# Fossil-Fuels Depletion

## Introduction

One often reads in the press and/or on the Internet that a certain fossil fuel is sufficiently available to last hundreds of years. That is a meaningless statement because it implies, if not explicitly stated, the assumption that the current rate of extraction will remain the same into the future, which will not be even close to reality.

Any mineral, such as a fossil fuel, follows a depletion curve in its extraction rate in that it rises quickly and then slows down to a peak and they falls rapidly either faster or slower than it rose. That is, the peaked depletion curve may be asymmetric. The area under the depletion curve is the amount that will eventually be extracted, which is the sum of the amount already extracted plus the true extractable reserves. See an excellent mathematical method to arrive at a depletion curve for any mineral. The basic equation is the Verhulst function:

is the amount to be eventually extracted, is the rising exponential time constant in years units, n is the falling exponential time constant and t1/2 is the time in years units at which the resource is one-half depleted. The parameter n determines the amount of skewing at large times. For n = 1 the extraction curve is symmetrical and the peak occurs at t1/2. The deviation of the peak time from t1/2 is negative for n > 1 (skewed toward large times) and is positive for n < 1 (skewed toward small times).

The sum is due to the fact that the extraction rate may have more than one peak.

Any study of fossil fuel extraction that claims to predict the future of the extraction, to be honest, must present the predicted depletion curve, not some meaningless statement about the future extraction. Then any study that refutes that prediction must show a depletion curve that disagrees with the one being refuted. The area under the refuting depletion curve must be equal to the sum of the amount already extracted plus a defensible estimate of the reserves. The best estimates of reserves for fossil fuels is given and regularly updated by the Energy Information Agency (EIA) of the United States Department of Energy. If the area under a depletion curve greatly deviates from the EIA value, a rational explanation must be given why. Here is an example of how the reserves value is used to determine the future shape of a depletion curve:

In this case of crude-oil extraction for the United States, the blue area labeled "Reserves" is larger than the EIA stated reserves, which is required to fit the measured extraction data. Reserves' values are rough estimates, so are not expected to be accurate. In the depletion curves given below the values of the amount "already extracted", the amount "to be extracted" and the "total" amount extracted will be given below each graph. The amount "to be extracted" is often larger than the "reserves" of necessity to fit the extraction data with the Verhulst function.

In this article depletion curves for coal, crude oil and natural gas will be presented for the United States and the world using the Verhulst function to fit the extraction data using the EIA reserves' values. If anyone disagrees with these predictions of future extraction of fossil fuels, they should present competing depletion curves and rationally explain why the reserves' values differ from the EIA values.

## Coal Extraction

### Coal Extraction in the United States

The 2010 recoverable coal reserves value for current-existing mines in the United States given by the EIA is 17.937x109 short tons (tons/ST). Yearly Coal extraction data are given by EIA. Using these numbers one gets the following coal depletion curve for coal extraction in the United States:

Already extracted by 2010 = 77.22x109 tons, to be extracted = 18.78x109 tons, total = 96x109 tons.

Note that three Verhulst functions are used to fit the extraction-rate data. It is possible that more peaks will occur as the average extraction rate falls.

The conclusion is that coal extraction in the United States is peaking and will fall off rapidly in the future, which is good news for reducing global warming. There is not even 50 years supply of coal from current mines, let alone "250 years supply of coal"!

The 2010 recoverable coal reserves value including possible new mines in the United States given by the EIA is 259.5x109 short tons (tons/ST). Using these numbers one gets the following coal depletion curve for coal extraction in the United States:

This is the maximum that can be expected. The conclusion is that coal extraction in the United States is peaking and will fall off in the future, but not rapidly enough to be good news for reducing global warming. In 100 years the extraction rate will be ~67% of the current peak; in 200 years the extraction rate will be ~42% of the current rate; in 300 years the extraction rate will be ~25% of the current rate. It is misleading to state that there is "250 years supply of coal".

For more details see http://www.roperld.com/science/minerals/CoalExtractionUS.pdf.

### Coal Extraction for the World

World coal extraction-rate data and reserves are given by EIA. The 2008 reserves value for the world is 948x109 short tons (tons/ST). Using these numbers one gets the following coal depletion curve for extraction for the world:

Already extracted by 2008 = 326x109 tons, to be extracted = 938x109 tons, total = 1,260x109 tons.

Note that three Verhulst functions are used to fit the extraction-rate data. It is possible that more peaks will occur as the average extraction rate falls.

Probably the shape of the future curve will not be as smooth as shown here, but the average extraction over years may peak soon and then fall off rapidly. It could peak later and higher and fall off more rapidly. As time progresses the reserves value may change either up or down. This does not bode well for reducing global warming.

For more details see http://www.roperld.com/science/minerals/FossilFuels.htm#WorldCoal.

## Crude-Oil Extraction

### Crude-Oil Extraction in the United States

The 2010 recoverable crude-oil reserves value for the United States given by the EIA is 23.3x109 barrels. Yearly crude-oil extraction data are given by EIA. Using these numbers one gets the following depletion curves for crude-oil extraction in the United States:

The red curve is for the 2010 EIA reserves estimate (23.3x109 barrels). Reserves values are rough estimates, so are not expected to be accurate. The blue curve is for tripling the reserves to 75 x109 barrels.

The recent rise in extraction will probably peak before 2020 and then decline rapidly.

Obviously, there is no hope for long-term crude-oil independence for the United States.

For more details see

### Crude-Oil Extraction for the World

World crude-oil extraction-rate data and reserves are given by EIA. The 2009 reserves value for the world is 1,342x109 barrels. Using these numbers one gets the following depletion curve for crude-oil extraction for the world:

Already extracted by 2009 = 1,110x109 barrels, to be extracted = 1,500x109 barrels, total = 2,610x109 barrels.

Note that two Verhulst functions are used to fit the extraction-rate data. It is possible that more peaks will occur as the average extraction rate falls.

In this case of crude-oil extraction for the world, the area under the curve is larger than the amount already extracted plus the EIA stated reserves, which is required to fit the measured extraction data. Reserves' values are rough estimates, so are not expected to be accurate.

There may be a slight rise in crude-oil extraction in the future because of extracting oil from oil sands. See http://www.roperld.com/science/minerals/CanadaOilSands.htm.

## Natural-Gas Extraction

### Natural-Gas Extraction in the United States

United States natural-gas extraction-rate data and reserves are given by EIA. The 2009 reserves value for the United States is 272.5x1012 ft3. Using these numbers one gets the following depletion curve for natural-gas extraction in the United States:

Already extracted by 2009 = 1,289x1012 ft3, to be extracted = 521x1012 ft3, total = 1,810x1012 ft3.

Note that three Verhulst functions are used to fit the extraction-rate data. It is possible that more peaks will occur as the average extraction rate falls.

The peak at ~2014 year was obtained by fitting the fast-rising shale-gas extraction data using 110x1012 ft3 as the area under the curve, which is slightly more than,the 2010 shale-gas reserves, 97.449x1012 ft3. Obviously, shale-gas can only supply about a decade of consumption, not a century!

In this case of natural-gas extraction for the world, the area under the curve is larger than the amount already extracted plus the EIA stated reserves, which is required to fit the measured extraction data. Reserves' values are rough estimates, so are not expected to be accurate.

For more details see:

### Natural-Gas Extraction for the World

World natural-gas extraction-rate data and reserves are given by EIA. The 2009 reserves value for the world is 6,289x1012 ft3. Using these numbers one gets the following depletion curve for natural-gas extraction for the world:

Already extracted by 2009 = 3,185x1012 ft3, to be extracted = 6,326x1012 ft3, total = 9,600x1012 ft3.

Note that two Verhulst functions are used to fit the extraction-rate data.

If the reserves value given for world natural gas is correct, world extraction of natural gas will peak ~2021 year. It could peak later and higher and fall off more rapidly.

There may be a sizeable decade-long shale-gas peak similar to the case for the United States. It may not be as relatively large to the total curve because other countries may require more environmental controls on fracking for shale gas than does the United States. However, to get an idea of how shale gas might contribute to world natural-gas extraction rate assume that its peak is at the same ratio to non-shale-gas extraction as is the case for the United States, that the peak occurs about ten years later than for the United States and that it is about 50% wider:

## Conclusion

The result of this study are:

• Coal extraction is peaking in the United States but will continue to rise for the world for at least another decade, unless humans decide to stop burning it in order to stop global warming. There is not "250 years supply of coal", either for the United States or the World.
• Crude-oil extraction peaked at ~1970 in the United States and is peaking about now for the world. It is not true that "U.S. oil independence (is) no longer a joke".
• Natural-gas extraction in the United States is rising rapidly due to fracking for shale gas, which according to the EIA reserves value will peak at ~2014 and then fall rapidly. It appears that natural-gas extraction for the world will peak in about a decade; there may be a small, short peak due to fracking. It is not true that "Shale gas could supply 100 years of consumption."

All who disagree with these conclusions need to present their depletion curves and give rational explanations why the areas under the curves correspond to larger values for the reserves compared to the Energy Information Agency reserves' values.

Our descendants will reprimand us for burning valuable fossil hydrocarbons instead of using them to make useful objects and then recycling the material many times over to make more useful objects; especially since burning fossil fuels causes disastrous global warming.

### References

L. David Roper interdisciplinary studies