Control Optimization of Oil Production under Geological Uncertainty

¹´²´³Agus Hasan, ²´³Bjarne Foss,¹´³Jon Kleppe

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¹Department of Petroleum Engineering, NTNU²Department of Cybernetics Engineering, NTNU

³Center for Integrated Operations in Petroleum Industry

Nordic Process Control Workshop 2009Porsgrunn, Norway29-30 January 2009

Outline

04/19/23 NPCW 2009NTNU

Objectives and Motivations Closed-loop Reservoir Management Case Study Part 1 Optimization

Optimization MethodsReservoir Control StructureBinary Integer ProgrammingOptimization Results

Part 2 UncertaintyGeological UncertaintyHistory MatchingResults

Conclusions and Recomendations

Objectives and Motivations

• Efficient: Fast enough• Accurate• Robust• Applicable: can be used in practical way

Which optimization method should we choose in our problem?

Objective function: Net Present Value (NPV)

injProd, ,

, ,1 1 1

, , , ,

1n

n n NNNo o j w o j n

w inj inj itn j i

r q x u m r q x u mNPV r q

b

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.

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Closed-Loop Reservoir Management

Production System

(Reservoir, Well)

Reservoir Simulator

Optimization

Optimization

Calc.NPV

Data

Identification and Updating

Identification and Updating

Control andOptimization

GeologicalUncertainty

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Case StudyGrid cells : 45 x 45 x 1 = 2025

2-phases : Oil-Water

Assumptions:

1 Injector and 1 Producer well

Each well was divide into 45 segments

Each segments was modeled as a separated “smart well”

No flow boundaries

Incompressible and Immiscible fluids flow

No capillary pressure

No gravity effect

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(Brouwer 2004)

Initial Data• 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

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Mass balance

Darcy’s Law

Saturation Equation

Pressure Equation

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 ControlDelay water breakthrough

Binary Integer Programming (BIP)On-off valves setting

min

.

0,1

T

xc x

s t

A x b

x Z

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Reservoir Control Structure

0 200 400 600 800 [days]

Start Finish

45 well segment aggregated into 9 control segments. Allow one segmentto 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

1 Open

0 Closed

z

z

1

9

z

z

z

1

9

o

o

o

q

Q

q

1 98 9z z

Constrain:

max

. .

To

zz Q

s t

Az b

min

. .

To

zz Q

s t

Az b

1 1 1

1 1 1A

9

8b

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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

Mathematical model (linear model) Measurement devices (well loging, surface facilities, etc) Reservoir geology (porosity, permeability, fault, etc)

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EnKF Bayesian Inversion History matching etc.

Origins:

Treatments:

Geological UncertaintyPermeability Realizations

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History Matching (Using 200 day production data)

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History Matching (Cont’d)

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”True” permeability fields Selected permeability fields from ”Realizations”

”True” saturation profile (200 days) Saturation profile from ”Realizations” (200 days)

Unit in million USD

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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 %

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Results (Cont’d)Saturation profile without Uncertainty (800 days)

Saturation profile with Uncertainty (800 days)

Conclusions A new production optimization technique has been presented.Optimization proces based on Binary Integer Programming has beensuccesfuly applied and gives improvement in Net Present Value. BinaryInteger Programming gives more benets in the sense of NPV improvementthen regular Reactive or Proactive Control. Binary Integer Programming is a robust optimization technique undergealogical uncertainty such as permeability distribution. The optimizationprocess also showed that water saturation at breakthrough was observed tobe more uniformly distributed across the reservoir after the optimizationprocess as compared with the unoptimized case. The scope for improvement depends on the type of heterogeneity in thepermeability field. Because the NPV performance of the optimal waterflood depends less on geological features than that of a conventional waterflood, the scope for improvement partly depends on the performance ofthe conventional water flood. The scope for improvement depends on the relative magnitudes of the oilprice 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 notinvestigated in this study.

Results obtained in this study may therefore only be representativefor situations were gravity and capillary effects are relatively small. Gravity maypositively or negatively affect the sweep efficiency. The scope for improvement andthe shape of the optimal control functions may thus change if capillary or gravityforces are signicant. Therefore, their exact effects should be investigated.

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