World Fossil-Fuels Depletion

L. David Roper
http://arts.bev.net/RoperLDavid/
21 December, 2011

Oil: Not Exactly Dead Dinosaurs

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Using the Depletion Theory that I have previously developed, I show here fits to United States and World extraction of crude oil, natural gas and coal. The depletion equation used to fit the extraction data is the Verhulst function:

The Q parameter is the total amount eventually to be extracted. The n parameter is a measure of the asymmetry: symmetric is n=1, skewed to early times is n<1 and skewed to later times is n>1.

United States Crude-Oil extraction
These data came from http://www.eia.doe.gov/pub/international/iealf/table24.xls.

United States Crude-Oil Extraction

U.S. crude-oil discoveries ( http://www.durangobill.com/Rollover.html) and a Verhulst-function fit to the data.
The total amount of U.S. crude oil to be discovered is about 253x109 barrels.

Fit of the Verhulst function to U.S. crude oil extraction. Note that the peak occurred 1975-8. This is the best example of crude-oil depletion.:

The total amount to be extracted is 250x109 barrels, almost exactly the same as for the fit to the U.S. crude-oil discoveries. The rising exponential time constant () is 15.8 years and the falling exponential time constant (n) is 27.3 years. The peak date is 1974.6 .

Fit of the Verhulst function to U.S. crude oil extraction and projection to 2100:

When natural resources peak they usually oscillate around the peak.

U.S. Crude-Oil Extraction with sinx/x oscillations on both sides of the peak:

The oscillation is mathematically represented by two sinx/x functions, one before the peak and one after the peak; they are added to the Verhulst function. An equally good fit can be obtained by using two Gaussian functions instead of sinx/x functions.

My reasoning for the oscillation is that, when starting to peak, great effort is made to keep the extraction increasing; after that fails and extraction starts to fall, great effort again is made to keep it from falling. Eventually that final great effort also fails.

Fit of the Verhulst function to U.S. crude oil offshore extraction and projection to 2100:

The red curve is the best fit, which is considerably higher than the result when the EIA 2009 estimate of offshore reserves (4129x106 barrels) is used to constrain the fit, shown by the blue curve.

BP Deepwater Horizon Oil Spill and Offshore Drilling
Comparison of U.S. offshore crude-oil extraction to total extraction:
Best fit to U.S. offshore crude-oil extraction of the total extraction:

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This shows the change in U.S. crude oil extraction since 1945. The biggest recent yearly decrease was -6.7% in 1989 during the BushGHW administration. The average yearly decrease was -3.1% for the BushGHW administration and -2.7% during the Clinton administration. Note that the yearly changes oscillate depending on many factors, but the general trend is downward. No administration should be blamed for most of these factors and no administration can change the fact that the U.S. is running out of economically feasible crude oil.

Alaska Crude-Oil Extraction

Data are from: http://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=PET&s=MCRFPAK1&f=M http://www.tax.alaska.gov/programs/documentviewer/viewer.aspx?426

The extraction peak occurred in less than 2 decades after the big Prudhoe Bay discovery.

Possible Alaska ANWAR crude-oil extraction:

A high-value assumption has been made that the eventual total extraction will be 1010 barrels. Further assumptions are that the initial speed of extraction will be ~30% less than the Prudhoe-Bay speed and that the asymmetry will be the same as for Prudhoe-Bay extraction.


United States Natural-Gas Extraction

Fit of the Verhulst function to U.S. natural gas extraction.

The short large blip is shale gas. So, shale natural gas adds a short large blip to the natural-gas extraction for the United States. It could be reduced in size and stretched out over a larger time interval, but I doubt it will be. The U.S. will probably extract and use it as fast as possible.

The jump just before 1950 is because the previous data did not include wet natural gas.

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United States Petroleum Consumption

These data came from http://www.eia.doe.gov/pub/oil_gas/petroleum/data_publications/petroleum_supply_monthly/current/txt/table_s02_a.txt. U.S. petroleum consumption since 1949. Note the sharp downward turn during the Carter administration (1977-1980); but then the increases started again by the end of Reagan's first term (1981-1988). Then consumption leveled off during the Bush administration (1989-1992) and then continued the upward trend during the Clinton administration (1993-2000). Note how the onset of Alaska extraction caused a temporary rise in U.S. extraction; but then, after a decade, began to decline. The Arctic National Wildlife Refuge is estimated to contain 7 x 109 bbl of oil. This is about one year's consumption, but it will probably be extracted over a decade or longer, which will be a negligible blip on these curves.

United States Petroleum Imports

United States Petroleum imports since 1960. Note the sharp downward trend during the Carter administration (1977-1980); but then the increases started again by the end of Reagan's first term (1981-1988). Then the imports leveled off during the Bush administration (1989-1992) and then continued the upward trend during the Clinton administration (1993-2000). Of course, when consumption increased as U.S. extraction went down, the shortfall had to made up by imports and a little taken from stock.

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United States Coal Extraction


The 340,000 curve is closest to the reported reserves + amount already extracted.

The blue curve is for total eventual extraction of 280 x 109 tons, which is the reserves given in http://www.eia.doe.gov/fuelcoal.html. (Click on Reserves below International Data at the bottom left.) The black curve is for twice that amount and the red curve is for half that amount.

Here is a fit with three Verhulst functions:

The amount to be extracted (area under the curve) is 562,000x10^6 ST (486,100x10^6) ST reserves in 2009 + 72,495x10^6 ST already extracted by 2009). (I.e., about 14% has already been extracted.) I suspect that the currently-shown “peak” will go higher, which means that the drop will then be faster. And there might be later peaks, which would be followed by a faster drop.

U.S. Coal energy/volume and a hyperbolic-tangent function fit to the data:

As seen below the final asymptote is somewhat above the energy content of lignite (14 MBtu/ST), as it should be. The initial asymptote is equivalent to mostly bituminous (20.5 MBtu/St), as it should be.

Putting the last two graphs together, the energy available from coal in the U.S. is

Although U. S. coal extraction peaks at ~2020, U.S. coal energy peaks at ~2005.

The energy contents of the three different classes of coal are (1 MBtu/ST = 0.8598 MJ/kg):

Coal energy density:
MJ/kg
MBtu/ST
Anthracite
32.50

28.0
Bituminous
24.00
20.5
Lignite
16.50

14.0

Most of the coal mined in the U.S. is bituminous, with a little lignite. Anthracite extraction is almost negligible:

U.S. Coal Areas:

Central 
Appalachia
12,500 Btu/lb, 
1.2 SO2/lb		 Northern 
Appalachia
13,000 Btu/lb, 
<3.0 SO2/lb		 Illinois Basin
11,800 Btu/lb, 
5.0 SO2/lb		 Powder 
River Basin 
8,800 Btu/lb, 
0.8 SO2/lb		 Uinta Basin
11,700 Btu/lb,
0.8 SO2/lb

1 Btu = 1055.056 joules = 2.930711x10-4 kWh
1 lb = 0.45359237 kg
1 MJ/kg = 429.9226 Btu/lb

Coal Prices Prediction

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World Crude-Oil Extraction

World crude-oil discoveries ( http://www.durangobill.com/Rollover.html) and a Verhulst-function fit to the data.
The total amount of World crude oil to be discovered is slightly less than 2 x 1012 (2 trillion) barrels.

World crude-oil extraction rate and a Verhulst-function fit to the data obtained by fitting the discoveries data and the extraction data together with a common value for the amount to discovered and extracted. That value searched to 1.965x1012 barrels.

The total amount to be extracted was fixed at 2 x 1012 (2 trillion) barrels, which is slightly more than for the fit to the discoveries data. The rising exponential time constant () is 4.1 years and the falling exponential time constant (n) is 54.2 years. The peak date is 1997.2 .

World crude-oil extraction per capita. The extrapolation into the future is obtain by using a fit to World population extrapolated into the future (http://arts.bev.net/roperldavid/WorldPop.htm).

Comparison of world oil discoveries and extraction.

The amount under both curves is about 2x1012 barrels.

This graph contains information that probably will have the greatest effect on those now living and born in the future. Crude Oil cannot be extracted if it has not been discovered! This graph shows very clearly why it is very unlikely that the final amount to be extracted will exceed 2x1012 barrels. So far the amount extracted has exceeded 1x1012 barrels, so we are more than halfway there!

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Monthly world oil extraction.

The amount extracted per month has been nearly level for three years.

World crude-oil prices

Possibly a better way to project future crude-oil prices is to fit the product of the past prices and the past extraction rate, which yields a world total cost in dollars for crude oil for each year. Neglecting inflation (which could be accounted for by an inflation index as a function of time), it is reasonable to assume that there is a maximum total value, represented by dollars, that the world will assign to crude oil as it becomes depleted. That is, a hyperbolic-tangent function fit to the product might be a reasonable projection to the product. The following graph shows such a fit:

Using the projection of world crude-oil extraction into the future, and the fit in the graph above of the product of price times extraction rate, the projected price of crude oil is:

Another way to project future crude-oil prices is to fit the product of the past prices and the past extraction rate and divide by the population for each year, which yields a world cost in dollars per person for crude oil for each year. Neglecting inflation (which could be accounted for by an inflation index as a function of time), it is reasonable to assume that there is a maximum total value, represented by dollars, that the average person inthe world will assign to crude oil as it becomes depleted. That is, a hyperbolic-tangent function fit to the product/quotient might be a reasonable projection to the product. The following graph shows such a fit:

Using the projection of world crude-oil extraction into the future, the projected world population, and the fit in the graph above of the product of price times extraction rate divided by the population, the projected price of crude oil is the blue curve in the following graph.:


The red curve is the same curve as in the third graph above.

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An interesting analyis of the effect of oil prices on financial markets. This paper inspired me to look at oil prices in a different way: It seems reasonable that the price of a non-renewable mineral will be an inverse power function of the amount left to be extracted. I did such a fit to the price of oil in the first week of January since 1978 as shown below.

The amount of crude oil left to be extracted for my best fit to the World extraction data & the discovery rate is given by the red curve here:

The price data for the first week in January fitted by the inverse power function:


The power searched to 4.388.

The prediction of the inverse-function fit for years up to 2030 is:

I expect that there will be fluctuations around the average curve, especially as panic sets in. For example, the price on 1 Jun 2009 was $126 and later that month it went as high as $140 or so. However, the price on 1 January 2009 was $93, which is the price used in this fit.

The prices fitted (blue dots in data above) are yearly 1 January prices, so the fit only prodicts prices for 1 January. You need to wait until the end of a year to get points to compare to the fit. (Since the price has been level at about $70 for the last several months, I assumed a for 1 January 2010 of $70. Each years as the 1 January price is known, I can refit the curve to get a better prediction for future years.

Gasoline Prices in the United States

This result can be used to predict the future price of gasoline in the United States for 1 January; it should be approximately linear in the price per barrel of crude oil. Here are those two prices:

A linear fit of the U.S. regular gasoline price to the fit to crude oil price obtained above yields:

The predicted U.S. regular gasoline price to 2030 is:

See the book $20 Per Gallon: How the Inevitable Rise in the Price of Gasoline Will Change Our Lives for the Better by Christopher Steiner.

Correlations of Energy-Minerals Prices and Consumer Energy Prices

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Saudi Arabia crude-oil extraction

This is a single-Verhults and a double-Verhulst fit to the Saudi Arabia crude-oil extraction data with Q=400x109 barrels, which is slightly more than the reported reserves (262x109 barrels) plus the amount already extracted (about 100x109 barrels).

Saudi Arabia crude-oil extraction extrapolated to the year 2100 for the double-Verhults fit and single-Verhulst fit:

The dashed curve is for Q=600x109 barrels, which corresponds to a reserve of about 500x109 barrels.

Apparently recent extraction has overshot the depletion curve, which implies that there will be fast decline in extraction to the depletion curve.

Kuwait crude-oil extraction

This is a two-Verhulst fit to the Kuwait crude-oil extraction data. The total amount to be extracted searched to Q=140x109 barrels, which is very close to the reported reserves (101x109 barrels) plus the amount already extracted (about 37x109 barrels). The single-Verhulst fit was made with the same Q=140x109 barrels value.

United Arab Emirates crude-oil extraction

This is a two-Verhulst fit to the UAE crude-oil extraction data. The total amount to be extracted was set at Q=200x109 barrels, which is somewhat above the reported reserves (98x109 barrels) plus the amount already extracted (about 72x109 barrels). The single-Verhulst fit was made with the same Q=200x109 barrels value.


The dashed curve is for Q=300x109 barrels, which corresponds to a reserve of about 230x109 barrels.

Iran crude-oil extraction

The total amount to be extracted is set at about 190x109 barrels, which is the reported reserves (132x109 barrels) plus the amount already extracted (58x109 barrels).

Iran crude-oil extraction extrapolated to the year 2100:
The dashed curve is for total extraction of about double (400x109 barrels) the solid curve,
which corresponds to a reserve of about 240 x109 barrels.

The large dip in crude-oil extraction due to the Iranian/Islamic Revolution put Iran in a good position for future crude-oil extraction, causing its peak to be delayed until at least 2015.

Iraq crude-oil extraction

The Verhulst fits have a total amount to be extracted set to Q=200x109 barrels, which is slightly more than the estimated reserves (115x109 barrels) plus the amount already extracted (30x109 barrels).

Due to the animosity between three ethnic groups in Iraq, it appears unlikely that there will be another large peak in crude-oil extraction in Iraq. The more likely scenario is that future crude-oil extraction will oscillate around its depletion curve.

Nigeria crude-oil extraction

This is a two-Verhulst fit to the Nigeria crude-oil extraction data and earlier data no longer available on the Internet. The three curves in the graph below are for reserves values:

  • 37x109 barrels, the reserves value given by EIA in 2011.
  • 75x109 barrels, about twice the given reserves value.
  • 110x109 barrels, about three times the given reserves value.

Note that all three curves fit the data about equally well and that increasing the reserves from the 2011 given value by two and three times does not change the fact that crude-oil extraction in Nigeria will decline in future years. The conclusion is that even much larger reserves will not stop the decline if no other peaks occur. If another peak occurs, the decline after that peak will be even faster.

Angola crude-oil extraction

The total amount to be extracted was set at 19.1x109 barrels for a 2-Verhulst fit, which is equal to the reported reserves amount (9.1x109 barrels) plus the amount already extracted (~1010 barrels).

A larger amount to be extracted (larger reserves) would yield a larger asymmetric tail.

Libya crude-oil extraction

The total amount to be extracted was set at 60x109 barrels for the double-Verhulst fit, which is equal to the reported reserves amount (~45x109 barrels) plus the amount already extracted (~15x109 barrels).

Syria crude-oil extraction

The total amount to be extracted was set at 8x109 barrels for the double-Verhulst fit, which is equal to the reported reserves amount (~3x109 barrels) plus the amount already extracted (~5x109 barrels).

Venezuela crude-oil extraction

The total amount to be extracted searched to 163x109 barrels for the single-Verhulst fit, which is greater than the reported reserves amount (80x109 barrels) plus the amount already extracted (53x109 barrels). The 2-Verhulst fit yielded 70x109 barrels; so there will probably be another extraction peak when Venezuela settles down politically.
Venezuela crude-oil extraction extrapolated to the year 2100:

Mexico crude-oil extraction.

For the 2-Verhulst fit he total amount to be extracted searched to 56x109 barrels, which is more than the reported reserves amount (11x109 barrels) plus the amount already extracted (36x109 barrels).

Also shown is a single-Verhulst fit with Q=56x109 barrels.

References:

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Brazil crude-oil extraction

The total amount to be extracted searched to 22.4x109 barrels for the 1-Verhulst fit, very close to the reported reserves amount (12.6x109 barrels) plus the amount already extracted (8.8x109 barrels). The 2-Verhulst fit yielded 21.6x109 barrels.

The reserves used in this calculation were posted by the U.S. Energy Information Agency in March 2009. Obviously, it does not include the recent off-shore discoveries called Pre-sal, with estimates up to 100x109 barrels. It is too early to tell how much is really recoverable. I was able to obtain a good fit to the data with an amount to be extracted of 78x109 barrels:

The best article I found about Pre-sal is :http://www.economist.com/displayStory.cfm?story_id=13348824. I think that it is very uncertain as to how much oil can actually be recovered from Pre-sal. The Economist article mentions many problems with extracting oil from Pre-sal.

Countries almost always greatly exaggerate oil discoveries. 50x109 barrels or more would be an amazing discovery. None that large have been discovered for over 40 years. I don't believe the numbers given by Petrobras for the Pre-sal discovery.

Columbia crude-oil extraction

The total amount to be extracted searched to 6.18x109 barrels for the single-Verhulst fit, which is greater than the reported reserves amount (1.5x109 barrels) plus the amount already extracted (~4.6x109 barrels). The 2-Verhulst fit yielded 70x109 barrels; so there will probably be another extraction peak when Venezuela settles down politically.

Soviet-Union/Russia crude-oil extraction.

The total amount to be extracted searched to 207x109 barrels for the 1-Verhulst fit, very close to the reported reserves amount (75x109 barrels) plus the amount already extracted (144x109 barrels). The 2-Verhulst fit yielded 167x109 barrels; so there will probably be another extraction peak.


Note the drastic drop when the Soviet Union collapsed.

Of course, the first peak is for the entire Soviet Union and the second peak is for Russia alone.

Soviet-Union/Russia crude-oil extraction extrapolated to the year 2100:

The dashed curve is for total extraction of about double (400x109 barrels) the solid curve.

China crude-oil extraction

The reserves reported for China (16x109 barrels) appears to be much too low. (See Verhulst-50 fit below.) The best Verhulst fit yields Q=425x109 barrels, which corresponds to reserves of 390x109 barrels, given that about 35x109 barrels have already been extracted.

United Kingdom crude-oil extraction

The total amount to be extracted for the 2-Verhulst fit searched to 31x109 barrels, slightly more than the reported reserves amount (4x109 barrels) plus the amount already extracted (23x109 barrels)

The single-Verhulst fit is fixed at Q=45x109 barrels, about 50% more than the 2-Verhulst fit.

Canada crude-oil extraction

The reserves reported for Canada (16x109 barrels) appears to be much too low. (See Verhulst-50 fit below.) A fit for 50% more eventually to be extracted is also show (Verhulst-75 for Q=75x109 barrels, which corresponds to reserves of 43x109 barrels, given that about 32x109 barrels have already been extracted.

Canada Oil from Oil Sands

Norway crude-oil extraction

The reserves reported for Norway (9x109 barrels) matches very closely the Q value (28.5x109 barrels) minus the amount already extracted (20x109 barrels). The crude-oil extraction curve for Norway is the closest to symmetrical of any nation. A fit for 50% more eventually to be extracted is also shown (Verhulst-45 for Q=45x109 barrels, which corresponds to reserves of 25x109 barrels, given that about 20x109 barrels have already been extracted.

World Natural-Gas Extraction


The blue curve corresponds to known resources. The red curve doubles the known resources.

This does not include uncertain shale gas; see below.

World Natural-Gas Discoveries

This and the curve below for world natural-gas extraction were fitted together with a common value for amount eventually discovered and extracted (7.8x1015 ft3).

Comparison of world natural-gas discoveries and extraction.

This does not include shale gas. The amount under both curves is about 7.8 x 1015 ft3.

This graph contains information that probably will have the greatest effect on those now living and born in the future. Natural gas cannot be extracted if it has not been discovered! This graph shows very clearly why it is very unlikely that the final amount to be extracted will exceed 8x1015 ft3. So far the amount extracted is about 3x1015 ft3, so we are more than one-third of the way there!

This does not include uncertain shale gas; see below.

Adding in uncertain shale gas:

The short large blip is shale gas. So, shale natural gas adds a short large blip to the natural-gas extraction for the World. It could be reduced in size and stretched out over a larger time interval, but I doubt it will be. The world will probably extract and use it as fast as possible.

China Natural-Gas Extraction

l

The blue curve is the best fit to the data (final extraction of 440x1012 ft3) and the red curve is a fit using the reserves value of 107x1012 ft3.

Russia Natural-Gas Extraction

The fit to the data (1, 2) uses the reserves value 1680x1012 ft3.

Iran Natural-Gas Extraction

The fit to the data uses the reserves value 1046x1012 ft3.
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World Coal Extraction

This Verhulst fit was made to extraction and reserves data from the USA EIA. There are some indications that the estimated reserves value is too high; if that is so, the peak will occur sooner than 2050.

China Coal Extraction

The 18 Nov 2010 issue of Nature (468, pp.367-369) gives two different possible values for coal reserves in China: 187 x 109 or 115 x 109 short tons. The following shows fits of the Verhulst function to the China coal extraction data for those two reserves values.

It either case coal extraction in China will peak around year 2020.

United Kingdom Coal Extraction

The UK is the best example of coal depletion:

The data are taken from:

Coal Prices Prediction

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