### URR of Discovery/Shock Model

Some commenters on the last post asked about the seemingly large number I selected for a discovery URR of 3.43 trillion barrels. This overshoots the generally accepted number bandied about of 2.1 to 2.6 up to numbers as high as 3.345 trillion barrels according to a USGS estimate. So if anything, the Discovery/Shock model overshoots the low end wildly and the USGS estimate only slightly.

I think I can explain the reason for the discrepancy from the lower pessimistic estimates. Most of the numbers in the 2 to 3 trillion range come about from Hubbert Linearization estimates taken as we near the peak.

That takes it closer to the 2.1 to 2.3 trillion barrels normally quoted by Peak Oil experts than the 3 trillion expected by more optimistic analysts.However, since HL does rely on a symmetric profile, out year data becomes inconsequential. You can see this if I try to do a Hubbert Linearization of the Discovery/Shock model data (actually the Discovery part only):

The red line extrapolation near the "halfway" point puts the URR at a little less than 2.6 trillion but the "hockey stick" or "dog leg" up pushes the actual URR out to 3.4. Note that this purely reflects the discovery model, which shows long tails caused by the apparent reserve growth discoveries.

To answer another question: in the previous post, I fit to the data set shown in this figure that Khebab posted at TOD, solving for CumulativeDiscoveries(2005) - CumulativeDiscoveries(1945) = D(2005) - D(1945), which gave me the 3.4 trillion.

Now that I see how close I am to the USGS estimates, and knowing how overly optimistically many analysts treat their interpretation, I get a little worried on the veracity of my own estimates. But then again we have to recall that the long tails have absolutely no impact on hitting a peak at this instant; it can only serve to delay the downturn if we can crank up the extraction rate. But does the proverbial world have the technical and political wherewithal to accomplish that? ... or do we instead choose a soft landing?

## 14 Comments:

Thanks for the clarification. The question of reserve growth was discussed in detail in the Oil Drum post by khebab, but I thought the conclusion was that the higher URR estimates of CERA, USGS, et al was a result of questionable (at best) reserve growth estimates, specifically as illustrated here and here. However, as you say, the increased extraction rates (and higher URR) can only serve to delay and steepen the inevitable decline. Thanks again and keep up the good work.

thanks. Good catch on picking up my old TOP post. In those days, I had a poor grasp on reserve growth or for that matter how new discoveries would play out. The steepness of the decline is of course much more severe with no future incomings.

Hi WHT,

What allowance for declining EROEI is factored into the long tail? Also I do not believe based on the available evidence (greed and procreation increasing unabated) that a soft landing is possible given that we are consuming the fuels that brought modern society into existence, and allow it to function.

Cheers.

Nothing on declining Eroei into the tail, unless we consider that this is the physical analog (searching larger and larger volumes for smaller payoff) of a perhaps related economic concept (applying more and more energy to generate smaller energy outputs).

That's actually an interesting question, the harder a deposit is to extract the worse the EROEI. You've done an excellent job of modelling the increasing difficulty of locating deposits as a negative feedback term in the discovery model, and of modelling the increasing difficulty of producing depleted deposits as an exponential extraction decline. What about the difficulty of producing from deposits that are in increasingly remote and/or inhospitable locations (polar, ultra deepwater, etc)? Would that be an additional negative feedback term in the production model?

My knee-jerk reaction is to think it difficult to separate the effects of remote and inhospitable locations from that of picking up the vestiges and fringes of the finite reservoir we are exploring (which is what this discovery model essentially does).

On second thought, this in fact may be more amenable as a declining extraction rate, i.e. we know where the stuff is but it gets harder to exploit.

Spot on question though.

On second thought, this in fact may be more amenable as a declining extraction rate, i.e. we know where the stuff is but it gets harder to exploit.Aha! If that's the case then the larger question of "is there a place in the physical model for EROEI" becomes highly relevant.

On a gut level it's easy to see that you need to burn oil to pump oil, and so it just makes sense that somehow it should be subtracted from the production. One way to look at it would be as though removing a portion of oil from every barrel is the "cost" of producing that barrel, a portion never to be seen again as though you burned it right there at the wellhead. It would follow then that the harder, faster, longer you increase production (i.e. secondary recovery, etc.) then the higher the cost of producing each barrel.

This is manifest in the real world as the relentlessly decreasing EROEI of oil production over time, down to something like 1:10 or 1:15 now from a high in the past of as much as 1:100 in KSA, and still headed even lower to the dismal 1:2 or 1:3 of the Alberta tar sands.

Adding such a cost would accomplish two things, first it would explicitly model the diminishing returns of both the increasing difficulty of maintaining high production in depleted fields and the increasingly difficult locations of new discovery, and second it would provide a mechanism for modeling the magical 1:1 "threshold" of EROEI beyond which production is pointless. Each barrel becomes so costly to produce that, using the analogy above, you would burn the entire barrel as soon as it came out of the ground!

Easy to model if the "burned" energy goes poof. Just add on a transition arc to the data flow model where a portion of the flow of extracted oil goes into the bit bucket.

This is a really good idea and one I will likely follow on because it fits in so nicely with the shock model framework.

Outstanding, I'm glad you like it. The only question remaining is "what portion?" for which I may have hit on a relatively painless answer. Globally the energy mix is roughly 40% oil, so a very conservative estimate would be 1/3 of energy invested is itself oil. For an EROEI of 1:1 about 14 of each 42 gallons in a barrel would go poof. This pushes the aforementioned threshold out to 3:1, the other two barrels being some other source of energy, but that actually fits with the popular observation that "burning natural gas to melt tar sands is like turning gold into lead".

On an unrelated note I just noticed something remarkable about your latest chart. One of Hubberts original insights was that the area under the production curve must equal the area under the discovery curve. Looking at charts like this any simian can see that, on our current trajectory, we have a LONG way to go before total production starts to match backdated discovery. And yet in three years of reading peak-oil websites I've never seen a production curve that came close to acknowledging that simple reality. Until now.

Absolutely top notch work.

In the best case the area under the production curve should match the area under the discovery curve. If we siphon some of that away as Eroei losses we forego that equivalence. We also lose it if we find that a portion of the discovered oil is unrecoverable.

If we siphon some of that away as Eroei losses we forego that equivalenceExcellent point. If EROEI is subtracted after production perhaps that calls for a second curve that tracks "net oil"? Just a thought.

We also lose it if we find that a portion of the discovered oil is unrecoverableNow I'm a bit confused again. Did you mean "a portion of the

original estimateis unrecoverable"? As I'm sure you well know one never recovers 100% of the oil from a field, usually only 30%, maybe 50% with EOR, obviously that is the very reason for URR being such a black art (as well as a moving target), and why we have reserve "growth" despite no new oil being created. But you already knew all that, so I'll shut up now.Yes, this only occurs in the non-URR case (i.e. non ultimately recoverable reserves). So you have to make that point.

To be honest I was a little surprised you found the proposition disagreeable. If I were a modeler I would welcome the idea because it gives me a dead simple way to sanity check my equations. For any given projection of URR and production, if the area under the two curves is roughly equal, then my model is plausible. Or at least not totally absurd.

That being said, I can see at least one case where it would not hold true and that would be If the human race suddenly stopped using oil, in which case production would drop to zero and some portion of URR would remain in the ground, but I won't speculate on how likely that is. OK, enough of that, I promise this time I really will shut up.

Mathematically, I agree 100%. The way the equations are set up, probability is conserved and the areas under the two curves (Discovery and Production) have to be equivalent. So yes, it's the way I usually sanity check results.

But like you said, this assumes that all discoveries fall under the "recoverable" class, which is basically a conservative estimator and gives the best possible (i.e. optimistic) outcome. If some is not recoverable, conservation is not assured and we then generate a pessimistic outcome.

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