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Chemical Engineering Journal 168 (2011) 1217–1226

Contents lists available at ScienceDirect

Chemical Engineering Journal

journa l homepage: www.e lsev ier .com/ locate /ce j

FD simulation of natural gas sweetening in a gas–liquid hollow-fiberembrane contactor

ashallah Rezakazemi, Zahra Niazi, Mojtaba Mirfendereski, Saeed Shirazian,oraj Mohammadi ∗, Afshin Pak

esearch Centre for Membrane Separation Processes, Faculty of Chemical Engineering, Iran University of Science and Technology (IUST), Narmak, Tehran, Iran

r t i c l e i n f o

rticle history:eceived 19 October 2010eceived in revised form 9 February 2011ccepted 10 February 2011

eywords:

a b s t r a c t

Chemical absorption of CO2 and H2S from natural gas was studied theoretically and experimentallyusing a hollow-fiber membrane contactor (HFMC) in this work. A 2D mathematical model was proposedto study simultaneous transport of CO2 and H2S through a HFMC using methyldiethanolamine (MDEA)as chemical absorbent. The model considers axial and radial diffusion in the HFMC. It also considersconvection in tube and shell sides with chemical reaction. CFD techniques were applied to solve the model

atural gas sweeteningumerical simulationollow-fiber membrane contactormine aqueous solution

equations involving continuity and momentum equations. Modeling predictions were validated with theexperimental data and it was found that there is a good agreement between them for different values ofgas and liquid velocities. The simulation results showed that the removal of H2S with aqueous solutionof MDEA was very high and indicated almost total removal of H2S. Experimental and simulation resultsindicated that the membrane module was very efficient in the removal of trace H2S at high gas/liquidflow ratio. The removal of H2S was almost complete with recovery of higher than 96%. The proposed

he pe

model is able to predict t

. Introduction

Removal of sour gas impurities such as H2S and CO2 from gasixtures is of vital importance for chemical industries. Natural gas

NG) usually contains H2S and CO2 as major gas impurities. In ordero use NG for energy generation, H2S and CO2 must be removedrom NG.

CO2 is an unwanted component in NG and can reduce its energyfficiency. H2S is a toxic and corrosive gas and also known as a poi-on. [1]. Therefore, from environmental view-point, it is importanto separate CO2 and H2S from NG. Current H2S and CO2 separationrocesses include absorption, adsorption, cryogenic and membraneechniques [2]. Conventional processes suffer from many problemsuch as flooding, foaming, entraining, channeling, and high capitalnd operating cost. Therefore, many researchers have studied theossibility of enhancing the efficiency of these processes [2].

Recently, new processes using gas–liquid membrane contactorss gas absorption devices have been a subject of great interest. In

hese processes, the membrane contactor mainly acts as a physi-al barrier between two phases (gas and liquid) without significantffect in selectivity, i.e. the membrane does not change the parti-ion coefficient. Being the two phases separate by the membrane,

∗ Corresponding author. Tel.: +98 21 789 6621; fax: +98 21 789 6620.E-mail address: torajmohammadi@iust.ac.ir (T. Mohammadi).

385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.cej.2011.02.019

rformance of CO2 and H2S absorption in HFMCs.© 2011 Elsevier B.V. All rights reserved.

there is no phases mixing and dispersion phenomena do not occur.The gases are transferred from one phase to the other only by diffu-sion. The membranes are usually mesoporous and symmetric andare always hydrophobic. Hydrophobicity of gas–liquid membranecontactors increases mass transfer rates and separation efficiency.The membranes do not allow the liquid phase to penetrate throughthe membrane pores and thus the gas phase fills the membranespores. Diffusion coefficient through gases is higher than in liquids;this means that in the former case, the membrane mass transferresistance (the reciprocal of the diffusivity) is smaller [3].

Among the diversity of membrane geometries availablefor membrane contactors, hollow-fiber membrane contactors(HFMCs) are favored because they provide a very high sur-face/volume ratio for separation. These contactors offer a greatnumber of advantages upon other classical gas absorption devicessuch as dispersion columns. The interfacial mass transfer area ismuch higher and better controlled. Therefore, the main advantageof HFMCs is that they allow a contact without dispersion of twophases. In addition, the velocities of both phases can be chosenindependently, so that neither flooding nor unloading problemsarise [2].

Some experimental and modeling studies have been done on gasseparation using HFMCs. Qi and Cussler first studied these devices[4]. They studied operational theory of the HFMCs, and calculatedmass transfer coefficients in liquid phase. They also obtained over-all mass transfer coefficients, including resistances in both liquid

1218 M. Rezakazemi et al. / Chemical Engineer

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)CH2S−shell H2S concentration in the shell (mol/m3)CH2S−tube H2S concentration in the tube (mol/m3)Ci concentration of any species (mol/m3)Ci-tube concentration of any species in the tube (m2/s)Cin absorbent concentration at the inlet (mol/m3)Cinlet inlet concentration of CO2 in the shell (mol/m3)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 mem-

brane (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 fibersP pressure (Pa)Qg gas flow rate (L/h)Ql liquid flow rate (L/h)r1 tube inner radius (m)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)Tg gas temperature (K)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

apHmHr

filemf

from Sarakhs petrochemical complex with purity of 99%. Distilled

� surface tension of the liquid (N/m)� contact angle (◦)

nd membrane, and compared performance of hollow fibers withacked towers. The separation of CO2 from offshore gas usingFMCs was studied by Falk-Pederson and Dannström [5], who opti-ized the process. Many authors have studied the applications ofFMCs for absorption of CO2 in hydroxide solution [6], and CO2

emoval using amino acid salts [7].Other authors [8–11] investigated separation of CO2 and SO2

rom CO2/N2 and SO2/air gas mixtures, using water as an absorbentn a parallel module employing mesoporous polypropylene hol-

ow fibers. A similar process has been recently studied by Zhangt al. [12] for co-current gas–liquid contact in a parallel hollow-fiberodule. In both studies, the authors assumed negligible axial dif-

usion, which may not be a good assumption, especially at low gas

ing Journal 168 (2011) 1217–1226

velocities. Kim and Yang [13] investigated the separation of CO2/N2mixtures using HFMCs theoretically and experimentally. Althoughthere was an agreement between model findings with experimen-tal results, the authors assumed a linear reduction of gas flow ratefor the simulation purposes.

Recently, Faiz and Al-Marzouqi [1] developed a 2D mass trans-fer model for simultaneous absorption of CO2 and H2S using MEAin hollow fiber membrane contactors. They studied these con-tactors theoretically. Their model was accurate and could predictremoval of H2S and CO2 in HFMCs. The gas flow rates consideredin their work were small and could not achieve reasonable val-ues for industrial applications purposes. No one has yet consideredsimultaneous separation of H2S and CO2 at high gas/liquid ratioin order to fulfill the needs at industrial applications. Separationat high gas/liquid ratio is needed for industrial applications. Also,removal of CO2 and H2S in trace amount is really difficult to achieveand is a challenge for researchers who study in the field of gasseparation.

Kieffer et al. [14] simulated mass transfer in a liquid–liquidmembrane contactor for laminar flow conditions. They used CFDtechniques for solving the governing equations. Their resultsshowed that HFMCs have a very narrow mixing zone due to theirinner diameter. Numerical simulation of momentum and masstransfers in a HFMC showed that mixing is obtained when bothcomponents diffuse along the streamlines.

Ghidossi et al. [15] overviewed state of the art CFD methodsapplied on membrane processes. On their study, two approacheswere particularly investigated: hydrodynamics and mass transfer.The hydrodynamics increases the shear stress near the wall. Theauthors considered the momentum and mass transfers only in thelumen side of the membrane contactor. For practical purposes, allHFMC subdomains including lumen, fiber and shell sides should beconsidered in the simulations.

The present research was performed in order to achieve an effi-cient and selective removal of H2S and CO2 from CH4 as a NGmodel. The gas stream consisted of trace concentrations of CO2 andH2S in CH4. The absorption medium used was an aqueous solu-tion of methyldiethanolamine (MDEA) and the contactor employedwas a hollow-fiber membrane module. Experiments were carriedout at high gas/liquid ratio so that reasonable flow rates could beachieved. Furthermore, a mass transfer model was proposed forabsorption of CO2 and H2S in the HFMC. Axial and radial diffu-sion inside the tube side, through the membrane, and within theshell side of the membrane contactor were considered in the modelequations. Convection was also considered in the shell and tube aswell as chemical reaction. CFD techniques were then applied tosolve the model equations. The main goal of the simulation wasto predict concentrations of the gas components in the membranecontactor. The effect of various process parameters on the masstransfer of CO2 and H2S were also investigated. Chemical absorp-tion was considered for absorption of CO2 and H2S in aqueoussolution of MDEA. Finally, the model predictions were validatedwith experimental data.

2. Materials and methods

The modeling predictions were validated with experimentaldata by comparing the results of CO2 and H2S removal from CH4by MDEA aqueous solution as the liquid solvent using polypropy-lene hollow fibers obtained from Liqui-Cel. MDEA was purchased

water was used for making the aqueous solutions. CO2, having99.5% purity, was purchased from Farafan Gas Corp., Tehran, Iran.H2S with 99.99% purity and CH4 as NG model with purity of 99.5%were supplied by Technical Gas Services, Inc.

M. Rezakazemi et al. / Chemical Engineering Journal 168 (2011) 1217–1226 1219

famtafguwCt

ulcd

wtvttt

3

tra

THe

Fig. 1. Schematic drawing of experimental setup.

The experimental setup is shown schematically in Fig. 1. Theeed gas was passed through the tube side and its flow rate wasdjusted using mass flow controllers (Brooks mass flow controllersodel 5850). The liquid absorbent was fed counter currently

hrough the shell. The module was set at a constant temperature,nd the experiments were conducted at ambient temperature. Theeed gas pressure was about 1 atm. It slightly changed with theas flow rate. The liquid inlet pressure was varied with the liq-id flow rate by adjusting the liquid outlet valve. CO2 compositionsere measured by a gas chromatogram purchased from Teif Gostarompany (Iran) which provided accurate (±2%) measurements ofhe gas components.

H2S concentration, as a toxic and corrosive gas, was analyzedsing a H2S analyzer (GFG, Germany). To trace H2S leakage in the

aboratory, a H2S sensor equipped with an alarm was used. Theharacteristics of the hollow-fiber contactor and operational con-itions are presented in Table 1.

Furthermore, in all the experiments, the liquid phase pressureas maintained higher than the gas phase pressure to establish

he interface at the pores adjacent the liquid phase. This also pre-ented dispersion of the gas phase in the liquid phase. Therefore,he aqueous phase could not penetrate the membrane pores duringhe experiments. So the membrane pores could not be wetted withhe liquid solvent in the range of operating conditions.

. Mass transfer model

A comprehensive 2D mathematical model was proposed forransport of CO2 and H2S through the HFMC. In this work, sepa-ation of CO2 and H2S from CH4 using MDEA aqueous solution asbsorbent in the HFMC was studied. The model was based on “non-

able 1ollow-fiber membrane module characteristic and operational conditions ofxperiments.

Parameter Symbol Value

Membrane module Liqui-Cel extra flow (2.5 × 8) –Fiber inner radius (�m) r1 110Fiber outer radius (�m) r2 150Fiber porosity (%) ε 25Fiber tortuositya � 4Module inner radius (cm) � 3.325Fiber length (cm) L 18.58Number of fibers n 8000Pore diameter (�m) d 0.03Shell side geometric void fraction – 0.40Effective area (m2) S 1.4Gas inlet pressure (atm) p 1Temperature (K) T 298Gas flow rate (L/h) Qg 360–480Liquid flow rate (L/h) Ql 0.5–3.5

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

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

wetted mode” in which the gas mixture fills the membrane poresfor counter-current gas–liquid contact. The liquid absorbent flowsin the shell side, whereas the gas feed (CO2, H2S, and CH4) is fedto the tube side of the HFMC. Laminar parabolic velocity distribu-tion is used for the gas flow in the tube side; whereas, the liquidflow field in the shell side was determined using Navier–Stokesequations. Axial and radial diffusions inside the tube side, throughthe membrane, and within the shell side of the HFMC are consid-ered in the model equations. The model also considers chemicalreaction between CO2 and MDEA in the shell side while the reac-tion between H2S and MDEA is assumed to be instantaneous[11,16].

3.1. Model equations

A mass transfer model is used for a hollow fiber, as shown inFig. 2a. The gas mixture (CO2/H2S/CH4) flows with a fully developedlaminar velocity inside the hollow fibers. Fig. 2b shows cross sec-tional area of the HFMC. Based on Happel’s free surface model [17],only a portion of fluid surrounding the fiber is considered and maybe approximated as a circular cross section. Therefore, the HFMCconsists of three sections: tube side, membrane, and shell side. Thesteady state 2D mass balances are carried out for all three sectionsof the HFMC. The gas mixture is fed to the tube side (at z = 0), whilethe absorbent is passed through the shell side (at z = L). CO2 andH2S are removed from the gas mixture by diffusing through the gasbulk, 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.

1220 M. Rezakazemi et al. / Chemical Engineer

Ftr

3

s

wctd

H

D

wrti

t

V

wr

l

a

a

ig. 3. Model domain and meshes used for simulation. The three domains from lefto right are tube (gas channel) side, membrane and shell (absorbent channel) side,espectively.

.1.1. Tube side equationsThe continuity equation for all species in a reactive absorption

ystem can be expressed as [18]:

∂Ci

∂t= −(∇ · CiV) − (∇ · Ji) + Ri (1)

here Ci (mol/m3), Ji (mol/m2 s), Ri (mol/m3 s), V (m/s) and t (s) areoncentration, diffusive flux, reaction rate of species i, velocity andime, respectively. Fick’s law of diffusion is used to determine theiffusive fluxes of species i.

The steady-state continuity equation for transport of CO2 and2S in the tube side may be written as:

i−tube

[∂2Ci−tube

∂r2+ 1

r

∂Ci−tube

∂r+ ∂2Ci−tube

∂z2

]= Vz−tube

∂Ci−tube

∂z− Ri

(2)

here i refer to CO2 or H2S and Ri is reaction rate. r and z also refer toadial and axial coordinates, respectively. The reaction term in theube side is not considered because there is no chemical reactionn the tube side of the HFMC.

Velocity distribution in the tube side is assumed to follow New-onian laminar flow [18]:

z−tube = 2u

[1 −

(r

r1

)2]

(3)

here u (m/s) is average velocity in the tube side and r1 is the inneradius of fibers (see Fig. 3).

The boundary conditions assumed for the tube side are as fol-ows:

t z = 0, CCO2−tube = CCO2,0, CH2S−tube = CH2S,0 (Inlet boundary)

(4)

t z = L, Convective flux

ing Journal 168 (2011) 1217–1226

The convective flux boundary condition assumes that all masspassing through this boundary is convection-dominated. Thisfirstly assumes that any mass flux due to diffusion across thisboundary is zero.

at r = r1, CCO2−tube = CCO2−membrane, CH2S−tube = CH2S−membrane

(Membrane pores) (5)

at r = 0,∂CCO2−tube

∂r= ∂CH2S−tube

∂r= 0 (Symmetry) (6)

3.1.2. Concentration equations in the shell sideThe steady state continuity equation with chemical reaction

for CO2 in the shell side of the HFMC in cylindrical coordinate isobtained using Fick’s law of diffusion for estimation of diffusiveflux:

DCO2−shell

[∂2CCO2−shell

∂r2+ 1

r

∂CCO2−shell

∂r+ ∂2CCO2−shell

∂z2

]

= Vz−shell

∂CCO2−shell

∂z(7)

Velocity distribution in the shell side is obtained by solving themomentum equation, i.e. Navier–Stokes equations. Therefore, themomentum and the continuity equations should be coupled andsolved simultaneously to obtain concentration distribution of thesolutes. The Navier–Stokes equations describe flow in viscous fluidsthrough momentum balances for each of the components. Theyalso assume that density and viscosity of the modeled fluids areconstant, which yields to a continuity condition. The Navier–Stokesequations are defined as follows [18]:

−∇ · (∇Vz−shell + (∇Vz−shell)T ) + (Vz−shell.∇)Vz−shell + ∇p = F

∇.Vz−shell = 0(8)

where , V and denote fluid dynamic viscosity (kg/m s), velocityvector (m/s), density (kg/m3), respectively; p is pressure (Pa) and Fis a body force term (N).

Happel’s free surface model can be used to estimate the radius ofshell side [17]. The radius of free surface (r3 in Fig. 3) can be definedas:

r3 =(

11 − �

)1/2r2 (9)

In which � is volume fraction of the void. It can be calculated asfollows:

1 − � = nr22

�2(10)

where n is the number of fibers and � is the module inner radius.Happel’s free surface model can also be used to determine theshell side velocity. In Happel’s model, the fluid flow in the shellside of the membrane contactor is configured as fluid envelopearound the fiber and there is no interaction between the fibers.Some researchers used Happel’s free surface model [10,19]. How-ever, Navier–Stokes equations provided general methodology fordetermination of velocity in the shell side and were used for allmembrane geometries [14,20].

The reaction rate between H2S and MDEA is assumed to beinstantaneous [11,21] and therefore H2S concentration of in the

shell side is negligible. Therefore, the continuity equation for H2Stransport 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)

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a

a

A

3

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3

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a

a

a

a

3

sCfiemsnab2t

M. Rezakazemi et al. / Chemical En

t z = 0, Convective flux, p = patm (Outlet boundary) (12)

t r = r3,∂CCO2–shell

∂r= 0 (Symmetry boundary)

(No slip condition), (13)

t r = r2, CCO2−shell = m × CCO2−membrane (Henry’law)

(No slip condition), (14)

The reaction rates between CO2 and MDEA are given in Appendix. m is the physical solubility of gas in the liquid solvent.

.1.3. Membrane equationsThe steady-state continuity equation for transport of CO2 and

2S inside the membrane, which is considered to be due to diffusionlone, may be written as:

i−membrane

[∂2Ci−membrane

∂r2+ 1

r

∂Ci−membrane

∂r+ ∂2Ci−membrane

∂z2

]= 0

(15)

Boundary conditions are given as:

t r = r1, Ci−membrane = Ci−shell (16)

t r = r2, CCO2−membrane = CCO2−shell

m(Henrys’law), CH2S−membrane = 0

(17)

here m is solubility of CO2 in the absorbent.

.1.4. Amine equationsThe steady state continuity for amine (MDEA) in the shell side

f the HFMC may be written as:

MDEA−shell

[∂2CMDEA−shell

∂r2+ 1

r

∂CMDEA−shell

∂r+ ∂2CMDEA−shell

∂z2

]

= Vz−shell∂CMDEA−shell

∂z(18)

Boundary conditions for the shell side are given as:

t z = L, CMDEA−shell = CM0 (Inlet boundary), (19)

t z = 0, Convective flux (Outlet boundary), (20)

t r = r3,∂CMDEA−shell

∂r= 0 (Symmetry boundary), (21)

t r = r2,∂CMDEA−shell

∂r= 0 (Insulation boundary) (22)

.2. Numerical solution of model equations

The model equations related to shell side, membrane and tubeide with the appropriate boundary conditions were solved usingOMSOL Multiphysics version 3.2 software (Sweden), which usesnite element method (FEM) for numerical solutions of the modelquations. The finite element analysis is combined with adaptiveeshing and error control using numerical solver of UMFPACK ver-

ion 4.2. This solver is well suited for solving stiff and non-stiff

on-linear boundary value problems. The applicability, robustnessnd accuracy of this method for membrane contactors were provedy some authors [9,19,20]. An IBM-PC-Pentium 4 (CPU speed is800 MHz) was used to solve the set of equations. The computa-ional time for solving the set of equations was about 10 min. Fig. 3

ing Journal 168 (2011) 1217–1226 1221

shows a segment of the mesh used to determine the gas transportbehavior in HFMC. It should be pointed out that the COMSOL meshgenerator creates triangular meshes that are isotropic in size. Alarge number of elements are then created with scaling. A scalingfactor of 500 was employed in z direction due to a large differencebetween r and z. COMSOL automatically scales back the geometryafter meshing. This generates an anisotropic mesh around 3000 ele-ments. Adaptive mesh refinement in COMSOL, which generates thebest and minimal meshes, was used to mesh the HFMC geometry.

4. Results and discussions

4.1. Model validation

The simulation results for the separation of CO2 and H2S fromCH4 using the HFMC were compared with the experimental data inorder to validate the mass transfer 2D model proposed. The CO2 andH2S outlet concentrations in HFMC for different values of liquid andgas velocities are presented in Table 2. As shown, increasing liquidvelocity in the shell side of the HFMC increases the mass transferrate of CO2 in the membrane. The liquid velocity affects the convec-tion contribution in the mass transfer (continuity equation) in theshell side which in turn changes the overall mass transfer of CO2.Table 2 also reveals that the liquid velocity has significant effecton the mass transfer of CO2. However, it does not affect the masstransfer of H2S because its concentration in the liquid phase wasassumed to be negligible due to instantaneous reaction betweenH2S and MDEA. Table 2 also shows that the model predictions are ingood agreement with the experimental values for different valuesof gas and liquid velocities.

4.2. Velocity field

The velocity field and profile in the shell side of the HFMC areshown in Figs. 4 and 5, where the liquid absorbent flows. The veloc-ity profile in the shell side of the HFMC was simulated by solving theNavier–Stokes equations. In the gas–liquid membrane contactorsfor gas separation the liquid phase plays crucial role in mass trans-fer because it is the controlling phase. In the absence of chemicalreaction, the mass transfer of gas is controlled by the liquid solvent.Chemical reaction increases the mass transfer rate of gas phase anddecreases resistance of the liquid phase. Therefore, the velocity pro-file for the liquid phase must be accurately obtained. The velocityprofile is almost parabolic with a mean velocity which increaseswith 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, themodel considers the inlet effects on the hydrodynamics of fluid flowin the shell side.

4.3. Concentration distribution of CO2 and H2S in the HFMC

Fig. 6 presents the dimensionless concentration distribution(C/C0) of CO2 and H2S in the tube side, the membrane and the shellside of the HFMC. The gas mixture containing CO2/H2S/CH4 flowsfrom one side of the HFMC (z = 0) where the concentrations of CO2and H2S are the highest, whereas the liquid solvent (MDEA) flowsfrom the other side (z = L) where the concentrations of gases areassumed to be zero. As the gas mixture flows through the tubeside, it is transferred towards the membrane due to concentration

difference (driving force) [20]. The mechanisms of mass transferin the tube and shell sides are convection and diffusion. In thez-direction, the predominant mass transfer mechanism is convec-tion because fluid flows in the z-direction, while in the r-direction,diffusion occurs because of large concentration differences in the

1222 M. Rezakazemi et al. / Chemical Engineering Journal 168 (2011) 1217–1226

Table 2Comparison of experimental results with simulation results.

Inlet conditions Experimental CFD simulation

Gas flow rate (L/h) Liquid flow rate (L/h) H2S (vol.%) CO2 (vol.%) H2S (vol.%) CO2 (vol.%) H2S (vol.%) CO2 (vol.%)

360 0.5 2.45 8.61 0.0014 2.96 0.0011 2.55360 2.5 0.31 8.43 0.0007 2.00 0.0004 1.89420 0.5 0.84 4.73 0.1173 3.40 0.1138 3.21420 2.5 1.45 4.77 0.0036 1.30 0.0022 1.25480 0.5 1.36 1.51 0.1173 0.70 0.1159 0.65

rdt

tso

4

bss

F(ca

480 1.5 0.31 8.43480 3.5 2.45 8.61

-direction. The gas is transferred through the membrane only byiffusion mechanism and then absorbed by the moving solvent inhe shell side.

Fig. 7 illustrates the axial concentration profile of H2S and CO2 inhe tube side of HFMC. Fig. 7 indicates that H2S concentration dropsuddenly at the inlet of the membrane because of low concentrationf H2S in the feed and high reaction rate of H2S with MDEA.

.4. Concentration distribution of MDEA in the HFMC

A representation of the dimensionless concentration distri-ution of amine (MDEA) in the shell side of the HFMC ishown in Fig. 8. The amine solution flows through the shellide (z = L) and reacts with CO2 and H2S which come from the

ig. 4. Velocity field in the shell side of the HFMC. Gas flow rate = 480L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 vol.%; H2S inletoncentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temper-ture = 298 K.

0.0763 3.54 0.0750 3.340.0029 1.37 0.0015 1.25

membrane pores due to the concentration difference betweenthe two sides of the membrane. The amine concentrationdecreases significantly in the gas–liquid interface zone. Thevariation of MDEA concentration along the HFMC is also sig-nificantly high due to the reaction mainly between CO2 andMDEA.

Fig. 9 also indicates axial concentration profile of MDEA alongthe HFMC in the shell side. Figs. 8 and 9 show that almost all MDEAis consumed in the process. This is because of highly effective con-tact between the gas and liquid phases and the contact time is longenough to achieve a reasonable separation even at high gas veloc-ities. The most important advantage of this HFMC is its effectiveoperation 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 fol-lowing equation:

% CO2 removal = 100(� × C)inlet − (� × C)Outlet

(� × C)inlet= 100

(1 − Coutlet

Cinlet

)

(23)

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

Fig. 5. Velocity profile in the shell side along the membrane length. Gas flowrate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 wt.%; H2Sinlet concentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; tem-perature = 298 K.

M. Rezakazemi et al. / Chemical Engineering Journal 168 (2011) 1217–1226 1223

F ) in tht on = 0.

g

C

wflb

ttmtplrl

iri

4

wethasc

As the porosity-to-tortuosity ratio increases, the membrane diffu-sivity and thus the mass transfer of CO2 through the membraneincreases; i.e. the CO2 outlet concentration decreases. Indeed,when the porosity-to-tortuosity ratio increases, the membranemass transfer resistance decreases. Therefore, the total resistance

ig. 6. Representation of the concentration distribution of (a) CO2 and (b) H2S (C/C0

ion = 50 wt.%; H2S inlet concentration = 0.31 vol.%; amine (MDEA) inlet concentrati

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

outlet =

r=r1∫r=0

∫C(r)dA

r=r1∫r=0

∫dA

∣∣∣∣∣∣∣∣∣∣∣z=L

(24)

here A is area of the tube side (m2). The change in volumetric gasow rate is assumed to be negligible and thus % CO2 removal cane approximated by Eq. (17).

In Fig. 10, the CO2 outlet concentration in the gas phase (theube side) is plotted as functions of the liquid (absorbent) andhe gas (feed) flow rates. As the absorbent flow rate increases, the

ass transfer rate of CO2 into the liquid phase increases becausehe concentration gradients of CO2 and absorbent in the liquidhase increase, which in turn results in reduction of the CO2 out-

et concentration in the gas phase. It can also be observed that theeduction rate of CO2 outlet concentration is much sharper at higheriquid flow rates.

The effect of gas flow rate on CO2 outlet concentration is alsollustrated in Fig. 10. As expected, increasing the gas flow rateeduces the residence time of the gas phase in the HFMC, whichn turn reduces the mass transfer of CO2 in the HFMC.

.6. Effect of porosity-to-tortuosity ratio

Variation of the porosity-to-tortuosity ratio between 0.1 and 0.9as also considered in the simulations in order to investigate the

ffect of this parameter on the mass transfer of CO2. The values for

his ratio correspond to those of current porous membranes whichave porosities between 0.15 and 0.75 and tortuosity between 2nd 3 (values reported by Gabelman and Hwang [2]). Fig. 11 repre-ents the effect of the porosity-to-tortuosity ratio on the CO2 outletoncentration. As observed, the CO2 outlet concentration decreases

e HFMC. Gas flow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentra-5 mol/L; temperature = 298 K.

from 4 to 0.6 vol.% as this ratio increases from 0.1 to 0.9. The effec-tive diffusion coefficient of CO2 (DCO2−membrane) in the membrane iscalculated through the membrane porosity and tortuosity, whichis 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 gasdiffusivity in the gas phase (tube side). As seen, the effective diffu-sion coefficient is a function of membrane porosity and tortuosity.

Fig. 7. Axial concentration distribution of H2S and CO2 in the tube side of HFMC. Gasflow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 vol.%;H2S inlet concentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L;temperature = 298 K. “L” is length of a fiber (m).

1224 M. Rezakazemi et al. / Chemical Engineering Journal 168 (2011) 1217–1226

Fig. 8. Dimensionless concentration of MDEA (CMDEA−shell/CM0) in the shell sideocc

tco

fbi

Fig. 9. Axial concentration distribution of MDEA in the shell side of the HFMC. Gasflow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 vol.%;H2S inlet concentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L;temperature = 298 K; “L” is length of a fiber (m).

increasing absorbent concentration increases CO2 removal by

Fc

f the HFMC. Gas flow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inletoncentration = 50 wt.%; H2S inlet concentration = 0.32 vol.%; amine (MDEA) inletoncentration = 0.5 mol/L; temperature = 298 K.

o the mass transfer of CO2 reduces. The simulation results indi-ated that the porosity-to-tortuosity ratio does not have any effectn the H2S removal.

It should be pointed out that Knudsen diffusion was neglectedor calculation of mass transfer flux across membrane pores. This isecause its contribution to overall mass transfer across membrane

s negligible [12,19,20].

ig. 11. Effect of porosity-to-tortuosity ratio on concentration of CO2. Gas flow rate = 4oncentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temperature = 2

Fig. 10. Relationship between CO2 outlet concentration and gas and liquid flowrates. CO2 inlet concentration = 50 vol.%; H2S 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 H2Sremoval

Fig. 12 illustrates the effect of the absorbent concentration onCO2 outlet stream in the tube side of the HFMC. As observed,

reducing CO2 outlet concentration. Since reaction kinetics of MDEAwith CO2 is elementary, it depends directly on absorbent con-centration. Increasing absorbent concentration increases reactionrate between CO2 and absorbent and this reduces CO2 outlet con-

80 (L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 wt.%; H2S inlet98 K.

M. Rezakazemi et al. / Chemical Engineer

F(ca

chtwe

nc

4

itocdtFb

phmmf

Focc

ig. 12. Effect of absorbent concentration on CO2 removal. Gas flow rate = 480L/h); liquid flow rate = 3.5 (L/h); CO2 inlet concentration = 50 vol.%; H2S inletoncentration = 0.32 vol.%; amine (MDEA) inlet concentration = 0.5 mol/L; temper-ture = 298 K.

entration. The results also confirm that absorbent concentrationas significant effect on CO2 removal and plays a key role inhe separation process. Improving liquid phase mass transfer rateith increasing liquid phase velocity or absorbent concentration,

nhances CO2 removal efficiency.The results indicated that the amine (MDEA) concentration does

ot have any effect on H2S removal. Therefore, the effect of MDEAoncentration on H2S outlet concentration is not shown here.

.8. Flux distribution in the HFMC

Mass transfer flux distribution in the gas phase of the HFMC isllustrated in Fig. 13. Both diffusive and convective fluxes for CO2 inhe tube side are shown in Fig. 13 to demonstrate the contributionf axial diffusion in the simulation. As observed, contribution ofonvective flux in the z-direction is predominant compared to axialiffusive flux. That is due to the fact that in the axial direction,he velocity is significant and causes high convective flux for CO2.ig. 13 also indicates that both fluxes decrease along the contactorecause of driving force reduction in the z-direction.

It should be pointed out here that the hollow fibers are made of

olypropylene (PP) which is a hydrophobic polymer. Generally, inydrophobic HFMCs the aqueous phase cannot penetrate into theembrane pores because of hydrophobic nature of the fibers. Inembrane contactors, membrane wettability depends on several

actors including membrane pore diameter, contact angle, surface

ig. 13. Axial diffusive and convective flux distribution of CO2 in the tube sidef the HFMC. Gas flow rate = 480 (L/h); liquid flow rate = 3.5 (L/h); CO2 inletoncentration = 50 vol.%; H2S inlet concentration = 0.32 vol.%; amine (MDEA) inletoncentration = 0.5 mol/L; temperature = 298 K; “L” is length of a fiber (m).

ing Journal 168 (2011) 1217–1226 1225

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

�P = −4� cos (�)dmax

(26)

where � is surface tension of the liquid phase that is equal to72.3 × 10−3 (N/m) and � refers to the contact angle between the liq-uid phase and the membrane that is equal to 117.7◦ for a water–PPsystem [23]. Since the liquid pressure was 2 bar, the pore diame-ter could be estimated using Eq. (26) to be 0.66 �m. Therefore, themembrane wettability occurs for any pore larger than 0.66 �m. Themembrane pore size is 0.03 �m, so the membrane pores cannot bewetted 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 maintainedhigher than the gas phase to establish the interface at the poresadjacent the liquid phase. This also prevented the dispersion of gasphase into the liquid phase. Therefore, the aqueous phase could notpenetrate into the membrane pores during the experiments.

5. Conclusions

Chemical absorption of CO2 and H2S in a HFMC was studiedin this work. A 2D mathematical model was proposed to describesimultaneous absorption of CO2 and H2S in the HFMC. The modelwas based on solving the conservation equations for gas compo-nents in three sections of the HFMC. The FEM was applied to solvethe differential equations of mass transfer. Absorption medium wasamine (MDEA) aqueous solution. The simulation results revealedthat the H2S removal with aqueous solution of MDEA is almostcomplete. The model was validated with the experimental resultsfor absorption of CO2 and H2S in MDEA aqueous solution. The mod-eling predictions were in good agreement with the experimentaldata for different values of gas and liquid velocities. The simula-tion results for absorption of CO2 in MDEA aqueous indicated thatthe CO2 removal increases with increasing liquid phase velocityand MDEA concentration in the HFMC. The simulation results alsorevealed that H2S removal was almost complete using the HFMC.

The results of this work indicated that the proposed mass trans-fer model is capable to predict the performance of HFMCs for NGsweetening. The proposed simulation can also take into accountcomplex chemical reaction schemes. The developed model thus canbe used to predict the mass transfer performance of the HFMCs forother reactive as well as non-reactive systems. Eventually, the pro-posed mass transfer model provides a preliminary design tool formulti-component membrane gas absorption processes.

Appendix A.

A.1. Reaction rate of CO2 with amines

See Table A.1.

Table A.1Rate expression of amines.

Aqueous amine solution Ri (mol/m3 s) k (m3/mol s) Refs.

MDEA kCCO2 CAmine 8.40 × 10−3 [24,25]

1 gineer

A

s

m

A

s

D

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[dioxide, nitrous oxide) in aqueous alkanolamine solutions, Journal of Chemical& Engineering Data 33 (1988) 29–34.

226 M. Rezakazemi et al. / Chemical En

.2. CO2 solubility

The distribution coefficient of CO2 in water was taken from Ver-teeg and van Swaaij [26]:

w,CO2 = 3.59 × 10−7 RT exp(

2044T

)(A.1)

.3. CO2 diffusivity

The diffusivity of CO2 in pure water Dw,CO2 was taken from Ver-teeg and van Swaaij [26].

w,CO2 = 2.35 × 10−6 exp(−2119

T

)(A.2)

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