Cost modeling of photocatalytic decomposition of atmospheric methane and nitrous oxide

The photocatalytic decomposition of atmospheric methane (CH4) and nitrous oxide (N2O) could be valuable tools for mitigating climate change; however, to date, few photocatalyst deployment strategies have had their costs modeled. Here, we construct basic cost models of three photocatalytic CH4 and N2O decomposition systems: (1) a ground-based solar system with natural airflow over photocatalyst-painted rooftops, (2) a ground-based LED-lit system with fan-driven airflow, and (3) an aerosol-based solar system on solid particles dispersed in the atmosphere. Each model takes as inputs the photocatalyst’s apparent quantum yield (AQY; a measure of how efficiently photons drive a desired chemical reaction) and the local CH4 or N2O concentration. Each model calculates an overall rate of greenhouse gas (GHG) drawdown and returns a levelized cost of GHG removal per equivalent ton of carbon dioxide (tCO2e). Based on prior studies of atmospheric carbon dioxide removal, we adopt $100/tCO2e as a target cost. We estimate that painting rooftops with photocatalysts might meet the target cost for decomposition of >10 ppm CH4 with catalyst AQYs >4%. If painting and cleaning costs were reduced by a factor of ∼3 from our scenario, removal of ambient CH4 could meet the cost target with AQYs >1% and removal of ambient N2O could do so with AQYs >0.1%. Fan-driven systems with LED illumination appear to be very challenging, achieving removal costs <$100/tCO2e only for AQYs of >10% for CH4 and >1% for N2O. Dispersing photocatalytic aerosols in the troposphere could be cost-effective with AQYs of >0.4% for ambient CH4 or >0.04% for ambient N2O. However, the mass of aerosols required is large and their side effects and social acceptability are uncertain. We note that, for any system, AQYs on the order of 1% will likely be extremely challenging to achieve with such dilute reagents.


Introduction
Limiting Earth's average temperature rise to 2 • C requires a rapid, massive decrease in both the net releases and the atmospheric stocks of greenhouse gases (GHGs).Though most attention is justifiably dedicated towards mitigating carbon dioxide (CO 2 ) emissions, non-CO 2 GHGs are powerful levers for climate mitigation.Of these, methane (CH 4 ) and nitrous oxide (N 2 O) are the most substantial.
The atmospheric stock of CH 4 in 2019 contributed 0.54 ± 0.25 W m −2 of radiative forcing over preindustrial levels, compared to 2.16± 0.35 W m −2 from CO 2 and 0.21± 0.03 W m −2 from N 2 O [1].The same years CH 4 concentration of 1866 ppb and N 2 O concentration of 332 ppb were respectively 156% and 23% above pre-industrial levels, with both concentrations still rising [2].
The past decade has seen increasing interest in removing atmospheric CO 2 .Literature exists for the engineering, economics, and impacts of various removal approaches, including mechanical direct air capture of CO 2 (CO 2 -DAC) [3][4][5].Numerous companies are attempting to scale CO 2 -DAC, with systems currently operating at kiloton-per-year scale and planned at the megaton-per-year scale [6].In contrast, the removal of atmospheric CH 4 and N 2 O have seen comparatively less activity, in part because of their dilute concentrations compared to CO 2 [7][8][9].
While there are many feasible ways to reduce CH 4 and N 2 O emissions, some sources, especially lowconcentration emissions in nature and agriculture, are challenging to mitigate directly [10].Just as atmospheric CO 2 removal can help offset the emissions of 'hard-to-decarbonize' sectors, CH 4 or N 2 O removal could be used to offset CH 4 or N 2 O emissions that are hard to stop at their source, and in the case of long-lived N 2 O could also reverse historical emissions.Inexpensive and rapidly scalable CH 4 removal, if developed, would be especially valuable in limiting the planet's near-term warming, to which CH 4 contributes disproportionately [11].
Other factors make the decomposition of atmospheric CH 4 and N 2 O compelling.Both gases cause more radiative forcing per unit mass than CO 2 , with CH 4 having 20-and 100 year global warming potentials (GWPs) of 81 and 27 respectively and N 2 O having a 20-and 100 year GWP of 273 [12].Interventions targeting CH 4 or N 2 O might thus still be useful at high costs per unit of GHG decomposed.In contrast to CO2 that must be captured and sequestered, CH 4 and N 2 O may be decomposed in place with most of the same climate benefits (equations (1) and ( 2)), a process that we term 'removal' when conducted on outdoor air.Decomposing CH 4 or N 2 O avoids the permanent gigaton-scale sequestration of captured GHGs required by CO 2 removal.It may also be possible to target CH 4 -rich outdoor air near emitters (∼10 ppm very near to cattle herds, rice paddies, and landfills), which should improve kinetics and process economics compared to targeting the ∼2 ppm background in the atmosphere [8].However, it thus far unclear whether and how these benefits can outweigh the challenges to create cost-effective CH 4 and N 2 O mitigation strategies.
Previous studies have identified many promising materials for dilute CH 4 and N 2 O decomposition and many ways to deploy them.Proposed approaches for the oxidation of dilute (⩽100 ppm) CH 4 include thermocatalysis using noble metal-based catalysts; surface photocatalysis using semiconductors such as TiO 2 and ZnO; generating gaseous hydroxyl and chlorine radicals; and biofiltration by microorganisms [8,13].Candidate materials for dilute CH 4 oxidation have been identified in each of those categories [14 -17].Multiple known photocatalysts are also capable of decomposing dilute N 2 O [18][19][20].Proposed ways to expose such materials to large volumes of outdoor air include stand-alone fan-driven units, passive systems using natural wind, additions to CO 2 -DAC machines, and solar updraft towers [10].
Several works have discussed the advantages and estimated the costs of different potential CH 4 and N 2 O removal systems.One study gives rough cost figures for zeolite thermocatalysis, photocatalysis, and radical generation based mainly on researchers' unpublished models [13].Air flows, CH 4 removal rates, and costs have been modeled in detail for solar updraft towers with photocatalytic active phases [21,22].The lifecycle CH 4 removal of a passive solar photocatalytic device has also been modeled previously [23].The overall economic feasibility of 2 ppm CH 4 removal via fan-driven machines has been questioned based on the empirical trend that separation costs often rise linearly with target substance dilution [9].However, most proposed CH 4 /N 2 O removal systems lack published cost estimates that transparently account for reaction rates, mass transfer, and capital/operating costs.
Here, we provide cost estimates for three photocatalyst-based CH 4 /N 2 O removal strategies that previously lacked such estimates.We aim to provide straightforward and reproducible cost models describing each strategy's cost as a function of photocatalyst performance.We hope to clarify which strategies might be viable under scenarios of photocatalyst improvement and to set performance targets for researchers developing photocatalytic materials.
Photocatalysts are appealing because of their ability to decompose CH 4 and N 2 O under ambient conditions and their potential for cheap and scalable deployment [23][24][25].They can also degrade local air pollutants, especially volatile organic compounds, meaning that CH 4 or N 2 O removal systems might have health co-benefits for local people if deployed in areas with poor air quality [24].However, whether these traits can translate into a practical GHG removal system is unknown.

Methods
We model three candidate photocatalytic GHGremoval systems (figure 1).We emphasize photocatalysts because they are known to decompose various dilute pollutants at room temperature and pressure [26].We emphasize systems where we can project the costs of widespread deployment by analogy to existing industries (e.g.commercial painting and agricultural Our models compute the levelized costs of GHG removal in similar ways (figure 2).We assume a certain unit size for each system, an assumption that in our model does not affect the levelized cost of GHG removal: 1 m 2 for the rooftop system, a size giving a drawdown of 1 mole of GHG per second for the fandriven system, and 1000 kg of particles for the aerosol system.Each model computes the cost of the system over some period of time (1 year for the groundbased systems, with capital costs inflation-adjusted to 2023 dollars and annualized as discussed below, or the particles' atmospheric residence time for the aerosolbased system).Each estimate then finds the system's total GHG drawdown during the same period, evaluating whether surface reaction or convective mass transfer is the rate-limiting step (shared approach in supplementary notes 1 and 3).The total costs are divided by the total GHG drawdown to give the levelized cost per ton of GHG removed over that time period.The models are discussed in detail and their levelized cost formulae are derived in their respective sections below.While we discuss our assumptions for values of the more important model variables in the main text, we describe how we arrived at every input's value in detail in supplementary tables 1-4.
Throughout, we assume the use of ultraviolet (UV)-active photocatalysts similar to those that have been studied for photocatalytic air purification [24,27,28].These photocatalysts are semiconductors like ZnO and TiO 2 that absorb photons, generating charge carriers (electrons and holes) that migrate to the surface and cause reactions, often aided by cocatalysts such as silver or other metals.
We use the apparent quantum yield under UV light (AQY; equation (3)) as our main figure of merit for photocatalysts.We specifically refer to the 'intrinsic' AQY that would be observed in a benchtop trial of a photocatalyst in the absence of gas-phase mass transfer limitations, equal to the intrinsic reaction rate (R reaction ; moles m −2 s −1 ) divided by the incident UV photon flux (Φ UV ; moles m 2 s −1 ).R reaction and the AQY are properties of the catalyst at a given light flux and gas composition, independent of the deployment configuration (supplementary note 1).Treating the intrinsic AQY as an independent variable allows us to model systems with both known photocatalysts and hypothetical future photocatalysts, AQY = 100% • Number of target GHG molecules decomposed Number of photons (< 365 nm) incident on the photocatalyst Figure 2. The high-level flow of variables through our models, whose structures are similar even though the systems' underlying cost models, air flows, and mass transport behaviors vary.For the rooftop and aerosol-based systems, all modeled costs are attributable to mounting or dispersing the catalyst, whether on fixed surfaces or on scattered aerosols, respectively.The ground-based LED-driven system also consumes electricity to light the photocatalyst and circulate air; its model uses an iterative solver to find the air speed, removal fraction, and packing channel size that minimize the levelized GHG removal cost for a given input GHG concentration.
The term 'quantum yield' can also refer to other quantities [29].It may sometimes refer to a yield of charge carriers that participate in a reaction rather than a yield of reacted molecules [15].Quantum yields may also be defined under other spectra of light, such as a full solar spectrum.We use the AQY under UV light because most CH 4 and N 2 Odecomposing photocatalysts to date are predominantly UV-active.We also define our AQY to include the effects of CH 4 /N 2 O adsorption.At dilute GHG concentrations, the intrinsic reaction rate might be limited by GHG adsorption onto the catalyst surface, causing low AQYs even if many charge carriers are generated and reach the surface (supplementary note 2) [30].
For a given UV flux, the AQY is directly proportional to the reaction rate.For example, since an AM1.5 g solar spectrum contains 6.3 • 10 −5 moles m −2 s −1 of photons with wavelengths <365 nm (supplementary table 2), an AQY of 3% under our definition corresponds to a reaction rate of 1.9 • 10 −6 moles m −2 s −1 under 1 sun of UV radiation.
The best reported CH 4 -oxidizing photocatalyst has an AQY of ∼1% t 5000 ppm CH 4 , whereas the best known N 2 O-decomposing photocatalyst has an AQY of ∼9% at 1000 ppm N 2 O [15,31].Those catalysts' AQYs and reaction rates at CH 4 or N 2 O concentrations <100 ppm have not to our knowledge been reported.Since many photocatalytic reactions are described by Langmuir-Hinshelwood rate laws, whose rates decrease at low reagent concentra-tions due to low surface coverage of the catalyst with the reagent, one would expect low rates and AQYs with dilute CH 4 and N 2 O [30].However, the system costs achievable with known photocatalysts at low or ambient CH 4 and N 2 O concentrations remain uncertain until such measurements are made, and upper bounds of future catalysts' performance are therefore unknown.
We use a simplified model of the transition between reaction and mass transfer-limited regimes.In reality, as the reaction rate approaches the mass transfer limit, the concentration of GHG molecules near the surface drops, reducing the fraction of catalyst surface covered in GHG and consequently slowing the reaction rate to equilibrate with the mass transfer rate (supplementary note 2) [32].Whether there is a sharp or gradual transition, and how closely the catalyst can approach the mass transfer limit, depends strongly on the catalyst's affinity for the GHG.For simplicity and generality, and consistent with previous work, we model an abrupt transition between the two rate-limiting steps (supplementary equation ( 1)) [21].
We generally assume that GHG-decomposing reactions take place on or very near the photocatalyst surface.Though photocatalysts often generate radicals (e.g.hydroxyl or superoxide) that can exist in gaseous form, a study of TiO 2 found that few of those radicals traveled far from the catalyst surface [24,33].In our models, the AQY accounts for reactions driven both by charge carriers on the surface and by any radicals that are present.
We assume that photocatalysts resist deactivating or fouling, because we aim to evaluate these materials' potential under a future best-case scenario.The rooftop system is modeled to replace its catalysts every ∼20 years and the fan-driven system every ∼6 years, whereas the aerosolized catalysts need only last ∼21 d.More research would be required to realize such durable photocatalysts because many photocatalysts undergo full or partial deactivation after only months in outdoor air [23,24,[32][33][34].Moreover, current photocatalytic roof treatments (intended to reduce moss growth) require reapplication every year [35].
For similar reasons, we do not consider full lifecycle emissions (e.g. from construction) from these processes, despite their importance in evaluating negative-emissions technologies [8].Doing so properly would be complex: painting rooftops affects buildings' heating and cooling energy use in locationdependent ways, aerosols and rooftops have direct effects on planetary albedo, and many processes' and inputs' carbon intensities will decrease as fossil fuel use declines [36][37][38].Any processes that look promising here should be subjected to detailed lifecycle analyses in the future; in contrast, processes that seem implausible here are unlikely to perform better once full lifecycle emissions are considered.
Where a photocatalyst cost is required, we use $4500/ton, based on recent prices of ∼$3000/ton for a TiO 2 or ZnO base material and an assumed cost of $1500 per ton of photocatalyst from cocatalysts and synthesis [39,40].For general validation of the latter assumption, the 0.1% by weight of silver in the stateof-the-art CH 4 -oxidizing catalyst reported by Chen et al would cost roughly $700 per ton of catalyst at 2022's average silver price, though non-material bulk synthesis costs are difficult to estimate [15,41].
For ground-based systems, capital costs are annualized using a capital recovery factor (CRF; equation ( 4)).CRFs convert the overnight capital cost of a project into estimated annual loan payments, abstracting away repayment periods, interest rates, and project finance structures [42].We use a CRF of 7.5%/yr.throughout, an optimistic value corresponding to a commercially de-risked technology [43].In contrast to the ground-based systems, the aerosol process incurs only operating costs.
We report mitigation costs in dollars per equivalent ton of carbon dioxide ($/tCO 2 e), converting using 20 year GWPs of 81.2 for CH 4 and 273 for N 2 O [12].We use a 20 year GWP for CH 4 because, given CH 4 's short atmospheric lifetime and large near-term warming effect, rapidly-deployable CH 4 removal might be most useful to limit near-term warming and 'overshoot' of the planet's long-term stable temperature.If CH 4 removal were considered to stabilize long-term temperatures, e.g. to negate increasing natural emissions, a 100 year GWP of 27.9 might be more appropriate.Under 100 year GWP for CH 4 , all of our reported CH 4 removal costs would increase by a factor of ∼2.9, making those solutions less attractive.N 2 O has the same warming potential on 20 or 100 year time scales, so the valuation of near-or long-term warming does not affect its results.
We use $100/tCO 2 e as a rough cost target for GHG removal based on the frequent use of $100/tCO 2 as a cost target for CO 2 -DAC [3,44,45].The Inflation Reduction Act in the USA will create a methane price of $900/tCH 4 ($11/tCO 2 e) starting in 2024 that rises to $1500/tCH 4 ($18/tCO 2 e) in 2026, giving another possible target for CH 4 removal costs [46].

Rooftop-based solar photocatalysis with natural airflow
The simplest possible photoreactor consists of a photocatalyst surface exposed to sunlight and natural airflow.A few such systems have already been proposed or studied for GHG mitigation, including purposebuilt solar photoreactors and buildings covered in photocatalytic paint [8,9,23].We analyze a system in which photocatalytic paint covers the rooftop of a warehouse or commercial building (figure 1(a)).As wind blows over the rooftop, GHG molecules convect to the photocatalyst, where they react under sunlight.Although we assume that the photocatalyst does not chemically deteriorate, we include the cost of annual pressure-washing to remove accumulated dirt.This system's levelized cost of GHG removal (LCOR; $/mole) is calculated using equation (5), which is derived and evaluated in detail in supplementary note 4 using the values and assumptions in supplementary tables 1 and 2. The numerator of equation (5) represents the system's annualized costs per unit area of photocatalyst, whereas the denominator represents its annual rate of GHG drawdown per unit area of photocatalyst.CRF (%/yr.) is the capital recovery factor.CAPEX painting,m 2 ($/m 2 ) is the cost to apply 1 m 2 of paint to a commercial rooftop, while CAPEX catalyst,m 2 ($/m 2 ) is the cost of the paint itself.OPEX m 2 yr.($/m 2 -yr.) is the cost of pressure-washing 1 m 2 of rooftop.UF (%) is the device's utilization factor, which accounts for variations in solar intensity, cloud cover, and day/night cycles [47].R reaction and R ṁ (moles m −2 s −1 ) are the reaction and mass transfer fluxes illustrated in figure 3, one of which is the rate-limiting step for the GHG drawdown process (supplementary note  Each plot shows a target cost of $100/tCO2e for reference.The AQY is the number of moles of methane or nitrous oxide decomposed per mole of incident ultraviolet photons.(a) shows costs for systems targeting CH4 at atmospheric concentrations ranging from atmospheric background to 30 ppm.Outdoor 10 ppm CH4 may sometimes be found close to coal mines, rice paddies, wetlands, and landfills; 30 ppm CH4 can sometimes be found in indoor dairies and close to concentrated cattle feedlots [8].(b) shows costs of systems targeting atmospheric background N2O.In the reaction-limited regime at lower AQYs, GHG removal costs decrease with increasing quantum yields.In the mass transfer-limited regime above a certain AQY, higher quantum yields do not increase the GHG drawdown rate or decrease the system cost.We do not model the transition regime in detail.Higher ambient GHG concentrations or wind speeds boost the maximum mass transfer rate, lowering the system costs achievable at higher quantum yields.) Figure 4 shows the modeled cost of ground-based solar GHG-removal systems under varying ambient conditions and catalyst attributes.Average wind speeds of 2-6 m s −1 are found at a height of 10 m above ground level, about the height of a commercial roof, in many locations [48].
Systems targeting atmospheric CH 4 and N 2 O are modeled to approach ∼$300/tCO 2 e at high quantum yields (>1% for CH 4 and >0.1% for N 2 O), well above a $100/tCO 2 e target.The costs are roughly 37% initial painting, 3% catalyst, and 60% annual washing.Reductions in these costs or additional value streams (e.g.white roofs that reduce HVAC costs) might help achieve $100/tCO 2 e [49].The costs are also proportional to the capital recovery factor.Systems targeting elevated (>10 ppm) CH 4 concentrations also might be cost-effective.
We also considered mounting panels of solar photocatalysts on standalone structures that resemble utility-scale fixed-tilt photovoltaic arrays.However, we estimated that the construction cost per square meter of exposed photocatalyst would be ∼7 times that of painting rooftops, making the system unlikely to be cost-effective (supplementary table 2) [47].

Ground-based LED photocatalysis with fan-driven airflow
Fan-driven machines with artificial illumination are another option for photocatalytic systems, offering the potential for compact footprints and, unlike solar systems, 24 hour operation.We envision a machine generally resembling the 'slab-style' CO 2 -DAC contactor described by Holmes and Keith in 2012 and since commercialized by Carbon Engineering Ltd. (figure 5(a)) [50].More recent pilot and engineering studies based on that work have generally validated its cost projections [43].We model the cost in two decoupled components: (1) that of the air contactor, which blows air over the photocatalyst and whose cost (capital and energy) depends strongly on the inlet GHG concentration and the photocatalyst's reaction rates, and (2) that of the LED system, whose size and cost depend mainly on the photocatalyst's AQY.
Holmes and Keith [50] modeled the reaction of gaseous CO 2 with an aqueous hydroxide solution using off-the-shelf crossflow tower packing that provides excellent contact between flowing gases and trickling liquids.The packing is made of stacked sheets of inexpensive heat-formed plastic.Since our reactions are gas-solid instead of gas-liquid, we instead imagine 'monolith-style' packing consisting of many straight, square, photocatalyst-coated channels.These types of channels offer fast mass transfer at low pressure drops [51].We envision channels made of stacked heat-formed plastic sheets with volumetric costs similar to Holmes et al's crossflow packing.
The photocatalyst-coated channels could be illuminated in various ways [24].UV-transparent packing could be used, or LEDs or optical fibers could be embedded in the plastic layers.We treat LED costs separately from the volumetric cost of packing, assuming that the LEDs can be integrated inexpensively.We assume that the packing is coated in a 1 µm layer of photocatalyst and is replaced whenever the LEDs are replaced (every 6 years).The packing contributes <5% of contacting costs in all scenarios modeled, so replacing the catalyst more frequently might not be cost-prohibitive.We assume that the light intensity is always set so that the photochemical reaction rate matches the convective mass transfer rate of GHGs to the catalyst surface.
We model the fan-driven air contactor using Holmes and Keith approach [50].Key variables are labeled in figure 5. We first define an expression (equation ( 6)) for the levelized cost of GHG removal (LCOR; $/tCO 2 e).We later minimize that expression at a fixed inlet GHG concentration (C GHG,In ; ppm) and electricity price (LCOE; $/kWh) by adjusting the air velocity (V air ; m/s), channel width (W channel ; m), and outlet GHG concentration (C GHG,Out ; ppm).
The numerator on the right side of equation ( 6) is the plant's total annualized cost, which includes its construction cost (CAPEX Construction ; $) adjusted by a construction contingency ratio (F Contingency ; %) and annualized using a capital recovery factor (CRF; %/yr), as well as the annual operating and energy cost (OPEX Annual ; %/yr).The denominator is its annual GHG drawdown in moles, which includes its designed removal capacity (RC; moles s −1 ) and utilization factor (UF; %).
Evaluating equation ( 6) requires calculating various intermediates (figure 5).Holding the machine's overall GHG removal capacity fixed, we compute the contactor's frontal area, depth, internal surface area, and electricity demand as functions of V air , W channel , and C GHG,Out using pressure drop, mass transfer, reaction rate, and mass balance relations.The contactor's frontal area, internal volume, and internal surface area each determine components of its construction cost (CAPEX Construction ), while the fan electricity cost, LED electricity cost, and ongoing LED and packing replacement costs are components of operating cost (OPEX Annual ).Supplementary note 5 and Figure 5.We envision a system resembling some devices for the direct air capture of carbon dioxide, using a slab-style contactor where fans blow air through straight, square, photocatalyst-coated channels studded with LEDs.(a) Our model for this device's cost takes air velocity, channel width, and outlet GHG concentration (V air , W channel , and CGHG,out) as arguments while assuming a fixed inlet GHG concentration (C GHG,in ) and total GHG removal capacity.Based on these inputs, the required pressure drop, packing depth, frontal area, and fan power (∆P, D packing , A frontal , and E fan ) and other intermediate values are calculated, leading to an estimate of the levelized system cost.V air , W channel , and CGHG,out are finally optimized to find the minimum system cost at a given C GHG,in .(b) We model the overall GHG decomposition flux to be limited either by the reaction flux on the surface (R reaction ) or by the flux of GHG mass transfer to the surface (R ṁ).The reaction flux is calculated using a first-order rate law from an assumed or observed reaction rate at the ambient GHG concentration (1.8 ppm for CH4; 0.33 ppm for N2O).The maximum mass transfer rate is calculated for a fully developed fluid flow in a square pipe with a given average velocity (V air ) and average GHG concentration (C GHG,bulk ).
supplementary table 3 describe these calculations in detail.
Unlike in the solar systems, multiple suns of UV light may be used to boost rates and decrease the system footprint.However, increasing the light flux gives diminishing returns in terms of the reaction rate (i.e. an arbitrarily high light flux does not lead to an arbitrarily high rate), since other aspects of reaction kinetics limit the rate even when charge carriers are abundant on the surface [30].To capture this behavior, each model is given the photocatalyst's reaction rate at ambient GHG concentrations (1.8 ppm for CH 4 or 0.33 ppm for N 2 O) under a high UV flux.Ideally, this rate and the AQY would be experimentally measured for a specific photocatalyst under a fixed light intensity, e.g. 10 suns of UV.However, one can also choose an 'upper bound' rate, such as the expected reaction rate of 2 ppm CO 2 with a film of aqueous NaOH solution, a rapid reaction whose rate photocatalysts are unlikely to exceed [50].Figures 6(a) and (c) show this parameter's effect.
The LCOR is minimized over of V air , W channel , and C GHG,Out at a given C GHG,In and electricity price (equation ( 7)) to find the lowest-cost GHG removal system under those conditions, whose cost we report.
Our model tends to choose similar device traits across a range of conditions.As an example, the lowest-cost device for an elevated inlet CH 4 concentration of 20 ppm, an LCOE of 4 c kWh −1 , and a catalyst with a reaction rate of 0.1 µmol m −2 s −1 at 1.8 ppm has monolith channels 2.0 cm wide and 12.6 m deep.It blows air at 3.1 m s −1 through a 151 Pa pressure drop, achieving an outlet CH 4 concentration of 6.6 ppm.The flow is turbulent (Re ≈ 4200) inside the channels.Fan electricity and the contactor frame respectively contribute 23% and 34% of the total contacting cost.
Figures 6(a)/(c) and 6(b)/(d) respectively show the costs of the air contacting and lighting subsystems, which can be summed to estimate the total cost of a GHG-removing system.For both CH 4 and N 2 O, Figure 6.Costs of ground-based, fan-driven GHG removal systems with LED illumination.Such devices contain an air contacting subsystem, whose costs depend mainly on the inlet GHG concentration and the photocatalyst's activity, estimated in (a) for CH4 and (c) for N2O, and a lighting subsystem, whose costs depend mainly on the photocatalyst quantum yield and are estimated in (b) for CH4 and (d) for N2O.The contacting and lighting subsystem costs can be added to estimate the total cost of a GHG removal system.Atmospheric background concentrations of CH4 and N2O are marked, as are subsystem cost targets of $100/tCO2e.In each of (a) and (c), the lowest line represents a rate close to the mass-transfer limit in which every GHG molecule that touches the catalyst is decomposed, while the second-lowest line represents a rate close to that of the reaction between CO2 and the surface of an aqueous 1-2 M NaOH solution (∼0.2 µmol m −2 s −1 at 1.8 ppm) [50].The upper two lines are more likely to represent the rates of existing photocatalysts [21].In (a) and (c), a base-case LCOE of 4 c kWh −1 is used.Using an LCOE of 2 c kWh −1 decreases the modeled contactor costs by ∼10%, while using one of 6 c kWh −1 increases them by ∼10%.extremely high reaction rates are required to achieve contacting costs below $100/tCO 2 e at ambient GHG concentrations.Lower rates necessitate larger and more expensive contactors.Even a rate constant as high as that of the reaction between CO 2 and aqueous ∼1 M NaOH, which Keith et al exploit for their CO 2 -DAC system and which would be very difficult to replicate with a photocatalyst, leads to system costs well over $100/tCO 2 e for 1.8 ppm CH 4 , consistent with others' concerns about the expense of fan-driven contactors for ambient CH 4 [9,50].
One might also combine CH 4 or N 2 O removal with CO 2 -DAC [10].In the best case, the LEDs and photocatalyst would be added to unused surfaces within the CO 2 -DAC system, incurring no additional pressure drop.The lighting subsystem cost in figures 6(b) and (d) can be considered a lower bound on such a modification's cost, to which catalysts and construction expenses would be added.Even in an ideal scenario, very high CH 4 AQYs and high N 2 O AQYs would be required to achieve <$100/tCO 2 e costs.

Aerosol-based solar photocatalysis
Rather than moving air across a photocatalyst surface, one could in principle 'bring the catalyst to the atmosphere' by dispersing aerosolized photocatalysts.Fine powders have extremely high specific surface areas, allowing fast mass transfer and rapid reactions.Figure 7(a) illustrates the general process we envision and Supplementary Note 6 describes it in greater detail.We model the physical processes only, without considering social factors in whether deployment of such a technology would or should be allowed.
We model particles as either pure photocatalyst (⩽2 µm particles) or a 1 µm layer of photocatalyst around a silica core (>2 µm particles), with the photocatalyst assumed to cost $4500/ton.We model aircraft dispersing catalyst particles either in the lower troposphere (altitudes 0.5-1.5 km) or upper troposphere (>1.5 km).We estimate particle dispersal costs of $760/ton, calculated using industry figures from aerial pesticide application (supplementary note 6) [53].This value is about half the projected cost per ton of launching aerosols at higher altitudes of ∼20 km with jet aircraft [54,55].
A variety of other dispersion methods might be possible with modest engineering improvements, including guyed masts (up to ∼500 m), tethered balloons, and kites like those used for airborne wind power generation [55][56][57][58].Aerosols could also be lofted in the heated gases from existing smokestacks [59].We model airplanes because they are a proven technology.Even if cheaper launch systems are possible, the particles in this system are a much greater driver of overall cost.
We estimate the levelized cost of GHG removal using equation (8), which is derived and evaluated in detail in supplementary note 6 using the values in supplementary tables 1 and 4. The numerator represents the total cost per unit mass of aerosol dispersed and the denominator represents the lifetime GHG drawdown per unit mass of aerosol dispersed.OPEX Synthesis ($/ton) is the cost to manufacture the particles and OPEX Launch ($/ton) is the cost to disperse them.AF (%) is the sunlight availability factor, which accounts for temporal variations in solar intensity including clouds and day-night cycles.SSA (m 2 /ton) is the mass-specific surface area of the particles.L particle (s) is the aerosol's atmospheric residence time, which varies with the particles' diameter and altitude [60].Particles between about 0.1 and 1 µm last ∼7 d in the lower troposphere and 21 d in the upper troposphere, with larger particles settling faster.R reaction and R ṁ (moles m −2 s −1 ) are the average reaction and mass transfer fluxes over the particle surface, illustrated in figure 7, one of which is the ratelimiting step for the GHG drawdown process.

LCOR =
OPEX Synthesis + OPEX Launch AF • SSA.L particle • min (R reaction , R in ) . (8) Figures 8(a) and (b) show the projected costs for CH 4 and N 2 O removal using photocatalytic aerosols.Costs are fairly low even at modest quantum yields, despite the particles' short lifespans.Assuming 1 µm particles dispersed in the lower troposphere, $100/tCO 2 e removal costs are attainable at AQYs of ∼1.0% when targeting 1.9 ppm CH 4 and ∼0.10% when targeting 330 ppb N 2 O.We note that removal costs are sensitive to particle costs; doubling the particles' cost, for instance, would increase all removal costs by 88%.
We also compared the airplanes' CO 2 emissions to the GHG drawdown effected by the particles and found that they are small compared to the overall climate benefit (supplementary note 7).If the particles contain photocatalysts with AQYs giving $100/tCO 2 e removal costs in the lower troposphere, the planes' CO 2 emissions negate ∼0.3% of the process's climate benefit.
One concern with this approach is the effect of small aerosol particles on human and ecosystem health.Particles <10 µm in size can irritate tissues in respiratory tracts, with smaller particles usually causing greater harm [61].PM 10 (<10 µm particles) and PM 2.5 (<2.5 µm particles) are wellstudied types of air pollution; a process generating them would be unlikely to be deployed if people might inhale the particles downwind.Simply making the particles larger is costly (figure 8(c)): going from 1 µm particles to pollen-sized 20 µm particles raises removal costs by ∼40x.Dispersing particles in remote areas, e.g. over oceans, could mitigate human exposure, though animals and ecosystems might still be affected.
The total amount of aerosols required is another challenge.Removing 1 gigaton of CO 2 equivalent using 1 µm particles with AQYs of 0.8% would require dispersing 19 megatons of aerosols in the lower troposphere at a cost of $100/tCO 2 e or 7.6 megatons in the upper troposphere at a cost of $40/tCO 2 e (supplementary note 7).For comparison, California's 2021 wildfires released around 1 megaton of PM 2.5 [62].While gigaton-scale drawdown is valuable, dispersing such a mass of aerosols may be impractical due to environmental impacts and social considerations.Because the cost and the required aerosol mass are inversely proportional to each particle's lifetime GHG drawdown, higher quantum yields or smaller particles would reduce the required mass of aerosols considerably.The maximum reaction rate is calculated based on an assumed or observed quantum yield at a given GHG concentration (C GHG,bulk ) and photon flux in a certain spectrum (Φ solar ).The maximum mass transfer rate is calculated using a closed-form solution for mass transfer to a spherical particle with a known GHG concentration (C GHG,bulk ) in the bulk air.

Discussion
Several of the GHG decomposition systems we analyzed might achieve our target of <$100/tCO 2 e in optimistic scenarios.The removal of atmospheric background CH 4 and N 2 O using photocatalytic paint could be cost-effective with excellent AQYs and lower painting costs.N 2 O removal using fan-driven machines like those for CO 2 DAC might be plausible with greatly improved photocatalysts.Using such devices to decompose CH 4 seems unlikely without elevated local CH 4 concentrations, cost declines in LEDs, and extremely efficient photocatalysts.While higher CH 4 concentrations might boost the reaction rates of both rooftop-based and fan-driven systems, finding suitable project sites where CH 4 levels remain elevated for years may be difficult.Finally, aerosol-based CH 4 and N 2 O removal could be costeffective, though the mass of particles required would be substantial.
We emphasize the uncertainty in our cost estimates for untried technologies.Outputs are also quite sensitive to the assumed values of a few key cost drivers, as discussed in each section.Labor, component, and raw material prices can vary considerably by country and economic conditions.Though most of our estimates are from North America, many inputs may be cheaper elsewhere.Macroeconomic conditions affect the capital recovery factor, to which ground-based systems are sensitive.Additionally, although our study considers the systems' direct GHG drawdowns, future studies should consider all lifecycle climate effects.These include rooftop paint's effects on heating and cooling energy use, rooftops' and aerosols' direct effect on planetary albedo, and all systems' construction, energy, and material emissions.They could also consider any local air quality benefits in addition to climate benefits.Moreover, all of our outputs are highly sensitive to the GWP used: using a 100 year instead of our 20 year GWP for CH 4 increases costs by a factor of ∼2.9.
All systems we modeled appear to require greatly improved photocatalysts to be cost-effective.The quantum yield at the relevant GHG concentration and the photocatalyst lifetime are the most critical figures to improve.Whereas state-of-the-art photocatalysts have >1% AQYs at >1000 ppm of CH 4 or N 2 O, their efficiency will likely drop considerably at single-ppm GHG concentrations.Measuring known catalysts' rates at dilute concentrations would be a useful first step.Given the low (0.01%-0.1%)AQYs often observed for photocatalysts reacting other dilute substances like volatile organic compounds, achieving the AQY targets that this study sets, especially those ⩾1%, would require fundamental research to greatly increase photocatalysts' AQYs [63,64].Reductions in photocatalyst fouling and deactivation would also be essential for any ground-based system but matter less for aerosols, which only stay active for days.
We found throughout that for a given cost target, targeting ambient N 2 O requires a considerably (a) Removal of atmospheric background CH4 could achieve a cost target of $100/tCO2e on 1 µm particles with a catalyst quantum yield of ∼1.0% in the lower troposphere or ∼0.4% in the upper troposphere.(b) Removal of atmospheric background N2O could attain the same cost target on the same size of particle with quantum yields of only ∼0.10% in the lower troposphere or ∼0.04% in the upper troposphere.(c) Greenhouse gas removal costs are lower with smaller particles due to their longer atmospheric residence times and greater surface area-to-mass ratios.However, particles smaller than 10 µm, and especially those smaller than 2.5 µm, could have adverse health effects if dispersed in large quantities near human settlements.In all cases, particles in the upper troposphere last longer than particles in the lower troposphere, leading to lower costs.lower AQY than targeting ambient CH 4 .However, photodecomposition of 330 ppb N 2 O and 1.9 ppm CH 4 are distinct processes with different mechanisms whose AQYs cannot be compared side-by-side, and it remains unclear which-if either-is closer to practicality.
Pursuit of aerosol-based GHG photodecomposition would require serious evaluation and mitigation of unintended environmental and health effects.Improved photocatalyst quantum yields could decrease the mass of particles required to remove a given amount of GHG.In addition, it would be essential to begin exploring now whether, how, and under what conditions this strategy might gain social license to operate.
In recent years, numerous strategies for removal of atmospheric CH 4 and (to a lesser extent) N 2 O have been proposed.Cost-effectiveness will be one of many criteria that will help select the options that could plausibly be deployed in a relevant timeframe.While photocatalytic CH 4 /N 2 O removal may one day be possible with improved materials, the challenges are considerable.Study of photochemical and all other CH 4 /N 2 O removal approaches should continue, while mitigation of CH 4 and N 2 O sources continues as the greater priority.DGE-1656518.Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Figure 1 .
Figure 1.Graphical summaries of the three greenhouse gas photodecomposition systems considered here.Methane is shown, but N2O could be substituted for CH4 in each panel.The systems are (a) a photocatalyst-painted rooftop under sunlight and natural, passive airflow; (b) a ground-based electrically driven device using forced airflow and internal LED illumination (drawn with a cutaway to show the internal photocatalyst channels and LEDs); and (c) an aerosol-based system using sunlight and photocatalytic particles dispersed in the troposphere.

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Figure 3 .
Figure 3.We envision a flat commercial rooftop painted with a uniform layer of photocatalytic paint, sketched in full in figure 1.We model the overall GHG decomposition flux to be limited either by the reaction flux on the surface (R reaction ) or by the flux of GHG mass transfer to the surface (R ṁ).The maximum reaction rate is calculated based on an assumed or observed quantum yield at a given GHG concentration (C GHG,bulk ) and photon flux in a certain spectrum (Φ solar ).The maximum mass transfer rate is calculated using a mass transfer correlation for fluid flow over a flat rooftop with a given velocity (V air ) and GHG concentration (C GHG,bulk ) in the free stream.

Figure 4 .
Figure 4. Costs of ground-based solar GHG removal systems at varying wind speeds and ambient GHG concentrations.Each plot shows a target cost of $100/tCO2e for reference.The AQY is the number of moles of methane or nitrous oxide decomposed per mole of incident ultraviolet photons.(a) shows costs for systems targeting CH4 at atmospheric concentrations ranging from atmospheric background to 30 ppm.Outdoor 10 ppm CH4 may sometimes be found close to coal mines, rice paddies, wetlands, and landfills; 30 ppm CH4 can sometimes be found in indoor dairies and close to concentrated cattle feedlots[8].(b) shows costs of systems targeting atmospheric background N2O.In the reaction-limited regime at lower AQYs, GHG removal costs decrease with increasing quantum yields.In the mass transfer-limited regime above a certain AQY, higher quantum yields do not increase the GHG drawdown rate or decrease the system cost.We do not model the transition regime in detail.Higher ambient GHG concentrations or wind speeds boost the maximum mass transfer rate, lowering the system costs achievable at higher quantum yields.

Figure 7 .
Figure 7.The modeled aerosol-based system using sunlight and photocatalytic powders dispersed by aircraft.(a) The process modeled involves several steps.(I) The aerosol powder is synthesized, with each particle consisting either of agglomerated photocatalyst nanoparticles or of a layer of photocatalyst nanoparticles around an inert core.(II) The particles are dispersed in the troposphere.We model dispersal via small aircraft like those used for crop-dusting, though other approaches like towers or kites may be possible.(III) While the particles remain suspended, the target GHG diffuses to the surface and reacts in sunlight.(IV) The particles exit the atmosphere, usually after a few days, through some combination of wet and dry deposition.(b) We model the overall GHG decomposition flux to be limited either by the reaction flux on the surface (R reaction ) or by the flux of GHG mass transfer to the surface (R ṁ).The maximum reaction rate is calculated based on an assumed or observed quantum yield at a given GHG concentration (C GHG,bulk ) and photon flux in a certain spectrum (Φ solar ).The maximum mass transfer rate is calculated using a closed-form solution for mass transfer to a spherical particle with a known GHG concentration (C GHG,bulk ) in the bulk air.

Figure 8 .
Figure8.Costs of aerosol-based solar GHG removal systems with varying target gases, altitudes, particle sizes, and quantum yields.(a) Removal of atmospheric background CH4 could achieve a cost target of $100/tCO2e on 1 µm particles with a catalyst quantum yield of ∼1.0% in the lower troposphere or ∼0.4% in the upper troposphere.(b) Removal of atmospheric background N2O could attain the same cost target on the same size of particle with quantum yields of only ∼0.10% in the lower troposphere or ∼0.04% in the upper troposphere.(c) Greenhouse gas removal costs are lower with smaller particles due to their longer atmospheric residence times and greater surface area-to-mass ratios.However, particles smaller than 10 µm, and especially those smaller than 2.5 µm, could have adverse health effects if dispersed in large quantities near human settlements.In all cases, particles in the upper troposphere last longer than particles in the lower troposphere, leading to lower costs.