Mathematical characterization of scenarios of fluid flow and solute transport in porous media by discriminated nondimensionalization

The nondimensionalization of the partial differential equations that define the mathematical model of any physical process is the first step towards obtaining rapid information on the dimensionless parameters that influence the solution of the problem. In this paper we apply this technique, in its discriminated form, to derive these parameters for the engineering problem of fluid flow coupled with solute transport in anisotropic porous media. In contrast to classical nondimensionmalization, the discrimination generally leads to a lower number of independent dimensionless groups, which means a notable improvement for the researcher. Classical groups, generally assumed to be independent, such as the so-named form factors or aspect ratios, do not emerge as such when discrimination is applied. In addition, the resulting discriminated groups have a clear meaning in terms of balance between the characteristic quantities, referring to the same domain of the problem. To demonstrate the advantages of this mathematical technique, intrusion scenarios, numerically simulated by the network method, are studied.

► Flow and solute transport scenarios are characterized by dimensionless numbers.
► Discriminated nondimensionalization applies to obtain the dimensionless numbers.
► The less number of dimensionless groups are deduced.
► Resulting dimensionless groups are different from those of classical studies.
► Dimensionless numbers are interpreted in terms of balances in the domain.