Synthetic Jet Fuel

Fig. 1:Given η1 = 0, points in (cag, η 2) space are colored according to their ability to satisfy the airline industry demand for carbon. The blue points can fuel the fiducial airline industry given 100% Fischer-Tropsch efficiency. The yellow points can fuel the fiducial airline industry given 50% or greater Fischer-Tropsch efficiency.

Renewable energy technologies are supplying an increasing fraction of the global energy budget. [1] Many state actors have set goals of reducing their net carbon emissions to zero during this century. [2] Indeed, there is more than enough renewable energy available to replace carbon emitting power sources: the solar power incident upon Earth's atmosphere is 4.4 × 10¹⁶ Watts, for a total of 10²⁴ Joules per year. [3] Of this, about 70% reaches the Earth's surface for a total of 0.9 million exajoules per year (9.72 × 10²³ J y^-1). [4] Humanity currently uses roughly 6.0 × 10²⁰ Joules per year, which is far less than the amount of solar power available. [1] This might lead an observer to believe that supplying the global energy budget is merely a problem of the politics and economic costs of capturing enough of the renewable energy available to us. While this may be the case for many applications, there are significant technical challenges in using renewable energy for applications that are highly sensitive to the mass of the power system. In particular, the weight of batteries poses a great difficulty to creating battery powered airplanes or rockets. Current batteries are able to store roughly two orders of magnitude less energy per kilogram than carbon based propellants. [6] Replacing such carbon fuel systems with batteries would therefore dramatically decrease the payload of the airplane or rocket, making it a much less useful (and more expensive) way to transport people and goods.

An alternative is to synthesize jet fuel from biological hydrocarbons. Given that this is possible, the speed and convenience of air travel over other forms of long distance transportation lead us to believe that flight will always be available to the ultra-rich. In fact, it is plausible that harvesting carbon from trees and converting it into synthetic jet fuel will allow for a large-scale, carbon-neutral aviation industry. In this work, we will investigate the resources needed for fuel production at this scale and the challenges that this industry would face.

We will first explain why advances in battery technology will not make batteries competitive with carbon-based fuel for aviation applications. We then introduce the Fischer-Tropsch process to synthesize jet fuel from biomass. Next, we argue that the amount of carbon contained in present day forests is significantly more than the demand of the aviation industry, but accessing this carbon would be extremely difficult. Finally, we will analyze the possibility of harvesting carbon from forests in a variety of possible futures. We argue that land will become a scarce resource and that the usage of this land will be crucial for achieving an equitable and stable future. If this challenge is not met, air travel and even food will be limited to the wealthier citizens of the world. On the other hand, dramatic change in agricultural practices would allow for a significant amount of carbon to be harvested from trees planted on land that is currently used for agriculture.

Batteries vs. Carbon Fuels

As mentioned previously, the abundance of solar energy makes batteries a particularly appealing way to store energy. Unfortunately, the difficulty of battery-powered flight is a fundamental physical limitation of the technology. The theoretical maximum energy density of a lithium-ion battery is still about 60 times less than gasoline; while other types of batteries have better theoretical limits, they are still less energy dense than gasoline [5]. Furthermore, a battery also has substantial mass added in the form of the casing and internal structure of the battery; reducing this mass would increase the energy density of the battery, but it would also decrease the structural integrity of the battery. It is this structural integrity that prevents the chemicals in the battery from combusting directly, so there is a limit to how much this weight may be safely decreased. This compounds with the fact that batteries typically use metals in their electrodes and current collectors, which are much heavier than carbon based fuel. As a result of these considerations, we can see that batteries are inherently less energy dense than carbon based fuels; no amount of technological progress can overcome this fundamental limitation.

Given these limitations of battery technology, we are forced to turn to synthesis of carbon-based fuels. It is in fact clear that this can be done, because such technology is already used commercially (and has been for some time) [6]. A reaction called the Fischer-Tropsch process allows for the conversion of hydrocarbons into synthetic diesel fuel [6]. At present, commercially viable production of synthetic diesel uses fossil fuels to supply hydrocarbon input because fossil fuels are much cheaper than other sources of hydrocarbon. However, this is an economic constraint; there is no technical reason that other hydrocarbons cannot be used as a fuel [7]. If the carbon used in this input to the Fischer-Tropsch process ultimately came from the atmosphere, then burning the resulting synthetic fuel would not result in an overall increase in the concentration of carbon in the atmosphere.

Biological Carbon Resources

To create synthetic jet fuel without changing atmospheric carbon levels, we need a way to extract carbon from the atmosphere. Some work is currently being done on direct extraction of carbon from the atmosphere. However, this technology is still in early stages of development. [10] We will focus on the possibility of using trees as a convenient source of hydrocarbons that ultimately come from the atmosphere.

If we are interested in using biomass to fuel a widespread airline industry, we should first ask if the world's forests store enough carbon to meet the current industry demands for carbon.

We wish to explore an equilibrium solution to this problem, so our maximum harvesting rate of trees for biofuel must be equal to the growth rate of the trees we are harvesting.

Then the amount of carbon we can sustainably harvest from biomass of trees per year is bounded by

where T_tree is the time (in years) that it takes the average tree to mature.

Ecological studies estimate that 363 gigatons of carbon are contained in the live biomass of trees. [9] We will take T_tree = 40 years as a fiducial value, yielding C_yearly = 9 gigatons of carbon (GtC) per year.

The global airline industry currently emits about a gigaton of carbon dioxide per year. [10] Since CO₂ is 6/22 carbon by mass, this corresponds to consumption of about 0.27 gigatons of carbon per year.

So we see that Earth's forests hold far more carbon than the airline industry consumes. However, there are many difficulties in accessing this carbon. This calculation assumes that we are harvesting carbon from all of the world's forests and converting it to biofuel with 100% efficiency. In reality, the Fischer-Tropsch process currently has an efficiency closer to 50%. [7] Additionally, there is a nontrivial social and environmental cost to turning a natural forest into a commercialized biofuel farm, so we should expect that significant swathes of forest will be protected. Furthermore, the remote nature of many forests would pose a substantial technical challenge to harvesting carbon from these forests. Even if all of these challenges could be overcome, we would be left with an infrastructure project on an extraordinary scale: the amount of land covered by forest is about 4 Gha (4.0 × 10¹³ m²). [11,12] For comparison, all of humanity's agricultural production occupies about 4.8 Gha (4.8 × 10¹³ m²) of land. [11,12] Building the infrastructure necessary to manage this much land for commercial biofuels would be a monumental task.

In fact, the problem is even harder than that. In the calculation above, we assumed that every tree that dies contributes to the creation of biofuel and is replaced by another tree that will grow to take its place and maintain the population equilibrium. However, forest fires will remove trees from the population without allowing us to use their biomass as a carbon source. To keep the tree population constant, we must replace these trees and count them in our total of harvested trees. Furthermore, the land occupied by these forests is itself a valuable resource. As mentioned above, the amount of land used for agriculture exceeds the amount of land occupied by forests. As the global population continues to increase, we should expect the amount of land used by agriculture to increase. Much of this land will have to come from deforestation, as the habitable land that is not currently used for agriculture or urban development is essentially all either forest or shrubland. [11,12] This reduction in the global tree population will reduce the amount of carbon available for biofuels; the size of this effect will depend heavily on the size of the population increase and the average global diets at the time.

Consequently, the amount of carbon that can realistically be harvested from trees is vastly less than 9 GtC per year. For now, we will simply take this to mean that 9 GtC per year is an (extremely optimistic) upper bound. Later, we will introduce a few parameters to quantify these effects.

Land Resources

As we have discussed, one of the primary resources that a biofuel industry must compete for is land. Presently, agriculture is the largest driver of land use; competition between these two industries will present a major challenge for widespread commercial biofuels. Unfortunately, the details of how much land agriculture will use in the distant future is very difficult to predict, as it depends heavily on the global population (which is predicted to peak at 10 billion) and the diet of the population. [13] To illustrate the problem, we will compute how much land would be required to feed a population of ten billion people eating an average American diet and flying as frequently as the average American.

The average American diet requires about a hectare (1.0 × 10⁴ m²) of land per person to produce. [14] Thus, we would need 10 Gha of agricultural land to provide for this population. Currently, 4.8 Gha of Earth's land are agricultural. [11,12] The remaining habitable land is composed of 4 Gha of forest and 1.7 Gha of shrubland for a total of 5.7 Gha of wild land. [11,12,15] To accommodate 10 Gha of agricultural land, we would need to convert 5.2 Gha of this wild land into agricultural land. If we conservatively say that we consume all of the world's remaining shrubland, then we have 0.5 Gha of forest remaining.

The yearly carbon available in that case is

The total carbon emissions from flights (domestic and international) leaving the US per year is about 0.185 gigatons of CO₂, or 0.0505 gigatons of carbon. [16] We will call this the total carbon demand for the American aviation industry. There are 331 million Americans, so this is a demand of 0.000152 gigatons per million people. [17] The carbon demand to supply a population of 10 billion people with the average American flight habits would be therefore be

So we conclude that even if all of the problems with harvesting biomass described in the previous section could be overcome perfectly, the total amount of habitable land on Earth is insufficient to support a population of 10 billion people with American diets and flight habits using synthetic biofuels. This shows us that if wealthy nations do not change their dietary or flight habits, they risk using all of the world's land, leaving the rest of the planet without the ability to grow biofuels or even food.

Having outlined this extreme, we will now explore the other extreme. If global land usage is managed efficiently and equitably, could widespread global aviation be supported?

The maximal efficiency gain in agricultural land usage that could be achieved (without significant technological advances) is conversion of animal agriculture to plant-based agriculture. Currently, the land used for grazing animals and growing their feedstock accounts for 77% of the land devoted to animal agriculture, whereas it only accounts for 18% of the global calorie supply and only 37% of the global protein supply. [11]

How much would our land usage change if all agriculture were plant-based? Suppose that all calorie production was achieved via plant-based agriculture rather than animal-based agriculture. Let N₈ be the number of calories that we currently use to feed 8 billion people. We find that 82% of these calories are produced by 1.1 Gha of cropland. [11] Then we have that current plant-based agriculture requires 1.1 Gha to produce 0.82 × N₈ calories (or 1.34 Gha per N₈ calories).

This tells us how much land we would need to use to feed 8 billion people eating only plants, given the current global caloric consumption and agricultural yields. Then, keeping these things constant, we need (land use per capita) × population = (1.34 Gha/8 billion people) × 10 billion people = 1.68 Gha to feed 10 billion people.

Recall that we presently use 4.8 Gha of land for agriculture.[11,12] Of this land, 1.6 Gha is used for growing crops (including those fed to livestock) and 3.2 Gha is used for grazing animals. [11,12] Of these grazing lands, it is estimated that 0.6849 Gha are suitable for growing crops. [15] This gives us a total of 2.285 Gha of land that is currently used for agriculture that could be used for growing crops or trees.

Then the maximum amount of land currently used for agriculture that we could use for cultivating tree biomass is

To determine how much carbon we could harvest from these lands, we need to know how much carbon a forest stores per Gha. At present, the Earth has 363 GtC in forest biomass [11] and 4 Gha of forest [11,12]. This tells us that the average forest stores about 90 GtC per Gha.

Computing the yearly carbon budget we could harvest from this converted land, we find that

This is still less than the amount of carbon we would require for a population of 10 billion to fly as much as the average American. However, it is enough for a population of 10 billion to fly as much as the average person does now: the global airline industry consumes about 0.27 GtC for 8 billion people, which would correspond to

So we conclude that widespread adoption of plant based agriculture would provide the land resources necessary for a significant amount of carbon biomass to be harvested from trees. Whether or not this would be sufficient to fuel a global airline industry without harvesting from forests that are already in existence depends on the average flying habits of the population, as well as the efficiency of harvesting these trees and converting them into biofuel.

To sketch an idea of how the answer to this question depends upon these efficiencies, we will introduce a few parameters to our simple model. These parameters are simply conversion factors whose values we don't know, as they depend on the details of the future. By introducing these as variables, we can answer questions about a wide range of future scenarios with a single equation.

Let η₁ be the effective efficiency of harvesting all forests that currently exist. Let η₂ be the effective efficiency of harvesting all forests planted on the land converted from agriculture. These efficiencies allow us to distill the complexities described in section two (forest fires, protected forests, inaccessibility of remote forests, lack of infrastructure, etc.) into two simple parameters. While we do not know the future values of these parameters, we do expect η₂ to be significantly greater than η₁; forests planted on former cropland should be less remote, have more infrastructure already built, and be less protected than currently existing forests.

Finally, we want to understand the effects of agricultural change on this calculation. Let c_ag = future agricultural land usage per capita/(1.68 Gha per 10 billion people). Assuming a future population of 10 billion people, that means that c_ag = future agricultural land usage/1.68 Gha. (Recall that 1.68Gha is the amount of land we would need for plant- based agriculture to feed 10 billion people, given the agricultural yield rates and calories per capita of the present day; thus c_ag = 1 can be interpreted as a population of 10 billion people subsisting entirely on plant-based agriculture, with crop yields and calories per capita equal to those of the present). Thus the future agricultural land use is c_ag × 1.68 Gha. This variable expresses the fact that we don't know how much agricultural land will be used per capita; this depends on things like crop yields, calories consumed per capita, and global diets. Increasing crop yields would decrease c_ag, increasing the global calories per capita would increase c_ag, and the existence of a substantial amount of animal-based agriculture would dramatically increase c_ag.

Assuming that c_ag is sufficiently close to 1 that some land is converted from agriculture to growing trees for biofuel, we see that

Cyearly = [η1 × carbon biomass of existing forests + η2 × carbon mass of newly planted forests per Gha × (Gha of newly planted forests)]/Ttree = [η1 × carbon biomass of existing forests + η2 × carbon mass of newly planted forests per Gha × (land available for agriculture - land used for agriculture in the future)]/Ttree = [η1 × 363 + η2 × 90 × (2.285 - 1.68 cag)]/Ttree

(7)

Suppose that η₁ = 0 (i.e., we wish to consider the case where only forests planted on converted agricultural land are used for biofuel production). Figure one plots the parameter space of (c_ag, η₂) and colors points by their ability to meet carbon production demands for an airline industry. The answer to whether or not an airline industry can be supported in a future with those parameters depends on the size of the industry; for simplicity, we will take the airline carbon demand per capita to be the same as it is now. Thus the fiducial future airline carbon demand is 0.3375 GtC per year (see Eq. (6)).

We color each point in parameter space according to the answer to the following questions. Can a future with these parameters sustain the fiducial airline industry with 50% Fischer- Tropsch synthesis efficiency? Can a future with these parameters sustain the fiducial airline industry with 100% Fischer-Tropsch synthesis efficiency? If the answer to both questions is yes, we color the point yellow. If the answer to the second question is yes (but the answer to the first is no), we color the point blue. If the answer to both questions is no, the point is left uncolored.

Then the plot conveys the following information: conversion to plant-based agriculture coupled with high harvesting efficiencies of newly planted forests would produce a significant fraction of the carbon demanded by the airline industry. Whether or not this source of carbon would be enough to entirely meet the demands of the airline industry depends on the details of the agricultural conversion, biomass harvesting efficiency, and fuel synthesis efficiency. For some c_ag (i.e., for some agricultural practices), the carbon demand of the airline industry can be entirely met by harvesting newly planted forests (without increasing the Fischer-Tropsch synthesis efficiency). For some c_ag on the plot, we require an increase in Fischer-Tropsch synthesis efficiency to fuel the fiducial airline industry.

Discussion

From our above calculations, we conclude that sustaining a widely accessible global airline industry via synthesis of jet fuel from tree biomass is a difficult (but possible) proposition. A growing demand for agricultural land could cause significant deforestation, thereby eliminating much of the world's harvestable carbon biomass. To harvest a sufficient amount of biomass, humanity must either develop the infrastructure needed to harvest trees from a significant amount of the current forested land on Earth (and prevent agriculture from consuming all of this land) or achieve sufficient dietary change that some lands that are currently used for agriculture can be used for biomass production. To make flying more accessible globally than it is now, our results indicate that it is likely that both problems must be solved.

Our calculations show that widespread conversion to plant-based agriculture would allow for a substantial amount of new forest to be planted; if these forests were efficiently harvested for carbon biomass, they would provide a significant amount of the carbon needed for an airline industry based on synthetic fuel. From this, we conclude that Earth does have the land resources to provide for a well-fed population of 10 billion and sustain a large airline industry if available land is used efficiently. However, if this challenge is not effectively addressed, the scarcity of land and the difficulty of densely storing energy threaten to drastically reduce the accessibility of air travel for much of humanity, rendering it affordable only to the wealthiest citizens of the globe. In the worst case, land resources needed for food may be denied to some of the world's population. The stark differences between these possibilities indicate that this issue ought to be actively and vigorously addressed.

© Nicolas Ferree. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

References

[1] "BP Statistical Review of World Energy 2022," British Petroleum, June 2022.

[2] "Paris Agreement," United Nations, 2015.

[3] "The Balance of Power in the Earth-Sun System," U.S. National Aeronautics and Space Administration, 2005.

[4] G. L. Stephens et al. "The Albedo of Earth," Rev. Geophys. 53, 141 (2015).

[5] A. A. Naqvi et al., "Aprotic Lithium Ion Batteries With Oxygen-Selective Membranes." Mater. Renew. Sustain. Energy 11, 33 (2022).

[6] G. J. Suppes and T. S. Storvick, eds., Sustainable Nuclear Power (Elsevier, 2007), pp. 75-117.

[7] N. H. Leibbrant et al., "Process Efficiency of Biofuel Production via Gasification and Fischer-Tropsch Synthesis," Fuel 109, 484 (2013).

[8] Negative Emissions Technologies and Reliable Sequestration: A Research Agenda (National Academies Press, 2018).

[9] Y. Pan et al., "A Large and Persistent Carbon Sink in the World's Forests," Science 333, 988 (2011).

[10] D. S. Lee et al., "The Contribution of Global Aviation to Anthropogenic Climate Forcing for 2000 to 2018,". Atmospheric Environment 244, 117834 (2021).

[11] "Statistical Yearbook - World Food and Agriculture 2022," Food and Agriculture Organization of the United Nations, 2022.

[12] P. Potapov et al., "The Global 2000-2020 Land Cover and Land Use Change Dataset Derived From the Landsat Archive: First Results," Frontiers in Remote Sensing 3, 856903 (2022).

[13] S. E. Vollset et al., "Fertility, Mortality, Migration, and Population Scenarios for 195 Countries and Territories From 2017 to 2100: A Forecasting Analysis for the Global Burden of Disease Study," The Lancet 396, 1285 (2020).

[14] C. J. Peters et al., "Carrying Capacity of US Agricultural Land: Ten Diet Scenarios," Elementa 4, 000116 (2016).

[15] A. Mottet et al., "Livestock: On Our Plates or Eating at Our Table? A New Analysis of the Feed/Food Debate," Glob. Food Sec. 14, 1 (2017).

[16] X. S. Zheng and D. Rutherford, "Reducing Aircraft CO₂ Emissions: The Role of U.S. Federal, State, and Local Policies," International Council on Clean Transportation, February 2021.

[17] B. Epstein and D. Lofquist, "Congressional Apportionment: 2020 Census Briefs". U.S. Census Bureau, C2020BR-01, May 2023.