# Energy cannibalism

## Idea

Energy cannibalism refers to an effect where rapid growth of an energy-producing industry creates a need for energy that uses (or ‘cannibalizes’) the energy of existing power plants. Thus during rapid growth the industry as a whole produces no net energy. This of course may change in the long term as the building of new plants levels off.

## Details

This idea was given a simple quantitative analysis by Joshua Pearce, summarized nicely here:

Briefly:

Energy cannibalism occurs when more energy goes into building these plants than the plants will generate.

A criterion for this involves the concept of energy payback time: the time that the individual power plant takes to pay for itself in terms of energy. For a plant that produces power at a constant rate, this is the total energy invested in the plant (over the entire life cycle), divided by energy produced (or fossil fuel energy saved) per year.

Energy cannibalism occurs when the number of power plants of some type grows exponentially so fast that the growth rate (measured in units of inverse time) has a reciprocal less than the energy payback time.

The solar breeder is an attempt to get around energy cannibalism.

### Illustrative simulations

To gain some understanding of how the contributions interact to give energy cannibalism, let’s look at some toy examples, considering identical renewable plants of some type which are assumed to emit no carbon dioxide when up-and-running.

To simplify things, let’s pick units of time so that the plant takes 1 unit of time to build and energy so that the plant produces 1 unit of energy in 1 unit of time. Finally we choose the unit of $CO_2$ to be the amount of emitted by an existing polluting power station to produce 1 unit of energy.

Then the major variable is $c$, namely how much energy an renewable plant takes to build. For the moment let’s consider the case where it takes 6 times as much energy to build the plant as its energy output in 1 time unit. Let’s suppose the world wants 2047 renewable plants built and the building rate doubles each year until all those plants have been built (so that 10 “time units” of building occur before the programme ends).

#### Net energy

Firstly, let’s consider net energy cannibalism for identical renewable plants using some particular technology. We’ll also assume we’ve got a huge number of polluting plants we’re prepared to use to build these new more eco-friendly renewable plants. Various quantities are plotted below for the $c=6$, doubling building rate each generation programme:

The red line is the amount of energy generated by the renewable plants in the current time period, and the green line is the amount of energy to build the renewable plants being built in the current year (negative as it takes away from net energy). The blue line is thus the current year’s net energy (i.e., energy generated - energy used in building). Finally the magenta line is the running average of the net energy generated so far (ie the sum of the net energy so far divided by the time). Intuitively, in the limit of the renewable plants running forever after being built this magenta line will tend towards the red line of renewable output.

However, it can be seen that, with this relatively modest 6 times energy output required for construction, there is a huge net deficit (approximately the “plant building energy” times larger than the final renewable plant output) that needs to be provided by older energy generation technologies which “peaks” in the final year of the building program. For these particular parameters, note that the historical average net energy generated, and hence the cumulative net energy generated, does not even become positve until “build periods” after the building programme has finished.

#### Carbon dioxide emissions

Secondly, we can look at carbon dioxide releases. We’ll also suppose the reason 2047 renewable plants are being built is because there is (at least) 2047 units of energy currently being used by consumers. Thus initially there are 2047 units of $CO_2$ emissions attributable to satisfying this demand. As more renewable plants are built more of this demand can be fulfilled with zero carbon dioxide emissions, but the building of these plants will require energy from old carbon dioxide emitting power plants. The graph below combines these effects for the same $c=6$ and building scheme as the first graph, showing the current $CO_2$ emissions at a given point in time:

(It can be seen that, as expected from the model, these are the same curves as the first graph but with different orientations and offsets.)

The red line shows the amount of $CO_2$ emitted in order to fulfill the consumer demand, the green line shows the amount of $CO_2$ emitted in building the current set of renewable plants. Finally the blue line shows the net $CO_2$ emissions. As can be seen, whilst the red line drops the green line is rising faster, so that the blue net $CO_2$ keeps rising even above the initial emissions level right until the building program has finished.

#### Avoiding problems by using only energy from previous plants

Suppose we try and avoid these cannibalisation effects by requiring that, after building some initial renewable plants, the production of the next set of renewable plants must use only energy from previously completed renewable plants. For these purposes we’ll keep the same units as in the previous sections. If we start out with some number of plants $n(0)$, how many plants can be built at each point in time? From the functional equation (which assumes no energy losses anywhere)

$c n(T)=\sum_{t=0}^{T-1} n(t)$

we find that

$n(t)=\left(\frac{c+1}{c}\right)^{t-1} \frac{n(0)}{c}$

Thus the number of plants being built increases geometrically with parameter $(c+1)/c$. This appears to require $c$ is much less than the energy generated by a plant over a the length of time it takes to build a plant for a self-sustaining rapid build out.

Question: Are there any feasible technologies, other than nuclear power, that actually satisfy this constraint?

### Further complications

“Types of energy” are only fungible at a conversion cost. This may compound the energy cannibalism effect. For example, consider a programme of building wind turbines. A major contribution to the energy cost of building a wind turbine is in smelting metal ores to form the blades and tower. A smelting plant generally needs to be run continuously (in order to avoid issues arising from molten metals cooling within the plant). As such, it requires electrical inputs which are reliable and continuous. In contrast, a wind farm generates intermittent electricity, and thus can only be used for smelting if its energy can be transferred to an temporary storage medium (eg, CAES storage). Thus the wind farm programme will result in some combination of

• taking a portion of the continuous power generation capacity away from general use replacing it with less generally useful intermittent power,

• contribute less power to the wind turbine building programme than their “naive capacity” (due to conversion losses).

This is not a fatal problem, but highlights the need for detailed modelling of very large scale build-out schemes in order to understand these effects in advance.

## References

Also see Energy return on energy invested.

category: energy