Control Optimization of Oil Production
under Geological Uncertainty
¹´²´³Agus Hasan, ²´³Bjarne Foss,
¹´³Jon Kleppe
¹Department of Petroleum Engineering, NTNU
²Department of Cybernetics Engineering, NTNU
³Center for Integrated Operations in Petroleum Industry
Nordic Process Control Workshop 2009
Porsgrunn, Norway
29-30 January 2009
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Outline
 Objectives and Motivations
 Closed-loop Reservoir Management
 Case Study
 Part 1 Optimization
Optimization Methods
Reservoir Control Structure
Binary Integer Programming
Optimization Results
 Part 2 Uncertainty
Geological Uncertainty
History Matching
Results
 Conclusions and Recomendations
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Objectives and Motivations
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.
Objective function: Net Present Value (NPV)
 NProd  r q n  x, u, m   r q n  x, u, m   Ninj

o o, j
w o, j
n
   rw,inj qinj ,i 
NPV     
tn

 i 1
n 1  j 1 
1  b 

 

N
Which optimization method should we choose in our problem?
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•
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Efficient: Fast enough
Accurate
Robust
Applicable: can be used in practical way
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Closed-Loop Reservoir Management
Production
System
(Reservoir, Well)
Optimiza
tion
Data
Control and
Optimization
Calc.
NPV
Identification and
Updating
Reservoir Simulator
Geological
Uncertainty
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Case Study
Grid cells : 45 x 45 x 1 = 2025
2-phases : Oil-Water
Assumptions:
Incompressible and Immiscible fluids flow
No flow boundaries
No capillary pressure
No gravity effect
(Brouwer 2004)
1 Injector and 1 Producer well
Each well was divide into 45 segments
Each segments was modeled as a separated “smart well”
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Initial Data
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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:
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Reservoir Simulator
Mass balance
Darcy’s Law
Saturation Equation
Pressure Equation
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Non-optimized Results
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PART 1 Optimization
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Optimization Methods
 Reactive Control
Shut-in well with water cut above some threshold
 Proactive Control
Delay water breakthrough
 Binary Integer Programming (BIP)
On-off valves setting
min cT x
x
s.t
A x  b
x  Z  0,1
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Reservoir Control Structure
Start
0
Finish
200
400
600
800 [days]
45 well segment aggregated into 9 control segments. Allow one segment
to be closed at 200, 400, and 600 days.
Which well segment should be closed?
(Optimize the shut in sequence)
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Binary Integer Programming
z  1  Open
 z1 
 
 
z   
 
 
z 
 9
 qo1 
 
 
Qo    
 
 
q 
 o9 
Constrain:
8  z1 
 z9  9
z  0  Closed
max z T Qo
min  z T Qo
s.t.
s.t.
Az  b
Az  b
z
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z
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 1 1
A
 1  1
1 

 1
9
b 
8
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Results (Water saturation after 800 days)
Non-optimize Case
Reactive
Proactive
BIP
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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
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PART 2 Uncertainty
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Uncertainty
Origins:
 Mathematical model (linear model)
 Measurement devices (well loging, surface facilities, etc)
 Reservoir geology (porosity, permeability, fault, etc)
Treatments:
 EnKF
 Bayesian Inversion
 History matching
 etc.
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Geological Uncertainty
Permeability Realizations
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History Matching (Using 200 day
production data)
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History Matching (Cont’d)
”True” permeability fields
Selected permeability fields from ”Realizations”
”True” saturation profile (200 days)
Saturation profile from ”Realizations” (200 days)
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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 %
Unit in million USD
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Results (Cont’d)
Saturation profile without Uncertainty (800 days)
Saturation profile with Uncertainty (800 days)
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Conclusions
 A new production optimization technique has been presented.
Optimization proces based on Binary Integer Programming has been
succesfuly applied and gives improvement in Net Present Value. Binary
Integer Programming gives more benets in the sense of NPV improvement
then regular Reactive or Proactive Control.
 Binary Integer Programming is a robust optimization technique under
gealogical uncertainty such as permeability distribution. The optimization
process also showed that water saturation at breakthrough was observed to
be more uniformly distributed across the reservoir after the optimization
process as compared with the unoptimized case.
 The scope for improvement depends on the type of heterogeneity in the
permeability field. Because the NPV performance of the optimal water
flood depends less on geological features than that of a conventional water
flood, the scope for improvement partly depends on the performance of
the conventional water flood.
 The scope for improvement depends on the relative magnitudes of the oil
price and the water cost, and on the length of the optimization window.
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Recommendations
The effects of capillary pressure, compressibility, and gravity were not
investigated in this study.
Results obtained in this study may therefore only be representative
for situations were gravity and capillary effects are relatively small. Gravity may
positively or negatively affect the sweep efficiency. The scope for improvement and
the shape of the optimal control functions may thus change if capillary or gravity
forces are signicant. Therefore, their exact effects should be investigated.
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