Exponential Growth

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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 year Populations 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?
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Q0 initial quantity R percent rate
of growth percent change per time r decimal
rate of growth fractional change per time r
/ 100 Then
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Doubling time T2 T2
time for quantity to increase to twice current
value Approximate rule of thumb
T2 70/( rate of
growth)
5
1
2
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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
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Some Basic Definitions Q(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
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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.
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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.
11
Laherrère J.H. 1998 "The evolution of the world's
hydrocarbons reserves" translation of SPE June
17, http//dieoff.com/page178.htm
12
http//www.eia.doe.gov/pub/oil_gas/petroleum/prese
ntations/2000/long_term_supply/LongTermOilSupplyPr
esentation.ppt
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Laherrère J.H. 1998 "The evolution of the world's
hydrocarbons reserves" translation of SPE June
17, http//dieoff.com/page178.htm
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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
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BPs Position?
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Shell Downsizes
Shell Cuts Oil and Gas Reserves for the Fifth
Time by M.Carr T.Coulter
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.
Published on 5 Feb 2005 by Bloomberg.
17
OPEC Bulletin, February 1996, pp 7-11
http//www.oilcrisis.com/laherrere/disctrnd.htm
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OPEC Bulletin, February 1996, pp 7-11
http//www.oilcrisis.com/laherrere/disctrnd.htm
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Laherrère J.H. 1998 "The evolution of the world's
hydrocarbons reserves" translation of SPE June
17, http//dieoff.com/page178.htm
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http//www.iiasa.ac.at/Research/ECS/IEW2001/pdffil
es/Papers/Laherrere-long.pdf
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Net Oil
Billions of Barrels
Figure II
-
1. Net Difference Between Annual World Oil
Reserves Additions a
nd Annual Consumption
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Published Estimates of World Oil Ultimate Recovery
USGS 5 2000
USGS Mean 2000
USGS 95 2000
Campbell 1995
Masters 1994
Campbell 1992
Bookout 1989
Masters 1987
Martin 1984
Nehring 1982
Halbouty 1981
Meyerhoff 1979
Nehring 1978
Nelson 1977
Folinsbee 1976
Adams Kirby 1975
Linden 1973
Moody 1972
Moody 1970
Shell 1968
Weeks 1959
MacNaughton 1953
Weeks 1948
Pratt 1942
0
0.5
1
1.5
2
2.5
3
3.5
4
Trillions of Barrels
Source USGS and Colin Campbell
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http//production.investis.com/bp2/ia/stat/
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Member States of the Organization of Petroleum
Exporting Countries   State membership, Date of
membership and Status Iran - September 1960
Founder Member Iraq - September 1960 Founder
Member Kuwait - September 1960 Founder
Member Saudi Arabia - September 1960 Founder
Member Venezuela - September 1960 Founder
Member Qatar - December 1960 Full Member Libya -
December 1962 Full Member Indonesia - December
1962 Full Member United Arab Emirates November
1967 Full Member Algeria July 1969 Full
Member Nigeria July 1971 Full Member Ecuador
November 1973 Full Member (Left OPEC in
1992) Gabon December 1973 Associate Member