Wednesday, June 8, 2011

Atmospheric temperature increase due to coal combustion

I remember reading, ages ago, an article that estimated the global atmospheric temperature increase due to the combustion of a small amount of fossil fuels.  Or, put another way, if combustion releases x units of energy (and of course some CO2, which traps further heat), then the atmospheric heat content eventually increases by y units of energy.  My recollection is that y/x was large.

I’ve tried without success to find that article; perhaps a reader can help me?

Whatever, in the spirit of enquiry, I thought I’d make my own estimate.  Here is the task: if we burn 1 kg of coal, what is the resultant eventual increase in the atmospheric temperature and heat content?

Let’s start with a few assumptions and some results from the literature:

Fraction of Carbon in coal: 0.7 (but depends on the type of coal)
Energy content of coal: 28 MJ/kg (but depends on the type of coal)
Mass of the atmosphere [1]: 5.144 × 10^18 kg
Mass of CO2 in the atmosphere [2]: 3.16× 10^15 kg
Current CO2 concentration [3]: 387 ppmv
Pre-industrial CO2 concentration [3]: 280 ppmv
Climate sensitivity [4]: 2.0 – 4.5 °C per doubling of CO2 concentration from pre-industrial levels
Specific heat capacity of air at constant pressure: 1005 J/(kg.°C)
Molar mass of Carbon: 0.012 kg
Molar mass of CO2: 0.044 kg

By the way, the climate sensitivity is a topic of immense importance and interest.  Reference [4] gives a readable account of the current state of knowledge.

Let’s proceed with the estimates …

The mass of CO2 produced by combustion of 1 kg coal is
0.7 × 0.044/0.012 = 2.57 kg

The mass of CO2 in the pre-industrial atmosphere is
(280/387) × 3.16 × 10^15 = 2.286 × 10^15 kg

The fractional increase in the atmosphere’s CO2 due to the combustion of 1 kg coal is
2.57/(2.286 × 10^15) = 1.124 × 10^-15


[Note added (26 April 2012):  Upon further consideration, I realise this fractional increase needs to be modified.  Not all of the CO2 will remain in the atmosphere; indeed the Airborne Fraction is usually reckoned to be a little less than 0.5, with the remainder of the CO2 absorbed by oceans, land and plants.  For that reason, all the following estimates need to be scaled down by a factor of approximately 2.]

The resulting increase in the atmospheric temperature is in the range
1.124 × 10^-15 × {2.0 to 4.5} °C,
that is, in the range
{2.248 to 5.058} × 10^-15 °C.

The resulting increase in the heat content of the atmosphere is in the range
{2.248 to 5.058}× 10^-15 × 1005 × 5.144 × 10^18  J,
that is, in the range
{11.6 to 26.1} MJ

Each kg of coal produces 28 MJ directly from combustion. Through complicated atmospheric processes, somewhere between half and the full amount of that heat will remain permanently in the atmosphere.  This estimate seems less dramatic than I indicated in my opening paragraph.  But maybe readers can shed light on that matter?

What is the effect of all the coal burned in the world?  According to reference [5], 2009 world coal production (both hard coal and brown coal/lignite) was 6.903 billion metric tonnes per yr.  That would lead to an annual increase in the global temperature in the range
6.903 × 10^12 × {2.248 to 5.058} × 10^-15 °C/yr, or
{15.5 to 34.9} × 10^-3 °C/yr, or
{0.155 to 0.349} °C/decade.

In an earlier post (see 2011-03-15), I showed the world’s current coal reserves can be expected to last for around 75 years at current rates of fossil fuel consumption.  The temperature rise due to coal consumption would therefore be in the range {1.2 to 2.6} °C.  The effect of consumption of oil and gas would be additional.

According to the 2009 BP Statistical Review of World Energy, Australia has around 9% of the world’s coal (and current production is around 6% of the world’s total).  Under a business-as-usual scenario in which we mine all our coal, we could anticipate that Australia’s contribution to global warming from coal alone over 75 years would be in the range {0.1 to 0.24} °C.

To conclude, let me comment on my other activities.  If you follow this blog, you’ll know that I’ve invented a new thermodynamic cycle for power generation.  I’m currently trying to commercialise one variant of this invention, in which I propose to boost the power of open-cycle gas turbines for power generation at peak demand in the electricity grid.  To help me get traction with my commercialisation efforts, please mention my work to anyone who designs, manufactures or uses such gas turbines.  Successful commercialisation will definitely lead to a big saving on global CO2 emissions.  I need help!

For details, please see http://www.sunoba.com.au/ and follow the link to “Expansion-Cycle Evaporation Turbine”.

References:

[1] K.E. Trenberth & C.J. Guillemot, J Geophysical Research, 99 (1994), 23079-23088
[4] http://www.skepticalscience.com/christy-crock-6-climate-sensitivity.html
[5] http://www.worldcoal.org/resources/coal-statistics/

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