L. David Roper
http://www.roperld.com/personal/RoperLDavid.htm
5 March, 2018
World Fossil Fuels Depletion
The U.S. state of North Dakota is having a boom in extracting crude oil 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 North Dakota 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 North Dakota since 1981. Earlier data are available back to 1952.
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 1977 to 2011 for crude-oil extraction in North Dakota, which are shown here by black dots for years 2005 to 2011:
The curve is a fit to the estimates using the Verhulst function described in the next section, assuming that the curve will be symmetrical. The fit is done to get a rough estimate of the peak value of the peak reserves estimate, which is ~6 x 109 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:
.
One needs an estimate of the amount of asymmetry, described by the parameter n, for the future peak due to fracking for shale natural gas for the Marcellus play, which can be obtained from the macro-analysis of the Bakken play by J. David Hughes (Drilling Deeper).
J. David Hughes (Drilling Deeper) has done a micro-analysis of the Bakken tight-oil play, which is very largely in North Dakota:
“Most Likely Rate” scenario of Bakken tight-oil extraction including both North Dakota and Montana which rate is very small.
Hughes' Bakken curve is asymmetric; i.e., n > 1..
I fitted a Verhulst function to the Hughes Bakken curve to get the asymmetric parameter n:
The asymmetric parameter is 3.4.
Then a Verhulst fit was done to the North Dakota tight-oil extraction data with the asymmetric parameter fixed at 3.4:
For the red curve all Verhulst parameters were varied. For the blue curve all Verhulst parameters were varied except the n parameter for the future peak, which was set at 3.4, the Hughes value. The calculated 2016 reserves for the blue curve is
5.23 x 109 barrels and for the red cuve 4.32 x 109 barrels, close to the estimated reserves value (16 x x 109 barrels) given above.
The extraction appears to have peaked already and will fall rapidly in future years.
Even for very high estimates of crude-oil reserves for its extraction in North Dakota, the current boom will turn into a bust in less than a decade.
It would be wise for North Dakota 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 power in North Dakota has a good start already. Solar power in North Dakota is far behind most other states.
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 government of North Dakota 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