Equivalence analysis of non-linear partial differential equations of fluid flow through porous media

INTRODUCTION; The physico-mathematical background of the flowing phases through homogeneous and heterogeneous porous media is discussed in this chapter which is necessary to understand the author's investigations presented in the subsequent chapters. The fundamental definitions of piezometric head, piezometricalope, filtration (Seepage) velocity and seepage face are given. The basic Darey's law governing the flow of fluid through porous media is stated; its range of validity and general forms are discussed. Further, we have introduced basic flow equations describing a poro-hydrodynamical systems, viz., generalized Darey's law, the equation of continuity applied to each phase individually, the relation between capillary pressure and phase saturation [Fig.l] together with necessary boundary and initial conditions which are sufficient for a complete specification of the flow system.