Energy Policy
Arithmetic, Population and Energy, Part 4
Revision A
For the love of the human
race.
Tuesday, March 25, 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.”[i]
1.
What time is
it?
A. It’s 11:59, 1 minute before noon.
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.”[ii]
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.”[iii]
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) *
bt – y0 / ln (b):
factoring
R
= A (t) = y0 / ln (b) *
(bt – 1): solving for (bt
– 1)
(bt
– 1) = 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.”[iv] 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.[v]
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.[vi] 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.”[vii]
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.[viii] 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.
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
[i]
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
[ii] 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.
[iii] 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.
[iv]
Falkie, Thomas, Energy Fuels Corporation, June, 1976. http://www.aimehq.org/programs/award/bio/thomas-v-falkie
[v]
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.
[vi] 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.
[vii]
Dr. Bartlett
[viii]
http://en.wikipedia.org/wiki/Terra_preta, and http://news.nationalgeographic.com/news/2008/11/081119-lost-cities-amazon_2.html
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