Page 56 - Principles of Catalyst Development

Part I: Reservoir Engineering Primer 3?

of the basic three-dimensional, three-phase black oil simulator equations.
Equivalent but much simpler appearing forms of the flow equations are presented
in terms of vector operators as

- V (427)

q 3
™ - - • (4,28)
and

- V
Pgsc
(4.29)
}
+1? * "
dt

where the symbol V • v for the divergence of the velocity vector is shorthand
for the expression
_
d d d
—
+
- v = — v + —v y + —-v z. (430)
+
—v
—-v x
dx dy dz
A review of vector analysis can be found in many references, such as Kreyszig
[1999] and Fanchi [2000].
Exercises

Exercise 4.1 Suppose the unit of density p osc is mass per volume at standard
conditions, and the unit of Darcy velocity is length per time. Use dimensional
analysis to determine the unit of flux in Eq. (4.7).

Exercise 4.2 The densities in Eqs. (4.14) and (4.15) include gas dissolution.
Rewrite Eqs. (4.19), (4.23), and (4.29) for a system with no gas dissolved in
either the oil or water phases.