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?

Answer : About 3 billion would starve .

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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