Closed Loop Reservoir Management

SPE Golden Gate Section, 8 December 2010 1

Closed-loop reservoir management

Jan-Dirk Jansen

Delft University of TechnologyDepartment of Geotechnology

Cox visiting professorStanford UniversityDepartment of Energy Resources Engineering


Closed-loop reservoir management a.k.a. Smart Fields, i-Fields, e-Fields, etc.

Jan-Dirk Jansen

Delft University of TechnologyDepartment of Geotechnology

Cox visiting professorStanford UniversityDepartment of Energy Resources Engineering


Delft University of Technology

Founded 184216000 students2700 scientific staff250 PhDs/yr8 faculties

Faculty of Civil Engineering and Geosciences – Department of Geotechnology

http://beeldarchief.fd.tudelft.nl/ipsearch/gallery_detail.asp?mmobject_id=14102






Closed-loop reservoir management - Project history

Controllable

input

Data

assimilationalgorithms

Low-order modelswith or w/o physics High-order

modelsup/downscaling

Geology, seismics,well logs, well tests,fluid properties, etc.

Noise OutputInput NoiseSystem (reservoir, wells

& facilities)

Optimizationalgorithms Sensors

2000: Smart wells

Shell:We have those new toys. How can we use them?

2001: TUD - optimal control

2004: CLoReM workshop with Stanford

2010: Recovery FFactory (Shell)

2005: ISAPP 1 (TNO, TUD, Shell)

2003: VALUE project subsidized

2002: Shell launches Smart Fields

2010: ISAPP 2 (TNO,ENI, …)



• Hypothesis: recovery can be significantly increased by changing reservoir management from a ‘batch-type’ to a near-continuous model-based controlled activity

• Key elements:• Optimization under physical constraints and

geological uncertainties• Data assimilation aimed at continuous updating of

system models

• Inspiration:• Measurement and control theory• Meteorology and oceanography



Dataassimilationalgorithms


& facilities)


System models

Predicted output Measured output

Controllableinput


Start, 1) Open-loop, 2) Robust, 3) Closed-loop, 4) Hierarchical, 5) Two-level, 6) Systems theory, 7) Conclusions


CLoReM

perspectives

• Geoscience-focused Maximize subsurface knowledgeRelevant for field development planningGeological model(s) at the core

• Production-focusedMaximize financial outcomeRelevant for surveillance and interventionFlow model(s) at the core




& facilities)


System model


Controllableinput


1) Open-loop flooding optimization



Optimization techniques

• Global versus local• Gradient-based versus gradient-free• Constrained versus non-constrained• ‘Classical’ versus ‘non-classical’ (genetic algorithms,

simulated annealing)

• We use ‘optimal control theory’ – local, gradient-based• Has been proposed for history matching (Chen et al.

1974, Chavent et al. 1975, Li, Reynolds and Oliver 2003 ) and for flooding optimization (Ramirez 1987, Asheim 1988, Virnovski 1991, Zakirov et al. 1996, Sudaryanto and Yortsos, 1998, Brouwer et al. 2002, Sarma et al. 2004)


Optimal control theory, summary• Gradient based optimization technique – local optimum• Objective function: NPV or ultimate recovery• Controls: injection/production rates, pressures or valve

openings (102 to 103 control variables, 104 – 106 states )• Gradients of objective function with respect to controls

obtained from ‘adjoint’ equation (implicit differentiation) • Results in dynamic control strategy, i.e. controls change

over time• Computational effort independent of number of controls• Rate and pressure constraints (path constraints) not

trivial; various techniques used: GRG, augmented Lagrangian, Zoutendijk’s method, constraint lumping


12-well example

• 3D reservoir• High-permeability channels• 8 injectors, rate-controlled• 4 producers, BHP-controlled• Production period of 10 years• 12 wells x 10 x 12 time steps gives 1440 optimization parameters

• Optimization of monetary value Van Essen et al., 2006

( ) ( ) ( )

( )

, , ,1 1

1 1

inj prod

k

N N

wi wi i wp wp j o o jK k k ki j

k ktk

r u r y r yJ J t

b τ

= =

=

⎧ ⎫⎡ ⎤× + × + ×⎪ ⎪⎣ ⎦⎪ ⎪= Δ⎨ ⎬⎪ ⎪+⎪ ⎪⎩ ⎭

∑ ∑∑


Run animation 1


Why this wouldn’t work

• Real wells are sparse and far apart• Real wells have more complicated constraints• Field management is usually production-focused• Long-term optimization may jeopardize short-term profit• Production engineers don’t trust reservoir models anyway

• We do not know the reservoir!


2) Robust open-loop flooding optimization



& facilities)


System models


Controllableinput




Robust optimization example

• 100 realizations• Optimize expectation of objective function

Van Essen et al., 2006

( )1:

1: 1:1

1max , ,r

K

Ni

K K iir

JN =∑u

y u θ


Robust optimization results

3 control strategies applied to set of 100 realizations:reactive control, nominal optimization, robust optimization



3) Closed-loop flooding optimization



& facilities)


System models


Controllableinput




Computer-assisted history matching (data assimilation, parameter estimation)

• Very ill-posed problem: many parameters, little info

• Variational methods – minimization of mismatch

• Ensemble Kalman filtering – sequential methods

• Reservoir-specific methodsStreamline-based sensitivitiesGradual deformation Probability perturbation

• ‘Non-classical’ methods – simulated annealing, GAs, …

• Monte Carlo methods – MCMC with proxies

• We use Ensemble Kalman filtering (sequential assimilation)


Closed-loop –

example 1 Ensemble updates at different times


Virtual asset model



& facilities)


System models


Controllableinput



Closed-loop –

example 1 NPV and contributions from water & oil production

1 2 3 4 5 68.5

9

9.5

10

10.5x 107

NPV, $

1 2 3 4 5 6-2

-1.5

-1.0

-0.5

0

Dis

coun

ted

wat

er c

osts

, $

1 2 3 4 5 68.5

9

9.5

10

10.5x 107

Dis

coun

ted

oil r

even

ues,

$

reactive

open-loop

1 month 1 year 2 years 4 years


110 x 110 grid blocks

10 inj. segments (x)

10 prod. segments (o)

1100 m

1100 m

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Closed-loop optimization –

example 2 Virtual asset



example 2 Results

Saturation for conventional waterflooding.

Saturation for optimized waterflooding with updated permeability field.

Estimated permeability field. [20 – 7000 mD]

Injection rates. The total injection rate is constant and 2600 m3/day

46 days

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

116 days

1

2

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6

7

8

9

10

1

2

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5

6

7

8

9

10

463 days

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

750 days

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

0 days

1

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5

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10

1

2

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9

10



example 2 Permeability estimates

1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

‘True’ permeability field Estimated average permeability field


4) Link with short-term optimization



& facilities)


System models


Controllableinput




Run animation 2


Hierarchical optimization

• Take production objectives into account by incorporating them as additional optimization criteria:

• Formal solution:• Order objectives according to importance• Optimize objectives sequentially• Optimality of upper objective constrains optimization of

lower one

• Only possible if there are redundant degrees of freedom in input parameters after meeting primary objective


Objective function with ridges


Example: Hierarchical optimization using null-space approach (1)

• 3D reservoir• 8 injection / 4 production wells• Period of 10 years • Producers at constant BHP• Rates in injectors optimized

• Primary objective: undiscounted NPV over the life of the field

•Secondary objective: NPV with very high discount factor (25%) to emphasize importance of short term production



20 40 60 80 10024

25

26

27

28

29

30

31

32

Iterations

Net P

rese

nt V

alue

- D

iscou

nted

[M$]

Secondary Objective Function

20 40 60 80 10040

41

42

43

44

45

46

47

48

Iterations

Net

Pre

sent

Val

ue -

Und

iscou

nted

[M$]

Primary Objective Function

50 100 150 20024

25

26

27

28

29

30

31

32

Iterations

Net P

rese

nt V

alue

- D

iscou

nted

[M$]

Secondary Objective Function

50 100 150 20040

41

42

43

44

45

46

47

48

Iterations

Net

Pre

sent

Val

ue -

Und

iscou

nted

[M$]

Primary Objective Function

Optimization of secondary objective function - constrained to null-space

of primary objective

Optimization of secondary objective function - unconstrained

+28.2 %

+28.2 %

-0.3%

-5.0%


0 900 1800 2700 36000

5

10

15

20

25

30

35

40

45

50

time [days]

NPV

ove

r Ti

me

- Und

isco

unte

d [1

0 6 $

]

~~

value of objective function J1 resulting from uθ* .

value of objective function J1 resulting from uθ*

value of objective function J1 resulting from uθ



5) Two-level CLoReM



& facilities)


System models


Controllableinput




• Full cycle of assisted history matching and robust optimization too labor-intensive to apply frequently

• Poor short-term prediction quality of large-scale reservoir model (poor near-well bore modeling)

• Optimal inputs may be difficult to implement in practice• Cultural barriers to use reservoir simulation as a basis

for production-related decisions• Proposed solution: two-level control strategy

• Outer loop to determine optimal ouput trajectory (life-cycle horizon, periodically updated)

• Inner loop to stay close to optimal output (short- term horizon, frequently updated)

• Can be interpreted as ‘disturbance rejection’

Two-level CLoReM

–

motivation & idea


Two-level CLoReM

–

elements

• Model-predictive controller (MPC) to track optimal output

• Data-driven low-order system model

• State estimator (observer)

• Short-term objective function: mismatch between optimal and actual (estimated) output


Optimizationalgorithms

High-ordersystem models



& facilities)

Sensors Low-order

system model

MPCcontroller

Observer

J = |(yopt* - ylo )|2

J = NPV

States & parameters

Statesyopt

ylo


Local grid refinement

Error in main flow direction

Synthetic ‘truth’time step size: 0.25 days

8 injection wells, 4 production wells

High-order system modeltime step size: 30 days

Model errors due to geological uncertainty & undermodeling of fast, local dynamics

Two-level CLoReM

–

example


Low-order modeling (system identification)

Persistently exciting inputs

= Injection rates

&Producer

BHP’s

Virtual asset

System Identification

Subspace model

Liquid production flow

rates


Two-level CLoReM

–

results

500 1000 1500 2000 2500 3000 3500 40000

2000

4000

6000

8000

10000

12000

14000

producer 1

time [days]

liqui

d flo

w ra

te [b

bl/d

ay] reference

open-loopMPC controlled

500 1000 1500 2000 2500 3000 3500 40000

0.5

1

1.5

2

2.5

3

3.5x 104 producer 2

time [days]

liqui

d flo

w ra

te [b

bl/d

ay] reference

open-loopMPC controlled

Small tracking error due to bottom-hole pressure constraint

Small tracking error due to water

break-through in producer 2



6) System-theoretical aspects



& facilities)


Low-ordersystem models


Controllableinput


up/downscaling

High-ordersystem models



1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

Why do such crude models sometimes work so well?

System-theoretical aspects


Observability, controllability, identifiability

Controllability of a dynamic system is the ability to influence the states through manipulation of the inputs.

Observability of a dynamic system is the ability to determine the states through observation of the outputs.

Identifiablity of a dynamic system is the ability to determine the parameters from the input-output behavior.

See Zandvliet et al., Computational Geosciences, 2008, 12

(4) 808-822.

System model

state (p,S)parameters (k,φ,…)

output (pwf ,qw ,qo )input (pwf ,qt )



For our system the (few) identifiable parameter patterns correspond just to the (few) controllable state patterns

Reservoir dynamics ‘lives’ in a state space of a much smaller dimension than the number of model grid blocks

=> Large scope for reduced-order modeling to speed up iterative optimization, history matching


Control-relevant grid-coarsening

• one layer of SPE 10 model Vakili 2010

• 0.0001 < k < 17000 mD• 60 x 220 = 13200 gridblocks• Dominant nr. of Hankel singular values: O(100)

1

2

1

1

2

1


Do we still need geology?


For our system the (few) identifiable parameter patterns correspond just to the (few) controllable state patterns

Reservoir dynamics ‘lives’ in a state space of a much smaller dimension than the number of model grid blocks

=> Large scope for reduced-order modeling to speed up iterative optimization, history matching



Yes, we do need geology!

• Interpreting the history match results requires geological insight

• Well location-optimization requires a geological model

• However, we need to focus on the relevant geology:

Which geological features are identifiable?

Which geological features influence controllability?


CLoReM

–

conclusions so far

• Size of the prize still unknown (open-loop and closed-loop) • Adjoint based-optimization techniques work well; constraints,

regularization, storage, efficiency, still to be improved• Specific data assimilation methods less important than

workflow & human interpretation of results• Many history matching efforts too much focused on history &

models, not on forecast and decisions • Field acceptance of closed-loop approach will require

combination with short-term production optimization• Reservoir dynamics lives in low-order space. Wide scope for

reduced-order, control-relevant modeling



CLoReM

–

current focus areas• Develop workflows for geoscience- and production-focused

CLoReM• Develop means for joint assimilation (production data, 4D

seismics, passive, EM, gravity, etc. • Quantify flow/control/decision-relevant aspects of geology• Continue reduced-order modeling of reservoir flow• Address computational aspects: HPC (infrastructure, multi

run) and physics-based pre-conditioning (link to ROM)• Develop multi-level optimization methods to reconcile

production optimization and reservoir management• Extend to EOR applications (Recovery Factory program)• Develop tools and apply to field cases (ISAPP 2 program)


AcknowledgmentsOkko

Bosgra2

Paul van den Hof2

Arnold Heemink3

Roald Brouwer5

Sippe

Douma5

Marielba

Rojas3

Hans Kraaijevanger5 Rob Arts1,6

Remus

Hanea1,6

Renato

Markovinivić1

Joris

Rommelse1,3

Maarten Zandvliet1,2

Jorn

van Doren1,2

Gijs

van Essen1,2

Justyna

Przybysz1,4

Ali Vakili1

Gosia

Kaleta1,2

Gerben

de Jager1

Maryia

Krymskaya1,2

Mario Trani1

Victoria Lawniczak1,2

1)

TUD –

Geotechnology 2)

TUD –

Delft Institute for Measurement and Control3)

TUD –

Delft Institute for Applied Mathematics4)

TUD –

Applied Physics5

)

Shell International Exploration & Production6)

TNO –

Built Environment and GeosciencesSponsors:• VALUE & ISAPP 1 –

TNO & Shell , ISAPP 2 –

TNO & ENI• Recovery Factory –

Shell• Delphi consortium –

BGP, BP, CGG-Veritas, Chevron, Conoco Phillips, ExxonMobil, Fugro

Jason, Petrobras, Petronas, PGS,

Saudi Aramco, Shell, Statoil, TNO, WesternGeco


www.citg.tudelft.nl/smart

Questions?

http://www.citg.tudelft.nl/smart

Documents

Closed Loop Reservoir Management