## Tuesday, January 4, 2011

### The Problem with EROI: Instead we should be Maximizing the Rate of Return on Work Invested

There have been quite a few journal articles and web posts about the idea of Energy Return on Energy Investment (EROI).
According to the definition of EROI that I pulled from the group that uses it the most,
http://www.eoearth.org/article/Energy_return_on_investment_%28EROI%29

EROI = (Quantity of Energy supplied) / (Quantity of energy used in supply process)

I find the this definition of EROI to be vague and confusing. Perhaps the people who use this definition a lot know what they mean by EROI, but this seems like a poorly defined quantity. Energy is one of least well defined terms out there because it can sometimes mean gibbs free energy, potential energy, work, chemical energy, thermal energy, or ever perhaps exergy.

Another problem I have with EROI is that it's not actually what we're trying to maximize. It may be useful as a ballpark number to determine whether the work spent on a project can be recovered (since many alternative energy concepts can't even meet this criterion.) But it doesn't help the investment community or our politicians because it's not what we should be maximizing.
What we're trying to maximize is the Average Rate of Return on Work Investment. By Work, I mean force times distance, such as electrical or mechanical work. The Net Work Generated (for a power plant) is the gross electrical energy generated over its lifetime minus reoccurring work spent in labor, maintenance, fuel costs, and pollution credits. The work spent on these items can be calculated easily if the US had an electricity-backed money supply (if not the calculations are a little harder.) If the US had an electricity-backed money supply, the work would be calculated by multiplying by the factor that converts dollars into kW-hr's. (see my earlier post on Electricity-based Currency)

EROI doesn't tell us anything about how long it takes to realize the return on investment. Insteead, we should always chose the option with the highest average rate of return on investment (as long as that value is correctly calculated and includes costs associated with decommissioning and pollution control.)

The goal is to increase the amount of work we can do as a society. The average rate of return on work investment tells us how quickly we can increase the amount of work that our society can accomplish.

So, why do we want to increase the amount of work our society can do?
1) Knowledge requires work (in order to increase our knowledge of the universe, we need to increase the amount of work our society is capable of generating.)
2) (as per my earlier blogs) The purpose of life is to increase the amount of entropy production in the universe. Ironically, this is done by increasing the amount of work available to a society. Why? Because the increased amount of work can be used to generate more work, and along the way, the entropy of the universe increases. The entropy production actually occurs faster when you are continuously trying to generate more work. Because of the exponential nature of generating work when you try to maximize ARROWI, you end up increasing entropy at a faster rate than if you just wasted the work by turning it directly into thermal energy.

So, maximizing the average rate of return of work invested is actually another way of maximizing the production of entropy.

As I've mentioned in previous posts, there is no way to prove that you are maximizing the production of entropy (unless you're near equilibrium), so there is no way to prove that you are maximizing the return on investment. All you can do is to maximize the ARROWI with respect to certain free variables. For example, if you are drilling a well for natural gas, you might try to calculate at which depth you end up maximizing the rate of return on work investment.

Our society is expanding our knowledge of the universe and expanding our capability to do work. Ironically, this is but a means to an end. The end goal is really to increase the entropy of the universe so that the universe reaches equilibrium sooner. Either way you think about, the way to reach the goal is to maximize the average rate of return of work invested (ARROWI).

#### 1 comment:

1. I've seen a variable called ERORI. It shows up in a lot journal articles.
Does anybody know how to calculate ERORI?
What does the energy stand for in ERORI?
Energy can not be created or destroyed, so what does ERORI mean?