The Hubbert curve is an approximation of the production rate of a resource over time. It is a symmetric
logistic distribution curve,
often confused with the "normal"
gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function (mathematics), function of the base form
f(x) = \exp (-x^2)
and with parametric extension
f(x) = a \exp\left( -\frac \right)
for arbitrary real number, rea ...
. It first appeared in "Nuclear Energy and the Fossil Fuels," geologist
M. King Hubbert'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 extraction of petroleum, production, oil refinery, refinement, pipeline ...
, as an idealized symmetric curve, during his tenure at the
Shell Oil Company.
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, 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, also known as the U.S. mainland, officially referred to as the conterminous United States, consists of the 48 adjoining U.S. states and the District of Columbia of the United States in central North America. The te ...
would peak around 1970.
Shape
The prototypical Hubbert curve is a
probability density function
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a Function (mathematics), function whose value at any given sample (or point) in the sample space (the s ...
of a
logistic distribution curve. It is not a
gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function (mathematics), function of the base form
f(x) = \exp (-x^2)
and with parametric extension
f(x) = a \exp\left( -\frac \right)
for arbitrary real number, rea ...
(which is used to plot
normal distribution
In probability theory and 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 ...
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", 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 fossil gas, methane gas, and gas) is a naturally occurring compound of gaseous hydrocarbons, primarily methane (95%), small amounts of higher alkanes, and traces of carbon dioxide and nitrogen, hydrogen sulfide and helium ...
(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 Chemical element, elements, chiefly hydrogen, sulfur, oxygen, and nitrogen.
Coal i ...
,
fissionable materials,
Helium
Helium (from ) is a chemical element; it has chemical symbol, symbol He and atomic number 2. It is a colorless, odorless, non-toxic, inert gas, inert, monatomic gas and the first in the noble gas group in the periodic table. Its boiling point is ...
, transition metals (such as
copper
Copper is a chemical element; it has symbol Cu (from Latin ) 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 pinkish-orang ...
), and
water
Water is an inorganic compound with the chemical formula . It is a transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance. It is the main constituent of Earth's hydrosphere and the fluids of all known liv ...
. At least one researcher has attempted to create a Hubbert curve for the
whaling
Whaling is the hunting of whales for their products such as meat and blubber, which can be turned into a type of oil that was important in the Industrial Revolution. Whaling was practiced as an organized industry as early as 875 AD. By the 16t ...
industry and caviar, while another applied it to
cod.
[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 and gas) reservoirs, or unconventional resources (resource plays) are Petroleum geology, accumulations where oil and gas Phase (matter), phases are tightly bound to the rock fabric by strong capillary action, capillary forces, ...
, resulting in individual Hubbert cycles.
The Hubbert Curve for US oil production is generally measured in years.
See also
*
Bioeconomics (biophysical)
*
Energy accounting
*
Gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function (mathematics), function of the base form
f(x) = \exp (-x^2)
and with parametric extension
f(x) = a \exp\left( -\frac \right)
for arbitrary real number, rea ...
, a "bell curve" shape
*
Thermoeconomics
References
External links
The Hubbert Curve: Its Strengths And Weaknessesarticle by
Jean Laherrère.
Hubbert Mathfurther mathematical manipulations by a Stanford professor
{{Webarchive, url=https://web.archive.org/web/20190801024938/http://www.hubbertpeak.com/hubbert/Bibliography.htm , date=2019-08-01
1956 introductions
Equations
Economics curves
Peak oil
Continuous distributions