## 1 Introduction
The proposed linear state-space formation can be applied properly for advanced controller techniques, such as multi-linear model predictive control (MMPC). The previous discussion highlights the increasing interest in the off-design behavior of CO\({}_{2}\) capture systems and also shows that this is mainly approached through the use of rigorous dynamic and/or rate-based models in dynamic mode along with a suitable control structure. Such models are indispensable for the accurate determination and evaluation of the process operation under varying conditions but often require intense effort to construct and execute. This is greatly amplified when there is a need to investigate the performance of multiple different solvents and further enhanced when such solvents include mixtures exhibiting liquid-liquid phase-change behavior. The next observation was that almost all contributions listed in Table 1 focus on MEA, except three cases that consider up to four other conventional solvents. The importance of both solvent mixtures and phase-change solvents in CO\({}_{2}\) capture indicates that their off-design performance needs to be investigated before selecting the most appropriate option. However, the off-design operation of neither conventional solvent mixtures nor phase-change solvents is yet to be addressed in published literature. This is mainly due to the high complexity of the models required for their simulation and the prediction of their phase-change behavior. This work employed for the first time a systematic approach that enabled the efficient screening and selection from multi-component sets of solvents and mixtures exhibiting non-ideal, multiphase behavior. It fits into the wider need to evaluate any type of material in off-design process conditions as an additional criterion for material selection. This was first highlighted in [PERSON] and [PERSON] [37] and then in [PERSON] et al. [38]. [PERSON] and [PERSON] [37] showed that any type of material, including solvents, used to enhance the operation of a process, may exhibit significantly different performance under the influence of variability compared to steady-state operation under nominal conditions. In the case of CO\({}_{2}\) capture solvents, it is necessary to select the ones that operate as close as possible to the economically desirable set-points and facilitate the minimization of resources required using the employed controller to bring the process back to its set-point under disturbances. In this work, the enhanced, shortcut model of [PERSON] et al. [13] was exploited to identify solvents that exhibit favorable performance under off-design conditions. The model was very suitable for use with the method proposed in this work as it came with the advantages demonstrated in the case of nominal operating conditions [13]; it captured the non-ideal solvent-water-CO\({}_{2}\) behavior, it was much easier to develop and use than the corresponding rigorous models, and the obtained predictions were in very good agreement with the experimental data. It is therefore reasonably expected to provide valid insights regarding the off-design performance of various solvents and mixtures examined here. More specifically, the approach of [PERSON] et al. [38] was used within a framework that considers CO\({}_{2}\) capture process operability using steady-state, nonlinear sensitivity with an implicit consideration of a controller scheme [39]. A very inclusive set of controlled variables was used in the context of disturbance scenarios to assess their deviation from their desired, nominal setpoints. The employed approach could simultaneously evaluate the effects of multiple and simultaneous disturbances on the controlled and manipulated variables for a wide set of solvents and solvent mixtures. It also identified the disturbances that have major, detrimental effects on all the controlled variables for each solvent and the controlled variables that have the highest sensitivity.