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That's a good question. It depends on what happens to costs. If costs of extraction rise at the same rate as prices rise, then the economics are no different. In particular, energy prices have a big input to general inflation. You end up chasing your own tail.
Surely if the energy ROI is positive, then so would be the financial ROI?
Apologies, I haven't thoroughly read all of the reports, I was wondering if there was a quick answer to the question that the peak oil skeptics like to use - i.e. 'It's not economic at the moment'
For some production scale, yes.
But the minimum scale depends on salaries, non-energetic inputs, interest and ERoEI. And the dependence on ERoEI grows very fast when ERoEI approaches 1.
Surely if the energy ROI is positive, then so would be the financial ROI?
There is a lot of overlap, but it's not 1:1. For example, if you are producing gas from a well but don't have infrastructure to deliver it to a market, the gas is flared. Therefore it may have a high EROEI, but would have poor ROI.
Conversely, if you can use the gas to turn tar sand into syncrude, which can be more easily transported to a market, then the tar sand has a positive ROI even if it has a poor EROEI.
In general though, a back of the envelope formula is
C = nP + F
where C is the cost of producing a barrel of oil equivalent, n is the number of BOE used, P is the price per BOE, and F is non-energy (fixed) cost.
then the required price for break-even is:
P = F / (1-n)
Here I have assumed that the non-energy costs are fixed, which may not be the case. In practice, these costs may also rise, e.g. rising cost of steel.
Note this equation incorporates EROEI.
To illustrate how this works, an example. With an oil price of $40/bbl, I estimate that my turkey offal syncrude costs $80/bbl to produce. At what oil price do I break-even? The answer is not $80/bbl. Of my costs, let's say $20 is direct energy cost, and $60 are fixed costs (plant etc). Therefore
P = $60 / (1-0.5) = $120
In this example the EROEI was 2:1. As EROEI decreases, the break even price increases.
I see you are saying n = 1/EROEI so that 0.5 = 1/(2). This works for fuels not wind and solar where depreciation has to be converted to energy equivalents, with interest being a somewhat fixed cost. In the case of corn ethanol (say EROEI = 1.25, n = 0.8) the sale price in effect gets an add-on from the tax credit.
I think mechanised coal mining will stop when it gets into the EROEI range of 2 to 4. Gubmints just won't have the revenue to subsidise it.