Energy Return On Energy Invested and its variations is a metric frequently used to look at our efficiency in harvesting energy with respect to the energy input.
As an aside, regarding fossil fuels in day to day use we talk about energy production when strictly speaking we don’t produce coal/oil/gas but extract it and sometimes convert it. Strictly technically speaking fossil fuels as well as renewables are solar energy; one is previously accumulated stock and the other is flow. Think balance sheet versus income statement.
EROEI is an attractive concept but has a number of issues which can reduce its utility significantly. The main issue with EROEI is that it suffers from boundary issues along a number of vectors.
1. The first boundary issue is that although it is relatively easy to measure the energy produced it is significantly more difficult to determine the energy consumed in producing the energy. Should only direct energy inputs be counted (for example the energy to turn the drill on an oil rig), or should second order inputs (the energy the workers on the rig used going to work) or even third order inputs (the energy used to make the car which the worker uses to go to the rig) count?
2. Another boundary issue is that of the input fuel source. If the Input energy is fossil fuel based the EROEI analysis will tell you how efficient the energy extraction process is with respect to energy use, and therefore how much energy ultimately can be extracted. If, however, the input energy is renewable even if the energy conversion process is seemingly inefficient in at the end of the process one has in total more energy than one started, which is quite the opposite from when the input was fossil fuel based.
3. Another consideration is that of the energy density of the fuel produced/ extracted. Generally the higher the energy density of a fuel the higher its utility is. Methanol and gasoline are both liquid fuels but one has a higher utility because of its higher energy density. Specifically, in mobile applications the energy density of the fuel you carry has a very direct impact on the end user utility.
Aside from boundary issues EROEI does not take into account the different utility associated with different energy carriers. Instead there is an implicit assumption that all BTUs are created equal. In real life though some BTUs are more equal than others.
Once you move from an entropic system (where energy flows from a highly concentrated state to a less concentrated state) to a negative entropy system (where you capture some form of diffuse solar energy and concentrate it) everything changes. Instead of running down finite energy sources you are now adding to the quantity of energy available. There will be other limits, but not energy per se. In a system relying on non-renewable energy, no matter what your EROEI is eventually you'll run out of fuel. In an open system therefore EROEI is interesting as a conversion efficiency measure, but irrelevant with respect to sustainability of the energy input of energy production.
If humanity wants to continue to exist in a form recognizable to us making the switch from an entropic energy supply to a negative entropy energy supply is unavoidable. Without making that switch the game will be over at some point. We are starting to feel the first hints of limits to growth along a number of vectors, both on the input side as well as the output side of economic activity. Specifically, what you're seeing now is that there is a tension between a financial system which requires growth to exist and a natural system (resources) which naturally deplete and which have an extraction rate which at some point can no longer be increased. Switching to a negative entropy energy system would be an important step towards dealing with this problem.