Energy Returned Over Energy Invested – a concept introduced in a paper by Dr John Morgan, which I found in Principia Scientific under the heading The Catch-22 of Energy Storage.


Michael Hohmann | LMH Design

Reprinted with permission from the Clean Energy Pundit blog:
Energy Returned Over Energy Invested – a concept introduced in a paper by Dr John Morgan, which I found in Principia Scientific under the heading The Catch-22 of Energy Storage. I was sure that it would not only make me sit up and consider its possible implication for all matters of energy provision, and republished it as Reality Check #6 on my blogsite.
This made me reach for what I still think is one of the most important books on energy:
Basic Books, New York, 2005
Having now recapped on Huber & Mills, together with some further looks at what is available online about EROEI, I could not help thinking that there ought to be a better way to come to understand this concept – like knowing that ‘a picture is worth a thousand words’ rather than words alone.  So here goes with some thoughts in that direction.
EROEI expressed as a formula would look like this:  ER / EI = U, where U denotes a measure of Usefulness (for humans). We can leave out the E, because shown thus it really applies not only to all human activities, but also to all events in the universe, come to think of it, leaving us with R/I=U. Simplifying further in simple IN and OUT concepts, we are left with O/I=U when following the EROEI acronym sequence.
But that irks me, because
a)     on a timeline, Input must always precede Output.  Time Fact.
b)    When then written I/O=U, we become immediately aware that the Input ‘I’ must always, and without exception, exceed the Output ‘O’ in order to achieve any Usefulness ‘U’. Thermodynamic Fact.  In other words, the investment ‘I’ is always borrowed, resulting in an IOU to the environment – but will show as such only when we set the input boundary at this ‘Mother Nature’ level. [For practical purposes see the further discussion of FOWIand Output Tentacle A when I come to Octopus Diagrams]. Therefore, the description for the formula for calculating should always be known as I/O=IOU, and shown and used as
c)     The formula IOU=I/O also provides not only a familiar acronym for this method of calculating ‘usefulness to humans’ as in ‘IOU’ [I owe you], but also provides an instant reminder that whatever energy we use, we also owe it to the environment which provides it for us – however closely or widely one chooses or is forced to consider the term ‘environment’. We can only transform whatever we find, and live with the inevitable entropy losses when extracting and converting energy sources for usefulness. No human, however sapiens, has yet ‘created’ any energy ab initio, or is ever likely to.
 By Order of the Universe [1], as in Thomas Payne: THE AGE OF REASON 
“The Creation speaketh an universal language, independently of human speech or human language, multiplied and various as they may be. It is an ever-existing original, which every man can read. It cannot be forged; it cannot be counterfeited; it cannot be lost; it cannot be altered; it cannot be suppressed. It does not depend upon the will of man whether it shall be published or not; it publishes itself from one end of the earth to the other.”
Staying with energy matters, we need to use measurements and dimensions for them. For purposes of measuring energy (and work and heat) the SI unit is the joule  (which in turn is short for Nm).  I prefer here to use kWh because everyone is used to these from their energy bills – and multiplied by the cost charged for their kWh on everyone’s respective utility bill in any location and situation, gives an instant feel for the amount of energy under discussion and their incurred costs.
So, from dimensional consistency requirements, we measure IOU as I/O=IOU 
or kWh/kWh=kWh.  So the value IOU always has a dimension which should be stated.
But kWh ǂ kWh, they come in vastly different forms and qualities; for example, a barrel of oil delivered to your door may well contain about 1650 kWh in thermal energy, but you can’t run your television with it. Unless the QUALITY of U is known, described or even specified for its actual or intended use, the whole concept of IOU, or EROEI for that matter, or indeed any other discussion about uses of energy, is just about meaningless.
So, what does IOU actually mean when calculated as in I/O=IOU?
·         It is a measure of the INPUT COST for one unit of useful benefit when both are measured in energy terms.
·         the kind of, and the dimension always needs to be quoted, both for input as well as for output.
o    In the laser example shown below, the usefulness IOU is the cost of energy input when converted from oil (ex well head, say) in terms of kWh (thermal) to achieve a single unit in terms of kWh (power) in the form of laser photons. In the example illustrated, the IOU cost is IOU=I/O=330 kWhth.
o     For the same amount of usefulness provided by 1 kWhconverted from the direct output of electrons ex solar PV panels on the roof would certainly be different for an IOU= ? kWhp.
Unit dimensions, kind and descriptions for all three terms in the formula IOU=I/O always need to be stated or remain useless.  Back to your utility’s energy bill:  both gas and electricity consumptions are measured in kWh, but you certainly would not like your gas kWhth to be charged at the same rate as your electricity kWhp.
For a hunter-gatherer, Usefulness would mean finding enough berries, vegetables, and killing enough deer or other animals to feed himself, plus fending for family, shelter, clothing, firewood, provided from the quality of flora and fauna, and area of roaming range etc. Here is the energy pyramid for this situation:
IOU=I/O= ~140 Btu/m2/year
A hunter-gatherer would be an omnivore, let’s say halfway between a herbivore and first-level carnivore, to find his physical strength and stamina for his only input, giving an IOU ratio of 150000/1100=136.4; here measured in Btu/m2/year; which when used on both sides of the equation still gives a valid ratio between input and output. But again, the QUALITY (kind) of input needs to be known or specified; here we start with Plants – not with, say electrons coming directly from a solar PV panel. And another measure appears: area of land required as ‘input’ for plant-life energy. So even our single hunter-gatherer level human is, in energy terms, permanently in hock to the environment to the tune of, say 140 times his own possible adult input valour. The term ‘environment’ can be any four-dimensional region (time always plays a role, even when kept tacit) between the tip of your nose and the furthest region of the universe; we are all just stardust on that ‘boundary’ assumption. A realistic boundary needs to be defined before making meaningful comparisons between different situations – to be discussed below.
At the other extreme of a situation to be assessed, providing 20 kWh of laser quality photons for, say eye surgery, requires app. 6,600 kWh thermal energy at start of the chain of conversion and refinement necessary from coal, oil or gas, that is I/O=U  or 6600/20=330/1  or an IOU ratio of 330 kWh Input for every single kWh of laser output.
Again, this is most intuitively understandable when shown graphically:
     IOUkWhp=I/O=330 kWhth
One last example for comparison:  the SUV version of the horseless carriage:
The author’s 2% stated usefulness from the original oil source, giving an    IOU=I/O=132 kWhth
Where does all this Input energy disappear to with so little Output energy ending up asUseful for us humans? Best illustrated with Sankey diagrams [try].
Here is the first one I ever saw, created in 1949 showing the World’s Energy Flux in 1937:
When I first saw this, I was reminded of seeing an octopus and called it an Octopus Diagram, with the octopus’ head at the input end at left, and the tentacles on the right, in between digesting and distributing everything that the various mouths at the head can gobble up.                                                  
 The next thing I liked was the distinction of input groupings as RECURRING energy sources versus IRREPLACABLE energy sources.  Buckminster Fuller describes the same two groups as INCOME energies versus CAPITAL energies.  ‘Renewable’ energy is plainly a Newspeak misnomer and should be disused:  energy just isn’t renewable – by Order of the Universe as already noted above. The term RECURRING also has the immediate reminder of the element of time: if the recurrence happens at a slower rate than use, result: misery, if faster, result is happiness – ala Micawber.  IRREPLACABLE similarly embodies the time element in the sense of being finite – at some time, sooner or later, there will be NIL food at one or more mouths of that kraken sized octopus.
The other advantage is the possibility to arrive at boundary definitions for arrival of energy sources at the various ‘mouths’, from where they enter the octopus’ digestive system.
Perhaps a simple convention for all entry boundaries could be the first entry level to wholesale points, Free at Top-level Onshore Wholesale Intake – FOWI perhaps – from where only direct distribution levels, routes and conduits to reach any end user depart, albeit via further intermediate refinement and conversion operators and processes [most notably for electricity generation, as identified in the US 2009 diagram below].
If on further scrutiny, FOWI would form a practicable boundary definition for the ‘food’ intake at the various mouths of any Octopus, it would also be the point of total energy expenditure needed to provide its different kinds of ‘food’, in order to arrive from whatever source found in the environment at a comparable level of entry into the Octopus’ metabolism.    
One entry shown in the 1937 World Energy Octopus is the tentacle labelled A in the black CONSUMED box at the output end of the diagram, labelled ‘extraction of raw materials’.
 I propose to retain a tentacle A as in this 1937 Octopus of energy use perhaps as label A1 because it is, after all an output used, and not just as ‘extraction of raw materials’ but including all energy expenditure for ‘food’ right up to the ‘mouths’ identified as FOWI gates. A1 uses need to be known when used for calculating energy embodiments in their respective primary energy headings by the time they arrive at FOWI input boundaries. Further tendrils  at tentacle A, say as A2. A3… An   might collectively be described as Culture uses, which would include headings like education from kindergarten to university and beyond, science, fundamental research (Iter, Cern, Fusion etc), all of the Arts, leisure activities, etc etc; in short anything using energy not suitably classifiable as belonging strictly under headings like Electricity Generation, Residential, Commercial, Industrial and Transportation as categorized in the 2009 US diagram.
One fundamental other resource is needed for our Octopuses just as for any other creature, including humans, with all their bodily internal and external transformation processes  – and that is WATER.  In discussions of IRREPLACABLE energy sources, often the use of Peak Oil, Peak Coal appears  for any other irreplaceable source peaking and then beginning to become unavailable for ever.  Yet Water is never explicitly mentioned in spite of being essential in the extraction, transformation and as processing ingredient in all primary energy sources and their uses. I have made a rough-and-ready assessment of the water requirements of electricity production and came to surprising results, peaking in PEAK WATER becoming apparent.  While water is not strictly irreplaceable, – with oceans and polar ice caps being about as limitless as could be desired – but water will (where it not already is) become a very energy-hungry resource due to  transportation, desalination and waste-water treatment and purification necessities.. 
After all, no one has described the essence of the design objective for all of us, better than Buckminster Fuller in his address to the 1963 Congress of the International Union of Architects in Paris:
".... to render the total chemical and energy resources* of the world, which are now exclusively preoccupied in serving only 44% of humanity, adequate to the service of 100% of humanity, at higher standards of living and total enjoyment than any man has yet experienced."
*I think we should include information resources
Back to the original Octopus version, figures for which are given in Millions of Millions of Kilowatt-hours/year (1937).
During that year, the world used – for other than food – (0.3 +0.2  +1.8 +0.9 +3.6 +0.1 +0.7 +10.9) =18.5^12 kWh/y , of which (0.3+1.8+0.8+0.8)=3.7^12 kWh/y were useful, giving an
IOU=5^12 kWh/y, or as plain ratio with identical I and O dimensions assumed, an
Overall, during that year the World Octopus gobbled up (7.0+16.2) = 23.2 trillion kWh and ‘excreted’ (23.2-3.7) =19,5 trillion of these, that is a seeming ‘waste’, but better called
entropy* = 84%
because that ‘waste’ is not wasted: without it there would be NIL output;
 useful output = 16% 
* Entropy is a thermodynamic property that is a measure of the energy not available for work in a 
thermodynamic process. It is defined by the second law of thermodynamics
A more recent Sankey diagram for US energy in 2009:
IOU=94.62/39.97=    IOU = 2.37 
entropy is 54.64/94.62=            entropy = 58%
useful output = 42%
These two diagrams are different in size, time and construction and are not strictly comparable in detail, kind or volume, but seen as a type comparison, they do show, that the US had about half the IOU ratio of energy drawn from the environment with an efficiency of conversion processes of ~40% useful output with ~60% incurred entropy losses, compared to the whole World conversion process (1937) showing an efficiency  of ~20% useful output with ~80% incurred entropy losses from an IOU ratio of energy drawn from the environment
about twice that of the US 2009 situation. 
A notable difference between the two Sankey diagrams shown, is that US 2009 does not contain any mention of Octopus mouths for Food and Fuel  for whichsay artificial fertilizers amongst other needs for processes might be seen as a significant energy input requirement. In the discussion of water needs below, agriculture would be a major contributer to Peak Water.
There is one other enlightening use of octopuses. Using the 2009 US diagram, the annual Residential consumption is shown as 11.26 Quads/y, derived from (0.01 +8.35 +2.68 +0.7 +0.37 +23.37 +19.76 +3.88) = 59.12 Quads/y applicable national primary inputs. Some assumptions here: Residential is taken to include everything from construction, use and maintenance and demolition during that year. The pure lighting use is probably no more than 1% of that total, but is pure electricity. It is therefore arriving from the inputs to Electricity Generation of 38.19 Quads/y. Saving 1% (assumption, here purely for illustration purposes) of residential energy use from changing ‘lightbulbs’ would save 1.126 Quads/y [that is equal to 329,998,039,833 kWh/y, or 330 billion kWh/y] out of 38.19 Quads/y, or 0.3% of national electricity production costs in energy terms.  Out of total national primary energy, those 330 billion kWh/y saved would represent a national saving in primary energy of 1.126/59.12 = 0.2%. This is just to illustrate one other useful aspect of making use of Sankey diagrams by following any end (or inter-process stage) use  upstream to see what effect any change will have on primary input.
I would like to quote from the inside cover blurb of this ‘Basic Book’ that triggered me to think of octopuses and IOUs:
“For all the talk about energy prices, and energy policy on both sides of the political aisle we actually know very little about what’s really at stake. In their explosive new book The Bottomless Well, Peter W Huber and Mark R Mills shatter the prevailing myths and show that across the board, energy isn’t the problem – energy is the solution.
Writing in take-no-prisoners, urgently compelling prose, Huber &    Mills explain:
--   why demand for energy will never go down
            --   why most of what we think of as “energy waste” actually benefits us
            --   why more efficient cars, engines, and bulbs will never lower demand
            --   why energy supply is infinite
            --   why gasoline prices matter less and less
--   and why hybrid engines will most likely lead us to cars propelled by the
     coal-fired and uranium-fired grid.
As for the much-maligned power grid itself, it’s the Worst system we could have except for all the pro-posed alternatives. Expanding energy supplies mean higher productivity, more jobs, and a growing GDP. The Bottomless Well shows how a better understanding of energy should radically change our views and policies on a number of highly controversial issues.
           I hope this trailer sounds intriguing enough to make you reach for this book, from which all illustrations but the US 2009 diagram, have been borrowed.
 WIRED magazine [UK Edition OCT 14] provides, as always, fascinating reading; making inter alia no less of an announcement on the front cover than:   
Enticing no doubt, but would be digressing here because on page 139 surfaces an article by Jeremy White [WIRED’s Product Editor] from which I would like to quote an excerpt relevant to the IOU discussion here:
“From Henry Ford’s industrial production model to the introduction of robots in the late 20th century, there has been significant change in the way mass-market cars are made….
Take BMW. The German company was aware that the assembly of its i Series of electric and hybrid vehicles (the i3 was launched in November 2013, the i8 in June this year) required a new approach to manufacturing. So, between 2009 and 2012, it spent €400 million (£310 million) building a new factory near Leipzig in east central Germany.
The company claims that the facility, which covers an area of 2.1 million m2, is one of the most sustainable automobile plants in the world. The differences with the older plants are striking. On the new line, there is no need for a paint shop as the thermoplastic outer body panels can be sprayed in small, shed-like rooms. A traditional press shop is absent because the construction of the passenger section of the vehicles doesn’t require steel or aluminium. In the body shop, there is no more welding, just robots silently applying glue.
The result is that making the i models requires 50 per cent less power and 70 per cent less water per car compared to the BMW production average which, in 2011, was 2.43 MWh per vehicle. All of the electricity needed for the i models is generated on-site using wind power from four 2.5 MW turbines. Generating around 26 GWh per year, these turbines produce 2GWh more electricity than is required for the i Series. The surplus is channelled into other areas of the plant….”
WOW, I thought what a topical real-life example for exploring with IOU analyses:  an on-site windmill powered industrial plant, usually thought of necessarily being hooked to that ‘baseload grid’, producing surplus energy for export, perhaps on a 24hour production basis (?) using what (?) for wind power variability bridging, comparing its installed IOU with the same 26 GWh/y output derived from Baltic or North Sea offshore wind, or from a possible grid connection, or what-if from solar PV perhaps on factory roofs – using the IOU calculation method here described together with the graphical views like the Pyramids and Octopus diagrams to compare and understand the various options? 

Have some fun with that :-) 


I can see a liberal necessity for ‘midnight oil’ coming up…

Added on 16 March 2015:
On 17 January 2015 The Economist published a Special Report on Energy and Technology. The first article in this report, headed Let there be light  included this Sankey diagram
Source: The Economist 17 JAN 2015, Special Report: Let there be light
IOU = I/O = 97.14/38.4 =      IOU = 2.63
entropy is 59.0/97.14 = entropy = 61%
useful output = 39%
Converting all energy units to TWh as in the first Octopus for the World Energy use in 1937, we can make the following comparison:
WORLD 1937
Total IN:                     23.2 TWh                                = 100%                     IOU = 5.49
Useful OUT:               3.7 TWh                                 =   16%                 entropy = 84%
USA 2009: 
Total IN:                     94.62 Quads = 27 730 TWh = 100%                         IOU = 2.37
Useful OUT:              39.97 Quads = 11 714 TWh  =   42%                     entropy = 58%
USA 2013:
Total IN:                     97.14 Quads = 28 469 TWh  = 100%                        IOU 2.53
Useful OUT:                38.40 Quads = 11 254 TWh =   39%                     entropy = 61%
Which together show these useful order-of-magnitude comparisons:
--    in 2013, the USA alone consumed 1227 times as much energy as the whole World did in 1937,  with a 231% improved conversion efficiency (measured by the IOU ratio, after the 2.9 TWh used for ‘food’ in the 1937 world total – not used in the USA diagrams – has been allowed for)
--    USA consumption had increased by 2.66% since 2009,  with a 7% entropy increase over 2009 (= loss in conversion efficiency = IOU ratio).
[1] PS added 01 DEC 2014
Oxford University Press Inc, New York, 2007
Addendum 07 July 2016:
Since writing this essay about three years ago, the IOU concept has led to further insights from a fuller understanding of Peter Atkins' FOUR LAWS when combined with the BIRTH OF THERMODYNAMICS at ,
which in turn led to an expanded edition of SUSTAINABILITY – THE FULL MONTY, 
All of which finally allowed me to arrive at a definition of SUSTAINABILITY, now added to the earlier definition of CLEAN ENERGY
And not to forget: 'sustaining itself in future' is, of course, the ultimate definition of 

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