Oye'd! to Carbon

Okay, let's try this again for my benefit:

Coal Gasification

The chemical reaction for coal gasification is
H₂O + C → CO + H₂, ΔH = +131 kJ
CO + H₂O → CO₂ + H₂, ΔH = -41 kJ

So overall we turn 1 mole of Carbon into 2 moles of diatomic Hydrogen and 1 mole of Carbon Dioxide for an ideal energy input of 90 kJ.

Thus the ideal energy input is 47 kJ/mol of H₂ = 22.32 MJ/kg of H₂. The ratio of Hydrogen to Carbon by mass is 1 kg:5.96 kg.

Burning Carbon

Carbon is burned to Carbon Monoxide and then Carbon Dioxide:
2C + O₂ → 2CO, ΔH = - 221 kJ
2CO + O₂ → 2CO₂, ΔH = -566 kJ

Therefore pure carbon yields 393.5 kJ/mol = 32.76 MJ/kg

In contrast, coal is not nearly so good a fuel because it contains water and other contaminants. I picked Illinois bituminous coal at 11,800 Btu/lbs. This coal is equivalent to 27.5 MJ/kg. This is basically why coal is not considered a transport fuel. Note that this is basically the highest quality coal that we burn for fuel. The best stuff is saved for steel manufacture. The carbon content would be about 65 %. Oxygen and Nitrogen constituents take up many bond positions and lower the overall recoverable energy. Hydrogen adds some energy with much of that bound as water, and Sulfur a very tiny amount.

More info on coal available here:

http://www.eia.doe.gov/cneaf/coal/quarterly/co2_article/co2.html

Note this article states that Illinois bitluminous coal produces 203.5 lbs. of CO₂/MBtu. With 11,800 Btu/lbs. the mass ratio coal:CO₂ is 1:2.4013, which you can use to confirm the carbon content of 65 %.

Gasification Inputs

As mentioned before, the ideal input is 22.32 MJ of heat and 5.96 kg of Carbon to produce a single kilogram of Hydrogen gas.
1. Heating input: 22.32 MJ of heat at 55 % cycle efficiency is 40.58 MJ. Given energy content of 5.63 MJ/kg, a total of 7.2 kg of coal must be burned for fuel. Now obviously the efficiency of this stage can be challenged.
2. Chemical input: 5.95 kg of carbon is needed, and the coal has 65 % Carbon content, for a total input of 9.154 kg. This stage should be around 99 % efficient.

TOTAL COAL INPUT = 7.2 kg + 9.15 kg = 16.35 kg of coal / kg of H₂

Cost Input

Coal is priced at $40/short ton = $0.02/lbs. = $0.0442/kg.

So our 16 kg of coal costs $0.723.

Obviously I made some sort of bad error in my last post. I will probably have to stop trying to run through multiple calculations using just my calculator since I'm generating too many lazy errors. :-) Of course, this took about five times as long to write.

CO₂ Pollution Credits

With 16.35 kg of coal consumed and 65 % Carbon content the total carbon combusted is 10.63 kg. This works out to 38.94 kg of CO₂. Recall, again, this is for one kilogram of H₂. We can check this with the EIA derived ratio of 1 kg coal:2.4 kg CO₂ → 39.25 kg of CO₂ .

I'll examine two potential electolysis costs. $40/MWh is ultra-cheap electricity derived from a high quality wind resource. $74/MWh was the average cost of electricity in the states for 2003. At $40/MWh electrolysis H₂ is $2.10/kg; at $74/MWh it's $3.885/kg. The difference between gasified coal and electrolysis is $1.38/kg and $3.162/kg respectively. Obviously the cost of electricity is a very sensitive parameter!

The cost to buy CO₂ credits to make up the difference is now $35.4/ton for the $40/MWh case and $81.2/ton for the $74/MWh case.

I can actually make up a formula for this to see how the cost of electricity varies the CO₂ price point:

Cost CO₂ credit = [1.346/tonMwh] P_Elec - $18.5/ton

where P_Elec is the price of electricity in $/MWh.

--

I'll take a look at steam reforming again later. I probably made the same error there. The electrolysis numbers are still correct.