Single-Atom Solvent for Enhanced CO₂ Capture: Process Modeling and Multi-Objective Optimization

Abstract

This work addresses the post-combustion CO₂ capture demand, employing a single-atom solvent as the absorbent to conduct systematic research on process modeling, energy consumption analysis, and multi-objective optimization. The energy consumption of the single-atom solvent-enhanced CO₂ capture process was reduced to 2.864 GJ/t, representing a 26.9% reduction compared with that of the conventional solution. The effects of solvent flow rate, gas flow rate, rich solvent temperature, reflux ratio, and extraction ratio on the energy consumption, annual total utility consumption, CO₂ equivalent emissions, and total annual cost were systematically investigated. The results indicate that rich solvent temperature and reflux ratio are the most sensitive parameters affecting system energy consumption variations; increasing solvent flow rate linearly elevates the reboiler duty, whereas gas flow rate variations exert negligible influence on system performance. The energy consumption was further reduced to 1.84 GJ/t CO₂ after process parameter optimization. A multi-objective optimization approach coupling the NSGA-II with Aspen Plus process simulation was developed for economic–energy–environmental optimization. Annual total utility consumption was reduced by 12.75%, CO₂ equivalent emissions per unit of product were reduced by 47.87%, and total annual cost was reduced by 13.09% after optimization. The optimal operating conditions under multi-objective optimization were determined simultaneously. This study provides an optimization strategy for the industrial application of CO₂ capture technology.

1. Introduction

Global climate change has become one of the most severe challenges facing humanity in the 21st century. According to the 2023 CO₂ Emissions Report released by the International Energy Agency (IEA) [1], global energy-related CO₂ emissions increased by 1.1% in 2023 [1], reaching a historic high of 37.4 billion tons, with coal-fired power plants contributing over 65% of the emissions increase [2,3]. The concentration of CO₂ in the flue gas of coal-fired power plants is usually 12–15%. Efficient capture and storage of CO₂ in coal-fired power plants is a key path to achieving carbon neutrality goals. Among numerous carbon capture technologies, the chemical absorption method is widely recognized as the most promising post-combustion capture technology due to its high technological maturity, capture efficiency of over 90%, and strong adaptability. However, the core bottleneck of this technology lies in the high energy consumption of solvent regeneration. The specific reboiler duty of the traditional monoethanolamine (MEA) based process is as high as 3.5–4.5 GJ/t CO₂ [4], resulting in a 23–29.5% decrease in net output power of the power plant [5], and an increase in operating costs of about 70%, which seriously restricts its large-scale commercial application [6].

To overcome the above bottlenecks, the development of solvents for chemical absorption methods has evolved from traditional single-component amines to high-performance mixed amines. Although MEA solvents, widely used in the early days, have the advantages of fast reaction rate and large absorption capacity, their high regeneration energy consumption (measured heat of CO₂ desorption reaction about 80.2–85.6 kJ/mol CO₂) [7,8], strong corrosiveness, and easy degradation have prompted researchers to develop various alternative solvents. Methyl diethanolamine (MDEA), as a representative tertiary amine, has a reaction enthalpy of only 61 kJ/mol CO₂ [8], low corrosiveness, and good stability, but a slow absorption rate. Moreover, PZ accelerates CO₂ absorption via rapid carbamate formation and shifts the liquid-phase speciation equilibrium as an activator, which lowers the apparent reaction heat per unit CO₂ and allows operation at a reduced solvent circulation rate; the combined reduction in reaction, sensible, and latent heat duties directly decreases the specific reboiler duty and overall regeneration cost. Otitoju et al. [4] studied the capture of piperazine PZ based combustion in a 250 MW natural gas combined cycle power plant, and found that the energy consumption of the standard process reboiler was 3.56–5.34 GJ/t CO₂. After adding PZ as an activator to the MDEA system, the reaction enthalpy of the PZ/MDEA mixed solvent decreased to about 70 kJ/mol CO₂, a decrease of 26.3% compared to MEA. The specific reboiler duty can be reduced to 2.39–3.0 GJ/t CO₂ [8,9].

Moreover, new solvents such as amino acid salts and ionic liquids have shown potential for low energy consumption and low volatility. The specific reboiler duty of ionic liquid-based solvents has been reduced to 2.5–2.8 GJ/t CO₂ [10,11]. Zhou et al. [12] reviewed stimuli-responsive organic polymers and frameworks that enable non-thermal regeneration through light, redox, or pH switching, dramatically reducing energy penalties compared to conventional thermal methods. On the molecular-design front, Yang et al. [13] demonstrated that amino-functionalized porous organic polymers achieve superior CO₂/N₂ selectivity via synergistic carbamate formation and electrostatic interactions, as elucidated by DFT calculations. Complementing these strategies, Ravi et al. [14] showed that melamine post-functionalization of high-surface-area aromatic carbonyl polymers introduces dense nitrogen sites, yielding both high CO₂ affinity and stable cyclic performance under ambient regeneration. However, relying solely on solvent modification is difficult to fundamentally solve the energy consumption problem, and it is necessary to combine solvent performance improvement with process system optimization [10].

In recent years, multi-objective optimization methods that combine intelligent optimization algorithms with process simulation have become an important research direction for energy conservation and consumption reduction in CO₂ capture systems [15]. Eslick et al. [16] used the NSGA-II to conduct a multi-objective analysis on multiple amine solvents, optimizing operating conditions with net power output and capital cost as objective functions. Khaidzir et al. [17] coupled Aspen Plus process simulation with NSGA-II to achieve synergistic optimization of cost, emissions, and technical performance of a CO₂ capture utilization integrated system. Wang et al. [18] systematically evaluated the impact of different desorber configurations on the energy consumption of the reboiler, providing a theoretical basis for process structure optimization. Existing research has shown that optimizing key operating parameters such as solvent flow rate, reflux ratio, extraction ratio, and rich solution temperature [19] can significantly reduce system energy consumption and environmental impact while ensuring CO₂ capture rate. However, existing research has mostly focused on traditional amine solvent systems, and there is still a lack of process optimization research for new high-performance solvents, especially a systematic research framework that couples solvent characteristics, process parameters, and economic and environmental indicators.

Single-atom solvent (SAS), as an emerging functionalized absorbent, can significantly improve CO₂ absorption capacity and selectivity by anchoring single metal atoms or active sites in porous carriers or ionic liquid frameworks, while reducing regeneration energy consumption. Single atoms are atomically dispersed and stabilized within the solvent matrix through coordination interactions. The single metal atom (Cu/Pt/Cr/Ni) is coordinated with functional groups from PANI (polyaniline) and TEMPO (2,2,6,6-tetramethylpiperidine-1-oxyl), forming a well-defined coordination environment that prevents metal aggregation. The concentration of the single-atom Cu species has been quantified and reported. The advantages of single-atom solvents for carbon capture processes are summarized in

Table 1. Summary of the advantages of single-atom solvents in carbon capture processes.

Characteristic	Advantage	Note
Absorption reaction	Fast absorption rate and large absorption capacity [20,23]	It is suitable for low-concentration CO2 capture in coal-fired power plants
Desorption reaction	The heat of the desorption reaction is 55.5 kJ/mol [24]	Compared with 30 wt% MEA aqueous solution, it decreased by 30.8%
Energy consumption for regeneration	2.0–2.5 GJ/t CO2 [25]	Energy consumption values verified through small-scale and pilot-scale experiments.

. Compared with traditional amine solvents, single-atom solvents have unique advantages such as high absorption capacity (up to 2–3 times that of traditional solvents) [20], low regeneration temperature (can be reduced by 20–30 °C) [21], and excellent thermal stability [22]. Single-atom species under the temperature swing of the absorption–desorption cycle generate a thermoelectric effect. This effect provides an additional driving force that reduces the apparent heat requirement for CO₂ desorption, thereby lowering the reaction heat of the desorption process. Introducing single-atom solvents into the chemical absorption carbon capture process is expected to fundamentally break through the bottleneck of high energy consumption in traditional solvent regeneration. However, the application of single-atom solvents is still in the laboratory stage, and there have been no reports on the systematic optimization of their processes. How to translate the excellent intrinsic properties of single-atom solvents into economic and environmental benefits of actual processes is a key scientific problem that urgently needs to be solved.

Based on the above background, this work constructs a CO₂ capture process for coal-fired power plants using a single-atom solvent as an absorbent. Aspen Plus is used for steady-state process simulation to systematically investigate the impact of key operating parameters such as solvent flow rate (Flux_S), gas flow rate (Flux_G), rich solution temperature (T_R), reflux ratio (RR_M), and extraction ratio (ER_D) on energy consumption (Econ), annual total utility cost (ATU), CO₂ emission intensity (CO₂ e), and annual total cost (TAC). A multi-objective optimization method coupled with NSGA-II and process simulation is used to determine the optimal operating parameters of the system. The objective function is to minimize (ATU, CO₂ e, and TAC), obtain the Pareto optimal solution set, and use the LINMAP (Linear Programming Technique for Multidimensional Analysis of Preference) method to determine the optimal point. This study aims to reveal the quantitative relationship between operating parameters and energy consumption and cost emission indicators in single-atom solvent carbon capture processes, and to establish a multi-objective optimization framework for single-atom solvent enhanced carbon capture processes based on NSGA-II, achieving global optimization of process parameters. This work provides theoretical guidance and technical support for the transition of single-atom solvents from laboratory to industrial applications, and promotes the update and development of chemical absorption carbon capture technology.

2. Process Modeling

2.1. Model Description

This work is modeled using Aspen Plus simulation software V11, and the simulation process of SAS-enhanced carbon dioxide capture technology is shown in Figure 1. The process description is as follows: After entering the bottom of the absorber, the flue gas comes into countercurrent contact with the fresh absorbent/regenerated lean solution flowing out from the top of the absorber, and then removes carbon dioxide. The solvent carried out by the flue gas is removed by the gas–liquid separator, and the decarbonized carbon tail gas in the gas phase of the gas–liquid separator is directly discharged. The rich solution that has absorbed CO₂ is heated to a specified temperature by a power pump installed at the bottom outlet of the absorber and a lean-rich liquid heat exchanger, and then enters the upper part of the desorber. The rich solution enters the upper part of the desorber for desorption and regeneration. The rich liquid in the lower part of the desorber is heated to the specified temperature by the reboiler and desorbed for regeneration. The carbon dioxide gas desorbed from the top of the desorber is cooled by the condenser, and the separated condensate is returned to the system for reuse. The separated 99% high-purity carbon dioxide gas enters the downstream carbon dioxide utilization unit. The lean solution obtained from the desorber bottom is subjected to heat exchange with the rich solution through a heat exchanger to around 120 °C, and then cooled to around 30–40 °C through a lean solution cooler. Together with the liquid phase from the gas–liquid separation tank at the top of the absorber, it forms a circulating solvent and enters the system for reuse. The circulating solvent enters the top of the absorber again and comes into countercurrent contact with the flue gas to absorb carbon dioxide.

This work is aimed at the design of CO₂ capture technology for experimental bench scale, with an annual CO₂ capture capacity of about 10 tons. The detailed design parameters are shown in

Table 2. Basic design parameters and design requirements.

Parameters	Unit	Value
Flue gas components (Volume fraction)	/	CO2: 0.125, O2: 0.068, N2: 0.807
Flow rate	kg/h	7.15
Temperature	°C	40
Pressure	MPa	0.1
CO2 capture rate	%	99
Solvent components (Mass fraction)	/	MEA: 0.3, DMF: 0.6974, PANI: 0.001, TEMPO: 0.0001, CuH: 0.00159, H2O: 1 × 10−5
Annual operating hours	h	8000
Annual CO2 capture capacity	Ton/year	~10
CO2 products purity	%	>99

. The chemical absorption method technology with single-atom solvent as the absorbent is adopted, and the composition of the single-atom solvent is shown in Table 2. The preparation of single-atom solvent can be found in published works [26,27]. SAS is prepared from 65.5 g N, N-Dimethylformamide, 0.1 g Copper (I) hydride, 0.1 g polyaniline, 0.1 g 4-hydroxy-TEMPO, and 28.1 g MEA. The solvent is prepared by the electrochemical method [22].

The simulation of the absorber and desorber is based on equilibrium-stage modeling. The main chemical reactions considered in the model are water dissociation, the reaction between CO₂ and MEA, and the equation for CO₂ desorption. The desorption reaction in the desorber is independently set to kinetic mode. The kinetic parameters are based on experimentally determined SAS-CO₂ desorption reaction heat-corrected kinetic parameters. Through previously published research [24], the heat of the SAS-CO₂ desorption reaction was experimentally measured to be 55.5 kJ/mol, which is 30.8% lower than the MEA aqueous solution [7].

Table 3. Chemical reactions and kinetic parameters involved in this work.

Reaction	Type	k	Ea (Cal/mol)
MEA+ + H2O $\leftrightarrow$ MEA + H3O+	EQUIL	/	/
H2O $\leftrightarrow$ OH− + H+	EQUIL	/	/
HCO3− $\leftrightarrow$ CO32− + H+	EQUIL	/	/
CO2 + OH− $\to$ HCO3−	KINETIC	4.32 × 1013	13,249
HCO3− $\to$ CO2 + OH−	KINETIC	2.38 × 1017	29,451
MEA + CO2 $\to$ MEACOO− + H+	KINETIC	9.77 × 1010	9855.8
MEACOO− + H+ $\to$ MEA + CO2	KINETIC	4.99 × 106	13,214

displays the chemical reactions and kinetic parameters involved in the simulation.

2.2. Physical Property Method

This work uses the ENRTL-RK physical property method in Aspen Plus software for simulation calculations. The ENRTL-RK method can handle liquid-phase systems containing electrolytes. ENRTL-RK can effectively describe the interactions between ions. ENRTL-RK considers the non-ideality of electrolyte solutions and corrects the activity coefficient by introducing the concept of local composition. The fitted gas–liquid equilibrium data can be well matched with experimental values through calculation. The Redlich–Kwong equation of state calculation method is used for the gas phase. For common non-polar or weakly polar gases such as CO₂, N₂, and O₂ in carbon capture systems, the RK equation can fully describe the PVT relationship of molecules. All binary interaction parameters for the relevant pairs—MEA–DMF, CO₂–MEA–DMF, and those involving PANI, TEMPO, and CuH—were taken directly from the Aspen Plus built-in databank (specifically, the ELECNRTL and NRTL parameter libraries).

2.3. Thermodynamics Verification

SAS uses DMF instead of traditional water as the solvent, which shows better solubility in the process of capturing CO₂. The CO₂–DMF binary data are used to regress the non-reactive VLE/Henry’s law parameters. DMF is the dominant solvent by mass; therefore, the physical solubility of CO₂ is governed primarily by CO₂–DMF interactions. This study compares the gas–liquid equilibrium data of CO₂ in DMF with published experimental research data (20–65 °C and 0.2–4.5 MPa) [28,29] to demonstrate the reliability of the thermodynamic calculation results selected for simulation. The comparison between the CO₂-SAS thermodynamic model calculation results of Aspen Plus software and experimental data is shown in Figure 2.

It can be seen from Figure 2 that as the temperature increases, the solubility of CO₂ in SAS decreases, which is consistent with published research conclusions [24,28,29]. The model accuracy is high under low-temperature conditions, and the experimental points almost coincide with the model lines, indicating that thermodynamic models can be used to describe the process of single-atom solvent absorption of carbon dioxide.

3. Process Evaluation Indicators and Optimization

3.1. Process Performance

To evaluate the absorption performance of the SAS-enhanced CO₂ capture process, the CO₂ capture rate was used to quantify the absorption performance. Process energy consumption was calculated using the energy consumption index of the desorber reboiler per unit of carbon dioxide product. The specific calculation is shown in Equations (1) and (2).

$${\mathrm{CR}}_{{\mathrm{CO}}_2}={\displaystyle \frac{\mathrm{G}{\mathrm{asIN}}_{{\mathrm{CO}}_2}-{\mathrm{GasOUT}}_{{\mathrm{CO}}_2}}{\mathrm{G}{\mathrm{asIN}}_{{\mathrm{CO}}_2}}}$$

(1)

$${\mathrm{E}}_{\mathrm{con}}={\displaystyle \frac{Q_{reboiler}}{{\mathrm{Pro}}_{{\mathrm{CO}}_2}}}$$

(2)

3.2. System Energy Consumption

Energy consumption is an important indicator for evaluating the economic performance of industrial processes. The basis of energy analysis is the law of conservation of mass and energy, expressed as Equations (3) and (4):

$$\sum m_i=0$$

(3)

$$\sum Q+\sum \mathrm{W}+\sum {n_{i}h}_i=0$$

(4)

The energy consumption involved in the carbon capture process established in this article includes the power consumption of the pump, the cold utility consumption of the condenser, the hot utility consumption of the reboiler, and the cold and hot utility consumption of the heating or cooling heat exchanger. The annual total utility consumption (ATU) consists of total heating utility (THU), total cooling utility (TCU), and electricity consumption of equipment. ATU can be calculated by the following Equation (5).

$$\mathrm{A}\mathrm{T}\mathrm{U}=\mathrm{T}\mathrm{H}\mathrm{U}+\mathrm{T}\mathrm{C}\mathrm{U}+\sum \mathrm{W}$$

(5)

3.3. Environmental Impact

Quantifying the environmental impact of this work was done using CO₂ equivalent emissions, which include direct carbon emissions generated throughout the process and indirect carbon emissions caused by system utility consumption. The total annual CO₂ equivalent emissions (${\mathrm{TOT}}_{{\mathrm{CO}}_2\mathrm{e}}$) of the process system are divided into two parts: carbon emissions caused by coal consumption used in the system’s utilities (${\mathrm{M}}_{{\text{utility-CO}}_2}$) and carbon emissions directly emitted into the atmosphere $({\mathrm{M}}_{{\text{stream-CO}}_2}$). The carbon dioxide equivalent emissions per unit product (CO₂ e) is the ratio of annual carbon dioxide equivalent emissions to product output. The detailed calculation process of CO₂ e is shown in Equations (6)–(9). Specifically, the utility emission factor depends on the type of utility (heating/cooling utility or electricity); the emission factor of electricity is taken as 0.6 kg CO₂ e/kWh, and the emission factor of steam is 0.09 kg CO₂ e/MJ. The efficiency factor is taken as 0.6, and the global warming potential factor of CO₂ is taken as 1.

$${\mathrm{TOT}}_{{\mathrm{CO}}_2\mathrm{e}}={\mathrm{M}}_{{\text{utility-CO}}_2}+{\mathrm{M}}_{{\text{stream-CO}}_2}$$

(6)

$${\mathrm{M}}_{{\text{utility-CO}}_2}={\phi }_{{\mathrm{CO}}_2}{\mathsf{\xi }}_{{\mathrm{CO}}_2}{\mathrm{Q}}_{\mathrm{duty}}$$

(7)

$${\mathrm{M}}_{{\text{stream-CO}}_2}={\mathrm{m}}_{\mathrm{i}}{\mathsf{\theta }}_{{\mathrm{CO}}_2}$$

(8)

$${\mathrm{CO}}_2\mathrm{e}={\displaystyle \raisebox{1ex}{${\mathrm{TOT}}_{{\mathrm{CO}}_2\mathrm{e}}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{Pro}}_{{\mathrm{CO}}_2}$}\right.}$$

(9)

3.4. Economic Investment

The total annual cost (TAC) is introduced to evaluate the economic performance of the three processes. TAC is the sum of cash cost of production (CCOP) and annual cost of capital (ACC). Cash cost of production (CCOP) is the sum of the variable cost of production (VCOP) and fixed cost of production (FCOP). The annual capital charge ratio (ACCR) can be used to convert the total capital cost (TCC) into an annual capital cost (ACC). The detailed calculation process is shown in Equations (10)–(12). The total annual variable cost of production (VCOP) is estimated as Equation (13).

TAC = CCOP + ACC

(10)

CCOP = VCOP + FCOP

(11)

ACC = ACCR × TCC

(12)

VCOP = C_f + C_c

(13)

The total capital cost (TCC) is the capital cost of all equipment, including heat exchangers, towers, pumps, separators, etc. The cost correlations summary of the economic analysis is listed in

Table 4. Cost correlations summary of economic analysis.

Equipment/Utilities/Materials		Cost Correlation	Reference
Equipment	Column trays	${\mathrm{C}}_{\mathrm{tray}}=568.94\times {\mathrm{D}}^{1.55}\times {\mathrm{h}}_{\mathrm{tray}}$ ${\mathrm{h}}_{\mathrm{tray}}=0.6096\times (\mathrm{NT}-2)$	[30]
	Column shells	${\mathrm{C}}_{\mathrm{shell}}=22,930.82\times {\mathrm{D}}^{1.066}\times {{\mathrm{h}}_{\mathrm{col}}}^{0.802}$ ${\mathrm{h}}_{\mathrm{col}}=1.2\times 0.6096\times (\mathrm{NT}-2)$	[30]
	Condenser	${\mathrm{C}}_{\mathrm{con}}=9414.568\times {\left({\displaystyle \frac{{\mathrm{Q}}_{\mathrm{c}}}{0.852\times ∆{\mathrm{T}}_{\mathrm{c}}}}\right)}^{0.65}$	[30]
	Reboiler	${\mathrm{C}}_{\mathrm{reb}}=10,386.54\times {\left({\displaystyle \frac{{\mathrm{Q}}_{\mathrm{r}}}{0.568\times ∆{\mathrm{T}}_{\mathrm{r}}}}\right)}^{0.65}$	[30]
	Heat exchanger	${\mathrm{C}}_{\mathrm{Hex}}=9414.568\times {\left({\displaystyle \frac{{\mathrm{Q}}_{\mathrm{H}}}{0.852\times ∆{\mathrm{T}}_{\mathrm{H}}}}\right)}^{0.65}$	[30]
	Pump	${\mathrm{C}}_{\mathrm{P}}=3099\times {\left({\displaystyle \frac{\mathrm{PP}}{4}}\right)}^{0.55}$	[30]
	Separator	${\mathrm{C}}_{\mathrm{sep}}=149,100\times {\left({\displaystyle \frac{{\mathrm{Q}}_{\mathrm{sep}}}{0.15}}\right)}^{0.55}$	[30]
Utilities	CW	2.12 × 10−10, $/J Tin: 20 °C, Tout: 25 °C	[31]
	MP	2.2 × 10−9, $/J Tin: 175 °C, Tout: 174 °C	[31]
	Refrigeration	2.5 × 10−9, $/Cal Tin: −25 °C, Tout: −24 °C	[31]
	Electricity	2.15 × 10−8, $/J	[31]
Materials	H2O	0.412 $/ton	[32]
	MEA	1400 $/ton	[32]
	DMF	4500 $/ton	[33]
Interest rate		12%	[34]
Plant lifetime		30 years	[34]

. MEA and DMF are the main components of the solvent system, accounting for over 99% of the total solvent mass. Therefore, it is assumed that the solvent cost is approximately the cost of MEA and DMF in the economic analysis.

The total annual fixed cost of production (FCOP) can be approximated as TCC multiplied by the fixed cost of production coefficient ($\omega$) ($\omega$ = 25%) [34].

3.5. Multi-Objective Optimization

Figure 3 shows the multi-objective optimization framework coupled with MATLAB R2016a and Aspen Plus V11. The left MATLAB platform runs the NSGA-II (non-dominated sorting, selection/crossover/mutation, Euclidean distance calculation), which communicates bidirectionally with the intermediate data exchange layer through the COM/ActiveX interface. The decision variables (feed ratio, temperature, pressure, reflux ratio, etc.) are input into Aspen Plus for steady-state process simulation. Aspen completes the sequential module calculation and returns the results of TAC, energy consumption, CO₂ emissions, product purity, etc., to MATLAB. After updating the iteration counter, it enters the next generation of evolution and finally outputs the Pareto optimal solution set. The NSGA-II initial parameters are set to a population size of 60 and 30 generations of evolution. The detailed information about NSGA-II used in multi-objective optimization is shown in

Table A1. The detailed information about NSGA-II used in multi-objective optimization.

Algorithmic Component	Detail Provided
Population size	60
Number of generations	30
Crossover probability	0.9
Mutation probability	0.2
Crossover operator	Simulated Binary Crossover
Mutation operator	Polynomial Mutation
Distribution index for crossover	20
Distribution index for mutation	20
Initialization strategy	Random uniform sampling within variable bounds
Selection operator	Binary tournament selection
Constraint-handling procedure	Constraint Dominance Principle
Stopping/convergence criterion	Maximum number of generations
Random seed	Fixed to ensure reproducibility
Number of independent optimization runs	10
Size of final non-dominated population	60

in the Appendix A.

3.5.1. Objective Functions

TAC, CO₂ e, and ATU represent the quantitative indicators of economic investment, environmental impact, and energy consumption of the SAS-enhanced CO₂ capture process established in this work. They are set as three objective functions for multi-objective optimization, as shown in Equations (14)–(16).

Obj.Func.I = TAC = C_f + C_c + 0.374 × TCC

(14)

$$\mathrm{Obj}.\mathrm{Func}.\mathrm{II}={\mathrm{CO}}_2\mathrm{e}={\displaystyle \raisebox{1ex}{${\mathrm{TOT}}_{{\mathrm{CO}}_2\mathrm{e}}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{Pro}}_{{\mathrm{CO}}_2}$}\right.}$$

(15)

Obj.Func.III = ATU = THU + TCU + ∑W

(16)

3.5.2. Decision Variables

Five important parameters, including flue gas flow rate, solvent flow rate, mass reflux ratio of the top of the desorber, temperature of rich liquid entering the desorber, and extraction ratio of the bottom of the desorber, are taken as decision variables; the purity and yield of CO₂ products are used as constraints for multi-objective optimization.

3.5.3. Determination of Optimal Solution

The Pareto front of multi-objective optimization can be obtained by Aspen Plus and MATLAB after multiple interactive operations. The famous LINMAP is used to find the optimal solution in the Pareto solution set. The ideal point is the extreme point of the objective function in the solution set. At the ideal point, each objective obtains an ideal optimal value. The LINMAP method computes the Euclidean distance (${\mathrm{ED}}_{i+}$) between each point in the Pareto solution set and the ideal point to evaluate each solution. The solution corresponding to the minimum Euclidean distance value is considered the optimal point on the Pareto solution set [31,35]. The Euclidean distance is calculated as shown in Equations (17) and (18). Specifically, all objective functions were normalized using min–max normalization to eliminate scale differences. Equal weights were assigned to the three objectives.

$$f_{\mathit{ij}}^{\mathit{norm}}={\displaystyle \frac{f_{\mathit{ij}}-\mathit{min}(f_{\mathit{ij}})}{\mathit{max}\left(f_{\mathit{ij}}\right)-\mathit{min}(f_{\mathit{ij}})}}$$

(17)

$${\mathrm{ED}}_{i+}=\sqrt{{\displaystyle \sum _{j=1}^n}{{(f}_{\mathit{ij}}^{\mathit{norm}}-f_{\mathit{ij}}^{\mathit{ideal}})}^2}$$

(18)

4. Results and Discussion

4.1. Model Validation

Table 5. Comparison between the results of this work and the literature.

Design/Output Parameter	Unit	This Work	Reference	Relative Error
CO2 concentration (Volume fraction)	%	12.5	12.5% [36]	0%
Inlet temperature of absorbent	°C	40	39.4 °C [37]
Desorption temperature	°C	120	120 °C [36]
Liquid-to-gas ratios (L/G)	kg/kg	3.5	3.66 [38]	3.14%
Desorption pressure	MPa	0.12	0.122 [37]	1.67%
CO2 capture rate	%	99	92% [36]	7.07%
Lean CO2 loadings	mol CO2 mol−1 MEA	0.22	0.21 [18]	4.55%
Reboiler duty	GJ/t CO2	2.864	2.98 [39]	3.89%

shows the comparison results between this study and the reference values in the literature, verifying the reliability of the model. Specifically, key operating parameters such as CO₂ volume fraction (12.5%), absorbent inlet temperature (40 °C), desorption pressure (0.12 MPa), and desorption temperature (120 °C) are almost consistent with the literature values, while the output parameters of CO₂ capture rate and liquid-to-gas ratio deviate by 7.07% and 3.14%, respectively. It is worth noting that the CO₂ capture rate in this study reached 99%, which is 7.07% higher than the reference value in the literature (92%). This indicates that while ensuring the accuracy of the model, the single-atom solvent used to enhance the CO₂ absorption and desorption process has significant advantages in CO₂ capture efficiency.

Moreover, the simulated lean loading ([0.22 mol CO₂ mol⁻¹ MEA]) is now explicitly compared with the calculated values reported in the literature [18] ([0.21 mol CO₂ mol⁻¹ MEA]). The relative deviations are within 5%, indicating the simulation’s satisfactory agreement with the calculation data. The predicted specific reboiler duty (2.864 GJ t⁻¹ CO₂) is compared with the literature [39] (2.98 GJ t⁻¹ CO₂), showing good agreement.

4.2. Summary of Process Simulation

The process flow data obtained from the Aspen Plus simulation are shown in

Table 6. Simulation results of mass balance.

Stream	G-IN	GOU	LIQ1	R-2	CO2	LIQ	LEAN-1	S-IN
T/°C	40	20	20	64.15265	10	10	164.7308	40
P/MPa	0.10	0.12	0.12	0.2	0.12	0.12	0.12	0.1
Mass enthalpy /KJ/kg	−1610.62	−24.85	−3350.05	−3819.77	−8955.18	−3422.79	−3275.39	−3547.58
Mass density kg/m3	1.21	1.75	954.53	935.38	2.39	968.87	811.16	954.62
Average molecular weight	30.28	28.45	72.136	67.18	44.00	72.01	69.05	69.02
Mass flow kg/hr	7.15	5.89	0.11	26.15	1.28	0.026	24.84	25.00
Mass fraction
H2O	0	9.82 × 10−7	1.99 × 10−5	9.26 × 10−6	1.37 × 10−5	0.001716	7.23 × 10−6	8.93 × 10−6
CuH	0	0	0	0.0015	0	0	0.0016	0.0016
PANI	0	8.76 × 10−8	0.00018	0.00096	1.02 × 10−11	1.82 × 10−7	0.0010	0.001
MEA	0	3.65 × 10−5	0.067	0.22	2.01 × 10−7	0.0054	0.30	0.30
N2	0.746	0.906	8.19 × 10−5	4.76 × 10−5	0.000971	1.09 × 10−7	0	0
O2	0.0718	0.0871	2.16 × 10−5	1.26 × 10−5	0.000256	7.92 × 10−8	9.03 × 10−26	0
CO2	0.182	0	0	4.99 × 10−9	0.998	0.0133	3.04 × 10−12	0
MEA+	0	0	7.64 × 10−7	0.00108	0	0	0.00113	3.68 × 10−6
MEACOO−	0	0	0	0.117457	0	0	0.001901	0
DMF	0	0.00717	0.933	0.661	0.00116	0.980	0.695	0.697
H+	0	0	0	0.00112	0	0	0	0

. The operating results and parameters of key equipment are shown in

Table 7. Simulation results of the equipment.

Name	Module	T/°C	P/MPa	Heat Load (kW)	Notes
B7	Heater	40	0.1	−0.901	/
B7-PUMP	Pump	64	0.2	0.00263	/
B5	Flash	20	0.15	−0.0533	/
B6	HeatX	120	0.2	1.0353	Temperature of rich liquid entering desorber
B5-ABS	RadFrac	40 → 63 top → bottom	0.1	0	Number of trays: 12 Feed stage: 1 and 12
B9-DES	RadFrac	111 → 165 top → bottom	0.12	/	From top to bottom Number of trays: 13 Feed stage: 6
DES-Condenser	Heater	10	0.12	−0.181	Mass reflux ratio: 0.75
DES-Reboiler	Heater	164.730761	0.12	1.017	Reboiler ratio: 0.925

. The process performance indicators are shown in

Table 8. Summary of process performance indicators.

Indicator	Unit	Value
CRCO2	%	99.99
Econ	GJ/t CO2	2.864
ATU	GJ/year	79.49
CO2 e	kg CO2/kg CO2	0.403
TAC	$/year	3709.07

.

From Table 6, it can be seen that the mass flow rate of the CO₂ product corresponding to the CO2 stream is 1.28 kg/h, and the CO₂ purity is 99.8%, which meets the design requirements in Table 2, indicating that the modeling results are usable. The energy consumption of carbon dioxide capture is 2.864 GJ/t CO₂, which is 26.9% lower than that of 30 wt% MEA aqueous solution (3.92 GJ/t CO₂) [18], indicating the significant advantages of using single-atom solvents for the CO₂ absorption–desorption process. After process optimization, it can be further reduced.

4.3. Effect of Operating Parameters on Energy Consumption

Figure 4 shows the response surface of the energy consumption with key operating parameters (ER_D, Flux_S, and RR_M). From Figure 4a, it can be seen that as ER_D increases from 0.935 to 0.95, the energy consumption decreases from about 4.0 to 2.6 GJ/t CO₂. As Flux_S increases from 25 to 35 kg/h, the overall energy consumption rises, and the surface tilts upward along the Y-axis direction. The lowest energy consumption is located in the lower left corner of the surface, at the maximum ER_D (0.95) and the minimum Flux_S (25 kg/h). This indicates that an increase in ER_D and a decrease in Flux_S are beneficial for reducing energy consumption. This is because when the extraction ratio increases, the decrease in liquid level at the bottom of the tower results in a decrease in the load of the reboiler [40,41]. An increase in the solvent feed flow rate to the absorber means an increase in the total amount of solvent entering the desorber. The reboiler must heat more solvent to complete CO₂ desorption, resulting in an increase in the shared heat per unit product, which is consistent with the research findings in the literature [41,42].

Figure 4b shows that as ER_D increases, energy consumption increases from approximately 3.0 to 5.0 GJ/t CO₂. When the RR_M increases, the energy consumption also increases significantly. At lower levels of ER_D, the amplification effect of Econ by increasing RR_M is more prominent. On the contrary, the lowest energy consumption zone is located in the lower left corner. Comparing the Z-axis range of Figure 4a, the increase in RR_M has a greater impact on the increase in Econ than on the increase in Flux_S, indicating that RR_M has a more severe effect on energy consumption than Flux_S.

Therefore, it can be concluded that, while meeting the requirements of CO₂ capture rate and product purity, it is advisable to use higher ER_D combined with lower Flux_S and RR_M, but the premise is to minimize the solvent flow rate and increase ER_D to a limited extent while meeting the capture conditions.

Figure 5 shows the response surface of the energy consumption per unit product of the desorber reboiler as a function of key operating parameters (ER_D, RR_M, and T_R). From Figure 5a, it can be seen that as ER_D increases, energy consumption increases from about 2.0 GJ/t CO₂ to 5.5 GJ/t CO₂, and as T_R increases, energy consumption sharply decreases from about 6.0 GJ/t CO₂ to about 2.0 GJ/t CO₂. The slope of the surface along the T_R direction (Y-axis) is much greater than the slope along the ER_D direction (X-axis). When the T_R decreases from 140 °C to 100 °C, the energy consumption increases by more than three times. When the T_R is fixed, the ER_D increases from 0.936 to 0.952, and the energy consumption increases by about 20–30%. Therefore, the impact of T_R on Econ is greater than that of ER_D. The lowest energy consumption can be as low as 1.84 GJ/t CO₂.

From Figure 5b, when RR_M increases from 0.2 to 1.0, the energy consumption increases by about 2–2.5 times, and the energy consumption amplification effect is more prominent at lower T_R levels. Comparing Figure 5a, T_R has the most significant pulling effect on energy consumption, followed by RR_M, and ER_D has the smallest impact on energy consumption. The higher the rich liquid temperature, the less additional heating heat gap the reboiler needs to provide, resulting in a decrease in the reboiler load [19]. However, when the reflux ratio decreases, the reboiler heat load significantly decreases because the liquid phase flow rate that needs to be vaporized and refluxed to maintain the separation accuracy inside the tower is significantly reduced, which is consistent with the research conclusions in the literature [43,44].

Therefore, it can be concluded that increasing ER_D and T_R while reducing RR_M can reduce the unit product heat load of the reboiler, while meeting the requirements of CO₂ capture rate and product purity.

Figure 6 shows the response surface of the energy consumption per unit product of the desorber reboiler as a function of three key operating parameters (Flux_S, T_R, and RR_M). From Figure 6a, it can be seen that when the solvent flow rate increases from 31 to 35 kg/h, the energy consumption increases from about 2.0 to about 5.5 GJ/t CO₂. The slope of the surface along the TR direction (Y-axis) is much greater than the slope along the Flux_S direction (X-axis). Under a fixed TR, Flux_S increased from 31 to 35 kg/h, with an energy consumption increase of about 20–30%, indicating that T_R has a greater impact on Econ than Flux_S. The minimum energy consumption is 1.84 GJ/t-CO₂, which is 35.8% lower than before optimization and 53.1% lower than 30 wt% MEA aqueous solution [18].

Similarly, from Figure 6b, it can be seen that when RRM increases from 0.2 to 1.0, the energy consumption increases by about 2–2.5 times. Comparing Figure 6a and Figure 6b, it can be clearly concluded that the increase in Flux_S has a weaker effect on energy consumption than the decrease in T_R and the increase in RR_M. The increase in Flux_S raises the reboiler duty because fresh solvent must be heated to the reboiler’s operating temperature. Although an increase in feed temperature is beneficial for reducing reboiler energy consumption, as the rich liquid temperature increases, it will cause more solvent thermal decomposition, thereby affecting the reabsorption effect of the rich liquid after desorbing CO₂ and circulating it back to the absorber.

From Figure 4, Figure 5 and Figure 6, it can be concluded that there is a significant correlation between energy consumption and all investigated operating parameters. Among them, T_R is the most sensitive to Econ, followed by the reflux ratio at the top of the desorber. The influence of ER_D and Flux_S is relatively weak. The ways to reduce the energy consumption of the regeneration tower while meeting the capture rate and CO₂ product purity can be summarized as increasing T_R and ER_D, and reducing Flux_S and RR_M. From the optimization results of the response surface mentioned above, the energy consumption of the reboiler can be fully reduced to 1.84 GJ/t CO₂. It is worth noting that in the actual engineering operation process, it is not enough to solely pursue the reduction in energy consumption of the regeneration tower reboiler. It is necessary to consider the energy consumption, economic performance, and environmental impact of the overall process. Therefore, the determination of the optimal operating parameters needs to be based on the results of multi-objective collaborative optimization.

4.4. Effect on 3E Performance

This section evaluates the impact of key parameters on the 3E (Energy–Economic–Environment) objective functions to analyze the optimization direction for improving the 3E objective functions.

Figure 7 shows the influence of Flux_S and Flux_G on 3E objectives. ATU significantly increases with the increase in Flux_S, from 2.75 to 3.5 kW. In contrast, with the increase in Flux_G, ATU shows a slightly decreasing trend (reduced by about 0.5%) and remains almost unchanged. When Flux_S increased from 25 to 30 kg/h, ATU increased linearly by about 27%. The increase in reboiler load is the main cause of the increase in ATU. When Flux_G changes, ATU remains relatively constant, indicating that within the experimental range, the impact of gas flow rate changes on utility demand is offset by other factors.

CO₂ e significantly increased with the increase in Flux_S, from 0.40 to 0.48. In contrast, the carbon dioxide equivalent emissions slightly decreased and remained almost unchanged with the increase in Flux_G. This is because although increasing the flow rate can improve the CO₂ capture rate, increasing the solvent flow rate after the capture rate approaches 100% leads to an overall increase in reboiler heat load and the corresponding increase in heat utilities [19]. Therefore, CO₂ e increases with the increase in Flux_S. The change in gas flow rate has no significant impact on carbon emission intensity, indicating that the system has a certain robustness to gas load fluctuations.

TAC significantly increases with the increase in Flux_S, with a slope of approximately 20 $/(kg·h⁻¹). The increase in Flux_G only leads to a slight increase in TAC, with a slope of approximately 2.5 $/(kg·h⁻¹). As Flux_S increases, the rise in system energy consumption leads to an increase in utility costs, resulting in an increase in TAC. Therefore, it can be concluded that Flux_S is the most sensitive parameter for system economy and environmental performance [45]. Flux_G has a weak impact on system performance within its range of variation, so it can be flexibly adjusted within a certain range in actual production to adapt to upstream flue gas flow fluctuations. As shown above, minimizing solvent circulation is the key to reducing system energy consumption and costs while meeting the CO₂ capture rate.

Figure 8 shows the influence of RR_M and ER_D on 3E objective functions. From the three solid lines in the figure, ATU, CO₂ e, and TAC all significantly increase with the increase in RR_M, with increases of about 33%, 61%, and 2.5%, respectively. Among them, CO₂ e has the largest increase, indicating that the increase in reflux ratio directly converts the reboiler load into higher carbon emission intensity, which is consistent with published research conclusions [46]. Secondly, the ATU increased by 33%, which is consistent with the previous response surface graph in Section 4.3, where the increase in RR_M led to a sharp increase in reboiler energy consumption.

From the three dashed lines in Figure 8, the increase in ER_D, ATU, CO₂ e, and TAC all show a decreasing trend, with reductions of 26%, 35%, and 2.6%, respectively. Among them, CO₂ e is the most sensitive to ER_D, indicating that increasing ER_D can maximize system efficiency and effectively reduce CO₂ e [19]. The reduction in ATU is 26%, which is consistent with the pattern in the response surface graph of Section 4.3, where an increase in ER_D leads to a decrease in reboiler energy consumption. Therefore, an increase in ER_D and a decrease in RR_M can optimize the ATU, CO₂ e, and TAC indicators.

Figure 9 shows the influence of T_R on 3E objective functions. From Figure 9, ATU, CO₂ e, and TAC all show a decreasing trend with increasing T_R, with decreases of 36%, 33%, and 4.9%, respectively. ATU is most sensitive to T_R, with a decrease of 36%, indicating that the temperature of the rich solvent is a strongly correlated parameter for total energy consumption. CO₂ e is highly sensitive to T_R with a decrease of 33%, indicating that the reduction in energy consumption directly translates into a reduction in carbon emissions. The more complete the heat exchange is before the rich liquid enters the desorber, the less additional heat the reboiler needs to provide. At the same time, the amount of lean liquid cooling utility returning to the absorber decreases synchronously. It is worth noting that the high temperature of the rich liquid increases the risk of solvent pyrolysis. Therefore, while meeting the constraints of equipment corrosion and solvent degradation, increasing the temperature of the rich solution entering the desorber as much as possible is an effective strategy to reduce system energy consumption and costs.

4.5. Three Objective Functions Optimization

From Section 4.3 and Section 4.4, the influence trend of five parameters on the performance of Econ and 3E has been confirmed. To improve computational efficiency and convergence of NSGA-II, the range of using five operational parameters as decision variables for multi-objective optimization has been further improved.

Table 9. Decision variables and constraints for multi-objective optimization.

Parameters	Unit	Value
Decision variables:
FluxS	kg/h	25–30
FluxG	kg/h	7.0–8.5
TR	°C	100–140
RRM	/	0.5–1.5
ERD	/	0.91–0.95
Constraints:
CO2 product purity	/	0.90–1.0
CO2 production	kg/h	≥1

lists the decision variables and constraints for the multi-objective optimization. The key operating parameters of the CO₂ absorption–desorption system are optimized with the goal of minimizing ATU, CO₂ e, and TAC. The Pareto front of the multi-objective optimization is obtained as shown in Figure 10. From Figure 10, the Pareto front exhibits a non-linear surface distribution, indicating a complex trade-off relationship among the three objectives. The front edge converges from the lower-left corner direction, which conforms to the typical characteristics of multi-objective optimization. The optimal solution is very close to the ideal solution, indicating that the NSGA-II optimization algorithm has found a high-quality compromise solution.

Table 10. Comparison of operation variables and objective function before and after multi-objective optimization.

Parameter	Unit	Initial Solution	Optimum Solution	Comparison
Objective functions
ATU	GJ/year	79.46	69.32	↓ 12.75%
CO2 e/	kg CO2/kg CO2	0.403	0.210	↓ 47.87%
TAC	$/year	3709.07	3223.73	↓ 13.09%
Operation variables
FluxS	kg/h	25.00	25.981	/
FluxG	kg/h	7.15	7.497	/
TR	°C	120	123.158	/
RRM	/	0.75	0.500	/
ERD	/	0.925	0.950	/
CO2 capture rate	%	99.99	99.99	/
CO2 product purity	/	0.998	0.999	constraint satisfaction
CO2 production	kg/h	1.28	1.29	constraint satisfaction
Econ	GJ/t CO2	2.864	2.156	24.72%

Note: ↓ and ↑ indicate a decrease and an increase in the corresponding indicator after optimization, respectively.

shows the comparison between the manipulated variables and the objective function before and after multi-objective optimization. After calculation, the CO₂ emission intensity after conversion is 0.210 kgCO₂/kgCO₂, which is 56.3–61.8% lower than the traditional MEA process (0.48–0.55) [4,47,48]. The decrease in CO₂ e by 47.87% compared to before optimization indicates that the carbon footprint of the optimized system has almost halved, and the environmental benefits are most prominent. ATU and TAC have similar declines and are highly correlated, as utility costs are an important component of the annual total cost. By comparing the corresponding operating parameters, reducing the reflux ratio, moderately increasing the rich liquid temperature and extraction ratio, and flexibly adjusting the solvent and gas flow rates are the key paths to achieve economic–environmental synergistic optimization of the CO₂ capture system, while meeting the requirements of CO₂ capture rate and product purity.

5. Conclusions and Outlook

5.1. Conclusions

This work focuses on the single-atom solvent-enhanced CO₂ capture process and conducts systematic research in three aspects: process modeling, energy consumption analysis, and multi-objective optimization. A steady-state process simulation model was established based on Aspen Plus, and the error between key parameters and the literature values was controlled within 3.5%. The CO₂ capture rate reached 99%, verifying the reliability of the model. The influence of operating parameters was revealed through single-factor and response surface analysis. The study showed that the rich liquid temperature and reflux ratio were the most sensitive parameters for energy consumption, followed by solvent flow rate and gas flow rate. The method of coupling NSGA-II with process simulation was used for multi-objective Pareto optimization, and the optimal parameter set under economic–environment–energy optimal conditions was obtained. The optimal solution can reduce ATU by 12.75%, CO₂ e by 47.87%, and TAC by 13.09%, achieving synergistic improvement in energy consumption, economic cost, and environmental impact. In summary, this study provides a systematic theoretical framework and optimization strategy for the scale-up application of single-atom solvent carbon capture technology.

5.2. Limitations of the Present Study

Although this study systematically modeled and multi-objective optimized the SAS-enhanced CO₂ capture process, there are still the following limitations:

(1)

This study is based on the steady-state process simulation of an experimental platform with an annual capture capacity of about 10 tons, and has not yet conducted industrial-scale (such as coal-fired power plant level) scale-up research. The steady-state model is difficult to reflect the impact of load fluctuations, start-stop conditions, and dynamic disturbances on system performance in actual industrial operation.

(2)

The long-term stability and degradation mechanism of solvents have not been fully considered. The article points out that increasing the temperature of the rich solution (T_R) can reduce system energy consumption, but at the same time, it will increase the risk of solvent thermal decomposition. However, this study has not yet quantitatively analyzed the thermal and oxidative degradation products of SAS during long-term cyclic operation, as well as their attenuation patterns on absorption performance.

(3)

The calculation of CO₂ e in this study mainly focuses on indirect emissions related to system energy consumption and direct emissions from process streams and has not yet conducted a full life cycle assessment (LCA), which does not cover the implicit carbon emissions and environmental impacts during solvent production, transportation, waste treatment, and equipment manufacturing stages.

5.3. Future Research Directions

(1)

It is suggested to extend the existing steady-state model to industrial scale (such as the capture device for a 300 MW coal-fired unit) and establish a dynamic simulation model to investigate the effects of variable load operation, solvent circulation cumulative effects, and control strategies on system robustness, providing theoretical support for engineering scaling up.

(2)

Conduct degradation kinetics experiments of SAS under long-term thermal cycling conditions for solvent stability systems to clarify the types and generation rates of degradation products; develop anti-degradation additives or new carrier structures, establish solvent loss replenishment strategies, and ensure the long-term stable operation of industrial equipment.

(3)

Carry out a cradle-to-grave LCA study to comprehensively assess the environmental footprint of the entire process of solvent synthesis, plant construction, operation and maintenance, and decommissioning and disposal; introduce uncertainty analysis and sensitivity analysis to establish a more realistic economic evaluation model.