CHEMICAL ENGINEERING TRANSACTIONS VOL. 76, 2019 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Petar S. Varbanov, Timothy G. Walmsley, Jiří J. Klemeš, Panos Seferlis Copyright © 2019, AIDIC Servizi S.r.l. ISBN 978-88-95608-73-0; ISSN 2283-9216 Rate-Based Modelling and Validation of an Absorber and Stripper in an Amine-Based Post-Combustion CO2 Capture Process He Jin, Jianlin Li, Pei Liu*, Zheng Li State Key Lab of Power Systems, Department of Energy and Power Engineering, Tsinghua University, Beijing, 100084, China liu_pei@tsinghua.edu.cn Carbon emissions capture and storage is regarded as an essential approach to mitigate the greenhouse effect led by carbon dioxide emissions from the fossil fuels combustion. Amine-based post-combustion CO2 capture technologies have great potential for retrofitting existing coal-fired power plants. In this paper, a mathematical model for a packed absorber and stripper in a CO2 capture process are developed. Typical aqueous monoethanolamine (MEA) with 30 wt.% concentration is selected as the absorbent. A rate-based method is implemented to represent the mass and heat transfer in carbon dioxide absorption and desorption processes. In addition, the heat of CO2 is derived by Gibbs-Helmholtz equation. In this way, the effect of chemical equilibrium and thermodynamic equilibrium on absorption capacity and absorption heat can be obtained. Finally, these models are validated by literature data in different plant operating conditions. The present mathematical models can be used to analyse the mass and heat transfer behaviour and to improve the overall performance of the CO2 process. 1. Introduction Carbon dioxide is regarded as the predominant greenhouse gas that leads to global warming. The Intergovernmental Panel on Climate Change (IPCC) claims that the massive emissions of carbon dioxide contribute over half of increased temperature in recent decades (Oliver, 2013). The main source of carbon dioxide emissions is fossil fuels combustion. Therefore, it is essential to integrate carbon capture technologies with the large-scale emission source, such as coal-fired power plants, to mitigate CO2 emissions (Yaumi et al., 2017). Amine-based post-combustion CO2 capture technology is considered as an effective way and owns a great potential for further commercial application (Wang et al., 2017). Considering the energy consumption and operation flexibility, the simulation of post-combustion carbon capture process is necessary to study the feasibility for the real industrial application. Kvamsdal et al. (2009) developed a stand-alone CO2 absorber model and used steady-state data of the temperature profiles, rich solvent loading and CO2 capture rate from a pilot plant to validate the model. This work emphasized the necessity of the modelling the absorber to understand the complexities of real plant operation. Gaspar et al. (2012) set up a dynamic absorption/desorption model and also validated it by steady-state plant data. As the supplement and extension of the previous work, Gaspar et al. (2016) validated the model with the transient data in response to the flue gas flow rate changes in a pilot plant. Flø et al. (2015) set up a rated-based model of the CO2 absorption process in Matlab and validated the model with steady-state and transient pilot plant data from the pilot plant in Norwegian University of Science and Technology. Manaf et al. (2016) utilized the system identification method with the transient pilot plant data to set up a black box model, instead of physical mechanism model. Zhao et al. (2017) used the equilibrium stage model in Aspen Plus to analyze the energy flow in the carbon capture process with different absorbent. According to this research, the aqueous MDEA solution with lower absorption heat is a better choice than typical MEA solution for the energy consideration. Montañés et al. (2017) developed a dynamic model based on conventional amine-based configuration, considering the size, geometry and materials of the key equipment. This model was validated steady state and dynamic plant data from the Technology DOI: 10.3303/CET1976136 Paper Received: 13/03/2019; Revised: 13/05/2019; Accepted: 14/05/2019 Please cite this article as: Jin H., Li J., Liu P., Li Z., 2019, Rate-Based Modelling and Validation of an Absorber and Stripper in an Amine-Based Post-Combustion CO2 Capture Process, Chemical Engineering Transactions, 76, 811-816 DOI:10.3303/CET1976136 811 Centre Mongstad carbon capture plant. Bui et al. (2018) developed a dynamic model by the gCCS modules to study the interaction between the key process parameters, such as liquid to gas ratio and capture rate, during the dynamic amine-based carbon capture process. In this paper, a rate-based model for a packed absorber and stripper is implemented in gPROMS. The typical solution, aqueous MEA with 30 wt.% concentration, is chosen as the absorbent in this model. The modeling method is introduced in section 2. To simplify the thermodynamic calculation, the equilibrium partial pressure of CO2 is expressed by a function of temperature and carbon loading by Chen et al. (2011) approach. This equilibrium method was not used for overall performance calculation of absorber and stripper. The heat of CO2 is derived by Gibbs-Helmholtz equation. Validation of the model is conducted by comparing the simulation results with the data from a pilot plant in section 3 and conclusions from this work are given in section 4. 2. Model development A typical amine-based CO2 absorption system mainly includes an absorber, a stripper, and a rich/lean heat exchanger (RLHX). The absorption/desorption process is presented in Figure 1. In this process, flue gas enters the absorber from the bottom and contacts with the countercurrent lean absorbent from the top of the absorber. The majority of CO2 in flue gas is eliminated and vent gas exits from the top of the absorber. The rich solvent after absorption is preheated in the RLHX for heat recovery by the lean solvent at the bottom of the stripper. Then CO2 in the rich solvent is regenerated during the desorption reaction in the stripper. Then the lean solvent is introduced to the top of the absorber to form a closed loop. The absorber and stripper are the key equipment in the carbon capture process. The column is discretized along the height and the control volume contains vapor and liquid phase. The following assumptions are used in this model. ⚫ Plug flow regime is considered in each control volume. ⚫ Liquid and vapor phases are considered as ideal phases. ⚫ Both columns are adiabatic. ⚫ Mass and heat transfer are described by the two-film theory and rate-based model. ⚫ Mass transfer of inert gas, such as N2 and O2, is negligible. ⚫ Figure 1: Flow diagram of a conventional CO2 capture process 2.1 Conservation equations Conservation equations are the main control equations in this model, including mass, component and energy balances. Mass and component conservation equations are described as follows: 0 = 1 𝐴 𝑢𝑠 𝐿 𝜕𝑐𝑡𝑜𝑡 𝐿 𝜕𝑧 + 1 𝐴 𝑐𝑡𝑜𝑡 𝐿 𝜕𝑢𝑠 𝐿 𝜕𝑧 + ∑ 𝐽𝑖 𝑖 𝑎𝑝𝑒 (1) 0 = − 1 𝐴 𝑢𝑠 𝑉 𝜕𝑐𝑡𝑜𝑡 𝑉 𝜕𝑧 − 1 𝐴 𝑐𝑡𝑜𝑡 𝑉 𝜕𝑢𝑠 𝑉 𝜕𝑧 − ∑ 𝐽𝑖 𝑖 𝑎𝑝𝑒 (2) 0 = 1 𝐴 𝑢𝑠 𝐿 𝜕𝑐𝑖 𝐿 𝜕𝑧 + 1 𝐴 𝑐𝑖 𝐿 𝜕𝑢𝑠 𝐿 𝜕𝑧 + 𝐽𝑖 𝑎𝑝𝑒 (3) 812 0 = − 1 𝐴 𝑢𝑠 𝑉 𝜕𝑐𝑖 𝑉 𝜕𝑧 − 1 𝐴 𝑐𝑖 𝑉 𝜕𝑢𝑠 𝑉 𝜕𝑧 − 𝐽𝑖 𝑎𝑝𝑒 (4) where the subscripts 𝑖 denote components H2O and CO2, superscripts 𝐿 and 𝑉 denote liquid and vapor phases respectively, 𝑐𝑡𝑜𝑡 is the total concentration of a phase, 𝑢𝑠 is superficial velocity, 𝐽 is mass transfer flux, 𝑎𝑝𝑒 is effective specific area of the packing between liquid and vapor phases for mass transfer, 𝐴 is the interface area between liquid and vapor phases. Energy conservation equations are described as follows: 0 = 𝑢𝑠 𝐿 𝜕𝑇 𝐿 𝜕𝑧 + ℎ𝑐𝑜𝑒𝑓𝑓 𝑎𝑝𝑒 𝐶𝑝𝑚 𝐿 𝜌𝐿 (𝑇 𝑣 − 𝑇 𝐿 ) + 𝐽𝐶𝑂2 𝑎𝑝𝑒 ℎ𝐿𝐹 𝐶𝑝𝑚 𝐿 𝜌𝐿 ∆𝐻𝑎𝑏𝑠 + 𝐽𝐻2𝑂 𝑎𝑝𝑒 ℎ𝐿𝐹 𝐶𝑝𝑚 𝐿 𝜌𝐿 ∆𝐻𝑣𝑎𝑝 (5) 0 = −𝑢𝑠 𝑉 𝜕𝑇 𝑉 𝜕𝑧 − ℎ𝑐𝑜𝑒𝑓𝑓 𝑎𝑝𝑒 𝐶𝑝𝑚 𝑉 𝜌𝑉 (𝑇 𝑉 − 𝑇 𝐿 ) (6) where 𝑇 is temperature, ℎ𝑐𝑜𝑒𝑓𝑓 is the heat transfer coefficient between liquid and vapor phases, 𝐶𝑝𝑚 is the specific heat capacity on mass basis , 𝜌 is density, ∆𝐻𝑎𝑏𝑠 stands for the absorption heat of CO2, ∆𝐻𝑣𝑎𝑝 stands for the heat of vaporization of H2O. 2.2 Mass transfer equations Mass transfer for the components CO2 and H2O can be described by the two-film theory as Figure 2 shows. The transfer resistance consists of vapor and liquid resistance. The flux of mass transfer is calculated by the following equation: 𝐽𝑖 = 𝐾𝑖 𝑜𝑣 (𝑐𝑖 𝑉 − 𝑐𝑖 𝐿∗) (7) where the superscript * denotes the state of thermodynamic equilibrium, 𝐾𝑖 𝑜𝑣 represents the overall mass transfer coefficient. Figure 2: Illustration of the two-film model The overall mass transfer coefficient for H2O equals the mass transfer coefficient of the vapor phase side because the resistance of the vapor phase side is far more than that of liquid phase side. As for the component CO2, the method of enhancement factor is used in rate-based model. The overall mass transfer coefficient is calculated by the following equation: 𝐾𝐶𝑂2 𝑜𝑣 = 1 ( 1 𝐾𝐶𝑂2 𝑉 + 𝐻𝐶𝑂2 𝐸𝐾𝐶𝑂2 𝐿 ) (8) 813 where 𝐻𝐶𝑂2 is the Henry’s constant, 𝐾𝐶𝑂2 𝑉 and 𝐾𝐶𝑂2 𝐿 represent the mass transfer coefficient in vapor and liquid phase respectively, 𝐸 is the enhancement factor which presents the effect of the existence chemical reaction upon the absorption process. The mass transfer coefficient can be calculated by the correlations in previous literature (Onda et al., 1968; Bravo et al., 1992). 2.3 Thermodynamic equations In this work, a semi-empirical thermodynamic equilibrium model is implemented to reduce the amount of calculation (Chen et al., 2011), as Equation 9 shows. In this model, the equilibrium partial pressure of CO2 is assumed as a function of temperature 𝑇 and solvent carbon loading 𝛼. Therefore, the calculation of activity coefficient can be avoided. The constants 𝑎, 𝑏, 𝑐, 𝑑, 𝑒 are fitting coefficient for amines. In terms of the MEA, a, b, c, d, e equal to 36.61, -11152, -7.46, 2389, 26.69. ln 𝑃𝐶𝑂2 ∗ = 𝑎 + 𝑏 𝑇 + 𝑐𝛼 + 𝑑𝛼 𝑇 + 𝑒𝛼2 (9) Thereby, the expression of CO2 absorption heat ∆𝐻𝑎𝑏𝑠 is obtained by Gibbs-Helmholtz equation: ∆𝐻𝑎𝑏𝑠 = −𝑅 𝑑(ln 𝑃𝐶𝑂2 ∗ ) 𝑑 ( 1 𝑇 ) = −𝑅(𝑏 + 𝑑𝛼) (10) where CO2 absorption heat is a function of solvent carbon loading 𝛼. 3. Model validation Feasibility of the above mathematical model needs to be tested by comparing simulation results and literature data. In this work, the practical operation data is selected from the pilot plant experiments in the University of Texas, Austin (Dugas, 2006). The information of the absorber and stripper is listed in Table 1. For the modelling verification, the main performance in experiments data need to be distribute in a relatively wide range. The following five typical cases in different working conditions are chose to validate the column model, in which the reboiler duty is from 30% to 100% based on case 1. The information of the working conditions in these cases is listed in Table 2. Table 1: Main parameters for absorbers and strippers Unit Absorber Stripper Operating pressure bar 1.01 1.66 Packing type - IMTP FLEXIPAC Packing height m 6.1 6.1 Column diameter m 0.427 0.427 Table 2: Working conditions in different cases Unit Case 1 Case 2 Case 3 Case 4 Case 5 CO2 concentration in flue gas vol.% 16.6 16.5 16.0 17.7 17.5 Flue gas temperature ℃ 55 48 54 47 53 Flue gas flow rate m3/h 660 660 660 330 330 Lean solvent carbon loading mol/mol 0.278 0.290 0.231 0.279 0.284 Lean solvent temperature ℃ 40 40 40 40 40 Lean solvent flow rate m3/h 6.25 4.63 2.36 2.44 2.57 Rich solvent temperature ℃ 69 73 80 86 85 Reboiler duty kW 469 366 209 152 155 Temperature profiles of the absorber and stripper are shown in Figure 3 and Figure 4 respectively. The simulation results are in accordance with the pilot plant data. Validation of simulation results of rich solvent carbon loading, CO2 capture rate, lean solvent carbon loading are depicted in Figure 5. Similarly, the model calculation results are in line with the experimental data. 814 Figure 3: Temperature profiles of the absorber in different cases Figure 4: Temperature profiles of the stripper in different cases (a) (b) (c) Figure 5: Validation of simulation results of rich solvent carbon loading (a), CO2 capture rate (b), lean solvent carbon loading (c) 0 2 4 6 40 50 60 70 T e m p e ra tu re ( °C ) Height (m) Case 1 Model Experiment 0 2 4 6 40 50 60 70 T e m p e ra tu re ( °C ) Height (m) Case 2 Model Experiment 0 2 4 6 40 50 60 70 80 90 T e m p e ra tu re ( °C ) Height (m) Case 3 Model Experiment 0 2 4 6 40 60 80 100 T e m p e ra tu re ( °C ) Height (m) Case 4 Model Experiment 0 2 4 6 40 50 60 70 80 T e m p e ra tu re ( °C ) Height (m) Case 5 Model Experiment 0 2 4 6 70 90 110 130 T e m p e ra tu re ( °C ) Height (m) Case 1 Model Experiment 0 2 4 6 70 90 110 130 T e m p e ra tu re ( °C ) Height (m) Case 2 Model Experiment 0 2 4 6 70 90 110 130 T e m p e ra tu re ( °C ) Height (m) Case 3 Model Experiment 0 2 4 6 70 90 110 130 T e m p e ra tu re ( °C ) Height (m) Case 4 Model Experiment 0 2 4 6 70 90 110 130 T e m p e ra tu re ( °C ) Height (m) Case 5 Model Experiment 0.30 0.35 0.40 0.45 0.50 0.30 0.35 0.40 0.45 0.50 M o d e l Experiment 0.7 0.8 0.9 1.0 0.7 0.8 0.9 1.0 M o d e l Experiment 0.20 0.25 0.30 0.35 0.20 0.25 0.30 0.35 M o d e l Experiment 815 4. Conclusions This paper developed a model for an absorber and stripper in the post-combustion CO2 capture process based on the physical mechanism method. The control equations mainly consist of conservation, mass transfer and thermodynamic equations. A rate-based model based on the enhancement factor method is implemented to calculate the mass transfer flux. For maintain the flexibility and simplicity of the model, a semi-empirical model of equilibrium partial pressure of CO2 is used in thermodynamic calculation. The equilibrium model correlates the CO2 pressure with temperature and load and provides the heat of absorption required in the energy balance. Since the modelling approach doesn’t include the rigorous electrolyte calculation, the electrolyte concentration distribution along the height of absorber and stripper cannot be reflected in this model. However, in terms of the overall performance calculation, such as carbon capture rate and carbon loading, the mathematical model for an absorber and stripper is feasible by the validation of the experimental data in different cases from a pilot plant. This work provides a foundation for further dynamic model development with an agreeable dynamic performance. Acknowledgments The authors gratefully acknowledge the support by The National Key Research and Development of China (2016YFE0102500), Shanxi Key Research and Development Program (201603D312001), National Natural Science Foundation of China (71690245), and the Phase Ⅲ Collaboration between BP and Tsinghua University. References Bravo J.L., Patwardhan A.A., Edgar T.F., 1992, Influence of effective interfacial areas in the operation and control of packed distillation columns, Industrial & Engineering Chemistry Research, 31(2), 604-608. Bui M., Tait P., Lucquiaud M., Mac Dowell N., 2018, Dynamic operation and modelling of amine-based CO2 capture at pilot scale, International Journal of Greenhouse Gas Control, 79, 134-153. Chen X., Closmann F., Rochelle G. T., 2011, Accurate screening of amines by the wetted wall column, Energy Procedia, 4, 101-108. Dugas R.E., 2006, Pilot plant study of carbon dioxide capture by aqueous monoethanolamine, MSE Thesis, University of Texas at Austin, USA. Flø N.E., Knuutila H., Kvamsdal H.M., Hillestad M., 2015, Dynamic model validation of the post-combustion CO2 absorption process, International Journal of Greenhouse Gas Control, 41, 127-141. Gaspar J., Cormos A.M., 2012, Dynamic modeling and absorption capacity assessment of CO2 capture process, International Journal of Greenhouse Gas Control, 8, 45-55. Gaspar J., Gladis A., Jørgensen J.B., Thomsen K., von Solms N., Fosbøl P.L., 2016, Dynamic operation and simulation of post-combustion CO2 capture, Energy Procedia, 86, 205-214. Kvamsdal H.M., Jakobsen J.P., Hoff K.A., 2009, Dynamic modeling and simulation of a CO2 absorber column for post-combustion CO2 capture. Chemical Engineering and Processing: Process Intensification, 48(1), 135-144. Manaf N.A., Cousins A., Feron P., Abbas A., 2016, Dynamic modelling, identification and preliminary control analysis of an amine-based post-combustion CO2 capture pilot plant, Journal of Cleaner Production, 113, 635-653. Montañés R., Flø N., Nord L., 2017, Dynamic process model validation and control of the amine plant at CO2 Technology Centre Mongstad, Energies, 10(10), 1527. Oliver J.E., 2013, Intergovernmental Panel in Climate Change (IPCC), Encyclopedia of Energy Natural Resource & Environmental Economics, 26(2), 48-56. Onda K., Takeuchi H., Okumoto Y., 1968, Mass transfer coefficients between gas and liquid phases in packed columns, Journal of Chemical Engineering of Japan, 1(1), 56-62. Wang T., Yu W, Le Moullec Y., Liu F., Xiong Y., 2017, Solvent regeneration by novel direct non-aqueous gas stripping process for post-combustion CO2 capture, Applied Energy, 205, 23-32. Yaumi, A.L., Bakar M.Z.A., Hameed B.H., 2017, Recent advances in functionalized composite solid materials for carbon dioxide capture, Energy, 124, 461-480. Zhao B., Liu F., Cui Z., Liu C., Yue H., Tang S., Liang B., 2017, Enhancing the energetic efficiency of MDEA/PZ- based CO2 capture technology for a 650 MW power plant: Process improvement, Applied Energy, 185, 362- 375. 816