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A novel fitted thermodynamic model for the capture of CO2 from flue gas by the hydrate method
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Research Article
A novel fitted thermodynamic model for the capture of CO2 from flue gas by the hydrate method*,** Li Luling a,*, Zhao Jinzhou a, Li Haitao a, Zhang Liehui a, Fan Shuanshi a,b, Li Qingping c, Pang Weixin c, Lu¨ Xin c, Zheng Lijun c & Wei Na a State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, China b CNOOC Research Institute, Beijing 100027, China c MOE Key Laboratory of Heat Transfer Enhancement and Process Energy Conservation, South China University of Technology, Guangzhou, Guangdong 510006, China a
Received 5 November 2018; accepted 25 April 2019
Abstract The hydrate-based gas separation for capturing CO2 from flue gas has the characteristics of low energy consumption, simple operation and convenience for the subsequent CO2 storage and utilization. In order to reduce the total cumulative deviation of multi-stage hydration reaction, it is of great importance to establish an accurate thermodynamic model. Based on the vdWeP þ CPA model, therefore, we refitted the parameters of the thermodynamic model considering the association between CO2 and H2O. Firstly, the energy parameter a0.5 of H2O and CO2 are developed as the cubic function and the linear function of [1-(T/Tc)0.5], respectively. Then, the calculation parameters of Langmuir absorption coefficient of vdWeP model is refitted based on the temperature dependent binary interaction parameters kij. The following research results are obtained. First, when the novel fitted thermodynamic model is used to predict the density of saturated fluid, the average absolute deviation (AAD) of H2O drops from 1.84% to 0.08% and that of CO2 drops from 4.06% to 2.09%. Second, when it is used to predict the phase equilibrium pressure of the hydrate generated from pure CO2 and pure N2, the AAD is 0.86% and 0.82%, respectively. Third, when it is used to calculate the phase equilibrium condition of hydrate generated from flue gas with different compositions, the AAD is decreased from 15.16% to 5.02%. In conclusion, this novel fitted thermodynamic model is of higher accuracy and it, to some extent, can decrease the total accumulative deviation of multi-stage hydration reaction. The research results provide reference for the actual application of the hydrate-based gas separation for capturing CO2 from flue gas. © 2019 Sichuan Petroleum Administration. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Hydrate-based gas separation; Flue gas; CO2 capture; CO2 thermodynamic model; Multi-stage hydration reaction; Energy parameter; Langmuir absorption coefficient; Prediction
0. Introduction
* Project supported by the National Natural Science Foundation Project “Study on methane storage, separation and sequestration of carbon dioxide in exploitation and utilization of marine gas hydrate” (No.: 21736005), China Postdoctoral Science Foundation Project (No.: 2017M623060, 2019T120860). ** This is the English version of the originally published article in Natural Gas Industry (in Chinese), which can be found at https://doi.org/10.3787/j.issn. 1000-0976.2019.04.014. * Corresponding author. E-mail address: [email protected] (Li LL). Peer review under responsibility of Sichuan Petroleum Administration.
The flue gas discharged from fossil-fuel power plants contains a large amount of CO2, accounting for about 75% of the total CO2 emissions [1,2]. CO2 is a harmful greenhouse gas to the environment, but it is also a type of valuable resource [3,4]. Therefore, it is necessary to capture CO2 from flue gas. Common CO2 capture processes includes chemical absorption [5,6], physical absorption [7e10], membrane separation [11], and cryogenic separation [12]. The hydrate-based gas separation method [12], one of the cryogenic separation methods, is considered to be one of the most promising CO2
https://doi.org/10.1016/j.ngib.2019.04.006 2352-8540/© 2019 Sichuan Petroleum Administration. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: Li LL et al., A novel fitted thermodynamic model for the capture of CO2 from flue gas by the hydrate method, Natural Gas Industry B (2019), https://doi.org/10.1016/j.ngib.2019.04.006
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capture processes because it is low in energy consumption, simple in operation and favorable for subsequent CO2 storage and utilization [13e15]. In order to meet the requirements of CO2 capture, it is necessary to use multi-stage hydration reaction. A thermodynamic model is usually used to determine the operating conditions of hydration reactions at all stages. Therefore, an accurate thermodynamic model is particularly important in order to reduce the total accumulative deviation by multi-stage reactions. The establishment of a thermodynamic model is based on the principle that the chemical potential difference or fugacity of the same substance in each phase is equal when the system reaches equilibrium. The commonly used gaseliquid models mainly include SRK equation, PR equation, CPA equation, SAFT equation and DA equation. The hydrate phase models mainly include vdWeP model [16] and CheneGuo model. Herslund et al. [17] used the vdWeP þ CPA model to calculate the phase equilibrium pressure of hydrate generated from CO2eN2, and found that for low-concentration CO2 flue gas, the deviation is larger. Zhang et al. [18] revised the vdWeP þ PR model to predict the phase equilibrium conditions of hydrate generated from CO2eN2 under the action of accelerators. The results show that the accuracy of the model is lower when the generating pressure is predicted with given temperature. Herri et al. [19] calculated the Langmuir absorption coefficient based on vdWeP þ SRK model and three methods, and found that the average absolute deviation of calculating phase equilibrium pressure of flue gas is higher than 8%. Thus, the accuracy of the existing thermodynamic models needs to be improved [20]. In this paper, the vdWeP þ CPA model is revised and its accuracy is verified. 1. Thermodynamic model 1.1. Gaseliquid phase model The perturbation expansion of the residual Helmholtz free energy term (Ares) in the CPA equation is as follows [21]: Ares ¼ A Aphy ¼ Aassoc
ð1Þ
where, " # Aassoc X X XAi 1 ¼ xi lnXAi þ Mi 2 RT 2 i Ai , XAi ¼ 1
X X Ai Bj 1 þ V 1 xj XBi m D j
calculated using the SRK equation in this paper; Aassoc: the Helmholtz free energy of associative term, J/mol; R: the universal gas constant, 8.314 J/(mol$K); T: the temperature, K; xi: the molar fraction of the ith component; Ai: the associating position A of the ith component; Mi: the number of associating positions of the ith component; XAi: the unoccupied molar fraction of A coordination on the ith molecule; Vm: the molar volume, m3/mol; XBi: the unoccupied molar fraction of B coordination on the ith molecule; DAiBj is the associating strength between the A coordination on the ith molecule and the B coordination on the jth molecule, m3/mol; bAiBj: the energy parameter; b: the volume parameter, m3/mol; εAiBj: the associating volume, (Pa$m3)/mol; g(1/Vm): the radial distribution function. 1.2. Hydrate phase model The chemical potential difference (Dmw,H) between hydrate phase and base hydrate phase in the vdWeP model can be calculated by using the following equation: ! X X Dmw;H ¼ RT ni ln 1 qij ð2Þ i
where, qij ¼
j
where, Vi is the number of type i pores connected by a single water molecule; similarly, qij: the occupation ratio of guest molecule j in type i pores; fj: the fugacity of guest molecule j, Pa; Cij: the Langmuir absorption coefficient of guest molecule j on type i pores. Parrish and Prausnitz [22] proposed the following formulas for calculating the Langmuir absorption coefficient: Ak;i Bk;i Ck;i ¼ exp ð3Þ T T where, Ak,i and Bk, i are fitting parameters. Moreover, Saito et al. [23] proposed the calculation method of the chemical potential difference of water in liquid phase Dmw,L: Dmw;L ¼ Dm0w;L RT lnaw
D
Ai Bj ε ¼ gð1=Vm Þ exp 1 bij bAi Bj RT
gð1 = Vm Þ ¼ 64V 3m 8V 2m b ð4Vm bÞ3 where, A is the total Helmholtz free energy, J/mol; similarly, Aphy: the Helmholtz free energy of physical term, J/mol, which is
ð4Þ Z
Dm0w;L Dm0w ¼ RT RT0 ZT þ
T
ZT Dhw;bI þ Dhw;LI þ
DCpw dT T0
RT 2 T0
Ai Bj
Cij fj P 1 þ Cij fj
!
Bi
j
dT ð5Þ
Dvw;bI þ Dvw;LI ðdPR = dTÞdT RT
T0
where, PR ¼ A þ B=T þ DlnT
Please cite this article in press as: Li LL et al., A novel fitted thermodynamic model for the capture of CO2 from flue gas by the hydrate method, Natural Gas Industry B (2019), https://doi.org/10.1016/j.ngib.2019.04.006
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where, Dm0w is the chemical potential difference between hydrate phase and b phase under standard conditions, J/mol; similarly, aw: the water activity in liquid phase; T0: the temperature under standard conditions, K; Dhw,beI: the molar enthalpy change of water in solid phase and b phase under standard conditions, J/mol; Dhw,LeI: the molar enthalpy change of water in solid ice phase and liquid phase under standard conditions, J/mol; DCpw: the change of heat capacity of water, J/(mol$K); Dvw,beI: the molar volume difference between b phase and solid ice phase, m3/mol; Dvw,LeI: the molar volume difference between hydrate, m3/mol; PR: the reference hydrate formation pressure at temperature T, Pa; A, B and D are related parameters [22]. According to Dmw,H ¼ Dmw,L, Equations (2)e(5) can be used to predict the phase equilibrium conditions for hydrate formation in the system. 2. Fitting of model parameters In the CPA equation reported in Refs. [17,24], only the interactive association between water molecules is considered, while CO2 and N2 are considered as non-associated molecules. By contrast, Tsivintzelis et al. [25] found that the accuracy is higher when CO2 is a solvent molecule and there is an accepting electron position associated only with the molecule of H2O. Therefore, in order to improve the accuracy of the thermodynamic model, we consider H2O as a 4C-linked molecule, CO2 molecule as a solvent molecule with an accepting electron position, and N2 as a non-associated molecule. On this basis, we re-fitted the model parameters. 2.1. Energy parameter a The CPA equation considers that CO2 is a non-polar molecule without association, and the energy parameter a can be calculated by directly using the absolute temperature, absolute pressure and eccentricity factor of CO2. Also, it is considered that H2O is a type 4C molecule, and its energy parameter a0.5 is a linear function of [1-(T/Tc)0.5]. Mathias et al. [26] reports that the calculation results are more accurate when the energy parameter a0.5 of polar components is a cubic function of [1-(T/Tc)0.5], while the calculation results are more accurate when the energy parameter a0.5 of polar components is a linear function of [1-(T/Tc)0.5] for nonpolar molecules with intermolecular association. Therefore, based on the data of saturated liquid density and saturated vapor pressure of CO2 and H2O in DIPPR database [27], the energy parameter a in CPA equation is regressed, and optimum calculation is conducted by matlab. The objective function can be calculated by using the following formula: ( " 2 DIPPR 2 #) N X pDIPPR pCal: ri rCal: i i i OF ¼ min þ pDIPPR rDIPPR i i i¼1 ð6Þ
3
where, pi is the system pressure of the ith group, Pa; similarly, ri: the saturated liquid density of the ith group, kmol/m3; the superscript DIPPR: the experimental data from the DIPPR database; the superscript ‘Cal.’: the calculated value of the model; N: there are N sets of data totally. The energy parameter a of H2O and CO2 can be expressed separately as: h pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi 2 a1 ¼ 0:094 1þ1:278 1 Tr;1 þ4:974 1 Tr;1 ð7Þ pffiffiffiffiffiffiffi 3 i2 18:085 1 Tr;1 pffiffiffiffiffiffiffi 2
a2 ¼ 0:391 1 þ 1:435 1 Tr;2
ð8Þ
where, a1 is the energy parameter of H2O, Pa/(m6$mol2); similarly, a2: the energy parameter of CO2, Pa/(m6$mol2); Tr,1: the correspondence temperature of H2O; Tr,2: the correspondence temperature of CO2. In order to verify the accuracy of the fitting results, it is necessary to calculate the saturated liquid densities of CO2 and H2O using the novel fitted energy parameters and the original energy parameters [28], respectively, and compare them with the DIPPR data (Fig. 1). It is noteworthy that the experimental data selected to verify the accuracy of the model are not used for parameter fitting. As shown in Fig. 1, both models can well describe the relationship between saturated liquid density and temperature of CO2 and H2O. For H2O, when the temperature is higher than 420 K or less than 320 K, the influence of polarity of water molecules on saturated liquid density becomes more and more obvious, so the accuracy of the initial model decreases; but the accuracy of the novel fitted model is higher in the range of investigation, especially at low temperature. For CO2, since the initial model considers it to be a non-polar molecule without association, if its energy parameter is calculated directly by absolute temperature, absolute pressure and eccentricity factor, it results in a large deviation between the saturated liquid density and the experimental value at low temperature. The a0.5 of CO2 is fitted as a linear function of [1-(T/Tc)0.5], and the accuracy of calculation results is higher. When the temperature is higher, the calculated result of the novel fitted model is slightly higher than the experimental value, while the result of the initial model is closer to the experimental value. The reason may be that the association of CO2 becomes weaker at high temperature, then it is more reasonable to consider CO2 as a non-polar molecule without association. As the hydrate system is a low temperature system, the novel fitted model is more suitable. For comparison, Equation (9) is used to determine the average absolute deviation (AAD). As for H2O, the AAD is only 0.08% for the novel fitted model and is 1.84% for the initial model; As for CO2, the AAD is 2.09% and 4.06% respectively. Clearly, the novel fitted model is more accurate in predicting the saturated liquid phase densities of H2O and CO2, and more suitable for cryogenic systems.
Please cite this article in press as: Li LL et al., A novel fitted thermodynamic model for the capture of CO2 from flue gas by the hydrate method, Natural Gas Industry B (2019), https://doi.org/10.1016/j.ngib.2019.04.006
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Fig. 1. Comparison of saturated liquid density of H2O and CO2 calculated by the initial model and novel fitted model.
AAD% ¼
N exp: cal: 1X xi x xexp: 100 i i N i¼1
ð9Þ
where, xi is the molar content of component i of the system; the superscript ‘exp.’ represents the experimental data reported in the literature. 2.2. Binary interaction parameter kij This parameter reflects the influence of the interaction between different molecules on the thermodynamic properties of the system. Ruffine et al. [29] find through experiments that kij is greatly affected by temperature. Therefore, using the temperature dependent kij can help to improve the accuracy of model calculation. kij fitting and verification process for CO2eH2O system and N2eH2O system have been described in detail in the previous study [30], thus no further elaboration will be made here. The fitting result is: kCO2 H2 O ¼ 2:09 105 T 2 þ 0:011T 1:28
ð10Þ
kN2 H2 O ¼ 7:09 105 T 2 þ 0:04T 6:47
ð11Þ
As the interaction between CO2 and N2 molecules is smaller, kCO2eN2 is taken as 0 [17]. 2.3. Calculating parameters of Langmuir adsorption coefficient Langmuir absorption coefficient is usually fitted by the thermodynamic model based on phase equilibrium conditions of hydrate generated from pure gas. Therefore, when the gaseliquid phase model changes, the Langmuir absorption coefficient should also change. Determination of the Langmuir absorption coefficients of large pores and small pores simultaneously is the key to calculation. Because most CO2 exists in large pores and N2 exists in large and small pores when gas hydrate is formed by the CO2 and N2 mixture, it is considered that the Langmuir absorption coefficient of small pores is very small for CO2, that of large pores is larger, and that of N2 is similar for large pores and small pores. In order to simplify the calculation process, it is considered that the Langmuir absorption coefficients of small pores of CO2 and N2 have little
changes. The absorption coefficients of large pores are fitted by using the phase equilibrium conditions of hydrate formation from pure gas [31e35], and the parameters are obtained by using the fitting results. The results are shown in Table 1. In order to verify the accuracy of the fitting results, it is necessary to substitute the fitting parameters into the thermodynamic model to calculate the phase equilibrium conditions of pure CO2 and N2, respectively. The results are compared with the experimental data reported in the literature. The results are shown in Fig. 2. In Fig. 2, the phase equilibrium pressures of CO2 and N2 increase with the temperature. At the same temperature, the phase equilibrium pressure of N2 is obviously higher than that of CO2, which again verifies that CO2 and N2 can be separated by the hydrate-based method. The Langmuir absorption coefficient is calculated by using the parameters fitted in this paper. The calculated results of the model are in good agreement with the experimental results reported in literature. The calculated results show that AAD is 0.86% and 0.82% respectively for predicting the equilibrium pressures of CO2 and N2. It can be concluded that the parameters fitted in this paper for the Langmuir absorption coefficient can ensure the accuracy of vdWeP model in calculating the thermodynamic properties of pure hydrate phase. 3. Model verification In order to verify the accuracy of the established thermodynamic model, it is necessary to calculate the phase equilibrium pressures of hydrate generated from flue gas at given temperatures by using the novel model and the VeP model [16], respectively, and compare them with the experimental data reported in literatures [32,36,37]. As the experimental data in Table 1 Parameters in Equation (8). Hydrate type
Component
Small pore A/(K$MPa
Type I Type II
CO2 N2 CO2 N2
1.159 3.007 1.265 2.839
Large pore 1
)
2
10 10 10 10
2 2 2
B/K
A/(K$MPa
2861 2139 2790 2175
1.097 2.184 3.036 2.364
1
)
10 102 101 102
B/K 1855 2879 3059 2215
Please cite this article in press as: Li LL et al., A novel fitted thermodynamic model for the capture of CO2 from flue gas by the hydrate method, Natural Gas Industry B (2019), https://doi.org/10.1016/j.ngib.2019.04.006
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Fig. 2. Comparison between the calculated values of pure CO2 and pure N2 phase equilibrium conditions by the novel fitted model and the experimental data reported in literatures [31e35].
the literatures are reported on the feeding liquid fraction, and the feeding liquid fraction has little influence on the calculation results of phase equilibrium conditions, it is assumed that the feeding liquid fraction is 0.5 based on the relevant literatures [38,39]. The calculation results are shown in Fig. 3.
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In Fig. 3, both models can well describe the relationship between phase equilibrium pressure and temperature of hydrate generated from flue gas. By considering the interaction association between CO2 and H2O molecules, a and kij in the CPA equation and the calculation parameters of Langmuir absorption coefficient in the vdWeP model are re-fitted. The accuracy of the novel fitted model in calculating the phase equilibrium conditions of flue gas is higher than that of the initial model. For most gas samples, especially those with about 50% CO2 content, the deviation between the calculated results and the experimental values of the novel fitted model is less affected by temperature. The reason may be that the temperature-related binary interaction parameters reduce the influence of temperature on the accuracy of the calculated results. Meanwhile, the calculation accuracy of gaseliquid phase composition is improved by considering the interaction association between CO2 and H2O molecules. The AAD of the two models are calculated separately, and the results are shown in Table 2. In Table 2, the average value of AAD of the novel fitted model decreased from 15.16% to 5.02% compared with that of the literature model. However, for the mixed gas with 6.63% CO2 content, the AAD of the novel fitted model is higher than that of the VeP model. The possible reason is that the novel fitted model overestimates the influence of N2 on the phase equilibrium conditions of hydrate generated from the mixed
Fig. 3. Comparisons between the calculated and experimental values of the two models for the phase equilibrium conditions of hydrate generated from CO2þN2 mixed gas. Please cite this article in press as: Li LL et al., A novel fitted thermodynamic model for the capture of CO2 from flue gas by the hydrate method, Natural Gas Industry B (2019), https://doi.org/10.1016/j.ngib.2019.04.006
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Table 2 Comparison of AAD calculation results between the VeP model and the novel fitted model. CO2 content (%)
Temperature (K)
96.59 85.32 77.80 48.15 45.24 36.24 25.10 20.03 18.00 11.59 10.10 6.63
274.95e283.55 276.20e284.01 274.00e284.25 273.75e282.00 274.34e283.15 273.80e282.32 273.60e277.60 273.80e282.00 273.50e277.40 274.25e278.95 273.40e276.80 273.95e278.25
Mean
AAD VeP model (%)
Novel fitted model (%)
12.71 20.93 23.11 20.31 17.15 17.04 16.26 7.35 20.43 4.98 9.23 9.72
8.97 5.50 9.21 4.02 2.05 0.97 1.09 2.86 6.96 1.54 4.99 12.04
15.16
5.02
gas, which results in the decreased accuracy of the model when the CO2 content is lower. The prediction result deviation of the phase equilibrium conditions is larger for forming type I hydrate generated from the mixed gas by the VeP model, while the deviation for type II hydrate is smaller. When the CO2 content is more than 75%, the AAD of the novel fitted model is relatively large (10e5%). The possible reason is that under this condition, the mixed gas produces type I hydrate. N2 occupies 512 small pores due to pressure, while CO2 content is bigger and partial pressure is higher, N2 will compete with N2 to occupy 512 small pores as a result of pressure. However, the model neglects the interaction between N2 and CO2, resulting in a slight decrease in accuracy. With the decrease of CO2 content, the partial pressure of CO2 decreases, the competition between two molecules decreases, and AAD drops. Especially for the mixed gas with 20e48% CO2 content, AAD is about 2%. It is noteworthy that the AAD values of both models are larger when the CO2 content is about 18%, possibly because the transition from type I to type II of hydrate generated from the mixed gas is a gradual process, and the calculation accuracy of the model decreases with the 15% CO2 content as the boundary in this paper. In a word, the accuracy of the novel fitted model has been improved to some extent, especially for the mixed gas with 25.1e48.15% CO2 content. 4. Conclusions 1) By fitting the energy parameter a0.5 of H2O and CO2 into the cubic and linear functions of [1-(T/Tc)0.5], the results show that AAD decreases from 1.84% to 0.08% and from 4.06% to 2.09% respectively in predicting saturated liquid density. 2) On this basis, the calculation parameters of the Langmuir absorption coefficient in the vdWeP model are refitted. It is verified that the AAD of the new model is only 0.86% and 0.82% respectively in predicting the
phase equilibrium pressure of hydrate generated from pure CO2 and pure N2. 3) The phase equilibrium conditions of hydrate generated from flue gas with different compositions are calculated by using the novel fitted model and the VeP model, and compared with the experimental data. It is found that the accuracy of the novel fitted model is much higher than that of the VeP model. AAD decreases from 15.16% to 5.02%. Especially for the mixed gas with 25.1e48.15% CO2 content, the novel fitted model has a higher calculation accuracy. 4) For the flue gas with 18% CO2 content, there is big deviation in the calculation results of the two models. The reason is that the transition of gas hydrate from type I to type II is a gradual process. In this paper, 15% CO2 content is taken as the boundary, which results in the decrease of calculation accuracy in this range. In a word, by considering the interactive association between CO2 and H2O molecules, the initial model is modified, and the accuracy of the novel fitted model is improved to a certain extent, which provides a reference for the practical application of the hydrate-based method. References [1] Yang H, Xu Z, Fan M, Gupta R, Slimane RB, Bland AE, et al. Progress in carbon dioxide separation and capture: a review. J Environ Sci 2008;20(1):14e27. [2] Zhu Lin, He Yangdong, Li Luling, Lu¨ Liping & He Jinling. Thermodynamic assessment of SNG and power polygeneration with the goal of zero CO2 emission. Energy 2018;149:34e46. [3] Shi Bohui, Yang Liang, Fan Shuanshi & Lou Xia. An investigation on repeated methane hydrates formation in porous hydrogel particles. Fuel 2017;194:395e405. [4] Tang LG, Xiao R, Huang C, Feng ZP & Fan SS. Experimental investigation of production behavior of gas hydrate under thermal stimulation in unconsolidated sediment. Energy Fuel 2005;19(6):2402e7. [5] El Hadri N, Quang DV, Goetheer ELV & Abu Zahra MRM. Aqueous amine solution characterization for post-combustion CO2 capture process. Appl Energy 2017;185:1433e49. [6] Zhu Lin, Li Luling, Zhang Zheng, Chen Hu, Zhang Le & Wang Feng. Thermodynamics of hydrogen production based on coal gasification integrated with a dual chemical looping process. Chem Eng Technol 2016;39(10):1912e20. [7] Yu Gan. Study on removal of carbon dioxide from biogas by chemical absorption/pressure swing adsorption. Hangzhou: Zhejiang University of Technology; 2013. [8] Ofori-Boateng C & Kwofie E. Water scrubbing: a better option for biogas purification for effective storage. World Appl Sci J 2009;5(3):122e5. [9] Rasi S, L€antel€a J & Rintala J. Upgrading landfill gas using a high pressure water absorption process. Fuel 2014;115:539e43. [10] Zhu Lin, He Yangdong, Li Luling & Wu Pengbin. Tech-economic assessment of second-generation CCS: chemical looping combustion. Energy 2018;144:915e27. [11] Ding Xiaoli, Hua Mingming, Zhao Hongyong, Yang Pingping, Chen Xiaolu, Xin Qingping, et al. Poly (ethylene oxide) composite membrane synthesized by UV-initiated free radical photopolymerization for CO2 separation. J Membr Sci 2017;531:129e37. [12] Dashti H, Zhehao YL & Lou Xia. Recent advances in gas hydrate-based CO2 capture. J Nat Gas Sci Eng 2015;23:195e207. [13] Wei Na, Sun Wantong, Meng Yingfeng, Zhou Shouwei, Li Gao, Guo Ping, et al. Sensitivity analysis of multiphase flow in annulus during
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global trial production of marine natural gas hydrates through solid fluidization. Nat Gas Ind B 2018;5(2):118e31. Li Luling, Fan Shuanshi, Chen Qiuxiong, Yang Guang, Zhao Jinzhou, Wei Na, et al. Simulation of post-combustion CO2 capture process by non-equilibrium stage hydrate-based gas separation technology. Int J Greenh Gas Contr 2018;79:25e33. Oliveira MB, Coutinho JAP & Queimada AJ. Mutual solubilities of hydrocarbons and water with the CPA EoS. Fluid Phase Equilib 2007;258(1):58e66. Ruffine L, Mougin P & Barreau A. How to represent hydrogen sulfide within the CPA equation of state. Ind Eng Chem Res 2006;45(22):7688e99. Li Luling, Zhu Lin & Fan Junming. The application of CPAevdWP to the phase equilibrium modeling of methane-rich sour natural gas hydrates. Fluid Phase Equilib 2016;409:291e300. Sabil KM, Witkamp GJ & Peters CJ. Phase equilibria in ternary (carbon dioxide þ tetrahydrofuran þ water) system in hydrate-forming region: effects of carbon dioxide concentration and the occurrence of pseudoretrograde hydrate phenomenon. J Chem Thermodyn 2010;42(1):8e16. Ruffine L & Trusler JPM. Phase behaviour of mixed-gas hydrate systems containing carbon dioxide. J Chem Thermodyn 2010;42(5):605e11. Jhaveri J & Robinson DB. Hydrates in the methaneenitrogen system. Can J Chem Eng 1965;43(2):75e8. Cleeff VA & Diepen GAM. Gas hydrates of nitrogen and oxygen. I. eRecueil des Travaux Chimiques des PayseBas 1960;79(6):582e6. Cleeff VA & Diepen GAM. Gas hydrates of nitrogen and oxygen. II. Recl Trav Chim Pays-Bas 1965;84(8):1085e93. Kang SP, Lee H, Lee CS & Sung WM. Hydrate phase equilibria of the guest mixtures containing CO2, N2 and tetrahydrofuran. Fluid Phase Equilib 2001;185(1/2):101e9. Sun Shicai, Liu Changling & Meng Qingguo. Hydrate phase equilibrium of binary guest-mixtures containing CO2 and N2 in various systems. J Chem Thermodyn 2015;84:1e6. Herslund PJ, Thomsen K, Abildskov J & Solms VN. Modelling of tetrahydrofuran promoted gas hydrate systems for carbon dioxide capture processes. Fluid Phase Equilib 2014;375:45e65. Herslund PJ, Thomsen K, Abildskov J & Solms VN. Modelling of cyclopentane promoted gas hydrate systems for carbon dioxide capture processes. Fluid Phase Equilib 2014;375:89e103.
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Research Article
A novel fitted thermodynamic model for the capture of CO2 from flue gas by the hydrate method*,** Li Luling a,*, Zhao Jinzhou a, Li Haitao a, Zhang Liehui a, Fan Shuanshi a,b, Li Qingping c, Pang Weixin c, Lu¨ Xin c, Zheng Lijun c & Wei Na a State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, China b CNOOC Research Institute, Beijing 100027, China c MOE Key Laboratory of Heat Transfer Enhancement and Process Energy Conservation, South China University of Technology, Guangzhou, Guangdong 510006, China a
Received 5 November 2018; accepted 25 April 2019
Abstract The hydrate-based gas separation for capturing CO2 from flue gas has the characteristics of low energy consumption, simple operation and convenience for the subsequent CO2 storage and utilization. In order to reduce the total cumulative deviation of multi-stage hydration reaction, it is of great importance to establish an accurate thermodynamic model. Based on the vdWeP þ CPA model, therefore, we refitted the parameters of the thermodynamic model considering the association between CO2 and H2O. Firstly, the energy parameter a0.5 of H2O and CO2 are developed as the cubic function and the linear function of [1-(T/Tc)0.5], respectively. Then, the calculation parameters of Langmuir absorption coefficient of vdWeP model is refitted based on the temperature dependent binary interaction parameters kij. The following research results are obtained. First, when the novel fitted thermodynamic model is used to predict the density of saturated fluid, the average absolute deviation (AAD) of H2O drops from 1.84% to 0.08% and that of CO2 drops from 4.06% to 2.09%. Second, when it is used to predict the phase equilibrium pressure of the hydrate generated from pure CO2 and pure N2, the AAD is 0.86% and 0.82%, respectively. Third, when it is used to calculate the phase equilibrium condition of hydrate generated from flue gas with different compositions, the AAD is decreased from 15.16% to 5.02%. In conclusion, this novel fitted thermodynamic model is of higher accuracy and it, to some extent, can decrease the total accumulative deviation of multi-stage hydration reaction. The research results provide reference for the actual application of the hydrate-based gas separation for capturing CO2 from flue gas. © 2019 Sichuan Petroleum Administration. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Hydrate-based gas separation; Flue gas; CO2 capture; CO2 thermodynamic model; Multi-stage hydration reaction; Energy parameter; Langmuir absorption coefficient; Prediction
0. Introduction
* Project supported by the National Natural Science Foundation Project “Study on methane storage, separation and sequestration of carbon dioxide in exploitation and utilization of marine gas hydrate” (No.: 21736005), China Postdoctoral Science Foundation Project (No.: 2017M623060, 2019T120860). ** This is the English version of the originally published article in Natural Gas Industry (in Chinese), which can be found at https://doi.org/10.3787/j.issn. 1000-0976.2019.04.014. * Corresponding author. E-mail address: [email protected] (Li LL). Peer review under responsibility of Sichuan Petroleum Administration.
The flue gas discharged from fossil-fuel power plants contains a large amount of CO2, accounting for about 75% of the total CO2 emissions [1,2]. CO2 is a harmful greenhouse gas to the environment, but it is also a type of valuable resource [3,4]. Therefore, it is necessary to capture CO2 from flue gas. Common CO2 capture processes includes chemical absorption [5,6], physical absorption [7e10], membrane separation [11], and cryogenic separation [12]. The hydrate-based gas separation method [12], one of the cryogenic separation methods, is considered to be one of the most promising CO2
https://doi.org/10.1016/j.ngib.2019.04.006 2352-8540/© 2019 Sichuan Petroleum Administration. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: Li LL et al., A novel fitted thermodynamic model for the capture of CO2 from flue gas by the hydrate method, Natural Gas Industry B (2019), https://doi.org/10.1016/j.ngib.2019.04.006
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capture processes because it is low in energy consumption, simple in operation and favorable for subsequent CO2 storage and utilization [13e15]. In order to meet the requirements of CO2 capture, it is necessary to use multi-stage hydration reaction. A thermodynamic model is usually used to determine the operating conditions of hydration reactions at all stages. Therefore, an accurate thermodynamic model is particularly important in order to reduce the total accumulative deviation by multi-stage reactions. The establishment of a thermodynamic model is based on the principle that the chemical potential difference or fugacity of the same substance in each phase is equal when the system reaches equilibrium. The commonly used gaseliquid models mainly include SRK equation, PR equation, CPA equation, SAFT equation and DA equation. The hydrate phase models mainly include vdWeP model [16] and CheneGuo model. Herslund et al. [17] used the vdWeP þ CPA model to calculate the phase equilibrium pressure of hydrate generated from CO2eN2, and found that for low-concentration CO2 flue gas, the deviation is larger. Zhang et al. [18] revised the vdWeP þ PR model to predict the phase equilibrium conditions of hydrate generated from CO2eN2 under the action of accelerators. The results show that the accuracy of the model is lower when the generating pressure is predicted with given temperature. Herri et al. [19] calculated the Langmuir absorption coefficient based on vdWeP þ SRK model and three methods, and found that the average absolute deviation of calculating phase equilibrium pressure of flue gas is higher than 8%. Thus, the accuracy of the existing thermodynamic models needs to be improved [20]. In this paper, the vdWeP þ CPA model is revised and its accuracy is verified. 1. Thermodynamic model 1.1. Gaseliquid phase model The perturbation expansion of the residual Helmholtz free energy term (Ares) in the CPA equation is as follows [21]: Ares ¼ A Aphy ¼ Aassoc
ð1Þ
where, " # Aassoc X X XAi 1 ¼ xi lnXAi þ Mi 2 RT 2 i Ai , XAi ¼ 1
X X Ai Bj 1 þ V 1 xj XBi m D j
calculated using the SRK equation in this paper; Aassoc: the Helmholtz free energy of associative term, J/mol; R: the universal gas constant, 8.314 J/(mol$K); T: the temperature, K; xi: the molar fraction of the ith component; Ai: the associating position A of the ith component; Mi: the number of associating positions of the ith component; XAi: the unoccupied molar fraction of A coordination on the ith molecule; Vm: the molar volume, m3/mol; XBi: the unoccupied molar fraction of B coordination on the ith molecule; DAiBj is the associating strength between the A coordination on the ith molecule and the B coordination on the jth molecule, m3/mol; bAiBj: the energy parameter; b: the volume parameter, m3/mol; εAiBj: the associating volume, (Pa$m3)/mol; g(1/Vm): the radial distribution function. 1.2. Hydrate phase model The chemical potential difference (Dmw,H) between hydrate phase and base hydrate phase in the vdWeP model can be calculated by using the following equation: ! X X Dmw;H ¼ RT ni ln 1 qij ð2Þ i
where, qij ¼
j
where, Vi is the number of type i pores connected by a single water molecule; similarly, qij: the occupation ratio of guest molecule j in type i pores; fj: the fugacity of guest molecule j, Pa; Cij: the Langmuir absorption coefficient of guest molecule j on type i pores. Parrish and Prausnitz [22] proposed the following formulas for calculating the Langmuir absorption coefficient: Ak;i Bk;i Ck;i ¼ exp ð3Þ T T where, Ak,i and Bk, i are fitting parameters. Moreover, Saito et al. [23] proposed the calculation method of the chemical potential difference of water in liquid phase Dmw,L: Dmw;L ¼ Dm0w;L RT lnaw
D
Ai Bj ε ¼ gð1=Vm Þ exp 1 bij bAi Bj RT
gð1 = Vm Þ ¼ 64V 3m 8V 2m b ð4Vm bÞ3 where, A is the total Helmholtz free energy, J/mol; similarly, Aphy: the Helmholtz free energy of physical term, J/mol, which is
ð4Þ Z
Dm0w;L Dm0w ¼ RT RT0 ZT þ
T
ZT Dhw;bI þ Dhw;LI þ
DCpw dT T0
RT 2 T0
Ai Bj
Cij fj P 1 þ Cij fj
!
Bi
j
dT ð5Þ
Dvw;bI þ Dvw;LI ðdPR = dTÞdT RT
T0
where, PR ¼ A þ B=T þ DlnT
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where, Dm0w is the chemical potential difference between hydrate phase and b phase under standard conditions, J/mol; similarly, aw: the water activity in liquid phase; T0: the temperature under standard conditions, K; Dhw,beI: the molar enthalpy change of water in solid phase and b phase under standard conditions, J/mol; Dhw,LeI: the molar enthalpy change of water in solid ice phase and liquid phase under standard conditions, J/mol; DCpw: the change of heat capacity of water, J/(mol$K); Dvw,beI: the molar volume difference between b phase and solid ice phase, m3/mol; Dvw,LeI: the molar volume difference between hydrate, m3/mol; PR: the reference hydrate formation pressure at temperature T, Pa; A, B and D are related parameters [22]. According to Dmw,H ¼ Dmw,L, Equations (2)e(5) can be used to predict the phase equilibrium conditions for hydrate formation in the system. 2. Fitting of model parameters In the CPA equation reported in Refs. [17,24], only the interactive association between water molecules is considered, while CO2 and N2 are considered as non-associated molecules. By contrast, Tsivintzelis et al. [25] found that the accuracy is higher when CO2 is a solvent molecule and there is an accepting electron position associated only with the molecule of H2O. Therefore, in order to improve the accuracy of the thermodynamic model, we consider H2O as a 4C-linked molecule, CO2 molecule as a solvent molecule with an accepting electron position, and N2 as a non-associated molecule. On this basis, we re-fitted the model parameters. 2.1. Energy parameter a The CPA equation considers that CO2 is a non-polar molecule without association, and the energy parameter a can be calculated by directly using the absolute temperature, absolute pressure and eccentricity factor of CO2. Also, it is considered that H2O is a type 4C molecule, and its energy parameter a0.5 is a linear function of [1-(T/Tc)0.5]. Mathias et al. [26] reports that the calculation results are more accurate when the energy parameter a0.5 of polar components is a cubic function of [1-(T/Tc)0.5], while the calculation results are more accurate when the energy parameter a0.5 of polar components is a linear function of [1-(T/Tc)0.5] for nonpolar molecules with intermolecular association. Therefore, based on the data of saturated liquid density and saturated vapor pressure of CO2 and H2O in DIPPR database [27], the energy parameter a in CPA equation is regressed, and optimum calculation is conducted by matlab. The objective function can be calculated by using the following formula: ( " 2 DIPPR 2 #) N X pDIPPR pCal: ri rCal: i i i OF ¼ min þ pDIPPR rDIPPR i i i¼1 ð6Þ
3
where, pi is the system pressure of the ith group, Pa; similarly, ri: the saturated liquid density of the ith group, kmol/m3; the superscript DIPPR: the experimental data from the DIPPR database; the superscript ‘Cal.’: the calculated value of the model; N: there are N sets of data totally. The energy parameter a of H2O and CO2 can be expressed separately as: h pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi 2 a1 ¼ 0:094 1þ1:278 1 Tr;1 þ4:974 1 Tr;1 ð7Þ pffiffiffiffiffiffiffi 3 i2 18:085 1 Tr;1 pffiffiffiffiffiffiffi 2
a2 ¼ 0:391 1 þ 1:435 1 Tr;2
ð8Þ
where, a1 is the energy parameter of H2O, Pa/(m6$mol2); similarly, a2: the energy parameter of CO2, Pa/(m6$mol2); Tr,1: the correspondence temperature of H2O; Tr,2: the correspondence temperature of CO2. In order to verify the accuracy of the fitting results, it is necessary to calculate the saturated liquid densities of CO2 and H2O using the novel fitted energy parameters and the original energy parameters [28], respectively, and compare them with the DIPPR data (Fig. 1). It is noteworthy that the experimental data selected to verify the accuracy of the model are not used for parameter fitting. As shown in Fig. 1, both models can well describe the relationship between saturated liquid density and temperature of CO2 and H2O. For H2O, when the temperature is higher than 420 K or less than 320 K, the influence of polarity of water molecules on saturated liquid density becomes more and more obvious, so the accuracy of the initial model decreases; but the accuracy of the novel fitted model is higher in the range of investigation, especially at low temperature. For CO2, since the initial model considers it to be a non-polar molecule without association, if its energy parameter is calculated directly by absolute temperature, absolute pressure and eccentricity factor, it results in a large deviation between the saturated liquid density and the experimental value at low temperature. The a0.5 of CO2 is fitted as a linear function of [1-(T/Tc)0.5], and the accuracy of calculation results is higher. When the temperature is higher, the calculated result of the novel fitted model is slightly higher than the experimental value, while the result of the initial model is closer to the experimental value. The reason may be that the association of CO2 becomes weaker at high temperature, then it is more reasonable to consider CO2 as a non-polar molecule without association. As the hydrate system is a low temperature system, the novel fitted model is more suitable. For comparison, Equation (9) is used to determine the average absolute deviation (AAD). As for H2O, the AAD is only 0.08% for the novel fitted model and is 1.84% for the initial model; As for CO2, the AAD is 2.09% and 4.06% respectively. Clearly, the novel fitted model is more accurate in predicting the saturated liquid phase densities of H2O and CO2, and more suitable for cryogenic systems.
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Fig. 1. Comparison of saturated liquid density of H2O and CO2 calculated by the initial model and novel fitted model.
AAD% ¼
N exp: cal: 1X xi x xexp: 100 i i N i¼1
ð9Þ
where, xi is the molar content of component i of the system; the superscript ‘exp.’ represents the experimental data reported in the literature. 2.2. Binary interaction parameter kij This parameter reflects the influence of the interaction between different molecules on the thermodynamic properties of the system. Ruffine et al. [29] find through experiments that kij is greatly affected by temperature. Therefore, using the temperature dependent kij can help to improve the accuracy of model calculation. kij fitting and verification process for CO2eH2O system and N2eH2O system have been described in detail in the previous study [30], thus no further elaboration will be made here. The fitting result is: kCO2 H2 O ¼ 2:09 105 T 2 þ 0:011T 1:28
ð10Þ
kN2 H2 O ¼ 7:09 105 T 2 þ 0:04T 6:47
ð11Þ
As the interaction between CO2 and N2 molecules is smaller, kCO2eN2 is taken as 0 [17]. 2.3. Calculating parameters of Langmuir adsorption coefficient Langmuir absorption coefficient is usually fitted by the thermodynamic model based on phase equilibrium conditions of hydrate generated from pure gas. Therefore, when the gaseliquid phase model changes, the Langmuir absorption coefficient should also change. Determination of the Langmuir absorption coefficients of large pores and small pores simultaneously is the key to calculation. Because most CO2 exists in large pores and N2 exists in large and small pores when gas hydrate is formed by the CO2 and N2 mixture, it is considered that the Langmuir absorption coefficient of small pores is very small for CO2, that of large pores is larger, and that of N2 is similar for large pores and small pores. In order to simplify the calculation process, it is considered that the Langmuir absorption coefficients of small pores of CO2 and N2 have little
changes. The absorption coefficients of large pores are fitted by using the phase equilibrium conditions of hydrate formation from pure gas [31e35], and the parameters are obtained by using the fitting results. The results are shown in Table 1. In order to verify the accuracy of the fitting results, it is necessary to substitute the fitting parameters into the thermodynamic model to calculate the phase equilibrium conditions of pure CO2 and N2, respectively. The results are compared with the experimental data reported in the literature. The results are shown in Fig. 2. In Fig. 2, the phase equilibrium pressures of CO2 and N2 increase with the temperature. At the same temperature, the phase equilibrium pressure of N2 is obviously higher than that of CO2, which again verifies that CO2 and N2 can be separated by the hydrate-based method. The Langmuir absorption coefficient is calculated by using the parameters fitted in this paper. The calculated results of the model are in good agreement with the experimental results reported in literature. The calculated results show that AAD is 0.86% and 0.82% respectively for predicting the equilibrium pressures of CO2 and N2. It can be concluded that the parameters fitted in this paper for the Langmuir absorption coefficient can ensure the accuracy of vdWeP model in calculating the thermodynamic properties of pure hydrate phase. 3. Model verification In order to verify the accuracy of the established thermodynamic model, it is necessary to calculate the phase equilibrium pressures of hydrate generated from flue gas at given temperatures by using the novel model and the VeP model [16], respectively, and compare them with the experimental data reported in literatures [32,36,37]. As the experimental data in Table 1 Parameters in Equation (8). Hydrate type
Component
Small pore A/(K$MPa
Type I Type II
CO2 N2 CO2 N2
1.159 3.007 1.265 2.839
Large pore 1
)
2
10 10 10 10
2 2 2
B/K
A/(K$MPa
2861 2139 2790 2175
1.097 2.184 3.036 2.364
1
)
10 102 101 102
B/K 1855 2879 3059 2215
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Fig. 2. Comparison between the calculated values of pure CO2 and pure N2 phase equilibrium conditions by the novel fitted model and the experimental data reported in literatures [31e35].
the literatures are reported on the feeding liquid fraction, and the feeding liquid fraction has little influence on the calculation results of phase equilibrium conditions, it is assumed that the feeding liquid fraction is 0.5 based on the relevant literatures [38,39]. The calculation results are shown in Fig. 3.
5
In Fig. 3, both models can well describe the relationship between phase equilibrium pressure and temperature of hydrate generated from flue gas. By considering the interaction association between CO2 and H2O molecules, a and kij in the CPA equation and the calculation parameters of Langmuir absorption coefficient in the vdWeP model are re-fitted. The accuracy of the novel fitted model in calculating the phase equilibrium conditions of flue gas is higher than that of the initial model. For most gas samples, especially those with about 50% CO2 content, the deviation between the calculated results and the experimental values of the novel fitted model is less affected by temperature. The reason may be that the temperature-related binary interaction parameters reduce the influence of temperature on the accuracy of the calculated results. Meanwhile, the calculation accuracy of gaseliquid phase composition is improved by considering the interaction association between CO2 and H2O molecules. The AAD of the two models are calculated separately, and the results are shown in Table 2. In Table 2, the average value of AAD of the novel fitted model decreased from 15.16% to 5.02% compared with that of the literature model. However, for the mixed gas with 6.63% CO2 content, the AAD of the novel fitted model is higher than that of the VeP model. The possible reason is that the novel fitted model overestimates the influence of N2 on the phase equilibrium conditions of hydrate generated from the mixed
Fig. 3. Comparisons between the calculated and experimental values of the two models for the phase equilibrium conditions of hydrate generated from CO2þN2 mixed gas. Please cite this article in press as: Li LL et al., A novel fitted thermodynamic model for the capture of CO2 from flue gas by the hydrate method, Natural Gas Industry B (2019), https://doi.org/10.1016/j.ngib.2019.04.006
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Table 2 Comparison of AAD calculation results between the VeP model and the novel fitted model. CO2 content (%)
Temperature (K)
96.59 85.32 77.80 48.15 45.24 36.24 25.10 20.03 18.00 11.59 10.10 6.63
274.95e283.55 276.20e284.01 274.00e284.25 273.75e282.00 274.34e283.15 273.80e282.32 273.60e277.60 273.80e282.00 273.50e277.40 274.25e278.95 273.40e276.80 273.95e278.25
Mean
AAD VeP model (%)
Novel fitted model (%)
12.71 20.93 23.11 20.31 17.15 17.04 16.26 7.35 20.43 4.98 9.23 9.72
8.97 5.50 9.21 4.02 2.05 0.97 1.09 2.86 6.96 1.54 4.99 12.04
15.16
5.02
gas, which results in the decreased accuracy of the model when the CO2 content is lower. The prediction result deviation of the phase equilibrium conditions is larger for forming type I hydrate generated from the mixed gas by the VeP model, while the deviation for type II hydrate is smaller. When the CO2 content is more than 75%, the AAD of the novel fitted model is relatively large (10e5%). The possible reason is that under this condition, the mixed gas produces type I hydrate. N2 occupies 512 small pores due to pressure, while CO2 content is bigger and partial pressure is higher, N2 will compete with N2 to occupy 512 small pores as a result of pressure. However, the model neglects the interaction between N2 and CO2, resulting in a slight decrease in accuracy. With the decrease of CO2 content, the partial pressure of CO2 decreases, the competition between two molecules decreases, and AAD drops. Especially for the mixed gas with 20e48% CO2 content, AAD is about 2%. It is noteworthy that the AAD values of both models are larger when the CO2 content is about 18%, possibly because the transition from type I to type II of hydrate generated from the mixed gas is a gradual process, and the calculation accuracy of the model decreases with the 15% CO2 content as the boundary in this paper. In a word, the accuracy of the novel fitted model has been improved to some extent, especially for the mixed gas with 25.1e48.15% CO2 content. 4. Conclusions 1) By fitting the energy parameter a0.5 of H2O and CO2 into the cubic and linear functions of [1-(T/Tc)0.5], the results show that AAD decreases from 1.84% to 0.08% and from 4.06% to 2.09% respectively in predicting saturated liquid density. 2) On this basis, the calculation parameters of the Langmuir absorption coefficient in the vdWeP model are refitted. It is verified that the AAD of the new model is only 0.86% and 0.82% respectively in predicting the
phase equilibrium pressure of hydrate generated from pure CO2 and pure N2. 3) The phase equilibrium conditions of hydrate generated from flue gas with different compositions are calculated by using the novel fitted model and the VeP model, and compared with the experimental data. It is found that the accuracy of the novel fitted model is much higher than that of the VeP model. AAD decreases from 15.16% to 5.02%. Especially for the mixed gas with 25.1e48.15% CO2 content, the novel fitted model has a higher calculation accuracy. 4) For the flue gas with 18% CO2 content, there is big deviation in the calculation results of the two models. The reason is that the transition of gas hydrate from type I to type II is a gradual process. In this paper, 15% CO2 content is taken as the boundary, which results in the decrease of calculation accuracy in this range. In a word, by considering the interactive association between CO2 and H2O molecules, the initial model is modified, and the accuracy of the novel fitted model is improved to a certain extent, which provides a reference for the practical application of the hydrate-based method. References [1] Yang H, Xu Z, Fan M, Gupta R, Slimane RB, Bland AE, et al. Progress in carbon dioxide separation and capture: a review. J Environ Sci 2008;20(1):14e27. [2] Zhu Lin, He Yangdong, Li Luling, Lu¨ Liping & He Jinling. Thermodynamic assessment of SNG and power polygeneration with the goal of zero CO2 emission. Energy 2018;149:34e46. [3] Shi Bohui, Yang Liang, Fan Shuanshi & Lou Xia. An investigation on repeated methane hydrates formation in porous hydrogel particles. Fuel 2017;194:395e405. [4] Tang LG, Xiao R, Huang C, Feng ZP & Fan SS. Experimental investigation of production behavior of gas hydrate under thermal stimulation in unconsolidated sediment. Energy Fuel 2005;19(6):2402e7. [5] El Hadri N, Quang DV, Goetheer ELV & Abu Zahra MRM. Aqueous amine solution characterization for post-combustion CO2 capture process. Appl Energy 2017;185:1433e49. [6] Zhu Lin, Li Luling, Zhang Zheng, Chen Hu, Zhang Le & Wang Feng. Thermodynamics of hydrogen production based on coal gasification integrated with a dual chemical looping process. Chem Eng Technol 2016;39(10):1912e20. [7] Yu Gan. Study on removal of carbon dioxide from biogas by chemical absorption/pressure swing adsorption. Hangzhou: Zhejiang University of Technology; 2013. [8] Ofori-Boateng C & Kwofie E. Water scrubbing: a better option for biogas purification for effective storage. World Appl Sci J 2009;5(3):122e5. [9] Rasi S, L€antel€a J & Rintala J. Upgrading landfill gas using a high pressure water absorption process. Fuel 2014;115:539e43. [10] Zhu Lin, He Yangdong, Li Luling & Wu Pengbin. Tech-economic assessment of second-generation CCS: chemical looping combustion. Energy 2018;144:915e27. [11] Ding Xiaoli, Hua Mingming, Zhao Hongyong, Yang Pingping, Chen Xiaolu, Xin Qingping, et al. Poly (ethylene oxide) composite membrane synthesized by UV-initiated free radical photopolymerization for CO2 separation. J Membr Sci 2017;531:129e37. [12] Dashti H, Zhehao YL & Lou Xia. Recent advances in gas hydrate-based CO2 capture. J Nat Gas Sci Eng 2015;23:195e207. [13] Wei Na, Sun Wantong, Meng Yingfeng, Zhou Shouwei, Li Gao, Guo Ping, et al. Sensitivity analysis of multiphase flow in annulus during
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Please cite this article in press as: Li LL et al., A novel fitted thermodynamic model for the capture of CO2 from flue gas by the hydrate method, Natural Gas Industry B (2019), https://doi.org/10.1016/j.ngib.2019.04.006