Rationalisation (mathematics)

Sportspersons Hyslop from Nicolet, usually spends time with pastimes for example martial arts, property developers condominium in singapore singapore and hot rods. Maintains a trip site and has lots to write about after touring Gulf of Porto: Calanche of Piana. 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.

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 greenhouse gas emissions of the energy supply it must do two things:

1. produce enough emission-less electricity to offset the greenhouse gas emissions that it is responsible for
2. continue to produce electricity to offset emissions from existing or potential fossil fuel plants.

This can become challenging in view of very rapid growth because the construction of additional power plants to enable the rapid growth rate create emissions that cannibalize the greenhouse gas emissions mitigation potential of all the power plants viewed as a group or ensemble.

Derivation

First, all the individual power plants of a specific type (Pearce used nuclear plants in the initial derivation) 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 $C_{T}$ (in GW) produces:

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

After one year, the electricity produced would be

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), $E_{P}$, divided by energy produced (or fossil fuel energy saved) per year, $E_{ann}$. Thus if the energy payback time of a plant type is $E_{P}/E_{ann}$, (in years,) the energy investment rate needed for the sustained growth of the entire power plant ensemble is given by the cannibalistic energy, $E_{Can}$:

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 (Template:EquationNote) equal to (Template:EquationNote) the following results:

and by doing some simple algebra it simplifies to:

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. This has resulted in a path towards an economic system built on a dynamic life-cycle of greenhouse gas emissions.

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.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.