Page 123 - Intelligent Digital Oil And Gas Fields

90 Intelligent Digital Oil and Gas Fields

Standard deviation (σ): σ ¼U t /2
Initial balance (Bal): A-B-C¼0
Yield between B and C: Y¼B/C
2

y y i
i
Penalty of measurement (P m ): P m ¼
σ
Objective function (f (y) ) minimization of the total penalties:
2

i
P n y y i
f y ¼ ¼ 0:0
i¼1 σ
where
• y i is the initial measurement at point A, B, or C using the flow rate tool,
either device or calculations.
• y i * is the measurement at point A, B, or C after reconciliation.
• %Tol is the manufacture tolerance in percentage.
• U t is the uncertainty calculation of measurement
• Y is the yield between points B and C
• σ is the standard deviation calculated as the half value of the uncertainty.
• Bal is the initial balance in the total sum of the independent measure-
ments, which should be 0.0. If the total sum is different than 0.0, then
we need reconciliation.
• P m is the penalty function of the measurement or device.
• f (y) is the total objective function, which should be minimized to 0.0 if
condition of Bal¼0.0.
Table3.1showsthefinalvaluesafterreconciliation.NotethatCoriolishasbeen
affected by +116bbl/d (14% error), virtual meter by 103bbl/d (8% error),

Table 3.1 Reconciliation Method Among a Coriolis Meter Setup in Well C, A Virtual
Meter Setup in Well B, and the Total Fluid Measured in Point A With An MPFM (Note That
There is a Mismatch Between the MPFM and Other Meters)
Measured Uncertainty Reconciled
Flow Rate U t (95% Standard Value Penalty, Measurement
Well Flowmeter (Bls/d) Confidence) Deviation (Bls/d) PM Error (%)

A MPFM 2265 68 34.0 2163 8.9 4
B Virtual 1300 78 39.0 1197 6.9 8
meter
C Coriolis 850 85 42.5 966 7.5 +14
meter
B+C 2150 Objective function—minimize 23.3
penalty➜
Imbalance 115 Imbalance after reconciliation➜ 0.0
(A-B-C)
Yield Y¼B/C 57 New yield % 55.3