Abstract
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.
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