Configurations and deployment scenarios

We model six unique DAC plant configurations, where a configuration is a pairing of DAC process and heat supply (Supplementary Tables 5–7). Three of these configurations involve high-temperature (HT) liquid solvent process coupled to kilns that employ oxy-fired natural gas (HT-gas or “HT-g”), electricity (HT-electric or “HT-e”), or hydrogen (HT-hydrogen or “HT-h”). Three configurations are comprised of low-temperature (LT) solid sorbent process coupled to either a natural gas combustion-fired boiler (LT-g), a supply of waste heat (LT-w), or electric heat pumps (LT-hp). Geothermal heating, actively considered in some places⁵⁴, is location-constrained, while our focus is scalable options. Extant pilot plants have been sized <1000 tCO₂ yr^–1; the plants considered in this analysis are of commercial size with capacity 1-MtCO₂ yr^–1. Hardware, fuel use, and carbon flows differ by configuration (Supplementary Figs. 3 and 4), as do the equations governing the system. We track differences by defining six disjoint sets that distinguish scenarios s by their configuration, i.e., \(s \in {\cal{S}}_{{\mathrm{HT}}-{\mathrm{g}}} \cup {\cal{S}}_{{\mathrm{HT}}-{\mathrm{e}}} \cup {\cal{S}}_{{\mathrm{HT}}-{\mathrm{h}}} \cup {\cal{S}}_{{\mathrm{LT}}-{\mathrm{g}}} \cup {\cal{S}}_{{\mathrm{LT}}-{\mathrm{w}}} \cup {\cal{S}}_{{\mathrm{LT}}-{\mathrm{hp}}}\). DAC deployment modeling is implemented in Matlab.

Deployment scenarios are formed by pairing each of the six configurations with one of several non-proximate electricity sources along with an appropriation regime that funds deployment. Electricity supplies include renewables, hydroelectric power, CCGT, CCGT with CCS, SMRs, or hybrids thereof (Supplementary Tables 8–10). An appropriation is the amount of funding made available for deployment. Each scenario—294 in total—is a combination of DAC type, heat source, electricity source, and appropriation.

The modeling period t = {2025, 2030, ..., 2105} runs through end-of-century and is defined by T = 16 periods lasting Δ = 5 years. Results are, in general, denoted with vectors v_i of length T or matrices m_i,k of size T-by-T. Results can vary by period k ∈ {1, …, T} and by DAC vintage i ∈ {1, …, T}, where a vintage is the set of plants deployed (brought into operation) in period t_i. Plants operate over the period \(t_{{\mathrm{{\Omega} }}_i}\), where \({\Omega} _i = \{ i, \ldots ,i + L{\mathrm{/}}{\Delta} - 1\}\) and L is the plant operating lifetime in years.

Appropriation

The appropriation for DAC deployment in period t_k is given by \(A_k = A_1{\Delta} \mathop {\prod}\nolimits_{u = 1}^k {1 + g_u}\), where A₁ is the initial (year-one) appropriation defined by a funding regime (Supplementary Tables 1–3) and g_u ∈ [0, 1] is the appropriation growth rate in period t_u, with g₁ = 0 (Supplementary Table 4). An appropriation A_i funds DAC vintage i over the vintage’s operating lifetime, with A_i allocated equally (annualized) over periods \(t_{{\mathrm{{\Omega} }}_i}\), given by \(\alpha _{i,k} = A_iL^{ - 1}\,\forall k \in {\Omega} _i\) and 0 otherwise. It follows that the appropriation “disbursed” in period k (in Fig. 2a) is given by \(\hat \alpha _k = \mathop {\sum}\nolimits_{u,v = 1}^k {a_{u,v}}\).

Energy use, CO₂ emissions and removal, and cost

Calculation of DAC deployment and of associated energy use, CO₂ removal, and cost is iterative by DAC vintage and follows four steps broadly: calculation of plant-level totals, calculation of new deployment and retirement, application of technological learning-by-doing, and, after the iteration process is completed, calculation of fleet-aggregated totals and levelized totals (Supplementary Fig. 2).

Electricity use by DAC is given by \(\eta _{i,k}^{{\mathrm{dac}}} = \dot E_i^{{\mathrm{dac}}}U{\Delta} \,\forall {\mathrm{k}} \in {\Omega} _{\mathrm{i}}\), where \(\dot E^{{\mathrm{dac}}} = E^{{\mathrm{dac}}}R^{{\mathrm{dac}}}8760^{-1}\) is the electricity demand of the DAC process in kWh h^–1, and \(U = \min \{ U^{{\mathrm{dac}}},U^{{\mathrm{elec}}} + U^{{\mathrm{es}}}\} \in [0,8760]\) is the plant uptime (availability) in hours of annual operation and constrained by either the uptime of the DAC process U^dac or the total electricity resource U^elec + U^es (electric grid “elec” plus energy storage “es”). E^dac includes the compressor load, which compresses CO₂ to 15 MPa for pipeline injection and is identical across configurations. Electricity is also consumed by heat pumps, \(\eta _{i,k}^{{\mathrm{hp}}} = 0.0036r_i^{{\mathrm{hp}}}\beta _i^{-1}{\mathrm{U}}{\Delta} \,\forall {\mathrm{k}} \in {\Omega} _{\mathrm{i}}\), where r^hp is the is the capacity of installed heat pumps in GJ-thermal (GJt), with \(r_i^{{\mathrm{hp}}} = \dot H_i^{{\mathrm{dac}}}\,\forall s \in {\cal{S}}_{{\mathrm{LT}}-{\mathrm{hp}}}\) and 0 otherwise, \(\dot H^{{\mathrm{dac}}} = H^{{\mathrm{dac}}}R^{{\mathrm{dac}}}8760^{-1}\) is the low-temperature heat demand in GJ h^–1, and β is the heat pump coefficient of performance in GJt GJe^–1. It follows that total electricity consumption at the DAC plant is \(\eta = \eta ^{{\mathrm{dac}}} + \eta ^{{\mathrm{hp}}}\).

Natural gas is combusted for process heat in scenarios \(s \in \{ {\cal{S}}_{{\mathrm{HT}}-{\mathrm{g}}},{\cal{S}}_{{\mathrm{LT}}-{\mathrm{g}}}\}\). For HT-g DAC, gas use is given by \(\gamma _{i,k}^{{\mathrm{dac}}} = {\mathrm{LHV}}^{-1}\dot G_i^{{\mathrm{dac}}}U{\Delta} \,\forall {\mathrm{k}} \in {\Omega} _{\mathrm{i}}\), where LHV is the lower heating value of natural gas in GJ t^–1; for LT-g DAC, \(\gamma _{i,k}^{{\mathrm{dac}}} = {\mathrm{HHV}}^{-1}{\mathrm{Eff}}^{{\mathrm{boil}}^{ - 1}}\dot H_i^{{\mathrm{dac}}}U{\Delta} \,\forall {\mathrm{k}} \in {\Omega} _{\mathrm{i}}\), where Eff^boil is the boiler efficiency. For all other configurations, γ^dac = 0. HT-g DAC is defined by a gas requirement \(\dot G^{{\mathrm{dac}}} = G^{{\mathrm{dac}}}R^{{\mathrm{dac}}}8760^{-1}\) (GJ h^–1), whereas LT DAC is defined by the low-temperature heat requirement \(\dot H^{{\mathrm{dac}}}\) (GJ h^–1) that can be supplied via gas combustion or otherwise (e.g., waste heat or heat pumps). Combined cycle gas turbines (CCGT) consume natural gas when serving as the electricity source, given by \(\gamma _{i,k}^{{\mathrm{ccgt}}} = \tilde \eta _{i,k}^{{\mathrm{grid}}}q_k{\mathrm{LHV}}^{-1}\), where \(\tilde \eta _{i,k}^{{\mathrm{grid}}} = \eta _{i,k}U^{-1}\left( {U^{{\mathrm{elec}}} + U^{{\mathrm{es}}}{\mathrm{Eff}}^{{\mathrm{es}}^{-1}}} \right)\) is power supplied by the grid to the DAC plant and energy storage system, where Eff^es is the roundtrip efficiency of energy storage, and q is the CCGT net heat rate in GJ kWh^–1 (where “net” is inclusive of parasitic load for capture and compression to 15 MPa; see Supplementary Tables 9 and 10 for electricity source parameters); otherwise, γ^ccgt = 0.

Plant CO₂ emissions derive from electricity generation and production of process heat, given by \({\it{\epsilon }}_{i,k}^{{\mathrm{elec}}} = \tilde \eta _{i,k}^{{\mathrm{grid}}}{\mathrm{CI}}_k^{{\mathrm{elec}}}\) and \({\it{\epsilon }}_{i,k}^{{\mathrm{heat}}} = \gamma _{i,k}^{{\mathrm{dac}}}{\mathrm{LHV}}\,{\mathrm{CI}}_i^{{\mathrm{heat}}}\), respectively, where \({\mathrm{CI}}_k^{{\mathrm{elec}}}\) and \({\mathrm{CI}}_i^{{\mathrm{heat}}}\) are the carbon intensities of electricity generation and heat production, in tCO₂ kWh^–1 and tCO₂ GJ^–1, respectively (Supplementary Tables 7 and 9). Combustion emissions originate from within the plant boundary (they are direct emissions), while emissions from electricity generation are indirect, but both are attributable in the calculation of net CO₂ removal. Fugitive leaks of methane from natural gas infrastructure are given by \({\it{\epsilon }}_{i,k}^{{\mathrm{CH}}4} = \lambda \left( {\gamma _{i,k}^{{\mathrm{dac}}} + \gamma _{i,k}^{{\mathrm{ccgt}}}} \right)\), where λ ∈ [0, 1] is the fraction of leakage from production, gathering, processing, transmission, and storage (Supplementary Table 11).

CO₂ captured from the atmosphere is given by \(\chi _{i,k}^{{\mathrm{atm}}} = R^{{\mathrm{dac}}}U{\Delta} {\mathrm{/}}8760\,\forall {\mathrm{k}} \in {\Omega} _{\mathrm{i}}\). For scenarios \(s \in {\cal{S}}_{{\mathrm{HT}}-{\mathrm{g}}}\), 100% of CO₂ is captured from the oxy-fuel combustion process, given by \(\chi _{i,k}^{{\mathrm{heat}}} = \dot G_i^{{\mathrm{dac}}}\mu {\mathrm{HHV}}^{-1}U{\Delta} \,\forall {\mathrm{k}} \in {\Omega} _{\mathrm{i}}\), where μ = 2.744 gCO₂ gCH₄^–1 is the ratio of molecular weights of CO₂ to CH₄, HHV is the higher heating value of methane, and assuming 100% conversion of CH₄ to CO₂; for all other scenarios, CO₂ is not captured from heat production, i.e., χ^heat = 0. CO₂ is captured when CCGT with post-combustion capture serves as the electricity source, given by \(\chi _{i,k}^{{\mathrm{elec}}} = \tilde \eta _{i,k}^{{\mathrm{grid}}}{\mathrm{CC}}_k^{{\mathrm{elec}}}\), where CC^elec is the carbon capture factor in tCO₂-captured per kWh electricity supplied (Supplementary Note 1); otherwise, CC^elec = 0. Gross CO₂ removal from the atmosphere is equivalent to χ^atm, total CO₂ captured at the DAC plant is given by χ^dac = χ^atm + χ^heat, and net CO₂ removal from the atmosphere, i.e., gross removal less process emissions, is given by \(\rho = \chi ^{{\mathrm{atm}}}-{\it{\epsilon }}^{{\mathrm{elec}}}-{\it{\epsilon }}^{{\mathrm{heat}}}\). Capturing CO₂ from energy generation, though not counted toward gross atmospheric CO₂ removal, is nevertheless important for maximizing ρ.

The total plant cost c_i,k gives the cost of a DAC plant deployed in period i during each period of operation k ∈ Ω_i. The total cost is comprised of capital and operating costs for the DAC system c^dac and means of heat production c^heat, energy costs for electricity c^elec and natural gas c^ngas, and CO₂ disposal costs c^seq, given by

It follows that the lifetime cost of a plant of vintage i is \(\mathop {\sum}\nolimits_k {c_{i,k}}\). DAC costs are expressed as \(c_{i,k}^{{\mathrm{dac}}} = C_i^{{\mathrm{dac}},{\mathrm{cap}}}R^{{\mathrm{dac}}}\,{\mathrm{CRF}}{\Delta} + C_i^{{\mathrm{dac}},{\mathrm{om}}}R^{{\mathrm{dac}}}{\Delta} \,\forall {\mathrm{k}} \in {\Omega} _{\mathrm{i}}\), where C^dac,cap is the plant capital cost in $ tCO₂^–1 yr^–1, C^dac,om is the plant operating cost in $ tCO₂^–1, \({\mathrm{CRF}} = {\mathrm{WACC}}\left( {1 + {\mathrm{WACC}}} \right)^L\left( {\left( {1 + {\mathrm{WACC}}} \right)^L - 1} \right)^{ - 1}\) is the capital recovery factor in yr^–1, and WACC is the weighted average cost of capital. Costs are inclusive of CO₂ compressor costs. Heat production costs are given by \(c_{i,k}^{{\mathrm{heat}}} = C_i^{{\mathrm{boil}},{\mathrm{cap}}}r_{\mathrm{i}}^{{\mathrm{boil}}}{\mathrm{CRF}}{\Delta} + C_i^{{\mathrm{hp}},{\mathrm{cap}}}r_{\mathrm{i}}^{{\mathrm{hp}}}{\mathrm{CRF}}{\Delta} + C^{{\mathrm{hp}},{\mathrm{om}}}r_i^{{\mathrm{hp}}}U{\Delta} \,\forall {\mathrm{k}} \in {\Omega} _{\mathrm{i}}\), where \(C^{ \cdot ,{\mathrm{cap}}}\), \(C^{ \cdot ,{\mathrm{om}}}\), and \(r^{( \cdot )}\) denote the capital cost, operating cost, and capacity of the boiler “boil” and heat pumps “hp”. Waste heat is taken to have zero cost. Electricity and natural gas costs are given by \(c_{i,k}^{{\mathrm{elec}}} = \eta _{i,k}^{{\mathrm{dac}}}U^{-1}\left( {U^{{\mathrm{elec}}}{\mathrm{MC}}_k^{{\mathrm{elec}}} + U^{{\mathrm{es}}}{\mathrm{MC}}_k^{{\mathrm{es}}}} \right)\) and \(c_{i,k}^{{\mathrm{ngas}}} = \gamma _{i,k}^{{\mathrm{dac}}}{\mathrm{HHV}}\,{\mathrm{MC}}_k^{{\mathrm{ngas}}}\), respectively, where MC^(·) is commodity marginal cost (electricity “elec”, $ kWh^–1; energy storage “es”, $ kWh^–1; natural gas “ngas”, $ GJ^–1). Natural gas costs are attributed only to gas consumed for heat production; fuel costs for electricity generation are included in MC^elec. The cost of sequestration is given by \(c_{i,k}^{{\mathrm{seq}}} = \chi _{i,k}^{{\mathrm{dac}}}{\mathrm{MC}}_k^{{\mathrm{seq}}}\), where MC^seq is the marginal cost of CO₂ transport and sequestration in $ tCO₂^–1 (Supplementary Table 12). Sequestration costs are applied only to CO₂ captured within the plant boundary; the costs of capturing CO₂ from electricity generation are included in MC^elec. All costs are set to a 2018$ basis.

In our framework DAC plants are treated as government-mandated expenses and thus bear no capital risk beyond any other highly credible government mandate; hence we set WACC to zero. Supplementary Figure 20 explores the importance of risk-adjusted capital costs, showing sensitivity to variation in WACC over the full span of U.S. long-term Treasury Bills covering the last three decades.

Deployment

Deployment of DAC plants is tracked by vintage. Plants are constructed, placed into service for their operating lifetime \(t_{{\mathrm{{\Omega} }}_i}\), then retired. Deployment and fleet size are tracked via the number of new plants deployed \(\pi _i^{{\mathrm{new}}}\), retired \(\pi _i^{{\mathrm{ret}}}\), and operating π_i. New deployment is constrained either by available funding or the rate at which the DAC industry can scale. Given plant total cost c_i,k, the appropriation a_i permits construction of \(\mathop {\sum}\nolimits_k {\alpha _i{\mathrm{/}}c_{i,k}}\) new plants in period t_i. Industry growth is defined with a maximum initial deployment and growth rate. The initial deployment is a ceiling n on the number of plants that can be deployed at the start of the program, i.e., \(\pi _1^{{\mathrm{new}}} \le n\) and we set n = 5. A dynamic diffusion constraint relates the construction of plants in period i to the previous period i – 1, given by \(\pi _i^{{\mathrm{new}}} \le \pi _{i-1}^{{\mathrm{new}}}\left( {1 + p} \right)\), where \(p \in \left[ {0,1} \right]\) is the maximum industry growth rate. We set p = 0.2, in line with prior use and historical growth of energy technologies²¹. The number of plants deployed in period t_i is therefore given by \(\pi _i^{{\mathrm{new}}} = \min \left\{ {\mathop {\sum}\nolimits_k {\alpha _i{\mathrm{/}}c_{i,k}} ,\pi _{i-1}^{{\mathrm{new}}}\left( {1 + p} \right)} \right\}\). Plants are retired at end-of-operating-life, given by \(\pi _i^{{\mathrm{ret}}} = \pi _{i - L/{\Delta} }^{{\mathrm{new}}}\,\forall i {\,}> {\,} L{\mathrm{/}}{\Delta}\) and 0 otherwise. Constraints on deployment lead to the logistic (“S”-shaped) growth characteristic of industries that emerge, expand, and saturate in the marketplace. The total number of plants operating in period t_i is the cumulative sum of prior deployments and retirements, i.e., \(\pi _i = \mathop {\sum}\nolimits_{u = 1}^i {\pi _u^{{\mathrm{new}}}-\pi _u^{{\mathrm{ret}}}}\).

Learning

DAC attributes for cost (C^dac,cap, C^dac,om) and energy demand (electricity E^dac, natural gas G^dac, and heat H^dac) improve endogenously through investment and learning, given by

where ϕ represents, independently, each of the five parameters; ϕ₁ is the parameter value in period one; \(\chi _{1,1}^{{\mathrm{atm}}}\) is gross atmospheric CO₂ removal in period one; and LR^(ϕ) is the learning rate associated with parameter ϕ, i.e., the fractional reduction in ϕ associated with a doubling of gross removal. Learning effects accrue with each new DAC vintage and are bound by floor estimates on performance and cost. Exogenous learning is applied per forecasts (Supplementary Table 13) for energy supply technologies: CCGT with and without CCS (heat rate, marginal cost, carbon intensity, carbon capture factor), SMRs (marginal cost), lithium-ion battery storage (marginal cost), and heat pumps (capital cost, coefficient of performance).

Levelized cost of removal and energy use

After the iterative calculations are completed for the modeling period t, the marginal levelized cost of net CO₂ removal (LCOR), in 2018$ tCO₂^–1, as well as marginal energy consumption per tCO₂ net removal EC, in GJ tCO₂^–1, are calculated:

where \({\mathrm{{\Xi} }} = 0.0036\tilde \eta ^{{\mathrm{grid}}} + {\mathrm{LHV}}\left( {\gamma ^{{\mathrm{dac}}} + \gamma ^{{\mathrm{ccgt}}}} \right)\) is the total energy use in GJ yr^–1. Marginal values give the lifetime cost and performance by DAC vintage.

Climate modeling

Two quantities—fleet-aggregated net CO₂ removal, given by \(\hat \rho _k = \mathop {\sum}\nolimits_i {\pi _i^{{\mathrm{new}}}\rho _{i,k}}\), along with fugitive methane emissions attributable to DAC, given by \({{\hat \epsilon }}_k^{{\mathrm{CH}}4} = \mathop {\sum}\nolimits_i {\pi _i^{{\mathrm{new}}}{\it{\epsilon }}_{i,k}^{{\mathrm{CH}}4}}\)—are input to two climate models to calculate the impact of removals on net global CO₂ emissions, atmospheric CO₂ concentration, and global mean temperature. The impact of removals is quantified relative to baseline futures (for emissions, concentration, and temperature) defined by SSPs⁴⁹; that is, we assume DAC deployment is pursued in concert with mitigation efforts, not in place of them. When calculating impacts beyond 2100, we assume SSP emissions, DAC CO₂ removals, and fugitive CH₄ emissions in 2100 remain constant thereafter.

The two climate models, which have been developed independently, simulate the growth rate of atmospheric CO₂, radiative forcing, and realized global mean warming as a function of time, given an evolution of CO₂ emissions. The first is a climate-carbon-geochemistry model and has been tested extensively for use in climate mitigation studies^39,55,56,57. It contains a carbon cycle model and a one-layer energy balance model. The second is the Minimum Complexity Earth Simulator (MiCES)⁴⁰, which has also been comprehensively tested⁵⁸. It features the coupling of a simpler carbon cycle model and two-layer ocean energy balance model. We include two independent climate models in this study to track variations that stem from model structural difference.

Climate responses to changes in emissions remain an important area of uncertainty in climate science. The two climate models we use match well to past warming. To facilitate comparisons we document how these models compare with MAGICC, which was used to estimate warming for the SSPs. Within the realm of unknowns about the carbon cycle and climate response, our climate models produce CO₂ concentrations and temperatures in 2100 with mean absolute difference of 14% and 6%, respectively, relative to MAGICC (Supplementary Fig. 21).

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.