The dimensional character of permeability. Dimensionless groups that govern Darcy’s flow in anisotropic porous media

The dimensional character of permeability in anisotropic porous media, that is,its dimension or dimensional equation, is an information that allows setting thedimensionless groups that govern the solution of the flow equation in terms ofhydraulic potential patterns. However, employing the dimensional basis {L, M,T} (length, mass, time), the dimensionless groups containing the anisotropic per-meability do not behave as independent monomials that rule the solutions. Inthis work, the contributions appearing in the literature on the dimensional char-acter of permeability are discussed and a new approach based on discriminatedand general dimensional analysis is presented. This approach leads to the emer-gence of a new and accurate dimensionless group,kxkyl∗2yl∗2x, a ratio of permeabilitiescorrected by the squared value of an aspect factor, beingl∗xandl∗ytwo arbitrarylengths of the domain in the directions that are indicated in their subscripts. Spe-cific values of this lengths, which we name ‘hidden characteristic lengths’, arealso discussed in this article. To check the validity of this dimensionless group,numericalsimulationsoftwoillustrative2-Dseepagescenarioshavebeensolved. The authors would like to thank SéNeCa Foundation for the support given to this research and for the scholarships awarded to Martínez-Moreno E. to carry out her doctoral thesis.