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In the formulation of basic equations for single-phase flow in porous media, one must consider the type of fluid and the flow geometry expected to be dominant. Flow equations are written in a certain geometry and in a certain number of dimensions in view of the reservoir’s structural characteristics and well-completion techniques. For example, 1D radial-cylindrical flow geometry is most-widely used in single vertical-well applications. If the well is horizontal or a single well is hydraulically fractured with vertical fracture planes, an elliptical-cylindrical flow geometry is expected to develop and, hence, the use of an elliptical-cylindrical coordinate system is warranted. In field-scale simulation models with the presence of many wells located in the computational domain, rectangular flow geometry in one, two, or three dimensions typically is used. One important thing to keep in mind is the shape of the equipotential lines and streamlines. In an orthogonal-coordinate system, the elemental volume should conform to these two important elements of the flow problem. In doing so, it will also be possible to minimize the grid-orientation effects.

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