Coal is a Hydrocarbon (Sort Of)

While coal is largely graphite along with water, there are a significant number of Hydrogen-Carbon bonds that contribute to the heating value of coal as a fuel. This is an issue for coal gasification, because this Hydrogen is essentially "free". If we are running coal gasification plants for the production of Hydrogen the H-C bound material can increase the effective efficiency of the chemical process above 100 %.

ΔH(C) = -32.7 MJ/kg

ΔH(Coal) = -27.5 MJ/kg, % C = 65% by mass

therefore only 21.255 MJ/kg of energy from coal is derived from burning carbon. The remainder must come from either the combustion of Sulfur or Hydrogen. Sulfur is a fairly trivial component, being 1-2 % by mass and it only provides ΔH = -4.63 MJ/kg.

This means that roughly 27.5 MJ/kg - 21.25 MJ/kg = 6.2 MJ/kg of the heating energy is derived from Hydrogen. The only other potential energy source is Carbon double bonds but I have no way of estimating the frequency of those. Since the H-C bond and H-H bond are quite close in terms of energy I'll just assume that all of this energy is provided by the production of water at 141.9 MJ/kg. That gives a Hydrogen yield of 0.0437 kg(H₂/kg(coal). This is surprisingly high -- it suggests my reference coal is almost the equivalent of Benzene. There's only 1.35 C atoms for every H atom. I am mildly suspicious of this result. It is in the right order of magnitude from this table for Australian coal.

This changes the chemical yield of coal gasification slightly. If %C = 0.65 and %H₂ = 0.044 then each kilogram of coal yields 0.109 kg(H₂) + 0.044 kg(H₂) = 0.15276 kg (H₂). This represents a 40 % increased chemical yield over my original coal gasification figures! The coal → Hydrogen yield is now 6.54 kg/kg.

Including heating input (7.2 kg/kg), the total coal input drops to 13.75 kg/kg. The fuel cost of Hydrogen derived from gasification drops from $0.72/kg to %0.61/kg. The CO₂ production drops to 33 kg(CO₂)/kg(H₂).

We can run the comparisons to electrolysis at the two price levels once again:

Electricity Price	$40/MWh	$74/MWh
Gasification Price delta	$1.49/kg	$3.28/kg
Gasification CO2 Price (33 kg CO2:1 kg H2)	$45/ton	$100/ton

The average improvement is about 25% over my previous calculations in favour of gasification. Further improvements to the thermal efficiency of the process will only make minor improvements in the cost of coal derived Hydrogen, but it will further depress the CO₂ production and make it more difficult for electrolysis to compete.