Moving beyond 90% Carbon Capture by Highly Selective Membrane Processes

A membrane-based system with a retentate recycle process in tandem with an enriching cascade was studied for >90% carbon capture from coal flue gas. A highly CO2-selective facilitated transport membrane (FTM) was utilized particularly to enhance the CO2 separation efficiency from the CO2-lean gases for a high capture degree. A techno-economic analysis showed that the retentate recycle process was advantageous for ≤90% capture owing to the reduced parasitic energy consumption and membrane area. At >90% capture, the enriching cascade outperformed the retentate recycle process since a higher feed-to-permeate pressure ratio could be applied. An overall 99% capture degree could be achieved by combining the two processes, which yielded a low capture cost of USD47.2/tonne, whereas that would be USD 42.0/tonne for 90% capture. This FTM-based approach for deep carbon capture and storage can direct air capture for the mitigation of carbon emissions in the energy sector.


Introduction
In the past two decades, methods to accelerate the decarbonization of the energy sector have been extensively investigated in order to limit the impact of global warming [1]. The removal of CO 2 from fossil fuel combustion and the subsequent underground storage, commonly known as carbon capture and storage (CCS), is regarded as one of the most reliable and affordable options [2]. In this context, a target of "90% capture" has become ubiquitous not only in academic studies [3], but also in sustainability policies [4,5]. However, residual emissions still escape from the capture system, which need to be captured by "negative emissions" technologies such as direct air capture (DAC) [6] and bioenergy with carbon capture and storage (BECCS) [7]. Compared with carbon capture from large stationary sources, the negative emissions technologies often involve the separation or bioconversion of CO 2 from air; nevertheless, the low CO 2 concentration (ca. 410 ppm) requires energyintensive separation systems with sizable footprints, which, in turn, exacerbate the energy sustainability [8][9][10].
Alternatively, a deep CCS concept with >90% capture has been proposed as a necessary pathway to decarbonize the power generations [11]. This scheme aims for a higher degree of CO 2 removal so that the CO 2 concentration in the exhaust flue gas approaches to that in air. For instance, coal flue gases typically contain ca. 13% CO 2 [12,13], and residual emissions with 1-2% CO 2 can slip through the capture system after 90% CO 2 removal. If the capture is increased to 99%, the CO 2 concentration in the resultant residual flue gas can be reduced to 0.1-0.2%. In order to achieve a carbon-neutral scenario, 99.7% of the CO 2 must be captured. To distinguish from negative emissions technologies, methods capable of >90% capture from stationary sources are usually referred to as "near-zero emissions" technologies. Figure 1 shows the schematic of the primary and secondary membrane systems for >90% CO 2 capture. The supercritical coal-fired power plant produces a flue gas containing 13.2% CO 2 with particulate matter filtered by a baghouse collector and SO 2 removed down to ca. 40 ppm by a flue gas desulfurization (FGD) unit. The SO 2 is polished down to 3 ppm by an SO 2 caustic scrubber (SCS) containing an aqueous solution of 20 wt.% NaOH. The flue gas is then first treated by the primary capture system aiming for 90% capture. The primary system features a two-stage process, with retentate recycle at the first stage, proposed in our previous work [32]. The flue gas is pressurized by blower BL-01 and enriched by the first membrane stage MB-01. After the energy recovery by the turboexpander EX-01, the CO 2 -depleted but N 2 -rich retentate is partially recycled to the permeate side as an internal sweep gas. The MB-01 permeate is repressurized by blower BL-02 and fed to the second membrane stage MB-02 with a permeate vacuum VAC-01, which further enriches the CO 2 to ≥95% purity (dry basis). The retentate of MB-02 is recycled back to the feed side of MB-01.  The residual emissions from the primary capture system typically contain ca. 1.8% CO2. Should it be further decarbonized, a two-stage enriching cascade detailed in our previous publication [38] is used as the secondary capture system. In this case, the majority of MB-01 retentate is not expanded and is sent to the secondary capture system directly. Rather, only the portion used as the retentate recycle for MB-01 is expanded as shown in Figure 1. In the secondary capture system, another blower BL-03 further elevates the feed pressure for the enriching membrane stage MB-03. A vacuum VAC-02 is pulled on the permeate side in order to provide a higher transmembrane driving force. If the secondary system aims for 90% capture (i.e., 99% capture from the combined primary and secondary systems), the CO2 concentration in the MB-03 retentate can be reduced to ca. 0.18%, which is expanded by turboexpander EX-02. The permeate is compressed by blower BL-04 and further enriched to ≥95% purity by membrane stage MB-04. The MB-04 retentate is recycled back to the MB-03 feed.
Not shown in Figure 1 are the interstage cooling and heat integration of the blowers. One example is given by Figure 2, where the designs of the rotating equipment associated with MB-01 and MB-02 are detailed for capture using the primary system only. As shown, both BL-01 and EX-01 are split into two stages with interstage cooling and heating, respectively, in order to avoid excessive gas heating and to reduce the energy consumption. The expanded MB-01 retentate is used for the interstage cooling in BL-01, which reduces the cooling water demand of the capture system. Although BL-02 must involve water cooling, the heat duty is much less than that of BL-01 due to the much lower gas flow rate. A similar design principle is applied to the combined systems in tandem. Recall that EX-01 only expands the recycled retentate, and the remaining high-pressure retentate exiting MB-01 is mildly compressed by BL-03 and eventually expanded by EX-02. The expanded retentate in EX-02 is heat exchanged with BL-01 and BL-03 subsequently. Water cooling is used for BL-04 similar to that of BL-02. The residual emissions from the primary capture system typically contain ca. 1.8% CO 2 . Should it be further decarbonized, a two-stage enriching cascade detailed in our previous publication [38] is used as the secondary capture system. In this case, the majority of MB-01 retentate is not expanded and is sent to the secondary capture system directly. Rather, only the portion used as the retentate recycle for MB-01 is expanded as shown in Figure 1. In the secondary capture system, another blower BL-03 further elevates the feed pressure for the enriching membrane stage MB-03. A vacuum VAC-02 is pulled on the permeate side in order to provide a higher transmembrane driving force. If the secondary system aims for 90% capture (i.e., 99% capture from the combined primary and secondary systems), the CO 2 concentration in the MB-03 retentate can be reduced to ca. 0.18%, which is expanded by turboexpander EX-02. The permeate is compressed by blower BL-04 and further enriched to ≥95% purity by membrane stage MB-04. The MB-04 retentate is recycled back to the MB-03 feed.
Not shown in Figure 1 are the interstage cooling and heat integration of the blowers. One example is given by Figure 2, where the designs of the rotating equipment associated with MB-01 and MB-02 are detailed for capture using the primary system only. As shown, both BL-01 and EX-01 are split into two stages with interstage cooling and heating, respectively, in order to avoid excessive gas heating and to reduce the energy consumption. The expanded MB-01 retentate is used for the interstage cooling in BL-01, which reduces the cooling water demand of the capture system. Although BL-02 must involve water cooling, the heat duty is much less than that of BL-01 due to the much lower gas flow rate. A similar design principle is applied to the combined systems in tandem. Recall that EX-01 only expands the recycled retentate, and the remaining high-pressure retentate exiting MB-01 is mildly compressed by BL-03 and eventually expanded by EX-02. The expanded retentate in EX-02 is heat exchanged with BL-01 and BL-03 subsequently. Water cooling is used for BL-04 similar to that of BL-02.

FTM Modeling
It is known that the performance of an FTM depends on the CO2 partial pressure. Often, the CO2 permeance and CO2/N2 selectivity increases with the reduction in the partial pressure of CO2 due to the mitigated carrier saturation [32,33,37]. A homogeneous reactive diffusion model is used to describe the composition-dependent CO2 permeation [32]: where is the CO2 permeance in a unit of GPU (1 GPU = 10 -6 cm 3 (STP) cm -2 s -1 cmHg -1 ), is the permeance at full carrier saturation, is the effective factor of facilitated transport, * is the onset carrier saturation partial pressure, and is the CO2 partial pressure on the feed side. The N2 permeance ( ) is assumed as a constant; therefore, the ideal CO2/N2 selectivity at full carrier saturation is defined as = .
Equation (1) implies that the local feed CO2 partial pressure dictates the CO2 permeance. Therefore, the CO2 permeance must be treated as a variable in the module modeling. Such a treatment has been detailed by the countercurrent and crossflow models

FTM Modeling
It is known that the performance of an FTM depends on the CO 2 partial pressure. Often, the CO 2 permeance and CO 2 /N 2 selectivity increases with the reduction in the partial pressure of CO 2 due to the mitigated carrier saturation [32,33,37]. A homogeneous reactive diffusion model is used to describe the composition-dependent CO 2 permeation [32]: where P CO 2 is the CO 2 permeance in a unit of GPU (1 GPU = 10 -6 cm 3 (STP) cm -2 s -1 cmHg -1 ), P 0 CO 2 is the permeance at full carrier saturation, η CO 2 is the effective factor of facilitated transport, p * CO 2 is the onset carrier saturation partial pressure, and p h CO 2 is the CO 2 partial pressure on the feed side. The N 2 permeance (P N 2 ) is assumed as a constant; therefore, the ideal CO 2 /N 2 selectivity at full carrier saturation is defined as α 0 = P 0 CO 2 /P N 2 . Equation (1) implies that the local feed CO 2 partial pressure dictates the CO 2 permeance. Therefore, the CO 2 permeance must be treated as a variable in the module modeling. Such a treatment has been detailed by the countercurrent and crossflow models developed in our previous work [32,40]. In this study, the countercurrent model was used for MB-01 while the crossflow model was employed for MB-02, MB-03, and MB-04.

Process Modeling
The operating conditions for the power plant, the primary and secondary membrane capture systems, and the benchmark FTM are listed in Table 1. Case B5A in the Cost and Performance Baseline for Fossil Energy Plants Volume 1: Bituminous Coal and Natural Gas to Electricity (Revision 4, 2019) [5] was used as the reference power plant with a net power of 650 MW e . The facilitated transport characteristics of the benchmark FTM were obtained by fitting the experimental data [38] using Equation (1), which will be further discussed in Section 3.1. For conciseness, the readers are referred to our previous publications for the detailed equipment schedules of the retentate recycle process [32] and the enriching cascade process [38]. All process simulations were performed using a MATLAB code developed in house with the Soave-Redlich-Kwong equation as the thermodynamic model for process streams [41,42]. Unless otherwise noted, the conditions summarized in Table 1 were used as the default. 7.5 kPa † The residual flue gas is fully saturated with water vapor at 67 • C and 354.6 kPa (3.5 atm). It is then compressed by BL-03 and a minor amount of water is knocked out during the compression. ‡ Default operating conditions. * A lower heat transfer coefficient is assigned when the expanded retentate gas is used as the coolant in comparison with cooling water [43].

Costing Modeling
Case B5B in the Performance Baseline [5] was followed for the cost modeling. The detailed costing procedures have been reported in our previous publications [32,38]. All costs are reported in 2018 US. Dollars (USD). The key assumptions are as follows: 1.
An installed membrane skid cost of USD 44.6/m 2 membrane area was assigned, including USD 21.5/m 2 membrane element cost, USD 5.4/m 2 housing cost, and 17.7/m 2 installation cost, based on commercial-scale reverse osmosis plants [44]; 2.
A membrane lifetime of 4 years was assumed with a membrane replacement cost of USD 5.4/m 2 /yr; 3.
A capital charge factor of 0.125 was applied to calculate the capital cost [5].

Performance of the Benchmark FTM
The mitigated carrier saturation of the benchmark FTM is illustrated in Figure 3. The CO 2 permeances and CO 2 /N 2 selectivities at different feed CO 2 partial pressure values were reported by Han and Ho [38]. Equation (1) was used to fit the experimental data, and the fitting parameters, as listed in Table 1, were used for the process simulations. The benchmark FTM exhibited clear uprising trends of CO 2 permeance and CO 2 /N 2 selectivity with reductions in CO 2 partial pressure. In other words, the CO 2 separation became more selective upon the CO 2 removal in the membrane module. An onset saturation pressure (p * CO 2 ) of 7.5 kPa was obtained. This value was close to the CO 2 partial pressure in the residual flue gas from the primary capture system (90% capture and 354.6 kPa (3.5 atm) feed pressure as in Table 1). Consequently, the secondary capture system could be considerably more selective than the primary one, which was well-suited to treat the dilute CO 2 gas. For instance, with a partial pressure reduction from 38 to 7.5 kPa, the permeance increased from 1473 to 1684 GPU and the selectivity increased from 186 to 217. At a further reduced partial pressure of 0.4 kPa, the FTM showed an even greater permeance of 3832 GPU with a high selectivity of 472.
Membranes 2022, 12, x FOR PEER REVIEW 6 of 13 2. A membrane lifetime of 4 years was assumed with a membrane replacement cost of USD 5.4/m 2 /yr; 3. A capital charge factor of 0.125 was applied to calculate the capital cost [5].

Performance of the Benchmark FTM
The mitigated carrier saturation of the benchmark FTM is illustrated in Figure 3. The CO2 permeances and CO2/N2 selectivities at different feed CO2 partial pressure values were reported by Han and Ho [38]. Equation (1) was used to fit the experimental data, and the fitting parameters, as listed in Table 1, were used for the process simulations. The benchmark FTM exhibited clear uprising trends of CO2 permeance and CO2/N2 selectivity with reductions in CO2 partial pressure. In other words, the CO2 separation became more selective upon the CO2 removal in the membrane module. An onset saturation pressure ( * ) of 7.5 kPa was obtained. This value was close to the CO2 partial pressure in the residual flue gas from the primary capture system (90% capture and 354.6 kPa (3.5 atm) feed pressure as in Table 1). Consequently, the secondary capture system could be considerably more selective than the primary one, which was well-suited to treat the dilute CO2 gas. For instance, with a partial pressure reduction from 38 to 7.5 kPa, the permeance increased from 1473 to 1684 GPU and the selectivity increased from 186 to 217. At a further reduced partial pressure of 0.4 kPa, the FTM showed an even greater permeance of 3832 GPU with a high selectivity of 472.

Effect of Retentate Recycle
In principle, the two-stage enriching cascade (see Figure 1) could be used for the primary carbon capture (i.e., removing 90% CO2 from the flue gas) [45,46]. Our recent work has also shown that it can achieve an overall 99% capture degree. Therefore, the necessity of the combined primary and secondary capture systems pivots on whether the retentate recycle process is more cost-effective for ca. 90% carbon capture. To this end, the CO2/N2 separation performance of the retentate recycle process was studied for 85-95% capture degrees. As one of the most important operating parameters, the percentage of the retentate recycle ( ) varied between 0 and20%. At = 0, the retentate recycle process reduced to the two-stage enriching cascade. Based on the process optimization conducted in our . Increasing CO 2 permeance and CO 2 /N 2 selectivity with a decreasing partial pressure of the CO 2 of the benchmark FTM as reported by Han and Ho [38]. The best fits and uncertainties based on Equation (1) are shown as solid lines and blue shades, respectively.

Effect of Retentate Recycle
In principle, the two-stage enriching cascade (see Figure 1) could be used for the primary carbon capture (i.e., removing 90% CO 2 from the flue gas) [45,46]. Our recent work has also shown that it can achieve an overall 99% capture degree. Therefore, the necessity of the combined primary and secondary capture systems pivots on whether the retentate recycle process is more cost-effective for ca. 90% carbon capture. To this end, the CO 2 /N 2 separation performance of the retentate recycle process was studied for 85-95% capture degrees. As one of the most important operating parameters, the percentage of the retentate recycle (X r ) varied between 0 and20%. At X r = 0, the retentate recycle process reduced to the two-stage enriching cascade. Based on the process optimization conducted in our previous work [32,38], a feed pressure (p h ) of 354.6 kPa (3.5 atm) was used for both MB-01 and MB-02, while a permeate pressure (p l ) of 81.0 kPa (0.8 atm) was applied to MB-02. All results presented in this section had a CO 2 purity ≥95% through the primary capture system.
where A 0 is the membrane area and n h A=0 the feed molar flow rate. The N 2 permeation, or N 2 loss, is defined as the percentage of N 2 in the flue gas that permeates through MB-01 to the permeate side instead of through the retentate recycle. This value, in part, reflects the parasitic energy consumption of the retentate recycle process, or how much the compression energy of BL-01 can be recovered by EX-01. The flue gas (mainly N 2 ) is pressurized to 354.6 kPa (3.5 atm) through the work of BL-01. With the thermal expansion in EX-01, the thermodynamic availability (i.e., work potential) carried by the N 2 in the retentate can be recovered. However, the portion of the N 2 that permeates through the membrane to the low-pressure side cannot be utilized for energy recovery. Consequently, the parasitic energy is adversely related to the N 2 loss. As shown in Figure 4a, at a given capture degree, the N 2 loss reduced considerably with increasing X r . Therefore, the retentate recycle process (i.e., X r > 0) is advantageous over the enriching cascade (i.e., X r = 0) in terms of energy efficiency for treating the flue gas. For a fixed X r , however, a higher N 2 loss was observed at a higher capture. Therefore, the optimal X r value (based on the minimized capture cost) increased with the increasing capture as depicted by the solid lines in Figure 4. previous work [32,38], a feed pressure ( ) of 354.6 kPa (3.5 atm) was used for both MB-01 and MB-02, while a permeate pressure ( ) of 81.0 kPa (0.8 atm) was applied to MB-02. All results presented in this section had a CO2 purity ≥95% through the primary capture system. Figure 4 shows the percentage of N2 permeated through MB-01, the CO2 concentration of MB-02 feed, and the normalized membrane area ( = [32]) of MB-01, where is the membrane area and the feed molar flow rate. The N2 permeation, or N2 loss, is defined as the percentage of N2 in the flue gas that permeates through MB-01 to the permeate side instead of through the retentate recycle. This value, in part, reflects the parasitic energy consumption of the retentate recycle process, or how much the compression energy of BL-01 can be recovered by EX-01. The flue gas (mainly N2) is pressurized to 354.6 kPa (3.5 atm) through the work of BL-01. With the thermal expansion in EX-01, the thermodynamic availability (i.e., work potential) carried by the N2 in the retentate can be recovered. However, the portion of the N2 that permeates through the membrane to the low-pressure side cannot be utilized for energy recovery. Consequently, the parasitic energy is adversely related to the N2 loss. As shown in Figure 4a, at a given capture degree, the N2 loss reduced considerably with increasing . Therefore, the retentate recycle process (i.e., > 0) is advantageous over the enriching cascade (i.e., = 0) in terms of energy efficiency for treating the flue gas. For a fixed , however, a higher N2 loss was observed at a higher capture. Therefore, the optimal value (based on the minimized capture cost) increased with the increasing capture as depicted by the solid lines in Figure 4. It is worth noting that a proper amount of retentate recycle retards the N2 permeation but does not dilute the CO2 fed to MB-02. As seen in Figure 4b, the retentate recycle slightly increased the MB-2 feed CO2 concentration vs. the case with = 0, and it remained undiluted until the value was much higher than the optimal. Therefore, the separation performance of MB-02 was not adversely affected by the retentate recycle. Another feature exemplified in Figure 4b is that the optimal curve coincided with the second inflection points of the concentration isolines on the capture-plane. Therefore, the optimized system should possess the lowest possible N2 loss but not at the expense of the dilution of the MB-02 feed. It is worth noting that a proper amount of retentate recycle retards the N 2 permeation but does not dilute the CO 2 fed to MB-02. As seen in Figure 4b, the retentate recycle slightly increased the MB-2 feed CO 2 concentration vs. the case with X r = 0, and it remained undiluted until the X r value was much higher than the optimal. Therefore, the separation performance of MB-02 was not adversely affected by the retentate recycle. Another feature exemplified in Figure 4b is that the optimal X r curve coincided with the second inflection points of the concentration isolines on the capture-X r plane. Therefore, the optimized system should possess the lowest possible N 2 loss but not at the expense of the dilution of the MB-02 feed.
Although a proper retentate recycle did not change the CO 2 concentration at the permeate outlet of MB-01, the internally recycled N 2 -rich effectively altered the permeate side flow pattern from the crossflow to the countercurrent, which particularly lowered the permeate CO 2 concentration near the sweep inlet. Consequently, the retentate recycle drastically reduced the MB-01 membrane area as shown in Figure 4c. For instance, at 90% capture, the s 0 reduced by ca. three times after increasing X r from 0 to 15%.

Costs at Different Capture Degrees
The analysis in Figure 4 clearly shows that the retentate recycle process is superior to the enriching cascade for ca. 90% capture. However, the optimal X r curve tended to flatten out at a high CO 2 capture degree. Increasing the capture from 90 to 95% led to ca. 22% more N 2 loss and 7% less CO 2 to MB-02 as feed, and more importantly, a 30% increase in the membrane area. The deteriorated energy efficiency and the more capital-intensive system resulted in a drastically increased capture cost beyond 90% capture. As illustrated in Figure 5, the capture cost increased from USD 42.0/tonne to USD 76.5/tonne when the capture degree was increased from 90 to 95%. At 97% capture, a prohibitively high capture cost of USD 111.6/tonne was observed even with retentate recycle.
the membrane area. The deteriorated energy efficiency and the more capital-intensive system resulted in a drastically increased capture cost beyond 90% capture. As illustrated in Figure 5, the capture cost increased from USD 42.0/tonne to USD 76.5/tonne when the capture degree was increased from 90 to 95%. At 97% capture, a prohibitively high capture cost of USD 111.6/tonne was observed even with retentate recycle.
The above results indicate that a higher transmembrane driving force is needed for a capture degree greater than 90%. Such an effect was demonstrated by setting = 0 and pulling a vacuum of 20.3 kPa (0.2 atm) on the permeate side of MB-01. Effectively, this system is equivalent to an enriching cascade with a feed-to-permeate pressure ratio ( = ⁄ ) of 17.5. The capture costs at different CO2 capture degrees were calculated for this system and the results are also shown in Figure 5. As expected, this system was not as competitive as the retentate recycle process at a lower capture degree of <95%. However, its capture cost did not increase as drastically on the high capture end, resulting in lower capture costs for >95% capture. For instance, a capture cost of USD 81.6/tonne was attained at 97% capture, and a further increase to 99% capture only led to a capture cost of USD 93.8/tonne. Apparently, the transmembrane driving force should be optimized based on the range of capture degrees. This observation motivated the use of the combined primary and secondary capture systems in tandem.  The above results indicate that a higher transmembrane driving force is needed for a capture degree greater than 90%. Such an effect was demonstrated by setting X r = 0 and pulling a vacuum of 20.3 kPa (0.2 atm) on the permeate side of MB-01. Effectively, this system is equivalent to an enriching cascade with a feed-to-permeate pressure ratio (γ = p h /p l ) of 17.5. The capture costs at different CO 2 capture degrees were calculated for this system and the results are also shown in Figure 5. As expected, this system was not as competitive as the retentate recycle process at a lower capture degree of <95%. However, its capture cost did not increase as drastically on the high capture end, resulting in lower capture costs for >95% capture. For instance, a capture cost of USD 81.6/tonne was attained at 97% capture, and a further increase to 99% capture only led to a capture cost of USD 93.8/tonne. Apparently, the transmembrane driving force should be optimized based on the range of capture degrees. This observation motivated the use of the combined primary and secondary capture systems in tandem.

Separation Performance of the Secondary System
The separation performance of the secondary system was studied by assuming that 90% of the CO 2 from the flue gas had been removed by the primary capture system with X r = 15% (see Table 1). In order to analyze the separation performance of the secondary system for treating the residual flue gas (1.85% CO 2 ), the permeate CO 2 purity and the dimensionless area of MB-03 were calculated for capture degrees of 50-90% and γ values of 10-25. The γ value was adjusted by varying the p h between 202.6 and 506.5 kPa (2 and Membranes 2022, 12, 399 9 of 13 5 atm) while maintaining the p l at 20.3 kPa (0.2 atm). Combined with the 90% capture from the primary system, the overall capture, therefore, was 95-99%. Figure 6a shows the calculated CO 2 purities (dry basis) in the MB-03 permeate; the uncolored region represents the cases where ≥95% purity in the final CO 2 product was unattainable. At a given capture degree, the MB-03 purity increased with increasing γ. In order to achieve 90% capture in the secondary system, the minimum γ required was ca. 16.5. In comparison, MB-01 in the primary system only employed a γ of 3.5, which further emphasized the different compression requirements of the two systems. In general, the residual flue gas could be enriched by MB-03 up to 40-50% at 50% capture, and the CO 2 purity was at best ca. 20% at 90% capture. Nevertheless, the ≥20% CO 2 stream fed as the feed to MB-04 yielded a permeate with >95% CO 2 . The limited driving force at high capture also affected the membrane area of MB-03. As shown in Figure 6b, a drastic increase in s 0 (i.e., denser, lighter isolines) was observed when the capture approached 90%. Even at γ = 25, increasing the capture from 50 to 90% led to a 7-time increase in the membrane area.
The separation performance of the secondary system was studied by assuming that 90% of the CO2 from the flue gas had been removed by the primary capture system with = 15% (see Table 1). In order to analyze the separation performance of the secondary system for treating the residual flue gas (1.85% CO2), the permeate CO2 purity and the dimensionless area of MB-03 were calculated for capture degrees of 50-90% and values of 10-25. The value was adjusted by varying the between 202.6 and 506.5 kPa (2 and 5 atm) while maintaining the at 20.3 kPa (0.2 atm). Combined with the 90% capture from the primary system, the overall capture, therefore, was 95-99%. Figure 6a shows the calculated CO2 purities (dry basis) in the MB-03 permeate; the uncolored region represents the cases where ≥95% purity in the final CO2 product was unattainable. At a given capture degree, the MB-03 purity increased with increasing . In order to achieve 90% capture in the secondary system, the minimum required was ca. 16.5. In comparison, MB-01 in the primary system only employed a of 3.5, which further emphasized the different compression requirements of the two systems. In general, the residual flue gas could be enriched by MB-03 up to 40-50% at 50% capture, and the CO2 purity was at best ca. 20% at 90% capture. Nevertheless, the ≥20% CO2 stream fed as the feed to MB-04 yielded a permeate with >95% CO2. The limited driving force at high capture also affected the membrane area of MB-03. As shown in Figure 6b, a drastic increase in (i.e., denser, lighter isolines) was observed when the capture approached 90%. Even at = 25, increasing the capture from 50 to 90% led to a 7-time increase in the membrane area. Figure 6. Effects of CO2 capture degree and feed-to-permeate pressure ratio ( ) on (a) the permeate CO2 purity (dry basis) and (b) dimensionless area ( ) of MB-03 in the secondary capture system. The uncolored represents the regions where ≥95% purity in the final CO2 product is unattainable.

Process Economics
The results in Figure 6 are consistent with our previous study on the enriching cascade [38], where a ≥ 22.5 (i.e., ≥ 4.5) is required for MB-03, especially at 90% capture. Despite the stringent operating conditions, the compression requirement of BL-03 could be significantly lower than that of BL-01 since the residual flue gas (i.e., the MB-01 retentate that is not recycled) was not expanded and thus delivered to the secondary system at Figure 6. Effects of CO 2 capture degree and feed-to-permeate pressure ratio (γ) on (a) the permeate CO 2 purity (dry basis) and (b) dimensionless area (s 0 ) of MB-03 in the secondary capture system. The uncolored represents the regions where ≥95% purity in the final CO 2 product is unattainable.

Process Economics
The results in Figure 6 are consistent with our previous study on the enriching cascade [38], where a γ ≥ 22.5 (i.e., p h ≥ 4.5) is required for MB-03, especially at 90% capture. Despite the stringent operating conditions, the compression requirement of BL-03 could be significantly lower than that of BL-01 since the residual flue gas (i.e., the MB-01 retentate that is not recycled) was not expanded and thus delivered to the secondary system at 354.6 kPa (3.5 atm). Therefore, the compression ratio of BL-03 was reduced to 1.28, which could be achieved by a single-stage compression. In this regard, it is more advantageous for the secondary membrane system to be used in tandem with a membrane-based, pressure-driven primary system than other temperature-swing technologies such as solvents or sorbents.
The process economics of the combined process with the primary and secondary systems in tandem are shown in comparison with the primary system only in Figure 7a. The primary system with the retentate recycle process was used alone mainly for ≤90% capture, while the combined process was used for >90% capture. As seen, the combined process only led to a less pronounced cost increase from USD 42.0/tonne at 90% capture to USD 47.2/tonne at 99% capture. The 12% cost increase was significantly lower than using the primary system only throughout this range of capture, which makes the combined process attractive for deep CCS.
the secondary system. At 90% capture, the marginal cost of the primary system was already as high as USD 1.8/tonne/%. Switching to the secondary system for the residual flue gas effectively reduced the marginal cost to <USD 0.1/tonne/%, which accounted for the significantly reduced overall capture cost. Even at 99% capture, the marginal cost was only USD 1.6/tonne/%. In comparison, our previous study showed a higher marginal cost of USD 8.9/tonne/% at 99% capture by using the secondary system alone [38]. This difference mainly stems from the relaxed compression ratio of BL-03 while in tandem with the primary system. Figure 7b also illustrates the relative scales of CO2 captured by the primary and secondary systems. At 99% capture, the marginal costs incurred by the secondary system only accounted for ca. 10% of the total CO2 captured. Therefore, the capture cost was less sensitive to the marginal cost of the secondary system.  It is worth noting that it was difficult to clearly discern the relative contributions of the primary and secondary systems to the capture cost because of the relocation of EX-01 and the shared use of EX-02. Instead of a guesstimate approach, we calculated the marginal cost in a similar fashion as Brandl et al. [14]: where C and θ are the capture cost and overall capture degree, respectively. Figure 7b shows the marginal costs of the combined systems plotted against the CO 2 captured annually from the reference power plant as shown in Table 1. As seen, two distinct branches of marginal costs were observed with a crossover around 90% capture. Therefore, we assigned the left branch (blue color) to the primary system and the right one (red color) to the secondary system. At 90% capture, the marginal cost of the primary system was already as high as USD 1.8/tonne/%. Switching to the secondary system for the residual flue gas effectively reduced the marginal cost to <USD 0.1/tonne/%, which accounted for the significantly reduced overall capture cost. Even at 99% capture, the marginal cost was only USD 1.6/tonne/%. In comparison, our previous study showed a higher marginal cost of USD 8.9/tonne/% at 99% capture by using the secondary system alone [38]. This difference mainly stems from the relaxed compression ratio of BL-03 while in tandem with the primary system. Figure 7b also illustrates the relative scales of CO 2 captured by the primary and secondary systems. At 99% capture, the marginal costs incurred by the secondary system only accounted for ca. 10% of the total CO 2 captured. Therefore, the capture cost was less sensitive to the marginal cost of the secondary system. Lastly, the importance of beyond 90% capture was demonstrated by a comparison with DAC. The marginal cost analysis suggested only a slight increase in capture cost by increasing the capture from 90 to 95%. Even for the extreme case where the capture increased from 98 to 99%, an additional capture cost of USD 1.6/tonne was needed, which was considerably lower than the USD 150-200/tonne for DAC [8,47,48]. Consequently, the deep CCS scheme in large stationary sources is useful to DAC for mitigating the carbon emissions in the energy sector.