The input biomass has 17.4 EJ/yr heat of combustion (initial chemical energy). Full gasification of 450 million MT of carbon with water yields 1.05 gigatons of carbon monoxide and 0.075 gigatons of hydrogen, a molecular ratio of 1:1. The difference between the energy of the input biomass and the cold syngas product is 4.15 EJ/year. This comes out to about 132 GW thermal power, not including sensible heat losses; this is not much more than the electric output of the US nuclear fleet, so it appears highly likely that it could be supplied via electric power and the raw processing done as a distributed system. This yields a CO-H2 mix which is highly toxic, but there's a potential fix for that. If half of the CO was converted to CO2 and H2 via the water-gas shift reaction, the remaining CO could be converted to methanol using the hydrogen. The mixture of CO2 and MeOH would be far less toxic and could be shipped by pipeline, after local needs were satisfied. The MeOH is usable immediately, the CO2 is storable and provides a reservoir of carbon for reaction with H2 produced later. So long as all the carbon is recently extracted from the atmosphere, the system would be carbon neutral.
An additional 0.075 gigatons of hydrogen is required to reach the 2:1 H:CO ratio required to make methanol or hydrocarbons, for a total of 0.150 GT of H2 overall. This yields 32.49 EJ heat of combustion, or 30.79 quads. If converted to methanol, it would yield 25.8 quads of liquid fuel. Converted to hydrocarbons via F-T synthesis, it would yield less.
In 2019, the USA only consumed about 38 quads of petroleum for all purposes. 17.2 quads of that was motor gasoline, of which at least 70% can be replaced by electricity using PHEVs. (I'm getting closer to 80%, and the infrastructure isn't really in place yet.) This reduces net petroleum consumption to roughly 26 quads all by itself.
New nuclear technologies would help. If we could engineer nuclear plants which operate at perhaps 1200°C, they could supply the required process heat directly with a reactor fleet of net power just a fraction of what we're operating today. Of course, wind and solar could assist via e.g. plasma-arc gasification of biomass as a dump load, but the nuclear pathway would have a much smaller environmental footprint (and probably lower capital costs).
Such high-temperature reactors could also drive open-cycle gas turbines which need no cooling water. I shouldn't need to mention just how well a heat-driven biomass conversion process meshes as a thermal dump load in lieu of electric generation, allowing a great deal of flexibility as to load-following on the grid.
Supplying the additional 75 mmt of H2 per year is a somewhat bigger challenge. Producing this hydrogen via electrolysis of water at 50 kWh/kg H2 requires 3750 TWh of electric power, an amount roughly equal to total annual electric consumption in the USA. Using high-temperature steam electrolysis this would be reduced by about 35%, to roughly 2440 TWh (still about 60% of annual US electric generation).
So far I'm only describing a carbon-neutral fuel scheme, but it's possible to do better. Carbon monoxide can be steam-reformed to CO2 and hydrogen, and the CO2 can potentially be sequestered. 1.05 GT of CO plus 0.675 GT of steam reacts to 1.65 GT of CO2 plus 0.075 GT of H2, with a consequent increase in HHV of 0.6 EJ. This isn't much but it isn't quite trivial either. Of course, a nuclear steam supply would be ideal for feeding a water gas shift reactor.
This also solves the energy-stockpile problem. Sudden spikes in demand such as are caused by heat waves and cold snaps are a poor match for capital-intensive energy sources. Stockpiling energy as methanol, dimethyl ether or hydrogen is one way to get full utilization out of such sources while maintaining the ability to follow demand surges. Methanol in particular is handy, as it's a room temperature liquid which can be easily cracked to CO and H2 at temperatures even LWRs can reach; then the CO can be reformed to H2 with a bit of steam. This yields a carbon-free stream of fuel which can be generated from bulk-storable stockpiles upon demand and distributed by pipeline.
Next step: learning how to use matplotlib to generate Sankey diagrams of this stuff!
Update: I found my spreadsheet of chemical properties. I also found an EPA document on the solubility of CO2 in methanol at various temperatures. Upshot: at room temperature, a 1:1 molecular ratio of MeOH and CO2 can be held as a liquid at less than 40 bar. This is definitely a mixture which can be transported either by tankers or by pipeline, retaining 100% of the carbon either for re-use or for sequestration.
On the chemical end: at 1000°C, the enthalpies of H2O, H2 and CO are -204.09, 28.08 and -79.59 kJ/mol, respectively. At 25 C the numbers for H2 and CO are 0.01 and -110.52 kJ/mol; my coefficients for calculating the enthalpy of water aren't valid at such a low temperature, so I'm going to assume -285.82 kJ/mol (heat of formation of liquid water). Assuming 0.2 mol of excess water (steam) for each mol of CO+H2 produced, there is (28.08-0.01)+(-79.59+110.52)+0.2*(-204.09+285.82) = 75.346 kJ/mol of sensible heat that is lost in the cooling of the product gas. 450 million metric tons of carbon is roughly 37.5 teramoles, for a total sensible energy loss of 2.826 EJ. Processing 450 million metric tons of biomass carbon loses sensible heat in the quenching process at a rate of 89.5 megawatts. This is a rounding error, thank goodness.
Still trying to understand the Sankey function of matplotlib.
Update 2: I slipped a decimal point and thought I was calculating joules/watts when I was actually calculating kJ/kW. The sensible heat losses will come to 89.5 GW, not MW. Some process heat reclamation will definitely be in order.
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