CFD simulation of natural gas sweetening in a gas–liquid hollow-fiber membrane contactor

Chemical Engineering Journal 168 (2011) 1217–1226

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CFD simulation of natural gas sweetening in a gas–liquid hollow-fiber membrane contactor Mashallah Rezakazemi, Zahra Niazi, Mojtaba Mirfendereski, Saeed Shirazian, Toraj Mohammadi ∗ , Afshin Pak Research Centre for Membrane Separation Processes, Faculty of Chemical Engineering, Iran University of Science and Technology (IUST), Narmak, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 19 October 2010 Received in revised form 9 February 2011 Accepted 10 February 2011 Keywords: Natural gas sweetening Numerical simulation Hollow-fiber membrane contactor Amine aqueous solution

a b s t r a c t Chemical absorption of CO2 and H2 S from natural gas was studied theoretically and experimentally using a hollow-fiber membrane contactor (HFMC) in this work. A 2D mathematical model was proposed to study simultaneous transport of CO2 and H2 S through a HFMC using methyldiethanolamine (MDEA) as chemical absorbent. The model considers axial and radial diffusion in the HFMC. It also considers convection in tube and shell sides with chemical reaction. CFD techniques were applied to solve the model equations involving continuity and momentum equations. Modeling predictions were validated with the experimental data and it was found that there is a good agreement between them for different values of gas and liquid velocities. The simulation results showed that the removal of H2 S with aqueous solution of MDEA was very high and indicated almost total removal of H2 S. Experimental and simulation results indicated that the membrane module was very efficient in the removal of trace H2 S at high gas/liquid flow ratio. The removal of H2 S was almost complete with recovery of higher than 96%. The proposed model is able to predict the performance of CO2 and H2 S absorption in HFMCs. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Removal of sour gas impurities such as H2 S and CO2 from gas mixtures is of vital importance for chemical industries. Natural gas (NG) usually contains H2 S and CO2 as major gas impurities. In order to use NG for energy generation, H2 S and CO2 must be removed from NG. CO2 is an unwanted component in NG and can reduce its energy efficiency. H2 S is a toxic and corrosive gas and also known as a poison. [1]. Therefore, from environmental view-point, it is important to separate CO2 and H2 S from NG. Current H2 S and CO2 separation processes include absorption, adsorption, cryogenic and membrane techniques [2]. Conventional processes suffer from many problems such as flooding, foaming, entraining, channeling, and high capital and operating cost. Therefore, many researchers have studied the possibility of enhancing the efficiency of these processes [2]. Recently, new processes using gas–liquid membrane contactors as gas absorption devices have been a subject of great interest. In these processes, the membrane contactor mainly acts as a physical barrier between two phases (gas and liquid) without significant effect in selectivity, i.e. the membrane does not change the partition coefficient. Being the two phases separate by the membrane,

∗ Corresponding author. Tel.: +98 21 789 6621; fax: +98 21 789 6620. E-mail address: [email protected] (T. Mohammadi). 1385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cej.2011.02.019

there is no phases mixing and dispersion phenomena do not occur. The gases are transferred from one phase to the other only by diffusion. The membranes are usually mesoporous and symmetric and are always hydrophobic. Hydrophobicity of gas–liquid membrane contactors increases mass transfer rates and separation efficiency. The membranes do not allow the liquid phase to penetrate through the membrane pores and thus the gas phase fills the membranes pores. Diffusion coefficient through gases is higher than in liquids; this means that in the former case, the membrane mass transfer resistance (the reciprocal of the diffusivity) is smaller [3]. Among the diversity of membrane geometries available for membrane contactors, hollow-fiber membrane contactors (HFMCs) are favored because they provide a very high surface/volume ratio for separation. These contactors offer a great number of advantages upon other classical gas absorption devices such as dispersion columns. The interfacial mass transfer area is much higher and better controlled. Therefore, the main advantage of HFMCs is that they allow a contact without dispersion of two phases. In addition, the velocities of both phases can be chosen independently, so that neither flooding nor unloading problems arise [2]. Some experimental and modeling studies have been done on gas separation using HFMCs. Qi and Cussler first studied these devices [4]. They studied operational theory of the HFMCs, and calculated mass transfer coefficients in liquid phase. They also obtained overall mass transfer coefficients, including resistances in both liquid

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Nomenclature A cross section of shell (m2 ) C0 inlet concentration (mol/m3 ) C concentration (mol/m3 ) CCO2 −shell CO2 concentration in the shell (mol/m3 ) CCO2 −tube CO2 concentration in the tube (mol/m3 ) CH2 S−shell H2 S concentration in the shell (mol/m3 ) CH2 S−tube H2 S concentration in the tube (mol/m3 ) Ci concentration of any species (mol/m3 ) Ci-tube concentration of any species in the tube (m2 /s) absorbent concentration at the inlet (mol/m3 ) Cin inlet concentration of CO2 in the shell (mol/m3 ) Cinlet Coutlet outlet concentration of CO2 in the shell (mol/m3 ) CMDEA–shell MDEA (amine) concentration (mol/m3 ) CM0 inlet MDEA concentration (mol/m3 ) D diffusion coefficient (m2 /s) Di-membrane diffusion coefficient of any species in the membrane (m2 /s) Di-tube diffusion coefficient of any species in the tube (m2 /s) Ji diffusive flux of any species (mol/m2 s) k reaction rate coefficient of CO2 with absorbent (m3 /mol s) L length of a fiber (m) m physical solubility (–) n number of fibers P pressure (Pa) Qg gas flow rate (L/h) Ql liquid flow rate (L/h) tube inner radius (m) r1 r2 tube outer radius (m) r3 inner shell radius (m) r radial coordinate (m)  module inner radius (m) Ri overall reaction rate of any species (mol/m3 s) S effective area (m2 ) t time (s) T temperature (K) Tl liquid temperature (K) gas temperature (K) Tg u average velocity (m/s) V velocity in the module (m/s) Vz-shell z-velocity in the shell (m/s) Vz-tube z-velocity in the tube (m/s) z axial coordinate (m)  volumetric flow rate of gas phase (m3 /s)  module volume fraction  surface tension of the liquid (N/m)  contact angle (◦ )

and membrane, and compared performance of hollow fibers with packed towers. The separation of CO2 from offshore gas using HFMCs was studied by Falk-Pederson and Dannström [5], who optimized the process. Many authors have studied the applications of HFMCs for absorption of CO2 in hydroxide solution [6], and CO2 removal using amino acid salts [7]. Other authors [8–11] investigated separation of CO2 and SO2 from CO2 /N2 and SO2 /air gas mixtures, using water as an absorbent in a parallel module employing mesoporous polypropylene hollow fibers. A similar process has been recently studied by Zhang et al. [12] for co-current gas–liquid contact in a parallel hollow-fiber module. In both studies, the authors assumed negligible axial diffusion, which may not be a good assumption, especially at low gas

velocities. Kim and Yang [13] investigated the separation of CO2 /N2 mixtures using HFMCs theoretically and experimentally. Although there was an agreement between model findings with experimental results, the authors assumed a linear reduction of gas flow rate for the simulation purposes. Recently, Faiz and Al-Marzouqi [1] developed a 2D mass transfer model for simultaneous absorption of CO2 and H2 S using MEA in hollow fiber membrane contactors. They studied these contactors theoretically. Their model was accurate and could predict removal of H2 S and CO2 in HFMCs. The gas flow rates considered in their work were small and could not achieve reasonable values for industrial applications purposes. No one has yet considered simultaneous separation of H2 S and CO2 at high gas/liquid ratio in order to fulfill the needs at industrial applications. Separation at high gas/liquid ratio is needed for industrial applications. Also, removal of CO2 and H2 S in trace amount is really difficult to achieve and is a challenge for researchers who study in the field of gas separation. Kieffer et al. [14] simulated mass transfer in a liquid–liquid membrane contactor for laminar flow conditions. They used CFD techniques for solving the governing equations. Their results showed that HFMCs have a very narrow mixing zone due to their inner diameter. Numerical simulation of momentum and mass transfers in a HFMC showed that mixing is obtained when both components diffuse along the streamlines. Ghidossi et al. [15] overviewed state of the art CFD methods applied on membrane processes. On their study, two approaches were particularly investigated: hydrodynamics and mass transfer. The hydrodynamics increases the shear stress near the wall. The authors considered the momentum and mass transfers only in the lumen side of the membrane contactor. For practical purposes, all HFMC subdomains including lumen, fiber and shell sides should be considered in the simulations. The present research was performed in order to achieve an efficient and selective removal of H2 S and CO2 from CH4 as a NG model. The gas stream consisted of trace concentrations of CO2 and H2 S in CH4 . The absorption medium used was an aqueous solution of methyldiethanolamine (MDEA) and the contactor employed was a hollow-fiber membrane module. Experiments were carried out at high gas/liquid ratio so that reasonable flow rates could be achieved. Furthermore, a mass transfer model was proposed for absorption of CO2 and H2 S in the HFMC. Axial and radial diffusion inside the tube side, through the membrane, and within the shell side of the membrane contactor were considered in the model equations. Convection was also considered in the shell and tube as well as chemical reaction. CFD techniques were then applied to solve the model equations. The main goal of the simulation was to predict concentrations of the gas components in the membrane contactor. The effect of various process parameters on the mass transfer of CO2 and H2 S were also investigated. Chemical absorption was considered for absorption of CO2 and H2 S in aqueous solution of MDEA. Finally, the model predictions were validated with experimental data.

2. Materials and methods The modeling predictions were validated with experimental data by comparing the results of CO2 and H2 S removal from CH4 by MDEA aqueous solution as the liquid solvent using polypropylene hollow fibers obtained from Liqui-Cel. MDEA was purchased from Sarakhs petrochemical complex with purity of 99%. Distilled water was used for making the aqueous solutions. CO2 , having 99.5% purity, was purchased from Farafan Gas Corp., Tehran, Iran. H2 S with 99.99% purity and CH4 as NG model with purity of 99.5% were supplied by Technical Gas Services, Inc.

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Fig. 1. Schematic drawing of experimental setup.

The experimental setup is shown schematically in Fig. 1. The feed gas was passed through the tube side and its flow rate was adjusted using mass flow controllers (Brooks mass flow controllers model 5850). The liquid absorbent was fed counter currently through the shell. The module was set at a constant temperature, and the experiments were conducted at ambient temperature. The feed gas pressure was about 1 atm. It slightly changed with the gas flow rate. The liquid inlet pressure was varied with the liquid flow rate by adjusting the liquid outlet valve. CO2 compositions were measured by a gas chromatogram purchased from Teif Gostar Company (Iran) which provided accurate (±2%) measurements of the gas components. H2 S concentration, as a toxic and corrosive gas, was analyzed using a H2 S analyzer (GFG, Germany). To trace H2 S leakage in the laboratory, a H2 S sensor equipped with an alarm was used. The characteristics of the hollow-fiber contactor and operational conditions are presented in Table 1. Furthermore, in all the experiments, the liquid phase pressure was maintained higher than the gas phase pressure to establish the interface at the pores adjacent the liquid phase. This also prevented dispersion of the gas phase in the liquid phase. Therefore, the aqueous phase could not penetrate the membrane pores during the experiments. So the membrane pores could not be wetted with the liquid solvent in the range of operating conditions.

Fig. 2. (a) A schematic diagram for the HFMC. (b) Cross sectional area of the membrane contactor and a circular approximation of a portion of the fluid surrounding the hollow fibers.

wetted mode” in which the gas mixture fills the membrane pores for counter-current gas–liquid contact. The liquid absorbent flows in the shell side, whereas the gas feed (CO2 , H2 S, and CH4 ) is fed to the tube side of the HFMC. Laminar parabolic velocity distribution is used for the gas flow in the tube side; whereas, the liquid flow field in the shell side was determined using Navier–Stokes equations. Axial and radial diffusions inside the tube side, through the membrane, and within the shell side of the HFMC are considered in the model equations. The model also considers chemical reaction between CO2 and MDEA in the shell side while the reaction between H2 S and MDEA is assumed to be instantaneous [11,16]. 3.1. Model equations

3. Mass transfer model A comprehensive 2D mathematical model was proposed for transport of CO2 and H2 S through the HFMC. In this work, separation of CO2 and H2 S from CH4 using MDEA aqueous solution as absorbent in the HFMC was studied. The model was based on “nonTable 1 Hollow-fiber membrane module characteristic and operational conditions of experiments. Parameter

Symbol

Value

Membrane module Fiber inner radius (␮m) Fiber outer radius (␮m) Fiber porosity (%) Fiber tortuositya Module inner radius (cm) Fiber length (cm) Number of fibers Pore diameter (␮m) Shell side geometric void fraction Effective area (m2 ) Gas inlet pressure (atm) Temperature (K) Gas flow rate (L/h) Liquid flow rate (L/h)

Liqui-Cel extra flow (2.5 × 8) r1 r2 ε   L n d – S p T Qg Ql

– 110 150 25 4 3.325 18.58 8000 0.03 0.40 1.4 1 298 360–480 0.5–3.5

a

Estimated from Wakao–Smith equation ( = 1/ε) [27].

A mass transfer model is used for a hollow fiber, as shown in Fig. 2a. The gas mixture (CO2 /H2 S/CH4 ) flows with a fully developed laminar velocity inside the hollow fibers. Fig. 2b shows cross sectional area of the HFMC. Based on Happel’s free surface model [17], only a portion of fluid surrounding the fiber is considered and may be approximated as a circular cross section. Therefore, the HFMC consists of three sections: tube side, membrane, and shell side. The steady state 2D mass balances are carried out for all three sections of the HFMC. The gas mixture is fed to the tube side (at z = 0), while the absorbent is passed through the shell side (at z = L). CO2 and H2 S are removed from the gas mixture by diffusing through the gas bulk, membrane and then are absorbed in the liquid solvent. The model is built considering the following assumptions: 1. Steady state and isothermal conditions. 2. Fully developed parabolic gas velocity profile in the HFMC. 3. Ideal gas behavior is imposed. 4. Henry’s law is applicable for gas–liquid interface. 5. Laminar flow for gas and liquid phases in the HFMC. 6. Non-wetted mode in which the gas mixture fills the membrane pores. 7. CH4 is not dissolved in the liquid solvent. 8. No homogeneous reaction takes place in the tube side.

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The convective flux boundary condition assumes that all mass passing through this boundary is convection-dominated. This firstly assumes that any mass flux due to diffusion across this boundary is zero. CCO2 −tube = CCO2 −membrane , CH2 S−tube = CH2 S−membrane

at r = r1 ,

(Membrane pores)

∂CCO2 −tube

at r = 0,

∂r

(5)

=

∂CH2 S−tube ∂r

=0

(Symmetry)

(6)

3.1.2. Concentration equations in the shell side The steady state continuity equation with chemical reaction for CO2 in the shell side of the HFMC in cylindrical coordinate is obtained using Fick’s law of diffusion for estimation of diffusive flux:



DCO2 −shell

∂r 2

= Vz−shell

Fig. 3. Model domain and meshes used for simulation. The three domains from left to right are tube (gas channel) side, membrane and shell (absorbent channel) side, respectively.

3.1.1. Tube side equations The continuity equation for all species in a reactive absorption system can be expressed as [18]: ∂Ci = −(∇ · Ci V ) − (∇ · Ji ) + Ri ∂t

(1)

where Ci (mol/m3 ), Ji (mol/m2 s), Ri (mol/m3 s), V (m/s) and t (s) are concentration, diffusive flux, reaction rate of species i, velocity and time, respectively. Fick’s law of diffusion is used to determine the diffusive fluxes of species i. The steady-state continuity equation for transport of CO2 and H2 S in the tube side may be written as:



Di−tube

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



= Vz−tube

∂Ci−tube − Ri ∂z (2)

where i refer to CO2 or H2 S and Ri is reaction rate. r and z also refer to radial and axial coordinates, respectively. The reaction term in the tube side is not considered because there is no chemical reaction in the tube side of the HFMC. Velocity distribution in the tube side is assumed to follow Newtonian laminar flow [18]:



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. 3). The boundary conditions assumed for the tube side are as follows: at z = 0,

CCO2 −tube = CCO2 ,0 , CH2 S−tube = CH2 S,0

(Inlet boundary) (4)

at z = L,

Convective flux

∂2 CCO2 −shell

+

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



∂CCO2 −shell

(7)

∂z

Velocity distribution in the shell side is obtained by solving the momentum equation, i.e. Navier–Stokes equations. Therefore, the momentum and the continuity equations should be coupled and solved simultaneously to obtain concentration distribution of the solutes. The Navier–Stokes equations describe flow in viscous fluids through momentum balances for each of the components. They also 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 [18]: −∇ · (∇ Vz−shell + (∇ Vz−shell )T ) + (Vz−shell .∇ )Vz−shell + ∇ p = F (8) ∇ .Vz−shell = 0 where , V and denote fluid dynamic viscosity (kg/m s), velocity vector (m/s), density (kg/m3 ), respectively; p is pressure (Pa) and F is a body force term (N). Happel’s free surface model can be used to estimate the radius of shell side [17]. The radius of free surface (r3 in Fig. 3) can be defined as: r3 =

 1 1/2 1−

r2

(9)

In which  is volume fraction of the void. It can be calculated as follows: 1− =

nr22

(10)

2

where n is the number of fibers and  is the module inner radius. Happel’s free surface model can also be used to determine the shell side velocity. In Happel’s model, the fluid flow in the shell side of the membrane contactor is configured as fluid envelope around the fiber and there is no interaction between the fibers. Some researchers used Happel’s free surface model [10,19]. However, Navier–Stokes equations provided general methodology for determination of velocity in the shell side and were used for all membrane geometries [14,20]. The reaction rate between H2 S and MDEA is assumed to be instantaneous [11,21] and therefore H2 S concentration of in the shell side is negligible. Therefore, the continuity equation for H2 S transport in the shell side is not considered. Boundary conditions for the shell side are given as: at z = L,

CCO2 −shell = 0,

Vz−shell = V0

(Inlet boundary)

(11)

M. Rezakazemi et al. / Chemical Engineering Journal 168 (2011) 1217–1226

at z = 0, at r = r3 ,

Convective flux, p = patm ∂CCO2 –shell ∂r

=0

(Outlet boundary)

(12)

(Symmetry boundary)

(No slip condition),

(13)

CCO2 −shell = m × CCO2 −membrane

at r = r2 ,

(Henry’law)

(No slip condition),

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shows a segment of the mesh used to determine the gas transport behavior in HFMC. It should be pointed out that the COMSOL mesh generator creates triangular meshes that are isotropic in size. A large number of elements are then created with scaling. A scaling factor of 500 was employed in z direction due to a large difference between r and z. COMSOL automatically scales back the geometry after meshing. This generates an anisotropic mesh around 3000 elements. Adaptive mesh refinement in COMSOL, which generates the best and minimal meshes, was used to mesh the HFMC geometry.

(14) 4. Results and discussions

The reaction rates between CO2 and MDEA are given in Appendix A. m is the physical solubility of gas in the liquid solvent. 3.1.3. Membrane equations The steady-state continuity equation for transport of CO2 and H2 S inside the membrane, which is considered to be due to diffusion alone, may be written as:



Di−membrane

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



=0 (15)

Boundary conditions are given as: at r = r1 ,

Ci−membrane = Ci−shell

at r = r2 ,

CCO2 −membrane =

CCO2 −shell m(Henrys’law)

(16) ,

CH2 S−membrane = 0 (17)

4.1. Model validation The simulation results for the separation of CO2 and H2 S from CH4 using the HFMC were compared with the experimental data in order to validate the mass transfer 2D model proposed. The CO2 and H2 S outlet concentrations in HFMC for different values of liquid and gas velocities are presented in Table 2. As shown, increasing liquid velocity in the shell side of the HFMC increases the mass transfer rate of CO2 in the membrane. The liquid velocity affects the convection contribution in the mass transfer (continuity equation) in the shell side which in turn changes the overall mass transfer of CO2 . Table 2 also reveals that the liquid velocity has significant effect on the mass transfer of CO2. However, it does not affect the mass transfer of H2 S because its concentration in the liquid phase was assumed to be negligible due to instantaneous reaction between H2 S and MDEA. Table 2 also shows that the model predictions are in good agreement with the experimental values for different values of gas and liquid velocities.

where m is solubility of CO2 in the absorbent.

4.2. Velocity field

3.1.4. Amine equations The steady state continuity for amine (MDEA) in the shell side of the HFMC may be written as:

The velocity field and profile in the shell side of the HFMC are shown in Figs. 4 and 5, where the liquid absorbent flows. The velocity profile in the shell side of the HFMC was simulated by solving the Navier–Stokes equations. In the gas–liquid membrane contactors for gas separation the liquid phase plays crucial role in mass transfer because it is the controlling phase. In the absence of chemical reaction, the mass transfer of gas is controlled by the liquid solvent. Chemical reaction increases the mass transfer rate of gas phase and decreases resistance of the liquid phase. Therefore, the velocity profile for the liquid phase must be accurately obtained. The velocity profile is almost parabolic with a mean velocity which increases with the membrane length because of continuous fluid permeation. Figs. 4 and 5 also reveal that at the inlet regions in the shell side, the velocity is not developed. After a short distance from the inlet, the velocity profile is fully developed (see Fig. 5). As observed, the model considers the inlet effects on the hydrodynamics of fluid flow in the shell side.



DMDEA−shell = Vz−shell

∂2 CMDEA−shell ∂2 CMDEA−shell 1 ∂CMDEA−shell + + 2 r ∂r ∂r ∂z 2

∂CMDEA−shell ∂z



(18)

Boundary conditions for the shell side are given as: at z = L,

CMDEA−shell = CM0

(Inlet boundary),

(19)

at z = 0,

Convective flux

(Outlet boundary),

(20)

at r = r3 ,

∂CMDEA−shell =0 ∂r

(Symmetry boundary),

(21)

at r = r2 ,

∂CMDEA−shell =0 ∂r

(Insulation boundary)

(22)

4.3. Concentration distribution of CO2 and H2 S in the HFMC

3.2. Numerical solution of model equations The model equations related to shell side, membrane and tube side with the appropriate boundary conditions were solved using COMSOL Multiphysics version 3.2 software (Sweden), which uses finite element method (FEM) for numerical solutions of the model equations. The finite element analysis is combined with adaptive meshing and error control using numerical solver of UMFPACK version 4.2. This solver is well suited for solving stiff and non-stiff non-linear boundary value problems. The applicability, robustness and accuracy of this method for membrane contactors were proved by some authors [9,19,20]. An IBM-PC-Pentium 4 (CPU speed is 2800 MHz) was used to solve the set of equations. The computational time for solving the set of equations was about 10 min. Fig. 3

Fig. 6 presents the dimensionless concentration distribution (C/C0 ) of CO2 and H2 S in the tube side, the membrane and the shell side of the HFMC. The gas mixture containing CO2 /H2 S/CH4 flows from one side of the HFMC (z = 0) where the concentrations of CO2 and H2 S are the highest, whereas the liquid solvent (MDEA) flows from the other side (z = L) where the concentrations of gases are assumed to be zero. As the gas mixture flows through the tube side, it is transferred towards the membrane due to concentration difference (driving force) [20]. The mechanisms of mass transfer in the tube and shell sides are convection and diffusion. In the z-direction, the predominant mass transfer mechanism is convection because fluid flows in the z-direction, while in the r-direction, diffusion occurs because of large concentration differences in the

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Table 2 Comparison of experimental results with simulation results. Inlet conditions

Experimental

CFD simulation

Gas flow rate (L/h)

Liquid flow rate (L/h)

H2 S (vol.%)

CO2 (vol.%)

H2 S (vol.%)

CO2 (vol.%)

H2 S (vol.%)

CO2 (vol.%)

360 360 420 420 480 480 480

0.5 2.5 0.5 2.5 0.5 1.5 3.5

2.45 0.31 0.84 1.45 1.36 0.31 2.45

8.61 8.43 4.73 4.77 1.51 8.43 8.61

0.0014 0.0007 0.1173 0.0036 0.1173 0.0763 0.0029

2.96 2.00 3.40 1.30 0.70 3.54 1.37

0.0011 0.0004 0.1138 0.0022 0.1159 0.0750 0.0015

2.55 1.89 3.21 1.25 0.65 3.34 1.25

r-direction. The gas is transferred through the membrane only by diffusion mechanism and then absorbed by the moving solvent in the shell side. Fig. 7 illustrates the axial concentration profile of H2 S and CO2 in the tube side of HFMC. Fig. 7 indicates that H2 S concentration drops suddenly at the inlet of the membrane because of low concentration of H2 S in the feed and high reaction rate of H2 S with MDEA. 4.4. Concentration distribution of MDEA in the HFMC A representation of the dimensionless concentration distribution of amine (MDEA) in the shell side of the HFMC is shown in Fig. 8. The amine solution flows through the shell side (z = L) and reacts with CO2 and H2 S which come from the

membrane pores due to the concentration difference between the two sides of the membrane. The amine concentration decreases significantly in the gas–liquid interface zone. The variation of MDEA concentration along the HFMC is also significantly high due to the reaction mainly between CO2 and MDEA. Fig. 9 also indicates axial concentration profile of MDEA along the HFMC in the shell side. Figs. 8 and 9 show that almost all MDEA is consumed in the process. This is because of highly effective contact between the gas and liquid phases and the contact time is long enough to achieve a reasonable separation even at high gas velocities. The most important advantage of this HFMC is its effective operation at high gas velocities.

4.5. Effects of liquid and gas flow rates on CO2 absorption The percentage removal of CO2 can be calculated using the following equation:

% CO2 removal = 100



( × C)inlet − ( × C)Outlet C = 100 1 − outlet Cinlet ( × C)inlet



(23) where  (m3 /s) and C (mol/m3 ) are volumetric gas flow rate and concentration, respectively. Coutlet (mol/m3 ) is calculated by inte-

Fig. 4. Velocity field in the shell side of the HFMC. Gas flow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 vol.%; H2 S inlet concentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temperature = 298 K.

Fig. 5. Velocity profile in the shell side along the membrane length. Gas flow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 wt.%; H2 S inlet concentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temperature = 298 K.

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Fig. 6. Representation of the concentration distribution of (a) CO2 and (b) H2 S (C/C0 ) in the HFMC. Gas flow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 wt.%; H2 S inlet concentration = 0.31 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temperature = 298 K.

grating the local concentration at the outlet of the tube side (z = L):

   C(r)dA    r=0 = r=r  1   dA   

r=r1

Coutlet

r=0

(24)

z=L

(m2 ).

The change in volumetric gas where A is area of the tube side flow rate is assumed to be negligible and thus % CO2 removal can be approximated by Eq. (17). In Fig. 10, the CO2 outlet concentration in the gas phase (the tube side) is plotted as functions of the liquid (absorbent) and the gas (feed) flow rates. As the absorbent flow rate increases, the mass transfer rate of CO2 into the liquid phase increases because the concentration gradients of CO2 and absorbent in the liquid phase increase, which in turn results in reduction of the CO2 outlet concentration in the gas phase. It can also be observed that the reduction rate of CO2 outlet concentration is much sharper at higher liquid flow rates. The effect of gas flow rate on CO2 outlet concentration is also illustrated in Fig. 10. As expected, increasing the gas flow rate reduces the residence time of the gas phase in the HFMC, which in turn reduces the mass transfer of CO2 in the HFMC.

from 4 to 0.6 vol.% as this ratio increases from 0.1 to 0.9. The effective diffusion coefficient of CO2 (DCO2 −membrane ) in the membrane is calculated through the membrane porosity and tortuosity, which is provided by the membrane manufacturer [2]: DCO2 −membrane = DCO2 −tube

ε 

(25)

where DCO2 −tube is CO2 diffusivity in the gas phase. Chapman–Enskog theory [18] was used for estimation of gas diffusivity in the gas phase (tube side). As seen, the effective diffusion coefficient is a function of membrane porosity and tortuosity. As the porosity-to-tortuosity ratio increases, the membrane diffusivity and thus the mass transfer of CO2 through the membrane increases; i.e. the CO2 outlet concentration decreases. Indeed, when the porosity-to-tortuosity ratio increases, the membrane mass transfer resistance decreases. Therefore, the total resistance

4.6. Effect of porosity-to-tortuosity ratio Variation of the porosity-to-tortuosity ratio between 0.1 and 0.9 was also considered in the simulations in order to investigate the effect of this parameter on the mass transfer of CO2 . The values for this ratio correspond to those of current porous membranes which have porosities between 0.15 and 0.75 and tortuosity between 2 and 3 (values reported by Gabelman and Hwang [2]). Fig. 11 represents the effect of the porosity-to-tortuosity ratio on the CO2 outlet concentration. As observed, the CO2 outlet concentration decreases

Fig. 7. Axial concentration distribution of H2 S and CO2 in the tube side of HFMC. Gas flow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 vol.%; H2 S inlet concentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temperature = 298 K. “L” is length of a fiber (m).

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Fig. 9. Axial concentration distribution of MDEA in the shell side of the HFMC. Gas flow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 vol.%; H2 S inlet concentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temperature = 298 K; “L” is length of a fiber (m).

Fig. 8. Dimensionless concentration of MDEA (CMDEA−shell /CM0 ) in the shell side of the HFMC. Gas flow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 wt.%; H2 S inlet concentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temperature = 298 K.

to the mass transfer of CO2 reduces. The simulation results indicated that the porosity-to-tortuosity ratio does not have any effect on the H2 S removal. It should be pointed out that Knudsen diffusion was neglected for calculation of mass transfer flux across membrane pores. This is because its contribution to overall mass transfer across membrane is negligible [12,19,20].

Fig. 10. Relationship between CO2 outlet concentration and gas and liquid flow rates. CO2 inlet concentration = 50 vol.%; H2 S inlet concentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temperature = 298 K.

4.7. Effect of absorbent (MDEA) concentration on CO2 and H2 S removal Fig. 12 illustrates the effect of the absorbent concentration on CO2 outlet stream in the tube side of the HFMC. As observed, increasing absorbent concentration increases CO2 removal by reducing CO2 outlet concentration. Since reaction kinetics of MDEA with CO2 is elementary, it depends directly on absorbent concentration. Increasing absorbent concentration increases reaction rate between CO2 and absorbent and this reduces CO2 outlet con-

Fig. 11. Effect of porosity-to-tortuosity ratio on concentration of CO2 . Gas flow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 wt.%; H2 S inlet concentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temperature = 298 K.

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tension and breakthrough pressure. The pore diameter can be calculated using Laplace–Young equation [22]:

P = −

Fig. 12. Effect of absorbent concentration on CO2 removal. Gas flow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 vol.%; H2 S inlet concentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temperature = 298 K.

centration. The results also confirm that absorbent concentration has significant effect on CO2 removal and plays a key role in the separation process. Improving liquid phase mass transfer rate with increasing liquid phase velocity or absorbent concentration, enhances CO2 removal efficiency. The results indicated that the amine (MDEA) concentration does not have any effect on H2 S removal. Therefore, the effect of MDEA concentration on H2 S outlet concentration is not shown here. 4.8. Flux distribution in the HFMC Mass transfer flux distribution in the gas phase of the HFMC is illustrated in Fig. 13. Both diffusive and convective fluxes for CO2 in the tube side are shown in Fig. 13 to demonstrate the contribution of axial diffusion in the simulation. As observed, contribution of convective flux in the z-direction is predominant compared to axial diffusive flux. That is due to the fact that in the axial direction, the velocity is significant and causes high convective flux for CO2 . Fig. 13 also indicates that both fluxes decrease along the contactor because of driving force reduction in the z-direction. It should be pointed out here that the hollow fibers are made of polypropylene (PP) which is a hydrophobic polymer. Generally, in hydrophobic HFMCs the aqueous phase cannot penetrate into the membrane pores because of hydrophobic nature of the fibers. In membrane contactors, membrane wettability depends on several factors including membrane pore diameter, contact angle, surface

4 cos () dmax

(26)

where  is surface tension of the liquid phase that is equal to 72.3 × 10−3 (N/m) and  refers to the contact angle between the liquid phase and the membrane that is equal to 117.7◦ for a water–PP system [23]. Since the liquid pressure was 2 bar, the pore diameter could be estimated using Eq. (26) to be 0.66 ␮m. Therefore, the membrane wettability occurs for any pore larger than 0.66 ␮m. The membrane pore size is 0.03 ␮m, so the membrane pores cannot be wetted with the liquid solvent in the range of operating pressure. Since low concentration of MDEA was used in all the experiments, it was assumed that the contact angle was never lower than 90◦ , so that no pore penetration of the solvent did occur. Furthermore, in all the experiments the liquid phase pressure was maintained higher than the gas phase to establish the interface at the pores adjacent the liquid phase. This also prevented the dispersion of gas phase into the liquid phase. Therefore, the aqueous phase could not penetrate into the membrane pores during the experiments.

5. Conclusions Chemical absorption of CO2 and H2 S in a HFMC was studied in this work. A 2D mathematical model was proposed to describe simultaneous absorption of CO2 and H2 S in the HFMC. The model was based on solving the conservation equations for gas components in three sections of the HFMC. The FEM was applied to solve the differential equations of mass transfer. Absorption medium was amine (MDEA) aqueous solution. The simulation results revealed that the H2 S removal with aqueous solution of MDEA is almost complete. The model was validated with the experimental results for absorption of CO2 and H2 S in MDEA aqueous solution. The modeling predictions were in good agreement with the experimental data for different values of gas and liquid velocities. The simulation results for absorption of CO2 in MDEA aqueous indicated that the CO2 removal increases with increasing liquid phase velocity and MDEA concentration in the HFMC. The simulation results also revealed that H2 S removal was almost complete using the HFMC. The results of this work indicated that the proposed mass transfer model is capable to predict the performance of HFMCs for NG sweetening. The proposed simulation can also take into account complex chemical reaction schemes. The developed model thus can be used to predict the mass transfer performance of the HFMCs for other reactive as well as non-reactive systems. Eventually, the proposed mass transfer model provides a preliminary design tool for multi-component membrane gas absorption processes.

Appendix A. A.1. Reaction rate of CO2 with amines See Table A.1.

Fig. 13. Axial diffusive and convective flux distribution of CO2 in the tube side of the HFMC. Gas flow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 vol.%; H2 S inlet concentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temperature = 298 K; “L” is length of a fiber (m).

Table A.1 Rate expression of amines. Aqueous amine solution

Ri (mol/m3 s)

k (m3 /mol s)

Refs.

MDEA

kCCO2 CAmine

8.40 × 10−3

[24,25]

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A.2. CO2 solubility The distribution coefficient of CO2 in water was taken from Versteeg and van Swaaij [26]: mw,CO2 = 3.59 × 10−7 RT exp

 2044  T

(A.1)

A.3. CO2 diffusivity The diffusivity of CO2 in pure water Dw,CO2 was taken from Versteeg and van Swaaij [26]. Dw,CO2 = 2.35 × 10−6 exp

 −2119  T

(A.2)

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