Page 46 - Principles of Applied Reservoir Simulation 2E

Chapter 4

Derivation of the Flow Equations

Many derivations of the oil, water, and gas fluid flow equations exist in
the literature [for example, see Crichlow, 1977; Peaceman, 1977]. Consequently,
only a brief discussion will be presented here. It closely follows the presentation
originally published in Fanchi, et al. [1982].

4.1 Conservation of Mass

We begin by considering the flow of fluid into and out of a single reservoir
block (Figure 4-1). Let the symbol J denote fluid flux. Flux is defined as the rate

A /

j, — ** i i J X+AX fmnm—^nm^^. j£
y
^^-
7 T
z

Figure 4-1. Reservoir block: the coordinate
convention follows Sawyer and Mercer [1978].

of flow of mass per unit cross-sectional area normal to the direction of flow,
which is the x direction in the present case. Assume fluid flows into the block
atx (J x) and out of the block at ;c + A x +&x)- By conservation of mass, we have
(J x
the equality:

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