multivariate production systems optimization - Stanford University
multivariate production systems optimization - Stanford University
multivariate production systems optimization - Stanford University
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ut the estimation of this term would be impractical. Instead, we use arithmetic averages<br />
ROAVG = ROK + ROK-1<br />
2<br />
RGAVG = RGK + RGK-1<br />
2<br />
Once we have solved for ΔNOO<br />
"<br />
, we can solve for the total incremental oil and gas<br />
<strong>production</strong> for the time step as<br />
ΔNP " = ΔNOO<br />
"<br />
ΔGP " = ΔNOO<br />
"<br />
ROAVG<br />
RGAVG<br />
Substituting Equations 2.46 and 2.47 into Equations 2.41 and 2.42 yields<br />
14<br />
(2.44)<br />
(2.45)<br />
(2.46)<br />
(2.47)<br />
AOK - AOK-1 + ΔNP " = 0 (2.48)<br />
AGK - AGK-1 + ΔGP " = 0 (2.49)<br />
Thus, the material balance errors for the oil and gas material balance equations may be<br />
expressed as<br />
ΔEO = AOK - AOK-1 + ΔNP "<br />
ΔEG = AGK - AGK-1 + ΔGP "<br />
The solution procedure for the generalized material balance method when the preferred<br />
phase is oil is as follows:<br />
1. Specify the constant oil rate, q O " , and the time step length, Δt.<br />
2. Determine the total incremental oil <strong>production</strong>, ΔNP " .<br />
ΔN P " = qO " Δt<br />
(2.50)<br />
(2.51)