Journal of Membrane Science 429 (2013) 396–408
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Rate based modeling for CO2 absorption using monoethanolamine solution in a hollow fiber membrane contactor Wichitpan Rongwong a, Suttichai Assabumrungrat b, Ratana Jiraratananon a,n a b
Department of Chemical Engineering, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand Department of Chemical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 May 2012 Received in revised form 19 November 2012 Accepted 21 November 2012 Available online 30 November 2012
This work presents a rate based model to estimate the performance of CO2 absorption by monoethanolamine (MEA) solution using a hollow fiber membrane contactor. The predicted CO2 fluxes were validated with the experimental data of both polytetrafluoroethylene (PTFE) and polyvinylidene fluoride (PVDF) membranes from the literature. The simulation results of the PTFE membrane showed that the CO2 flux could be predicted by the rate based model with a deviation less than 4% for a nonwetted mode of operation. For the PVDF membrane, the model predicted the CO2 fluxes fairly well under partially-wetted mode of operation. The simulated concentration profiles in both the gas and liquid phases, as well as the liquid temperature profile of PTFE membrane, corresponded well with the experimental data. A study of parameter sensitivity analysis revealed that the proposed model is most sensitive to Henry’s constant and when the reaction regime between CO2 and MEA changes from intermediate fast-instantaneous to instantaneous, when the membrane is 20% wetted. A comparison between the CO2 fluxes of the non-wetted and partially wetted modes showed that the increase of CO2 flux in the non-wetted mode with an increasing gas composition and liquid temperature is more significant than that of the partially wetted mode. & 2012 Elsevier B.V. All rights reserved.
Keywords: Carbon dioxide Chemical absorption Membrane contactor Rate based modeling
1. Introduction Nowadays, fossil fuels are still the most important energy source worldwide. The combustion of fossil fuels releases a huge volume of carbon dioxide (CO2), one of the major greenhouse gases, to the atmosphere. Therefore, the capture of CO2 from flue gas before venting is important in order to reduce global warming problems. Membrane contactors are an alternative method for capturing CO2 from the gas mixtures. It is a hybrid of gas absorption and membrane separation processes. The use of membranes as a mass transfer contactor offers a number of advantages, including a high surface area per unit volume. Reed et al. [1] reported that the surface area per unit volume of a membrane contactor is typically 500–2000 ft 1 compared to 10–100 ft 1 found in packed or trayed columns. Membrane contactors are also flexible for scale-up and easy to operate because of the independent gas and liquid flow rates, which results in no flooding or foaming [2]. Gas absorption using membrane contacting processes has been widely studied by a number of researchers, especially in the past decade. Topics of interest such as the effect of operating parameters, types of
n
Corresponding author. Tel.: þ66 2470 9222; fax: þ 66 2428 3534. E-mail address:
[email protected] (R. Jiraratananon).
0376-7388/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.memsci.2012.11.050
absorbents, and membrane wetting have been extensively investigated [3–7]. In addition to experimental studies, modeling studies of CO2 absorption in hollow fiber membrane contactors have received much interest. Many researchers have proposed mathematical models to predict CO2 flux, and study the effect of membrane wetting [8–11]. For liquid flow in fibers, the two-dimensional diffusion model has been applied. Karoor and Sirkar [9] proposed mathematical models for CO2 and SO2 absorption into water using a membrane contactor. Both non-wetted and wetted modes were investigated. The results showed that the overall liquid phase mass transfer coeficient (KLa in s 1) of the membrane contactor was higher and the height of transfer unit (HTU) was lower than those found in conventional contactors. Hoff et al. [10] performed both modeling and experimental studies on CO2 absorption into monoethanolamine (MEA) and methyldiethanolamine (MDEA) solutions using PTFE hollow fiber membranes. The simulation results of their two-dimensional model were in good agreement with the experimental data. Faiz and Al-Marzouqi [11] developed a comprehensive two-dimensional mathematical model for the simultaneous absorption of CO2 and H2S into MEA solution or water using PVDF membranes. The model simulation, using water as an absorbent, fitted well with the experimental data for the non-wetted mode. Meanwhile, the model results for MEA solutions corresponded with the experimental data when the simulation was performed
W. Rongwong et al. / Journal of Membrane Science 429 (2013) 396–408
under a partially wetted mode. Wang et al. [12] also proposed a two-dimensional model for CO2 absorption by 2-amino-2-methyl1-methanol (AMP), diethanolamine (DEA) and MDEA solutions by membrane contacting processes. They found that the absorptions of CO2 into AMP and DEA solutions were instantaneous and the mass transfer was not limited by the chemical kinetics. Although the two-dimensional diffusion model can accurately predict the experimental results, solving the two-dimensional differential mass balance with a liquid velocity profile can be very complex. It is even more complicated when the heat effect are considered because of the nonlinear partial-differential equations. Therefore, in many membrane contactor models, the heat effect is neglected and the process is considered isothermal. However, the real operation of a CO2 absorption process is non-isothermal, the temperatures of the gas stream and absorbent could be different [13], espcially since heat is generated in the absorber due to the exothermic reaction and is lost due to the vaporization of the absorbents. An easier way to estimate the performance of a nonisothermal absorption process is to use a rate-based model, rather than the two-dimensional diffusion model. The use of a rate based model to take into account the heat effect was first applied for a hollow fiber membrane contactor by deMontigny et al. [14]. They applied a mathematical model developed for gas absorption in a packed column to estimate the performance of CO2 absorption by MEA solution in a membrane contacting process. The model predicted the experimental data with an average deviation of only 1.9%. Khaisri et al. [15] used a rate based model to estimate and compare the performance of a membrane contactor operated under the non-wetted and partially wetted modes. The simulation results showed that the CO2 flux of the partially wetted mode (10% membrane wetting) was more than 50% lower than that of the non-wetted mode. Although the energy balance equations were included in the models of deMontigny et al. [14] and Khaisri et al. [15], detailed calculations of heat transfer coefficients and the parameters involved were not presented in either work. The simulation results of the temperature profile were also not shown or validated with the experimental data. This work proposes a comprehensive rate based model for the simulation of CO2 absorption with aqueous MEA solution in a hollow fiber membrane contactor. The overall mass and heat transfer coefficients were calculated from the resistance-in-series model. The individual gas, membrane and liquid phase mass and heat transfer resistances were taken into account in the model. The heat transfer model and the involved heat transfer correlations are presented. The simulation results of the gas–liquid temperature profiles were validated with the experimental data of both PTFE and PVDF membranes from the literature [7,16] to demonstrate the reliability of the proposed model. A parametric sensitivity analysis was performed in order to study the influence of the system’s parameters on the mass transfer with chemical reaction and to identify the key parameters for a better process optimization. Two operating conditions found in gas absorption by a membrane contactor, namely the non-wetted and partially wetted modes were investigated. Additionally, the effect of operating parameters, i.e., gas concentration, liquid temperature and liquid velocity, on the CO2 flux and the enhancement factor of the non-wetted and partially wetted modes were studied.
2. Theory 2.1. Mass transfer with chemical reaction in the membrane contactor For a non-wetted mode of operation, the mass transfer occurs in three steps, i.e., (1) diffusion from the bulk gas phase to the
397
pCO2,GM
pCO2,G
pCO2,I CCO2,B
CCO2,I
Absorbent
Bulk liquid
Gas stream Liquid film
membrane
Gas Film
pCO2,GM CCO2,I CCO2,B
Bulk gas
pCO2,G
pCO2,I
CCO2,ML
Absorbent Gas stream
Bulk
Liquid
liquid
film
membrane
Gas
Bulk
Film
gas
Fig. 1. Mass transfer in membrane contactor (a) for the non-wetted mode (b) for partially-wetted mode.
outer surface of the membrane, (2) diffusion through membrane pores, and (3) dissolution into the liquid absorbent. Fig. 1 shows the concentration profile for the transfer of CO2 from the bulk gas to the bulk liquid. CO2 absorption flux (NCO2 ) into chemical solution can be expressed in term of the overall driving force based on the liquid phase (Eq. (1)), or the local driving forces of gas, membrane and liquid phases (Eq. (2)), as the following [17]: NCO2 ¼ K L HpCO2 ,G C CO2 ,B ð1Þ NCO2 di ¼ kG =RT do pCO2 ,G pCO2 ,GM 0 ¼ kM =RT dln pCO2 ,GM pCO2 ,I ¼ EkL di C CO2 ,I C CO2 ,B
ð2Þ
For a partially-wetted mode, the wetted membrane mass transfer resistance is included, and Eq. (2) can be rewritten as: NCO2 dint ¼ kG =RT do pCO2 ,G pCO2 ,GM ¼ kM =RT dln pCO2 ,GM pCO2 ,I 0 0 ð3Þ ¼ Ek0M dln C CO2 ,I C CO2 ,ML ¼ EkL di C CO2 ,ML C CO2 ,B where K L is overall mass transfer coefficient based on liquid 0 0 phase. kG , kM , kM and k L are the individual mass transfer coefficients of the gas phase, non-wetted membrane, wetted membrane and liquid phase (physical absorption), respectively. pCO2 ,G , pCO2 ,GM , and pCO2 ,I are the partial pressures of CO2 at bulk gas, gas-side membrane surface and gas–liquid interface, respectively. C CO2 ,I , C CO2 ,ML and C CO2 ,B are CO2 concentrations at the
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gas–liquid interface, liquid-side membrane surface, and liquid 0 bulk, respectively. di , dint , do , dln and dln are the inner, interfacial, outer, and the logarithmic mean diameters of the non-wetted and the wetted part of the membrane, respectively. T is temperature and R is gas constant. H is the Henry’s constant and E is the enhancement factor. Eqs. (4) and (5) express the resistance-in-series model for the non-wetted mode and for a partially wetted mode of the hollow fiber contactor, respectively. 1 1 RTH RTH ¼ 0 þ þ K L di k k d M G do ln EkL di
ð4Þ
1 1 1 RTH RTH ¼ 0 þ 0 0 þ þ K L dint k k d d Ek M G do ln EkL di M ln
ð5Þ
The above equations refer to liquid flow in the tube side and gas flow in the shell side. 2.2. Individual mass transfer coefficients 2.2.1. Liquid side mass transfer For liquid flow in the tube side of the membrane, the wellknown Graetz–Leveque mass transfer correlation has been widely 0 used to predict the tube side mass-transfer coefficient (kL ) [2]: 1=3 0 k d d ð6Þ Sh ¼ L i ¼ 1:62 i Re Sc DCO2 ,L Z where Sh, Re, Sc are the Sherwood, Reynolds and Schmidt numbers, respectively. Z is membrane length and DCO2 ,L is the diffusivity of CO2 in the liquid phase. 2.2.2. Gas side mass transfer For gas flow in the shell side, Yang and Cussler [18] proposed the following correlation to predict the gas side mass transfer coefficient for gas absorption and stripping: 0:93 kG de de Re ¼ 1:25 Sc0:33 ð7Þ Sh ¼ DCO2 ,G Z where de is the hydraulic diameter and DCO2 ,G is the diffusivity of CO2 in gas phase. 2.2.3. Membrane mass transfer In the case of a non-wetted mode, the membrane mass transfer coefficient (kM) can be calculated using the following equation: kM ¼
DG,ef f eM
tM dnon-wetted
ð8Þ
For a wetted mode, the wetted membrane mass transfer coefficient can be expressed as: 0
kM ¼ DCO2, eMCO , 2
tM dwetted
ð9Þ
where eM , is the membrane porosity, dnon-wetted and dwetted are the thicknesses of non-wetted and wetted parts of the membrane pores, respectively, and tM is the tortuosity. DG,ef f is the effective diffusion coefficient of gas in the pores, which is calculated by the combination of molecular and Knudsen diffusivities as shown in Eq. (10). 1 DG,ef f
¼
1 1 þ DM DKn
2.3. Enhancement factor The enhancement factor (E) is a variable that accounts for the effect of reaction on mass transfer. It is a function of the Hatta number (Ha) and the infinite enhancement factor (E1 ). Assuming that the reaction between CO2 and MEA is irreversible, the enhancement factor can be calculated by the expression proposed by DeCoursey [19] as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ha2 Ha4 E1 Ha2 þ þ1 ð11Þ þ E¼ 2ðE1 1Þ 4ðE1 1Þ2 ðE1 1Þ The Hatta number is the ratio of maximum reactive conversion rate to the maximum diffusion mass transfer rate in the liquid film. It is defined as: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k2,MEA DCO2 ,L C MEA ð12Þ Ha ¼ kL,ext where k2,MEA is the second-order reaction rate constant, C MEA is the MEA concentration. kL,ext is the liquid phase mass transfer coefficient, which for in a partially wetted mode includes the wetted portion of the 0
membrane pore. For a non-wetted mode kL,ext is the same as kL , while for the partially wetted mode it can be expressed as 0 0 0 0 kL,ext ¼ kL =1 þ kL =kM di =dln [15]. The infinite enhancement factor (E1 ) is defined as the maximum attainable enhancement factor when the reaction between absorbed gas and absorbent becomes instantaneous and the mass transfer does not depend on the rate of the reaction. The E1 based on Leveque’s model with the presence of a velocity gradient in the mass transfer zone is given by the following [20]: DCO2 ,L 1=3 C MEA DMEA,L E1 ¼ 1 þ ð13Þ nR C CO2 ,I DCO2 ,L DMEA,L where DMEA,L is the diffusivity of MEA in MEA solution, vR is the stoichiometric coefficient of overall reaction and C CO2 ,I can be calculated by the expression proposed by Khaisri et al. [15] as follows: pCO2 ,G þ ðkL,ext ðdi =do ÞE=kG,ext ÞC CO2 ,B H ð14Þ C CO2 ,I ¼ 1 þðkL,ext ðdi =do ÞE=HkG,ext Þ where kG, ext is the combined gas and membrane mass transfer coefficient. It is calculated from the following equation: kG,ext ¼
kG =RT 1 þ kG =kM do =dln
ð15Þ
From the values of Ha and E1 , we can categorize the regime of the reaction between CO2 and alkanolamines as fast, instantaneous or intermediate fast-instantaneous [21]. The reaction is considered to take place in the fast regime when Ha 42 and Hao oE1 . In this regime, the value of E is close to Ha. The reactive conversion rate in the liquid film has a significant effect on the rate of CO2 absorption. The instantaneous reaction occurs when Ha42 and Ha 4 4E1 . The value of E will almost reach E1 and the rate of mass transfer in the liquid film is independent of the rate of the reaction. In the intermediate fast-instantaneous absorption regime, the values of Ha and E1 are not much different. The CO2 absorption rate and the enhancement factor are dependent on both the reaction and the diffusion rates in the liquid film. 2.4. Equilibrium model for the CO2–MEA–water system
ð10Þ
where DM and DKn are the molecular and Knudsen diffusion coefficients, respectively.
Generally, when the enhancement factor is introduced into the calculation of overall mass transfer coefficient, the reactions between absorbed gas and aqueous absorbent in the bulk liquid
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are considered to be at equilibrium. The equilibrium reactions in the system consisting of CO2, MEA (HOCH2 CH2 NH2 ) and water are as follows [22]: K1
2H2 O2OH þ H3 O þ
ð16Þ
K2
CO2 þ 2H2 O2HCO3 þH3 O þ
ð17Þ
K3
HCO3 þ H2 O2CO3 2 þH3 O þ
ð18Þ
K4
HOCH2 CH2 NHCOO þ H2 O2HOCH2 CH2 NH2 þHCO3 HOCH2 CH2 NH3þ
K5
þH2 O2HOCH2 CH2 NH2 þH3 O
þ
ð19Þ ð20Þ
where Ki are the equilibrium constants of the reactions. In order to evaluate the CO2 concentration in the liquid bulk (C CO2 ,B ), the overall material and charge balances of all species in the liquid phase must be solved simultaneously. MEA balance: C MEA,B þC MEA H þ ,B þ C MEA COO ,B ¼ C 0MEA
ð21Þ
2.5. Heat transfer in gas absorption using hollow fiber membrane contactors The physical and chemical properties involved in the system can be influenced by the temperature changes due to the heat effect from heat transfer between phases, chemical reaction, and vaporization of the absorbent. Therefore, in addition to the mass balance, the energy balance equations should be considered in order to obtain more accurate prediction of the mass transfer flux. The heat transfer flux (Q) is given as follows: Q ¼ U ol ðT G T L Þ
ð29Þ
where U ol is the overall heat transfer coefficient. T G and T L are the temperatures of the bulk gas and liquid, respectively. The resistance-in-series model can also be applied to determine the overall heat transfer coefficients (U ol ) of the non-wetted and partially wetted modes: 1 1 1 1 ¼ þ þ U ol di hG do hM dln hL di
ð30Þ
1 1 1 1 1 ¼ þ þ þ U ol dint hG do hM dln h0lM d0ln hL di
ð31Þ
0
where hG , hM , hM and hL are heat transfer coefficients of gas, nonwetted membrane, wetted membrane and liquid phase, respectively.
Carbon balance: C CO2 ,B þC HCO3 ,B þ C CO2 ,B þ C MEA COO ,B ¼ X CO2 C 0MEA 3
ð22Þ
Charge balance: C MEA H þ ,B þC H3 O þ ,B ¼ C HCO3 ,B þ C OH ,B þ 2C CO2 ,B þC MEA COO ,B 3
ð23Þ For simplification, the concentrations of OH , H3 O þ and CO3 2 are neglected due to very small values at equilibrium. In a CO2– MEA–water system, the concentration of OH- is very small due to its rapid reactions with CO2 and HOCH2 CH2 NHCOO . Increasing CO2 loading also decreases the concentration of OH and reduces the significance of the reaction of CO2 þ OH 2HCO3 in the CO2– MEA–H2O system [10]. The vapor–liquid equilibrium model (VLE), which calculated the concentration of all eight species in the liquid phase, including OH , was proposed by Aboudheir et al. [22]. Their simulation results showed that the concentrations of OH , CO23 and H3O þ were very close to zero. In this work, the CO2 and other species concentrations in liquid phase are calculated by the equilibrium model based on Astarita et al. [23] as follows: C HOCH2 CH2 NH þ ,B ¼ X CO2 C 0HOCH2 CH2 NH2 3
ð24Þ
C HCO3 ,B ¼ X CO2 C 0HOCH2 CH2 NH2 C HOCH2 CH2 NHCOO ,B
ð25Þ
C HOCH2 CH2 NH2 ,B ¼ C 0HOCH2 CH2 NH2 1X CO2 C HOCH2 CH2 NHCOO ,B
ð26Þ
C HOCH2 CH2 NHCOO ,B ¼
2 2
C 0HOCH2 CH2 NH2 þ K 4 C 0HOCH2 CH2 NH2 þ K 4 4X CO2 1X CO2 C 0HOCH2 CH2 NH2
K 5 K 4 CHOCH2 CH2 NHCOO ,B CHOCH2 CH2 NH3þ ,B K2 CHOCH2 CH2 NH2 ,B 2
2.5.1. The heat transfer coefficient of the gas phase The heat transfer coefficient in gas phase (hG ) can be obtained from the mass transfer coefficient using the Chilton–Colburn analogy as the following equation [24]: !1=3 rC P l2G hG ¼ kG ð32Þ DCO2 , G2 where r is the density of the gas mixture. C P is the specific heat capacity and lG is the thermal conductivity of the gas mixture. 2.5.2. The heat transfer coefficient of the membrane phase The non-wetted and wetted heat transfer coefficients of 0 membrane (hM and hM ) are determined based on the conductivities of the polymer in the solid phase, and the gas or liquid trapped within the membrane pores by the following equations [25]: hM ¼ 0
hM ¼
eM lG þ ð1eM ÞlM dnon-wetted
eM lL þ ð1eM ÞlM dwetted
ð33Þ
ð34Þ
where lG , lM and lL are the thermal conductivities of gas, membrane and liquid phases, respectively. 2.5.3. The heat transfer coefficient of the liquid phase For the liquid flow in the fiber, the heat tranfer coefficient is calculated using following equation [26]: ! 0:085 RePrdi =Z lL nB 0:14 hL ¼ 3:658 þ ð35Þ 0:67 di nML 1 þ0:047 RePrdi =Z
ð27Þ
where Pr is the Prandtl number. nB and nML are kinemetic viscosities in the bulk and at the membrane surface, respectively.
ð28Þ
3. Model development
2
C CO2 ,B ¼
399
where X CO2 is the CO2 loading in the liquid phase. The C CO2 ,B from Eq. (25) and partial pressure of CO2 are used to evaluate the driving force of the process (Eq. (1)).
The rate based and plug flow model for CO2 absorption with chemical solvent using hollow fiber membrane contactors is proposed in this work. The schematic diagram of a differential
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reactions 17, 19 and 20) as follows:
section of the membrane contactor is shown in Fig. 2. The mass and energy balance equations around the section are included in the simulation. A counter-current mode is considered for the model development. The important assumptions used to derive the main equations are summarized below:
CO2 þ2HOCH2 CH2 NH2 2HOCH2 CH2 NH3þ þ HOCH2 CH2 NHCOO ð36Þ Thus, the mass balances of gas and liquid phases are calculated by the following equations:
(1). Ideal gas and liquid behavior. (2). Steady state and adiabatic conditions. (3). Constant total pressure in gas and liquid phase along the fiber length. (4). Membrane properties are uniform along the fiber length. (5). The interfacial area is the same for both mass and heat transfer. (6). The liquid volume flow rate is constant.
3.1. Main model equations
Membrane phase
NCO2∆Z NH2O∆Z
dX CO2 npd ¼ 0 N CO2 dZ LC MEA
ð39Þ
dC MEA 2npd NCO2 ¼þ L dZ
ð40Þ
FCO2+Δ FCO2 TG+ Δ TG
MATLAB (version 7.7.0) was employed in solving the proposed model. The set of main equations including mass and energy balances were simultaneously solved using a built-in solver ODE15S.
Fig. 2. The schematic diagram of a differential section in the hollow fiber membrane.
start Input feed gas and liquid conditions, physical and chemical properties and TGin and TLin I Assume TL,out Give a guessed outlet CO2 concentration in gas phase (yCO2 I) Calculate inlet XCO2 Solve set of ODEs. Eq. (37)-(42). Calculate outlet CO2 concentration in gas phase (yCO2 II) and TLin II if yCO2 II - yCO2 I ≤ error Yes Adjust the value of TL,out
ð42Þ
3.2. Numerical solutions
Absorbent
No
ð41Þ
where C P, CO2 , C P, H2 O , C P, air and C P,L are the heat capacities of CO2, water vapor, air and MEA solution, respectively. Lm is the liquid mass flow rate. DHr ,DHl are the heat of reaction between CO2 and MEA and vaporization of water, respectively.
Q∆Z Z+ΔZ
L(CMEA+ΔCMEA) XCO2 +Δ XCO2 TL+ Δ TL
ð38Þ
dT L npd ¼ Q þ NCO2 C P,CO2 þN H2 O C P,H2 O T G T ref Lm C P,L dZ N CO2 DHr NH2 O DHl Þ
Gas phase
Liquid phase
dF H2 O ¼ npdN H2 O dZ
dT G npdQ ¼ F CO2 C P,CO2 þF H2 O C P,H2 O þ F air C P,air dZ
F CO2 kmolCO2/s TG kJ/s Z
Gas
ð37Þ
where F CO2 and F H2 O are CO2 and H2O mole flow rates, respectively. n is the number of fibers. L is the liquid volume flow rate, and d is di and dint in the case of the non-wetted and partiallywetted modes, respectively. The energy balances for the gas and liquid phases are:
The relation between the absorption flux of CO2 (N CO2 ) to the change in concentration of MEA in liquid phase is indicated by the stoichiometry of overall reaction of CO2 and MEA (by combining LCMEA kmolMEA/s XCO2 molCO2/molMEA TL kJ/s
dF CO2 ¼ npdN CO2 dZ
if TL,in II - TL,in I ≤ error Yes Calculate CO2 flux End Fig. 3. Computational flow chart.
No
Adjust the value of yCO 2 I
W. Rongwong et al. / Journal of Membrane Science 429 (2013) 396–408
The shooting method was applied to solve the problem. Fig. 3 shows the computational flow chart used to solve the set of equations. At the initial step, the simulation starts at the top of the absorber with a guessed outlet liquid temperature. The concentration and temperature profiles of both the gas and liquid phases are calculated from the top to the bottom of the absorber (from the gas inlet to the outlet). Then, the calculated inlet liquid temperature (TL, in II) is compared with the experimental values (TL, in I) and the new outlet liquid temperature is guessed. The simulation is repeated until the calculated inlet liquid temperature is equal to the experimental value with an error less than 0.1%.
401
simulation. It can be seen that for most parameters the changes in values are not significant, except for Ha,E1 and E, resulting in an obvious change in the overall mass transfer coefficient based on liquid phase (K L ). 5.1.1. CO2 fluxes in PTFE and PVDF membranes For gas absorption using membrane contactors, two types of membranes commonly applied are PTFE and PVDF. To validate the proposed model, the experimental data reported by Khaisri [16] for PTFE and Atchariyawut et al.[7] for PVDF were used to Table 2 Typical values of the important parameters used in the simulation.
4. Physical and chemical properties Parameters
The physical and chemical properties of the MEA solution and gas mixture, and the equilibrium constants of the CO2–MEA reaction used in the simulation with the literature source, are shown in Table 1. Since the model is adiabatic, the values of these parameters change with the temperature and the concentration of MEA and gases along the module length.
Non-wetted mode
2
1.497 10 5–1.514 10 5 1.043 10 5–1.054 10 5 1.245 10 5–1.249 10 5 1.31 10 9–1.315 10 9 7.054 10 10–7.132 10 10 3.608 10 8–3.618 10 8 4.631 10 3–4.807 10 3 1.889 10 3–1.905 10 3 1.054 10 5–1.057 10 5
DCO2 , G (m /s) DM (m2/s) DKn (m2/s) DCO2 , L (m2/s) DMEA, L (m2/s) H(kmol/m3 atm) kG (m/s) kM (m/s) 0
kL (m/s) Ha E1 E K L (m/s)
5. Results and discussion 5.1. Model validation Table 2 displays the ranges of the values of important parameters obtained under the operating conditions used in the
200.3–214.4 102.9–166.1 84.67–117 3.266 10 4–4.092 10 4
(15 %v/v CO2 in air, liquid velocity is 5.89 cm/s, PTFE membrane TG and TL are 296 and 293 K, respectively).
Table 1 The equations and the values for the physical and chemical properties used for the simulation. Parameters
Sources
Equations
Density of MEA solution (g/cm3)
Weiland et al. [27]
r¼
xMEA M MEA þ xH2 O M H2 O þ xCO2 M CO2 xMEA V MEA þ xH2 O V H2 O þ xCO2 V CO2 þ xMEA xH2 O V n þ xMEA xCO2 V nn
V j ¼ M j =rj r ¼ a1 þ a2 T þ a3 T 2
Viscosity of MEA solution (mPa s)
Weiland et al. [27] 2
Diffusivity of CO2 in MEA solution (cm /s)
Versteeg et al. [28], Ko et al. [29]
Diffusivity of MEA in MEA solution (cm2/s)
Versteeg et al. [28]
Diffusivity of CO2 in gas mixture (cm2/s)
Poling et al. [30] Welty et al. [31]
Z ZH2 O
¼ exp ½ðaO þ bÞT þ ðcO þ dTÞ½2aðeO þ f T þ g Þ þ 1O DCO2 ¼ DN2 O, MEA DCO2 =DN2 O water b3 þ b4 C MEA DN2 O,MEA ¼ b0 þ b1 C MEA þ b2 C MEA 2 exp T DCO2 ,water ¼ 2:35 102 exp 2119=T
DN2 O,water ¼ 5:07 102 exp 2371=T C MEA ,mol=dm3 0:6 DMEA ¼ DMEA,H2 O ZH2 O =ZMEA DCO2 mixture ¼
1 y0air =DCO2 air þ y0water =DCO2 water
DCO2 air ¼
Second order rate constant (m3/kmol s)
Jamal et al. [32] 3
Henry’s constant for CO2–MEA system (kPa m /kmol)
Tsai et al. [33], Wang et al. [34], Versteeg et al. [28]
0:00266T 3=2 P2½ 1=M CO2 þ 1=M air 1 s2CO2 air OD
k2,MEA ¼ 3:951 1013 exp 6863:8 T H ¼ HN2 O HCO2 water =HN2 Owater water lnH1,S ¼ R23 þ HCO2 water ¼ 2:82 106 exp
X3 2
Fj lnH1,j
2044 T
HN2 Owater ¼ 8:55 106 exp
Heat capacity of gases (J/kmol K) Heat capacity of MEA solution (J/g K) Heat of absorption (J/kmol CO2) Equilibrium constants Reaction (16)–(18) Reaction (19) and (20) n
2284 T
Welty et al. [31] Weiland et al. [35] Gabrielsen et al. [36]
CO2: 3.69 104, water vapor: 3.36 104 and air: 2.92 104 at 296 K. 3.67 DHr ¼ 10584 R
Edwards et al. [37] Kent and Eisenberg [38]
ln K ¼ a1 =TðKÞ þ a2 ln TðKÞ þ a3
Please refer to the individual publications for the values of parameters.
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Table 3 The characteristics of hollow fiber membranes used in the simulation [16,7]. Membrane
PTFE [16]
PVDF [7]
Fiber o.d. (cm) Fiber i.d. (cm) Module i.d. (cm) Number of fiber Module length (cm) Porosity Tortuosity pore size (mm) Thermal conductivity (W/m k) [13]
0.2 0.1 2.8 57 36.7 0.5 3 2.5 0.22
0.1 0.065 1 35 27 0.75 4 0.2 0.18
CO2 flux (mol/m2.s)
4.00E-03
3.00E-03
2.00E-03 Experimental 1.00E-03
[7]
Faiz and Marzouqui's model [11] Present model
0.00E+00 0
50
100
150
200
250
Liquid velocity (cm/s)
CO2 flux (mol/m2.s)
2.10E-03
Fig. 5. Model validation using PVDF membrane (50% wetting). (Pure CO2, Gas flow rate (F CO2 ) 200 mL/min, 2 M MEA, gas and absorbent temperatures are 30 1C.) [7].
1.70E-03
1.30E-03 Experiment [15,16] Simulation 9.00E-04
5.00E-04 0
2
4
6
8
Liquid velocity (cm/s) Fig. 4. Model validation using PTFE membrane. (15 %v/v CO2 in balance of air, inert gas (air) flow rate (Fair) 0.3 mol/min, 3 M MEA and 0.3 CO2 loading) [15,16].
compare with the predicted results. The specifications of the membranes and modules used are shown in Table 3. 5.1.1.1. PTFE membrane. The experiments of Khaisri [16] were performed with the gas mixture (15 %v/v CO2 in the balance of air) fed to the shell side, counter-current, to the absorbent, which flowed in the tube side of the module. The absorbent used was 3 M MEA with CO2 loading of 0.3 mol CO2/mol MEA. The inert gas (air) flow rate (Fair) was 0.3 mol/min and the liquid velocities ranged from 1.45 to 7.36 m/s. Since the PTFE membrane has a high hydrophobicity [39], the simulation was performed via the non-wetted mode operation. Fig. 4 shows the experimental and simulation CO2 fluxes as a function of liquid velocity. The simulation results fitted the experimental data well with maximum deviation less than 4%. This shows that the rate-based model can provide sufficient accuracy for predicting the CO2 absorption flux in membrane contactor using PTFE membranes without using the percentage of wetting as the fitting parameter. It was found that the both model and experimental CO2 fluxes were enhanced with an increasing liquid velocity due to the mass transfer coefficient in the liquid phase being enhanced [7,40]. The inclusion of energy balance equations (Eqs. (38) and (39)) does improve the accuracy of the model prediction, especially at low liquid velocity. At liquid velocities of 1.45 and 2.69 m/s, the deviations between experimental and simulation CO2 fluxes under adiabatic condition are only 3.71% and 1.8%, while the deviations between experimental and simulation CO2 fluxes under isothermal conditions are 8.47% and 5.17%, respectively. The validations of temperature profiles of gas and liquid phases of these experiments are shown in Section 5.1.2. 5.1.1.2. PVDF membrane. In the experiments of Atchariyawut et al. [7], pure CO2 and 2 M MEA counter-currently flowed through the hollow fiber module. The feed gas flow rate was 200 mL/min and
the liquid velocities were 65.6–211.5 cm/s. The liquid and gas temperatures were 303 K. The characteristics of the hollow fiber membrane are shown in Table 3. Faiz and Al-Marzouqi [11] also used the results of these experiments [7] to validate their mathematical model. The nonlinear two-dimensional material balance in both gas and liquid phases using diffusion coefficients was employed in their work. Considering the fact that the PVDF membrane can be partially wetted by an organic absorbent like MEA solution, several models [41–43] of the CO2 absorption using PVDF membranes considered the partiallywetted mode operation and applied the percentage of membrane wetting as a fitting parameter to compare the model results with the experimental data. The comparisons between the experimental CO2 fluxes and simulation results calculated from the models of the present work, and Faiz and Al-Marzouqi’s [11] work, are shown in Fig. 5. It was found that the prediction results considering 50% membrane wetting in this work, and Faiz and Marzouqi’s work [11], were in good agreement with the experimental data. The increase of simulated CO2 flux with 50% membrane wetting with the liquid velocity was lower than the experimental CO2 flux and the large deviation between the experimental and simulation fluxes was found at low liquid velocity. This is because the wetted membrane resistance controlled the mass transfer when the 50% membrane wetting was introduced in the simulation. The percentage of wetted membrane phase resistance was higher than 87% of the total resistance. The higher deviation of the fluxes at low velocity is due to the assumption of no concentration gradient of the MEA in the mass transfer zone was used in order to calculate the enhancement factor according to Eq. (11) [44]. However, at low velocity this assumption may not be valid because the supply of MEA solution for the reaction between MEA and CO2 at the interface is less than that at high velocity and this could result in the concentration gradient of MEA in the mass transfer zone, resulting in the higher predicted CO2 flux from the model. This difference will be more significant in the prediction of CO2 flux in a partially-wetted mode because of the low diffusivity of the MEA in the liquid-filled membrane pores in the case of the partially wetted mode, compared with diffusivity of the MEA in the in bulk solution case of the non-wetted mode (DMEA,pore ¼ DMEA,L eM =tM ).[45]
5.1.2. Concentration and temperature profiles The experimental results from Khaisri [16] were used to compare with the simulated data. The experimental and simulation profiles of CO2 concentration in gas phase and CO2 loading in liquid phase at a liquid velocity 5.89 cm/s are shown in Fig. 6. The CO2 concentration in the gas phase and CO2 loading in the liquid phase are highest at the top of the absorber because the gas and liquid flow counter-currently. A good agreement can be
W. Rongwong et al. / Journal of Membrane Science 429 (2013) 396–408
0.45
Table 4 The comparison between the measured and simulated data of gas and liquid phase temperatures [16].
15 0.4
14 13
0.35
12 0.3
11 10
CO2 loading
% CO2 in gas phase (%v/v)
16
9 0.2 0
0.1
0.2
0.3
0.4
Exp. %CO2 (g)
Exp. CO2 loading
Sim. CO2 loading
297.00
298
296.00
297 296
294.00 295 293.00 294
292.00
293
291.00
292
290.00 0
0.1
0.2
0.3
Liquid phase temperature (K)
Gas inlet
Exp. gas outlet
Sim. gas outlet
Liquid inlet
Exp. liquid outlet
Sim. liquid outlet
295.15 296.93 295.65 294.61
294.15 295.21 294.61 294.34
294.06 293.62 293.52 293.46
293.33 293.15 293.15 293.15
295.91 295.45 294.89 294.7
296.7 295.56 295.12 294.77
Table 5 Heat transfer coefficients and percentage contribution to the total heat transfer resistances of gas, membrane and liquid phases.
2
Liquid temperature (K)
Gas temperature (K)
Fig. 6. Concentration profiles of CO2 in gas phase (%v/v) and CO2 loading in liquid phase (mol CO2/mol MEA), 15 %v/v CO2 in air and PTFE membrane [16].
295.00
Gas phase temperature (K)
(Fair ¼0.3 mol/min, 3 M MEA and 0.3 CO2 loading).
Z (m) Sim. %CO2 (g)
Liquid velocities
2.69 4.69 5.89 7.36
0.25
8
403
Heat transfer coeficient (W/m K) % contribution of heat tranfer resistance
Gas
Membrane
Liquid
Overall
7.58 95.3
246 4.07
2265 0.63
7.29 100
(Fair ¼0.3 mol/min, nL ¼2.69 m/s, TG ¼ 295.15 K, TL ¼293 K, PTFE membrane).
membrane phases. This is because the thermal conductivity and density of the liquid are higher than those of the gas phase. Therefore, in the other parts of this work, only the gas and membrane heat transfer resistances were included in the simulation.
0.4
5.2. Sensitivity analysis
Z (m) Sim. TG
Exp. TG
Exp. TL
Sim. TL
Fig. 7. Temperature profiles of gas and liquid phase. (15 %v/v CO2 in air and PTFE membrane at liquid velocity 5.89 cm/s) [16].
observed between the simulated and experimental profiles for both CO2 concentration in gas phase and CO2 loading in liquid phase. The maximum deviation was not more than 2%. Fig. 7 depicts the experimental and simulated temperature profiles of gas and liquid phases along the length of the module. The experimental temperature of the inlet gas was slightly higher than that of the inlet liquid. The values were 295.7 and 294.9 K, respectively. In the simulation, the inlet gas and liquid temperatures are specified and used as the boundary values to simulate the temperature profiles along the module length and also the outlet temperatures of gas and liquid phases. The results show that the model prediction matched well with the experimental profiles of liquid temperature, as well as liquid outlet temperature, while a slight deviation was found in the model simulation of gas temperature profile. Table 4 compares the measured and simulated outlet gas and liquid temperatures at different liquid velocities. The agreement between simulated and experimental liquid phase temperatures was better than that of the gas phase. The measured gas temperatures were higher than the simulated results of all runs. This is possibly due to the heat transfer from the surroundings that increased the experimental gas temperature. Several adiabatic modeling works [46,47] also found a slight deviation between simulated and experimental temperatures. They recommended that heat from the surroundings, or heat loss terms, should be added in the energy balance equation in order to improve the accuracy of model. The individual and overall heat transfer coefficient values and percentages of the heat transfer resistances in gas, membrane and liquid phases at liquid velocity 2.69 m/s are shown in Table 5. The liquid phase heat transfer resistance is very small when compared with the gas and
A parameter sensitivity analysis is important in order to better understand the influence of the relevant parameters on gas absorption with chemical solvent in hollow fiber membrane contactors. Although sensitivity analysis has been performed in several modeling studies [48,49], there is no report on the determination of the reaction regime in the membrane contactor operating under non-wetted and partially wetted modes. The aims of this study were to (a) determine the reaction regime between CO2 and MEA solution, (b) investigate the effect of partially wetted membranes on the change of the reaction regime, and (c) identify the important parameters in the process. The experimental conditions of Khaisri [16] (15 %v/v CO2 in balance of air, MEA 3 M, 0.3 CO2 loading and at liquid velocity 5.89 m/s) were used in the simulation. The parameters used to calculate the overall mass transfer coefficient were selected to study the sensitivity of the model. In operation, these parameters can change due to varying liquid absorbent temperature, MEA concentration and liquid CO2 loading. The non-wetted mode of operation was compared to partially wetted modes of operation (20 and 40%). The values of the studied parameters were increased by 20% to observe changes in the CO2 flux in order to investigate the sensitivity of the model by the studied parameters. The results of the sensitivity analysis are shown in Table 6. First, we examined the parameters that directly influence the enhancement factor in order to determine the reaction regime including k2, MEA , which is related to the Hatta number (Ha), DMEA, L and DCO2 , G , which are related to the infinite enhancement factor (E1 ). For the non-wetted mode, the increase of these three parameters significantly enhances the CO2 flux and the enhancement factor is considerably influenced by both the Hatta number and the E1 . It indicates that the reaction of CO2 with MEA in this condition is in the intermediate fast-instantaneous regime. Hoff et al. [49] also found in their work that CO2 absorption into MEA solution using hollow fiber membrane contactors occurred in the region close to the instantaneous regime. For the partially wetted
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Table 6 Percentage change of CO2 flux when the input parameters are increased by 20%. Input parameters
Percentage deviation of CO2 flux Non-wetted mode
Second order rate constant (k2, MEA ) Diffusivity of MEA in MEA solution (DMEA, L ) Diffusivity of CO2 in MEA solution (DCO2 , L ) Diffusivity of CO2 in gas phase (DCO2 , G ) Effective diffusion coefficient of gas (DG, ef f ) Henry’s constant (H)
Partially wetted mode
2.57 5.5 2.67 0.33 1.68 10.94
20% wetting
40% wetting
0.04 12.41 5.24 0.1 0.03 16.23
0.01 12.59 5.78 0.1 0.02 16.3
(Fair ¼0.3 mol/min, 3 M MEA, 0.3 CO2 loading and PTFE membrane).
5.2.1. Effect of CO2 concentration in the gas phase Fig. 8 shows the effect of CO2 concentration in air (5–30 %v/v) on CO2 flux and the enhancement factor of the non-wetted mode and the partially wetted mode with 20% membrane wetting, respectively. It is obvious that, the CO2 flux of the non-wetted mode greatly increases from 7.69 10 4 to 2.63 10 3 mol/m2 s while the flux of the partially wetted mode slightly increases from 4.53 10 4 to 4.85 10 4 mol/m2 s when the CO2 concentration is increased from 5 to 30 %v/v. For the non-wetted mode, especially at low CO2 concentration, the reaction takes place in the region close to fast reaction regime. The absorption flux is proportional to the gas concentration [21] since the overall mass transfer coefficient and the enhancement factor are influenced by Ha more than the E1 . While, for the partially-wetted mode, the reaction between CO2 and MEA is instantaneous and the value of E is close to E1 . From Eq. (13), when gas concentration is increased, E1 is reduced, resulting in smaller E (Eq. (11)). Therefore, from Eq. (5), the overall mass transfer coefficient based on liquid phase (K L ) is decreased. However, flux is
200 160
2.00E-03
Flux
120
E 80 1.00E-03
Enhancement factor
CO2 flux (mol/m2.s)
3.00E-03
40 0.00E+00
0 0
10
20
30
CO2 concentration in gas phase (%v/v)
5.00E-04
400
4.80E-04
300
4.60E-04
Flux E
200
4.40E-04 100
4.20E-04 4.00E-04
Enhancement factor
CO2 flux (mol/m2.s)
mode, the CO2 flux is less affected by the increase of k2, MEA , while it is more sensitive to the increase of DMEA, L . Therefore, the reaction occurs in the instantaneous regime and the rate of absorption is limited by the diffusivity of the absorbent [21]. The absorption regime changes from the intermediate to the instantaneous when the membrane is partially wetted due to the large increase of the Hatta number (Eq. (12)) from 213.6 to 3627.95 when the percentage of membrane wetting is increased from 0% to 40%. In the partially wetted mode, there are two important mass transfer resistances including wetted membrane and liquid phase resistances (see Fig. 1b). When the wetted membrane resistance is increased, the combined wetted membrane and liquid phases mass transfer coefficient. (kL, ext ) is reduced and greatly increases the Hatta number (Ha). Thus, the reaction occurs instantaneously at the gas–liquid interface, which is in the membrane pores. From Table 6 it is clear that the proposed models for both the non-wetted and partially-wetted modes are most sensitive to the value of Henry’s constant (H). The same result was also obtained by Gabrielsen et al. [50] who performed the sensitivity analysis of the rate based model of CO2 absorption using a packed column. The increase of H reduces the CO2 flux because it increases the mass transfer resistance in gas and membrane phase (Eqs. (4) and (5)). It is also evident that the increase of H affects the CO2 fluxes of the partially wetted mode more than that of the non-wetted mode because, for the partially wetted mode, the absorption takes place in the instantaneous regime in which the enhancement factor is close to the infinite enhancement factor (E1 ). The increase of H, leads to higher CO2 concentration at gas–liquid interface (C CO2 , I ), and reduces both E and EN.
0 0
10 20 30 CO2 concentration in gas phase (%v/v)
Fig. 8. Effect of CO2 concentration in gas phase on the CO2 flux and the enhancement factor of the non-wetted mode (a) and the partially wetted mode with 20 % wetting (b). (15 %v/v CO2 in air, liquid velocity is 10 cm/s, PTFE membrane and TG and TL are 296 K and 293 K, respectively).
still slightly enhanced due to the increase of the driving force (Eq. (1)). The enhancement factors of both the non-wetted and partially-wetted modes reduce with increasing gas concentration because the increase of dissolved CO2 at gas–liquid interface enhances the contribution of physical absorption to the overall mass transfer in the liquid film [51]. The reductions of the enhancement factors of the partially wetted mode are more significant than that of the non-wetted mode, 85% and 66%, respectively, when the CO2 concentration is increased from 5 to 30 %v/v. This is due to the decrease of E1 , which significantly affects the absorption in the instantaneous regime of the
W. Rongwong et al. / Journal of Membrane Science 429 (2013) 396–408
Non-wetted mode
110
40% wetting
CO2 flux (mol/m2.s)
2.50E-03 2.00E-03 1.50E-03 1.00E-03 5.00E-04 0.00E+00 283
100
2.00E-03
90 1.50E-03
Flux
80
E
70
1.00E-03
60 50
303
323
343
363
5.00E-04
Temperature (K)
5.2.3. Effect of liquid velocity The effects of liquid velocity on the CO2 fluxes and the enhancement factors of the non-wetted mode (see Fig. 10) are not straightforward. At low liquid velocity (0–5 cm/s), the reaction between CO2 and MEA solution is instantaneous (E is close to E1 ) because the high liquid phase mass transfer resistance causes the reactions to occur immediately at the gas–liquid interface. The CO2 fluxes at low liquid velocities are strongly influenced by the liquid velocity since the liquid phase mass transfer coefficient with chemical reaction (EkL ) is proportional to the liquid velocity. At higher liquid velocity, the increase of CO2 flux is low because the reduction of the liquid phase mass transfer resistance changes the absorption regime from the instantaneous to the intermediate fast-instantaneous (as Ha is decreased). In this region, the enhancement factor starts to drop with liquid velocity and reduces the significance of liquid phase mass transfer resistance because the enhancement factor is influenced by the decrease in the Ha. The different effects of liquid velocity on the CO2 absorption in fast and instantaneous regimes using membrane contactors were also investigated by Dindore et al. [52]. Their simulation results showed that the increase of liquid
10
15
6.00E-04
CO2 flux (mol/m2.s)
5.2.2. Effect of liquid temperature From Fig. 9, both CO2 fluxes of the non-wetted and partially wetted modes increase with increasing inlet liquid temperatures. However, in the range of 293–333 K, it seems that the enhancement of CO2 flux in the non-wetted mode is more significant because the increase of liquid temperature that directly enhances the rate constant and influences the absorption in the intermediate fast-instantaneous regime more than in the instantaneous regime. The increase of liquid temperature does not change the absorption regime of the non-wetted mode to be instantaneous because E1 also increases with the liquid temperature. The values of Ha and E1 are increased from 214 to 296 and 135 to 199, respectively, when the liquid temperature is increased from 293 to 323 K. However, at temperatures above 333 K, the CO2 fluxes of the non-wetted mode started to decline because the reduction in driving force along the length of the absorber due to the reversibility of the CO2–MEA reaction is pronounced and the CO2 concentration in the bulk liquid is then increased. While, for the partially wetted mode, the CO2 fluxes do not decline in this region due to the increases of CO2 loading and the CO2 concentration in the bulk liquid are smaller than that of the non-wetted mode.
5
Liquid velocity (cm/s)
Fig. 9. Effect of inlet liquid temperature on the CO2 flux of the non-wetted mode and partially wetted mode (20% and 40 % wetting). (15%v/v CO2 in air, liquid velocity is 5.89 cm/s, PTFE membrane and TG is 296 K).
partially-wetted mode compared to that of the absorption in the intermediate regime of the non-wetted mode.
40 0
95 94
5.00E-04
93 92
4.00E-04
Flux
91
E
90
3.00E-04
Enhancement factor
CO2 flux (mol/m2.s)
120
2.50E-03
20% wetting
3.00E-03
Enhancement factor
3.50E-03
405
89 2.00E-04
88 0
5
10
15
Liquid velocity (cm/s) Fig. 10. Effect of liquid velocities on the CO2 flux and the enhancement factor of the non-wetted mode (a) and the partially wetted mode with 20 % wetting (b). (15 %v/v CO2 in air, PTFE membrane and TG and TL are 296 K and 293 K, respectively).
velocity did not influence the CO2 flux in the fast reaction regime but strongly increased the flux in the instantaneous reaction regime. For the partially wetted mode (Fig. 10b), the enhancement factor increases with liquid velocity because the absorption occurs in the instantaneous regime. The increase of liquid velocity slightly affects the flux because the wetted membrane resistance reduces the role of liquid phase resistance on the mass transfer.
6. Conclusion A rate-based model has been developed for estimating the CO2 fluxes of PTFE and PVDF membranes using MEA solution in hollow fiber membrane contactors. The predicted CO2 fluxes in PTFE and PVDF membranes were validated with the experimental data from the literature. For PTFE membranes, the simulation results fitted the experimental data well without using the percentage of wetting as a fitting parameter. While for PVDF membrane, the model results were in good agreement with the experimental data when considering the effect of membrane wetting. A parameter sensitivity analysis has been carried out and the results showed that the proposed models of both the nonwetted and partially-wetted modes are most sensitive to the value of Henry’s constant. The results also showed that the reaction between CO2 and MEA in the non-wetted mode takes place in the intermediate fast-instantaneous regime, and it is changes to the instantaneous regime when the membrane is partially wetted. The effect of operating parameters on the CO2 fluxes of the non-wetted and partially wetted modes were
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compared and the results showed that the increases of CO2 flux in the non-wetted mode with an increasing of CO2 concentration in gas phase and liquid temperature, was more significant than that of the partially-wetted mode.
xi yCO2 Z
mole fraction of species i (dimensionless) CO2 concentration in gas phase (%v/v) membrane length (m)
Greek letters
Ci CP C P,L DG,ef f Di DKn DM de di dint dln dln0 do E E1 Fi H Ha DHl DHr h Ki KL k2, kG kG, 0
k
MEA
ext
L
kL,
ext
kM 0 kM L Lm Mi NCO2 n P Pr pi Q R Re Sc Sh T U ol Vi Vn, Vnn vL X CO2
concentration of species i (kmol/m3) heat capacity (J/kmol K) heat capacities MEA solution (J/g K) effective diffusion coefficient of gas (m2/s) diffusivity of species i (m2/s) Knudsen diffusion coefficient (m2/s) molecular diffusion coefficient (m2/s) hydraulic diameter (m) inner diameter of membrane (m) interfacial diameter of the membrane (m) (di þ %wetting=100 ðdo di Þ) logarithmic mean diameters of the non-wetted pert of membrane (m) ( ðdo dint Þ=ln do =dint Þ) logarithmic mean diameters of the wetted pert of membrane (m) ( ðdint di Þ=ln dint =di Þ) outer diameter of membrane (m) enhancement factor (dimensionless) infinite enhancement factor (dimensionless) mole flow rates of species i (kmol/s) 3 Henry’s constant atm) ffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p(kmol/m Hatta number ( k2,MEA DCO2 ,L C MEA =kL,ext , dimensionless) heat of vaporization of water (J/kmol H2O) heat of reaction between CO2 and MEA and vaporization of water (J/kmol CO2) heat transfer coefficients (J/m2 s K) equilibrium constants of the reaction (dimensionless) overall mass transfer coefficient based on liquid phase (m/s) second-order reaction rate constant (m3/kmol s) gas phase mass transfer coefficients (m/s) combined gas and membrane phase mass transfer coefficient (m/s) liquid phase mass transfer coefficients (physical absorption) (m/s) combined wetted membrane and physical liquid phases mass transfer coefficients (m/s) non-wetted membrane mass transfer coefficient (m/s) wetted membrane mass transfer coefficient (m/s) liquid volume flow rate. (m3/s) liquid mass flow rate (g/s) Molecular weight of species i (g/mol) CO2 absorption flux (kmol/m2 s) number of fiber (dimensionless) total system pressure (atm) Prandtl number (ZC P,L =l, dimensionless) partial pressure of species i (atm) heat transfer flux (J/m2 s) gas constant (8.206 m3 atm/K kmol) Reynolds number (rvL di =Z, dimensionless) Schmidt number (Z=rDi , dimensionless) Sherwood number (kdi =Di , dimensionless) Temperatures (K) overall heat transfer coefficient (J/m2 s K) molar volume of species i (mL/mol) molar volume associated with the interaction between H2O and MEA and between CO2 and MEA liquid velocity (m/s) CO2 loading (mol CO2/mol MEA)
thicknesses of membrane (m) membrane porosity (dimensionless) tortuosity (dimensionless) ˚ collision diameter (A)
d
eM tM s Z
dynamic viscosity (Pa s) thermal conductivity (J/m s K) density (kg/m3) kinetic viscosity (m2/s) stoichiometric coefficient of overall reaction of CO2 and MEA (dimensionless) volume fraction of species i (dimensionless) mass percentage of MEA collision integral for diffusion (dimensionless)
l
r n vR
Fi O
OD Subscript B G GM I i L M ML I II
liquid bulk gas phase gas–membrane surface gas–liquid interface component i or inside (diameter) liquid membrane phase membrane–liquid surface experimental value calculated value
Superscripts 0
initial condition
Acknowledgments The authors gratefully acknowledge the financial support from the Royal Golden Jubilee program and the Senior Research Scholar Grant from Thailand Research Fund (TRF).
10000 CO2 Partial pressure (kPa)
Nomenclature
1000 100 Song et al. [53]
10
Austgen and Rochelle [54] Shen and Li [55]
1
Present work (model) 0.1 0.01 0.2
0.4
0.6
0.8
1
CO2 loading (molCO2/molMEA) Fig. A1. CO2 partial pressure at equilibrium condition in 2.5 M MEA solution and liquid temperature 313.2 K. Model validation with the experimental data from Song et al.[53], Austgen and Rochelle [54] and Shen and Li [55] .
W. Rongwong et al. / Journal of Membrane Science 429 (2013) 396–408
Appendix A.1. CO2 concentration in liquid phase at equilibrium The accuracy of the simple equilibrium model for CO2–MEA– water system (Eqs. (24)–(28)) was checked by comparison with the experimental data from the literature. Fig. A.1 compares the predicted values of CO2 partial pressure (pCO2 ¼ H C CO2 , B ) and experimental data for CO2 partial pressure in equilibrium over a 2.5 M MEA solution. The results show that the predicted values are in good agreement with the experimental data, suggesting that this model is sufficiently accurate to be used in actual processes. See Appendix Fig. A1
Appendix B. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.memsci.2012. 11.050.
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