4 - Transient saturated flow

Abstract

This chapter discusses about the transient, single-phase fluid flow in random porous media and introduces several methods to formulate and solve moment equations that are applied to this problem. Partial differential equations govern the statistical moments of flow quantities with perturbative expansions. As an alternative to the partial differential equations, moment equations in terms of integrodifferential representations are also formulated with the aid of Green's function. There are two ways to derive moment integrodifferential equations for transient flow. The first is to derive exact but unclosed moment equations, and then close the equations by closure approximations or perturbation schemes; and the second is to invoke the perturbation schemes from the onset, and then formulate the moment integrodifferential equations. In adjoint state equations, the original equations are first discretized on specified grids by using finite differences or finite elements, and then the resulting equation is used to derive statistical moments of flow quantities by adjoint state method. Transient effective hydraulic conductivity is defined as the tensor that relates the expected values of flux and hydraulic head gradient.