There have certainly been production increases after declines, but has any major producing area (with at least 50 Gb or so in recoverable reserves) shown a production increase after hitting about 55% of Qt, based on P/Q versus Q?  

Based on the data I have seen, the answer is no.  

The current key case history is Saudi Arabia--at 55% of Qt.

The "nonscientific" label is interesting.  One of Lynch's cohorts, Peter Huber, asserts that our energy consumption will increase--forever.   Huber, if pressed, will admit that some energy sources, like conventional oil, will eventually peak and decline, but he still asserts that aggregate energy consumption--from a group of finite energy sources--will increase forever.   Let's see, infinite energy from a group of finite energy sources--yep, that makes a lot of sense.  

but has any major producing area (with at least 50 Gb or so in recoverable reserves) shown a production increase after hitting about 55% of Qt, based on P/Q versus Q?
 
Only if you do the linearization too early. For example
http://www.theoildrum.com/story/2005/9/30/21818/2120
You can't model UK production with a single logistic model.

Two cycles of discovery -> Two logistic models.

The US crossed 50% Qt in 1971 and crossed 55% of Qt in 1978 (using 220gb as Qt) yet our production increased each year from 1976 to 1985 (except 1981 small drop). Yes that was Alaska for the most part, so your 'geologic' point is sound.(if you include Alaska in north america as a whole I dont think this still holds). But on a country basis, here is one example. Perhaps there are others.
The Lower 48 peaked before serious production even began in Alaska.  In terms of timing of development, geology and distance, Alaska might as well be in the Middle East.  

The key to developing a useful model is to set reasonable geographic limits.  In time, the world--a geographically limited area--will show the same type of production behavior as our geographically limited models--Lower 48; Texas and the North Sea.  

Texas peaked at 54% of Qt (66 Gb), and production has steadily fallen.

The Lower 48 peaked at 48% of Qt (200 Gb), and production has steadily fallen.

The North Sea peaked at 52% of Qt (60 Gb), and production has steadily fallen. Furthermore, the North Sea P/Q intercept accurately predicted that the North Sea would have a steeper decline rate than Texas and the Lower 48.

The peaks significantly before 50% of Qt, e.g. Iran, have corresponded to political problems.

My proposed ground rules are:  (1)  reasonable geographic limits; (2)  decades of serious production and (3)  a Qt of at least 50 Gb.  

Within those limits, has any region shown production increases beyond 55% of Qt?

The multi-trillion dollar question is Saudi Arabia, currently at 55% of Qt.

It certainly sounds reasonable that once a field has gotten past a certain point, it has not been economical to try to force an actual increase in production. It would probably be possible to do so, if you spent enough money, but it makes more sense to spend that money on newer fields which will give you a much greater return on your investment.

This is why I have urged caution in extending these principles into the environment of a worldwide peak. Once we get to the point where there are no other fields to go to, where the only possibility is to spend more to improve production from existing fields, then incentives will be different and we may well see different results.

In the near-peak and post-peak periods, oil will rapidly increase in value and oil owners will try much, much harder than we have ever seen before to improve extraction from their fields. I don't know how much success they will have, but you can't extrapolate from past failures to resurrect declining fields and assume that this will remain true once we hit a worldwide peak.

Oil companies in Texas have had considerable incentives to increase production from existing fields.  We have tried everything known to the oil industry.  The same thing is true in the North Sea.  In both cases, it's been all downhill once production peaked at around 50% of Qt.  Note that these two peaks were 27 years apart (1972 and 1999).  

The best example of the true problem is the East Texas Field, which is now producing 1.2 million bpd of water, with a 1% oil cut (12,000 bpd).  What can technology do to increase production from a field that has watered out? This is precisely the same problem facing the Saudis in the Ghawar Field.

At Matt Simmons has documented, better technology has primarily given us faster production rates--and faster decline rates once production peaks.

As we approach peak you would expect to see all available rigs jump out of cold storage and drill for hydrocarbons. That has happened. More money will not provide the world with hardly any more rigs in the near term. Meanwhile, reduced production/ng well has resulted in high prices for ng, which in turn has distracted the US rigs such that 85%, up from 50%, are now drilling for ng. Higher oil prices will just compete with high ng prices for available rigs - total US production will continue declining regardless of price. The same situation exists all around the world - Saudi poached deep sea rigs from our gulf to drill in theirs.
I'm pretty sure that if you ask a geologist why the number of rigs drilling for NG is relatively higher, she/he'll say that it is not because they had a choice between drilling either an oil well OR drilling a gas well, but that they (geologists) see a 5.67 times higher successful completion percentage (or would it be 5.67 x the # completions x expected profit/completion?  Anyway...) in recommending that they try drilling for gas rather than try to drill for increasingly scarce oil with holes that have increasing probabilities of coming up dry.
Its simpler than this. ng companiew bid against oil companies for rigs, and can afford to bid more because ng has increased much more than oil over the bast couple of years.
Actually that used to be true but now isnt. Since Jan of 2003, Nat gas has gone from $5.10 to $9.20 or up about 80% -(in November it was at $15.70+) During the same period WTI crude has gone from $32 to $68 or about $115%. If price is the switching impetus, expect the # of rigs drilling for gas to decline -
I thought that somebody would bring that up, which is why I included the semi-formula for maximizing expected returns if gas price had increased overproportionally to oil in recent times, rather than just having left it with the formula based on  choosing X from the total available possibilities, so there was really no possibility of a wrong answer as I kinda' suggested both could be driving factors, but anyway... I know that there's a hellova' lot more gas fields than oil and its a long-held geologist's (shall we say) "superstition" that its always easier to hit a producer (oil or gas) near the ones you already know are winners.  Usually they'll try that unitl its even plainly obvious to the investors that there just aint any more to be found here and they can't trust the geologist's recommendations any longer, 'cause the geologists are still saying to drill the next 40 acres right there, even if the last 10 came up dry.  Nobody's more optimistic than a geologist.  (I don't mean that in a poor way.  I have much respect and know I don't have X-ray vision either.  Just that the continously optimistic production forecasts made it real hard for me to optimize the gathering system when the wells would make 30 MMCFD for 30 days than fall off to 50,000 CFD in the next couple of weeks and stay there for the next 2 years.  Granted, it wasn't the best producing formations they were drilling on either.)

I see there's another one that agrees.

I think we're talking about increasing production ABOVE the highest amount before 55% Qt was extracted. Sure you can increase production one year over another, but to actually reach a higher Bbl output after "peak" would seem to be impossible (in addition to never happening thus far). Its kind of like thermodynamics. No variations have ever been observed in nature, unless your research is funded by oil companies, you don't do science, or really really really want to believe in cornocopia.
The UK, if you were just looking at the linearization, you'd have thought you were well past Qt/2 and then been surprised by the second peak.  So you have to have some awareness of the discoveries in the pipeline.
Note that the UK by itself falls short of my 50 Gb limit, but the UK and Norway together have a Qt of 60 Gb.  FYI--I used crude + condensate for the Qt estimate.
And there is the second large mistake that Lynch is using. He looks at production curves of nations and concludes from that that nations do not have an neat gaussian production curve. Then Lynch states that oil production is influenced by politics more then by geolological restraints.

See this UK graph

But Lynch doesn't realise that by looking at nations he specificaly is looking at political units while large culsters of oilfields most often do not lie in a single political unit. If you look at production curves of the North Sea in total you come to the astonishing conclusion that even when the UK's production curve might not fit a gaussian curve, the Northsea's resembles it far more closely.

Iraq is another example of a "wierd" production curve which is influenced by politics. Yet the world production curve is driven by demand, so if one poltical unit fails to deliver another will come up with the difference.

By looking at the production curves of nations political influences on the world are wildly exaggerated.

That last sentence should have been:

By looking at the production curves of nations political influences on the world production is wildly exaggerated.

Sorry..

Good point.  

Perhaps ASPO should do analyses of geological regions, rather than analyzing individual countries a second time around.