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.