### Decomposing Reserve Growth

The likelihood of reserve growth adds a bit of complexity to the oil shock model but nothing it can't handle. The "enigma" of reserve growth, at least in the USA, shows a fairly fast rise in estimates in the first 10 years and then a slower growth spanning perhaps over the course of 90 years. I showed that it graphically follows a self-limiting parabolic growth model in a previous post. If you look carefully at the growth, it appears to decompose into a fast exponential to which we superimpose a much more slowly damped exponential growth curve. If we assume that a fraction of the reserves get discovered early and the rest gets "discovered" as reserves later, then we can use the shock model to evaluate the effects on production by separating the two modes.

For demonstration purposes, I used a single spike of discovery in 1899. The fast reserve growth comprises 45% of the discovery, while the slow reserve growth comprises 55%.

To model the production curve, I used 8 years for the fallow, build, and maturation phases for the quick growth. I replaced the maturation phase with a value of 40 years for the slow growth model. I chose an extraction rate of 5% of remaining reserves per year for both modes. The linear properties of this stochastic model allow us to decompose or compose the two modes freely.

Note that the peak changes by at most 5 years with the addition of a significant long term reserve growth component. The model makes the assumption that the reserve growth actually comes about from continual discoveries or improvements in recovery technology over time. This tends to extend the tails out quite a bit and suppresses the height of production peak if we hold the proportional extraction rate constant.

Whether this assumption holds true world-wide, we probably can't yet say. We know that off-shore fields do not show extensive reserve growth because they shut down on the hint of production decrease. The same holds true for fields in other inhospitable or harsh regions or in fields that have had poor management practices over the years, in particular, via excessive water cuts. If the fraction of slow growth global reserves decreases with respect to the USA proportion, the broad peak will shrink.

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