Excerpts from your post:

So, what is the downside of increasing the extraction rate?

Answer: The downside is the downslope. Quite literally, upping the extraction rate under a limited supply makes the downslope that much more pronounced. The Gompertz shows a marked asymmetry that more closely aligns to exponential rise and collapse than the typical symmetric Hubbert curve.

These are two representations of what the world oil production curve might look like, if we actually managed to pump harder. (The Gompertz curve is the rounder one, closer to the Hubbert curve we are used to).

You also fitted a Gompertz curve to phosphate production:

Click for larger images. Read the whole post for better understanding of that WebHubbleTelescope is saying.

Hello WHT,

Thxs for your hard work on phosphates. I don't know if this will help on any future analysis, but remember the guanos are activated phosphorus[P]--beneficiated by the birds and bats; thus equivalent to modern superphosphate from processed ores:

http://en.wikipedia.org/wiki/Superphosphate

We are now reliant upon raw ores PLUS THE BENEFICIATION PROCESS. The key to this is Sulfur-->sulfuric acid-->phosphoric acid-->high potency, high NPK-ratio finished products.

Much more energy is now required than for guano. Lawes knew about this chem-process a long time ago, but couldn't find the energy to power a large scale operation--thus the ships had to sail around the world for guano, instead of the short hop to Morocco.

Thus, as sour crude and sour natgas depletes, IMO, it will have a great impact on I-NPK flowrates, with the greatest effect upon activated-P flowrates [as that is where most sulfur is directed].

Some people will say we will never run out of sulfur to mine. I counter with the USGS argument that mining raw sulfur is much more energy intensive plus environmentally destructive than refining it from FFs [56-page PDF Warning]:

http://pubs.usgs.gov/of/2002/of02-298/of02-298.pdf
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[Page 15] Recovered Sulfur

In the context of this report, recovered sulfur is defined as the elemental sulfur recovered for environmental reasons during the
processing of natural gas and petroleum refining. The U.S. Bureau of Mines first reported recovered sulfur production data for the
United States in 1938; prior to that time, unspecified quantities of sulfur were produced, especially during treatment of natural gas, but
disposed of as waste. Sulfur recovery has grown in importance over the years to become the leading source of sulfur in the United
States starting in 1982 and the only source of elemental sulfur with the closure of the last domestic sulfur mine in August 2000.
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As FFs deplete, I suspect the shrinking energy and sulfur will impact the P-flowrate, but I have no idea how to math extrapolate this out.

Hopefully, you can find time to give this a go....Thxs in advance.

Bob Shaw in Phx,Az Are Humans Smarter than Yeast?