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An Experiment To Evaluate Methods For Estimating
Fossil Fuel Resources
John D. Sterman George P. Richardson
Sloan School of Management Wheaton College
Massachusetts Institute of Technology
April 1983
Revised September 1984
ABSTRACT
Estimates of petroleum and natural gas resources
vary substantially, both over time and across estimation methods.
This paper develops a simulation model of global oil resources to
evaluate different resource estimation techniques. Protocols for
the Hubbert life cycle and USGS geologic analogy methods are
developed and applied to synthetic data generated by the model.
It is shown that the Hubbert method can generate an accurate
estimate as early as twenty years before the peak of global
production, but the geologic analogy approach overestimates the
true resource base over the life cycle of the resource. The
results show the applicability of simulation and the synthetic
data approach to the problem of evaluating forecasting methods.
"Oil is a finite commodity...once it has gone, it
cannot be replaced."
"It just isn't going to happen...The more you use,
the more there is."
(Christian Science Monitor,
11 March 1983, 1)
The estimation of petroleum resources is perhaps one of the most
controversial and important of all forecasting activities. As illustrated
by the quotations from oil market analysts cited above, there are
fundamentally divergent views on the nature of petroleum resources, the
role of technology, and the appropriate sources of information for
estimating the resource base. The uncertainty, combined with the
importance of oil, have spawned a minor industry which since 1973 has
witnessed a proliferation of forecasts, models, and estimation procedures
(for surveys and reviews see Mathtech 1978, MIT 1982, Grenon 1975, and
Meyer 1977). The effort devoted to resource estimation, however, has not
veduced the uncertainty or settled the debate. Estimates of ultimate
Forthcoming in the Journal of Forecasting
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recoverable petroleum resources vary substantially, both across
estimation methods and over time (Meyer 1977, Odell and Rosing 1980).
Worse, the traditional approach to evaluating forecasting methods, repeated
comparison of forecasts to actual outcomes, is of little use because the
true resource base will not be known for decades.
The research reported here contributes to the development of methods for
evaluating forecasting techniques before actual outcomes are known. The
approach is based on the use of synthetic data generated by a model of the
processes being forecasted (Richardson 1982).
A wide variety of estimation techniques currently exist, including life
cycle (Hubbert 1956, 1962, 1982; Ryan 1966; Wiorkowski 1981), geologic
analogy (Zapp 1962, Hendricks 1965, USGS 1975, Jones 1975, Energy, Mines,
and Resources Bureau (Canada) 1977, Semenovich et al. 1977), rate of effort
(Hubbert 1974) econometric (Khazzoom 1971, MacAvoy and Pindyck 1973), and
discovery process methods (Arps and Roberts 1958, Ryan 1973, Barouch and
Kaufman 1977). The techniques range from the basin and play level to
continental and global aggregation, from detailed structural and process
models to curve-fitting. Despite the differences, all estimation
procedures can be thought of as information processing schemes which take
certain data as input and produce an estimate of the resource base as the
output. Previous appreciations of estimation methods (e.g. Mathtech 1978,
MIT 1982) have focused on the logical structure, parameter estimation, and
data requirements of the methods. But to compare the various methods it is
necessary to apply them to a consistent set of data. This is done by
generating data through a simulation model of global oil discovery,
development, and production.
To demonstrate the approach, we have chosen to evaluate the Hubbert
life-cycle method and the geologic analogy method. First, the estimation
methods are formalized. The resulting protocols specify in an exact and
reproducible manner the way in which information is processed to yield an
estimate. Second, the protocols are applied to synthetic data generated by
the model, and a dynamic path of the estimates is generated. The evolution
of resource estimates over time is then compared to the resource base
assumed in the model, and the accuracy of the estimation protocols is
evaluated. But will a good estimation method perform well on the synthetic
data? And will a flawed method perform poorly? The answer to both
questions is yes, if the data-generating model corresponds closely enough
to the real petroleum system. "Closely enough" in this context means that
the behavior of the information inputs to each estimation method must be
broadly consistent with history. More important than historical fit,
however, the resource development scenarios generated by the model must be
both feasible anid internally consistent. To insure feasibility and
consistency, the data-generating model should portray the physical
structure of the resource system and the decisionmaking procedures used by
the actors. As described below, the model portrays technical, geologic,
economic, and other factors which interact to endogenously produce the
lifecycle of world petroleum. If the model appropriately mimics the real
system, then the synthetic data will constitute a fair test of the
estimation methods.
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The History of Petroleum Estimates: Excelsior!
Serious estimates of world ultimate recoverable petroleum resources date
from at least the 1940s, and show a clearly rising trend over time (exhibit
1). A similar pattern exists for estimates of the ultimate recoverable
resource (URR) in the United States (exhibit 2). The rising trend reflects
increasing knowledge of geology, improvements (actual and anticipated) in
recovery technology, and, of course, increases in discoveries and
recoverable reserves.
In general, there are two polar responses to the rising pattern of
estimates. The more conservative response is typified by Warman (1972,
292) who states
It is interesting to note that estimates have increased with time and
it is fair to ask whether we are still underestimating. There are
some good reasons for believing that during the time span of these
estimates our knowledge has increased to a point where future
continued expansion on the same scale seems unlikely.
Warman concludes that the URR is likely to be 1,800 billion barrels. In
contrast, some see in the rising trend of estimates justification for
assuming the ultimate recoverable amount is much greater. Peter Odell
(1973, 454) extrapolated the past estimates and concludes
«..the resource base,...given the extrapolation of the
calculated trend, would reach almost 4,000 x 10° barrels...by the
year 2000. In brief, the oil resource base in relation to reasonable
expectations of demand gives very little apparent cause for concern,
not only for the remainder of this century, but also thereafter well
into the twenty-first century at rates of consumption which will then
be five or more times their present level.
Because the endowment of nature-made petroleum (oil-in-place) is finite,
estimates of URR should eventually level off. Given that it takes time to
develop the knowledge and experience that permit accurate estimates to be
made, the ideal pattern would be a gradual approach to the (correct) URR.
Alternatively, estimates might overshoot the URR, gradually approaching the
true resource base from above as more knowledge is gained (exhibit 3).
Close examination of the estimates for the United States (exhibit 2)
reveals an apparent peak in the early 1960s at a level of 500 to 600
billion barrels, compared to more recent estimates in the range of 160 to
300 billion barrels.
The consequences of overestimation are potentially serious. Overestimation
may lead to inefficient allocation of ‘exploration effort, overvalued lease
tracts, and complacency in the development of oil substitutes. It is
important, therefore, to identify possible sources of overshoot in the
estimation methods currently in use.
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Modeling The Estimation Process
The model described below is but one of many that could conceivably be used
to generate the synthetic data for the experiment. Not all models of the
oil supply process are appropriate, however. In addition to the obvious
constraint that the model must generate data at an appropriate level of
aggregation for the estimation protocols, the model should have the
following characteristics.
First, it should be a structural model. Tt should attempt to represent the
physical and causal structure of the processes modeled, as opposed to a
model based on historical correlations. Nonlinearities and constraints may
alter historical correlations in the future. Physical delays, such as the
time required to develop an oil field or build a synfuel plant, should be
represented explicitly.
Second, it should be a behavioral model, portraying the information
available to actors and the procedures they use to process it and arrive at
decisions. The petroleum system is characterized by imperfect information,
uncertainty, and distributed decisionmaking. If the model is to respond to
changes in the environment in the same way the real actors do, this bounded
rationality should be incorporated (Simon 1979, Hogarth 1980, Morecroft
1983).
Third, the model should generate its behavior endogenously. The discovery
and production process is tightly interconnected with energy price, demand,
substitution, and technology. A change in one part of the system may have
ramifications throughout. A model that relies on exogenous variables is
Likely to produce inconsistent results as the feedback effects are ignored.
A model that generates the petroleum life cycle endogenously constitutes an
internally consistent theory that is subject to analysis, refutation, and
revision (Bell and Senge 1980).
In addition to these general considerations, a model of petroleum resources
to be used in forecast evaluation should include the following specific
features as endogenous components:
1. Technology: The ultimate recoverable resource depends heavily on the
recovery factor. Only 30 to 40 percent of oil-in-place can be
recovered economically with current technology, but the fraction
recoverable has been rising and may rise substantially in the future.
2. Economic incentives: Economic incentives (primarily determined by the
price of oil) play a large role in determining proved reserves,
exploration, and production. Oil that is subeconomic at $10 per barrel
may be highly profitable at $30 per barrel. Regions that were not even
considered for exploration may be prime candidates for test wells ata
higher price.
3. Price: Because the price has a strong influence on the incentives for
exploration and development, it must be modeled explicitly. The
effects of production costs, supply and demand, and market
imperfections should be incorporated.
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4. Demand and Substitution: Petroleum demand is sensitive to price. As
prices rise, the demand for oil will be depressed, and the production
of substitutes ("backstops" [Nordhaus 1973]) such as synfuels will be
stimulated. The pattern of demand and substitution will have a strong
influence on production and investment in exploration. Delays in the
response of demand and in the development of the backstop industry
should be explicit.
5. Depletion: The total initial quantity of oil-in-place is finite. As it
is consumed, the quantity remaining inevitably declines, and the
marginal cost increases, ceteris paribus. Though improving technology
may offset depletion and cause the real price of oil to decline, the
limited nature of the resource base and its depletion must be treated
explicitly.
The Data-Generating Model
The criteria proposed above impose strong constraints. The model described
below should be thought of as a step towards an endogenous, structural
theory of petroleum geology, economics, and technology.
The system dynamics approach to simulation is used (Forrester 1961,
Richardson and Pugh 1981). Application of system dynamics to energy
include Naill (1973, 1977), Backus et al. (1979), Choucri (1981), and
Sterman (1983). A documented listing of the model is available from the
authors and has been lodged with the editors. The model is divided into
five basic sectors: (1) exploration; (2) production; (3) technology; (4)
revenue and investment; and (5) demand and substitution (exhibit 4).
1. Exploration: The model divides the total quantity of oil-in-place into
three basic categories: as yet undiscovered oil, identified resources, and
cumulative production. Within these broad categories, several finer
divisions are portrayed. The disaggregation of the resource base follows
standard resource classification shown in the McKelvey box format (USGS
1976) in exhibit 5. The McKelvey box is a useful but static
characterization of the resource base. Over time, exploration and
production activity shift the boundaries in the McKelvey box. Successful
exploration shifts the boundary between identified and undiscovered
resources to the right; improvements in technology or increases in the real
price of oil shift the boundary between economic and subeconomic resources
towards the bottom. Production shrinks the reserve base.
As an example, the determinants of the exploration rate are shown in
exhibit 6. The rate at which undiscovered resources are identified is
determined by investment in exploration and the productivity or yield of
that investment. Note that additions to the identified resource include
all oil-in-place identified through exploration and not just the economic,
proven part that is immediately producible, which is often mis-labeled
"discoveries" (MIT 1982, part IT). Additions to the identified resource
depend on investment expenditure and the desired discovery rate. To
represent the time required to identify and explore a prospective oil-
bearing region, the potential discovery rate is given by lagged investment
expenditure. The rate of investment, in turn, depends on the desired
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discovery rate, modified by profitability. If the expected revenues from
exploration activity do not justify the cost, or if the cost of developing
new reserves exceeds the expected cost of oil substitutes, exploration is
curtailed. Conversely, higher than normal return induces entry and
expansion of exploration efforts. The desired discovery rate is the rate
at which resources need to be identified to meet anticipated production and
expected growth in production, and to provide the reserve levels required
to meet anticipated production.
The cost of exploration activity is determined directly by the yield or
productivity, which depends on technological and geological factors. At
the dawn of the oil era, only a small fraction of oil-in-place was
discoverable. As the ability to drill deeper wells was developed, a larger
fraction of oil-in-place in a given region could be identified. As the
ability to drill offshore and in increasingly hostile environments was
developed, a larger fraction of the potential oil-bearing area of the globe
could be economically explored. And as the sophistication of seismic
detection technology grew, smaller and smaller oil deposits, for example,
in stratigraphic traps, could be identified.
At the same time, however, depletion reduces the productivity of
exploration efforts. Producers naturally follow a Ricardian resource
exploitation strategy, exploring those areas they believe most likely to
yield oil first, drilling shallow wells and tapping giant oilfields when
possible before moving on to less accessible and more expensive regions.
To the extent producers are able to identify oil at a better than random
rate, the productivity of future exploration activity is necessarily
reduced (ceteris paribus), as future additions to the identified resource
will involve more dry holes, deeper wells, and increasingly, drilling
offshore or in distant and hostile locations. The evidence suggests
exploration activity in the United States historically has been 2.75 times
more effective than chance drilling (McCray 1975, 229). Hubbert and others
(Hall and Clevelend 1981) have documented a significant decline in yield
per foot drilled both as a function of time and as a function of cumulative
exploratory effort for the United States:
In fact, ‘finding rates' had fallen sharply since the late 1930's as
oilmen skimmed the cream off the prospects in Texas, Oklahoma, and
California. From a high of 276 barrels per foot of exploratory
drilling, discoveries have fallen to about 35 barrels per foot by
1955 and to 30 in 1972 (Gillette 1974, 129).
Though depletion causes yield to decline, close examination of the U.S.
data show actual yields increased in the 1920s and again in recent years,
illustrating the shifting dominance of technical, economic, and geological
factors. These factors are represented in the model and, as shown below,
the simulated yield to exploration first rises with technology and then
falls with depletion.
2. Production: Production in the model is determined by three major
factors: the quantity of identified resource remaining, recovery
technology, and investment in production facilities. Investment in
production facilities depends on anticipated demand for natural pretroleum,
modified by profitability. As in the exploration decision, higher than
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normal returns cause expansion of production. An insufficient return
causes a cutback in production as existing wells are shut down and plans
for new wells cancelled. Investment in production capacity is also
constrained by the technically recoverable quantity of oil. Limitations on
the rate of flow and on the density of producing wells constrain useful
investment in producing wells, though it is assumed in the model that
production/reserve ratios can be increased somewhat above normal levels in
a situation of high demand or profit.
3. Technology: Technology in the model is endogenously generated. As
shown in exhibit 7, the model distinguishes between the fraction of oil-in-
place that is discoverable with current technology and the fraction of the
identified resource recoverable with current technology. The fraction
discoverable represents the feasible depth of wells, the ability to drill
offshore and in hostile environments, and the effectiveness of geologic
survey and identification technology. The fraction recoverable represents
the effectiveness of secondary and tertiary recovery techniques.
Each type of technology improves as the result of research effort.
Improvements in technology take time, and an average delay of six years is
assumed between an increase in expenditures on research and development and
the resulting improvement in technology. Expenditures on R&D are assumed
to be a fixed fraction of industry revenues. The effectiveness of
investment in technology is variable. As the level of technology improves,
the marginal improvement in technology per dollar of research effort
declines. The total R&D effort is allocated between discovery and recovery
technology on the basis of the perceived marginal benefit to each.
Initially, the majority of research is devoted to improved exploration
technology designed to increase the fraction discoverable. As the fraction
discoverable rises, research effort gradually shifts to improving the
recovery factors from developed fields.
4. Revenues and Price: Revenues are given by the price and production of
natural petroleum. The price of natural petroleum is determined by
production and exploration costs and by relative supply and demand. When
supply and demand are in balance, the price equilibrates at a level
sufficient to cover exploration and production costs and to provide the
required return on investment. Investment expenditures are allocated among
exploration, production, and R&D on the basis of the relative need for
funds.
5. Demand and Substitution: The demand for petroleum is endogenously
portrayed in the model (exhibit 8). The total demand for oil is determined
by the stock of capital in the economy and the oil intensity of that
capital. Capital is assumed to grow at an exogenous rate. The oil
intensity of the capital stock is determined by the average price of oil.
The average price is given by the prices and market shares of natural and
synthetic petroleum. An average lag of fifteen years is assumed between a
change in the price of oil and its full effect on demand. The fifteen year
lag is somewhat shorter than the twenty year average life of energy
consuming capital (Coen 1975, Sterman 1981), to represent the potential for
retrofitting existing capital.
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The market share of natural petroleum is determined by its price relative
to the price of synthetic substitutes. The share responds to changes in
the relative prices of natural and synthetic oil with an average lag of ten
years, representing the time required to develop a synthetic fuel industry.
The real price of synthetic substitutes is assumed to be constant.
Model Calibration
The model used in these experiments has been calibrated to represent the
global petroleum system. The major quantitative assumptions are listed in
exhibit 9. The simulation results reproduce the global experience fairly
accurately. However, the key aspect of the simulations is not the specific
values of parameters or variables. The evolution of the petroleum system
to date is but one draw from a large number of possibilities: the world's
endowment of petroleum could have been different, discoveries could have
occurred earlier or later, recovery technology could have developed at a
different pace, and so on. A good estimation procedure should be able to
produce accurate estimates for any consistent resource development
scenario, and must not depend on the realization of a particular scenario.
Thus, the results presented here are not contingent on the precision with
which the model reproduces the past history of oil discovery and use. The
purpose of the model is not to estimate the resource base. Our focus is
the relationship between estimates of the resource base and the assumed
resource base, not the absolute magnitude of the resource base or other
parameters.
The total quantity of oil-in-place in 1900 is assumed to be slightly
greater than 5000 billion barrels. It is assumed technology can improve so
that all oil-in-place is potentially discoverable and that the recovery
factor can rise to as high as 60 percent. The maximum ultimate recoverable
resource is therefore about 3000 billion barrels, consistent with
contemporary estimates. Note that the actual values of the discovery and
recovery factors are endogenous and may not attain their maxima; likewise,
the ultimate quantity produced may be less than the potential due to the
substitution of backstop technologies before exhaustion of the resource.
Results
Simulation results are shown in exhibit 10. The simulation starts in 1900
and runs until 2100. With the sole exception of the exogenous growth rate
of energy consuming capital, the behavior is endogenously generated over
the two hundred year life cycle of the resource.
In the early years of the century, simulated demand and production grow
rapidly (exhibit 10a). Growth of the industry stimulates R&D, and the
fraction discoverable rises rapidly (exhibit 10c). Between 1900 and 1940,
improving technology causes the yield to exploration effort to rise from an
initial value of about 60 barrels per foot to nearly 200 barrels per foot
exhibit 10c). As a result, the rate at which resources are identified
greatly exceeds production (exhibit 10a), causing recoverable resources and
the reserve-production ratio to rise, especially after 1940 (exhibit 10b).
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The improvement in technology and yield causes the real price of oil to
decline by over sixty percent between 1900 and 1950 (exhibit 10d). The
reduction in the real price of oil causes demand to grow faster than
capital stock, and the average oil intensity rises.
After 1940, simulated yield begins to drop: though discovery technology is
still improving rapidly, the very effectiveness of exploration in locating
oil implies future efforts will be less successful. As the giant oilfields
and shallow deposits are found, additional exploration yields more dry
holes and smaller finds. By the mid-1960s, the rate of addition to
identified resources reaches its maximum. But though new finds are
declining, they remain well above production, and reserves continue to
grow.
Initially, R&D activity was focused on discovery technology, and the
fraction recoverable grows only slightly (exhibit 10c). But as discovery
technology becomes more effective, R&D effort is shifted to enhancing
recovery factors. After 1940, the fraction recoverable begins to rise
rapidly, reflecting the development of secondary and tertiary recovery
techniques.
By the 1980s, the industry has reached a turning point. Declining yield
has caused real prices to begin to rise, and the higher price begins to
suppress demand and stimulate the development of substitutes, though
natural petroleum still dominates the market. Over two-thirds of the total
oil-in-place has been identified, and additions to identified resources are
falling. But because recovery technology is improving rapidly, reaching 35
percent in 1980, recoverable reserves continue to grow, and the reserve-
production ratio reaches a peak of more than 34 years in 1985.
In the next twenty years, newly identified resources drop below production,
proved reserves peak and begin to decline, and the reserve-production ratio
falls. Production, though still rising, grows at a diminishing rate.
Improving technology boosts the fraction discoverable to over 85 percent
and the fraction recoverable to over 50 percent. Nevertheless, the real
price continues to rise reaching nearly $20 per barrgl by 2000, though
transitory periods of glut cause temporary plateaus. Significant
investment in substitutes is undertaken, but due to the long construction
lags, natural petroleum loses market share only slowly.
After 2000 the transition to substitutes accelerates. The market share of
synthetics rises to 25 percent by 2016 and exceeds 75 percent by 2045.
Production of natural petroleum peaks about 2020 near 40 billion barrels
per year and falls rapidly. Additions to identified resources are
stimulated somewhat by higher prices, but as substitutes begin to be
competitive, investment is curtailed, and exploration activity is virtually
zero after 2050. The reserve-production ratio falls to 20 years by 2020
and to 16 years by 2050 as falling reserves force production down.
The real price of natural petroleum continues to rise, exceeding the
assumed substitute price of $30 per barrel by 2020, and rising to $60 per
barrel before stabilizing after 2060. The average price of oil (both
natural and synthetic) grows less rapidly than that of natural petroleum as
substitutes come on stream. But because of the development delays, the
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average price of oil overshoots the cost of the substitutes, remaining over
$33 per barrel for nearly thirty years. The overshoot of energy prices as
a consequence of delays in substitution is consistent with the results of
several other models of the energy transition (Sterman 1983, Energy
Modeling Forum 1981, DOE 1979).
By 2060 the petroleum era in the model is largely over. Production is
about six billion barrels per year and falling. Substitutes account for 90
percent of the market, and the remaining petroleum demand is for premium
uses only. Reviewing the entire life cycle highlights the following
points:
1. The life cycle of production follows a roughly bell-shaped path, though
it is definitely asymmetrical, with production falling off faster than
it grew (exhibit 10a).
2. Consistent with the United States experience, the yield to exploration
first rises, as a consequence of improving technology, and then falls
as a consequence of depletion (exhibit 10c).
3. Likewise, improvements in technology first cause the real price to
decline, but eventually depletion dominates technology and the real
price rises (exhibit 10d).
4. Substitution to backstop technologies limits the average price of oil,
but substitution delays cause an extended period of price overshoot in
which the economy must continue to depend on natural petroleum even
though it is more expensive than the substitutes (exhibit 10d).
5. Though the ultimate recoverable resource could have reached as high as
3000 billion barrels, the actual resource recovered by 2100 is
approximately 2700 billion barrels. Substitution to the backstop
causes production and investment in technology to stop before the
ultimate limits are reached (exhibit 10b).
The Estimation Protocols
We have evaluated two estimation procedures, the Hubbert life cycle
approach and the geologic analogy approach used by the USGS and others.
Each of these techniques can be applied to the aggregate data generated by
the model.
The Hubbert Method: Hubbert has actually developed two methods to estimate
ultimate recoverable resources, the original life cycle approach and a
later rate-of-effort approach. We consider here the life cycle approach.
It was the first method he developed, the most controversial, and also the
most accurate to date in projecting production and reserves in the United
States.
Hubbert's method has been extensively described, criticized, and analyzed
elsewhere (MIT 1982, Mathtech 1978). To apply the method to the
model-generated data, we developed the following protocol:
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1. Define cumulative proved discoveries as cumulative production
plus technically recoverable reserves,
2. Assume cumulative proved discoveries follow a logistic path
given by:
*
6. x sseuse Q (41)
t 1 + a*exp(db t-t_))
where °
*
= ultimate recoverable resource
GW oF cumulative proved discoveries at time t
a, b= parameters to be estimated
tie = an arbitrary initial time
3. Rearrange equation (H1) as
in (Q"/Q,)-1] = In(a) + d(t-t,) (Ha)
4, Estimate the parameters of equation (H2) by ordinary least
*
squares regression for various values of Q , and
* 2
select Q from the regression that yields the highest R-.
In Hubbert's original work, Q* was estimated by "a trial and error
graphical method" in which he plotted the data on semi-log paper and,
judging by eye, chose the Q* that best fit the data (MIT 1982, III-2-10).
We have used regression so that our results are reproducible. Hubbert's
graphical method is equivalent to the regression technique if-one is
willing to assume that the "best" fit judging by eye is roughly equivalent
to the least squares estimates of the parameters in equation (H2). No
measurement error is introduced, as we are primarily concerned with the
tendency of estimation methods to overshoot even when perfect information
is assumed. The robustness of the protocols in the face of process noise
and measurement error is left as a topic for future research.
Values of Q* were estimated by the protocol above using the model generated
data from 1900 to 1970, 1900 to 1980, and so on. The results are
shown in exhibit 11, compared against the "true" ultimate recoverable
resource. The Hubbert method eventually provides an unbiased estimate of
URR, settling within 11 percent of the true value by 2000 and reaching it
by 2040. However, before the year 2000, the estimated value of Q* exceeds
the true value considerably. Up to 1970, the best fit to the logistic
curve actually yields an infinite value for Q*. Up to that year,
cumulative discoveries have been growing at an increasing exponential rate,
rather than the continuously declining exponential rate presumed by a
logistic curve. Between 1900 and 1970, the rate of economic growth
accelerated, causing total demand for oil to grow at an increasing rate.
In addition, the declining real price of oil encouraged growth of oil
demand over and above the rate of economic growth, further adding to the
growth rate of production. Finally, improving technology caused reserves
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to grow faster than production, in contrast to Hubbert's original model
which presumes a constant average reserve~production ratio.
After 1970, the rate of growth of cumulative proved discoveries slows, and
the estimated Q* falls rapidly. By 1980, Q* has dropped to between 5500
and 6500 billion barrels; by 1990 it is between 3500 and 3800 billion
barrels. As the life cycle unfolds, the estimate falls towards the true
value, and the range of uncertainty shrinks.
The life cycle approach relies on the fact that the finite nature of the
resource necessarily implies a roughly S-shaped path for cumulative
production and discoveries. The logistic model satisfies this requirement,
but imposes the constraint that the fractional rate of growth declines
continuously throughout the life cycle. In order to estimate the logistic
successfully, therefore, the data must continuously reflect the decline in
the growth rate caused by depletion. As demonstrated by the simulation,
this need not be the case even when depletion of the resource is in fact
strictly monotonic. Because rising rates of demand growth and improving
technology dominate over the depletion effect in the first third of the
life cycle, depletion, though occurring continuously, is masked in the
aggregate data.
The life cycle approach, therefore, is only likely to give accurate
estimates after the depletion effect dominates over other forces that may
conspire to cause the fractional rate of production or discovery to rise.
In the simulation, that shift in dominance occurs between 1980 and 2000.
By 2000, eighteen years before the peak in production, the Hubbert estimate
is within 11 percent of the true value. The results suggest the life cycle
approach is only now becoming a reasonable guide to estimating the world's
ultimate recoverable resource, at least at the global level of aggregation.
It is interesting to compare the results above to Hubbert's astonishingly
accurate forecast of production in the United States. In 1956, Hubbert
forecast that the ultimate recoverable resource for the lower 48 states and
adjacent offshore areas would be between 150 and 200 billion barrels, and
projected "the peak in production should probably occur within the interval
1966-1971" (Hubbert 1975, 371). At the same time, the USGS, using the
geologic analogy method (Zapp 1962) projected ultimate recoverable
resources of 590 billion barrels, and concluded that
...the size of the resource base would not limit domestic production
eapacity ‘in the next 10 to 20 years at least, and probably [not] for
a much longer time’ (Gillette 1974, 129).
Production actually peaked in 1970, and, as Renshaw and Renshaw (1980, 58)
have pointed out, Hubbert's "projected values for cumulative discoveries
and production have not yet been exceeded." Assuming 1970 was the true
peak of production, Hubbert's 1956 forecast leads the peak by some fourteen
years, well within the twenty-year lead generated in the experiment.
The Geologic Analogy Method: Geologic analogy methods, sometimes called
volumetric methods, are a common approach to estimating ultimate
recoverable resources. In essence, the method consists of
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++-projecting average yield factors (barrels of oil per cubic mile of
sedimentary rock or per square mile of surface area) uniformly over a
sedimentary rock stratum (Mathtech 1978, ITI-297).
The USGS estimates of 1975 present one of the most comprehensive and
detailed uses of these techniques to date. The essence of the method was
described by the Survey as follows:
Estimates of recoverable oil and gas resources are based upon a
series of resource appraisal techniques....The techniques used
include: (1) an extrapolation of known producibility into untested
sediments of similar geology for a well-developed area; (2)
volumetric techniques using geologic analogs and setting upper and
lower yield limits through comparisons with a number of known areas;
(3) volumetric estimates with an arbitrary general yield factor
applied when direct analogs were unknown; (4) Hendricks’ (1965)
potential area categories; and (5) comprehensive comparisons of all
known published estimates for each area to all estimates generated by
the above methods (USGS 1975, cited in MIT 1982, III-5-13).
Despite the apparent rigor, the USGS study actually involved a high degree
of subjective judgment and discussion, and the protocols used to reach
consensus have been criticized as "mismanaged" (MIT 1982, ITI-5-19). Our
representation of the process abstracts from the subjective and political
nature of the process to focus on the sources of information for the
economic, technical, and geologic assumptions made in the study.
The survey divided the resource base into the standard classifications of
the McKelvey box, and assumed
«..that undiscovered recoverable resources will be found in the
future under conditions represented by a continuation of price/cost
relationships and technological trends generally prevailing in
therecent years prior to 1974. Price/cost relationships since 1974
were not taken into account because of the yet undetermined effect
these may have on resource estimates....
These assumed conditions permit the appraisal of recoverable oil and
gas resources to be made on the basis of: (1) relevant past history
and experience concerning recovery factors; (2) the geology favorable
to the occurrence of producible hydrocarbons; and (3) the size and
type of reservoirs which have geen found, developed, and produced....
The economic recovery factor used was based on a current national
average of approximately 32 percent....Sub-economic identified
resources of crude oil were calculated on the following assumptions:
(1) that on the average, 32 percent of original oil-in-place is rec-
overable if there are no substantial changes in present economic
relationships and known production technology, and (2) that
ultimately the recovery factor could be as large as 60 percent....
It is extremely optimistic to assume that 60 percent of the
oil-in-place will eventually be recovered. If [this] becomes a
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reality, it is likely to occur only through gradual development over
an extended time period. The remaining 40 percent of oil-in-place is
not included as it is considered to be nonrecoverable.... (USGS 1975,
cited in MIT 1982, III-5-9, 10).
The protocol used to test the geologic analogy method appears in the
appendix. The protocol assumes far better information than is actually
available to real estimators. Cumulative production, technically
recoverable reserves, cumulative identified oil-in-place, the current
recovery factor, and the area explored are assumed to be known exactly.
The only potential sources of error are in the estimation of the future
recovery fraction and in the expected yield of oil-in-place in unexplored
areas. In both of these cases, the model, like the Survey, assumes "a
continuation of price/cost relationships and technological trends generally
prevailing in...recent years...."
Applying the geologic analogy protocol to the data generated by the model
yields the path of estimates summarized in exhibit 12. The components of
the estimates are shown in exhibit 13. The estimates start low, rise
rapidly, overshoot the ultimate quantity recovered, and settle at a level
in excess of the ultimate quantity recovered.
Exhibit 13 tells the following tale. In 1900 the estimates are very low--
only a small fraction of the sedimentary basins in the world have been
surveyed, both discovery and recovery technology are primitive, and little
of the resource has been identified. With increasing exploration
experience, improving exploration technology, and growing knowledge of
sedimentary basins, the estimates steadily rise, reaching almost 600
billion barrels by 1940. In 1940, reserves are small and recovery
technology has not grown enough to warrant substantial forecasts of future
improvement. The majority of the estimate consists of probable recovery
from unidentified resources--the quantity expected at current recovery
factors from know sedimentary basins that are as yet unexplored, assuming
historic yields.
Between 1940 and 1960 the estimate more than triples, reaching nearly 2000
billion barrels. Though all components of estimated ultimate recovery are
growing, the bulk of the estimate (60 percent) is still due to probable
future discoveries. By 1960, the accelerating growth of recovery
technology is beginning to cause the expected recovery fraction to exceed
the current fraction. Expectations of technical improvement for both the
identified and estimated unidentified resource is still quite cautious,
however, accounting for less than 20 percent of the estimate.
The estimate continues to grow between 1960 and 1980, surpassing the
ultimate quantity ultimately recovered in the early 1970s. In contrast to
previous years, the majority of the growth is due to expectations of
continuing improvement in recovery technology. Between 1960 and 1980, the
fraction recoverable rises from 24 percent to 35 percent; based on that
growth, the expected fraction recoverable doubles, rising from 29 to 60
percent. In fact, the USGS estimated the recovery fraction might rise to
as high as 60 percent when the recovery factor was actually 32 percent (see
appendix). As a result, the estimated ultimate recoverable resource rises
to 3280 billion barrels, of which 15 percent has already been produced and
fully 40 percent is based on the expectation of continued technical
progress.
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By 1980, the estimated quantity of oil-in-place remaining to be identified
is declining, the combination of declining area unexplored and particularly
of declining yield. The decline in yield that began in the 1940s has
accelerated, causing the expected yield to fall as well. Nevertheless, as
a consequence of the lags in recognizing and adapting to lower yields, the
expected yield is 36 percent higher than the actual yield in 1980.
After 1980, growth of the estimate slows as the unexplored area and
expected yield to exploration continue to drop. Recovery technology
continues to improve, however, which causes the expected recovery factor to
overshoot the true value. The expected fraction recoverable peaks at 73
percent in 2019, compared to the true long-run value of 59 percent. The
vesulting overestimate of recovery helps boost the estimated URR to a peak
of about 3550 billion barrels. After 2010, the expected recovery fraction
approaches the actual fraction, and the estimated recoverable resource
declines to an equilibrium value of about 3000 billion barrels,
approximately equal to the ultimate quantity that could have been recovered
if the resource had been fully exploited.
Simulation of the geologic analogy method produces estimates which are
consistent with the historical estimates of world ultimate recoverable
resources (exhibit 14). Nevertheless, the geologic analogy method
substantially overshoots the true ultimate quantity recovered. The
overshoot begins in the 1970s and reaches a peak over 30 percent greater
than the ultimate resource recovered. The overshoot is caused by two major
factors, visible in exhibit 13. First, the extrapolation of past
improvements in recovery technology leads to forecasts of ultimate recovery
factors that exceed the true factor. Second, lags in the recognition of
declining yields to future exploration activity cause the estimates of
unidentified oil-in-place to overshoot the true quantity. And when the
extrapolation of recovery technology is applied to the estimated
unidentified oil-in-place, the overestimation is compounded.
Viewed from another perspective, however, the estimation procedure does not
perform badly. Exhibit 15 compares simulated estimated recoverable
resource remaining to simulated true recoverable resource remaining. The
history of resource estimation divides into two distinct phases. At first,
estimates rise steeply as more kmowledge is gained. The estimated
recoverable resource remaining overtakes the true quantity remaining in the
1970s. The estimates then reverse and fall as the true quantity remaining
falls. The estimates lag behind the true quantity remaining due to the
expectations of continued technical progress and near-historical yields.
Viewed as a learning process in the presence of limited and uncertain
information, the estimation procedure performs rather well. Note, however,
that though there is no change in the way estimates are being made, there
is a dramatic shift in perspective between 1970 and 1990. Within twenty
years, the historic trend of growing estimates reverses.. The result of
such a shift is likely to be conflicting estimates and methodological
disagreements.
Interestingly, the USGS recently lowered its estimate of world ultimate
recoverable petroleum resources (Science, 27 January 1984, 382). Citing
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continued disappointments in finding rates as the main reason for the
decline, the USGS report may represent the beginning of an overshoot in
actual estimates of world petroleum resources.
Implications: the Accuracy of the Estimation Methods
The synthetic data used in this experiment to evaluate the estimation
methods represent but one of many possible scenarios for the development of
world petroleum. Other scenarios can and should be developed to test the
robustness of the results. Yet the estimates generated by the two methods
are sufficiently different to warrant comment (exhibit 16).
Hubbert's method has been criticized as merely an exercise in fitting data
to an arbitrary curve. Yet these results show the life cycle approach can
yield an accurate estimate of the ultimate recoverable resource, provided
the resource is far enough into its life cycle so that the depletion effect
begins to dominate other factors and depress the growth rate of cumulative
discoveries. In the scenario tested, this point is reached approximately
twenty years before the peak in production. Before then, the life cycle
method overestimates the ultimate recoverable resource. The results are
consistent with the impressive accuracy of Hubbert's projections for the
United States but suggest the method may only now become useful for
estimating world resources. It is worthwhile noting that Hubbert presumed
a logistic curve and has been criticized for not using a more flexible
functional form that allows the data to dictate the presence of asymmetries
(MIT 1982, TII-2). The model used to generate the synthetic data does not
presume a logistic curve, nor does it generate one,,but Hubbert's approach
eventually produces accurate estimates nonetheless.
Analysis of the geologic analogy approach shows the history of rising
estimates of world ultimate recoverable petroleum resources can be
explained in terms of the information sources available to resource
estimators and the estimation procedures used. Though ostensibly superior
to the Hubbert method, because it involves the use of disaggregate, primary
geologic data, the analogy method actually involves a high degree of
judgment, extrapolation of past trends, and educated guessing. Results
show the analogy method can lead to a substantial overshoot of the world
ultimate recoverable resource, even when a high degree of perfect
information is assumed.
The results demonstrate that the pattern of rising estimates is perfectly
consistent with the continuous depletion of the resource, and show it is
quite possible that estimates may have already exceeded the true resource
base. Further, the results suggest there is absolutely no basis, other
than faith, for estimating the ultimate recoverable resource by
extrapolating past estimates. Odell's statement, quoted earlier, that
++.the resource base,...given the exfrapolation of the calculated
trend, would reach almost 4,000 x 10° barrels by the year 2000....
reveals a potentially serious confusion between the estimated resource base
and the actual resource base. The estimated resource base may rise, but
the actual resource base is constant and the remaining quantity of oil-in-
place is monotonically declining. To illustrate, extrapolation of the
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D-3432-1
model-generated analogy estimates would exceed Odell's figure by the year
2000, increasing the overshoot to more than fifty percent. Indeed, given
the historic rising trend of estimates, any simple extrapolation of past
estimates must necessarily overshoot the true resource, even if the
estimates themselves do not. And when the estimates themselves show the
potential for overshoot, as shown by the model and by the experience in the
United States, the error in extrapolating is magnified even further.
Methodological Conclusions
Most previous critiques of resource estimation techniques have focused on
the sources of information, the statistical procedures, and the analytic
framework used by the various estimators. This work suggests that a
complementary approach based on simulation of the various methods offers
important insights into the dynamics of the resource estimation process.
By formalizing the protocols for making estimates and applying them to
synthetic data, it is possible to assess the tendency for an estimation
technique to overshoot the true resource before the true resource base is
known. Further, it may be possible, as in the Hubbert case, to identify
time frames in which the method is accurate.
The work reported here demonstrates the potential of the synthetic data
approach. More work needs to be done both refining the model and the
estimation protocols. Other estimation methods, such as rate-of-effort,
need to be examined. The model could be calibrated to portray the United
States to see if the pattern of overshoot can be generated. The robustness
of the results in the presence of process noise and measurement error
should be explored. Other models of the resource life cycle should be used
to generate the synthetic data used by the estimation protocols to see if
these results can be replicated.
This work opens a line of research that could contribute to increasing the
reliability of resource estimation methods. It is possible to develop
causal, structural models of nonrenewable resources that incorporate
geologic, technical, and economic factors, and which endogenously generate
the complete life cycle. We have shown that it is possible to use such
models to evaluate various methods of estimating resources. The approach
helps resolve the apparent paradox of rising estimates and inexorably
declining resources. .
+~919-
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APPENDIX: PROTOCOL FOR THE GEOLOGIC ANALOGY METHOD
In the equations, the prefix 'G' denotes a quantity estimated by the
geologic analogy protocol; other variables denote the true values generated
by the model. A '<P>' denotes the assumption of perfect information.
GEURR, = GCUMPR, + GTRRR + GEATRR, + GEPD, (G1)
<P> GCUMPR, = CUMPR, (G2)
<P> GTRRR, = T!
RRR, = TRRR, (G3)
where
GEURR Estimated ultimate recoverable resource (bbls)
Hou
GCUMPR Estimated cumulative production (bbls)
GTRRR = Estimated technically recoverable resource remaining (bbls)
GEATRR = Gu additions to technically recoverable resource
bbls
GEFD = Estimated future discoveries (bbls)
CUMPR = Cumulative production (bbls)
TRRR = Technically recoverable resource remaining (bbls)
The expected ultimate recoverable resource is divided into four basic
eategories: cumulative production, technically recoverable reserves,
expected additions to technically recoverable reserves, and expected future
discoveries. The estimated values of cumulative production and technically
recoverable reserves are assumed to be equal to the true values.
GEATRR, = GETRRR, - GTRRR, (G4)
GETRRR, = GCUMATR *GEFR - GCUMPR, (G5)
<P> GCUMAIR, = CUMAIR, (G6)
GEFR, = GFR, + GETFR, (G7)
<P> GFR, = FR, (G8)
GEIFR, = (1-GFR)*£, (GEGFR,) £,(0)=0, £,'20 (G9)
GEGFR, = TREND(GFR,) (610)
where
GEATRR = Estimated additions to technically recoverable resource
(bbls)
GETRRR = Estimated expected technically recoverable resources
remaining (bbls)
GTRRR = Estimated technically recoverable resource remaining (bbls)
GCUMAIR = Estimated cumulative additions to identified resource
(bbls)
CUMALR = Cumulative additions to identifed resource (bbls)
GEFR Expected fraction recoverable (dimensionless)
GCUMPR Estimated cumulative production (bbls)
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GFR Estimated current fraction recoverable (dimensionless)
FR Fraction recoverable (dimensionless)
GEIFR = Expected increase in fraction recoverable (dimensionless)
GEGFR Expected growth in fraction recoverable (1/years)
TREND = Funetion to estimate growth rate of a variable
Technically recoverable reserves include all the known resource that can be
recovered with current technology, whether it is currently economic to do
so or not. Expected additions to technically recoverable reserves
represents the additional recovery from currently identified resources due
to anticipated advances in recovery technology. The expected addition is
given by the difference between what could be recovered at anticipated
levels of technology and what is currently recoverable. We assume perfect
knowledge of the quantity of identified resource and of the cumulative
original oil-in-place identified. Similarly, the current fraction
recoverable is assumed known.
The expected increase in the fraction recoverable is based on the expected
rate of technical progress. The expected rate of technical improvement is
based on the trend in the recovery fraction over the past ten years. We
assume changes in the trend in recovery factors are incorporated in the
forecast after an average lag of ten years. The lag stems from the time
required to become aware of new recovery techniques, to evaluate and build
confidence in their effectiveness, and for that information to diffuse
through the geological community and become enough a part of "conventional
wisdom" to be included in government projections.
The maximum possible addition to the fraction recoverable is, of course,
the fraction unrecoverable. The fraction of this maximum improvement that
is expected is nonlinearly related to the expected rate of technical
improvement. When the recovery fraction is not growing, no improvement in
technology is expected and the anticipated increase in the recovery
fraction is zero. When the growth rate is higher than 1.5 percent per
year, the expected increment in the fraction recoverable reaches a maximum,
assumed to be 49 percent of the fraction unrecoverable. (The USGS assumed
A maximum potential recovery factor of 60 percent compared to an average of
32 percent in 1975. Thus the anticipated improvement was expected to be 28
percentage points out of a maximum of 68, or .41 of the maximum.)
GEFD, = GPED, + GSED, (G11)
GPFD, = GFR *GEUR (G12)
GSFD, = GELFR,*GEUR, (G13)
where
GEFD = Expected future discoveries (bbls)
GPFD = Probable future discoveries (bbls)
GSFD = Speculative future discoveries (bbls)
GFR = Estimated current fraction recoverable (dimensionless)
GEUR = Estimated undiscovered resource (bbls)
GEIFR = Expected increase in fraction recoverable (dimensionless)
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Expected future recovery from unexplored areas is the least certain
component of any resource estimate. We have disaggregated the total into
two components: (1) the quantity of currently unidentified oil expected to
be recovered at current recovery factors (GPFD) and (2) the additional
quantity expected to be recovered at anticipated recovery levels (GSFD).
Both of these quantities depend directly on the estimate of unidentified
oil-in-place (GEUR).
GEUR, = GAU,*GFD, *GEYUA, (G14)
GAU, = GAS, - GAEL (615)
<P> GAB, = AB, (G16)
GAS, = £,(t) £,120 (617)
= 6
<P> GED, = FD, (618)
where
GEUR Estimated undiscovered resource (bbls)
GAU Estimated area unexplored (sq. mi.)
GFD = Estimated fraction discoverable (dimensionless)
GEYUA = Expected yield from unexplored area (bbls/sq. mi.)
GAS = Surveyed area of sedimentary basins (sq. mi)
GAE Estimated area explored (sq. mi.)
AE Area explored (sq. mi.)
FD = Fraction discoverable (dimensionless)
Estimated unidentified oil-in-place is the product of the area unexplored,
the fraction of that area in which exploration is feasible given current
technology, and the expected yield in that area. The fraction of
oil-in-place that is currently discoverable is assumed to be known exactly.
The area unexplored is given by the total global area in which sedimentary
basins are known to exist less the area already explored. The area in
which sedimentary basins are known to exist is specified exogenously.
Assumed to be quite small in 1900, knowledge of sedimentary basins expands
to 25 million square miles by 1980 (Grossling 1977) and is assumed to rise
an additional 20 percent to 30 million square miles by 2020. The area
actually explored is endogenously generated by the model and is related to
the cumulative resource identified. If oil were distributed uniformly over
the total area of sedimentary basins, and if exploration activity were no
better than random, the relationship between area explored and identified
oil-in-place would be linear. However, oil is distributed very unevenly,
and exploration activity is better than random. Giant and supergiant
fields account for one percent of known fields but 75 percent of known
reserves and 55 to 70 percent of current production (Klemme 1977). The
assumed curve is therefore highly nonlinear.
GEYUA, = GHD*GAWD*CRYE, (G19)
GWD = .5 (619.1)
GAWD = 6000 (619.2)
= GHYE, *GPHYS
GEYE, = GHYE, *GPHYS, (G20)
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GHYE = DLINE3(YE, ,GTARY) (G21)
GTAEY = 10 (21.1)
EHYE,. = £ f = '
GFHYE,. 3(6TY,) 300) 1, £5120 (G22)
GTY, = TREND(YE,) (G23)
where
GEYUA = Expected yield from unexplored area (bbls/sq. mi.)
GWD = Estimated well density (wells/sq. mi.)
GAWD = Estimated average well depth (ft/well)
GEYE = Expected yield to exploration (bbls/ft)
GHYE = Estimated historical yield to exploration (bbls/ft)
GFHYE = Fraction of historical yield expected (dimensionless)
DLINF3 = Third order exponential information smoothing
YE = Yield to exploration (bbls/ft)
GTAEY = Time to adjust estimates of historical yield (years)
GTY Estimated trend in yield to exploration (1/years)
TREND = Function to estimate growth rate of a variable
The expected yield of oil-in-place per square mile of unexplored area is
based on the density of wells, the average well depth required to explore a
region fully, and the expected yield per foot drilled. We assume average
well density and depth to be one well every two square miles and 6000 feet
per well, respectively (Gillette 1974). Expected yield per well is based
on historic yields, discounted according to past trends in the yield. The
historic yield is assumed to lag the actual yield by ten years. The delay
reflects the time required to compile yield data, to separate a systematic
change in the yield from the noise, and for the revised yield estimates to
become accepted throughout the geologic community. For example, the
largest decline in yield per foot drilled in the United States occurred
between 1940 and 1950. Hubbert pointed out the declining trend in yield
per foot in the United States in 1962. Until 1955, the USGS continued to
use the so-called "Zapp hypothesis" of constant future yield. Even then
soeye assumed a value that exceeded more recent yields (Gillette 1974,
129):
That year, the USGS noted a 'definite decline’ in discoveries and
postulated now that oil would, on the average, prove to be only
half--not equally--as abundant in unexplored rock as in explored
rock. Now this number is in contention, with Hubbert claiming that
it's at least five times too large for onshore terrain. fuses
director] McKelvey acknowledges that the figure of one-half was
largely a 'subjective judgnent' and another official describes it as
‘mostly a guess.!
It is assumed in the model that the expected yield in unexplored areas is
discounted below the historic yield when the yield is perceived to be
falling. In the USGS study, the choice of the discount factor was highly
subjective. The Survey acknowledged that
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D-3432-1
++.the proper [discount factor] is open to conjecture. The fraction
can range from one (or greater) to zero. Precedents exist for both
1.0 and 0.5. Qualitatively, 1.0 seems optimistic but not
unreasonable; 0.5 seems conservative; less than 9.5 seems pessimistic
(Mallory, 'Synopsis of Procedure' cited in MIT 1982, TII-3-12).
The assumed discount becomes progressively larger as the decline rate
grows.
NOTES
Oo. We gratefully acknowledge the helpful criticisms of M. K. Hubbert,
Gordon Kaufman, Robert Fildes, and three anonymous referees.
1. The discussion of Warman's and Odell's views is based on Seidl 1977.
2. The oscillation stems from delays in adjusting energy demand to price
and in bringing investment in exploration to fruition. No
significance should be attached to the timing of the resulting gluts.
3. An interesting extension of the present work would apply alternative
functional forms which do not presume a symmetrical life cycle, such
as the Gompertz, Weibull, or Richards curves, to see if the lead
provided by the logistic curve can be extended.
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Dynamics Modeling With DYNAMO. Cambridge: The MIT Press.
~926-
D-3432-1
Ryan, J. M. (1966) "Limitations of Statistical Methods for Predicting
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1450-A, Washington, D.C.
2
Warman, H. R. (1972) "The Future of 011," Geographical Journal 138, 287-97.
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Zapp, A. D. (1962) "Future Petroleum Producing Capacity of the United
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-927~
D-3432-1
(BILLION BARRELS)
4000
3000
2000 ° °
1000
L £ 1 5
1940 1950 1960 1970 1980
YEAR A-32%0
Exhibit 1: Estimates of the world’s ultimate
recoverable petroleum resource. Source: Seidl 1977.
D-3432-1 908
(BILLION BARRELS )
in the coterminous United States and adjacent offshore
area. Source: MIT 1982, II-1-3.
ESTIMATES OF THE
ULTIMATE RECOVERABLE
RESOURCE
ULTIMATE
RECOVERABLE - ~
RESOURCE \ #7 ~S
/ ty
-
Soe
o ue
re] Va
c a
= 4
a va
7
al
L CUMULATIVE
PRODUCTION
1940 Tine
A. 3203
Exhibit 3: Possible paths of estimates of the world
ultimate recoverable resource.
600,
°
o. i
500} . \
|
. :
o° i
400+ . :
300-
re
200; °
: H. :
1ooF 3
3 og 1 n n n n 5
1900 1910 1920 1930 1940 1950 1960 1970 1980
YEAR means
Exhibit 2: Estimates of ultimate recoverable petroleum
-929-
D-3432-1
EXPLORATION
ANDO DISCOVERY
PRODUCTION ANDO
USAGE
IDENTIFIED AND
RECOVERABLE
RESOURCES
PRODUCTION RATE
RESERVE /
PRODUCTION RATIO
UNDISCOVERED
RESOURCES
DISCOVERY RATE
YIELD
° CAPACITY
UTILIZATION
IDENTIFICATION
OF RESOURCE
* capacity
UTILIZATION
\ REVENUES
EONS. 7-19 \ EONS. 20-35
ee és costs San ET
4 ‘ \ INVESTMENT | a
U INVESTMENT IN { IN PRODUCTION | | .
| EXPLORATION y \ .
1
' PRICE, REVENUE, costs | ’
\ ANO INVESTMENT ’ \ \
1 {
! '
PRICE INFORMATION
REVENUE
INVESTMENT
DECISIONS IN
EXPLORATION,
PRODUCTION, AND
TECHNOLOGY
'
EFFECTIVENESS
OF DISCOVERY — — —
TECHNOLOGY
a7 4
i
EFFECTIVENESS.
—— — OF RECOVERY
TECHNOLOGY
Ly
1
I
t
1
1
SUPPLY i
1
1
1
!
i
|
i)
DEMAND
INFORMATION
EONS. 56-72 Ne
INVESTMENT
1
S 1
IN TECHNOLOGY ERCE !
TECHNOLOGY q OEMAND AND
1 SUBSTITUTION
*@ FRACTION
DISCOVERABLE CAPITAL STOCK
FRACTION ’
RECOVERABLE Ol NTENSIT OF
PROOUCTIVITY OF
INVESTMENTS IN SUBSTITUTE PRICE
EXPLORATION ENERGY MARKET
AND DISCOVERY SHARES.
Ae 3zar
_ £ONS. 46-55
f
\
1
\
1
\
\
\
!
i)
\
t
'
\
\
1
i)
'
1
\
f
EONS. 36-45 |
. !
4: Model overview.
-930-
D-3432-1
cr
CLASSIFICATION CF RESOURCES
TOTAL RESOURCES
tOERTIFIED | URDISCOVERED
DER CRSTRATED LYPOTKETICAL SFECULATIVE
(i CROWS UR UNDISCOVERED
REASURED IMGICATED INFERRED DISTRICTS) DISTRICTS)
3 F A
=
2 RESERVE
8 BASE Yf
o
“ | 1} +. Siz
z q i wa [S
z #\s
g oie
els ais
=/= ot
Sie zig
Ste ale
ote wie
wi] = 2/2
aie ois
alé zie
<
4
2 | i l !
INCREASIKG DECREE OF
GEOLOGIC ASSURARCE
SOURCE. BUREAU OF MINES A - 330%
~-931-
id
FRACTI
nse’
ENT
IN EXPLORATION, 13
UNIT COST OF
ee
EXPLORATION, 61 Co
DESIRED INVESTMENT
UNIT COST OF
PRODUCTION, 62
COSTS, 60
ADDITIONS TO
IDENTIFIED
RESOURCE, & PRODUCTION, 2t
UNDISCOVERED . IDENTIFIED
RESOURCE RESOURCE
CAPACITY UTILIZATION
IN EXPLORATION, 9
/ oe \
/ ‘
/ DESIRED
DISCOVERY
POTENTIAL RATE, 69
DISCOVERY EXPECTED
RATE, 13 GROWTH IN
PRODUCTION,
72
IN EXPLORATION, 67
<
SUBSTITUTE
PRICE, 43.1
INVESTMENT IN
EXPLORATION, 12
NATURAL
PETROLEUM RISE
PRICE, 58
D-34352-1
~932-
REVENUES, 57 FRACTION OF REVENUES
INVESTED IN TECHNOLOGY,
fo 56.1
INVESTMENT IN.
TECHNOLOGY, 56
INVESTMENT INVESTMENT
iN DISCOVERY IN RECOVERY
TECHNOLOGY, $3 TECRNOLOGY, 54
DISCOVERY RECOVERY
TECHNOLOGY FRACTION TECHNOLOGY
DEVELOPMENT, INVESTED IN DEVELOPMENT
TIME, 49.1 DISCOVERY. TIME, 52.1
TECHNOLOGY, 55
FRACTION FRACTION
DISCOVERABLE RECOVERABLE
a7| soy
UNDISCOVERED IDENTIFIED
RESOURCE, 7 \ yo 18
TECHNICALLY DISCOVERABLE TECHNICALLY RECOVERABLE.
RESOURCE REMAINING , 16
CUMULATIVE, ff
RESOURCE
IDENTIFIED, 17
PRODUCTIVITY OF
INVESTMENT IN
EXPLORATION, 13
RESOURCE REMAINING, 19.
\ CUMULATIVE
PRODUCTION, 20
PRODUCTIVITY OF
INVESTMENT IN
PRODUCTION,
29
9335
NATURAL PETROLEUM
CEMANO, 36
4 ‘
\
—_—,
TOTAL PETROLEUM
DEMAND, 37 MARKET
SHARE
44
SUBSTITUTE
CAPITAL
gapiTa 7" PRICE, 43.1
3e INTENSITY
OF CAPITAL NATURAL
40 PETROLEUM
PRICE, 58
AVERAGE wa \
PETROLEUM costs, 60
PRICE, 43
FRACTIONAL
GROWTH IN,
CAPITAL, 39
3300
-934-
D=3432-1
Exhibit 9. Major Parametric Assumptions
Quantity Value
Total resource (billion bbls) 5042
Initial undiscovered resource (billion bbls) 5000
Exploration development delay (years) 4
Average technology development time (years) 6
Initial fraction discoverable (dimensionless) 0.1
Maximum fraction discoverable (dimensionless) 1.0
Initial fraction recoverable (dimensionless) 0.2
Maximum fraction recoverable (dimensionless) 0.6
Growth rate of capital stock (1/years)*
1900 204
1925 2045
1950 205
1975 205
2000 O04
2025 +03
2050 202
2075 201
2100 0.00
Long run price elasticity of petroleum demand
(dimensionless) 0.75
Average lag in adjustment of petroleum demand
to price (years) 15
Price of petroleum substitutes ($/bb1) 30
Average lag in development of petroleum
substitutes (years) 10
Linear interpolation between values.
-935-
Exhibit 10b:
YEAR
reserve/production ratio.
Base run - resource levels and the
D-3432-4
100 1
ADDITIONS TO an TOTAL
IDENTIFIED —_ | oN PETROLEM
RESOURCE ~~}, \ DEMAND F
7 \ 2
= 75 ( 4 2
qt z 1
WwW fH ‘
= ! \ SYNTHETIC
a i \ PETROLEUM
ra ! ‘ PRODUCTION
!
<q 50 ,
ao 1
3 i
3 / NATURAL PETROLEUM 4]
2 fi PRODUCTION f
cS fe 4
a) az .
.
i ost |
a i
1900 1940 1980 2020 2060 2100
YEAR
Ca: Ease run = petroleum dex » Production,
and discovery.
5000 ; 40
oN RESERVE / PRODUCTION
| UNDISCOVERED ee al | |
_ | RESOURCE i Wns x | | 3
a ! ‘ ! q
Zi 3750 t <> + 1 30
& l | l
< : S| | 3
oO t nN } a
z ; S| a
g | | ie |
g 2500 b me = +20
a “Semaine: ae if 1
S | IDENTIFIED
a RESOURCE i
2 | [RECOVERABLE | i
a i [RESOURCE \
(1250! ~ ; ———| 110
e | fF} i i
=a i
—
O be a
1900 1940 1980 2020 2080 2100
RESERVE/ PRODUCTION RATIO (YEARS)
FRACTIONS DISCOVERABLE & RECOVERABLE
PETROLEUM PRICE ($/8BL)
-936-
D-3432-1
100 200
eT i
ae
7 FRACTION DISCOVERABLE 4
75 | 21150
‘ IN r\
; / y, |_- FRACTION RECOVERABLE
50 a 100
”
a
e g
2
YIELD FROM EXPLORATION q
125 1 i 50
! |
| |
OL_ °
1900 1940 1980 2020 2060 2100
YEAR
Base run ~ technology and yield.
80 — 100
ne —.
! NATURAL
NATURAL /- . PETROLEUM fl
PETROLEUM \ PRICE #
MARKET SHARE ‘
60 75
AVERAGE.
PETROLEUM
Exhibit 10d:
YEAR
Base run - prices and market shares.
YIELD FROM EXPLORATION (8BLS./FOOT)
MARKET SHARE (PERCENT)
-937-
D-3432-1
Exhibit 11. Estimates of Ultimate Recoverable Resource
by the Hubbert Life Cycle Method
Range Estimated Q* a Re Percent Error?
(billion bbls)
1900 - 1970 + co +99947
6000 299918
1900 - 1980 6600 «99937
4 9300 +999358 141
5500 +99938 104
5400 +99937
1900 - 1990 3900 +99930
3800 °99932
+ 2700 99932 37
3600 99932 34
3500 «99932
3400 +99930
1900 - 2000 3100 +99923
+ 3000 -99925 11
2900 -99921
1900 - 2010 2850 99924
+ 2800 -99927 4
2750 99921
1900 - 2020 2800 299912
+ 2750 +99933 2
2700 299922
1900 - 2030 2800 ~99869
+ 2750 99941 2
2700 -99902
1900 - 2040 2750 -99873
+ 2700 -99906 )
* 2650 97445
4900 - 2050 2750 .97461
+ 2700 299947 0
2650 99644
® a's! indicates the optimal estimate.
* * *
100*(Estimated Q - True Q )/True Q
-938-
® Error computed by comparison with ultimate quantity recovered.
D-3432-1
Exhibit 12, Estimates of the Ultimate Recoverable Resource
by the Geologic Analogy Method
Year GEU; Error* GEFR FR GEYE YE
(10° bbls) (%) (dimensionless) (bbls/ft) (bbls/ft)
1900 16 -99 20 +20 66 66
1940 598 -78 223 221 175 196
1950 4177 56 225 222 192 187
1960 1952 -28 029 024 181 140
1970 2668 -1 -40 227 124 81
1980 3280 21 -60 35 66 48
1990 3361 24 .67 44 40 43
2000 3521 30 70 251 32 27
2010 3552 32 73 55 22 25
2020 3545 31 72 57 24 20
2030 3217 19 266 58 17 19
2040 3061 13 62 58 19 23
2050 3008 11 -60 259 23 26
2060 3012 12 -60 259 26 28
2070 3019 12 59 +59 28 29
. 2080 3024 12 59 59 29 30
2090 3026 12 259 259 30 30
2100 3028 12 59 259 30 30
GEUR = Estimated Ultimate Recoverable Resource
GEFR = Expected Fraction Recoverable
FR = Fraction Recoverable
GEYE = Expected Yield to Exploration
YE = Yield to Exploration
D-3432-1
(BILLION BARRELS)
(BILLION BARRELS)
4000
3000
2000
1000
4000
3000
2000
1000
-939-
T
ESTIMATED ULTIMATE
RECOVERABLE RESOURCE
SPECULATIVE
FUTURE
DISCOVERIES
ie}
1900
CUMULATIVE
PRODUCTION
a
|
1940
2020
YEAR
13:
recoverable resource.
Geologic analogy estimates of the ultimate
MODEL - GENERATED
ESTIMATES
HISTORICAL
ESTIMATES ° ——
OrL
Exhibit 14:
historically observed estimates.
1960
Comparison of model-generated estimates and
(BILLION BARRELS)
(BILLION BARRELS)
-940-
D-3432=4
4000 =] — aaa
RECOVERABLE RESOURCE
REMAINING
4
3000 S|
GEOLOGIC ANALOGY
ESTIMATE OF
RECOVERABLE 4
RESOURCE 4
REMAINING si
| :
if
|
- i
i
“2060 2100
4000 T
e
GEOLOGIC 3
ANALOGY a
ESTIMATE a
301 f ae =
00 d
/| fo |
/ HUBBERT :
ESTIMATE |
2000 7
, t
/ | 1 o\ : i
/ i | cumuvative | i
/ : : PRODUCTION |
son of
ates and true
Qo
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