## 3 Implementation
### Controlled Variables and Disturbance Scenarios
These nominal points are reported in Table 4.  
The steps and the overall range of the above parameters are represented through \(\zeta\), which is varied within the range \([-\zeta_{\text{max}},\zeta_{\text{max}}]\). The limit in the \(\zeta\) coordinate depends on the solvent or mixture of solvents; variations may result from variability in the steam availability in the reboiler, problems in the rich-lean heat exchanger, and so forth. Plotting \(\Omega(\zeta,d)\) vs. \(\zeta\) for different ranges can help determine the \(\zeta_{\text{max}}\) value. This plot indicates that solvents with the steepest slope are the most sensitive to variability. The underlying process and thermodynamic model are non-linear, hence the \(\Omega(\zeta,d)\) vs. \(\zeta\) profile for every solvent may change non-linearly. The selected range for \(\zeta\) values should therefore capture the plant operating patterns. With respect to the selection of the \(\zeta\) value, to implement step 6, a value close to \(\zeta=0\) usually provides a good indication about the solvents that are sensitive even under small variations. Inspection of the \(\Omega(\zeta,d)\) vs. \(\zeta\) profile for all solvents guides the selection of this value. This work considered three different sets of performance indices:  
* Set 1 included \(Y_{1}\ =\ Q_{\text{\emph{green}}}\), \(Y_{2}\ =\ m_{\text{\emph{am}}}\), and \(Y_{3}\ =\ \Delta\alpha\). * Set 2 included \(Y_{1}\ =\ NEP\), \(Y_{2}\ =\ m_{\text{\emph{am}}}\), and \(Y_{3}\ =\ \Delta\alpha\). * Set 3 included \(Y_{1}\ =\ R_{\text{\emph{lost}}}\), \(Y_{2}\ =\ C_{\text{\emph{sol}}}\), and \(Y_{3}\ =\ \Delta\alpha\). In Set 2, \(Q_{\text{\emph{green}}}\) was replaced by \(NEP\), which incorporates \(Q_{\text{\emph{regon}}}\) together with other process parameters, such as the reboiler temperature and pressure. In Set 3, \(NEP\) was replaced by \(R_{\text{\emph{lost}}}\) and \(m_{\text{\emph{am}}}\) by \(C_{\text{\emph{sol}}}\), hence transforming the operating indices to economic ones. This investigation had two goals: first, to assess the sensitivity of the different solvents to disturbances, and second, to assess how different performance indices may affect the assessment of the solvents based on their sensitivity to disturbances. The latter is important because performance indices, such as the reboiler duty and mass flow rate, are often used as criteria for solvent selection. The choice of reboiler duty overlooks other important parameters, such as the reboiler temperature and pressure, which directly impact the process's economics. The use of solvent mass flow rate as a selection criterion assumes that all solvents have the same purchase value, whereas in practice, the prices of amines vary quite significantly. Each set was used for the calculation of the corresponding sensitivity indices \(\Omega_{1}\), \(\Omega_{2}\), and \(\Omega_{3}\), per step 5. Results are reported for all indices in Section 4.2, whereas step 6 was implemented only for \(\Omega_{3}\) (i.e., set 3). Pareto fronts based on two criteria were developed by considering \(\Omega_{3}\) and \(R_{\text{\emph{lost}}}\), \(C_{\text{\emph{sol}}}\), \(\Delta\alpha\), \(Q_{\text{\emph{green}}}\), and \(NEP\) for both a selected positive and negative \(\zeta\). This served to finally select a set of very few candidates that exhibited good trade-offs between nominal and off-design performance.