**Peak Coal: How Much Remains Economically Recoverable? by Ron Patterson, OilPrice.com**

The eventual peak in world fossil fuel output is a potentially serious problem for human civilization. Many people have studied this problem, including Jean Laherrere, Steve Mohr, Paul Pukite (aka Webhubbletelescope), and David Rutledge.

I have found Steve Mohr’s work the most comprehensive as he covered coal, oil, and natural gas from both the supply and demand perspective in his PhD Thesis. Jean Laherrere has studied the problem extensively with his focus primarily on oil and natural gas, but with some exploration of the coal resource as well. David Rutledge has studied the coal resource using linearization techniques on the production data (which he calls logit and probit).

Paul Pukite introduced the Shock Model with dispersive discovery which he has used primarily to look at how oil and natural gas resources are developed and extracted over time. In the past I have attempted to apply Paul Pukite’s Shock Model (in a simplified form) to the discovery data found in Jean Laherrere’s work for both oil and natural gas, using the analysis of Steve Mohr as a guide for the URR of my low and high scenarios along with the insight gleaned from Hubbert Linearization.

In the current post I will apply the Shock model to the coal resource, again trying to build on the work of Mohr, Rutledge, Laherrere, and Pukite.

A summary of URR estimates for world coal are below:

The “Laherrere+Rutledge” estimate uses the Rutledge best estimate for the low case and Laherrere’s low and medium cases for the medium and high cases. Laherrere also has a high case of 750 Gtoe for the world coal URR, which seems too optimistic in my opinion. The “high” estimate of Steve Mohr has been reduced from his “Case 3” estimate of 670 Gtoe by 40 Gtoe because I have assumed lignite and black coal resources are lower than his high estimate.

An update of David Rutledge’s estimate using the latest BP data through 2014 gives a URR of about 400 billion tonnes of oil equivalent (Gtoe) for coal. The Rutledge 2009 estimate was about 350 Gtoe.

My initial estimate was in billions of tonnes (Gt) of coal at 800 Gt for the low estimate (a round number near Steve Mohr’s low estimate of 770 Gt) and 1300 Gt for the high estimate (about the same as Steve Mohr’s high estimate), my medium estimate was simply the average of the high and low estimates. I came across Jean Laherrere’s estimate after I had developed my model, surprisingly his medium estimate is a little higher than my guess, which is usually not the case (for other fossil fuels).

I do not have access to discovery data for coal, but based on World Resource estimates gathered by David Rutledge, most coal resources had been discovered by the 1930s. I developed simple dispersive discovery models with peak discovery around 1900 for each of the three cases, these are rough estimates, I only know that coal was discovered over time. The cumulative coal discovery models in Gtoe are shown in the chart below for the low, medium and high URR cases.

In each case about 75% of coal discovery was prior to 1940.

Coal resources have been developed very slowly, especially since the discovery of oil and natural gas. As a simplification I assume that the rate that the discovered coal is developed remains constant over time.

A maximum entropy probability density function with a mean time from discovery to first production of 100 years is used to approximate how quickly new proved developed producing reserves are added to any reserves already producing each year. For example a 1000 million tonne of oil equivalent (1 Gtoe) coal discovery would be developed (on average) as shown in the chart below:

Reading from the chart, about 9 Mtoe of new producing reserves would be developed from this 1850 discovery in 1860 and about 5 Mtoe of new producing reserves would be developed in 1920. About half of the 1000 Mt discovered in 1850 would have become producing reserves by 1920, so the median time from discovery to producing reserve is about 70 years (the mean is 100 years due to the long tail of the exponential probability density function).

The model takes all the discoveries for each year and applies the probability density function (pdf) above to each year’s discoveries (the pdf is 1000 less than shown in the chart because we multiplied the pdf by 1000 to show the new producing reserves in Mtoe.) Then the new producing reserves from each year’s discoveries are simply added together in a spreadsheet, not complicated, just an accounting exercise.

The new producing reserves curve (when everything is added up) is shown below for the medium URR case (510 Gtoe):

Each year new producing reserves are added to the pool of producing reserves while some of these reserves are produced and become fossil fuel output. This is indicated schematically below:

If the Fossil fuel output is less than the new producing reserves added in any year, then the producing reserves would increase during that year, if the reverse is true they would decrease.

The fossil fuel output divided by the producing reserves is called the extraction rate.

Using data from David Rutledge for fossil fuel output to 1980 and data from BP’s Statistical Review of World Energy from 1981 to 2014, I extrapolated the extraction rate trend from 2000 to 2014 to estimate future coal output. The chart below shows the discovery curve, new producing reserves curve, and the output curve for the scenario with a URR of 510 Gtoe.

Note that when new producing reserves are more than output the producing reserves will increase (up to 1986), after 1993 output is higher than the new producing reserves added each year so producing reserves start to decrease. Producing reserves are in the following chart for the medium scenario (URR=510 Gtoe).

The fall in producing reserves combined with increased world output of coal from 2000 to 2013 required an increase in extraction rates from 1.5% to 2.9%. I assume after 2014 that this increase in extraction rates continues at a similar rate until reaching 4% in 2026 and then extraction rates gradually flatten, reaching 5.1% in 2070.

Clearly I do not know the future extraction rate, this is an estimate assuming recent trends continue. For this scenario with a coal URR of 510 Gtoe output peaks in 2026 at about 4250 Mtoe/year.

For the low and high URR cases the details of the analysis are covered at the end of the