A new strategy for membrane-based direct air capture

Direct CO2 capture from the air, so-called direct air capture (DAC), has become inevitable to reduce the concentration of CO2 in the atmosphere. Current DAC technologies consider only sorbent-based systems. Recently, there have been reports that show ultrahigh CO2 permeances in gas separation membranes and thus membrane separation could be a potential new technology for DAC in addition to sorbent-based CO2 capture. The simulation of chemical processes has been well established and is commonly used for the development and performance assessment of industrial chemical processes. These simulations offer a credible assessment of the feasibility of membrane-based DAC (m-DAC). In this paper, we discuss the potential of m-DAC considering the state-of-the-art performance of organic polymer membranes. The multistage membrane separation process was employed in process simulation to estimate the energy requirements for m-DAC. Based on the analysis, we propose the target membrane separation performance required for m-DAC with competitive energy expenses. Finally, we discuss the direction of future membrane development for DAC. Direct CO2 capture from the air (DAC), is inevitable to reduce the concentration of CO2 in the atmosphere. Recent reports of ultrahigh CO2 permeances in gas separation membranes indicate a potential of new technology for DAC (m-DAC). In this paper, we use chemical process simulation to discuss the potential of m-DAC considering the state-of-the-art performance of organic polymer membranes. Based on the analysis, we propose the target properties for separation membranes required for m-DAC with competitive energy expenses as well as the direction of future membrane development for DAC.


Introduction
Carbon dioxide emissions into the atmosphere are the main reason for climate change. Drastic reductions in CO 2 emissions into the atmosphere are unavoidable to meet the 1.5°C scenario recommended by the Intergovernmental Panel on Climate Change [1]. Unfortunately, it has become apparent that the 1.5°C scenario cannot be achieved simply by reducing CO 2 emissions to the atmosphere [2][3][4]. This has led to the need for a more progressive approach, called negative emission technologies. These technologies include direct CO 2 capture (direct air capture (DAC)) from ambient air by chem-or physisorption processes and other approaches, such as the use of bioderived energy combined with carbon capture and storage (BECCS), enhanced weathering of minerals, afforestation, and reforestation [5][6][7][8]. Among these technologies, DAC has a removal capacity comparable to that of BECCS (~3.3 Gt-C/year), which requires a large amount of land and water [9][10][11]. While the potential of DAC based on sorption technologies has been proven, it requires considerable energy to desorb CO 2 from the sorbents [12,13].
Membrane separation is also one of the major technologies for capturing CO 2 . Compared to other conventional capture methods, CO 2 capture by permselective membranes has advantages because of its smaller footprint and simpler setup and operation. However, large-scale membrane separation is still in its infancy, with only a few pilot plants operating at CO 2 mass emission points, such as coal-fired power plants that emit flue gases containing 10-15% CO 2 [14]. Merkel et al. concluded that improved gas permeance in membranes is more critical for reducing capture cost than enhanced selectivity [15]. Compared to concentrated CO 2 emission sources, the partial pressure of CO 2 in the air is only 40 Pa, which is considered too small to pass CO 2 through membranes effectively. Keith et al. also mentioned that DAC by membranes seems implausible, given the relatively low molecular fluxes through membranes [16]. Based on these considerations, membrane-based DAC (m-DAC) has never been considered [6].
Recently, many efforts have been devoted to the development of polymeric materials with high CO 2 permeance. For example, Yoo et al. reported defect-free Teflon-based membranes possessing a CO 2 permeance of~31,500 GPU (GPU: gas permeance unit, 1 GPU = 7.5 × 10 −12 m 3 (STP) m −2 s −1 Pa −1 , STP: standard temperature and pressure) with a CO 2 /N 2 selectivity of 3.3 [17]. We have also reported freestanding siloxane nanomembranes with high CO 2 permeances exceeding 40,000 GPU [18]. Such membranes with ultrahigh gas permeance and selectivity would have the potential to capture CO 2 efficiently, even from the air, since the gas permeance resistance through the membranes is quite small. Based on recent achievements in the membrane field, it is meaningful to evaluate the potential of membrane separation as an alternative DAC process. Analysis of membrane separation using process simulation has been well established based on chemical engineering aspects. This process analysis based on computational chemical engineering can assess the performance and feasibility of m-DAC from a realistic standpoint.
In this paper, we explored the potential of m-DAC based on process simulation with consideration of the state-of-theart CO 2 separation membrane performance. The future direction of membrane development for DAC is discussed.

Preliminary feasibility evaluation of m-DAC
For the initial investigation of the feasibility of m-DAC, we assumed a membrane with a permeance of 40,000 GPU and selectivity of 70, for which performances have been separately achieved in different membranes [18,19]. Aspen Plus V11 (AspenTech, USA) flowsheeting software with the Peng-Robinson state equation thermodynamic model was used. The membrane separation process was modeled using the third-party unit operation MEMSIC, acquired from the University of Lorraine [20]. The following conditions were used for the process simulation: (1) The CO 2 concentration of the retentate gas should bẽ 300 ppm, which is the level in the preindustrial period.
(2) The pressures of the feed and permeate sides are 101.3 kPa (atmospheric pressure) and 5 kPa, respectively. (3) Multistage separation with four membrane separation units connected in series was considered ( Fig. 1). (4) The process is driven by vacuum pumps, which are units of the process that require energy. (5) The outcomes of the energy requirements and required membrane area are normalized on the mass of CO 2 in the product stream.
The results of the process simulation are summarized in Table 1. The relevant CO 2 concentration of >10% in the permeate is reached by three-and four-stage separations, while single-or two-stage separation remains below 3% CO 2 . Concerning the membrane area, the required membrane area for four-stage separation is only~3.2 m 2 /kg CO 2 /day as a flat sheet. This membrane area can be assembled into the membrane module with a volume of less than 0.01 m 3 (for 1 kg-CO 2 capture per day) estimated from the empirical membrane surface-tovolume ratio for plate-and-frame modules (~100-150 ft 2 /ft 3 ) [21]. Notably, the amount of CO 2 emissions estimated from the energy used by the separation process is only~0.6 kg/1 kg-CO 2 captured, leading to negative emission of CO 2 . These simple process simulation results encouraged us to explore more realistic membrane performances and process conditions for m-DAC.

Key parameters in the CO 2 separation by membranes
In the membrane separation process, both membrane properties and process parameters play an important role in determining the overall performance of the process. In addition to the gas permeance and selectivity of membranes, stage cut and the pressure ratio between the feed and the permeate sides are important.

Gas permeance
The gas permeance property is important because the required membrane area is inversely proportional to this value. Therefore, only high permeance separation membranes can be considered as a practical option for DAC with realistic size and pressure conditions. It is noteworthy that membranes with high permeance would allow for the building of multistage separation processes with a reasonable membrane size, as shown in Table 1.

CO 2 selectivity of membranes
The selectivity of membranes for CO 2 capture is also critical. Single-step membrane separation can hardly exceed more than 1% of 400 ppm CO 2 in air, even with a high CO 2 / N 2 selectivity of 70. However, the high CO 2 permeance of the membrane enables the application of multistage separation, making it feasible even with relatively low membrane selectivity for CO 2 over other gas species. Figure 2a shows a three-stage membrane separation process used to analyze the effect of the CO 2 selectivity on the CO 2 purity in the product gas. The CO 2 permeances of all membranes are assumed to be 10,000 GPU. The pressures of the feed and permeate sides at each separation step are 110 and 2 kPa, respectively. The CO 2 selectivity of membranes over other gases is a variable parameter, but the same membrane performances at every stage are used for the analysis.
In this model, the membrane size was adjusted to maintain the CO 2 concentration of 300 ppm in the retentate of each stage. As seen in Fig. 2b, the final CO 2 concentration does not exceed more than 10% when the CO 2 selectivity is less than 20, even after three-stage separation. Higher CO 2 selectivity results in higher CO 2 concentrations in the permeate gas. However, the enhancement of CO 2 purity in the product becomes moderate for the selectivity of more than 30. The required power of the pump at the first stage is the largest, and subsequent separation stages consume less energy since the gas volume after the first stage is significantly reduced (Fig. 2c). Higher CO 2 selectivity contributes to the reduction of the pump energy, although the reduction rate becomes lower at selectivities greater than 30 (the black diamonds in Fig. 2c).
These results clearly show that the CO 2 selectivity over other gases has a definitive and critical impact on the performance of m-DAC.

Pressure ratio
Process conditions also play an important role in determining the process performance in addition to the intrinsic membrane properties. The pressure ratio (φ), defined in Eq.
(1), is a particularly important factor in the membrane separation process [22] φ where p f and p p are the total pressure at the feed and permeate sides of the membrane. By considering the mass balances in a single membrane separation process, the partial pressure of CO 2 in the permeate cannot exceed the partial pressure of CO 2 in the feed; therefore, the following equation should be satisfied: where C p and C f are the mole fractions of CO 2 at the permeate and feed side, respectively. Hence, the following relation defines the permeate concentration with feed concentration and pressure ratio: This equation implies that the pressure ratio limits the mole fraction of CO 2 at the permeate side, independent of the membrane selectivity. Figure 3a shows the effect of the pressure ratio on the CO 2 concentration at the permeate (product) and the retentate sides in the single-step separation from the air. The small pressure ratio has a large impact on the CO 2 concentration in the permeate and retentate streams, but the trend plateaus in the high-pressure ratio a The utilization of photovoltaic electricity (PV-e) considered for separation process, and the amount of CO 2 emissions relevant to the required energy is calculated from the carbon intensity of PV-e in Japan (0.038 kg/kWh) [33] region (φ > 30). This result demonstrates the importance of the pressure ratio in determining the CO 2 concentrations after membrane separation. The pressure ratio is also related to the energy needed for vacuuming. Figure 3b shows the required energy (per kg-CO 2 ), and there is an optimum pressure ratio for having local minimum energy at pressure ratios of 10-15, which is similar to the optimum pressure ratio for postcombustion CO 2 capture [15].

Stage cut
In membrane separation, the feed gas flows along the membrane surface, and the CO 2 concentration gradually decreases since CO 2 selectively permeates across a membrane, leading to a reduced driving force for permeation.
In contrast, the concentrations of other (less permeable) gases in the residue stream are relatively sustained, resulting in a stable driving force. Especially for high gas-permeable membranes, this effect becomes increasingly significant. A larger membrane area and slower feed flow allow for more efficient permeation of gas across a membrane. Therefore, the degree of separation has a trade-off relationship between purity and recovery that can be controlled by the flow rates and membrane area, which is known as the stage cut (θ), which is defined as the ratio of permeate to feed flow. Figure 3c shows the effect of stage cut on the CO 2 concentration of the permeate and feed sides. In the region of a relatively small stage cut, a higher CO 2 concentration at the permeate side is obtained. However, the portion of CO 2 separated from the feed gas (recovery rate) inevitably decreases and vice Fig. 2 a Scheme of the three-stage membrane process for CO 2 separation from air. b Dependence of CO 2 purity in the product stream on membrane selectivity. c Requirements for the vacuum pump power (circles) and total daily energy/per kg of CO 2 (diamonds) depending on membrane selectivity (the setting for pressure ratio: φ = 50) versa for relatively large stage cuts. Specifically, one can see that product purity and recovery of CO 2 from air show a trade-off relationship (Fig. 3c, d). The stage cut factor can be controlled by the membrane area (at a stable feed flow) and should be optimized to achieve a target separation.

The design strategy of m-DAC and sensitivity analysis
By considering the importance of the factors described above, the membrane process for DAC was investigated as follows.
Target CO 2 concentration for m-DAC CO 2 capture is one component of the process of CO 2 capture, utilization, and sequestration (CCUS). Thus, the target conditions for CO 2 capture depend on the subsequent CO 2 treatment process. For transport and geological sequestration, a nearly pure CO 2 stream is required [23]. On the other hand, there are no specific concentration requirements for CO 2 utilization. A high concentration of CO 2 is certainly desirable in CO 2 conversion reactions to value-added materials. However, high purity at the CO 2 separation step is not necessary if subsequent conversion steps can still proceed efficiently. Indeed, Kim et al. showed the potential for electrochemical conversion of low-purity CO 2 [24]. They used CO 2 gas diluted with N 2 as a feedstock for the electrochemical reduction of CO 2 and achieved efficient conversion reactions to CO, even at feed CO 2 concentrations as low as 20%. Kumagai et al. also achieved CO 2 conversion even at only 1000 ppm CO 2 [25]. These results make it apparent that it is not necessary to produce a highpurity CO 2 stream by membrane separation. Based on these considerations, for the subsequent analysis, the target CO 2 Fig. 3 Influence of the pressure ratio φ and stage cut (θ) on the CO 2 separation from the air using a CO 2 selective membrane. a Dependence of CO 2 concentration in permeate and retentate streams and b CO 2 -mass normalized daily energy requirements on pressure ratio (other parameters: stage cut θ~5-10 and selectivity CO 2 /X = 30, where X identifies other components of air (N 2 , O 2 , Ar). c Dependence of CO 2 concentration in permeate and retentate streams and d CO 2mass normalized daily energy requirements on stage cut (other parameters: pressure ratio, φ = 20; selectivity CO 2 /X = 30, where X identifies other components of air (N 2 , O 2 , Ar) purity in the final gas was set to 40%, which is 1000 times its concentration in the air.

Stage cut and pressure ratio
The main purpose of DAC is to reduce the CO 2 concentration in the air by removing historical emissions and to offset the emissions that are difficult to avoid. Generally, membrane separation emits a retentate gas to the external air. Therefore, the CO 2 concentration of the retentate gas should be less than 300 ppm (characteristic atmospheric CO 2 concentration of the preindustrial period) by adjusting the stage cut (controlled by membrane area). The pressure ratio also impacts the total performance of the DAC membranes. As shown in Fig. 3b, the pressure ratios ranging from~10 to 20, which is a local minimum of the consumed energy, would be reasonable for analysis. However, the final concentration of CO 2 within this pressure ratio range cannot reach 40% even after four-stage separation. When the pressure at the permeate side is 4 kPa (φ = 25), the final CO 2 concentration can exceed 40% ( Table 2). Although the final concentration of CO 2 also depends on the membrane selectivity, as shown in Fig. 3a, pressure ratios higher than 30 in the membrane separation seem to be needed.

Influence of the gas permeance and selectivity on the m-DAC performance
Once the concentration of retentate CO 2 concentration is defined, the volume of the permeate gas is simultaneously determined according to mass-balance constraints. The size of a membrane with relatively high gas permeance becomes small and vice versa if the separation parameters are identical. Therefore, the high gas permeance contributes to the reduction of the required membrane size and allows for one to build relatively small modules for multistage separation with practical sizes.
Membrane selectivity to CO 2 also plays an important role in building a feasible m-DAC process. As shown in Fig. 2, membranes with CO 2 selectivity of more than 70 can achieve the target CO 2 concentration of 40% with a pressure ratio of 22 (in the three-stage process). However, the total performance of m-DAC depends on the parameters described above, and there may be a window of CO 2 selectivity to satisfy the current target (1000 times CO 2 concentration). To explore the range of CO 2 selectivity, the following conditions were considered.
The obtained results are standardized for capturing 1 kg of CO 2 per day.
As summarized in Table 3, membrane separation with a relatively realistic CO 2 selectivity of 30 can reach the target CO 2 concentration (more than 40%). The total amount of CO 2 emissions through this process is less than 1 kg, leading to negative emission of CO 2 with a membrane size of less than 5 m 2 /kg-CO 2 /day. In the separation with relatively low selectivity, other gases also permeate faster, resulting in a rapid increase in the CO 2 concentration of the  The utilization of photovoltaic electricity (PV-e) considered for separation process, and the amount of CO 2 emissions relevant to the required energy is calculated from the carbon intensity of PV-e in Japan (0.038 kg/kWh) [33] retentate stream. Thus, the area of the membrane with lower selectivity should be smaller than that with higher selectivity to release the retentate gas with a CO 2 concentration of less than 300 ppm. Highly CO 2 selective membranes show relatively lower energy for vacuuming and CO 2 emission through the DAC process. These analyses imply that there is space to achieve the current target, 1000-fold preconcentration of the CO 2 from air, by optimizing parameters, which has never been considered before. As a short summary, the membrane performances and process factors need to satisfy the following conditions: (1) CO 2 permeance: more than 10,000 GPU to achieve realistic membrane sizes. (2) CO 2 selectivity >30 (higher selectivity is preferred).
One can claim that the discussion of CO 2 capture in kg mass range may be negligible to reduce the CO 2 concentration in the air since the amount of already emitted CO 2 is incredibly large. However, once we have such membranes, they can be considered for relatively large CO 2 capture facilities. For example, the required membrane for one ton of CO 2 capture per day is estimated to be less than 5000 m 2 , leading to less than 15.2 m 3 (~2.5 m × 2.5 m × 2.5 m in size) for the volume of the membrane unit. The massive installation of such membrane separation units would therefore have the potential to reduce the CO 2 concentration in the air meaningfully.
In the present analysis, the electricity generated by the photovoltaic system was considered for m-DAC operation and to estimate the amount of CO 2 emissions through the process. The price of PV electricity was $0.068/kWh in 2019 and predicted to average $0.039/kWh in 2021 [26], meaning that the cost of m-DAC can also be expected to fit within the socially acceptable price range. This paper aimed to evaluate the technical aspects of m-DAC and exploring the required membrane performances, and the analysis of the cost performance was not the main purpose. In addition, a large number of scenarios concerning electricity should be considered for detailed techno-economic analysis, including not only operational expenses but also capital expenses. Therefore, we did not examine the cost aspect of m-DAC in this paper. The reported estimates of cost (energy) of other DAC technologies vary from 50 to 1000 $/t-CO 2 , and the most detailed report describes the DAC process used by Carbon Engineering Ltd. (CE) relying on CO 2 capture by strong bases (KOH) interacting with air through the plastic contactor. The levelized cost of CO 2 capture from 94 to 232 $/t-CO 2 was reported and was strongly dependent on financial assumptions and energy cost [13]. The CE design required 8.81 GJ of natural gas or 5.25 GJ of gas and 366 kWhr of electricity per t-CO 2 . Earlier studies of similar processes provided costlier estimates, namely, 610 and 780 $/t-CO 2 in optimistic and realistic scenarios, respectively, [5]. Another recent report provided an estimate of the energies required in solid adsorbent-based DAC varying from ca. 15 to 60 MJ/kg-CO 2 (4.5-17 kWhr/kg-CO 2 ) [12], and these energy requirements are similar to those described here for m-DAC.

Concluding remarks
In general, the DAC process has been considered in form of large-scale systems to process a vast amount of air efficiently. Although there is no question about deploying large and integrated systems for reducing the CO 2 concentration in the air, expensive initial costs and specific site conditions for the plant installation limit the rapid and massive deployment of DAC systems. To meet the recommendation from the IPCC for achieving the 1.5°C scenario, other approaches should be proposed as much as possible. In this context, membrane separation has several advantages compared to the conventional sorbent-based DAC process. Generally, membrane separation is considered the most energy-efficient technique for CO 2 separation among the various separation technologies. Moreover, this approach does not require special chemicals or sorbents for CO 2 capture. The greatest advantage is that membrane separation systems are scalable and can be installed in a variety of locations. These characteristics of membrane separation can enable m-DAC to be the most suitable technology for ubiquitous and ambient DAC. This uniqueness of m-DAC provides opportunities to capture CO 2 that have never been considered before. For example, the CO 2 concentration in the school classroom often exceeds more than 1000 ppm without ventilation since human beings emit CO 2 at a rate of 1 kg per person per day [27]. In such places of higher CO 2 concentrations, CO 2 capture by membranes becomes relatively efficient since the driving force of CO 2 is larger. Recently, Dittmeyer et al. discussed the potential of an air conditioner system with a CO 2 capture function [28]. Their argument is based on existing DAC technologies that use CO 2 absorption and adsorption. The energy cost of CO 2 recovery is still high and it is essentially identical to the large-scale system, and specific chemicals for CO 2 capture are required. This situation makes it difficult to introduce conventional systems into offices and private residences. Therefore, for a truly distributed and scalable DAC system, m-DAC would be the most suitable technology.
As discussed above, the permeance of CO 2 and selectivity toward other gases (N 2 , O 2 ) together with the process parameters (pressure ratio and stage cut) will define the degree of preconcentration and required energy in the m-DAC system. Membrane materials play a large role in capital investments, as the required membrane areas are relatively large. Therefore, the materials used should be suitable for thin-film fabrication. Considering the specific materials, thermally reversed polymers and polymers of intrinsic microporosity (PIMs) have shown superior CO 2 permeability, breaking the upper bound [29], but higher CO 2 selectivity is desired. Moreover, PIMs manifest accelerated physical aging when fabricated as submicronthick membranes [30]. By combining specific fillers and polymers, mixed-matrix membranes (MMMs) can reach both high CO 2 permeability and selectivity. However, for the m-DAC process to be practical, the permeance is the key parameter (not permeability), which leads to the requirement of~100 nm membrane thicknesses. Most MMMs cannot be fabricated at this thickness. Facilitated transport membranes are promising, especially for the first step of separation with a low concentration of CO 2 in the feed, but may lack performance in later stages where the CO 2 concentration is higher.
Although the target properties of membranes for m-DAC are challenging, recently, a thin-film composite membrane approach was used to improve the performance [30,31]. In this approach, the CO 2 selective thin layer is deposited on the highly gas-permeable support layer, the so-called gutter layer, and assembled on a porous support (Fig. 4). We believe it is promising to provide membranes for m-DAC because the layers are often made of versatile, low-cost polymers that can be fabricated with thicknesses of a few tens of nanometers without losing the performance [18], while the selectivity can be improved by surface modification [19]. Moreover, for m-DAC, it is important to study all materials that show promising bulk performance in the form of thin membranes or thin composites to determine whether the separation is influenced by the thickness and whether large-scale, mechanically stable membranes can be fabricated.
In addition, CO 2 /O 2 separation becomes important, especially for the CO 2 conversion process, since oxygen prevents efficient CO 2 reduction [32]. To the best of our knowledge, CO 2 /O 2 separation by membranes has rarely been addressed in the literature, and most previous research on membrane-based CO 2 separation was devoted to postcombustion capture (separation of CO 2 and N 2 ), precombustion capture (CO 2 and H 2 ), and natural gas sweetening (CO 2 and CH 4 ). Although much research is related to oxygen-enriching membranes, for example, that based on oxygen ion conductive materials, silicone-based polymers, or other organic polymers, most of the studies focus on O 2 separation over N 2 and do not report preferential CO 2 permeation over O 2 . All CO 2 capture technologies, including this m-DAC process, should be combined with successive processes to manage captured CO 2 . Chemical conversion is one of the major processes to circulate CO 2 as a carbon source. In the process of CO 2 conversion, it is chemically reduced to other value-added compounds, such as CO and CH 4 . O 2 inhibits the conversion of CO 2 to the corresponding reduced form since it is a strong oxidant. Therefore, the product gas from the m-DAC system should not only achieve a relevant concentration of CO 2 but also significantly reduce concentrations of O 2 , which emphasize the requirement of high CO 2 /O 2 selectivity, in addition to CO 2 /N 2 selectivity, although such a separation situation has never been considered.
As described above, the CO 2 capture process is one component of CCUS and thus the subsequent process after DAC by membranes should be considered carefully. The target performance of the membrane for DAC depends on the requirements in the subsequent utilization processes. The simplicity of membrane separation offers many opportunities to capture and utilize CO 2, and this versatile ability of the m-DAC process has great potential to establish a future sustainable and circular economy enabled by carbon recycling and negative carbon emissions. article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons. org/licenses/by/4.0/.