multivariate production systems optimization - Stanford University

The reservoir model is constrained by both pressure and flowrate. In addition to specifying
a minimum flowing well pressure, two flowrates must be specified: a minimum flowrate
and a maximum target flowrate. The model attempts to satisfy the target flowrate without
violating the minimum flowing well pressure.
2.1 Reservoir Material Balance
Reproduced here is the theory and procedure of the “generalized” material balance method
as implemented in the reservoir model developed by Borthne (1986). For a more
exhaustive treatment on the subject, the reader is referred to Borthne’s thesis.
For the following discussion, a simple notation scheme is employed. A variable
may be given a superscript of S or R, denoting standard conditions or reservoir conditions,
respectively. Those without a superscript are implied to be standard conditions. In
addition, a variable may be given a two letter subscript, such as OO, OG, GO, or GG. The
first letter of the subscript indicates the current phase of the variable and the second letter
indicates the source phase of this variable. For example,
S
ρGO is the standard density of gas derived from free reservoir oil. Similarly,
is the reservoir volume of oil, and
V O R
QOO
is the standard volumetric flow rate of oil derived from free reservoir oil.
Using this notation scheme, the formation volume factors may be expressed as
BO = V O R
V OO S
BG = V G R
The solution phase ratios may be expressed as
V GG S
8
(2.1)
(2.2)