Do EROEI ratios matter a lot?

I have recently been discussing how important EROEI ratios for economic prosperity. We are soon going to exhaust all high EROEI fossil fuel sources. So we will have really no choice but to switch to lower grade energy sources. Is this a big deal?


Obviously there are big issues with such a transition (mainly due to the more polluting nature of some alternative sources), but is the lower EROEI a source of concern?


I think the standard economic reply to that question is that it would simply stimulate investment. A lower EROEI source requires a higher ratio of capital vs income (or investment vs consumption). This is not necessarily bad, given that most economic models assume that you can accumulate an infinite amount of capital. Lower EROEI requires a bigger physical capital structure and such capital structure is always achievable. Provided the lower EROEI source is infinite, you will reach a new equilibrium, where the higher capital will generate enough return for the previous level of consumption and the investment necessary to renew or expand the capital base. I think that various renewable technologies (solar, algae bio-fuels, etc...) could be that infinite EROEI source.


I think it might be interesting to calculate what rate of return is implied by a certain EROEI. I think I can use the simple model in the previous post. With such a simple exponential decay, EROEI is simply equal to productivity divided by decay.

We can now solve a simple equation to calculate the internal rate of return for such a return profile:

The solution is simply:

What can we say about this equation? Well the first question is what are reasonable values for d. To be honest I am not entirely sure... I would guess between 3% and 10%, corresponding to half-life between 7 and 25 years. Taking 5% as a guess, it gives us a 15% rate of return for a EROEI of 3 (I think this is the current estimates for tar sands). I think that this compares quite well with standard equity rate of return. Certainly EROEIs below 2 look difficult to sustain, especially on very long dated projects. Market real returns have been on a secular down trend, so you never know, but it looks tricky.

The above analysis is implicitly assuming that the energy I put into the project will be worth as much as the energy I take out. Historically this hasn't been the case to be honest, with highly volatile energy prices creating significant uncertainty which stopped investment.

Such rates of return would seem to suggest there should always be massive investment in energy production, but for a large part of recent past, lack of demand for oil was the real bottleneck, with producers in the 1990 having to cut supply in order to maintain prices. The joint effect of slow investment and the physical depletion of known reserves has now change that equilibrium and we are observing an increase in prices and investment, be it wind/solar, tar sands and gas fracking.

Is the energy trap possible?

I have enjoyed reading this blog. I agree with many of the opinions listed there and I have learned quite a few things.

But I really cannot agree with one of his worries: the energy trap.

Let me describe the basic idea: as fossil fuel production starts declining in the future, people will be unwilling to divert their now scarce energy resources into renewable energy investment, since this would depress their current consumption even further.

While I bow to Tim Murphy's scientific knowledge, the energy trap is basically a theory of human behaviour. As such I think that it needs to be judged based on observed human behaviour (current and past).

The first question we need to ask is: is energy consumption consumption in the economic sense?

In economics production is allocated between consumption and investment. As a simple example, a farmer splits his harvest between seeds and food. The allocation between the two depends on many factors, such as productivity, time preferences, risk appetite, etc... You can see here that investment is roughly 20-25% of world GDP. The number is not constant through time, but it's always a significant amount. This is a constant feature of economic activity and one of the engines of growth, as accumulated capital goods (such as railways, bridges, etc...) help increase production.


What is the relative energy intensity of consumption vs investment? If the energy intensity of investment is zero, the above point would be irrelevant. I find this conjecture hard to believe. If anything my intuition would argue the opposite as most capital goods are highly energy intensive. 70% of the economy is services to each other (doctors, lawyers, accountants, etc...) which are mostly consumed immediately. I doubt such activity has the same energy intensity as building a house or a factory. But even if the energy intensity is the same, this leaves us with a large investment budget.

So there is a large component of energy usage which could be easily re-directed without actually requiring anyone sacrificing their shower. Is 25% of energy usage enough to power a conversion to renewable energy? I guess not always. Let's build a toy model:

y(t) = f(t) + r(t)*pr
d f(t) / d t =  - kf * f(t)
d r(t) / d t  = - kr * r(t) + i * y(t)

f = fossil fuel production
r = energy invested in renewable capacity
pr = productivity of renewable capacity
i = investment ratio

We want to calculate in which circumstances the first derivative of y(t) at time 0 is negative. So:
EROEI = pr/kr
d y(t) / d t = d f(t) / dt + pr * d r(t) / dt
d y(t) / d t =  - kf * f(t) - pr * kr * r(t) + pr * i * y(t)

Assuming r(0) = 0, we can simplify and we get simply:
pr * i > kf


As we saw, a reasonable value for i is 25%. Assuming a EROEI of 4 and kr of 10%, we get 40% productivity. This parameters would require an annual  10% drop in fossil energy production in order to force anyone to actually change their consumption patterns. Is that possible? Are the others parameters too optimistic? I know little about geology, but 10% decrease seems far fetched. Investment patterns would be massively changed, but that's kind of normal, new investment is always somewhat different.

Now our toy model has assumed fixed parameters, which is obviously silly. What is reasonable to expect? Most parameters in the model are more or less determined by physics and geology, so I have nothing to add, but investment ratio is clearly not, it's a matter of human preferences. I acknowledge there is no perfect parallel for this, but I think there is a class of events which are somewhat similar.

The energy trap must be a function of an unexpected drop in fossil fuel production. We were too optimistic about available fossil fuel reserves and we have over consumed. This realization is really equivalent to a drop in wealth. We believed our stock of fossil energy was higher than it was. Wealth losses (at a society level) are not that common, but do occur. The most common are natural disasters. What is the standard reaction to natural disaster? An increase in GDP driven by a jump in investment. This is not universally true, as poor society have no storage capacity and no ability to devote resources to further investment.

Are there any other possible factors? A recent, but very powerful phenomenon is the increase of time devoted to leisure, mostly through longer retirement. This development is only sustainable if we increase saving rates, in order to fund our retirement consumption. Given that saving and investment are two-sided of the same coin, this requires increasing investment rates. By how much? As a back of the envelope calculation, investment needs to be equal to the share of life spent not working: so roughly 30-40% in the developed world. We are currently far from this and we will probably disappoint some pensioners, but that's a different matter.

So I think the energy trap is very unlikely, given current available technology and current investment preferences.