Analysis of CO2 Separation with Aqueous Potassium Carbonate

Mar 4, 2013 - ... Elizabeth Glogowski , William C. Floyd , Carlos A. Valdez , William L. Smith , Joe H. Satcher , William L. Bourcier , Christopher M...
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Analysis of CO2 Separation with Aqueous Potassium Carbonate Solution in a Hollow Fiber Membrane Contactor M. Mehdipour, M. R. Karami, P. Keshavarz,* and S. Ayatollahi Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran ABSTRACT: Hot potassium carbonate solution is a promising absorbent for economical sequestration of CO2 from flue gas. In the present study, a 2D mathematical model was developed to analyze the absorption of carbon dioxide from a gas mixture into an aqueous solution of potassium carbonate using a microporous hollow fiber membrane contactor operated under nonwetted or partially wetted conditions. The set of partial differential equations for the liquid, membrane and gas phases were solved by applying a numerical procedure, and the model results were validated with available experimental data in the literature. A parametric study was done using the validated model in order to achieve an optimized CO2 capture. It was found that the rate of absorption increases significantly with increasing the liquid temperature, and there is an optimum carbonate concentration which gives maximum absorption flux at each solution temperature. A comparison between potassium carbonate and diethanolamine solutions was done under nonwetted and partially wetted conditions. The results revealed that potassium carbonate can give higher CO2 recovery at optimum conditions. Considering the other advantages of K2CO3 solution over alkanolamines such as lower cost and easier regeneration, it can be a suitable choice for CO2 absorption by hollow fiber membrane contactors. evaluated the influence of various factors such as porosity, fiber diameter, liquid viscosity, and chemical reaction on the rate of mass transfer in a hollow fiber membrane contactor. Karoor and Sirkar4 studied the absorption of CO2 and SO2 from various gas mixtures by water in a microporous hydrophobic hollow fiber membrane contactor. Rangwala9 showed that the use of hollow fiber membrane contactors instead of conventional packed towers caused a 3- to 9-fold increase in the overall mass transfer rate. Wang et al.10−12 did several studies on CO2 capture by various amine solutions in the hollow fiber membrane modules. They investigated the influence of many factors such as type and concentration of the liquid absorbent, gas and liquid flow rates, and membrane wetting on CO2 absorption experimentally and theoretically. Keshavarz et al.13−15 simulated the chemical absorption of CO2 in a hollow fiber membrane module and investigated the effect of membrane wetting on the CO2 absorption flux as well as the simultaneous absorption of CO2 and H2S in a hollow fiber membrane contactor. One of the most important parameters in CO2 absorption by hollow fiber membrane contactors is the selection of liquid absorbent. Some of the criteria that should be considered for absorbent selection are as follows:3,16,17 (i) There should be a rapid reaction with CO2 to increase absorption flux and decrease the mass transfer resistance of liquid phase. (ii) It has a high surface tension because the liquid with low surface tension has a greater tendency to penetrate into the pores of the membrane that cause the membrane wetting phenomenon. (iii) It should be chemically compatible with the membrane material, because the reaction of a chemical absorbent with a membrane can change the membrane pore structures and cause

1. INTRODUCTION Environmental pollution is one of the greatest challenges that humans have ever faced. Carbon dioxide is the most important of the greenhouse gases which are contributing to global warming and climate change. Therefore, it is necessary to find convenient methods for CO2 removal from various gas streams. At present, several methods are available for CO2 capture from gas streams such as adsorption on solids, cryogenic distillation, chemical and physical absorption, and membrane separation.1 Among these methods, chemical absorption with amine solutions using traditional contactors such as packed or tray columns are very common the separation of CO2 from gas streams. Another absorbent that can be used in these conventional contactors is an aqueous solution of potassium carbonate at high temperatures (hot potassium carbonate solution). The main advantages of aqueous K2CO3 in comparison with alkanolamines are its low cost and easier regeneration. Gas−liquid membrane contactors have been considered for gas absorption in recent years because of many advantages over traditional equipment. Some of these advantages include much higher surface area per unit volume of contactor and more flexibility in operation, because liquid and gas flow rates can be controlled independently without any problems such as flooding, weeping, foaming, or entrainment. Furthermore, gas−liquid interfacial area is constant and independent of operating conditions such as temperature or flow rates. Due to modularity of membrane contactors, they can be easily scaled up or down linearly, and they are more economical because of less space and consumption of less energy.2−4 These advantages have led to several investigations in the field of gas absorption with membrane contactors. Zhang and Cussler5,6 were the pioneers who used gas−liquid membrane contactors for gas absorption. They studied the absorption of CO2 by aqueous NaOH solution in a microporous polypropylene hollow fiber membrane module. Kreulen et al.7,8 © 2013 American Chemical Society

Received: January 11, 2013 Revised: February 28, 2013 Published: March 4, 2013 2185

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Figure 1. Schematic diagram of the liquid and gas flow in a hollow fiber.

membrane wetting. (iv) Since the flue gas temperature is very high, an absorbent for sequestration of CO2 should be able to absorb CO2 effectively under hot conditions. Therefore, the solvent should be thermally stable and have a low vapor pressure to prevent the lost of solvent. (v) It can be easily regenerated because the process would be much more economical in this case. Previous research has mainly used alkanolamine solutions as the absorbent in the hollow fiber membrane contactors for CO2 separation. Aqueous solution of K2CO3 can be a good alternative to amines solutions for CO2 absorption. It is thermally more stable than amine solutions; thus the process can work at higher temperatures (hot potassium carbonate process). One of the biggest advantages of K2CO3 solution is its lower cost of regeneration especially at higher concentrations of CO2, which makes it a promising absorbent for economical sequestration of CO2 from flue gas.18 It is also a nonorganic solution with greater surface tension than amine solutions with lower tendency for membrane wetting. One of the first investigations of the CO2 absorption using aqueous K2CO3 solution in hollow fiber membrane modules was done by Nii and Takeuchi.18 They studied absorption of CO2 and SO2 by aqueous solutions of NaOH, K2CO3, Na2SO3, and alkanolamines in a hollow fiber membrane contactor experimentally. Lee et al.19 modeled the CO2 absorption by potassium carbonate solution using membrane contactors and tried to find an optimal absorbent flow rate. They studied the effects of some parameters using their models; however the model was not validated with experimental data and some factors such as gas phase resistance, membrane resistance, and partial wetting of membrane were not considered. Recently, Faiz and AlMarzouqi20 studied the simultaneous absorption of CO2 and H2S with an aqueous solution of K2CO3 using nonwet membrane contactors. They found that a complete removal of CO2 and H2S was possible by using two membrane modules in series with a fresh 1 M carbonate solution in each module. In this paper, a mathematical model is presented for CO2 absorption from a CO2/N2 gas mixture using an aqueous solution of K2CO3 in a microporous hollow fiber membrane contactor, operated under nonwetted or partially wetted conditions. By applying a material balance for each diffusing component, the governing equations in the gas phase, liquid phase, and gas and/or liquid filled membrane phases were developed. A numerical scheme was prepared to solve the simultaneous nonlinear mathematical expressions, and the results of the model were validated with the experimental data of Nii and Takeuchi.18 The effects of temperature and

concentration of aqueous K2CO3 solution, important parameters that have not been studied in previous works, were investigated in order to achieve an optimal CO2 capture. In addition, partial wetting of the membrane was modeled for an aqueous solution of K2CO3 as well as a diethanolamine solution (DEA) to compare their absorption performance under different conditions.

2. MODEL DESCRIPTION A mathematical model is developed here to describe CO2 capture from a gas mixture by aqueous solution of K2CO3. The liquid absorbent is assumed to flow inside the fibers, and the gas mixture of CO2/N2 flows in the shell side cocurrently, which is schematically shown in Figure 1. The mass transfer process consists of four steps: (1) diffusion from the bulk gas phase to the outer surface of the membrane, (2) diffusion into the gas-filled pores of the membrane, (3) dissolution into the liquid absorbent and diffusion with chemical reaction into the liquid-filled pores of the membrane, and (4) diffusion with chemical reaction in the liquid phase. The following assumptions have been applied in the mathematical model: • a laminar parabolic velocity profile within the fibers • steady state and isothermal conditions • ideal gas behavior • uniform pore size distributions and membrane wall thickness • no axial diffusion • applicability of Henry’s law Since the fiber length is not very long, the contact time between gas and liquid phases is short. Also, these phases are not in direct contact with each other. Therefore, the assumption of the isothermal condition seems to be reasonable. It should be noted that, to consider a nonisothermal condition, the detailed thermal properties of fibers must be addressed, which were not available for the applied modules in this modeling. 2.1. Reaction of CO2 with Aqueous K2CO3 Solution. Potassium carbonate ionized into K+ and CO32− ions when it is dissolved in water. Various reactions that occur during the CO2 absorption in aqueous K2CO3 solution are presented below with the assumption that the ratio of bicarbonate to carbonate is negligible:21 k1

CO2 + H 2O XoooY H+ + HCO−3 k −1

(1)

k2

CO2 + OH− XoooY HCO−3 k −2

K3

HCO−3 ⇄ H+ + CO32 − Kw

H 2O XooY H+ + OH−

(2) (3) (4)

The overall reaction of CO2 in carbonate solution can be written as 2186

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CO2 + CO32 − + H 2O ↔ 2HCO−3

∂CjL

(5)

∂r

The rate controlling reactions for the absorption process are reactions 1 and 2.21 Reactions 3 and 4 are very fast and are assumed to be at equilibrium. On the basis of these assumptions, the reaction rate of CO2 consumption has been obtained as follows:21

rCO2

⎛ K [CO32 −] ⎞ ⎟ − [HCO−3 ] = [CO2 ]⎜k1 + k 2 w K3[HCO−3 ] ⎠ ⎝ ⎛ ⎞ [HCO−3 ] ⎜k −1K3 ⎟ + k − 2 [CO32 −] ⎝ ⎠

Dj L

(6) Dj L

log k1 = 329.85 − 110.541 log T −17265.4/T log k2 = 13.635− 2895/T log K1 = 14.843− 0.03279T − 3404.7/T K2 = K1/Kw log K3 = 6.498 − 0.0238T − 2902.4/T log Kw = 61.2062 − 22.4773 log T − 5839.5/T Dw,CO2 = (2.35 × 10−6) exp(−2119/T)

22 22 22 22 22 23 24

DCO2

25

DHCO−3

DCO2/Dw,CO2 = 1 − (0.154[K2CO3] + 0.0723[KHCO3]) DHCO3− = DCO32− = DCO2(MCO2/MHCO3−)−1/2

Hw,CO2

Hw,CO2 = [3.59 × 10−7]RT exp(2044/T)

24

h

log(Hw,CO2/HCO2) = (0.0959 + h)[K ] + (0.0839 = h) [OH−] + (0.0967 + h)[HCO3−] + (0.1423 + h) [CO32−] h = −0.0172 − 3.38 × 10−4 (T = −298.15)

∂Cj L ∂r

x=

27

(13)

−

(14)

(15)

δL δ

(16)

(17)

The diffusion coefficient of each diffusing component in the wetted part of membrane can be defined as:

27

DjLε (18)

τ

2.3.2. Nonwetted Part of the Membrane. To describe the CO2 transport into the part of membrane that is occupied by gas, eq 17 can be used without a reaction term. Because of very small membrane pore size, the gas diffusion in the nonwetted part of the membrane is affected by the pore wall; therefore the Knudsen diffusion must be considered to obtain the effective diffusion coefficient.

1 1 1 = + DjGe DjG Djk

(9)

where rj is the rate of reaction for component j. The liquid flow inside the fibers is laminar, and the velocity profile can be written as

(19)

To calculate the diffusion coefficient of each diffusing component in the nonwetted part of the membrane, the effective diffusion coefficient from eq 19 must be replaced with the ordinary diffusion coefficient in eq 18. The Knudsen diffusion coefficient is written as29 ⎛ T ⎞1/2 Djk = 0.485d p⎜ ⎟ ⎝M⎠

(10)

Equation 9 should be written for all necessary components in the liquid phase. Since the reaction rate depends on the concentration of the various components, the set of partial differential equations must be solved simultaneously. The initial condition for each diffusing component in the lumen is specified as

Cj L = Cj L,in for z = 0

=0

⎛ ∂ 2C ⎞ 1 ∂Cjm ⎟ jm − rj = 0 Djm⎜⎜ 2 + r ∂r ⎟⎠ ⎝ ∂r

26

∂Cj L

⎛ ⎛ r ⎞2 ⎞ Uz(r ) = 2UavL⎜⎜1 − ⎜ ⎟ ⎟⎟ ⎝ Ri ⎠ ⎠ ⎝

for r = R i and all z

By considering the chemical reaction in liquid filled pores, eq 17 is obtained for mass transport in the membrane phase:

2.2. Mass Transfer with Chemical Reaction in the Liquid Phase. By applying a component material balance for each diffusing component, the two-dimensional partial differential equation is obtained as follows: ⎛ ∂ 2C ⎞ 1 ∂Cj L ⎟ jL = Dj L⎜⎜ 2 + − rj ∂z r ∂r ⎟⎠ ⎝ ∂r

∂r

2.3. Mass Transfer in the Microporous Membrane. When the membrane porosity is high (more than 10%), the diffusion process into the membrane is basically one-dimensional, as it has been checked by Keller and Stein.28 The governing equations for the mass transport inside the membrane by applying the steady-state material balance can be achieved. 2.3.1. Wetted Part of the Membrane. Under wetted conditions, parts of membrane pores are filled by liquid, and this causes the additional resistance to appear on the way to mass transfer, and the efficiency of absorption decreases dramatically. The membrane wetting fraction (x) can be defined as

Djm =

Uz(r )

∂Cjm

CCO2,L = HCCO2,G

reference

k1 k2 K1 K2 K3 Kw Dw,CO2

HCO2

= Djm

Also, Henry’s law can be applied at the gas−liquid interface for the solubility of CO2 in the K2CO3 solution:

Table 1. Kinetic and Equilibrium Constants, Diffusion, and Solubility Coefficients Used in Calculations

+

∂r

and HCO3 that do not diffuse to the gas For species such as phase, eq 14 can be used as boundary condition at the gas−liquid interface:

(8)

equation

∂Cj L

CO32−

The kinetic parameters, equilibrium constants, and diffusion and solubility coefficients used in calculations are given in Table 1.

parameter

(12)

At the membrane-liquid interface, material balance for each diffusing component leads to following boundary condition:

According to the overall reaction in eq 5, the reaction rate equations of CO32− and HCO3− can be written as rCO32 − = rCO2 (7)

rHCO−3 = − 2rCO2

= 0 for r = 0 and all z

(20)

2.4. Governing Equations in the Gas Phase. The fluid flow inside the shell is usually very complex. In this study, Happel’s free surface model30 is used to describe the shell side velocity profile. This model is given by the following equations: ⎛ ⎛ R ⎞2 ⎞ Uz(r ) = 2UavG⎜⎜1 − ⎜ o ⎟ ⎟⎟β(r ) ⎝ Re ⎠ ⎠ ⎝

(11)

At the center of each fiber, because of symmetry in the radial direction, eq 12 can be used as a boundary condition: 2187

(21)

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Table 2. Specifications of Hollow Fiber Membrane Modules module no.

fiber o.d. (μm)

fiber i.d. (μm)

fiber length (cm)

no. of fibers

pore size (μm)

packing fraction

tortuosity

porosity

ref

1 2 3

300 1800 300

240 1000 220

30 30.5 11.3

132 14 1100

0.03 2 0.04

0.4887 0.157 0.4

2.5 2 3.5

0.4 0.5 0.4

4 18 11

β(r ) =

(r /R e)2 − (R o/R e)2 + ln(R o/r ) 3 + (R o/R e)4 − 4(R o/R e)2 + 4 ln(R o/r )

(22)

where Re and Ro are the radius of the free surface and fiber outer radius, respectively. Re is defined as Re =

⎛ 1 ⎞0.5 ⎜ ⎟ R ⎝θ⎠ o

(23)

By applying a material balance for CO2 transport in the shell side, the following partial differential equation is obtained:

⎡ ⎛ ∂ 2C ⎞ ⎛ R ⎞2 ⎤ ∂CjG 1 ∂CjG ⎟ jG 2UavG⎢1 − ⎜ o ⎟ ⎥β(r ) = DjG⎜⎜ 2 + ⎢⎣ ∂z r ∂r ⎟⎠ ⎝ R e ⎠ ⎥⎦ ⎝ ∂r

(24)

At the free surface, the following boundary condition can be used: ∂CjG ∂r

= 0 for r = R e and all z

(25)

The specifications of hollow fiber membrane modules which have been modeled in this study are presented in Table 2.

Figure 2. Pure CO2 absorption in water under wetted and nonwetted cases (gas flow rate: 75 cc/min, module 1).

3. NUMERICAL SCHEME The presented mathematical relations in the liquid, membrane, and gas phases contain a set of partial differential equations that must be solved simultaneously to find the liquid and gas concentration profiles in radial and axial directions. The partial differential equations in the liquid phase are nonlinear because of nonlinear reaction terms. Due to the mathematical complexity of the proposed system, a numerical method should be applied to solve the equations. A finite difference method was applied to solve the equations by using MATLAB.31 The diffusion terms were discretized implicitly, which generated sets of simultaneous nonlinear algebraic equations. Because of the very large number of nodes, the reaction terms in each node were rewritten based on this fact that the species concentrations do not have sharp variation in the axial direction.13 By applying this assumption the nonlinear chemical reaction terms were linearized. Then, the linearized algebraic equations in the radial direction, which form a tridiagonal matrix, were solved simultaneously using the Thomas algorithm as an initial guess.32 A material balance error was applied at the end of the program to check the accuracy of the numerical method. The average error is around ±0.03%, which is acceptable for a finite difference method.

Figure 3. Effect of CO2 partial pressure on absorption flux (feed conditions: T = 294 K, UL = 0.011 m/s, UG = 0.1 m/s; module 2).

4. RESULTS AND DISCUSSION 4.1. Model Validation. To evaluate the model validation, the physical absorption of pure CO2 in water was analyzed initially by using the model and checked with experimental results of Karoor and Sirkar4 in Figure 2. As can be seen from this figure, the concentration of CO2 in the liquid outlet decreases with increasing the liquid flow rate, and model results are in good agreement with experimental data for both wetted and nonwetted modes. Figure 3 shows a comparison between the model results and experimental data of Nii and Takeuchi18 for CO2 absorption from a gas mixture of CO2/N2 with 2 M aqueous K2CO3 solution. This figure presents CO2 absorption flux as a function of the partial pressure of CO2. It is indicated that the absorption flux predicted by the model increases with increasing partial

pressure of CO2, which is in good agreement with the experimental data. 4.2. Effects of Liquid Temperature and Liquid Concentration. In all upcoming sections, module 3 is applied for modeling because it is available commercially. Furthermore, its higher number of fibers makes it possible for the model to undertake a wider range of operations. The effect of solution temperature on the concentration distribution of CO2 along the fibers in the gas phase is given in Figure 4, when a 1 M K2CO3 solution is used as the absorbent. As shown in this figure, CO2 removal increases from the gas phase with increasing temperature of the liquid absorbent. A higher temperature of K2CO3 solution causes two different effects on the absorption parameters; reaction rate and diffusion coefficients increase, and 2188

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the CO2 absorption flux increases with the liquid velocity at low temperatures. Because of a high reaction rate at higher temperatures, the mass transfer resistance in the liquid phase reduces in this condition. Therefore, the CO2 flux is almost not affected by the liquid velocity at 348 K. Figure 6 presents the effect of concentration and temperature of the K2CO3 solution on the CO2 absorption flux. At a specific temperature, the absorption flux initially increases fast and then decreases slowly with increasing the concentration of K2CO3 solution. There are two important factors that act in opposition to each other by changing the K2CO3 concentration. While the K2CO3 concentration is increased, the reaction rate increases as well; however, the solubility of CO2 in the liquid phase also reduces significantly. At low concentrations of potassium carbonate, the reaction rate and thus the flux are very low. Under this condition, a small increase of K2CO3 concentration will enhance the reaction rate and the flux significantly. However, after a specific concentration, the solubility becomes more important, and the absorption flux is decreased with concentration. Therefore, at each temperature, there is an optimum concentration at which the absorption flux is maximum. The figure also shows that the reduction of absorption flux after the optimum concentration is slower at higher temperatures. Figure 7 shows the optimum concentration for CO2 absorption at various temperatures of K2CO3 solution. This figure reveals that the optimum concentration increases with solution temperature. As shown in this figure, the optimum concentration increases with a sharp slope at temperatures more than 363 K. At high temperatures, the reaction rate increases extremely, and its positive effect on absorption rate prevents the negative effects of solubility. It provides the possibility of using more concentrated solutions to achieve maximum absorption of CO2. According to these results, the optimum concentration should be considered as an important parameter for CO2 absorption using potassium carbonate solution. Figure 8 presents the variation of the maximum absorption flux of CO2 with the temperature at optimum concentrations of K2CO3 solution. The figure reveals that increasing the temperature significantly affects the maximum absorption flux. Under the operating conditions applied in the model, all CO2 in the gas phase is absorbed at 348 K. Therefore, increasing the temperature of K2CO3 solution higher than this value does not affect the maximum absorption flux. 4.3. Effect of Gas Flow Rate. Figure 9 shows the CO2 concentration profiles of the gas phase (average in the radial direction) along the module at various gas velocities. According to Figure 7, the optimum concentration of K2CO3 solution at 298 K is 0.6 M; therefore this concentration is considered in this part. As seen in Figure 9, the CO2 removal efficiency decreases with increasing gas phase velocity, because the CO2 in the gas phase has less time to contact liquid absorbent. The influence of gas velocity on the CO2 absorption flux is depicted in Figure 10. The CO2 flux increases with gas phase velocity, which is due to higher amounts of CO2 in the shell side. On the basis of the obtained results, the gas phase velocity should be selected in such a way that in addition to having a high removal efficiency of CO2, an acceptable absorption flux is also obtained. 4.4. Effect of Membrane Wetting on CO2 Absorption Using K2CO3 and DEA Solutions. One of the important issues in gas absorption by the hollow fiber membrane contactors is the membrane wetting phenomenon. In the

Figure 4. Gas phase concentration distribution of CO2 along the hollow fiber at different temperatures of K2CO3 solution (feed gas, 20/ 80 CO2/N2 mixture, UG = 0.1 m/s; absorbent, 1 M aqueous K2CO3, UL = 0.15 m/s).

on the other hand, solubility of CO2 in the liquid phase decreases. For potassium carbonate solution, the predominant parameter is the reaction rate; therefore the rate of CO2 absorption increases with increasing the temperature of the K2CO3 solution. Figure 4 reveals that a rise in temperature of about 50 °C increases the CO2 capture from the gas phase up to 80%. It demonstrates that the use of hot potassium carbonate solution is more effective at removing CO2. In addition, at high temperatures of the liquid phase, higher concentrations of potassium carbonate can be used without precipitating the bicarbonate.33,34 The effects of liquid velocities on CO2 absorption flux at different temperatures is presented in Figure 5. As seen from this figure, the absorption flux increases by increasing the temperature of the K2CO3 solution. This figure also shows that

Figure 5. Effect of liquid velocity on CO2 absorption flux at different temperatures of K2CO3 solution (feed gas, 20/80 CO2/N2, UG = 0.1 m/s; absorbent, 1 M aqueous K2CO3). 2189

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Figure 6. Effect of concentration and temperature of K2CO3 solution on CO2 absorption flux (feed gas, 20/80 CO2/N2, UG = 0.1 m/s; UL = 0.15 m/ s).

Figure 7. Effect of liquid temperature on optimum concentration of K2CO3 solution for CO2 absorption (feed gas, 20/80 CO2/N2, UG = 0.1 m/s; UL = 0.15 m/s).

Figure 8. Effect of liquid temperature on maximum absorption flux of CO2 (feed gas, 20/80 CO2/N2, UG = 0.1 m/s; absorbent, aqueous K2CO3, UL = 0.15 m/s).

previous sections, the effects of membrane wetting on the CO2 absorption have not been considered. Initially, a comparison between aqueous solutions of K2CO3 and diethanolamine (DEA) has been done under nonwetted conditions in Figure 11. The K2CO3 solution at 363 K (similar to hot potassium carbonate condition) and the concentration of 0.8 M (its optimum concentration) is considered to compare with a 2 M DEA solution at 298 K.13 The figure shows that at low gas velocities the recovery of CO2 by both of these solutions is almost the same. The CO2 recovery decreased with an increase in the gas velocity for both absorbents. However, at high gas velocities, K2CO3 solution under hot conditions and optimum

concentration is more effective than DEA solution for CO2 capture in hollow fiber membrane contactors. The membrane wetting significantly depends on the surface tension of the liquid absorbent. The liquid with low surface tension has a greater tendency to penetrate into the membrane pores that cause the membrane wetting. The surface tension of K2CO3 and DEA solutions as a function of concentration is given in Table 3. According to the data that are presented in this table, the surface tension increases with increasing K2CO3 concentration; however it decreases with increasing DEA concentration. Therefore, it would be expected that the membrane wetting is higher if the DEA solution is used as an absorbent. Here, it is assumed that K2CO3 solution does not wet the membrane and 2190

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Table 3. Surface Tension of K2CO3 and DEA Solutions at 298 K σ (mN m−1) wt %

K2CO3

DEA

0 10 20 30 40 50 ref

72 75.1 78.6 83.8 91.4 103.8 35

72 66.70 63.25 60.75 58.82 57.20 36

DEA solution wets the membrane with different percents. By applying this assumption, the results of CO2 removal are presented in Figure 12. The figure shows that the membrane Figure 9. Gas phase concentration distribution of CO2 along the hollow fiber at different gas velocities (feed gas, 20/80 CO2/N2 mixture; absorbent, 0.6 M aqueous K2CO3, UL = 0.15 m/s).

Figure 12. Effect of membrane wetting on CO2 absorption (feed gas, 20/80 CO2/N2 mixture, UG = 0.1 m/s; absorbent, 0.8 M aqueous K2CO3 at 363 K and 2 M aqueous DEA at 298 K, UL = 0.15 m/s).

Figure 10. Effect of gas velocity on CO2 absorption flux (feed gas, 20/ 80 CO2/N2; absorbent, 0.6 M aqueous K2CO3, UL = 0.15 m/s).

wetting reduces dramatically the efficiency of CO2 absorption using DEA solution. It is well-known that potassium carbonate solution has some advantages compared to alkanolamines, especially its lower regeneration cost. However, its recovery is usually considered lower than amine solutions due to a lower reaction rate. The presented results reveal that applying the solution of potassium carbonate may even give higher CO2 recovery using hollow fiber membrane contactors. 4.5. Effect of Water Evaporation on Absorption Flux. In order to achieve an effective CO2 capture with aqueous K2CO3 solution, the liquid absorbent should be used at relatively high temperatures. One problem that may occur under this operating condition is the evaporation of water and the penetration of that water vapor into the pores of the membrane. The main effect of this phenomenon is the reduction of effective diffusivity of CO2 in the membrane phase. To study this effect, it was assumed that the effective diffusion coefficient of CO2 in the membrane phase decreased with different ratios due to the presence of water vapor. As can be seen in Figure 13, reducing the diffusion coefficient does not affect the absorption flux significantly, which is because of

Figure 11. Effect of gas velocity on CO2 recovery (feed gas, 20/80 CO2/N2; absorbent, 0.8 M aqueous K2CO3 at 363 K and 2 M aqueous DEA at 298 K, UL = 0.15 m/s).

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negligible membrane resistance compared to the main module resistance.

Article

AUTHOR INFORMATION

Corresponding Author

*Tel.: +987116133713. Fax: +987116473180. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

Figure 13. Effect of water vapor penetration into the membrane pores on CO2 absorption flux (feed gas, 20/80 CO2/N2 mixture; absorbent, 0.8 M aqueous K2CO3 at 363 K, UL = 0.15 m/s).

While Figure 13 reveals that water evaporation does not affect the module performance, however, this evaporated water can decrease the absorption flux considerably if water condensation occurs inside the membrane pores. For instance, water vapor can condense in the pores if the flue gas temperature becomes much lower than the temperature of potassium carbonate solution. Such water condensation has the same effect of partial wetting of the membrane and can affect the module performance considerably according to Figure 12. It should be noted that the drawback effects of water condensation can be even more than partial wetting, because the condensed water is pure (without K2CO3), and therefore there is no chemical reaction in the region in which water is condensed. However, when the flue gas temperature is high enough, which is practical in industrial applications, the water condensation will not essentially occur.

NOMENCLATURE C = concentration (mol m−3) d = diameter (m) D = diffusivity (m2 s−1) Djk = Knudsen diffusivity of species j (m2 s−1) h = gas-specific parameter (m3 kmol−1) H = Henry’s constant (mol mol−1) k1 = forward reaction rate constant of reaction 1 (s−1) k2 = forward reaction rate constant of reaction 2 (m3 kmol−1 s−1) K1 = equilibrium constant of reaction 1 (kmol m−3) K2 = equilibrium constant of reaction 2 (m3 kmol−1) K3 = equilibrium constant of reaction 3 (kmol m−3) Kw = ionization constant of water (kmol2 m−6) M = molecular weight (kg kmol−1) r = radial coordinate (m) rj = reaction rate of component j (mol m−3 s−1) Re = free surface radius of fiber (m) Ri = inner radius of fiber (m) Ro = outer radius of fiber (m) T = temperature (K) U = velocity (m s−1) x = wetting fraction z = axial coordinate (m)

Greek letters

δ = membrane thickness (m) ε = membrane porosity θ = packing fraction τ = tortuosity Subscripts

5. CONCLUSION In this study, a 2D mathematical model was developed for CO2 absorption from a CO2/N2 gas mixture in the aqueous solution of K2CO3 by hollow fiber membrane contactors. The model results were in good agreement with the available experimental data. The effects of temperature and concentration of K2CO3 solution and membrane wetting on the removal efficiency of CO2 were investigated. Increasing the temperature of K2CO3 solution enhanced the rate of CO2 absorption significantly. It was shown that there was an optimum concentration at each solution temperature. The results also showed that potassium carbonate, under its optimum conditions, can give higher CO2 recovery than diethanolamine solution, especially if DEA wets the membrane. These results, as well as other advantages of K2CO3 solution such as lower cost and easier regeneration, make it a good alternative solution compared to alkanolamines such as DEA for CO2 separation in hollow fiber membrane contactors.

■

av = average e = effective G = gas in = input j = any diffusing species L = liquid m = membrane p = pore w = water wv = water vapor

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