The Oil Drum

This is a guest post by WebHubbleTelescope.

In school, we used to do horrendously difficult mathematical "word" problems routinely. I remember occasionally getting one right, but more often ended up punting on the problem, and then waiting for the teacher to explain the solution in all its elegant simplicity. Of course, just about every real-world problem contains inherent ambiguities and incomplete information. So we rarely get to see the elegant solution in our day-to-day work life. Sometimes we get lucky and nail a problem, but in the majority of cases, we eventually resort to creating a limited model of the problem domain and deal with that.

The problem that I have recently wrestled with has to do with predicting future oil discoveries based on historical dynamics. Ideally, I want to reduce it to a solution that has the elegance of a word problem, and not have to deal with messy economic and geologic factors that would quickly turn it into a rat's nest of complexity. Call me an optimist in this regard, but my intuition tells me that the solution remains as simple as ... finding needles in a haystack.

WebHubbleTelescope, a long time TOD poster, has been one of the most active in the blogosphere in the area of oil production modeling. He has advocated a more physically based approach instead of a heuristic curve fitting approach such as the Hubbert Linearization. He proposed an original method, the so called Shock Model, that has a clear physical interpretation and that is making use of both the production profile and the discovery data. I think that a review of the Shock Model is long overdue.

I also propose three modifications or extensions:

1. Originally, the instantaneous extraction rate function E(t) has to be provided by the user. I propose a method to estimate E(t) directly from the observed production profile.
2. Reserve growth is modeled as a fourth convolution function based on an empirical parabolic cumulative growth functions (this will be detailed in part II).
3. A new way to project future extraction rate (in part II).

In summary, the shock model is a simple and intuitive model that is making use of both the production profile and the discovery curve. In this essay, the method is applied on the world conventional crude oil production (crude oil + condensate) and the ASPO backdated discovery data. Interestingly, the derived Reserve to Production ratio (R/P) seems to match the values obtained when using the proven reserve numbers (BP) once corrected for Middle-East spurious reserve revisions (in 1985, 1988 and 1990). In addition, R/P values are presently at a record low levels and below what have been observed during the previous oil shocks.

The code in R language is provided at the end of this post.

[editor's note, by Prof. Goose] This is a guest post by Rembrandt Koppelaar, Chairman of ASPO Netherlands.

In the discussion about the date of peak oil production there is often a lack of a common framework. This makes it difficult to compare arguments concerning the date of peak oil / liquids production. In this post I outline a set of clear suppositions that, I hope, will help to understand the issue better.

There's been some discussion lately about reserve additions due to new discoveries and the trends there. This topic came up in some comments on Stuart's Predicting US Production with Gaussians--for example here). WebHubbleTelescope over at Mobjectivist has done a couple posts lately on this topic. In Monte Carlo Discoveries, he comes to a rather important conclusion.

The main thing to note relates to the essential noise characteristic in the system [discovery curves]. The fluctuation excursions fairly well match that of the real data (see the first diagram at the top of this post), with the occasional Ghawar super-giant showing up in the simulations, at about the rate expected for a log-normal distribution. But the truly significant observation relates to the disappearance of the noise on the downslope, in particular look at the noise after about 1980.

Remember what I said initially about noise telling us something? The fact that the noise starts to disappear should make us worry. That noise-free downslope tells us that we have pretty effectively mined the giants and super-giants out there and that oil exploration has resorted to back-up strategies and a second pass over already explored territory or to more difficult regions that have a tighter distribution of field sizes.

I'll leave the heavy duty mathematics & modelling to Stuart, WHT, Khebab and others to argue over. This includes the mysterious assumption first used by M. King Hubbert that

The discovery curve mirrors approximately the production curve with a lag that varies from country to country. The US-48, for example, had a lag of 41 years whilst the UK North Sea production, with its urgency and technological basis had a lag of 25 years. The World's lag is estimated to be 36 years.

noted at (among other places) Wolf At The Door. Here instead I will check in with the real world data over the last twenty years and particularly since 1994 using a favorite source, presentations from IHS Energy, to see what's been happening lately on the tail end of the discoveries curve. I feel it's always a good idea to remain a part of the reality-based community, so let's look at some data and look closely at what the recent trends are. Do they confirm the modelling?