## 3 Model Development
### Steady-State Model Development
#### 3.2.4 Absorber Design  
After being cooled, the flue gas enters an absorption tower from the bottom stages, where it meets the down-coming lean amine solvent that captures the CO\({}_{2}\) component in the flue gas. The clean flue gas rises to the top of the absorber and leaves the unit into the atmosphere, while rich amine goes to the bottom of the absorber exiting the unit to be pumped and sent to the cross-heat exchanger. The term lean amine refers to the solvent after being stripped of the CO\({}_{2}\) and enters the top of the absorber; the loading of the lean amine is maintained at 0.2 moles of CO\({}_{2}\) per moles of MEA solvent, as per [PERSON] et al. [37] and [PERSON] et al. [19]. The stream leaving the absorber after being loaded with CO\({}_{2}\) is referred to as rich amine and has a loading of 0.48. The solvent loading determines the required flow rate to achieve the desired capture rate. The higher the lean loading the higher the flow rate required, as the capacity for CO\({}_{2}\) absorption decreases. The minimum required flow rate is calculated empirically using Equation (12):  
\[\mathrm{F_{lean}}=\frac{\mathrm{F_{FG}}x_{\mathrm{CO_{2}}}\mathrm{F_{CO_{2}}}} {100z(\alpha_{\mathrm{Rich}}-\alpha_{\mathrm{lean}})}\bigg{(}\frac{M_{Amine}} {44.009}\bigg{[}1+\frac{1-\omega_{Amine}}{\omega_{Amine}}\bigg{]}+z\alpha_{ lean}\bigg{)} \tag{12}\]  
where \(\mathrm{F_{lean}}\) is the mass flow rate of the lean amine, \(\mathrm{F_{FG}}\) is the mass flow rate of the flue gas, \(x_{\mathrm{CO_{2}}}\) is the mass fraction of the CO\({}_{2}\) in the flue gas, \(\mathrm{F_{CO_{2}}}\) is the % of the CO\({}_{2}\) in the flue gas recovered, \(M_{Amine}\) is the molar mass of amine, \(\alpha_{\mathrm{Rich}}\) / \(\alpha_{\mathrm{lean}}\) is the rich and lean amine loading respectively, and \(z\) is the number of equivalents per mole of the amine (1 for MEA). The resulting flow rate value is then implemented in the model as an initial guess value for the given loading, any increase or decrease than the calculated flow rate will increase or decrease the capture rate, respectively. To achieve the required 90% capture rate, a solvent flow rate of 763,058 kg/h is required. [PERSON], [PERSON], and [PERSON] [15] state that a quick rough initial guess for calculating the mass flow of MEA is around five times the mass flow of the flue gas feed. The absorber and stripper units were modeled as RadFrac rate-based columns similar to the DCC unit; Aspen allows the choice between the trap and packed columns in the design stage. In this study, the column is designed with structured packing material. The packing material provides the required surface area for contact and thus determines the final rich loading achievable, which in turn affects the reboiler duty. The uniform arrangement of the structured packing has several advantages over the random packing or column trays. Structured packing provides lower pressure drop through the column, as low as 0.5 mbar/equilibrium stage [38], and higher capacity leading to a smaller column diameter. The metal FiexiPac structured packing was used in this study with the dimension of 250Y (315 mm HETP or 12.4 in) and a nominal inclination angle of 45\({}^{\circ}\). More details about the packing material can be found in the KOCH vendor technical article [39]. Decreasing the temperature of the solvent would improve the absorption driving force, but it would also affect the rate of reactions and diffusivity. The temperature does not influence the reboiler duty and does not have a major effect on the performance of the system since the exothermic nature of the absorption reaction raises the solvent temperature upon contact with the CO\({}_{2}\)-rich flue gas. The maximum temperature rise is observed at the top stages of the absorber where the lean solvent enters, indicating the highest rate of reaction. The MEA solvent has low specific heat capacity and quickly absorbs the heat of reaction thus causing the temperature to rise sharply towards the top of the tower, as shown in Figure 11 in Appendix B.