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This chapter explains how fluid flow in porous media can be translated into a mathematical statement and how mathematical analysis can be used to answer transient-flow problems. This broad area is common to many other disciplines, such as heat conduction in solids and groundwater hydrology. The objective of this chapter is to introduce the fundamentals of transient analysis, present examples, and guide the interested reader to relevant references. Most physical phenomena in the domain of transient fluid flow in porous media can be described generally by partial differential equations (PDEs). With appropriate boundary conditions and sometimes with simplifying assumptions, the PDE leads to an initial boundary value problem (IBVP) that is solved to find a mathematical statement of the resulting flow in the porous medium. Figure 1.1 โ Arbitrary closed surface ฮ in porous medium. The initial condition is normally expressed in terms of a known pressure distribution at time zero; that is, ....................(3.26) The most common initial condition is the uniform pressure distribution in the entire porous medium; that is, f (x, y, z) pi. The boundary conditions are specified at the inner (wellbore) and outer boundaries of the reservoir.
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