CO2 absorption using aqueous solution of potassium carbonate: Experimental measurement and thermodynamic modeling

Fluid Phase Equilibria 447 (2017) 132e141

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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

CO2 absorption using aqueous solution of potassium carbonate: Experimental measurement and thermodynamic modeling M.R. Bohloul a, M. Arab Sadeghabadi b, S.M. Peyghambarzadeh c, *, M.R. Dehghani b a

Young Researchers and Elite Club, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran Thermodynamic Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran, Iran c Department of Chemical Engineering, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 February 2017 Received in revised form 20 May 2017 Accepted 26 May 2017 Available online 1 June 2017

Potassium carbonate solution is a widely used solvent for CO2 removal due to its benefit in energy consumption and other economic concerns like degradation and corrosion problem. In this study, the solubility of CO2 in aqueous solutions of potassium carbonate was measured using pressure-decay method at temperatures of 313.15 K, 323.15 K, and 333.15 K, different pressures (up to 1.2 MPa), and different solution concentrations of 15 %wt., 20 %wt., and 30 %wt. Also, two equations of state were utilized to anticipate CO2 solubility in aqueous solution of potassium carbonate. The model is a combination of chemical equilibrium in the liquid phase and physical equilibrium between the liquid and vapor phases. For vapor-liquid equilibrium calculations, Peng-Robinson equation of state (PR-EOS) was used to present the fugacity coefficient in the vapor phase. The activity coefficient in the liquid phase was presented by Pitzer equation. Also, the values of the primitive interaction coefficients (lCO2 ;K þ and mCO2 ;CO2 ;K þ ) were optimized using the available literature data of the similar system. The results demonstrated that the performance of the thermodynamic modeling procedure was acceptable and the average absolute relative deviation (AARD) between the experimental and the predicted data was less than 2.7%. © 2017 Elsevier B.V. All rights reserved.

Keywords: Potassium carbonate solution Solubility of CO2 Pitzer equation Primitive interaction coefficients

1. Introduction Global warming and climate change are widely attributed to the build-up greenhouse gases such as CO2. As global warming becomes an important issue, many countries are looking to limit their emission of greenhouse gases, with carbon dioxide being the main focus. As a result of this, CO2 capture and sequestration is considered an important option to mitigate CO2 emissions in recent years [1]. In other words, the elimination of acidic gases such as CO2, H2S, and COS from gas streams played prominent role in the petrochemical plants, natural gas purification plants, fossil fuel-fired power plant, oil refineries, and steel and cement industry. There exists many applicable processes like chemical absorption, physical absorption, adsorption, and physical separation processes [2]. The common techniques for the removal of CO2 are based on the absorption processes. One of the chemical solvents for the gas sweetening process is aqueous potassium carbonate solution that is

* Corresponding author. E-mail address: [email protected] (S.M. Peyghambarzadeh). http://dx.doi.org/10.1016/j.fluid.2017.05.023 0378-3812/© 2017 Elsevier B.V. All rights reserved.

commonly used in hot carbonate processes especially for bulk CO2 removal. This is because of their appropriate cost, high absorption rate, and simple and convenient regeneration. The existence of chemical reactions between the solvent and the acidic gases leads to high absorption rate. In this process, low partial pressure of acidic gas is restricting operating condition to achieve high purity separation [3,4]. Thermodynamic modeling of the absorption process is one of most effective methods for process development, design, and optimization. Also, the modeling of electrolyte systems, such as aqueous potassium carbonate solution and CO2 system, is very important because this kind of systems are widely used in many processes. Rashed et al. [5] used the electrolyte-UNIQUAC model to demonstrate the thermodynamic behavior of CO2 and H2S in mixed DEA/MEA alkanolamine solutions to determine activity coefficients of liquid phase. Also, for determining the fugacity coefficient in the vapor phase, they used the Soave-Redlich-Kwong (SRK) equation. Their results showed that the model predictions were dramatically compatible with the experimental measurements. Vahidi et al. [6] studied the solubility of CO2 in N-methyldiethanolamine and piperazine aqueous solution using extended

M.R. Bohloul et al. / Fluid Phase Equilibria 447 (2017) 132e141

Debye-Hückel model. Also, the fugacity coefficient of CO2 was calculated by using the Peng-Robinson equation of state. According to their experimental data, they calculated the extended DebyeHückel interaction parameters at different temperatures (313 K 343 K) and concentrations (2.52 kmol/m3 - 4.28 kmol/m3). Their results showed that the average absolute relative deviation between the experimental data and the predicted values for all data points were 8.11%. Cullinane et al. [7] investigated the thermodynamic modeling of aqueous potassium carbonate, piperazine and carbon dioxide in a wetted wall column at different concentrations. They used ENRTL equation in order to determine the equilibrium condition of the solvent. Moreover, several thermodynamic models have been developed to represent the vapor-liquid equilibrium in mixed solvent, electrolyte systems and non-electrolyte systems, such as: CO2 in N-methyldiethanolamine solution using electrolyte PC-SAFT equation of state [8], CO2 and H2S in DIPA solutions using electrolyte NRTL model [9], CO2 in aqueous MEA solutions using electrolyte NRTL model [10], CO2 and H2S in aqueous alkanolamine solutions using Debye-Hückel model [11], CO2 in aqueous methyldiethanolamine solutions using Chain-SAFT equation of state [12], and CO2 in N-methyldiethanolamine solution using extended UNIQUAC model [13]. The first purpose of this study is to present the values of solubility of CO2 in aqueous solutions of potassium carbonate at different operating conditions. The second purpose is the thermodynamic modeling of this complicated electrolyte system. In this regard, Peng-Robinson equation of state and Pitzer correlation were applied to determine the fugacity coefficient in the vapor phase and the activity coefficient in the liquid phase, respectively. 2. Experimental 2.1. Materials The specifications of the chemicals used in this study were Table 1 The specifications of materials. Material

Purity

Company

Potassium carbonate (K2CO3) Carbon dioxide (CO2) Deionized water

99.5 %wt. 99.9 %mol. 99.9 %mol.

Merck Balon Gas Co. Behnogen Co.

133

summarized in Table 1. All the chemicals were utilized without future purification and their purities were obtained from suppliers. 2.2. Experimental apparatus and procedure Fig. 1 shows a schematic representation of the experimental apparatus. The experimental apparatus and procedure are similar to that reported in our previous papers and detail of experimental procedure are given in them [14e16]. In this apparatus, the inlet gas was preheated prior to entering the middle and absorption cells. The gas was sent into the middle cell to adjust the temperature. Afterward, it enters the absorption cell and the gas absorption process begins. The pressure change of CO2 during absorption course was measured and recorded, and the solubility of CO2 is evaluated by measuring the difference between initial and final pressures (equilibrium point) in the absorption cell. Before each experiment, residual gas was evacuated from apparatus by a vacuum pump. In all of the experiments, to rise the mass transfer rate and reduce the absorption time, a magnetic stirrer was used in absorption cell with constant speed. The main advantage of the middle cell is adjustment of gas temperature before absorption process. In order to control gas temperature during absorption process, the middle and absorption cells were placed in a water bath. In this study, experimental data on the solubility of CO2 in aqueous solutions of potassium carbonate was presented at temperatures of 313.15 K, 323.15 K, and 333.15 K, and K2CO3 concentrations of 15, 20 and 30 %wt. The real gas law is applied to determine the number of absorbed moles of CO2:

nCO2 ¼

Pi Vi Pf Vf V  ¼ G RTZi RTZf RT

Pi Pf  Zi Zf

! (1)

where nCO2 represents the number of moles of CO2 in the solvent, Pi and Pf are initial and final pressure (or equilibrium pressure, Peq) of CO2, Vi and Vf are initial and final volumes of the gas, and Zi and Zf are compressibility factors of CO2 at initial and final stage of the absorption process. Before and after each experiment, the volume of solvent is measured. The results showed that the volume of solvent has not changed, thus, Vi¼Vf¼VG. Compressibility factors were calculated using PR-EOS [17]. It should be mentioned that the advantages of PR-EOS is that it can accurately and easily represent the relation among temperature, pressure and phase compositions in binary and multicomponent system. The success of the equation

Fig. 1. Schematic diagram of the experimental apparatus.

134

M.R. Bohloul et al. / Fluid Phase Equilibria 447 (2017) 132e141

is restricted to the estimation of vapor pressure and it cannot always calculate the volumetric properties with high accuracy [18]. However, PR-EOS has been utilized in the literature for the calculation of phase equilibria [19,20,21and22] and its results was acceptable. Solution loading was measured using the following equation:

a1 ¼

nCO2 nK2 CO3

these repetitions showed that the Moffat's procedure has acceptable accuracy.

3. Experimental results 3.1. Kinetic of absorption

(2)

where a1 is the loading of CO2. The evaporation of water into gas phase is insignificant. This is due to the volume of solution is measured before and after each experiment and the results showed that the volume of solution has not changed. 2.3. Uncertainty analysis In order to reduce experimental error, uncertainty analysis was fulfilled by computing the error of the experimental data, based on procedure explained by Moffat [23]. According to the results of the uncertainty analysis, we figured out the measurement error of the solution loading was ±2%. Thereafter, some runs were repeated and the results showed that the maximum deviation from initial runs were less than 1.5%. Also,

Fig. 2 demonstrated the values of instantaneous pressure during absorption process of CO2 at different concentrations and initial pressures at the constant temperature of 313.15 K. According to Eq. (1), the number of absorbed moles of CO2 was calculated by measuring the difference between the initial and final pressures (final pressure is assumed to be the equilibrium pressure, Peq) in the absorption cell. The profound point to be mentioned is that the pressure reduction will continue until such time as the solution becomes saturated with gas and it is the emblem of equilibrium between the two phases. The time of equilibrium was different for each concentration of solution. As shown in Fig. 2, the time of equilibrium for concentration of 15 %wt. was about 110 min, 20 %wt. about 130 min, and 30 %wt. about 170 min. The reason for this difference is the concentration of solution and its absorption capacity. It is obvious that the CO2 absorption capacity and the equilibrium time rise when the

Fig. 2. Pressure reduction during absorption process at different concentrations of aqueous solution of potassium carbonate (15, 20 and 30 %wt) and different initial pressures (a: 14.30 (bar), b: 11.80 (bar), c: 8.60 (bar)) at 313.15 K.

M.R. Bohloul et al. / Fluid Phase Equilibria 447 (2017) 132e141

135

It should be mentioned that Peq in Figs. 3e6 is the equilibrium pressure at equilibrium point.

concentration of solution increases. 3.2. The equilibrium data The equilibrium data of CO2 capture using aqueous potassium carbonate solutions is presented in Figs. 3e5. Also, all the experimental data are reported in Table 2. In addition to the uncertainty analysis for the verification of accuracy, the present equilibrium data were compared with the published equilibrium data [24,25and26]. Although the range of operating condition was different, appropriate agreement can be seen. For all concentrations of solution, the results manifested that at a given pressure, the solution loading declines with the rise of temperature. Also, the solution loading increases with the rise of pressure at constant temperature. Fig. 6 illustrates that at a given temperature and pressure, the number of absorbed moles of CO2 rises with the increasing of concentration of potassium carbonate in the solution.

1.2

Solution loading of CO2 (α1)

1

4. Thermodynamic modeling In thermodynamic modeling of the CO2-K2CO3-H2O system, two types of equilibrium existed which consisted of chemical reaction and vapor-liquid equilibrium (VLE). Thus, these equations must be solved simultaneously.

4.1. Chemical reaction equilibrium As CO2 dissolved in the aqueous solution of potassium carbonate, the following equilibrium reactions occur [27,28]: þ  H2 O⇔HðaqÞ þ OHðaqÞ

(3)

þ CO2 þ H2 O⇔HðaqÞ þ HCO 3ðaqÞ

(4)

2 þ HCO 3ðaqÞ ⇔HðaqÞ þ CO3ðaqÞ

(5)

0.8

From these reactions, the following equilibrium relations can be written as:

0.6

K1 ¼

0.4

K2 ¼

T=313.15 K [This work] T=323.15 K [This wok]

aHþ aOH ðmHþ gHþ ÞðmOH gOH Þ ¼ aH2 O aH2 O aHþ aHCO3 aH2 O aCO2

T=333.15 K [This work]

0.2

T=333.15 K [24]

K3 ¼

T=353.15 K [24]

aHþ aCO2 3

aHCO3

0 0

0.2

0.4

0.6

0.8

1

1.2

Peq (MPa) Fig. 3. The equilibrium data for CO2 capture in aqueous solution of 15 %wt. K2CO3.

  ðmHþ gHþ Þ mHCO3 gHCO   3 ¼ aH2 O mCO2 gCO2

(7)

  ðmHþ gHþ Þ mCO2 gCO2 3 3   ¼ mHCO3 gHCO

(8)

3

where K is the equilibrium constant. The activities (ai) of aqueous solute species are usually defined on the basis of molalities. The activities (ai) are expressed by the following equation:

1.4

1.4

1.2

1.2

1

Solution loading of CO2 (α1)

Solution loading of CO2 (α1)

(6)

0.8

0.6

0.4

T=313.15 K [This work]

1

0.8

0.6

T=313.15 K [This work] T=323.15 K [This work]

0.4

T=333.15 K [This work]

T=323.15 K [This work] 0.2

T=373.2 K [25] 0.2

T=333.15 K [This work]

T=383.15 K [26]

T=333.15 K [24]

T=393.2 K [25]

0 0

0.2

0.4

0.6

0.8

1

1.2

Peq (MPa) Fig. 4. The equilibrium data for CO2 capture in aqueous solution of 20 %wt. K2CO3.

0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

Peq (MPa) Fig. 5. The equilibrium data for CO2 capture in aqueous solution of 30 %wt. K2CO3.

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M.R. Bohloul et al. / Fluid Phase Equilibria 447 (2017) 132e141

Table 2 Experimental equilibrium data for temperature (T), equilibrium pressure (Peq), aqueous solutions of K2CO3 (w2) and solution loading (a1) for the system CO2 (1) þ potassium carbonate (2) with standard uncertainty (u).a w2b

Peq(MPa)

a1

Peq(MPa)

T ¼ 313.15 K 15 %wt

20 %wt

30 %wt

a1

Peq(MPa)

T ¼ 323.15 K

expressed as [29]:

lnðKi Þ ¼ Ai þ

a1

T ¼ 333.15 K

1.09 1.02 0.9 0.75 0.64 0.51 0.18 0.1 0.05 0.03

1 0.99 0.98 0.95 0.93 0.89 0.6 0.52 0.48 0.45

1.09 0.97 0.88 0.75 0.62 0.53 0.19 0.11 0.09 0.05

0.95 0.94 0.94 0.91 0.88 0.83 0.57 0.53 0.48 0.45

1.12 0.97 0.89 0.8 0.64 0.55 0.13 0.09 0.06 0.03

0.82 0.81 0.81 0.75 0.7 0.68 0.54 0.5 0.46 0.41

0.93 0.82 0.73 0.65 0.53 0.41 0.15 0.1 0.05 0.03

1.25 1.25 1.22 1.19 1.1 1.02 0.77 0.73 0.71 0.68

0.99 0.92 0.81 0.73 0.54 0.41 0.15 0.1 0.06 0.03

0.98 0.96 0.95 0.91 0.84 0.79 0.62 0.57 0.55 0.53

0.93 0.9 0.81 0.7 0.54 0.39 0.13 0.09 0.07 0.04

0.79 0.79 0.78 0.76 0.71 0.65 0.55 0.5 0.44 0.4

0.78 0.65 0.59 0.49 0.32 0.23 0.15 0.1 0.04

1.16 1.15 1.13 1.1 1.05 1.02 0.97 0.94 0.88

0.81 0.66 0.57 0.47 0.35 0.25 0.16 0.09 0.05

1.1 1.1 1.08 1.04 1.01 0.95 0.94 0.91 0.86

0.79 0.64 0.55 0.45 0.33 0.24 0.17 0.1 0.06

1.07 1.05 1.03 1 0.95 0.91 0.9 0.85 0.82

a a1 ¼ mol CO2/mol K2CO3, Standard uncertainties u are u(T) ¼ 0.2 K, u(Peq) ¼ 0.001 MPa u(w2) ¼ 0.1 and u(a1) ¼ 0.02. b w2 is mass fraction of K2CO3 in aqueous solution.

0.25

Bi E þ Ci lnðTÞ þ Di T þ 2i T T

(10)

where Ai to Ei are constants, and T is temperature (in K). The values of these constants for the reactions were presented in Table 3. Also, based on these reactions, the following conservation relations may be obtained: (i) Charge balance:

mHþ þ mK þ ¼ mOH þ mHCO3 þ 2mCO2

(11)

3

(ii) Molality balance for carbon:

mHCO3 þ mCO3 þ mCO2 ¼

nCO2 þ mK2 CO3 mH2 O

(12)

(iii) Molality balance for Kþ [30]:

mK þ ¼ 2mK2 CO3

(13)

4.2. Vapor-liquid equilibrium The equilibrium between gaseous CO2 molecules and CO2 molecules in the aqueous solution of potassium carbonate can be expressed by Henry's law at given temperature and pressure [31]:

PyCO2 fCO2 ¼ xCO2 gCO2 HCO2

(14)

where P is total pressure, yCO2 is CO2 mole fraction in vapor phase, fCO2 is CO2 fugacity coefficient in the vapor phase, HCO2 is Henry's law constant of CO2 in the mixed solvent of water and potassium carbonate, xCO2 is CO2 mole fraction in the liquid phase, and gCO2 is the activity coefficient of CO2 in the liquid phase. The Henry's law constants are calculated using the following equation [32]:

Number of absorbed moles of CO2

0.2

HCO2 ¼ 0.15

0.1

15 %wt

0.05

20 %wt 30 %wt 0 0

0.2

0.4

0.6

0.8

1

1.2

Peq (MPa)

PCO2 xCO2

(15)

where PCO2 the equilibrium pressure of CO2 and xCO2 is the mole fraction of CO2 at equilibrium state. The values of Henry's law constant as a function of temperature for CO2 and aqueous solution of potassium carbonate are calculated using experimental data. It should be mentioned that the vapor phase is pure because the vapor pressure of water, based on Table 4, is very low in these operating conditions [33]. Also, before and after each experiment, the volume of solvent is measured and the results showed that the volume of solvent has not changed. Also, it shows that the water in the solution do not vaporize. As a result, the vapor phase has only one component (CO2). The vapor phase fugacity coefficient for a pure component in Eq. (14) is calculated using Peng-Robinson equation of state [14]:

Fig. 6. The number of absorbed moles of CO2 in aqueous solution of potassium carbonate at 313.15 K. Table 3 The values of the coefficients for the reaction equilibrium constants used in this work.

ai ¼ mi gi

(9)

which mi is molal concentration and gi is molal activity coefficient. The temperature dependence of the equilibrium constants is

Parameter

Ai

Bi

Ci

Di

Ei

Ref.

K1 K2 K3

140.93 1203.01 175.36

13445.90 68359.60 7230.60

22.47 188.44 30.65

0.0 0.20 0.01

0.0 4712910 372805

[29] [29] [29]

M.R. Bohloul et al. / Fluid Phase Equilibria 447 (2017) 132e141 Table 4 The values of vapor pressure of water at different temperatures [33]. Temperature (K)

ln gN ¼ 2

X

313.15 323.15 333.15

mn lNn þ 2

n

Vapor pressure (MPa)



0.007 0.012 0.019

137

X

X c

mn mc mNnc þ 6

c

þ3

    A Z þ 2:414B ln fCO2 ¼ Z  1  lnðZ  BÞ  pffiffiffi ln Z  0:414B 2 2B

X

m2a mNaa þ 6

c0 > c

(16)



mc mc0 mNcc0 þ 6

m2n mNnn

n



All the parameters in Eq. (16) are defined in Appendix A.

X

ma lNa þ 6

a

X

m2c mNcc

c

mc ma mNca þ 6

X

a

a

X n

mn ma mNna þ 3

X X

X

þ6

X

a

XX c

X X

XX n

a



mc lNc þ 2

a0 > a

c

ma ma0 mNaa0 þ 3

mN mn mNNn þ 6

nsN

X nsN

mn mn0 mNnn0

n0 sN

(21)

4.3. Activity coefficient model Activity coefficients are required in aqueous phase chemical equilibrium calculations and vapor-liquid equilibrium (VLE) calculations. In this study, Pitzer model was used to calculate these activity coefficients. According to Pitzer model, the activity coefficient of a cation ðgM Þ and the activity coefficient of an anion ðgX Þ are as follows [34]:

lnðgM Þ ¼ z2M F þ þ

X

XX

ma ð2BMa þZCMa Þþ

a

X

mc 24Mc þ

c

ma ma0 jMaa0 þzM

XX

a
c

X

! ma jMca

a

mc ma Cca

a

(17)

lnðgX Þ ¼ z2X F þ þ

X

XX c < c0

mc ð2BcX þ ZCcX Þ þ

c

X

ma 24Xa þ

a

mc mc0 jcc0 X þ jzX j

XX c

X

! mc jcXa

c

mc ma Cca

a

(18) The summations in Eqs. (17) and (18) over c and a are summations over the cations and the anions present in the solution, respectively. z is the charge of the ion considered in the unit of elementary units. Jijk is a model parameter that is assigned to each cation-cation-anion triplet and to each cation-anion-anion triplet. To facilitate direct programing, the remaining quantities in the activity coefficient equations are listed in Appendix B. Also, Pitzer model describes the activity of water in terms of the osmotic coefficient ð4Þ.

ð4  1Þ

X i

XX   X 2A4 I 1:5 mi ¼  þ mc ma B4ca þ ZCca þ 0:5 1 þ bI c a c0 ! X X X  mc mc0 44cc0 þ ma Jcc0 a þ c > c0



X

a

ma ma0

a > a0

44aa0

þ

X

!

a0

mc Jca0 a

c

(19) and the relation between the osmotic coefficient and the activity of water is:

X   ln aH2 O ¼ 4MwH2 O mi

(20)

i

For neutral species like CO2, the activity coefficient ðgN Þ is given by Ref. [35]:

This equation shows the activity coefficient of a neutral species in terms of all possible second order (l) and third order (m) primitive interaction coefficients [36]. For CO2 and aqueous solution of potassium carbonate system, Eq. (21) decreases to following equation:

ln gCO2 ¼ 2mK þ lCO2 ;K þ þ 6mCO2 mK þ mCO2 ;CO2 ;K þ

(22)

where lCO2 ;K þ and mCO2 ;CO2 ;K þ are primitive interaction coefficients that can be obtained from optimization of these parameters. These parameters are usually obtained through solubility of CO2 matching to experimental data. In these equations, a few parameters have not been defined. These parameters include temperature independent and temperature dependent parameters. In Table 5, the temperature independent parameters are summarized and the interaction parameters have been included in Table 6. 4.4. Thermodynamic modeling procedure The algorithm followed in the thermodynamic modeling of this study is shown in Fig. 7. The accuracy of the algorithm was examined by modeling of CO2 solubility in aqueous potassium carbonate solution. The procedure involves the calculation of the liquid phase composition (CO2 solubility) and the primitive interaction coefficients (lCO2 ;K þ and mCO2 ;CO2 ;K þ ). According to the model structure, the optimum values of the primitive interaction coefficients were Table 5 Mixture independent parameters of the Pitzer model [37]. Parameter

Numerical value

sq þ þ H ;K sq þ þ H ;H sq þ þ K ;K sq  OH ;OH sq  OH ;HCO 3 sq OH ;CO2 3 sq HCO ;CO2 3 3 sq HCO ;HCO 3 3 sq CO2 ;CO2 3 3 CH4 þ ;OH CH4 þ ;HCO 3 CH4 þ ;CO2 3 CK4þ ;OH CK4þ ;HCO 3 CK4þ ;CO2 3

0.005 0 0 0 0

All the JMMX

JK þ ;OH ;CO2 3 JK þ ;HCO3 ;CO2 3 Other JMXX

0.01 0.089 0 0 0 0 0 0.0041 0 0.0005 0 0.01 0.036 0

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M.R. Bohloul et al. / Fluid Phase Equilibria 447 (2017) 132e141

Table 6 Interaction parameters of Pitzer model [38].

bð0Þ MX

bð0Þ MX ð298:15KÞ

db dT

d2 b dT 2

H þ ; OH  H þ ; HCO 3 H þ ; CO2 3

0 0 0

0 0 0

0 0 0

K þ ; CO2 3

0.1298 0.01070 0.1288

0 0.001 0.0011

0 0 1.02E-5

bð1Þ MX

bð1Þ MX ð298:15 KÞ

db dT

d2 b dT 2

H þ ; OH  H þ ; HCO 3 H þ ; CO2 3

0 0 0

0 0 0

0 0 0

K þ ; CO2 3

0.32 0.0478 1.433

0 0.0011 0.00436

0 0 4.14E-5

K þ ; OH K þ ; HCO 3

K þ ; OH K þ ; HCO 3

*

db b ¼ bð298:15 KÞ þ dT ðT  298:15Þ þ 12

** All

ð0Þ

d2 b ðT dT 2

ð0Þ

ð1Þ

these parameters must be obtained by fitting experimental. So, they are quantity parameters and can positive or negative values [40]. For optimization of the primitive interaction coefficients and prediction of CO2 solubility, the experimental data was used. The optimized values of the primitive interaction coefficients at different concentrations of solution and temperatures are presented in Table 7. 5.2. Prediction of CO2 solubility

ð1Þ

 298:15Þ2 .

for this study are zero. bð2Þ MX

obtained by minimizing the average absolute relative deviation (AARD) with respect to mole fraction [39].

M acal  aexp 100 X AARDð%Þ ¼ M i¼1 aexp i

The main objective of this model is the prediction of CO2 solubility in aqueous potassium carbonate solution. Thus, to validate the applied method, the predicted solubility of CO2 in aqueous solution of potassium carbonate at different equilibrium pressures, temperatures and concentrations compared to the available experimental data of the similar system. Figs. 8e10, show the graphical comparison between the experimental solubility of CO2 in aqueous potassium carbonate solution and the predicted results. Also, such consistency was quantified by calculating the average absolute relative deviation (AARD) between the experimental data and the predicted values by Pitzer model which was less than 2.7%. Finally, the results showed that the applied method were validated and found to give acceptable accuracy.

(23) 6. Conclusion

where M is the number of data points, and acal and aexp are the calculated and the experimental values of the mole fraction of CO2, respectively. 5. Modeling results 5.1. Optimization of the primitive interaction coefficients The primitive interaction parameters are completely empirical

The solubility of CO2 in aqueous potassium carbonate solution was measured at different temperatures, pressures and solution concentrations. The experimental solution loading data showed that at a similar pressure, the solution loading decreased with increasing temperature. Also, the solution loading increased with increasing pressure at a given temperature. For the thermodynamic modeling of the hot potassium carbonate process, also known as Benfiled process, Pitzer model has been successfully applied to predict the CO2 solubility in aqueous solution of potassium

Fig. 7. Schematic overview of the model structure.

M.R. Bohloul et al. / Fluid Phase Equilibria 447 (2017) 132e141

1.2

Table 7 The optimized values of the primitive interaction coefficients (lCO2 ;K þ and mCO2 ;CO2 ;K þ ) at different concentrations (w2).a

w2 ¼ 15 wt% 313.15 323.15 333.15 w2 ¼ 20 wt% 313.15 323.15 333.15 w2 ¼ 30 wt% 313.15 323.15 333.15 a

lCO2 ;K þ

mCO2 ;CO2 ;K þ

AARD (%)

0.5015 0.2624 0.4932

0.1243 0.7361 0.0412

1.35 2.62 0.49

0.3930 0.3270 0.1133

0.0796 0.1311 0.6727

3.96 0.42 1.30

0.1374 0.0044 0.2241

0.1374 0.6110 0.2333

2.98 3.33 1.33

1.1

Solution loading of CO2 (α1)

T (K)

139

1

0.9

T=313.15 K

0.8

w2 is mass fraction of K2CO3 in aqueous solution.

T=323.15 K T=333.15 K

1.1

0.7 0

0.2

0.6

0.8

1

Peq (MPa)

1

Solution loading of CO2 (α1)

0.4

Fig. 10. Comparison of the model results (curves) and experimental data for aqueous solution of 30 %wt K2CO3.

0.9 0.8

carbonate at different operating conditions. The result showed that the average absolute relative deviation between the experimental and the predicted data was less than 2.7% and the calculation yielded satisfactory results.

0.7 0.6

Acknowledgement 0.5 T=313.15 K T=323.15 K

0.4

T=333.15 K 0.3

0

0.2

0.4

0.6

0.8

1

1.2

Peq (MPa) Fig. 8. Comparison of the model results (curves) and experimental data for aqueous solution of 15 %wt K2CO3.

The authors of this paper would like to appreciate the financial support provided by Islamic Azad University, Mahshahr branch for completing the research project entitled: “Experimental study of the effect of different additives to solvent on the thermodynamics and kinetics of carbon dioxide absorption“. Appendix A. The parameters of the vapor phase fugacity coefficient The all parameters in the vapor phase fugacity coefficient are defined as follows [14and17]:

1.4

A¼

aCO2 P R2 T 2

(A.1)

B¼

bCO2 P RT

(A.2)

Solution loading of CO2 (α1)

1.2

1

aCO2

0.8

! R2 Tc2 ¼ 0:45724 k Pc 

0.6

b ¼ 0:0778 T=313.15 K

0.4

T=323.15 K T=333.15 K

0.2 0

0.2

0.4

0.6

0.8

1

1.2

Peq (MPa) Fig. 9. Comparison of the model results (curves) and experimental data for aqueous solution of 20 %wt K2CO3.

RTc Pc

(A.3)

 (A.4)

i2 h  k ¼ 1 þ m 1  Tr 0:5

(A.5)

m ¼ 0:37464 þ 1:55226u  0:26992u2

(A.6)

where Tc and Pc are critical temperature and pressure, respectively, u is acentric factor. Tr ¼ T/Tc is reduced temperature. The critical properties and acentric factor for CO2 are listed in Table A1.

140

M.R. Bohloul et al. / Fluid Phase Equilibria 447 (2017) 132e141

Table A.1 The values of critical properties and acentric factor for CO2 [14]

ffij ¼ s qij þ E qij ðIÞ þ I E qij ðIÞ

Tc (K)

P (MPa)

u

304.12

7.374

0.225

The quantities in the activity coefficient equations are defined as follows [41]:

#  X XX 1 2  F ¼ A4 þ ln 1 þ bI2 mc ma B0 ca þ þ 1 b 1 þ bI 2 c a c0 X X X 0 0  mc mc 4cc0 þ ma ma 4aa0 1

a0

E

qij ¼

  zi zj   1 1   J xij  Jðxii Þ  J xjj 2 2 4I

(B.11)

where

I2

c > c0

(B.10)

4 CMX is another model parameter assigned to each cation-anion pair.s qij is a model parameter assigned to each cation-cation pair and to each anion-anion pair, andE qij is an electrostatic term.

Appendix B. The quantities in the activity coefficient equations

"

44ij ¼ s qij þ E qij ðIÞ

(B.9)

1

a > a0

(B.1)

xij ¼ 6zi zj A4 I 2

(B.12)

  i1 h  JðxÞ ¼ x 4 þ 4:581 x0:7231 exp 0:012x0:528

(B.13)

where b is a constant and I is the ionic strength (mole/kg solvent) [42]. Nomenclature

1X I¼ mi jzi j2 2 i Z¼

X

(B.2)

mi jzi j

(B.3)

i

 1  1 ð0Þ ð1Þ 2 BMX ¼ bMX þ bMX g a1 I 2 þ bMX g a2 I 2

(B.4)

in which

gðxÞ ¼

 2 1  ð1  xÞex x2

(B.5)

 1  1 ð1Þ 2 B0 MX ¼ bMX g0 a1 I 2 þ bMX g 0 a2 I 2

(B.6)

a bðnÞ ij sq ij

in which



2 1  1 þ x þ 12x2 ex g 0 ðxÞ ¼  x2



(B.7)

ð1Þ ð2Þ bð0Þ , bij and bij are interaction parameters. One of each parameter ij

is assigned to each cation-anion pair. The value of some other parameters of Pitzer model were presented in Table B1.

Table B.1 Pitzer's model parameters [41]. Parameter

Numerical value

A4 at 313.15 K A4 at 323.15 K A4 at 333.15 K b

0.3652 0.3483 0.3328 1.2 2 12

a1 a2 *

CMX ¼

1

2jzM zX j2

A4 Pc Tr T X xCO2 yCO2 zi

Jijk bij

fi ffij 44ij

qij

4

l m

The unit of the all parameters is (kg/mole)0.5. 4 CMX

ai CO2 CO2 3 4 CMX H2 O Hþ HCO 3 I Ki K2CO3 Mw mi M n P V

(B.8)

Peq Z R HCO2

activity carbon dioxide carbonate Pitzer's model parameter Water Hydron bicarbonate ionic strength on the molality scale(mol/kg solvent) equilibrium reaction constant potassium carbonate molecular weight (kg/kmol) molality of an ion i (mol/kg solvent) cation number of moles (mol) system pressure (bar) volume of the gas solution loading interaction parameter of cation-anion pair model parameter of cation-cation pair Debye-Hückel parameter critical pressure reduced temperature temperature (K) anion liquid phase mole fraction of CO2 vapor phase mole fraction of CO2 charge number of an ion i Pitzer model parameter Interaction parameter of Pitzer model vapor phase fugacity coefficient Pitzer model parameter Pitzer model parameter Pitzer model parameter osmotic coefficient primitive interaction coefficient primitive interaction coefficient equilibrium pressure (MPa) compressibility factor of CO2 universal gas constant Henry's law constant of CO2

M.R. Bohloul et al. / Fluid Phase Equilibria 447 (2017) 132e141 Eq ij

Tc

u

electrostatic term critical temperature acentric factor

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