I did find some historical data on platform rigs. Because of Federal law regulating wells, the Bureau of Ocean Energy Management, U.S. Department of the Interior, keeps records of oil spills for platforms in the outer continental shelf (OCS). There were 251 spills reported of amounts greater than 50 barrels (bbl) from 1964 through 2009. A total of 261,052 bbl (10.96 million gallons) were reported spilled over this time period (if the spill was greater than 50 bbl). Beginning in 1970, reports were required for spills between 10 and 50 bbl. This second data base contains information on an additional 449 spills with a total 8,972 bbl. These two data bases can be found at:
The data for 251 large oil spills on platforms in the OCS are shown in condensed form in the video here (http://www.archive.org/details/PlatformOilSpillHistory). It displays the water depth of the well on the vertical axis and the total amount spilled on the horizontal axis. The year is shown running below the horizontal axis. Both scales are logarithmic. This is the raw data that people in the field would see as events occurred. To make this video I used a Google Gadget, Motion Graph, and Google Docs.
In order to determine if the platform system is a critical state system, it’s instructive to look at the distribution of the magnitude of the spills. If it is a complex system in a critical state, that distribution should be an inverse power law.
The distribution is shown below for the large spill data set. Note that I eliminated all the data with exactly 50 bbl, the lower limited of the required reporting, as suspicious. And, to make the data easier to display on a graph and subsequent analysis, I eliminated data over 8,000 bbl (9 data points). As you will see later in this report, this makes little difference to the analysis.
First, you will note that this curve does look like an inverse power law (1/XN). Additionally, it has a very long tail, especially if you remember that there are 9 data points beyond the upper limit extending to 160,000 bbl. This indicates that, based on historical data, even though the majority of the spills are relatively small, there is a small but finite probability that a very large spill can occur.
Analysis of these data indicates that the distribution is indeed an inverse power law with a power of 1.56.
Performing the same analysis on the small spill (less than 50bbl) data set, over a different time period and different range of data, showed that the results were nearly identical. The power was -1.53 with a correlation coefficient of 0.94. This is a strong indication that something similar to a complex system in a critical state exists for this system as this suggests scale invariance, i.e. it looks the same at any scale.
However, that is hidden chaotic behavior if you look at the details and not just averages.
In this graph, all the data is shown as logarithms. On a log – log plot, a power curve shows up as a straight line. Note that the left edge of the envelope is almost exactly an inverse square relationship, how earthquakes present themselves. However, for spills larger than 500 bbl, the behavior appears chaotic. Unfortunately, the data indicates that for spills over 1,000 bbl, it’s just as likely that the spill will be 1,000 or 160,000 bbl.
There are several reasons why these data could indicate this apparent chaotic behavior:
- We don’t have a large enough data set. Given the extremely long tail of this distribution, the apparent chaotic behavior could be the result of sampling error. In which case the last statement about probabilities would be invalid.
- There could be a problem in estimating spills over 1,000 bbl.
- There are variables in the response to the spill that could turn a 1,000 bbl spill to 160,000 bbl.
- The specific conditions of the large spills are significantly different.
- The data set includes the performance of many platforms over a long time span. Behavior of the different systems above 1,000 bbl could be different. Behavior of systems could change over time.
- The system becomes chaotic under the conditions of a large spill. The above curve is reminiscent of the logistic map that demonstrates regions of chaotic behavior.
- Cause and effect are disconnected. As Buchanan wrote, “...that the greatest of events have no special or exceptional causes.”
- A power law can only be generated by some process that is steeped in history. “...the future emerges out of a string of accidents, each leaving its indelible trace on the course of events,” Buchanan commented.
- The complex system in a critical state exhibits the property of self similarity or scale invariance. It looks the same at all scales. Again, referring to Buchanan, “...the Gutenberg-Richter power law says that the process behind earthquakes is scale invariant, and the unavoidable implication is that the great quakes are no more special or unusual than the tiny shudders constantly rippling beneath our feet.”
- Systems that exhibit self organizing critically are ubiquitous.
- A new type of statistics has to be applied to complex systems in a critical state. They do not follow normal, i.e. Gaussian, statistics. Large events are a lot more likely to occur than a normal distribution would predict. Nassim Nicholas Taleb wrote in The Black Swan, “A Black Swan is a highly improbable event with three characteristics: It is unpredictable; it carries a massive impact; and after the fact, we concoct an explanation that makes it appear less random, and more predictable than it was.”
- The results of attempts to “improve” the behavior of a complex system in a critical state are unpredictable and can actual make the performance worse. Since the 1890's the forest service had a policy of stamping out a forest fire as quickly as possible. The logic behind that policy was that it was better to catch a fire small before it became big. In 1998 the Yellowstone fire consumed almost 800,000 acres, 36% of the park, and the number and intensity of forest fires was increasing everywhere. Also in 1998, the geologists Bruce Malamud, Gleb Morein, and Donald Turcotte of Cornell University gathered extensive data on forest fires. They demonstrated that the number of acres consumed in a forest fire followed an inverse power law of 2.48. A forest is a complex system in a critical state, at least for forest fires. The actions of the forest service were inadvertently making the critical state more dangerous by not allowing the small naturally occurring fires to keep the system in its natural state.
You can download a copy of this article here.
For more information about complexity, read my article “1, 2, a Few, Many”. Or, clcik on the term complexity in the left sidebar of this blog.