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Off-Design Operation of Conventional and Phase-Change CO_{2} Capture Solvents and Mixtures: A Systematic Assessment Approach

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## Abstract

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_{2}capture technologies hold promise for future implementation but conventional solvents incur significant energy penalties and capture costs. Phase-change solvents enable a significant reduction in the regeneration energy but their performance has only been investigated under steady-state operation. In the current work, we employed a systematic approach for the evaluation of conventional solvents and mixtures, as well as phase-change solvents under the influence of disturbances. Sensitivity analysis was used to identify the impact that operating parameter variations and different solvents exert on multiple CO

_{2}capture performance indicators within a wide operating range. The resulting capture process performance was then assessed for each solvent within a multi-criteria approach, which simultaneously accounted for off-design conditions and nominal operation. The considered performance criteria included the regeneration energy, solvent mass flow rate, cost and cyclic capacity, net energy penalty from integration with an upstream power plant, and lost revenue from parasitic losses. The 10 investigated solvents included the phase-change solvents methyl-cyclohexylamine (MCA) and 2-(diethylamino)ethanol/3-(methylamino)propylamine (DEEA/MAPA). We found that the conventional mixture diethanolamine/methyldiethanolamine (DEA/MDEA) and the phase-change solvent DEEA/MAPA exhibited both resilience to disturbances and desirable nominal operation for multiple performance indicators simultaneously.

## 1. Introduction

_{2}abatement systems is widely pursued as a means of mitigating the detrimental effects of global warming [1]. Currently, intense research efforts are focusing on CO

_{2}capture technologies, such as membrane processes [2], adsorption systems [3], and materials- [4,5] and solvent-based absorption/desorption processes [6]. The latter represents a technology with significant potential, which has been demonstrated even in large-scale plants [7,8]. The selection of efficient solvents or mixtures in solvent-based CO

_{2}capture plays an important role in the process configuration, the regeneration energy requirements, and the process economics [9]. While the development of new solvents has been an active research field, the ones proposed to date have not managed to reduce the regeneration energy requirements by more than 25% compared to the reference monoethanolamine (MEA) solvent, with detrimental effects on the reduction of capture costs [1]. In recent years, a new class of solvents called phase-change solvents [10] has indicated experimentally verified regeneration energy reductions of approximately 43% compared to MEA [11,12]. Unlike conventional solvents, phase-change solvents undergo a phase separation upon reaction with CO

_{2}or a change in temperature. The resulting CO

_{2}-lean phase may be mechanically separated and recycled to the absorber using insignificant amounts of energy, whereas the CO

_{2}-rich phase is introduced into a desorption process. This reduction in the solvent flow rate that undergoes thermal separation, and in some cases, desorption at lower than 90 °C [6], enables the corresponding reduction in regeneration energy requirements.

_{2}within a specific range of temperature enables the utilization of the advantages that this type of solvents bring in the reduction of the overall energy penalty for CO

_{2}capture. Zarogiannis et al. [13] compared phase-change solvent mixtures to conventional solvents based on their performance regarding CO

_{2}capture using the cyclic solvent capacity, the parasitic electricity losses, and the regeneration energy as criteria. Phase-change solvents showed improved performance in all aspects except the solvent cost due to the small industrial production for such solvents. For this purpose, a short-cut model for the absorption–desorption system has been utilized, initially developed by Kim et al. [14] but extended by Zarogiannis et al. [13] to account for phase-change solvents. However, the evaluation of the performance metrics has been accomplished by considering only the optimal design operating point at steady-state operation. Flue gas streams are usually susceptible to variabilities in their conditions, such as the flow rate, composition, concentration, and temperature, due to either production changes (e.g., variable power plant operation, fuel type change, and so forth) or other disturbances affecting the plant. The variability in the flue gas stream affects the operation of the capture plant by deviating the plant’s operating conditions from the cost-effective design point with potentially detrimental effects on the achieved process and economic performance. In addition, several other factors may influence the operating efficiency of the capture plant, such as solvent degradation, solvent losses, and heat exchanger inefficiencies. It is therefore imperative to investigate the performance of candidate CO

_{2}capture solvents and mixtures, not only at the nominal design point but also for a wide range of off-design conditions.

_{2}capture solvents and eventually select the solvent or solvent mixture that enables economically optimal operation over a wide range of operating conditions.

_{2}capture systems but only for a few conventional (non-phase-change) solvents (Table 1). Different process flowsheets and proposed control strategies are assessed according to the respective dynamic response. Table 1 presents an organized overview of published works based on the modeling approach, the investigated amine solvents, and the development of operating or control strategies.

_{2}capture process. Gaspar and Cormos [15] reported that absorption performance depends on the reaction rate and the mass transfer rate for four common amine solvents, namely monoethanolamine (MEA), diethanolamine (DEA), methyl diethanolamine (MDEA), and 2-amino-2-methyl-1-propanol (AMP). They developed a dynamic model to investigate the behavior and to evaluate the absorption capacity of solvents. Jayarantha et al. [16] considered a sensitivity analysis of an absorber for a post-combustion CO

_{2}capture plant. They concluded that the correlations used to describe the reactions and mass transfer are important factors that affect the efficiency of the model. The effects of the lean solvent flow rate on the CO

_{2}capture process were also investigated using a dynamic model with SAFT-VR (Statistical Associating Fluid Theory for potentials of Variable Range ) for the determination of thermo-physical properties [17].

^{®}and validated their results using pilot plant data. Enaasen Flø et al. [21] performed a dynamic model validation of the post-combustion CO

_{2}absorption process. They claimed that changes in the flue gas and solvent flow rate affect the process more than changes in the reboiler duty. Cormos and Daraban [22] developed and validated a dynamic, rate-based model of a CO

_{2}capture process in an aqueous solution of AMP using experimental data.

_{2}capture process performance, there is also an increasing number of studies on the development of control strategies for absorption–desorption CO

_{2}capture. Lin et al. [23] investigated the plantwide control of a post-combustion CO

_{2}capture process using MEA. The CO

_{2}removal ratio was controlled by manipulating the lean solvent recycle rate. The flexibility in power plants integrated with CO

_{2}capture systems was also investigated by Lin et al. [24] in a commercial process simulator with two proposed control strategies. They recommended that the lean solvent flow rate and loading were considered the key variables for the process performance. Simulation studies in commercial simulators were presented by Nittaya et al. [25]. They developed a mechanistic dynamic model using MEA as a solvent and proposed three decentralized control schemes, where the first was based on the relative gain array (RGA), while the others were based on heuristics. Sensitivity analysis was performed to unveil the most suitable controlled and manipulated variables. The study showed that heuristic-based control exhibits better performance than the RGA analysis. Abdul Manaf et al. [26] employed a black-box model to investigate the transient behavior of equipment, such as the absorber, the desorber, and the lean/rich heat exchanger for the determination of the process control strategy. A preliminary analysis expressed as relative gain analysis proposed the control of the CO

_{2}capture rate and the regeneration energy performance through the manipulation of the lean solvent flow rate and the reboiler duty. Gaspar et al. [27] reported a decentralized control scheme using proportional-integral (PI) controllers for the piperazine (PZ) and MEA as candidate solvents for CO

_{2}capture. Variations in the lean solvent flow rate and reboiler duty affected the performance of the process. It was proposed that PZ is a better candidate than MEA since it compensated for the disturbances in the lean solvent flow rate, recycle flow rate, reboiler duty, and stripper’s feed. Damartzis et al. [28] proposed a framework that includes a generalized process representation and an operability assessment by considering the steady-state controllability and dynamic evaluation of the process. The employed models were developed using the orthogonal collocation on finite elements (OCFE) technique in both assessment stages to efficiently manage the necessary rigorous models and to facilitate computations. Three amines were investigated, namely MEA, DEA, and monopropanolamine (MPA). Damartzis et al. [28] also illustrated that the combination of the choice of solvent and flowsheet features affects the dynamic performance of the process and thus the control scheme proposed to compensate for the possible disturbances. MPA achieved better performance under variability. Panahi and Skogestad [29] proposed a control design approach using a cost index that combines the energy utilization with a penalty for leaving CO

_{2}to the air by considering self-optimizing control variables for three operational regions. A dynamic simulation was reported by Mechleri et al. [30] using MEA for natural gas combined-cycle power plants. They investigated and applied an appropriate control structure to achieve flexible operation. Leonard et al. [31] proposed the control of the water balance by manipulating the temperature of flue gas in the absorber washing stage. Dynamic studies using MEA as a solvent were presented by Lawal et al. [32]. They shed light on the dynamics of a post-combustion CO

_{2}capture process for a 500 MWe power plant. It was shown that the power plant exhibits a faster response than the capture plant.

_{2}capture. The proposed approach first identifies local linear models at typical operating points. Subsequently, the nonlinearity distribution of the process was investigated for the change of the CO

_{2}capture rate and the change of mass flow of the flue gas. Finally, the multi-linear model was developed based on the nonlinearity distribution. The proposed linear state-space formation can be applied properly for advanced controller techniques, such as multi-linear model predictive control (MMPC).

_{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.

_{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 Zarogiannis 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.

_{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. This is a very useful feature because fewer solvents and disturbances, as well as controlled and manipulated variables exhibiting high sensitivity, can be selected and subsequently examined in a more rigorous solvent, process, and control design problem, hence reducing the computational effort associated with it.

_{2}capture solvents were evaluated in terms of their performance under off-design conditions. The nonlinear sensitivity assessment highlights that certain economically desirable solvents may not be as attractive under off-design conditions.

## 2. Materials and Methods

#### 2.1. Overview of the Controllability Assessment Framework

- A set of controlled variables associated with process performance indicators may be maintained within pre-defined levels for a set of disturbance scenarios, by calculating the necessary steady-state effort from a set of manipulated variables.
- Large variations in the steady-state position of the manipulated variables required for the compensation of relatively small disturbances indicate a limited ability by the solvent–process design configuration to address the disturbances and imply a compromise in the achieved dynamic performance by the control system.

_{2}capture solvents and mixtures is approached through a systematic non-linear sensitivity analysis method that investigates the static operability performance of each solvent in the process under disturbance variations along a direction in which the process exhibits the greatest sensitivity. The most sensitive directions in the disturbance space are derived using the decomposition of the sensitivity matrix, which incorporates the derivatives of multiple process performance measures (e.g., reboiler duty, net energy penalty, cyclic capacity, and so forth) with respect to the operating parameters for each solvent system. The sensitivity matrix constitutes a measure of the process’s operating variation under the influence of infinitesimal changes imposed on the selected parameters. The sensitivity matrix is decomposed into major directions of variability represented by the eigenvectors associated with the respective eigenvalues of the sensitivity matrix. The eigenvector direction that is associated with the largest-magnitude eigenvalue represents the dominant direction of variability for the system that causes the largest change in the performance measures. The entries in the dominant eigenvector determine the major direction of variability in the multi-parametric space and indicate the impact of each parameter in this direction. Having identified this direction, it is not necessary to explore all directions of variability (i.e., combinations of parameters) arbitrarily, hence reducing the dimensionality of the sensitivity analysis problem. The dominant eigenvector direction is then applied to the capture system for the evaluation of an aggregate performance indicator that encompasses all individual criteria for a wide variation range.

#### 2.2. Detailed Description

- Define a vector ${\mathit{E}}^{\mathit{n}\mathit{o}\mathit{m}}$ that represents the nominal process design and operating conditions of an absorption–desorption process system that will be subjected to variability, a set $\mathit{D}$ that includes the candidate solvents and mixtures, a vector $\mathit{X}$ of state variables of the CO
_{2}capture process represented through vectors $\mathit{h}\left(\mathit{X},d,\mathit{E}\right)$, $\mathit{g}\left(\mathit{X},d,\mathit{E}\right)\forall d\in \mathit{D}$ that describe the process equality and inequality constraints, and a vector $\mathit{Y}$ representing the controlled variables associated to the process performance criteria. - Variability can be represented by considering disturbance scenarios through a vector of infinitesimal deviations $\mathit{d}\mathit{E}$ such that each element of vector ${\mathit{E}}^{\mathit{n}\mathit{o}\mathit{m}}$ is represented as ${\epsilon}_{i}^{nom}={\epsilon}_{i}+d{\epsilon}_{i}$ $\forall i\in \left\{1,\dots ,{N}_{\epsilon}\right\}$, with vector $\mathit{Y}$ calculated as follows:$$\begin{array}{c}\underset{\forall d\in \mathit{D}}{\mathrm{Calculate}}{Y}_{1}\left(\mathit{X},d,\mathit{E}\right),\dots ,{Y}_{N}\left(\mathit{X},d,\mathit{E}\right),\\ s.t.\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}h\left(\mathit{X},d,\mathit{E}\right)=0,\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}g\left(\mathit{X},d,\mathit{E}\right)\le 0,\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathit{E}={\mathit{E}}^{\mathit{n}\mathit{o}\mathit{m}}+\mathit{d}\mathit{E},\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\mathit{X}}^{L}\le \mathit{X}\le {\mathit{X}}^{U}.\end{array}$$
- The most sensitive process performance indicators in $\mathit{Y}$ can then be identified by generating a local scaled sensitivity matrix $\mathit{P}$ around ${\mathit{E}}^{\mathit{n}\mathit{o}\mathit{m}}$ as described below:$$\mathit{P}={\left[\begin{array}{ccc}\frac{d\mathrm{ln}{F}_{1}}{d\mathrm{ln}{\epsilon}_{1}}& \cdots & \frac{d\mathrm{ln}{F}_{N}}{d\mathrm{ln}{\epsilon}_{1}}\\ \vdots & \ddots & \vdots \\ \frac{d\mathrm{ln}{F}_{1}}{d\mathrm{ln}{\epsilon}_{{N}_{\epsilon}}}& \cdots & \frac{d\mathrm{ln}{F}_{N}}{d\mathrm{ln}{\epsilon}_{{N}_{\epsilon}}}\end{array}\right]}_{d},$$
- The main directions of variability are obtained by calculating the eigenvalues of the matrix ${\mathit{P}}^{T}\mathit{P}$ and then used to rank-order the resulting eigenvectors $\left\{{\theta}_{i}\right\}\hspace{0.17em}\forall i\in \left\{1,\dots ,{N}_{\epsilon}\right\}$ based on the magnitude of the corresponding eigenvalues. The eigenvector corresponding to the largest-magnitude eigenvalue indicates the main direction of process variability under the influence of disturbances in the multi-parametric space defined by ${\mathit{E}}^{\mathit{n}\mathit{o}\mathit{m}}$.
- Using the dominant eigenvector, the sensitivity index $\Omega \left(\zeta ,d\right)$ is calculated with the use of a relevant appropriate parameter $\zeta $, which represents the magnitude of the disturbance magnitude along the eigenvector direction ${\theta}_{1}$ with respect to ${\mathit{E}}^{\mathit{n}\mathit{o}\mathit{m}}$, as described below:$$\begin{array}{c}\underset{\forall d\in \mathit{D},\zeta}{\mathrm{Calculate}\hspace{0.17em}}\Omega \left(\zeta ,d\right)={w}^{\Omega}\left(\zeta \right){\displaystyle \sum _{i=1}^{N}}\left|\frac{{F}_{i}\left(\mathit{X},d,\mathit{E}\left(\zeta \right)\right)-{F}_{i}\left(\mathit{X},d,{\mathit{E}}^{\mathit{n}\mathit{o}\mathit{m}}\right)}{{F}_{i}\left(\mathit{X},d,{\mathit{E}}^{\mathit{n}\mathit{o}\mathit{m}}\right)}\right|,\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}s.t.\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathit{h}\left(\mathit{X},d,\mathit{E}\left(\zeta \right)\right)=0,\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}g\left(\mathit{X},d,\mathit{E}\left(\zeta \right)\right)\le 0,\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\epsilon}_{i}\left(\zeta \right)={\theta}_{1,i}\cdot \zeta \cdot \hspace{0.17em}{\epsilon}_{i}^{nom}+\hspace{0.17em}{\epsilon}_{i}^{nom}\forall i\in \left\{1,\cdots ,{N}_{\epsilon}\right\},\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\mathit{X}}^{L}\le \mathit{X}\le {\mathit{X}}^{U}.\end{array}$$The maximum variation along the direction is determined by the final value of ${\zeta}_{\mathrm{max}}$, which is varied within the range $\left[-{\zeta}_{\mathrm{max}},{\zeta}_{\mathrm{max}}\right]$. The limits in the $\zeta $ coordinate are selected based on the variability of the process’s system. It is worth noting that the nominal value of the parameter ${\epsilon}_{i}^{nom}$ used in sensitivity analysis is considered when $\zeta $ equals zero, ${\epsilon}_{i}^{nom}\equiv {\epsilon}_{i}\left(\zeta =0\right)$. This procedure is repeated for every selected solvent or mixture of solvents. The algorithmic steps are illustrated in Figure 1.After the implementation of the proposed sensitivity analysis for the assessment of the process operability, an appropriate $\zeta \prime $ is selected for all the solvents. This is used to calculate the sensitivity index $\Omega \left(\zeta \prime ,d\right)$. A multi-criteria selection problem is formulated using the indices employed for the calculation of $\Omega \left(\zeta \prime ,d\right)$, as described in step 6.
- For every solvent $d\in \mathit{D}$, select $\Omega \left(\zeta \prime ,d\right)$ at the desired point $\zeta \prime $ and develop an augmented vector such that ${Y}^{a}=\left[Y\left(d,\epsilon \left(0\right)\right),Y\left(\zeta \prime ,d\right)\right]$. ${Y}^{a}$ is considered a combination of the optimal objective function values obtained during nominal operation and of the controllability index for each solvent. Use the elements of ${Y}^{a}$ in a multi-criteria problem formulation that considers the solvents in $\mathit{D}$ as the decision parameters to select the ones that simultaneously minimize all performance indices in $\mathit{Y}$ and the sensitivity index (or indices) in $\Omega $ by generating a Pareto front as follows:$$\begin{array}{c}\underset{\forall d\in \mathit{D}}{\mathrm{Minimize}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{Y}_{1}^{a}}\left(d,\epsilon \left(0\right)\right),{Y}_{2}^{a}\left(d,{\zeta}^{\prime}\right),\\ s.t.\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{Y}_{j}^{a}\left({d}^{*}\right)\le {Y}_{j}^{a}\left(d\right)\hspace{0.17em}\hspace{0.17em}\forall \hspace{0.17em}\hspace{0.17em}j\in \left\{1,2\right\}\wedge \exists l\in \left\{1,2\right\}:{Y}_{l}^{a}\left({d}^{*}\right)\le {Y}_{l}^{a}\left(d\right).\end{array}$$In step 6, the constraint of Equation (4) implies in a formal mathematical way that a solvent or mixture $d$ in $\mathit{D}$ is called a Pareto optimum or non-dominated solution if there exists no other solvent or mixture ${d}^{*}$ in $\mathit{D}$ satisfying this constraint. The constraint is illustrated for two objective functions, i.e., ${Y}_{1}^{a}\left(d,\epsilon \left(0\right)\right)\equiv Y\left(d,\epsilon \left(0\right)\right)$ and ${Y}_{2}^{a}\left(d,\zeta \prime \right)\equiv Y\left(\zeta \prime ,d\right)$. The former represents one performance index under nominal operation and the latter represents the sensitivity index for all performance indices during the variability. Multiple performance indices under nominal operation can also be considered as part of Equation (4). The Pareto optimality condition represents a minimization problem in Equation (4); however, a maximization or combinations may be similarly defined and solved by changing the direction of the inequality signs as appropriate. Note that step 6 is implemented after all calculations of Figure 1 are completed.

## 3. Implementation

#### 3.1. Overview of the Process and the Amine Solvents

_{2}capture solvents and were retrieved from the published literature. Phase-change solvents are characterized by the presence of a vapor–liquid–liquid equilibrium, where after the phase split, one liquid phase is rich in CO

_{2}, while the other phase is lean in CO

_{2}and rich in amine. MCA is selected as a representative of phase-change solvents requiring a liquid–liquid phase separator after the intermediate heat exchanger (HX) in the absorption–desorption flowsheet (Figure 2a), whereas DEEA-MAPA requires the liquid–liquid separator before the intermediate heat exchanger (Figure 2b).

_{2}and enthalpy as functions of the loading and temperature. For MEA, the models were from Oyenekan [40], whereas for AMP and AMP/PZ, they were from Oexman [41]. For DEA, MEA/MDEA, DEA/MDEA, and MPA/MDEA, the models were derived from equilibrium data obtained from gSAFT software [42]. For MPA/MDEA, the software uses an equation of state (EoS) called SAFT-γ Mie [43,44]. For the other three solvents, the model uses the SAFT-VR EoS [45]. For MAPA and DEEA/MAPA, models were derived from equilibrium data obtained from Arshad [46]. For MCA, the models were derived from equilibrium data obtained from Tzirakis et al. [47] and Jeon et al. [48].

#### 3.2. Controlled Variables and Disturbance Scenarios

_{2}, which would otherwise be sold to generate revenues. Parameter $NEP$ was calculated through a correlation proposed in Zarogiannis et al. [13] for stripper pressures of 1 and 1.5 bar. The former pressure was considered for MCA due to the availability of thermodynamic data, whereas the latter pressure was used in all other solvents. Parameter ${R}_{lost}$ was calculated for a 620 MW coal-fired power plant. All the other data are available in Zarogiannis et al. [13].

- ${\epsilon}_{1}$ = ${y}_{in}^{C{O}_{2}}$ is the content of CO
_{2}in the flue gas that enters the process. The nominal value is ${\epsilon}_{1}\left(0\right)$ = 15 vol%. - ${\epsilon}_{2}$ = ${\alpha}_{lean}$ is the CO
_{2}loading of the absorption–desorption process after the stripper. Its value depends on the selected solvents and their physico-chemical characteristics. The nominal values for each solvent were reported by Zarogiannis et al. [13]. ${\alpha}_{lean}$ can be adjusted by the reboiler duty in the stripper, which subsequently has an impact on the performance criteria. - ${\epsilon}_{3}$ = ${T}_{1}$ is the temperature of the inlet stream that enters the heat exchanger after the absorber. The nominal temperature is set to ${\epsilon}_{3}\left(0\right)$ = 40 °C. This can be adjusted by the possible cooling effort in the absorber and the amine flow rate in the system.

_{2}content of the flue gas may be attributed to a random disturbance or variability in the quality of the fuel or the operating regime of the power plant. Disturbance scenarios also involve a decrease or increase in ${\alpha}_{lean}$ and increase or decrease in the temperature of the inlet stream. These variations create inclinations in the operating process and help to understand potential disturbance rejection compensations that are necessary for each solvent. The starting point for every considered scenario constitutes the nominal, “desired” point, as calculated by Zarogiannis et al. [13]. The latter corresponds to operation in which there is a desired constant CO

_{2}capture rate at 90% with the ${Q}_{regen}$ at its lowest value. These nominal points are reported in Table 4.

- Set 1 included ${Y}_{1}={Q}_{regen}$, ${Y}_{2}={m}_{am}$, and ${Y}_{3}=\mathrm{\Delta}\alpha $.
- Set 2 included ${Y}_{1}=NEP$, ${Y}_{2}={m}_{am}$, and ${Y}_{3}=\mathrm{\Delta}\alpha $.
- Set 3 included ${Y}_{1}={R}_{lost}$, ${Y}_{2}={C}_{sol}$, and ${Y}_{3}=\mathrm{\Delta}\alpha $.

## 4. Results and Discussion

#### 4.1. Influence of Parameters on the Process Operability

#### 4.2. Sensitivity Index

_{2}capture as they exhibited the ability to alleviate the effects of disturbances. In Figure 3, Figure 4 and Figure 5, we designated the area of positive $\zeta $ as an unfavorable scenario because disturbances caused deterioration in the performance indicators. For example, ${Q}_{regen}$, $NEP$, etc. increase in that direction, which was undesired. On the other hand, when a performance indicator improved due to disturbances (e.g., a reduction of ${Q}_{regen}$), this direction of variability was designated as a favorable scenario. It could be argued that in this case, solvents with a high sensitivity to variability would be desirable as they appeared to exploit the effects of disturbances. However, such a conclusion would require a more detailed analysis of other issues, such as the duration of variability and the dynamic solvent behavior. It is generally desired to avoid solvents and operating conditions that deviate significantly from the intended system operation.

#### 4.3. Selection of Solvents

_{2}capture process, it was beneficial to combine the sensitivity analysis with the performance indices of ${R}_{lost}$, ${C}_{sol}$, $\mathrm{\Delta}\alpha $, ${Q}_{regen}$, and $NEP$ at nominal conditions. In this context, a Pareto front of the sensitivity index ${\Omega}_{3}\left(\zeta \prime \right)$ at an appropriate $\zeta \prime $ for all the solvents with respect to the aforementioned performance criteria could be implemented (Figure 6 and Figure 7). The selected $\zeta \prime $s were 0.2 and −0.15 to include all the proposed mixtures. The minimization of the sensitivity index with respect to the minimization of ${R}_{lost}$, ${C}_{sol}$, $\mathrm{\Delta}\alpha $, ${Q}_{regen}$, and $NEP$, along with the maximization of $\mathrm{\Delta}\alpha $, formed the respective Pareto fronts. Pareto optimal mixtures presented remarkably low sensitivity and good process performance from the nominal economic perspective.

_{3}and the nominal process performance were DEA/MDEA and DEEA/MAPA, as they appear with a very high frequency. It is also worth noting that DEA and AMP also appeared quite frequently in the Pareto fronts in the positive direction, i.e., they were quite resilient under unfavorable conditions.

## 5. Conclusions

_{2}capture process and certain solvents that were subjected to variations of CO

_{2}content in the flue gas, lean loading, and the temperature of the inlet stream. The parameters adopted here as performance indices consisted of the reboiler duty, the net efficiency energy penalty, the cyclic capacity, the solvent mass flow rate, the solvent purchase cost, and the lost revenue from parasitic electricity. All these parameters had direct or indirect impacts on the process economics. Furthermore, the sensitivity index provided valid insights regarding the sensitivity of each solvent within a wide range. Sharp profile changes indicated that a particular solvent was unsuitable because the achieved performance would be diminished under variability. Finally, the proposed multi-criteria assessment approach identified trade-offs between the solvents, pointing to those with the highest overall performance and the minimum sensitivity to variability.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Logical diagram of the sensitivity analysis approach used for the process operability assessment.

**Figure 2.**CO

_{2}capture flowsheet for phase-change solvents with phase separation (

**a**) after the intermediate heat exchanger and (

**b**) before the intermediate heat exchanger. The figures have been adapted from Zarogiannis et al. [13] with permission from Elsevier. HX: Heat exchanger.

**Figure 3.**Sensitivity index ${\Omega}_{1}\left(\zeta \right)$ versus the parametric variation magnitude cοordinate $\zeta $.

**Figure 4.**Sensitivity index ${\Omega}_{2}\left(\zeta \right)$ versus the parametric variation magnitude cοordinate $\zeta $.

**Figure 5.**Sensitivity index ${\Omega}_{3}\left(\zeta \right)$ versus the parametric variation magnitude cοordinate $\zeta $.

**Figure 6.**Pareto front between the sensitivity index ${\Omega}_{3}\left(\zeta \prime =0.2\right)$ and (

**a**) ${R}_{lost}$, (

**b**) ${C}_{sol}$, (

**c**) $\mathrm{\Delta}\alpha $, (

**d**) ${Q}_{regen}$, and (

**e**) $NEP$. Marks other than colored circles indicate undesirable solvents.

**Figure 7.**Pareto front between the sensitivity index ${\Omega}_{3}\left(\zeta \prime =-0.15\right)$ and (

**a**) ${R}_{lost}$, (

**b**) ${C}_{sol}$, (

**c**) $\mathrm{\Delta}\alpha $, (

**d**) ${Q}_{regen}$, and (

**e**) $NEP$. Marks other than colored circles indicate undesirable solvents.

**Figure 8.**Change in the performance criteria for solvents DEEA/MAPA and DEA/MDEA for the investigated $\zeta \prime =0.2$ and $\zeta \prime =-0.15$.

**Table 1.**Overview of the literature regarding the development of dynamic models, the employed amine solution, and their scope.

Reference | Model Used | Investigated Solvents | Purpose |
---|---|---|---|

[15] | Dynamic (Matlab/Simulink) | MEA, DEA, MDEA, AMP | Investigation of the dynamic process behavior of solvents |

[16] | Dynamic (Matlab) | MEA | Sensitivity analysis and dynamic simulations |

[17] | Dynamic (gPROMS) | MEA | Dynamic simulation |

[18] | Dynamic (gPROMS) | MEA | Different dynamic simulation approaches |

[19] | Dynamic (gPROMS) | MEA | Steady-state and dynamic process validation |

[20] | Dynamic (Aspen) | MEA | Dynamic simulation |

[21] | Dynamic (Matlab) | MEA | Dynamic model validation |

[22] | Dynamic (Matlab/Simulink) | AMP | Dynamic simulation and validation |

[23] | Dynamic (Aspen Dynamics) | MEA | Plantwide control |

[24] | Dynamic (Aspen Plus) | MEA | Investigation of a control strategy |

[25] | Mechanistic process model (gPROMS–Aspen Plus) | MEA | Investigation of decentralized control schemes |

[26] | Non-linear autoregressive model with exogenous input (NLARX) | MEA | Preliminary control analysis |

[27] | Dynamic, rate-based model (Matlab) | PZ, MEA | Investigation of decentralized control structure |

[28] | Custom steady-state and dynamic models using OCFE | MEA, DEA, MPA | Steady-state controllability assessment and evaluation of the process dynamic response for different solvents |

[29] | Dynamic (Unisim) | MEA | Investigation of operating strategy with self-optimizing control variables |

[30] | Aspen HYSYS Dynamics | MEA | Investigation of control structure |

[31] | Dynamic (Aspen Plus Dynamics) | MEA | Investigation of control strategy |

[32] | Dynamic (gPROMS) | MEA | Control design |

[33] | Dynamic, rate-based model (Aspen HYSYS) | MEA | Controllability analysis using MPC |

[34] | Dynamic (Unisim) | MEA | Control strategy with alternative control structures |

[35] | Dynamic (gPROMS) | MEA | Different control architectures |

[36] | Dynamic (gCCS) | MEA | Multi-model modeling for advanced control design using MMPC |

ID | Single Amine |
---|---|

MEA | |

AMP | |

DEA | |

MAPA | |

MCA |

**Table 3.**Mixtures employed in this work. 2-(Diethylamino)ethanol (DEEA)/MAPA is a phase-change mixture.

Component 1 | Component 2 | ||
---|---|---|---|

MEA | | MDEA | |

MPA | MDEA | ||

DEA | MDEA | ||

AMP | PZ | ||

DEEA | MAPA |

**Table 4.**Representative results of nominal operation for the investigated solvents in the performance indicators.

Solvent | ${\mathit{Q}}_{\mathit{r}\mathit{e}\mathit{g}\mathit{e}\mathit{n}}$ (GJ/ton CO _{2})
| $\mathit{N}\mathit{E}\mathit{P}$ (%-pts.) | $\mathbf{\Delta}\mathit{\alpha}$ | ${\mathit{m}}_{\mathit{a}\mathit{m}}(\mathbf{ton}/\mathbf{ton}{\mathbf{CO}}_{2})$ | ${\mathit{C}}_{\mathit{s}\mathit{o}\mathit{l}}$ (k€/ton CO _{2} | ${\mathit{R}}_{\mathit{l}\mathit{o}\mathit{s}\mathit{t}}(\mathbf{M}\u20ac/\mathbf{yr})$ |
---|---|---|---|---|---|---|

MEA | 3.72 | 11.2 | 0.3 | 4.7 | 76.3 | 290.1 |

MCA | 2.12 | 8.8 | 0.22 | 13.83 | 3929.7 | 150.1 |

MAPA/DEEA | 2.10 | 8.1 | 0.58 | 13.03 | 656.0 | 140.8 |

AMP | 3.13 | 9.4 | 0.28 | 7.35 | 238.7 | 206.5 |

AMP/PZ | 3.10 | 9.7 | 0.17 | 9.12 | 362.8 | 216.0 |

DEA | 3.47 | 10.2 | 0.18 | 13.48 | 328.5 | 240.7 |

MAPA | 4.56 | 12.6 | 0.49 | 4.15 | 573.3 | 361.3 |

MDEA/DEA | 3.74 | 11.1 | 0.28 | 9.52 | 401.9 | 293.8 |

MEA/MDEA | 4.28 | 11.5 | 0.13 | 17.67 | 746.0 | 302.0 |

MPA/MDEA | 3.32 | 9.8 | 0.18 | 13.02 | 687.0 | 221.2 |

**Table 5.**Ranking of the parameters that affected ${Q}_{regen}$, ${m}_{am}$, and $\mathrm{\Delta}\alpha $, with descending eigenvector entries from left to right. The highest absolute values are shown in bold. Underlined symbols indicate the eigenvector direction that corresponded to the second-largest eigenvalue, which is of a similar order of magnitude as the highest eigenvalues. The signs in brackets indicate the directions of change for the parameters (opposite signs indicate a change in the opposite direction).

Solvent | Order of Parameters | Solvent | Order of Parameters |
---|---|---|---|

MEA | ${\mathit{y}}_{\mathit{i}\mathit{n}}^{\mathit{C}{\mathit{O}}_{2}}$ (+), ${a}_{lean}$ (+), ${T}_{1}$ (−) | DEEA/MAPA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${y}_{in}^{C{O}_{2}}$ (−), ${T}_{1}$ (−) |

AMP | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), $\underset{\xaf}{{y}_{in}^{C{O}_{2}}}$ (−), ${T}_{1}$ _{(0)} | MEA/MDEA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${T}_{1}$ (−) |

DEA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), $\underset{\xaf}{{y}_{in}^{C{O}_{2}}}$ (−), ${T}_{1}$ _{(0)} | MPA/MDEA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${T}_{1}$ (−) |

MAPA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), $\underset{\xaf}{{y}_{in}^{C{O}_{2}}}$ (−), ${T}_{1}$ _{(0)} | DEA/MDEA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${T}_{1}$ _{(0)} |

MCA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−)_{,} ${T}_{1}$ _{(0)} | AMP/PZ | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${y}_{in}^{C{O}_{2}}$ (−) |

**Table 6.**Ranking of the parameters that affected the performance indices of $NEP$, ${m}_{am}$, and $\mathrm{\Delta}\alpha $.

Solvent | Order of Parameters | Solvent | Order of Parameters |
---|---|---|---|

MEA | ${\mathit{y}}_{\mathit{i}\mathit{n}}^{\mathit{C}{\mathit{O}}_{2}}$ (+), $\underset{\xaf}{{a}_{lean}}$ (+), ${T}_{1}$ _{(0)} | DEEA/MAPA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${y}_{in}^{C{O}_{2}}$ (−), ${T}_{1}$ (−) |

AMP | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), $\underset{\xaf}{{y}_{in}^{C{O}_{2}}}$ (−) | MEA/MDEA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${T}_{1}$ (−) |

DEA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), $\underset{\xaf}{{y}_{in}^{C{O}_{2}}}$ (−) | MPA/MDEA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${T}_{1}$ (−) |

MAPA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), $\underset{\xaf}{{y}_{in}^{C{O}_{2}}}$ (−), ${T}_{1}$ _{(0)} | DEA/MDEA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${T}_{1}$ _{(0)} |

MCA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−) | AMP/PZ | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${y}_{in}^{C{O}_{2}}$ (−) |

**Table 7.**Ranking of the parameters that affected the performance indices of ${R}_{lost}$, ${C}_{sol}$, and $\mathrm{\Delta}\alpha $.

Solvent | Order of Parameters | Solvent | Order of Parameters |
---|---|---|---|

MEA | ${\mathit{y}}_{\mathit{i}\mathit{n}}^{\mathit{C}{\mathit{O}}_{2}}$ (+), $\underset{\xaf}{{a}_{lean}}$ (+), ${T}_{1}$ _{(0)} | DEEA/MAPA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${y}_{in}^{C{O}_{2}}$ (−), ${T}_{1}$ (−) |

AMP | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), $\underset{\xaf}{{y}_{in}^{C{O}_{2}}}$ (−), ${T}_{1}$ _{(0)} | MEA/MDEA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${T}_{1}$ (−) |

DEA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), $\underset{\xaf}{{y}_{in}^{C{O}_{2}}}$ (−) | MPA/MDEA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${T}_{1}$ (−) |

MAPA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), $\underset{\xaf}{{y}_{in}^{C{O}_{2}}}$ (−), ${T}_{1}$ _{(0)} | DEA/MDEA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−), ${T}_{1}$ _{(0)} |

MCA | ${\mathit{a}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{n}}$ (−) | AMP/PZ |

**Table 8.**Mixtures presenting the optimal trade-off between performance and sensitivity at $\zeta \prime =0.2$ and $\zeta \prime =-0.15$.

$\mathit{\zeta}\prime $ | ${\mathit{R}}_{\mathit{l}\mathit{o}\mathit{s}\mathit{t}}$ | ${\mathit{C}}_{\mathit{s}\mathit{o}\mathit{l}}$ | $\mathbf{\Delta}\mathit{\alpha}$ | ${\mathit{Q}}_{\mathit{r}\mathit{e}\mathit{g}\mathit{e}\mathit{n}}$ | $\mathit{N}\mathit{E}\mathit{P}$ |
---|---|---|---|---|---|

0.2 | DEEA/MAPA DEA/MDEA MCA AMP DEA | DEA/MDEA MEA AMP DEA | DEEA/MAPA DEA/MDEA MAPA | DEEA/MAPA DEA/MDEA MCA AMP DEA | DEEA/MAPA DEA/MDEA AMP DEA |

−0.15 | DEEA/MAPA DEA/MDEA | DEA/MDEA MEA AMP DEA | DEEA/MAPA DEA/MDEA | DEEA/MAPA DEA/MDEA | DEEA/MAPA DEA/MDEA |

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Zarogiannis, T.; Papadopoulos, A.I.; Seferlis, P.
Off-Design Operation of Conventional and Phase-Change CO_{2} Capture Solvents and Mixtures: A Systematic Assessment Approach. *Appl. Sci.* **2020**, *10*, 5316.
https://doi.org/10.3390/app10155316

**AMA Style**

Zarogiannis T, Papadopoulos AI, Seferlis P.
Off-Design Operation of Conventional and Phase-Change CO_{2} Capture Solvents and Mixtures: A Systematic Assessment Approach. *Applied Sciences*. 2020; 10(15):5316.
https://doi.org/10.3390/app10155316

**Chicago/Turabian Style**

Zarogiannis, Theodoros, Athanasios I. Papadopoulos, and Panos Seferlis.
2020. "Off-Design Operation of Conventional and Phase-Change CO_{2} Capture Solvents and Mixtures: A Systematic Assessment Approach" *Applied Sciences* 10, no. 15: 5316.
https://doi.org/10.3390/app10155316