Parabolic Adjustment for Idle Capacity in the
World Conventional Oil Production System

John H. Walsh
Energy Advisor

Note: The two figures of this paper are not included with the text below. These may be obtained in hard copy form by contacting the author at


This paper has been prepared to estimate the uncertainty in the parabolic projection of world oil production from conventional sources arising from idle capacity in the system. A second parabola is staged using the most recent year for which production data is available. Under the assumption that all idle capacity will be brought into service by the time the peak is reached, a new peak is calculated by adding the estimate of this capacity to the peak computed in the usual way. The timing of the new peak is then compared with the original peak.

The estimates employed of present idle capacity ranging from 0.5 to 5 million barrels per day lead to a delay in reaching the peak in world conventional oil production of no more than an extra 3.3 years. Bringing the idle capacity into service before the peak is reached results in the production of more oil sooner than otherwise which in turn leads to lower output in the late decades of this century.


The forward-looking staged parabolic technique was devised to estimate the magnitude and the timing of the peak in world conventional oil production based upon geological estimates of the ultimate recoverable resource. Unlike other projection methods, in this appoach the past pattern of production before a chosen staging date does not influence the result because only the cumulative production up to this time is relevant. The recent comprehensive assessment of the world's conventional petroleum resources by the U.S. Geological Survey (U.S.G.S.) provides updated data for such projections.1

The staging year is normally chosen at some convenient time safely after the dislocating events of the 1970's. In the underlying paper, the parabola is based upon 1988 because a reliable value for cumulative world production is available up to this date and because production has increased more-or-less regularly since this time.2 The production-time parabola is chosen from the staging point that both encompasses the requisite quantity of oil and passes through the actual production for the most recent date for which output data is available. Computational details of the application of this technique to world conventional oil resources have been given previously.3

This paper addresses an uncertainty faced by this and other such projection methods arising from the existence of appreciable idle capacity in the world oil production system. It has long been true that the already discovered resources could support a greater production of oil than the actual output for a given year were the necessary facilities to be installed. Reserves-to-production ratios can fall as low as about nine in mature oil producing countries such as the U.S.

Here the issue is not the possible output supportable by the reserve base at any one time but rather the uncertainty in the operation of the already installed capacity and its expected rate of gradual absorption in the production system over time. This problem arises because the actual production data chosen to anchor the parabola at both the staging year and the forward year may be lower than if the system were operating at capacity. To not take this capacity into account is in effect to underestimate both the magnitude of the peak and the production during the years immediately around it. In the case of oil this non-operational capacity is mainly due to the policy actions of OPEC and some special situations such as the Sanctions instituted by the United Nations against Iraq. In the natural gas system, the same problem may arise due to the discovery of `stranded' gas ready for production but not yet connected to distribution channels for exploitation for either geographical or economic reasons or both. When significant idle capacity exists, the actual production in the years reported chosen for both staging and for the forward definition of the parabola are less than both could be. Worse, the extent of the idle capacity may vary significantly from year-to-year. This factor introduces an uncertainty into the parabolic projection and the purpose of this paper is to estimate the probable extent of this possible discrepancy.

Idle capacity is thought of in this paper as facilities in existence that could supply oil on one hundred days notice of requirement. Any capacity that at any time could or did produce oil is considered idle under this definition. There is some recent evidence that the inactive capacity has fallen into a state of disrepair in some countries and by allowing some time for refurbishment, sterile debates over the extent of this issue are avoided. Industry operating, planning or financial requirements may require other definitions of idle capacity.


The three attributes of oil-the ability to fill essentially all energy needs in a convenient liquid form, the low cost of transport of the contained energy on both land and sea so that its price before taxes does not vary greatly from one place to another, and the unusual inverse supply pattern-result in its production to depend more upon the magnitude of the discovered resource base than any other factor. This author has shown that the world per capita consumption of oil, now well past its peak, has been nearly constant at 4.43 barrels per person for the last seventeen years.4

Two main changes are expected after the peak has passed. First, with one notable exception, there is no reason for idle capacity to exist in the conventional supply system because part of the oil requirement at that time will be met by more expensive non- conventional sources such as from the oil sands in Canada, the heavy oils of Venezuela, and possibly the synthesis of ultra-low sulphur transportation liquids from stranded natural gas. In a rational world, the cheaper source is used first. Nevertheless, Saudi Arabia, because of its very large resources, may well have idle capacity for some time into the post-peak period and this possibility is recognized as a source of uncertainty in this paper.

Second, there is no reason for the inverse supply pattern to persist after the peak is passed. Currently, large reservoirs with very low technical costs of production are idling in the Middle East although expensive oil sands plants are now operating at capacity and are in fact being expanded. Though it has persisted for many years, this inverse supply situation is inherently unstable and could turn right-side-up tomorrow.5 After the peak is passed, with the higher prices expected then, there is less incentive to to keep low-cost production from reaching the market. In any case, production deliberately withheld at that time would in effect reduce the peak and the time required to reach it. For the maximum effect therefore, it is assumed in this paper that all the idle capacity is in productive service by the time the peak is reached with the possible exception of Saudi Arabia already noted. Though prices may be higher in this period, the system should behave more rationally after the peak in conventional oil production.

This assumption permits an estimate to be made of the effect of the idle capacity on the timing of the peak in the world's conventional oil supply system. The magnitude of the peak is first computed in the normal way ignoring the idle capacity. To this value is added an estimate of the size of this non-operational capacity. The parabolic calculation is then repeated using the most recent year for which production data is available as the staging year (here 1999). The new parabola chosen is the one whose peak equals the sum of the original peak plus the estimate of idle capacity. This calculation is repeated for each estimate made for the idle capacity over the probable range.

This method of estimation implies a gradual reduction in the idle capacity over the years until it is in full production at the time the peak is reached. Were this non-operating capacity to be brought into service more rapidly, the peak would in fact be less and consequently the delay in reaching it would also be less.

Thus at both extremes, whether production is withheld from the market after the peak is reached or whether it is brought into full production before the peak, the result is the same. Both the peak and the time to reach it are reduced in either case. The assumption of full operation of the idle capacity at the time of the peak gives the highest value for both the peak and the delay in reaching it. For these reasons the estimate that follows is a maxium and so a safe estimate of the delay.


The technique was applied to the results of Case 1 in the earlier paper which was based upon the Mean Value of the U.S.G.S. Year 2000 Assessment.2 The reserves addition was assumed to be only operative after the peak has passed in all cases when the generally higher prices to be expected for oil at that time would justify the application of higher-cost recovery procedures. The peak in world conventional oil production of 29.38 GB/year predicted for 2017.1 in Reference 2 is replotted in Figure 1. Four cases of 0.5, 1, 3, to 5 million barrels per day were assumed for the range of the present idle capacity of interest. The lowest Case 1/0.5 was not shown in Figure 1 for reasons of clarity because the increase was so small. These values were added individually to the original peak in turn and a set of parabolas was then drawn from the most recent year (1999) serving as the staging point for the four cases. Each parabola was then calculated to pass through its own respective new peak as illustrated in Figure 1.

In the highest Case 1/5, a present idle capacity of five million barrels per day delayed the arrival of the peak a maximum of 3.3 years. The other cases were proportionately less.

To illustrate this extension of the time-to-peak more clearly, the assumed values for the idle production capacity are plotted versus the year of each predicted peak in Figure 2. The effect is relatively small and does not lead to large errors but is perhaps worth noting. It is somewhat counter-intuitive in that as the idle capacity increases, both the magnitude of the peak and the time to reach it increases. This must involve the production of more oil sooner than would otherwise be the case. Because the calculation is applied to a fixed quantity of oil-the resource endowment specified by the geological assessment-the production curves must cross at a later date. It may be seen in Figure 1 that the cross-over points occur as late as 2070. This transfer of the time of production is an inevitable consequence of the parabolic projection method.

The delay of the peak 3.3 years when the idle capacity was set at a maximum five million barrels per day in Case 1/5 may be contrasted with the delay of 9.8 years in Case 2 in Reference 2. In Case 2, the reserves addition was distributed uniformly over time as compared with Case 1 and its four sub-cases in this paper where the reserves addition was only assumed operative after the peak had passed.

Summary and Conclusion

A modification to the parabolic technique for projecting oil production from geological resource assessments has been devised to estimate the uncertainty arising from the existence of idle capacity in the world production of oil from conventional sources. An estimate is made of the magnitude of the idle capacity in the most recent year for which production data is available. This value is added to the peak computed when no allowance is made for idle capacity and a second parabola is drawn such that it passes through the revised peak under the assumption that there is no reason for significant idle capacity to exist at that time except perhaps in Saudi Arabia.

The expected range of idle capacity assumed up to five million barrels per day increases peak production moderately and delays its onset by 3.3 years in the high case at the expense of lower production in the late decades of this century. The error introduced by the idle capacity is not large in terms of timing but the somewhat higher values for the peak computed may well prove a close approximation to the actual situation as the future unfolds.


  1. United States Geological Survey World Petroleum Assessment 2000, Four CD-ROM Set, Version 1.0, DDS-60.
  2. J.H. Walsh, Parabolic Projection of World Conventional Oil Production Based on Year 2000 Assessment of the U.S. Geological Survey, April 2000. (Abridged version on Web at
  3. J.H. Walsh, Two World Oil Production Parabolas Staged at 1988, Proceedings of the Canadian Association of the Club of Rome, Series 1, Number 28, Winter 1998-99.
  4. J.H. Walsh. World Per Capita Oil Consumption 1965-1999. Updated June 2000.
  5. J.H. Walsh, The Future for the Fossil Fuels, Proceedings of the Canadian Association of the Club of Rome, Series 2, Number 2, Autumn 1999.

September 2000
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