L. David Roper
http://www.roperld.com/personal/RoperLDavid.htm
6 March, 2018
World Fossil Fuels Depletion
The U.S. state of North Dakota is having a boom in extracting natural gas 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 natural-gas 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 natural-gas extraction data for North Dakota since 1981. Earlier data are available back to 1961.
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 2016 for natural-gas extraction in North Dakota, which are shown here by black dots for years 2005 to 2016:
The curve is a fit to the 2005-2016 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 2008, the fit is done to get a rough estimate of the peak value of the reserves estimate in the future, which is ~6.5 x 1012 ft3.
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
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 shale-gas 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 5.76. (The Y-axis has been changed from 10^9 ft^3/day to 10^12 ft^3/yr.)
Then a Verhulst fit was done to the North Dakota tight-oil extraction data with the asymmetric parameter n fixed at 5.76:
All Verhulst parameters were varied except the n parameter for the future peak, which was set at 5.76. The calculated 2015 reserves for this curve is ~19 x 1012 ft3, greater than the estimated reserves value (~6.5 x 1012 ft3) given above.
The extraction is projected to peak at about 2017 and then fall rapidly in future years.
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.Go to the top.
Much natural gas has been "lost" (vented, flared and otherwise lost) into the atmosphere in North Dakota:
The ratio of natural-gas "lost" to natural-gas extracted is:
Natural gas released into the atmosphere is very dangerous for global warming.
Even for very high estimates of natural-gas reserves for its extraction in North Dakota, the current boom will turn into a bust in much less than a decade.
It would be wise for North Dakota to use the current natural-gas 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 North Dakota has a good start already.
See http://www.roperld.com/science/RenewableEnergyElectricityDemand.pdf.
It would be wise for the government of North Dakota to do some decade-long planning about how to best manage the coming natural-gas-extraction bust. A tax on natural-gas 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/
6 March, 2018