In ﬂ uence of ﬁ ve model parameters on the performance of a CO 2 absorber column by a loaded aqueous MEA solution

. Rigorous packed-bed absorber modeling and simulation are signi ﬁ cant for post-combustion CO 2 capture processes design. Hence, a good knowledge and judicious selection of model parameters are essential to ensure reliable predictions. In this paper, the reactive absorption of CO 2 into loaded aqueous monoethanolamine solution was modeled, furthermore, the effects of ﬁ ve different parameters (kinetic model, enhancement factor, enthalpy of absorption, CO 2 diffusivity, and vapor pressure) were investigated. Finally, this study revealed that some model parameters have a large in ﬂ uence on the column performance, contrary to others. In addition, methods and correlations that generally provide more accurate predictions of the empirical data relative to the other cases involved in this research were determined for each model parameter. It was also found that the model deviation was reduced by 18% and 4% for the liquid temperature and liquids CO 2 loading pro ﬁ les, respectively, while comparing between the worst and the best case.


Introduction
Significant efforts have been made to reduce greenhouse gas emissions and mitigate the global warming IPCC (2007). In this area, particular attention has been given to carbon dioxide removal using the post-combustion process on the basis of the absorption-desorption with chemical solvents.
In recent years, remarkable progress has been made in this area of research. New solvents that increase the CO 2 absorption and desorption of CO 2 have been developed such as the nanoparticle additives and biphasic solvents (Liu et al., 2019;Mehassouel et al., 2018;Wang et al., 2016). Despite that, aqueous solution of monoethanolamine is undoubtedly still the most extensive, mature, appropriate, and well-documented chemical solvent for the CO 2 capture in post-combustion processes (Akinola et al., 2019;Ali Saleh Bairq et al., 2019;Gheni et al., 2018;Mohammadpour et al., 2019;Wang et al., 2019).
Reliable dimensioning, scaling, and monitoring postcombustion processes require the use of an accurate packed bed absorber modeling and simulation (Llano-Restrepo and Araujo-Lopez, 2015). Therefore, a good knowledge and judicious selection of model parameters are essential to ensure rigorous predictions. In this context, several studies on diverse process parameters have been published in literature (Abu-Zahra et al., 2007;Mofarahi, 2013, 2014;Khan et al., 2011;Kvamsdal and Rochelle, 2008;Kvamsdal and Hillestad, 2012;Mofarahi et al., 2008;Wu et al., 2010). Abu-Zahra et al. (2007) investigated absorber inlet temperature, lean amine loading, concentration, and stripper pressure sensitivities. Furthermore, the process that recovers carbon dioxide from flue gas was studied by Mofarahi et al. (2008) where the effect of both operating conditions and design parameters on the absorber and stripper columns was presented. In addition, a statistical analysis and a combination between the sensitivity analysis and the neural networks modeling were carried out by Wu et al. (2010) to investigate the interactions between similar main process parameters. However, the studies on the selection of rate-based model parameter correlations in packed columns are scarce. Khan et al. (2011) applied the rate-based model to perform a sensitivity analysis using different mass transfer coefficients in a packed column. Furthermore, in the aim of determining the temperature bulge position and magnitude, Kvamsdal and Rochelle (2008) carried out a comparative analysis between diverse methods that compute mass transfer coefficient, liquid heat capacity, and liquid density. Moreover, Kvamsdal and Hillestad (2012) focused on the selection of the rate-based model parameter correlations for prediction of physical properties and kinetics, they investigated also their effects on mass and energy balances. Mofarahi (2013, 2014) performed a rate-based model sensitivity analysis, once by varying different mass transfer correlations, and another time by combining these correlations with different kinetic models.
In the current paper, the reactive absorption of CO 2 with loaded aqueous monoethanolamine solution in a packed-bed absorber was modeled and simulated, in addition, the effects of five different parameters (kinetic model, enhancement factor, enthalpy of absorption, CO 2 diffusivity in aqueous solution of MEA, and vapor pressure) on the column performance were investigated by performing a parametric study based on step-by-step approach.
2 Rate-based model For modeling the CO 2 absorption in a packed column, three forms of the rate-based model were developed: the Continuous Differential Contactor (CDC) model, the Continuous Film Reaction (CFR) model, and Non-Equilibrium Stage (NEqS) model. In this study, the last version of the CDC model was applied, indicating that this model was first proposed by Pandya (1983) based on the differential-change approach suggested by Treybal (1969) which was largely employed by many authors, and since it presents some inconsistent simplifications or assumptions, Llano-Restrepo and Araujo-Lopez (2015) revised the model using the finite difference approach and introduced a new improved version as shown below: CO 2 and water vapor balances for the gas phase: The mole fractions of CO 2 and water vapor y A.I and y S.I , respectively, at the interface are given below: Noting that, the model considers the liquid phase as an ideal solution. Thus c S = 1 and Raoult's law y S: A total mole balance for both liquid and gas phases: Temperature gradients for the gas and liquid phases: Indicating that the energy balance neglects heat losses through the wall of the absorber column (an adiabatic column is assumed). For the resolution of these differential equations a computer program was coded in Matlab software.
The correlations used for estimating the different physicochemical and transport properties are listed in Table A1.

Heat of absorption
Although MEA is believed to be the most commonly used solvent for the CO 2 removal, only limited data on the direct measurements of the heat of absorption of the reaction between CO 2 and aqueous solutions of MEA have been published (Arcis et al., 2011;Carson et al., 2000;Kim, 2009;Kim and Svendsen, 2007;Mathonat et al., 1998).
Few researchers, in their works, used fixed values for the enthalpy of absorption prediction (Kohl and Nielsen, 1997;Kvamsdal and Rochelle, 2008;Pandya, 1983), however, others have developed new correlations to calculate the enthalpy of absorption on the basis of existing empirical data available in literature (Kim, 2009, Llano-Restrepo andAraujo-Lopez, 2015). All these correlations and fixed values for the heat of absorption estimation are summarized in Table A4.

Vapor pressure
Over the years, various temperature dependent equations for water vapor pressure estimation have been developed. In this study, we will consider the ones that are most commonly used in literature (Ambrose and Walton, 1989, Antoine, 1888, Riedel, 1954. These correlations are written in Table A5.

CO 2 diffusivity in aqueous solutions of MEA
Because of the reaction occurring between CO 2 and the amine solutions, the CO 2 diffusivity in the MEA solution cannot be determined directly. Therefore, Clarke (1964) proposed the N 2 O analogy method which has been then adopted by many researchers. This approach can be expressed as follows: Various measurements have been reported in literature on the N 2 O diffusivity in aqueous solutions of MEA on a broad range of MEA concentration and temperature (Clarke, 1964;Cullen and Davidson, 1957;Sada et al., 1978;Li and Lai, 1995;Ko et al., 2001;Ying and Eimer, 2012). Based on these experimental data, different correlations have been developed which are listed in Table A6.

Parametric study
The effects of changing the empirical correlations or fixed values on the column performance (liquid temperature and liquid CO 2 loading profiles) were investigated for each model parameter following step-by-step approach, that  Yeramian et al. (1970) based on penetration theory (d) Yeramian et al. (1970) based on surface renewal theory (e) Wellek et al. (1978) (f) Last and Stichlmair (2002) Gaspar and Fosbøl (2015) Llano-Restrepo and Araujo-Lopez (2015) based on Arcis et al.  means, each time the best correlation for the parameter X calculation is determined then used (or fixed) to study the next parameter, and so on. For a better understanding, Table 1 shows the different methods used for model parameters calculation in each case. In this paper, the average relative deviation percentage ARD% was the criterion used to compare model predictions with experiments, and it was computed by using the following equation: 9 Results and discussion In this research work, the model simulation was based on the experimental data reported in the literature by Sonderby et al. (2013) using a pilot-scale CO 2 absorption column, where 23 experiments were performed, denoted (R1-R23). However, in this study, only 9 runs (R 3, 8, 13-15, 18, 21-23) were taken into account, as shown in Table 2. This selection was founded on two criteria: a low experimental error and a large number of points (measurements) in each run.
All the simulation results, displayed in terms of liquid temperature and liquid CO 2 loading average relative deviation percentages (ARD%s) for all runs (R 3, 8, 13-15, 18, 21-23) and all cases (21 cases), are summarized in Table 2.
In this section, the results presented in Table 2 are discussed in general terms, that means, they will be discussed only in respect of the simulation deviation between the different runs, and then a detailed discussion is given for each parameter separately (in Sects. 9.1-9.5).
The Case 5-c is selected as a base case for this discussion because it represents a combination between the correlations that provide the lowest ARD%. Accordingly, it has been noticed that for the liquid CO 2 loadings, the ARDS% are in the range of 1-6%. A maximum ARD% of ±5% is obtained for runs (R13-15), while the minimum ARD% of ±2% is obtained for runs (R18, 21-23). Furthermore, for the liquid temperature, the ARDS% for the different runs are varying also between 1% and 6%. A maximum ARD% of ±5% is obtained for Run 18, an ARD% of 4.260% is also given by Run 8, while the other runs (R3, 13-15, 21-23) have an ARD% of ±2%. This difference in ARD%s between the different runs might be cause by the experimental errors which are different from a run to another, and it is believed that the reasons of these deviations are: The use of manual instruments instead of digital readouts which require a calibration prior to each run. Moreover, the difficulty to reach the adiabatic conditions at the laboratory scale which is assumed in the model development. Finally, pressure and heat losses along the column.

Kinetic model
A sensible selection of kinetic models is important for obtaining accurate predictions. In regards to this area, the liquid-phase temperature and liquid CO 2 loading have been simulated using two different kinetic models (Aboudheir et al., 2003, Luo et al., 2015. Figure 1 illustrates the simulation results in respect of the empirical values obtained from runs R21 and R22 of Sonderby et al. (2013). According to this figure, it has been noticed that the liquid temperature and the liquid CO 2 loading profiles simulated by using the kinetic model suggested by Luo et al. (2015) are more accurate than the ones obtained while using the kinetic model of Aboudheir et al. (2003). The use of the kinetic model of Aboudheir et al. (2003) is somewhat under predicts the liquid temperature and the liquid CO 2 loading. This low accuracy presented by this kinetic model might be affected by the instrumental methods employed to obtain kinetic data, and the empirical correlations of physical properties (CO 2 diffusivity and solubility in aqueous solutions) employed for kinetic model development. Furthermore, it has been also observed that the kinetic models have a large influence on both, liquid CO 2 loading and liquid temperature. And according to the results obtained from Cases 1.a to 1.b for all runs, presented in Table 2, the same conclusions are found.

Enhancement factor
On the basis of the results presented in Table 2 for the Cases 2.a-2.h, it can be deduced that the effect of the different enhancement factor models on the performance of the columns is not very significant. The ARD%s between the simulation results and pilot-plant measured data are very close for all cases, the difference is in the order of ±0.1% for both liquid temperature and liquid CO 2 loading. The lowest ARD% is obtained by using the model developed by Van Krevelen and Hoftijzer (1948), while the highest ARD% is given from the model suggested by Cussler (2009).

Enthalpy of absorption
The simulated liquid temperature and liquid CO 2 loading profiles were compared with measurements taken from runs R21 and R22 of Sonderby et al. (2013), as shown in Figure 2, to study the effect of the enthalpy of absorption on the absorber performance.
Accordingly, it has been noticed that the influence of the enthalpy of absorption on the liquid CO 2 loading is very small, the different profiles obtained for R21 and R22 are almost overlapped, there is just a slight difference in the last 3 m of the absorber height, where the lowest ARD% is obtained from the correlation of Llano-Restrepo and Araujo-Lopez (2015) based on Arcis et al. (2011). On the other hand, the effect is very high for the liquid temperature profiles. It has been observed that the use of the fixed value of 118.2 kJ/mol, given by Kohl and Nielsen (1997), underpredicts the liquid temperature profile for both runs R21 and R22 with ARD%s of 5.573% and 5.746%, respectively. Furthermore, the liquid temperature profiles obtained by using the fixed value of 84.4 kJ/mol reported by Pandya (1983) and the two correlations developed by Kim (2009) and Llano-Restrepo and Araujo-Lopez (2015) based on Kim and Svendsen (2007) data are closely superposed with ARDs% of 7.793, 7.925, and 8.114%, respectively, for R21, and ARDs% of 5.881, 5.944 and 6.118%, respectively, for R22, they exhibit a good accord with experimental data in the initial 3 m then they overpredict the liquid temperature for the rest of the column. Finally, the correlation suggested by Llano-Restrepo and Araujo-Lopez (2015) based on Arcis et al. (2011) data provides the lowest ARD% of 2.522% and 2.521%, with respect to R21 and R22, the overall agreement in this case between simulated liquid temperature profile and measurements is generally good.
From the results of Table 2, regarding the Cases 3.a-3.e for all runs, it has been noticed that it leads to the same conclusions.

Vapor pressure
Different correlations for vapor pressure estimation (see Tab. A5) were employed to simulate the liquid temperature and the liquid CO 2 loading using the experimental data of Sonderby et al. (2013), the results for R21 and R22 are illustrated in Figure 3.
As shown in Figure 3, the influence of the vapor pressure on both, the liquid temperature and the liquid CO 2 loading is important. According to runs R21 and R22, the results obtained while using the correlation developed by Antoine (1888) show a good agreement with experimental data, contrary to the correlation suggested by Riedel (1954) Riedel (1954), and (c) Ambrose and Walton (1989).
where the ARD% is very large (see Tab. 2), it overestimates the liquid temperature and the liquid CO 2 loading, while the use of Ambrose and Walton (1989) correlation under-predicts them. All in all, and according to these results as well as the results shown in Table 2 for the Cases 4.a-4.d, it has been concluded that the correlation developed by Antoine (1888) leads to the most accurate simulation results.

CO 2 diffusivity in aqueous solutions of MEA
The influence of CO 2 diffusivity in aqueous solutions of MEA on the column performance is studied by using the measurements taken from Sonderby et al. (2013). The results, shown in Figure 4, are presented in terms of liquid temperature and liquid CO 2 loading.
According to this figure, It has been noticed that the influence of the CO 2 diffusivity in aqueous MEA solution on the column performance is not very large, all the three correlations show a good agreement with experimental data, the profiles obtained from the correlations of Ko et al. (2001) and Ying and Eimer (2012) are almost overlapped with very close ARD%s (see Tab. 2). However, the use of the correlation of Jamal (2002) under-predicts both, liquid temperature and liquid CO 2 loadings profiles. The lowest ARD% is obtained from the correlation suggested by Ying and Eimer (2012), while the highest ARD% is given from the correlation developed by Jamal (2002), and according to Table 2 for the cases 5.a-5.c, the same is observed for the other runs.

The added value of this study to the modeling and simulation
In general, the experimental techniques, the number of measurements, as well as the assumptions behind the different model parameter correlations are the main reason of the discrepancies between experimental data and simulated profiles, therefore, a good selection of such correlations is of high importance which is the key objective of this parametric study. And in order to prove its significance on obtaining reliable modeling and simulation results, a comparison between a combination of different model parameters that present the highest and the lowest ARDs% was performed (only this two cases were chosen since the number of possible combinations is very large), in other words, the difference in deviation between the worst case and the best one is investigated in this section, Table 3 summarized the model parameter correlations used in each case.
According to the comparison results illustrated in Figure 5, for different runs (R 3, 8, 13-15, 18, 21-23) of Sonderby et al. (2013), we can come up with the following conclusions: In general, the decrease of the model deviation between both cases is very large, it can reach more than 18% and 4% for the liquid temperature and liquid CO 2 loading profiles, respectively, which is more important for the liquid temperature than for the liquid CO 2 loading. This could be explained by the fact that almost all the model parameters studied in this paper have a great impact on the liquid temperature contrary to the liquid CO 2 loading where the influence is minor. Finally, this comparison shows clearly the significance of this study on obtaining reliable model predictions seen the important reduction of the model deviation obtained while estimating the model parameters by the means of the most accurate correlations.

Conclusion
One of the challenges faced while modeling and simulating the reactive absorption of CO 2 into loaded aqueous monoethanolamine solution in a packed-bed absorber is the proper calculation of the model parameters, hence, a parametric study was performed by using different cases of five different model parameters (kinetic model, enhancement factor, heat of absorption, CO 2 diffusivity in aqueous solutions of MEA, and vapor pressure). Consequently, the following points can be deduced: Among the model parameters studied in this paper, only kinetic model and vapor pressure have a large influence on the liquid CO 2 loading. Some parameters present a large influence on the liquid temperature (kinetic model, heat of absorption, and vapor pressure). Therefore, they should be chosen very carefully. The effect of the enhancement factor and CO 2 diffusivity is not very important, hence, a wrong choice of the model does not lead to severe deviation. The kinetic model introduced by Luo et al. (2015), the widely used model developed by Van Krevelen and Hoftijzer (1948) for the enhancement factor prediction, the developed correlation of Llano-Restrepo and Araujo-Lopez (2015) on the basis of Arcis et al. (2011) data for the heat of absorption estimation, vapor pressure expression of Antoine (1888), and the correlation of Ying and Eimer (2012) for the diffusivity of CO 2 in loaded aqueous MEA solution calculation generally provide more accurate predictions of the empirical values relative to the other cases employed in this analysis. This combination of correlations is obtained using the step-by step approach where the coupling between different processes or phenomena is neglected. Therefore, another optimum model could be found while using another methods of performing the paramedic study.
In addition, the comparison between the two combinations of different model parameters that present the highest and the lowest ARDs% revealed that the model deviation   Vapor pressure Riedel (1954) Antoine (1888) CO 2 diffusivity Jamal (2002) Ying and Eimer (2012) could be reduced by 18% and 4% for the liquid temperature and liquid CO 2 loading profiles, respectively.