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Successful enhanced oil recovery (EOR) requires knowledge of equal parts of chemistry, physics, geology, and engineering. Each of these enters our understanding through elements of the equations that describe flow through permeable media. Each EOR process involves at least one flowing phase that may contain several components. Moreover, because of varying temperature, pressure, and composition, these components may mix completely in some regions of the flow domain, causing the disappearance of a phase in those regions. Atmospheric pollution, groundwater flow, and chemical and nuclear waste storage lead to similar problems.

This chapter gives the equations that describe multiphase, multicomponent fluid flow through permeable media on the basis of conservation laws for mass, energy, entropy, and linear constitutive theory. Initially, we strive for the most generality possible by considering the transport of each component in each phase. Then, we obtain special cases from the general equations by making additional assumptions. The approach in arriving at the special equations is as important as the equations themselves because it will help to understand the specific assumptions—and the limitations—that are being imposed for a particular application.

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