I made the following assumptions:
- Electricity at $40/MWh from wind.
- Natural gas at $15/GJ.
- Illinois coal at 23.6 Mbtu/short ton, cost of $40.00 per short ton.
| H2 Source | Ideal Energy Input (MJ/kg) | Expected Efficiency (%) | Real Energy Input (MJ/kg) | Unit Cost ($/GJ) | H2 Cost ($/kg) |
| Electrolysis | 142 | 75 | 189 | 11.1 | $2.10 |
| Methane | 20.5 | 55 | 37.3 | 15.0 | $0.56 |
| Coal | 22.3 | 55 | 40.6 | 1.6 | $0.065 |
As we can see, the cost of coal-derived Hydrogen is vastly lower than that of methane or electrolysis derived Hydrogen. The question I want to know is, in some carbon-trading scheme like Kyoto, what rate does CO2 have to trade at for electrolysis to become viable?
I figured out the amount of CO2 produced from the combination of actual material input and the heating requirement. For example, methane, with a heating value of 55.7 MJ/kg has a heating input of 0.67 kg of methane per kg of Hydrogen (which is about 1.8 kg of CO2), and 22 kg of CO2 are produced from the actual chemical reaction to split the methane.
| H2 Source | CO2 Produced (kg CO2 / kg H2) | Marginal CO2 Cost (relative to CH4) ($/ton) | Marginal CO2 Cost (relative to coal) ($/ton) |
| Electrolysis | 0 | 62.1 | 42.0 |
| Methane | 24.8 | 0 | 20.9 |
| Coal | 48.5 | -20.8 | 0 |
As you can see, Methane is the winner even with its assumed high price. Carbon dioxide needs to be trading at $62/ton in order for electrolysis produced Hydrogen to be competitive. Obviously I'm being rather kind to Hydrogen by giving it cheap wind power and pushing the cost of natural gas well above the world average (if not so much above the North American average).
Note that the implications for sequesterization are clear. If CO2 can be sequestered for less than $60/ton, methane should remain the preferred feedstock for Hydrogen. If it can be sequestered for less than $20/ton, coal is the winner.
6 comments:
I don't quite get where your numbers in the first table came from. How do you get MJ/kg for electricity? And I think your efficiencies are a bit low; cold-gas efficiency for the E-gas coal gasifier is about 76%, and shift conversion from CO + H2O to CO2 + H2 isn't all that lossy. IIRC, the waste heat from the gasifier is roughly enough to power the air separation plant so no big costs there either.
Good to see someone going over the data from a different perspective, always enlightening.
Hydrogen derived from electrolysis has to pay the full chemical potential of transforming water to H2 and O2. That's 141.9 MJ/kg of Hydrogen.
I used the following publication from the International Journal of Hydrogen Energy for efficiency numbers:
http://dx.doi.org/10.1016/j.ijhydene.2004.06.001
It gives the cycle efficiency a rating of about 55 % for coal gasification and 50 % for methane steam reforming. I'm sure you can find different numbers in a different publication. :-( They actually state that the overall efficiency is far lower but they aren't recovering as many inputs as they could.
On the basis sequesterization break-even points, system is mostly sensitive to the CO2 production. Most CO2 production doesn't come from the need for heat. The vast majority of CO2 is from the moles of carbon need to break up water. It wouldn't be very sensitive to variations in the price of coal.
The most sensitive input parameter is clearly the cost of electricity simply due to the fact that the energy inputs for electrolysis are about 4x higher.
Okay so according to the DoE the average electricity rate in the USA for 2003 was $74/MWh or $20.56 / GJ. Obviously I was being intentionally generous to electrolysis by providing dirt cheap power. The cost break for steam methane reforming then jumps way up to $135 / ton of CO2. Now if we say at $74 /MWh for electricity but knock the price of natural gas up to $27.75 / GJ (same 85 % increase as for electricity) the price break only drops to $116 / ton of CO2.
As mentioned before, the European trade price for CO2 usually is around 30 Euros.
It looks like you aren't counting the energy in the input fuel against the cost of the output. Are you only counting losses in the processing? That's not clear, and if so it's not obvious what you're trying to demonstrate.
Using your figures of 23.6 mmBTU/ton and $40/ton for coal, I get:
590,000 BTU/$
~149 megacalories/$
2106 moles-H2 equivalent/$ @ 70600 cal/mol
1158 moles/$ @ 55%, or $.43/kg.
Those numbers look solid to me after re-examination. I'll let you do the numbers for natural gas.
I may have dropped the carbon content of the coal to match the energy content.
I'll go over my calculations again but are you need to account for two things:
1. The enthapy change -- have to burn fuel to produce heat.
2. The carbon/methane necessary for the chemical reaction that produces hydrogen.
I did account for that; it's taken care of by your 55% efficiency multiplier.
I still get a coal-hydrogen cost more than six times as high as you did.
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