Modeling and simulation of CO2 removal from power plant flue gas by PG solution in a hollow fiber membrane contactor

Advances in Engineering Software 42 (2011) 612–620

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Modeling and simulation of CO2 removal from power plant flue gas by PG solution in a hollow fiber membrane contactor S. Eslami a, S.M. Mousavi b,⇑, S. Danesh a, H. Banazadeh b a b

Department of Civil Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran Department of Chemical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

a r t i c l e

i n f o

Article history: Received 17 February 2011 Received in revised form 14 April 2011 Accepted 1 May 2011 Available online 25 May 2011 Keywords: Modeling Membrane contactor Absorption Flue gas Power plant Potassium glycinate

a b s t r a c t The absorption of carbon dioxide from nitrogen–carbon dioxide mixture was investigated in a polytetrafluoroethylene (PTFE) hollow fiber membrane module using potassium glycinate (PG) aqueous solution. A mathematical model was developed to simulate the behavior of CO2 removal by PG solution in hollow fiber module and solved for the non-wetted operation mode. The simulation results showed that both CO2 mass transfer rate and removal efficiency were favored by concentration of PG, liquid flow rate and liquid temperature, and while the gas temperature having no push on the removal efficiency, increase in gas flow rate and initial CO2 concentration will reversely affect the capture process. Comparison of different diameters for the fibers of contactor and also different number of fibers showed that there is conditions of number and diameter of fibers which results in highest removal efficiency. Moreover, the simulation results agreed well with the expected theoretical trends. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction It is well known that emission of carbon dioxide is amongst the most important reasons of global warming [1]. Fossil fuel power plants are considered a major contributor to carbon dioxide emissions. Therefore, CO2 capture from flue gas of power plants will be an effective way to control these emissions [2]. Several techniques have been introduced for CO2 removal from power plant flue gases; including adsorption, chemical and physical absorption, cryogenic method and membrane separation process, the most common of which is chemical absorption with alkanolamine solutions such as monoethanol amine (MEA), diethanol amine (DEA), triethanol amine (TEA) and methyldiethanol amine (MDEA) in absorption columns [3–7]. However, conventional absorption columns suffer from many drawbacks such as foaming, flooding, air entrainment, channeling and also high capital and operational costs. Numerous searches have been performed for the cause that led to the introduction of membrane contactor systems, which are proved to be capable of overcoming the above shortcomings and improve system function in terms of mass transfer [8]. Absorption of CO2 occurs in a membrane contactor when the gas stream contacts with the liquid phase flowing on the opposite side of the membrane. Due to absence of interpenetration of two phases with membrane acting as a barrier between liquid and gas stream, problems such

⇑ Corresponding author. Tel./fax: +98 511 8816840. E-mail address: [email protected] (S.M. Mousavi). 0965-9978/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.advengsoft.2011.05.002

as foaming that are associated with dispersion of two phases are not likely to occur any longer. The efficiency of membrane contactors for CO2 capture has been extensively studied in recent years [9–11]. According to Li and Chen [12], the idea of CO2 absorption by chemical solvent in a hollow fiber membrane contactor (HFMC) was first proposed by Qi and Cussler. HFMCs have also been a subject of study in recent years [12–16]. The membrane can be either porous or nonporous; the advantage of using nonporous membrane is that it has a greater potential to improve the selectivity for CO2 [12,13]. However, in this case the membrane resistance is high to control the permeation rate. As a consequence, most of the previous research was focused on the porous membranes. The advantages and disadvantages of membrane contactors have been discussed in more detail by Gabelman and Hwang [13]. The membrane contactor systems using alkanol amine solutions have proved to suffer from wetting problem [17]. PTFE HFMCs happen to show good resistance when wetting is a matter of importance [18]. Studies also have been made in order to evaluate new absorption liquids based on amino acid salts that minimize the risk of wetting in membrane contactors [19]. Yan et al. studied the Potassium Glycinate solutions as absorbent liquid in contactor systems. In comparison with water, MEA and MDEA, PG proved to have higher surface tension and less likely to wet the membrane [20]. Much works have been performed to study the removal of CO2 from flue gas using various absorbent solutions in membrane contractors. Lee et al. [21] performed a numerical analysis to investigate the removal behavior of carbon dioxide using aqueous potassium carbonate solution in a hollow fiber membrane contactor.

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Dindore et al. [22] also studied the CO2 capture process in a polypropylene (PP) hollow fiber membrane contactor using potassium carbonate solution both theoretically and experimentally. Wang et al. [23] investigated the absorption of CO2 using three typical solutions AMP, DEA, MDEA in hollow fiber membrane contactors. Al-Marzouqi et al. [24] studied CO2 absorption using MEA and NaOH in hollow fiber membrane contactors. Atchariyawut et al. [25] used MEA and NaOH as the absorbent solvents for CO2 absorption from CH4 using membrane contactors. Faiz and Al-Marzouqi [26] also studied the simultaneous CO2/H2S absorption using MEA in a hollow fiber membrane contactor. Yet still, in spite of PG solution being proved an advantageous absorbent, a mathematical model for the removal of carbon dioxide from flue gas using PG solution as absorbing liquid has not been published in literature. This work is aimed to develop and solve such a model. 2. Model development In the current study, a two dimensional mathematical model for the transport of CO2 through membrane contactor has been developed assuming PG as absorbent liquid. Due to high resistance of PTFE membranes for membrane wetting and also low tendency of PG solution to wet the membrane, non-wetting conditions are considered. 2.1. Material balance A material balance has been carried out on membrane contactor system to develop the main equations for the mathematical model. The model is developed for a single hollow fiber through which the liquid flows with a fully developed laminar parabolic velocity profile. The fiber is surrounded by a laminar countercurrent gas flow. According to Happel’s free surface model [27], only a portion of the fluid surrounding the fiber is considered which may be approximated as circular cross section. Therefore, as illustrated in Fig. 1 the membrane contactor consists of three sections: tube, membrane, and shell sides. The steady state two dimensional material balances are carried out for all three sections. The gas mixture is fed to the shell side (at z = L), while the solvent is passed through the tube side (at z = 0). Carbon dioxide is removed from the mixture by diffusing through the membrane and then undergoing reaction with the solvent. 2.1.1. Tube side The steady state continuity equation for each species during the simultaneous mass transfer and chemical reaction in a reactive absorption system can be expressed as below:

@C i ¼  r  N i þ Ri @t

ð1Þ

where Ci, Ni, Ri, are the concentration, flux and reaction rate of species i respectively. Fick’s law of diffusion can be used for the determination of fluxes of species i:

Ni ¼ Di rC i þ C i V z

ð2Þ

where Di and Vz are the diffusion coefficient and axial velocity along the membrane module length, respectively. Combining the Eqs. (1) and (2), the overall mass transfer equation will be as follows:

@C i ¼ Di r2 C i  r  C i V z þ Ri @t

ð3Þ

Material balance for transfer of CO2 through the tube at steady state will be given by the following equation:

Ditube

" @ 2 C itube @00722

þ

# 1 @C itube @ 2 C itube @C itube þ Ri ¼ V ztube þ r @r @z2 @z

ð4Þ

where r and z are radial and axial components, respectively and i is either CO2 or PG. The left-hand side of the above equation represents the diffusion and reaction terms, whereas the right-hand side of the equation is the convection term. The velocity distribution in the tube is assumed to follow Newtonian laminar flow pattern [28].

" V z-tube ¼ 2V tube

 2 # r 1 r1

ð5Þ

where V tube and r1 are average liquid flow rate in tube side and fiber inner radius, respectively. Boundary conditions are given as:

z ¼ 0;

C CO2 -tube ¼ 0;

C PG-tube ¼ C initial

ð6Þ

z ¼ L;

Ni ¼ C i V z-tube ðconvective fluxÞ

ð7Þ

r ¼ 0;

@C i-tube ¼0 @r

ð8Þ

r ¼ r1 ;

C CO2 -tube ¼ C CO2 -membrane  m;

@C PG ¼0 @r

ð9Þ

where m is the dimensionless Henry Constant (mol mol1) and defined using Eqs. (10)–(13) [29]; and i is either PG or CO2. It should be noticed that convection is the dominant mass flow through the boundary with respect to the convective flux boundary condition. In other words, the mass flux due to diffusion across this boundary is zero.

m ¼ 8:314 

T HCO2

ð10Þ

where HCO2 is the Henry Constant for CO2 in PG solution (Pa mol1 m3) and T is gas temperature (K).

HCO2 ¼ HCO2 ;w  10ðaC o;PG Þ

ð11Þ

where HCO2 ;w is the Henry constant for CO2 in water (Pa mol1 m3) and a is a coefficient (mol1 dm3).

HCO2 ;w ¼

Fig. 1. A schematic diagram of a single hollow fiber for the model.

a¼

expð2044=TÞ 3:54  107

62:183098  0:111175 T

ð12Þ

ð13Þ

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2.1.2. Membrane side As long as wetting is not considered, only the gas phase exists in the membrane. The overall mass transfer equation at steady state for transport of carbon dioxide in the membrane is as follows:

" # @ 2 C CO2 -membrane 1 @C CO2 -membrane @ 2 C CO2 -membrane ¼0 DCO2 -membrane þ þ r @r2 @r @z2 ð14Þ The membrane diffusion coefficient, DCO2 -membrane includes the effect of such factors as membrane porosity and tortuosity and will be given by below equation [26]:

DCO2 -membrane ¼

DCO2 -shell  e

s

r ¼ r1 ;

C CO2 -membrane ¼

C CO2 -tube m

ð16Þ

r ¼ r2 ;

C CO2 -membrane ¼ C CO2 -shell

ð17Þ ð18Þ

where r2 is fiber outer radius.

" # @ 2 C CO2 -shell 1 @C CO2 -shell @ 2 C CO2 -shell DCO2 shell þ þ r @r2 @r @z2 @C CO2 -shell @z

ð19Þ

ð20Þ

where V shell and r3 are the average gas flow rate in shell side and shell effective radius, respectively.

r3 ¼ r2

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=ð1  /Þ

ð26Þ

Deprotonation of zwitterions by a base also follows the below reaction: kB

OOCþ H2 N—CH2 —COO Kþ þ Bi !  OOCHN—CH2 —COO Kþ þ Bi Hþ ð27Þ where Bi is the base in solution which is able to deprotonate the zwitterions. In amino acid salt solution, these bases are generally H2O, OH, and the amino acid salt H2NCH2COOK+ [30]. Reaction of CO2 with PG has been studied and reported by Portugal et al. [31]. The reported overall kinetic constant points out that PG is a fast absorbent compared to other absorbing solutions such as MEA (13,400 s1 for PG at 298 K for 1 M solution compared to 5920 s1 at the same conditions for MEA). The reaction rate is first order regarding the concentration of CO2. The rate constant and reaction rate equation are given by Eqs. (28) and (29), respectively [31]:

  8544 expð0:44C PG Þ T

r CO2 ¼ 2:42  1016 exp



 8544 expð0:44C PG ÞC PG C CO2 T

ð28Þ

ð29Þ

where T is the liquid temperature (K).

Assuming Happel’s free surface for the model [27], the velocity profile in the shell will follow the below equation:

h i V z-shell ¼ 2V shell 1  ðr 2 =r 3 Þ2 " # ðr=r 3 Þ2  ðr 2 =r 3 Þ2 þ 2 lnðr 2 =rÞ  3 þ ðr 2 =r 3 Þ4  4ðr 2 =r 3 Þ2 þ 4 lnðr 2 =r 3 Þ

k1

kov ¼ 2:42  1016 exp

2.1.3. Shell side The overall mass transfer equation for steady state transport of carbon dioxide in shell side will be:

¼ V z-shell

k2

H2 —CH2 —COO Kþ þ CO2 ¢  OOC þ H2 N—CH2 —COO Kþ

ð15Þ

where e and s are the porosity and tortuosity of the membrane, respectively. Boundary conditions for the membrane will be as follows:

z ¼ 0 and z ¼ L; rC CO2 -membrane ¼ 0 ðInsulationÞ

zwitterions mechanism reported by Caplow (1968) is generally applied, according to which CO2 reacts with amino acid salt, PG solution in this study, forming a zwitterions, which subsequently is deprotonated by a base from the solution. The formation of zwitterions follows the below reaction:

ð21Þ

where / is the volume fraction of the void. Boundary conditions for the shell side will be as follows:

z ¼ L;

C CO2 -shell ¼ C CO2 -initial

ð22Þ

z ¼ 0;

NCO2 ¼ C CO2 V z-shell ðconvective fluxÞ

ð23Þ

r ¼ r3 ;

@C CO2 -shell ¼0 @r

ð24Þ

r ¼ r2 ;

C CO2 -shell ¼ C CO2 -membrane

ð25Þ

3. Numerical solution The dimensionless model equations associated with the tube, membrane and shell sides with considering appropriate boundary conditions, physical and chemical properties, and reaction rate equations were solved using COMSOL software. This software takes use of finite element method for numerical solutions of partial differential equations. For the finite element analysis, mapped meshing was applied (Fig. 2) and among a variety of numerical solvers, the UMFPACK was adapted due to memory efficiency. Physical and chemical properties for the gas mixture and the liquid solvent that are needed to solve the above set of equations with the boundary conditions are provided in Table 1. These properties include: the gas physical solubility in the liquid solution, the gas and liquid phase diffusion coefficients in addition to adapted dimensions of the membrane contactor. Conditions such as gas and liquid flow rates, gas and liquid temperatures, CO2 concentration in feed gas and PG concentration are as listed in Table 2 except where indicated either in text or in figure captions. 4. Results and discussion

2.2. Reaction mechanism The reaction rate equation and rate constant of chemical absorption of CO2 in PG solution are of the main importance in developing the mathematical model. In order to model the carbon dioxide absorption into aqueous solutions of amino acid salt, the

The mathematical model was solved for different gas and liquid flow rates, temperatures and PG and CO2 concentrations. The objective of simulation is to study the effect of operational conditions on removal system behavior. The simulation results are illustrated either in term of CO2 mass transfer rate or removal efficiency using equations below, respectively [7]:

J CO2 ¼

ðQ in  C in  Q out  C out Þ  273:15  1000 22:4  T g  S

ð30Þ

S. Eslami et al. / Advances in Engineering Software 42 (2011) 612–620

R r3 C out ¼

r2

Cðr; 0Þdr R r3 dr r2

615

ð32Þ

The concentration gradient and the total flux vectors of CO2 in the tube, membrane and shell sides of the contactor are shown in Fig. 3. The gas mixture flows into the shell side of the contactor at (z = L) where the concentration of CO2 is the highest, while PG solution flows into the tube side at (z = 0) where the concentration of CO2 is assumed to be zero. As the gas flows through the shell side, it moves to the membrane side due to the concentration difference, and then it is absorbed by the flowing solvent in the tube side where it reacts and gets consumed. In tube and shell compartments, the flux vectors are in both r and z directions due to convection and diffusion; whereas within the membrane, the flux vectors are in two directions due to only diffusion. 4.1. Axial and radial concentration profile

Fig. 2. Mapped meshing for the simulation of CO2 capture in HFMC by PG solution.

Table 1 Physical and chemical data for the model.

The axial concentration of CO2 along the tube-membrane interface is illustrated in Fig. 4. The CO2 concentration decreases nearly linearly along the tube-membrane interface till it reaches the minimum value at the exit. The radial concentration profile at z/L = 0.5 is also presented in Fig. 5 which shows that the CO2 concentration has a negligible decrease cross the shell side, while it drops significantly and linearly cross the membrane side till it reaches the minimum at tube-membrane interface. 4.2. Effect of PG concentration

Parameter

Value

References

Module inner diameter (m) Fibers outer diameter (lm) Fibers inner diameter (lm) Fibers length (m) Membrane area (m2) Number of fibers Membrane porosity Membrane tortuosity DCO2 -shell (m2 s1) DCO2 -tube (m2 s1) DPG (m2 s1)

0.08 442 344 0.15 6.05 7000 0.45 2 1.8  105 1.5  109 6  1010

[20] [20] [20] adapted [20] [20] [20] [20] [26] [32] [26]

The effect of solvent concentration on removal efficiency and mass transfer rate has been illustrated in Figs. 6 and 7, respectively. It is evident that increasing the solvent concentration directly improves the removal efficiency and also the mass transfer rate of CO2. This happens because the active absorption of carbon dioxide at liquid boundary layer is increased with increasing solvent concentration. Moreover, increasing PG concentration will lead to increase in surface tension, which is associated with wetting phenomenon in a reverse fashion, and therefore positively affects both the removal efficiency and the mass transfer rate. 4.3. Effect of gas temperature

Table 2 Values of system operational parameters. Parameter

Value

Unit

C CO2 in CPG in

14 1 0.05

(%) (mol/lit) (m/s)

0.211

(m/s)

298 308

(°C) (°C)

V tube (=vliquid) V shell (=vgas) Tgas Tliquid

g ¼ 100

  Q in  C in  Q out  C out C out ¼ 100 1  Q in  C in C in

CO2 removal efficiency for different values of gas temperature has been illustrated in Fig. 8 which shows that the gas temperature has almost no effect on the removal process. That is evident since despite the slight reduction of gas concentration due to temperature increase of 20 °C, the subsequent effect of gas concentration on removal process is not significant, because there is concentration term in both numerator and denominator of Eq. (28) too. Regarding the mass transfer rate equation on which the gas temperature has a reverse effect and also the slight variations of gas concentration, the CO2 mass transfer rate decreases as in Fig. 9. 4.4. Effect of gas flow rate

ð31Þ

where JCO2 is the mass transfer rate of CO2 (mol/m2 h), Tg is the gas temperature (K), S is the total membrane area (m2), Q in and Q out are the gas volumetric flow rates (m3/h) and Cin and Cout are the CO2 volumetric concentrations in the gas phase (%) at the inlet and outlet, respectively and g is the CO2 removal efficiency (%). Since the maximum CO2 concentration of the gas mixture at the inlet is very low, the change in volumetric flow rate is assumed to be negligible and thus removal efficiency can be approximated by Eq. (31). Cout is derived by means of COMSOL through the following formula:

Fig. 10 shows the effect of gas velocity on CO2 removal efficiency. It can be seen that the removal efficiency reduces with increasing gas velocity. This is due to the reducing detention time of CO2 in the shell and further reduction of CO2 availability for the reactive absorption. 4.5. Effect of liquid temperature System behavior at different amounts of liquid temperature is illustrated in Fig. 11. Regarding the liquid temperature being

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Fig. 3. Model solution for CO2 capture.

Fig. 4. Axial CO2 concentration profile at tube-membrane interface.

involved in Arrhenius equation as well as its effect on the diffusion phenomenon, the observed increase in CO2 mass transfer could be explained. It should be noticed that increasing the solvent temperature could discourage gas solubility and enhance liquid evaporation which leads to a reduction in mass transfer. Increasing the liquid temperature may cause different results at different conditions depending on which of the situations explained being

dominant. The changes in CO2 removal efficiency will also follow a similar trend. 4.6. Effect of liquid flow rate The CO2 mass transfer rate at different liquid flow rates is illustrated in Fig. 12. The increase in the mass transfer is due to faster

S. Eslami et al. / Advances in Engineering Software 42 (2011) 612–620

Fig. 5. Radial CO2 concentration profile at z/L = 0.5.

Fig. 6. Effect of PG concentration on removal efficiency.

Fig. 7. Effect of PG concentration on CO2 mass transfer rate.

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Fig. 8. Effect of gas temperature on removal efficiency (vliquid = 0.1 m/s).

Fig. 12. Effect of PG flow rate on CO2 mass transfer rate.

Fig. 13. Effect of CO2 concentration in feed gas on mass transfer rate (CPG in = 0.5 mol/l). Fig. 9. Effect of gas temperature on CO2 mass transfer rate (vliquid = 0.1 m/s).

Fig. 14. Effect of CO2 concentration in feed gas on removal efficiency (CPG in = 0.5 mol/l). Fig. 10. Effect of gas flow rate on removal efficiency.

Figs. 13 and 14. Increase in CO2 content in the feed gas encourages mass transfer due to higher availability of carbon dioxide in the system. At the other hand, by increasing the CO2 content in the feed gas while keeping the solvent concentration constant, the amount of un-absorbed CO2 in the system is increased with consequent reduction in removal efficiency.

Fig. 11. Effect of PG temperature on CO2 mass transfer rate (CPG in = 0.5 mol/l).

substitution of reacted PG which results in better availability of the absorbent at the liquid boundary layer. 4.7. Effect of CO2 concentration in the feed gas The effect of CO2 volumetric concentration in the feed gas on the mass transfer rate and removal efficiency is represented in

Fig. 15. Effect of fiber diameter on removal efficiency (CPG in = 0.5 mol/l).

S. Eslami et al. / Advances in Engineering Software 42 (2011) 612–620

619

Regarding the simultaneous effect of increased amount of absorbed carbon dioxide and also increase of mass transfer interface which is represented by S in mass transfer rate equation, the changes in CO2 mass transfer rate will be as in Fig. 18.

5. Conclusion

Fig. 16. Effect of fiber diameter on CO2 mass transfer rate (CPG in = 0.5 mol/l).

A comprehensive two dimensional mathematical model was developed for the transport of CO2 in HFMCs using PG as the absorbent solvent. The model was established considering nonwetted condition for countercurrent gas–liquid flow arrangement. Axial and radial diffusion were considered inside the fiber, through the membrane, and within the shell. No experimental data were available for validation. The effect of PG concentrations, gas and liquid flow rates, gas and liquid temperature as well as CO2 content in the feed gas on the removal efficiency and mass transfer rate of CO2 were studied. The removal percentage of CO2 increased while increasing the PG concentration. Both liquid temperature and flow rate encouraged the removal process. While the gas temperature being neutral to removal process, gas flow rate will have a reverse effect.

References Fig. 17. Effect of number of fibers on removal efficiency (vliquid = 0.1 m/s, CPG in = 0.5 mol/l).

Fig. 18. Effect of number of fibers on CO2 mass transfer rate (vliquid = 0.1 m/s, CPG in = 0.5 mol/l).

4.8. Effect of fiber diameter In order to simulate the effect of fiber diameter, the inner and outer diameters of the original fiber are simultaneously multiplied by a factor, a, and consequent shell diameter is then calculated and considered in velocity profiles in both the shell and tube side. Fig. 15 illustrates the positive effect of fiber diameter on the CO2 removal efficiency. This effect is obvious since the available mass transfer interface increases due to increase in fiber diameter. Elsewhere, regarding the simultaneous effect of increased amount of absorbed carbon dioxide and also increase of mass transfer interface which is represented by S in mass transfer rate equation, the changes in CO2 mass transfer rate will be as in Fig. 16. It should be noted that the highest mass transfer rate coincides with original fiber dimensions, (i.e. a = 1).

4.9. Effect of number of fibers Changing the number of fiber used in a module will directly alter the mass transfer interface. Thus, as illustrated in Fig. 17, increasing the number of fibers in module will encourage the removal efficiency.

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