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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
2Precise Production Forecasting for Improved Portfolio Management, 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
3Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
4Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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!
5Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
““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”
6Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
7Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
8Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
9Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
10Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
Sum of the throw of two dice
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
11Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
Sum of the throw of two dice
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
12Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
13Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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?
14Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
Field AField A
15Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
Field A: Field A: Probability TreeProbability Tree
LARGELARGEMODERATEMODERATE
NONENONE
000
000
000
SEALSEAL
LARGELARGEMODERATEMODERATE
NONENONE
13.37713.10412.831
0.0040.0150.001
0.05350.19660.0128
LEAKLEAK
LARGELARGEMODERATEMODERATE
NONENONE
000
000
000
SEALSEAL
LARGELARGEMODERATEMODERATE
NONENONE
44.49927.30021.294
0.0160.0600.004
0.71201.63800.0852
LEAKLEAK
LARGELARGEMODERATEMODERATE
NONENONE
10.1019.5558.736
0.00720.02700.0018
0.07270.25800.0157
SEALSEAL
LARGELARGEMODERATEMODERATE
NONENONE
14.46913.65012.831
0.01680.06300.0042
0.24310.86000.0539
LEAKLEAK
LARGELARGEMODERATEMODERATE
NONENONE
31.39521.02118.837
0.02880.10800.0072
0.90422.27030.1356
SEALSEAL
LARGELARGEMODERATEMODERATE
NONENONE
30.03023.20520.475
0.06720.25200.0168
2.01805.84770.3440
LEAKLEAK
LARGELARGEMODERATEMODERATE
NONENONE
12.28512.01211.875
0.01080.04050.0027
0.13270.48650.0321
SEALSEAL
LARGELARGEMODERATEMODERATE
NONENONE
13.10412.28511.875
0.00120.00450.0003
0.01570.05530.0034
LEAKLEAK
LARGELARGEMODERATEMODERATE
NONENONE
15.01515.01515.015
0.04320.16200.0108
0.64862.43240.1622
SEALSEAL
LARGELARGEMODERATEMODERATE
NONENONE
29.48423.47820.202
0.00480.01800.0012
0.14150.42260.0242
LEAKLEAK
OUTOUT
OIL-FILLEDOIL-FILLED
OUTOUT
OIL-FILLEDOIL-FILLED
OUTOUT
OIL-FILLEDOIL-FILLED
VERTICAL BARRIERVERTICAL BARRIER
2 CHANNEL2 CHANNEL
CONTINUOUSCONTINUOUS
AQUIFERAQUIFERSUPPORTSUPPORT
OILOILRECOVEREDRECOVERED
PROBABILITYPROBABILITY Pxoil rec.Pxoil rec.(MMstb)(MMstb)
BARRIERSBARRIERSGOCGOCMODELMODEL
1.0000 20.3000
16Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
17Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
18Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
19Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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)
20Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
21Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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
22Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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)
(%)
23Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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?
24Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005
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)