Early in the history of fossil-fuels extraction the energy available in the minerals extracted was high. However, as the more-easily extractable minerals are no longer available the emery return over energy invested (EROEI) decreases. Eventually, the EROEI goes to zero, at which point extraction no longer occurs for the purposes of using it for energy. Of course, it still will be extracted for its material value until solar materials replace it.
Reference 3 gives the following approximate values for EROEI for world crude oil:
I fitted a hyperbolic tangent to these "data":
The fit equation is 39284{1-tanh[(t-1715)/72.01]}/2.
To get the amount of energy available from extracted crude oil for the world multiply the extraction rate multiplied by this function:
The blue curve shows the extraction rate in 10^9 barrels per year, which peaks at about 2011. The red curve shows the approximate energy (in arbitrary unit) available from the extracted crude oil, which peaked at about 1975.
Applying the same EROEI function to the crude-oil extraction data for the United States:
Although the extraction peak occurred at ~1975, the energy availability peak was at ~1955.
The EROEI for tar-sands oil is ~5. The EROEI for shale oil is ~3. Applying the EROEI for tar-sands oil to the fit to the extraction data we get:
Oil extracted from Canadian oil sands is a blip on world extraction, but the energy blip is much smaller; essentially negligible. Oil extracted from shale and coal will be even less important for future energy.
Charles Hall and David Murphy give a curve for estimated EROEI at the city gate. I have fitted a function containing three hyperbolic-tangent functions to their curve:
The best fit gave a final EROEI of 6.87. However, more data are needed to determine that number. So, I have also included two other options, final EROEI=0 and final EROEI=3.
Applying the EROEI for world natural gas, including shale gas, to the fit to the extraction data we get:
The left axis is for the black extraction curve and the right axis is for the three colored energy curves. Of course, the energy available at the city gates is very sensitive to the final EROEI.
L. David Roper, http://arts.bev.net/RoperLDavid/; roperld@vt.edu
24-apr-13