Intensified CO₂ Absorption Process Using a Green Solvent: Rate-Based Modelling, Sensitivity Analysis, and Scale-Up

Abstract

Ionic liquids (ILs) are recognized as environmentally friendly solvents due to their high CO₂ absorption capacity, ease of recovery, and chemical stability, making them a promising alternative to conventional solvents for CO₂ capture. In this study, a rate-based mathematical model was developed for a rotating packed bed (RPB) absorber employing 1-n-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF₆]) as the solvent. The model incorporates mass, energy, and momentum balances, coupled with a thermodynamic model whose parameters were determined using experimental data. The rate-based model was validated against experimental results obtained from the RPB absorber. To enhance predictive accuracy, a sensitivity analysis of various mass transfer correlations was conducted, and simulations were performed based on the outcomes of this analysis. The model provided detailed radial profiles of pressure, gas and liquid flow rates, CO₂ concentration, temperature, volumetric mass transfer coefficients, and both gas- and liquid-phase resistances. The results indicated that the CO₂ capture efficiency and mass transfer coefficients in both phases increased with rotational speed along the bed’s radial direction. Furthermore, the RPB was designed for a flue gas stream from a fired heater in a petrochemical unit containing 10.74 mol % CO₂. The optimal liquid-to-gas ratio at a large scale was found to be 0.3 kg/kg, achieving a CO₂ removal efficiency of 98%. Under these conditions, the required motor power at an outer radius of 1.55 m was approximately 24.6 kW. Furthermore, comparison with a conventional packed bed showed that the liquid-phase volumetric mass transfer coefficient in the RPB was significantly higher, confirming its superior mass transfer performance.

1. Introduction

1.1. Background

Over the past century, the atmospheric concentration of CO₂ has increased significantly due to the growing energy consumption in the industrial sector. The majority of CO₂ emissions originate from the combustion of fossil fuels, which is recognized as one of the primary drivers of climate change and global warming [1,2,3,4]. To achieve the targets set by the Paris Agreement, CO₂ emissions must be strictly controlled in the short term, before 2050, to slow down the pace of global warming. In the long term, large-scale CO₂ capture and storage (CCS) is required to reduce the overall concentration of CO₂ in the atmosphere. Therefore, the development of environmentally safe and stable technologies and approaches for CCS is both urgent and essential [5]. Conventional solutions for reducing CO₂ in the atmosphere include CCS, efficient utilization of existing energy resources, and the use of non-fossil fuels such as renewable energy and hydrogen [6]. The carbon capture, utilization, and storage (CCUS) technology has been recognized as an effective and promising approach for large-scale CO₂ mitigation, enabling the continued use of fossil fuels, at least in the short to medium term [7,8].

Selecting optimal methods for CO₂ capture is crucial in terms of both operational and capital costs. A wide range of approaches, including pressure-swing adsorption, absorption, membrane separation, and cryogenic distillation, have been proposed for CO₂ capture [9].

Among the various technologies available, CO₂ capture using solvents is a well-established and user-friendly method. Its industrial applications include dehydration, natural gas sweetening, carbon capture, and so on [10].

Current CO₂ capture systems at an industrial scale predominantly utilize amine-based absorbents, owing to their significant reactivity with CO₂. However, several drawbacks, such as high regeneration heat demand, significant solvent losses, and corrosiveness, are associated with amine-based systems due to their intrinsic properties. These environmental and economic challenges have motivated researchers to explore alternative processes and novel absorbents [11].

The core of absorption processes lies in the use of high-performance solvents; therefore, exploring advanced new solvents to enhance the efficiency of absorption systems is essential [10]. In recent years, advances in green chemical technologies have led to the development of a new class of compounds known as ILs [12].

Due to their unique advantages, such as adequate thermal stability, a wide liquid range, very low vapor pressure, and high and tunable absorption capacity, ILs have attracted increasing attention as absorbents in gas separation processes [13].

In other words, ILs represent a new class of molten salts with melting points near room temperature. Owing to their non-volatility, they are appealing for a wide range of applications, including extraction processes, electrolytic media, heat transfer fluids, and thermal storage media [14,15].

They are entirely composed of anions and cations. The most commonly used ILs are formed by cations such as phosphonium, ammonium, pyridinium, and imidazolium combined with inorganic or organic anions such as nitrate, ethanoate, halide, or tetrafluoroborate [12,14].

Moreover, numerous combinations of anions and cations can produce ILs, and this structural flexibility allows for tuning their physical and chemical properties, making them suitable for designing high-energy-efficiency liquid absorbents for CO₂ capture processes [15].

Specifically, ILs are being extensively investigated as absorbents for CO₂ capture, aiming to overcome the drawbacks associated with amine-based systems and to advance next-generation absorption technologies [13].

Overall, IL-based absorbents exhibit significantly lower CO₂ absorption enthalpies compared to amine solvents, resulting in reduced energy requirements for solvent regeneration. In addition, the low volatility and thermal stability of ILs may decrease the release of volatile components and reduce solvent make-up costs. Finally, ILs are less likely to produce impurities during their reaction with CO₂ and are less corrosive [11]. ILs are typically high-viscosity fluids with poor fluidity. A significant limitation for their large-scale application in CO₂ absorption processes is the low gas–liquid mass transfer rate in conventional gas–liquid contactors, as well as the high mass transfer resistance due to their elevated viscosity. Therefore, the use of an RPB as an efficient contactor with high mass transfer performance is crucial for such high-viscosity systems. RPBs have been successfully employed in processes such as reactive crystallization, polymer devolatilization, distillation, absorption, and others [3]. Next, the studies conducted on the application of IL-based solvents for the CO₂ capture process are reviewed.

1.2. Literature Survey

Researchers have extensively studied ILs containing ammonium and imidazolium for CO₂ absorption. Blanchard et al. [16] studied the solubility of CO₂ in the IL such as [bmim][PF₆] and reported this solvent as a green and environmentally friendly option. Cadena et al. [17] measured the solubility of CO₂ in several ILs, including [bmim][PF₆], [bmim][BF₄], and [emim][Tf₂N]. Their results demonstrated that ILs containing the [PF₆]⁻ anion exhibit higher CO₂ absorption due to strong interactions with CO₂.

Shiflett and Yokozeki [18] measured the CO₂ solubility in [bmim][PF₆] and [bmim][BF₄] over a temperature range of 283.15–348.15 K and at pressures below 2 MPa. Their results indicated that CO₂ solubility decreases with increasing temperature, whereas it increases with increasing pressure.

Ziobrowski et al. [19] studied CO₂ absorption in traditional packed beds using ILs and compared them with a 15 wt.% MEA solution. Their results showed that ILs and MEA exhibit comparable CO₂ absorption capacities, although the liquid-side mass transfer coefficients for ILs are several times lower, highlighting the need for low-viscosity ILs with improved chemisorption properties.

Seo et al. [11] developed an integrated rate-based and thermodynamic modeling framework for CO₂ capture in packed-bed absorbers using ILs. The framework was applied for economic optimization and sensitivity analysis, highlighting the influence of key IL properties—including chemical absorption enthalpy, viscosity, heat capacity, and molar volume—on process performance and providing insights relevant for comparison with advanced amine-based processes.

Afkhamipour et al. [20] applied a rate-based model, incorporating the Deshmukh–Mather thermodynamic method, to simulate CO₂ absorption in a packed column using a Diethylenetriamine (DETA) solution and the ionic liquid [bmim][PF₆]. Sensitivity analysis was performed to assess the impact of mass transfer correlations on temperature and concentration profiles. The performance of DETA was compared with that of the ionic solvent, revealing that [bmim][PF₆] exhibits higher absorption efficiency under the same conditions. The study emphasizes the importance of optimizing absorber column parameters to maximize CO₂ removal efficiency while considering the specific advantages and limitations of each.

Hospital-Benito et al. [21] conducted a process modeling study of integrated absorber–stripper systems using six different ILs for CO₂ capture. Targeting a 90% CO₂ recovery, they evaluated the ILs based on solvent demand, regeneration energy, and column size. Their findings highlighted that the viscosity of ILs and their reaction enthalpy with CO₂ are key parameters governing solvent selection and overall process performance.

1.3. Motivation of the Current Study

The lack of modeling studies on CO₂ absorption using green solvents highlights the importance of the present research. While amine-based CO₂ absorption processes have been extensively investigated, previous findings indicate that the development of IL-based absorption systems could offer significant operational advantages over conventional chemical absorption. However, to date, no comprehensive investigation has been reported on CO₂ absorption processes employing green solvents in RPBs, covering the pathway from laboratory-scale validation to industrial-scale applications. This study aims to evaluate the performance of an RPB for CO₂ absorption and to assess the feasibility of process intensification for capturing CO₂ from flue gas at an industrial scale, thereby highlighting the advantages of HiGee technology over conventional absorption processes. For the first time, this work investigates the variations in key parameters, including K_Ga, K_La, CO₂ concentration in the gas phase, gas and liquid flow rates, gas-phase temperature, CO₂ removal efficiency, gas- and liquid-phase resistances, pressure drop, and liquid holdup along the packing. Furthermore, the influence of different mass transfer correlations on the system performance is systematically evaluated. In addition, to evaluate the effectiveness of applying HiGee technology with green solvents, a rigorous iterative approach was implemented to estimate the dimensions of the RPB at an industrial scale. During the scale-up process, the optimal L/G ratio, the rotor’s optimal power consumption, and the variation of CO₂ removal efficiency were thoroughly analyzed. Finally, the performance of the RPB absorber using the [bmim][PF₆] solvent was compared with that of conventional packed columns. This comparison aims to provide a clearer perspective on the potential adoption and effectiveness of green solvents in RPB-based CO₂ absorption processes at both laboratory and industrial scales.

2. Methodology

The rate-based and thermodynamic models are developed in MATLAB software (V14) by considering relevant equations and parameters.

2.1. Thermodynamic Modeling

Determining the mass transfer flux requires knowledge of both the driving force and the mass transfer coefficient. The driving force is defined as the difference between the CO₂ concentration in the gas phase and its equilibrium concentration in the liquid phase [22]. In this study, the equilibrium CO₂ concentration in the liquid phase was estimated using the UNIQUAC model, following the approach adopted by Yunus et al. [23], for CO₂ solubility in a pyridinium-based ionic liquid system. The absorption of CO₂ by [bmim][PF₆] was analyzed using available solubility data to determine the unknown parameters in the model equations. All relevant equations employed for the thermodynamic modeling in this study are as follows [18]:

$$f_2^L=f_2^G⟹x_2{\gamma }_2{f}_2^{\circ }=y_{2}P$$

(1)

$$f_2^{\circ }={\displaystyle \frac{{He}_{2,r}}{{\gamma }_{2,r}^{\infty }}}⟹x_2={\displaystyle \frac{y_{2}p}{{He}_{2,r}({\gamma }_2/{\gamma }_{2,r}^{\infty })}}$$

(2)

$$ln{\gamma }_i=ln{\gamma }_i^C+ln{\gamma }_i^R$$

(3)

$$\begin{gathered} ln{\gamma }_i^C=ln{\displaystyle \frac{{\Phi }_i}{x_i}}+{\displaystyle \frac{z}{2}}{q}_{i}ln{\displaystyle \frac{{\theta }_i}{{\Phi }_i}}+l_i-{\displaystyle \frac{{\Phi }_i}{x_i}}\sum _j{x}_j{l}_j \\ {l}_i={\displaystyle \frac{z}{2}}\left(r_i-q_i\right)-\left(r_i-1\right);z=10;r_i=\sum _k{\nu }_k^{\left(i\right)}{R}_k;q_i=\sum _k{\nu }_k^{\left(i\right)}{Q}_k \\ {\Phi }_i=x_i{r}_i/\sum _j{x}_j{r}_j;{\theta }_i=x_i{q}_i/\sum _j{x}_j{q}_j \end{gathered}$$

(4)

$$\begin{gathered} \mathit{ln}{\gamma }_i^R=q_i\left[1-ln\left(\sum _j{\theta }_j{\tau }_{ji}\right)-\sum _j\left({\theta }_j{\tau }_{ij}/\sum _k{\theta }_k{\tau }_{kj}\right)\right] \\ {\tau }_{ji}=exp\left(-{\displaystyle \frac{a_{ji}}{T}}\right)and{\tau }_{ij}=exp\left(-{\displaystyle \frac{a_{ij}}{T}}\right) \end{gathered}$$

(5)

$$OF={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{\left[{\displaystyle \frac{{x_2}_{exp}-{x_2}_{cal}}{{x_2}_{exp}}}\right]}^2$$

(6)

Equation (1) shows that, at equilibrium, the fugacity of the gas phase is equal to that of the liquid phase when a gaseous solute (component 2) dissolves in a liquid solvent (component 1). Here, x₂ and γ₂ represent the mole fraction and activity coefficient of the gaseous component 2 in solvent 1, respectively. When the temperature exceeds the critical temperature of the gas, the parameter $f_2^{\circ }$ corresponds to the fugacity of a hypothetical pure liquid. Since $f_2^{\circ }$ cannot be determined experimentally, the expression is reformulated to estimate Henry’s law constant for a reference solvent. In Equation (2), ${\gamma }_{2,\mathrm{r}}^{\mathrm{\infty }}$ denotes the infinite dilution activity coefficient of the gas in the reference solvent, while ${\mathrm{H}\mathrm{e}}_{2,\mathrm{r}}$represents Henry’s law constant of the gas in that solvent.

The UNIQUAC model is employed in this study to determine the activity coefficient. Equation (3) presents the activity coefficient of component i, where $\mathrm{l}\mathrm{n}{\gamma }_{\mathrm{i}}^{\mathrm{C}}$ represents the combinatorial contribution and $\mathrm{l}\mathrm{n}{\gamma }_{\mathrm{i}}^{\mathrm{R}}$ accounts for the residual contribution. The combinatorial term, given by Equation (4), is defined using ${\mathrm{\Phi }}_{\mathrm{i}}$, the segment fraction, and ${\mathrm{\theta }}_{\mathrm{i}}$, the area fraction. The volume and surface area parameters for component i are denoted by ${\mathrm{r}}_{\mathrm{i}}$ and ${\mathrm{q}}_{\mathrm{i}}$, respectively. The residual contribution of the UNIQUAC equation is calculated using Equation (5), where ${\mathrm{\tau }}_{\mathrm{j}\mathrm{i}}$ represents the binary interaction parameter. Thus, a_ji and a_ij are the two interaction parameters required by the UNIQUAC model for a binary mixture. To minimize errors in estimating these interaction parameters, an objective function (OF), as shown in Equation (6), was employed. Using the UNIQUAC equations, ${\mathrm{\gamma }}_2$ and ${\mathrm{x}}_2$can be calculated, representing the activity coefficient and solubility of CO₂ in the ionic liquid, respectively. The optimized model parameters, including the binary interaction parameters (a_ij (K)), volume parameters (${\mathrm{r}}_{\mathrm{i}}$), and surface area parameters (${\mathrm{q}}_{\mathrm{i}}$), were obtained in this study and are summarized in

Table 1. Optimized parameters for the thermodynamic model.

r-IL	q-IL	r-CO2	q-CO2	a (CO2-IL)	a (IL-CO2)
7.108	4.5	3.139	1.020	5.314	2.153

.

2.2. Process Modeling

Traditional absorption columns are associated with operational challenges and high costs due to their large size compared to RPBs. The use of a suitable solvent and an appropriate rotational speed—taking into account the solvent’s viscosity—can enhance mass transfer and consequently reduce operating costs. Modeling and simulating such processes using a detailed rate-based approach significantly improves the accuracy of process design and performance analysis [22,24]. Depending on the system configuration, the gas–liquid flow may occur in co-current, counter-current, or cross-current modes [25]. In this study, a counter-current flow configuration was considered for model development, based on the available experimental data for CO₂ absorption in [bmim][PF₆] [3].

Figure 1 illustrates the counter-current flow in an RPB for CO₂ absorption using [bmim][PF₆]. The liquid enters the column and is distributed radially from the inner to the outer radius across the packing surface, while the gas enters from the outer radius and comes into radial contact with the liquid. This liquid distribution is driven by the centrifugal force generated by the rotor and the resulting pressure gradient. Under the modelling assumptions, a differential volume element is defined, and mass and energy balances are derived for this element in the radial direction. Prior to formulating the governing balance equations, the following assumptions were considered in the modeling of the absorber column:

• The system operates under steady-state conditions.
• The gas phase follows ideal behavior, whereas the liquid phase demonstrates non-ideal thermodynamic characteristics.
• The absorber operates under adiabatic conditions.
• Variations in both liquid and gas flow rates along the column are incorporated into the modeling equations.

The main equations developed for the process modeling of CO₂ absorption using [bmim][PF₆] in an RPB are presented as follows:

$${\displaystyle \frac{dG}{dr}}=-2\pi rH{j}_{{CO}_2}{a}_e{ϵ}_G$$

(7)

$${\displaystyle \frac{dL}{dr}}=-2\pi rH{j}_{{CO}_2}{a}_e{ϵ}_L$$

(8)

$${\displaystyle \frac{d{y}_{{CO}_2}}{dr}}={\displaystyle \frac{2\pi rH{a}_e{ϵ}_G}{G}}\left(\left(y_{{CO}_2}+1\right)j_{{CO}_2}\right)$$

(9)

$${\displaystyle \frac{d{x}_{{CO}_2}}{dr}}={\displaystyle \frac{2\pi rH{a}_e{ϵ}_L}{L}}\left((x_{{CO}_2}-1)j_{{CO}_2}\right)$$

(10)

$${\displaystyle \frac{d{x}_{IL}}{dr}}={\displaystyle \frac{2\pi rH{a}_e{ϵ}_L}{L}}\left((x_{IL}-1)j_{{CO}_2}\right)$$

(11)

$${\displaystyle \frac{d{T}_G}{dr}}={\displaystyle \frac{-2\pi rH{a}_e{h}_G{ϵ}_G}{C_{p_G}G}}\left(T_G-T_L\right)$$

(12)

$${\displaystyle \frac{d{T}_L}{dr}}=2\pi rH{a}_e{ϵ}_L({\displaystyle \frac{j_{{CO}_2}{T}_L{ϵ}_L}{L}}-{\displaystyle \frac{j_{{CO}_2}{T}_G}{C_{p_L}L}}-{\displaystyle \frac{h_G\left(T_G-T_L\right)}{C_{p_L}L}})$$

(13)

Since the first-order ordinary differential equations for mass, energy, and momentum balances require initial conditions, these were taken as the operating conditions at the inlet of the packed bed for both the gas and liquid phases. The mass transfer flux of CO₂ ($j_{{CO}_2}$) was calculated using the film theory, as expressed by the following equation:

$${\mathrm{j}}_{{\mathrm{C}\mathrm{O}}_2}={\mathrm{K}}_{G,{\mathrm{C}\mathrm{O}}_2}({\mathrm{P}}_{{\mathrm{C}\mathrm{O}}_2}-{\mathrm{P}}_{{\mathrm{C}\mathrm{O}}_2}^{\mathrm{*}})$$

(14)

The calculation of the CO₂ mass flux requires evaluation of ${\mathrm{K}}_{G,{\mathrm{C}\mathrm{O}}_2}$, which accounts for resistances in both phases. Since the ionic liquid solvent is highly viscous, the resistance is often dominated by the liquid phase, and the gas-phase resistance may be neglected. However, for greater accuracy, both resistances are considered, as expressed by the following equation:

$${\displaystyle \frac{1}{K_{G,{CO}_2}}}={\displaystyle \frac{1}{k_{G,{CO}_2}}}+{\displaystyle \frac{{He}_{{CO}_{2-IL}}}{k_{L,{CO}_2}}}$$

(15)

Here, the terms ${He}_{{CO}_{2-IL}}\mathrm{/}{\mathrm{k}}_{L,{\mathrm{C}\mathrm{O}}_2}$ and $1\mathrm{/}{\mathrm{k}}_{G,{\mathrm{C}\mathrm{O}}_2}$ represent the liquid- and gas-phase mass transfer resistances, respectively. The gas-phase mass transfer coefficient, ${\mathrm{k}}_{G,{\mathrm{C}\mathrm{O}}_2}$, was calculated using the correlation proposed by Onda et al. [26]. For the liquid-side mass transfer coefficient, ${\mathrm{k}}_{L,{\mathrm{C}\mathrm{O}}_2}$, two correlations were adopted, as reported by Onda et al. [26] and Tung and Mah [27]. A sensitivity analysis was performed using these two correlations for ${\mathrm{k}}_{L,{\mathrm{C}\mathrm{O}}_2}$ and five correlations for the effective interfacial area,${\mathrm{a}}_{\mathrm{e}}$, as detailed in

Table 2. Mass transfer correlations set used in the developed model.

	Authors	Correlations	Ref.
${\mathit{k}}_{\mathit{G}}$
	Onda et al.	${\displaystyle \frac{k_{G}RT}{a_t{D}_G}}=5.23{\left({\displaystyle \frac{V_m^{\mathrm{*}}}{{\mu }_G{a}_t}}\right)}^{0.7}{\left({\displaystyle \frac{{\mu }_G}{{\rho }_G{D}_G}}\right)}^{{\displaystyle \frac{1}{3}}}{\left(a_t{d}_p\right)}^{-2}$	[26]
${\mathit{k}}_{\mathit{L}}$
1	Tung and Mah	${\displaystyle \frac{k_L{d}_p}{D_L}}=0.918{\left({\displaystyle \frac{{\mu }_L}{D_L{\rho }_L}}\right)}^{{\displaystyle \frac{1}{2}}}{\left({\displaystyle \frac{L_m^{\mathrm{*}}}{{\mu }_L{a}_t}}\right)}^{{\displaystyle \frac{1}{3}}}{\left({\displaystyle \frac{a_t}{a_e}}\right)}^{{\displaystyle \frac{1}{3}}}{\left({\displaystyle \frac{d_p^3{\rho }_L^{2}r{\omega }^2}{{\mu }_L^2}}\right)}^{{\displaystyle \frac{1}{6}}}$	[27]
2	Onda et al.	$k_L{\left({\displaystyle \frac{{\rho }_L}{{\mu }_{L}r{\omega }^2}}\right)}^{{\displaystyle \frac{1}{3}}}=0.0051{\left({\displaystyle \frac{L_m^{\mathrm{*}}}{\mathrm{a}{\mu }_L}}\right)}^{{\displaystyle \frac{2}{3}}}{\left({\displaystyle \frac{{\mu }_L}{{\rho }_L{D}_L}}\right)}^{-{\displaystyle \frac{1}{2}}}{\left(a_t{d}_p\right)}^{0.4}$	[26]
${\mathit{a}}_{\mathit{e}}$
1	Billets and Schultes	${\displaystyle \frac{a_e}{a_t}}=1.5{\left(a_t{d}_h\right)}^{-0.5}{\left({\displaystyle \frac{{\rho }_L{u}_L{d}_h}{{\mu }_L}}\right)}^{-0.2}{\left({\displaystyle \frac{{\rho }_L{u}_L^2{d}_h}{{\sigma }_L}}\right)}^{0.75}{\left({\displaystyle \frac{u_L^2}{r{\omega }^2{d}_h}}\right)}^{-0.45}$	[29]
2	Onda et al.	${\displaystyle \frac{a_e}{a_t}}=1-\mathrm{e}\mathrm{x}\mathrm{p}\left[-1.45{\left({\displaystyle \frac{{\sigma }_c}{{\sigma }_L}}\right)}^{0.75}{\left({\displaystyle \frac{L_m^{\mathrm{*}}}{a_t{\mu }_L}}\right)}^{0.1}{\left({\displaystyle \frac{a_t{L}_m^{2*}}{r{\omega }^2{\rho }_L^2}}\right)}^{-0.05}{\left({\displaystyle \frac{L_m^{2\mathrm{*}}}{{\sigma }_L{\rho }_L{a}_t}}\right)}^{0.2}\right]$	[26]
3	Rajan et al.	${\displaystyle \frac{a_e}{a_t}}=54999{\left({\displaystyle \frac{{\rho }_L{d}_p{u}_L}{{\mu }_L}}\right)}^{-2.2186}{\left({\displaystyle \frac{{u_L}^2}{r{\omega }^2{d}_p}}\right)}^{-0.1748}{({\displaystyle \frac{{\rho }_L{d}_p{u_L}^2}{{\sigma }_L}})}^{1.3160}$	[30]
4	Puranik and Vogelpohl	${\displaystyle \frac{a_e}{a_t}}=1.045{\left({\displaystyle \frac{L_m^{\mathrm{*}}}{a_t{\mu }_L}}\right)}^{0.041}{\left({\displaystyle \frac{L_m^{2\mathrm{*}}}{{\sigma }_L{\rho }_L{a}_t}}\right)}^{0.133}{\left({\displaystyle \frac{{\sigma }_{\mathrm{C}}}{{\sigma }_L}}\right)}^{0.182}$	[31]
5	Kolev	${\displaystyle \frac{a_e}{a_t}}=0.584{\left({\displaystyle \frac{a_t{u_L}^2}{r{\omega }^2}}\right)}^{0.196}{\left({\displaystyle \frac{{\rho }_{L}r{\omega }^2}{{a_t}^2{\gamma }_L}}\right)}^{0.49}{\left(a_t{d}_p\right)}^{0.42}$	[32]

. The purpose of the sensitivity analysis was to evaluate the model’s response to the selected correlations, which have been previously employed by various researchers in absorption column studies [20,22,24,28]. To ensure the accuracy of the results, the model was first validated, and all subsequent predictions and design calculations were carried out using the most appropriate mass transfer correlations. Accurate estimation of the heat and mass transfer coefficients requires detailed knowledge of key physical and hydrodynamic properties, including the density, viscosity, surface tension, and heat capacity of the ionic solvent, as well as gas diffusivity and liquid holdup. The relevant equations and parameters are summarized in

Table 3. Physical and hydrodynamic properties utilized in the developed model.

Property	Correlations/Method	Ref.
[bmim][PF6] density, kg/m3	${\rho }_{\mathrm{I}\mathrm{L}}=-1.19T+1721.1$	[3]
[bmim][PF6] surface tension, N/m	${\sigma }_{\mathrm{I}\mathrm{L}}=-2.81\times {10}^{-4}T+0.1305$	[3]
[bmim][PF6] viscosity, Pa·s	${\mu }_{\mathrm{I}\mathrm{L}}=2.55\times {10}^{-6}\exp \left({\displaystyle \frac{3091}{T}}\right)$	[3]
Diffusivity of CO2 in IL solvent, m2/s	$D_{C{O}_2-IL}=4.0\times 10^{-33}{T}^{8.9507}$	[3]
Heat capacity of IL, J/kmol·K	${Cp}_{\mathrm{I}\mathrm{L}}=\left(388.01-4.016\times {10}^{-1}T+1.567\times {10}^{-3}{T}^2\right)\times 1000$	[33]
Henry’s constant of CO2 in [bmim][PF6], Pa	${He}_{{CO}_{2-IL}}=(0.0042T^3-3.7734T^2+1132.5T-113406)\times 10^6$	[34]
Molar heat capacity of gas, J/kmol·K	DIPPR method (empirical equation)	[35]
Thermal conductivity of the gas, W/m·K	DIPPR method (empirical equation)	[35]
Gas viscosity	Herning–Zipperer method	[36]
Gas diffusivity	Fuller correlation	[37]
Pressure drop	${\Delta P}_{RPB}={\displaystyle \frac{150{\mu }_G{\left(1-\epsilon \right)}^2}{{d_P}^2{\epsilon }^3}}\left({\displaystyle \frac{Q_G}{2\mathbf{п}H}}\right)ln{\displaystyle \frac{r_o}{r_i}}$ $+\epsilon \left(-0.08-Q_G+\left(2000{\left(RPM\right)}^{1.22}+{\omega }^{1.22}\right){Q_G}^2\right)$ $+{\displaystyle \frac{1.75\left(1-\epsilon \right){\rho }_L}{d_P{\epsilon }^3}}{\left({\displaystyle \frac{Q_G}{2\mathbf{п}H}}\right)}^2\left({\displaystyle \frac{1}{r_i}}-{\displaystyle \frac{1}{r_o}}\right)+{\displaystyle \frac{1}{2}}{\rho }_G{\omega }^2\left({r_o}^2-{r_i}^2\right)$	[38]
Holdup	$\epsilon =0.039{\left({\displaystyle \frac{g}{g_0}}\right)}^{-0.05}{\left({\displaystyle \frac{U_L}{U_0}}\right)}^{0.6}{({\displaystyle \frac{v_L}{v_0}})}^{0.22}$	[39]
Rotation energy	$P_{motor}=1.2+1.1\times {10}^{-3}{\rho }_L{r}_o^2{\omega }^2{Q}_L$	[40]

. The regressed correlations for viscosity, density, surface tension, and diffusion coefficient were derived from the experimental data reported by Zhang et al. [3], covering a temperature range of 293–336 K. The other correlations required for modeling the RPB absorber are provided in Table 3.

2.2.1. Numerical Solution

The CO₂ absorption system using an ionic liquid in an RPB was modelled by simultaneously solving Equations (7)–(15) under the stated assumptions. Given the counter-current flow configuration, the operating conditions of the gas stream were defined at the outer radius, while those of the IL were specified at the inner radius. In this study, these equations are first-order ordinary differential equations (ODEs) that require initial conditions for their solution. The initial conditions correspond to the operating conditions of the inlet gas and solvent entering the RPB. Since the calculations begin at the outer radius, where only the gas inlet conditions are known and the solvent outlet conditions are unknown, initial guesses for the solvent outflow at this radius were assumed using the shooting method. Once the initial conditions at the outer radius are estimated, the equations are solved using the finite difference method, and the results are computed point by point along the radial direction until the inner radius is reached, where the predicted solvent inlet conditions are compared with the operational conditions obtained from experimental data. The error is then defined and iteratively minimized until convergence is achieved, ensuring the accuracy of the predicted outcomes.

2.2.2. Experimental Data Source

Based on the experimental data reported by Zhang et al. [3], the CO₂ absorption using [bmim][PF₆] in an RPB equipped with stainless steel wire mesh packing was modelled and simulated. The operating conditions and other parameters of the packed bed, used as inputs for the model, are summarized in

Table 4. Operating parameters are used for modeling the RPB.

Operating Variables	Value
Temperature, K	293
Pressure, atm	1
Liquid flow rate, mL/min	29.2−102.2
Gas flow rate, L/min	0.6−1.0
CO2 mole fraction	0.1
Solvent mole fraction	1.0 (pure)
Pressure drop in the bed, kPa	<2

and

Table 5. Dimensions of the RPB.

Parameter	Value
$r_i$, cm	1
$r_o$, cm	3
H, cm	2
Packing type	Stainless wire mesh

.

2.3. Sensitivity Analysis

Sensitivity analysis was performed using the correlations summarized in Table 2. Among the various correlations available in the literature, those proposed by Tung and Mah [27] and Onda et al. [26] were adopted to estimate the liquid-phase mass transfer coefficient within the framework of the rate-based model. This approach is adopted because the absorption process with ionic solvents is film-controlled. In addition, five correlations were selected for the effective surface area, as detailed in Table 2. For the gas phase, the correlation developed by Onda et al. [26] was applied in all sensitivity analysis cases.

2.4. Iterative RPB Scale-Up Approach

A rigorous design methodology, proposed by Shamsi et al. [41], was employed in this study to estimate the dimensions of the RPB absorber at an industrial scale. The corresponding iterative procedure is illustrated in Figure 2. The inlet flue gas operating conditions for the RPB absorber were based on those of an existing industrial unit in a petrochemical complex [42].

Key operating parameters of the flue gas are summarized in

Table 6. Operating conditions of flue gas from the petrochemical complex [42].

Flue Gas Specifications
Temperature, °C	40
Pressure, bar abs	1
Total flow, kmol/h	6447.8
Component (mole %)
CO2	10.74
N2	65.73
O2	1.53
H2O	21.18
Ar	0.82

. Following the proposed methodology, the internal radius of the packing was first estimated using the correlation reported by Agarwal et al. [43]. After determining the specific surface area of the packing and the liquid holdup, the gas superficial velocity at flooding conditions was calculated using the correlation established by Jassim et al. [44]. The axial height (H) of the RPB absorber was then estimated based on the superficial gas velocity, assuming operation at approximately 80% of the flooding velocity. Accordingly, the RPB was designed to operate below flooding conditions to ensure efficient and stable performance. Initially, a value for $r_o$was assumed. After calculating the mass transfer coefficients and Henry’s constant, the NTU and ATU were subsequently determined using Equations (16) and (17).

$$\mathrm{N}\mathrm{T}\mathrm{U}=\mathit{ln}{\displaystyle \frac{Y_2}{Y_1}}$$

(16)

$$\mathrm{A}\mathrm{T}\mathrm{U}={\displaystyle \frac{F_G}{HP{K}_G}}$$

(17)

Finally, the $r_{o,new}$ is determined through an iterative approach, as detailed in Figure 2. As can be seen, the design of an RPB absorber for dimension estimation, specifically regarding axial height, outer radius, and inner radius, depends on the correlations, which significantly affect its separation performance at the industrial scale.

3. Results and Discussion

3.1. Thermodynamic Modeling Outcomes

The validity of the thermodynamic model for CO₂ absorption by [bmim][PF6] was assessed using experimental data reported by Shiflett and Yokozeki [18], as shown in Figure 3. As evident from the figure, the results are plotted for different temperatures; each of them is a specific isotherm. For each isotherm, solubility increases with increasing pressure, whereas at a constant pressure, solubility decreases with rising temperature. At 348 K, the decrease in solubility is sufficiently pronounced that the corresponding plot appears nearly linear. In this study, data were evaluated over a pressure range from low pressures up to 2025 kPa. Data in the low-pressure range are particularly critical for the rate-based model, as they enable accurate prediction of CO₂ solubility and improve the estimation of Henry’s constant. Given the low partial pressure of CO₂ in feed gas, the rate-based model primarily relies on low-pressure solubility data. In contrast, the thermodynamic model was validated over a broader pressure range to provide sufficient information for accurate parameter fitting. By encompassing the entire pressure range, the thermodynamic model can be effectively integrated with the rate-based model, enabling it to utilize low-pressure data while also accommodating higher pressures.

3.2. Process Modeling Outcomes

Figure 4 illustrates the validation of the developed model for CO₂ absorption in an RPB by comparing the predicted and experimental k_la values as a function of rpm at different liquid and gas flow rates. As shown, the model accurately reproduces the experimental data reported by Zhang et al. [3] under operating conditions of G = 0.95 L.min⁻¹ and L = 43.8 mL.min⁻¹, with an AARD of 7.29%, and at G = 0.85 L.min⁻¹ and L = 43.8 mL.min⁻¹, with an AARD of 6.11%. These outcomes confirm the strong predictive capability of the model. Increasing the rotational speed from 1000 to 3300 r/min consistently enhances k_la. However, k_La values are lower at higher gas flow rates, primarily due to the increased liquid-phase resistance during CO₂ absorption by the [bmim][PF₆] solvent.

Figure 5 illustrates the validation of the developed model for the physical absorption process. As shown, the developed model for CO₂ absorption in the RPB accurately predicts the experimental k_La vs. temperature data, achieving an AARD of 7.88% at L = 43.8 mL.min⁻¹ and 8.64% at L = 58.4 mL.min⁻¹. In both cases, increasing the temperature from 293 to 335 K leads to a rise in k_La. This enhancement in the liquid-side mass transfer coefficient is attributed to the reduction in the viscosity of the ionic solvent with rising temperature, which leads to an enhancement in the diffusion coefficient of CO₂ in the solvent.

Following validation and confirmation of the model’s accuracy for CO₂ absorption, the effects of different parameters along the radial direction of the packing were investigated. As shown in Figure 6, k_La decreases along the radial direction at all rotational speeds. The mass transfer efficiency reaches its maximum near the inner radius of the bed due to the longer contact time between the gas and liquid phases and then declines toward the outer periphery, where the effective interfacial contact is reduced. At any given radial position, increasing the rotational speed (from 1100 to 3300 r/min) leads to an increase in k_La due to the reduction in ${He}_{{CO}_{2-IL}}/{\mathrm{k}}_{L,{CO}_2}$ for the CO₂-IL system. Higher rpm increases the centrifugal force, which in turn enlarges the gas–liquid interfacial area and turbulence, thereby enhancing mass transfer. This demonstrates a direct correlation between rotational speed and mass transfer performance. The reduction in mass transfer resistance can be attributed to a decreased diffusion depth, a thinner liquid film, and smaller liquid droplets, all of which contribute to improved k_La. However, an excessive increase in rotational speed has a limited effect on k_La, as the reduction in mass transfer resistance is offset by the decreased gas–liquid contact time, which is unfavorable for the absorption process [3].

Figure 7 illustrates the variation in the k_Ga along the radial packing length at different rotational speeds. As can be seen, the value of k_Ga decreases along the radius direction (from r_i to r_o) at all rotational speeds. The k_Ga is a function of the L/G ratio, solvent concentration, and rotational speed. Increasing the rotational speed leads to a reduction in mass transfer resistance, enhanced liquid dispersion, smaller droplet sizes, and an increased effective contact area [24]. Consequently, k_Ga increases with higher motor speed, indicating a direct correlation between rotational speed and k_Ga in this system.

Figure 8 shows the radial distribution of CO₂ mole fraction for different inlet concentrations of flue gas, ranging from 0.05 to 0.2. As the gas passes through the packing, CO₂ is efficiently absorbed by the IL, resulting in a significant decrease in its concentration up to a radial distance of approximately 0.02 m. Beyond this radial position, toward the inner radius, the flue gas exits the packed bed with nearly negligible CO₂ levels. A steeper radial gradient in CO₂ mole fraction is observed at higher inlet concentrations, reflecting the strong absorption capacity of the [bmim][PF₆] solvent over a wide range of flue gas compositions. These results demonstrate the effectiveness of the system in handling flue gases with varying CO₂ content.

Figure 9 illustrates the radial distribution of the gas-phase flow rate for various inlet flue gas flow rates entering the absorber bed. As noted earlier, the highest CO₂ concentration and mass transfer driving force are observed near the external radius of the bed. Due to the counter-current radial flow configuration, where the gas and liquid phases move in opposite directions, CO₂ from the incoming flue gas is progressively absorbed as it passes through the packing of the RPB. Consequently, both the CO₂ concentration and the gas-phase flow rate decrease along the radial direction, with the treated gas ultimately exiting the system at the inner radius. As shown in Figure 9, a higher inlet flue gas flow rate causes a steeper initial gradient in the gas-phase flow rate along the radial direction. The gradient then levels off near the mid-radius of the packing, with the exact position of this transition determined by the inlet gas flow rate.

Figure 10 illustrates the variation in the liquid-phase flow rate along the packing length at different inlet solvent flow rates. As shown, the liquid flow rate increases from the internal radius toward the external radius due to CO₂ absorption by the solvent. In this system, mass transfer resistance is predominantly in the liquid phase, causing k_La to increase from the outer to the inner radius. This rise in k_La reduces the mass transfer driving force, which explains the observed trend in the liquid-phase flow rate.

Figure 11 illustrates the radial temperature distribution of the IL-based absorption system for different inlet gas temperatures. As the flue gas flows through the packing, its temperature increases along the radial direction due to heat exchange with the liquid phase. Once thermal equilibrium is reached, the gas exits the packing from the inner radius with a nearly constant temperature. As the inlet gas temperature rises, the temperature difference between the packing’s inlet and outlet also grows. For instance, when the gas enters the packing at 293 K, the temperature difference is approximately 2.8 K, whereas for an inlet temperature of 323 K, it increases to about 9 K. Although increasing the temperature lowers the solvent viscosity and enhances the gas diffusion coefficient, it simultaneously decreases the gas solubility in the solvent. Generally, in such systems, an increase in temperature leads to a decrease in absorption efficiency. Although increasing the temperature lowers the solvent viscosity and enhances the gas diffusion coefficient, it simultaneously decreases the gas solubility in the solvent. Therefore, it is preferable to operate the system at lower temperatures, especially given the high rotational speed of the system. For the IL-based solvent, operating close to ambient temperature is preferred to maximize CO₂ absorption performance.

Figure 12 shows the CO₂ capture level along the radial position at diverse motor speeds. The gradual absorption of CO₂ throughout the packing bed results in solvent saturation, a reduction in the driving force, and the establishment of equilibrium, ultimately leading to improved overall absorption efficiency along the radial path. Increasing the rotational speed in RPB absorbers promotes the formation of smaller liquid droplets, enlarges the gas–liquid interfacial area, and reduces mass transfer resistance, all of which contribute to enhanced CO₂ removal performance [22]. As shown in Figure 12, at a rotational speed of 3500 r/min, the absorption efficiency reaches nearly 100% around the mid-radius of the packing (r ≈ 0.02 m) due to the increased centrifugal force and intensified mass transfer. In this system, the unique physical properties of the IL-based solvent—compared to those of conventional chemical solvents—enable the use of higher rotational speeds. However, in centrifugal systems such as RPBs, excessively high rotational speeds increase energy consumption without a proportional improvement in removal efficiency. Therefore, determining the optimal rotational speed is essential to minimizing energy penalties and ensuring efficient operation.

Figure 13a,b illustrate the influence of rotational speed on the mass transfer resistance in the liquid and gas phases along the radial direction of the packing. The liquid-phase resistance constitutes the dominant contribution, while the gas-phase resistance remains the lowest, confirming that the process is governed by liquid film control. Across all examined rotational speeds (1000–3500 rpm), the liquid-phase mass transfer resistance decreases along the radial direction from the external to the internal radius of the packing. At the outer radius, the liquid film thickens due to CO₂ absorption, which reduces the liquid velocity and consequently increases the mass transfer resistance compared to the inner radius.

In contrast, the gas-phase resistance exhibits an opposite trend, decreasing toward the outer radius. The high viscosity of the IL-based solvent suppresses diffusion in the liquid phase, thereby lowering the mass transfer coefficient and increasing the overall resistance. In this system, an inverse relationship exists between the rotational speed and the thickness of the liquid film and droplets, directly influencing the mass transfer coefficient. However, given the quantitatively small thickness of the liquid film, increasing the rotational speed does not significantly alter the liquid-phase resistance. Consequently, as shown in Figure 13, the high viscosity of the fluid results in a narrow range of resistance variation, with values remaining tightly clustered.

At any given rotational speed, the liquid-phase mass transfer resistance increases from the inner to the outer region of the packing. This behavior can be attributed to a reduction in both the liquid film thickness and the liquid-phase mass transfer coefficient. Conversely, the gas-phase resistance decreases due to an increase in its mass transfer coefficient.

Figure 14 illustrates the radial variation in pressure drop across the packing bed under different rotational speeds. Since pressure drop directly influences energy consumption, design optimization, and the selection of suitable packing materials, its analysis is crucial for evaluating the performance of an RPB [22]. The pressure drop in an RPB is influenced by several factors, including rotational speed, packing characteristics (type and size), fluid flow rates, and liquid viscosity. This pressure loss arises from the resistance the gas phase encounters while flowing through the packed bed, which becomes more pronounced at elevated rotational speeds.

The effects of the rotational speeds on holdup at two distinct liquid flow rates are shown in Figure 15. Several parameters, including rotational speed, liquid flow rate, and solvent viscosity, influence the holdup in an RPB. Increasing the rotational speed promotes the formation of dispersed liquid droplets, diminishes the viscous resistance encountered by the liquid, and thins the liquid film on the packing surface [22]. Consequently, the holdup within the bed decreases as the flow regime transitions from the pore regime to the film regime. Moreover, at a constant temperature, increasing the liquid flow rate results in a corresponding rise in holdup. Overall, near the inner radius of the packing, where the local liquid flow rate is higher, the holdup attains its maximum value and then gradually decreases along the radial direction. This behavior underscores the positive influence of liquid flow rate and the inverse effect of rotational speed on holdup.

3.3. Sensitivity Analysis Results

Figure 16 illustrates the impact of rotational speed on the k_la, based on experimental data reported in the literature [3]. In this analysis, the liquid-phase mass transfer coefficient was determined using the correlation proposed by Tung and Mah [27]. Five simulation runs were conducted using the effective interfacial area (a_e) values listed in Table 2, corresponding to five distinct case studies. The best agreement between model predictions and experimental data was achieved for Case 1, where the correlation proposed by Billet and Schultes [29] was applied to estimate a_e. Consequently, Case 1 was selected to validate the model’s performance. The purpose of this section is to identify and evaluate the most relevant empirical correlations reported in the literature for the present system. Furthermore, the rate-based model predictions presented here were obtained using the set of correlations associated with Case 1.

Figure 17 illustrates the radial variation in the k_La for five distinct case studies. In Figure 17a, k_la is calculated using the correlation proposed by Onda et al. [26], while Figure 17b shows the results based on the correlation by Tung and Mah [27]. Both subfigures reveal an increasing trend in k_La from radially inward, consistent with the trend previously discussed in Figure 6. Among the five cases, Case 1 exhibits the best performance across the packing, as corroborated by comparison with the experimental data shown in Figure 16.

3.4. Scale-Up Results

Figure 18 depicts the variation in the outer radius as a function of the liquid-to-gas ratio. The scale-up results were derived using the iterative procedure outlined in the flowchart shown in Figure 2. Mass transfer coefficients were calculated based on the correlations from Case 1 of the sensitivity analysis, conducted at a rotational speed of 2000 rpm. One of the main challenges in scaling up an RPB absorber is determining the optimal L/G ratio. Figure 18 illustrates the impact of varying the L/G ratio from 0.1 to 1.0 vs. the external radius of the packing. At the optimal L/G ratio, the estimated industrial-scale dimensions of the RPB absorber, calculated based on the flue gas operating conditions provided in Table 6, are an axial height of 0.48 m, an outer radius of 1.55 m, and an inner radius of 0.53 m.

Figure 19 illustrates the radial profile of CO₂ removal efficiency in the large-scale RPB absorber. The lowest CO₂ removal efficiency is observed at the outer radius, where the flue gas enters the packing. Efficiency increases progressively along the radial direction, reaching approximately 98% at the inner radius, where the treated gas exits. This high removal efficiency underscores the effective performance of the selected IL solvent under industrial-scale operating conditions.

The relationship between motor power consumption and the external radius of the packing in the RPB absorber is presented in Figure 20. At an outer radius of 1.55 m, the power consumption reaches an optimal value of 24.6 kW. This finding corroborates the optimal outer radius determined via the rigorous design approach, confirming its suitability for industrial-scale operation. It should be noted that due to the higher viscosity of ILs, reducing drag forces requires higher rotational speeds compared to amine systems; consequently, greater motor power is clearly needed.

3.5. Comparison of k_La Value Between RPB and Conventional PB

To evaluate and compare the mass transfer performance of a conventional absorption column and an RPB using an IL solvent, k_La values were calculated for both systems under identical operating conditions, as presented in

Table 7. Comparison of RPB and PB based on the rate-based model for CO₂ absorption by IL solvent.

Operating Parameters	RPB	PB
Liquid flow rate, mL/min	50	50
Gas flow rate, L/min	0.5	0.5
CO2 concentration, mol %	10	10
Packing surface area, m2/m3	850	2000
Packing volume, cm3	50.26	98.17
Pressure, atm	1	1
Temperature, K	298	298
kLa, 1/s	0.024 at rpm = 2000 0.032 at rpm = 3000	0.0019

. The operating parameters in Table 7 were derived from the values reported in Table 4 and Table 5. Based on the modeling and simulation results for the RPB at two distinct rotational speeds, the data in Table 7 indicate that the mass transfer coefficients are substantially higher than those of the conventional packed bed, confirming the superior performance of the RPB system. These simulation results further demonstrate the model’s capability to accurately predict and compare the performance of both column types across a wide range of operating conditions, offering valuable insights for process optimization.

4. Conclusions and Recommendations for Future Work

A rate-based mathematical model was developed to simulate CO₂ absorption in an RPB using [bmim][PF₆] as the solvent. The UNIQUAC model parameters were optimized, and the validated results showed excellent agreement with experimental data. The rate-based model accurately predicts experimental outcomes under various operating conditions, achieving an AARD of 7.48%, thereby confirming its robustness. Increasing the rotational speed from 1100 to 3300 r/min enhances mass transfer by reducing liquid-phase resistance, improving liquid distribution, and enlarging the effective interfacial area, which collectively lead to higher values of both k_La and k_Ga. Additionally, higher gas flow rates cause a more pronounced initial decline in flow velocity, which stabilizes around the mid-radius of the packing, while the liquid flow rate increases toward the outer radius due to CO₂ absorption. Although elevated temperatures reduce solvent viscosity and enhance gas diffusivity, they simultaneously decrease CO₂ solubility, indicating that lower operating temperatures are more favorable, particularly at high rotational speeds. As the rotational speed increases, liquid-phase mass transfer resistance rises because of liquid film thinning and a reduction in the liquid-side mass transfer coefficient, whereas gas-phase resistance decreases. Liquid holdup increases with higher liquid flow rates but decreases with increasing rotational speed. Sensitivity analysis identified the correlations of Tung and Mah [27] for the liquid-side mass transfer coefficient, Onda et al. [26] for the gas-side, and Billet and Schultes [29] for the interfacial area as the most reliable. These findings highlight the potential of RPB technology for intensified CO₂ capture, particularly when utilizing IL solvents. For future research, it is recommended to conduct an economic assessment of green solvents in comparison to conventional chemical solvents. Such an evaluation would provide clearer insights into the industrial-scale adoption of HiGee technology and support more informed decision-making for stakeholders in the field of carbon capture.