Definitions

# EROEI

In physics, energy economics and ecological energetics, EROEI (Energy Returned on Energy Invested), ERoEI, EROI (Energy Return On Investment) or less frequently, eMergy, is the ratio of the amount of usable energy acquired from a particular energy resource to the amount of energy expended to obtain that energy resource. When the EROEI of a resource is equal to or lower than 1, that energy source becomes an "energy sink", and can no longer be used as a primary source of energy.

The natural or original sources of energy are not usually included in the calculation of energy invested, only the human-applied sources. For example in the case of biofuels the solar insolation driving photosynthesis is not included, and the energy used in the stellar synthesis of fissile elements is not included for nuclear fission. The energy returned includes any usable energy and not wasted heat for example.

## Relationship to net energy gain

EROEI and Net energy (gain) measure the same quality of an energy source or sink in numerically different ways. Net energy describes the amounts, while EROEI measures the ratio or efficiency of the process. They are related simply by

$\left(hbox\left\{NetEnergy\right\} + hbox\left\{EnergyExpended\right\} \right) div hbox\left\{EnergyExpended\right\} = EROEI$

or

$\left(hbox\left\{NetEnergy\right\} div hbox\left\{EnergyExpended\right\} \right) + 1 = EROEI$

For example given a process with an EROEI of 5, expending 1 unit of energy yields a net energy gain of 4 units. The break-even point happens with an EROEI of 1 or a net energy gain of 0.

## The economic influence of EROEI

High per-capita energy use is considered desirable as it is associated with a high standard of living based on energy-intensive machines. A society will generally exploit the highest available EROEI energy sources first, as these provide the most energy for the least effort. With non-renewable sources, progressively lower EROEI sources are then used as the higher-quality ones are exhausted.

For example, when oil was originally discovered, it took on average one barrel of oil to find, extract, and process about 100 barrels of oil. That ratio has declined steadily over the last century to about three barrels gained for one barrel used up in the U.S. (and about ten for one in Saudi Arabia). Currently (2006) the EROEI of wind energy in North America and Europe is about 20:1 which has driven its adoption.

Although many qualities of an energy source matter (for example oil is energy-dense and transportable, while wind is variable), when the EROEI of the main sources of energy for an economy fall energy becomes more difficult to obtain and its value rises relative to other resources and goods. Therefore the EROEI gains importance when comparing energy alternatives. Since expenditure of energy to obtain energy requires productive effort, as the EROEI falls an increasing proportion of the economy has to be devoted to obtaining the same amount of net energy.

Since the discovery of fire, humans have increasingly used exogenous sources of energy to multiply human muscle-power and improve living standards. Some historians have attributed our improved quality of life since then largely to more easily exploited (i.e. higher EROEI) energy sources, which is related to the concept of energy slaves. Thomas Homer-Dixon demonstrates that a falling EROEI 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 EROEI analysis provides a basis for the analysis of the rise and fall of civilisations. Looking at the maximum extent of the Roman Empire, (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 per day per person. It comes out roughly equal to the area of food production at its height. But ecological damage (deforestation, soil fertility loss particularly in southern Spain, southern Italy, Sicily and especially north Africa) saw a collapse in the system beginning in the 2nd century, as EROEI began to fall. It bottomed in 1084 when Rome's population, which had peaked under Trajan at 1.5 million, was only 15,000. Evidence also fits the cycle of Mayan and Cambodian collapse too. Joseph Tainter suggests that diminishing returns of the EROEI is a chief cause of the collapse of complex societies. Falling EROEI due to depletion of non-renewable resources also poses a difficult challenge for industrial economies.

## Criticism of EROEI

Measuring the EROEI of a single physical process is unambiguous, but there is no agreed standard on which activities should be included in measuring the EROEI of an economic process. 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 EROEI of less than one, but could still be desirable due to the benefits of liquid fuels.

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 steelworker's 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.

Energy return on Energy invested does not take into account the factor of time. Energy invested in creating a solar panel may have consumed energy from a high power source like coal, but the return happens very slowly, i.e. over many years. If energy is increasing in relative value this should favour delayed returns. Some believe this means the EROEI measure should be refined further.

Conventional economic analysis has no formal accounting rules for the consideration of waste products that are created in the production of the ultimate output. For example, differing economic and energy values placed on the waste products generated in the production of ethanol makes the calculation of this fuel's true EROEI extremely difficult.

EROEI is only one consideration and may not be the most important one in energy policy. Energy independence (reducing international competition for limited natural resources), freedom from pollution (including carbon dioxide and other green house gases), and affordability could be more important, particularly when considering secondary energy sources. While a nation's primary energy source is not sustainable unless it uses less energy than it creates, the same is not true for secondary energy supplies. Some of the energy surplus from the primary energy source can be used to create the fuel for secondary energy sources, such as for transportation.