World Oil Depletion: Diffusion Models, Price Effects, Strategic and Technological Interventions

Renato Guseo ASPO-5 San Rossore 18-19 July 2006, Italy

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World Oil Depletion: Diffusion Models, Price Effects, Strategic and Technological Interventions

Department of Statistical Sciences

Renato Guseo

University of Padova, Italy

5-th International ASPO Conference,San Rossore, 18-19 July 2006, Italy


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World Crude Oil Production

0

10000

20000

30000

40000

50000

60000

70000

80000

1900 10 20 30 40 50 60 70 80 90 2000

Thousand barrels daily

Global

OPEC

USA (NGL)

FSU

CSI


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World Production and Prices

Crude Oil Production and Prices per Barrel

year

VariablesProduction (barrel x 1000)Price (dollars, 2002)

1900 1920 1940 1960 1980 2000 20200

2

4

6

8(X 10000)

0

20

40

60

80

Fonte: BP Statistical Review of World Energy, 2004


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Growth and Development after World War II -1-

• Cohen, J.E. (2003) Human Population: The next Half Century, Science, 203, 1172-1175;

• Exceptional demographic expansion;• Rural population peak in rich countries: 1950;• Increse of world average life: 30 years in 1900

and 65 years in 2000;• Population: 6.3 billion in 2004; United Nations

Population Division: 8.9 billion in 2050 (ex medium variant scenario forecasting);

• Regional population contraction in 2050: Japan -24%; Italy -22%; FSU -29%;


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• USA dominance in oil estraction and refining: shock 1918 (positive with local memory);

• Decisive military advantage. Competitive advantage after World War II;

• American way of life;• Energetic Surplus based on cheap crude oil;• Structural change in sustainable economic

evolution based on non-renewable resources;


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• Today risk: physical restrictions towards expansion in oil production due to emergent demand by China and India;

• Risk of a late migration towards renewable energetic resources;

• Emerging technologies are not completely sustainable and efficient (fuel-cells, hydrogen, photovoltaic systems, solar thermal systems, eolic systems, etc.).


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Recent strategic researches

1. Morse, E.L. e Jaffe, A.M. (2001). “Strategic Energy Policy Challenges for the 21st Century”; (2000 - aprile 2001); James A. Baker III Institute for Public Policy of Rice University, Texas; Council of Foreign Relations of USA

2. National Energy Policy Development Group, (2001, Task Force supervised by D. Cheney).

• USA energetic policy since 1940 – security -;• Global Economic growth based on a production surplus

with cheap prices;• New emerging world oil demand; • Supply dependence (Midle East).


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Non-Renewable Resources Depletion: Hubbert and recent

developtments• Hubbert, M.K. (1949). Energy from fossil fuels, Science, 4,

103-109.

• In 1956 Hubbert forecasts the peak of annual production within 48-lower states in USA by year 1970;

• Campbell, C. e Laherrère, J. (1998). The End of Cheap Oil, Scientific American, March 1998.

• Laherrère, J. (2003). Modelling future oil production, population and the economy, ASPO 2nd international workshop on oil and gas, Paris, 26-27.

• ASPO (Association for the Study of Peak Oil and Gas);


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Economic and financial “estimation” of oil reserves: inflated figures

• Warranties on international long-term loans;

• Investments on production plants;

• OPEC restrictions overcoming: export is proportional to the “declared” reserves.

BP - Statistical Review of World Energy

Source: BP Statistical Review of World Energy


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Ultimate Recoverable Resouce: URR• URR: total amount of a finite resource obtainable at the end of

extraction process;

• Geologic estimates of Oil URR during the life- cycle of resource extraction:

1. Production to date. Oil heterogeneity. (weight 100%);2. Proven reserves. Ex-post recovery factor 35% is a median and

today’s variability is very large. Revision principles and “reserves growth” (USGS) enlarge uncertainties;

3. Probable and possible reserves: undiscoverd petroleum based on subjective assessments (probability, e.g. 5%).

•Could we do a simple weighted sum of such components? Probably not


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Recent statistical modeling • Guseo, R. (2004) Interventi strategici e aspetti competitivi nel

ciclo di vita di innovazioni, Working Paper Series, 11, Department of Statistical Sciences, University of Padua.

• Guidolin, M. (2004) Cicli energetici e diffusione delle innovazioni. Il ruolo dei modelli di Marchetti e di Bass, Thesis, University of Padua.

• Guseo, R and Dalla Valle, A. (2005) Oil and Gas Depletion: Diffusion Models and Forecasting under Strategic Intervention, Statistical Methods and Applications, 14(3), 375-387;

• Guseo, R., Dalla Valle, A. and Guidolin, M. (2006) World Oil Depletion Models: Price effects compared with strategic or technological interventions, Technological Forecasting and Social Change (in press);

• Guseo, R. (2006) Bass-let Detection of Automobile Successive Generations: Evidence from the Italian Case (submitted).


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Crude Oil Production: Diffusion of an Innovation

• Oil production is modulated by the dynamics of international demand;

• Oil demand is a function of the diffusion processes related to basical technologies (transport, chemical industries, heating, etc.);

• Diffusion of technological innovations is conditioned by social communication structure: innovators and imitators (word-of-mouth)


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Bass Equation: BM• z’(t) = mf(t) = m[p+qF(t)][1-F(t)] or• z’(t) = pm+(q-p)z(t) - (q/m) z(t)2 (Riccati)

• z’(t)=mf(t) (instantaneous adoptions); • f(t)=F’(t) • z(t)=m F(t) (cumulative adoptions);

F(t)=z(t)/m• f(t)/[1-F(t)]=p+qF(t) Bass Hazard rate • m=potential market; carrying capacity; URR• p=innovation coefficient, p>=0• q=imitation coefficient, q>=0


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Normalized Bass models: BM and GBM

BM: f(t)/[1-F(t)]=[p+qF(t)] “Standard”

GBM: f(t)/[1-F(t)]=[p+qF(t)] x(t) “GBM”

x(t) is a quite general intervention function: integrable, positive and “centered” around unitary “neutral pole”: 1.

Representation of temporal price variations, of advertising pressure, of political, strategic, legal, environmental interventions.


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Equation Solution: GBM

IIII btatbtatcctx

)()(2)()(12211

1)(

Exp. shocks

Rect. shocks

Mixed shocks

IecIec aab

aabtx

t

t

t

t

)(

)(

2)(

)(

12

22

1

111)(

IIcIec baaabtx

ttt

t

)()(2)(

)(

1221

111)(

e

et

p

q

t

mtz

txzmm

zqptz

dxqp

dxqp

0

0

)()(

)()(

1

1)(

)())(()('


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Plot of Fitted Model

t

GBb

pC

0 20 40 60 800

0,5

1

1,5

2

2,5

3(X 1000)

Great Britain: GBM, 2 mixed sh.Estimation method: MarquardtEstimation stopped after maximum iterations reached.Number of iterations: 31Number of function calls: 330Estimation Results Asymptotic 95,0% Asymptotic Confidence IntervalParameter Estimate Standard Error Lower Upper----------------------------------------------------------------------------m 4513,39 154,806 4196,77 4830,0p 0,0000708436 0,0000324773 0,00000441993 0,000137267q 0,111872 0,00516425 0,10131 0,122434c1 8,54019 1,02935 6,43493 10,6454b1 -0,250721 0,0114596 -0,274159 -0,227284a1 10,7677 0,458356 9,83028 11,7052c2 -0,331417 0,0175489 -0,367309 -0,295526a2 23,4341 0,190843 23,0438 23,8245b2 28,6819 0,164258 28,3459 29,0178----------------------------------------------------------------------------Analysis of VarianceSource Sum of Squares Df Mean Square Model 6,52091E7 9 7,24545E6Residual 657,546 29 22,674-----------------------------------------------------Total 6,52097E7 38Total (Corr.) 3,31712E7 37R-Squared = 99,998 percentR-Squared (adjusted for d.f.) = 99,9975 percentStandard Error of Est. = 4,76172Mean absolute error = 3,10566Durbin-Watson statistic = 0,889298

Positive Shock with local memory


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Great Britain: analysis• The “saddle” 1987-

1991-1999 is perfectly absorbed by a rectangular shock:

• a) Petroleum Reven Tax modification;

• b) pipelines restructuring 1986-1991; symmetric behaviour confirms ordinary regime;

• c) partial production stall due to the reduction of new discoveries.

Multiple X-Y Plot

t

Variables GBbp DIFF(PRED) DIFF(FOR)

0 20 40 60 80 0

30

60

90

120

150


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USA: 48 lower States and Alaska,one exponential shock

Estimation Results---------------------------------------------------------------------------- Asymptotic 95,0% Asymptotic Confidence IntervalParameter Estimate Standard Error Lower Upper----------------------------------------------------------------------------m 224,885 0,784401 223,328 226,442p 0,000445866 0,0000177788 0,000410571 0,000481162q 0,0571941 0,000403937 0,0563922 0,057996c1 0,682617 0,0735348 0,536632 0,828602b1 -0,0852885 0,00948373 -0,104116 -0,0664609a1 18,0477 0,981086 16,1 19,9954---------------------------------------------------------------------------- Analysis of Variance-----------------------------------------------------Source Sum of Squares Df Mean Square -----------------------------------------------------Model 735809,0 6 122635,0Residual 7,39124 95 0,0778026-----------------------------------------------------Total 735817,0 101Total (Corr.) 352880,0 100 R-Squared = 99,9979 percentR-Squared (adjusted for d.f.) = 99,9978 percentStandard Error of Est. = 0,278931Mean absolute error = 0,207909Durbin-Watson statistic = 0,173839

Plot of Fitted Model

t

cum

0 20 40 60 80 100 1200

40

80

120

160

200

Multiple X-Y Plot

t

VariablesbariliDIFF(PREDb1)DIFF(PREDbe1)

0 20 40 60 80 100 1200

1

2

3

4

Positive shock with local memory


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USA: 48 lower States and Alaska, ARMAX(4,0,2) sharpening

Forecasting - bariliAnalysis SummaryData variable: bariliNumber of observations = 101Start index = 1,0Sampling interval = 1,0 Forecast Summary----------------Forecast model selected: ARIMA(4,0,2) + 1 regressorNumber of forecasts generated: 40Number of periods withheld for validation: 0 ARIMA Model SummaryParameter Estimate Stnd. Error t P-value----------------------------------------------------------------------------AR(1) 1,21416 0,691695 1,75534 0,082426AR(2) -0,140994 1,11031 -0,126986 0,899220AR(3) -0,146337 0,49692 -0,294488 0,769028AR(4) -0,132467 0,0891259 -1,48629 0,140514MA(1) 0,591549 0,68527 0,863235 0,390183MA(2) 0,299352 0,650254 0,460362 0,646308DIFF(PREDbe1) 0,20426 0,0890786 2,29303 0,024052----------------------------------------------------------------------------Backforecasting: yesEstimated white noise variance = 0,00495321 with 95 degrees of freedomEstimated white noise standard deviation = 0,0703791Number of iterations: 17

Time Sequence Plot for bariliARIMA(4,0,2) + 1 regressor

baril

i

actualforecast95,0% limits

0 30 60 90 120 150-1

0

1

2

3

4

Shock: 1918


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Alaska: ARMAX(2,0,1) sharpening

Multiple X-Y Plot

t

Variables alaskap DIFF(FORar2ma1)

0 20 40 60 80 0

0,4

0,8

1,2

1,6

2

2,4 Residual Autocorrelations for alaskac

ARIMA(2,0,1) with constant + 1 regressor

lag

Aut

ocor

rela

tions

0 3 6 9 12 15-1

-0,6

-0,2

0,2

0,6

1

ARIMA Model SummaryParameter Estimate Stnd. Error t P-value----------------------------------------------------------------------------AR(1) 0,323713 0,100318 3,22686 0,002667AR(2) -0,172177 0,054492 -3,15967 0,003195MA(1) -0,818595 0,102552 -7,98224 0,000000PREDbme1 0,847508 0,0501864 16,8872 0,000000Mean -0,0143829 0,0282678 -0,508809 0,613990Constant -0,0122034 ----------------------------------------------------------------------------Backforecasting: yesEstimated white noise variance = 0,00281514 with 36 degrees of freedomEstimated white noise standard deviation = 0,0530579Number of iterations: 20


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World Oil data:Daily Production

Sources:

• Industriedatenbank 2001 (1900 – 1986)

• BP Statistical Review of World Energy (1987- 2002)


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GBM: x(t) pure prices control


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GBM exp shocks + price effect


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Guidolin (2004): GBM, 2 exp shocks

World Oil Depletion Models

year

VariablesProduction datagbm2e+for

1950

1960

1970

1980

1990

2000

2010

0

2

4

6

8(X 10000)


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GBM: 3 exp shocks (memory persistence)

World Oil Depletion Models

year

VariablesProduction datagbm3e+for

1950

1960

1970

1980

1990

2000

2010

0

2

4

6

8(X 10000)


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GBM 3 exp shocks: estimates(memory persistence)

q/p = 608 Qp=1%;

999994708,02 R

06,17)1951/.( parzmF


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World Oil Depletion: GBM with three shocks vs Hubbert-Bass

Oil Peak: 2007

Depletion time 90% : 2019 Depletion time 95% : 2023

URR=1524 Gbo


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Oil market Operators: prices growth

• Demand and supply self-control similar to 1973 and 1979-’83 behaviour. Extension of crude oil economic life cycle;

• Limited techonological efficiency margins due to the improvementes of 70’s , 80’s and 90’s;

• Savings through “life styles” modification: this is the central dilemma in industrialized countries;

• Sluggishness of middle class whose life style is based on an expected irreversible and indefinite growth and development.


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New Emergent Economies

• Increase in crude oil requirements by recent emergent economies: China, India, and other Asiatic countries;

• US EIA (Energy Information Administration) “forecasts” a world oil demand of 40 Gbo/year (or 109.6 milion daily barrels) in 2020;

• Guseo, Dalla Valle, Guidolin (2006) and Bakhtiari (2004) forecast, in 2019-20, only 55 milion daily barrels.


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Crude Oil: Area consumption

Consumi medi giornalieri (in barrel X 1000)

Anno

Variables

North Ame

Europe Eurasia

Asia Pacific

South Central Ame

Middle East

Africa

1960 1970 1980 1990 2000 20100

0,5

1

1,5

2

2,5

3(X 10000)


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Outlook• Nuclear fission perspective is probably a tardy

strategy with known collateral externalities. A new plant in Italy can be launched after 13-15 years;

• Technological, political and economic efforts must be distributed in different areas: photovoltaic, solar thermal, bio-fuel, biomass, eolic, hydrogen, etc.;

• Electric sector: distributed investments (photovoltaic, micro-cogeneration, etc.).

• Individual and collective mobility.


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World Oil Depletion: GBM with three shocks vs Hubbert-Bass vs five shocks scenario


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World Oil Depletion: GBM with three shocks vs five shocks vs four shocks scenarios

Shock 2008 (sim. 1951)

Depletion time 90% : 2017

Documents

World Oil Depletion: Diffusion Models, Price Effects, Strategic and Technological Interventions