Mathematical modeling and simulation of CO2 stripping from monoethanolamine solution using nano porous membrane contactors

International Journal of Greenhouse Gas Control 13 (2013) 1–8

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Mathematical modeling and simulation of CO2 stripping from monoethanolamine solution using nano porous membrane contactors Mehdi Ghadiri, Azam Marjani ∗ , Saeed Shirazian Islamic Azad University, Arak Branch, Department of Chemistry, Arak, Iran

a r t i c l e

i n f o

Article history: Received 31 July 2012 Received in revised form 22 November 2012 Accepted 28 November 2012 Available online 10 January 2013 Keywords: Membranes Mathematical modeling Mass transfer CFD Simulation

a b s t r a c t A novel model based on the finite element analysis by COMSOL software is built to simulate the flow and concentration in a membrane contactor for stripping of CO2 at high operating temperature. A CFD model was developed by solving the 2D Navier–Stokes equations as well as mass conservation equations for steady-state conditions in polymeric membrane contactors. The model prognosticates the velocity fields and the concentration of CO2 along the membrane under laminar flow regime. The membrane contactor was divided into three compartments, i.e. tube, shell and microporous membrane. The model findings for the stripping of CO2 using the membrane contactor were compared with the experimental data in order to validate the proposed mass transfer model and showed great agreement. Moreover, the simulation results showed that mass transfer resistance of gas phase has a minor effect on the CO2 stripping flux. Increasing temperature and liquid phase velocity cause enhancement of CO2 stripping flux. © 2012 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, the restriction of greenhouse gases emissions to the environment has become a main issue in industrial processes (Medina-Gonzalez et al., 2012; Porcheron and Drozdz, 2009). CO2 has been recognized as the most important greenhouse gas which is released mostly by industrial activities. Absorption of CO2 into amine solutions has been used as the most effective method for capture of CO2 . Back-absorption (stripping) of CO2 from amine solvents is a major section of absorption–stripping process. The traditional separation process for removal of CO2 from gas mixtures usually takes place in two separated contacting columns; the first for CO2 absorption and the second for CO2 back-absorption or stripping. These two units together form the CO2 removal plant. In fact, amine absorption system, for example Petronas Fertilizer Co. in Malaysia and Sleipner project in Norway are the most current CO2 capture plants. Therefore, amine absorption of CO2 has been attracted a lot of in-depth research (Chang and Shih, 2005; Koonaphapdeelert et al., 2009). Membrane contactors provide a dispersive-free contact between gas and liquid phases via a microporous membrane for the purpose of gas absorption or liquid extraction. In these novel devices, the interfacial area is known and constant. The latter

∗ Corresponding author. Tel.: +98 861 3663041; fax: +98 861 3663057. E-mail address: [email protected] (A. Marjani). 1750-5836/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijggc.2012.11.030

allows performance to be predicted more easily compared to conventional dispersed phase contactors. Moreover, the scale-up of membrane contactors can be practically linear (Mansourizadeh and Ismail, 2011; Yeon et al., 2003). The mass transfer through membrane contactors has been investigated by several researchers. The resistance-in-series model is usually applied to explain mass transfer in membrane contactors at steady-state condition and to determine the individual mass transfer coefficients for each phase (Gabelman and Hwang, 1999; Phattaranawik et al., 2005). The other modeling approach is based on solving conservation equations for the specie in all phases. In this method, conservation equations including continuity, energy and momentum equations are derived and solved by appropriate numerical method based on computational fluid dynamics (CFD) techniques. A number of authors have used this method to simulate the gas separation and solvent extraction carried out in HFMCs. Their results show good agreements between the experimental and simulation results (Al-Marzouqi et al., 2008a,b; Fasihi et al., 2012; Marjani and Shirazian, 2011; Rezakazemi et al., 2011a,b; Shirazian et al., 2009, 2011, 2012; Sohrabi et al., 2011). this work, modeling of CO2 stripping from In monoethanolamine (MEA) solution using polytetrafluoroethylene (PTFE) hollow-fiber membranes was investigated by numerical methods. In order to validate the simulation results, experimental data reported by Khaisri et al. (Khaisri et al., 2011) were used. The developed model considers both axial and radial diffusions in the tube, membrane, and shell parts of the membrane contactor.

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Nomenclature cross section of tube, m2 constant used for CO2 -MEA VLE correlation constant used for CO2 -MEA VLE correlation constant used for CO2 -MEA VLE correlation concentration, mol/m3 inlet concentration, mol/m3 concentration of CO2 in the tube side, mol/m3 concentration of CO2 in the shell side, mol/m3 outlet concentration of CO2 in the tube side, mol/m3 inlet concentration of CO2 in the tube side, mol/m3 concentration of any species in the tube side, mol/m3 Ci-shell concentration of any species in the shell side, mol/m3 Ci-membrane concentration of any species in the membrane, mol/m3 CMEA -tube MEA concentration, mol/m3 CMEA morality of MEA solution, mol/dm3 D diffusion coefficient, m2 /s diffusion coefficient of any species in the shell, m2 /s Di-shell Di-tube diffusion coefficient of any species in the tube, m2 /s Di-membrane diffusion coefficient of any species in the membrane, m2 /s DCO2 ,MEA diffusivity of CO2 in MEA solution, m2 /s DN2 O,MEA diffusivity of N2 O in MEA solution, m2 /s DCO2 ,H2 O diffusivity correlations of CO2 in water, m2 /s DN2 O,H2 O diffusivity correlations of N2 O in water, m2 /s diffusive flux of any species, mol/m2 s Ji L length of the fiber, m solubility, dimensionless m H Henry’s constant, kPadm3 mol−1 or dimensionless HCO2 ,MEA Henry’s constant of CO2 in MEA solution, kPadm3 mol−1 HN2 O,MEA Henry’s constant of N2 O in MEA solution, kPadm3 mol−1 HCO2 ,H2 O Henry’s constant correlations of CO2 in water, kPadm3 mol−1 HN2 O,H2 O Henry’s constant correlations of N2 O in water, kPadm3 mol−1 E H Excess Henry’s constant, kPadm3 mol−1 or dimensionless number of fibers, dimensionless n p pressure, Pa ∗ PCO CO2 partial pressure, bar A a b c C C0 CCO2 -tube CCO2 -shell Coutlet Cintlet Ci-tube

2

Q Qg Ql r R1 R2 R3  T u

vi

i y V Vz-shell Vz-tube z

volumetric flow rate, m3 /s gas flow rate, m3 /s liquid flow rate, m3 /s radial coordinate, m inner tube radius, m outer tube radius, m inner shell radius, m module inner radius, m temperature, K average velocity, m/s molar volume of pure solvent i mole fraction of solvent i mole fractions velocity in the module, m/s z-velocity in the shell, m/s z-velocity in the tube, m/s axial coordinate, m

F M

body force, N molecular weight

Greek symbols ε membrane porosity  tortuosity factor collision integral for molecular diffusion ˝D  viscosity, mPa s  characteristic length that depends on the intermolecular force  two-body interaction  module volume fraction density, kg/m3

fluid dynamic viscosity, kg/m s Abbreviations computational fluid dynamics CFD FEM finite element method monoethanolamine MEA HFMC hollow-fiber membrane contactor

The operating conditions that affect system performance such as gas and liquid velocities, rich solution temperature were studied to investigate the mass transfer of process. 2. Model development To predict transport of CO2 through the hollow-fiber membrane contactors in stripping process, a transport model was developed. In this study, stripping of CO2 from monoethanolamine (MEA) aqueous solution using N2 in a hollow-fiber membrane contactor (HFMC) was investigated theoretically. The model is based on “nonwetted mode”. This model considers that the gas phase fills the pores of membrane and liquid cannot penetrate membrane pores. The latter is due to hydrophobic nature of membrane used in the experiments. Fig. 1 shows a hollow fiber of length L and radius R (2D geometry) in a cylindrical coordinate system. The liquid stream containing aqueous solution of MEA was fed to the bottom of the module and flowed upwards. The gas stream was fed through the shell-side of contactor. Laminar parabolic velocity distribution is applied for the liquid flow in the tube side. The gas flow in the shell side was determined through solving the Navier–Stokes equations. Axial and radial diffusions inside the tube side, through the membrane, and within the shell side of the HFMC are considered to simulate the stripping of CO2 . 2.1. Equations of change The model is constructed based on the following assumptions: 1. Isothermal and steady-state conditions. 2. The Newtonian fluid with constant physical properties and transport coefficients. 3. Laminar flow with fully developed parabolic liquid velocity profile in the membrane contactor. 4. Henry’s law is applicable for gas–liquid interface. 5. Non-wetted condition. Mass transfer model is applied for a hollow fiber, as shown in Fig. 1b. As observed, the liquid phase containing dissolved CO2 passes with a fully developed laminar velocity inside the tube. To develop the transport model, the single fiber is divided into three sections, i.e. tube side, membrane, and shell side. The steady-state

M. Ghadiri et al. / International Journal of Greenhouse Gas Control 13 (2013) 1–8

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Fig. 1. A schematic diagram for the hollow-fiber membrane contactor used for stripping of CO2 .

2D mass balances are taken for all three sections of the fiber. The liquid phase enters to the tube side (at z = 0), while the gas phase (pure N2 ) is passed through the shell side (at z = L). CO2 is removed from the absorbent by diffusing through the liquid bulk, membrane and then are desorbed in the gas phase. 2.1.1. Equations of tube side The continuity equation for CO2 in desorption system can be expressed as (Bird et al., 2002) ∂Ci = −[(∇ .Ci V ) + (∇ .Ji )] ∂t

(1)

Di-tube

∂2 Ci-tube ∂2 Ci-tube 1 ∂Ci-tube + + r ∂r ∂r 2 ∂z 2



∂C = Vz-tube i-tube ∂z

(2)

where i refers to CO2 . r and z also refer to radial and axial coordinates, respectively. It should be noted that the convection in r-direction is omitted in Eq. (2) because the velocity is considered in z-direction and r-velocity is negligible in the tube side of contactor. Velocity distribution in the tube side is assumed to follow Newtonian laminar flow (Bird et al., 2002):



Vz-tube = 2u 1 −

 r 2  R1

(3)

where u (m/s) is average velocity in the tube side and R1 is the inner radius of fibers (see Fig. 1b). The boundary conditions assumed for the tube side are as follows: at z = 0, CCO2 -tube = CCO2 ,0 (Intel boundary) at z = L, Convective flux at r = 0,

∂CCO2 -tube ∂r

= 0 (Symmetry)

at r = R1 , CCO2 -tube =

CCO2 -membrane m (Henrys’ law)

2.1.2. Equations of membrane The steady-state continuity equation for transport of CO2 through the pores of membrane may be written as



Di-membrane

∂2 Ci-membrane ∂2 Ci-membrane 1 ∂Ci-membrane + + 2 r ∂r ∂r ∂z 2



=0 (7)

where Ci (mol/m3 ), Ji (mol/m2 s), V (m/s), and t (s) are concentration, diffusive flux of CO2 , velocity and time, respectively. Fick’s law of diffusion is used to calculate the diffusive fluxes of CO2 in the tube section. Therefore, the steady-state continuity equation for transport of CO2 in the tube side may be written as



boundary condition for mass transfer equations postulates that all mass passing through this boundary is convection-dominated. The latter means that any mass flux due to diffusion across this boundary is zero.

(4)

(5) (6)

m is the solubility of gas in the liquid solvent that are given in Appendix A. It should be pointed out that the convective flux

It should be noted that transport of CO2 through the membrane pores is considered to be due to diffusion alone. Boundary conditions are given as at r = R1 , CCO2 -membrane = m (Henrys’ law) × CCO2 -tube

(8)

at r = R2 , CCO2 -membrane = CCO2 -shell

(9)

CO2 effective diffusivity in membrane pores is calculated from the following equation (Bird et al., 2002): DCO2 -membrane = DCO2 -N2

ε

(10)



where ε and  denote membrane porosity and tortuosity, respectively. 2.1.3. Equations of shell side The steady-state continuity equation for CO2 transfer in the shell side of the membrane contactor in cylindrical coordinate is calculated using Fick’s law of diffusion for prediction of diffusive flux:



DCO2 -shell = Vz-shell

∂2 CCO2 -shell ∂r 2 ∂CCO2 -shell ∂z

∂2 CCO2 -shell 1 ∂CCO2 -shell + + r ∂r ∂z 2



(11)

Velocity distribution in the shell side is characterized by numerical solution of the Navier–Stokes equations. Therefore, the momentum and the continuity equations should be coupled and solved to calculate concentration distribution of CO2 in all sections of membrane contactor. The Navier–Stokes equations depict flow in viscous fluids through momentum balances for CO2 . They also

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Table 1 The characteristics of the hollow-fiber contactor and operational conditions used in simulation (Khaisri et al., 2011; Koonaphapdeelert et al., 2009). Parameter

Symbol

Value

Membrane module Fiber inner radius (mm) Fiber outer radius (mm) Fiber porosity (%) Fiber tortuosity Module inner radius (mm) Fiber length (cm) Number of fibers Pore diameter (␮m) Shell side geometric void fraction Pressure (atm) Temperature (K) Gas flow rate (cm/s) Liquid flow rate (cm/s) Carbonation ratio Partial pressure (bar) (Appendix A.5)

Markel Corporation R1 R2 ε ␶  L n d – p T Qg Ql ␣ ∗ PCO

– 0.813 1.0035 0.23 3 12 14 or 28 50 0.161 65.03 1 atm 90–100 10–18 0.5–3.5 0.45 0.78

2

assume that density and viscosity of the modeled fluids are constant, which yields to a continuity condition. The Navier–Stokes equations are defined as follows (Bird et al., 2002):

∂Vz − ∇ . (∇ Vz + (∇ Vz )T ) + (Vz .∇ )Vz + ∇ p = F ∇ .Vz = 0 ∂t

(12)

where Vz , ␩, ␳, p, and F denote velocity vector in z-direction (m/s), fluid dynamic viscosity (kg/m s), density (kg/m3 ), pressure (Pa), and body force term (N), respectively. The boundary conditions for the shell side are given as Fig. 2. The meshes generated to simulate the CO2 stripping behavior in HFMCs.

• Continuity equation at r = R2 , CCO2 -shell = CCO2 -membrane at r = R3 ,

∂CCO2 -shell ∂r

= 0 (Symmetry)

(13)

3. Results and discussion

(14)

3.1. Concentration distribution of CO2 in the HFMC

at z = 0, Convective flux

(15)

at z = L, Concentration

(16)

• Momentum equation at r = R2 , Wall, No slip

(17)

at r = R3 , Wall, No slip

(18)

at z = 0, Outlet

(19)

at z = L, Inlet

(20)

The characteristics of the hollow-fiber contactor and operational conditions are presented in Table 1. 2.2. Numerical solution of model equations The model equations considering the boundary conditions were solved using COMSOL Multiphysics version 3.5 software. The latter utilizes finite element method (FEM) for numerical solutions of the differential equations developed in the mathematical model. The numerical solver of UMFPACK version 4.2 was used as linear solver in the calculations. This solver is well suited for solving stiff and non-stiff non-linear boundary value problems. A system with the specifications of RAM 4.00 GB (2.98 GB usable) and Intel® CoreTM i5CPU M 480 @ 2.67 GHz and 32-bit operating system was used to solve the model equations. Fig. 2 demonstrates the mesh used to determine the CO2 stripping behavior in the contactor. It should be pointed out that the COMSOL mesh generator creates triangular meshes that are isotropic in size.

Numerical solution of model equations results in determining the concentration distribution of CO2 in the membrane contactor. The surface concentration distribution of CO2 in all sections of membrane contactor is illustrated in Fig. 3. The concentration is shown in dimensionless form, i.e. C/C0 . Fig. 3 also shows the total flux (diffusive and convective) of CO2 in the tube, porous membrane and shell side of the contactor. As observed, the rich MEA solution passes from one side of the contactor (z = 0) where the concentration of CO2 is the highest (C0 ). The stripping phase (N2 ) flows from the other side (z = L) where the concentration of CO2 is considered to be negligible. As the MEA solution flows through the tube side, it moves to the membrane pores due to the concentration gradient, and then it is desorbed by the moving gas phase. The CO2 is transferred in the tube side by convection and diffusion mechanisms. Diffusive flux causes the transport of CO2 toward the membrane–tube interface. 3.2. Velocity field The velocity field and profile in the shell side of the membrane contactor are shown in Figs. 4 and 5, where the stripping gas phase passes. It is notable that the velocity profile in the shell side of the membrane contactor was simulated by solving the Navier–Stokes equations. It is clearly observed that the velocity profile in the shell side is almost parabolic with a mean velocity increasing with membrane length because of continuous permeation of CO2 from feed phase into the shell side. Figs. 4 and 5 also reveal that at the inlet regions in the shell side, the velocity is not fully developed. After a short distance from the inlet of shell side, the velocity profile becomes fully developed (see Fig. 5). The latter confirms that the

M. Ghadiri et al. / International Journal of Greenhouse Gas Control 13 (2013) 1–8

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Fig. 5. Velocity profile in the shell side along the membrane length. Liquid phase velocity = 1 cm/s; gas phase velocity = 10 cm/s; CO2 inlet concentration = 26.56 mol/m3 , temperature = 373 K, pressure = 1 atm. Fig. 3. Concentration distribution of CO2 (C/C0 ) in the HFMC. Feed velocity = 1 cm/s, gas phase velocity = 10 cm/s, inlet concentration of solute = 26.57 mol/m3 , temperature = 373 K, pressure = 1 atm.

developed model considers the entry effects on the hydrodynamics of fluid flow in the shell side of contactor. 3.3. Concentration profile in radial direction Radial concentration profile of CO2 in all sections of membrane contactor is depicted in Fig. 6. It can be observed that the radial

Fig. 4. Velocity field in the shell side of HFMC. Liquid phase velocity = 1 cm/s, gas phase = 10 cm/s, inlet concentration of solute = 26.56 mol/m3 , temperature = 373 K, pressure = 1 atm.

concentration changes in the membrane and shell sides are not appreciable. On the other hand, a sharp decrease in concentration of CO2 can be seen in the tube side of the module, as illustrated in Fig. 6. The reason for such behavior is due to that fact that diffusion coefficients of CO2 inside the membrane pores and also the gas phase are much higher than the diffusion coefficient in the tube side (liquid phase). Thus mass transfer resistance to CO2 transport in the membrane and shell sides is much smaller than that in the liquid phase. Khaisri et al. (Khaisri et al., 2011) showed experimentally that the liquid phase mass transfer resistance accounted for roughly 90% of the overall mass transfer resistance. Therefore, mass transfer resistance of liquid phase is the controlling resistance in the system. The dimensionless CO2 concentration along the length of the module for different values of MEA solution velocities is presented in Fig. 7. As expected, the increase in the MEA solution velocity reduces the residence time of liquid phase in the module, which in turn reduces the concentration gradient along the length of the module (Al-Marzouqi et al., 2008a).

Fig. 6. CO2 concentration in the radial direction at the middle of membrane contactor (z/L = 0.5) for CO2 –MEA system.

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Fig. 9. Effect of stripping gas velocity on CO2 desorption flux. Liquid phase velocity = 1 cm/s, temperature = 373 K.

Fig. 7. CO2 concentration in the axial direction at different values of MEA solution velocity for CO2 –MEA system.

Figs. 9 and 10. Comparisons were carried out for a wide range of liquid and gas phase velocities. The desorption flux of CO2 (J) which were used to evaluate membrane performance can be calculated as (Khaisri et al., 2011) G(Yout − Yin ) A

3.4. Effect of temperature on CO2 desorption

J=

The influence of feed temperature on CO2 desorption flux is shown in Fig. 8. As it can be seen from the figure, the CO2 stripping flux increases with increasing operating temperature in the membrane contactor. Temperature has influence on physical and chemical parameters including the CO2 equilibrium partial pressure, chemical reaction equilibrium constant and diffusion coefficient. Increasing temperature would increase the equilibrium partial pressure of CO2 exponentially (see Eq. (A.16)). Consequently, the equilibrium constant decreases due to the enhancement of equilibrium partial pressure of CO2 . The latter confirms that increasing operating temperature leads to an increase in the driving force for stripping of CO2 from the MEA solution (Khaisri et al., 2011).

where G is the gas flow rate, Y is the mole ratio of CO2 in the gas phase, and A is the mass transfer area. The stripping flux of CO2 as a function of gas velocity for liquid temperature of 373 K is presented in Fig. 9. As seen, the changes in CO2 desorption flux with increasing gas velocity are negligible and desorption flux remains almost constant over a wide range of gas velocities. This reason for this observation is due to that the main mass transfer resistance which is located in the liquid phase and gas phase has negligible effect on mass transfer of CO2 (Khaisri et al., 2011). Effect of liquid velocity on desorption flux is also represented in Fig. 10. It is clearly seen that an increase in the liquid phase velocity leads to increase in the CO2 desorption flux. This could be attributed to this fact that an increase in the liquid velocity leads to a decrease in the liquid film mass transfer resistance. Therefore, desorption flux of CO2 and the overall mass transfer coefficient increase with increment of liquid velocity (Khaisri et al., 2011). Moreover, Figs. 9 and 10 reveal that the modeling findings are in

3.5. Model validation To validate the mass transfer model developed in this study, CO2 desorption flux calculated using the mathematical model developed here were compared with the experimental data reported by Khaisri et al. (Khaisri et al., 2011). The results are shown in

Fig. 8. Effect of rich solution temperature on CO2 desorption flux (MEA concentration = 3.0 kmol/m3 , gas phase velocity = 10 cm/s).

(21)

Fig. 10. Effect of MEA solution velocity on CO2 desorption flux. Gas phase velocity = 10 cm/s, temperature = 373 K.

M. Ghadiri et al. / International Journal of Greenhouse Gas Control 13 (2013) 1–8

good agreement with the experimental data for a wide range of gas and liquid velocities. 4. Conclusions A mass transfer model for simulation of membrane-based stripping unit was developed to study recovery of CO2 from CO2 -loaded monoethanolamine solutions. The model was based on solving the conservation equations for CO2 in three sections of the single fiber. The finite element analysis was adopted to solve the differential equations of mass transfer. The model prognosticates the velocity fields and the concentration of CO2 in the membrane contactor. The simulation results revealed that the CO2 stripping flux increased with an increase in the liquid velocity and feed temperature. Moreover, the gas phase mass transfer resistance in gas stripping membranes was found to have a minor effect on the CO2 desorption flux. Moreover, the simulation results for the stripping of CO2 using the membrane contactor were compared with the experimental data in order to validate the developed mass transfer model and showed good agreement. Appendix A. A.1. Diffusion coefficient of CO2 in the MEA solution



DCO2 ,MEA = DN2 O,MEA



DCO2 ,H2 O

(A.1)

DN2 O,H2 O

where DCO2 and DN2 O are the diffusivity of CO2 and N2 O in MEA solution, respectively. The diffusivity correlations of CO2 and N2 O in water were proposed (Versteeg and Van Swaalj, 1988): DCO2 ,H2 O = 2.35 × 10−2 exp DN2 O,H2 O = 2.35 × 10−2 exp

 −2119 

(A.2)

T

 −2371 

(A.3)

T

where the diffusivity is in the unit of cm2 /s and T is temperature in Kelvin. The N2 O diffusivity in MEA solution correlation was presented by Ko et al. (Ko et al., 2000). The correlation is shown as follows [19]: 2 DN2 O,MEA = (5.07 × 10−2 + 8.65 × 10−3 CMEA + 2.78 × 10−3 CMEA )

× exp

 −2371 + (−93.4C

MEA )

T



(A.4)

where DN2 O,MEA is the diffusivity of N2 O in MEA solution in cm2 /s, CMEA is the molarity of MEA solution in (mol/dm3 ), and T is the temperature in Kelvin. A.2. CO2 diffusivity in N2 CO2 diffusivity in N2 gas is calculated from the following equation (Welty et al., 2001): DAB =

0.001858T 3/2 [(1/MA ) + (1/MB )] 2 ˝ PAB D

A.3. Density and viscosity of gas mixtures In order to calculate Reynolds and Schmidt numbers, the density and viscosity of gas mixtures are also needed. The density of gas mixtures can be estimated by imposing ideal gas law. The viscosity for binary gas mixtures of A and B can be calculated from the following equations (Welty et al., 2001): AB =

yA A yB B + yA + yB AB yB + yA BA

−1 = AB = BA

(1/2)

(A.5)

where the units of DAB are cm2 /s, P is the pressure in atm, T is the temperature in Kelvin, MA and MB are the molecular weight of A and B, respectively. ␴AB is the characteristic length that depends on the intermolecular force. D is the collision integral for diffusion.

(A.6)

 M 1/2 B

(A.7)

MA

where ␮AB , ␮A , and ␮B are the viscosities (mPa s) of gas mixtures and pure component A and B, respectively. yA and yB are mole fractions of A and B, respectively. MA and MB are the molecular weight of component A and B, respectively. A.4. Henry’s constant (H) The Henry’s constant is also important in simulation of gas stripping. Due to the chemical reaction between CO2 and amines, the N2 O analogy is used to determine the free-gas solubility of CO2 in amine solution (Versteeg and Van Swaalj, 1988).



The diffusion coefficient of CO2 in the MEA solution can be calculated from N2 O analogy. The N2 O analogy can be written for the CO2 diffusivity in amine solutions as follows (Versteeg and Van Swaalj, 1988):

7

HCO2 ,MEA = HN2 O,MEA



HCO2 ,H2 O

(A.8)

HN2 O,H2 O

HCO2 ,H2 O = 2.82 × 106 exp HN2 O,H2 O = 8.55 × 106 exp

 −2044  T

 −2284  T

(A.9) (A.10)

where HCO2 ,MEA and HN2 O,MEA are the Henry’s constant of CO2 and N2 O, respectively, in MEA solution. The units of HN2 O,MEA and HN2 O,H2 O are kPadm3 mol−1 and T is in Kelvin. Tsai et al. (Tsai et al., 2000) used a semi empirical model of excess Henry’s constant to correlate the solubility of N2 O in amine solutions. The solubility of N2 O in amine solution can be calculated from the following equations: ln H1,S = H E +

3 

i ln H1,i

(A.11)

i=2

Here the subscript 1 stands for N2 O absorbed gas, 2 stands for pure amine, 3 stands for water, and S stands for amine aqueous solution. HE is the excess Henry’s constant and i is the volume fraction of solvent i. The volume faction and excess Henry’s constant are defined as a function of volume fraction: v (A.12) i = 3 i i v i=2 i i H E = 2 3 23

(A.13)

where vi is the molar volume of pure solvent i, ␹i is the mole fraction of solvent i, and ␭23 is the two-body interaction parameter for the MEA-H2 O: 23 = 4.793 − 7.44 × 10−3 T − 2.2013

(A.14)

where 3 is the volume faction of water. The Henry’s constant for N2 O in pure MEA can be calculated from the following expression: HN2 O,MEA = 1.207 × 105 exp

 −1136.5  T

(A.15)

where the units are in kPadm3 mol−1 and T is the temperature in kelvin.

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Table A.1 The parameters used for CO2 -MEA VLE correlation (Koonaphapdeelert et al., 2009). Parameter

Value

a b c

−47.91 + 112.8␣ 0.7615 − 1.668␣ −0.0029 + 0.007␣

A.5. Calculation of equilibrium CO2 partial pressure Equilibrium CO2 partial pressure is estimated from the equation below (Koonaphapdeelert et al., 2009): ∗ PCO = exp[a + bT + cT 2 ]/760 2

(A.16)

∗ PCO 2

is the partial pressure(bar) and T is liquid temperature where (◦ C). The constants a, b, and c are defined in Table A.1. References Al-Marzouqi, M., El-Naas, M., Marzouk, S., Abdullatif, N., 2008a. Modeling of chemical absorption of CO2 in membrane contactors. Separation and Purification Technology 62, 499–506. Al-Marzouqi, M.H., El-Naas, M.H., Marzouk, S.A.M., Al-Zarooni, M.A., Abdullatif, N., Faiz, R., 2008b. Modeling of CO2 absorption in membrane contactors. Separation and Purification Technology 59, 286–293. Bird, R.B., Stewart, W.E., Lightfoot, E.N., 2002. Transport Phenomena. John Wiley & Sons, New York. Chang, H., Shih, C.M., 2005. Simulation and optimization for power plant flue gas CO2 absorption-stripping systems. Separation Science and Technology 40, 877–909. Fasihi, M., Shirazian, S., Marjani, A., Rezakazemi, M., 2012. Computational fluid dynamics simulation of transport phenomena in ceramic membranes for SO2 separation. Mathematical and Computer Modelling 56, 278–286. Gabelman, A., Hwang, S.-T., 1999. Hollow fiber membrane contactors. Journal of Membrane Science 159, 61–106. Khaisri, S., deMontigny, D., Tontiwachwuthikul, P., Jiraratananon, R., 2011. CO2 stripping from monoethanolamine using a membrane contactor. Journal of Membrane Science 376, 110–118. Ko, J.-J., Tsai, T.-C., Lin, C.-Y., Wang, H.-M., Li, M.-H., 2000. Diffusivity of nitrous oxide in aqueous alkanolamine solutions. Journal of Chemical & Engineering Data 46, 160–165.

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