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■ These lecture notes can be seen as a reasonable supplement for the lecture “Advanced Petroleum Economics”.
■ Because of didactic reasons placeholder can be found instead of most figures in these lecture notes. The figures are presented and discussed in the lessons. Subsequently this is not a complete manuscript and consequently not sufficient for the final examination.
■ For further reading and examination prparation the following books are recommended:▪ Allen, F.H.; Seba, R. (1993): Economics of Worldwide Petroleum
Types of Cost Estimates▪ Linked to the stage of development
▪ Based on the available information
■ Order of Magnitude Estimate
▪ Data: Location, weather conditions, water depth (offshore), terrain conditions (onshore), distances, recoverable reserves estimate, number and type of wells required, reservoir mechanism, hydrocarbon properties
■ Optimization Study Estimate
▪ Also based on scaling rules but with more information and for individual parts
■ Budget Estimate
▪ Engineers create a basis of design (BOD)
▪ Contractors are invited for bidding
▪ Result is a budget estimate
■ Control Estimate
▪ Actual expenditure is monitored versus the budget estimate
▪ If new information is available, then the development plan is updated
■ Three which ignore time-value of money:▪ Net Profit▪ Payout (PO)▪ Return on Investment (undiscounted profit-to-investment ratio)
■ Others which recognize time-value of money:▪ Net present value profit▪ Internal rate of return (IRR)▪ Discounted Return on Investment (DROI)▪ Appreciation of equity rate of return
■ Some criteria might have alternate names, but these are the common ones in petroleum economics
■ Strengths:▪ All advantages of NPV (such as realistic reinvestment rate, not trail and
error procedure)▪ Providing a measure of profitability per dollar invested ▪ Suitable for ranking investment opportunities▪ Only meaningful if both signs of the ratio are positive
■ Ranking investments with DROI gives a simple and often good enough portfolio
■ But there are a couple of considerations around that might optimize one’s portfolio:▪ Synergies▪ Fractional participation▪ Strategic and option values▪ Game-theoretical thoughts
Example “Addition Rules”■ Assume 50 wells have been drilled in an area with blanket
sands. The drilling resulted in (a) 8 productive wells in Zone A, (b) 11 productive wells in Zone B, and (c) 4 productive wells in both Zones. With the help of Venn diagrams and probability rules, calculate the following:1. Number of wells productive in Zone A only,2. Number of wells productive in Zone B only,3. Number of wells discovered, and4. Number of dry holes.
■ 10 prospective leases have been acquired. Seismic surveys conducted on the leases show that three of the leases are expected to result in commercial discoveries. The leases have equal chances of success. If drilling of one well is planned for each lease, calculate the probability of drilling the first two wells as successful discoveries.
■ Solution: ▪ W1 is the first, W2 the second well.
■ One box contains 3 green and 2 red pencils. A second box contains 1 green and 3 red pencils. A single fair die is rolled and if 1 or 2 comes up, a pencil is drawn from the first box; if 3, 4, 5 or 6 comes up, then a pencil is drawn from the second. If the pencil drawn is green, then what is the probability it has been from the first box?
■ Solution:▪ P(B1)=1/3 and P(B2)=2/3▪ In box 1: P(G)=3/5 and P(R)=2/5▪ In box 2: P(G)=1/4 and P(R)=3/4
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Page 57Cf. Mian (2002b), p. 84ff.
Fig. 43: Probability tree for the theoretical example“Bayes’ Rule”
■ We have made a geological and engineering analysis of a new offshore concession containing 12 seismic anomalies all about equal size. We are uncertain about how many of the anomalies will contain oil and hypothesize several possible states of nature as follows: ▪ E1: 7 anomalies contain no oil and 5 anomalies contain oil▪ E2: 9 anomalies contain no oil and 3 anomalies contain oil
■ Based on the very little information we have, we judge that E2 is twice as probable as E1.
■ Then we drill a wildcat and it turns out to be a dry hole. The question is: “How can this new information be used to revise our initial judgement of the likelihood of the hypothesized state of nature?”
■ Applicable if an event has two possible outcomes■ Equations:
▪ Where,▪ P(x)=probability of obtaining exactly x successes in n trails,▪ p=probability of success,▪ q=probability of failure,▪ n=number of trails considered and▪ x=number of successes
■ Example:▪ A company is planning six exploratory wells with an estimated chance of
success of 15%.What is the probability that (a) the drilling will result in exactly two discoveries and (b) there will be more than three successful wells.
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Cf. Mian (2002b), p. 99ff.
Fig. 45: Solution of the “six exploratory wells” example
■ In a certain prospect, the company has grouped the possible outcomes of an exploratory well into three general classes as (a) dry hole (zero reserve), (b) discovery with 12 MMBbls reserves, and (c) discovery with 18 MMBbls reserves. Each of these categories probabilities of 0.5, 0.35, and 0.15 were assigned, respectively. If the company plans to drill three additional wells, what will be the probabilities of discovering various total reserves with these three additional wells?
■ Solution:▪ m=3; N=3; P1=0.5; P2=0.35; P3=0.15▪ k1=number of wells giving reserves of zero▪ k2=number of wells giving reserves of 12 MMBbls ▪ k3=number of wells giving reserves of 18 MMBbls
■ Application in statistical sampling, if trails are dependent and selected, is from a finite population without replacement
■ Equation:
▪ Where,▪ N=number of items in the population▪ C=number of total successes in the
population▪ n=number of trails (size of the sample)▪ x=number of successes observed in the
sample■ Example:
▪ A company has 10 exploration prospects, 4 of which are expected to be productive. What is the probability 1 well will be productive if 3 wells are drilled.
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Cf. Mian (2002b), p. 99ff.
Fig. 46: Solution of the “Hypergeometric distribution”example
■ Good for representing a particular event over time or space
■ Equation:
▪ Where,▪ λ=average number of occurrence per interval of time or space▪ x=number of occurrences per basic unit of measure▪ P(x)=probability of exactly x occurrences
■ Examples:▪ Assume Poisson distribution!1. If a pipeline averages 3leaks per year, what is the probability of having
exactly 4 leaks next year?2. If a pipeline averages 5 leaks per 1000 miles, what is the probability of
having no leaks in the first 100 miles?
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Cf. Mian (2002b), p. 99ff.
Fig. 47: Solutions of the “Poisson distribution” examples
■ Probability density function:▪ Where,▪ μ=mean▪ σ=standard deviation
■ Example:▪ Porosities calculated from porosity logs of a
certain formation show a mean porosity of 12% with standard deviation of 2.5%. What is the probability that the formation’s porosity will be (a) between 12% and 15% and (b) greater than 16%.
■ Solution:▪ By means of the standard normal derivate (Z)
and probability tables
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Cf. Campbell et al. (2007) p. 218ff and Mian (2002b), p. 99ff.
Fig. 48: Solutions of the “Normal distribution” example
■ Linear systems, like NCF, approximate a normal distribution, regardless of the shape of subordinate variables like OPEX, CAPEX, taxes, etc…
Cf. Campbell et al. (2007) p. 218ff and Mian (2002b), p. 99ff.
Fig. 49: Lognormal distribution
■ The occurrence of oil and gas reserves is approximately lognormal distributed (the same as return on investments, insurance claims, core permeability and formation thickness)
Cf. Campbell et al. (2007) p. 218ff and Mian (2002b), p. 99ff.
Fig. 51: Probability density function and cumulative distribution function of a triangulardistribution
■ Used if an upper limit, a lower limit, and a most likely value can be specified
■ Equation:
■ Example:▪ A bit record in a certain area shows the minimum and
maximum footage, drilled by the bit to be 100 and 200 feet, respectively. The drilling engineer has estimated, that the most probable value of the footage drilled by a bit will be 130 feet, and the footage which is drilled follows triangular distribution. What is the probability that the bit fails within 110 feet?
Risk Management in E&P Projects■ Example for key points of a risk management policy:
Risk management is an integrated part of project managementEvery project faces risks from the very beginningThe ability to influence and manage risk is higher the earlier identifiedRisk management supports the achievement of the project’s objectivesThe project manager – and development manager in case of composite projects – is ac-countable for managing project’s risksRisk management is a continuous processThe selective application of risk management tools supports risk managementProper risk management involves multi-discipline teamsTaking calculated risk consciously generates valueRisk can be quantified by multiplying the probability that the unfavourable event happens with the severity (financial exposure) of possible consequencesRisk auditing is subject to project peer reviewing
■ In risk analysis one can distinguish between:Qualitative risk analysisQuantitative risk analysis
■ Risk management is understood asIdentifying potential project threats,Reducing the probability that negative events occur (prevention), andMinimizing the impact of the occurrence of negative events (mitigation).
Bow-tie diagrams are used for in depth analysis of major risk issues. Especially when the cause-effect-chain of a risk issue is too complicated to be overlooked due to multiple threats, consequences, and barrier opportunities, bow-ties reduce the complexity and help to understand the coherence of the risk issue.
Cf. Zettl (2000), p. 43 and Newendorp, Schuyler (2000), p. 397ff.
Input Data
Sampling of Input Data via Probability
Distributions
Computing Outputs
(e.g.: NPV)
Evaluation ofOutput Probability
Distribution
Result Interpretation and Decision
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In Monte Carlo simulations risky events and values are modelled by means of probability distributions and repeating relevant calculations a sufficiently number of times using random numbers in order to end up with calculated probability distributions for output variables.
■ Sources of random numbers:Mechanical experimentNoise in nature (really random)Table of random number (boring book!)(Pseudo) Random number generator (pseudo random)
■ Uniformly distributed numbers between 0 and 1■ If computers offer to set the “seed” value, the
■ The result is a probability distribution of the output value■ Received statistical measures:
Measures of location: mean, median, mode…Measures of dispersion: range, interquantile range, standard deviation, variance…Measures of shape: modality, skewness, kurtosis…
Fig. 57: Hidden relationship between input and output shape of distribution Fig. 58: Possible output probability distribution of a Monte-Carlo-Simulation
Selected Measures of Risk■ Risk Adjusted Capital (RAC)
Maximum amount of money that can be lost (with a certain confidence)
■ Value-at-Risk (VaR)Difference between the mean and the maximum amount of money that can be lost (with a certain confidence)
■ Return on Risk Adjusted Capital (RORAC)Relation between expected profit (e.g. mean) and the maximum amount of money that can be lost (with a certain confidence)
LiteratureAllen, F.H.; Seba, R. (1993): Economics of Worldwide Petroleum Production, Tulsa: OGCI Publications.Campbell Jr., J.M.; Campbell Sr., J.M.; Campbell, R.A. (2007): Analysing and Managing Risky Investments, Norman: John M. Campbell.Clo, A. (2000): Oil Economics and Policy, Boston/Dordrecht/London: Kluwer Academic Publisher.Dahl, C.A. (2004): International Energy Market - Understanding Pricing, Politics and Profits, Tulsa: Penn Well.Deffeyes, K.S. (2005): Beyond Oil - The view from Hubbert's Peak, New York: Hill and Wang.Dias, M.A.G. (1997): The Timing of Investment in E&P: Uncertainty, Irreversibility, Learning, and Strategic Considerations. In: 1997 SPE Hydrocarbon Economics and Evaluation Symposium. Dallas, TX: SPE.Dixit, A.K.; Nalebuff, B.J. (1997): Spieltheorie für Einsteiger - Strategisches Know-how für Gewinner, Stuttgart: Schäffer-Poeschel Verlag.Gleißner, W. (2004): Die Aggregation von Risiken im Kontext der Unternehmensplanung. In: Zeitschrift für Controlling und Management. Vol. 48, Nr. 5: S. 350-359.Homburg, C.; Stephan, J. (2004): Kennzahlenbasiertes Risikocontrolling in Industrie und Handelsunternehmen. In: Zeitschrift für Controlling und Management. Vol. 48, Nr. 5: S. 313-325.Johnston, D. (2003): International Exploration Economics, Risk, and Contract Analysis, Tulsa: Pann Well.Laux, H. (2003): Entscheidungstheorie. 5. Auflage, Berlin Heidelberg: Springer.Mian, A.M. (2002a): Project Economics and Decision Analysis - Volume I: Deterministic Models, Tulsa: PennWell.Mian, A.M. (2002b): Project Economics and Decision Analysis - Volume II: Probabilistic Models, Tulsa: PennWell.Newendorp, P.; Schuyler, J. (2000): Decision Analysis for Petroleum Exploration. Vol. 2nd Edition, Aurora: Planning Press.PalisadeCorporation (2002): @Risk - Advanced Risk Analysis for Spreadsheets. Vol. Version 4.5, Newfield: Palisade Corporation.Zettl, M. (2000): Application of Option Pricing Theory for the Valuation of Exploration and Production Projects in the Petroleum Industry. Leoben: Montanuniversität Leoben, Dissertation.