## Sunday, June 15, 2008

### Petroleum and Population

Petroleum and Population
Andre Willers
11 June 2008

What will happen to the teeming billions on Earth if Petroleum should suddenly vanish?

How do we get to this figure ?
We look in the past ( 1800 – 1900 ) when petroleum did not play a big role . We then calculate the estimated population in 2000 AD using the Exponential Growth Rate Constant of this period ( 1800 – 1900 ) .

Fundamental assumptions used in the calculation:
Exponential curve .
See the Appendix for the derivations .
The population size is described by the exponential equation of the form
Population = M * e^(K*t)
Where M is a constant , K is the important Exponential Growth Rate Constant and t is years (ie t=2000 at 2000 AD) .

Populations are usually more exactly described using a S shaped curve , but the populations we are talking about show no signs yet of inflection into the top half of the S-curve . Exponential growth is a close enough fit for the bottom half of this curve , especially given the approximate nature of the data .

Malthus :
We assume that populations expanded at the maximum rate made possible by their technologies . This is the historical experience .
This means that , if we extrapolate the same growth rate forward , it will be at the limits of that technology . The population we arrive at will be near the maximum sustainable by that technology .

Any piece of ground does not have an innate human , animal or plant population carrying capacity . This capacity varies with the technology of it’s inhabitants . This technology includes the bodies of the inhabitants . (Eg teeth , digestive systems , salt tolerance , etc ,etc)

Saying that we need another 1.6 or 2 Earths is meaningless without specifying the technological level .

Technological Levels .

A : Medieval : 1500 – 1700 . Animal power , Pre-medicine , Pre-industrial , Pre-Coal , Pre-Petroleum . The old Era.
Start period world population (in billions) : 0.425
End period world population (in billions) : 0.600
Exponential Growth Rate Constant (K) : 0.0017
Estimated world population in 2000AD at this growth rate (in billions) : 1.0

B : The Age of Reason : 1700 – 1800 . . Science . Medicine and Industrial revolutions start . Pre-Coal , Pre-Petroleum .
Start period world population (in billions) : 0.600
End period world population (in billions) : 0.813
Exponential Growth Rate Constant (K) : 0.00303
Estimated world population in 2000AD at this growth rate (in billions) : 1.5

C : Industrial revolution : 1800 – 1900 . The Age of Coal. Pre-Petroleum .
Start period world population (in billions) : 0.813
End period world population (in billions) : 1.550
Exponential Growth Rate Constant (K) : 0.00645
Estimated world population in 2000AD at this growth rate (in billions) : 3.0

D : Petroleum Age : 1900 – 2000 .
Start period world population (in billions) : 1.550
End period world population (in billions) : 6.1
Exponential Growth Rate Constant (K) : 0.0137
Estimated world population in 2000AD at this growth rate (in billions) : 6.1

A Table will make it clearer :

A B C D
K{x10^(-3)} 1.7 3.03 6.45 13.7
Pop2000(bn) 1.0 1.5 3.0 6.5

Corollaries at 2000AD and with present technology:

C . Without Petroleum the planet can support 3 billion .
Without Petroleum and coal the planet can support 1.5 billion .
Without Petroleum , coal , industry or medicine the planet can support 1.0 billion . This is also the estimate of the basal carrying capacity of the planet .
Almost by definition , as only animal power is used . The population will probably be near or past the inflexion point for this tech–level .

Note the near-doubling of K at each technological paradigm-shift . I suspect that this is because of the fractal nature of the development stages of the world population .

The Vanishing Act of Petroleum .
Of course , petroleum won’t vanish overnight . But , after Hubbert’s Peak has been reached (when rate of new discoveries are less than rate of usage) , the oil in the ground appreciates faster than returns to be gotten by selling it .
This point has already been passed .(+- 2005)

Hoarding .
Producers down the whole supply-chain hoard product . Prices rocket , encouraging more hoarding in a vicious positive feedback cycle .

This is a well-known mechanism usually seen in famines when warehouses are full of food and people starve . ( Eg 1942-1943 in Bengal , 4 to 6 million people starved to death even though there was a good harvest . The war made merchants expect higher prices , so they locked up the food in warehouses . The incompetent and corrupt British administration allowed it .)

Of course , one person’s hoarding is another person’s optimization of profits . The only way out of this impasse is by political leadership , not a quality in great supply at the moment .

Prognosis: Not good .
Prices shoot up non-linearly . Then , hiccups develop in the supply-chain and actual physical shortages result . This is the equivalent of inventory build-up . This has disasterous consequences on an economic system optimized on Just-in-Time deliveries . National and Military interests seize the only reserves in the system . The bubble collapses . Markets collapse . The demise of Capitalism and Democracy . (A-la-USSR)

Even huge multi-national oil companies can be bankrupted . They sit on huge inventories of oil-products , but their customers can no longer afford to buy .
Non-food producing nations starve .
Genocidal war and volkewanderung (already happening in Africa) .
Civil wars (a-la-Yugoslavia) in artificial states . Even established states with ethnically diverse populations (US ,China , India , UK,Iraq,etc) can be torn apart by diverse interests as groups battle to eat .

All this against the background of climate change , as well as nuclear and biological weapons .

I have described this scenario in previous posts on the collapse of the Late Bronze Age . See
http://andreswhy.blogspot.com

In Interregnums like these leadership is critical . Even small actions can have huge effects . The whole system has gone non-linear .

Andre Willers

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Appendix
The population size is described by the exponential equation of the form
Population = M * e^(K*t)
(This can be described as the left-hand side of the S-shaped population curve known as activation or logistic functions in Neural Networks . Also known as squash functions .)

P(1)=M*e^(K*t(1) )
P(2)=M*e^(K*t(2) )

P(2)/P(1)= e^(K(t(2) –t(1) ) )

K=ln (P(2)/P(1) ) / ( (t(2) –t(1) )

Solving for M and substituting in above gives

P(3) = P(2) * [ [ P(2)/P(1) ] ^ [ {t(3) –t(2)} / {t(2) –t(1)} ] ]

Where
P(1) , P(2) and P(3) are populations at times t(1) , t(2) and t(3) respectively
M is a constant , K is the important Exponential Growth Rate Constant and t is years (ie t=2000 at 2000 AD) .

Populations (from UN , McEvedy)
Year Billion
1500 0.425
1700 0.600
1800 0.813
1900 1.550
2000 6.100

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