Thermodynamic modelling using e-UNIQUAC model

Fluid Phase Equilibria 473 (2018) 50e69

Contents lists available at ScienceDirect

Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d

Thermodynamic modelling using e-UNIQUAC model for CO2 absorption by novel amine solutions: 1-Dimethylamino- 2-propanol (1DMA2P), 3-dimethylamino-1-propanol (3DMA1P) and 4diethylamino-2-butanol (DEAB) Morteza Afkhamipour a, Masoud Mofarahi a, b, *, Chang-Ha Lee b a

Department of Chemical Engineering, Faculty of Petroleum, Gas and Petrochemical Engineering, Persian Gulf University, P.O. Box 75169-13798, Bushehr, Iran b Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 120-749, Republic of Korea

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 January 2018 Received in revised form 21 May 2018 Accepted 25 May 2018 Available online 31 May 2018

The proper selection of thermodynamic models is an important step in the design and simulation of CO2 removal processes using amine solutions. In this study, we aim to study the thermodynamic behaviour of the CO2 removal process by employing the extended-universal quasichemical (e-UNIQUAC) model for three novel amine systems, namely CO2þ1DMA2P þ H2O, CO2þ3DMA1P þ H2O, and CO2þDEAB þ H2O. The thermodynamic behaviour was studied in terms of the CO2 loading of amines, the ion speciation profiles, the isothermal pressure-composition (Pxy) profiles, and the pH of the amine solutions. Adjustable parameters of the model include binary interaction parameters, and the volume and surface area parameters of the amine and protonated amine were determined using different objective functions based on the experimental data available in the literature. The ion and molecular speciation profiles are obtained and compared with nuclear magnetic resonance (NMR) data for CO2þ1DMA2P þ H2O and CO2þDEAB þ H2O systems. The model predicted the experimental data with average absolute relative deviations (AARDs) of 8.06%, 13.39% and 16.50% for CO2 loading values of DEAB, 1DMA2P, and 3DMA1P, respectively. In addition, the results of Pxy profiles at different temperatures show that the azeotrope does not form in the 3DMA1P þ H2O system. The adjustable parameters and predicted data of the applied e-UNIQUAC model may contribute to the rate-based simulation of CO2 absorption processes using novel amine systems. © 2018 Elsevier B.V. All rights reserved.

Keywords: e-UNIQUAC Amine CO2 loading Adjustable parameters Chemical speciation

1. Introduction The CO2 emissions that result from the burning of fossil fuels are the primary causes of global warming and climate change [1]. Therefore, the development of good technologies which perform functions such as carbon capture and storage may be effective for reducing these emissions [2]. CO2 capture can be achieved by using a variety of methods including physical or chemical absorption, adsorption, membrane separation, and low-temperature distillation [3]. Economically, chemical absorption is superior to the other

* Corresponding author. Department of Chemical Engineering, Faculty of Petroleum, Gas and Petrochemical Engineering, Persian Gulf University, P.O. Box 7516913798, Bushehr, Iran. E-mail address: [email protected] (M. Mofarahi). https://doi.org/10.1016/j.fluid.2018.05.026 0378-3812/© 2018 Elsevier B.V. All rights reserved.

mentioned methods in post-combustion capture [4]. Most of the chemical solvents used in the chemical absorption process are amine-based solvents [5]. These amines can be categorized as conventional amines (monoethanolamine (MEA), diethanolamine (DEA), methyldiethanolamine (MDEA), and 2- amino-2-methyl-1propanol (AMP) and newly developed amines (N,N-diethylethanolamine (DEEA), 4-diethylamino-2 butanol (DEAB), diethylenetriamine (DETA), 3-dimethylamino-1-propanol (3DMA1P), and 1-dimethylamino-2-propanol (1DMA2P)). Many researchers have performed various scientific and practical studies about various amines [6]. Among the amines studied, tertiary amines exhibit a high absorption capacity for CO2, low flow rate of amine circulation, low-energy consumption for regeneration, and low degradation and corrosion rates [3,7]. In addition, their low reaction rate with CO2 can be overcome by adding amine activators [8].

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

Together with the absorption capacity for CO2 in tertiary amines, which is defined in terms of CO2 loading in amine, many studies have been performed for conventional tertiary amines. Thermodynamic models are required for the design and simulation of CO2 absorption processes with amines [9e11]. Rayer et al. [10] reviewed the thermodynamic models and categorized them from simple models to rigorous models. The simple models are Kent-Eisenberg or modified Kent-Eisenberg, which are based on stoichiometric correlations. The rigorous models are categorized based on the excess Gibbs energy, which accounts for short-range and long-range forces between chemical species presented in amine systems. The most commonly applied rigorous models in the literature for CO2 absorption by amines are Deshmukh-Mather, Pitzer, extended universal quasichemical (e-UNIQUAC) and electrolyte-NRTL [12]. The e-NRTL and the e-UNIQUAC are based on the local composition models. In comparison between these two models, the expressions for calculating of activity coefficients and the structure of parameters of e-UNIQUAC model are simpler than the electrolyte-NRTL model. In addition, the identical activity coefficient expressions are used for cations, anions and molecular species in the e-UNIQUAC model. Therefore, these advantages could make e-UNIQUAC model far easier to apply in comparison with electrolyte-NRTL based model [13]. These models have primarily been applied for conventional amines, while a few have been applied to newly developed amines. For example, we recently applied the Kent-Eisenberg, the modified Kent-Eisenberg and the Deshmukh-Mather models for newly tertiary amines such as 1DMA2P, 1-diethylamino-2-propanol (1DEA2P), DEEA, and DEAB [14]. In the literature, the e-UNIQUAC model has been applied for CO2 absorption using tertiary conventional amine solutions such as MDEA. Faramarzi et al. [15] used the e-UNIQUAC model for CO2 absorption in aqueous solution of MDEA. They adjusted thirteen parameters of the model based on the different types of experimental data obtained from the literature, including the vapoureliquid equilibrium (VLE), freezing-point depression and molar excess enthalpy ðH E Þ of amine aqueous solution. The concentration of different chemical species in the CO2þMDEA þ H2O system was also estimated using this model, and it was compared with NMR spectroscopy results. Aronu et al. [16] have applied the e-UNIQUAC model for CO2 absorption in an aqueous solution of MEA. The parameters of model were obtained by regression analysis based on the LevenbergeMarquardt algorithm. For this purpose, they used their VLE experimental data for CO2þMEA þ H2O system as well as VLE data and H E for MEA þ H2O system. They validated the model in comparison with experimental data for total pressure and CO2 partial pressure in various concentrations of MEA within average absolute relative deviations (AARDs) of 11.7% and 24.3%, respectively. In addition, the concentration of different chemical species in the CO2þMEA þ H2O system was also obtained, and it was compared with NMR spectroscopy data. Mehdizadeh et al. [17] have provided a set of model parameters using the e-UNIQUAC model for the CO2þAMP þ H2O system by relating computational chemistry and their experimental data. The computational chemistry was used to obtain the equilibrium constant of the AMP carbamate reaction. A combination of pattern search and Nelder-med method was used as an optimization method to tune the model parameters for CO2 loaded and unloaded of AMP þ H2O system. Their model predicted CO2 partial pressure, speciation and heat of absorption. In another work of Mehdizadeh et al. [18], similar their previous model, they provided a set of model parameters for CO2þ Piperazine (PZ)þH2O system using the eUNIQUAC model and computational chemistry. Biget et al. [19] have used the e-UNIQUAC model for CO2 absorption in aqueous

51

solutions of MEA, MDEA and AMP. The parameters of model were obtained by an optimization method based on the combination of a genetic algorithm and a quasi-newton method. For this purpose, they used different sets of experimental data of amine systems from literature, including the total pressure, H E of amine þ H2O system and VLE data of CO2 loaded of amines. For obtaining of model parameters, a sensitivity analysis on each parameter was performed to determine the significance of regressed parameters. They validated the model for MEA with an average absolute relative deviation (AARD) of 20% obtained for 639 experimental points. They used the e-UNIQUAC model to determine the model parameters for MDEA and AMP. Recently, Sadegh, et al. [20] improved the work of Faramarzi et al. [15] by optimizing the model parameters of the e-UNIQUAC model for the CO2þMDEA þ H2O system. To adjust the model parameters, they used various sets of experimental data of amine systems, including the pure vapour pressure of amine ðP vap Þ, VLE, freezing point, H E , and heat capacity of the amine solution. The obtained parameters were valid for a temperature ranging from 15  C to 200  C and a concentration range of 5e75 wt%. In their study, two different algorithms for optimizing the parameters were used: Levenberg-Marquardt and Nelder-Mead. They concluded that the model correctly represents the thermodynamic and thermal properties for the CO2þMDEA þ H2O system with an AARD of 16.0%. Together with novel tertiary amines, Zaidy [13] applied the eUNIQUAC model for the CO2þDEEA þ H2O system using the data of VLE, P vap , and H E to predict the CO2 loading in the DEEA solution at two concentrations, i.e. 2 M and 5 M. The adjustable parameters in the CO2þDEEA þ H2O system could be reduced by using the parameters from a binary system (DEEA þ H2O), such as binary interaction parameters between amine and water as well as the volume and the surface-area parameters of DEEA. Modfit as an optimization algorithm in MATAB software was used for optimizing the parameters. An AARD of 26.5% was obtained between predicted results and experimental data in the CO2þDEEA þ H2O system. On the other hand, rigorous modelling and thermodynamic study for CO2þ1DMA2P þ H2O, CO2þ3DMA1P þ H2O, and CO2þDEAB þ H2O systems has not been reported in terms of the CO2 loading in amine solutions, the ion speciation profiles, the Pxy profiles, or the pH of amine solutions. The aim of this study is to investigate the thermodynamic behaviour of the mentioned amine systems by employing the eUNIQUAC model. To adjust the model parameters, different types of experimental data were used, such as VLE data of a binary system, H E data, VLE data of a ternary system, NMR data, and pH data. The adjustable parameters obtained in this study are binary interaction parameters, the volume and surface-area parameters of amine and protonated amine, and the equilibrium constant parameters for protonated amine reaction (only for 3DMA1P). In addition, the azeotrope formation was studied for available VLE data of the 3DMA1P þ H2O system. The adjustable parameters of the presented models were obtained from the minimization of objective function using the Simplex optimization algorithm in MATAB software [21]. Different types of objective functions based on the available experimental data were defined for three of the abovementioned systems. After finding the adjustable parameters, the Newton's method was used to solve the nonlinear algebraic equations of the applied model. The results of the model were validated with experimental data, and the model prediction was carried out for new observation data. Furthermore, the NMR spectroscopic data and pH data were obtained for amine systems, and the effect of temperature and amine concentration on the profiles of chemical species in the liquid phase was investigated.

52

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

Table 1 Experimental data obtained from the literature for the optimization of parameters and modelling predictions. System

Data type

Number of data

Concentration range

Temperature range (K)

Source

3DMA1P þ H2O 3DMA1P þ H2O

VLE

81 27

0.0e1.0 (mole fraction) 0.1e0.9 (mole fraction)

283e363 298e333

[41] [25]

45 54 61 27

13 (mol/L) 1,2, and 5 (mol/L) 2,3 and 4 (mol/L) 0.1e0.9 (mole fraction)

298e333 298e333 298e333 298e333

[27] [22] [26] [25]

56 41 60 128

1.5, 2.5 and 4 (mol/L) 0.5e2 (mol/L) 15 (mol/L) 0.52e1.97 (mol/L)

298e313 301 298e333 298

[23] [24] [28] [29]

HE VLE VLE VLE

CO2þ3DMA1P þ H2O CO2þ1DMA2P þ H2O CO2þ1DMA2P þ H2O 1DMA2P þ H2O

HE pH pH VLE NMR

CO2þ1DMA2P þ H2O CO2þ1DMA2P þ H2O CO2þDEAB þ H2O CO2þDEAB þ H2O

Table 2 Parameters for equilibrium constants. Ki

A

B

C

D

Temperature range ( C)

Source

K1 ð3DMA1PÞ K1 ðDEABÞ K1 ð1DMA2PÞ K2 K3 K4

5239.0 3237.24 4278.0 12092.1 12431.7 13445.9

0.009 9.53 0 36.7816 35.4819 22.4773

0.0876 0 0 0 0 0

0.0110 105.260 8.108 235.482 220.067 140.932

25e60 25e60 25e60 0e225 0e225 0e225

This work [14] [14] [30] [30] [30]

2. Experimental data sources The experimental data used for optimization of parameters in the model were taken from the literature, and are presented in Table 1. Details of these data are described as follows: For the CO2þ1DMA2P þ H2O system, Liu, et al. [22] conducted the experiments to determine the CO2 equilibrium solubility of the 1DMA2P solution for concentrations of 1 M, 2 M, and 5 M at CO2 partialpressure values ranging from 8 to 101 kPa, and at temperatures ranging from 298 K to 333 K. Liu et al. [23] reported the pH values of the 1DMA2P solution with concentrations of 1.5 M, 2.5 M, and 4 M when CO2 was loaded in the range of 0e0.8 mol CO2/mol amine from 298 K to 313 K. They used the pH values of the 1DMA2P solution to calculate the concentrations of molecules and ions by incorporating the mass balances (charge, carbon, and amine balances) of the CO2þH2Oþ1DMA2P system. Recently, Liu, et al. [24] measured the concentration of chemical species such as 1DMA2P, 2 1DMA2PHþ , HCO 3 , and CO3 , for a CO2þH2Oþ1DMA2P system 13 using the C NMR method, and they also reported the pH values. Their experiments were performed at fixed temperatures of 301 K and 298 K, and for concentration values ranging from 0.5 M to 2.0 M, and CO2 loading range of 0e1.0 mol CO2/mol. They also reported the new pH values of the 1DMA2P solution with concentrations ranging from 0.5 M to 2.0 M, at a fixed temperature of 301 K as the CO2 loading range was 0e0.96 mol CO2/mol amine. Nezamloo [25] reported the H E data for the 1DMA2P þ H2O system over the entire range of amine mole fractions at 298 K, 313 K, and 333 K. Recently, we reported the solubility data of CO2 in 1DMA2P solution with concentrations of 2 M, 3 M, and 4 M at temperatures ranging from 298 K to 333 K, and CO2 partial pressures ranging from 3.0 to 167 kPa as well as the density and viscosity data at different temperatures and concentrations [26]. For the CO2þ3DMA1P þ H2O system, Li, et al. [27] conducted experiments for the CO2 equilibrium solubility of the 3DMA1P solution at concentrations ranging from 1 M to 3 M, CO2 partial pressures ranging from 8 to 101 kPa, and at temperatures ranging from 298 K to 333 K. Nezamloo [25] reported the H E data for the 3DMA1P þ H2O system over the entire range of amine mole fractions at 298 K, 313 K, and 333 K. For the CO2þH2O þ DEAB system,

Table 3 e-UNIQUAC parameters (volume (r) and surface area (q)) for all species obtained from literature or obtained in this study. Species

r

q

References

DEAB DEABHþ 3DMA1P 3DMA1PHþ 1DMA2P 1DMA2PHþ H2 O CO2 OH Hþ HCO 3

0.32 2.0 0.26 3.41 0.32 2.0 0.92 0.1 9.39 0.137 8.07 10.82

1.0 1.97 0.99 3.86 1.0 2.1 1.4 1.1 8.81 10e15 8.68 10.76

This study This study This study This study This study This study [20,34] This study [20,34] [20,34] [20,34] [20,34]

CO2 3

the data used was the experimental data reported by Sema et al. [28]. They experimentally obtained the equilibrium solubility data of CO2 in DEAB solution over the temperature range of 298 Ke333 K, CO2 partial pressure range of 10e100 kPa, and DEAB concentration range of 1e5 M. In addition, Shi, et al. [29] reported NMR data for the CO2þH2O þ DEAB system at different amine concentrations at a fixed temperature of 298 K.

3. Thermodynamic framework In the CO2þamine þ H2O system, when the absorption of the molecular solute CO2 takes place in the amine solution, CO2 dissolves and reacts into the amine solution. The unreacted CO2 in the amine solution phase is in physical equilibrium with its corresponding vapour-phase partial pressure. Therefore, the chemical and physical equilibria occur simultaneously in system [10]. In the same way, the water partial pressure in the vapour phase is in equilibrium with the water in the liquid phase. The thermodynamic framework for the CO2þamine þ H2O system is evaluated based on the chemical reaction equilibrium and phase equilibrium, the mass balances of chemical species, and the electro-neutrality of bulk electrolyte solution.

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

53

Table 4 e-UNIQUAC interaction parameters obtained using Equation (27) for CO2þ1DMA2P þ H2O system; u0ji ¼ u0ij . Species

H2 O

CO2

1DAM2P

OH

Hþ

HCO 3

CO2 3

H2 O CO2 1DAM2P OH  Hþ HCO 3

0 137.35 8.79045 4.271546 104 20.73042 3.21145

302.25 1010 2500 1010 526.31 2500

1.09555 1010 1010 1010 1010

1562.88 1010 1010 1588.03

0 1010 1010

771.38 800.008

1458.34

37.7055

29.98359

1010

1010

1010

1010

1010

CO2 3

1DAM2PHþ

1DAM2PHþ

0

Values in italic are fixed to their default. Table 5 e-UNIQUAC interaction parameters obtained using Equation (27) for CO2þ1DMA2P þ H2O system; uTji ¼ uTij . Species

H2 O

CO2

1DAM2P

OH

Hþ

HCO 3

CO2 3

H2 O CO2 1DAM2P OH  Hþ HCO 3

0 6.0907 10.312 4.14915 0 28.6312 5.10399

0.3587 5.5011 2.15337 46.5673 57.3802 51.2543

45.9307 50.8685 113.6825 23.9454 15.0949

5.6169 0 0 2.5176

0 0 0

¡0.0198 1.7241

¡1.3448

45.82435

12.945

78.2494

0

0

0

0

CO2 3 1DAM2PHþ

1DAM2PHþ

0

Values are in italic fixed to their default. Table 6 e-UNIQUAC interaction parameters obtained using Equation (27) for CO2þDEAB þ H2O system; u0ji ¼ u0ij . Species

H2 O

CO2

DEAB

OH

Hþ

HCO 3

CO2 3

H2 O CO2 DEAB OH  Hþ HCO 3

0 137.35 3.3297 ¡24.7896 104 517 361.387

302.25 1010 2500 1010 526.31 2500

6.0082 1010 1010 1010 1010

1562.88 1010 1010 1588.03

0 1010 1010

771.38 800.008

1458.34

5.6082

2.9405

1010

1010

1010

1010

1010

0

CO2 3

DEABHþ

CO2 3

DEABHþ

DEABHþ

Values in italic are fixed to their default. Table 7 e-UNIQUAC interaction parameters obtained using Equation (27) for CO2þDEAB þ H2O system; uTji ¼ uTij . Species

H2 O

CO2

DEAB

OH

Hþ

HCO 3

H2 O CO2 DEAB OH  Hþ HCO 3

0 6.0907 11.2778 4.6855 0 12.2746 ¡2.3149

0.3587 4.8349 ¡3.5672 15.1598 ¡77.3342 0.4658

8.1880 37.8952 0.7284 ¡12.5831 0.77857

5.6169 0 0 2.5176

0 0 0

¡0.0198 1.7241

¡1.3448

3.3297

18.1043

¡3.9620

0

0

0

0

CO2 3

DEABHþ

0

Values in italic are fixed to their default.

3.1. Chemical equilibrium equations K3

The chemical reactions in the CO2þAM þ H2O system (here, AM is 1DMA2P, 3DMA1P, and DEAB) can be considered as follows [22,27]:

K1

AM








!
AMHþ þ Hþ

K2

þ CO2 þ H2 O








!
HCO 3 þH

(1)

(2)

þ HCO




!
CO2 3



3 þH

K4

H2 O








!
OH þ Hþ

(3)

(4)

From the above reactions, the equilibrium constants (Ki) as a function of the activity of chemical species can be obtained from the following equations:

K1 ¼

aHþ aAMHþ aAM

(5)

54

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

Table 8 e-UNIQUAC interaction parameters obtained using Equation (27) for CO2þ3DMA1P þ H2O system; u0ji ¼ u0ij . Species

H2 O

CO2

3DMA1P

OH

Hþ

HCO 3

CO2 3

H2 O CO2 3DMA1P OH  Hþ HCO 3

0 ¡137.35 ¡19.4740 600.49 104 517 361.387

302.25 1010 2500 1010 526.31 2500

6.5993 1010 1010 1010 1010

1562.88 1010 1010 1588.03

0 1010 1010

771.38 800.008

1458.34

0.1683

¡12.3455

1010

1010

1010

1010

1010

CO2 3

3DMA1PHþ

3DMA1PHþ

0

Values in italic are fixed to their default.

Table 9 e-UNIQUAC interaction parameters obtained using Equation (27) for CO2þ3DMA1P þ H2O system; uTji ¼ uTij . Species

H2 O

CO2

3DMA1P

OH 

Hþ

HCO 3

CO2 3

H2 O CO2 3DMA1P OH  Hþ HCO 3

0 6.0907 3.6924 8.5455 0 15.3560 8.8433

0.3587 7.5994 ¡12.2671 ¡5.6168 ¡71.4636 ¡1.8009

¡2.2140 ¡11.7269 12.0186 57.5354 20.91945

5.6169 0 0 2.5176

0 0 0

¡0.0198 1.7241

¡1.3448

8.5607

13.5500

¡0.0805

0

0

0

0

CO2 3 3DMA1PHþ

3DMA1PHþ

0

Values in italic are fixed to their default.

1000

1.0

DEAB (AARD=8.06%) 3DMA1P (AARD=16.51%) 1DMA2P (AARD=13.39%) E-line

0.9 0.8

CO2 partial pressure (kPa)

Predicted data of CO2 loading(mol CO2 /mol amine

1.1

0.7 0.6 0.5 0.4 0.3 0.2

T=298K T=313K

100

T=323K T=333K

10

0.1

1

0.0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0

0.2

Expt data of CO2 loading (mol CO2 /mol amine)

aHþ aHCO3 aCO2 aH2 O

1

1.2

Fig. 2. Capability of the model to predict CO2 loading for 3- M solution of DEAB at different temperatures.

considered in the following temperature-dependent equation [30]:

lnðKi Þ ¼ (7)

aHþ aOH aH2 O

(8)

where ai is the activity for ions and molecules presented in the amine solution phase, and it is considered in the mole fraction scale as:

ai ¼ gi xi

0.8

(6)

aHþ aCO2 3 K3 ¼ aHCO3 K4 ¼

0.6

CO2 loading (mol CO2/mol DEAB)

Fig. 1. Plot of predicted CO2 loading data of amines vs. experimental data (see Table 1) of CO2 loading of amines using e-UNIQUAC model.

K2 ¼

0.4

(9)

where xi is the mole fraction of species i, and gi is the activity coefficient of species i. The equilibrium constant for each reaction is

A þ B lnðTÞ þ CðTÞ þ D ðTÞ

(10)

In the above equation, the parameters A; B; C; and D for Equations (2)e(4) were either taken from the literature [30] or regressed in this study using VLE experimental data for Equation (1). These parameters are listed in Table 2 along with their temperature range. The concentration of the chemical species, which exists in the amine solution phase, can be obtained by the following balances based on the mole-fraction scale [31]:  Charge balance:

xHþ þ xAMHþ ¼ xHCO3 þ xOH þ 2xCO2 3

(11)

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

 Amine balance:

 m0AM

nw Mw 1000 nt

 ¼ xAM þ xAMHþ

(12)

 Carbon balance:

 m0AM

nw Mw 1000 nt

55

PCO2 fCO2 ¼ g*CO2 HeCO2 xCO2

(19)

 .  s PH2 O fH2 O fsH2 O ¼ gH2 O PH x 2 O H2 O

(20)

where PCO2 is the partial pressure of CO2, fCO2 is the fugacity co-

efficient of CO2, g*CO2 is the activity coefficient of CO2 in the un-

 : aCO2 ¼ xCO2 þ xHCO3 þ xCO2

(13)

3

symmetrical reference state, HeCO2 is the Henry's law constant of CO2 in water, and PH2 O is the partial pressure of water. The factor fH2 O =fsH2 O is the ratio of the fugacity coefficient of water in solution to the fugacity coefficient of water at its vapour pressure, gH2 O is the s is the vapour pressure of water. activity coefficient of H2 O, and PH 2O

 Water balance:

2nw ¼ 2xH2 O þ xHþ þ xAMHþ þ xOH þ xHCO3 nt

(14)

The summation of mole fractions for all species is equal to unity, as follows:

xHþ þ xAMHþ þ xOH þ xCO2 þ xHCO3 þ xCO2 þ xAM þ xH2 O ¼ 1

In this study, at low-to-moderate pressures, for both Equation (19) and Equation (20), the Poynting correction factor was set equal to one, and both factors, i.e. fCO2 and fH2 O =fsH2 O , were assumed to be unity [32]. To calculate HeCO2 , the correlation was taken from literature based on the mole-fraction scale [33].

3

(15) m0AM

In the above equations, is the initial concentration of amine, aCO2 is the CO2 loading of amine, nw is the total number of moles of water in the amine solution phase, nt is the total number of moles of the mixture, and Mw is the molecular weight of water. 3.2. Phase equilibrium Molecular solutes, such as CO2, H2O, and amine, in a closed system under equilibrium conditions can be distributed between the amine-solution phase and vapour phase by the following equilibrium reactions [31]:

H2 O ðgÞ#H2 O ðaqÞ

(16)

CO2 ðgÞ#CO2 ðaqÞ

(17)

AMðgÞ#AM ðaqÞ

(18)

4. Extended-UNIQUAC (e-UNIQUAC) model The e-UNIQUAC model was first proposed by Thomsen and Rasmussen [34], and it was developed for aqueous-solution systems including ammonia or CO2 along with various salts. This model is a combination of the original UNIQUAC model, which was developed by Abrams and Prausnitz [35], and the term that accounts for electrolyte systems, which is called the Debye-Hückel formula. In this study, we applied the e-UNIQUAC model for CO2þAM þ H2O systems based on the work developed by Thomsen [36] and Zaidy [13]. In the e-UNIQUAC model, besides the combinatorial (entropic) and residual (enthalpic) terms, the electrostatic term is the Debye-Hückel formula, which accounts for long-range interaction parameters. The total excess Gibbs energy related to three above-mentioned terms are as follows:

GE ¼ RT

To calculate the phase equilibrium for the above equations, the presence of amine in the vapour phase was neglected, so Equation (18) was not considered in this study. For water and CO2, the following equations were used for the phase-equilibrium calculations [10,31].



 GE RT Combinatorial; UNIQUAC Entropic  E  E G G þ þ RT Residual; UNIQUAC Enthalpic RT Extended DebyeHu€ ckel (21)

The combinatorial term is related to the size and shape of

1000

1000

CO2 partial pressure (kPa)

CO2 partial pressure (kPa)

T=298K

100

T=298K T=313K

10

T=323K T=333K

T=313K 100

T=323K T=333K

10

1

1 0

0.2

0.4

0.6

0.8

1

1.2

CO2 loading (mol CO2/mol 3DMA1P) Fig. 3. Capability of the model to predict CO2 loading for 5-M solution of 3DMA1P at different temperatures.

0

0.2

0.4

0.6

0.8

1

1.2

CO2 loading (mol CO2/mol 1DMA2P) Fig. 4. Capability of the model to predict CO2 loading for 2.5-M solution of 1DMA2P at different temperatures.

56

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

Table 10 Experimental data and model results for CO2þH2O þ DEAB system. T (K) PCO2(kPa) C(M) Exp data for CO2 loading Model results for CO2 loading xCO2 298 11

1

0.83

0.72

298 13

1

0.87

0.88

298 35

1

0.89

0.92

298 60

1

0.9

0.98

298 71

1

0.92

0.99

298 99

1

0.93

1.00

313 11

1

0.78

0.66

313 15

1

0.8

0.67

313 36

1

0.83

0.76

313 57

1

0.89

0.93

313 66

1

0.89

0.96

313 78

1

0.9

0.98

313 100

1

0.91

0.99

333 11

1

0.52

0.45

333 13

1

0.56

0.48

333 33

1

0.63

0.54

333 62

1

0.71

0.59

333 72

1

0.75

0.60

333 99

1

0.81

0.68

298 10

2

0.92

0.99

298 15

2

0.94

1.00

298 31

2

0.95

1.01

298 51

2

0.97

1.02

298 76

2

0.98

1.02

298 100

2

1

1.04

313 10

2

0.83

0.78

313 15

2

0.88

0.88

313 30

2

0.92

0.99

313 51

2

0.95

1.01

313 76

2

0.97

1.02

313 100

2

0.99

1.04

333 10

2

0.76

0.61

333 15

2

0.79

0.67

333 30

2

0.81

0.70

333 51

2

0.83

0.79

333 76

2

0.88

0.90

333 100

2

0.93

1.00

xCO2 3

xDEAB

xDEABHþ xHCO3

xOH

0.00019 0.00091 0.01247 0.01771 0.01156 8.43E11 0.00023 0.00065 0.01362 0.01770 0.01298 6.80E11 0.00062 0.00006 0.01694 0.01769 0.01688 1.37E11 0.00106 0.00002 0.01737 0.01768 0.01735 5.50E12 0.00125 0.00001 0.01744 0.01767 0.01743 4.14E12 0.00174 0.00001 0.01753 0.01766 0.01752 2.32E12 0.00013 0.00194 0.00937 0.01773 0.00743 1.66E12 0.00017 0.00130 0.01180 0.01772 0.01050 1.28E12 0.00041 0.00014 0.01648 0.01769 0.01634 3.38E13 0.00066 0.00004 0.01720 0.01769 0.01716 1.43E13 0.00076 0.00002 0.01732 0.01768 0.01729 1.09E13 0.00090 0.00001 0.01741 0.01768 0.01740 7.94E14 0.00115 0.00001 0.01751 0.01768 0.01750 4.98E14 0.00008 0.00134 0.00902 0.01772 0.00768 2.07E13 0.00010 0.00117 0.01049 0.01772 0.00932 1.74E13 0.00024 0.00001 0.01731 0.01769 0.01730 1.36E14 0.00046 0.00001 0.01795 0.01769 0.01794 1.17E14 0.00053 0.00001 0.01795 0.01769 0.01794 1.20E14 0.00073 0.00001 0.01791 0.01768 0.01790 1.05E14 0.00017 0.00411 0.02268 0.03492 0.01857 2.94E10 0.00026 0.00211 0.02773 0.03484 0.02563 1.88E10 0.00053 0.00044 0.03266 0.03477 0.03222 6.45E11 0.00087 0.00015 0.03381 0.03475 0.03366 2.98E11 0.00129 0.00007 0.03422 0.03473 0.03415 1.62E11 0.00170 0.00004 0.03437 0.03472 0.03433 1.07E11 0.00011 0.00673 0.01776 0.03501 0.01104 4.96E12 0.00017 0.00468 0.02277 0.03494 0.01808 3.85E12 0.00033 0.00117 0.03078 0.03481 0.02961 1.65E12 0.00057 0.00029 0.03336 0.03477 0.03307 6.78E13 0.00085 0.00010 0.03408 0.03475 0.03398 3.42E13 0.00111 0.00005 0.03432 0.03474 0.03427 2.16E13 0.00007 0.00587 0.01534 0.03498 0.00948 7.16E13 0.00011 0.00522 0.02012 0.03496 0.01490 5.28E13 0.00021 0.00134 0.03012 0.03482 0.02878 2.20E13 0.00036 0.00009 0.03401 0.03477 0.03392 5.11E14 0.00054 0.00000 0.03472 0.03476 0.03472 3.08E15 0.00071 0.00000 0.03485 0.03475 0.03485 8.71E15

xHþ

Error for loading data (%)

7.45E11 9.41E11 4.69E10 1.10E09 1.44E09 2.43E09 8.33E11 1.16E10 4.98E10 1.19E09 1.56E09 2.11E09 3.30E09 1.22E10 1.49E10 2.43E09 3.22E09 3.19E09 3.72E09 3.98E11 6.48E11 1.91E10 4.00E10 7.04E10 1.03E09 5.08E11 7.24E11 1.89E10 4.71E10 9.27E10 1.45E09 6.44E11 9.42E11 2.71E10 1.32E09 2.31E08 8.37E09

13.26 0.87 3.35 8.68 7.84 7.51 14.84 16.35 8.94 4.21 7.49 9.08 8.78 13.00 13.95 14.04 16.67 19.59 15.91 7.91 6.68 5.97 4.82 4.43 4.11 5.83 0.07 8.06 6.40 5.33 4.73 19.59 15.60 14.01 5.21 2.23 7.74

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

57

Table 10 (continued ) T (K) PCO2(kPa) C(M) Exp data for CO2 loading Model results for CO2 loading xCO2 298 11

2.5

0.95

1.01

298 13

2.5

0.96

1.01

298 35

2.5

1

1.04

298 60

2.5

1.01

1.05

298 70

2.5

1.02

1.06

298 99

2.5

1.03

1.09

313 11

2.5

0.89

0.96

313 15

2.5

0.92

1.00

313 36

2.5

0.98

1.02

313 57

2.5

0.98

1.02

313 66

2.5

0.99

1.04

313 78

2.5

1

1.05

313 100

2.5

1.02

1.06

333 11

2.5

0.83

0.81

333 13

2.5

0.85

0.85

333 33

2.5

0.89

0.96

333 62

2.5

0.94

1.00

333 72

2.5

0.96

1.02

333 99

2.5

0.98

1.03

298 9

5

0.59

0.52

298 16

5

0.61

0.52

298 21

5

0.62

0.53

298 30

5

0.64

0.56

xCO2

xDEAB

3

xDEABHþ xHCO3

xOH

0.00018 0.00534 0.02933 0.04333 0.02399 3.80E10 0.00022 0.00417 0.03190 0.04327 0.02772 3.21E10 0.00059 0.00056 0.04079 0.04310 0.04023 8.07E11 0.00100 0.00019 0.04208 0.04306 0.04189 3.57E11 0.00117 0.00014 0.04227 0.04305 0.04213 2.84E11 0.00166 0.00008 0.04255 0.04303 0.04248 1.71E11 0.00012 0.00888 0.02343 0.04349 0.01455 6.46E12 0.00017 0.00675 0.02794 0.04339 0.02120 5.34E12 0.00039 0.00119 0.03936 0.04313 0.03818 1.82E12 0.00062 0.00036 0.04156 0.04308 0.04119 8.46E13 0.00072 0.00025 0.04192 0.04308 0.04166 6.61E13 0.00085 0.00017 0.04221 0.04307 0.04204 5.01E13 0.00109 0.00010 0.04250 0.04305 0.04240 3.33E13 0.00008 0.00860 0.02021 0.04348 0.01161 9.30E13 0.00009 0.00836 0.02230 0.04347 0.01394 8.27E13 0.00023 0.00196 0.03744 0.04317 0.03548 3.00E13 0.00043 0.00009 0.04240 0.04308 0.04231 5.64E14 0.00050 0.00003 0.04274 0.04308 0.04271 3.07E14 0.00069 0.00000 0.04306 0.04307 0.04306 3.73E16 0.00014 0.01872 0.04856 0.08427 0.02984 1.18E09 0.00025 0.01013 0.06272 0.08351 0.05259 7.46E10 0.00033 0.00659 0.06885 0.08319 0.06225 5.47E10 0.00046 0.00344 0.07470 0.08290 0.07126 3.42E10

xHþ

Error for loading data (%)

3.78E11 4.55E11 1.84E10 4.00E10 4.95E10 7.89E10 4.84E11 6.32E11 2.10E10 4.57E10 5.83E10 7.66E10 1.14E09 6.08E11 7.05E11 2.45E10 1.48E09 2.78E09 2.35E07 2.06E11 3.45E11 4.74E11 7.57E11

6.44 5.66 4.37 4.42 3.61 6.07 7.60 8.21 4.49 4.51 5.15 4.54 3.81 2.15 0.31 8.29 6.88 5.74 5.07 12.02 14.17 14.31 12.78

AARD ¼ 8.06%.

individual chemical species in the amine solution, and is given as follows:



GE RT

 ¼ Combinatorial

X i

    ∅i Z X ∅i  xi ln qi xi ln 2 I xi qi

(22)

taken from the literature. The residual term is related to the energetic interactions between unlike and like chemical species, and is given as follows:



GE RT

 ¼ Residual

X

0 xi qi ln@

X

1 xj jji A

(25)

Z is called the coordination number, and it was set to 10. ∅i and qi are the volume fraction and the surface-area fraction of the component i, respectively, as follows:

jji is the adjustable parameter, and is given as:

xr ∅i ¼ P i i j xj rj

(23)

jji ¼ exp 

x qi j xj qj

(24)

In the above equation, we considered the adjustable interaction energy parameters to be temperature dependent, similar to other works in the literature [13,15,20] using the following equation:

qi ¼ P i

In the above equations, r and q are respectively the volume and surface-area parameters for the components i and j. For all chemical species presented in the amine-solution phase, these adjustable parameters, i.e. r and q, were regressed by experimental data or



i

uji  uii T

j



uji ¼ u0ji þ uTji  ðT  298:15Þ

(26)

(27)

In this study, both u0ji and uTji were regressed for each pair of

58

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

Table 11 Experimental data and model results for CO2þH2Oþ3DMA1P system. T (K) PCO2(kPa) C(M) Exp data for CO2 loading Model results for CO2 loading xCO2 298 2.7

1

0.62

0.43

298 8.2

1

0.70

0.49

298 14.5

1

0.75

0.54

298 30.3

1

0.78

0.64

298 101.0

1

0.82

0.91

313 3.6

1

0.46

0.43

313 8.2

1

0.64

0.49

313 15.4

1

0.71

0.55

313 29.9

1

0.73

0.63

313 101.4

1

0.79

0.89

333 3.0

1

0.21

0.23

333 7.7

1

0.41

0.45

333 14.0

1

0.53

0.51

333 29.4

1

0.61

0.61

333 100.5

1

0.73

0.87

298 2.5

2

0.57

0.45

298 8.0

2

0.69

0.49

298 14.8

2

0.74

0.52

298 29.6

2

0.79

0.57

298 101.4

2

0.87

0.74

313 3.0

2

0.43

0.45

313 8.5

2

0.58

0.50

313 15.6

2

0.67

0.53

313 30.0

2

0.76

0.58

313 101.0

2

0.80

0.75

333 2.9

2

0.14

0.15

333 7.6

2

0.35

0.48

333 13.9

2

0.44

0.52

333 29.6

2

0.58

0.57

333 100.6

2

0.72

0.75

298 2.6

3

0.52

0.46

298 7.9

3

0.69

0.49

298 14.9

3

0.71

0.52

298 29.8

3

0.84

0.55

298 101.6

3

0.90

0.67

313 2.6

3

0.31

0.36

313 8.3

3

0.49

0.50

xCO2 3

x3DMA1P x3DMA1P þ xHCO3

xOH

0.00002 0.00051 0.01622 0.01771 0.00041 2.13E10 0.00005 0.00197 0.01178 0.01773 0.00184 1.73E10 0.00009 0.00213 0.00886 0.01773 0.00441 1.51E10 0.00018 0.00101 0.00451 0.01771 0.01101 9.03E11 0.00061 0.00006 0.00068 0.01769 0.01686 1.40E11 0.00002 0.00039 0.01638 0.01770 0.00049 3.36E12 0.00003 0.00135 0.01355 0.01772 0.00134 2.77E12 0.00006 0.00226 0.01003 0.01774 0.00298 2.24E12 0.00012 0.00198 0.00635 0.01773 0.00722 1.68E12 0.00042 0.00013 0.00100 0.01769 0.01638 3.30E13 0.00001 0.00013 0.01698 0.01770 0.00043 4.96E13 0.00002 0.00047 0.01521 0.01770 0.00148 4.21E13 0.00004 0.00100 0.01237 0.01771 0.00320 3.37E13 0.00008 0.00132 0.00699 0.01772 0.00789 2.02E13 0.00028 0.00000 0.00005 0.01769 0.01764 1.87E15 0.00001 0.00225 0.02923 0.03486 0.00080 7.53E10 0.00005 0.00669 0.01759 0.03501 0.00327 5.12E10 0.00009 0.00688 0.01264 0.03502 0.00774 4.33E10 0.00017 0.00405 0.00729 0.03492 0.01877 2.91E10 0.00059 0.00034 0.00128 0.03477 0.03267 5.42E11 0.00001 0.00149 0.03077 0.03483 0.00082 1.23E11 0.00003 0.00539 0.02084 0.03497 0.00265 8.36E12 0.00006 0.00734 0.01424 0.03504 0.00527 6.28E12 0.00012 0.00643 0.00909 0.03500 0.01219 4.77E12 0.00040 0.00071 0.00184 0.03479 0.03132 1.21E12 0.00001 0.00074 0.03235 0.03480 0.00082 1.80E12 0.00002 0.00233 0.02725 0.03486 0.00252 1.45E12 0.00004 0.00435 0.02061 0.03493 0.00492 1.09E12 0.00008 0.00585 0.01158 0.03498 0.01085 6.55E13 0.00027 0.00046 0.00159 0.03478 0.03210 1.24E13 0.00001 0.00542 0.03842 0.05156 0.00126 1.47E09 0.00004 0.01227 0.02119 0.05193 0.00438 9.18E10 0.00008 0.01241 0.01484 0.05193 0.01033 7.60E10 0.00017 0.00795 0.00892 0.05169 0.02515 5.33E10 0.00057 0.00087 0.00178 0.05129 0.04743 1.14E10 0.00001 0.00312 0.04341 0.05144 0.00110 2.56E11 0.00003 0.01042 0.02568 0.05183 0.00364 1.53E11

xHþ

Error for loading data (%)

1.94E11 2.67E11 3.54E11 6.90E11 4.58E10 3.19E11 3.85E11 5.18E11 8.16E11 5.11E10 5.21E11 5.81E11 7.13E11 1.26E10 1.84E08 1.02E11 1.69E11 2.35E11 4.02E11 2.26E10 1.61E11 2.37E11 3.46E11 5.39E11 2.61E10 2.59E11 3.08E11 4.05E11 7.18E11 5.12E10 7.39E12 1.34E11 1.90E11 3.11E11 1.53E10 1.08E11 1.83E11

31.61 29.03 27.41 18.09 10.96 7.17 23.76 23.27 13.76 12.67 5.02 8.88 2.83 0.19 19.34 20.89 28.59 29.35 27.79 14.63 5.80 14.15 20.71 23.59 6.83 6.61 37.21 16.36 1.38 4.10 10.81 28.52 27.88 34.65 25.24 17.55 2.26

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

59

Table 11 (continued ) T (K) PCO2(kPa) C(M) Exp data for CO2 loading Model results for CO2 loading xCO2 313 15.3

3

0.60

0.52

313 29.8

3

0.71

0.56

313 101.6

3

0.83

0.68

333 3.0

3

0.08

0.10

333 7.9

3

0.23

0.26

333 14.5

3

0.33

0.34

333 29.3

3

0.46

0.56

333 100.7

3

0.68

0.69

xCO2 3

x3DMA1P x3DMA1P þ xHCO3

xOH

0.00006 0.01315 0.01690 0.05197 0.00689 1.11E11 0.00012 0.01169 0.01074 0.05189 0.01585 8.38E12 0.00039 0.00168 0.00246 0.05134 0.04495 2.42E12 0.00001 0.00196 0.04575 0.05138 0.00121 3.69E12 0.00002 0.00558 0.03563 0.05157 0.00355 2.77E12 0.00004 0.00922 0.02515 0.05176 0.00646 1.96E12 0.00008 0.01145 0.01418 0.05188 0.01285 1.19E12 0.00027 0.00199 0.00286 0.05137 0.04387 3.31E13

xHþ

Error for loading data (%)

2.77E11 4.32E11 1.83E10 1.74E11 2.23E11 3.15E11 5.56E11 2.67E10

13.55 22.05 18.30 14.42 14.37 1.45 20.13 0.67

AARD ¼ 16.5%.

chemical species. The third term is the Debye-Hückel formula, and is as follows:



GE RT

 € ckel Extended DebyeH u

¼ xw Mw

  pffiffi  pffiffi b2 I 4A ln 1 þ b I  b Iþ 2 b3

coefficients by applying the following equation for solutes [34]:

  ln g*i unsymmetric ¼ ðln gi ÞCombinatorial  ðln gi Þ∞ Combinatorial

 þ ðln gi ÞResidual  ðln gi Þ∞ Residual þ ðln gi ÞExtended DebyeHuckel

(28) where xw and Mw are the mole fraction of water and the molecular weight of water, respectively. In the above equation, the parameter A was considered with a polynomial approximation as a function of temperature based on the work of Thomsen [36], and the parameter b was fixed at a constant value of 1.2, which is similar to the results reported in literature for other amine systems [26]. I is the ionic strength calculated based on the work by Arshad et al. [37]. By applying the partial molar differentiation to Equation (22) and Equation (25), the symmetrical activity coefficients for combinatorial and residual terms can be obtained from Ref. [34]:







∅i ∅i þ1 ðln gi ÞCombinatorial ¼ ln xi xi



     Z ∅i ∅i  qi ln þ1 2 qi qi

(33) In the above equation, the infinite dilution activity coefficients can be obtained by setting the mole fraction of water to be equal to unity in Equation (29) and Equation (30) as follows:

       ri ri Z ri qw q þ1  ln þ1 ðln gi Þ∞ ¼ ln Combinatorial 2 i rw rw rw qi   r qw  i rw qi ðln gi Þ∞ Residual ¼ qi ½1  lnðjwi Þ  lnðjiw Þ

(34) (35)

(29) 2

0

ðln gi ÞResidual ¼ qi 41  ln@

X

1

qj jji A 

j

X j

5. Regression method

3

qj jij 5 k qk jkj

P

(30)

Moreover, for the electrostatic term, by applying the partial molar differentiation to Equation (28), the unsymmetrical activity coefficients for ions and water are as follows:

ðln gi ÞExtended DebyeHuckel ¼ 

ln gw ¼ 2A Mw



pffiffi AZi2 I pffiffi 1þb I

(31)

 pffiffi  pffiffi 1 pffiffi 

1þb I  1þb I  2ln 1 þ b I b3 (32)

The activity coefficients, which can be obtained from Equation (29) and Equation (30), are symmetric activity coefficients, but Equation (31) accounts for the unsymmetrical activity coefficients. Therefore, to obtain the unsymmetrical activity coefficients for solutes in the investigated systems, the combinatorial and residual terms were also converted to the unsymmetrical activity

The adjustable parameters in the applied model were found by using fminsearch in MATLAB software as an optimization algorithm [21,38]. Based on the available experimental data for investigated amine systems (see Table 1), we have defined different objective functions. For the CO2þ3DMA1P þ H2O system, the objective function (OF) that was employed to obtain the parameters was minimized according to the following equation:

OF ¼

X h

Exp aCal CO2  aCO2

.

aExp CO2

i2

VLE data

þ

. i X h Exp Exp 2 Cal Pvap Pvap  Pvap

pvap data

þ

. i2 X h HECal  HEExp HEExp

(36)

H E data

In the above equation, the errors between the calculated ðCalÞ data and experimental ðExpÞ data for three variables, i.e. the CO2 loading of amine (aCO2 Þ, vapour pressure of amine (Pvap Þ, and H E were minimized. For the CO2þDEAB þ H2O system, the aCO2 and

60

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

Table 12 Experimental data and model results for CO2þH2Oþ1DMA2P system. T (K) PCO2(kPa) C(M) Exp data for CO2 loading Model results for CO2 loading xCO2

xCO2 3

x1DAM2P x1DMA2PHþ xHCO3

298 8.2

1

0.85

0.54

0.00005 0.00320 0.00482 0.00950

298 11

1

0.89

0.61

0.00007 0.00301 0.00392 0.01060

298 15

1

0.93

0.68

0.00009 0.00260 0.00312 0.01182

298 30.1

1

0.96

0.83

0.00018 0.00143 0.00173 0.01443

298 60

1

0.98

0.93

0.00036 0.00065 0.00088 0.01610

298 101

1

1.02

0.98

0.00060 0.00036 0.00053 0.01676

313 8.2

1

0.73

0.58

0.00003 0.00246 0.00840 0.00667

313 11

1

0.76

0.45

0.00005 0.00278 0.00692 0.00783

313 15

1

0.82

0.52

0.00006 0.00291 0.00558 0.00903

313 30.1

1

0.87

0.68

0.00012 0.00234 0.00335 0.01186

313 60

1

0.91

0.84

0.00025 0.00123 0.00181 0.01455

313 101

1

0.92

0.93

0.00042 0.00064 0.00107 0.01591

333 8.2

1

0.50

0.39

0.00002 0.00099 0.01330 0.00330

333 11

1

0.54

0.45

0.00003 0.00134 0.01194 0.00428

333 15

1

0.56

0.32

0.00004 0.00175 0.01031 0.00548

333 30.1

1

0.67

0.48

0.00008 0.00247 0.00669 0.00836

333 60

1

0.77

0.65

0.00017 0.00217 0.00403 0.01133

333 101

1

0.84

0.79

0.00028 0.00140 0.00255 0.01361

298 3.03

2

0.53

0.41

0.00002 0.00802 0.01225 0.01392

298 8.2

2

0.66

0.57

0.00005 0.00910 0.00578 0.01933

298 7.51

2

0.70

0.55

0.00004 0.00918 0.00616 0.01887

298 11

2

0.72

0.61

0.00006 0.00858 0.00471 0.02092

298 15

2

0.73

0.67

0.00009 0.00765 0.00381 0.02275

298 13

2

0.75

0.64

0.00008 0.00812 0.00420 0.02188

298 18.78

2

0.78

0.71

0.00011 0.00681 0.00325 0.02417

298 22.57

2

0.82

0.74

0.00013 0.00606 0.00284 0.02535

298 30.1

2

0.82

0.79

0.00017 0.00489 0.00226 0.02715

298 40.31

2

0.85

0.84

0.00023 0.00380 0.00177 0.02879

298 60

2

0.93

0.90

0.00035 0.00262 0.00125 0.03060

298 101

2

0.95

0.95

0.00059 0.00157 0.00077 0.03221

298 106.13

2

0.97

0.95

0.00061 0.00150 0.00074 0.03232

298 138.65

2

1.01

0.97

0.00080 0.00116 0.00058 0.03286

298 162.31

2

1.01

0.98

0.00094 0.00099 0.00050 0.03312

313 4.11

2

0.47

0.32

0.00002 0.00602 0.01737 0.01081

313 8.2

2

0.61

0.45

0.00003 0.00814 0.01075 0.01529

313 11

2

0.65

0.50

0.00004 0.00861 0.00858 0.01699

313 15

2

0.66

0.55

0.00006 0.00869 0.00680 0.01871

xOH

0.00630 1.31E09 0.00760 8.11E10 0.00923 4.85E10 0.01300 1.39E10 0.01544 3.56E11 0.01640 1.22E11 0.00421 1.75E09 0.00505 1.08E09 0.00612 6.41E10 0.00952 1.98E10 0.01332 5.43E11 0.01527 1.81E11 0.00230 2.18E09 0.00295 1.46E09 0.00373 9.28E10 0.00589 3.00E10 0.00916 9.21E11 0.01221 3.46E11 0.00590 3.21E08 0.01023 5.79E09 0.00970 6.69E09 0.01234 3.59E09 0.01510 2.18E09 0.01376 2.74E09 0.01736 1.51E09 0.01929 1.11E09 0.02226 6.69E10 0.02499 3.93E10 0.02798 1.85E10 0.03063 6.72E11 0.03082 6.09E11 0.03170 3.59E11 0.03212 2.63E11 0.00479 2.61E08 0.00715 8.21E09 0.00838 4.91E09 0.01002 2.89E09

xH þ

Error for loading data (%)

6.64E11 8.15E11 1.02E10 1.84E10 3.59E10 5.99E10 6.32E11 7.66E11 9.49E11 1.58E10 2.90E10 4.92E10 6.76E11 7.52E11 8.71E11 1.34E10 2.21E10 3.48E10 2.48E11 5.23E11 4.92E11 6.41E11 7.90E11 7.17E11 9.25E11 1.06E10 1.32E10 1.68E10 2.39E10 3.82E10 4.00E10 5.10E10 5.88E10 2.90E11 4.67E11 5.84E11 7.36E11

36.00 31.30 27.38 13.78 4.84 3.84 19.97 41.05 36.72 21.42 7.20 0.51 21.47 16.88 43.98 27.69 14.72 5.66 23.52 13.72 21.39 15.17 9.12 14.10 9.63 9.30 3.38 0.57 3.56 0.28 1.68 3.55 2.82 31.81 26.53 22.84 16.38

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

61

Table 12 (continued ) T (K) PCO2(kPa) C(M) Exp data for CO2 loading Model results for CO2 loading xCO2

xCO2 3

x1DAM2P x1DMA2PHþ xHCO3

313 16.24

2

0.69

0.56

0.00007 0.00863 0.00642 0.01915

313 43.21

2

0.71

0.74

0.00017 0.00576 0.00315 0.02533

313 30.1

2

0.74

0.67

0.00012 0.00719 0.00414 0.02288

313 68.94

2

0.83

0.83

0.00028 0.00386 0.00213 0.02835

313 60

2

0.89

0.81

0.00024 0.00440 0.00241 0.02751

313 89.35

2

0.89

0.87

0.00036 0.00298 0.00168 0.02975

313 101

2

0.91

0.89

0.00040 0.00262 0.00150 0.03033

313 100.12

2

0.92

0.89

0.00040 0.00264 0.00151 0.03029

313 131.37

2

0.94

0.92

0.00053 0.00197 0.00117 0.03136

333 6.09

2

0.37

0.22

0.00002 0.00379 0.02315 0.00736

333 8.2

2

0.52

0.47

0.00002 0.00473 0.02028 0.00923

333 11

2

0.58

0.53

0.00003 0.00572 0.01724 0.01123

333 15

2

0.59

0.39

0.00004 0.00672 0.01406 0.01337

333 30.1

2

0.63

0.52

0.00008 0.00799 0.00836 0.01780

333 33.13

2

0.64

0.54

0.00009 0.00800 0.00778 0.01838

333 60

2

0.73

0.65

0.00016 0.00698 0.00503 0.02218

333 68.47

2

0.77

0.68

0.00019 0.00653 0.00455 0.02311

333 101

2

0.83

0.76

0.00028 0.00496 0.00334 0.02596

333 117.98

2

0.85

0.80

0.00032 0.00431 0.00291 0.02707

333 164.15

2

0.88

0.86

0.00045 0.00304 0.00214 0.02920

298 4.87

3

0.46

0.51

0.00003 0.01560 0.00912 0.02545

298 11.37

3

0.68

0.61

0.00006 0.01448 0.00492 0.03077

298 14.72

3

0.71

0.65

0.00008 0.01335 0.00415 0.03265

298 30.72

3

0.81

0.77

0.00017 0.00906 0.00249 0.03867

298 50.18

3

0.85

0.84

0.00028 0.00630 0.00169 0.04242

298 51.82

3

0.85

0.85

0.00029 0.00613 0.00165 0.04263

298 56.3

3

0.88

0.86

0.00032 0.00573 0.00154 0.04318

298 76.91

3

0.90

0.89

0.00043 0.00441 0.00118 0.04499

298 108

3

0.93

0.93

0.00061 0.00329 0.00088 0.04655

298 147

3

0.95

0.95

0.00082 0.00250 0.00067 0.04764

313 2.93

3

0.16

0.31

0.00001 0.01021 0.02451 0.01537

313 8.66

3

0.48

0.48

0.00003 0.01471 0.01115 0.02426

313 46.16

3

0.76

0.73

0.00018 0.01015 0.00331 0.03670

313 78.31

3

0.83

0.82

0.00030 0.00684 0.00218 0.04132

313 103.22

3

0.85

0.86

0.00040 0.00536 0.00172 0.04339

313 141.17

3

0.89

0.90

0.00055 0.00399 0.00130 0.04532

313 161.98

3

0.90

0.92

0.00063 0.00350 0.00115 0.04602

xOH

0.01052 2.52E09 0.01958 4.93E10 0.01569 9.11E10 0.02449 2.10E10 0.02311 2.72E10 0.02678 1.27E10 0.02771 9.92E11 0.02765 1.01E10 0.02939 5.81E11 0.00358 1.82E08 0.00450 1.20E08 0.00550 7.64E09 0.00665 4.60E09 0.00981 1.38E09 0.01038 1.17E09 0.01520 4.29E10 0.01658 3.43E10 0.02099 1.72E10 0.02276 1.29E10 0.02616 6.74E11 0.00985 3.23E08 0.01629 7.79E09 0.01930 5.17E09 0.02961 1.54E09 0.03612 6.44E10 0.03650 6.07E10 0.03745 5.21E10 0.04058 2.91E10 0.04327 1.52E10 0.04514 8.42E11 0.00516 1.08E07 0.00955 1.73E08 0.02656 1.04E09 0.03448 4.07E10 0.03803 2.41E10 0.04132 1.31E10 0.04252 9.96E11

xHþ

Error for loading data (%)

7.80E11 1.57E10 1.20E10 2.32E10 2.05E10 2.92E10 3.28E10 3.25E10 4.20E10 3.68E11 4.20E11 4.94E11 6.04E11 1.01E10 1.09E10 1.68E10 1.85E10 2.51E10 2.87E10 3.89E10 3.16E11 5.81E11 6.87E11 1.13E10 1.66E10 1.70E10 1.82E10 2.36E10 3.15E10 4.12E10 1.95E11 4.27E11 1.42E10 2.13E10 2.69E10 3.54E10 4.00E10

18.04 4.46 8.71 0.61 9.11 1.84 2.52 3.29 1.98 41.08 8.76 8.26 33.70 16.79 15.70 10.04 11.73 7.69 5.77 2.62 10.15 9.72 8.12 4.40 0.73 0.34 2.85 0.67 0.07 0.10 89.89 1.85 3.07 0.66 1.21 1.38 1.89 (continued on next page)

62

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

Table 12 (continued ) T (K) PCO2(kPa) C(M) Exp data for CO2 loading Model results for CO2 loading xCO2

xCO2 3

x1DAM2P x1DMA2PHþ xHCO3

333 3.42

3

0.18

0.18

0.00001 0.00587 0.03544 0.00904

333 12.28

3

0.35

0.40

0.00003 0.01200 0.01818 0.01984

333 14.69

3

0.37

0.43

0.00004 0.01275 0.01589 0.02138

333 19.17

3

0.43

0.47

0.00005 0.01363 0.01288 0.02354

333 88.2

3

0.70

0.71

0.00023 0.01033 0.00411 0.03567

333 111.74

3

0.74

0.76

0.00030 0.00876 0.00342 0.03799

333 131.33

3

0.77

0.79

0.00035 0.00768 0.00300 0.03956

298 6.71

4

0.47

0.55

0.00004 0.02210 0.00732 0.03613

298 14.1

4

0.61

0.64

0.00008 0.01932 0.00442 0.04167

298 52.51

4

0.80

0.83

0.00029 0.00965 0.00178 0.05423

298 84.32

4

0.86

0.88

0.00046 0.00678 0.00122 0.05796

298 111.1

4

0.88

0.91

0.00061 0.00546 0.00097 0.05971

298 159.63

4

0.92

0.94

0.00087 0.00407 0.00071 0.06156

313 9.1

4

0.38

0.50

0.00003 0.02137 0.01108 0.03300

313 30.14

4

0.58

0.65

0.00011 0.01832 0.00463 0.04240

313 58.93

4

0.70

0.76

0.00022 0.01306 0.00292 0.04941

313 86.47

4

0.77

0.82

0.00033 0.00997 0.00218 0.05345

313 115.18

4

0.80

0.86

0.00043 0.00793 0.00172 0.05615

333 16.09

4

0.29

0.26

0.00004 0.01954 0.01548 0.03027

333 52.16

4

0.50

0.61

0.00014 0.01906 0.00620 0.04007

333 59.14

4

0.53

0.63

0.00015 0.01836 0.00569 0.04126

333 121.44

4

0.66

0.76

0.00031 0.01264 0.00340 0.04933

333 168.09

4

0.71

0.81

0.00043 0.00979 0.00262 0.05315

298 8.2

5

0.29

0.57

0.00004 0.02787 0.00642 0.04597

298 11

5

0.47

0.60

0.00006 0.02657 0.00527 0.04832

298 15

5

0.61

0.64

0.00008 0.02457 0.00434 0.05113

298 30.1

5

0.71

0.73

0.00016 0.01854 0.00279 0.05860

298 60

5

0.79

0.82

0.00032 0.01238 0.00170 0.06621

298 101

5

0.83

0.88

0.00054 0.00863 0.00113 0.07098

313 8.2

5

0.27

0.20

0.00003 0.02767 0.01229 0.04021

313 11

5

0.31

0.33

0.00004 0.02798 0.00964 0.04260

313 15

5

0.43

0.56

0.00006 0.02759 0.00759 0.04503

313 30.1

5

0.53

0.64

0.00011 0.02394 0.00474 0.05130

313 60

5

0.71

0.74

0.00022 0.01752 0.00300 0.05940

313 101

5

0.77

0.82

0.00037 0.01247 0.00204 0.06573

333 8.2

5

0.14

0.19

0.00002 0.02219 0.02687 0.03066

333 11

5

0.19

0.23

0.00003 0.02412 0.02159 0.03411

333 15

5

0.24

0.27

0.00004 0.02572 0.01678 0.03744

xOH

0.00318 1.01E07 0.00784 1.54E08 0.00863 1.13E08 0.00991 7.04E09 0.02534 5.22E10 0.02923 3.45E10 0.03188 2.58E10 0.01402 3.29E08 0.02235 9.89E09 0.04458 1.11E09 0.05118 4.66E10 0.05425 2.78E10 0.05750 1.40E10 0.01163 2.82E08 0.02408 3.77E09 0.03635 1.25E09 0.04349 6.33E10 0.04822 3.72E10 0.01073 1.72E08 0.02101 2.22E09 0.02290 1.81E09 0.03669 5.45E10 0.04336 3.03E10 0.01810 3.66E08 0.02176 2.28E08 0.02656 1.40E08 0.04006 4.60E09 0.05382 1.40E09 0.06235 5.46E10 0.01255 5.29E08 0.01462 3.12E08 0.01744 1.82E08 0.02736 5.90E09 0.04188 1.92E09 0.05326 7.70E10 0.00847 8.66E08 0.00999 5.26E08 0.01171

xH þ

Error for loading data (%)

2.29E11 4.44E11 5.07E11 6.25E11 1.93E10 2.31E10 2.63E10 3.73E11 6.12E11 1.49E10 2.16E10 2.71E10 3.66E10 4.08E11 9.64E11 1.51E10 2.01E10 2.53E10 4.95E11 1.22E10 1.33E10 2.19E10 2.83E10 4.03E11 4.89E11 5.92E11 9.10E11 1.47E10 2.19E10 3.50E11 4.46E11 5.65E11 8.96E11 1.40E10 2.03E10 2.72E11 3.38E11

1.44 14.84 15.65 10.97 1.86 2.85 2.88 17.36 4.64 3.15 2.89 3.00 2.22 34.23 11.55 7.79 6.08 6.84 8.46 23.38 19.86 14.70 14.20 101.16 27.27 5.43 2.82 4.01 6.15 23.78 6.26 31.01 20.86 3.99 6.78 30.32 20.21 12.56

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

63

Table 12 (continued ) T (K) PCO2(kPa) C(M) Exp data for CO2 loading Model results for CO2 loading xCO2

xCO2 3

x1DAM2P x1DMA2PHþ xHCO3

333 30.1

5

0.28

0.35

0.00008 0.02694 0.00943 0.04373

333 60

5

0.38

0.43

0.00015 0.02401 0.00574 0.05018

333 101

5

0.44

0.51

0.00025 0.01925 0.00403 0.05655

xOH

3.04E08 0.01679 8.67E09 0.02616 2.75E09 0.03730 1.18E09

xHþ 4.35E11 7.69E11 1.25E10 1.76E10

Error for loading data (%)

23.41 13.09 16.68

AARD ¼ 13.39%.

NMR data, namely the mole-fraction concentrations 2 were used to minimize paðxi Þof DEABDEABH þ , HCO , and CO 3 3 rameters with the following OF:

OF ¼

X h

Exp aCal CO2  aCO2

VLE data

þ

.

aExp CO2

i2

h . i2 xCal xExp  xExp i i i

X

(37)

NMR data

For the CO2þ1DMA2P þ H2O system, the aCO2 ; pH data, and H E data were used to minimize parameters with the following OF:

OF ¼

X h

Exp aCal CO2  aCO2

.

aExp CO2

i2

VLE data

þ

. i2 X h pH Cal  pHExp pHExp

pH data

þ

X h

Exp

HECal  HE

. i Exp 2 HE

(38)

H E data

It should be noted that in all objective functions defined in Equations (36)e(38) the weights were considered one. In the eUNIQUAC model, the adjustable parameters are those in the residual term as a function of temperature as well as r and q for all species in the liquid phase. To reduce the number of parameters, we made some assumptions to determine the adjustable parameters in the model as follows: in Equation (27), u0ji ¼ u0ij and uTji ¼ uTij ; therefore, we reduced the number of adjustable parameters to 72. In accordance with the works of Sadegh et al. [20] and Zaidy [13] for their studied systems (CO2þMDEA þ H2O and CO2þDEEA þ H2O), the values for u0ji and uTji for our investigated system, which are less likely to coexist in liquid phase, were set to a large value and zero. In addition, in this study, some of the interaction parametric values which are related to CO2þH2O systems, and which were studied by Thomsen and Rasmussen [34], are similar to works by Sadegh et al. [20] and Zaidy [13]. The parameters r and q were optimized for amine and protonated amine, as well as the other species obtained from the literature [13,20,31,34].

related to the equilibrium constant for Equation (1) related to the 3DMA1P solution, the parameters ri and qi , and binary interactions for all mentioned systems. For DEAB and 1DMA2P solutions, the parameters for the equilibrium constant were taken from our previous study [14]; however, for the 3DMA1P solution, the parameters were adjusted by considering only the Debye-Hückel term in the applied model. Results for four parameters in the temperature range of 298e333 K and concentration range of 1e3 M of the 3DMA1P solution are listed in Table 2. The parameters ri and qi used in the eUNIQUAC model are listed in Table 3. The r and q parameters for 3DMA1P were obtained by optimizing the total pressure data for the 3DMA1P þ H2O system using the UNIQUAC model, and for 3DMA1PHþ, the parameters were adjusted by using the VLE data of the CO2þ3DMA1P þ H2O system. For DEAB and 1DMA2P, the values of r and q were adjusted using Equation (37) and Equation (38), respectively. The other parameters were taken from the literature, but for CO2, the values of r and q proposed by Thomsen and Rasmussen [34] were first set in the model. However, these values did not give the appropriate results. The values of r and q for CO2 were very sensitive to the model results; therefore, the sensitivity analysis was performed and the best values presented in Table 3. The values for the binary interaction parameters, u0ji and uTji , were found using Equations (36)e(38) as well as from the literature. The values of u0ji and uTji for three studied systems are listed in Tables 4e9. In this study, 24 possible binary parameters were regressed for the CO2þ1DMA2P þ H2O system (the values are in bold in Tables 4 and 5). Owing to the unavailability of VLE data for 1DMA2P þ H2O and DEAB þ H2O systems, all 24 parameters for the CO2þ1DMA2P þ H2O system were regressed using Equation (38). For the CO2þDEAB þ H2O system, 22 parameters were regressed based on Equation (37) (the values are in bold in Table 6 and Table 7). For the CO2þ3DMA1P þ H2O system, 20 parameters were regressed, and two of the 20 parameters obtained from the binary system (3DMA1P þ H2O) include: u0H2 O3DMA1P and uTH2 O3DMA1P by the UNIQUAC model (the values are in bold in Tables 8 and 9). Other binary-interaction parameters in Tables (4e9) were set to a large value and zero without affecting the results according to the works proposed by Sadegh et al. [20] and Zaidy [13]. It should be noted that the regression of parameters was done all-in-one for all systems investigated in this study.

6. Results and discussion 6.2. Model validation 6.1. Model parameters and model validation The assessment of the thermodynamic behaviour for CO2 absorption by the above-mentioned amine systems was validated using the CO2 loading data in the amine systems. Then, the model was used to obtain profiles of chemical species presented in amine solution, Pxy profiles, activity coefficients and pH data. The model parameters, which were adjusted in this study, are

Results of presented model were validated by the MDEA, as a reference solvent, with an AARD of 12.21% obtained for 719 VLE experimental data of CO2þH2O þ MDEA system. Therefore, the obtained errors in this study are in agreement with other presented works in literature [19,20,39]. For instance, our model results were compared with the work of Biget et al. [19]. In this study, AARDs of 12.21%, 1.07%, and 10.47% respectively for CO2 partial pressure, total

64

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

Fig. 5. Validation of model for concentration of species in CO2-loaded DEAB solution using the NMR data reported by Shi et al. [29]: (a) concentrations in 0.5-M solution of DEAB, (b) concentrations in 1-M solution of DEAB, and (c) concentration in 1.5-M solution of DEAB.

pressure, and H E were obtained for MDEA system, while these deviations in the work of [19] were 15%, 12%, and 5%. The details of results for CO2þH2O þ MDEA system including CO2 loading of MDEA and speciation, H E data, the isothermal pressurecomposition (Pxy) profile, total pressure data, and model parameters are presented in supplementary information. By incorporating the obtained adjustable parameters into the model, the model validation of CO2 loading data was also confirmed using the experimental data obtained for the three systems presented in Table 1. This validation is shown in Fig. 1 for the three systems. A good agreement between the predicted data of CO2 loading of 1DAM2P, 3DMA1P, and DEAB, and corresponding experimental data was shown within AARDs of 13.39%, 16.50%, and 8.06%, respectively.

Fig. 6. Comparison between the model results and experimental data of pH of 1DMA2P solution [23,24]: (a) concentration of 4-M solution of 1DMA2P and (b) concentration of 1-M solution of 1DMA2P.

Fig. 7. Validation of model for concentration of species in CO2-loaded 1DMA2P solution using the NMR data reported by Liu et al. [24] for a 1-M concentration of 1DMA2P solution.

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

65

Fig. 8. Effect of temperature on the profiles of chemical species in CO2þ1DMA2P þ H2O system at temperatures of: (a) 301 K, (b) 313 K, and (c) 333 K.

Fig. 9. Effect of concentration on the profiles of chemical species at concentrations of: (a) 1 M, (b) 2 M, and (c) 3 M.

The capability of the model was tested to predict new experimental data, which did not consider in the model development stage. Fig. 2 shows the predicted data of CO2 loading for DEAB at a concentration of 3 M and at four different temperatures. The data

were predicted CO2 partial pressures ranging from 0.001 to 300 kPa. In addition, the results obtained at different temperatures for 3DMA1P at a concentration of 5 M, and for 1DMA2P at a concentration of 2.5 M are shown in Fig. 3 and Fig. 4, respectively. As

66

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

Fig. 11. Capability of model to predict profiles for activity coefficients in CO2þDEAB þ H2O system at concentration of 2 M and at a temperature of 313 K.

Fig. 10. Capability of model to predict profiles for chemical species CO2þ3DMA1P þ H2O system at concentrations of: (a) 2 M and (b) 4 M.

in

can be seen from Figs. 2e4, as the equilibrium temperature decreases, the CO2 loading of amine increases when the partial pressure increases, as is expected for CO2 absorption by amine solutions. Details of the calculations, such as CO2 loading data (experimental and calculated data) and the concentration (mole fraction) of all chemical species, as well as absolute deviations between results of the model and experimental data for CO2 loading of amines, are listed in Tables 10e12 for the CO2þH2O þ DEAB system, CO2þH2Oþ3DMA1P system, and CO2þH2Oþ1DMA2P system, respectively. 6.3. Assessment of NMR spectroscopic data and pH data The concentration of different chemical species is important in the simulation and optimization of CO2 removal processes by amine solutions. The determination of these species in the amine solution phase can be applied in the rate-based model [11]. In addition, a knowledge of pH data for amine solutions is required to control the foaming and to protect equipment from corrosion in CO2 removal processes. First, the results of the model for chemical species were validated by using NMR spectroscopic data for two available systems (CO2þH2O þ DEAB and CO2þH2Oþ1DMA2P). The predicted profiles versus experimental data for different concentrations of DEAB at a temperature of 298 K are shown in Fig. 5(aec). As seen from these figures, there are several deviations between the model results and experimental data. There is usually some degree of deviation in these complicated systems. For example, similar deviation trends

were reported by Sema et al. 40 for chemical species for the CO2þH2O þ DEAB system. In this study, we predicted the experimental data of pH for the CO2þH2Oþ1DMA2P system using the e-UNIQUAC model at two different concentrations (1 M and 4 M). Fig. 6 (a and b) shows the profiles for the pH of the 1DMA2P solution versus the CO2 loading of 1DMA2P at concentrations of 1 M and 4 M. As can be seen in the figure, the CO2 loading of amine increases with a decrease in the pH values. This results from the acidity of the solution, which indicates an increased concentration of Hþ with the CO2 loading. Fig. 7 shows the results obtained by the model for profiles of chemical species in the CO2þH2Oþ1DMA2P system, and the results of the model compared with NMR spectroscopic data reported by Liu et al. [24]. It is obvious from the figure that the free concentration of 1DMA2P decreases as the CO2 loading increases. This is believed to be because the protonated concentration (1DMA2PHþ ) increases gradually by increasing the CO2 loading as CO2 reacts with 1DMA2P. Based on Equation (2), the concentration of HCO 3 increases as the CO2 loading increases. However, the profile of CO2 3 is different from other concentration profiles. It increases initially for a low range of values of the CO2 loading, and reaches a maximum value (at approximately 0.5 mol CO2/mol is decreased by amine). After that, the concentration of CO2 3 increasing the CO2 loading. The reason for this behaviour is that at a lower range of CO2 loading values, an excess amount of 1DMA2P is presented and the pH values are also high (see Fig. 6), which causes an increase in the amount of CO2 3 . At higher CO2 loading values, by decreasing the concentration of 1DMA2P (this results in decreases by lower values of pH), the concentration of CO2 3 converting to the HCO 3 based on Equation (3) (the reverse of the dissociation of bicarbonate ion). The effect of temperature and amine concentration on the profiles of chemical species for the CO2þH2Oþ1DMA2P system was also studied. Fig. 8(aec) and Fig. 9(aec) show the effect of temperature and amine concentration on the profiles of chemical species, respectively. In Fig. 8(aec), the results were obtained for three different temperatures (301 K, 313 K, and 333 K) and at a concentration of 2 M. As can be seen from Fig. 8(aec), by increasing the temperature from 301 K to 333 K, the values for the concentrations of species decrease when the CO2 loading increases. Therefore, by increasing the temperature, the shapes of profiles are changed. For example, the bulge of profiles for CO2 3 decreases by increasing the temperature. In Fig. 9(aec), the results were obtained for three different concentrations (1 M, 3 M, and 5 M) and at

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

67

Fig. 13. Plot of predicted data for total pressure vs. experimental data [41] using UNIQUAC model for 3DMA1P þ H2O system.

loading values near saturation point is due to the equilibrium between unreacted CO2 in the liquid phase and CO2 in the vapour phase. This means that the combinatorial and residual terms are responsible for more contributions than the Debye-Hückel term in the e-UNIQUAC model. 6.4. Assessment of binary system results

Fig. 12. Comparison between the model results (lines) of HE and the experimental data (markers) [25] for three different temperatures 298 K, 313 K, and 333 K: (a) 3DMA1P þ H2O system and (b) 1DMA2P þ H2O system.

a temperature of 313 K. As can be seen from these figures, by increasing the concentration from 1 M to 5 M, the values for concentrations of species decrease when the CO2 loading increases. It should be noted that the profiles in the above-mentioned figures were calculated for CO2 partial-pressure values ranging from 0.0001 to 101 kPa. For the CO2þH2Oþ3DMA1P system, there are no NMR data in the literature to validate the model. However, the capability of the model in the prediction of chemical species in this system is shown in Fig. 10(a and b). These profiles were predicted by the model at two different concentrations (2 M and 4 M) at a temperature of 313 K. Fig. 11 shows the activity coefficients of all species presented in liquid phase obtained by the model at a temperature of 298 K, a concentration of 1 M, and at CO2 partial-pressure values ranging from 0.0001 to 30 kPa with respect to CO2 loading for the CO2þH2O þ DEAB system. From Fig. 11, it can be inferred that the values of all activity coefficients for ions are less than one. This is because the Debye-Hückel term has the largest contribution for ions in the e-UNIQUAC model. However, for molecules, the activity coefficients depend on the CO2 loading of amine. For water, the activity coefficient is constant over the entire CO2 loading of amine. This is expected because of the presence of a high concentration of water in the CO2þamine þ water system. For amine (DEAB), the activity coefficient decreases with an increase of the CO2 loading from about 1.1 to 0.7. For CO2, the activity coefficient increases with an increase of the CO2 loading from about 0.45 to 1.6. The increase in the activity coefficient for CO2 at higher CO2

The parameters for the binary system are used to reduce the number of interaction parameters in the ternary system, or to obtain the parameters ri and qi in the e-UNIQUAC model. As mentioned in the previous sections, the parameters of the model for the 3DMA1P þ CO2þH2O system were found by the regression of required UNIQUAC parameters using total pressure data of the 3DMA1P þ H2O system and H E data. In addition, the q value of amine was found from HE data for the 1DMA2P þ CO2þH2O system. Fig. 12 (a and b) shows the isothermal H E trends for 3DMA1P þ H2O and 1DMA2P þ H2O systems versus the mole fraction of amine. The results of H E were predicted for three different temperatures, i.e. 298 K, 313 K, and 333 K over the entire mole fraction of amine solution. The AARDs of 6.6% and 9.8% were obtained between the model results for HE and experimental data

Fig. 14. Pxy diagram of 3DMA1P þ H2O system at three different temperatures, i.e. 313 K, 333 K, and 353 K over the entire mole fraction of amine solution. Markers are experimental data reported by Belabbaci et al. [41].

68

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69

7. Conclusions In this study, we applied the e-UNIQUAC model to assess the thermodynamic behaviour of three systems. The parameters of the model for three amine systems were determined based on the different objective functions defined in this study using different experimental data available in the literature. To reduce the number of parameters in the model for a ternary system, the binaryinteraction parameters were obtained between species using the data of a binary system. The CO2 loading data of amines and all chemical species data were obtained, and predictions were made for CO2 loading data of amines for new observation data at different temperatures and concentrations. In addition, the assessment of NMR spectroscopic data and pH data for amine systems were done using the applied model. The effect of temperature and amine concentration on the profiles of chemical species were investigated, and results showed that by increasing the temperature and amine concentration, the values of the concentrations of chemical species decrease over the CO2 loading range of 0e1.0 mol CO2/mol 1DMA2P. In summary, the model predicted the experimental data for CO2 loading of DEAB, 1DMA2P, and 3DMA1P with average absolute relative deviations (AARDs) of 8.06%, 13.39%, and 16.50%, respectively. In addition, the Pxy and activity-coefficient profiles for the 3DMA1P þ H2O system were predicted, and the results showed that there is no azeotrope formation in the 3DMA1P þ H2O system. Acknowledgment We thank the Persian Gulf University and the Converged Energy Materials Research Center, Yonsei University, for the financial support, and for granting the required approval for this study. Appendix A. Supplementary data

Fig. 15. Predicted profiles of activity coefficients of 3DMA1P and water over the entire range of mole fraction values of 3DMA1P system at temperatures of (a) 313 K and (b) 353 K.

of H E , as reported by Nezamloo [25], for the 1DMA2P þ H2O and 3DMA1P þ H2O systems, respectively. As can be seen from Fig. 12, in the 1DMA2P þ H2O and 3DMA1P þ H2O systems, the minimum values of H E take place near the amine mole fraction value of 0.5. This shows that the reason for highest exothermic mixing process is the interaction between the amine group in amine and the hydroxide group in water. The cross plot for the calculated data of total pressure for the 3DMA1P þ H2O system and corresponding experimental data is shown in Fig. 13. An AARD of 2.84% was obtained by the UNIQUAC model between model results and experimental data for the total pressure data. Fig. 14 shows the Pxy diagram for the 3DMA1P þ H2O system at three different temperatures, i.e. 313 K, 333 K, and 353 K over the entire mole fraction of amine solution in the liquid and gas phases. Compared with experimental data of total pressure, the predicted profiles show that there is no formation of azeotrope in the 3DMA1P þ H2O system at different temperatures. However, for 1DMA2P þ H2O and DEAB þ H2O systems, the VLE experimental data for binary systems are unavailable in the literature, preventing further study into the formation of azeotrope. Fig. 15(a and b) shows the profiles of activity coefficients of 3DMA1P and water over the entire range of mole fractions of 3DMA1P at temperatures of 313 K and 353 K. As can be seen from this figure, at higher temperatures, the activity-coefficient values are higher at low concentrations of amine solution.

Supplementary data related to this article can be found at https://doi.org/10.1016/j.fluid.2018.05.026. References [1] A.E. Creamer, B. Gao, Carbon Dioxide Capture: an Effective Way to Combat Global Warming, Springer, 2015. [2] R.S. Haszeldine, Carbon capture and storage: how green can black be? Science 325 (2009) 1647e1652. [3] M. Mofarahi, Y. Khojasteh, H. Khaledi, A. Farahnak, Design of CO 2 absorption plant for recovery of CO 2 from flue gases of gas turbine, Energy 33 (2008) 1311e1319. [4] R. Idem, T. Supap, H. Shi, D. Gelowitz, M. Ball, C. Campbell, P. Tontiwachwuthikul, Practical experience in post-combustion CO 2 capture using reactive solvents in large pilot and demonstration plants, Int. J. Greenh. Gas. Contr. 40 (2015) 6e25. [5] M. Afkhamipour, M. Mofarahi, Review on the mass transfer performance of CO 2 absorption by amine-based solvents in low-and high-pressure absorption packed columns, RSC Adv. 7 (2017) 17857e17872. [6] Z.H. Liang, W. Rongwong, H. Liu, K. Fu, H. Gao, F. Cao, R. Zhang, T. Sema, A. Henni, K. Sumon, Recent progress and new developments in postcombustion carbon-capture technology with amine based solvents, Int. J. Greenh. Gas. Contr. 40 (2015) 26e54. [7] F.A. Chowdhury, H. Yamada, T. Higashii, K. Goto, M. Onoda, CO2 capture by tertiary amine absorbents: a performance comparison study, Ind. Eng. Chem. Res. 52 (2013) 8323e8331. [8] X. Zhang, C.-F. Zhang, S.-J. Qin, Z.-S. Zheng, A kinetics study on the absorption of carbon dioxide into a mixed aqueous solution of methyldiethanolamine and piperazine, Ind. Eng. Chem. Res. 40 (2001) 3785e3791. [9] T.N.G. Borhani, A. Azarpour, V. Akbari, S.R.W. Alwi, Z.A. Manan, CO 2 capture with potassium carbonate solutions: a state-of-the-art review, Int. J. Greenh. Gas. Contr. 41 (2015) 142e162. [10] A.V. Rayer, K.Z. Sumon, T. Sema, A. Henni, R.O. Idem, P. Tontiwachwuthikul, Part 5c: solvent chemistry: solubility of CO2 in reactive solvents for postcombustion CO2, Carbon Manag. 3 (2012) 467e484. [11] M. Afkhamipour, M. Mofarahi, Rate-based modeling and sensitivity analysis of a packed column for post-combustion CO2 capture into a novel reactive 1dimethylamino-2-propanol (1DMA2P) solution, Int. J. Greenh. Gas. Contr. 65 (2017) 137e148.

M. Afkhamipour et al. / Fluid Phase Equilibria 473 (2018) 50e69 [12] H. Suleman, A.S. Maulud, Z. Man, Review and selection criteria of classical thermodynamic models for acid gas absorption in aqueous alkanolamines, Rev. Chem. Eng. 31 (2015) 599e639. [13] S.A.H. Zaidy, Vapor-liquid Equilibrium in DEEA/H2O/CO2 System; Experiments and Modeling. Master Thesis. Trondheim, Norwegian University of Science and Technology, Norway, 2011. [14] M. Afkhamipour, M. Mofarahi, A modeling-optimization framework for assessment of CO2 absorption capacity by novel amine solutions: 1DMA2P, 1DEA2P, DEEA, and DEAB, J. Clean. Prod. 171 (2018) 234e249. [15] L. Faramarzi, G.M. Kontogeorgis, K. Thomsen, E.H. Stenby, Extended UNIQUAC model for thermodynamic modeling of CO 2 absorption in aqueous alkanolamine solutions, Fluid Phase Equilibria 282 (2009) 121e132. [16] U.E. Aronu, S. Gondal, E.T. Hessen, T. Haug-Warberg, A. Hartono, K.A. Hoff, H.F. Svendsen, Solubility of CO2 in 15, 30, 45 and 60 mass% MEA from 40 to 120 C and model representation using the extended UNIQUAC framework, Chem. Eng. Sci. 66 (2011) 6393e6406. [17] H. Mehdizadeh, M. Gupta, I. Kim, E.F. Da Silva, T. Haug-Warberg, H.F. Svendsen, AMPeCO2ewater thermodynamics, a combination of UNIQUAC model, computational chemistry and experimental data, Int. J. Greenh. Gas. Contr. 18 (2013) 173e182. [18] H. Mehdizadeh, M. Gupta, E.F. Da Silva, H.F. Svendsen, Representation of piperazine-CO2-H2O system using extended-UNIQUAC and computational chemistry, Energy Procedia 37 (2013) 1871e1880. [19] A. Biget, T. Neveux, J.P. Corriou, Y.L. Moullec, Development of a thermodynamic identification tool for CO2 capture by chemical absorption, Can. J. Chem. Eng. 93 (2015) 297e303. [20] N. Sadegh, E.H. Stenby, K. Thomsen, Thermodynamic modeling of CO 2 absorption in aqueous N-Methyldiethanolamine using Extended UNIQUAC model, Fuel 144 (2015) 295e306. [21] S. Singer, J. Nelder, Nelder-Mead algorithm, Scholarpedia 4 (2009) 2928. [22] H. Liu, H. Gao, R. Idem, P. Tontiwachwuthikul, Z. Liang, Analysis of CO 2 solubility and absorption heat into 1-dimethylamino-2-propanol solution, Chem. Eng. Sci. 170 (2017) 3e15. [23] H. Liu, X. Luo, Z. Liang, P. Tontiwachwuthikul, Determination of vaporeliquid equilibrium (VLE) plots of 1-Dimethylamino-2-propanol solutions using the pH method, Ind. Eng. Chem. Res. 54 (2015) 4709e4716. [24] H. Liu, R. Idem, P. Tontiwachwuthikul, Z. Liang, Study of ion speciation of CO2 absorption into aqueous 1-Dimethylamino-2-propanol solution using the NMR technique, Ind. Eng. Chem. Res. 56 (2017) 8697e8704. [25] A. Nezamloo, Measurements of the Molar Heat Capacity and the Molar Excess Enthalpy for Various Alkanolamines in Aqueous Solutions, in, Faculty of Graduate Studies and Research, University of Regina, 2013. [26] M. Afkhamipour, M. Mofarahi, Experimental measurement and modeling study on CO 2 equilibrium solubility, density and viscosity for 1dimethylamino-2-propanol (1DMA2P) solution, Fluid Phase Equil. 457 (2018) 38e51.

69

[27] C. Li, H. Liu, M. Xiao, X. Luo, H. Gao, Z. Liang, Thermodynamics and ANN models for predication of the equilibrium CO 2 solubility in aqueous 3dimethylamino-1-propanol solution, Int. J. Greenh. Gas. Contr. 63 (2017) 77e85. [28] T. Sema, A. Naami, R. Idem, P. Tontiwachwuthikul, Correlations for equilibrium solubility of carbon dioxide in aqueous 4-(diethylamino)-2-butanol solutions, Ind. Eng. Chem. Res. 50 (2011) 14008e14015. [29] H. Shi, T. Sema, A. Naami, Z. Liang, R. Idem, P. Tontiwachwuthikul, 13C NMR spectroscopy of a novel amine species in the DEABeCO2eH2O system: VLE model, Ind. Eng. Chem. Res. 51 (2012) 8608e8615. [30] T. Edwards, G. Maurer, J. Newman, J. Prausnitz, Vapor-liquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes, AIChE J. 24 (1978) 966e976. [31] O.A. Al-Rashed, S.H. Ali, Modeling the solubility of CO 2 and H 2 S in DEAeMDEA alkanolamine solutions using the electrolyteeUNIQUAC model, Separ. Purif. Technol. 94 (2012) 71e83. [32] I. Kim, H.F. Svendsen, E. Børresen, Ebulliometric determination of vapor liquid equilibria for pure water, monoethanolamine, n-methyldiethanolamine, 3-(methylamino)-propylamine, and their binary and ternary solutions, J. Chem. Eng. Data 53 (2008) 2521e2531. [33] M.L. Posey, G.T. Rochelle, A thermodynamic model of Methyldiethanolamine CO2 H2S water, Ind. Eng. Chem. Res. 36 (1997) 3944e3953. [34] K. Thomsen, P. Rasmussen, Modeling of vaporeliquidesolid equilibrium in gaseaqueous electrolyte systems, Chem. Eng. Sci. 54 (1999) 1787e1802. [35] D.S. Abrams, J.M. Prausnitz, Statistical thermodynamics of liquid mixtures: a new expression for the excess Gibbs energy of partly or completely miscible systems, AIChE J. 21 (1975) 116e128. [36] K. Thomsen, Modeling electrolyte solutions with the extended universal quasichemical (UNIQUAC) model, Pure Appl. Chem. (2005) 531. [37] M.W. Arshad, N. von Solms, K. Thomsen, Thermodynamic modeling of liquideliquid phase change solvents for CO 2 capture, Int. J. Greenh. Gas. Contr. 53 (2016) 401e424. [38] Y. Lacouture, D. Cousineau, How to use MATLAB to fit the ex-Gaussian and other probability functions to a distribution of response times, Tutorials. Quant. Meth. Psychol. 4 (2008) 35e45. [39] L. Faramarzi, G.M. Kontogeorgis, K. Thomsen, E.H. Stenby, Extended UNIQUAC model for thermodynamic modeling of CO2 absorption in aqueous alkanolamine solutions, Fluid Phase Equil. 282 (2009) 121e132. [40] T. Sema, A. Naami, Z. Liang, R. Idem, P. Tontiwachwuthikul, H. Shi, P. Wattanaphan, A. Henni, Analysis of reaction kinetics of CO 2 absorption into a novel reactive 4-diethylamino-2-butanol solvent, Chem. Eng. Sci. 81 (2012) 251e259. [41] A. Belabbaci, N.C.-B. Ahmed, I. Mokbel, L. Negadi, Investigation of the isothermal (vapourþ liquid) equilibria of aqueous 2-amino-2-methyl-1propanol (AMP), N-benzylethanolamine, or 3-dimethylamino-1-propanol solutions at several temperatures, J. Chem. Therm. 42 (2010) 1158e1162.