Evaluation of an Industrial Absorption Process for Carbon Capture Using K₂CO₃ Promoted by Boric Acid

Abstract

Hot potassium carbonate (HPC) process aims to remove the CO₂ present on synthesis gas. This removal is done in an absorption process, where takes place the reaction of CO₂ with a K₂CO₃ solution. This reaction is slow and H₃BO₃ can be used to increase the rate of reaction. The rate-based model is the most suitable way to model the process. This approach uses different correlations to calculate important mass transfer and hydraulic parameters, such as: mass transfer coefficient, interfacial area, and liquid holdup. This paper aims to evaluate the performance of many correlations to represent the HPC process. An automatic procedure was developed to test a high number of equations, using MATLAB and Aspen Plus software. The best set of correlations was found after a comparison with industrial data. Correlations with errors less than 10% for the entire evaluated operating conditions were calculated for mass transfer coefficient and the interfacial area, as well as for liquid holdup.

Keywords:
carbon capture; rate-based model; potassium carbonate; liquid holdup; mass transfer; interfacial area; synthesis gas

Introduction

The hot potassium carbonate (HPC) process was developed in 1950s by Benson and Field to remove the carbon dioxide (CO₂) present in the synthesis gas. Since then, it is one of the most used processes for carbon capture in the industry, with more than 850 plants in operation around the world.¹

The solvent used in the HPC process is potassium carbonate (K₂CO₃). The main advantages of using K₂CO₃ are lower energy consumption when compared to other solvents; lower toxicity in comparison with ammonia (NH₃), and amines; lower capital cost, as it does not demand a high level of heat integration and it does not show serious corrosion problems.²

The HPC process has two main drawbacks: the K₂CO₃ concentration in the solution is limited due to precipitation of the bicarbonate salts; and the reaction kinetics of K₂CO₃ with CO₂ is quite slow when compared to other solvents. Promoters can be used to improve the reaction kinetics and boric acid (H₃BO₃) has shown excellent results, both on pilot and industrial scales.¹

To have an accurate representation of the HPC process, the rate-based model must be used. It is based on the Maxwell-Stefan equations³ and on the Two Films Theory⁴ and depends on the choice of mass transfer and hydraulic correlations. They are used to predict mass transfer coefficient, interfacial area, and liquid holdup.

Previous works investigated how those correlations impact the model prediction of a CO₂ capture process. Gaspar and Cormos⁵ evaluated different combinations of correlations to estimate the mass transfer coefficient, interfacial area, and liquid holdup for amine-based systems. The results were compared with experimental data from four different pilot plants and validated according to the CO₂ composition profile in the absorption column. The correlation proposed by Wang et al.⁶ provided the best results for the prediction of the mass transfer coefficient and the interfacial area, while the correlation of Rocha et al.⁷ showed the best performance for predicting liquid holdup.

Zhang and Chen⁸ used the equations proposed by Bravo and co-workers⁷ to calculate the mass transfer coefficients and evaluated the performance of these equations based on the results of 19 experiments using monoethanolamine (MEA) as solvent. The validation variables were the loading of the rich solution at the absorber bottom, the fraction of CO₂ removed, and the energy consumption in the stripper column. The authors obtained errors lower than 7% for all cases.

Qi et al.⁹ used the equations proposed by Onda et al.¹⁰ for the calculation of mass transfer coefficients and interfacial area, and the equation of Stichlmair et al.¹¹ for estimating liquid holdup. The model results were compared with experimental data from a CO₂ absorption column using NH₃ as solvent, and the validation variables were the CO₂ removal rate, NH₃ composition in the clean gas, absorber temperature profile, and the global mass transfer coefficient. The results showed significant errors for the estimation of the CO₂ removal rate and for the NH₃ composition in the clean gas.

Hemmati et al.¹² evaluated the combination of several correlations for calculating the mass transfer coefficient, interfacial area, and liquid holdup, to predict the behavior of the CO₂ capture process with a solution of methyldiethanolamine using piperazine as additive. The obtained results were compared to 24 experiments carried out in a pilot plant and indicated that the equation of Bravo and co-workers⁷ was the most suitable for the mass transfer coefficient and interfacial area calculations. To calculate the liquid holdup, the equations of Stichlmair et al.¹¹ and Billet and Schultes¹³ provided the same results. The validation variables were the absorber temperature profile, rich solution loading, and fraction of CO₂ captured.

Considering the carbon capture using potassium carbonate promoted with H₃BO₃, there is no study in the literature which says what are the suitable mass transfer and hydraulic correlations. This paper presents the Aspen Plus¹⁴ simulation of the HPC process and the assessment of several correlations to calculate mass transfer coefficient, liquid holdup, and interfacial area. The developed model was validated against plant data and the best set of correlations was found. As the assessment of many correlations is an exhaustive process, an automatic procedure was developed to do it.

Experimental

The HPC process investigated in this work is in an ethylene oxide industrial plant and it is highlighted in Figure 1. Carbon dioxide is a by-product of the ethylene oxide reactor, which should be removed to avoid a decrease in catalyst selectivity. The formation of CO₂ in the reactor increases when the lifetime catalyst approaches its end.¹⁵

Figure 1
Industrial process flow diagram of the hot potassium carbonate of an ethylene oxide industrial plant.

After leaving the ethylene oxide recovery column, the CO₂-rich gas (FGAS) exchanges heat with the lean solution (LSOL) and it is fed into the base of the absorption column (ABS), while the solution enters at the top. The contact between the phases occurs through a countercurrent flow inside the column, enabling the absorption and diffusion of CO₂ in the K₂CO₃ solution promoted with H₃BO₃ and the consequent gas purification.

The treated gas leaves the top of the absorption column and is partially condensed to remove water. The vapor stream (CLEANGAS) is recycled back to reactor, as shown in Figure 1.

The rich solution of K₂CO₃ that leaves the absorber at the bottom (RICHOUT) exchanges heat with the recirculated lean solution (LSOL-REC) and then enters in the top stage of the stripper column (STP). Low-pressure steam (FSTM) is fed directly into the stripper, promoting the CO₂ desorption, and regenerating the solution’s absorption capacity. The removed CO₂ (CO2) is sold to oxygen factories, and the lean solution is pumped back to top stage of the absorption column.

The focus of the paper (the absorption column and the stripper column) is the part highlighted in red, which is shown in Figure 2 (simulated in Aspen Plus). The specifications of each equipment are presented in Table 1.

Table 1
Absorption and stripper columns specifications

Equipment	Calculation routine	Specification
ABS	RateFrac	pressure: 20.7 kgf cm-2 stages number: 40 packing: structured MELLAPAK 250Y packing column diameter: 2.38 m
STP	RateFrac	pressure: 1.1 kgf cm-2 stages number: 35 packing: random FLEXIMAX 300 packing column diameter: 1.68 m steam (FSTM) feed stage: 34

ABS: absorber; STP: stripper; FSTM: low-pressure steam.

Figure 2
Process flowsheet diagram implemented in Aspen Plus software.

Figure 2 also presents the average data of the process variables, measured over 20 months of operation. These data are later used to validate the best set of correlations that should be used in the evaluated absorption process.

Modelling

The HPC process promoted with H₃BO₃ has a high number of electrolytes in the liquid phase. The suitable thermodynamic model to describe the behavior of this system is the electrolytic nonrandom two-liquid (ELECNRTL).²,⁵ As the absorption column operates at high pressures, the Redlich-Kwong equation of state is used for the vapor phase.

The chemical species defined as Henry components were argon (Ar), carbon dioxide (CO₂), nitrogen (N₂), oxygen (O₂), methane (CH₄), ethylene (C₂H₄), ethylene oxide (C₂H₄O), and ethane (C₂H₆). Under the process conditions, all these components are beyond their critical point, except ethylene oxide (C₂H₄O); however, due to its extremely low composition, the Henry’s law can also be applied to this component.

Equation 1 shows the calculation of Henry’s law constant (H_i,j) for a component i dissolved in a solvent j as a function of temperature (T):

(1) $$\ln \left({\mathrm{H}}_{\mathrm{i},\mathrm{j}}\right)={\mathrm{a}}_{\mathrm{i}\mathrm{j}}+\frac{{\mathrm{b}}_{\mathrm{i}\mathrm{j}}}{\mathrm{T}}+{\mathrm{c}}_{\mathrm{i}\mathrm{j}}\ln (\mathrm{T})+{\mathrm{d}}_{\mathrm{i}\mathrm{j}}\mathrm{T}$$

The parameters a_ij, b_ij, c_ij, and d_ij for C₂H₄O were obtained from Conway et al.,¹⁶ while the parameters of the components were determined through numerical regression from the Aspen Plus databank. Table 2 presents the parameters for the solute and solvent pairs regarding the process under study.

Table 2
Henry’s law binary parameters

Component i	Component j	aij	bij	cij	dij	Temperature unit	Pressure unit
CO2	H2O	159.2	-8477.7	-21.96	0.0058	°C	bar
N2	H2O	164.99	-8432.8	-21.56	-0.0084	°C	bar
O2	H2O	144.41	-7775.0	-18.4	-0.0094	°C	bar
CH4	H2O	183.78	-9111.7	-25.04	0.00014	°C	bar
C2H4	H2O	152.94	-7959.7	-20.51	0	°C	bar
Ar	H2O	169.48	-8137.13	-23.25	0.0031	°C	bar
C2H6	H2O	268.43	-13368.1	-37.55	0.0023	°C	bar
C2H4O	H2O	24.5	-3200	0	0	K	Pa
CO2	C2H6O2	-83.82	2941.4	14.05	0	°C	bar
N2	C2H6O2	10.21	0	0	0	°C	bar
O2	C2H6O2	9.89	0	0	0	°C	bar
CH4	C2H6O2	8.68	0	0	0	°C	bar
C2H4	C2H6O2	-1.99	2751.5	0	0	°C	bar
Ar	C2H6O2	8.86	161.1	0	0	°C	bar
C2H6	C2H6O2	10.24	-822.03	0	0	°C	bar

_ijijijij24et al¹⁴

Chemical reactions

The overall reaction of the CO₂ absorption process with a K₂CO₃ solution is described by reaction 2:¹⁷

(2) $${\mathrm{C}\mathrm{O}}_2+{\mathrm{K}}_2{\mathrm{C}\mathrm{O}}_3+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons 2{\mathrm{K}\mathrm{H}\mathrm{C}\mathrm{O}}_3$$

K₂CO₃ and KHCO₃ are strong electrolytes, which completely and quickly dissociate in contact with water; therefore, it is possible to consider that they are present in the liquid phase only in the form of K⁺ ions, according to the following reactions:¹⁷,¹⁸

(3) $${\mathrm{K}}_2{\mathrm{C}\mathrm{O}}_3\to 2{\mathrm{K}}^{+}+{\mathrm{C}\mathrm{O}}_3^{2-}$$

(4) $${\mathrm{K}\mathrm{H}\mathrm{C}\mathrm{O}}_3\to {\mathrm{K}}^{+}+{\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}$$

Therefore, the reaction 2 can be re-written in the form:

(5) $${\mathrm{C}\mathrm{O}}_2+{\mathrm{C}\mathrm{O}}_3^{2-}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons 2{\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}$$

Reaction 5 is not instantaneous; it occurs from a sequence of elementary reactions. There are two reaction mechanisms involved in the overall reaction, which are dependent on the pH of the solution. In alkaline conditions (pH > 8), which is the case of the present process, the reaction mechanism is based on the formation of HCO₃^- (reaction 6) and on the equilibrium reaction between bicarbonate and carbonate (reaction 7).¹⁷

(6) $${\mathrm{C}\mathrm{O}}_2+{\mathrm{O}\mathrm{H}}^{-}\rightleftharpoons {\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}$$

(7) $${\mathrm{C}\mathrm{O}}_3^{2-}+{\mathrm{H}}_3{\mathrm{O}}^{+}\rightleftharpoons {\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}+{\mathrm{H}}_2\mathrm{O}$$

The water dissociation (reaction 8) is also present in this mechanism:

(8) $$2{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{O}\mathrm{H}}^{-}$$

Reaction 6 was modeled by the forward (9) and reverse (10) reactions:¹⁸,¹⁹

(9) $${\mathrm{C}\mathrm{O}}_2+{\mathrm{O}\mathrm{H}}^{-}\to {\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}$$

(10) $${\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}\to {\mathrm{C}\mathrm{O}}_2+{\mathrm{O}\mathrm{H}}^{-}$$

It is well known that the explained reaction mechanism is quite slow. Aiming to increase the rate of reaction 7, and, consequently, the CO₂ removal efficiency of the process, a boric acid solution (H₃BO₃) is used, which acts as a catalyst in the process. Boron hydroxide(IV) (B(OH)₄^-) reacts with CO₂ to improve the formation of HCO₃^- through the following mechanism:¹⁹

(11) $${\mathrm{H}}_3{\mathrm{B}\mathrm{O}}_3+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons \mathrm{B}(\mathrm{O}\mathrm{H}{)}_4^{-}+{\mathrm{H}}^{+}$$

(12) $$\mathrm{B}(\mathrm{O}\mathrm{H}{)}_4^{-}+{\mathrm{C}\mathrm{O}}_2\to \mathrm{B}(\mathrm{O}\mathrm{H}{)}_4{\mathrm{C}\mathrm{O}}_2^{-}$$

(13) $$\mathrm{B}(\mathrm{O}\mathrm{H}{)}_4{\mathrm{C}\mathrm{O}}_2^{-}+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{H}}_3{\mathrm{B}\mathrm{O}}_3\cdot {\mathrm{H}}_2\mathrm{O}+{\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}$$

To model the reaction mechanism of H₃BO₃ in Aspen Plus, reactions 12 and 13 are replaced by a single global reaction, resulting in reaction 14:¹⁸

(14) $$\mathrm{B}(\mathrm{O}\mathrm{H}{)}_4^{-}+{\mathrm{C}\mathrm{O}}_2\to {\mathrm{H}}_3{\mathrm{B}\mathrm{O}}_3+{\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}$$

The ethylene oxide present in the vapor phase, when diffusing into the liquid phase, reacts with water to form monoethylene glycol (C₂H₆O₂), according to:

(15) $${\mathrm{C}}_2{\mathrm{H}}_4\mathrm{O}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{O}}_2$$

Only the direct path of reaction 15 is modeled because it occurs in a small extension. The power-law model was used to calculate the reaction rate. The kinetic parameters of the reactions 9, 10, 14, and 15 are presented in Table 3.

Table 3
Kinetic parameters of reactions 9, 10, 14, and 15

Reaction	k0 / s-1	Ea / (J kmol-1)	Reference
9	4.3 × 1013	5.5471 × 107	20
10	2.38 × 1017	1.23305 × 108	14
14	2.195 × 1013	6.74 × 107	19
15	338	7.8994 × 107	21

₀

The equilibrium constant (K_eq) of the reactions 7, 8, and 10 is calculated according to equation 16. All coefficients are shown in Table 4.

Table 4
Equilibrium constant parameters of reactions 7, 8, and 11

Reaction	A	B	C	Reference
7	132.899	-13445.9	-22.4773	22-24
8	216.049	-12431.7	-35.4819	22-24
11	177.6	-10266.5	-28.9	18

A, B and C: the parameters of the equilibrium constant used in Aspen Plus.

(16) $$\ln \left({\mathrm{K}}_{\mathrm{e}\mathrm{q}}\right)=\mathrm{A}+\frac{\mathrm{B}}{\mathrm{T}}+\mathrm{C}\ln (\mathrm{T})$$

where A, B and C are the parameters of the equilibrium constant used in Aspen Plus.

Rate-base model

The RateFrac routine is used to simulate the absorption and stripper columns. This routine uses the rate-based model for mass and energy balance calculations in columns where there is no thermodynamic equilibrium in the stages.²⁵ To correct deviations from equilibrium, the rate-based model considers the influence of chemical reactions on mass and energy transfer rates, based on Maxwell-Stefan ^equations3 and the Two-Film Theory.⁴ The reactions take place in the liquid phase, which should be discretized to increase the model’s accuracy, as shown in Figure 3. The film is discretized into 5 sections. According to the results of Schneider et al.,²⁶-²⁸ this value results in errors around 10^-5 in the composition profiles of the main species.

Figure 3
Visual scheme of two-film theory applied to this work.

Discretization also needs to be performed hetero­geneously because sections closer to the interface offer less resistance to mass transfer, while sections closer to the bulk solution offer greater resistance. This can be done through the film discretization ratio, which determines the ratio between the thickness of adjacent sections. In this work, the discretization ratio of the liquid film is 5: the section adjacent to the interface is five times smaller than the section adjacent to it and, subsequently to the last section in the direction of the bulk solution. The vapor phase does not require discretization, as no reactions occur in this phase.

Another important parameter for the rate-based model is the reaction condition factor, which is illustrated by the green point in Figure 3. This parameter determines the location, in each section of the discretized film, where reaction rates will be calculated. This factor works as a weight between the conditions at the interface and at the bulk solution, through equation 17.

(17) $${\mathrm{C}}_{\mathrm{a}\mathrm{v}\mathrm{g}}=\text{Factor}\ast {\mathrm{C}}_{\text{bulk}}+(1-\text{Factor})\ast {\mathrm{C}}_{\text{interface}}$$

where C represents variables such as concentration and temperature. Factors close to 1 indicate a greater influence of the conditions within the solution, while factors close to 0 indicate a greater influence of the interface’s conditions. The reaction condition factor adopted in this work is 0.9, indicating a greater influence of the conditions within the solution.

Mass transfer and hydraulic correlations

One of the most important steps of the development of a representative model is the choice of correct correlations to calculate the parameters of the rate-based model: mass transfer coefficients, interfacial area, and liquid holdup. Wrong choices of these correlations imply in inaccurate calculations of the mass transfer inside the column. Ultimately, these errors result in wrong estimations of composition and energy consumption.

Aspen Plus provides several correlations to calculate the rate-based parameters. In general, the choice of correct correlations is a function of column diameter, operational conditions, liquid and vapor transport properties, the type and geometry of packing used in the column. The evaluated correlations to calculate liquid holdup, interfacial area and mass transfer coefficients are shown in Tables 5, 6 and 7, respectively.

Table 5
Correlations evaluated for stage liquid holdup

Absorption column	Stripper column
Stichlmair et al.11 $${\mathrm{h}}_{\mathrm{L}}=0.555{\mathrm{Fr}}_{\mathrm{L}}^{1/3}(1+20\mathrm{\Delta }{\mathrm{P}}^2)\ast {\mathrm{h}}_{\mathrm{p}}\ast {\mathrm{A}}_{\mathrm{t}}$$	Stichlmair et al.11 $${\mathrm{h}}_{\mathrm{L}}=0.555{\mathrm{Fr}}_{\mathrm{L}}^{1/3}(1+20\mathrm{\Delta }{\mathrm{P}}^2)\ast {\mathrm{h}}_{\mathrm{p}}\ast {\mathrm{A}}_{\mathrm{t}}$$
Rocha et al.7 $${\mathrm{h}}_{\mathrm{L}}={\left(\frac{4{\mathrm{F}}_{\mathrm{t}}}{\mathrm{S}}\right)}^{2/3}{\left(\frac{3{\mu }^{\mathrm{L}}{\mathrm{u}}_{\mathrm{s}}^{\mathrm{L}}}{{\rho }_{\mathrm{t}}^{\mathrm{L}}{\mathrm{g}}_{\mathrm{e}\mathrm{f}\mathrm{f}}\sin \theta }\right)}^{1/3}\ast {\mathrm{h}}_{\mathrm{p}}{}^{\ast }{\mathrm{A}}_{\mathrm{t}}$$	Billet et al.13 $${\mathrm{h}}_{\mathrm{L}}={\left(\frac{12{\mu }^{\mathrm{L}}{\mathrm{a}}_{\mathrm{p}}^2{\mathrm{u}}_{\mathrm{s}}^{\mathrm{L}}}{{\rho }_{\mathrm{t}}^{\mathrm{L}}\mathrm{g}}\right)}^{1/3}\ast {\mathrm{h}}_{\mathrm{p}}\ast {\mathrm{A}}_{\mathrm{t}}$$
Billet et al.13 $${\mathrm{h}}_{\mathrm{L}}={\left(\frac{12{\mu }^{\mathrm{L}}{\mathrm{a}}_{\mathrm{p}}^2{\mathrm{u}}_{\mathrm{s}}^{\mathrm{L}}}{{\rho }_{\mathrm{t}}^{\mathrm{L}}\mathrm{g}}\right)}^{1/3}\ast {\mathrm{h}}_{\mathrm{p}}\ast {\mathrm{A}}_{\mathrm{t}}$$

_L³_pt²_L^L_s^L-1_t^L-3-2_eff^-2_p^2-3

Table 6
Correlations evaluated for interfacial area

Absorption column	Stripper column
Billet et al.13 $${\mathrm{a}}^{\mathrm{I}}=\frac{1.5}{\sqrt{{\mathrm{a}}_{\mathrm{p}}{\mathrm{d}}_{\mathrm{h}}}}{\left(\frac{{\mathrm{u}}_{\mathrm{s}}^{\mathrm{L}}{\mathrm{d}}_{\mathrm{h}}{\rho }_{\mathrm{t}}^{\mathrm{L}}}{{\mu }^{\mathrm{L}}}\right)}^{-0.2}{\left(\frac{{\left({\mathrm{u}}_{\mathrm{s}}^{\mathrm{L}}\right)}^2{\mathrm{d}}_{\mathrm{h}}{\rho }_{\mathrm{t}}^{\mathrm{L}}}{\sigma }\right)}^{0.75}{\left(\frac{{\left({\mathrm{u}}_{\mathrm{s}}^{\mathrm{L}}\right)}^2}{{\mathrm{g}\mathrm{d}}_{\mathrm{h}}}\right)}^{-0.45}\ast {\mathrm{a}}_{\mathrm{p}}\ast {\mathrm{h}}_{\mathrm{p}}\ast {\mathrm{A}}_{\mathrm{t}}$$	Onda et al.10 $${\mathrm{a}}^{\mathrm{I}}=[1-\exp (-1.45{\left(\frac{{\sigma }_{\mathrm{c}}}{\sigma }\right)}^{0.75}{\mathrm{Re}}_{\mathrm{L}}^{0.1}{\mathrm{F}\mathrm{r}}_{\mathrm{L}}^{-0.05}\mathrm{W}\mathrm{e}{\mathrm{L}}_{\mathrm{L}}^{0.2})]\ast {\mathrm{a}}_{\mathrm{p}}\ast {\mathrm{h}}_{\mathrm{p}}\ast {\mathrm{A}}_{\mathrm{t}}$$
Rocha et al.7$${\mathrm{a}}^1=\frac{29.12{\left({\mathrm{W}\mathrm{e}}_{\mathrm{L}}{\mathrm{F}\mathrm{r}}_{\mathrm{L}}\right)}^{0.15}{\mathrm{S}}^{0.359}}{{\mathrm{Re}}_{\mathrm{L}}^{0.2}{\epsilon }^{0.6}(\sin \theta {)}^{0.3}(1-0.93\cos \gamma )}\ast {\mathrm{a}}_{\mathrm{p}}\ast {\mathrm{F}}_{\mathrm{s}\mathrm{c}}\ast {\mathrm{h}}_{\mathrm{p}}\ast {\mathrm{A}}_{\mathrm{t}}$$	Billet et al.13 $${\mathrm{a}}^{\mathrm{I}}=\frac{1.5}{\sqrt{{\mathrm{a}}_{\mathrm{p}}{\mathrm{d}}_{\mathrm{h}}}}{\left(\frac{{\mathrm{u}}_{\mathrm{s}}^{\mathrm{L}}{\mathrm{d}}_{\mathrm{h}}{\rho }_{\mathrm{t}}^{\mathrm{L}}}{{\mu }^{\mathrm{L}}}\right)}^{-0.2}{\left(\frac{{\left({\mathrm{u}}_{\mathrm{s}}^{\mathrm{L}}\right)}^2{\mathrm{d}}_{\mathrm{h}}{\rho }_{\mathrm{t}}^{\mathrm{L}}}{\sigma }\right)}^{0.75}{\left(\frac{{\left({\mathrm{u}}_{\mathrm{s}}^{\mathrm{L}}\right)}^2}{{\mathrm{g}\mathrm{d}}_{\mathrm{h}}}\right)}^{-0.45}\ast {\mathrm{a}}_{\mathrm{p}}\ast {\mathrm{h}}_{\mathrm{p}}\ast {\mathrm{A}}_{\mathrm{t}}$$
Bravo et al.29 $$a^I=a_p^{\ast }{h}_p^{\ast }{A}_t$$	Bravo et al.29 $${\mathrm{a}}^{\mathrm{I}}=19.78{\mathrm{a}}_{\mathrm{p}}{\left({\mathrm{C}\mathrm{a}}_{\mathrm{L}}{\mathrm{Re}}_{\mathrm{V}}\right)}^{0.392}\ast \frac{{\sigma }^{0.5}}{{\mathrm{h}}_{\mathrm{p}}^{0.4}}\ast {\mathrm{A}}_{\mathrm{t}}\ast {\mathrm{h}}_{\mathrm{p}}$$
Tsai et al.30 $${\mathrm{a}}^{\mathrm{I}}=1.34{\left[\left({\mathrm{W}\mathrm{e}}_{\mathrm{L}}\right){\left({\mathrm{F}\mathrm{r}}_{\mathrm{L}}\right)}^{-1/3}\right]}^{0.116}$$	Tsai et al.30 $${\mathrm{a}}^{\mathrm{I}}=1.34{\left[\left({\mathrm{W}\mathrm{e}}_{\mathrm{L}}\right){\left({\mathrm{F}\mathrm{r}}_{\mathrm{L}}\right)}^{-1/3}\right]}^{0.116}$$

^I2_ht^L-3_s^L-1L-1_c^-1_p^2-3-2_pt²_LLLVset²_s^L-1_L

Table 7
Correlations evaluated for mass transfer coefficients

Absorption column	Stripper column
Rocha et al.7 $$\begin{array}{rl}& {\mathrm{k}}_{\mathrm{i},\mathrm{k}}^{\mathrm{L}}=2\sqrt{\frac{{\mathrm{D}}_{\mathrm{i},\mathrm{k}}^{\mathrm{L}}{\mathrm{u}}_{\mathrm{L}\mathrm{e}}}{\pi {\mathrm{S}\mathrm{C}}_{\mathrm{E}}}}\\ & {\mathrm{k}}_{\mathrm{r},\mathrm{k}}^{\mathrm{v}}=0.054\frac{{\mathrm{D}}_{\mathrm{l},\mathrm{k}}^{\mathrm{v}}}{\mathrm{S}}{\mathrm{Re}}_{\mathrm{v}}^{0.8}{\mathrm{S}\mathrm{c}}_{\mathrm{v},\mathrm{i},\mathrm{k}}^{0.333}\end{array}$$	Onda et al.10 $$\begin{array}{c}{\mathrm{k}}_{\mathrm{i},\mathrm{k}}^{\mathrm{L}}=0.0051{\left({\mathrm{Re}}_{\mathrm{L}}^{\mathrm{\prime }}\right)}^{0.667}{\mathrm{S}\mathrm{c}}_{\mathrm{L},\mathrm{i},\mathrm{k}}^{-0.5}{\left({\mathrm{a}}_{\mathrm{p}}{\mathrm{d}}_{\mathrm{p}}\right)}^{0.4}{\left(\frac{{\mu }^{\mathrm{L}}\mathrm{g}}{{\rho }_{\mathrm{t}}^{\mathrm{L}}}\right)}^{0.333}\\ {\mathrm{k}}_{\mathrm{i},\mathrm{k}}^{\mathrm{V}}=2{\mathrm{Re}}_{\mathrm{v}}^{0.7}{\mathrm{S}\mathrm{c}}_{\mathrm{V},\mathrm{i},\mathrm{k}}^{0.333}{\mathrm{a}}_{\mathrm{p}}{\mathrm{D}}_{\mathrm{i},\mathrm{k}}^{\mathrm{v}}{\left({\mathrm{a}}_{\mathrm{p}}{\mathrm{d}}_{\mathrm{p}}\right)}^{-2}\text{for}\mathrm{d}\mathrm{p}<0.015\mathrm{m}\\ {\mathrm{k}}_{\mathrm{i},\mathrm{k}}^{\mathrm{V}}=5.23{\mathrm{Re}}_{\mathrm{v}}^{0.7}{\mathrm{S}\mathrm{c}}_{\mathrm{V},\mathrm{i},\mathrm{k}}^{0.333}{\mathrm{a}}_{\mathrm{p}}{\mathrm{D}}_{\mathrm{i},\mathrm{k}}^{\mathrm{V}}{\left({\mathrm{a}}_{\mathrm{p}}{\mathrm{d}}_{\mathrm{p}}\right)}^{-2}\text{for}\mathrm{d}\mathrm{p}>0.015\mathrm{m}\end{array}$$
Bravo et al.29 $$\begin{array}{rl}& {\mathrm{k}}_{\mathrm{i},\mathrm{k}}^{\mathrm{L}}=2\sqrt{\frac{{\mathrm{D}}_{\mathrm{i},\mathrm{k}}^{\mathrm{L}}}{\pi {\mathrm{t}}_{\mathrm{L}}}}\\ & {\mathrm{k}}_{\mathrm{i},\mathrm{k}}^{\mathrm{V}}=0.0338\frac{{\mathrm{D}}_{\mathrm{i},\mathrm{k}}^{\mathrm{V}}}{{\mathrm{d}}_{\mathrm{e}\mathrm{q}}}{\mathrm{Re}}_{\mathrm{v}}^{0.8}{\mathrm{S}\mathrm{c}}_{\mathrm{v},\mathrm{i},\mathrm{k}}^{0.333}\end{array}$$	Bravo et al.29 $$\begin{array}{c}{\mathrm{k}}_{\mathrm{i},\mathrm{k}}^{\mathrm{L}}=0.0051{\left({\mathrm{Re}}_{\mathrm{L}}^{\mathrm{\prime }}\right)}^{0.667}{\mathrm{S}\mathrm{c}}_{\mathrm{L},\mathrm{i},\mathrm{k}}^{-0.5}{\left({\mathrm{a}}_{\mathrm{p}}{\mathrm{d}}_{\mathrm{p}}\right)}^{0.4}{\left(\frac{{\mu }^{\mathrm{L}}\mathrm{g}}{{\rho }_{\mathrm{t}}^{\mathrm{L}}}\right)}^{0.333}\\ {\mathrm{k}}_{\mathrm{i},\mathrm{k}}^{\mathrm{V}}=2{\mathrm{Re}}_{\mathrm{v}}^{0.7}{\mathrm{S}\mathrm{c}}_{\mathrm{V},\mathrm{i},\mathrm{k}}^{0.333}{\mathrm{a}}_{\mathrm{p}}{\mathrm{D}}_{\mathrm{i},\mathrm{k}}^{\mathrm{v}}{\left({\mathrm{a}}_{\mathrm{p}}{\mathrm{d}}_{\mathrm{p}}\right)}^{-2}\text{for}\mathrm{d}\mathrm{p}<0.015\mathrm{m}\\ {\mathrm{k}}_{\mathrm{i},\mathrm{k}}^{\mathrm{V}}=5.23{\mathrm{Re}}_{\mathrm{v}}^{0.7}{\mathrm{S}\mathrm{c}}_{\mathrm{V},\mathrm{i},\mathrm{k}}^{0.333}{\mathrm{a}}_{\mathrm{p}}{\mathrm{D}}_{\mathrm{i},\mathrm{k}}^{\mathrm{V}}{\left({\mathrm{a}}_{\mathrm{p}}{\mathrm{d}}_{\mathrm{p}}\right)}^{-2}\text{for}\mathrm{d}\mathrm{p}>0.015\mathrm{m}\end{array}$$

^L_i,k^-1V_i,k^-1V_i,k^-2L_i,k^-2_ELe^-1_{VV,i,kL,i,kLeqLp}^2-3_p^L-2_t^L-3

Correlation calculations require knowledge of several thermodynamic and transport properties. The main equations used to calculate these properties are presented in Table 8 and are widely available in the literature.

Table 8
Correlations used for thermodynamic and transport properties calculation

Property	Correlation
Pressure drop in the column	Wallis/Aspen31
Heat transfer coefficient	Chilton and Colburn32
Flow model	mixed
Density	Rackett, DIPPR32,33
Viscosity	DIPPR33
Superficial tension	DIPPR33
Binary diffusivity	Nernst-Hartley33
Thermal conductivity	DIPPR and NIST ThermoM33

DIPPR: Design Institute for Physical Property Research.

An exhausted try and error procedure could be used to find the best set of correlations that represents the HPC process in a suitable manner. A computational methodology was developed to reduce the user’s effort. The following procedure tests all the possible combinations (of correlations) that better model the process, in an automatic way. Data from Figure 2 is compared against the model results to validate the best set of correlations.

The conventional way to evaluate the influence of parameters in a mathematical model is through sensitivity analysis. However, Aspen Plus¹⁴ does not allow modification of correlations through the built-in tool. A MATLAB³⁴ script was developed, and the analysis can be performed automatically. It is necessary to create an interface that enables the communication between the two software, through the creation of a Component Object Model (COM). The MATLAB built-in function actxserver is used for the COM creation. Figure 4 presents the flowchart of the developed MATLAB script.

Figure 4
Communication between MATLAB and Aspen Plus software implemented to evaluate the studied correlations.

Once the interface between the software is created (highlighted by red lines), the sensitivity analysis determines the combination of correlations to be used. This information is fed to the Aspen Plus simulation through COM. Once the simulation is run, the results are imported into MATLAB via COM and the error is calculated for each used variable to validate the model. The procedure is repeated until every point of the sensitive analysis is evaluated. At the end, the results are saved in a spreadsheet file and the best combination is printed to the user.

Results and Discussion

The correlations presented in Tables 5 to 7 were evaluated in the Aspen Plus regarding their ability to represent the HPC process. By using the procedure mentioned in the experimental description, 384 combinations were analyzed. For didactic purposes, 12 combinations were selected for discussion, as shown in Table 9.

Table 9
Combinations of correlations selected

Combination	ABS column				STP column
	Mass transfer coefficient	Interfacial area	Liquid holdup		Mass transfer coefficient	Interfacial area	Liquid holdup
1	Rocha et al.7	Rocha et al.7	Stichlmair et al.11		Onda et al.10	Tsai et al.30	Stichlmair et al.11
2	Rocha et al.7	Rocha et al.7	Stichlmair et al.11		Bravo et al.29	Onda et al.10	Stichlmair et al.11
3	Rocha et al.7	Rocha et al.7	Stichlmair et al.11		Bravo et al.29	Bravo et al.29	Stichlmair et al.11
4	Rocha et al.7	Rocha et al.7	Stichlmair et al.11		Bravo et al.29	Billet et al.13	Stichlmair et al.11
5	Rocha et al.7	Rocha et al.7	Stichlmair et al.11		Bravo et al.29	Tsai et al.30	Stichlmair et al.11
6	Rocha et al.7	Rocha et al.7	Stichlmair et al.11		Bravo et al.29	Tsai et al.30	Billet et al.13
7	Rocha et al.7	Rocha et al.7	Bravo et al.35		Bravo et al.29	Tsai et al.30	Stichlmair et al.11
8	Rocha et al.7	Rocha et al.7	Billet et al.13		Bravo et al.29	Tsai et al.30	Stichlmair et al.11
9	Rocha et al.7	Bravo et al.35	Stichlmair et al.11		Bravo et al.29	Tsai et al.30	Stichlmair et al.11
10	Rocha et al.7	Billet et al.13	Stichlmair et al.11		Bravo et al.29	Tsai et al.30	Stichlmair et al.11
11	Rocha et al.7	Tsai et al.30	Stichlmair et al.11		Bravo et al.29	Tsai et al.30	Stichlmair et al.11
12	Bravo et al.35	Rocha et al.7	Stichlmair et al.11		Bravo et al.29	Tsai et al.30	Stichlmair et al.11

ABS: absorber; STP: stripper.

Figure 5 presents the errors of variables in the absorption column: CO₂ composition in clean gas, top and bottom temperatures. The combinations 2 to 8 obtained the best results with errors below 2.5%, considering all the variables. The choice of combinations does not significantly impact the prediction of top and bottom temperatures.

Figure 5
Relative error of main variables in the absorber column.

Figure 6 presents the errors of variables in the stripper column: reboiler steam consumption, top and bottom temperatures. Considering the steam consumption, the best results were obtained with combinations 3, 5, and 6. The prediction of top and bottom temperatures was not significantly affected by the combination of correlations.

Figure 6
Relative error of the main variables in the stripper column.

A more detailed discussion is presented in the next paragraphs. Table 10 shows the average CO₂/K₂CO₃ binary mass transfer coefficient in the absorption column for all combinations.

Table 10
Average mass transfer coefficients in the absorption column

Combination	CO2/K2CO3 overall mass transfer coefficient / (kmol h-1)
1-11 (Rocha et al.7)	13855.35
12 (Bravo et al.35)	3715.10

Considering the combinations 5 and 12, the difference between then is the correlation used to calculate the mass transfer coefficient in the absorption column: combination 5 uses Bravo et al.⁷ and 12 uses Bravo et al.³⁵ The choice by one or other has a strong impact in the prediction of CO₂ composition in the clean gas. In the first case, the relative error is 1.8% while in the last case, this error is 68.6%. The Bravo et al.³⁵ correlation is based on packing corrugation side dimension and the effective velocity. The Rocha et al.⁷ considers the liquid residence time but not the effective velocity. The considerations adopted by Rocha et al.⁷ correlation results in an increase in the mass transfer coefficient and lower errors. In this way, Rocha et al.⁷ is the most suitable correlation to calculate the mass transfer coefficient in the absorption column.

Considering the combinations 5, 9, 10, and 11, the difference between then is the used correlation to calculate the interfacial area in the absorption column, as shown in Table 11. According to Hemmati et al.,¹² this parameter mainly depends on gas flow rate and density. Liquid flow rate is proportional to effective area: greater liquid velocities results in a higher packing wettability. Therefore, the effective interfacial area is increased, resulting in a higher mass transfer.

Table 11
Average effective interfacial area in the absorption column

Combination	Interfacial area / m2
1-8 and 12 (Rocha et al.7)	166.7342
9 (Bravo et al.35)	36.1409
10 (Billet et al.13)	59.6639
11 (Tsai et al.30)	149.2431

The combination 9 showed the highest error for the absorption column. This can be attributed to the high number of used variables in correlations Bravo et al.³⁵ Moreover, the interfacial area calculated by this equation is affected by parameters that has a strong dependence of gas and liquid flow rates, as Reynolds number. The absorption column operates in a turbulent regime, which is characterized by a high surface velocity and a high Reynolds number (Re > 10.000).³³,³⁶ According to the Bravo et al.³⁵ correlation, the value of the interfacial area is inversely proportional to the Reynolds number, the higher the Reynolds number the lower the value of the interfacial area.

Considering the absorption column, the combinations 7 and 8 shows that the choice of correlation used to calculate liquid holdup does not significantly impact the model, as can be seen in Figure 5. In addition, Table 12 does not show any modification in the value of calculated liquid holdup.

Table 12
Average stage liquid holdup in the absorption column

Combination	Liquid holdup / m3
1-6 and 9-12 (Stichlmair et al.11)	102.19
7 (Bravo et al.35)	102.19
8 (Billet et al.13)	102.19

Examining the stripper column, as mentioned before, the lowest errors were obtained for combinations 3, 5 and 6, while the highest errors were combinations 9 and 10. However, combination 5 and 9 use the same set of correlations. How can they result in opposite outcomes? It suggests that correlations do not have any impact on the stripper column. The errors of the stripper are much more correlated to the errors of absorption column: the highest errors of absorber are for combinations 9, 10, 11 and 12; these errors are impact the stripper, resulting in wrong predictions of it. Dutta et al.³⁷ states that the stripper column operates close to the equilibrium conditions and can be modeled with equilibrium model. This explains why the correlations do not directly impact the desorption process.

Other operating conditions

With the definition of the best combination of correlations, the model was used to predict the process behavior under two different operational conditions: operation with catalyst at the beginning of the campaign (characterized by the lower production of CO₂ in the reactor); and operation with catalyst at the end of the campaign (characterized by the higher production of CO₂ in the reactor). Table 13 presents the results using combination 5 for the used correlations. Even with very different conditions, acceptable errors were obtained.

Table 13
Results for different operating conditions

Validation variables	Relative error for the case of low CO2 production in the reactor / %	Relative error for the case of high CO2 production in the reactor / %
CO2 composition	6.32	1.91
Temperature bottom (ABS)	1.68	1.02
Temperature top (ABS)	1.85	2.49
Steam consumption	1.03	0.68
Temperature bottom (STP)	5.06	1.58
Temperature top (STP)	4.02	2.43

ABS: absorber; STP: stripper.

Conclusions

In the present work, different combinations of correlations for calculating mass transfer coefficient, interfacial area and liquid holdup were evaluated and compared to estimate key parameters of an HPC process promoted with H₃BO₃. The best set of correlations is Bravo et al.²⁹ to calculate the mass transfer coefficients and interfacial area in the absorber; Stichlmair et al.¹¹ to calculate the liquid holdup in the absorber column. The stripper column was not affected by the correlation and can be modeled using equilibrium thermodynamic consideration. This work developed an automatic procedure to evaluate a high number of correlations, reducing time and effort during the process evaluation. Lastly, the industrial plant data used to validate the model is valuable for academic purposes.

Acknowledgments

The authors thank the National Council for Scientific and Technological Development (CNPq) for the financial support.

References

• ¹
  Smith, K. H.; Nicholas, N. J.; Stevens, G. W.; Absorption-Based Post-Combustion Capture of Carbon Dioxide; Feron, P. H. M., ed.; Woodhead: Cambidge, 2016, p. 145. [Crossref]
• ²
  Ayittey, F. K.; Saptoro, A.; Kumar, P.; Wong, M. K.; IOP Conf. Ser.: Mater. Sci. Eng. 2020, 778, 012082. [Crossref]
• ³
  Maxwell, J. C.; Philos. Trans. R. Soc. London 1867, 157, 49. [Crossref]
• ⁴
  Whitman, W. G.; Int. J. Heat Mass Transfer 1962, 5, 429. [Crossref]
• ⁵
  Gaspar, J.; Cormos, A.-M.; Int. J. Greenhouse Gas Control 2012, 8, 45. [Crossref]
• ⁶
  Wang, G. Q.; Yuan, X. G.; Yu, K. T.; Chem. Eng. Process.: Process Intensif. 2006, 45, 691. [Crossref]
• ⁷
  Rocha, J. A.; Bravo, J. L.; Fair, J. R.; Ind. Eng. Chem. Res. 1996, 35, 1660. [Crossref]
• ⁸
  Zhang, Y.; Chen, C.-C.; Energy Procedia 2013, 37, 1584. [Crossref]
• ⁹
  Qi, G.; Wang, S.; Yu, H.; Wardhaugh, L.; Feron, P.; Chen, C.; Int. J. Greenhouse Gas Control 2013, 17, 450. [Crossref]
• ¹⁰
  Onda, K.; Takeuchi, H.; Okumoto, Y.; J. Chem. Eng. Jpn. 1968, 1, 56. [Crossref]
• ¹¹
  Stichlmair, J.; Bravo, J. L.; Fair, J. R.; Gas Sep. Purif. 1989, 3, 19. [Crossref]
• ¹²
  Hemmati, A.; Farahzad, R.; Surendar, A.; Aminahmadi, B.; Process Saf. Environ. Prot. 2019, 126, 214. [Crossref]
• ¹³
  Billet, R.; Schultes, M.; Chem. Eng. Technol. 1993, 16, 1. [Crossref]
• ¹⁴
  Aspen Plus, v.10; Aspen Technology, Massachusetts Institute of Technology, USA, 2010.
• ¹⁵
  Khalfe, N. M.; Lahiri, S. K.; Sawke, S. K.; Chem. Ind. Chem. Eng. Q. 2011, 17, 17. [Crossref]
• ¹⁶
  Conway, R. A.; Waggy, G.T.; Spiegel, M. H.; Berglund, R. L.; Environ. Sci. Technol. 1983, 17, 107. [Crossref]
• ¹⁷
  Ahmadi, M.; Gomes, V. G.; Ngian, K.; Sep. Purif. Technol. 2008, 63, 107. [Crossref]
• ¹⁸
  Smith, K. H.; Anderson, C. J.; Tao, W.; Endo, K.; Mumford, K. A.; Kentish, S. E.; Qader, A.; Hooper, B.; Stevens, G. W.; Int. J. Greenhouse Gas Control 2012, 10, 64. [Crossref]
• ¹⁹
  Guo, D.; Thee, H.; da Silva, G.; Chen, J.; Fei, W.; Kentish, S.; Stevens, G. W.; Environ. Sci. Technol. 2011, 45, 4802. [Crossref]
• ²⁰
  Pinsent, B. R. W.; Pearson, L.; Roughton, F. J. W.; Trans. Faraday Soc. 1956, 52, 1512. [Crossref]
• ²¹
  An, W.; Lin, Z.; Chen, J.; Zhu, J.; Ind. Eng. Chem. Res. 2014, 53, 6056. [Crossref]
• ²²
  Jou, F.-Y.; Mather, A. E.; Otto’, F. D.; Ind. Eng. Chem. Process Des. Dev 1982, 21, 539. [Crossref]
• ²³
  Jou, F. Y.; Carroll, J. J.; Mather, A. E.; Otto, F. D.; J. Chem. Eng. Data 1993, 38, 75. [Crossref]
• ²⁴
  Jou, F. -Y; Carroll, J. J.; Mather, A. E.; Otto, F. D.; Can. J. Chem. Eng. 1993, 71, 264. [Crossref]
• ²⁵
  Léonard, G.: Optimal Design of a CO2 Capture Unit with Assessment of Solvent Degradation, PhD Thesis, University of Liege, 2013. [Link] accessed in September 2022
• ²⁶
  Schneider, R.; Sander, F.; Górak, A.; Chem. Eng. Process.: Process Intensif. 2003, 42, 955. [Crossref]
• ²⁷
  Kenig, E. Y.; Schneider, R.; Górak, A.; Chem. Eng. Sci. 2001, 56, 343. [Crossref]
• ²⁸
  Mayer, J.; Schneider, R.; Kenig, E.; Górak, A.; Wozny, G.; Comput. Chem. Eng. 1999, 23, S843. [Crossref]
• ²⁹
  Bravo, J. L.; Fair, J. R.; Ind. Eng. Chem. Process Des. Dev. 1982, 21, 162. [Crossref]
• ³⁰
  Tsai, R. E.; Seibert, A. F.; Eldridge, R. B.; Rochelle, G. T.; AIChE J. 2011, 57, 1173. [Crossref]
• ³¹
  Suess, P.; Spiegel, L.; Chem. Eng. Process. 1992, 31, 119. [Crossref]
• ³²
  Stewart, W. E.; AIChE J. 1993, 41, 202. [Crossref]
• ³³
  Poling, B. E.; Prausnitz, J. M.; The Properties of Gases and Liquids, vol. 1, 5^th ed.; Elsevier: London, UK, 2011.
• ³⁴
  MATLAB, v.R2018b; MathWorks, Stanford University, USA, 2018.
• ³⁵
  Bravo, J. L.; Rocha, J. R.; Fair, J. R.; Inst. Chem. Eng. Symp. Ser. 1992, 1, A489. [Link] accessed in September 2022
• ³⁶
  Li, W.; Yu, K.; Yuan, X.; Liu, B.; Int. J. Heat Mass Transfer 2015, 88, 775. [Crossref]
• ³⁷
  Dutta, R.; Nord, L. O.; Bolland, O.; Fuel 2017, 202, 85. [Crossref]

Edited by

Editor handled this article: Eduardo Carasek

Publication Dates

• Publication in this collection
  10 Mar 2023
• Date of issue
  Mar 2023

History

• Received
  16 May 2022
• Published
  21 Sept 2022