Economic and energetic analysis of capturing CO₂ from ambient air

In 1959, Thomas K. Sherwood published the original version of what is now commonly referred to as a Sherwood plot (5). His graph revealed an empirical relationship between the market price of a metal and its typical concentration in the ore from which it is extracted, using mature separation technologies. Later versions by others include additional substances that are separated from dilute mixtures, such as pollutants and valuable organic compounds (17, 18). Recently, Dahmus and Gutowski developed such a plot to help assess material recycling potentials (7).

In all of these analyses, it is clear that the cost to separate a given substance from a mixture scales inversely with the initial concentration of that substance. Dahmus and Gutowski (7) interpret this result as related to material extraction and processing costs that scale with the amount of material processed, which we parallel to the amount of gas to be processed for capturing CO₂. In Fig. 1, we present the updated Sherwood plot from Grübler (6), which includes three categories of materials to be separated: metals, organics, and pollutants. A line with the form P = A/C, can be drawn through each set of separated materials, where P is the price (dollars per kilogram), C is the initial concentration of the input stream (i.e., mass of product per mass of mixture), and A is a separation constant with units (dollars per kilogram initial mixture). Dahmus and Gutowski observe that A is approximately $1/kg of initial mixture (kg_i) for separating organics; approximately $0.01/kg_i for separating metals; and approximately $0.001/kg_i for separating pollutants from mixed gas streams (7).

We can use the estimated separation constant for separating pollutants from mixed gas streams (i.e., A = $0.001/kg_i) to estimate the cost, per unit of CO₂, to separate CO₂ from a variety of mixed streams. For example, the CO₂-mole fraction of flue gas from a coal-fired power plant is about 12%, or order 0.1. Using Dahmus and Gutowski’s constant and adjusting to 2008 dollars, we calculate that separating CO₂ from a coal-fired power plant will cost on the order of $10/tCO₂. Most estimates suggest that capturing, but not compressing, a stream of CO₂ from a coal-fired power plant will cost closer to about $30–$60/tCO₂ (13, 19, 20) on a per tonne captured basis. When applied to CO₂ separation from a natural gas-fired power plant, the separation constant (7) indicates that the cost of CO₂ purification would be approximately $25/tCO₂, which is also slightly lower than most reported values in the approximate $50/tCO₂ range (13). Thus, using the separation constants derived by Dahmus and Gutowski (7) yields the correct order of magnitude.

Application of the separation constant to air capture would suggest a cost of about $2,500/tCO₂. Just as types of materials scale (i.e., organics, metals, pollutants), according to Fig. 1, gases with similar chemical properties, such as acid gases, should also scale. For instance, after close inspection of Fig. 1, one can see that drawing a line through the cluster of acid gases (CO₂, SO_x, and NO_x) would result in a shallower slope than the $0.001/kg_i cited. To better constrain the cost projection for air capture, we constructed a Sherwood plot for mixed acid gas stream separation only (SI Appendix). The projected cost was consistently larger than $1,100/tCO₂ for air capture, whether different trace acid gas separation processes were included or not, indicating independence of separation cost on a particular process choice or process chemistry. Rather, as Lightfoot and Cockrem pointed out in 1987 (8), separation costs are more closely related to the “processing of valueless constituents.”

The theoretical minimum work required to achieve a change in thermodynamic states is the net change in work potential (i.e., thermodynamic availability or exergy) of the system (21). The change in work potential is minimized when a flowing system undergoes a reversible isothermal, isobaric change (22). Therefore, the absolute minimum work, W_min, required for a given separation process is equal to the difference between the work potential of the product and feed streams, which is equal to the difference in stream exergy:where Ψ_i is the exergy of stream i. For the isothermal, isobaric processes that we are considering, the change in work potential equals the change in the Gibbs free energy. In the simple case of a separation of one feed stream (stream 1) consisting of n substances into two product streams (streams 2 and 3, as in Fig. 2), where all streams consist of ideal mixtures, the minimum work reduces towhere N_j denotes the molar flow rate of stream j, and X_j,k denotes the molar concentration of substance k in stream j. Note that for nonideal mixtures (i.e., real gases and solutions), we must account for the excess properties that depend on interactions between molecules.

According to Eq. 2, the theoretical minimum work required to separate a stream of air with 400 ppm CO₂ into one stream with 200 ppm CO₂ and a second stream of highly concentrated (i.e., 99% purity) CO₂, all at the same temperature and pressure, is about 20 kJ/(mol CO₂). No real process can operate by expending only the theoretical minimum work, because reversibility—the thermodynamic requirement to achieve minimum work—requires infinitesimal mass transport driving forces, which in turn require theoretical equipment of infinite size and cost. As such, the capital costs of processes designed to expend close to the minimum work are excessive.

The second-law analysis uses only work, whereas real capture processes may use a combination of heat and work. The minimum work analysis, however, is still valid for those systems because the heat is associated with work potential. For example, many amine capture systems use steam extracted from the turbine as their source of heat. That steam extraction results in a loss of power generation, which is the real work penalty associated with that heat. If one used fuel to generate the heat directly, it would most likely result in an even bigger work penalty because extracting steam from a turbine is a form of cogeneration, which tends to be more energy efficient than making low pressure steam from fuel directly (23).

Real-world separation processes typically achieve second-law efficiencies (η), defined as the ratio of minimum to actual power consumption, in the 5–40% range (see Fig. 3). For these processes, η is the result of a design strategy to minimize the net present value of total costs. That optimization involves balancing capital costs, which tend to increase with η, and operating costs, which tend to decrease with η.

Fig. 3 plots concentration factor (i.e., the ratio of the material’s final concentration to its initial concentration) versus the second-law efficiency of several industrial separation processes. The data indicate that separation processes span a wide range of concentration factors and second-law efficiencies, but they never exhibit both high concentration factor and high second-law efficiency. That observation helps explain observations made by Sherwood et al. (5, 6) that the total costs scale with the concentration factor: As more material is processed, more work input is required for moving and arranging the additional material. The trend apparent in Fig. 3 suggests that, for air capture, the second-law thermodynamic efficiency is likely to be significantly below 10%. Indeed, unless a new technology is shown to substantially deviate from the efficiency frontier in Fig. 3, it is reasonable to assume that the second-law efficiency of an air capture system could be below 5%. Rather than conflict with Baciocchi et al.’s projection of a process with 13.5% second-law efficiency (24) (see Table 1), this empirical projection is indicative of the difference in performance between detailed process design with process components that have yet to be developed (i.e., Baciocchi et al.’s process, ref. 24) and as-built commercial processes as shown in Fig. 3.

If we assume a second-law efficiency of 5% for air capture systems, 400 kJ/(mol CO₂) of work will be required to separate CO₂ from the air. As a reference, a power plant fueled by natural gas, the least carbon-intensive fossil fuel, produces about 400 kJ of work for each mole of CO₂ emitted (see Table 2). Therefore, if one powered an air capture system with 5% second-law efficiency this way, then no net CO₂ would be removed from the atmosphere. Under such circumstances, air capture systems would need to be driven by nearly CO₂-free power sources, which are more expensive than today’s mix of CO₂ and non-CO₂ emitting power sources.

Determining the cost of CO₂-free work is not easy because the work can take many forms for different technological approaches. As an estimate, however, we use the Energy Information Agency’s 2009 Levelized Cost of New Generating Technologies (25), which we have incorporated into Table 2.

Table 2 indicates that carbon-free electricity will have a cost of electricity (COE) in the 10–20 ¢/kWh range in the foreseeable future. If we use a price of 10 ¢/kWh, then just the cost of required CO₂-free work is about $253/tCO₂ for the air capture system. Because additional capital investment that is unrelated to the cost of CO₂-free work (i.e., capture equipment, land, etc.,) is required, the total cost of air capture will be substantially higher than just the cost of the work.

Using a range of η and COE, Table 3 (which does not include capital cost) indicates that air capture cost estimates (including capital) of $100–$200/tCO₂ (see Table 3) will not be realized unless the capture system is shown to significantly deviate from the trends observed in Fig. 3.

In air, CO₂ is a trace gas (i.e., at 400 ppm, it is present at a very low concentration). Therefore, it is instructive to examine the thermodynamic work required to remove trace gases from mixed gas streams in commercial processes. We examined a class of processes that involve the removal of the trace gases by reaction (i.e., the trace gas is chemically transformed to eliminate it from the original stream). For example, the process for removing SO₂ from flue gas results in the conversion of SO₂ into CaSO₃. Such chemical processes are thermodynamically favorable, meaning that the processes could, in principle, be used to do useful work. Yet, in practice, these processes require substantial inputs of thermodynamic work, and the work requirements of these processes result from losses associated with the handling of the nonreactive material contained in the mixed gas stream. As such, it is useful to extend our investigation of the energetic dependence on initial concentration to processes that involve the thermodynamically favorable removal of minority gas species from mixed gas streams. In doing so, we characterized a relationship between the actual work used by various separation processes and the initial concentration of the trace gas that is to be removed (Table 4). Note that the actual work required to remove these trace gases from flue gas increases as the initial concentration of the trace gas decreases.

The removal of NO_x from flue gas, in particular, is worth considering because the initial concentration of NO_x in flue gas is approximately equal to that of CO₂ in ambient air. Typical NO_x-removing selective catalytic reduction (SCR) systems can reduce on average 80% of the NO_x from the flue gas (26) through the injection of reactive ammonia into the flue-gas stream. The overall reaction between ammonia and NO_x across an SCR catalyst, typically comprised of supported vanadia, to form H₂O and N₂ is thermodynamically favorable, meaning that, in theory, no work is required to remove NO_x from flue gas. In practice, however, nearly 500 kJ of work is expended per mole of NO_x removed to power the fan/blower system due to increased pressure drop across monoliths of catalyst. Additionally, the SCR unit is placed just downstream of the boiler exit so that reaction kinetics of reduction are enhanced by the elevated temperature of the flue gas.

In addition to the concentration similarity between NO_x in flue gas and CO₂ in air, both the removal of NO_x from flue gas and the removal of CO₂ from air use “end-of-pipe” cleanup techniques, and they both involve reaction on a solid surface (catalyst for NO_x, absorbent for CO₂). As such, the removal of NO_x from flue gas by commercial systems should provide insight into the thermodynamic work required to remove CO₂ from air. It is important to note, however, that NO_x removal differs from air capture because, aside from the physical differences of the substances, NO_x removal is a thermodynamically favorable process; NO_x removal does not produce a concentrated stream of NO_x; and NO_x removal benefits from the elevated temperature of the flue gas. Thus, all of the key differences between NO_x removal from flue gas and CO₂ removal from air indicate that air capture of CO₂ will require more thermodynamic work than NO_x removal. It is therefore very likely that CO₂ capture from air will require more thermodynamic work than the approximate 500 kJ/mol used for NO_x removal. As discussed in the prior section, an air capture process using greater than 400 kJ/mol is counterproductive unless powered by carbon-free energy.

Notably, there is an alternative indirect pathway for air capture that may ultimately offer a reasonable CO₂ offset: a biomass-based combustion power plant with CO₂ capture. Powered by the sun, CO₂ is captured from the air via photosynthesis and stored in the biomass, along with the solar energy. Next, the biomass is harvested and combusted to produce power. The relatively concentrated CO₂ in the flue gas (about 10%) is captured and stored, while the excess carbon-free power is available for sale. The net result is that solar energy is used to capture CO₂ from the air for storage in geologic reservoirs with production of CO₂-free electricity. Estimates for the total cost of capturing CO₂ from this process are in the range of $150–$400/tCO₂ (27).

One drawback to this approach will be scale, because an estimated 180,000 square miles of arable land (roughly 6% of the land area of the contiguous United States) will be required to capture one billion metric tons of CO₂ per year (28, 29). Another concern is the life-cycle carbon balance. Greenhouse gas emissions may be associated with growing, harvesting, and transporting the biomass, as well as land-use changes associated with growing energy crops. To account for these “fugitive” emissions, they must be subtracted from the gross amount of CO₂ captured. The low end of the cost range above assumes no fugitive CO₂ emissions, whereas the high end assumes the fugitive emissions equal 50% of the gross amount captured (27).

It should be noted that this process for removing CO₂ from the air does not violate the empirical trend that the efficiency of systems that remove trace substances from mixtures tends to scale inversely with the initial concentration because photosynthesis operates with a first-law efficiency seldom better than 2% (30, 31). So, in the case of biomass combustion with CCS, the total system does the same amount of material handling as industrial air capture systems; in the former, nature, rather inefficiently, does some of the material handling.

The 300-fold concentration difference of CO₂ in flue gas (12%) and air capture (0.04%) causes the minimum work to increase by only about a factor of three. As reported by Sherwood and others, however, the financial cost of separation tends to scale inversely to the initial concentration because of the large material handling requirements. Those large material handling requirements affect both the capital costs of the separation equipment as well as the process’s second-law efficiency. To better understand the empirical results presented above, this section looks at design trade-offs inherent in any CO₂ capture process based on traditional solvent/sorbent looping systems.

In the first step of any separation system, the air must be contacted with a solvent or sorbent to capture the CO₂. In conventional settings, contacting would be achieved by blowing the air through scrubber towers. To capture the same quantity of CO₂ as a flue-gas-capture plant, and assuming the same fractional CO₂ removal, an air capture plant would need to process 300 times the volume of gas. Given practical limits on gas velocities in traditional scrubbers (32), conventional scrubbers for air capture would need significantly greater cross-sectional areas, but unlike point-source scrubbers, may consist of an array of flat or short modules, rather than tall columns. In a conventional point-source scrubbing system, the solvent or sorbent loading and regeneration must maintain the pace dictated by the flue-gas flow rates, which are on the order of 3,000 t/h for a conventional 500-MW power plant, whereas the air capture system flow requirements will be dictated by the desired capture rates. Without major design modifications from the conventional, the expense of blowing or fan power may drive the cost of such a plant far above the order of magnitude estimates of the current work. Therefore, the air capture system will likely have to rely on a sorbent or solvent configuration that requires minimal effort to flow air through the system.

Whether the air is contacted with a solvent or sorbent via traditional blowers and scrubbers, or via more passive means, in a looping system, the solvent or sorbent must then be regenerated. That raises another issue because the driving force (i.e., the partial pressure of CO₂) for sorption in air capture absorbers is 300-fold less than in flue-gas absorbers. As a result, if one were to use the same solvents or sorbents in air capture as in flue gas, the sorption rates would be much lower, requiring much larger contact surface areas. Therefore, it is likely that the air capture system may require more selective binding, which can take the form of greater accessible surface area, faster kinetics, minimum diffusion constraints to the active site of adsorption or reaction, and/or enhanced binding to a given surface site or chemical solvent; otherwise, both the rich and lean solvent loadings will be lower, requiring significantly more energy to be expended in order to regenerate the solvent to the lower lean loadings (27), further driving up the potential costs of direct air capture. Stronger binding, however, may not be the best route because it will come at the expense of increased solvent regeneration cost and power. It becomes clear that, if the design and implementation of direct air capture plants were to move forward at the costs estimated in this work, they would have to be quite unique to the traditional gas scrubbing systems of point-source CO₂ emissions.

It has been suggested that, unlike a power plant, where a high recovery factor (i.e., the fraction of CO₂ in the gas stream that is captured) of 80–90% is an essential design constraint for point-source CCS to be a meaningful mitigation tool, the recovery factor for an air capture plant need not be so high (1). A lower recovery factor, however, is not necessarily beneficial. For example, operating with a recovery factor of only 45% (vs. 90%) will necessitate processing twice as much air (to capture the same tonne of CO₂), doubling the gas handling disadvantage from 300∶1 to 600∶1.