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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 1 Petro-Canada Our UK Investment Story A Practical Technique for Estimating a Probabilistic Range of Production Forecasts Based on Reservoir Simulation Sensitivity Studies Paul Armitage, Petro Canada 28 – 29 April, 2005

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 2 Talk Outline Introduction Introduction Problem to be Addressed Problem to be Addressed Theory Theory A Simple Example A Simple Example Methodology Methodology Applicability & Limitations Applicability & Limitations Example Field A Example Field A Example Field B Example Field B Summary & Conclusions Summary & Conclusions

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 3 Introduction 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 your analysis has barely begun? Provide facilities engineers with throughputs and other constraints before 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 estimates maybe a little quicker But here’s a strategy for arriving at some reasonably robust estimates maybe a little quicker

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 4 What’s the Problem? Simulation Studies Many sensitivity cases Many sensitivity cases Consolidation / estimation of range difficult Consolidation / estimation of range difficult Large investment needed to cover range fully Large investment needed to cover range fully Technique to estimate P90 – P50 – P10 Straightforward Straightforward Reduces simulation cases Reduces simulation cases Judgment still needed Judgment 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!

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 5 “Theory” Take a look in the England & Wales National Curriculum for GCSE Maths Take a look in the England & Wales National Curriculum for GCSE Maths Or a Maths GCSE Revision Guide Or a Maths GCSE Revision Guide Relative Frequency or “Experimental Probability” Relative Frequency or “Experimental Probability”

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 6 A Simple Example (1) Two dice thrown together – sum the dots What are the possible outcomes? What are the possible outcomes? And what are their probabilities? And what are their probabilities? 136 1/36 = 0.0277 112 2/36 = 0.0555 211 3/36 = 0.0833 310 4/36 = 0.1111 49 5/36 = 0.1388 58 6/36 = 0.1666 67 5/36 = 0.1388 56 4/36 = 0.1111 45 3/36 = 0.0833 34 2/36 = 0.0555 23 1/36 = 0.0277 12 ProbabilityNo. of waysNo. of dots

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 7 A Simple Example (2) Or 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 occurs Tally the no. of times each total occurs The greater N, the nearer to the actual probability the results should be The greater N, the nearer to the actual probability the results should be

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 8 A Simple Example: Tabulated Results 11100136 0.0250.000025012 0.0450.083345311 0.0980.111198410 0.1080.055510829 0.1560.194415678 0.1460.194414677 0.1580.194415876 0.1070.055510725 0.0790.02777914 0.0570.05555723 0.0220.02772212 Frequency N = 1001 Relative N = 36 No of ways N = 1001 No. of ways N = 36 No. of dots

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 9 A Simple Example: Graphical Representation 0 0.05 0.1 0.15 0.2 0.25 23456789101112 Sum of the throw of two dice Relative Frequency / Probability (fraction) Relative frequency (1001 trials) Relative frequency (36 trials) Theoretical

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 10 A Simple Example: 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 23456789101112 Sum of the throw of two dice 1-Relative Frequency or 1-Cumulative Probability (fraction) Relative frequency (1001 trials) Relative frequency (36 trials) Theoretical

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 11 Simple 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 23456789101112 Sum of the throw of two dice 1-Relative Frequency or 1-Cumulative Probability (fraction) P90P50P10 = 4 = 8 = 11

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 12 Simulation results Methodology 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

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 13 Applicability & Limitations Lack of (mathematical) rigour Lack of (mathematical) rigour Extrapolation Extrapolation Used so far Used so far Small fields Small fields Pre-development decisions Pre-development decisions Are there applications where inappropriate? Are there applications where inappropriate?

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 14 Field A

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 15 Field A: Probability Tree LARGEMODERATENONE 000000 000000 000000 SEAL LARGEMODERATENONE 13.377 13.104 12.831 0.004 0.015 0.001 0.0535 0.1966 0.0128 LEAK LARGEMODERATENONE 000000 000000 000000 SEAL LARGEMODERATENONE 44.499 27.300 21.294 0.016 0.060 0.004 0.7120 1.6380 0.0852 LEAK LARGEMODERATENONE 10.101 9.555 8.736 0.0072 0.0270 0.0018 0.0727 0.2580 0.0157 SEAL LARGEMODERATENONE 14.469 13.650 12.831 0.0168 0.0630 0.0042 0.2431 0.8600 0.0539 LEAK LARGEMODERATENONE 31.395 21.021 18.837 0.0288 0.1080 0.0072 0.9042 2.2703 0.1356 SEAL LARGEMODERATENONE 30.030 23.205 20.475 0.0672 0.2520 0.0168 2.0180 5.8477 0.3440 LEAK LARGEMODERATENONE 12.285 12.012 11.875 0.0108 0.0405 0.0027 0.1327 0.4865 0.0321 SEAL LARGEMODERATENONE 13.104 12.285 11.875 0.0012 0.0045 0.0003 0.0157 0.0553 0.0034 LEAK LARGEMODERATENONE 15.015 0.0432 0.1620 0.0108 0.6486 2.4324 0.1622 SEAL LARGEMODERATENONE 29.484 23.478 20.202 0.0048 0.0180 0.0012 0.1415 0.4226 0.0242 LEAK OUT OIL-FILLED OUT OIL-FILLED OUT OIL-FILLED VERTICAL BARRIER 2 CHANNEL CONTINUOUS AQUIFERSUPPORTOILRECOVEREDPROBABILITY Pxoil rec. (MMstb)BARRIERSGOCMODEL 1.000020.3000

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 16 Field A: Cumulative Relative Frequency 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 05101520253035404550 Oil Recovered (MMstb) 1-Cumulative Probability (fraction) P90MeanP50MLP10 = 13 MMstb = 20 MMstb = 21 MMstb = 23 MMstb = 30 MMstb

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 17 Methodology Simulation 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

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 18 Field B Single structural model simulated Single structural model simulated Min – ML – Max HCIIP estimated in static modelling Min – ML – Max HCIIP estimated in static modelling Simulation Sensitivity Study Simulation Sensitivity Study Relative Permeability Relative Permeability PVT PVT Permeability and its distribution Permeability and its distribution etc. etc. Various recovery factors Various recovery factors Estimate range and distribution Estimate range and distribution Min – ML – max; triangular Min – ML – max; triangular P90 – P50 – P10; normal P90 – P50 – P10; normal

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 19 Field B: Range of Recovery -30-20-10010203040 STOIIP hi STOIIP lo homo k k-phi Sorw lo Sorw hi oil viscosity krw' Difference in Ultimate Recovery from Base Case (MMstb)

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 20 Field B: Probabilistic Range of Recovery Monte Carlo method Monte Carlo method Statistical sampling technique to approximate solutions to quantitative problems Statistical sampling technique to approximate solutions to quantitative problems 2 or more variables 2 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 George S. Fishman “Monte Carlo Concepts, Algorithms and Applications” by George S. Fishman www.riskglossary.com/articles/monte-carlo-method.htm www.riskglossary.com/articles/monte-carlo-method.htm

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 21 Field B: Input to Monte Carlo Calculation 0 10 20 30 40 50 60 70 80 90 100 05101520253035404550 Recovery Factor (%) Probability or (100-Cumulative Probability) (%) 0 10 20 30 40 50 60 70 80 90 100 050100150200250300 STOIIP (MMstb) Probability or (100-Cumulative Proabability) (%) 350

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 22 Field B: Cumulative Relative Frequency 0 10 20 30 40 50 60 70 80 90 100 020406080100120140160 Ultimate Oil Recovery (MMstb) Probability or (100 - Cumulative Probability) (%)

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 23 Summary and Conclusions Largely empirical method developed Largely empirical method developed Estimate quickly P90 – P50 – P10 recoveries & profiles from a relatively small number of simulation cases Estimate quickly P90 – P50 – P10 recoveries & profiles from a relatively small number of simulation cases Can be extended to combine volumetric HCIIP ranges derived independently of simulation with simulation results Can be extended to combine volumetric HCIIP ranges derived independently of simulation with simulation results Important to exercise judgement throughout process Important to exercise judgement throughout process Critical that consensus developed if probabilities are to be assigned to different simulation sensitivities Critical that consensus developed if probabilities are to be assigned to different simulation sensitivities Technique has been used successfully for development decisions with respect to marginal fields Technique has been used successfully for development decisions with 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?

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Precise Production Forecasting for Improved Portfolio Management, 28 – 29 April, 2005 24 Summary and Conclusions: Field A 0 5000 10000 15000 20000 25000 30000 35000 Daily Dry Oil Production (stb) 246810121416182022242628303234363840424446485052545658600 Time (Days)

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Multiplication X 1 1 x 1 = 1 2 x 1 = 2 3 x 1 = 3 4 x 1 = 4 5 x 1 = 5 6 x 1 = 6 7 x 1 = 7 8 x 1 = 8 9 x 1 = 9 10 x 1 = 10 11 x 1 = 11 12 x 1 = 12 X 2 1.

Multiplication X 1 1 x 1 = 1 2 x 1 = 2 3 x 1 = 3 4 x 1 = 4 5 x 1 = 5 6 x 1 = 6 7 x 1 = 7 8 x 1 = 8 9 x 1 = 9 10 x 1 = 10 11 x 1 = 11 12 x 1 = 12 X 2 1.

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