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# Exponential Growth Exponential growth occurs when the rate of ...

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### Exponential Growth Exponential growth occurs when the rate of ...

1. 1. 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?
2. 2. Q 0 = initial quantity R= percent rate of growth= percent change per time r= decimal rate of growth = fractional change per time = r / 100 Then
3. 4. Doubling time T 2 T 2 = time for quantity to increase to twice current value Approximate rule of thumb T 2 = 70/(% rate of growth)
4. 5. 2 1 4 16 (8) 32 (16) 64 (32) 8 (4) 8 (4) (2)
5. 6. 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
6. 8. 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
7. 9. 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.
8. 10. 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.
9. 11. Laherrère J.H. 1998 &quot;The evolution of the world's hydrocarbons reserves&quot; translation of SPE June 17, http://dieoff.com/page178.htm
10. 12. http://www.eia.doe.gov/pub/oil_gas/petroleum/presentations/2000/long_term_supply/LongTermOilSupplyPresentation.ppt
11. 13. Laherrère J.H. 1998 &quot;The evolution of the world's hydrocarbons reserves&quot; translation of SPE June 17, http://dieoff.com/page178.htm
12. 14. “ Definition(s)” of Proved Reserves Laherrère J.H. 1998 &quot;The evolution of the world's hydrocarbons reserves&quot; translation of SPE June 17, http://dieoff.com/page178.htm
13. 15. 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.
14. 16. 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 Time by M.Carr & T.Coulter Published on 5 Feb 2005 by Bloomberg .
15. 17. OPEC Bulletin, February 1996, pp 7-11 http://www.oilcrisis.com/laherrere/disctrnd.htm
16. 18. OPEC Bulletin, February 1996, pp 7-11 http://www.oilcrisis.com/laherrere/disctrnd.htm
17. 19. Laherrère J.H. 1998 &quot;The evolution of the world's hydrocarbons reserves&quot; translation of SPE June 17, http://dieoff.com/page178.htm
18. 20. http://www.iiasa.ac.at/Research/ECS/IEW2001/pdffiles/Papers/Laherrere-long.pdf
19. 22. Net Oil Billions of Barrels Figure II - 1. Net Difference Between Annual World Oil Reserves Additions a nd Annual Consumption 0 - 20 20 40 1940 2000 Year
20. 24. 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% 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 Source: USGS and Colin Campbell
21. 25. http://production. investis .com/bp2/ ia /stat/
22. 26. 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