Finite-Element Modeling of Single-Fluid Phase Flows

First, a formal mathematical derivation of transient multidimensional flow and solute transport in subsurface media will be presented in this chapter. We attempt to include all important steps in the development to account for the assumptions and their bases and to incorporate boundary conditions as much as possible. Based on (1) the continuity of fluid, (2) the continuity of solid, (4) the motion of fluid (Darcy’s law), (4) the equation of the state, (5) the law of consolidation of media, (6) conservation of energy, and (7) the principle of mass balance, the governing equations can be derived for the distribution of pressure, temperature, and solute concentration for single-phase flow in subsurface media. Then, finite-element modeling of single-fluid phase flows under saturated and saturated-unsaturated conditions will be presented.