multivariate production systems optimization - Stanford University
multivariate production systems optimization - Stanford University
multivariate production systems optimization - Stanford University
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which is valid for steady-state, radial flow, and constant <strong>production</strong> rate. The expression<br />
may be modified for pseudosteady-state flow by the inclusion of a skin term<br />
qo =<br />
2 π k h<br />
ln re rw - 0.75 + S +Dqo<br />
Using the concept of pseudopressure, defined as<br />
m P =<br />
the above expression may be written as<br />
qo =<br />
0<br />
P<br />
17<br />
kRO<br />
μO BO<br />
2 π k h<br />
ln re rw - 0.75 + S +Dqo<br />
dP<br />
PR<br />
Pwf<br />
kRO<br />
μO BO<br />
dP<br />
(2.55)<br />
(2.56)<br />
m PR - m Pwf (2.57)<br />
The oil flow rate in this expression refers to the oil flow rate in the reservoir. The flow rate<br />
may be converted to a standard flowrate by expanding the pseudopressure integrand to<br />
include a term that accounts for oil originating from the reservoir gas.<br />
m P =<br />
0<br />
P<br />
kRO<br />
μO BO<br />
+ kRG rS<br />
μG BG<br />
dP<br />
(2.58)<br />
Notice that for a nonvolatile gas, where the oil-gas ratio, rS , is zero, the equation reduces to<br />
Equation 2.56. The corresponding equation for gas with oil in solution is<br />
m P =<br />
0<br />
P<br />
kRG<br />
μG BG<br />
+ kRO RS<br />
μO BO<br />
dP<br />
(2.59)<br />
We now have a flow equation in terms of modified pseudopressure. The pseudopressure<br />
is a function of both pressure and saturation. By assuming a constant producing gas-oil<br />
ratio, a relationship may be found between saturation and pressure. In the preceding<br />
discussion of the reservoir material balance, the producing gas-oil ratio, RP , was<br />
approximated by<br />
RP = ΔGP<br />
ΔNP<br />
(2.60)