Advanced Petroleum Economics Staber

© Economics and Business Management, University of Leoben, Stephan Staber

600.019 Advanced Petroleum EconomicsLecture Notes

Originaly prepared by Stephan Staber, 2007, Leoben

Revised by Stephan Staber, October 2008, Vienna

Revised by Stephan Staber, September 2009, Vienna

Revised by Stephan Staber, October 2010, Vienna

Revised by Stephan Staber, September 2011, Vienna


Preface

■ 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

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.▪ Newendorp, P.; Schuyler, J. (2000): Decision Analysis for Petroleum

Exploration. Vol. 2nd Edition, Aurora: Planning Press.■ The interested student finds the full list used literature at the end of

this document.


Why Advanced Petroleum Economics?

■ The content of teaching is based on your knowledge gained in the lecture „Petroleum Economics“!

■ Required knowledge:▪ Time Value of Money Concept

consult „Allg. Wirtschafts- und Betriebswissenschaften 1“ and „Petroleum Economics“

▪ Measures of Profitabilityconsult „Allg. Wirtschafts- und Betriebswissenschaften 1“ and „Petroleum Economics“

▪ Financial Reporting and Accounting Systemsconsult „Allg. Wirtschafts- und Betriebswissenschaften 2“ and „Petroleum Economics“

▪ Basic Probability Theory and Statisticsconsult „Statistik“ and „Petroleum Economics“

▪ Reserves Estimationconsult „Reservoir Engineering“ and „Petroleum Economics“


Lecture Outline

■ Cash Flow and Costs

■ Profitability and Performance Measures

■ Expected Value Concept

■ Decision Tree Analysis

■ Probability Theory

■ Risk Analysis

■ Sensitivity Analysis


Setting the scene…■ What are the core processes of an E&P company?

■ What are potential decision criteria/ decision influencing factors regarding e.g. a field development approval decision?

Fig. 0: Core processes in an E&P company

Cash Flow and Costs

© Economics and Business Management, University of Leoben

Cash Flow and Costs

■ Net Cash Flow=Net Annual Revenue – Net Annual Expenditure (both cash)

■ Costs:▪ Capital expenditure (CAPEX)

▪ Operating expenditure (OPEX)

▪ Abandonment Costs

▪ Sunk Costs

▪ Opportunity Costs

Cf. Allen and Seba (1993), p. Mian (2002a), p. 86ff.

Fig. 1: Cash Flow Projection


Capital Expenditure (CAPEX)■ …one-time costs

■ …occurring at the beginning of projects

■ Classification by purpose:▪ Exploration costs (capitalized portion)▪ Appraisal costs▪ Development costs▪ Running Business costs▪ Abandonment costs▪ Acquisition costs

■ Classification by purchased items:▪ Facility costs▪ Wells/ Drilling costs▪ Pipeline costs▪ G&G costs (mainly seismic)▪ Signature bonus

■ Classification and wording differ from company to company


Operational Expenditure (OPEX)■ …occur periodically ■ …are necessary for day-to-day operations■ …consist typically of:

▪ Utilities▪ Maintenance of facilities▪ Overheads▪ Production costs, e.g.:

▪ Treatment Costs▪ Interventions▪ Secondary recovery costs▪ Water treatment and disposal costs

▪ (Hydrocarbon-)Evacuation costs▪ Insurance costs

■ Classification and wording differ, but often:▪ Production cost per unit =

OPEX/production volume [USD/bbl]▪ Lifting cost per unit =

(OPEX + royalties + expl. expenses + depreciation)/sales volume [USD/bbl]

Cf. Mian (2002a), p. 126ff.


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

Cf. Mian (2002a), p. 139ff.


Accuracy and Cost Overrun

■ Main reasons for Cost Overrun

▪ Contractor delay

▪ Unforeseen difficulties

▪ New information may change the project

■ Accuracy improves over time

▪ Major improvement occurs when the BOD is frozen

From Mian (2002a), p. 139ff.

Fig. 2: Accuraccy of cost estimates

Fig. 3: Probability of cost overrun


Contingency and Allowance■ Contingency

▪ Budget for the unknown unknowns

■ Allowances▪ Budget for the known unknowns

▪ …are probable extra costs

▪ E.g. for material, identified risks, foreseeable market or weather conditions, new technology, growth…

▪ The value is often taken from the 10% probability budget estimate

Cf. Mian (2002a), p. 139ff.

Fig. 4: One possible statistical view on contingency and allowance

Measures of Profitability and Performance


Popular Criteria

■ 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

Cf. Newendorp, Schuyler (2000), p. 9ff.


Prospect Cashflow Example

■ This example helps to understand the measures of profitability (Taxation is excluded from this analysis for simplicity)

Investment: $268,600 for completed well; $200,000 for dry hole

Estimated recoverable reserves:

234,000 Bbls; 234 MMcf gas

Estimated average producing rate during first two years:

150 BOPD

Future Expenditures: Pumping Unit in year 3, $10,000; Workover in year 5, $20,000

Working interest in proposed well:

100%

Average investment opportunity rate:

10%

Type of discounting: Mid-project-year

Year Estimated oil Production, Bbls

Annual Net Revenue*

Future Expenditures

Net Cash Flow

1 54,750 $132,900 $132,900

2 54,750 132,900 132,900

3 44,600 107,600 10,000 97,600

4 29,200 69,200 69,200

5 18,900 43,500 20,000 23,500

6 12,900 28,600 28,600

7 7,800 15,900 15,900

8 5,200 9,400 9,400

9 3,700 5,600 5,600

10 2,200 1,900 1,900

234,000 $547,500 $30,000 $517,500

*Annual Net Revenue = Annual Gross Revenue – Royalties – Taxes – Operating expenses

From Newendorp, Schuyler (2000), p. 14f.


Net Profit

■ Net Profit=Revenues – Costs = Cash Receipts – Cash Disbursements

■ Prospect Cashflow Example:▪ $547,500 – $298,600 = $248,900

■ Strengths:▪ Simple

▪ Project profits can be weighted, e.g., (n x average = total)

■ Weaknesses:▪ Does not recognize the size of investment

▪ Does not recognize the timing of cash flows

Cf. Newendorp, Schuyler (2000),p. 9ff.


Payout (PO) 1/2

■ The length of time which elapses until the account balance is exactly zero is called payout time.

■ If one tracks the cumulative project account balance as a function of time he gets the so-called cash position curve.

Fig. 5: Cash position curve

■ All other factors equal a decision maker would invest in projects having the shortest possible payout time.



Prospect Cashflow Example

■ Unrecovered portion of the initial investment:

▪ $268,600 – $132,900 = $135,700

■ Unrecovered portion of the investment at the end of year 2:

▪ $135,700 – $132,900 = $2,800

■ Assuming constant cashflow rates the portion of year 3 required to recover this remaining balance:

▪ $2,800 / $97,600 = 0.029

■ Payout time:

▪ 2.029



Payout (PO) 2/2■ Strengths:

▪ Simple▪ Measures an impact on liquidity

■ Weaknesses:1. Payout considers cashflows only up to

the point of payback.2. Especially troublesome with large

abandonment costs3. Project profits cannot be weighted: (n x

average ≠ total)

Fig. 6: Weakness 1

Fig. 7: Weakness 2

Fig. 8: Weakness 3

Fig. 9: Variation 1 Fig. 10: Variation 2 Fig. 11: Variation 3



Return on Investment (ROI)

■ Reflects total profitability!

■ Sometimes called:▪ (undiscounted) profit-to-investment ratio

■ Strengths:▪ Recognizes a profit in relation to the size of investment

▪ Simple

■ Weaknesses:▪ Accounting inconsistencies

▪ Continuing investment is not represented properly

▪ Project ROI cannot be weighted: (n x average ROI ≠ total ROI)

InvestmentNCF

ROI ∑=



Return on Investment (ROI) - Variations

1. Using “maximum out-of-pocket cash” instead of investment

2. Return on Assets (ROA):

■ Prospect Cash Flow Example:▪ ($517,500 – $268,600) /

$268,600 = 0.927

tkInvestmenAverageBooIncomeAverageNetROA =

Fig. 12: Maximum out-of-pocket cash

Fig. 13: ROA



Net Present Value

■ Money received sooner is more worth than money received later!

■ The money can be reinvest in the meantime! (Opportunity cost of capital)

■ The present value can be found by:▪ PV = FV (1+i)-t

▪ PV… Present Value of future cashflows▪ FV… Future Value▪ i… Interest or discount rate▪ t… Time in years▪ (1+i)-t… Discount factor



Discount rate

■ Two philosophies what this rate should be:

1. Opportunity cost of capital (OCC)▪ The average yield we can expect from funding other projects. This

is the rate at which one can reinvest future cash.

2. Weighted-average cost of capital (WACC)▪ The marginal cost of funding the next project. This is calculated

as an weighted-average cost of a mixture of equity and debt.



Net Present Value

■ Prospect Cash Flow Example:

Year Net cashflow

Discount factor 10%

10% discounted cashflow

0 -$268,600 1.000 -$268,600

1 +$132,900 0.953 +$126,700

2 +$132,900 0.867 +$115,200

3 +$97,600 0.788 +$76,900

4 +$69,200 0.716 +$49,500

5 +$23,500 0.651 +$15,300

6 +$28,600 0.592 +$16,900

7 +$15,900 0.538 +$8,600

8 +$9,400 0.489 +$4,600

9 +$5,600 0.445 +$2,500

10 +$1,900 0.404 +$800

$148,400

= NPV @ 10%

Fig. 14: e.g. profitable, but neg. NPV

Fig. 15: Major weakness of NPV



(Internal) Rate of Return (IRR)

■ Sometimes:▪ Discounted rate of return

▪ Internal yield

▪ Sometimes: Profitability index (PI)

■ IRR is the discount rate such that the NPV is zero

■ Prospect Cash Flow Example: (trail-and-error procedure)

Year Net cashflow

Discount factor 40%

40% discounted cashflow

0 -$268,600 1.000 -$268,600

1 +$132,900 0.845 +$112,300

2 +$132,900 0.604 +$80,300

3 +$97,600 0.431 +$42,100

4 +$69,200 0.308 +$21,300

5 +$23,500 0.220 +$5,200

6 +$28,600 0.157 +$4,500

7 +$15,900 0.112 +$1,800

8 +$9,400 0.080 +$700

9 +$5,600 0.057 +$300

10 +$1,900 0.041 +$100

$0

IRR = 40%



Discounted Return on Investment (DROI)

■ Sometimes:▪ Discounted profit to investment ratio

(DPR, DPI, or DPIR)

▪ Present value index (PVI)

▪ Sometimes: Profatibility Index (PI)

■ DROI is the ratio obtained by dividing the NPV by the present value of the investment

■ Prospect Cash Flow Example: ▪ DROI = $148,400 / 268,600 = 0.553

InvestmentofPVNPVDROI__

=



Discounted Return on Investment (DROI)

■ 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



Appreciation of Equity Rate of Return

■ Also: Growth rate of return■ Idea:

▪ Reflecting the overall net earning power of an investment▪ Assumes the reinvestment at a lower rate (e.g. 10%) than the true rate

of return (e.g. 40%)▪ As a consequence the overall rate of return is less!

■ Baldwin Method:1. Calculate a compound interest factor for each year: (1+i)n ,

where i is the discount rate for the opportunity cost of capitaland n is always the number of years reinvested (midyear)

2. Calculate the appreciated value of the net cash flows. The sum is the total value of the cash flows at the end of the last project year.

3. Solve this equation for iae: Investment*(1+iae)N=Σ Αppr. value of NCFs



Appreciation of Equity Rate of Return

■ Prospect Cash Flow Example using the Baldwin Method:

Year Net cashflow

Number of years reinvested

Compound interest factor, 10%

Appreciated value of net cashfliws as of end of project

1 +$132,900 9.5 2.475 +$328,900

2 +$132,900 8.5 2.247 +$298,600

3 +$97,600 7.5 2.045 +$199,600

4 +$69,200 6.5 1.859 +$128,600

5 +$23,500 5.5 1.689 +$39,700

6 +$28,600 4.5 1.536 +$43,900

7 +$15,900 3.5 1.397 +$22,200

8 +$9,400 2.5 1.269 +$11,900

9 +$5,600 1.5 1.153 +$6,500

10 +$1,900 0.5 1.049 +$2000

$1,081,900


■ $268,600 (1+iae)10=$1,081,900

■ Appreciation of equity rate of return = iae = 0.1495


Net Present Value Profile Curve

■ NPV and rate of return not necessarily prefer the same ranking!

Fig. 16: Net Present Value Profile Curve



Net Present Value Portfolios

■ Due to limited statements of single measures portfolios are established

■ Common are “x” vs. NPV portfolios

Fig. 17: IRR vs. NPV Portfolio Fig. 18: DROI vs. NPV Portfolio Fig. 19: Cash Out vs. NPV Portfolio


Rate Acceleration Investments

■ Typical for the petroleum industry!■ Investments which accelerate the cashflow schedule■ Examples:

▪ Infill drilling▪ Installing large volume lift equipment

■ Simple calculation example:Year Present

cashflowAccelerated cashflow

Incremental cashflow

Discount factor, 10%

Discounted incremental cashflows, 10%

0 0 -$50 -$50 1.000 -$50.00

1 +$300 +$500 +$200 0.953 +$190.60

2 +$200 +$400 +$200 0.867 +$173.40

3 +$200 0 -$200 0.788 -$157.60

4 +$100 0 -$100 0.716 -$71.60

5 +$100 0 -$100 0.651 -$65.10

+$19.70



Multiple choice review questions

Past costs which have already been incurred and cannot be recovered are called…

O CAPEX.

O OPEX.

O Abandonment costs.

O Sunk costs.



The expected return forgone by bypassing of other potential investment projects for a given capital is called…

O weighted average cost of capital (WACC).

O opportunity cost of capital.

O profit.

O half-life.



The length of time which elapses until the account is balanced of e.g. a development project is called…

O maximum-out-of-pocket-cash.

O net present value.

O return on investment.

O payout.

Expected Value Concept


Expected Value Concept (EVC)

■ Previously discussed measures were all “no risk”parameters

■ But petroleum exploration involves a high degree of risk!

■ Two way out:▪ Doing intuitive risk analysis or

▪ trying to consider risk and uncertainty in a logical, quantitative manner.

■ Expected value concept combines profitability estimates and risk estimates



Risk and Uncertainty

■ Risk:▪ Addresses discrete events (e.g. discovery or dry hole)▪ Can be both: A threat or an opportunity

■ Uncertainty:▪ Result depends on unknown circumstances (e.g. oil price)▪ Occurrence probability of an event is not quantifiable

■ Deterministic:▪ Calculations using exact values for their parameters are called

deterministic

■ Stochastic:▪ Calculations which use probabilities within their model are

called stochastic

Cf. Newendorp, Schuyler (2000), p. 71ff and Laux (2003), p. 105.


Definitions and EVC

■ Expected Value (EV):▪ The EV is the probability-weighted value of all possible outcomes.

■ Expected Monetary Value (EMV):▪ The EMV is the expected value of the present values of the net

cashflows▪ EMV = EV (NPV)

■ “Conditional”▪ In this context “conditional” means that a value will be received only if

a particular outcome occurs.▪ Often it is omitted!

■ Simple Example:▪ EV Cost of Stuck Pipe = P(Stuck Pipe) * (Cost to remedy Stuck Pipe)

■ More generally: ∑ ×=iall

iOutcomeNPVioutcomePEMV_

_)_(



EMV Example■ Situation in a drilling prospect evaluation:

▪ Probability of a successful well 0.6

▪ Two decision alternatives:▪ Farm out: A producer is worth $50,000, a dry hole causes no profit or loss

▪ Drilling the well: A dry hole casts $200,000, a hit brings (after all costs) $600,000

■ EMV Decision Rule:

▪ When choosing among several mutually exclusive decision alternatives, select the alternative having the greatest EMV.

Decision Alternatives

Drill Farm Out

Outcome Probability outcome will occur

Conditional monetary value

Expected monetary value

Conditional monetary value

Expected monetary value

Dry hole 0.4 -$200,000 -$80,000 0 0

Producer 0.6 +$600,000 +$360,000 +$50,000 +$30,000

+$280,000 +$30,000


=EMV (farm out)=EMV (drill)

Fig. 20: Cumulative result for drill decisions


Characteristics of the EVC

■ Mutually exclusive outcomes

■ Collectively exhaustive outcomes

■ The sum of probabilities for one event must be one

■ Any number of alternatives can be considered

■ Normally values are expressed in monetary profit, therefore “expected monetary value”

■ The EMV does not necessarily have to be a possible outcome



Risked DROI

■ Reasonable under limited capital constraints

)__(_

InvestmentofPVEVEMVDROIRisked =

InvestmentofPVNPVDROI__

=


Cf.


Concerns about the EV Concept

■ Is there a need to quantify risk at all?■ No benefit seen in using the EV!■ We don’t have probabilities anyway…■ Every drilling prospect is unique,

therefore we have no repeated trail!■ Isn’t EV only suitable for large

companies?■ For sure other concerns override EV!

■ “…EMV is not perfect. It is not an oil-finding tool, and it is not (…) the ‘ultimate’ decision parameter.”

Cf. Newendorp, Schuyler (2000), p. 71ff.Newendorp, Schuyler (2000), p. 119.

Decision Tree Analysis


Simple Decision Tree Example

■ Decision trees are necessary if sequent decision must be made

■ Decision tree analysis is an extension of the EMV concept

■ There is no scale to decision trees

Decision Alternatives

Drill Don‘t Drill

Possible Outcome

Probability outcome will occur

Outcome Expected monetary value

Outcome Expected monetary value

Dry hole 0.7 -$50,000 -$35,000 0 0

2 Bcf 0.2 +$100,000 -$20,000 0 0

5 Bcf 0.1 +$250,000 -$25,000 0 0

1.0 EMV = +$10,000 EMV = $0


Fig. 21: Simple decision tree (partially completed)


Decision Tree Symbols

■ There exist two different nodes (forks)▪ Decision node (or activity node) - squares

▪ Chance node (or event node) - circles▪ Terminal nodes (last chance node of a branch)


Fig. 22: Simple decision tree (partially completed with correct symbols)


Decision Tree Completion

■ Associate probabilities to all chance nodes■ Place the outcome value to all branch ends

■ Three important rules:▪ Normalization requirement: The sum of all probabilities around a

chance node must be 1.0▪ There are no probabilities around decision nodes▪ The end nodes are mutually exclusive


Fig. 23: Simple decision tree (completed)


Decision Tree Solution

■ Start at the back of the tree and calculate the EMV for the last chance node.

■ The expected value is written above the node

■ The decision rule for a decision node is to choose the branch with the higher EMV


Fig. 24: Simple decision tree (solved)


Case Study: Decision Tree Analysis


Fig. 25: Case Study: Decision Tree


Advantages of Decision Tree Analysis

■ The complexity of a decision is reduced

■ Provides a consistent action plan

■ Decision problems of any size can be analysed

■ Forces us to think ahead

■ If conditions change the situation can be re-analysed

■ Logical, straight-forward an easy to use


Probability Theory


Concept of Probability▪ Probability Theory enables a person to make an educated guess

■ Objective Probability1. Classical approach:

▪ Derives Probability measures from undisputed laws of nature

▪ Requires the identification of the total number of possible outcomes (n)

▪ Requires the number of possible outcomes of a wanted event (m)

▪ Probability of occurrence of an event: P(A)=m/n

▪ Three basic condition must be fulfilled: equally likely, collectively exhaustive and mutually exclusive

2. Empirical approach:▪ Derives Probability measures from the events long-run frequency of occurrence

▪ The observation is random

▪ A large number of observations is necessary

▪ The following mathematical relationship is valid: P(A)=limn ∞ (m/n)

■ Subjective Probability▪ Based on impressions of individuals

Cf. Mian (2002b), p. 84ff.


Probability Rules■ Complementation Rule:

▪ P(A)+P(Ā)=1

■ Addition Rule:▪ For simultaneous trails1. Events are mutually exclusive:

▪ P(A∪B)=P(A)+P(B)

▪ P(A∩B)=0

2. Events are partly overlapping:▪ P(A∪B)=P(A)+P(B)-P(A∩B)

▪ P(A∩B)=P(A)+P(B)-P(A∪B) (=P(AB))

■ Multiplication Rule:▪ For consecutive trails▪ Independent events:

▪ P(AB)=P(A) x P(B)

▪ Dependent events:▪ P(AB)=P(A) x P(B|A)

Cf. Mian (2002b), p. 84ff. and http://cnx.org/content/m38378/latest/?collection=col11326/latest

Fig. 39: Vann diagram showing two mutually exclusive events

Fig. 40: Vann diagram showing of partly overlappingevents

Fig. 41: Vann diagram showing union two events


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.

■ Solution: ▪ n(S)=50; n(A)=8; n(B)=11; n(A∩B)=4 1. n(A∩B)=n(A) - n(A∩B)=8 - 4=42. n(Ā∩B)=n(B) - n(A∩B)=11 - 4=73. n(A∪B)= n(A) + n(B) - n(A∩B)=8+11 - 4=154. n(S) - n(A∪B)=50 - 15=35

Cf. Mian (2002b), p. 84ff.

Fig. 42: Vann diagram for example “Addition Rules”


Example “Multiplication Rules”

■ 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.

▪ P(W1)=3/10

▪ P(W2|W1)=2/9

▪ P(W1W2)= 3/10 x 2/9=6,67%

Cf. Mian (2002b), p. 84ff.


Bayes’ Rule

■ Beyesian analysis addresses the probability of an earlier event conditioned on the occurrence of a later event

■ Where: ▪ P(Ai|B)=posterior probabilities and▪ P(Ai)=prior event probabilities

■ Bayes’ theorem is used if additional information results in revised probabilities.

( ) ( ) ( )

( ) ( )∑=

⋅

⋅= k

iii

iii

APABP

APABPBAP

1

Cf. Mian (2002b), p. 84ff.


Theoretical Example “Bayes’ Rule”

■ 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

( ) ( ) ( )

( ) ( )%55,54

116

32

41

31

53

31

53

1

==⎟⎠⎞

⎜⎝⎛⋅⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛⋅⎟

⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛⋅⎟

⎠⎞

⎜⎝⎛

=⋅

⋅=

∑=

k

iii

iii

BPBGP

BPBGPGBP

Page 57Cf. Mian (2002b), p. 84ff.

Fig. 43: Probability tree for the theoretical example“Bayes’ Rule”


Offshore Concession 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?”



Offshore Concession Example “Bayes’ Rule”

Fig. 44: Solution of the offshore concession example


Probability Distributions■ Stochastic or random variable:

▪ The pattern of variation is described by a probability distribution

■ Probability distributions:▪ Discrete

(Stochastic variable can take only a finite number of values)Widely used in petroleum economics:▪ Binomial▪ Multinomial▪ Hypergeometric▪ Poisson

▪ Continuous (Stochastic variable can take infinite values)

▪ Widely used in petroleum economics:▪ Normal▪ Lognormal▪ Uniform▪ Triangular

Cf. Mian (2002b), p. 99ff.


Binomial Distributions

■ 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.

( ) xnxnx qpCxP −⋅⋅= ( )!!

!xnx

nCnx −⋅

=

Cf. Mian (2002b), p. 99ff.

Fig. 45: Solution of the “six exploratory wells” example


Multinomial Distributions

■ Applicable if an event has more than two possible outcomes

■ Equations:▪ Where,

▪ P(S)=probability of the particular sample,

▪ p=probabilities of drawing types 1, 2, …m from population,

▪ N=k1+k2+…+km=size of sample,

▪ k1, k2, …,km=total number of outcomes of type 1, 2, …,m

▪ m=number of different types

( ) mkm

kk

m

PPPkkk

NSP ...!!...!

!21

2121

=

Cf. Mian (2002b), p. 99ff.


Multinomial Distributions - Example 1/2

■ 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

▪ Corresponding reserves=2x0+1x12+0x18=12MMbbls▪ Expected reserves=0.263x12MMBbls=3.15MMBbls

( ) 263.0135.025.01112

12315.035.05.0!0!1!2

!3!!!

! 012321

321

321 =⋅⋅⋅⋅⋅⋅

⋅⋅=== kkk PPP

kkkNSP

Cf. Mian (2002b), p. 99ff.


Multinomial Distributions - Example 2/2

Probability Reserves Probability Exp. Reserves

k1 k2 k3 P(S) [MMBbls] Of Reserves ≥ [MMBbls]

3 0 0 0.125 0 1.000 0.000

2 1 0 0.263 12 0.875 3.150

2 0 1 0.113 18 0.613 2.025

1 2 0 0.184 24 0.500 4.410

1 1 1 0.158 30 0.316 4.725

1 0 2 0.034 36 0.159 1.215

0 3 0 0.043 36 ---“--- 1.544

0 2 1 0.055 42 0.082 2.315

0 1 2 0.024 48 0.027 1.134

0 0 3 0.003 54 0.003 0.182

1,000 20.700

Cf. Mian (2002b), p. 99ff.


Hypergeometric Distributions

■ 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.

( )⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

⎟⎟⎠

⎞⎜⎜⎝

⎛

=

nN

xnCN

xC

xP

Cf. Mian (2002b), p. 99ff.

Fig. 46: Solution of the “Hypergeometric distribution”example


Poisson Distributions

■ 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?

( ) λλ −= ex

xPx

!

Cf. Mian (2002b), p. 99ff.

Fig. 47: Solutions of the “Poisson distribution” examples


Normal Distributions

■ 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

( )2

21

21 ⎟

⎠⎞

⎜⎝⎛ −

−= σ

μ

πσ

x

exf

σμ−

=XZ

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…


Lognormal Distributions


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)

■ Y=ln(X) …is normal distributed


Uniform Distributions

( )minmax

1xx

xf−

=


Fig. 50: Probability density function and cumulative distribution function of a uniform distribution

■ Equal probability between a minimum and a maximum


Triangular Distributions

( )

⎪⎪

⎩

⎪⎪

⎨

⎧

≥≥⎟⎟⎠

⎞⎜⎜⎝

⎛−−

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−

−−

≥≥⎟⎟⎠

⎞⎜⎜⎝

⎛−−

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−

−

=

maxmodminmax

modmax

2

modmax

max

modminminmax

minmod

2

minmod

min

,1

,

XXXXXXX

XXXX

XXXXXXX

XXXX

xF

( ) %33.3033.0100200100130

100130100110 2

minmax

minmod

2

minmod

min ==⎟⎠⎞

⎜⎝⎛

−−

⋅⎟⎠⎞

⎜⎝⎛

−−

=⎟⎟⎠

⎞⎜⎜⎝

⎛−−

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=

XXXX

XXXXxF


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?

■ Solution:Xmin=100; Xmod=130; Xmax=200; X=110


Tests of Goodness of Fit

Cf. Mian (2002b), p. 99ff and PalisadeCorporation (2002), p. 148ff.

■ With these tests one can analyse whether a sample emanates from a certain population or not.

■ Chi-squared-TestFor continuous and discrete dataNeed to define bins

■ Kolmogoroff-Smirnow-TestFor continuousNo need to define bins

■ Anderson-Darling-TestFor continuousNo need to define bins

■ Root-Mean-Square-ErrorFor continuous and discrete dataNo need to define bins

■ The probability of a sample data drawn from a certain distribution is measured by P-values (called observed significance level)

Risk Analysis


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


Qualitative 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).

■ The process:

Policy

StandardsIdentification

Asses

smen

tResponse Planning

Mon

itorin

gPolicy

StandardsIdentification

Asses

smen

tResponse Planning

Mon

itorin

g


Bow-Tie Diagram

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.

Fig. 51a: Bow-Tie Diagram


Risk Matrix (for projects)

Fig. 51b: Bow-Tie Diagram

Never heard of in E&P industry

Heard of in E&P industry

Has occured in company

Has occured several times in

company

Occurs frequently in

company

A B C D E

Improbable Unlikely Seldom Probable Frequent

1 Catastrophic

2 Major High

3 Moderate Medium

4 Minor Low

5 Slight

Probability

Cost Schedule Scope

>= EUR 10 mn > 6 months delay

Total change in project scope or leading to desastrous quality

>= EUR 2 mn up to < 10 mn

2 - 6 months delay

Major change in project scope or

leading to bad project quality

>= EUR 100.000 up to < 2 mn

2 week - 2 month delay

Moderate change in project scope or leading to inferior

quality

>= EUR 10.000 up to < 100.000

2 days - 2 weeks delay

Minor change in project scope or leading to inferior

quality

< EUR 10.000 < 2 days delay

Marginal change in project scope and

quality

No consequence No consequence No consequence

Con

sequ

ence


Basic Problems of Risk Analysis■ Incomplete understanding■ Not independent trails■ Little data or experience■ Price instability■ Geology as an art

■ These factors make the judgement of probabilities in petroleum exploration difficult.



Judging Probability of Recovery■ What is the wildcat success ratio?

■ Derive from past success rates■ Calculate the geologic risk factor

Considered factors:SourceMigrationTimingThermal MaturityReservoir (porosity and permeability)TrapSeal

■ P(wildcat discovery)=P(trap) x P(source) x P(porosity and permeability) x etc.



Three Level Estimation of Risk

■ Is used instead of two discrete levels:Dry hole Average discovery

■ The three levels are:Low MediumHigh



Monte Carlo Simulation

■ Numerical procedure■ Random numbers provide computer-aided an

artificial sample■ Pioneers:

Earl George Buffon John von Neumann

■ Software packages in use:@RiskCristal Ball


Monte Carlo Process

■ Workflow:Define variables

Develop the deterministic projection model

Sort the input variables in two groups

Define distributions for random numbers

Perform the simulation trails

Calculate EMV and preparing graphical displays

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

i=n?no

yes

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.


Random Numbers

■ 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

random numbers are reproducible



Sampling■ Monte Carlo Sampling

■ Latin Hypercube Sampling


Fig. 52: Monte Carlo Sampling

Fig. 53: Latin Hypercube Sampling


Result Interpretation

■ 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


Main Fields of Application

■ Risked Costs

■ Risked Economics

■ Risked Schedule


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)

■ Different definition in literature!

Cf. Gleißner (2004) and Homberg, Stephan (2004)

Fig. 59: Selected Measures of Risk


Risked Schedules

■ Stochastic Inputs:Durations of project tasksStart dates of project tasksPredecessor linksCalendarGlobal variables

■ Outcome:Ranges, P10, P50, P90, and expected end datesProbability of meeting a deterministic schedule

Fig. 59a: Risked Gantt Chart

Fig. 59b: Important issue in risking schedules

Within probabilistic schedule analyses, a closer look on the project schedule is taken by means of a Monte Carlo simulation.

Sensitivity Analyses


Sensitivity Analysis

■ A way to handle uncertainty

■ Demonstrates the significance of uncertain elements in economic evaluations

■ Typical items for sensitivity analysis:Investment

Operating costs

Reserve size

Production rates

Prices

etc.

Cf. Allen, Seba (1993), p. 213.


Deterministic Sensitivity Analysis

■ Where the range of outcome is known but not the probability

■ Input parameters in an economic model are changed over a certain range

■ Y-axis represents an economic yardstick

■ X-axis represents the fractional change of the input parameters

■ Does not depict interrelations between input parameters

Cf. Allen, Seba (1993), p. 213ff.

Fig. 60: Spider Diagram


Probabilistic Sensitivity Analysis

■ The input parameters of an economic valuation model have probability distribution

■ Correlation- or Regression-Coefficients of every input parameter and the output are calculated

■ Visualisation is normally done in a tornado diagram

■ Does depict interrelations between input parameters

Fig. 62: Tornado Diagram

Fig. 61: Correlation diagram


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.

Advanced Petroleum Economics Staber

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