Exponential
I'm afraid in all coal gasification processes a lot of carbon ends up as CO2 which in conventional plants is released to the atmosphere. People are working of various means of sequestering this carbon source.
In surface coal gasification for making liquid fuels the CO2 is mostly produced from shifting the syngas composition to be more hydrogen rich which is necessary for the Fischer-Tropsch process. In this process you need more than two hydrogens for each carbon molecule, while the original coal has a ratio of around one to one.
In UCG the syngas is generally richer in hydrogen and so has a better ratio of H2:CO but due to the lower temperature of extraction there is much more CO2 in the actual syngas which is a fact of life from thermodyanmics unfortunately - about 30% of the syngas is CO2 on a mole basis from UCG.
Anyway I think on a carbon basis they have similar efficiencies when talking about CTL. So the possible benefit of UCG is lower capital cost mostly and no need for mining. But you have a much more dificult process to control. Nothing in life is free.
GLX
gulfx ltd
