Ali Taghvaie Nakhjiri,Amir Heydarinasab,*,Omid Bakhtiari,Toraj Mohammadi

1Department of Chemical Engineering,Science and Research Branch,Islamic Azad University,Tehran,Iran

2Membrane Research Center,Faculty of Chemical and Petroleum Engineering,Razi University,Kermanshah,Iran

3Research Center for Membrane Separation Processes,Faculty of Chemical Engineering,Iran University of Science and Technology(IUST),Narmak,Tehran,Iran

Keywords:CO2removal Membrane wettability Numerical simulation CO2/CH4gaseous mixture NaOH MEA and TEA liquid absorbents

A B S T R A C T The present paper renders a modeling and a 2D numerical simulation for the removal of CO2from CO2/CH4gaseous stream utilizing sodium hydroxide(NaOH), monoethanolamine(MEA)and triethanolamine(TEA)liquid absorbents inside the hollow fiber membrane contactor.Counter-current arrangement of absorbing agents and CO2/CH4gaseous mixture flows are implemented in the modeling and numerical simulation. Non-wetting and partial wetting modes of operation are considered where in the partial wetting mode,CO2/CH4gaseous mixture and liquid absorbents fill the membrane pores.The deteriorated removal of CO2in the partial wetting mode of operationis mainly due to the mass transfer resistance imposed by the liquid in the pores of membrane. The validation of numerical simulation is done based on the comparison of simulation results ofCO2removal using NaOH and experimental data under non-wetting mode of operation.The comparison illustrates a desirable agreement with an average deviation of less than 5%.According to the results,MEA provides higher efficiency for CO2removal in comparison with the other liquid absorbents.The order for CO2removal performance is MEA＞NaOH＞TEA.The influence of non-wetting and partial wetting modes of operation on CO2removal are evaluated in this article as one of the novelties.Besides,the percentage of CO2sequestration as a function of gas velocity for various percentages of membrane pores wetting ranging from0 (non-wetting mode of operation) to 100% (complete wetting mode of operation)is studied in this research paper,which can be proposed as the other novelty.The results indicate that increase in some operational parameters such as module length,membrane porosity and absorbents concentration encourage the removal percentage of CO2from CO2/CH4gaseous mixture while increasing in membrane tortuosity,gas velocity and initial CO2concentration has unfavorable influence on the separation efficiency of CO2.

1.Introduction

Having long been considered,the elimination of CO2from CO2/CH4gaseous stream is a momentous procedure in various industrial processes such as biogas purification,natural gas processing and the treatment of flue gas[1,2].The presence of CO2in natural gas is deleterious due to decreasing the heating value of gas and various operational problems such as corrosion because of its acidic feature.Membranes that are applied in membrane contacting processes are considered as a barrier and provide appropriate interfacial zones for gas–liquid phases.Thus,the removal efficiency substantially depends on the liquid absorbent and gas solute interaction.The scientific research on CO2removal from gas stream utilizing hollow fiber membrane contactor(HFMC)has been implemented since 1980.Qi and Cussler were the first investigators who developed the first membrane with the purpose of absorbing CO2acid gas from gaseous mixtures[3].The application of hollow fiber membrane contactors (HFMCs) renders numerous benefits such as simplicity to scale up, high surface area, small structural size and separate flow channels for both gas and liquid phases[4–6].Chemical elimination of CO2using alkanolamine absorbents such as MEA in packed columns is one of the most influential procedures[7].Albeit some disadvantages such as evaporation of solvents because of high temperature and high energy consumption should be considered during the use of alkanolamine aqueous solutions[8].Some investigators applied another class of liquid absorbents instead of alkanolamine solutions,namelyionic liquids in order to increase the efficiency of CO2separation from natural gas due to their admirable characters as like as acceptable thermal stability,good CO2solubility and trivial volatility[9,10].However,entrainment,channeling and flooding can be regarded as some of the mechanical and operational restrictions which can be happened during the utilization of these liquid absorbents in packed columns[11,12].Disparate procedures of CO2removal from natural gas including cryogenics,membrane gas adsorption are under the evaluation[8,13].The capture of CO2from natural gas using different chemical absorbent solvents such as alkanolamine solutions(MEA,DEA,MDEA…),ionic solvents and alkali solutions were modeled by various researchers[14–16].Fig.1 presents the molecular structures of liquid absorbents utilized in this research paper.Teplykov et al.proposed a theoretical simulation to study the purification of biogas(40%CH4and 60%CO2)applying polyvinyltrimethylsilane(PVTMS)non-porous membrane contactor[17].The efficiency of CO2elimination from natural gas using MEA,MDEA and deionized water In the HFMCs was evaluated by Yuexia et al.[18].Luis et al.developed a model related to the elimination of SO2in ceramic hollow fiber membrane contactor[19].Al-Marzouqi et al.rendered a comparison between the separation efficiency of different solutions using poly propylene(PP)mini module[20].Recently,various porous polymers such aspolysulfone(PSf),polypropylene(PP)and polyimide(PI)have been applied as membranes by numerous researchers[21–25].Approximately,all of the investigational papers developed by the authors presented the dynamic modeling of CO2removal from gaseous mixtures under non-wetting mode of operation while this condition is regarded as an ideal state for CO2removal[14,26–28].However in many cases, a part of membrane pores is wetted by liquid absorbents which increases the mass transfer resistance in the pores of membrane dramatically and eventuates in decreasing the removal efficiency of CO2from CO2/CH4gaseous mixture.

Recently,The use of finite element method(FEM)for analyzing the removal performance of greenhouse gases such as CO2,H2S and SO2from gaseous streams and also simulation of momentum,mass and heat transfer phenomenon were developed by different researchers and showed acceptable accuracy compared to experimental data[24,25,29–36].For instance,Eslami et al.,reported that UMFPACK was considered as an appropriate numerical solver due to its considerable memory efficiency[29].Besides,numerous investigators provided numerical simulation of CO2absorption from gaseous mixtures using COMSOL software which is based on FEM[25,27,29].They reported brilliant accuracy compared to experimental works.According to the mentioned items,COMSOL is used in this study to provide numerical analysis of CO2removal from CO2/CH4gaseous stream under nonwetting and partial wetting modes of operation.

According to the best of our knowledge,very few articles studied the effect of membrane pores wettability on the removal of CO2from CO2/CH4gaseous mixture using few liquid absorbents in the hollow fiber membrane contactor.As the novelty,this paper renders a dynamic modeling and a 2D numerical simulation for the absorption of CO2from CO2/CH4gaseous stream using NaOH,MEA and TEA liquid absorbents under both non-wetting and partial wetting modes of operation inside the porous PVDF hollow fiber membrane contactor(HFMC).Also,the effects of important operational parameters such as the velocities of gas and liquid,tortuosity and porosity of membrane,the concentration of liquid absorbents and module length on the separation efficiency of CO2from CO2/CH4gaseous mixture are investigated carefully.

2.Mathematical Model Development

This study renders material,momentum and energy transport equations in order to interpret the transport of chemical liquid absorbent solvents(NaOH,MEA and TEA)and gas mixture in porous Polyvinylidenefluoride (PVDF)hollow fiber membrane contactor.Each hollow fiber membrane contactor(HFMC)consists of three parts:tube side,porous membrane side and shell side.The schematic diagram of porous hollow fiber membrane module under non-wetting and partial wetting modes of operation is apparently presented in Fig.2.NaOH,MEA and TEA liquid solvents flow within the fiber considering a fully developed laminar parabolic velocity profile while in the opposite direction,gas moves through the shell.Fig.3,obviously demonstrates the cross sectional region of HFMC.According to the Happel's free surface model,just portion of the gas surrounding the fiber of porous membrane contactor is considered which is able to be estimated as circular cross section[37].

The development of the model is done on the basis of the assumptions as follows:

1)The model is developed under steady state condition,

2)The adoption of a fully developed laminar parabolic gas velocity profile in the shell side,and a laminar liquid flows in the lumen side of porous HFMC,

3)Considering the gas phase in the lumen side as an ideal gas,

4)The application of Henry's law for the gas–liquid surface,

5)The imposition of Isothermal condition,

6)The utilization of Happel's free surface model for predicting species velocity profile in the liquid phase,

7)The Newtonian liquid absorbent in the tube side of HFMC has constant physical properties,

8)Counter-current arrangement of liquid–gas flow.

Module specification,physicochemical properties and operating conditions of CO2acid gas and sodium hydroxide(NaOH),monoethanolamine(MEA)and triethanolamine(TEA)applied in the modeling and numerical simulation are presented in Tables 1 and 2,respectively.

2.1.Material balance in the shell side

The continuity equation Inside the shell region of hollow fiber membrane contactor may be estimated as follows:

Fig.1.Molecular structures of liquid absorbents used in this study.

Fig.2.Schematic diagram and model domain development for hydrophobic porous HFMC under(a)non-wetting and(b)partial wetting modes of operation.

where,in this equation,Ci,Riand Niare explained as the concentration,reaction rate and flux of species i along the length of membranereaction rate and flux of species i along the length of membrane,respectively.Fick's law of diffusion is denoted as follows with the purpose of defining the flux of species i.

In this equation,Diis denoted as the diffusion coefficient of components i along the length of hollow fiber membrane contactor(HFMC)and Vzis the axial velocity.The combination of Eqs.(1)and(2)eventuates in deriving the steady state material balance equation inside the shell segment of porous PVDF hollow fiber membrane contactor with the goal of gas molecules transport from CO2/CH4gaseous mixture which is derived as:

In this equation,DCO2,sand CCO2,scan be expressed as the diffusion coefficient and concentration of CO2inside the shell segment of HFMC.Based on the assumption of Happel's free surface model,the velocity profile in the shell side of HFMC(Vz,s)can be correlated applying following equation:

Fig.3.Cross sectional region of the porous PVDF hollow fiber membrane contactor and circular approximation.

Table 1Hollow fiber membrane contactor parameters and operating conditions utilized for numerical analysis[38,39]

Table 2CO2,NaOH,MEA and TEA physicochemical properties used for dynamic modeling and simulation

In this equation,V indicates the average velocity inside the shell region of hollow fiber membrane contactor(HFMC).r3is the effective radius of each shell unit of each fiber which can be derived considering active area and hexagonal shape shell unit around each fiber as follows:

where φ is interpreted as volume fraction of void.

2.2.Material balance inside the membrane section under non-wetting mode of operation

For non-wetting mode of operation across the membrane layer of porous HFMC,the steady state material balance equation with the purpose of gas molecules transport from CO2/CH4gaseous mixture is regarded because of diffusion,only.There is no reaction in the gas filled pores.Thus,the equation can be presented as follows:

where in this equation,DCO2,mand CCO2,mare defined as the diffusion coefficient and concentration of carbon dioxide(CO2)across the porous polyvinylidenefluoride(PVDF)membrane.The diffusion coefficient of carbon dioxide in the porous PVDF membrane depends on two important parameters:1)membrane porosity(ε)and 2)membrane tortuosity(τ)and can be rendered as:

2.3.Material balance inside the membrane section under partial wetting mode of operation

As can be seen in Fig. 4, due to the decrement in the surface tension, a portion of membrane pores may be wetted by the penetration of liquid solvents.Hence,in order to evaluate the steady state material balance for the transport of CO2inside the porous membrane along with liquid absorbents(NaOH,MEA and TEA),two parts(the gas filled and the liquid filled portions of the membrane)can be considered in the following sections below:

2.3.1.Material balance inside the gas filled portion

The gas filled portion of porous membrane is illustrated in the right side of Fig. 4. In this section, the only mechanism for the transport of CO2inside the porous membrane is diffusion.Hence,the steady state material balance is derived as follows:

2.3.2.Material balance inside the liquid filled portion

The liquid filled portion of porous membrane is depicted in the left side of Fig. 4. In this section, the governing mechanisms for the transport of CO2inside the porous membrane along with liquid absorbents(NaOH,MEA and TEA)are diffusion and reaction.Therefore,the steady state material balance is derived as follows:

Fig.4.A schematic diagram of the membrane thickness under partial wetting mode of operation.

Table 3Boundary conditions utilized for model development under non-wetting mode of operation

Due to the porosity of the membrane,the reactions which are taking place inside the membrane occur through the pores only.Therefore,the reaction inside the liquid portion of porous membrane is derived as:

2.4.Material balance in the tube segment

The steady state material balance equation for carbon dioxide(CO2),sodium hydroxide(NaOH),monoethanolamine(MEA)and triethanolamine(TEA) transport through the tube side of porous HFMC is due to diffusion,reaction and convection and is able to be derived as follows:

In this equation “i”shows carbon dioxide(CO2)and liquid absorbents(NaOH,MEA and TEA).The velocity distribution inside the tube region of hollow fiber membrane contactor is assumed to follow Newtonian laminar flow and can be presented as follows[48]:

Boundary conditions utilized inside the tube,porous membrane and shell segments of hollow fiber membrane contactor under both non wetting and partial wetting modes of operation are listed in Tables 3 and 4,respectively.

2.5.Numerical procedure

The principal aim of this study is to render a modeling and numerical simulation for the separation of carbon dioxide(CO2)from CO2/CH4gaseous mixture using sodium hydroxide(NaOH),monoethanolamine(MEA)and trirthanolamine(TEA)absorbent solvents in hydrophobic porous PVDF hollow fiber membrane contactor under non-wetting and partial wetting modes of operation.For this reason,COMSOL software which applies finite element method(FEM)was used to solve momentum,material and energy transport equations inside the tube,membrane and shell side of the hydrophobic porous HFMC with considering appropriate boundary conditions.This numerical simulation presents the transport of NaOH,MEA and TEA liquid solvents and CO2/CH4gaseous mixture in a countercurrent porous HFMC.The PARDISO solver is used among the variety of numerical solvers because of increasing the memory efficiency.Mapped meshing is used with the aim of studying and evaluating the results of simulation using finite element analysis which is depicted in Fig.5,apparently.Computer used for the numerical simulation had a 64-bit operating system,a4Gigabyte RAM and the computational duration for numerical simulation is approximately 1 min applying an Intel core?i5 4200U CPU.

Table 4Boundary conditions utilized for model development under partial wetting mode of operation

Fig.5.Mapped meshing for the simulation of CO2removal from CO2/CH4gaseous mixture in HFMC.

3.Results and Discussion

3.1.Model validation

On the basis of the authors' knowledge,there is no article that studied the separation of CO2from CO2/CH4gaseous mixture under both non-wetting and partial wetting modes of operation using NaOH,MEA and TEA liquid absorbent solvents in a hydrophobic PVDF hollow fiber membrane contactor(HFMC).Hence,the numerical simulation predictions for chemical absorption of carbon dioxide in NaOH liquid solvent(using a porous hydrophobic PVDF hollow fiber membrane contactor)under non-wetting mode of operation are compared with the experimental data which is illustrated in Figs.6 and 7[38].It is worth to mention that there is an excellent and rational agreement between the results of numerical simulation and experimental data with an average deviation of less than 5%.

Fig.6.Comparison of experimental data(triangle)and numerical simulation predictions(solid line)for carbon dioxide(CO2) flux at different velocities of NaOH in porous HFMC under non-wetting mode of operation.

Fig.7.Comparison of experimental data(triangle)and numerical simulation predictions(solid line)for carbon dioxide(CO2) flux at variable temperatures of NaOH in porous HFMC under non-wetting mode of operation.

3.2.Concentration distribution of CO2using NaOH,MEA and TEA inside the porous hydrophobic HFMC under non-wetting mode of operation

Whenever CO2/CH4gaseous mixture passes through the shell segment of porous hydrophobic HFMC(z=L)where CO2concentration is maximum,NaOH,MEA and TEA liquid absorbent solvents move inside the lumenside of HFMC(z=0)where the concentration of carbon dioxide is assumed zero.As CO2/CH4gaseous mixture flows inside the shell side of the contactor,it moves through the membrane side due to concentration gradient and then it is absorbed by NaOH,MEA and TEAmoving liquid absorbents. Concentration gradient of carbon dioxide(CO2)in the shell,membrane and tube segment of the porous PVDF hollow fiber membrane contactor considering various liquid absorbents are illustrated in Fig.8,conspicuously.It is worth quoting that the CO2/CH4gaseous mixture transport in the shell side of porous hydrophobic PVDF hollow fiber membrane contactor is due to the existence of two principal mechanisms(axial convection and radial diffusion)but in the tube segment of PVDF membrane contactor,diffusional mass transfer is the dominant mechanism.

3.3.Concentration distribution of NaOH,MEA and TEA at the tube-membrane interface under non-wetting mode of operation

Fig.9 apparently renders the concentration distribution of NaOH,MEA and TEA liquid absorbents at the tube-membrane interface of hydrophobic porous PVDF hollow fiber membrane contactor under non-wetting mode of operation. Whenever carbon dioxide diffuses inside the pores of membrane, it reacts with liquid absorbents which are flowing in the tube side.Consequently,due to the reaction of CO2with NaOH,MEA and TEA and also the consumption of liquid absorbents,the concentration of CO2at the tube-membrane interface reduces significantly while far from the tube-membrane interface the concentration of CO2is in the maximum amount because of the absence of CO2.

It can be understood from Fig.9 that the reaction of CO2with monoethanolamine(MEA)is faster than the reaction of CO2with NaOH and TEA.It can be shown from the figure that approximately all of MEA consumes at the tube membrane interface while the concentration of NaOH at the tube membrane interface declines from 1000 mol·m-3to 960mol·m-3and the concentration of TEA decreases from 1000mol·m-3to980mol·m-3which eventuates in better CO2removal performance using MEA in comparison with other liquid absorbents.

Fig.8.Concentration distribution of CO2using (a) NaOH (b)MEA and (c) TEA liquid absorbents inside the porous hydrophobic PVDF hollow fiber membrane contactor under non-wetting mode of operation,feed gas=20/80 CO2/CH4,CCO2,0=0.075 mol·m-3,Cabsorbents=1000 mol·m-3,Vg=0.07 m·s-1,Vl=2.3 m·s-1,T=303.15 K,P=1 MPa.

3.4.The influence of gas velocities on CO2removal using NaOH,MEA and TEA absorbents under non-wetting and partial wetting modes of operation

The influence of gas velocities on the removal of CO2from CO2/CH4gaseous stream applying NaOH,MEA and TEA liquid absorbents under non-wetting and partial wetting modes of operation is presented in Fig.10.The separation percentage of CO2from CO2/CH4gaseous mixture is derived from the following equation[50]:

As can be depicted,the removal efficiency of CO2from CO2/CH4gaseous mixture reduces significantly with increasing gas velocity.The increase in the gas velocity eventuates in decreasing the residence time in hydrophobic porous HFMC,which in turn decreases the carbon dioxide(CO2)separation rate,considerably.Also,by wetting the membrane pores of contactor,mass transfer resistance inside the membrane region of contactor increases substantially which results in the reduction of removal performance of CO2from gaseous mixture.

Table 5 presents the removal efficiency of CO2from CO2/CH4gaseous mixture utilizing different liquid absorbents under both non wetting and partial wetting modes of operation in a wide range of gas velocities.

3.5.The influence of module length on CO2removal using NaOH,MEA and TEA absorbents under non-wetting and partial wetting modes of operation

The influence of module length on the removal rate of CO2from CO2/CH4gaseous mixture in the porous hydrophobic PVDF hollow fiber membrane contactor applying three liquid absorbents(NaOH,MEA and TEA)under both non-wetting and partial wetting conditions is plotted in Fig.11.It is completely apparent from the figure that by increasing the module length, a significant improvement in the separation efficiency of CO2from CH4takes place due to enhancing the liquid–gas contact area and residence time.The removal rate of CO2from CO2/CH4gaseous mixture using NaOH,MEA and TEA absorbents under a wide range of module length can be illustrated in Table 6. Partial wetting of membrane pores and penetration of liquid into the pores causes a significant increase in mass transfer resistance which eventuates in decreasing the effective diffusion coefficient of CO2inside the membrane side and hence decreasing the removal performance of CO2in comparison with non-wetting mode of operation.

Fig.9.Concentration distribution of(a)NaOH(b)MEA and(c)TEA liquid absorbents at the tube-membrane interface under non-wetting mode of operation,feed gas=20/80 CO2/CH4,CCO2,0=0.075 mol·m-3,Vg=0.07 m·s-1,Vl=2.3 m·s-1,Cabsorbents=1000 mol·m-3,T=303.15 K,P=1 MPa,T=303.15 K,P=1 MPa.

3.6.The influence of membrane porosity and tortuosity on CO2removal using NaOH,MEA and TEA absorbents under non-wetting and partial wetting modes of operation

Fig.12 depict the influence of porosity of porous hydrophobic HFMC on the removal percentage of CO2utilizing sodium hydroxide(NaOH),monoethanolamine(MEA)and trirthanolamine(TEA)absorbent solvents under non-wetting and partial wetting modes of operation.It can be found from the Eq.(20)that there is a direct relation between the effective diffusion coefficient of CO2inside the membrane side(DCO2-mem)and membrane porosity[4,27].It means that increase in the porosity of hydrophobic membrane results in a significant increase in the membrane diffusivity.Consequently,by increasing the membrane diffusivity,the mass transfer of CO2inside the membrane side increases significantly which eventuates in an increase in the separation rate of CO2from CO2/CH4gaseous mixture.The effect of membrane porosity on removal efficiency of CO2using different liquid absorbents in a wide range under both non-wetting and partial wetting conditions is illustrated in Table 7,apparently.

Fig.10.The effect of gas velocity on CO2removal using (a)NaOH (b)MEA and (c) TEA liquid absorbents inside the porous hydrophobic PVDF hollow fiber membrane contactor under nonwetting (blue line) and partial wetting modes (40%wetting of membrane pores) (red line),feed gas=20/80CO2/CH4,r1=0.325 mm,rw=0.395mm,r2=0.5 mm,r3=5 mm CCO2,0=0.075 mol·m-3,Cabsorbents=1000 mol·m-3,Vl=2.3 m·s-1,T=303.15 K,P=1 MPa.

Table 5The removal efficiency of CO2from CO2/CH4gaseous mixture utilizing different liquid absorbents under both non-wetting and 40%partial wetting modes of operation in a wide range of gas velocity

Fig.11.The effect of module length on CO2removal using(a)NaOH(b)MEA and(c)TEA liquid absorbents inside the porous hydrophobic PVDF hollow fiber membrane contactor under non-wetting(blue line)and partial wetting modes(40%wetting of membrane pores)(red line),feed gas=20/80 CO2/CH4,r1=0.325 mm,rw=0.395 mm,r2=0.5 mm,r3=5 mm CCO2,0=0.075 mol·m-3,Cabsorbents=1000 mol·m-3,Vg=0.07 m·s-1,Vl=2.3 m·s-1,T=303.15 K,P=1 MPa.

Fig.13 shows the effect of membrane tortuosity of HFMC on the removal percentage of CO2utilizing NaOH, MEA and TEA liquid absorbents under non-wetting and partial wetting modes of operation. It can be perceived from Fig.13 that as the tortuosity of porous hydrophobic membrane increases,the mass transfer resistance of membrane increases substantially which results in a significant reduction in total mass transfer of CO2.Consequently,whenever the total mass transfer of CO2inside the hydrophobic membrane reduces the diffusivity of CO2gas in the membrane side declines which causes a considerable reduction in CO2removal percentage.Table 8 presents the effect of membrane tortuosity on removal efficiency of CO2using different liquid absorbents in a wide range under both modes(non-wetting and partial wetting).

Table 6The removal efficiency of CO2from CO2/CH4gaseous mixture utilizing different liquid absorbents under both non-wetting and 40%partial wetting modes of operation in a wide range of module length

3.7.The influence of CO2initial concentration on CO2removal using NaOH,MEA and TEA absorbents under non-wetting and partial wetting modes of operation

Fig.14 apparently demonstrates the effect of CO2concentration on the removal efficiency of CO2in porous HFMC under both nonwetting and partial wetting conditions.As CO2concentration in the CO2/CH4gaseous mixture increases mass transfer in the system improves due to higher accessibility of carbon dioxide.Consequently,by increasing the CO2concentration in CO2/CH4gaseous mixture with consideration of constant solvent concentration,the quantity of un-absorbed CO2in the system increases which eventuates in a substantial reduction in the separation efficiency.Also it can be understood from the figure that the existence of an extra mass transfer resistance due to partial wetting of membrane pores can be the reason of deteriorated removal performance of CO2in partial wetting mode of operation in comparison with non-wetting condition.The influence of initial CO2concentration on removal efficiency of CO2using different liquid absorbents in a wide range considering both no-wetting and partial wetting modes of operation is depicted in Table 9.

Fig.12.The effect of membrane porosity onCO2removal using(a)NaOH(b)MEA and(c)TEA liquid absorbents under non-wetting(blue line)and partial wetting modes(40%wetting of membrane pores)(red line),feed gas=20/80CO2/CH4,r1=0.325mm,rw=0.395mm,r2=0.5mm,r3=5mm,CCO2,0=0.075mol·m-3,Cabsorbents=1000mol·m-3,Vg=0.07m·s-1,Vl=2.3 m·s-1,T=303.15 K,P=1 MPa.

Table 7The removal efficiency of CO2from CO2/CH4gaseous mixture utilizing different liquid absorbents under both non-wetting and 40%partial wetting modes of operation in a wide range of membrane porosity

3.8.The influence of liquid absorbents concentration onCO2removal under non-wetting and partial wetting modes of operation

Fig.13.The effect of membrane tortuosity on CO2removal using (a)NaOH(b)MEA and (c) TEA liquid absorbents under non-wetting (blue line) and partial wetting modes (40%wetting of membrane pores) (red line), feed gas=20/80CO2/CH4,r1=0.325mm,rw=0.395mm,r2=0.5mm,r3=5mm,CCO2,0=0.075mol·m-3,Cabsorbents=1000mol·m-3,Vg=0.07m·s-1,Vl=2.3 m·s-1,T=303.15 K,P=1 MPa.

Table 8The removal efficiency of CO2from CO2/CH4gaseous mixture utilizing different liquid absorbents under both non-wetting and 40%partial wetting modes of operation in a wide range of membrane tortuosity

The effect of liquid absorbents concentration on removal efficiency of CO2is apparently illustrated in Fig.15.Increment in the absorbents concentration encourages the removal efficiency of CO2,directly.The increase in the removal performance of CO2happens due to this reality that by increasing the concentration of liquid solvents,the active absorption of CO2and also the surface tension at the boundary layer of liquid absorbents increases dramatically which positively affects the mass transfer rate and removal performance of CO2.Due to the increment of mass transfer resistance in the partial wetting mode of operation in comparison with non-wetting condition,increase in the removal of CO2in partial wetting condition is slower.

Fig.14.The effect of initial CO2concentration on CO2removal using(a)NaOH(b)MEA and(c)TEA liquid absorbents under non-wetting(blue line)and partial wetting modes(40%wetting of membrane pores)(red line),feed gas=20/80 CO2/CH4,r1=0.325 mm,rw=0.395 mm,r2=0.5 mm,r3=5 mm,Cabsorbents=1000 mol·m-3,Vg=0.07 m·s-1,Vl=2.3 m·s-1,T=303.15 K,P=1 MPa.

Table 9The removal efficiency of CO2from CO2/CH4gaseous mixture utilizing different liquid absorbents under both non-wetting and 40%partial wetting modes of operation in a wide range of CO2initial concentration

The influence of NaOH,MEA and TEA liquid absorbents concentration on removal efficiency of CO2in a wide range considering non-wetting and partial wetting modes of operation is presented in Table 10,obviously.

3.9.The influence of pore wetting ratio on CO2removal under non-wetting and partial wetting modes of operation

Fig.15.The effect of initial absorbents concentration on CO2removal using(a)NaOH(b)MEA and(c)TEA liquid absorbents under non-wetting(blue line)and partial wetting modes(40%wetting of membrane pores)(red line),feed gas=20/80 CO2/CH4,r1=0.325 mm,rw=0.395 mm,r2=0.5 mm,r3=5 mm,CCO2,0=0.075 mol·m-3,Vg=0.07 m·s-1,Vl=2.3 m·s-1,T=303.15 K,P=1 MPa.

Table 10The removal efficiency of CO2from CO2/CH4gaseous mixture utilizing different liquid absorbents under both non-wetting and 40%partial wetting modes of operation in a wide range of absorbents' concentration

Fig.16 clearly shows the simulation results of CO2sequestration as a function of gas velocity(Vg)for various percentages of membrane pores wetting ranging from 0(non-wetting mode of operation)to 100%(complete wetting mode of operation).Also this figure obviously illustrates the detrimental influence of membrane pores wettability on the removal of CO2applying the hollow fiber membrane contactor.The removal percentage of CO2from CO2/CH4gaseous mixture significantly decreases with increasing the membrane pores wettability.For instance,non-wetting mode of operation(0 wetting of membrane pores)leads in about 3.5 to 4.5 times higher removal efficiency in comparison with complete wetting mode(100%wetting of membrane pores)depending on the type of liquid absorbent.Also the results denotes that 40%wetting of membrane pores eventuates in about 27%to 33%decrement in the separation percentage of CO2using different liquid solvents which is in good agreement with the previous articles studied the influence of membrane wettability[51–53].This phenomenon can be justified due to the fact that the wettability of membrane pores enhances the resistance of CO2transport through the membrane and therefore declines the removal percentage of CO2.

Fig.16.The effect of pore wetting ratio on CO2removal as a function of gas velocity using(a)NaOH(b)MEA and(c)TEA liquid absorbents under non-wetting(blue line)and partial wetting modes(40%wetting of membrane pores)(red line),feed gas=20/80 CO2/CH4,r1=0.325 mm,rw=0.395 mm,r2=0.5 mm,r3=5 mm,CCO2,0=0.075 mol·m-3,Vl=2.3 m·s-1,T=303.15 K,P=1 MPa.

4.Conclusions

In this research article,a modeling and a two dimensional comprehensive numerical simulation was rendered with the aim of evaluating the removal performance of CO2from CO2/CH4gaseous mixture using NaOH,MEA and TEA absorbing agents inside the hydrophobic porous PVDF hollow fiber membrane contactor.The model was developed based on non-wetting and partial wetting modes of operation and counter-current arrangement of liquid–gas flows.Comparison of the results of numerical simulation and experimental data revealed a reasonable agreement with an average deviation of less than 5%.Based on the simulation results,MEA showed better efficiency in the removal of CO2in comparison with the other absorbents.As the novelty,the effect of membrane pores wettability(as a function of gas velocity)on the separation efficiency of CO2in a wide range of wetting percentage from 0(non-wetting mode of operation)to 100%(complete wetting mode of operation)is investigated in this paper.It is perceived from the results that 40%wetting of membrane pores causes 27%to 33%decrease in the removal performance of CO2depending on the type of absorbent.Also,non-wetting mode of operation(0 wetting of membrane pores)leads in about 3.5 to 4.5 times higher removal efficiency in comparison with complete wetting mode(100%wetting of membrane pores).Partial wetting mode of operation negatively affected the removal performance of CO2due to enhancing mass transfer resistance in the membrane pores.According to model results,The separation percentage of CO2reduced significantly whenever the gas velocity,initial CO2concentration and membrane tortuosity increased while increase in the module length,membrane porosity and liquid solvents concentration caused a significant increment in the removal efficiency of CO2from CO2/CH4gaseous stream.

Nomenclature

CCO2,0initial CO2concentration in the gas phase,mol·m-3

2D two dimensional

DCO2,Shelldiffusion coefficient of CO2inside the shell region,m2·s-1

DCO2,memdiffusion coefficient of CO2inside the membrane region,

m2·s-1

DCO2,NaOHdiffusion coefficient of CO2in the NaOH absorbent in the

tube region,m2·s-1

DCO2,TEAdiffusion coefficient of CO2in TEA absorbent inside the tube

region,m2·s-1

DCO2,TEAdiffusion coefficient of CO2in MEA absorbent inside the tube

region,m2·s-1

HFMC hollow fiber membrane contactor

kMEAreaction rate constant of MEA,m3·mol-1·s-1

kNaOHreaction rate constant of NaOH,m3·mol-1·s-1

kTEAreaction rate constant of TEA,m3·mol-1·s-1

L module length,m

MEA monoethanolamine

mCO2,NaOHCO2solubility in NaOH

mCO2,TEACO2solubility in TEA

mCO2,MEACO2solubility in MEA

n number of fibers

P pressure,Pa

rwwetting section of the membrane,m

r1the inner radius of tube,m

r2the outer radius of tube,m

r3the radius of Inner shell,m

T gas temperature,K

TEA triethanolamine

V average axial velocity of the liquid inside the shell region,m·s-1

ˉVaverage axial velocity of gas inside the tube region,m·s-1

Vggas velocity,m·s-1

Vlliquid velocity,m·s-1

ε membrane porosity

τ membrane tortuosity

φ volume fraction of the void inside the HFMC