Pittsylvania County Virginia

L. David Roper

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

2 July, 2016

When a new mine is proposed for an area, the company that is proposing the mine is obligated to present an estimated depletion curve for the mine. That is, a curve should be presented that shows estimates of how fast the mineral is expected to be extracted from the mine, when the extraction will peak and how fast extraction will decline. Such information is needed so that jurisdictions can better know the timing and magnitude of expected taxes and of needed cleanups due to accidents and cessation of mining.

The company that has proposed a uranium mine in Pittsylvania County Virginia has presented a study that gives some very rough estimates (p.11) of the mine's future as follows:

- The ore extraction estimate is divided into four time periods:
- The first year: 700,000 tons.
- Years 2 through 4: 1,050,000 tons.
- Years 5 through 25: 700,000 + 350,000 (mining previous pillars) = 1,050,000 tons.
- Years 26 through 35: 467,000 + 233,000 (mining previous pillars) = 700,000 tons.

- Concentration of U
_{3}O_{8}in the ore is extimated to range from 0.079% to 0.126%, with an average of 0.0965%. (The minimum and maximum average to 0.1025%, so more of the extraction is on the minimum side than the maximum side.) - The mining recovery rate is assumed to be 85%.
- The total U
_{3}O_{8}/year extraction is estimated to range from 1,225,000 lbs/year to 2,646,000 lbs/year, with an average of 1,885,000 lbs/year. In tons, the range is from 612.5 tons/year to 1323 tons/year, with an average of 942.5 tons/year. (The minimum and maximum average to 967.75 tons, so more of the extraction is on the minimum side than the maximum side.) Given 35 years for the lifetime of the mine, the estimated total amount to be mined is 942.5 tons/year x 35 years ~32,990 tons.

One can use linear equations to fit a quadratic function to the U_{3}O_{8} concentration in the ore such that the highest concentration, 0.126%, occurs at the beginning of mining, year 1, and the lowest concentration, 0.079%, occurs at the end of mining, year 35, and the average concentration is 0.0965%:

These concentrations can be used to calculate the U_{3}O_{8} extracted as a function of year:

The red curve is calculated by multiplying the concentration versus year times the amount of ore given in the study for each year.

The author of this article thinks that the large drop from year 25 to year 26 is unrealistic; in fact, the total amount of U_{3}O_{8} extracted is 27,340 tons instead of 32,990 tons calculated above. So, the blue curve is the result of smoothing out the U_{3}O_{8} extraction such that the total amount extracted over the 35 years is ~32,990 tons. The green curve is a Verhulst depletion function fitted to the blue curve.

The author of this article thinks that the fast rise in the early years is unrealistic. The purple curve is the author's estimate of a more realistic depletion curve such that the total amount extracted over the 35 years is ~32,990 tons. Of course, the mining may extend on past the 35 years, as shown here:

If the mining could be extended out to 75 years by this depletion curve, the amount of U_{3}O_{8} to be extracted would be ~44,180 tons.

Of course, circumstances such as nuclear accidents, wars and economic conditions would likely cause fluctuations from a smooth depletion curve, including major multiple peaks.

The price ($/lb) for U_{3}O_{8} versus year had a severe downturn in 2012:

It seem unlikely that the downturn will end soon. It is due to the Fukushima nuclear disaster in March 2011 and the subsequent decisions by Germany, Japan and France to diminish their dependence on nuclear energy in the future.

Using the purple curve in the second graph as the most realistic prediction for extraction of U_{3}O_{8} by the proposed Coles Hill mine and three realistic future prices of $40/lb, $30/lb and $20/lb the following curves show predictions for sales of U_{3}O_{8} from the mine:

The total sales in billions (10^9) of dollars after 35 years and 75 years would be:

Years |
$40/lb |
$30/lb |
$20/lb |

35 |
2.6 |
2.0 |
1.3 |

75 |
3.5 |
2.7 |
1.8 |

This is far below the $7 billion dollars mentioned in the media.