Exponential Growth

Exponential growth occurs when the rate of change of some quantity is proportional to the current amount of the quantity. Some familiar examples –

Bank account earning 5% per yearPopulations of some species (i.e. bacteria in a culture)GDP of some nation rising at 4% per year Decay of radioactive material

. . .P (production or extraction) of petroleum?

Q0= initial quantity R= percent rate of growth= percent change per timer= decimal rate of growth = fractional change per time = r / 100Then

1 0

22 1 0 0

2 33 2 0 0

1 0

* (1 )

* (1 ) * (1 )(1 ) * (1 )

* (1 ) * (1 ) (1 ) * (1 )

...

* (1 ) * (1 )nn n

Q Q r

Q Q r Q r r Q r

Q Q r Q r r Q r

Q Q r Q r

Doubling time T2

T2 = time for quantity to increase to twice current value Approximate rule of thumb T2 = 70/(% rate of growth)

2

1 4

16(8)

32(16)

64(32)

8(4) 8(4)

(2)

In a single doubling time there is more growth than that throughout all previous history.

... Producing oil is obviously a self-depleting activity. Every year you've got to find and develop reserves equal to your output just to stand still, just to stay even. This is as true for companies as well in the broader economic sense it is for the world … For the world as a whole, oil companies are expected to keep finding and developing enough oil to offset our seventy one million plus barrel a day of oil depletion, but also to meet new demand.

Vice-President Chaney at the London Institute of Petroleum Autumn lunch in 1999

http://www.energybulletin.net/349.html

World Population (Billions)http://www.un.org/esa/population/publications/sixbillion/sixbilpart1.pdf (p.5)

0

1

2

3

4

5

6

7

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

year (AD)

Some Basic DefinitionsQ(t) = cumulative production of oil to date (time t)

P(t) = rate of production (often in thousands of barrels/year)

Reserves = potentially recoverable oil yet in place

Discovery = estimate of oil yet to be discovered

Unrecoverable = oil that must be left behind due to physical,

economic reasons

EUR = Expected Ultimate Recovery = Q(t) after infinite time

EUR = Q(t) + reserves + discovery

R/P ratio = current reserves/ current production

Reserves

SEC- Companies reported on stock exchanges governed by SEC rules may list only proved reserves defined as amount of oil that lies near a producing well and with “reasonable certainty” can

be recovered profitably with current technology.

Reserve growth Given the stringent SEC rules stated “proved” reserves are often too low. As the field matures estimates of the proved reserves are revised upwards, a process known as reserve growth but often confused with new discoveries. Reserve growth most often does not represent improved knowledge of the reservoir.

Agencies or organizations not bound by SEC rules may use other definitions. One set uses classifications proved, probable and possible,each corresponding to a probability that level of reserve actually exists. Nominal values are roughly as follows:

P1 (proved) corresponds to about 90% likelihood.

P2 (probable) corresponds to about 50% likelihood.

P3 (possible) corresponds to about 10% likelihood.

As an example we will see the US Geologic Survey uses 95%, 50% and 5% as its definitions. Here there is no consistent set of definitions. Some argue that (portions of) the industry prefer the ambiguity.

Laherrère J.H. 1998 "The evolution of the world's hydrocarbons reserves" translation of SPE June 17, http://dieoff.com/page178.htm

Different Interpretations of a Hypothetical 6,000 Billion BarrelWorld Original Oil-in-Place Resource Base

0

1,000

2,000

3,000

4,000

5,000

6,000

USGS Approach 1995 Campbell/Laherrere Approach

Unrecoverable

ReservesGrowth

Undiscovered

ProvedReserves

CumulativeProduction

3,000Billion

Unrecovered

4,200Billion

Unrecovered

50%RecoveryFactor withReservesGrowth

30%RecoveryFactor

40%RecoveryFactorWithoutReservesGrowth

Reserves Growth Adds 10%

Bil

lio

n B

arr

els

http://www.eia.doe.gov/pub/oil_gas/petroleum/presentations/2000/long_term_supply/LongTermOilSupplyPresentation.ppt

Laherrère J.H. 1998 "The evolution of the world's hydrocarbons reserves" translation of SPE June 17, http://dieoff.com/page178.htm

“Definition(s)” of Proved Reserves

Laherrère J.H. 1998 "The evolution of the world's hydrocarbons reserves" translation of SPE June 17, http://dieoff.com/page178.htm

BP’s Position?

WORLD oil production is likely to peak in the next decade, much earlier than many international forecasts, a senior BP executive has told The Business.

BP exploration consultant Francis Harper said he estimated the world's total original usable oil resources - the amount of oil before drilling began - at about 2.4 trillion barrels of oil. This is considerably less than the 3 trillion assumed by bullish commentators such as the US government's Geological Survey. This points to oil production peaking between 2010 and 2020.

Shell Downsizes

Royal Dutch/Shell Group cut its reserves for a fifth time, showing its oil and gas holdings were at least a third lower than reported in 2002 after the company misled investors and failed to find new fields.

Shell Cuts Oil and Gas Reserves for the Fifth Timeby M.Carr & T.Coulter

Published on 5 Feb 2005 by Bloomberg.

OPEC Bulletin, February 1996, pp 7-11 http://www.oilcrisis.com/laherrere/disctrnd.htm

OPEC Bulletin, February 1996, pp 7-11 http://www.oilcrisis.com/laherrere/disctrnd.htm

Laherrère J.H. 1998 "The evolution of the world's hydrocarbons reserves" translation of SPE June 17, http://dieoff.com/page178.htm

http://www.iiasa.ac.at/Research/ECS/IEW2001/pdffiles/Papers/Laherrere-long.pdf

Oil Discovery Trend

Net Oil

Billions of Barrels

Figure II-1. Net Difference Between Annual World Oil Reserves Additions and Annual Consumption

0

-20

20

40

1940 2000Year

http://www.csis.org/energy/040224_simmons.pdf

Published Estimates of World Oil Ultimate Recovery

0 0.5 1 1.5 2 2.5 3 3.5 4

Trillions of Barrels

USGS 5% 2000USGS Mean 2000USGS 95% 2000Campbell 1995Masters 1994Campbell 1992Bookout 1989Masters 1987Martin 1984Nehring 1982Halbouty 1981Meyerhoff 1979Nehring 1978Nelson 1977Folinsbee 1976Adams & Kirby 1975Linden 1973Moody 1972Moody 1970Shell 1968Weeks 1959MacNaughton 1953Weeks 1948Pratt 1942

Source: USGS and Colin Campbell

http://production.investis.com/bp2/ia/stat/

Member States of the Organization of Petroleum Exporting Countries 

State membership, Date of membership and Status:

Iran - September 1960 Founder MemberIraq - September 1960 Founder MemberKuwait - September 1960 Founder MemberSaudi Arabia - September 1960 Founder MemberVenezuela - September 1960 Founder MemberQatar - December 1960 Full MemberLibya - December 1962 Full MemberIndonesia - December 1962 Full MemberUnited Arab Emirates – November 1967 Full MemberAlgeria – July 1969 Full MemberNigeria – July 1971 Full MemberEcuador – November 1973 Full Member (Left OPEC in 1992)Gabon – December 1973 Associate Member