Arithmetic, Population and Energy, Part 4

Energy Policy

Arithmetic, Population and Energy, Part 4

For the love of the human race.

Wednesday, February 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.

http://www.youtube.com/watch?v=umFnrvcS6AQ

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]

Discussion continues.  The Demonstrated Coal Reserve Base is around: R_b = 470 G-tons according to Dr. Bartlett’s charts.  The Recoverable Reserve is around: R_r = 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.

T_E ≅ 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 * b^t: the exponential curve

A(t) ≡ ∫ y(t) dt = ∫ a * b^t dt + C

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

z = b^t

ln(z) = ln(b^t) = t * ln(b)

dz / z = ln(b) dt

dz = ln(b) * z dt = ln(b) * b^t dt:integrating

∫ a * b^t dt = a / ln(b) ∫ ln(b) * b^t dt = a / ln(b) * b^t + C

At t = 0, A = 0, and a, always = y₀

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

C = - y₀ / ln(b): substituting and factoring

R = A = y₀ / ln(b) * b^t - y₀ / ln(b)
= y₀ / ln(b) * (b^t - 1): multiplying

(b^t - 1) = R * ln(b) / y₀ = ln(b) * R / y₀: adding

b^t = ln(b) * R / y₀ +1: taking the ln

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

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

We remember 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 construct 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.  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.”[6]

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.[7]  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.

“Corollary, The more optimistic the prediction, the greater is the probability that it’s based on faulty arithmetic or on no arithmetic at all.”⁶

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.

---

[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] Dr. Bartlett

[7] http://en.wikipedia.org/wiki/Terra_preta, and http://news.nationalgeographic.com/news/2008/11/081119-lost-cities-amazon_2.html