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The displacement of fluids in a porous medium in a waterflood project involves the simultaneous flow of two or more immiscible phases between an inner and an outer boundary. In this chapter, we introduce the mathematical models that have been developed for forecasting fluids migration and pressure performance within the drainage area. The diffusivity equation is derived by combining the law of conservation of mass and Darcy’s law for the isothermal flow of slightly compressible fluids, and the solutions are used to model the physics of the diffusion of pressure and/or fluid dynamics in accordance with a specific set of limiting or boundary conditions. One must be aware of the assumptions and boundary conditions included in the development of a particular flow equation to ensure its proper application when solving field problems. Rate equations form the basis of the oil, gas, and water inflow-performance relationships. Water-influx calculation methods, on the other hand, are founded on changing rates and pressures as a function of reservoir architecture.

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