2005
An upgraded porous medium coupled transport process algorithm
Ever since the Yuster (1951) watershed paper appeared more than half a century ago, viscous coupling subject matter as discussed recently by Wang (1997) has been one of many recent writings that has taken on the importance of serving as a paradigm example of the relevance of coupling phenomena in general that are of interest to geohydrologists and their companion reservoir engineers. And that is why the focus here is put on some additional practical ideas that are intended to be of at least passing interest to professionals involved in field-conducted porous media transport process simulation studies. Specifically, new ideas will be presented in this note about prospective (i.e., plausible but still to be proven) ways to devise and employ algorithms that perhaps in fact should facilitate laboratory and field work conducted by experimentalists who occasionally are interested in shortcut ways to validate theoretical presumptions about the nature of what are hoped to be macroscopically meaningful models governing specific transport processes of interest. And mention will also be made about the parallel work of those who engage in 'computerized games' as a logical way to forecast future reservoir performance outcomes by employing even simplistic variants of the classical Buckley-Leverett computational methodologies. The latter, for example, are of the sorts described in a contemporary sequel paper by Rose (2004). To be noted in particular, however, the analyses presented in what follows also support forecasting under field conditions future reservoir states which according to Gabrielli et al. (1996) can be made without the necessity of invoking any up-scaled principle of microscopic reversibility. This will be reasonable, for example, whenever there are no overriding needs to generate additional independent reciprocity relationships. In fact, the only constraint we shall be imposing here is that, for simplicity, attention will be limited only to some of those specific cases where linear polynomial relationships alone turn out to adequately describe the transport processes of specific interest, and this simply because they explicitly involve linearly related and macroscopically observable fluxes of mass, momentum and/or energy quanta that are sufficiently caused alone by attending conjugate thermodynamic driving forces. The computational algorithms to be described now (code-named here by a palindrome acronym, 'APTPA' to serve as a code name for 'A Prospective Transport Process Algorithm') are ones that makes it possible to simultaneously solve the given N independent transport relationships that can contain as many as N-2 stop initially unknown transport coefficients whenever the inequality, (M greater than or equal toN greater than or equal to 1) holds, with M being an integer which is larger than unity (but, however, typically still equal to ... or only a bit larger than N). In addition, the companion devices to measure necessary reservoir rock sample properties will be based on the laboratory procedural methodologies recommended by Rose (1997) and further described in Rose (2004), as will be shown in the discussions that follow.
Keywords:viscous and similar coupling phenomena;porous media transport systems;computational and laboratory procedural algorithms for simulating multi-fluid transport process properties