The claim that EROEI in and of itself determines the possible growth rate of an energy supply is incorrect. Of course if the energy balance is zero then you cannot obtain any useful energy whatsoever. Zero does indeed equal zero. However, the possible growth rate does not bear a simple relation ship to the energy balance.

For example, suppose that you are alone on an island, and you have figured out some way to produce fuel. Further suppose that the source of this fuel is so large that the only limitation on how much fuel you can produce is how many hours you dedicate the fuel extraction process. Suppose that in one hour of work you extract a gross output energy G and you consume an amount of energy I. Then your net energy production per hour is

N = G-I = G(G-I)/G = µG.

Where µ=(G-I)/G is the fraction of the gross output energy which is left over after the input energy has been subtracted (I call this number the energy utilization rate). In this case there is no energy growth issue whatsoever. The amount of energy you can harvest in a given year is simply proportional to fraction of your labor that you dedicate to producing energy. There is an issue of optimization of labor effort: How much time should be spent extracting energy and how much time should be spent using that energy to produce useful output?

Growth issues occur only when time delays come into the picture. If the energy payback on investment in natural gas exploration and drilling were instant, so that as soon as a new field had been found and drilled all of the energy from it was instantly available, then the only thing that would limit how much energy you could obtain in a given year would how much of your economic effort was dedicated to exploring and drilling. This would not be a growth issue but a resource allocation issue. Of course the energy balance would effect the optimum resource allocation via the energy utilization rate µ.

On the other hand, if a substantial period of time is required to recoup up front energy investments, then limits to growth issues arise. These limits cannot be analyzed in a simple way as a function of energy balance. What matters then is the time profile of the energy return relative to the time profile of the energy investment.