The media’s fascination with the prospect of peak oil has spread to another commodity — phosphorus. In Julian Cribb’s 2010 book, The Coming Famine: The Global Food Crisis and What We Can Do to Avoid It, Mr. Cribb highlights the 2007 work of Canadian physicist Patrick Déry, who applied the same analytical technique to world rock phosphate production that M. King Hubbert used to predict peak oil in the United States. Déry’s analysis suggested that the world reached peak rock phosphate production in 1989. Furthermore, the chart above demonstrates that the United States appears to have reached peak production long before that.
Curious, I decided to apply Hubbert’s analytical technique — so-called Hubbert Linearization — to the problem using more recent rock phosphate reserve and production data from the U.S. Geological Survey. What I found surprised me.
The Role of Phosphorus in Agriculture
Before delving into the details of my findings, it is important that I address why phosphorus is so important. The last century’s green revolution in food production succeeded because of the human application of mechanized equipment and systematic use of fertilizer on the farm. These two items drove tremendous leaps in agricultural productivity that helped sustain the world’s dramatic population increase in the twentieth century. One critical nutrient used in both fertilizer and animal feed that helped drive these crop yield improvements was phosphorus.
About ninety percent of industrial phosphorus makes its way to the agricultural industry. Of this ninety percent, animal feed accounts for about ten percent and fertilizer makes up the remaining ninety percent.
Perhaps because of a perceived peak in global rock phosphate production, prices have surged in recent years. But has the world really reached peak phosphorus production?
Applying Hubbert Linearization to Rock Phosphate Production
To answer this question, I first blindly applied the analytical technique to world rock phosphate production using data from 1900 to 2009. This technique provided a normal curve that suggests the world hit peak production in 1994 and that the ultimate amount of phosphoric rock ever recovered will be on the order of 8.9 billion metric tons. This number, the so-called ulimate recoverable reserves (URR) is supposed to equal the cumulative amount of phosphoric rock mined from 1900 to 2009 plus recoverable reserves still in the ground. My results are shown in the chart below.
Here is the problem. The U.S. Geological Survey 2010 estimates indicated that there were 16B metric tons of reserves in the world in 2009. Adding this 16B in reserves to the cumulative amount mined globally since 1900 yields a URR of about 23B, a number over two and a half times higher than the 8.9B figure implied by the “best-fit” curve.
Backsolving for the 23B figure and applying the same analytical technique yields the following result, which implies a peak production year of 2022 and a URR of 23.9B. This curve clearly does not have as nice a fit as the prior one, but it roughly foots to U.S. Geological Survey reserve estimates.
U.S. Geological Survey Quadruples Global Reserve Estimates in January 2011
While peaking rock phosphate production in 2022 is better having reached a peak in 1994, it still would be a concern for global food production. However, in January of this year, the U.S. Geological Survey more than quadrupled its reserve estimates from 16B metric tons to 65B metric tons. Using this revision, I again ran a Hubbert Linearization. When I tried to match the URR to that implied by the U.S. Geological Survey’s estimates of 72B, the normal curve fell out of view. So I assumed that countries would not be able to mine all of these reserves economically and fit the curve for a URR of 33B. This extremely conservative estimate implies that phosphoric rock will not peak until 2038, which suggests that global production has not peaked nor will it be peaking any time soon.
So the next time someone suggests that peak phoshorus is a looming concern, you can take comfort that the data does not seem to support their case.