Non-linear laws of fluid flow through anisotropic porous media

Non-linear laws of fluid flow through anisotropic porous media are written out in invariant tensor form for all crystallographic point symmetry groups. The equations, as is customary in seepage theory [1, 2], are represented by expressions containing the seepage velocity up to and including the third degree. Expressions defining non-linear flow resistances are given and it is shown that, when one transfers from linear to non-linear seepage laws, the symmetry group of the flow properties may change. For example, the isotropic flow properties manifested in Darcy's law may become essentially anisotropic in a non-linear law and display asymmetry, that is, they may be different along one straight line in the positive and negative directions. It is shown that, compared with linear seepage laws for anisotropic media, when flow properties may be defined by just four essentially different types of equation, in non-linear laws the appearance of anisotropy is highly diversified and the number of distinct types of equation increases considerably.