[khebab]

From the discussion in the thread "Help with deconstructing the EIA 2037 peak curve?" I decided to start a new one about the empirical relationship between the URR, the depletion rate and the PO date.

There are basically two major unknown factors in the depletion modeling problem:
- the URR which fluctuates between 1,800 Gb (ASPO) and 4,000 Gb (USGS)
- the world depletion rate which is expected to be between 1% and 5%

I assume the following:
- a geometric demand growth (+2%)
- a geometric depletion with different rates (1% to 5%);
Consequently, instead of assuming a particular curve model like in the Hubbert approach, I applied two exponential curves (EIA approach): A geometric demand growth prior to peak and a geometric depletion post-peak.

For each value of the URR and for each depletion rate, I compute the fraction of oil extracted before the peak (blue curves) and the year of the peak (red curves). The fraction of oil extracted indicates the degree of asymmetry of the curve (50% means a symmetric curve i.e. production midpoint= PO). The curve can be used as following: you fix your URR and you obtain a range of possible PO dates corresponding to different depletion rates. The blue curve will give you the degree of asymmetry.



The ASPO estimate give the most symmetric production curve. For a given URR, a higher depletion rate will push the PO date (technology improvements).

[pup55]

Good post, Khebab.

The really useful thing about this graph is you can see the sensitivity of the peak year calculation to changes in URR.. Interestingly the slope is higher for the lower reserve estimates--the change in peak between 2000 and 2500 gb is about ten years. The change in peak between 3000 and 3500 is about 5 years.

Looks like the individual red curves are asymptotic (the gap between curves is progressively smaller).

[khebab]

The really useful thing about this graph is you can see the sensitivity of the peak year calculation to changes in URR..

The idea is to visualize sensitivity in respect to the different variables and visualize also a locus of solutions instead of one particular instance. The advantage of the double exponential approach is that we can impose the depletion rate, therefore the shape of the post peak curve, which is hard to do with curve based model. The only limitation is that the peak is spiky and there is no plateau.

Interestingly the slope is higher for the lower reserve estimates--the change in peak between 2000 and 2500 gb is about ten years. The change in peak between 3000 and 3500 is about 5 years.

I guess because a small surface will be more sensitive to the parameter variations.

Looks like the individual red curves are asymptotic (the gap between curves is progressively smaller).

Good point! I would have to think about that one. Sensitivity to the depletion rate is greater between 1% and 2% and small beyond 4% even for small URR. Maybe because the area under the curve post peak is equal to the ratio of Pmax and the depletion rate.