# Energy consumption: fossil fuels and the growth issue

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1 Energy consumption: fossil fuels and the growth issue 1

2 Daily energy consumption per capita in 2005 WORLD United Arab Emirates Kuwait Canada USA Australia Netherlands Sweden Saudi Arabia Russian Federation France Japan Germany Switzerland United Kingdom Spain Denmark Venezuela Poland Mexico China Brazil India Philippines Megajoules per capita per day 2

3 Exajoules per year Annual world energy consumption Year 3

4 Average annual growth rates Country Group Annual Growth Rates (%) Population Energy consumption North America Latin America Western Europe Eastern Europe Africa Middle East and South Asia South-East Asia and the Pacific Far East

5 Exponential growth Let energy consumption be N at some time t It started as N 0 at time zero (t=0) Its growth rate is dn/dt (eg barrels of oil per year) Suppose its growth rate is always proportional to its present value Then dn/dt = constant.n = kn or dn/n = k.dt Integrate this: ln(n) = kt + constant So ln(n 0 ) = 0 +constant Hence the constant is just ln(n 0 ) 5

6 Ctd.. Therefore ln(n) = ln(n 0 ) + kt or ln (N/N 0 ) = kt 25 Or N = N 0 e kt k is called the growth constant N N t 6

7 Ctd.. If the percent growth rate is R then each year the multiplier is (1+R/100) and so N = N 0 (1+R/100) t But we have already N = N 0 e kt So k = ln (1+R/100) See example 2-1 in text 7

8 More doubling time How long to double the consumption if the growth constant is k? We call this the doubling time T D Set N = 2N 0 and so 2N 0 = N 0 e kt D Therefore e kt D = 2 or kt D = ln2 = or T D = 0.693/k (sometimes called T 2 ) 8

9 Semilog graphs ln N = ln N o + kt is same as y = const + gradient.x ie it is a rising straight line. Plot N versus t on on semilog paper and you get a straight line its slope tells you the k value Rn N Rn N 0 0 slope = k t 9

10 Exajoules per year Semi-log plot of world energy consumption Year This is a pretty good fit to a straight line with k = 0.03 yr -1 10

11 How long will a resource last (eg oil)? There are 2 extreme models: Constant production model (stupid model) Exponential growth model (unrealistic model in the long run) [Later we will look at a more sophisticated model due to M.K. Hubbert] Distinguish between RESERVES (known stuff, price OK) and RESOURCES (includes inferred and expected stuff, with some optimism about technology and price) 11

12 Constant production model This model just divides the resource by the present annual use to deduce the lifetime, ie it assumes there is no increase in use simple but wrong gives the most optimistic scenario Look at some examples : A signifies reserves B signifies resources 12

13 Fossil fuel reserves and resources (EJ) Region Oil reserves Oil resource N-gas reserves N-gas resource Coal reserves Coal resource World Canada USA production EJ/y Region Oil N-gas Coal World Canada USA

14 Fossil fuel lifetimes (in years) assuming constant production at 2005 level and based on Resource estimates Oil N-gas Coal World Canada USA

15 See textbook re: New fossil fuels 1 Tar sands and associated limestone deposits Oil shales Hydrates CANADIAN TAR SANDS - Bitumen is extracted from sandstone and dirt mostly by surface mining. 90% of deposits need in situ extraction eg drilling wells and injecting steam under pressure. Extraction has moved in 2 decades from a risky new technology to a major oil supply industry. Future direction includes adding solvents to the steam to decrease energy use and increase output. Huge energy and water inputs are needed; there are very large greenhouse gas emissions. 15

16 New fossil fuels 2 LIMESTONE DEPOSITS can t be mined and they dissolve in water. Very little progress to date. New interest in electrical heating methods in COLORADO OIL SHALES are hard rock containing more than 8 trillion barrels of oil. US gov t owns 70% of formations. Shell can produce fluid oil by deep-underground heating at 370 o C for 6 months: process is energyintensive. Chevron-LANL have gov t contract starting Sept 2006 to develop green chemical methods. US DOE 2004 report states that industry could start in 2010 and by 2020 would replace 35% of US crude oil imports 16

17 Liquefied natural gas (LNG) Despite expected export of northern Canadian resource, US expects supply-demand gap Several LNG terminals on ocean shore under construction or planning: new pipelines will radiate from them, especially in NE USA A US market share of 1% in 2002 could be 10% in 2020 By 2020 Europe will have to import 80% of its natural gas: reliance on Russia is troubling: Germany gets 30% of its energy from Russia, expects 70% by 2025 Hence European discussion of move to LNG imports from Qatar, Trinidad, Nigeria, Iran, Indonesia 17

18 Extensive resource data - see BPAmoco website Many useful charts one example follows The corresponding numerical data can be downloaded into an Excel spreadsheet. Regional data are broken down by country. There are charts and data for oil, gas, coal, nuclear, hydro and total energy. This appears to be an excellent resource but like all such data it should be treated cautiously. 18

19 19

20 Exponential growth model Does not seem realistic to expect continued exp growth right up to a complete crash - but it does show a worst case scenario Consider a resource that has amount Q T remaining now - set time now as t = 0 Set lifetime as T Then Q T will be equal to integrated area of production curve from t=0 to t=t 20

21 Annual Production Exponential growth model N (t ) )t time 21

22 Annual Production Area = Q T time T 22

23 Integrate the entire curve from 0 to T Q T = 0 T N0 e kt dt Q T = [ (N 0 /k) e kt ] T 0 = (N 0 /k) (e kt 1) Re-arrange: e kt = (kq T /N 0 ) + 1 And so kt = ln [ (kq T /N 0 ) + 1] Finally T = (1/k) ln [ (kq T /N 0 ) + 1] 23

24 T = (1/k) ln [ (kq T /N 0 ) + 1] Given the remaining resource Q T and the present production rate N 0, this equation provides the lifetime of the resource on the assumption of exponential growth right to the crash 24

25 Resource lifetimes with exponential growth 0% 2% 5% 10% Actual World oil % Canada oil % USA oil % World gas % Canada gas % USA gas % World coal % Can coal % USA coal % 25

26 Ctd. The above formalism was applied to our total RESOURCE estimates (see text). Try applying it yourself to the reserve data found in the BPAmoco website. And take a look at the data for other fossil fuels. 26

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