Dissertation on Peak Oil


by Charles Whalen


Very complex subject.  Peak Oil is not about running out of oil; it's about having reached maximum supply and production.  There's a big difference.  Basically what Peak Oil does is that it puts a cap on GDP, where the only way GDP can grow any further is through efficiency gains.  The practical effect of this is that we will see repeated cycles of rolling recessions (or worse, depressions) and recoveries, but without a longer term trendline of growth.  The longer term trendline will be flat.  This is exactly what we are seeing.  Global oil extraction and production peaked in 2005 and has fallen slightly since then.  We are now on a very slightly decreasing plateau and will likely not see larger declines in oil output for a few years, possibly until 2012-15, when the declines will get steeper.  There can be, and will be, lots of oil price volatility within this paradigm, with price basically determined by demand.  What we now have is a demand-destruction dynamic, where price will moderate demand and vice-versa, but where total supply is limited and capped by the global peak that is now clearly visible behind us in the rear-view mirror back in 2005.  Peak Oil is only visible in hindsight, and we've now got that hindsight to clearly see it.


There are mathematical models which explain the extreme price volatility we are seeing and will continue to see in the oil market.  In the absence of any widely developed and available, competing substitute for oil and with the supply of oil constrained and limited to the peak we have already seen behind us and unable to expand any further, I see mathematical queueing models as a good proxy and theoretical construct for explaining this price volatility.  In a queueing model, you have a demand rate and a supply rate, just as in the case of the oil market.  Mathematical queueing models do not directly incorporate price into them, but this can be done by proxy, as the length of the queue -- or equivalently, the waiting time in the queue (which is proportional to the length of the queue) -- can be thought of as a proxy for price, since price will likely be directly proportional to the length of the queue (or equivalently, waiting time in the queue).  This may be somewhat counter-intuitive to those without mathematical training, at least on first thought, but the length of the queue (and waiting time in it), and hence, by proxy, the price of oil, takes off exponentially and skyrockets as the demand rate approaches the limited, constrained, fixed supply rate.  In fact, the length of the queue, and hence price of oil, actually goes to infinity (in the mathematical model) as slack capacity completely disappears and the demand rate reaches 100% of supply, bumping up against the fixed supply constraint.  This can be seen mathematically, for the simplest M/M/1 queue, with the formula:


L(t) = 1/[µ(t)-λ(t)]




L(t) = length of the queue (as a proxy for price) at time t


λ(t) = demand rate at time t


µ(t) = supply rate at time t


This mathematical model is a good proxy in explaining the demand-destruction dynamic in a supply-constrained environment, as we now have with the oil market having reached maximum global ouput, and the resulting repeated cycles of rolling recessions and recoveries that we are seeing and will continue to see, with a flat longer-term GDP trendline, where demand continues to bump up against this fixed ceiling at the height of each recovery, causing the price of oil to skyrocket, which then results in demand destruction, leading to another recession and then subsequent recovery, and so on and so on.


As demand backs off of the fixed, constrained supply going into each recession, the mathematical model explains and demonstrates how the price of oil will drop precipitously with the more slack capacity that is freed up through demand destruction.  Basically what will happen is that with sufficient slack capacity (of supply over demand) in the global oil market, the price of oil will start to drop back down towards its cost of extraction and production, which is exactly what we are now seeing.


The only way we can get out of the vicious cycle of this paradigm (explained reasonably well by mathematical queueing models), which has stalled and flatlined long-term economic growth, is to develop a widely available competitive substitute for oil, which of course would be electrically-powered transportation, i.e. EVs.  That would remove the constraint and ceiling on economic growth and allow the global economy to once again expand.





Charles wrote this article, which first appeared on the FLEAA mailing list in response to a personal query to Charles from Fran Sullivan-Fahs. On the subject of Peak Oil, “what do you think, Charles?”  Fran asked the question after reading the following by Doug Korthof:




Doug is great source of energy and information and the response by Charles or my endorsement of it in no way indicates anything less than high regard for Doug and his opinion.  I just enjoyed the elegant simplicity and logic of Charles’ approach.



I relate to Charles approach because of my background in large scale computer operating systems design and programming.  As an operating systems designer, if you don’t understand Queuing Theory, you have poor performance or worse.  Up to this point I had not viewed Peak Oil in this way.  For me this approach helped.