SPE 26647 Application of Variable Formation Compressibility for Improved Reservoir Analysis
SELF-LEARNING RESERVOIR MANAGEMENT SPE 84064 … · SELF-LEARNING RESERVOIR MANAGEMENT SPE 84064...
Transcript of SELF-LEARNING RESERVOIR MANAGEMENT SPE 84064 … · SELF-LEARNING RESERVOIR MANAGEMENT SPE 84064...
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SELF-LEARNING RESERVOIR MANAGEMENTSPE 84064
L. Saputelli1,2,3, M. Nikolaou2, and M. J. Economides2,3
1PDVSA, 2University of Houston, 3SPE member
PRH 034 - Formação de Engenheiros nas Áreas de Automação, Controle, e Instrumentação do Petróleo e Gás -aciPG, participante do Programa de Recursos Humanos da ANP - Agência Nacional do Petróleo - para o setor
Petróleo e Gás - PRH - ANP/MME/MCT
October 21 2004; Florianopolis
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Agenda
• Motivation: The reservoir management challenge– What is the Problem?, – What have been done?– What are the challenges?
• Problem Formulation• The specific objectives and scope of this research• Reservoir modeling and identification• Model Predictive Control• Self Learning Reservoir Management• Conclusions• The Way Forward
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Objective of this presentation
• To review current petroleum production issues regarding real time decision making and,
• To present the results of a continuous self-learning optimization strategy to optimize field-wide productivity while satisfying reservoir physics, production and business constraints.
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The Reservoir Management ChallengeReservoir Management is about a careful orchestration of technology, people & resources
InjectionFacilities
Compression &Compression &Treatment PlantsTreatment PlantsProductionProduction
Well & FacilitiesWell & Facilities
DrainageDrainageAreaArea
Drill, build & OperateDrill, build & Operate
SubsurfaceCharacterizationSubsurfaceCharacterization Update ModelUpdate Model
ControlControl
MonitorMonitor
Establish or reviseOptimum Plan Establish or reviseOptimum Plan
Exploitation PlanWell location & numberRecovery mechanismSurface facilitiesWell intervention
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Motivation
Traditional ProblemsComplex & risky operations
(Drilling, Workover, Prod.)
Poor reservoir prediction &
production forecasting
Limited resources: injection
volumes, facilities, people.
Unpredictability of events:
gas or water, well damage.
Poor decision making ability
to tune systems, thus, not
optimized operations
More front-end engineering
and knowledge sharing
Integrated Characterization &
Modern visualization tools
Multivariable optimization,
reengineering.
Monitoring & control devices,
Beyond well measurements
Isolated optimization trials
with limited success.
Current ApproachMore data for analysis and
integration limitations.
Long-term studies, Ill-posed
tools, simple or incomplete.
Models are not linked among
different layers
Poor Justification, real time
analysis in early stage.
Decisions made only on few
pieces. Lack of Integration
between subsurface-surface
Challenges
Hydrocarbon production system suffering major technical problems
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Research Specific Objectives
• Model based control system used to continuously optimize three-phase fluid migration in a multi-layered reservoir
• A data-driven model that is continuously updated with collected production data.
• A self-learning and self-adaptive engine predicts the best operating points of a hydrocarbon-producing field, while integrating subsurface elements surface facilities and constraints (business, safety, quality, operability).
To develop a field-wide continuous self-learning optimization decision engine
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Research Framework
• Data handling– Data acquisition, filtering, de-trending, outliers detection
• Model building and identification– Gray box modeling: empirical reservoir modeling– Partial least square impulse response, neural network and sub-space
• Reservoir performance prediction– Real time Inflow performance and well restrictions– Havlena-Odeh Material Balance
• Bi-layer optimization of operating parameters– Reservoir best operating point based on the net present value optimization– Regulatory downhole sleeves and wellhead choke controls
• Closed-loop control with history-matched numerical reservoir model– Study of the system behavior in closed-loop
Combination of petroleum reservoir physics and process control technologies
DataHandling
DataHandling
ModelBuildingModel
BuildingSystem
IdentificationSystem
IdentificationReservoir
PerformanceReservoir
PerformanceBi-layer
OptimizationBi-layer
OptimizationClose-loop
ControlClose-loop
Control
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Problem Definition
• Control undesired fluid production
• Exploit efficiently multilayer horizons
• Characterize inter-well relationship
• Maximize reserves and production
• Control from surface measurement
• Optimization fluid production (< bottle-necks)
• Commingle multilayer reservoirs
• Minimize production costs
• Maximize reserves and production
• Control from surface measurement
Injector - Producer Profile Mngt.Injector - Producer Profile Mngt. Field-Wide ManagementField-Wide Management
Agua
Crudo
Gas
k1
kn
h1
hn
Attempt to solve two significant reservoir management challenges
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Traditional (Ideal) Integrated Management Approach
System:Reservoir, Wells &Surface Facilities
DatabaseParameters
Check ConditionApplications
Implementation
Well Model
Reservoir Model
BusinessModel
SurfaceModel
DataCollection
ExploitationOptions
Business Constraints
DecisionMaking Optimization
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3
4
5
6
7
8
9
By collecting data, a digital image is used to make decisions
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Reservoir Modeling: Fluid Transport in Porous media
rp pp p
p c p
k Sc p Z
g tφ
ρµ β
⎛ ⎞⎡ ⎤⎛ ⎞ ∂∇⋅ ∇ − ∇ = ⎜ ⎟⎢ ⎥⎜ ⎟ ⎜ ⎟∂⎝ ⎠⎣ ⎦ ⎝ ⎠
K g( ) 0c ct∂
+∇⋅ =∂
v
rpp p
p c
kp Z
gρ
µ⎛ ⎞
= − ∇ − ∇⎜ ⎟⎝ ⎠
p
K gv
p p pW
M p
A x S SMcV A x
φ β φβ
∆= = =
∆
Molar density in terms of Porous Volumes
Continuity Equation
Multiphase Darcy’s Law
Pressure Laplacian as a function of the saturation change
yi-1
yi+1∆yi zi+1
zi-1
∆zi
Spatial distribution of pressure as a time function of saturation
This realization is not used in this research, since it requires the knowledge of parameters that cannot be directly measured
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Reservoir Modeling: Flow through WellboreRadial Diffusivity Equation
Oil, water and gas flow as linear functions of the drawdown pressure
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2
1( )f
K p p pc c r r r tφµ
⎛ ⎞∂ ∂ ∂+ =⎜ ⎟+ ∂ ∂ ∂⎝ ⎠ re
rwh k
pwf
pe
rs( )2
,4 4
ti i
c rqp r t p Ekh kt
φµµπ
⎛ ⎞⎟⎜ ⎟= − ⎜ ⎟⎜ ⎟⎜⎝ ⎠
General Solution given by Exponential Integral
2
4ln4wf i
t w
q ktp pkh c rµπ γφµ
= −Wellbore flow given by logarithmic approximation
( )( ), 141.2 ln
ro e wf oo b
o o e w
kk h p pq
B r r sµ−
= ⎡ ⎤+⎣ ⎦
Steady-state Equation for the Undersaturated Oil-Flow
Inflow Performance (IPR) for Saturated reservoirs2*
, 1 0.2 0.81.8
wf wfbo o b
b b
p pp Jq qp p
⎡ ⎤⎛ ⎞ ⎛ ⎞⋅⎢ ⎥= + − −⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦
( )( )( )
2
0 1 2 3
2
0 1 2 3
2
0 1 2 3
k k k ko e wf wf
k k k kw e wf wf
k k k kg e wf wf
q a a p a p a p
q b b p b p b p
q c c p c p c p
= + ⋅ + ⋅ + ⋅
= + ⋅ + ⋅ + ⋅
= + ⋅ + ⋅ + ⋅
Proposed IPR for continuous monitoring
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Reservoir Modeling: Average Pressure ModelingAverage Reservoir Pressure is a function of net mass production
( ) ( )
( ) ( ) ( )
0 1 2 3 4
1 2 3 4
2 2110 1 2 1 3 1 5 2 6 2
, , ,p p p e
o w g wi
o w g wi
k k k k k k kwf wf wf wft
f p t g N G W W
p a a q a q a q a q
d p b q b q b q b qdt
p p c c p c p c p c p c p−
∆
⎡ ⎤ =⎣ ⎦
⇒ = + + + +
⇒ = + + +
⇒ − ≈ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅
∫ ∫ ∫ ∫
( ) ( ) ( ) ( )1 2 2
1 2 1 3 1 4 2 5 2
k k k k k kwf wf wf wfp p c c p c p c p c p
−= + + ⋅ + ⋅ + ⋅ + ⋅
Simplification
Material Balance Equation
Proposed Pressure Modeling for continuous monitoring
Expansion of Oil and Original dissolved gas, + Expansion of Gas Caps, Net Underground =
Withdrawal, + Reduction of Hydrocarbon Pore Volume,
+ Natural Water Influx,
o
g
fw
e
EE
F E
W
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Reservoir Modeling: Flow Through Pipes
0
2000
4000
6000
8000
10000
12000
14000
0 1000 2000 3000 4000 5000Pressure (psia)
Dep
th (f
t)
1,000 STB/D @ 500 SCF/STB; WOR=11,000 STB/D @ 1000 SCF/STB; WOR=11,000 STB/D @ 500 SCF/STB; WOR=01,000 STB/D @ 1000 SCF/STB; WOR=0
Vertical flow as non-linear functions of flow rates
220f
sc c c
f u dLdp udu g dz dWg g g Dρ
+ + + + =
Mechanical Energy Equation
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1 2
22
f
c c c
f u dLgp p p z ug g g D
ρρ∆ = − = ∆ + ∆ +
Single-Phase Solution, Incompressible
( )( )22
10 5
2144
7.413 10m cu gdp fm
dz zDρ ρ
ρ
∆= + +
∆×&
Two-Phase Solution, Hagerdorn & Brown (1965)
( ) ( ) ( ) ( )2 2 2
1 2 3 4 5 6
kk k k k k k kwf th o w g o w gp p b q b q b q b q b q b q− = + + + + +
Proposed Pressure Drop Modeling for Continuous Monitoring
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Tubing Performance
Reservoir Performance
Reservoir Modeling: Well Deliverability
Reservoir Pressure
Choke
Tubing Head Pressure
Fractional Flow of Phases
Bottomhole Flowing Pressure
Well operating point given by the intersection of reservoir and tubing performance
pwf , [psia]
q, [BPD]
pwf , [psia]
q, [BPD]
q, [BPD]
pwf , [psia]
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Reservoir as a Process Control System Structure
Agua
Crudo
Gas
MeasuredDisturbances
UnmeasuredDisturbances
Unmeasured Outputs
Measured Outputs
Well flowing Pressure: pwf
Reservoir Pressure: pres
Reservoir Saturations: So, Sw
Flow Impairment: S, Kr’s
Multiphase Flow: qo, qw, gq
Tubing Head Pressure: pTHP
Tubing Head Temperature: TTHT
Zone Multiphase Flow: qo, qw, gq
Solid Production, Water Analysis
Solvent InjectionGas Lift
ESP Speed
Water InjectionHeat InjectionGas Injection
Flow ChokeZone Control
Drainage Area: A
Manipulated Inputs
Controller
Feed forward path
Feed back path
Reservoir Rock HeterogeneityReservoir Fluid DistributionScheduling
BackpressureAmbient Temperature
Flow RestrictionsInjection Fluid Restriction
Knowing input-output relationships, reservoir could seen as a process plant
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Reservoir Model Identification
( )( )( )
2
0 1 2 3
2
0 1 2 3
2
0 1 2 3
k k k ko e wf wf
k k k kw e wf wf
k k k kg e wf wf
q a a p a p a p
q b b p b p b p
q c c p c p c p
= + ⋅ + ⋅ + ⋅
= + ⋅ + ⋅ + ⋅
= + ⋅ + ⋅ + ⋅ ( )
0 1 2 3
0 1 2 3
20 1 2 3
1k
koekkwwfk
g kwf
q a a a a pq b b b b pq c c c c
p
⎡ ⎤⎢ ⎥⎡ ⎤ ⎡ ⎤ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥= ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎣ ⎦⎣ ⎦ ⎢ ⎥⎢ ⎥⎣ ⎦
Recursive self-adaptive identification
,o optq
1 1,k kp q+ +
Reservoir Simulator
Reservoir Simulator
ModelIdentification
ModelIdentification
Reservoir ValueOptimization
Reservoir ValueOptimization
Measure
Interpret
Optimize
ControlImplementation
ControlImplementation Control
Physical System
Set point
Set point
| |1
ˆˆn N
k n j k i k n j i k ki n
y hu d+
+ + + + −= +
= +∑Model
spwf
spG
p
q
( )
( )( )
1
1
2
, 1
1, , 1
1
LS Optimization Loopˆˆ
min
, ... , ,...
, ... , ,...
k k
k k
N
ia b i
k ko g w T T
k kres n T T
q f p p q q
p f p p q q
−
−
=
−
−
+
⎧ ⎫⇒⎨ ⎬
⎩ ⎭⎧ =⎪⇔ ⎨
=⎪⎩
∑-1T T
Y = Xθ e
e X X X Y
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Example for Model Identification and Block Diagram
Reservoir Pressure: POil Rate: qoProducer Flowing Pressure, pwf1
Inputs (U)
Water Fraction: fw
qwinj qo
Water Injection Rate: qwi
Outputs (Y)
u1
u2
y1y2y3y4y5y6
Injector Flowing Pressure, pwf2
Gas Rate: qg
Water Rate: qw
o
w
g
qqqReservoir
(Simulator)Reservoir
(Simulator)
EmpiricalModel
EmpiricalModel
wfp+
d
IdentificationIdentificationEmpirical model whose structure is determined by first principles
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Model Identification Experimental Set-up
ReservoirNumerical
Model
GenerateDataFile
RunSummary
File
ConvertEclipse
To Excel
RunEclipse
RunMatlab
ReadExcelFile
AutoScale
cumsum(A)diff(A)
Select Input and Outputs
Split DataTest & Pred
x,y
Subspace Identification
NeuralNetwork
Plot RscCalculated
& Measured
RescaleParameters
FIR PLS
Windows and Eclipse Environment
Matlab Environment Level
01
xσ== U,Y c dA , A
A
Least SquaresEstimator
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Predictions Using Empirical Structured models
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Errors Using Empirical models
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Coefficients Using Empirical models
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Model Predictive ControlAt time k future predictions of the output y can be made as
| | |1 1
ˆ ˆˆ where n N n N
k n j k i k n j i k k k k k i k ii n i n
y hu d d y hu+ +
+ + + + − −= + = +
= + = −∑ ∑Minimization Problem to solve
Set Point Tracking ExampleAll Variables normalized so that They have zero mean and Std. Dev = 1
• Controls operation while optimizing performance
• Done over a receding or moving horizon
• Requires a setpoint from an upper level
MPC minimizes future prediction error while satisfying input constraints
( )2 2| 1|
1 1
m in | m ax
m in 1| m ax
| 1|
ˆm in
. .ˆ 1, ,
1, , , , 1
p mS P
k n j k k j kj j
k n j k
k j k
k i k k m k
y y R u
s ty y y j pu u u j mu u i m p
+ + + −= =
+ +
+ −
+ + −
⎡ ⎤⎧ ⎫− + ∆⎢ ⎥⎨ ⎬
⎩ ⎭⎢ ⎥⎢ ⎥⎢ ⎥
≤ ≤ =⎢ ⎥⎢ ⎥
≤ ≤ =⎢ ⎥⎢ ⎥= = −⎢ ⎥⎢ ⎥⎣ ⎦
∑ ∑
L
L
L
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Example for Control and Block Diagram
Reservoir Pressure: POil Rate Layer 1: qo1Producer Flowing Pressure, pwf1
Inputs (U)
Water Rate Layer 1: qw1
qwinj qoT
Water Injection Rate: qwi
Outputs (Y)
u1
u2
y1y2y3y4y5y6
Injection Flowing Rate, qwinj u3
Producer Flowing Pressure, pwf2Oil Rate Layer 2: qo2
Water Rate Layer 2: qw2
Layer 1, kh1
Layer 2, kh2
MPCController
MPCController
o
w
g
qqq
Reservoir(Simulator)Reservoir
(Simulator)
EmpiricalModel
EmpiricalModel
wfp,
,
,
o sp
w sp
g sp
qqq
oq∆+
-
+
d
PLS Impulse IdentificationPLS Impulse Identification
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Model Predictive Control ResponseMPC minimizes future prediction error by satisfying input constraints
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New Self-learning Reservoir Management TechniqueContinuous self-learning optimization decision engine
,o optq
1 1,k kp q+ +
Reservoir Simulator
Reservoir Simulator
ModelIdentification
ModelIdentification
Reservoir ValueOptimization
Reservoir ValueOptimization
Measure
Interpret
( )
{
, , 1
min , max
min max
, , ,
LP Optimization Loop
max , , ,$,
s.t.
ˆ ˆ ˆ, ,
o w g
N
o w gq q q
k p k
k p
o opt g opt w opt
f q q q T
p p p
q q q
q q q
+
+
⎧ ⎫= ∆⎨ ⎬⎩ ⎭
≤ ≤⎧⎪⎨ ≤ ≤⎪⎩
⇔
∑NPV
Optimize
ControlImplementation
ControlImplementation Control
Physical System
Set point
Set point
| |1
ˆˆn N
k n j k i k n j i k ki n
y hu d+
+ + + + −= +
= +∑Model
spwf
spG
p
q
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Multilayer Reservoir Control Model
MPCController
MPCController
o
w
g
qqq
Reservoir(Simulator)Reservoir
(Simulator)
EmpiricalModel
EmpiricalModel
wfp,
,
,
o sp
w sp
g sp
qqq
oq∆+
-
+
d
PLS Impulse IdentificationPLS Impulse Identification
Linear ProgrammingOptimizer
Linear ProgrammingOptimizer
Optimization Layer
Regulatory Layer
Upper optimization layer passes the best operating point to lower layer
Net Present ValueFunction
Net Present ValueFunction Reservoir ForecastsReservoir Forecasts
Information
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Total Liquid Rate, BPD
Reservoir Performance
Dow
n ho
le F
low
ing
Pres
sure
, ps
ia
Linear Optimization Problem
ql,max
VLP 2: fw,min +pTHP,min
pwf,min
pwf,max
ql,min
1
3
2
4
VLP 1: fw,min +pTHP,max
VLP 3: fw,max +pTHP,max
VLP 4: fw,max +pTHP,min
fw
2
pthp
( ) ( )( )1 365
1
1k
k k k k k k kN o o g g wp wp wi wi k T F
k Tk
q P q P q C q C T I C rNPV
i⋅∆
=
⎡ ⎤+ − − ∆ − − −⎣ ⎦=+
∑
( ), , 1
max , , ,$,o w g
N
o w gq q qf q q q T⎧ ⎫= ∆⎨ ⎬
⎩ ⎭∑NPV
Best operating point (LP) problem subject to well constraints
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Injector-producer Management Problem Results
Base Case No control
• Early water irruption reduced • High water cut reduced well’s vertical lift• Further recovery possible at a greater cost
Self Learning Case
• Water irruption detected and controlled • Zone shut off permitted better well’s vertical lift• Recovery accelerated at a minimum cost
Experimental Base: History-matched Model from El Furrial, HPHT, deep onshore, light oil
The self-learning cased permitted less water and more oil produced
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Field-wide life cycle comparison ResultsClear benefits from extra little oil but with a lot less effort.
Oil rate Oil Cumulative
Wp, Produced Water Cumulative
Water rate
Self-Learning
Non-Controlled
Self-Learning
Non-Controlled
Self-Learning
Non-Controlled
-78%
-55%
∆Np=500 Mbbls
∆Rev=$5 Million
∆Wp= -18 MMbbls∆Wi= -19 MMbbls
∆Rev= -$92.5 Million
5%
Wp Controlled
WpNon controlled
Winj Non controlled
Winj Controlled
Winj, Injected Water Cumulative
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New Self-learning Reservoir Management TechniqueContinuous self-learning optimization decision engine
,o optq
1 1,k kp q+ +
Reservoir Simulator
Reservoir Simulator
ModelIdentification
ModelIdentification
( )
( )( )
1
1
2
, 1
1, , 1
1
LS Optimization Loopˆˆ
min
, ... , ,...
, ... , ,...
k k
k k
ia b i
k ko g w T T
k kres n T T
q f p p q q
p f p p q q
−
−
∞
=
−
−
+
⎧ ⎫⇒⎨ ⎬
⎩ ⎭⎧ =⎪⇔ ⎨
=⎪⎩
∑-1T
Y = Xθ e
e X X XY
Reservoir ValueOptimization
Reservoir ValueOptimization
Measure
Interpret
( )
{
, , 1
min , max
min max
, , ,
LP Optimization Loop
max , , ,$,
s.t.
ˆ ˆ ˆ, ,
o w g
N
o w gq q q
k p k
k p
o opt g opt w opt
f q q q T
p p p
q q q
q q q
+
+
⎧ ⎫= ∆⎨ ⎬
⎩ ⎭≤ ≤⎧⎪
⎨ ≤ ≤⎪⎩
⇔
∑NPV
Optimize
ControlImplementation
ControlImplementation Control
Physical System
Set point
Set point
| |1
ˆˆn N
k n j k i k n j i k ki n
y hu d+
+ + + + −= +
= +∑
( )
[ ][ ]
[ ]
2 2
1 1
min | max
min | max
| 1|
QP Optimization Loop
ˆmin
. .ˆ ; 1,
; 1,
; ,
p mSP
k j k ju j j
k j k
k j k
k i k k m k
y y R u
s ty y y j p
u u u j m
u u i m p
+ +∆= =
+
+
+ + −
⎧ ⎫− + ∆⎨ ⎬
⎩ ⎭
≤ ≤ =
≤ ≤ =
= =
∑ ∑
Model
spwf
spG
p
q
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Summary & Conclusions
• Novel multilevel self adaptive reservoir performance optimization architecture– Upper level calculates the optimum operating point– Based on NPV– Optimum set point passed to underlying level
• Feasibility of the method demonstrated through a case study– Reservoir performance continuously optimized by an
adaptive self-learning decision engine– Method capitalizes on available remotely actuated devices
• Algorithm feasible for downhole implementation– Impart intelligent to downhole and surface actuation devices
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Acknowledgement
• Research work was done under the guidance of Dr. Michael J. Economides and Dr. Michael Nikolaou at the University of Houston
• Research partially funded by PDVSA and Cullen College of Engineering Research Foundation at the University of Houston
• Academic access to software technology: EPS, Stonebond Technologies, KBR’s Advanced Process Control framework.