EROEI as a Measure of Feasibility

(By the way, please see also, my “new” blog “Energy Returned over Energy Invested” at  when you finish reading this.)

Currently, I am trying to convince Charles Hall, Tom Robertson, Gail Tverberg, and the rest of the world that I have solved the problem of computing the ratio of energy returned to energy invested, i. e., ER/EI or EROEI or EROI, depending upon who is writing the term.  My latest effort to state the solution concisely is posted at, which has hyperlinks to longer discussions elsewhere.  The notion of the autonomous alternative energy district (AAED) originated in a section of “Energy in a Mark II Economy” that was posted at  In “Energy in a Mark II Economy”, I computed a series of subscripted EROIs beginning with the direct production expenses of the manufacturer in the energy-invested term and with each successive EROIi including more components.  The last should be recognized as the composition of the energy-invested term for the EROI in the AAED that determines feasibility.  Overwhelming sentiment dictates that I change EROI back to EROEI or ERoEI – regardless of the similarity of that term to EIEIO in the lyrics of Old MacDonald’s Farm. 

Note.  Actually, energy returned might be confused with net energy returned, denoted ER – EI in my papers except for; therefore, we should be referring to the energy produced.  The correct ratio to determine feasibility would be EPoEI; but, please, let’s not get into that.  Also, and this is more important, in I defined EROI so that it is the same as EROI  - 1 in  and

In a community that can subsidize a renewable energy technology with fossil fuel, it is especially important to use EROI* as discussed at because the lifestyles of the participants can be supported by fossil fuel.  Thus, the alternative energy technology might be able to produce energy, but the total amount of fossil fuel used by the community would be increased rather than diminished.  And, no one might ever know.

Before I ask you to read “EROI* as a Measure of Feasibility” copied from I need to emphasize a few key points: 

·        One of the correspondents claimed that EROI does not account for quality or convenience.  That is not true, provided that transformity is applied to the final product accounting for quality and for time and place of production to compute the emergy of the product in terms of a well-defined standard as I have done in my papers on emergy and EROI.  It is essential to combine emergy analysis with the computation of EROI to determine the feasibility and sustainability of the process under investigation. 

·        The price of energy should reflect the cost of preventing or repairing any changes to the environment that diminish the quality of life of mankind and other species or that compromise the sustainability of the relevant ecosystems including the magnitude of the storehouses of natural resources.  The quality of life depends upon aesthetics as well as pure material circumstances.

·        The energy-invested term should have an energy contribution corresponding to every monetary item that affects the price even if this reduces ERoEI* to less than 1.0. Research should continue until technologies with ERoEI greater than 1.0 are found.  This approach is mathematically rigorous as opposed to other approaches that merely state that an ERoEI must be greater than some unsupported number such as 3.0 to support the operations of civilization.

Revised April 29, 2011


EROI* as a Measure of Feasibility

If we wish to define an EROI that will indicate a feasible alternative energy technology if it is greater than 1.0, we must begin to think of society as a system the purpose of which is to keep high-grade energy flowing.  Let us begin by defining consumption in terms of emergy with an M.  For those who wish to know what I mean by emergy see  Thus, every citizen can be characterized by the community according to how much emergy he or she consumes strictly because he is employed, e. g., commuting costs, clothing costs, and meals away from home, and how much emergy he consumes otherwise.  Suppose, for the sake of analysis, that these quantities can be replaced by the average values in a few discrete strata.  Then, the system I used in Chapter 2 of On the Preservation of Species can be resurrected mutatis mutandis for our purposes.  It will not be necessary to take advantage of the distinction between personal emergy budget and work-related emergy budget until we begin to furlough people whose work is unnecessary to the well-being of the community.  At this point we may employ the notion of the Autonomous Alternative Energy District (AAED):

 Let us suppose that a group of people representing all of the trades and professions wishes to support itself completely by relying on a single alternative, renewable energy technology for all of its energy needs.  Let us suppose further that all of the natural resources necessary to do this are available within the AAED [and the repositories of such natural resources must be retained at steady state from the detritus of the AAED including superannuated installations of the technology].  Nothing is imported from outside the District whereas energy and only energy is exported.  If a man needs a car to drive from his home (in the District) to his job (in the District), the car is built, maintained, and fuelled in the District.  If his wife is sick the doctor in the District will treat her with medicine made in the District from chemicals produced there from raw materials mined there.  The EROI of the new energy technology is the total energy produced, ER, divided by the quantity ER minus the quantity EX, where EX is the energy exported; i. e., EX = ER – EI.  If the District is able to export any energy at all the EROI ratio exceeds one and the technology is feasible – at least.  In the case of a single energy technology, the energy produced by each technology can be assigned a transformity of unity and the value of emergy is quantitatively the same as the Gibbs availability, which, at room temperature, is the Gibbs free energy.  I prefer to report emergy values in units of emquads rather than quads, emjoules rather than joules, etc.  Thus, the units of transformity are emquads per quad, for example.

The actual situation in a self-contained US economy would be virtually identical to that of the AAED if the economy were to run exclusively on the alternative, renewable energy technology under investigation and there were precisely as many physicians, for example, as are needed to supply the needs of those whose purpose in life is to provide energy.  Thus, every ancillary and indirect expense of producing energy including the support of the workers and their dependents must be counted in computing energy invested if the EROI methodology is to be used to determine feasibility. 

In the broader economy, the pro-rated share of each workers energy budget that should be charged to energy invested is easily determined from the pro-rated share of his working hours and the consumption stratum to which he belongs.  If more than one technology is employed and the matching problem discussed in Chapter 2 of On the Preservation of Species has been solved, it is not necessary to convert one form of energy to another; therefore, a transformity of unity can be assigned to each form of energy produced.  Since, in addition, the fraction of personal energy and work-related energy served by each technology is usually known, this methodology can be extended easily to the more general situation.  To distinguish it from the superscripted EROIs in Energy in a Mark II Economy and to indicate its importance as the only EROI that determines feasibility, let us call it EROI*.

* Following Charles A. Hall, our name for the ratio of Energy Returned to Energy Invested is EROI rather than ERoEI.  

Tom Wayburn

December 14, 2008

Houston, Texas


P.S.  Remember to see my “new” blog “Energy Returned over Energy Invested” at