"Yet, even though we have these huge increases in search rate per year, we still keep finding fewer and fewer reservoirs on average per year."

You are right indeed. Situation, when exploration well spudding is based on sisemic data only exists for a long time. Today, as it was decades before, oil companies drill mostly dry exploration wells. Drilling success rate doesn’t overcome 25% on average. It means that three dry wells go to waste from each four drilled. It means also that discovery occurs too slowly today, but there is a highly productive exploration technology (Seismo-electromagnetic - SEM) for detection of hydrocarbon deposits. It provides a success rate close to 75%. In other words, 3 productive wells for each dry well. Obviously with the technology like this world oil industry could make three times more oil discoveries then using conventional technology, and this technology won't need more investment,time-frame and so on compare to a conventional one. It would significantly mitigate world energy problems.

Seismics---Prospects---Drilling---Discoveries: one in four
Funding --------project time-----------------------------------------
SEM--------Prospects---Drilling---Discoveries: three in four
www.binaryseismoem.weebly.com

The exponential distribution is definitely skewed. There is a finite probability of having delays of 20 years or more. As a matter of fact, the combination of the 4 latencies could conceivably push the peak location to beyond 30 and approaching 40 years. This occurs when you add in the 0.04 proportional extraction rate, which essentially provides a 25 year "shift".

As far as actual data, there is some data that we can infer parameters from:
http://mobjectivist.blogspot.com/2005/10/oil-production-ramp-up-times.html

We knew about oil in Alaska, but didn't develop it until US-48 started declining

The reasons for delays in developing the Alaska fields and the pipeline are given here, in a TIME article of 1971 (extracts):

Three years have lapsed since drillers struck oil on Alaska's North Slope, touching off a black-gold rush that promised to make the relatively poor state the "Kuwait of the North." What has happened to the promise?

Three years after one of history's richest oil discoveries, production is as bogged down as a truck convoy in tundra. The cause of the delay is the Department of Interior's refusal to grant a pipeline permit until the requirements of the 1970 Environmental Protection Act are met.

Some 57,000 Aleuts, Indians and Eskimos, protesting that the pipeline would pass through 641 miles of federal lands claimed to be theirs, demanded compensation. This has forced the Department of Interior to delay construction until the land claims can be settled.

Meanwhile, the boomer spirit has given way to despair. Near Anchorage, construction of the new Forum Hotel has halted. At the Anchorage airport, the Red Dodge Aviation Co. has abandoned its partially finished $2,000,000 freight terminal and has filed for reorganization under the bankruptcy law. Interior Airlines has also gone to court to stave off creditors. Alaska Airlines is in dire financial straits, as are several construction companies. Many corporations have overextended themselves. Bankers have begun to dry up financial pipelines that were once easily accessible to entrepreneurs

http://www.time.com/time/magazine/article/0,9171,877050,00.html

The Dispersive Discovery model takes future discoveries into account. By the time that the backside tail is reached, the search space traversal is 100's of times faster than it is on the frontside. I promised a few plots earlier. Here are a few examples of noisy discovery profiles and the smoothened Shock production curve (in red) that follows:




Compare against Khebab's Figure 3.

These are each Monte Carlo runs of 120,000 samples each (corresponding to number of reservoirs tapped) with a maximum reservoir size of 80 billion barrels and a minimum nucleated size of 2 million barrels. The key thing to note is that the amount of fluctuation does not affect the final shape after production convolution with the 3 stages plus the 0.04 proportional extraction rate. Yet these are all still random events in the sense that the DD profile provides a weighting for the sampling space.

I just caution on the interpretation of the IEA concave-up curve. Some of this is justified as it it making up for the concave down shape of previous discoveries. But of course they truncate the data before it reaches an expected maximum.