Let’s explore the concept of EROEI – Energy Return on Energy Invested is often cited as a metric to compare fossil fuels with renewables, typically with the claim that fossil fuels are way better with much higher EROEI and a global energy system based on renewables will crumble under the weight of its own internal energy demand because we will use more energy to build the renewables than we get back from them.

This is of course entirely false and has been debunked many times; in a nutshell:

1. Wind EROEI is ~20-30
2. Solar is typically ~10-15
3. Gas is ~5-15 depending on supply chain and usage specifics, e.g. LNG consumes ~10% of the product in liquefaction and transport.
4. Oil is ~3-8 by the time the energy consumed in extraction, transport and refining into useable products has been accounted for

But that isn’t the whole story because the EROEI equation is typically based on Primary energy, not exergy, and exergy describes the quality of the energy and is a whole load more valuable.

Exergy is essentially the useful work content of energy and electricity is effectively pure exergy, i.e., you can convert it into work with 100% thermodynamic efficiency, although in the real world the actual efficiency of converting electricity to work through a motor is between ~70-95%

Fossil fuels, on the other hand, are converted to work via combustion in a heat engine and hydrogen can similarly be combusted or oxidised in a fuel cell.  There are hard thermodynamic limits to how much exergy can be extracted from a chemical fuel used in a heat engine such that the maximum exergy than can be extracted from the primary energy is currently ~55-60% (based on the higher heating value (HHV) of the fuel) and in the case of an automotive ICE the delivered exergy is more like 35-45%.  That is not to say an ICE car is 45% efficient, as parasitic loads such as water and oil pumps and energy absorbed in the transmission system further reduce the actual work delivered to the wheels resulting in maximum real world efficiencies of ~25-35%

So, a better metric might be Exergy Returned on Exergy Invested – ExROExI?

However, this also has some issues as not all the energy consumed in manufacturing a product is converted into work; heat is often required in large quantities.  In fact, according to the IEA 2/3 of industrial energy consumption is heat, and fossil fuels and hydrogen are pretty good at delivering heat with typical efficiencies of 70-90% based on the HHV.  

However, our pure exergy electricity does even better with efficiencies of ~98% for high temperature resistive element heating, and for lower temperatures (<180C) we can do way better, using a heat pump to deliver multiples of the exergy we put into the system.

Let’s look at the impact all of the above has on our solar EROEI example if we draw the boundary at point of energy delivery.

The 15:1 EROEI ratio for solar is calculated based on the primary energy input to create and install the panel being largely fossil fuel based, as that is the current energy system we have.  If we consume 2/3 as heat and 1/3 as work our average conversion efficiency is ~(0.67 x 0.80) + (0.33 x 0.3)  ~64% 

If we replaced that primary energy with electricity with our average conversion efficiency is (0.67 x 0.98) + (0.33 x 0.8) ~92%.

So instead of putting in 1 unit of fossil fuel primary energy to get back 15 units of exergy, you would only need 0.64/0.92 = 0.7 units of electrical primary energy and therefore the EROEI for solar PV is ~20 and for a wind turbine would be ~40.

An excellent paper on the subject of EROEI and which addresses the issues above can be found here.

But this still isn’t the whole story around EROEI as there is a time factor which is important and has potential implications for speed of transition and rate of economic growth.