Kaya Identity Calculator Online

One of the big questions with simulations of future energy requirements is how realistic the various assumptions are - one can always express doubts about model inputs: for example how much efficiency improvements are built in is a critical issue, and future economic growth is of course hard to predict. A simple identity for better understanding all this is the "Kaya" relationship between CO2 output, population, GDP per capita, energy intensity, and carbon intensity of energy production. David Archer of realclimate.org has posted a simple online simulation of future CO2 production based on the "Kaya identity" on his website

See also his comments on realclimate.org.

From the parameters you give - maximum population, GDP per capita average growth rate, energy intensity decline rate, It automatically graphs up the following:

Carbon emissions (Gton/yr)
CO2 ppm in the atmosphere, compared against models to limit CO2 to certain levels
Carbon-free energy required for CO2 stabilization (in TW)

and several other graphs showing the more direct implications of the parameters you chose. Interesting stuff.

Satirical newspaper "The Onion" also has out a prediction of the energy situation in 2056: "SOLOPEC Nations Warn Sun's Output May Fall Short of Demand".

[Followup 24-Jun-05] Several people seem to be interpreting this in an overly optimistic way - that simply doing better on "efficiency" will solve all our problems. I gave a bit of an explanation why it's not so simple here; it seemed useful to reproduce those arguments here as well.


One confusion is that energy intensity relates directly to "efficiency", and that energy intensity improvements in individual nations have any direct relation to global energy intensity - that's simply not true because of the way GDP factors in. From Smil's "Energy at the Crossroads", China used some 33 MJ/$ of GDP (exchange rate valued), 3 times the energy intensity of the US (about 11 MJ/$) in 2001. So there would seem to be a lot of improvement available there - but it could be quite illusory. Let's look at some sample numbers here:

Year 1: $10 of GDP in US, using 110 MJ
$1 of GDP in China, using 33 MJ
total: $11 gross product, 143 MJ

Year 2: $9 of GDP in US, using 96 MJ (3% improvement)
$2 of GDP in China, using 64 MJ (3% improvement)
total: $11 gross product, 160 MJ

I.e. BOTH countries improved their energy intensity numbers by 3%, but the transfer of production from US to China resulted in an INCREASE in world energy use, not a decrease. World energy intensity actually went up, even though the energy intensity in both countries went down.

The energy intensity business is very complex, and full of subtleties not evident at first. The purchasing-power-parity issue is another one: if you measure China's GDP by PPP numbers rather than exchange-rates, it's actually very close to the US number of 11 MJ/$. But it's not improving much either by that measure.

One of the oddest things about energy intensities, despite definite significant improvements in efficiency of all sorts in the western world in the 20th century, is that the global ratio of world production to world energy use remained roughly constant throughout the 20th century - at about that 11 MJ/$ level.

I.e. the global energy intensity number that goes into the Kaya identity is not perhaps what you first think it is because of the GDP dependences. And improving at a much faster rate than the 1% or so typical of recent decades is going to be very, very, very hard.

The other big problem is the interdependence between efficiency and growth. Historically we've seen GDP growth rates of about 1.6%/year. China has had dependable growth rates in the 6-10% range or more for a long time; energy efficiency improvements around the world may spur even faster growth rates - and then we're right back at the same problem.

Much better to ensure we have the major carbon-free energy sources we will need under 99% of the realistic scenarios here.


On the limits to efficiency improvements: The efficiency of conversion of chemical (and nuclear) energy to electricity was pretty much stuck through most of the 20th century at about 35%, the Carnot (thermodynamic) efficiency limit for a steam turbine. A couple of things have allowed us to surpass that in recent years, through methods that convert the energy more directly rather than just burning to make heat: gas turbines (which use the mechanical energy of the burning gas much as an airplane jet engine does) and fuel cells.

For gas turbines we can use natural gas directly; this is already quite widespread, and efficiencies of well over 50% are typical. Theoretically this could go as high as 85%. We can also turn coal into gas as suggested; similarly we can turn natural gas or coal into hydrogen through chemical processes that lose some of the original energy; these are naturally less efficient overall, but still can be an improvement over burning coal directly.

Fuel cells also produce heat through their internal resistance - when run at the high power levels you'd need in a real power plant, efficiencies of 50-60% are typical, even though theoretically fuel cells can reach 90% or better.

In any case, we can certainly improve the 35% typical of the 20th century to 50% or more, and possibly as high as 85 or 90% efficiency in conversion of chemcial energy to electricity. So, in one of the heaviest uses of primary energy we have today, there's room for a factor of 1.5 to 2.5 improvement.

Now, suppose we have energy efficiency improvements (not the same as energy intensity, as explained earlier, but never mind that for now) of 3% per year. Compounding annually, we've hit the maximum 2.5 limit in just 30 years. How can we possibly expect to sustain that for a full century???

Even 1% continual improvements may be very hard to sustain for another century: 100 years at 1%/year is a factor of 2.7, more than is even theoretically available in chemical to electric conversion.

Created: 2005-06-22 16:52:44 by Arthur Smith
Modified: 2005-06-24 13:32:46 by Arthur Smith