TABLE OF CONTENTS Previous chapters describe much of the data that is needed by a reservoir simulator. Our goal here is to describe how the complex fluid flow equations presented in Chapter 9 are solved in practice. For a more detailed technical presentation, consult one of the many sources available in the literature [for example, see Aziz and Settari, 1979; Peaceman, 1977; Rosenberg, 1977; Thomas, 1982; Mattax and Dalton, 1990; Ertekin, et al, 2001; Munka and P pay, 2001]. The technique used to solve the set of IFLO equations is presented as an illustration of a simulator solution procedure.
Fluid flow equations are a set of nonlinear partial differential equations that must be solved by computer. The partial derivatives are replaced with finite differences, which are in turn derived from Taylor's series. Table 10-1 outlines this procedure. The spatial finite difference interval ? x along the x-axis is called the gridblock length, and the temporal finite difference interval ? t is called the timestep. Indices i, j, and k are ordinarily used to label grid locations along the x, y, and z coordinate axes, respectively. Index n labels the present time level, so that n+1 represents a future time level. If the finite difference representations of the partial derivatives are substituted into the original flow equations, the result is a set of equations that can be algebraically rearranged to form a set of equations that can be solved numerically.
