This is a guest post by Dennis Coyne.

The views expressed do not necessarily reflect the views of Ron Patterson.

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 is 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 post. The extraction rate trend from 2000 to 2014 was also extended until a peak was reached and then the increase in extraction rates were assumed to lessen until a constant rate of extraction was reached.

The three scenarios(low, medium, and high) are presented in the chart below.

The low scenario peaks in 2013 at about 4 Gtoe/a, the medium scenario peaks in 2025 at about 4.3 Gtoe/a, and the high scenario peaks in 2045 at about 4.9 Gtoe/a. Note that the medium scenario is not my best estimate, it is simply a scenario between possible low or high URR cases, reality might fall on any path between the high and low scenarios, depending on the eventual URR and extraction rates in the future.

A blog post by Luis de Sousa covered Jean Laherrere’s estimate of future coal output with URR between 550 Gtoe and 750 Gtoe.





For comparison, I have adjusted my chart (shown above) to have a similar scale as Jean Laherrere’s chart.

Note that only the two higher scenarios in my chart can be roughly compared with the lower two scenarios in Laherrere’s chart (510 compared with 550 Gtoe and 630 compared with 650 Gtoe). My scenarios peak at higher output at a later year and decline more steeply as a result.

The chart below is Steve Mohr’s medium independently dynamic scenario, where supply responds to coal demand.





The Chart above labelled C Case 2 is figure 5-8 from page 69 of Steve Mohr’s PhD Dissertation, the peak output is 210 EJ/year in 2019 (from Table 5-7 on page 71), Case 2 has a URR of 19.4 ZJ or 465 Gtoe (ZJ=zettajoule=1E21 J). My medium scenario (URR of 21.3 ZJ) has a lower peak output of 180 EJ/year, which occurs 6 years later than Mohr’s scenario. (1 Gtoe=41.868 EJ=4.1868E-2 ZJ).

It is interesting that Jean Laherrere’s larger URR scenario (550 Gtoe) has a peak of 4 Gtoe/year, while Mohr’s smaller URR (465 Gtoe) has a peak of 5 Gtoe/year. Mohr’s scenario was created in 2010 before the 2014 slowdown in Chinese coal consumption and he may have assumed that China and India would resume their rapid increase in coal consumption from 2010 to 2025. Jean Laherrere’s scenario was created in 2015 and in his 550 Gtoe scenario he may assume that the recent decrease in World coal output (in 2014) will continue in the future.

My medium scenario (510 Gtoe) is between Mohr’s medium (case 2) scenario and Laherrere’s low scenario. I have created two new scenarios using a URR of 510 Gtoe which match the peak output of Laherrere’s 550 Gtoe scenario and Mohr’s 465 Gtoe scenario. I have also created a “plateau” scenario with URR=510 Gtoe with World output remaining at the 2014 level until 2025. The various scenarios are presented in the chart below.

The extraction rates in the 4 different 510 Gtoe scenarios can be compared in the chart that follows.

Generally a higher peak in output leads to steeper annual decline rates, the chart below compares annual decline rates for the 4 different 510 Gtoe URR scenarios.

Summary

Coal is an important energy resource, but we do not know how the size of the economically recoverable resource that will eventually be recovered. The mainstream view is that there are extensive coal resources that are economically recoverable, research by Rutledge, Mohr, and Laherrere contradicts this view.

My estimates of the coal URR are based on the work of David Rutledge and Steve Mohr. Recent work by Jean Laherrere has coal URR estimates which are higher than my estimates, his medium scenario (650 Gtoe) is higher than my high case (630 Gtoe) and his estimates are usually conservative. My estimate may be too conservative, though my medium case (URR=510 Gtoe) is somewhat higher than the best estimate of Steve Mohr (465 Gtoe), whose work on coal is the best that I have found.

The average of the best estimate of Mohr and Laherrere’s medium case is about 550 Gtoe, a little higher than my medium case and similar to Laherrere’s low case. Based on the recent work by Laherrere, my best estimate would be 560 Gtoe (570 Gtoe is the average of my medium and high cases and 550 Gtoe is the average of the Mohr and Laherrere medium cases, the average of all 4 is 560 Gtoe).

The peak for world coal output will be sooner than most people think, the range is 2013 to 2045, my estimate is 2025 to 2030 with peak output between 4 and 5 Gtoe/year (2014 output was about 4 Gtoe/year).

Works Cited

De Sousa, Luis. “Peak Coal in China and the World, by Jean Laherrère.” attheedgeoftime.blogspot.com. Web. 11 March. 2016.

Mohr, Steve. Projection of world fossil fuel production with supply and demand interactions. 2010. Web. 11 March. 2016.

Oil Conundrum. theoilconundrum.com. Web. 11 March. 2016.

Rutledge, David. “Estimating long-term world coal production with logit and probit transforms.” International Journal of Coal Geology. 85 (2011): 23-33. Web. 11 March. 2016.

Appendix with details of Low and High cases

With links to Excel files at end of appendix

Low case-URR=390 Gtoe

High Case- URR=630 Gtoe

Further reading

Oil Shock Model Simplified

Oil Shock Model with Different URRs

Natural Gas Shock Model

Links to excel files with models

Low case

Medium case

High Case