Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 1 Petro-Canada Our UK Investment Story A Practical Technique for.

1Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005

Petro-CanadaOur UK Investment Story

A Practical Technique for Estimating a A Practical Technique for Estimating a Probabilistic Range of Production Forecasts Probabilistic Range of Production Forecasts Based on Reservoir Simulation Sensitivity Based on Reservoir Simulation Sensitivity StudiesStudies

Paul Armitage, Petro Canada

28 – 29 April, 2005


Talk OutlineTalk Outline

IntroductionIntroduction

Problem to be AddressedProblem to be Addressed

TheoryTheory

A Simple ExampleA Simple Example

MethodologyMethodology

Applicability & LimitationsApplicability & Limitations

Example Field A Example Field A

Example Field BExample Field B

Summary & ConclusionsSummary & Conclusions


IntroductionIntroduction

How many times have you had to……How many times have you had to…… Produce production forecasts before analysis complete?Produce production forecasts before analysis complete?

Provide facilities engineers with throughputs and other constraints before Provide facilities engineers with throughputs and other constraints before

your analysis has barely begun?your analysis has barely begun? Wished your simulation models would run quicker?Wished your simulation models would run quicker?

Well,…………….Well,…………….

Your problems aren’t over……………..Your problems aren’t over……………..

But here’s a strategy for arriving at some reasonably robust But here’s a strategy for arriving at some reasonably robust estimates maybe a little quickerestimates maybe a little quicker


What’s the Problem?What’s the Problem?

Simulation StudiesSimulation Studies Many sensitivity casesMany sensitivity cases

Consolidation / estimation of range difficultConsolidation / estimation of range difficult

Large investment needed to cover range fully Large investment needed to cover range fully

Technique to estimate P90 – P50 – P10Technique to estimate P90 – P50 – P10 StraightforwardStraightforward

Reduces simulation casesReduces simulation cases

Judgment still neededJudgment still needed

““Fit-for-purpose”Fit-for-purpose” You have to know what your purpose is first!You have to know what your purpose is first!


““Theory”Theory”

Take a look in the England & Wales National Take a look in the England & Wales National

Curriculum for GCSE MathsCurriculum for GCSE Maths

Or a Maths GCSE Revision GuideOr a Maths GCSE Revision Guide

Relative Frequency or “Experimental Probability”Relative Frequency or “Experimental Probability”


A Simple Example A Simple Example (1)(1)

Two dice thrown together – Two dice thrown together –

sum the dotssum the dots What are the possible What are the possible

outcomes?outcomes?

And what are their And what are their

probabilities?probabilities?

113636

1/36 = 0.021/36 = 0.027777111212

2/36 = 0.05552/36 = 0.0555221111

3/36 = 0.08333/36 = 0.0833331010

4/36 = 0.11114/36 = 0.11114499

5/36 = 0.13885/36 = 0.13885588

6/36 = 0.16666/36 = 0.16666677

5/36 = 0.13885/36 = 0.13885566

4/36 = 0.11114/36 = 0.11114455

3/36 = 0.08333/36 = 0.08333344

2/36 = 0.05552/36 = 0.05552233

1/36 = 0.021/36 = 0.0277771122

ProbabilityNo. of waysNo. of dots


A Simple Example A Simple Example (2)(2)

Or we could estimate probability in an experimentOr we could estimate probability in an experiment Throw the dice N times (N trials)Throw the dice N times (N trials)

Tally the no. of times each total occursTally the no. of times each total occurs

The greater N, the nearer to the actual probability the results The greater N, the nearer to the actual probability the results

should beshould be


A Simple Example: A Simple Example: Tabulated ResultsTabulated Results

1111100110013636

0.0250.0250.00000.00002525001212

0.0450.0450.08330.08334545331111

0.0980.0980.11110.11119898441010

0.1080.1080.05550.05551081082299

0.1560.1560.19440.19441561567788

0.1460.1460.19440.19441461467777

0.1580.1580.19440.19441581587766

0.1070.1070.05550.05551071072255

0.0790.0790.02770.027779791144

0.0570.0570.05550.055557572233

0.0220.02772212

Frequency

N = 1001

Relative

N = 36

No of ways

N = 1001

No. of ways

N = 36

No. of dots


A Simple Example: A Simple Example: Graphical RepresentationGraphical Representation

0

0.05

0.1

0.15

0.2

0.25

2 3 4 5 6 7 8 9 10 11 12

Sum of the throw of two dice

Rel

ati

ve

Fre

qu

ency

/ P

rob

abil

ity

(fra

ctio

n)

Relative frequency (1001 trials)Relative frequency (1001 trials)Relative frequency (36 trials)Relative frequency (36 trials)TheoreticalTheoretical


A Simple Example:A Simple Example:A More Familiar Graphical Representation?A More Familiar Graphical Representation?

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2 3 4 5 6 7 8 9 10 11 12


1-R

elat

ive

Fre

qu

en

cy o

r1-

Cu

mu

lati

ve P

rob

abil

ity

(fra

ctio

n)

Relative frequency (1001 trials)Relative frequency (1001 trials)Relative frequency (36 trials)Relative frequency (36 trials)TheoreticalTheoretical


Simple Example to Oil & Gas FieldsSimple Example to Oil & Gas Fields

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2 3 4 5 6 7 8 9 10 11 12


1-R

elat

ive

Fre

qu

en

cy o

r1-

Cu

mu

lati

ve P

rob

abil

ity

(fra

ctio

n) P90P90

P50P50P10P10

= 4= 4= 8= 8= 11= 11


Simulation results

Simulation results

MethodologyMethodology

Assign probability to

cases

Volumetric cases

simulated?

Build experimental

probability curve

Examine sensitivity to prob.

assumptions

Assign profiles from deterministic

cases

P90–P50–P10 to design /

economics

$$

No

Yes

Estimate Min-ML-Max

recovery factor

Confirm Min-ML-Max

volumetrics

Monte Carlo HCIIP & RF


Applicability & LimitationsApplicability & Limitations

Lack of (mathematical) rigourLack of (mathematical) rigour

ExtrapolationExtrapolation

Used so farUsed so far Small fieldsSmall fields

Pre-development decisionsPre-development decisions

Are there applications where inappropriate?Are there applications where inappropriate?


Field AField A


Field A: Field A: Probability TreeProbability Tree

LARGELARGEMODERATEMODERATE

NONENONE

000

000

000

SEALSEAL


NONENONE

13.37713.10412.831

0.0040.0150.001

0.05350.19660.0128

LEAKLEAK


NONENONE

000

000

000

SEALSEAL


NONENONE

44.49927.30021.294

0.0160.0600.004

0.71201.63800.0852

LEAKLEAK


NONENONE

10.1019.5558.736

0.00720.02700.0018

0.07270.25800.0157

SEALSEAL


NONENONE

14.46913.65012.831

0.01680.06300.0042

0.24310.86000.0539

LEAKLEAK


NONENONE

31.39521.02118.837

0.02880.10800.0072

0.90422.27030.1356

SEALSEAL


NONENONE

30.03023.20520.475

0.06720.25200.0168

2.01805.84770.3440

LEAKLEAK


NONENONE

12.28512.01211.875

0.01080.04050.0027

0.13270.48650.0321

SEALSEAL


NONENONE

13.10412.28511.875

0.00120.00450.0003

0.01570.05530.0034

LEAKLEAK


NONENONE

15.01515.01515.015

0.04320.16200.0108

0.64862.43240.1622

SEALSEAL


NONENONE

29.48423.47820.202

0.00480.01800.0012

0.14150.42260.0242

LEAKLEAK

OUTOUT

OIL-FILLEDOIL-FILLED

OUTOUT


OUTOUT


VERTICAL BARRIERVERTICAL BARRIER

2 CHANNEL2 CHANNEL

CONTINUOUSCONTINUOUS

AQUIFERAQUIFERSUPPORTSUPPORT

OILOILRECOVEREDRECOVERED

PROBABILITYPROBABILITY Pxoil rec.Pxoil rec.(MMstb)(MMstb)

BARRIERSBARRIERSGOCGOCMODELMODEL

1.0000 20.3000


Field A:Field A:Cumulative Relative FrequencyCumulative Relative Frequency

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 5 10 15 20 25 30 35 40 45 50

Oil Recovered (MMstb)

1-C

um

ula

tive

Pro

bab

ilit

y (f

ract

ion

)

P90P90MeanMean

P50P50MLML

P10P10

= 13 MMstb= 13 MMstb= 20 MMstb= 20 MMstb= 21 MMstb= 21 MMstb= 23 MMstb= 23 MMstb= 30 MMstb= 30 MMstb


MethodologyMethodologySimulation

resultsSimulation

results

Assign probability to

cases

Volumetric cases

simulated?

Build experimental

probability curve

Examine sensitivity to prob.

assumptions

Assign profiles from deterministic

cases

P90–P50–P10 to design /

economics

$$

No

Yes

Estimate Min-ML-Max

recovery factor

Confirm Min-ML-Max

volumetrics

Monte Carlo HCIIP & RF


Field BField B

Single structural model simulatedSingle structural model simulated

Min – ML – Max HCIIP estimated in static modellingMin – ML – Max HCIIP estimated in static modelling

Simulation Sensitivity StudySimulation Sensitivity Study Relative PermeabilityRelative Permeability

PVTPVT

Permeability and its distributionPermeability and its distribution

etc.etc.

Various recovery factorsVarious recovery factors Estimate range and distributionEstimate range and distribution

Min – ML – max; triangularMin – ML – max; triangular

P90 – P50 – P10; normalP90 – P50 – P10; normal


Field B:Field B:Range of RecoveryRange of Recovery

-30 -20 -10 0 10 20 30 40

STOIIP hiSTOIIP hi

STOIIP loSTOIIP lo

homo khomo k

k-phik-phi

Sorw loSorw lo

Sorw hiSorw hi

oil viscosityoil viscosity

krw'krw'

Difference in Ultimate Recovery from Base Case (MMstb)


Field B:Field B:Probabilistic Range of RecoveryProbabilistic Range of Recovery

Monte Carlo methodMonte Carlo method Statistical sampling technique to approximate solutions to Statistical sampling technique to approximate solutions to

quantitative problemsquantitative problems

2 or more variables2 or more variables

Specialist oil industry software or spreadsheet add-ins.Specialist oil industry software or spreadsheet add-ins.

““Monte Carlo Concepts, Algorithms and Applications” by Monte Carlo Concepts, Algorithms and Applications” by

George S. FishmanGeorge S. Fishman

www.riskglossary.com/articles/monte-carlo-method.htmwww.riskglossary.com/articles/monte-carlo-method.htm


Field B:Field B:Input to Monte Carlo CalculationInput to Monte Carlo Calculation

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30 35 40 45 50

Recovery Factor (%)

Pro

bab

ilit

y o

r (1

00-C

um

ula

tive

Pro

bab

ilit

y)

(%)

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300

STOIIP (MMstb)

Pro

bab

ilit

y o

r (1

00-C

um

ula

tive

Pro

abab

ilit

y)

(%)

350


Field B:Field B:Cumulative Relative FrequencyCumulative Relative Frequency

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100 120 140 160

Ultimate Oil Recovery (MMstb)

Pro

bab

ilit

y o

r (1

00 -

Cu

mu

lati

ve P

rob

abil

ity)

(%)


Summary and ConclusionsSummary and Conclusions

Largely empirical method developedLargely empirical method developed Estimate quickly P90 – P50 – P10 recoveries & profiles from a Estimate quickly P90 – P50 – P10 recoveries & profiles from a

relatively small number of simulation casesrelatively small number of simulation cases

Can be extended to combine volumetric HCIIP ranges derived Can be extended to combine volumetric HCIIP ranges derived

independently of simulation with simulation resultsindependently of simulation with simulation results

Important to exercise judgement throughout processImportant to exercise judgement throughout process

Critical that consensus developed if probabilities are to be Critical that consensus developed if probabilities are to be

assigned to different simulation sensitivitiesassigned to different simulation sensitivities

Technique has been used successfully for development decisions Technique has been used successfully for development decisions

with respect to marginal fieldswith respect to marginal fields

Is there a limit to the technique’s applicability? If so, what is it?Is there a limit to the technique’s applicability? If so, what is it?


Summary and Conclusions: Summary and Conclusions: Field AField A

0

5000

10000

15000

20000

25000

30000

35000

Dai

ly D

ry O

il P

rod

uct

ion

(st

b)

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600

Time (Days)

Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 1 Petro-Canada Our UK Investment Story A Practical Technique for.

Documents

precise production forecasting

improved portfolio management

frequency n

relative n

trials relative frequency

experimental probability

dice n times n trials

trials theoretical slide