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In previous chapters, we have learned finite-difference analogs of first-order and second-order derivatives. In Chapter 4, we learned the partial-differential equations (PDEs) that describe the single-phase flow of incompressible, slightly compressible, and compressible flow dynamics in porous media. Because these PDEs are all composed of first-order and second-order derivatives, writing the finite-difference representation of them is quite straightforward, using their respective finite-difference analogs. Because the finite-difference equations are implemented at preselected discrete points in the reservoir, a discretized representation of the reservoir also will be necessary. The discretized representation of the reservoir is achieved by superimposing gridblocks over the reservoir; this process is called gridding. In this chapter, we first will briefly review the different types of grids, and then we will learn how to couple the finite-difference approximations and the discretized (gridded) reservoir architecture.

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