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The only chemical inputs a Haber-Bosch plant needs are nitrogen and hydrogen. The nitrogen always comes from air and in this plant the hydrogen comes from electrolysis. The plant also needs electrical power to run compressors, but that can also be supplied by wind and it's minor compared to the embodied energy of the hydrogen input.
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Why would the HB plant be powered with fossil fuels? You can power that with wind power as well.
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Typically the natural gas is the source of the hydrogen. Usually natural gas is burned to form steam to split more natural gas (CH4) into carbon and hydrogen. That’s traditionally cheaper than electrolysis.
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