self-learning reservoir management 2004-10-21

8/4/2019 Self-learning Reservoir Management 2004-10-21

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SELF-LEARNING RESERVOIR MANAGEMENT

SPE 84064

L. Saputelli1,2,3, M. Nikolaou2, and M. J. Economides2,31PDVSA, 2University of Houston, 3SPE member

PRH 034 - Formao de Engenheiros nas reas de Automao, Controle, e Instrumentao do Petrleo e Gs -aciPG, participante do Programa de Recursos Humanos da ANP - Agncia Nacional do Petrleo - para o setor

Petrleo e Gs - 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 productionissues regarding real time decision making

and, To present the results of a continuous self-

learning optimization strategy to optimize

field-wide productivity while satisfyingreservoir physics, production and businessconstraints.


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The Reservoir Management Challenge

Reservoir Management is about a careful orchestration of technology, people & resources

InjectionFacilities

Compression &Compression &Treatment PlantsTreatment PlantsProductionProductionWell & FacilitiesWell & Facilities

DrainageDrainage

AreaArea

Drill, build & OperateDrill, build & Operate

SubsurfaceCharacterizationSubsurfaceCharacterization Update ModelUpdate Model

ControlControl

MonitorMonitor

Establish or reviseOptimum PlanEstablish or reviseOptimum Plan

Exploitation PlanWell location & numberRecovery mechanismSurface facilitiesWell intervention


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Motivation

Traditional Problems

Complex & 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 Approach

More 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 systemused to continuously

optimize three-phase fluid migration in a multi-layeredreservoir

A data-driven modelthat is continuously updated

with collected production data.

A self-learning and self-adaptive engine predicts thebest operating pointsof a hydrocarbon-producing

field, while integrating subsurface elements surfacefacilities 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

In jec t or - Producer Prof i le Mngt .In jec t or - Producer Prof i le Mngt . Field-Wide Mana gem entField -Wide Manag em ent

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

WellModel

ReservoirModel

BusinessModel

SurfaceModel

DataCollection

ExploitationOptions

BusinessConstraints

DecisionMaking

Optimization

12

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 p

p p

p c p

k Sc p Z

g t

=

K g

( )0

cc

t

+ =

v

rp

p p

p c

kp Z

g

=

p

K gv

p p pW

M p

A x S SMc

V A x

= = =

Molar density in terms of Porous Volumes

Continuity

Equation

Multiphase Darcys Law

Pressure Laplacian as a function of the saturation change

yi-1

yi+1yi zi+1

zi-1

zi

Spatial distribution of pressure as a time function of saturation

This realization is not used in thisresearch, since it requires theknowledge of parameters that cannotbe directly measured


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Reservoir Modeling: Flow through Wellbore

Radial Diffusivity Equation

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

2

2

1

( )f

K p p p

c c r r r t

+ =

+ re

rwh k

pwf

pe

rs( )

2

,4 4

ti i

c rq p r t p E

kh kt

=

General Solution given by Exponential Integral

2

4ln4

wf i

t w

q ktp p kh c r

=

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 s

=

+

Steady-state Equation for the Undersaturated Oil-Flow

Inflow Performance (IPR) for Saturated reservoirs2

*

, 1 0.2 0.81.8

wf wf bo o b

b b

p pp Jq q

p p

= +

( )

( )

( )

2

0 1 2 3

2

0 1 2 3

2

0 1 2 3

k k k k

o e wf wf

k k k k

w e wf wf

k k k k

g 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 Modeling

Average Reservoir Pressure is a function of net mass production

( ) ( )

( ) ( ) ( )

0 1 2 3 4

1 2 3 4

2 211

0 1 2 1 3 1 5 2 6 2

, , , p p p e

o w g wi

o w g wi

k k kk k k k

wf wf wf wf t

f p t g N G W W

p a a q a q a q a q

d pb q b q b q b q

dt

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 kk k k k

wf wf wf wf p 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

E

E

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 5000

Pressure (psia)

Depth(ft)

1,000 STB/D @ 500 SCF/STB; WOR=1

1,000 STB/D @ 1000 SCF/STB; WOR=1

1,000 STB/D @ 500 SCF/STB; WOR=0

1,000 STB/D @ 1000 SCF/STB; WOR=0

Vertical flow as non-linear functions of flow rates

220

f

s

c c c

f u dLdp udu gdz dW

g g g D+ + + + =

Mechanical Energy Equation

2

2

1 2

2

2

f

c c c

f u dLg p p p z u

g g g D

= = + +

Single-Phase Solution, Incompressible

( )( )22

10 5

2144

7.413 10

m cu gdp fm

dz zD

= + +

&

Two-Phase Solution, Hagerdorn & Brown (1965)

( ) ( ) ( ) ( )2 2 2

1 2 3 4 5 6

kk k k k k k k

wf 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, Krs

Multiphase Flow: qo, qw, gq

Tubing Head Pressure: pTHP

Tubing Head Temperature: TTHT

Zone Multiphase Flow: qo, qw, gq

Solid Production, Water Analysis

Solvent Injection

Gas Lift

ESP Speed

Water Injection

Heat Injection

Gas Injection

Flow Choke

Zone 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 k

o e w f wf

k k k k

w e wf wf

k k k k

g 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

koe

kkwwf

k

g k

wf

q a a a ap

q b b b bp

q c c c cp

=

Recursive self-adaptive identification

,o optq

1 1,k kp q+ +ReservoirSimulator

ReservoirSimulator

ModelIdentification

ModelIdentification

Reservoir Value

Optimization

Reservoir Value

Optimization

Measure

Interpret

Optimize

ControlImplementation


Control

Physical System

Set point

Set point

| |

1

n N

k n j k i k n j i k k

i n

y h u d +

+ + + + = +

= +Model

sp

wf

sp

G

p

q

( )

( )( )

1

1

2

,1

1, , 1

1

LS Optimization Loop

min

, ... , ,...

, ... , ,...

k k

k k

N

ia b

i

k ko g w T T

k k

res n T T

q f p p q q

p f p p q q

=

+

= =

-1

T T

Y = X e

e X X X Y


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Example for Model Identification and Block Diagram

Reservoir Pressure: P

Oil Rate: qoProducer Flowing Pressure, pwf1

Inputs (U)

Water Fraction: fw

qwinj qo

Water Injection Rate: qwi

Outputs (Y)

u1

u2

y1y2

y3y4y5y6

Injector Flowing Pressure, pwf2

Gas Rate: qg

Water Rate: qw

o

w

g

q

q

qReservoir

(Simulator)Reservoir

(Simulator)

EmpiricalModel

EmpiricalModel

wfp+

d

IdentificationIdentificationEmpirical model whosestructure is determinedby first principles


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Model Identification Experimental Set-up

Reservoir

NumericalModel

Generate

DataFile

Run

SummaryFile

Convert

EclipseTo Excel

Run

Eclipse

Run

Matlab

Read

ExcelFile

AutoScale

cumsum(A)diff(A)

Select Inputand Outputs

Split DataTest & Pred

x,y

Subspace

Identification

Neural

Network

Plot RscCalculated

& Measured

Rescale

ParametersFIR PLS

Windows and Eclipse Environment

Matlab Environment Level

0

1

x

=

= U,Yc d

A , AA

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 Control

At time kfuture predictions of the output ycan be made as

| | |

1 1

wheren N n N

k n j k i k n j i k k k k k i k i

i n i n

y h u d d y h u+ +

+ + + + = + = +

= + =

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|

m in

. .

1, ,

1, ,, , 1

p mS P

k n j k k j k

j j

k n j k

k j k

k i k k m k

y y R u

s t

y y y j p

u u u j mu u i m p

+ + + = =

+ +

+

+ +

+

=

= = =

L

L

L


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Example for Control and Block Diagram

Reservoir Pressure: P

Oil Rate Layer 1: qo1Producer Flowing Pressure, pwf1

Inputs (U)

Water Rate Layer 1: qw1

qwinj qoT

Water Injection Rate: qwi

Outputs (Y)

u1

u2

y1

y2y3y4y5y6

Injection Flowing Rate, qwinj u3

Producer Flowing Pressure, pwf2

Oil Rate Layer 2: qo2

Water Rate Layer 2: qw2

Layer 1, kh1

Layer 2, kh2

MPC

Controller

MPCController

o

w

g

q

q

q

Reservoir(Simulator)Reservoir

(Simulator)

EmpiricalModel

EmpiricalModel

wfp

,

,

,

o sp

w sp

g sp

q

q

q

oq+

-

+

d

PLS ImpulseIdentificationPLS ImpulseIdentification


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Model Predictive Control Response

MPC minimizes future prediction error by satisfying input constraints


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New Self-learning Reservoir Management Technique

Continuous self-learning optimization decision engine

,o optq


ReservoirSimulator

ModelIdentification

ModelIdentification

Reservoir Value

Optimization

Reservoir Value

Optimization

Measure

Interpret

( )

{

, ,1

min , max

min max

, , ,

LP Optimization Loop

max , , ,$,

s.t.

, ,

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



Control

Physical System

Set point

Set point

| |1

n N


i n

y h u d +

+ + + + = +

= +Model

sp

wf

sp

G

p

q


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Multilayer Reservoir Control Model

MPCController

MPCController

o

w

g

q

qq

Reservoir(Simulator)Reservoir

(Simulator)

EmpiricalModel

EmpiricalModel

wfp

,

,

,

o sp

w sp

g sp

q

q

q

oq+

-

+

d

PLS ImpulseIdentificationPLS ImpulseIdentification

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 Forecasts

Reservoir Forecasts

Information


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Total Liquid Rate, BPD

ReservoirPerformance

DownholeFlowingPressure

,psia

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 k N

o o g g wp wp wi wi k T F

k Tk

q P q P q C q C T I C r

NPVi

=

+

=+

( ), ,

1

max , , ,$,o w g

N

o w gq q q

f 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 wells vertical lift Further recovery possible at a greater cost

Self Learning Case

Water irruption detected and controlled Zone shut off permitted better wells 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 Results

Clear 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 MMbblsWi= -19 MMbbls

Rev= -$92.5 Million

5%

Wp Controlled

WpNonc

ontrolled

WinjNoncontrolled

Winj Controlled

Winj, Injected Water Cumulative

C


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New Self-learning Reservoir Management Technique

Continuous self-learning optimization decision engine

,o optq


ReservoirSimulator

ModelIdentification

ModelIdentification

( )

( )

( )

1

1

2

,1

1

, , 1

1

LS Optimization Loop

min

, ... , ,...

, ... , ,...

k k

k k

ia b

i

k k

o g w T T

k k

res n T T

q f p p q q

p f p p q q

=

+

=

=

-1

T

Y = X e

e X X XY

Reservoir Value

Optimization

Reservoir ValueOptimization

Measure

Interpret

( )

{

, ,1

min , max

min max

, , ,

LP Optimization Loop

max , , ,$,

s.t.

, ,

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



Control

Physical System

Set point

Set point

| |1

n N


i n

y h u d +

+ + + + = +

= +

( )

[ ]

[ ]

[ ]

22

1 1

min | max

min | max

| 1|

QP Optimization Loop

min

. .

; 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 t

y y y j p

u u u j m

u u i m p

+ +

= =

+

+

+ +

+

=

=

= =

Model

sp

wf

sp

G

p

q


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Summary & Conclusions

Novel multilevel self adaptive reservoir performanceoptimization 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 atthe University of Houston

Research partially funded by PDVSA and CullenCollege of Engineering Research Foundation at the

University of Houston

Academic access to software technology: EPS,

Stonebond Technologies, KBRs Advanced ProcessControl framework.

self-learning reservoir management 2004-10-21

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