by shortonoil » Wed 06 Jun 2012, 11:45:00
pstarr said:
$this->bbcode_second_pass_quote('', 'H')ow did you arrive at 7.3:1? Is that related to the the oil expense index, total-cost-of-crude/GDP?
This explanation is a little much for a post here, but I'll see if I can shorten it up a bit. The explanation lies with the implicit definition of ERoEI. When you pump oil from an oil well you do it by investing work - you are not investing energy.
Energy is a property of matter, work is the result of a process, and even though they are both measured with the same units (joules, BTU, ft-lbf, etc.) they are not the same thing. The energy that comes from the well head must be converted into work (goods and services) before it can be re-input. This conversion process always incurs losses; these losses are guaranteed to occur by the Second Law.
For the global oil system the energy to work conversion efficiency is 19.6%; derived through numerical analysis of cost and production data. (It is interesting to note that the US conversion process until 1971 took place with an efficiency of 22.9%. This we can be very confident of because we know almost exactly when US fields peaked). That is, it takes 5.1 BTU of energy from the well head to re-input 1 BTU of work back into the well.
One of the several ways we came up with 7.29:1 is this: using availability analysis (sometimes called exergy analysis) we computed the Maximum Theoretical Second Law Thermal Efficiency (MTSLTE) for the hydrocarbon crude oil. Even though MTSLTE depends somewhat on the molecular weight (MW) of the hydrocarbon being tested, using the median MW of 31.6 degree sweet crude under optimal conditions and adjusting for asphaltene components (which may not be refine-able) we get 70% (octane, C8H18, has an MTSLTE of 70.2%).
The Second Law says that the very best we can do is extract 70% of the 140,000 BTU that is in a gallon of oil. That is 98,000 BTU. If we reinvest all of the 98,000 at an efficiency of 19.6%, it produces 19,208 BTU of work. ERoEI = EG/EP: where EG = 140,000 BTU (internal energy per gallon, derived from EIA data) and EP is the work invested at the well head. ERoEI = 140,000/19,208 = 7.29:1.
7.3:1 is the world average ERoEI for which below refined fuels can no longer be produced. Of course, the distribution of individual field ERoEI will have some higher and some lower than 7.3:1, but 7.3:1 is important because at that point the higher ERoEI fields will no longer be able to subsidize the lower ERoEI fields when they decline further. Lower ERoEI fields must then be shut-in as they decline in-order to maintain the minimum allowable average. Since old fields will decline faster than new fields can be brought on line (which will have a higher ERoEI) oil production will go into a rapid permanent decline. The timing of all this is determinable from the ERoEI function, or the total accumulated production distribution (CDF).
Our study,
"A depletion model of world crude oil reserves", which "should" be out in a couple of months will go into this in much more detail. It is a "proved" model because its determinations can be validated by application of 1'st and 2'nd Law premises. In the meantime, I hope this answers some of your question.
The Hill's Group