The concept of energy return on investment (EROI), often called energy returned on energy invested (EROEI), is a simple and familiar one. Here is the short definition, from the Encyclopedia of Earth. To cite:
Energy return on investment (EROI) is the ratio of the energy delivered by a process to the energy used directly and indirectly in that process.
For example given a process with an EROI of 5, expending 1 unit of energy yields a net energy gain of 4 units. The break-even point happens with an EROI of 1 or a net energy gain of 0.
A common related concept is the energy payback period. Every energy system has initial investments of energy in the construction of facilities. The facility then produced an energy out for a number of years until it reaches the end of its effective lifetime. Along the way, additional energy costs are incurred in the operation and maintenance of the facility, including any self use of energy. The energy payback period is the time it takes a facility “pay back” or produce an amount of energy equivalent to that invested in its start-up.
Wiki also has a decent article about it, and it’s a source of much discussion on websites like The Oil Drum. In short, a simple concept, but fraught with debate. It is not my intention here to wade into the arguments on EROEI of individual energy sources — that would require many TCASE posts, and even after that, I’d be unlikely to get consensus. But feel free to hammer away on the ins and outs of EROEI in the comments.
What I want to do here is propose a simple method for estimating EREOI based on a life-cycle assessment of greenhouse gas emissions. This requires some assumptions, but is useful, I think, because LCA studies are readily available and widely cited, whereas explicit EREOIs via net energy analysis are harder to find and compare in a consistent way.
There have been many well-researched peer-reviewed studies looking at the life-cycle emissions of different energy technologies, expressed in terms of kilograms of CO2-e/MWh (commonly). For non-fossil fuel energy technologies, this is a useful benchmark for calculating EROEI, because their inputs mostly come from fossil fuels, yet they produce no CO2 when generating. So, let’s consider ‘clean energy’ EROEIs on this basis.
LCA on carbon emissions for nuclear (excluding weird outliers like SSL) is in the range of 5 – 80 kg CO2-e/MWh. This range is based on various assumptions about relative mixes of diffusion/centrifuge enrichment, embodied plant energy etc. (see WNA summary). For wind it’s ~30 kg CO2-e/MWh (without considering backup), solar thermal ~80 kg CO2-e/MWh, PV ~150 kg CO2-e/MWh. A more complete range of estimates, based on meta-analysis, are given here, in a detailed study by ISA (University of Sydney).
If we assume that about half the energy inputs comes from coal-fired electricity and the other half from oil (mostly diesel for mining) — a reasonable approximation, given the present fossil-fuel-dominated global economy — then the average emissions intensity for inputs will be roughly 900 kg CO2-e/MWh. With this number, we can then estimate the EROEI of various technologies:
Nuclear LWR = [900/5] to [900/80] = 180 to 11 EROEI; Wind = ~30, Solar Thermal = ~11, Solar PV = ~6, etc.
It is simple to then undertake a sensitivity analysis of the above, such as changing your assumption about the carbon intensity of the fossil-fuel inputs, and/or substituting different values you have for a nuclear/renewable CO2-e/MWh. For instance, if you assume 800 CO2-e/MWh for fossil-fuel inputs and a LCA of 50 for solar PV, the EROEI then becomes 800/50 = 16.
For a future closed-fuel-cycle nuclear technology, like the IFR, one can remove the inputs for mining, milling, enrichment and long-term waste management, retain those for plant construction and decomissioning, and add those for recycling of the fuel and short-term management of vitrified fission products. My rough estimate, using the breakdowns given here (Tables 1 and 2), is < 1 kg CO2-e/MWh, even if only fossil fuels are used for energy generation during the plant’s construction. There will be no direct emissions from fuel pyroprocessing, because it will be on-site, and so make use of the IFR’s power. Thus, the IFR’s EROEI is expected to be >900 — and it will be carbon-free, once fossil fuels are completely phased out.
With the EROEI to hand, energy payback time is a straightforward calculation. For example, if your technology’s EROEI is 15 and the power plant’s lifespan is 35 years, then the energy payback time can be approximated as 35/15 = 2.3 years or 28 months.
I’d appreciate any comments on the validity (or otherwise) of the above short-hand method I’ve used here for estimating EROEI and payback. Indeed, in the spirit of ‘blog-science’ review, I’m happy to stand corrected on any of the above, and revise accordingly, if I’m in error.
Finally, I’d like to propose some open questions for discussion in the comments section, below. These were first asked of me by regular BNC commenter Douglas Wise, so the credit — as devil’s advocate — goes to him:
1) Why are EROEI assessments so monumentally variable?
2) Why don’t high EROEIs necessarily (currently) translate into high ERO$I?
3) Will high EROEIs ever translate into high ERO$I?
Here is an early answer I gave to Douglas via email, which covers some of these points, from my perspective:
The EROEI for nuclear varies a lot depending on the assumptions you make. Realistic assessments using current high grade ores put it at over 100:1 with centrifuge enrichment and a little higher again with CANDU. With low grade ores and diffusion enrichment, it can be as low as 10 to 20:1. The world average, according to some recent figures I’ve seen, is ~50:1. This has been worked out in a number of comprehensive studies, using real-world mine data (e.g. Rossing, Olympic Dam), enrichment SWUs from France, US and Russia, and plant construction and operating data. As always in such matters, the numbers are available, publicly, for you to crunch yourself, if you have the time and tools. Don’t take such matters on faith — a lesson from Mackay.
Footnote: This article from EoE is well worth reading, Ten fundamental principles of net energy. Here are the headlines:
1. Net energy and energy surplus are important driving forces in ecology and economic systems
2. The size and rate of delivery of surplus energy is just as important as EROI
3. The unprecedented expansion of the human population, the global economy, and per capita living standards of the last 200 years was powered by high EROI, high energy surplus fossil fuels
4. The principal economic impact of a shift to a lower EROI energy system is the increased opportunity cost of energy delivery
5. Energy quality matters
6. Market imperfections that distort prices and cost also affect EROI
7. The methodologies to perform net energy analysis are well established
8. The relation between ‘peak oil’ and the EROI for world oil production is unknown
9. Technological change affects EROI just as it affects price and cost
10. Alternatives to the dominant energy and power systems show a wide range in EROI