# Analysis of Technologies for Carbon Dioxide Capture from the Air
###### Abstract
Generally, the minimum required thermodynamic work can be evaluated by the difference in stream energies, but for isothermal and isobaric processes it can be obtained by the Gibbs free energy, as shown in the following equation and Figure 1 [28, 29, 30] (see Equation (1)):  
\[ \begin{split} W_{min}=RT\Big{(}N_{B}^{CO2}lny_{B}^{CO2}+N_{B}^{B- CO2}lny_{B}^{B-CO2}\Big{)}+RT\Big{(}N_{C}^{CO2}lny_{C}^{CO2}+N_{C}^{C-CO2}lny_{C}^{C- CO2}\Big{)}\\ -RT\Big{(}N_{A}^{CO2}lny_{A}^{CO2}+N_{A}^{A-CO2}lny_{A}^{A-CO2} \Big{)}\end{split}  \tag{1}\]  
where \(W_{min}\) is the minimum separation work in kJ/mol, \(R\) is the universal gas constant 8.314 J/(molK), \(T\) is the temperature in K, n\({}_{i}\)CO\({}_{2}\) are CO\({}_{2}\) moles in stream i, n\({}_{i}\)i\({}^{-\text{CO2}}\) are the other moles in current i without CO\({}_{2}\), y\({}_{i}\)CO\({}_{2}\) is the CO\({}_{2}\) mole fraction in current i and y\({}_{i}\)i\({}^{-\text{CO2}}\) is the mole fraction of the remaining gas without CO\({}_{2}\) in stream i. A first calculation shows that the minimum thermodynamic work needed to separate a stream with 400 ppm of CO\({}_{2}\) into one stream that is poor in CO\({}_{2}\) and a second stream that is mostly CO\({}_{2}\), with a purity of 99%, is 21.86 kJ/molCO\({}_{2}\), while if the feed has a CO\({}_{2}\) concentration of 12%, the minimum thermodynamic work is 7.58 kJ/molCO\({}_{2}\)[31]. Given  
Figure 1: Diagram of the CO\({}_{2}\) separation process: CO\({}_{2}\) in the feed stream A is removed, resulting in a product stream B with more CO\({}_{2}\) and a product stream C with a small amount of CO\({}_{2}\). Reproduced with permission from [30]. this energy difference, it is preferred to capture CO\({}_{2}\) from a concentrated point instead of atmospheric air. [PERSON] et al. [32] evaluated the minimum thermodynamic work required to separate CO\({}_{2}\) from the air, natural gas combined cycle flue gas and pulverized coal combustion flue gas. The results are reported in Figure 2 as a function of CO\({}_{2}\) recovery and purity. From Figure 2, it is evident that the minimum thermodynamic work for CO\({}_{2}\) separation from the air is greater than its separation from flue gas, achieving values higher than 20 kJ/molCO\({}_{2}\) for higher CO\({}_{2}\) purities and recoveries. Only for CO\({}_{2}\) purities and CO\({}_{2}\) recoveries lower than 10% and 60%, respectively, is the minimum work for DAC in a range between 8 and 10 kJ/molCO\({}_{2}\), similar to that required for CO\({}_{2}\) separation from power plant flue gas with 90% recovery and 95% purity. With a higher amount of work required, a higher cost defines DAC systems in comparison with the traditional ones, as has been shown with a Sherwood plot, with costs reported as a function of dilution factor [29]. The Sherwood plot showed that new technologies can have costs 100 times higher than traditional post-combustion capture. However, a deeper economic analysis showed for the near term (within the next 25 years) an optimistic value for DAC costs of approximately 100 $/ton of CO\({}_{2}\). The pessimistic value was approximately 550 $/tonCO\({}_{2}\), while the median value was approximately 200 $/tonCO\({}_{2}\)[33]. Studies in the literature works have mainly been concerned with feasibility analysis of DAC systems, with economic and energetic analyses being undertaken especially for adsorption and absorption [34; 35; 36; 37], while the other technologies introduced above require more studies and investigations [22; 23; 24; 25; 26; 28; 29; 38; 40]. This present work aims to provide an interesting and cutting-edge review through a careful analysis of all the DAC systems suggested in the literature. Moreover, after a description and revision of these, attention is focused on DAC companies and key performance indicators (KPIs) in addition to social concerns about this emerging technology.