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Thursday, January 15, 2009

Boyle's Law and proprtionate natural gas extraction

I think I got this insight from commenter ElwoodElmore at TOD. He mentioned the use of the ideal gas law, also known as Boyle's Law to understand depletion from a reservoir of gaseous resources. Only material in the gas phase (such as natural gas) can compress with the following relationship between pressure (P) and volume (V):
PV = nRT
This basically says that when pressure increases, volume decreases proportionately, all other factors remaining equal. In other words, this basically states mathematically what we all intuitively understand in terms of compression -- we can compress gas but not liquids.

The other terms in the ideal gas law:
  • n = the number of moles of gas
  • R = the universal gas constant
  • T = the absolute temperature
form a constant only if the individual terms remain constant. Yet in reality, through the process of extraction, we do remove material from a pressurized reservoir. This causes the number of moles (n) to decrease; a mole defining a unit of dimension corresponding to about 6x1023 molecules of gas.

As pressure (P) defines the rate of release from a natural gas reservoir:
P = nRT/V
and the volume (V) stays constant in the cavern, then the pressure must decrease as material gets removed from the reservoir.

This gives us the proportionality, P = k*n, whereby we draw down from any reservoir a linear fraction of the amount (n) left. This forms an alternative basis for the proportionate extraction of the Oil Shock model, this time applying it to natural gas.

This brings up another interesting observation. Another commenter at TOD, Kalle, posted a link to this PDF paper The evolution of giant oil field production behaviour. The authors have gotten on the right track with a depletion rate approach. They essentially observe a characteristic depletion rate value at peak production for a range of oil fields. The variance of this value remains relatively small.

They refer to a "The Maximum Depletion Rate Model" paper in press which I can't get a hold of. I bet that it uses the same principles as I use in the Oil Shock model. The characteristic rate becomes a more-or-less constant factor across a range of fields, making it eminently suitable and a verification for the Markovian basis of the shock model.

So we can substantiate that both oil and natural gas follow this proportionate draw-down behavior, but not necessarily for the same reasons. But that's what happens with the typical probabilistic model.

As Simon-Pierre Laplace once said:
The theory of probabilities is at bottom nothing but common sense reduced to calculus.

Ref: Practical Enhanced Reservoir Engineering: Assisted with Simulation : This came out in 2008 and covers Boyle's Law, among other things in 600+ pages.

Sunday, January 11, 2009


This article lies behind a NY Times firewall:
Challenging the Crowd in Whispers, Not Shouts

It discusses how new ideas, in this case economics, have to overcome the obstacle of the groupthink wall.
... And why didn’t a consensus of economists at universities and other institutions warn that a crisis was on the way?

The field of social psychology provides a possible answer. In his classic 1972 book, “Groupthink,” Irving L. Janis, the Yale psychologist, explained how panels of experts could make colossal mistakes. People on these panels, he said, are forever worrying about their personal relevance and effectiveness, and feel that if they deviate too far from the consensus, they will not be given a serious role. They self-censor personal doubts about the emerging group consensus if they cannot express these doubts in a formal way that conforms with apparent assumptions held by the group.
Pretty sad. I think groupthink mixed with superstitious economic theorizing have lead us down this path.
"In 585BC, long before Jesus, the Greek philosopher Thales of Mellitus concluded that every observable effect must have a physical cause. The discovery of causality is now taken to mark the birth of science, and Thales is immortalized as its father. But causality also means the death of superstition." -- Robert Park, 2009