[Updated: In the comments Skipper points out a units error (Thanks!). That would be 20,000 nuclear plants, not 2,000!]

The central question can be found at the bottom of this long, technical post. In 1998 Hoffert et al. published a seminal paper in Nature (PDF) which argued that:

Stabilizing atmospheric CO2 at twice pre-industrial levels while meeting the economic assumptions of “business as usual” implies a massive transition to carbon-free power, particular in developing nations. There are no energy systems technologically ready at present to produce the required amounts of carbon-free power.

Hoffert et al. provide a figure which illustrates the amount of carbon-free energy that will be needed assuming that concentrations of carbon dioxide are to be stabilized at 550 ppm, and the global economy grows at 2.9% per year to 2025 and 2.3% per year thereafter. I have updated this figure to 2008 (estimated) values as indicated below.

The figure shows carbon free energy required to achieve stabilization at 550 ppm carbon dioxide as a function of the rate of average energy intensity decline. The figure also shows 1990 total energy consumption (about 11 terawatts, TW) and the share of this valuefrom carbon-free sources (about 1.2 TW). I have updated both of these values to 2008 using data from the EIA, which I extrapolated to 2008 values, for which I arrive at 17.4 TW of total energy consumption of which 2.4 TW are carbon-free.

Hoffert et al. estimated that we’d need 10-30 TW of carbon free primary energy production by 2050, assuming energy intensity declines of 1.0-2.0% over the first 5 decades of the 21st century. So far at least, that assumption has proved optimistic, as actual energy intensity has increased, as indicated by the blue dot on the leftward-extended horizontal axis. If energy intensity does not improve beyond this value then the world will need 22 TW of carbon-free energy by 2025, and if this value works out to a net 0.5% decline through 2025, then this figure would be halved to 11 TW. For 2050 the values are 51 and 25 TW respectively.

The units of energy can be difficult to interpret. How much is 10 TW of energy? A run-of-the-mill nuclear power plant provides about 500 megawatts; so if you have 2,000 of these then you have 1 terawatt. So 20,000 nuclear plants — or the equivalent — by 2025 would do the trick of providing 10 TW.

In a subsequent paper in Science 2002 Hoffert et al. discuss the options available to meet technological challenge of providing 10 TW of carbon-free energy:

Combating global warming by radical restructuring of the global energy system could be the technology challenge of the century. We have identified a portfolio of promising technologies here–some radical departures from our present fossil fuel system. Many concepts will fail, and staying the course will require leadership. Stabilizing climate is not easy. At the very least, it requires political will, targeted research and development, and international cooperation. Most of all, it requires the recognition that, although regulation can play a role, the fossil fuel greenhouse effect is an energy problem that cannot be simply regulated away.

They responded to critiques of their 2002 paper with this (emphasis added):

Market penetration rates of new technologies are not physical constants. They can be strongly impacted by targeted research and development, by ideology, and by economic incentives. Apollo 11 landed on the Moon less than a decade after the program started. We are confident that the world’s engineers and scientists can rise to the even greater challenge of stabilizing global warming. But it does not advance the mitigation cause to gloss over technical hurdles or to say that the technology problem is already solved.

Any discussion of the technologies needed to stabilize carbon dioxide concentrations is incomplete without showing the arithmetic of energy production and consumption. This simple math is too often overlooked in the highly politicized to and fro over mitigation.

The central question of the mitigation challenge is thus the following: What technologies will provide the world’s future power needs, and do so in a carbon-free manner? Show your work.