Thursday, November 20, 2014

Energy Policy, Analysis 5, rA


Energy Policy

Arithmetic, Population and Energy, Part 5


Revision A

For the love of the human race.

Thursday, November 20, 2014

Our Thesis


New and shifting data may require new mappings.  When situations are altered, new maps must be used.  There is nothing wrong with the old maps, they may simply be inapplicable to the new situation.  Failing to understand this is like trying to find a place in Denver from a map of Cleveland.

Nevertheless, opponents of truth persist in discrediting and marginalizing legitimate practices of mathematics and science, by conveniently ignoring the need for appropriate mapping.  This abuse is then made into the political or popular lever for claiming that the mathematics and science are incorrect, the mathematicians and scientists are to blame: they put forth a false theory, cried wolf, and lied to the populace.  However, it is not usually the mathematician or scientist who lied, but rather the individuals who found it powerful or profitable to spin the truth to their individual advantage.

Arithmetic, Population and Energy, Part 5


http://www.albartlett.org/presentations/arithmetic_population_energy_video1.html  Better results were achieved by playing the video clip directly from this site, rather than by linking through YouTube.  Click on the arrow in the middle of the picture, rather than on the black bar at the top.  This is Part 5.

“Energy industries agree that to achieve some form of energy self-sufficiency the U. S. must mine all the coal that it can.”[1]

Clearly, the editors at Time Magazine are full of hot air.

David Brower (1912-2000)[2] called this the policy of “strength through exhaustion.”

I liken this to driving at sixty miles per hour; learning that there is an immovable concrete barrier thirty miles ahead; then deciding to increase speed by 7% a mile.

Te = 1 / ln (b) * ln [ ln (b) * A / y0 + 1 ]
Te ≈ 1 / r * ln [ r * A / y0 + 1 ]

This reduces the remaining time until collision from 30 minutes to 16 minutes, increases the impact velocity to 182 miles per hour, and triples the momentum.  It also guarantees that no one will be maimed in the accident.  The 182 mile per hour impact velocity pretty much guarantees that all living occupants will be vaporized or reduced to dust.  Any remains for burial will have to be located with a sponge or a vacuum cleaner.  Instant cremation and dispersion of ashes in one swift motion.

Strength through exhaustion, simply won’t work.  The sensible person slows down and puts on the brakes.

“1994 was the first year in our nation’s history in which we had to import more oil than we were able to get out of our own ground.”[3]

Now Dr. Bartlett introduces the concept of peak growth.  Until this point our mapping has only considered exponential growth.  Government, business, industrial leaders, and many individuals assume the exponential growth will continue indefinitely.  These prognosticators are evidently oblivious to the cartoon where the exponential curve blows a hole in the ceiling.  If these movers and shakers could possibly be successful at selling their insane schemes of indefinite growth, they would proceed with their plans until every last ounce of any given commodity was consumed.  Then the graph would come to a screeching halt.  The car would hit the barricade.  Everyone on board would be killed and that would be that.

Such an infinitely sloped decrease or increase in mathematics is called a discontinuity.  It is easily drawn on a graph.  Fortunately, discontinuity is nearly impossible to achieve in nature.  Almost all things have some mass, even electrons, and they cannot be made to change direction abruptly.  In the case of our car crash model, we could observe this using high-speed, time-lapse photography, and we could watch the car and human bodies being reshaped as energy was dissipated.

In any case there can be no question that a peak was, or someday will be reached.  It is impossible to make exponential curves continue indefinitely: all of them approach infinity at terrifying speed.  Finite man, simply has no capacity for infinity, which is exactly what the word means.  Infinity is usually, perhaps always, the result of trying to divide by zero, it cannot be done.  So there must be a peak.  There must also be a path back downward to zero, either catastrophic or more sloped.  In our last session we showed how to calculate the maximum peak for an exponential curve.  Simply calculate Te using this formula.

Te = 1 / ln (b) * ln [ ln (b) * A / y0 + 1 ]

Then use Te to calculate the maximum peak from this formula.

y = a * bTe

The shape of the downward curve is determined largely by human decision, as is the case with the upward curve.  The mathematician and the scientist simply create a map to explain what is happening.  As human decisions change, new maps must be created.

This does not mean that either the math or the science was wrong.  It simply means that some decision makers changed their minds.  It is the height of foolishness to abandon or discredit the math because of a decision change made by business and political leaders.

A peak will occur.  Multiple peaks may occur.  The time and size of these peaks are determined by human decision and the availability of the remaining resource, and not by the mathematician or scientist.  The mathematician and scientist are simply trying to provide a reasonable means of prediction based on contemporary decision policy, and predicted reserves.

Even if the peak is reached abruptly, the crash will take some time as local storage is used up.  The resource producer will be the first to realize that he is out of business.  The end user will have his last tank to budget as he tries to plan his survival.  So a downward slope is inevitable.  It may be skewed, it may have bumps, it may be bimodal, it may be slow, but it probably won’t be abrupt.  Why?

We have a good idea where the remaining reserves are located, and what their size is.  Most of these reserves are not yet in production.  Starting production costs money and takes time.  Decision makers are the ones who determine when and where it is a good financial decision to open a new mine, buy new equipment, invest in a new process, or build a new refinery.  Several of these reserves are shale oil.  Shale oil is not processed the same way as crude bubbling up out of the ground.  Deep mines are operated differently than strip mines.

Technological obstacles also exist.  This is why we can only get 50% of the coal out of the ground.  Even if we know how, costs may be prohibitive.  The value of coal will have to increase dramatically to motivate going after it.  Not many years ago the depth of wells was limited by pressure to roughly 3,000 psi.  Hydraulic equipment was designed for those pressures.  When deeper drilling was desired, new technology was developed, pushing pressures beyond 3,000 toward 6,000 and even 10,000 psi.  Oil is a very dangerous substance at 3,000 psi: the presence of any air guarantees a fire.  At 6,000 or 10,000 psi explosions can be guaranteed, and the limits of material strength are being reached.  Common steel can only withstand around 36,000 psi: so things wear out more rapidly, it takes more force to pump at such pressures.  The costs go up, and progress goes down.  It takes time and money to solve such technological problems.

Popular obstacles also exist.  The neighbors will probably object to an operation destroying the view from their picture window, cutting down their favorite forest, muddying their water supply, or locating a nuclear reactor in their back yard.  Public outrage can slow, modify, or even stop a project.

All of these factors militate that the downward slope will become progressively slower as it becomes harder and harder to locate and develop new reserves.  The obvious mathematical map is some kind of a negative growth curve for much of its path.  An even better, more realistic map is that of a Gaussian curve, a bell curve, which accounts for the necessary negative growth rate changes on the bottom path.

So it is impossible to deny the reality of peak theory.  Granted, this is a bit like trying to map a bumpy emergency crash landing, but it would still be nice to have something to aim at: like a nice soft pasture, or a convenient highway with no traffic.

The problem with the Peak Oil theory.

Dr. Bartlett notes that possibly 3.2 G-bbl of crude oil exist in the Arctic Wildlife Refuge: about a 15 month supply at current consumption.  The peak in the extraction rate of U. S. crude oil was predicted to occur between 1966 and 1971.  This prediction was made by Dr. Hubbert in 1956 when oil consumption was still growing steadily at 7.04% per year.  The U. S. Department of Energy fixed the actual U. S. peak at about 3.5 G-bbl per year in 1970.  The Alaska reserves were discovered around 1982.

The curve development was dramatically shifted by the Alaskan discovery and OPEC increases in world oil prices, which prompted the U. S. energy crisis.

Dr. Bartlett continues.  “The estimated U. S. supply [of crude oil] from undiscovered resources and demonstrated reserves is 36 years at present rates of production or 19 years in the absence of imports.”[4]  We have demonstrated from 2012 data that the U. S. has only an estimated 10 year supply without considering imports.  The world is, at best, only good for 85 years.  “Please note that this is tracking faithfully down the back slope of the Peak Oil curve.”3  This will certainly continue to be a major problem for us, our children, grandchildren and great-grandchildren.  By refusing to deal with this emergency crisis we are mortgaging the future to the detriment of world society.

“…These reserves and the estimated undiscovered oil represent only a 16 years supply, with imports…providing 50% of U. S. needs…the domestic supply stretches to 32 years.”[5]

In 1998, U. S. Energy Secretary Federico Pena “issued his comprehensive … strategy … halting the slide in … production by 2005.”3  We conclude that Secretary Pena was forced to lie.

“Modern agriculture is the use of land to convert petroleum into food.”3

When the oil supply stops, food production will change dramatically.  Not only will we return to cultural conditions similar to those in 1850, we will do so with a startling deficit.  Along the way, in our rush to be wealthy, we have radically changed our environment.  We have reduced our oxygen levels.  We have created resistant bacteria, noxious insects, and noxious plants.  When the restraints of chemical herbicides and insecticides are removed, nature will strike back with vengeance.  Blights and diseases may reemerge as major plagues.  The land which we have abused, and depleted of nutrients, will not be able to sustain the food supply, without chemical fertilizers.  The bees, and other species that we have abused, will not be available to pollinate or attend plant life.  The waters that we have polluted, will not be fit to drink or irrigate.

The obvious solution is to reduce consumption drastically.

No one will (like this solution, but it is necessary to preserve life.  An additional $3.00 per gallon tax on gasoline will make people far more energy conscious.  Increasing that tax by another $3.00 per gallon per year until a maximum between $15 and $21 per gallon is reached should help bring consumption under control.  We should at least equalize our gasoline costs with those of Europe.  A hefty tax on cubic inches or milliliters of engine size should help consumers make better automobile, truck, ship, and industrial engine buying decisions.  Rationing fuel should be a final resort.  Other measures will also help: for example, the recall of all military to within U. S. borders.

We no longer have sufficient wealth to be the world’s enforcer of all things moral.  It’s time to face the fact that we are dying very rapidly.

In 1972 Dr. Hubbert predicted that the peak of world production would occur around 1995.  The U. S. Department of Energy observed the temporary world peak at about 23 G-bbl per year in 1979 with a second peak in 1990, the delay being caused by OPEC.  We are not yet over the actual peak.

Dr. Bartlett proceeds, “The consensus among petroleum geologists is that the total world supply of oil is around 2,000 G-bbl.”  This is an educated conjecture with an inherent uncertainty.  If we allow for errors of 50% and 100%, the total world supply of oil would be 3,000 G-bbl and 4,000 G-bbl, respectively.  Armed with these figures Dr. Bartlett is able to produce three different potential curve fits: with peak oil occurring in 2004, 2019, and 2030, depending on which total world supply of oil is chosen.  It is highly improbable that world peak oil would fall outside of this 26 year range.  Factors that influence the actual peak are: the actual total world supply of oil, oil prices, the timing of future discoveries, production technology, plant capacity, consumer demand.

We, the consumers of oil, can change the occurrence of peak oil by changing our use habits.  A 50% reduction in gasoline consumption would move the graph considerably.

Our Conclusion


Dr. Bartlett’s defense of Peak Oil theory is correct.  The attempts to discredit this theory will finally prove to be vain.  The final shape of the curve may not be known: the size and time of the peak, bimodal behavior, and a degree of skewness or kurtosis are all possible within the practical application of this math.  That being said, the peak or peaks have or will take place, and the downhill progression is inevitable.  The final shape of such bell shaped curves is ultimately determined by decision makers, not by scientists; but, once the downhill slide is begun it cannot be halted by decisions.  Instead of a crash, this is more like that sickening feeling you get when you run out of gas in the middle of nowhere.  You are hopelessly out of control as your engine sputters, and you coast to a stop.

Our leaders are not taking the sensible steps to put on the brakes and manage this crisis.  We should be operating on reduced growth conservation plans, negative percentages.  Our federal budget should be considering a -5% budget, instead of a +5% budget.  Our president should be pushing for cuts, rather than performing draconian theatrics to get the increases he wants.  Officers like Pena lied or were forced to lie to the American public.  The falsification of records continues, unabated.

Where are the real leaders who will stand up and face this crisis honestly and head on?



[1] Time Magazine, May 19, 1975, page 55
[2] http://en.wikipedia.org/wiki/David_Brower
[3] Dr. Bartlett
[4] Science, January 27, 1984, page 382
[5] 1989 oil reporting

Wednesday, November 19, 2014

Exponential Curve 4


Exponential Curve 4

Arithmetic, Population and Energy, Part 4


For the love of the human race.

Wednesday, November 19, 2014

Our Thesis


We are greatly indebted to Dr. Albert Allen Bartlett (1923-2013), former emeritus professor of physics at the University of Colorado, Boulder.[1]  These are Dr. Bartlett’s ideas, we are merely reporting them.  We have performed a lengthy analysis of Dr. Bartlett’s “arithmetic” elsewhere.[2]

One cannot investigate either energy policy or energy theory without a thorough understanding of the exponential curve.[3]

Arithmetic, Population and Energy, Part 4


Dr. Bartlett opens this part with a juicy quote from a very important Texas oil man, Michel T. Halbouty (1909-2004), “There is still as much oil to be found in the U. S. as has ever been produced.”[4]

1.    What time is it? 
A. It’s 11:59, 1 minute before noon.

Coal

Dr. Bartlett immediately turns the conversation to coal with this quote, “We’re sitting on half of the world’s known supply of coal, enough for over 500 years.”  A report to the Senate committee said this, “At current levels of output and recovery, these American coal reserves can be expected to last more than 500 years.”[5]

There is one of the most dangerous statements in the literature.  It’s dangerous because it’s true.  It isn’t the truth that makes it dangerous, the danger lies in the fact that people take the sentence apart: they just say coal will last 500 years.  They forget the caveat with which the sentence started.  Now, what were those opening words?  “At current levels.”  What does that mean?  That means, if and only if we maintain zero growth of coal production.”[6]

Dr. Bartlett’s discussion continues.  The Demonstrated Coal Reserve Base is around: Rb = 470 G-tons according to Dr. Bartlett’s charts.  The Recoverable Reserve is around: Rr = 240 G-tons (1991).  The significance of these two numbers is that we cannot practically reach over 50% of the total coal with existing technical equipment and methods.  Vastly improved technical equipment and methods can nearly double the realistic coal supply.

As with oil, Dr. Bartlett’s data (ca 1970) are hopelessly out of date.  So we will turn to fresh data studies in separate documents.

Extraction Time and Peak Production

Extraction time is the length of time we may expect a resource to last.  Peak Production is the highest level that can be reached with a given model.  The model that best fits reality is the result of business and political decisions.  Science has little or no influence on such decisions, it merely seeks to analyze and explain these decisions with clarity.

The Zero Growth Model

If we are evaluating a zero growth model the extraction time is simply the amount of the resource remaining, A, divided by its present rate of consumption, y0.  Te A / y0.

The peak production rate is y0, since the present rate of production is not growing.

This produces a rectangular graph, which is Te wide and y0 tall.  The area of the rectangle A / y0 x y0 is equal to the amount of the resource remaining, A.

Te at zero growth is the figure most commonly reported in public records, which conveniently ignore the fact that production rates can increase, or decrease, as well as remain constant.  Contemporary business and political attitudes mandate that production rates will increase.

The Positive Growth Model

If we are evaluating a positive growth model the extraction time is more complicated to calculate because we must account for the changing production rate.  We reason that the amount of the resource remaining, A, doesn’t change from one model to another, so the area under the exponential curve must also be A.  We need calculus to calculate this area, and the new Te under growth conditions.  Here is the result.

Te = 1 / ln (b) * ln [ ln (b) * A / y0 + 1 ]

We may approximate this time by remembering from part 1 that b = 1 + r, and that for small r (less than 0.10), ln (1 + r) r.

Te ≈ 1 / r * ln [ r * A / y0 + 1 ]

The peak production rate is now:

y = y0 * bTe

In this model the peak production rate is immediately followed by a catastrophic and instantaneous crash to zero.  It is the perfect “arithmetic” model for the Titanic.  Full speed ahead when you run into an immovable obstacle, killing nearly everyone on board.

The Negative Growth Model

If we are evaluating the negative growth model, specifically known as Sustained Availability, we may use the basic equation y(t) = y0 * e-kt.

k = 1 / Te

Theoretically a declining rate of k will make a resource last forever.  In actual practice we may expect somewhat less than this.  Instead of doubling time we calculate half-life: t = ln(2) / k, which is our old friend the Rule of Seventy.  As a practical rule of thumb we will be doing very well if we are able to extend the life of a resource to five times the half-life.

The peak production rate is y0 since the rate is declining steadily.

So, for example, if we have a 50 years supply of a resource; we may attempt to conserve that resource indefinitely by reducing consumption by 1 / 50, or 2% annually.  This will result in a half-life of approximately 70 / 2, or 35 years.  We will be able to extend the life of that resource from 50 to 175 years.  If reductions greater than k are practical, we can make a resource last even longer.  We will return to this topic under Sustainability.

The Gaussian Models

We will address the Gaussian models in part 5.

Utopian Mythology

Clearly, “We [do not] have coal coming out of our ears.”[7]  To achieve a mythical 500 year reserve time we have to throttle back to zero growth and develop technology that will use 100% of the Demonstrated Coal Reserve Base.  Using the 2008 data, we have at best 223 years of coal left, and very possibly as little as 30 years left.  Since the 1991, by 2008, a mere seventeen years, we have dropped from between 242/475 years of coal to 223 years of coal.

When gasoline and natural gas fail, their energy demand will be thrust upon coal.  Houses and factories will install coal burning furnaces as were common, even in the 1940’s.  Automobiles and trains will be powered by coal generated electricity, or by external combustion steam engines, ala 1850.  The demand on coal will roughly triple, quadruple, or even quintuple.  The reserve of 223 years will evaporate before our eyes to 223/3 less than 75 years; perhaps as little as 223/5, equals 45 years.  Under current economic plans this change will not be exponential, it will be sudden and catastrophic.

Wake Up and Smell The Reality

Don’t say it won’t happen.[8]  When the oil crisis struck in the 1970’s, there was no warning.  Overnight, the price of gasoline doubled.  Our leaders have repeatedly employed a policy that it is best to crash the system.  When the coal is gone we will turn to our forests.  Our children and grandchildren and great-grandchildren will be forced to cope with this disaster.

 “In the 1970’s there was great national concern about energy, but this concern disappeared in the 1980’s.  The concerns about energy in the 1970’s prompted experts, journalists and scientists to assure the American people that there was no reason to be concerned.”[9]

There is no question that additional reserves of coal can be found.  However, there is little incentive to pursue such reserves as long as gasoline and natural gas are the fuels of choice.  Nevertheless, it is likely that these new reserves of coal will be found under forests.  This means that we probably cannot get the coal without destroying the forests.

The continued devastation of forests will further deplete our life-giving supply of oxygen.  Moreover, in certain cases deep soil carbon provides the nutrients for vigorous and long sustained plant growth.[10]  It seems to me that if we are going to mine carbon out of the earth, we ought to be looking for judicious ways to put carbon back into the earth.  Terra-preta may well be a critical and essential ingredient in revitalizing our infertile and chemically dependent American soils, the answer to world hunger, and the solution to the oxygen depletion problem.  It may also enable us to grow healthier, more robust forests.

“Don't believe any prediction of the life expectancy of a non-renewable resource until you have confirmed the prediction by repeating the calculation [yourself].
“Corollary, The more optimistic the prediction, the greater is the probability that it’s based on faulty arithmetic or on no arithmetic at all.”9

Our Conclusion


Once again Dr. Bartlett’s “arithmetic” speaks with deadly accuracy.  We have examined his theorems with rigor, and proved them using standard mathematical methods.  We have lived with a system of utopian false hope: but at what cost?  Everybody likes positive attitudes and hopefulness.  The reality is that this, Titanic like, will cost many lives.

We also verified two very handy formulas that allow us to reevaluate the remaining time under any kind or percent of growth model.

Te = 1 / ln (b) * ln [ ln (b) * A / y0 + 1 ]
Te ≈ 1 / r * ln [ r * A / y0 + 1 ]

By putting this result for Te back into the basic exponential equation we calculate a maximum limit for peak production.  Peak production may be lower than this number, but it can only be made higher by increasing the growth rate or changing the data.

y (t) = a * bTe




[1] http://en.wikipedia.org/wiki/Albert_Allen_Bartlett
[2] http://swantec-ep.blogspot.com/2014/11/energy-policy-analysis-4-ra.html
[3] http://www.albartlett.org/presentations/arithmetic_population_energy_video1.html
[4] Halbouty, Michel, Time Magazine, October 29, 1990, Halbouty (1909-2004), a Texas wildcatter is responding to the question, “But haven’t many of our bigger fields been drilled nearly dry?”  http://en.wikipedia.org/wiki/Michel_T._Halbouty
[5] American Electric Power Company: This quote is possibly sourced in a report to the committee on Interior and Insular Affairs of the United States Senate.
[6] This is Bartlett’s profound and telling analysis.  It deserves our utmost attention.  In our “sound-bite” world we, typically, do not pay attention to what is actually said, we frequently drop conditional clauses; especially, when they are placed at the beginning of sentences and not emphasized.  We suspect that such a phenomenon is being deliberately used by expert communicators to manipulate readers; if conditional clauses are correctly positioned, they will almost always be overlooked.  Thus the public is played.  School reading programs often fail to teach the need to dissect sentences and analyze them.  Even with training, the rush of information is so great that critical information slips by us.  We desperately need to understand Dr. Bartlett’s method here, and learn to employ it ourselves.  The words, “if and only if,” are a standard mathematical expression indicating that the truth of the statement works both ways: if we have enough coal for over 500 years, we must be at zero growth conditions.  Mathematical logic statements are not usually true in both directions.
[7] Falkie, Thomas, Energy Fuels Corporation, June, 1976.  http://www.aimehq.org/programs/award/bio/thomas-v-falkie
[8] I started out in the steel business.  We were still using iron ore from the Mesabi Range.  Mining continues there, but for all intents and purposes, the once great steelmaking operations of the United States are gone.  Nobody was watching.  Today, most American steel is made from melted scrap.  When I was in engineering school in Wyoming (1965), CF&I was going strong as the tenth largest steel producer in the United States and biggest west of the Mississippi.
[9] Dr. Bartlett
[10] http://en.wikipedia.org/wiki/Terra_preta, and http://news.nationalgeographic.com/news/2008/11/081119-lost-cities-amazon_2.html
[11] If you have been blessed or helped by any of these meditations, please repost, share, or use any of them as you wish.  No rights are reserved.  They are designed and intended for your free participation.  They were freely received, and are freely given.  No other permission is required for their use.

Tuesday, November 18, 2014

Energy Policy, Analysis 4, rA


Energy Policy

Arithmetic, Population and Energy, Part 4


Revision A

For the love of the human race.

Wednesday, November 19, 2014

Our Thesis


We have investigated Dr. Bartlett’s mathematics with rigor and found that his use of mathematics is both correct and precise.  It is the task of the mathematician and the scientist to observe reality and explain exactly how and why it works.  This field is known as mapping; Dr. Bartlett’s mapping speaks with deadly accuracy: he has been faithful in this task.

We also investigated Dr. Bartlett’s data, and observed that his data need updating.  We attempted a partial update of the data, but this is an ongoing task that requires incessant continued surveillance.  Maintaining a good, up-to-date data set is the most difficult part of the mathematical problem.  GIGO explains why.

Arithmetic, Population and Energy, Part 4


http://www.albartlett.org/presentations/arithmetic_population_energy_video1.html  Better results were achieved by playing the video clip directly from this site, rather than by linking through YouTube.  Click on the arrow in the middle of the picture, rather than on the black bar at the top.  This is Part 4.

Dr. Bartlett opens this part with a juicy quote from a very important Texas oil man, Michel T. Halbouty (1909-2004), “There is still as much oil to be found in the U. S. as has ever been produced.”[1]

 

1.    What time is it? 
A. It’s 11:59, 1 minute before noon.

 

Then he turns the conversation immediately to coal with this quote, “We’re sitting on half of the world’s known supply of coal, enough for over 500 years.”[2]  A report to the Senate committee said this, “At current levels of output and recovery, these American coal reserves can be expected to last more than 500 years.”2

 

There is one of the most dangerous statements in the literature.  It’s dangerous because it’s true.  It isn’t the truth that makes it dangerous, the danger lies in the fact that people take the sentence apart: they just say coal will last 500 years.  They forget the caveat with which the sentence started.  Now, what were those opening words?  “At current levels.”  What does that mean?  That means, if and only if we maintain zero growth of coal production.”[3]

 

Dr. Bartlett’s discussion continues.  The Demonstrated Coal Reserve Base is around: Rb = 470 G-tons according to Dr. Bartlett’s charts.  The Recoverable Reserve is around: Rr = 240 G-tons (1991).  The significance of these two numbers is that we cannot practically reach over 50% of the total coal with existing technical equipment and methods.  Vastly improved technical equipment and methods can nearly double the realistic coal supply.

Extraction Rates.  In 1971 coal was extracted from mines at a rate of 560 M-tons per year.  In 1991 coal extraction rose to a rate of: 990 M-tons per year.  The Average Rate Growth in this period was roughly 2.86% per year.  Dr. Bartlett uses an equation to calculate the expiration time for any reserve, which he suggests may be derived by using first-year elementary calculus.  Let’s review our calculus to see if we can derive Dr. Bartlett’s equation.

TE 1 / k * ln (k * R / r0 + 1)

We begin by observing that: if exponential growth is in actual practice, that the reserve is equal to the area under the exponential curve.

y (t) = a * bt: the exponential curve

A (t) y (t) dt = a * bt dt + C

The initial value, a, or y0, is a constant.  Let z = bt.  We employ logarithmic differentiation:

z = bt: taking the logarithm and expanding the exponent

ln (z) = ln (bt) = t * ln (b): taking the differential

dz / z = ln (b) dt: multiplying by z and substituting z = bt

dz = ln (b) * z dt = ln (b) * bt dt: multiplying by ln (b) / ln (b)

a * bt dt = a * ln (b)/ln (b) * bt dt: simplifying

a * ln (b)/ln (b) * bt dt = a/ln (b) * ln (b) * bt dt: extracting a/ln (b)

a/ln (b) * ln (b) * bt dt = a/ln (b) * ln (b) * bt dt: integrating

A (t) = a/ln (b) * ln (b) * bt dt = a/ln (b) * bt + C: substituting values

At t = 0, A = 0, and always a = y0

0 = A (0) = y0 / ln (b) * b0 + C: solving for C

C = 0 – y0 / ln (b) * 1 = – y0 / ln (b): substituting

R = A (t) = y0 / ln (b) * bty0 / ln (b): factoring

R = A (t) = y0 / ln (b) * (bt1): solving for (bt1)

(bt1) = R * ln (b) / y0: solving for bt

bt = R * ln (b) / y0 + 1 = ln (b) * R / y0 + 1: taking the logarithm

ln (bt) = t * ln (b) = ln [ln (b) * R / y0 + 1]: solving for t

t = 1 / ln (b) * ln [ln (b) * R / y0 + 1]

We may approximate by remembering from before that b = 1 + r, and that for small r (less than 0.10), ln (1 + r) r: substituting….

T ≈ 1 / r * ln [r * R / y0 + 1]: QED

So, now we have both an exact formula that even applies to enormous values of r, and an approximation similar to the Rule of 70, which can be worked with a slide rule and a pencil.  Nowadays, we would simply grab our scientific pocket calculators and go for the exact solution.  We might even keep the formula in storage, so that we don’t have to remember it.

We reconstruct the following tables using Dr. Bartlett’s data, updating it with 2008 data, and filling in with the exact calculation for the T formula.

 

1971
1971
1991
1991
2008
Recoverable
Coal Reserve
(G-tons)
Demonstrated
Coal Reserve
Base (G-tons)
Recoverable
Coal Reserve
(G-tons)
Demonstrated
Coal Reserve
Base (G-tons)
Recoverable
Coal Reserve
(G-tons)
240
470
240
470
237
Extraction
Rate
(M-tons/year)
Extraction
Rate
(M-tons/year)
Extraction
Rate
(M-tons/year)
560
990
1,063

 

 

 

 

 

Growth
1971
Years of Recoverable Coal
1971
Years of Reserve Coal
1991
Years of Recoverable Coal
1991
Years of Reserve Coal
2008
Years of Reserve Coal
0%
429
839
242
475
223
1%
167
225
123
175
118
2%
114
145
89
118
85
2.86%
91
114
73
95
70
3%
88
110
71
92
69
4%
73
90
60
76
58
5%
63
77
52
65
51
6%
56
67
47
58
45
7%
50
60
42
52
41
8%
46
54
39
47
38

 

 

 

 

 

 

 

 

 

 

 

Clearly, “We [do not] have coal coming out of our ears.”[4]  To achieve a mythical 500 year reserve time we have to throttle back to zero growth and develop technology that will use 100% of the Demonstrated Coal Reserve Base.  Using the 2008 data, we have at best 223 years of coal left, and very possibly as little as 30 years left.  Since the 1991, by 2008, a mere seventeen years, we have dropped from between 242/475 years of coal to 223 years of coal.  This is amazing, it only took us seventeen years to consume nineteen or more years-worth of coal.[5]

When gasoline and natural gas fail, their energy demand will be thrust upon coal.  Houses and factories will install coal burning furnaces as were common, even in the 1940’s.  Automobiles and trains will be powered by coal generated electricity, or by external combustion steam engines, ala 1850.  The demand on coal will roughly triple, quadruple, or even quintuple.  The reserve of 223 years will evaporate before our eyes to 223/3 less than 75 years; perhaps as little as 223/5, equals 45 years.  Under current economic plans this change will not be exponential, it will be sudden and catastrophic.  Don’t say it won’t happen.[6]  When the oil crisis struck in the 1970’s, there was no warning.  Overnight, the price of gasoline doubled.  Our leaders have repeatedly employed a policy that it is best to crash the system.  When the coal is gone we will turn to our forests.  Our children and grandchildren and great-grandchildren will be forced to cope with this disaster.

Here is a 2008 data table for leading coal using nations:

Rank
Country
Reserves
(M-tons)
2008 Production
(M-tons/year)
Years of Reserve
1
United States
237,295
1,063
223
2
Russia
157,010
328.6
478
3
China
114,500
2,802
41
4
Australia
76,400
399.2
191
5
India
60,600
515.9
117
6
Germany
40,699
192.4
212
7
Ukraine
33,873
8
Kazakhstan
33,600
111.1
302
9
South Africa
30,156
252.6
119
10
Serbia
13,770
11
Columbia
6,746
12
Canada
6,528
13
Poland
5,709
144.0
40
14
Indonesia
5,529
240.2
23
15
Brazil
4,559

 

In 2008 the world’s known coal reserves are listed at 860,884 M-tons.  World production was at 6,795 M-tons/year.  This yields an average world supply of 127 years based on zero growth.

“In the 1970’s there was great national concern about energy, but this concern disappeared in the 1980’s.  The concerns about energy in the 1970’s prompted experts, journalists and scientists to assure the American people that there was no reason to be concerned.”[7]

 

There is no question that additional reserves of coal can be found.  However, there is little incentive to pursue such reserves as long as gasoline and natural gas are the fuels of choice.  Nevertheless, it is likely that these new reserves of coal will be found under forests.  This means that we probably cannot get the coal without destroying the forests.

The continued devastation of forests will further deplete our life-giving supply of oxygen.  Moreover, in certain cases deep soil carbon provides the nutrients for vigorous and long sustained plant growth.[8]  It seems to me that if we are going to mine carbon out of the earth, we ought to be looking for judicious ways to put carbon back into the earth.  Terra-preta may well be a critical and essential ingredient in revitalizing our infertile and chemically dependent American soils, the answer to world hunger, and the solution to the oxygen depletion problem.  It may also enable us to grow healthier, more robust forests.

 

“Don't believe any prediction of the life expectancy of a non-renewable resource until you have confirmed the prediction by repeating the calculation [yourself].
“Corollary, The more optimistic the prediction, the greater is the probability that it’s based on faulty arithmetic or on no arithmetic at all.”7

 

Our Conclusion


Once again Dr. Bartlett’s “arithmetic” speaks with deadly accuracy.  We have examined his theorems with rigor, and proved them using standard mathematical methods.  We have updated his data for coal, and found out that our coal reserves are not in much better shape than our oil reserves.  The main point made is that there is a broad willingness to manufacture and falsify data.  This is a public scandal.  It is nothing less than fraud.  Considering the life-threatening danger it imposes on the general population, this falsification of information must be classified as grand larceny, and even murder.  We have lived with a system of utopian false hope: but at what cost?  Everybody likes positive attitudes and hopefulness.  The reality is that this will take many lives.

We also verified these two very handy formulas.

t = 1 / ln (b) * ln [ln (b) * R / y0 + 1]
T ≈ 1 / r * ln [r * R / y0 + 1]

If we put this result for t back into the basic exponential curve, using the highest growth rate anticipated, we arrive at a maximum limit for peak production.  Peak production may be lower than this number, but it can only be made higher by increasing the growth rate or changing the data.

y (t) = a * bt

 



[1] Halbouty, Michel, Time Magazine, October 29, 1990, Halbouty (1909-2004), a Texas wildcatter is responding to the question, “But haven’t many of our bigger fields been drilled nearly dry?”  http://en.wikipedia.org/wiki/Michel_T._Halbouty
[2] American Electric Power Company: This quote is possibly sourced in a report to the committee on Interior and Insular Affairs of the United States Senate.
[3] This is Bartlett’s profound and telling analysis.  It deserves our utmost attention.  In our “sound-bite” world we, typically, do not pay attention to what is actually said, we frequently drop conditional clauses; especially, when they are placed at the beginning of sentences and not emphasized.  We suspect that the phenomenon is being used by expert communicators to manipulate readers; if conditional clauses are correctly constructed, they will almost always be overlooked: thus the public is played.  School reading programs often fail to teach the need to dissect sentences and analyze them.  Even with training, the rush of information is so great that critical information slips by us.  We desperately need to understand Dr. Bartlett’s method here, and learn to employ it ourselves.  The words, “if and only if,” are a standard mathematical expression indicating that the truth of the statement works both ways: if we have enough coal for over 500 years, we must be at zero growth conditions.  Mathematical logic statements are not usually true in both directions.
[4] Falkie, Thomas, Energy Fuels Corporation, June, 1976.  http://www.aimehq.org/programs/award/bio/thomas-v-falkie
[5] The top end figure is 252 years-worth of lost coal.  However, this number reduces to an inexplicable absurdity.  The 2008 report must be for recoverable coal only.  God help us, if this 2008 report includes even a portion of the Demonstrated Coal Reserve Base.
[6] I started out in the steel business.  We were still using iron ore from the Mesabi Range.  Mining continues there, but for all intents and purposes, the once great steelmaking operations of the United States are gone.  Nobody was watching.  Today, most American steel is made from melted scrap.  When I was in engineering school in Wyoming (1965), CF&I was going strong as the tenth largest steel producer in the United States and biggest west of the Mississippi.
[7] Dr. Bartlett
[8] http://en.wikipedia.org/wiki/Terra_preta, and http://news.nationalgeographic.com/news/2008/11/081119-lost-cities-amazon_2.html