The Hubbert curve is an approximation of the production rate of a resource over time. It is a symmetric
logistic distribution
Logistic may refer to:
Mathematics
* Logistic function, a sigmoid function used in many fields
** Logistic map, a recurrence relation that sometimes exhibits chaos
** Logistic regression, a statistical model using the logistic function
** Logit, ...
curve,
often confused with the "normal"
gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form
f(x) = \exp (-x^2)
and with parametric extension
f(x) = a \exp\left( -\frac \right)
for arbitrary real constants , and non-zero . It is n ...
. It first appeared in "Nuclear Energy and the Fossil Fuels," geologist
M. King Hubbert
Marion King Hubbert (October 5, 1903 – October 11, 1989) was an American geologist and geophysicist. He worked at the Shell research lab in Houston, Texas. He made several important contributions to geology, geophysics, and petroleum geolog ...
's 1956 presentation to the
American Petroleum Institute
The American Petroleum Institute (API) is the largest U.S. trade association for the oil and natural gas industry. It claims to represent nearly 600 corporations involved in production, refinement, distribution, and many other aspects of the pet ...
, as an idealized symmetric curve, during his tenure at the
Shell Oil Company
Shell USA, Inc. (formerly Shell Oil Company, Inc.) is the United States-based wholly owned subsidiary of Shell plc, a UK-based transnational corporation " oil major" which is amongst the largest oil companies in the world. Approximately 18,000 ...
.
It has gained a high degree of popularity in the scientific community for predicting the
depletion of various natural resources. The curve is the main component of
Hubbert peak theory
The Hubbert peak theory says that for any given geographical area, from an individual oil-producing region to the planet as a whole, the rate of petroleum production tends to follow a bell-shaped curve. It is one of the primary theories on peak ...
, which has led to the rise of
peak oil concerns. Basing his calculations on the peak of oil well discovery in 1948, Hubbert used his model in 1956 to create a curve which predicted that oil production in the
contiguous United States
The contiguous United States (officially the conterminous United States) consists of the 48 adjoining U.S. states and the Federal District of the United States of America. The term excludes the only two non-contiguous states, Alaska and Hawaii ...
would peak around 1970.
Shape
The prototypical Hubbert curve is a
probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can ...
of a
logistic distribution
Logistic may refer to:
Mathematics
* Logistic function, a sigmoid function used in many fields
** Logistic map, a recurrence relation that sometimes exhibits chaos
** Logistic regression, a statistical model using the logistic function
** Logit, ...
curve. It is not a
gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form
f(x) = \exp (-x^2)
and with parametric extension
f(x) = a \exp\left( -\frac \right)
for arbitrary real constants , and non-zero . It is n ...
(which is used to plot
normal distribution
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
:
f(x) = \frac e^
The parameter \mu ...
s), but the two have a similar appearance. The density of a Hubbert curve approaches zero more slowly than a gaussian function:
:
The graph of a Hubbert curve consists of three key elements:
# a gradual rise from zero resource production that then increases quickly
# a "
Hubbert peak
The Hubbert peak theory says that for any given geographical area, from an individual oil-producing region to the planet as a whole, the rate of petroleum production tends to follow a bell-shaped curve. It is one of the primary theories on peak ...
", representing the maximum production level
# a drop from the peak that then follows a steep production decline.
The actual shape of a graph of real world production trends is determined by various factors, such as development of enhanced production techniques, availability of competing resources, and government regulations on production or consumption. Because of such factors, real world Hubbert curves are often not symmetrical.
Application
Peak oil
Using the curve, Hubbert modeled the rate of petroleum production for several regions, determined by the rate of new oil well discovery, and extrapolated a world production curve.
The relative steepness of decline in this projection is the main concern in peak oil discussions. This is because a steep drop in the production implies that global oil production will decline so rapidly that the world will not have enough time to develop sources of energy to replace the energy now used from oil, possibly leading to drastic social and economic impacts.
Other resources
Hubbert models have been used to predict the production trends of various resources, such as
natural gas
Natural gas (also called fossil gas or simply gas) is a naturally occurring mixture of gaseous hydrocarbons consisting primarily of methane in addition to various smaller amounts of other higher alkanes. Low levels of trace gases like carbo ...
(Hubbert's attempt in the late 1970s resulted in an inaccurate prediction that natural gas production would fall dramatically in the 1980s),
Coal
Coal is a combustible black or brownish-black sedimentary rock, formed as rock strata called coal seams. Coal is mostly carbon with variable amounts of other elements, chiefly hydrogen, sulfur, oxygen, and nitrogen.
Coal is formed when dea ...
,
fissionable materials,
Helium
Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
, transition metals (such as
copper
Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkis ...
), and
water
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...
. At least one researcher has attempted to create a Hubbert curve for the
whaling
Whaling is the process of hunting of whales for their usable products such as meat and blubber, which can be turned into a type of oil that became increasingly important in the Industrial Revolution.
It was practiced as an organized industry ...
industry and caviar, while another applied it to
cod
Cod is the common name for the demersal fish genus '' Gadus'', belonging to the family Gadidae. Cod is also used as part of the common name for a number of other fish species, and one species that belongs to genus ''Gadus'' is commonly not call ...
.
[Jean Laherrere. ]
Multi-Hubbert Modeling
'' July, 1997.
Critique
After the predicted early-1970s peak of oil production in the U.S., production declined over the following 35 years in a pattern closely matching the Hubbert curve. However, new extraction methods began reversing this trend beginning in the mid-2000s decade, with production reaching 10.07 million b/d in November 2017 – the highest monthly level of crude oil production in U.S. history. As such, the Hubbert curve has to be calculated separately for different oil provinces, whose exploration has started at a different time, and oil extracted by new techniques, sometimes called
unconventional oil
Unconventional oil is petroleum produced or extracted using techniques other than the conventional method (oil well). Industry and governments across the globe are investing in unconventional oil sources due to the increasing scarcity of conventio ...
, resulting in individual Hubbert cycles.
The Hubbert Curve for US oil production is generally measured in years.
See also
*
Bioeconomics (biophysical)
Thermoeconomics, also referred to as biophysical economics, is a school of heterodox economics that applies the laws of statistical mechanics to economic theory. Thermoeconomics can be thought of as the statistical physics of economic value and ...
*
Energy accounting
*
Gaussian function, a "bell curve" shape
*
Thermoeconomics
Thermoeconomics, also referred to as biophysical economics, is a school of heterodox economics that applies the laws of statistical mechanics to economic theory. Thermoeconomics can be thought of as the statistical physics of economic value and ...
References
{{reflist
External links
The Hubbert Curve: Its Strengths And Weaknessesarticle by
Jean Laherrère Jean H. Laherrère (* May 30, 1931) is a petroleum engineer and consultant, best known as the co-author of an influential 1998 Scientific American article entitled ''The End of Cheap Oil''.
Career
Laherrère studied at the Ecole Polytechnique and ...
.
Hubbert Mathfurther mathematical manipulations by a Stanford professor
1956 introductions
Equations
Economics curves
Peak oil
Continuous distributions