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Wednesday, November 05, 2008

USA Field Size Distribution

This dated paper (circa 1986) on USA oil field size has a few interesting statistics. I don't have any of the charts, but the authors roll up a few of the numbers from the curves.
The distribution of about 14,000 United States oil fields (Figure 2)--a partial sample of those in the lower 48 states--illustrates the importance of the larger fields. The sample includes almost all larger fields as known about 1970 and excludes many tiny fields as well as all of the more recent discoveries. The lower dotted line is made of 13,985 points representing the fields ordered according to increasing reserves size. Only 440 fields, or about 3%, are major ones larger than 50 million bbl. The upper curve tracks the percentage of the total oil volume occurring in fields greater than each size. From this curve, we read that the major fields, constituting only 3% of the total number, contain 80% of the total oil. Obviously, in this type of distribution one can account for the bulk of the oil by assessing the larger field possibilities only.

Selecting an effective minimum field-size cutoff is very important, because it affects every major factor in the assessment--the prospects to be counted and the success and risk levels, as well as the average field size. Normally, the minimum size is taken at or just below the assumed economic minimum for the area. This approach ensures that all prospects of real interest are included. It also avoids getting bogged down in hundreds or thousands of fields that are inconsequential to early exploration stages. Furthermore, the comparative data base for assessing sub-economic fields is very weak, as the true sizes of these fields have rarely been scaled. If desired, one can assess the small fields by statistical extrapolation or by estimating a lump-sum proportion from a volume curve like that of Figure 2.

Economic limits always truncate the lower ends of observed field-size distributions (Arps and Roberts, 1958; Kaufman et al, 1975; Grender et al, 1978; Drew et al, 1982; Vinkovetsky and Rokhlin, 1982). In nature's distribution, numbers of deposits probably increase progressively in successively smaller sizes down to droplets and molecules; such a distribution is not lognormal. But we deal exclusively with artificially truncated distributions whose plots almost invariably curve upward near the low-side truncation point (upper curve, Figure 3). Our United States distribution (lower curve, Figure 2) has no data below 1,000 bbl, and many of the data points below 10,000 bbl, where the graph ends, are questionable. If the plot were continued to the left, it would ultimately curve upward at t e point of economic truncation beyond which there are no data.

We use the computational convenience of the lognormal distribution, appropriately truncated, but would not argue that this scheme is better or worse than other computational ones for strongly right-skewed distributions that have many more little fields than big fields. Some investigators (e.g., Ivanhoe, 1976; Folinsbee, 1977; Coustau, 1980) plot field size bilogarithmically against rank order. For our assessment approach, we must normalize field numbers at this stage by plotting "percent greater than" against log size. Depending on purpose and data, we may express field size as recoverable volumes of oil or of gas, or of oil plus gas on an energy-equivalent basis.

These numbers (the 50Mb and the less than 0.1Mb) fill in the following points on the previous post.

The authors state that 3% of the highest rank of fields contain 80% of the oil, which includes rank up to 440 in this chart. Or this means that 20% of the oil resides in the lowest 97% of the rank.
Up/U = (ln(1+Size/c) - 1/(1+Size/c)+ 1)/(ln(1+Max/c) - 1/(1+Max/c) + 1)
I would like to make sense of this but as I don't have the original charts, I am guessing as to whether the 80% makes sense. With the Dispersive Aggregation model for the extra 21,000 fields reported, the amount of oil contributed to those above 50Mb has dropped to 50%.

YearSizeFraction of Total
In the last 20 years, we probably have gained a lot of extra mileage from the low volume fields, but I can't say for certain without filling in the historical data points. If someone can get a hold of this Baker paper and post some of the charts, it would help immensely.

These authors also believed that the field size distribution followed a log-normal. The Dispersive Aggregation mimics the general shape of the log-normal under certain regimes, especially under a wide variance, while at the same time generating the heavy Pareto-like tail (i.e. 1/xp) that much of the data seems to indicate.

The following chart shows a cumulative field size distribution from the Canadian Williston Basin. The referenced article shows how they use a log-probability chart to map onto a log-normal curve; I pasted on a set of points corresponding to Dispersive Aggregation and as you can see, it mimics the behavior of a log-normal distribution.
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Baker, R.A., H. M. Gehman, W. R. James, D. A. White, 1986,
Geologic Field Number and Size Assessment of Oil and Gas Plays,
in Oil and Gas Assessment: Methods and Applications: AAPG Studies in Geology
No. 21, p. 25 – 31.


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