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energy economics Energy economics is a broad scientific subject area which includes topics related to supply and use of energy in societies. Considering the cost of energy services and associated value gives economic meaning to the efficiency at which energ ...
and
ecological energetics Energy flow is the flow of energy through living things within an ecosystem. All living organisms can be organized into producers and consumers, and those producers and consumers can further be organized into a food chain. Each of the levels wi ...
, energy return on investment (EROI), also sometimes called energy returned on energy invested (ERoEI), is the
ratio In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
of the amount of usable
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of ...
(the ''
exergy In thermodynamics, the exergy of a system is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir, reaching maximum entropy. When the surroundings are the reservoir, exergy is the pot ...
'') delivered from a particular energy resource to the amount of exergy used to obtain that energy resource. Arithmetically the EROI can be defined as: : EROI = \frac. When the EROI of a source of energy is less than or equal to one, that energy source becomes a net "energy sink", and can no longer be used as a source of energy. A related measure, called energy stored on energy invested (ESOEI), is used to analyse storage systems. To be considered viable as a prominent fuel or energy source a fuel or energy must have an EROI ratio of at least 3:1.


History

The energy analysis field of study is credited with being popularized by
Charles A. S. Hall Charles A. S. Hall (born 1943) is an American systems ecologist and ESF Foundation Distinguished Professor at State University of New York in the College of Environmental Science & Forestry. Biography Hall was born near Boston, and receiv ...
, a
Systems ecology Systems ecology is an interdisciplinary field of ecology, a subset of Earth system science, that takes a holistic approach to the study of ecological systems, especially ecosystems. Systems ecology can be seen as an application of general syst ...
and biophysical economics professor at the
State University of New York The State University of New York (SUNY, , ) is a system of public colleges and universities in the State of New York. It is one of the largest comprehensive system of universities, colleges, and community colleges in the United States. Led by ...
. Hall applied the biological methodology, developed at an Ecosystems Marine Biological Laboratory, and then adapted that method to research human industrial civilization. The concept would have its greatest exposure in 1984, with a paper by Hall that appeared on the cover of the journal ''Science''.


Application to various technologies


Photovoltaic

The issue is still subject of numerous studies, and prompting academic argument. That's mainly because the "energy invested" critically depends on technology, methodology, and system boundary assumptions, resulting in a range from a maximum of 2000 kWh/m2 of module area down to a minimum of 300 kWh/m2 with a median value of 585 kWh/m2 according to a meta-study from 2013. Regarding output, it obviously depends on the local
insolation Solar irradiance is the power per unit area ( surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument. Solar irradiance is measured in watts per square metre ...
, not just the system itself, so assumptions have to be made. Some studies (see below) include in their analysis that photovoltaic produce electricity, while the invested energy may be lower grade
primary energy Primary energy (PE) is an energy form found in nature that has not been subjected to any human engineered conversion process. It is energy contained in raw fuels, and other forms of energy, including waste, received as input to a system. Prim ...
. A 2015 review in
Renewable and Sustainable Energy Reviews ''Renewable and Sustainable Energy Reviews'' is a peer-reviewed scientific journal covering research on sustainable energy. It is published in 12 issues per year by Elsevier and the editor-in-chief is Aoife M. Foley (Queen's University Belfast). Ac ...
assessed the energy payback time and EROI of a variety of PV module technologies. In this study, which uses an insolation of 1700 kWh/m2/yr and a system lifetime of 30 years, mean harmonized EROIs between 8.7 and 34.2 were found. Mean harmonized energy payback time varied from 1.0 to 4.1 years. In 2021, the Fraunhofer Institute for Solar Energy Systems calculated an energy payback time of around 1 year for European PV installations (0.9 years for Catania in Southern Italy, 1.1 years for Brussels) with wafer-based silicon PERC cells.


Wind turbines

In the scientific literature EROIs wind turbines is around 16 unbuffered and 4 buffered. Data collected in 2018 found that the EROI of operational wind turbines averaged 19.8 with high variability depending on wind conditions and wind turbine size. EROIs tend to be higher for recent wind turbines compared to older technology wind turbines. Vestas reports an EROI of 31 for its V150 model wind turbine.


Oil sands

Because much of the energy required for producing oil from oil sands (bitumen) comes from low value fractions separated out by the upgrading process, there are two ways to calculate EROI, the higher value given by considering only the external energy inputs and the lower by considering all energy inputs, including self generated. One study found that in 1970 oil sands net energy returns was about 1.0 but by 2010 had increased to about 5.23.


Conventional oil

Conventional sources of oil have a rather large variation depending on various geologic factors. The EROI for refined fuel from conventional oil sources varies from around 18 to 43.


Shale oil

Due to the process heat input requirements for shale oil harvesting, the EROI is much lower than for conventional oil sources. Typically natural gas is used, either directly combusted for process heat or used to power an electricity generating turbine, which then uses electrical heating elements to heat the underground layers of shale to produce oil from the kerogen. Resulting EROI is typically around 1.4-1.5. Economically, oil shale might be viable due to the effectively free natural gas on site used for heating the kerogen, but opponents have debated that the natural gas could be extracted directly and used for relatively inexpensive transportation fuel rather than heating shale for a lower EROI and higher carbon emissions.


Oil liquids

The weighted average standard EROI of all oil liquids (including coal-to-liquids, gas-to-liquids, biofuels, etc.) is expected to decrease from 44.4 in 1950 to a plateau of 6.7 in 2050.


Natural gas

The standard EROI for natural gas is estimated to decrease from 141.5 in 1950 to an apparent plateau of 16.8 in 2050.


Non-manmade energy inputs

The natural or primary energy sources are not included in the calculation of energy invested, only the human-applied sources. For example, in the case of biofuels the
solar insolation Solar irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument. Solar irradiance is measured in watts per square metre ...
driving
photosynthesis Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities. Some of this chemical energy is stored in ...
is not included, and the energy used in the stellar synthesis of
fissile In nuclear engineering, fissile material is material capable of sustaining a nuclear fission chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of thermal energy. The predominant neutron energy may be t ...
elements is not included for
nuclear fission Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radio ...
. The energy returned includes only human usable energy and not wastes such as
waste heat Waste heat is heat that is produced by a machine, or other process that uses energy, as a byproduct of doing work. All such processes give off some waste heat as a fundamental result of the laws of thermodynamics. Waste heat has lower utilit ...
. Nevertheless, heat of any form can be counted where it is actually used for heating. However the use of waste heat in
district heating District heating (also known as heat networks or teleheating) is a system for distributing heat generated in a centralized location through a system of insulated pipes for residential and commercial heating requirements such as space heating ...
and
water desalination Desalination is a process that takes away mineral components from saline water. More generally, desalination refers to the removal of salts and minerals from a target substance, as in soil desalination, which is an issue for agriculture. Salt ...
in
cogeneration Cogeneration or combined heat and power (CHP) is the use of a heat engine or power station to generate electricity and useful heat at the same time. Cogeneration is a more efficient use of fuel or heat, because otherwise- wasted heat from elec ...
plants is rare, and in practice it is often excluded in EROI analysis of energy sources.


Competing methodology

In a 2010 paper by Murphy and Hall, the advised extended Ext"boundary protocol, for all future research on EROI, was detailed. In order to produce, what they consider, a more realistic assessment and generate greater consistency in comparisons, than what Hall and others view as the "weak points" in a competing methodology. In more recent years, however, a source of continued controversy is the creation of a different methodology endorsed by certain members of the IEA which for example most notably in the case of
photovoltaic solar panel A solar cell, or photovoltaic cell, is an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon.
s, controversially generates more favorable values. In the case of photovoltaic solar panels, the IEA method tends to focus on the energy used in the factory process alone. In 2016, Hall observed that much of the published work in this field is produced by advocates or persons with a connection to business interests among the competing technologies, and that government agencies had not yet provided adequate funding for rigorous analysis by more neutral observers.


Relationship to net energy gain

EROI and '' Net energy (gain)'' measure the same quality of an energy source or sink in numerically different ways. Net energy describes the amounts, while EROI measures the ratio or efficiency of the process. They are related simply by : \hbox \div \hbox = EROI or : (\hbox \div \hbox ) + 1 = EROI For example, given a process with an EROI of 5, expending 1 unit of energy yields a net energy gain of 4 units. The break-even point happens with an EROI of 1 or a net energy gain of 0. The
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
to reach this break-even point is called energy payback period (EPP) or
energy payback time Net Energy Gain (NEG) is a concept used in energy economics that refers to the difference between the energy expended to harvest an energy source and the amount of energy gained from that harvest. The net energy gain, which can be expressed in jo ...
(EPBT).


Economic influence

Although many qualities of an energy source matter (for example oil is energy-dense and transportable, while wind is variable), when the EROI of the main sources of energy for an economy fall that energy becomes more difficult to obtain and its
relative price A relative price is the price of a commodity such as a good or service in terms of another; i.e., the ratio of two prices. A relative price may be expressed in terms of a ratio between the prices of any two goods or the ratio between the price o ...
may increase. In regard to fossil fuels, when oil was originally discovered, it took on average one barrel of oil to find, extract, and process about 100 barrels of oil. The ratio, for discovery of fossil fuels in the United States, has declined steadily over the last century from about 1000:1 in 1919 to only 5:1 in the 2010s. Since the invention of agriculture, humans have increasingly used exogenous sources of energy to multiply human muscle-power. Some historians have attributed this largely to more easily exploited (i.e. higher EROI) energy sources, which is related to the concept of energy slaves.
Thomas Homer-Dixon Thomas Homer-Dixon (born 1956) is a Canadian political scientist and author who researches threats to global security. He is the founder and Executive Director of the Cascade Institute at Royal Roads University in Victoria, British Columbia. He is ...
argues that a falling EROI in the Later Roman Empire was one of the reasons for the collapse of the Western Empire in the fifth century CE. In "The Upside of Down" he suggests that EROI analysis provides a basis for the analysis of the rise and fall of civilisations. Looking at the maximum extent of the
Roman Empire The Roman Empire ( la, Imperium Romanum ; grc-gre, Βασιλεία τῶν Ῥωμαίων, Basileía tôn Rhōmaíōn) was the post-Roman Republic, Republican period of ancient Rome. As a polity, it included large territorial holdings aro ...
, (60 million) and its technological base the agrarian base of Rome was about 1:12 per hectare for wheat and 1:27 for alfalfa (giving a 1:2.7 production for oxen). One can then use this to calculate the population of the Roman Empire required at its height, on the basis of about 2,500–3,000
calories The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of ...
per day per person. It comes out roughly equal to the area of food production at its height. But ecological damage (
deforestation Deforestation or forest clearance is the removal of a forest or stand of trees from land that is then converted to non-forest use. Deforestation can involve conversion of forest land to farms, ranches, or urban use. The most concentrated ...
,
soil fertility Soil fertility refers to the ability of soil to sustain agricultural plant growth, i.e. to provide plant habitat and result in sustained and consistent yields of high quality.
loss particularly in southern Spain, southern Italy, Sicily and especially north Africa) saw a collapse in the system beginning in the 2nd century, as EROI began to fall. It bottomed in 1084 when Rome's population, which had peaked under
Trajan Trajan ( ; la, Caesar Nerva Traianus; 18 September 539/11 August 117) was Roman emperor from 98 to 117. Officially declared ''optimus princeps'' ("best ruler") by the senate, Trajan is remembered as a successful soldier-emperor who presi ...
at 1.5 million, was only 15,000. Evidence also fits the cycle of
Maya Maya may refer to: Civilizations * Maya peoples, of southern Mexico and northern Central America ** Maya civilization, the historical civilization of the Maya peoples ** Maya language, the languages of the Maya peoples * Maya (Ethiopia), a popul ...
n and Cambodian collapse too.
Joseph Tainter Joseph Anthony Tainter (born December 8, 1949) is an American anthropologist and historian. Biography Tainter studied anthropology at the University of California, Berkeley and Northwestern University, where he received his Ph.D. in 1975. he hol ...
suggests that diminishing returns of the EROI is a chief cause of the collapse of complex societies, which has been suggested as caused by peak wood in early societies. Falling EROI due to depletion of high quality fossil fuel resources also poses a difficult challenge for industrial economies, and could potentially lead to declining economic output and challenge the concept (which is very recent when considered from a historical perspective) of perpetual economic growth. Tim Garrett links EROI and
inflation In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reduct ...
directly, based on a
thermodynamic Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of ...
analysis that links current
world energy consumption World energy supply and consumption is global production and preparation of fuel, generation of electricity, energy transport, and energy consumption. It is a basic part of economic activity. It includes heat, but not energy from food. This art ...
(Watts) to a historical accumulation of inflation-adjusted global
wealth Wealth is the abundance of valuable financial assets or physical possessions which can be converted into a form that can be used for transactions. This includes the core meaning as held in the originating Old English word , which is from an I ...
(US dollars) known as the Garrett Relation. This economic growth model indicates that global EROI is the
inverse Inverse or invert may refer to: Science and mathematics * Inverse (logic), a type of conditional sentence which is an immediate inference made from another conditional sentence * Additive inverse (negation), the inverse of a number that, when a ...
of global inflation over a given time interval. Because the model aggregates supply chains globally, local EROI is outside its scope.


Criticism of EROI

EROI is calculated by dividing the energy output by the energy input. Measuring total energy output is often easy, especially in the case for an electrical output where some appropriate
electricity meter North American domestic analog electricity meter. Electricity meter with transparent plastic case (Israel) North American domestic electronic electricity meter An electricity meter, electric meter, electrical meter, energy meter, or kilowa ...
can be used. However, researchers disagree on how to determine energy input accurately and therefore arrive at different numbers for the same source of energy. How deep should the probing in the supply chain of the tools being used to generate energy go? For example, if steel is being used to drill for oil or construct a nuclear power plant, should the energy input of the steel be taken into account? Should the energy input into building the factory being used to construct the steel be taken into account and amortized? Should the energy input of the roads which are used to ferry the goods be taken into account? What about the energy used to cook the steelworkers' breakfasts? These are complex questions evading simple answers. A full accounting would require considerations of opportunity costs and comparing total energy expenditures in the presence and absence of this economic activity. However, when comparing two energy sources a standard practice for the supply chain energy input can be adopted. For example, consider the steel, but don't consider the energy invested in factories deeper than the first level in the supply chain. It is in part for these fully encompassed systems reasons, that in the conclusions of Murphy and Hall's paper in 2010, an EROI of 5 by their extended methodology is considered necessary to reach the minimum threshold of sustainability, while a value of 12-13 by Hall's methodology is considered the minimum value necessary for technological progress and a society supporting high art. Richards and Watt propose an ''Energy Yield Ratio'' for photovoltaic systems as an alternative to EROI (which they refer to as ''Energy Return Factor''). The difference is that it uses the design lifetime of the system, which is known in advance, rather than the actual lifetime. This also means that it can be adapted to multi-component systems where the components have different lifetimes. Another issue with EROI that many studies attempt to tackle is that the energy returned can be in different forms, and these forms can have different utility. For example, electricity can be converted more efficiently than thermal energy into motion, due to electricity's lower entropy. In addition, the form of energy of the input can be completely different from the output. For example, energy in the form of coal could be used in the production of ethanol. This might have an EROI of less than one, but could still be desirable due to the benefits of liquid fuels (assuming the latters are not used in the processes of extraction and transformation).


Additional EROI calculations

There are three prominent expanded EROI calculations, they are point of use, extended and societal. Point of Use EROI expands the calculation to include the cost of refining and transporting the fuel during the refining process. Since this expands the bounds of the calculation to include more production process EROI will decrease. Extended EROI includes point of use expansions as well as including the cost of creating the infrastructure needed for transportation of the energy or fuel once refined. Societal EROI is a sum of all the EROIs of all the fuels used in a society or nation. A societal EROI has never been calculated and researchers believe it may currently be impossible to know all variables necessary to complete the calculation, but attempted estimates have been made for some nations. Calculations are done by summing all of the EROIs for domestically produced and imported fuels and comparing the result to the
Human Development Index The Human Development Index (HDI) is a statistic composite index of life expectancy, education (mean years of schooling completed and expected years of schooling upon entering the education system), and per capita income indicators, w ...
(HDI), a tool often used to understand well-being in a society. According to this calculation, the amount of energy a society has available to them increases the quality of life for the people living in that country, and countries with less energy available also have a harder time satisfying citizens' basic needs. This is to say that societal EROI and overall quality of life are very closely linked.


EROI and payback periods of some types of power plants

The following table is a compilation of sources of energy from
German Wikipedia The German Wikipedia (german: Deutschsprachige Wikipedia) is the German-language edition of Wikipedia, a free and publicly editable online encyclopedia. Founded on March 16, 2001, it is the second-oldest Wikipedia (after the English Wikipedi ...
. The minimum requirement is a breakdown of the cumulative energy expenses according to material data. Frequently in literature harvest factors are reported, for which the origin of the values is not completely transparent. These are not included in this table. The bold numbers are those given in the respective literature source, the normal printed ones are derived (see Mathematical Description). :(a) The cost of fuel transportation is taken into account :(b) The values refer to the total energy output. The expense for storage power plants, seasonal reserves or conventional load balancing power plants is not taken into account. :(c) The data for the E-82 come from the manufacturer, but are confirmed by TÜV Rheinland.


ESOEI

ESOEI (or ESOIe) is used when EROI is below 1. "ESOIe is the ratio of electrical energy stored over the lifetime of a storage device to the amount of embodied electrical energy required to build the device." One of the notable outcomes of the
Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is conside ...
team's assessment on ESOI, was that if pumped storage was not available, the combination of wind energy and the commonly suggested pairing with battery technology as it presently exists, would not be sufficiently worth the investment, suggesting instead curtailment.


EROI under rapid growth

A related recent concern is energy cannibalism where energy technologies can have a limited growth rate if
climate neutrality Carbon neutrality is a state of net-zero carbon dioxide emissions. This can be achieved by balancing emissions of carbon dioxide with its removal (often through carbon offsetting) or by eliminating emissions from society (the transition to the " ...
is demanded. Many energy technologies are capable of replacing significant volumes of
fossil fuels A fossil fuel is a hydrocarbon-containing material formed naturally in the Earth's crust from the remains of dead plants and animals that is extracted and burned as a fuel. The main fossil fuels are coal, oil, and natural gas. Fossil fuels ma ...
and concomitant green house gas emissions. Unfortunately, neither the enormous scale of the current fossil fuel energy system nor the necessary growth rate of these technologies is well understood within the limits imposed by the
net energy Net Energy Gain (NEG) is a concept used in energy economics that refers to the difference between the energy expended to harvest an energy source and the amount of energy gained from that harvest. The net energy gain, which can be expressed in jo ...
produced for a growing industry. This technical limitation is known as energy cannibalism and refers to an effect where rapid growth of an entire energy producing or energy efficiency industry creates a need for energy that uses (or cannibalizes) the energy of existing power plants or production plants. The overcomes some of these problems. A solar breeder is a photovoltaic panel manufacturing plant which can be made energy-independent by using energy derived from its own roof using its own panels. Such a plant becomes not only energy self-sufficient but a major supplier of new energy, hence the name solar breeder. Research on the concept was conducted by Centre for Photovoltaic Engineering, University of New South Wales, Australia. The reported investigation establishes certain mathematical relationships for the solar breeder which clearly indicate that a vast amount of net energy is available from such a plant for the indefinite future. The solar module processing plant at
Frederick, Maryland Frederick is a city in and the county seat of Frederick County, Maryland. It is part of the Baltimore–Washington Metropolitan Area. Frederick has long been an important crossroads, located at the intersection of a major north–south Native ...
was originally planned as such a solar breeder. In 2009 the Sahara Solar Breeder Project was proposed by the ''Science Council of Japan'' as a cooperation between
Japan Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the n ...
and
Algeria ) , image_map = Algeria (centered orthographic projection).svg , map_caption = , image_map2 = , capital = Algiers , coordinates = , largest_city = capital , relig ...
with the highly ambitious goal of creating hundreds of GW of capacity within 30 years. Theoretically breeders of any kind can be developed. In practice, nuclear
breeder reactor A breeder reactor is a nuclear reactor that generates more fissile material than it consumes. Breeder reactors achieve this because their neutron economy is high enough to create more fissile fuel than they use, by irradiation of a fertile mate ...
s are the only large scale breeders that have been constructed as of 2014, with the 600 MWe BN-600 and 800 MWe
BN-800 reactor The BN-800 reactor (Russian: реактор БН–800) is a sodium-cooled fast breeder reactor, built at the Beloyarsk Nuclear Power Station, in Zarechny, Sverdlovsk Oblast, Russia. The reactor is designed to generate 880 MW of electrical po ...
, the two largest in operation.


See also

*
Cost of electricity by source Different methods of electricity generation can incur a variety of different costs, which can be divided into three general categories: 1) wholesale costs, or all costs paid by utilities associated with acquiring and distributing electricity to ...
– levelized cost of energy *
Embodied energy Embodied energy is the sum of all the energy required to produce any goods or services, considered as if that energy was incorporated or 'embodied' in the product itself. The concept can be useful in determining the effectiveness of energy-produ ...
* Emergy *
Energy balance Energy balance may refer to: * Earth's energy balance, the relationship between incoming solar radiation, outgoing radiation of all types, and global temperature change. * Energy accounting, a system used within industry, where measuring and anal ...
* Energy cannibalism *
Exergy In thermodynamics, the exergy of a system is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir, reaching maximum entropy. When the surroundings are the reservoir, exergy is the pot ...
– useful energy *
Jevons paradox In economics, the Jevons paradox (; sometimes Jevons effect) occurs when technological progress or government policy increases the efficiency with which a resource is used (reducing the amount necessary for any one use), but the falling cost of ...
– 1880s observation of the efficiency effect multiplier * Khazzoom-Brookes Postulate – 1980s updating of Jevons paradox * Net energy gain * Social metabolism * Thermoeconomics


References


External links


World-Nuclear.org
World Nuclear Association study on EROI with assumptions listed.

Wayback Archive of OilAnalytics.org, "EROI as a Measure of Energy Availability"
EOearth.org
Energy return on investment (EROI)
EOearth.org
Net energy analysis

Essay on H2-PV Breeder Synergies {{Bioenergy Peak oil Energy economics Emergy