Summary
Non-linear filtration is of considerable practical importance, since it arises, in particular, in connection with oil drilling operations. Thus, for example, flows of paraffin-based oils, of oils containing asphaltenes and of oil-water emulsions are characterized by deviations from linearity in the law relating the rate of filtration and the pressure gradient. Here, a variety of multi-parameter non-Darcian filtrations laws are constructed for which the hodograph system characterizing the non-linear filtration is reducible to a convenient canonical form (associated with theCauchy-Riemann equations). Available arbitrary constants in the non-linear filtration laws may be used to best approximate empirical filtration data for a diversity of permeable media for specified regions of variation of the rate of filtration. A wide class of non-linear filtration problems are thereby linked to situations described by the classicalDarcy Law.
As an application of the method, the general solution of a wide class of non-linear filtration problems involving a permeable medium with cavities is presented.
Résume
On construit une classe des lois non-linéaires à paramètre multiple d'un milieu poreux pour laquelle on peut réduire à une forme canonique les équations qui décrivent une certaine classe d'écoulements non-Darcians.
Zusammenfassung
Multiparametrische, nichtlineare Filtrationsgesetze werden untersucht, für die das regierende Gleichungssystem für eine Klasse nicht-darcyscher Strömungen auf kanonische Form reduziert werden kann.
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Rogers, C., Swetits, J.J. On a class of non-linear filtration laws. Rheol Acta 14, 842–849 (1975). https://doi.org/10.1007/BF01521413
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DOI: https://doi.org/10.1007/BF01521413