An air CO₂ capture system based on the passive carbonation of large Ca(OH)₂ structures

Abstract

Direct Air Capture (DAC) requires contacting a vast flow of air with a functional surface, which must be accommodated in a large and costly CO₂ capture device (i.e. at least 0.2–0.4 m³ of the reactor volume per t_CO2 per year). We propose in this paper a low-cost alternative that involves contactor volumes that are one or two orders larger, but require only the passive CO₂ carbonation of purpose-built porous structures of Ca(OH)₂. Such low-cost materials can be manufactured from natural limestone and/or from recycled carbonated structures by using oxy-calcination technologies, and then simply stacked in such a way as to leave gaps for air to pass through. On the basis of an analysis of the rate controlling factors of the carbonation reaction, we employed as the structural element sintered Ca(OH)₂ plates with an area of 2 × 2 m² and 3 cm thick with a porosity of 0.5, which can be fully carbonated in about 6 months. The cost of CO₂ captured from air is estimated to be between 140 and 340 $ per t_CO2 depending on assumed cost values for fuel, land use, structural materials manufacture & transport, and process and project contingencies.

---

1. Introduction

Direct CO₂ capture from air (DAC), combined with permanent CO₂ storage, is one of the negative emission technologies (NETs) that may be needed in the future to limit global warming to 1.5 °C.^1,2 The first conceptual designs of DAC systems were proposed 20 years ago,³ and research into novel concepts and materials is still continuing today.^3–22 The direct capture of CO₂ from air requires vast contacting surfaces with a great affinity and selectivity towards CO₂ (i.e. through a gas–liquid interface, the internal surface of a solid sorbent or through a membrane). Absorption methods generally use a strong alkaline aqueous solvent solution such as Ca(OH)₂,^3,10,11 NaOH^12–14 or KOH¹⁵ that reacts with CO₂ to yield carbonated salts. Such alkaline solutions are corrosive, require costly gas–liquid contactors and require a large amount of energy for their regeneration.^8,16 Adsorbent solids with a high selectivity for CO₂, such as amines supported on porous materials, ion-exchange resins, metal–organic frameworks, zeolites or activated carbons, have also been explored.^8,9,17,18 Other gas–solid contact options are membranes combined with KOH solutions,¹⁹ dispersed amines or ion-exchange resins.²⁰ An entirely different approach is to extract CO₂ from large flows of seawater by electrodialysis, after which the water is returned to the ocean to reabsorb more CO₂ from the air.^21,22

Some DAC technologies are being tested on increasingly larger scales to assess their technical and economic viability. Carbon Engineering operates a pilot plant designed to capture around 300 t CO₂ per year using aqueous solutions of NaOH or KOH coupled to a Ca(OH)₂/CaCO₃ loop.¹⁵ The estimated cost of the CO₂ captured in this process is around 230 $ per ton of CO₂ (in the case of “no revenues” for the CO₂ captured) depending on the type of fuel used, the cost of electricity or the fate of the CO₂ (storage or fuel synthesis).¹⁵ Climeworks has built a modular plant able to capture almost 1000 ton CO₂ per year using filters made up of porous granulates modified with amines. The process can deliver pure CO₂ for subsequent use in greenhouses or for geological storage/use at a cost of around 600 $ per tCO₂.²³ The largest DAC plant built to date, which is operated by Global Thermostat,²⁴ has been designed to capture around 4000 tCO₂ per year.²⁵ This facility is equipped with amine-based ceramic honeycombs able to produce a CO₂-rich gas of 98% purity.²⁶

The references to costs noted above were provided by developers and they are subject to a great degree of uncertainty. As pointed out in several studies dedicated to the analysis of the viability and cost of advanced DAC systems,^27–34 there are strong arguments for claiming that the cost of CO₂ captured from air will be in the range of 500–1000 $ per tCO₂, which is about one order of magnitude higher than that of their counterpart technologies for CO₂ capture from flue gases. Particularly relevant to the discussion in this work is the cost of the enormous capture device required to achieve the close contact of highly diluted molecules of CO₂ in the air with the surface of the material with a high affinity and selectivity towards CO₂. Fig. 1 represents the mass balance for a generic air capture device where 1 MtCO₂ per year is captured. As can be seen, a huge flow of air (about 45 000 m³ s⁻¹ STP) must flow through the DAC device even if a large capture efficiency (Δppmv_CO2 ≈ 400 ppm between the inlet and the outlet will require deep reactors) is assumed. The reduction of the cross-sectional area of the contactor (A_contact) by increasing the air velocity will be limited by kinetic constraints at the gas/sorbent (or solvent) interface, by the pressure drop along the contactor, and by other phenomena such as water and solvent losses due to evaporation or entrainment.³⁵

Fig. 1 Volumetric flow of air (Q_air in m³ s⁻¹ STP) required to achieve a CO₂ capture rate of 1 MtCO₂ per year for a reduction in the CO₂ concentration of Δppmv_CO2 (=ppmv_CO2in − ppmv_CO2out) in air as it circulates through the CO₂ capture system (arrow marks the particular design point of Carbon Engineering,¹⁵ in the design of Climeworks³⁶ the air flows range between 67 000 and 150 000 m³ s⁻¹).

In an attempt to overcome the costly barrier entailed by the capture device in large scale DAC systems, we propose in this work a passive CO₂ capture system involving the carbonation of large purpose-built porous structures of low-cost Ca(OH)₂. A basic cost analysis, which is mainly based on relatively well-known costs of oxy-combustion and hydration processes for obtaining Ca(OH)₂ from CaCO₃, demonstrates the economic feasibility of the proposed DAC process for a capture target of 1 MtCO₂ per year.

2. Passive direct air capture process concept

Fig. 2 shows the general scheme of the concept investigated in this work. The design target is to estimate the necessary volume and cost of the porous passive carbonation infrastructure (represented as a blue box on the left-hand side of Fig. 2), which is aimed at capturing 1 MtCO₂ per year, and the size, cost and energy requirements of the units needed to manufacture such structures in a continuous manner.

Fig. 2 The concept of passive CO₂ capture from air by the carbonation of a suitable structure of solid Ca(OH)₂ exposed to ambient air.

It should be noted that although in Fig. 2 we use the expression “CO₂ for storage or use”, the negative emission character of DAC technologies necessarily requires the permanent storage of CO₂, which must be added as a cost to account for avoided cost.³⁷ If CO₂ was used for the production of synthetic fuels with renewable energy, this would only lead to a maximum of 50% CO₂ captured,³⁸ which might be insufficient in future scenarios demanding negative emission technologies.²

The DAC concept shown in Fig. 2 is based on the known tendency of porous Ca(OH)₂ solids to slowly carbonate in contact with ambient air. Anecdotally, the passive carbonation of solid beds composed of Ca(OH)₂ is already commercially exploited for removing ambient CO₂ in order to preserve fruit in storage halls.^39,40 As a climate mitigation tool, the ambient carbonation of concrete and alkaline wastes obtained from steel, cement, lime and other solids containing free CaO and Ca(OH)₂ is another passive method for sequestering CO₂.^2,41–49 However, to our knowledge, a comprehensive design and cost analysis of a purpose-built passive DAC system, such as that represented in Fig. 2, has not yet been reported in the literature. As will be explained below in more detail, the very low specific cost and widespread geographical availability of natural limestone make it possible to manufacture derived calcium-based materials cheaply by means of calcination and hydration. In this study, porous Ca(OH)₂ has been chosen as the functional material for CO₂ capture due to its suitable mechanical stability when pelletized and favorable carbonation kinetics compared to CaO.^47,50,51

The slow kinetics of large porous carbonating structures can be modelled⁵² by accounting for the advance rate of a neat carbonation front according to Fick's law. In our case, where CO₂ diffuses through the porous CaCO₃ layer resulting from the carbonation of Ca(OH)₂, assuming that there is no expansion of the porous solid during carbonation (i.e. ρ_CaCO3(1 − ε_CaCO3) = ρ_Ca(OH)2(1 − ε_Ca(OH)2)), the mass balance can be represented as follows:

or in its integrated form:where z_CaCO3 is the thickness of the carbonated product layer (m), D_CO2 is the diffusion coefficient of CO₂ in the pores (m² s⁻¹), ρ_Ca(OH)2 and ρ_CaCO3 are the molar densities (i.e. 29.9 and 27.1 kmol m⁻³), respectively, ε_Ca(OH)2 and ε_CaCO3 are the corresponding porosities, C_CO2 is the CO₂ concentration at the external surface of the porous solid (i.e. assuming zero the concentration of CO₂ in the reaction front) and X_CaCO3 is the maximum carbonation conversion of the Ca(OH)₂ material. The advance of the carbonation with time represented in eqn (2) has been experimentally validated in several studies on the carbonation of concrete on time scales of years to decades.^44,53–55

Fig. 3 shows the evolution with time of the carbonated layer in a Ca(OH)₂-based solid according to eqn (2) for different values of Ca(OH)₂ solid porosity, ε_Ca(OH)2, and assuming a ppmv_CO2 gradient of 400 ppm (C_CO2 = ppmv_CO2/(RT × 10⁶) in mol m⁻³) between the external surface and the carbonation front. As can be seen, individual Ca(OH)₂ solids of thickness 5 mm (assuming ε_Ca(OH)2 = 0.5) would require around 15 days to approach total carbonation. This timescale is consistent with the experimental results of Erans et al.,⁴⁷ who obtained carbonation conversions of around 70% after 12.5 days in particles of hydrated lime exposed to ambient air in layers of 5 mm thickness. Fig. 3 extends to an arbitrary scale of 1 year the results for thicker and less porous solids.

Fig. 3 Evolution with time of the carbonated layer (z_CaCO3) in carbonated solids according to eqn (2), for different porosities (ε_Ca(OH)2) and assuming a CO₂ concentration gradient of 400 ppmv at 20 °C.

To take full advantage of such a slow passive carbonation process in a DAC system targeting 1 MtCO₂ per year, amounts of calcium-based sorbent on a megaton scale will be required. Such a carbonating material could take in principle many different forms, ranging from a vast number of pellets of several centimeters thick, simply dispersed on the ground, to purpose-designed porous structures/buildings for passive carbonation and eventual recycling. In the first case, the manufacture of non-recoverable Ca(OH)₂ pellets would involve the calcination of natural limestone to generate CaO (and eventually Ca(OH)₂) and a pure stream of CO₂ for permanent geological storage. Although there is evidence that soil liming provides nutrients for plant growth and contributes to acidity correction,⁵⁶ further experimental investigation would be required to determine the environmental implications of this option, and the possible constraints related to land availability. For this reason, the present work focuses on large-scale structural alternatives (e.g. stacked plates, beams etc.) that entail the recovery and regeneration of the carbonating solids once they have been completely carbonated. There are already commercial processes for manufacturing solid structures with a high porosity (as in the case of pervious concrete⁵⁷) and high mechanical stability (provided by the incorporation of cement-type additives^58,59). Consequently, details about the structural and mechanical properties of the porous solids have not been discussed in depth in this work. Similarly, the operations designed to produce CaO and a separated stream of pure CO₂ from limestone or carbonated solids are sufficiently well known from recent developments in clinker production with oxy-combustion^60,61 and CO₂ capture by Calcium Looping^62,63 and so will only be discussed in the cost section.

3. Estimation of the volume of passive carbonation structures

Of the wide range of possible arrangements for the Ca(OH)₂ structures, we have selected, for the purpose of illustration from the results of Fig. 3, flat plates 0.03 m thick with both sides exposed to the atmosphere and with a porosity ε_Ca(OH)2 = 0.5 that can achieve total carbonation in approximately 6 months. An external exposed area of 50.7 × 10⁶ m² of such solids would be needed to capture 1 MtCO₂ per year or, in other words, 761 000 m³ of porous plates. With a specific minimum capture contactor volume of almost 0.8 m³ per tCO₂ per year, this configuration is already 2–4 times larger than other competing air capture devices noted in the Introduction. However, it is possible to envisage recycling schemes (analogous to those already in operation for glass, metals, plastics etc.) promoting the deployment of disperse, but very large passive carbonation systems. In societies aiming at zero emission objectives, a person could reduce by 1 tCO₂ per year his per capita emissions by participating in such a recycling scheme, if he/she were responsible for maintaining exposed to the atmosphere (i.e. on a house, in a garden, terrace or on the roof of a building) 25.4 m² of plates exposed on both sides, and replaced approximately every 6 months. Much smaller surfaces or volumes of solids could also be considered if the thicknesses of the plates were reduced and the frequency of recycling was increased (see Fig. 3).

For the case of larger and centralized schemes, an important constraint affecting these carbonating structures is that they must be arranged in such a way that a continuous and renovated flow of air is in contact with the structure. To ensure this, further assumptions on the dimensions and the way the plates are stacked, including additional resistances other than those strictly related to the carbonation process inside the porous solids, must be taken into account (see Fig. 4).

Fig. 4 Evolution of the CO₂ concentration in air through the different CO₂ transport/diffusion stages, taking place at increasing scales from right to left: interior of a plate, individual plates, stacked plates and numerous stacked plates arranged in a field.

The volume of the overall structure increases as additional free space is required to facilitate the access of CO₂ from air to the external surface of each plate. Although the design decisions may differ considerably depending on local conditions (i.e. availability of wind and other atmospheric convective phenomena), the target is to design structures that are sufficiently expanded to ensure a high concentration of CO₂ on the external surface of each individual plate (large dot in Fig. 4). The volume occupied by the stacks of plates will be V_stack = V_carb/(1 − ε₂), where ε₂ is the volume fraction of the plates. In an oversimplification, it is assumed that CO₂ is transported horizontally by wind velocity (u₁) to the carbonating stacks. The actual velocity of the air circulating between the plates (u₂) is given by the net dynamic pressure exerted by the wind (at a velocity u₁) on the surface of the structure. This can be calculated by means of Bernoulli's equation and taking into account the friction factor and the geometry of the channel.⁶⁴ With the aim of achieving a value of u₂ > 0.5u₁, we have chosen squares that measure 2 × 2 m², arranged horizontally one on top of the other in the form of open structures 10 m high, with a space in between each plate that is twice their thickness (i.e. ε₂ = 0.67). With these dimensions, and a front open stack cross-section of 0.8 Mm² (=L_plateHε₂N_stacks), wind velocities u₁ below 0.8 m s⁻¹ (i.e. 3 km h⁻¹) are high enough to sustain an overall carbonation process controlled by Fick's diffusion as in Fig. 4 (since ppmv₃ − ppmv₀ will exceed 50 ppmv_CO2 for u₁ > 0.8 m s⁻¹). In many open field regions, average wind velocities of between 3 and 7 m s⁻¹ are common.^65,66 This will ensure a sufficient supply of air to the carbonating surfaces (except at the very beginning of the carbonation period, where z_CaCO3 is close to zero and the rate of carbonation may be limited by the value of u₁). Therefore, assuming a utilization factor for the carbonation structures of 1, a mass of 0.84 Mton of Ca(OH)₂ will need to be replaced every 6 months to remove from air 1 Mton of CO₂ per year. This amount of material will occupy a volume of about 761 000 m³ of porous plates, which is equivalent to around 2.3 Mm³ of open stacks. Finally, when the stacked plates are arranged in a specially assigned open field (left hand side of Fig. 4), an extra-large volume of the overall structure (V_structure = V_carb/((1 − ε₂)(1 − ε₁))) will be needed to take into account the resistance linked to Eddy diffusion, which is perceptible in large CO₂ sink areas, such as forests, where variations in the CO₂ concentration of between 25 and 35 ppm occur.^67,68 A value for ε₁ of 0.95 may be required to ensure that there is sufficient separation between the stacks to allow isolated roughness flow.⁶⁹ This will ensure the continuous renovation of CO₂ in the vicinity of the stacked plates. The DAC system will therefore need to occupy a total volume of 45.7 Mm³ which means 4.6 Mm² of land use when considering the height of stacked plates (i.e. H = 10 m).

To sum up, the specific contactor volumes necessary for the proposed passive air capture (which will range from 2.3 to 45.7 m³ per tCO₂ per year) for highly dispersed stacked structures and for a purpose-designed DAC field, respectively, will be between one and two orders of magnitude higher than the values reported for the competing DAC systems referred to in the Introduction. However, as it will be claimed in the next section, this DAC scheme could be sufficiently competitive in the context of a carbon-constrained world.

4. The cost of the full DAC system

To estimate the cost of capturing and removing from the atmosphere a tonne of CO₂ using the full DAC system shown in Fig. 2 we consider the following three main cost elements:

(i) The specific cost of capturing and storing CO₂ from the calcination of CaCO₃, which includes the total capital requirements (TCRs) for the purchase of the oxy-combustion equipment for calcination, energy recovery and compression and purification, all amortized at a certain capital charge factor (CCF). Also, following the standards in major CO₂ capture and storage (CCS) cost studies^37,70 the CCS cost includes terms for the fixed and variable operating cost (FOM and VOM), the fuel cost (FC), and the cost of transport and permanent geological storage of CO₂ (C_{CO2 T&S}).

(ii) The specific cost linked to the handling and transport of structural elements (C_handling) as well as their manufacturing cost (C_manufacture) from CaO generated in (i) and water.

(iii) The specific cost of the land occupied by the infrastructure (V_structure/H)C_land, which is amortized as other capital requirements in (i).

Therefore:

To gain transparency in the cost analysis carried out in this work, a set of minimum and maximum values of the specific cost of each cost component is adopted and justified below using references available in the literature, together with contingencies and other assumptions.

The specific cost of producing pure CO₂ and CaO from CaCO₃, and then transporting and storing geologically the captured CO₂, can be estimated from a basic simulation of the required oxy-combustion process (see Fig. 5). Oxy-fired Circulating Fluidized Bed (CFB) technology has been chosen for the calcination operation, due to the substantial amount of information available in the literature on the cost of these systems for power generation,^63,71 Calcium Looping processes⁶² or even cement plants.^61,72 However, other types of calciners (e.g. rotary kilns, entrained beds etc.) with CO₂ capture capability and different energy sources (i.e. gas, biomass, H₂ or solar energy) may be available for consideration in the future.

Fig. 5 General process scheme of the oxy-fired CFB calcination system and Ca(OH)₂ manufacture.

Fig. 5 represents a basic scheme of the proposed process. A flow of 72 kg s⁻¹ of CaCO₃ needs to be calcined to achieve the DAC capture target of 1 MtCO₂ per year. Following the cost estimation method reported by Guandalini et al.,⁶³ mass and energy balances have been solved, indicating energy requirements for the oxy-calcination operation of 225 MW_th (equivalent to 7.1 GJ per tCO₂ captured from air), assuming calcination at 900 °C, no-preheating of the inlet streams, biomass as a fuel (assuming a LHV value of 20 MJ kg⁻¹ and 41.4%C for these calculations) burnt with 10 vol% of excess O₂, including the use of the Air Separation Unit, ASU, and Compression and Purification Unit, CPU, of 210 kW h_e per tO₂ and 90 kW h_e per tCO₂, respectively, and including also the consumption of about 2.3% fuel input in the auxiliary units.⁶³ The waste heat extracted from the outlet CaO and CO₂-rich gas streams (assumed to be at 900 °C) drives a stream cycle (not shown in Fig. 5 for the sake of simplicity) that generates 34 MW_e, which is a sufficient power to cover the electricity consumed in the ASU, CPU and other auxiliary units. In other words, the system shown in Fig. 5 is designed as a small oxy-fired combustion boiler where parasitic power losses (mainly ASU and CPU electricity consumption) equal the gross power output, so that no electric power is exported or imported to run the system.

Reference costs for a typical oxy-combustion plant have been taken from Guandalini et al.⁶³ and have been updated assuming an inflation rate of 1.7%/annually.⁷³ The specific cost of a reference oxy-combustion plant of 550 MW_e (or 1697 MW_th) has been estimated to be about 4349 $ per kW_e (or 1626 $ per kW_th), which results in a total capital requirement (TCR) in 2011 USD of 2392 M$ (ref. 63) including process and project contingencies. Thus, when a scale factor of 0.7 is applied and the cost is updated to 2020 USD, the TCR for the proposed oxy-combustion system of 225 MW_th amounts to 671 M$. Assuming a capital charge factor (CCF) of 10.88% per year (ref. 63) and a capacity factor (CF) of 0.9, the CAPEX of the oxy-combustion plant amounts to 81 $ per tCO₂. Similarly and by comparison with the cost reported by Guandalini et al.,⁶³ a reference cost of 12 M$ per year has been calculated for fixed operation costs (FOM) by considering a scale factor of 0.65 and 1 for the labor and property taxed and insurance terms, respectively, resulting in a OPEX fixed of 14 $ per tCO₂. The variable costs (VOM) reported, without including the limestone cost, are about 9 $ per MW h_e,⁶³ resulting in about 3 $ per MW h_th when the electric efficiency and the inflation rate are applied. Considering that for a capture target of 1 MtCO₂ per year are required 225 MW_th, a variable OPEX of 7 $ per tCO₂ has been calculated. Contingency factors as high as 40–60% are used to account for cost uncertainties in other DAC systems.^29,35 We consider for this purpose, a maximum contingency factor of 40%, as the CAPEX and OPEX cost data used from Guandalini et al.⁶³ already include standard process and project contingencies and there is direct industrial experience in oxy-calcination, solids handling and all the energy recovery operations represented in Fig. 5. Note that the CAPEX range (min value of 81 and max 113 $ per tCO₂ in Table 1) can be considered conservative cost estimations compared to the CAPEX of the oxy-combustion calciner reported by Keith et al.¹⁵ claiming a cost at around 36 $ per tCO₂.

Table 1 Summary of the minimum and maximum costs of the main components of a passive CO₂ capture process, following the notation of eqn (3). All costs in 2020 US dollars

Cost component	Reference values				Cost CO2 captured ($ per tCO2)		%Total min–max
		Min	Max	Units	Min	Max
Oxy-combustion plant CAPEX	TCR	671	805	M$	81	113	59–33
Oxy-combustion plant OPEX fixed	FOM	12	15	M$ per year	14	20	10–6
Oxy-combustion plant OPEX variable	VOM	3	4	$ per MW hth	7	10	5–3
Fuel	FC	2	10	$ per GJ	14	71	10–21
CO2 transport & storage	C CO2 T&S	5	15	$ per tCO2	5	15	4–4
Handling & transport of structural elements	C handling	4	25	$ per tCaCO3	9	57	6–17
Pellets/plates manufacture	C manufacture	5	30	$ per tCa(OH)2	8	50	6–15
Land use	C land	0	10	$ per m^2	0	5	0–1
Total cost of CO 2 captured in $ per tCO 2					138	341

---

On the other hand, different fuels can be considered to cover the thermal requirements in the oxy-calciner and their cost will vary depending on their type and resource availability. Thus a fuel cost (FC) of between 2 and 10 $ per GJ has been taken as reference numbers, resulting in 14 to 71 $ per tCO₂ when considering that 7.1 GJ per ton of CO₂ captured from air are required in the subsystem of Fig. 5. Finally for the cost of the CO₂ transport and storage (C_{CO2 T&S}), 5 and 15 $ per tCO₂ have been taken to be consistent with published values.⁷⁰

Regarding those cost elements in Table 1 and eqn (3) linked to land use and handling and manufacture of structural elements, the similarity with other existing unit operations facilitates cost estimations. The US average market value of crushed limestone is about 8.4 $ per t.⁷⁴ Thus the minimum cost has been assumed as half the market value, accounting for a favourable scenario where CaCO₃ is provided directly from the quarry with a very short distance transport. Meanwhile, the maximum value for the sensitivity analysis is arbitrarily taken by multiplying by three this figure to 25 $ per t of carbonated material (or 57 $ per tCO₂ captured from air).

Regarding the manufacture of the Ca(OH)₂ structural elements or pellets, the cost is subjected to larger uncertainties (e.g. small pellets with modest mechanical stability or large porous structures with improved mechanical properties or other design characteristics). A wide cost range from 5 to 30 $ per ton of Ca(OH)₂ has been adopted as the manufacture cost (C_manufacture), which results in 8 to 50 $ per tCO₂.

Finally, since there are no special demands on the land to be used for the infrastructures, other than that of facilitating the exposure of a large volume of solids to the atmosphere, the minimum capital cost linked to land use can be assumed as zero. However, for more conservative scenarios, a royalty of C_land = 10 $ per m² has been taken as the upper bound, consistent with the land cost of extensive energy infrastructures in the US.⁷⁵ This results only in an increase of 5 $ per tCO₂ when the same CCF as for the oxy-combustion plant is applied.

As can be seen in Table 1, the cost of the passive CO₂ capture process from air will be between 140 and 340 $ per tCO₂. As expected, the main cost driver of the DAC system is the capture and storage of CO₂ generated from the oxy-combustion of CaCO₃, with a contribution to the total cost of between 67 and 88%. Thus, since there is substantial industrial experience in the operations involved in such operation, the system investigated in this work will be relatively insensitive to additional cost contingencies when compared to other proposed DAC systems involving large contactors for the CO₂ capture as discussed in Fig. 1.

5. Conclusions

The cost of Direct Air Capture (DAC) technologies is strongly influenced by the capital cost of a large device (i.e. about 0.2–0.4 m³ of the reactor volume per tCO₂ per year) that is needed to bring a vast flow of air into contact with a functional material with an affinity for CO₂. In an attempt to overcome this cost barrier, we have proposed design rules for a large-scale, purpose-built, passive carbonation system made up of porous structures of Ca(OH)₂ (i.e. plates or pellets with a thickness of 0.03 m and a porosity of 0.5). A DAC system of this type could adopt different forms of viability: from widely dispersed approaches involving the irreversible dissemination of Ca(OH)₂ pellets in the soil, or the public recycling of pellets/plates, to centralized schemes where vast structures of elements are stacked up in open fields. In the latter case, the volume of the structures must be able to increase (to up to 46 m³ per tCO₂ per year) to ensure that there are enough wind and natural atmospheric convection currents to sustain a given average rate of carbonation. However, the key advantage of the proposed scheme is that the required materials are available at an extremely low cost (i.e. limestone and/or recycled carbonated structures from the DAC scheme) and that the technology required to manufacture them, while generating a pure stream of CO₂, is already available (oxy-fuel combustion technologies for CaCO₃ calcination). The overall cost estimation of this DAC scheme is between 140 and 340 $ per tCO₂ captured, which is considerably less (subject to contingencies) than that of other competing DAC technologies.

Nomenclature

A contact	Air contactor cross-sectional area perpendicular to the air flow, m^2
CCF	Capital charge factor, per year
C CO2	CO2 concentration at the external surface of the porous solid, mol m^−3
C CO2 T&S	Cost of transport and permanent geological storage of CO2, $ per tCO2
CF	Capacity factor
C handling	Specific cost linked to the handling and transport of carbonated structural elements, $ per tCaCO3
C land	Specific cost linked to the land use occupied by the DAC system, $ m^−2
C manufacture	Specific cost linked to manufacturing pellets/plates, $ per tCa(OH)2
D CO2	Diffusion coefficient of CO2, m^2 s^−1
D Eddy	Eddy diffusion coefficient, m^2 s^−1
FC	Fuel cost, $ per GJ
FOM	Fixed operation costs of the oxy-combustion plant, M$ per year
H	Height of the stacked plates, m
LHV	Lower heating value of the fuel used in oxy-combustion, MJ kg^−1
L plate	Length of the plates, m
M i	Molecular weight of the compound i, kg kmol^−1
MWth	Required thermal input to the oxy-combustion plant, MWth
N stacks	Number of stacks in the DAC system
ppmv0	Atmospheric CO2 concentration, ppm
ppmv1	CO2 concentration in the vicinity of the overall structure, ppm
ppmv2	CO2 concentration outside the stacked plates, ppm
ppmv3	CO2 concentration at the surface of the plates, ppm
ppmv4	CO2 concentration in the carbonation reaction front in the interior of the porous plates or pellets, ppm
Q air	Volumetric air flow, m^3 s^−1 STP
R	Universal gas constant, atm L mol^−1 K^−1
T	Temperature, K
t CO2	CO2 capture rate, MtonCO2 per year
TCR	Total capital requirements of the oxy-combustion plant, M$
u 1	Wind velocity outside the stacked plates, m s^−1
u 2	Velocity of air moving in the space between the plates, m s^−1
VOM	Variable operation costs, $ per MW hth
V stack	Volume occupied by the stacks of plates, m^3
V structure	Volume of the overall DAC structures
X CaCO3	Maximum carbonation conversion of the Ca(OH)2 material
z	Flat plate thickness, m
z CaCO3	Thickness of the carbonated product layer, m
ε 1	Volume fraction between stacks
ε 2	Volume fraction between plates
ε Ca(OH)2	Porosity of the Ca(OH)2 layer
ε CaCO3	Porosity of the CaCO3 layer
ΔppmvCO2	Reduction in the CO2 concentration, ppm
ρ Ca(OH)2	Ca(OH)2 molar density, mol m^−3
ρ CaCO3	CaCO3 molar density, mol m^−3

Conflict of interest

There are no conflicts of interest to declare.

References

1. IPCC, Global Warming of 1.5 °C. An IPCC Special Report on the impacts of global warming of 1.5 °C above pre-industrial levels and related global greenhouse gas emission pathways, in the context of strengthening the global response to the threat of climate change, sustainable development, and efforts to eradicate poverty, Intergovernmental Panel on Climate Change, 2018.
2. C. Hepburn, E. Adlen, J. Beddington, E. A. Carter, S. Fuss, N. Mac Dowell, J. C. Minx, P. Smith and C. K. Williams, Nature, 2019, 575, 87–97.
3. K. S. Lackner, P. Grimes and H. J. Ziock, Presented in part at the 24th international technical conference on coal utilization and fuel systems, Clearwater, Florida (USA), 1999.
4. J. C. Minx, W. F. Lamb, M. W. Callaghan, L. Bornmann and S. Fuss, Environ. Res. Lett., 2017, 12, 035007.
5. National Academies of Sciences Engineering and Medicine, Negative Emissions Technologies and Reliable Sequestration: A Research Agenda, The National Academies Press, Washington, DC, 2019.
6. EASAC, Negative emission technologies: What role in meeting Paris Agreement targets? – EASAC policy report 35, European Academies' Science Advisory Council, Germany, 2018.
7. ICEF, Direct air capture of carbon dioxide, Innovation for Coal Earth Forum, 2018.
8. E. S. Sanz-Pérez, C. R. Murdock, S. A. Didas and C. W. Jones, Chem. Rev., 2016, 116, 11840–11876.
9. A. Goeppert, M. Czaun, G. K. Surya Prakash and G. A. Olah, Energy Environ. Sci., 2012, 5, 7833–7853.
10. S. Elliott, K. S. Lackner, H. J. Ziock, M. K. Dubey, H. P. Hanson, S. Barr, N. A. Ciszkowski and D. R. Blake, Geophys. Res. Lett., 2001, 28, 1235–1238.
11. D. W. Keith and M. Ha-Duong, in Greenhouse Gas Control Technologies – 6th International Conference, ed. J. Gale and Y. Kaya, Pergamon, Oxford, 2003, pp. 187–192,  DOI:10.1016/B978-008044276-1/50030-1.
12. F. Zeman, Environ. Sci. Technol., 2007, 41, 7558–7563.
13. D. W. Keith, M. Ha-Duong and J. K. Stolaroff, Clim. Change, 2006, 74, 17–45.
14. R. Baciocchi, G. Storti and M. Mazzotti, Chem. Eng. Process., 2006, 45, 1047–1058.
15. D. W. Keith, G. Holmes, D. St. Angelo and K. Heidel, Joule, 2018, 2, 1573–1594.
16. F. M. Brethomé, N. J. Williams, C. A. Seipp, M. K. Kidder and R. Custelcean, Nat. Energy, 2018, 3, 553–559.
17. B. Barkakaty, B. G. Sumpter, I. N. Ivanov, M. E. Potter, C. W. Jones and B. S. Lokitz, Environ. Tech. Innovations, 2017, 7, 30–43.
18. G. Santori, C. Charalambous, M. C. Ferrari and S. Brandani, Energy, 2018, 162, 1158–1168.
19. S. Stucki, A. Schuler and M. Constantinescu, Int. J. Hydrogen Energy, 1995, 20, 653–663.
20. K. S. Lackner, Eur. Phys. J.: Spec. Top., 2009, 176, 93–106.
21. C. F. de Lannoy, M. D. Eisaman, A. Jose, S. D. Karnitz, R. W. DeVaul, K. Hannun and J. L. B. Rivest, Int. J. Greenhouse Gas Control, 2018, 70, 243–253.
22. M. D. Eisaman, J. L. B. Rivest, S. D. Karnitz, C. F. de Lannoy, A. Jose, R. W. DeVaul and K. Hannun, Int. J. Greenhouse Gas Control, 2018, 70, 254–261.
23. Climeworks, Capturing CO₂ from airhttp://www.climeworks.com/.
24. Global Thermostat, Global Thermostat – A carbon negative solution, http://www.globalthermostat.com.
25. P. Eisenberger, US 9227153 B2, 2016.
26. B. Soltoff, Inside ExxonMobil's hookup with carbon removal venture Global Thermostat, https://www.greenbiz.com/article/inside-exxonmobils-hookup-carbon-removal-venture-global-thermostat.
27. M. Ranjan and H. J. Herzog, Energy Procedia, 2011, 4, 2869–2876.
28. K. Z. House, A. C. Baclig, M. Ranjan, E. A. van Nierop, J. Wilcox and H. J. Herzog, Proc. Natl. Acad. Sci. U. S. A., 2011, 108, 20428–20433.
29. M. Mazzotti, R. Baciocchi, M. J. Desmond and R. H. Socolow, Clim. Change, 2013, 118, 119–135.
30. P. Smith, S. J. Davis, F. Creutzig, S. Fuss, J. Minx, B. Gabrielle, E. Kato, R. B. Jackson, A. Cowie, E. Kriegler, D. P. van Vuuren, J. Rogelj, P. Ciais, J. Milne, J. G. Canadell, D. McCollum, G. Peters, R. Andrew, V. Krey, G. Shrestha, P. Friedlingstein, T. Gasser, A. Grübler, W. K. Heidug, M. Jonas, C. D. Jones, F. Kraxner, E. Littleton, J. Lowe, J. R. Moreira, N. Nakicenovic, M. Obersteiner, A. Patwardhan, M. Rogner, E. Rubin, A. Sharifi, A. Torvanger, Y. Yamagata, J. Edmonds and C. Yongsung, Nat. Clim. Change, 2016, 6, 42.
31. S. Fuss, W. F. Lamb, M. W. Callaghan, J. Hilaire, F. Creutzig, T. Amann, T. Beringer, W. de Oliveira Garcia, J. Hartmann, T. Khanna, G. Luderer, G. F. Nemet, J. Rogelj, P. Smith, J. L. V. Vicente, J. Wilcox, M. M. Zamora Dominguez and J. C. Minx, Environ. Res. Lett., 2018, 13, 063002.
32. M. Bui, C. S. Adjiman, A. Bardow, E. J. Anthony, A. Boston, S. Brown, P. S. Fennell, S. Fuss, A. Galindo, L. A. Hackett, J. P. Hallett, H. J. Herzog, G. Jackson, J. Kemper, S. Krevor, G. C. Maitland, M. Matuszewski, I. S. Metcalfe, C. Petit, G. Puxty, J. Reimer, D. M. Reiner, E. S. Rubin, S. A. Scott, N. Shah, B. Smit, J. P. M. Trusler, P. Webley, J. Wilcox and N. Mac Dowell, Energy Environ. Sci., 2018, 11, 1062–1176.
33. S. Brandani, Energy Environ., 2012, 23, 319–328.
34. C. Pritchard, A. Yang, P. Holmes and M. Wilkinson, Process Saf. Environ. Prot., 2015, 94, 188–195.
35. R. Socolow, M. Desmond, R. Aines, J. Blackstock, O. Bolland, T. Kaarsberg, N. Lewis, M. Mazzotti, A. Pfeffer, K. Sawyer, J. Siirola, B. Smit and J. Wilcox, Direct air capture of CO₂ with chemicals: A technology assessment for the APS Panel on Public Affairs, American Physical Society, Washington, DC, 2011.
36. C. Gebald, W. Meier, N. Repond, T. Ruesch and A. Wurzbacher, US2017/0106330A1, 2017.
37. IPCC, Special report on carbon dioxide capture and storage, Intergovernmental Panel on Climate Change, New York, USA, 2005.
38. J. C. Abanades, E. S. Rubin, M. Mazzotti and H. J. Herzog, Energy Environ. Sci., 2017, 10, 2491–2499.
39. Carmeuse, http://www.carmeuse-agriculture.com/our-products/fruitcal, accessed November 2019.
40. J. A. Bartsch, New York Fruit Quart., 2004, 12, 11–12.
41. V. Nikulshina, C. Gebald and A. Steinfeld, Chem. Eng. J., 2009, 146, 244–248.
42. A. Kirchofer, A. Becker, A. Brandt and J. Wilcox, Environ. Sci. Technol., 2013, 47, 7548–7554.
43. S. Talukdar and N. Banthia, Constr. Build. Mater., 2013, 40, 775–782.
44. F. Xi, S. J. Davis, P. Ciais, D. Crawford-Brown, D. Guan, C. Pade, T. Shi, M. Syddall, J. Lv, L. Ji, L. Bing, J. Wang, W. Wei, K.-H. Yang, B. Lagerblad, I. Galan, C. Andrade, Y. Zhang and Z. Liu, Nat. Geosci., 2016, 9, 880.
45. D. P. Hanak and V. Manovic, Energy Convers. Manage., 2018, 160, 455–466.
46. D. P. Hanak, B. G. Jenkins, T. Kruger and V. Manovic, Appl. Energy, 2017, 205, 1189–1201.
47. M. Erans, S. A. Nabavi and V. Manović, J. Cleaner Prod., 2020, 242, 118330.
48. M. Samari, F. Ridha, V. Manovic, A. Macchi and E. J. Anthony, Mitig. Adapt. Strat. Gl., 2019 DOI:10.1007/s11027-019-9845-0.
49. P. Renforth, Nat. Commun., 2019, 10, 1401.
50. R. M. Dheilly, J. Tudo and M. Quéneudec, J. Mater. Eng. Perform., 1998, 7, 789–795.
51. V. Morales-Flórez, A. Santos, I. Romero-Hermida and L. Esquivias, Chem. Eng. J., 2015, 265, 194–200.
52. H. Klopfer, Bautenschutz Bausanier, 1978, 1, 86–97.
53. H. Hilsdorf and J. Kropp, Performance criteria for concrete durability, CRC Press, London, United Kingdom, 1995.
54. B. Lagerblad, Carbon dioxide uptake during concrete life cycle – State of the art, NORDEN – Nordic Innovation Centre project, Stockholm, 2005.
55. W. Ashraf, Constr. Build. Mater., 2016, 120, 558–570.
56. D. J. Beerling, J. R. Leake, S. P. Long, J. D. Scholes, J. Ton, P. N. Nelson, M. Bird, E. Kantzas, L. L. Taylor, B. Sarkar, M. Kelland, E. DeLucia, I. Kantola, C. Müller, G. Rau and J. Hansen, Nat. Plants, 2018, 4, 138–147.
57. J. Mullaney and T. Lucke, CLEAN – Soil, Air, Water, 2014, 42, 111–124.
58. Y. A. Criado, M. Alonso and J. C. Abanades, Ind. Eng. Chem. Res., 2015, 54, 9314–9327.
59. K. G. Sakellariou, N. I. Tsongidis, G. Karagiannakis and A. G. Konstandopoulos, Energy Fuels, 2017, 31, 6548–6559.
60. M. Voldsund, S. O. Gardarsdottir, E. De Lena, J.-F. Pérez-Calvo, A. Jamali, D. Berstad, C. Fu, M. Romano, S. Roussanaly, R. Anantharaman, H. Hoppe, D. Sutter, M. Mazzotti, M. Gazzani, G. Cinti and K. Jordal, Energies, 2019, 12, 559.
61. S. O. Gardarsdottir, E. De Lena, M. Romano, S. Roussanaly, M. Voldsund, J.-F. Pérez-Calvo, D. Berstad, C. Fu, R. Anantharaman, D. Sutter, M. Gazzani, M. Mazzotti and G. Cinti, Energies, 2019, 12, 542.
62. J. C. Abanades, B. Arias, A. Lyngfelt, T. Mattisson, D. E. Wiley, H. Li, M. T. Ho, E. Mangano and S. Brandani, Int. J. Greenhouse Gas Control., 2015, 40, 126–166.
63. G. Guandalini, M. C. Romano, M. Ho, D. Wiley, E. S. Rubin and J. C. Abanades, Int. J. Greenhouse Gas Control, 2019, 84, 219–231.
64. R. B. Perry and D. W. Green, Perry's Chemical Engineers' Handbook, McGraw-Hill, 1999.
65. Global Wind Atlas, https://globalwindatlas.info/.
66. Windy, http://www.windy.com.
67. B. Chen, J. M. Chen, J. Liu, D. Chan, K. Higuchi and A. Shashkov, J. Geophys. Res.: Atmos., 2004, 109, D04306.
68. M. K. Dubey, H. Ziock, G. Rueff, S. Elliott, W. S. Smith, K. S. Lackner and N. A. Johnston, Fuel Chemistry Division Preprints, 2002, 47, 81–84.
69. T. R. Oke, Energy Build., 1988, 11, 103–113.
70. E. S. Rubin, J. E. Davison and H. J. Herzog, Int. J. Greenhouse Gas Control, 2015, 40, 378–400.
71. DOE/NETL, Cost and performance for low rank pulverized coal oxycombustion energy plants, Report DOE/NETL-401/093010 US Department of Energy, National Energy Technology Laboratory, 2010.
72. IEAGHG, CO₂ capture in the cement industry, Report 2008/3, International Energy Agency Greenhouse Gas R&D Programme, 2008.
73. Trading Economics, United States Inflation Rate, https://tradingeconomics.com/united-states/inflation-cpi.
74. USGS, Crushed stone statistics and information, https://www.usgs.gov/centers/nmic/crushed-stone-statistics-and-information, accessed November 2019.
75. DOE/NETL, Cost and performance baseline for fossil energy plants volume 1a: Bituminous coal (PC) and natural gas to electricity. Revision 3, Report DOE/NETL-2015/1723, US Department of Energy, National Energy Technology Laboratory, 2015.

---