1

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

2

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

3

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.

4

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

5

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

6

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

7

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

8

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

9

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

12

3

4

5

6

7

8

9

By collecting data, a digital image is used to make decisions

10

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

11

Reservoir Modeling: Flow through WellboreRadial Diffusivity Equation

Oil, water and gas flow as linear functions of the drawdown pressure

2

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

12

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

13

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

22

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]

15

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

16

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

17

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

18

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

19

Predictions Using Empirical Structured models

20

Errors Using Empirical models

21

Coefficients Using Empirical models

22

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

23

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

24

Model Predictive Control ResponseMPC minimizes future prediction error by satisfying input constraints

25

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

26

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

27

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

28

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

29

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

30

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

31

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

32

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.