# Energy cannibalism

Energy cannibalism refers to an effect where rapid growth of an entire 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 energy because new energy is used to fuel the embodied energy of future power plants.

## History

This term was first developed by J.M. Pearce in a paper discussing the potential for nuclear energy to offset greenhouse gas emissions and thus to mitigate climate change by replacing fossil fuel plants with nuclear plants.[1]

Energy cannibalism in this context is also true of any other energy source such as wind power, solar power, etc.

## Theoretical underpinnings

In order for an “emission free” power plant to have a net negative impact on the greenhouse gas emissions of the energy supply it must produce enough emission-less electricity to offset both greenhouse gas emissions that it is directly responsible for (e.g. from concrete used to construct a nuclear power plant) and to offset the greenhouse gas emissions from electricity generated for its construction (e.g. if coal is used to generate electricity while constructing a nuclear power plant). This can become challenging during rapid growth of the “emission free” technology because it may require the construction of additional power plants of the older technology simply to power the construction of the new “emission free” technology.

## Derivation

First, all the individual power plants of a specific type (Pearce used nuclear plants in the initial derivation)[1] can be viewed as a single aggregate plant or ensemble and can be observed for its ability to mitigate emissions as it grows. This ability is first dependent on the energy payback time of the plant. Aggregate plants with a total installed capacity of ${\displaystyle C_{T}}$ (in GW) produces:

${\displaystyle E_{T}=t\cdot C_{T}=t\cdot \sum _{n=1}^{N}C_{n}}$

(1)

of electricity, where ${\displaystyle t}$ (in hours per year) is the fraction of time the plant is running at full capacity, ${\displaystyle C_{n}}$ is the capacity of individual power plants and ${\displaystyle N}$ is the total number of plants. If we assume that the energy industry grows at a rate, ${\displaystyle r}$, (in units of 1/year, e.g. 10% growth = 0.1/year) it will produce additional capacity at a rate (in GW/year) of

${\displaystyle r\cdot C_{T}}$.

(2)

After one year, the electricity produced would be

${\displaystyle r\cdot C_{T}\cdot 8760\,h}$.

(3)

The time that the individual power plant takes to pay for itself in terms of energy it needs over its life cycle, or the energy payback time, is given by the principal energy invested (over the entire life cycle), ${\displaystyle E_{P}}$, divided by energy produced (or fossil fuel energy saved) per year, ${\displaystyle E_{ann}}$. Thus if the energy payback time of a plant type is ${\displaystyle E_{P}/E_{ann}}$, (in years,) the energy investment rate needed for the sustained growth of the entire power plant ensemble is given by the cannibalistic energy, ${\displaystyle E_{Can}}$:

${\displaystyle E_{Can}={\frac {E_{P}}{E_{ann}}}\cdot r\cdot C_{T}\cdot t}$

(4)

The power plant ensemble will not produce any net energy if the cannibalistic energy is equivalent to the total energy produced. So by setting equation (1) equal to (4) the following results:

${\displaystyle {\frac {E_{P}}{E_{ann}}}\cdot r\cdot C_{T}\cdot t=C_{T}\cdot t}$

(5)

and by doing some simple algebra it simplifies to:

${\displaystyle {\frac {E_{P}}{E_{ann}}}={\frac {1}{r}}}$

(6)

So if one over the growth rate is equal to the energy payback time, the aggregate type of energy plant produces no net energy until growth slows down.

## Greenhouse gas emissions

This analysis was for energy but the same analysis is true for greenhouse gas emissions. The principle greenhouse gas emissions emitted in order to provide for the power plant divided by the emissions offset every year must be equal to one over the growth rate of type of power to break even.

Recent work expands earlier work to generalize the GHG emission neutral growth rate limitation imposed by energy cannibalism to any renewable energy technology or any energy efficiency technology.[2] This has resulted in a path towards an economic system built on a dynamic life-cycle of greenhouse gas emissions.[3]

## Example

For example, if the energy payback is 5 years and the capacity growth is 20%, no net energy is produced and no greenhouse gas emissions are offset.

## Applications to the nuclear industry

In the article “Thermodynamic Limitations to Nuclear Energy Deployment as a Greenhouse Gas Mitigation Technology” the necessary growth rate, r, of the nuclear power industry was calculated to be 10.5%. This growth rate is very similar to the 10% limit due to energy payback example for the nuclear power industry in the United States calculated in the same article from a life cycle analysis for energy.

These results indicate that any energy policies with the intention of driving down greenhouse gas emissions with deployment of additional nuclear reactors will not be effective unless the nuclear energy industry in the U.S. improves its efficiency. An exception to these figures is the history of nuclear development in France. In ten years, nuclear power in France experienced a 15-fold increase that resulted in nuclear providing 70% of the country's electricity.[4]

## References

1. ^ a b Pearce, Joshua M. (2008). "Thermodynamic limitations to nuclear energy deployment as a greenhouse gas mitigation technology" (PDF). International Journal of Nuclear Governance, Economy and Ecology. 2 (1): 113–130. doi:10.1504/IJNGEE.2008.017358.
2. ^ Pearce, J.M. (2008). "Limitations of Greenhouse Gas Mitigation Technologies Set by Rapid Growth and Energy Cannibalism". Klima 2008. Archived from the original on August 17, 2009.
3. ^ Kenny, R.; Law, C.; Pearce, J.M. (2010). "Towards Real Energy Economics: Energy Policy Driven by Life-Cycle Carbon Emission" (PDF). Energy Policy. 38 (4): 1969–78. doi:10.1016/j.enpol.2009.11.078.
4. ^ http://pubs.giss.nasa.gov/docs/2013/2013_Kharecha_Hansen_2.pdf