Sunday, December 03, 2006

The Loglet Analysis Applied to the United Kingdom's Oil Production

Last week, Euan published on TOD a great compilation of UK forecasts. The UK production profile is a notoriously difficult case to model because it has two pronounced Hubbert cycles. The loglet analysis with two Logistic curves seems appropriate and gives the following result:


Fig. 1 Result of the loglet analysis (bi-logistic) in the standard Hubbert Linearization representation. The red line is the standard mono-logistic approach. Data is for crude oil plus condensate (source: DTI). mbpd= millions of barrels per day.


Fig. 2 Result of the loglet analysis (bi-logistic) and the mono-logistic curve derived from the Hubbert Linearization. Data is for crude oil plus condensate (source: DTI). mbpd= millions of barrels per day.

We can appreciate how accurate is the loglet analysis (Fig. 2) compared to the standard mono-logistic approach. The Ultimate Recoverable Resource (URR) is around 25 Gb for the loglets whereas the Hubbert Linearization gives 28.77 Gb. The production is predicted to reach 0.6 mbpd in 2010 (almost 50% of current levels). The parameters of the two logistic curves (or loglets) are the following:



Loglet 1Loglet 2
URR (Gb) 7.921 16.85
K (%)
42.85 22.72
Peak Date 1984.4 1998.7


The decline in production is dominated by the second logistic curve which has a fairly large logistic growth rate (K) at 22% especially compared with the result of the HL technique (K= 12.9%). When modeled by a logistic curve, the decline rate in production accelerates linearly with cumulative production and ultimately reaches the value K which can be considered as the ultimate decline rate value:


(dP/dt)/P=K(1-2Q/URR)=K(Reserve Fraction - Cum. Prod. Fraction)


For instance, when 75% of the URR has been extracted (Q=0.75xURR), the reserve fraction is equal to 25% and the cumulative production fraction is equal to 75% which implies that the decline rate reaches K/2.