L. David Roper

http://www.roperld.com/personal/RoperLDavid.htm

10 August, 2016

World Fossil Fuels Depletion

- Introduction
- Crude-Oil Extraction Data for Oklahoma
- Crude-Oil Reserves for Oklahoma
- Verhulst-Function Fit to Crude-Oil Extraction Data for Oklahoma
- Conclusions
- References

The U.S. state of Oklahoma has had many oil booms and busts. A new one is underway by the technique of fractionating ("fracking") shale/dolomite formations. A "boom" in nonrenewable resource extraction from the Earth is defined as a time period in which extraction is occurring very fast in a given area; thus, many workers come in from outside the area to man the drilling rigs, to build housing for the oil workers and to provide other services for the increased population.

This article shows mathematically that the current Oklahoma crude-oil boom will become a bust within a decade. A "bust" in nonrenewable resource extraction from the Earth is defined to begin at the time when extraction of the resource peaks and then falls to negligible amounts over a time period.

The U.S. Energy Information Administration gives monthly and annual crude-oil extraction data for Oklahoma since 1981. Earlier data are available back to 1905.

Those data are fitted by a depletion function, the Verhulst function, in this study to determine when the extraction will peak.

The data and the fits to the data are given in a later section.

A reliable estimate of reserves is needed to fit extraction data by a function for projecting into the future for a nonrenewable resource Here is a good definition of reserves of a nonrenewable resource.

The U.S. Energy Information Administration gives reserves estimates from 2006 to 2011 for crude-oil extraction in Oklahoma, which are shown here by black dots for years 2005 to 2014:

The curve is a fit to the 8 last data using the Verhulst function described in the next section, assuming that the curve will be symmetrical. Since the reserves estimates have been rising each year since 2007, the fit is done to get a rough estimate of the peak value of the reserves estimate in the future, which is ~3.9 x 10^{9} barrels.

The depletion function that is used in this article is the Verhulst function:

The asymmetry parameter, n, must be greater than 0.

where

The maximum of P(t) occurs at , which yields the peak value .

For the symmetric case (n=1): and .

For a depletion situation for which there are N peaks the depletion function is:

.

When a peak is symmetrical, the Verhulst function simplifies to

.

The depletion curve for crude-oil extraction for Oklahoma has essentially three peaks; so N=3 in the depletion equation. The fit to the extraction data using the reserves peak, ~5.2 x 10^{9} barrels, given in a previous section is:

The final large peak is assumed to be symmetric. Asymmetry would shift the peak backward for n > 1 (depletion curve skewed forward with a smaller peak) and forward for n < 1 (depletion curve skewed backward with a larger peak).

The area under the curve is equal to the amount already extracted (~15.6 x 10^{9} barrels) plus the reserves value (~3.9 x 10^{9} barrels).

Even if this very high reserves value (~3.9 x 10^{9} barrels) is correct, the final peak occurs at year ~2021. The onset of the bust could be extended out to later years by imposing environmental regulations and/or taxes on the extraction of natural gas, thereby reducing the extraction rate.

After getting the extraction curve above it occurred to the author that it would be interesting to see how the final peak value varies with the reserves amount. The following extraction curves were obtained for 7 different reserves values:

The area under each curve is equal to the amount already extracted (~15.4 x 10^{9} barrels) plus the reserves value.

The positions of the fimal peaks for 8 different reserves values are:

This has a logarithmic behavior as expected mathematically. That is, the rise in the peak year increases much less than linearly with the rise in reserves.

Even for an extremely high reserves value of 25 x 10^{9} barrels, the final peak position is ~2026 years, only 13 years from now! The reason the peaks occur so soon is because the extraction is occurring at a very high rate. The rising exponential rates for the final peak are:

The exponential rise rate approaches ~2.75 years as the reserves values get larger. This is a fast rise rate!

It is interesting to plot the chi square for the fit, which is a measure of the goodness of the function's fit to the extraction data, versus 9 reserves values::

The lower the chi square the better the fit.

Even for very high estimates of crude-oil reserves for its extraction in Oklahoma, the current boom will turn into a bust in about a decade.

It would be wise for Oklahoma to use the current crude-oil boom to build the policies and infrastructure for collecting energy from wind and solar, for encouraging drivers to drive electric vehicles and for fast charging stations for electric vehicles in personal and parking garages. Wind energy in Oklahoma has a good start already.

It would be wise for the govenment of Oklahoma to do some decade-long planning about how to best manage the coming crude-oil-extraction bust. A tax on crude-oil extraction to put in a fund to help manage the bust and to clean up the mess made by the extraction would be wise. Such tax might have an added benefit of slowing down the extraction so that the bust will not occur so soon, giving more time to prepare for it.

- A similar analysis has been done by the author for crude-oil extraction for Texas.
- A similar analysis has been done by the author for crude-oil extraction for North Dakota.
- A similar analysis has been done by the author for crude-oil extraction for United States.
- A similar analysis has been done by the author for natural-gas extraction for North Dakota.
- A similar analysis has been done by the author for natural-gas extraction for Pennsylvania.
- A similar analysis has been done by the author for natural-gas extraction for Colorado.
- A similar analysis has been done by the author for natural-gas extraction for Oklahoma.
- A similar analysis has been done by the author for natural-gas extraction for Texas.
- A similar analysis has been done by the author for natural-gas extraction for Louisiana.
- A similar analysis has been done by the author for natural-gas extraction for Arkansas.

- http://www.roperld.com/science/minerals/VerhulstFunction.htm
- Oklahoma First Energy Plan
- http://www.aei-ideas.org/2013/05/shale-oil-boom-spreads-to-wyoming-colorado-new-mexico-utah-and-oklahoma-combined-output-up-46-in-3-years/
- http://money.cnn.com/2011/12/06/pf/oil_boom_bust/index.htm?iid=SF_PF_River
- http://www.bloomberg.com/apps/news?pid=newsarchive&sid=ayj1uo_gdNI4
- http://www.climatecentral.org/news/fracking-boom-leading-to-fracking-bust-scientists-16680
- http://news.nationalgeographic.com/news/energy/2013/11/131111-north-dakota-wells-maintenance-water/
- Oil boomtown creates challenges
- http://www.motherjones.com/environment/2013/03/does-fracking-cause-earthquakes-wastewater-dewatering
- http://en.wikipedia.org/wiki/Wind_power_in_Oklahoma

L. David Roper interdisciplinary studies

World Fossil Fuels Depletion

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

10 August, 2016