The Oil Drum

Jeff,

Here are some thoughts and energy quality and EROEI:

The economic quality of energy production is always measured relative to the costs of some production resource that has to be expended in order to process energy into a usable form. With respect to a particular production resource (e.g. labor hours, cultivated land, irrigation water, etc) that unit of energy is best which requires the least resource expenditure to produce. The resource cost of producing one net unit of energy I call the resource intensity of net energy production.
Suppose that the gross energy output of an energy producing process is G. Since energy is used during the during the energy producing process, we must subtract this energy from the gross output energy in order to calculate net energy. Let us suppose that the energy consumed is f×G. If f<1 then the energy balance is positive. That is more energy is produced than is consumed. Finally let the amount of some non-energy resource expended to produce this output be given by R. Then the resource cost of producing one net unit of energy is given by:

Cn = R/(G-f×G)

This expression is the ratio of resource cost to energy profit. This resource cost or resource intensity of net energy production can be rewritten as follows:

Cn = (R/G)/(1-f) = Cg/µ

Cg (= R/G) is the resource cost of producing one gross unit of energy output. The quantity µ (=1-f), which I call the energy utilization rate, is the fraction of the gross output energy G which can be used for the production of goods and services other than energy. That is if we wish to run our energy producing process on an ongoing basis, a fraction f of our energy output must directed back into the energy producing process, thus leaving only a fraction 1-f available for the production of other economic goods and services. If multiple resources are involved in the energy production process then values of Cn can be calculated for each resource.
Both Cg and µ may play a role in determining the resource cost of net energy production. For example if we attempt to produce liquid hydrocarbon fuels from oil shale as conventional oil supplies decline, the energy utilization rate µ will drop because mining oil shale and thermally processing it to crack it into liquid hydrocarbons uses much more energy per unit of output than does pumping and refining conventional crude oil. In addition the resource costs (Cg) in terms of labor, fresh water, etc. of producing one unit of finished fuel will also increase. Note also that if the energy utilization rate approaches zero (energy output = energy input) then the resource cost of producing one net unit of energy will approach infinity.
The reciprocal of the resource intensity of net energy production, µ/Cg is also a useful parameter although I prefer to write it in a different form:

µ/Cg = µ/(R/G) = µ×(G/R) = µ×Pg

Pg is the unit productivity of the given resource with respect to gross energy production. That is, it is the amount gross output energy which results from the expenditure of one unit of resource. Naturally Pg has to be multiplied by the energy utilization rate µ in order to get the net energy production per unit of resource.
This quantity (µ/Cg or µ×Pg) is the ratio of energy profit to resource cost. In the terminology of economics this number is the efficiency of the resource in question with respect to the production of net energy. Both the energy utilization rate µ and the resource unit productivity Pg are likely to decrease as lower quality energy resources a exploited. If the energy utilization approaches zero the resource efficiency or productivity also approaches zero.
EROEI is defined as the ratio of energy output to energy input. At first glance this quantity appears to be the same kind of energy productivity that I have just described. It apparently describes the efficiency with which energy is turned into more energy. This conclusion is incorrect for two reasons. The numerator of EROEI is not the energy profit and the denominator is not the energy cost. These assertions can best be demonstrated by a concrete example.
Suppose a farmer produces biodiesel from some oil bearing crop. For simplicity we will assume that he manufactures the biodiesel on his own premises and sells it as a final product. We will further assume that the farm is run entirely off the energy of this biodiesel fuel. That is at the end of the production season the farmer holds back as much biodiesel as will be needed to run the farm during the coming year and the rest is sold to customers. We will assume that half the output has to be held back to run the farm in the coming year.
If we apply EROEI analysis to this production scheme we claim that the farmer’s total yearly output of biodiesel is his energy profit and the biodiesel used to run the farm is his energy cost which gives an EROEI of 2. While the farmer’s EROEI as defined is undoubtedly 2, the conclusions about profit and cost are clearly incorrect. The farmer’s profit is that part of his output which he sells to external customers, which is to say one half of his total output. His energy cost is zero. He does not purchase any energy. Of course the energy he uses to run the farm does detract from his total profits. Suppose he tries to improve his profit by maintaining his total yield but reducing his energy use. If he succeeds in cutting his energy use in half while maintaining his gross output then his EROEI will increase from 2 to 4, but his profit will only increase by from half of his total output to three quarters of his total output. In fact it is clear that his profit changes in proportion to the energy utilization rate µ which has increased from 0.5 to 0.75.
Suppose, on the other hand, the farm tries to improve his profit not by cutting his energy use, but by planting some new variety of crop which gives him increased twice the gross yield per hectare. Again his EROEI has increased from 2 to 4 and energy utilization rate has increased from 0.5 to 0.75. Energy utilization rate and EROEI have fixed relationship:

µ=(EROEI-1)/EROEI

In this case in addition to an increase in the energy utilization rate µ the resource unit productivity Pg has also increased; It has doubled from its previous value. If we use the size of the farmer’s original gross output as our measuring stick then his new profit is given 0.75×2 = 1.5. His energy profit has tripled. Again the productivity arithmetic I have outline above correctly describes the change in energy profit per hectare while EROEI does not.
I have artificially constructed this example so that it is clear that the energy costs are zero. However, the same conclusions apply even when external fuel purchases are made. Suppose that I purchase some fuel and use it to run an energy production process. If this process has a positive energy balance I will get back all of the energy I purchased plus some extra. For simplicity I will assume that all forms of energy are economically equivalent. Without this assumption simple energy balance calculations do not work, and one must inject energy quality factors into the analysis. If I make this simplifying assumption then I can take the energy which I have reproduced and sell it for the exact same price for which I purchased my original fuel. Therefore I have no energy cost. I only have an energy profit for the extra energy which I have produced.
Using energy to produce widgets and using energy to produce more energy are fundamentally different processes. If I spend energy to produce a widget, at the end of the process my energy is gone for good and in its place I have a widget. If I spend energy to produce more energy, then at the end of the process, all of the energy that I spent is returned to me plus some extra. The energy cost of producing energy is a meaningless concept.
EROEI defined as the ratio of energy output to energy input is not meaningless, but it does not have the significance of an economic efficiency. I am personally convinced that EROEI does not contain any information that is not contained the energy utilization rate µ in a more natural form.