# Natural-Gas Boom and Coming Bust in Arkansas

L. David Roper
http://www.roperld.com/personal/RoperLDavid.htm
2 July, 2016
World Fossil Fuels Depletion

## Introduction

The U.S. state of Arkansas 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 Arkansas 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.

## Natural-Gas Extraction Data for Arkansas

The U.S. Energy Information Administration gives monthly and annual natural-gas extraction data for Arkansas since 1981.

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.

## Natural-Gas Reserves for Arkansas

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 natural-gas extraction in Arkansas, which are shown here by black dots for years 2007 to 2011:

The curve is a fit to the 5 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 2004, the fit is done to get a rough estimate of the peak value of the reserves estimate in the future, which is ~19.1x 1012 ft3.

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## Verhulst-Function Fit to Natural-Gas Extraction Data for Arkansas

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:

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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, which can be obtained from the macro-analysis of the Fayetteville play by J. David Hughes (Drilling Deeper).

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## Hughes Fayetteville Micro-Analysis

J. David Hughes (Drilling Deeper) has done a micro-analysis of the Haynesville play, which is totally in Arkansas.:

I fitted a Verhulst function to the Hughes Arkansas curve to get the asymmetric parameter n:

The asymmetric parameter is 36. (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 Arkansas natural-gas extraction data with the asymmetric parameter fixed at 36:

All Verhulst parameters were varied except the n parameter for the future peak, which was set at 36. The calculated 2013 reserves for this curve is 40.6 x 1012 ft3, much larger than the estimated reserves value (19.1 x 1012 ft3) given above.

The extraction is projected to peak several years before 2015 and then fall rapidly in future years.

The fit to the data for early years:

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.

## Conclusion

Even for very high estimates of natural-gas reserves for its extraction in Arkansas, the current boom will turn into a bust in less than two decades.

It would be wise for Arkansas 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 Arkansas is off to a very slow start.

It would be wise for the government of Oklahoma 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.

• 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 Texas.
• A similar analysis has been done by the author for crude-oil extraction for Oklahoma.
• 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 Texas.
• 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 Louisiana.

## References

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L. David Roper, http://arts.bev.net/RoperLDavid/
2 July, 2016