1. Is there a physical model of oil depletion? Yes!
BUT Hubbert “analysis” is only curve fitting,
no predictive power, only appeal to precedent.
Not science!
Is there a physical model of oil depletion? Yes!
First simplification: separate discovery from extraction

2. Model of Oil Production
Field discovery is dispersed by fallow delay until infrastructure is built then full production
This plot adds a few
more steps
We model these intervals as distributions
over the historical range:
(Vertical axis is volume of oil in this state)
The process progresses as if the original
discovery is shifted in time &
smeared out …
Same area
State
of the
oil

3. Smoothing spreads a distribution
Two distributions, one is viewed thru a
window that is slid over other to form
weighted average output.
Their instantaneous product (= area) is
plotted as line, smoothing (spreading)
the original distribution.
Pattern of oil discovery, smoothed

4. Dispersed Delay on Campus
This is what each
delay looks like.
Triple smoothing
leads to last

5. Apply triple time-smoothing to discoveries D(t)
Field discovery “back-dated” to yr of initial discovery then dispersed gives D(t).
But actually several yrs to reach full operation: fallow delay then buildup infrastructure then full production
Apply triple time-smoothing to discoveries D(t)
Each smoothes D(t) more, with long tail.
So much for discovery,
what maps it to production?

6. Simply multiply by extraction rate E(t)
China
<- to map
discoveries to production
Opec
Texas
Railroad
Commission
to conserve
Oil during WW II
Discoveries
uncontrolled
Dynamics of recent oil production
seem to be very simple:
Petro engineers extract 2-3.5%
of what’s left annually

7. A random generated example
discovery
production
Increasing fraction of oil recovered barely shifts the peak right

8. A physical model makes testable predictions & gives uncertainties
Work in progress
by Foucher
(Logi Energy, NYC) ?
Official IEA 2010

9. Field-by-field depletion would tell us the whole PO story
That governments have not demanded these data from ME NOCs is telling
Numbers provided are suspiciously unchanged yr to yr
no published contingency plans for oil shortages
US strategic petroleum reserve = 44 days of full crude oil, then rationing
We remain very vulnerable to “oil shock” supply disruptions, especially refinery sabotage/damage

10. Coal
Land plants