control optimization of oil production under geological uncertainty ¹´²´³agus hasan,...
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Control Optimization of Oil Production under Geological Uncertainty
¹´²´³Agus Hasan, ²´³Bjarne Foss,¹´³Jon Kleppe
04/19/23 NPCW 2009NTNU
¹Department of Petroleum Engineering, NTNU²Department of Cybernetics Engineering, NTNU
³Center for Integrated Operations in Petroleum Industry
Nordic Process Control Workshop 2009Porsgrunn, Norway29-30 January 2009
Outline
04/19/23 NPCW 2009NTNU
Objectives and Motivations Closed-loop Reservoir Management Case Study Part 1 Optimization
Optimization MethodsReservoir Control StructureBinary Integer ProgrammingOptimization Results
Part 2 UncertaintyGeological UncertaintyHistory MatchingResults
Conclusions and Recomendations
Objectives and Motivations
• Efficient: Fast enough• Accurate• Robust• Applicable: can be used in practical way
Which optimization method should we choose in our problem?
Objective function: Net Present Value (NPV)
injProd, ,
, ,1 1 1
, , , ,
1n
n n NNNo o j w o j n
w inj inj itn j i
r q x u m r q x u mNPV r q
b
Objectives:
Find operating combination conditions of down-hole valve settings that optimize the water flood. Investigate potential for improvement as function of reservoir properties and operating constraints.
04/19/23 NPCW 2009NTNU
Closed-Loop Reservoir Management
Production System
(Reservoir, Well)
Reservoir Simulator
Optimization
Optimization
Calc.NPV
Data
Identification and Updating
Identification and Updating
Control andOptimization
GeologicalUncertainty
04/19/23 NPCW 2009NTNU
Case StudyGrid cells : 45 x 45 x 1 = 2025
2-phases : Oil-Water
Assumptions:
1 Injector and 1 Producer well
Each well was divide into 45 segments
Each segments was modeled as a separated “smart well”
No flow boundaries
Incompressible and Immiscible fluids flow
No capillary pressure
No gravity effect
04/19/23 NPCW 2009NTNU
(Brouwer 2004)
Initial Data• Porosity : 0.2 (uniformly distributed)• IOIP : 324000 sm3 = 2041200 bbl• Injection rate : 405 sm3/day• Water Injection price : $ 0 / bbl• Oil produced price : $ 60 / bbl• Water produced price : $ 10 /bbl• Discount rate : 0• Three different permeability cases:
04/19/23 NPCW 2009NTNU
Reservoir Simulator
04/19/23 NPCW 2009NTNU
Mass balance
Darcy’s Law
Saturation Equation
Pressure Equation
Optimization Methods
Reactive Control Shut-in well with water cut above some threshold
Proactive ControlDelay water breakthrough
Binary Integer Programming (BIP)On-off valves setting
min
.
0,1
T
xc x
s t
A x b
x Z
04/19/23 NPCW 2009NTNU
Reservoir Control Structure
0 200 400 600 800 [days]
Start Finish
45 well segment aggregated into 9 control segments. Allow one segmentto be closed at 200, 400, and 600 days.
Which well segment should be closed?(Optimize the shut in sequence)
04/19/23 NPCW 2009NTNU
Binary Integer Programming
1 Open
0 Closed
z
z
1
9
z
z
z
1
9
o
o
o
q
Q
q
1 98 9z z
Constrain:
max
. .
To
zz Q
s t
Az b
min
. .
To
zz Q
s t
Az b
1 1 1
1 1 1A
9
8b
04/19/23 NPCW 2009NTNU
Results (Water saturation after 800 days)
Non-optimize Case
Reactive
Proactive
BIP
04/19/23 NPCW 2009NTNU
Results (Water cut and NPV)
Type 1 Type 2 Type 3
Base Case 41,93 38,20 43,97
Reactive 47,67 45,52 49,82
Proactive 48,80 46,15 49,63
BIP 51,24 46,05 52,85
Unit in million USD
04/19/23 NPCW 2009NTNU
Uncertainty
Mathematical model (linear model) Measurement devices (well loging, surface facilities, etc) Reservoir geology (porosity, permeability, fault, etc)
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EnKF Bayesian Inversion History matching etc.
Origins:
Treatments:
History Matching (Cont’d)
04/19/23 NPCW 2009NTNU
”True” permeability fields Selected permeability fields from ”Realizations”
”True” saturation profile (200 days) Saturation profile from ”Realizations” (200 days)
Unit in million USD
04/19/23 NPCW 2009NTNU
Final Results (BIP with and without uncertainty)
Type 1 Type 2 Type 3
Base Case 41,93 38,20 43,97
BIP without UN 51,24 46,05 52,85
BIP with UN 48,62 46,16 51,62
Deviation (with and without UN)
5,05 % 0,24 % 1,35 %
04/19/23 NPCW 2009NTNU
Results (Cont’d)Saturation profile without Uncertainty (800 days)
Saturation profile with Uncertainty (800 days)
Conclusions A new production optimization technique has been presented.Optimization proces based on Binary Integer Programming has beensuccesfuly applied and gives improvement in Net Present Value. BinaryInteger Programming gives more benets in the sense of NPV improvementthen regular Reactive or Proactive Control. Binary Integer Programming is a robust optimization technique undergealogical uncertainty such as permeability distribution. The optimizationprocess also showed that water saturation at breakthrough was observed tobe more uniformly distributed across the reservoir after the optimizationprocess as compared with the unoptimized case. The scope for improvement depends on the type of heterogeneity in thepermeability field. Because the NPV performance of the optimal waterflood depends less on geological features than that of a conventional waterflood, the scope for improvement partly depends on the performance ofthe conventional water flood. The scope for improvement depends on the relative magnitudes of the oilprice and the water cost, and on the length of the optimization window.
04/19/23 NPCW 2009NTNU
Recommendations
The effects of capillary pressure, compressibility, and gravity were notinvestigated in this study.
Results obtained in this study may therefore only be representativefor situations were gravity and capillary effects are relatively small. Gravity maypositively or negatively affect the sweep efficiency. The scope for improvement andthe shape of the optimal control functions may thus change if capillary or gravityforces are signicant. Therefore, their exact effects should be investigated.
04/19/23 NPCW 2009NTNU