The Fischer-Tropsch (FT) process combines synthesis gas, H₂ plus CO, to make mostly straight chain hydrocarbons (Dry, 2004). The oxygen from the CO converts mainly into water but some oxygenated hydrocarbons can be produced as well. The process has been practiced since the Second World War, primarily using fossil fuels (coal, natural gas) as the source of input carbon, and process heat. The synthesis gas is fed to the Fischer-Tropsch reactor at high pressure and high temperature (∼500 K, ∼25 bar). Production of intermediate synthesis gas decouples the downstream fuel-synthesis process from the feedstock. Therefore, the Fischer-Tropsch reaction can meet ASTM D7566 specification for aviation fuel (ASTM International, 2021) from any source of synthesis gas, including renewable feedstocks (de Klerk, 2016).

The process makes steam and a broad distribution of hydrocarbons that must be separated and upgraded (e.g., hydrocracked) to make jet-range fuel, i.e., our nominal fuel surrogate: 12   CO   +   25   H 2   +   →   C 12 H 26   +   12 H 2 O           Δ G 0   =   - 1 , 684 . 9   kJ / mol Reaction 1

The FT process does make fuel molecules heavier than jet fuel, which might be hydrocracked into the jet range, however, we have ignored them in this first order analysis because their conversion into jet fuel will require additional hydrogen (Ostadi et al., 2019), which will only add to their cost. Selling those products as ultralow sulfur diesel fuel could lower the selling price of the jet fuel but, obviously, would then not directly increase the supply of jet fuel.

The process is approximately 50% carbon efficient (jet-fuel carbon produced/carbon input) (de Klerk, 2016; Gruber et al., 2019) and about 50% energy efficient (heating value of jet-fuel/heating value of biomass input) when the synthesis gas is produced by autothermal gasification of a biomass feedstock (Zhang et al., 2011; Ostadi et al., 2019). The gasification is illustrated simplistically by Reaction 2. The feedstock in Reaction 2 was assumed to have the elemental composition and heat of combustion of a soft wood such as pine; agricultural wastes contain more oxygen and have an enthalpy of combustion value closer to 15 MJ/kg (Hazel and Bardon, 2008)). CH 4 . 8 O 2 . 1   +   0 . 55   O 2   →   CO   +   2 . 4   H 2         Δ H reaction   =   - 153   kJ / mol Reaction 2

The carbon that is not converted to fuel or fuel precursors (e.g., tars that form) can be burned elsewhere in the process to generate heat. In Reaction 2 as written, the heating value of the “wood” −1,017 kJ/mol is converted into synthesis gas whose heat of combustion is about −860 kJ/mol, so a loss of about 15% of the input energy before consideration of any other sinks for the energy of the feedstock (e.g., compression, reaction selectivity). We note that steam reforming of the wood would produce the CO endothermically and autothermal reforming can be configured to be thermoneutral, but those conversions do not produce synthesis gas with the correct stoichiometry for Fischer Tropsch synthesis.

The process requires about twice the amount of input energy than reports to the fuel. Autothermal gasification of biomass is about 65–75% carbon efficient (Zhang et al., 2011). So, even if the FT process were 70% carbon efficient to making jet range fuels (it is actually closer to 50% carbon efficient (Gruber et al., 2019)), starting with biomass yields no more than a 50% overall carbon efficiency. Heavier (diesel-range, wax products) will require additional processing that will cost money. Selling those products might help offset the price of the SAF but won’t directly increase its supply. Because the heating value of lignocellulosic biomass is about 15–20 MJ/kg (Hazel and Bardon, 2008), making a year’s supply of jet fuel, 3.6 EJ, would require the input of about 480 Mt of biomass (= 2 × 3.6 EJ ÷ 15 MJ/kg). The long-term base-case of the updated Billion Ton Study (U.S. Department of Energy, 2016) comprises 826 Mt/year of biomass. So, more than half of the potentially available biomass-derived fuel feedstock would need to be devoted to jet fuel if the latter were produced by a process that involved production of the synthesis gas from the biomass.

In one estimate for a plant fed with coal (Reed et al., 2007), the production of 50,000 bbl/day of liquid fuel, was accompanied by an export of 125 MW of electricity. In that case, the net exportable electrical energy amounts to more than 10-times the energy resident in the liquid fuel: E e x p o r t E f u e l = 125   MW 50000   bbl / day = 125   MJ / s 50000   bbl / day × 6.1   GJ / bbl × 31.5 × 10 6 s 1   day = 12.9 (2)

That large ratio reflects the exothermicity of Reaction 1 plus recovery of process heat generated from the partial oxidation of about half the feedstock to produce the synthesis gas. The estimate is germane also to thermal gasification of biomass (Shahabuddin et al., 2020), where it represents both an opportunity (generation of renewable electricity) and a problem (low carbon yield of fuel) that could be balanced against each other according to higher-level optimization criteria (Tock et al., 2010).

If, instead, the energy for producing the synthesis gas could be added directly from renewable sources to renewable materials (Samavati et al., 2018; Gruber et al., 2019; Hannula et al., 2020; Korberg et al., 2021), then the overall process could, in principle, be much more carbon and energy efficient.

For example, concentrated CO₂, perhaps from an ethanol refinery or from the recycle stream in a CO₂-fed Fischer-Tropsch process (Hannula et al., 2020), could be converted into carbon monoxide, CO, using renewable electricity (Reaction 3, potentials referenced to the reversible hydrogen electrode (Kortlever et al., 2015)): CO 2   →   CO   +   1 / 2 O 2         E 0   =   - 1 . 33   V,   Δ G 0   =   257 . 1   kJ / mol Reaction 3

Similarly, H₂ could be produced by electrolysis of water (Reaction 4): H 2 O   →   H 2   +   1 / 2 O 2           E 0   =   - 1 . 23   V,   Δ G 0   =   237 . 1   kJ / mol Reaction 4

Just making sufficient CO and H₂ from CO₂ and H₂O to synthesize dodecane would require a minimum input energy, ΔG _min , that can be calculated from the stoichiometry of Reaction 1: Δ G min   =   12 × 257.1 kJ / mol + 25 × 237.1 kJ / mol = 9.0 MJ / mol dodecane (3)

To perform the reaction practically, however, that energy must be increased, slightly, by the work required to compress the gas to process conditions (about 20 kJ/mol = RT ln (25 bar/1 bar)) and, significantly, to overcome activation barriers of the constituent reactions. The practical electrochemical overpotentials for Reactions 3, 4 are each about 0.6 V (Rakowski-Dubois and Dubois, 2009), so the practical input energies must be increased by about 50% to ∼2 V and 1.8 V respectively. The process would still be only about 50% efficient towards the production of jet-range fuel (because of the broad distribution of products in the Fischer Tropsch process. Multiplying ΔG _min by 1.5 and doubling M _min, the mass of carbon incorporated in the fuel, represent reasonable lower bounds on the renewable energy and renewable carbon required to generate aviation fuel by this route. The inefficient utilization of the feedstock, however, means that the practical energy input, 1.5 × 9.0 MJ/mol = 13.5 MJ/mol, must also be doubled to adjust for the extra feedstock. Therefore, the adjusted, practical energy input, ΔG _practical will be 2 × 13.5 MJ/mol = 27 MJ/mol, which is the reason that we stated above that ≳2 J of input energy is needed for every 1 J of SAF.

The enthalpy of combustion of dodecane (and jet fuel) is about 8 MJ/mol. Therefore, this route would use approximately 27 MJ/mol of energy (from the biomass, electrical power, and other inputs) to make 8 MJ/mol worth of jet fuel. Given that this “electrofuel” would be intended for use in a jet engine whose efficiency would be around 40% (National Academies of Sciences E and Medicine., 2016), the 27 MJ/mol of input energy would result in ∼3 MJ/mol of work, a significant degradation that argues for the direct use, where possible of the input electrical energy. As discussed above, however, direct electrification of the propulsion of aircraft cannot yet achieve the desired range of travel. Therefore, we next discuss another route to sustainable aviation fuel that promises to be more energy- and mass-frugal.

Both methanol and ethanol can be oligomerized to make fuel range hydrocarbons. The methanol-to-gasoline process invented by ExxonMobil in the 1970s (Chang, 2007; Gogate, 2019) produces, using a small pore zeolite as the conversion catalyst, an unsaturated liquid (olefins, aromatics). The unsaturated intermediate can be hydrogenated to make a liquid fuel fungible with petroleum-derived gasoline. Similarly, ethanol can be converted into gasoline-range molecules through a homologous intermediate. However, ethanol also offers other chemistries (e.g., dehydration to the olefin, Guerbet reaction), that provide effective routes to the heavier molecules that comprise aviation fuel (Brooks et al., 2016).

The source of the ethanol is nearly irrelevant to its downstream conversion into jet fuel (Handler et al., 2015). There are, however, life-cycle differences among the different feedstocks (ethanol from fermentation of sugars derived from biomass, ethanol from waste industrial gas, ethanol from landfill gas). Roughly, the savings in greenhouse gases for each feedstock vary inversely with the cost of the feedstock (Table 1).

Those feedstock costs should be compared to the wholesale price of jet fuel, which recently (U.S. Energy Information Administration, 2020) has averaged close to 1.80 USD/gal (= 13.8 USD/GJ). The difference between the feedstock cost and the wholesale price is the amount available for operating costs and amortized capital costs and profit. Despite the low feedstock price of corn stover, it has not played a large role in the production of fuel ethanol, because of the still challenging conversion of cellulose into ethanol (Lamers et al., 2021).

The currently unused amount of potentially available, lignocellulosic feedstocks presented in Table 1 has been estimated to be 826 Mt/year in the long term (2040), base case scenario of the Billion Ton Study (U.S. Department of Energy, 2016). That material is composed primarily of sugars, e.g., C₆H₁₂O₆, which have a molecular weight of 180 g/mol, and lignin (roughly ²/₃ of the waste cellulosic feedstock is polysaccharides). The sugar provides the carbon that goes into the growing cells and the product fuel. Usually, the lignin is just burned for process heat (e.g., for distillation). That amount of material would be sufficient to make 0.40 Tmol/year of our surrogate, paraffinic fuel, C₁₂H₂₆, if it could be made by fermenting the sugars, C₆H₁₂O₆, into ethanol followed by oligomerization of the ethanol (3 sugar molecules per fuel molecule): C 6 H 12 O 6   →   2   C 2 H 5 OH   +   2   CO 2 Reaction 5 6   CH 3 CH 2 OH   +   H 2   →   C 12 H 26   +   6   H 2 O Reaction 6 826   MT biomass / year × 2   t sugar 3   t biomass × 10 9 kg Mt × 1   mol sugar 0.18   kg 1   mol fuel 3   mol sugar = 1 T m o l fuel / year (4)

Recall from the introduction that the U.S. uses “only” 0.46 Tmol of jet fuel, therefore, in principle there could be enough feedstock to satisfy this route. However, there are mass inefficiencies in both the fermentation process (72% in one study of making ethanol from wood (Zhu et al., 2010)) and the oligomerization process (∼75% carbon efficient to jet fuel and ∼90% to jet fuel plus diesel-range fuel in one patent (Lilga et al., 2017). The concatenation of those inefficiencies implies that more than the projected, currently unused supply of lignocellulosic feedstocks would be needed to satisfy the U.S. consumption of jet fuel.

A similar calculation can be made for a route that starts with CO that is produced by the steel industry. In steel making, the U.S. uses about 0.39 EJ worth of metallurgical coke as a reagent (i.e., not as a fuel) (U.S. Energy Information Administration, 2021e). The heating value of that coke is approximately that of pure carbon, 394 kJ/mol so, in the U.S., the manufacture of steel (110 Mt/year, (U.S. Geological Survey, 2020)) could produce approximately 1 Tmol of CO (Eq. 5). A small fraction of the carbon is incorporated into the metal, <0.5 wt% (MIT Department of Civil and Environmental Engineering, 1999) (Eq. 6): n C O = 0.39   EJ 394 kJ / mol C = 1   Tmol C × 1   mol CO mol C (5) n i n c o r p o r a t e d = 0.5 wt % × 110 Mt / year ÷ 0.012 kg / mol = 46   Gmol (6)

In the LanzaTech process the microbes use CO for energy and as a carbon source in a metabolic process that, formally, is equivalent to water-gas shift. Without suggesting the actual biochemical mechanisms, the overall stoichiometry for converting CO into C₁₂H₂₆, our surrogate for jet fuel is, minimally: 6   CO   +   3   H 2 O   →   CH 3 CH 2 OH   +   4   CO 2         Δ G reaction   =   - 216   kJ / mol Reaction 7

Combining Reaction 7 with Reaction 6 (ethanol oligomerization which, again, is about 75% efficient towards jet range products) implies that the 1 Tmol of CO possibly available from the U.S. steel industry could make, 1 Tmol_CO × 1 mol_dodecane/36 mol_CO × 0.75 = 21 Gmol of jet fuel and thus satisfy only about 5% of the U.S. demand (0.45 Tmol/year). Gas from a partial combustion fluidized catalytic cracking units in refineries could be a significant source of additional CO (U.S. Environmental Protection Agency, 2010) but we do not have a ready estimate of the available annual flow rates nor of the amenability of refineries to alter their operations to divert such streams away from their usual utility as fuel gas (Babcock and Wilcox Company, 2015).

Other, carbon-containing waste gases (e.g., from ethanol fermentation, refining, landfill, wastewater treatment) might also be considered as an input to this process. For example, CO and H₂ could be sourced electrochemically as discussed above in Section 3.2. In that case, the energy balance and carbon balance will depend on the specific stoichiometry of the inlet synthesis gas (Table 2).

Ethanol production, ∼16 billion gal/year in the U.S. (U.S. Energy Information Administration, 2021c), produces about 46 Mt/year of CO₂ (≈1.04 Tmol_CO₂). Consider converting all the carbon dioxide produced by the fermentation of ethanol into a sustainable aviation fuel by a three-step process. In the envisioned process, first, make the synthesis gas electrochemically (Reaction 3), then employ fermentation to convert that synthesis gas into ethanol (Reaction 5), and finally oligomerize the waste gas-derived ethanol to make jet fuel (Reaction 6). The energy input per mol of fuel would be derived from Reaction 3 (electrolysis of CO₂ to make CO) and the stoichiometries (and carbon efficiencies) of Reactions 5, 6. This route might satisfy 4.7% of the U.S. demand for jet fuel but would require inputting 19 EJ/year of renewable electricity or 3.6 times the amount of noncarbogenic electricity currently produced in the U.S. (see the Excel worksheet in the Supplemental Information for the detailed calculation).

The quantity of fuel produced can be increased and the electrical input can be decreased by adding H₂ to the feed to the CO fermenter. The addition of external H₂ provides a new energy source for the organism, allowing nearly all the carbon to be shunted into ethanol (Reaction 8). A minor portion of carbon will go to producing biomass: 2   CO   +   4 H 2   →   CH 3 CH 2 OH   +   H 2 O         Δ G reaction   =   - 135   kJ / mol Reaction 8

Combining Reaction 8 with Reaction 6 (ethanol oligomerization) yields an overall stoichiometric ratio of 12 CO and 24 H₂ per nominal dodecane instead of 12 and 25 respectively. Therefore, the minimum electrical energy required for the electrolysis will be nearly the same as before (Eq. 3), which still must be multiplied by 1.5 owing to the overpotentials for the two electrolyses. There will also still be a penalty owing to the selectivity of the oligomerization process (Lilga et al., 2017). However we can now expect a nearly stoichiometric utilization of the carbon in the fermentation process (Kopke and Simpson, 2020). Obviating the reverse water gas shift reaction could also accelerate the kinetics of the overall conversion. Δ G min = 12 × 257.1   kJ / mol + 24 × 237.1   kJ / mol = 8.8 MJ / mol dodecane (7)

Therefore, the practical energy input will be roughly 17 MJ/mol_dodecane = 1.5 ÷ 0.75 × 8.8 MJ/mol_dodecane instead of 28 MJ/mol that was employed in less efficient Fischer-Tropsch conversion. Moreover, the process now benefits from reaction conditions that involve near ambient pressures and temperatures instead of the high pressures and temperatures and low carbon utilization of a process that relies on Fischer-Tropsch chemistry. Because of the enhanced utilization of the carbon, this route applied to the CO₂ produced by ethanol fermentation could produce almost 13% of the U.S. demand for jet fuel but would require inputting 17 EJ/year in renewable electricity, which is about 3.2 times the ∼5.4 EJ/year of noncarbogenic energy produced in the U.S.

Given a renewable and frugal source of H₂ plus highly competent microorganisms maintained in a well-engineered reactor, one could even imagine using a combination of CO₂ and CO as the source of carbon instead of CO: CO 2   +   CO   +   5 H 2   →   CH 3 CH 2 OH   +   2 H 2 O         Δ G reaction   =   - 115   kJ / mol Reaction 9

In that case the minimum input energy would be smaller because it would, again, be the organisms that would undertake the equivalent of the reverse water gas shift reaction to generate the carbon that reports to the product ethanol The stoichiometric coefficients are derived from Reaction 9. Δ G min = 6 × 257.1   kJ / mol + 30 × 237.1   kJ / mol = 8.7   MJ / mol dodecane (8)

However, the practical energy would still be about 2 times larger, ΔG _practical = 16 MJ/mol from the electrochemical overpotential and the penalty arising from the selectivity of the oligomerization process. The process would benefit again from near ambient reaction conditions (temperature, pressure), very effective utilization of the input carbon, and further from the elimination of the electrochemical production of some of the CO. If this process were applied to the roughly 180 Mt/year of CO₂ produced in the refining of petroleum (U.S. Environmental Protection Agency, 2020) then it could satisfy about half the demand for jet fuel but would consume about 10 times the present amount of renewable electricity produced in the U.S. each year (53 EJ/year ÷ 5.4 EJ/year).