Doly said:
Unfortunately, I'm not convinced that you have the right result, either. I don't deny that it's the best fit that your maths software could find, but the decay curve is asymptotic to a level around 22:1, or in plain English, it's saying that EROEI will remain close to 22:1 for ever and ever. This is against what we all believe about EROEI: that it will keep declining until it's below 1:1. I can't really believe you found the best fit.
Excellent observation
Doly. This very issue prevented me from posting these results for almost two years! There is, however, an explanation:
The ERoEI curve is asymptotic to the X axis. It is presently declining by 0.47 points per year. US fields peaked at 21.9:1 in 1971 (some say ‘70). This is the ERoEI at the well head. The important factor to be determined, however, is the ERoEI for these products at the consumer. The amount of energy available to the society to do work, is the critical variable to be considered.
Cleveland puts the decline in ERoEI from the well head to the consumer at 10 - 14 to 1. My investigations show that this loss could be as high as 16 points for some products and some fields. This puts the ERoEI to the end consumer, (the actual critical value point) at 11.9:1 for the US fields at peak (using an average loss in ERoEI from well head to end user of 10).
Assuming that the ERoEI declines at a steady 0.47 points per year (which it probably doesn’t, but the estimate is adequate short term), we have: where ERoEI is at the end user,
- Code: Select all
Year ERoEI Energy Loss
1972 11.43 0.039
1973 10.96 0.041
1974 10.49 0.043
1975 10.02 0.045
1976 9.55 0.047
1977 9.08 0.049
1978 8.61 0.052
1979 8.14 0.055
1980 7.67 0.058
1981 7.20 0.061
.
.
.
1985 5.32
1986 4.85 0.088
As you can see the energy loss is increasing geometrically; growing from 3.9 % per year in ‘72 to 8.8% in ‘86.
I believe that this is the best fit for two reasons: First: Cleveland’s data set (the one the curve is derived from) is the best that has ever been assembled. He used a bottoms up analysis directly from producer data. The second reason: the ERoEI curve can be mathematically derived directly from the logistic curve. They are both compelling evidence and together produce what has to be considered a slam dunk.
Both the conventional interpretation of ERoEI and the
Available Energy Model arrive at the same destination at about the same time, they just use slightly different routes to get there.