Richard Nehring
NRG Associates
Colorado Springs
This is the third and final part of a three-part article that addresses the question: Does the Hubbert method provide a reliable means of predicting future oil production?
The key word in this question is “reliable.”
We are not asking whether the Hubbert method has provided a few valid predictions in the past, such as Hubbert’s own often cited prediction that US oil production would peak around 1970. We are asking whether the method is sufficiently robust to provide consistently valid predictions across a diverse range of circumstances.
Validity in predicting production has two dimensions:
1. Predicting when and at what level production will peak.
2. Predicting the post-peak rate of decline.
As Hubbert clearly recognized, valid predictions of future production depend on valid estimates of ultimate recovery.
For the two basins examined in the first two parts of this article, the San Joaquin and Permian basins, the Hubbert method clearly fails to predict future production accurately. All six predictions made prior to the actual peak in production fail to forecast the peak. Five of the six even indicate that the peak had already occurred.
All predictions, whether prepeak or postpeak, consistently overstate the rate of decline.
Moreover, the divergence between actual and predicted production is very large. Only two of the eight predictions as of 1964 and 1982 are even within 50% of actual production as of 2000 (and they just barely meet this standard, both being 52.5% of actual). Three of the eight predictions for 2000 are less than 20% of the actual. One of these predictions is even an order of magnitude less than actual production.
This consistent underprediction of future production occurs even in the half of the predictions that use the sophisticated version of the Hubbert method, namely one in which recent discoveries are adjusted for the future growth in their sizes that is likely to occur as these discoveries are fully developed.
Predicted production from the adjusted data is more accurate than predicted production made from the unadjusted data but is still significantly less than actual production.
The examples used, moreover, were ones that should be considered favorable for the Hubbert method. Both the Permian Basin and the San Joaquin Valley were clearly mature basins by 1960. The exploration process was highly advanced in each, discoveries being well past their peak.
Neither incurred a subsequent expansion in area, a problem that historically has bedeviled the Hubbert method. For example, deepwater oil discoveries, most of which have occurred since 1985, have increased cumulative oil discoveries in the Gulf of Mexico by more than 50%. With both future deepwater discoveries and full development of recent discoveries, ultimate recovery in the Gulf of Mexico should more than double because of this technologically driven expansion in the productive area of the Gulf of Mexico basin.
Neither the San Joaquin Valley nor Permian Basin can be considered a trivial example. These two basins are among the five largest US oil provinces.
As of 2000, the Permian Basin contained 17.8% and the San Joaquin Valley contained 8.2% of the known recovery of 196.5 billion bbl of crude oil in the US. The two combined provided an even greater share of US oil production in 2000, the Permian Basin providing 333 million bbl (17.7%) and the San Joaquin Valley providing 215 million bbl (11.4%) of the 1.88 billion bbl national total.
Why the method fails
Why does the Hubbert method fail to predict future oil production accurately?
The answer is simple. The method consistently underestimates future production because it consistently underestimates ultimate recovery. It underestimates ultimate recovery because it is incapable of estimating the appreciation (growth) in ultimate recovery that occurs in older fields.
Even the use of the correction factors (which focus on the growth that occurs in recently discovered fields until they become fully developed) provides no mechanism within the Hubbert method for accurately estimating growth in older fields.
The magnitude of this omission becomes clear when we consider the composition of the increase in ultimate recovery in both the Permian Basin and the San Joaquin Valley from 1964 to 2000.
In the Permian Basin, observed cumulative discoveries grew by 17.653 billion bbl. Of this amount, 14.583 billion bbl (82.6%) occurred in fields discovered by 1950. Use of the correction factors predicted 2.227 billion bbl of this pre-1951 appreciation, leaving 12.356 billion bbl (84.7% of the increase during this period) unexplained.
In the San Joaquin Valley, observed cumulative discoveries grew by 8.323 billion bbl. Growth in fields discovered by 1950 was 8.19 billion bbl, 98.4% of this total. The appreciation factors predicted 461 million bbl of this amount, leaving 7.729 billion bbl (92.9%) unexplained by the Hubbert method.
The Hubbert method assumes, as did all the thinking of his time and still too much of the thinking of our own, that future additions to reserves come wholly from new discoveries and the gradual completion of the development of recent discoveries. The history of reserve additions in the US since 1970 clearly indicates that this assumption is no longer valid.
Appreciation (growth) in the ultimate recovery of older fields not only invalidates the basic assumption of the Hubbert method; it also eviscerates its vital parts. If the Hubbert method is to forecast production accurately, his argument that production follows discovery with a relatively short lag time (5 to 15 years) needs to be valid.
For both the Permian Basin and the San Joaquin Valley, this relatively short lag time appeared to be correct as of 1964 (Figs. 3a and 8a). By 2000, it was clearly wrong in both basins (Figs. 5a and 10a). In each basin, the peak in discovery had moved to the left (backward in time), while the peak in production had moved to the right (forward in time).
The resulting lag between the two peaks thus increased to 40-80 years, a span of time that makes the temporal linkage between discovery and production so tenuous that it renders this linkage useless for predicting future production. When the Hubbert method is employed at the basin level (or used for even smaller levels of analysis), this is likely to be a universal problem.
Hubbert, especially in his later papers, argued that both the annual discovery and the annual production curves are horizontally symmetric. Yet on the basin and smaller level, the discovery curve will invariably be asymmetric to the left. That this is so stems from two of the few firm conclusions of petroleum resource assessment.
The first of these is that the petroleum resources of a basin are concentrated in a relatively small number of giant and large fields. The second is that most, if not all, of these giant and large fields are discovered early in the exploration of the basin.
As the preceding discussions indicate, both of these conclusions are firmly borne out in the composition of ultimate recovery by field size and the discovery history of fields by size in both the Permian Basin and San Joaquin Valley. A necessary corollary of these two conclusions is that the annual discovery curve in a mature developed basin will be highly asymmetric to the left.
Theoretically, the discovery curve could be symmetric on the continental, hemispheric, or world scale. However, this requires such an improbable combination of circumstances, primarily involving the order of discovery by basin size of individual basins, that it has to be considered an extremely unlikely case.
Because petroleum exploration in the US began very early, because initial exploration and discoveries occurred in what has proved to be relatively minor basins, because early drilling technology was very limited in its drilling depth capabilities, and because discoveries in the major basins only hit their stride between 1910 and 1950, the US comes closest to having a symmetric discovery curve of any major oil producing country or region.
On the other hand, the shape of the annual production curve could easily be symmetric, asymmetric to the right, or asymmetric to the left, depending on how a variety of economic, technological, and political factors shape production over its history.
Peak annual oil production in the San Joaquin Valley occurred in 1985 when cumulative production was 9.47 billion bbl. This cumulative is 57.3% of known recovery as of 2004. In other words, the annual production curve we observe currently for the San Joaquin Valley is somewhat asymmetric to the right.
As known recovery continues to grow, the peak on the annual production curve moves to the left, the cumulative at the peak being 52.6% of an ultimate of 18 billion bbl, 47.4% of an ultimate of 20 billion bbl, and 43.0% of an ultimate of 22 billion bbl.
The San Joaquin Valley is clearly a special case. Its shallow heavy oil fields were discovered early, but these fields could not be produced commercially in substantial amounts until after 1975.
Peak annual oil production in the Permian Basin occurred in 1974 when cumulative production was 17.9 billion bbl, 49.6% of 2004 known recovery of 36.1 billion bbl. As recovery continues to grow in the Permian Basin, this cumulative at the peak of production will move to the left, being 44.8% of recovery at 40 billion bbl, 39.8% of recovery at 45 billion bbl, and 35.8% of recovery at 50 billion bbl.
These two limited examples suggest that ultimate annual production curves are likely to be slightly to moderately asymmetric to the left. More provinces need to be examined however to validate this tentative conclusion.
Hubbert argued explicitly that both the annual discovery and the annual production curves were horizontally symmetric, that is, that their peaks would occur at the midpoint of ultimate recovery. He also suggested (as in the precursors to Fig. 1) that the two curves were also vertically symmetric, that is, they peaked at approximately the same amount.
Both the evidence from these two basins and general theoretical considerations regarding the discovery process indicate that this suggestion is clearly false. The annual peaks in discovery (without being dampened by the use of moving averages) are very high in both the San Joaquin Valley and the Permian Basin.
The three peak years of discovery in the San Joaquin Valley as of 2000 account for 22.5% (1901), 20.2% (1911), and 14.3% (1894) of 2000 known recovery. The three peak years of discovery in the Permian Basin as of 2000 account for 19% (1936), 12.6% (1926), and 7.5% (1929) of 2000 known recovery.
The high concentration of discovered amounts in just a few years is of course a consequence of the concentration of ultimate resources in a few giant fields and the early discovery of these fields in the exploration history of a basin.
By comparison, peak annual production in the San Joaquin Valley is only 1.69% of known recovery as of 2000. Peak annual production in the Permian Basin is 2.12% of 2000 known recovery. As known recovery increases in each basin, the percentage of the peak in annual production to ultimate recovery can only decrease, possibly to as low as 1.25% in the San Joaquin Valley and to 1.5% in the Permian Basin.
The order of magnitude difference between the percentage of ultimate recovery in the peak discovery year and the percentage of ultimate recovery in the peak production year is typical of most productive basins worldwide. Ultimate annual discovery curves are thus likely to be highly vertically asymmetric to the annual production curves.
The only way Hubbert discussed estimating ultimate recovery that is intrinsic to his method is to use the cumulative discovery curve. Once a basin has entered the phase of exploration maturity, the cumulative discovery curve begins to flatten out, indicating an asymptote that cumulative discoveries will gradually approach. This asymptote provides the estimate of ultimate recovery.
One consequence of growth in the ultimate recovery in older fields is that the cumulative discovery curve moves upward over time (see Figs. 6 and 11). This continuous upward movement in the cumulative discovery curve makes this curve useless as a tool for predicting ultimate recovery.
Estimates of ultimate recovery derived from cumulative discovery curves are only valid if one can guarantee that there will be no further increases in the ultimate recovery of discovered fields (other than those predicted by a correction factor for recent discoveries). In the present circumstances, especially when we appear to be entering a permanent realm of higher oil prices, no such guarantee can credibly be made.
An alternative to using the cumulative discovery curve is to use cumulative production at the peak of production to predict ultimate recovery. For this to work, the area being examined must be at a high level of exploration maturity with production indisputably past its peak. The annual production curve must also be horizontally symmetric.
Both the Permian Basin and the San Joaquin Valley clearly meet the first of these conditions. Whether either will meet the second is questionable.
Cumulative crude oil production in the Permian Basin at its annual peak in 1974 was 17.902 billion bbl. Doubling this amount suggests an ultimate recovery of 35.8 billion bbl. Cumulative discoveries as of 2004 were 36.098 billion bbl, an amount already exceeding this estimate of ultimate recovery. At the suggested ultimate recoveries of 40 to 50 billion bbl for the basin, ultimate recoveries are 12 to 40% higher than those suggested by this approach.
Cumulative crude oil production in the San Joaquin Valley at its peak in 1985 was 9.473 billion bbl. Doubling this amount suggests an ultimate recovery of 18.946 billion bbl. At the suggested ultimate recoveries of 18 to 22 billion bbl for the basin, ultimate recovery would between 5% less to 16% more than that suggested by this approach.
A range of estimates from 10% less to 40% more for ultimate recovery might appear to be a reasonable range of uncertainty. However, given that such estimates are being made when cumulative production already exceeds 80% of cumulative discoveries, the differences for remaining ultimate reserves (what remains to be produced) are great.
Remaining ultimate reserves at the high end of this range are double remaining ultimate reserves on the low end. A difference of this magnitude in remaining ultimate reserves results in quite different future production profiles, particularly when projected out to 40 years or more.
The problems that growth in ultimate recovery in older fields create for the Hubbert method are not just specific to the Hubbert method. They apply to all methods of resource assessment, such as discovery process models, that depend wholly or largely on historical data relating to the sizes of fields and reservoirs. Growth is the monkey wrench in the works of all such methods, particularly when it is irregularly distributed among fields and reservoirs (as it almost always is).
Attempted rebuttals
Growth in the ultimate recovery of older fields creates a backbreaking challenge to proponents of the Hubbert method.
Beginning with Hubbert himself, these proponents have been aware of this challenge. Their responses fall into three basic categories.
The first response has been one of denial. Growth simply does not occur, or as Hubbert (being a more careful thinker than his current disciples) would argue, major growth is very unlikely.
In the 1960s, when Hubbert was formulating his arguments, such an argument was clearly viable. In an environment of low, stable prices with only slow, incremental improvements in exploration and production technology, conditions which essentially characterized the quarter century from 1946 to 1970 in the upstream petroleum industry, growth in old fields was at most a minor component of reserve additions.
The experience of the industry since 1970, in a different economic and technological environment, provides overwhelming evidence that massive growth does occur. As Figs. 6 and 11 clearly demonstrate, what Galileo allegedly muttered after being forced to recant his argument that the earth rotated around the sun (“Eppur’ si muove!”-“Yet it moves!”) applies with equal force to the asymptote indicating ultimate recovery.
The second response is that growth does occur, but that it can be accommodated by backdating all growth to the year of field discovery.
In the preceding analysis, this procedure was carefully followed for both the Permian Basin and the San Joaquin Valley for the 1984 and 2000 data.
Backdating growth clearly helps the Hubbert method explain past production. Yet it does not help it predict the future. Sound predictions of future production require accurate predictions of future growth. Backdating is a technique that only helps us understand what has already happened; it provides no clues as to what will happen.
Moreover, backdating creates its own problems for the Hubbert method. As noted earlier, growth (backdated to the year of field discovery) increases the lag between discovery and production. As this lag lengthens, the causal linkage between discovery and production weakens, gradually rendering one of the key components of the Hubbert method useless for guiding predictions.
The third and final response is that growth occurs, but since it is mostly unconventional, it can be ignored. If we could apply the Hubbert method to only conventional oil resources, it works quite well in predicting future oil production. This response does indeed save the method.
If one could delete growth from infill drilling, advanced secondary recovery, and enhanced oil recovery in the Permian Basin and growth from heavy oil reservoirs through the application of thermal recovery methods in the San Joaquin Valley (and the associated production from each), the Hubbert method would have provided fairly accurate estimates of future conventional production in each basin after 1964.
This tactic, however, is one of desperation. It only saves the method by destroying its relevance. What has been considered the near nonconventional oil resources, whether defined by liquid quality (heavy oil and natural gas liquids), recovery method (advanced secondary and enhanced), or geographic location (Arctic and deepwater), have become the dominant sources of both reserve additions and oil production in the Western Hemisphere over the past three decades.
The more distant nonconventional resources, such as extra heavy oils (like those in the Orinoco region in Venezuela) and tar sands (such as those in Alberta) will be prominent oil resources throughout the 21st century.
The response of any knowledgeable student of world oil resources to the argument that the Hubbert method still accurately predicts future conventional oil production is simply, “So what?,” with an accompanying shrug of the shoulders.
The problem we face is that of accurately predicting the resources and production of all types of liquid hydrocarbons, not simply predicting a steadily diminishing component of world oil such as the so-called conventional resources.
Closing thoughts
We develop our methods and models to help us understand the world. Yet paradoxically our methods and models are also limited by those same understandings. At best, methods and models provide a systematic and logical rendition of our current knowledge. Often, the process of putting what we know in a systematic and logical form helps us to understand more fully the implications of our current knowledge.
As our knowledge changes, particularly in substantial ways, our methods and models need to change as well. Unfortunately, there is often a substantial lag between changes in our knowledge and changes in our methods and models.
Methodologists and modelers can become so enamored with the aesthetic properties of their creations that they focus all their attention and effort on polishing existing methods and models instead of developing new and more relevant ones.
When Hubbert developed his method between 1955 and 1965, it was an accurate reflection of how the process of petroleum discovery and development and their implications for production were understood at the time. His work clearly laid out clearly the implications of that understanding.
In the four decades since, our knowledge of petroleum discovery and development has changed significantly. We now recognize the existence and importance of recovery growth, especially in older and larger fields.
The task facing us now is not to continue to use an obsolete and increasingly irrelevant method but to develop further our understanding of recovery growth and create new methods and models of estimating ultimate petroleum recovery and forecasting production that incorporate that improved understanding.
Acknowledgments
The original idea for this article came from the author’s reflections on several projections of ultimate resources and production he made in the 1970s-80s using Hubbert’s methods. Because these projections consistently understated both future production and ultimate recovery, reprints from the publications in which they appeared are not available from the author. The more immediate ideas for this article grew from the author’s participation in the first USGS Conference on Reserve Growth in August 2004. I thank Tim Klett of the USGS for organizing these excellent conferences. Thanks to Keith King of ExxonMobil Corp. for several stimulating conversations on the Hubbert approach.✦
Bibliography
Hubbert, M.K., “Degree of Advancement of Petroleum Exploration in the US,” AAPG Bull., Vol. 51, No. 11, November 1967, pp. 2,207-27.
Hubbert, M.K., “Energy Resources,” in “Resources and Man,” Committee on Resources and Man, National Academy of Sciences-National Research Council, 1969, pp. 157-242.
