Introduction

The atmospheric concentration of CO2 has reached 410 parts per million by volume (ppm), an increase of almost 20 ppm in the last 10 years1,2. As current emission levels exceed 35 GtCO2 year−13,4, a diverse portfolio of CO2 mitigation technologies must be developed and strategically deployed to avoid more than a 2 °C increase in Earth’s temperature5. Due to global reliance on fossil fuels, and because it is unlikely our global economy will completely eliminate all emissions, this portfolio will include technologies that remove CO2 from the atmosphere (negative emission technologies, NETs)6,7,8. Some NETs propose accelerating natural processes such as CO2 uptake in oceans and terrestrial carbon sinks (soils, forests, minerals), or bioenergy with carbon capture and storage. The work described here is germane to NETs that use sorbents to scrub greenhouse gases from the atmosphere, also known as direct air capture (DAC) with storage7. Prior to deployment of these technologies, it is important to understand their potential economic, social, political, and environmental impact. This study presents an overview of, and technoeconomic analysis for, a process that pairs enhanced weathering with calcination for the repeated use of mineral feedstocks to remove CO2 from the atmosphere.

Enhanced weathering, emulating and accelerating natural weathering processes, was first proposed by Walter Seifritz in 19909. In natural weathering, silicate minerals are transformed into alkalinity-containing carbonate minerals on geologic timescales10,11,12. The generalized natural weathering reaction is described below in Eq. (1)13:

$${\mathrm{MeO}}\left( {{\mathrm{SiO}}_2} \right) + {\mathrm{CO}}_2 \to {\mathrm{MeCO}}_3 + \left( {{\mathrm{SiO}}_2} \right) + {\mathrm{Energy}},$$
(1)

where Me represents a divalent metal cation (typically magnesium (Mg2+) and calcium (Ca2+)), where suitable feedstocks include rocks (containing olivine and serpentine) as well as industrial byproducts, such as mine tailings and steel slag14. Since natural weathering occurs on geological timescales, researchers have explored methods to accelerate CO2 mineralization15,16,17,18,19. Conversely, in calcination, solid carbonate minerals are heated to decompose into metal oxides and CO2. The generalized calcination reaction is shown below in Eq. (2):

$${\mathrm{MeCO}}_3 + {\mathrm{Energy}} \to {\mathrm{MeO}} + {\mathrm{CO}}_2.$$
(2)

By pairing enhanced weathering with calcination, mineral feedstocks can be repeatedly used to capture and evolve CO2.

Systems for CO2 removal using carbonation reactions have been previously investigated. In 2011, the American Physical Society (APS) evaluated a system where CO2 is absorbed by sodium hydroxide (NaOH) and subsequently reacted with calcium hydroxide (Ca(OH)2) to produce solid calcium carbonate (CaCO3) 2. The CaCO3 is calcined in an oxy-fired calciner to release CO2. Keith et al.20 propose a continuous looping process consisting of an aqueous potassium hydroxide (KOH) sorbent coupled with a calcium caustic recovery loop. The KOH sorbent reacts with CO2 in air to produce aqueous potassium carbonate (K2CO3). K2CO3 then reacts with Ca(OH)2, produced by calcining solid CaCO3, to reproduce KOH and CaCO3 20. These types of aqueous looping systems have been primarily evaluated using calcium-based sorbents21,22,23. Calcium looping systems have also been demonstrated for flue gas capture, where the CO2 concentration typically ranges from 4% (natural gas combined cycle) to 10–15% (pulverized coal combustion). Manovic and Anthony24 explored using CaO/CuO-based solid sorbents for capture of CO2 from concentrated streams. Additionally, Kheshgi25, Renforth et al.26, Renforth and Kruger27 propose an ocean liming process that deposits lime (CaO produced by calcining carbonate minerals) into the ocean to react with carbonic acid currently in the ocean. This process increases oceanic alkalinity and leads to storage of carbon in the ocean as bicarbonate ions, reducing atmospheric CO2 concentration. Alternative systems consider reactions between minerals and concentrated CO2 in high temperature/pressure reactors or through multistep extraction28,29,30.

Researchers have also investigated using magnesia (MgO) in looping processes. The calcination temperature of magnesite (MgCO3) is lower than CaCO3, with a 66% lower enthalpy of decarbonization, potentially leading to a lower energy cost. Magnesium is also attractive as there are large deposits of magnesium silicate minerals throughout the world10,31,32. Song et al.33 synthesized MgO from magnesite by varying calcination temperatures from 400 to 600 °C when calcining for 2 h. MgO synthesized at higher calcination temperatures had a lower surface area, larger pore size, and a decrease in overall CO2 uptake capacity. Researchers have also investigated forming MgO with properties optimized for CO2 capture at ambient conditions, achieving higher specific surface areas (330.5 m2 g−1) than commercially available MgO and increased CO2 uptake capacity (6.18 wt% at 25 °C)34. Additional work focused on CO2 uptake by mesoporous MgO promoted by sodium salts, such as NaNO3 and Na2CO335, as well as KNO336 demonstrating capture capacities of up to 19.8 mmol g−1 (or 80% of the theoretical capacity)37,38.

Previous investigations of Ca- and Mg-looping focused on rapid carbon mineralization, for example in fluidized bed reactors39,40. The costs of building and operating such reactors contribute significantly to integrated looping cost. In this analysis, to reduce costs and ensure simple scalability, we do not include an engineered sorption/desorption-based process. Instead, we focus on land-based, enhanced weathering that could remove significant quantities of CO2 from air at a relatively low cost, with an area requirement comparable to other potential CO2 removal methods. Specifically, we consider using magnesite (MgCO3) as the source of MgO in a looping system that removes CO2 from air via enhanced weathering. We show that this process could cost approximately $46–$159 tCO2−1 net removed from air, considering both grid and solar electricity resources without including postprocessing costs. This technology may achieve lower costs than optimistic projections for other more highly engineered DAC methods and may be used to remove significant amounts of CO2 from air.

Results

Process concept and overview

In this process, MgCO3 is calcined to produce caustic MgO and high-purity CO2. The MgO is spread over land to react with atmospheric CO2 to form magnesite (MgCO3) and other Mg-carbonate minerals over the course of a year. After renewed formation of Mg-carbonate minerals, the weathered material is collected and calcined again, producing a nearly pure stream of CO2 together with an amorphous, solid MgO residue (caustic magnesia, i.e. caustic MgO). The resulting MgO can be exposed to weathering again, and so on.

The produced MgO is assumed to have the same reactivity as mineral brucite (Mg(OH)2). The rate of formation of magnesium carbonate via reaction of aqueous brucite is on the order of 3 × 10−8 moles m−2 s−1 when mineral dissolution kinetics are rate limiting7,41,42. Thus, for example, grains of brucite with a diameter of 10–100 μm (1.7 × 10−10–1.7 × 10−7 moles, 1.25 × 10−9–1.25 × 10−7 m2, assuming spherical grains), are predicted to be completely transformed to magnesite in less than a year. In practice, larger porous grains with a higher surface area to volume ratio than spheres would also be transformed in a year.

Existing data suggest that under conditions of near 100% relative humidity, conversion of MgO to Mg(OH)2 can occur on the order of hours, indicating that over the course of a year the hydration reaction is not rate limiting43. This conversion is further dependent on the specific surface area and relative humidity of the system (or water vapor partial pressure) with higher partial pressures resulting in faster conversion. Since conversion of MgO to Mg(OH)2 in the presence of water is much faster than the rate of carbonation of Mg(OH)2, we assume the carbonation step is rate limiting. Thus, the rate of carbonation can be assumed to be the effective rate for the system.

Based on these considerations, we made the conservative assumption that 20 µm particles of caustic magnesia achieve 90% carbonation in a year. The number of carbonation plots in our analysis is optimized to keep the calciner continuously operational, avoiding startup and shutdown expenses. Overall, the process analyzed here is divided into five main steps: mineral acquisition, magnesite calcination, onsite transportation, caustic magnesia carbonation, and mineral recollection (Fig. 1). A complete mass and energy balance for the system is shown in Supplementary Fig. 1 and described in Supplementary Note 1.

Fig. 1: Simplified schematic of the MgO looping process.
figure 1

The initial magnesite feedstock is fed into the calciner where the mineral is heated to produce CO2 and MgO. The produced MgO is then transported to land plots where it is deposited and allowed to carbonate over a year. The weathered material is then recollected, primarily in the form of magnesium carbonate, and transported back to the calciner. Here, the material is fed to the calciner with additional magnesite feedstock to make up for environmental losses from the previous cycle. In the calciner, the material is once again heated to produce CO2 and MgO. The process is then repeated.

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The major process assumptions and parameters for the upper and lower bounds of the analysis are outlined in Table 1. Postprocessing of CO2 (i.e., compression, transportation, geological sequestration or utilization) is not accounted for in this analysis. The upper and lower bounds correspond to the effect of each parameter on overall process cost, not necessarily the magnitude of each parameter value.

Table 1 Assumptions and parameters used for the upper and lower bounds in the process model.
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Three scenarios are explored in this analysis, related to the type, cost and emissions of electricity used. The first scenario uses grid electricity, assuming electricity is taken directly from the commercial grid. The second scenario uses solar electricity, assuming electricity is obtained via utility solar plants at the current market price. The third scenario uses a projected cost of solar electricity, assuming a decrease in utility solar electricity cost by 2030 as projected by the DOE44. The cost of electricity and associated emissions for each scenario are outlined in Table 1.

For this analysis, magnesite is considered to be the feedstock material, with 50,000 tons of raw mineral per carbonation plot. The emissions from mining magnesite are 10 kgCO2 tMgCO3−1, within the high end of the typical range of 1.3–12.5 kgCO2 tmineral−126. The process costs are not sensitive to the feedstock cost or to the mining emissions, due to repeated reuse of MgO from the feedstock. For this analysis, it is assumed the feedstock is available at the desired particle size of 20 µm or that this particle size is attained in the first calcination step.

Magnesite feedstock is generally calcined at 500–1200 °C45. For this analysis, two sets of calcination conditions are used: 600 °C for 2 h (lower bound) and 1200 °C for 0.5 h (upper bound). Calcining at 600 °C for 2 h yields a higher specific surface area (93.07 m2 g−1 for a 2–5 mm feed precalcination), which aids in subsequent carbonation reactions45. Calcination at 1200 °C for 0.5 h results in a decreased surface area (10.9 m2 g−1 for a 2–5 mm feed precalcination). Calcination yields MgO and a high-purity stream of CO2. The calciner is continuously operational with a capacity factor of 90% to account for routine maintenance. The number of carbonation plots was determined to meet this operational capacity. Additionally, an oxy-fired calciner was used. The oxy-fired calciner requires two additional pieces of equipment: an air separation unit (to feed high-purity oxygen to the system) and a condenser (to condense water from the calciner exhaust stream).

Combustion energy and CO2 outputs are estimated for oxidation of pure methane. Following combined combustion and calcination, the gas stream is fed into the condenser where water is removed. Since oxy-fired calcination is used, the flue gas is mainly composed of CO2 and water vapor, yielding a high-purity stream of CO2 after H2O condensation. The condensation step produces 0.3 tonnes of H2O per tCO2 captured from air, which can be sold as a byproduct. CO2 removed from Mg-carbonates, and CO2 produced from combustion, can be compressed and permanently stored or sold. The cost of compression—not included in our analysis—may add ~$8 tCO2−1 to the net removed cost, depending on proximity to, and infrastructure at, a storage site7.

To move calcined MgO to the plot of land used for weathering, an electric conveyor is used, as is ubiquitous in the mineral extraction industry. These conveyors act as connections between the calcination plant and carbonation plots for spreading MgO. Additionally, the conveyors will transport weathered, carbonated product from the plots to the calcination plant each year. A potential layout of the carbonation plots is shown in Supplementary Fig. 2. Transportation operating costs are related to electricity used by the conveyor system which was determined using motor power details for commercially available mining conveyors (373 kW (500 HP) with a capacity of 454 t h−1)46.

Weathering in this process takes place on land at ambient conditions. MgO is spread on land in layers 0.1 m thick and stirred daily. Since stirring equipment for large plots of land is not industrially available, values for the capital costs of this equipment are approximated using costs of large-scale agricultural tillage equipment (Table 2).

Table 2 Estimated capital expenditures (CAPEX) for the MgO looping process.
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The system analyzed here has between 3504 (lower bound) and 10,512 (upper bound) carbonation plots, each with ~21,500 tMgO from the original 50,000 tMgCO3 feedstock. The number of carbonation plots is optimized for continuous calciner operation. Since the upper bound and lower bound have 30-min and 2-h calcination cycles, respectively, more plots are processed per year in the upper bound scenario. Since each plot is populated with MgO at different times during the year, they will also be recollected and calcined at different times. Additionally, it was assumed that 90–95% of the MgO will be recollected as MgCO3 or unreacted MgO, while 5–10% of this material will be lost to the environment. We calculate that losses of MgCO3 will be 0.03–0.05% per year and MgO losses will be 3–4% per year (assumptions and results in Supplementary Note 2).

For recollection and delivery to conveyors, the associated pieces of equipment are assumed to be commercially available front-loading tractors. The conveyors will bring MgCO3 from the carbonation plots back to the calcination plant and the MgO will be regenerated in the calcination reactor for continued use. By staggering plot maturation times, the central calcination equipment can be used continuously for multiple carbonation plots throughout the year. This also allows for more CO2 capture without increasing the required operational scale (i.e., equipment sizing or throughput).

After undergoing repeated calcination, sintering may have a significant effect on MgO reactivity47. Studies evaluating capacity losses for magnesium-based adsorbents suggest that after ten cycles, CO2 uptake capacity diminishes by 5–7%48,49. This would correspond to a capacity loss between 2 and 17% over the plant lifetime, depending on the amount of makeup material and the number of cycles undergone by material lost to the environment (assumptions and results in Supplementary Table 1 and Supplementary Note 3). This analysis assumes 5–10% losses in each cycle, accounting for both environmental losses and possible sintering effects so the initial MgO lasts for 10–20 cycles. The periodic replacement of MgO via addition of MgCO3 feedstock is included in the system operating costs as makeup minerals, but capacity losses are not accounted for.

Cost calculations

The cost estimates presented in this section include capture of CO2 from ambient air and subsequent evolution of CO2 via a mineral calcination process, not including postprocessing CO2 costs. The largest contributions to the capital costs of the system are raw material costs at 81–86% of capital costs, the oxy-fired calciner at ~10% of capital costs, and the air separation unit and condenser at 2–7% of the capital costs. The costing method and scaling factor used for each piece of equipment are presented in Table 2.

Each capital cost value is scaled to the individual process conditions. Here, the upper bound is processing 0.18 Gt CO2 year−1 using 10,512 carbonation plots, while the lower bound is processing 0.06 Gt CO2 year−1 using 3504 carbonation plots. Since the upper bound is processing about three times more CO2 than the lower bound, the capital cost per tonne CO2 is significantly less for the lower bound compared to the upper bound.

Table 3 shows the energy requirements and energy type for each unit operation. The main energy demand of the process is for calcination, which depends on calcining temperature. Therefore, the energy requirements per tonne CO2 vary between the lower and upper bounds.

Table 3 Energy requirements for the MgO looping process.
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Table 4 details the operating costs for the MgO looping system, while Fig. 2 illustrates the breakdown of operating costs by type. There are no variations in the cost between grid and solar electricity scenarios as the cost of electricity is identical. Variations between these energy resource scenarios arise when considering CO2 emissions.

Table 4 Operating expenditures (OPEX) for the MgO looping process.
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Fig. 2: Distribution of operating costs for the enhanced weathering system.
figure 2

Color gradient indicates the difference between the lower and upper operating cost values. Two pie charts are presented representing the operating cost distribution for both the lower (darker color palette) and upper (lighter color palette) bounds of the analysis. Source data are provided as a Source Data file.

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The largest contribution to operating costs is the natural gas required to power the calciner, making up 45–62% of operating costs for all scenarios. This indicates process operating costs are sensitive to the price of natural gas. Additionally, electricity makes up 8–16% of operating costs. Other major contributions to operation costs are maintenance (15–34%) and labor (5–10%), which are directly correlated to capital costs.

Cost of CO2

The cost of CO2 combines the capital and operating costs presented in the previous sections to develop a process cost per tCO2 as outlined in the “Methods” section. These costs are shown in Table 5. In addition, costs for a smaller scale system (10,000 tMgCO3 per plot) and reduced layer thickness (0.01 m) are provided in Supplementary Tables 2 and 3, respectively. The sensitivity of process costs to key parameters is shown in Supplementary Fig. 3 and discussed in Supplementary Note 4.

Table 5 Summary of CO2 capture costs for the MgO looping process using costs as defined in the section “Calculating the cost of CO2”.
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While the cost of capture for the solar electricity scenario is the same as for the grid electricity scenario, the cost of CO2 net removed is ~4% less for the solar scenario compared to the grid scenario. This minor difference is due to the lower CO2 emissions associated with solar versus grid electricity. Additionally, when accounting for projected cost reduction of solar electricity, the CO2 net removed process cost is reduced by ~7% compared to grid electricity.

Discussion

This study explores a process by which a magnesite feedstock can be repeatedly calcined and carbonated to remove CO2 from air, to evaluate the feasibility of this process as a DAC technology. Here, we discuss important factors affecting feasibility, including estimated costs, opportunities for cost reduction, land use, magnesite availability and potential use of alternative feedstocks.

For the process presented here, the cost of CO2 net removed ranges from $46 to $159 tCO2−1 using current costs of grid and solar electricity, while the cost of CO2 produced ranges from $24 to $79 tCO2−1. Using future cost projections for solar electricity yields $43–$149 tCO2−1 net removed and $23–$77 tCO2−1 produced. These estimates can be compared to published values for other processes. Currently, DAC processes using synthetic sorbents or solvents have been demonstrated on pilot scales, with costs of CO2 net removed reported to be $500–$600 tCO2−1 captured using low-carbon energy50. Aside from industrial-scale initiatives, estimated costs of DAC technologies using combined carbonation and calcination processes have been described. The American Physical Society (APS) estimated a cost of $610–$780 tCO2−1 net removed for an aqueous calcium looping system using sodium hydroxide and a cost of electricity of $71 MWh−1 (or $19.7 GJ−1)2. By varying packing materials and optimizing the process around this new material, Mazzotti et al.51 estimated $510–$568 tCO2−1 net removed for a similar process. Using natural gas thermal and electric energy, the National Academies of Science, Engineering and Medicine (NASEM) estimated the cost of solvent- and sorbent-based DAC systems tCO2−1 net removed as $199–$357 tCO2−1 and $124–$407, respectively7. When using solar electric energy and natural gas thermal energy, these values become $165–$295 and $113–$326 tCO2−1 net removed, respectively. For a process using potassium hydroxide and calcium oxide, Keith et al. estimated costs ranging from $94 to $232 tCO2−1 captured with a cost of electricity of $30 MWh−1 ($8.34 GJ−1) and $60 MWh−1 ($16.7 GJ−1). The $94 tCO2−1 captured cost is for an Nth-of-a-kind plant optimized specifically for air-to-fuels20, and is approximately the same as the estimated cost of removing CO2 from air via MgO looping in this study.

In summary, CO2 removal from air via the MgO looping process described in this paper could have a similar or lower estimated cost compared to published estimates for CO2 removal using DAC with synthetic sorbents or solvents, within the uncertainties for all of these techniques. Additionally, the proposed process integrates CO2 capture from oxy-fired calcination. This reduces the produced cost of CO2 and provides a competitive price, if produced CO2 were to be sold for use.

As technology continues to develop, there are multiple opportunities to reduce the cost of the enhanced weathering process analyzed here, perhaps most notably by using a solar calciner. The calcination step requires the most process energy. As an alternative to capturing emissions associated with oxy-fired calcination, solar calcination may largely avoid these emissions. Currently, solar calcination is not an industrially available technology. However, research is currently underway to develop high temperature solar kilns for calcination52,53. Additionally, adoption and scale-up of industrial-scale electric calciners may allow for low-carbon energy to power the calcination step. Incorporating an experimental calcination process would increase initial capital investment. However, when solar or electric calcination technology becomes established, it could provide a lower-cost, sustainable alternative to oxy-fired calcination, aiding the transition away from fossil fuels.

The process evaluated in this study uses carbonation plots, each with ~21,500 tMgO in a layer 0.1 m thick, using 11 ha of land. For comparison, a small family farm in the US has an average size of 93 ha while large family farms average ~600 ha54. Using this approximation, 0.15–0.9 MtCO2 year−1 could be removed from air on a family farm, equivalent to 160 kgCO2 m−2 yr−1. For additional comparison, biomass-based production usually removes between 1 and 10 kgCO2 m−2 yr−1 55. The upper bound in this analysis would require 0.11 Mha (sequestering 180 million tCO2), while the lower bound would require 0.04 Mha (sequestering 64 million tCO2). To sequester 1 GtCO2 would require ~0.61 Mha (6100 km2) of land area.

The land area for electricity generation can also be incorporated into this analysis. The process consumes 0.3 GJ of electricity per tCO2 captured. The land area footprint for electrical generation, using natural gas combined cycle (NGCC) methods, is 0.14 ha MW−1, while for solar electricity the land requirement is 12.7 ha MW−1 56. Therefore, the upper bound would require 290 ha for NGCC electricity and 26,100 ha for solar electricity to remove 180 million tCO2 from air. The lower bound would require 91 ha for NGCC electricity and 8300 ha for solar electricity to remove 64 million tCO2. To remove 1 GtCO2 from the air per year with NGCC would require ~1500 ha (15 km2) for electrical generation, while a solar electricity generation would require ~0.14 Mha (1400 km2). The land energy requirements for the system coupled to solar and grid electricity are shown in Table 6.

Table 6 Land area requirements for the MgO looping process.
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In total, the lower and upper bound facilities using natural gas as the source for thermal and electrical requirements have a land area footprint between 0.04 and 0.11 Mha respectively. A facility using solar electricity and natural gas thermal energy has a land area footprint between 0.05 and 0.12 Mha for the lower and upper bounds. The small difference between the land area footprints arises from the small contribution of the footprint for electrical generation to the overall land area requirement (~2% for NGCC electricity and ~18% for solar electricity). To remove 1 GtCO2 from air requires 0.61 Mha (~6100 km2) for natural gas electricity and thermal energy and 0.75 Mha for solar electricity and natural gas thermal energy (0.02% of the 3.25 billion ha of global marginal land57).

These values are similar to the estimated footprints of DAC with synthetic sorbents or solvents7. To put these requirements into context, the Nevada Test Site plus the surrounding Nevada Test & Training Range occupy 15,000 km2, roughly enough to remove 2.5 GtCO2 from air per year via weathering of MgO. That area is about 5.2% of Nevada (286,380 km2), 0.15% of the USA (9,833,520 km2)58, 0.05% of global marginal land (~32,000,000 km2)57 or 0.01% of global land area (127,343,220 km2)59.

While this process would never be done on arable land, we used the cost of arable land here because price estimates are readily available. Additionally, our comparison to farm size is for illustrative purposes only. Since arable land is in high demand and is essential for food supplies, our proposed process would use inexpensive marginal land, so that our approximation yields an upper bound cost. Moreover, our upper bound for the cost of land in this analysis is still <1% of the overall capital costs.

When estimating magnesite requirements for this system, there are two main considerations: the initial supply of magnesite to each carbonation facility and the makeup supply of magnesite each subsequent year of facility operation. For the initial supply of magnesite, there are two cases: the lower bound utilizing 3,504 carbonation plots with 5% environmental losses and the upper bound utilizing 10,512 carbonation plots with 10% environmental losses. For both cases, the initial plots are each populated with 50,000 tMgCO3. The upper bound requires 525 MtMgCO3 to capture 180 MtCO2, or 6.2% of global reserves (estimated to be 8.5 billion tons of known, economically and legally producible magnesite)60. A graphical representation of global magnesite reserves by country is provided in Supplementary Fig. 4. Additionally, with 10% environmental losses, the lower bound process would require 53 MtMgCO3 in replacement magnesite each year or 0.6% of global reserves.

For the lower bound, the initial mineral requirement is 175 MtMgCO3 or 2% of global magnesite reserves to capture 64 MtCO2. For makeup minerals, the lower bound assumed 5% environmental losses, corresponding to an additional 8.7 MtMgCO3 per year or 0.1% of global reserves. Removing 1 GtCO2 from air per year would initially require 2.9 GtMgCO3 or roughly 29% of global magnesite reserves. The makeup supply would require between 0.15 and 0.29 GtMgCO3 per year, or roughly 1.7–3.4% of global magnesite reserves.

Magnesite is not the only mineral that can be used in this process. Another potential source of alkalinity is sodium carbonate, Na2CO3. According to the US Geological Survey, global reserves are about 25 billion tons, of which about 60 wt% is Na2O 60. If all of this were used for CO2 removal from air, that would yield almost 10 GtCO2 per year. It is not clear how practical this might be, since sodium carbonate is very soluble in water, and only preserved in arid climates. Additionally, alkaline industrial wastes may be able to remove ~1 GtCO2 per year, based on current production, and this may increase to more than 3 GtCO2 capacity per year by 210014.

Limestone (CaCO3) and dolomite (CaMg(CO3)2) are highly abundant, much less labile sources of alkalinity. The reserves of rock commodities are such that they are simply described as very large by the US Geological Survey. Hayes and Waldbauer61, estimate that the inventory of sedimentary carbon in the Earth’s crust is ~1022 moles. Much more than 10% of this is in limestone and dolomite, corresponding to more than 108 billion tons of rock, about half of which is CaO and MgO.

Finally, or in parallel, Mg-silicates from ultramafic rocks—olivine-rich peridotite from the Earth’s mantle and its hydrated equivalent, serpentinite—could be used as a source of MgO. For simplicity, peridotite can be simplified as nearly pure Mg-olivine (Mg2SiO4), and serpentinite as serpentine (Mg3Si2O5(OH)4) and brucite (Mg(OH)2). There are abundant legacy tailings of partially hydrated (serpentinized) peridotite, and the on-land resource of peridotite and serpentinite exceeds 100–1000 trillion tons within 3 km of the surface10. There is a large literature on heat-treating serpentinite to create a reactive material for CO2 capture and storage62,63,64,65,66,67. To produce MgO for weathering as envisioned in this paper, one would calcine serpentinite, driving off H2O and minor CO2, to create reactive material composed of MgO and amorphous Mg3Si2O7. After a few weathering and calcining cycles, this would become MgO and SiO2. One could then use MgO as described throughout this paper.

In summary, there are many natural sources of alkalinity (MgO, CaO, Na2O) that could be weathered and calcined, to remove CO2 from air as described in this paper. For example, the US Geological Survey reports that resources from which magnesium compounds can be recovered range from large to virtually unlimited and are globally widespread60. However, because the various feedstocks listed here undergo calcining and/or weathering at different rates and conditions compared to those for magnesite, additional calculations would need to be performed to investigate the economic feasibility using the alternatives.

CO2 removal from air via the process described in this paper has a similar or lower cost than CO2 removal using DAC with synthetic sorbents or solvents, within uncertainty of estimates for both techniques. The net removed cost associated with grid electricity ($48–$159 tCO2−1) is slightly higher than that of solar electricity ($46–$152 tCO2−1, or $43–$149 tCO2−1 when incorporating predicted cost decreases) due to the CO2 emissions associated with grid electricity. The process is relatively simple and robust and is feasible at a reasonable cost using existing technology. Additionally, the proposed process integrates CO2 capture from the oxy-fired calcination unit, so the cost of produced CO2, both removed from air and captured from combustion, is competitive with other sources. While addressing the greenhouse gas problem requires permanent storage of huge amounts of CO2, this is not currently profitable. For storage, the integrated CO2 capture from the calciner will increase the costs associated with storage—with storage costs of approximately $9–$20 tCO2−1 stored7. However, in the short term, sale of CO2 may provide an income stream that attracts the investment required to support research and development of a range of technologies for CO2 removal from air.

Finally, we wish to emphasize that DAC technologies, including the MgO looping process analyzed in this paper, are not as effective as point source emissions reductions. However, CO2 removal from air will probably be required to limit global warming to less than 2 °C by 2100. In this context, MgO looping offers a practical and relatively inexpensive carbon dioxide removal method.

Methods

Equipment scaling and capital costs

Major unit operations in this process include: physical preprocessing, air separation, condenser, oxy-fired calciner, land use, and transportation equipment. Costs for these were developed from two sources. First, quotes from industry for available equipment were used. This includes pricing for raw materials, the transportation conveyor system, and stirring and recollection equipment. For novel or new types of equipment, capital costs were determined based on corresponding literature values. Both of these types of equipment costs were scaled to process 50,000 tMgCO3 feedstock per cycle per plot (or 18 ktCO2 cycle−1 plot−1) using the relationship in Eq. (3).

$$\frac{{{\mathrm{Cost}}_1}}{{{\mathrm{Cost}}_2}} = \left( {\frac{{{\mathrm{Scale}}_1}}{{{\mathrm{Scale}}_2}}} \right)^\alpha,$$
(3)

where α is a scaling factor. Traditionally, 0.60 is used as a scaling factor for most industrial equipment. However, for reaction vessels, this scaling factor is conventionally 0.68 68. Additionally, to account for the installed cost of the equipment, a multiplication factor was included. This factor was 1.5× for commercially available equipment and 4.5× for new technology or new applications. Finally, capital expenditures for the process were annualized using capital recovery factors of 7.4% for the lower bound and 12.6% for the upper bound.

Energy requirements and operating costs

Energy costs associated with the process were calculated for each unit operation based on operating time, equipment capacities, and periodic nature of the process. Operations energy requirements were determined for a single carbonation cycle and scaled to the required number of plots. From the energy analysis on each unit operation, operating costs for the system were developed. The operating costs were determined using $16.7 GJ−1 for grid and utility solar electricity. Additionally, a third scenario was developed using a projected solar electricity cost of $8 GJ−1. Parameters for energy costs and associated emissions are outlined in Table 1.

Calculating the cost of CO2

The costs of CO2 determined in this analysis considers three different scenarios. First, a general case is presented where grid electricity is used. Second, the current industrial cost of electricity generated by solar photovoltaic cells was used. Finally, process costs were anticipated using the projected price of solar electricity, which is expected to reach $8 GJ−1 ($0.03 kWh−1) by 203044. Solar electricity is not entirely carbon-free as there are emissions during fabrication, mainly associated with manufacturing of solar cells7. While these emissions are significantly less than for a comparable amount of grid electricity, they must still be included in the analysis.

Three different costs of CO2 are calculated for each scenario: the cost of capturing CO2, the cost of CO2 net removed from the atmosphere, and the produced cost of CO269. The cost of capturing CO2 is the direct cost of the process and is calculated in accordance with Eq. (4). This value represents how much it would cost for the process to remove 1 tCO2 directly from the atmosphere.

$${\mathrm{Cost}}[{\mathrm{\$}}\,{\mathrm{tCO}}_2^{ - 1}] = \frac{{{\mathrm{Process}}\,{\mathrm{cost}}\,[{\mathrm{\$ }}]}}{{{\mathrm{CO}}_2\,{\mathrm{capture}}\,{\mathrm{from}}\,{\mathrm{air}}\,[{\mathrm{tCO}}_2]}}.$$
(4)

The cost of CO2 net removed takes the cost of capturing CO2 and adjusts for emissions produced in the process, and not captured onsite. For each step in the process, some amount of energy in the form of electricity, natural gas, or fuel is required. With each energy source, there are associated CO2 emissions. We have assumed that electricity will be generated off site, and that the emissions from generation are not captured. Since the goal of the process is to remove CO2 from the atmosphere, it is important to consider emissions from the process itself. The cost of CO2 net removed includes the emissions as a result of the process and scales the cost of capturing CO2 to develop a cost that represents a net capture of 1 tCO2 as follows:

$$ {\mathrm{Net}}\,{\mathrm{removed}}\,{\mathrm{cost}}[{\mathrm{\$ }}\,{\mathrm{tCO}}_2^{ - 1}] \\ \qquad\qquad = \frac{{{\mathrm{Process}}\,{\mathrm{cost}}\,[{\mathrm{\$ }}]}}{{{\mathrm{CO}}_2\,{\mathrm{capture}}\,{\mathrm{from}}\,{\mathrm{air}}\,[{\mathrm{tCO}}_2] - {\mathrm{CO}}_2{\mathrm{released}}\,{\mathrm{by}}\,{\mathrm{process}}\,[{\mathrm{tCO}}_2]}}.$$
(5)

Finally, the produced cost of CO2 uses the cost of capturing CO2 and adjusts for additional CO2 captured onsite, specifically CO2 captured from natural gas combustion in the oxy-fired calcination unit. Ultimately, the produced cost of CO2 is equivalent to the price at which CO2 could be sold for the process to break-even. This is described in Eq. (6).

$$ {\mathrm{Produced}}\,{\mathrm{cost}}\,[{\mathrm{\$ }}\,{\mathrm{tCO}}_2^{ - 1}] \\ \qquad= \frac{{{\mathrm{Process}}\,{\mathrm{cost}}\,[{\mathrm{\$ }}]}}{{{\mathrm{CO}}_2\,{\mathrm{capture}}\,{\mathrm{from}}\,{\mathrm{air}}\,[{\mathrm{tCO}}_2] + {\mathrm{additional}}\,{\mathrm{CO}}_2\,{\mathrm{captured}}\,{\mathrm{by}}\,{\mathrm{process}}\,[{\mathrm{tCO}}_2]}}.$$
(6)

Sensitivity analysis

A sensitivity analysis was performed on the proposed system with respect to six important parameters: carbonation efficiency, environmental losses, calcination temperature, calcination time, and the number of carbonation plots. The sensitivity analysis was performed in MATLAB by iteratively solving the process simulation between designated parameter values. This was performed for both the lower and upper bounds of the analysis. The complete sensitivity analysis is presented in Supplementary Fig. 3 and described in Supplementary Note 4.

Reporting summary

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