01 June 2006

Energy Return on Energy Invested (EROEI)

The energy return on energy invested − abbreviated EROEI − is commonly used to describe the net energy gain for an energy system normalized by the input. This can be applied to many renewable systems in a straight-forward manner or to the full lifecycles of biofuels, nuclear power plants, etc. Mathematically, EROEI is defined as,
EROEI = ΔE / Ein = (Eout - Ein) / Ein
Simplifying yields,
EROEI = Eout / Ein − 1
However, as most of you are probably aware when you see a listed EROEI number the above equation isn't what's used. What you actually are typically given is the Energy Return Ratio (ERR).
ERR = Eout / Ein
Obviously the two are quite similar except for the -1 in the definition for EROEI. If you've ever heard, for example, that the EROEI (actually ERR) of corn ethanol is 0.87 and that's 'negative' you may not have quite understood. On the other hand, if you use the proper EROEI definition then an ERR 0f 0.87 is an EROEI of -0.13. For ERR the break-even point is 1 while it's 0 for to proper definition of EROEI.

Since the error in definition is pretty widespread I don't think there's any point to trying to combat it. I don't bother and I freely call the energy return ratio, EROEI. Still it's useful to keep in the back of your mind. If it does bug you just use ERR and try to remove EROEI from the vocabulary. On the other hand, if you want to use EROEI to model exponential growth, you better use the EROEI rather than the ERR or you'll get a wrong answer.

I don't mean to be pedantic on the subject but I need to make this clear because I've been looking at NREL's soy biodiesel study and there's some funny definitions going on.


Anonymous said...


Robert McLeod said...

Smacks head and corrects error

Fat Man said...

"ERR = Eout/Eout"

Eout/Eout = 1 because a number divided by it self is unity.

Or am I missing something?

Robert McLeod said...

Not my best day.

Anonymous said...

To Robert Mcleod,

Would like to discuss Biodiesel. Reply at joe_villar2000@yahoo.com