L. David Roper
http://www.roperld.com/personal/RoperLDavid.htm
5 March, 2018
World Fossil Fuels Depletion
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 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 the Verhulst function using estimated reserves in this study to project when the extraction will peak in the future.
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 1977 to 2016 for crude-oil extraction in Oklahoma, which are shown here by black dots:
The curve is a fit to the 2007-2016 estimates using the Verhulst function described in the next section, assuming that the curve will be symmetrical. Since the reserves estimates have been rising on the average since 2007, the fit is done to get a rough estimate of the peak value of the reserves estimate in the future, which is ~5.0 x 109 barrels, an optimistic estimate.
The 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 fit to the extraction data using the reserves peak value, ~5 x 109 barrels, given in a previous section is:
The final large peak in the red curve is assumed to be symmetric (n=1). Asymmetry would shift the peak backward for n > 1 (a smaller peak) and forward for n < 1 (a larger peak). The blue curve is for n=5, a value that is close to what J. David Hughes finds in his detailed micro-analysis of extraction of tight oil by fracking in the U.S.
The area under the curve is equal to the amount already extracted (~15.8 x 109 barrels) plus the reserves value (~5 x 109 barrels), about 21 x 109 barrels total crude-oil extraction for Oklahoma..
If this very high reserves value (~5 x 109 barrels) is correct, the final peak occurs at year ~2026 for n=1 and ~2024.5 for n=5.. The onset of the bust could be extended out to later years by imposing environmental regulations and/or taxes on the extraction of crude oil, thereby reducing the extraction rate.
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 pwer in Oklahoma has an excellent start already. Solar power in Oklahoma is way behind many other states, but is accelerating.
Crude oil should be used to make products rather than burning it for energy and releasing carbon dioxide, which increases global warming. Also, methane release during crude-oil extraction should be minimized because it causes greater global warming than does carbon dioxide.
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.
L. David Roper interdisciplinary studies
World Fossil Fuels Depletion
L. David Roper, http://arts.bev.net/RoperLDavid/
5 March, 2018