Petrophysics laws as invariants of filtration model

Abstract

In this paper the methods of Lie group analysis are used to investigate symmetry properties of differential equations that describe filtration of a two-phase liquid in a porous media. Lie algebra of operators of a group of equivalence transformations is calculated. Invariants with respect to a subgroup of the group of equivalence transformations are used for constructing the functional dependencies which define arbitrary parameters of the model. It is shown that one of the invariants of a subalgebra of operators of equivalence transformations is the Timur's law, describing a relation between absolute permeability, porosity and residual water saturation.