by WebHubbleTelescope » Fri 27 Jan 2006, 23:19:51
$this->bbcode_second_pass_quote('ReserveGrowthRulz', 'M')y response is this....
Read the paper...the claim by the authors and their method, which you haven't said a single thing about, using all of the data you quoted is what? 10X 15X?
Seems like compounding reserve growth through time has a cumulative effect over, say, 100 years, similar to compounding interest.
Not compound growth by any stretch of the imagination. Compound growth in the traditional sense has a fixed proportional rate. This would give an accelerating slope. However, reserve growth has a decreasing rate which leads to a decelerating slope. Think of it this way -- if the growth rate follows 1/x, then any increase in x gets counterbalanced by a smaller proportional amount or ~(1+1/x)[sup]x[/sup]. I plotted a 0.5/x curve (in green) on top of the moving-average fit below.
Having been away in Silicon Valley on business the past few days, I haven't had a chance to respond more quickly, but oddly enough, there is a strong silicon analogy to what I see in the way this works. Take for example, the work of Andy Grove, one of the co-founders of Intel, who did his thesis work in diffusion-limited oxide growth. In a nutshell, silicon dioxide needs a source of silicon to form, but as the SiO2 layer gets thicker, it becomes harder and takes longer for the Si atoms to diffuse to the surface and react with oxygen. This leads to a law of the following form, where F(t) is thickness as a function of time:
$this->bbcode_second_pass_code('', 'dF/dt = k/F(t)
F = sqrt (2kt)')
Note that the fractional rate can be expressed as:
$this->bbcode_second_pass_code('', 'dF/dt / F = 0.5/t
')
Note that this follows the "reserve growth" curve fit fairly well, where the fractional growth is inversely proportional to time. This is called the
parabolic growth law. For the Google-challenged, you can look it up in any standard microelectronics textbooks.
Now if we were stupid semiconductor neophytes living in the 1950's and thought that the oxide growth could only be "guessed" at, then we would never have been able to advance through the microelectronics revolution and process unpredictability would have killed us. We would still be working with crystal radio sets. None of the multi-million gate circuits would have ever gotten made!
But the fact was that material scientists and engineers like Andy Grove were able to characterize the phenomena within a few years time (mid to late 1960's) and get their process down to a gnat's eyelash speaks volumes about the difference between real engineers and the geologists who believe in magical, enigmatic reserve growth. (I don't know any fab engineer in a bunny suit who believes in "enigmatic" oxide growth)
I have a suggestion for the geologists and petroleum engineers. Figure out what the heck is going on in your measurements and estimates, and then perfect the formula to eliminate the magical guess work. The more I look at it, the more I seriously think that no one has figured out how to do estimates of volume correctly. Could they all be measuring the volume as an approximation to how much they have extracted, with the increase over time caused by diminishing returns? Much like a thick SiO2 layer prevents fast oxidation, that drilling "deeper" into a field starts to slows down further depletion and you need to work harder and wait longer times to get at it? It almost sounds as if no one wants to admit that a parabolic growth law has any kind of importance.
If done correctly, reserve growth would transform from magic to a measure of extractability over time. And this is all I have been saying on how crudely the estimates have been made in the past.