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Energies 2021, 14, 3582 10 of 15 based on the settings of the maximum CO2 purity, maximum CO2 recovery, and minimum energy consumption. Table 8. Operating parameters. Variables. A: Feed pressure (atm) B: Vacuum pressure (atm) C: Vent pressure (atm) D: Surrounding temperature (K) E: Step 1/4/7 (cocurrent depressurization) time (s) F: Step 2/5/8 (vacuum) time (s) G: Bed length (m) - 0 + 2.0 3.0 4.0 0.05 0.075 0.1 0.2 0.3 0.4 288.14 305.64 40 80 120 250 300 350 0.3 0.4 0.5 Equations (7)–(9) present the regression equations for the bottom product CO2 purity, bottom product CO2 recovery, and energy consumption, respectively, which can be used for optimization. The coefficient multiplied by each factor is the regression coefficient, and the factor multiplication term indicates the interaction between the two factors. When the coefficient is large, the effect of this term on the response value is significant. In Figure 8, the red line represents the optimal values of the seven variables. Moreover, these optimal values are provided as inputs to the simulation program to compare the results. The optimization results using the setting value from Figure 8 are presented in Tables 9 and 10. Purity (%) = 208.683 + 8.44694 (1/atm) A − 136.4 (1/atm) B − 10.6067 (1/atm) C − 1.03797 (1/K) D + 0.254009 (1/s) E + 0.0168206 (1/s) F + 0.753353 (1/cm) G − 1.11434 (1/atm2) A · A + 303.611 (1/atm2) B · B − 14.7843 (1/atm3) C · C + 0.00176753 (1/K2) D · D − 0.00158675 (1/s2) E · E + 0.0001 (1/s2) F · F + 0.000643 (1/cm2) G · G − 0.31307 (1/atm2) A · B + 12.9433 (1/atm2) A · C + 0.000388 (1/atm·K) A · D + 0.015792 (1/atm · s) A · E + 0.00384 (1/atm · s) A · F − 0.08853 (1/atm · cm) A · G − 45.2696 (1/atm2) B · C + 0.436755 (1/atm · K) B · D + 0.499657 (1/atm · s) B · E − 0.239613 (1/atm · s) B · F − 0.862748 (1/atm · cm) B · G − 0.0234598 (1/atm · K) C · D − 0.323612 (1/atm · s) C · E − 0.0206273 (1/atm · s) C · F + 0.103386 (1/atm · cm) C · G + 0.0004568 (1/K · s) D · E −4.61·10−5 (1/K·s)D·F−0.00292673(1/K·cm)D·G−1.59·10−4 (1/s2)E·F +0.00148013(1/s·cm)E·G−2.7·10−4 (1/s·cm)F·G Recovery (%) = −54.8248 + 5.70294 (1/atm) A − 290.665 (1/atm) B − 1.79674 (1/atm) C + 0.949833 (1/K) D − 0.100019 (1/s) E − 0.0570018 (1/s) F − 1.02886 (1/cm) G − 1.816 (1/atm2) A · A − 1406.76 (1/atm2) B · B − 29.2673 (1/atm2) C · C − 0.0016378 (1/K2) D · D − 1.65144·10−5 (1/s2)E·E−2.19·10−4 (1/s2)F·F−0.0115602(1/cm2)G·G + 95.1987 (1/atm2) A · B − 4.91901 (1/atm2) A · C − 0.001048 (1/atm·K) A · D − 0.0285889 (1/atm · s) A · E − 0.00544839 (1/atm · s) A · F + 0.186206 (1/atm · cm) A · G + 163.14 (1/atm2) B · C − 0.403525 (1/atm · K) B · D − 0.9026 (1/atm · s) B · E − 0.269244 (1/atm · s) B · F + 3.48384 (1/atm · cm) B · G − 0.0252969 (1/atm · K) C · D + 0.240571 (1/atm · s) C · E + 0.0666479 (1/atm · s) C · F + 0.135799 (1/atm · cm) C · G + 7.99·10−5 (1/K·s)D·E+1.60842·10−4 (1/K·s)D·F+ 0.00265063 (1/K · cm) D · G − 1.21 · 10−4 (1/s2) E · F + 0.0029009 (1/s · cm) E · G + 0.0012076 (1/s · cm) F · G (7) 323.14 (8)PDF Image | CO2 captured from flue gas using the PSA process
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