Mass Transfer Coefficients for CO2 Absorption into Aqueous Ammonia

Article pubs.acs.org/IECR

Mass Transfer Coefficients for CO2 Absorption into Aqueous Ammonia Using Structured Packing Wenbin Li, Xingjian Zhao, Botan Liu,* and Zhongli Tang State Key Laboratory for Chemical Engineering and School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China ABSTRACT: In this study, the gas phase volumetric overall mass transfer coefficients (KGae) for CO2 absorption into aqueous ammonia solutions were measured to explore the mass transfer performance of a column packed with structured packing. The KGae values were evaluated over ranges of main operating variables, that are, 1400−2300 m3·m−2·h−1 gas flow rate, 20−39 m3· m−2·h−1 liquid flow rate, up to 8 kPa partial pressure of CO2, and 0.27−0.72 kmol·m−3 ammonia concentration. The results show that higher liquid loading and concentration of aqueous ammonia are beneficial to enhance the KGae values. On the contrary, KGae value decreases as the CO2 partial pressure increases. The results also show that gas loading has little influence on KGae. To allow the mass transfer data to be readily utilized, an empirical KGae correlation for this system was developed. Finally, Simulations were made for the absorption of CO2 into aqueous ammonia solutions by using the currently developed computational mass transfer model along with the proposed correlation for KGae. The simulation results on the gas phase CO2 concentration are found to be in satisfactory agreement with the experimental measurements. Yeh and Bai.12 It was shown that both the CO2 removal efficiency and absorption capacity of ammonia solvent are better than those of MEA solvent under the operating conditions in their study. As stated by Yeh et al.,13 the use of ammonia seems to have avoided the shortcomings of the MEA solvent. Generally speaking, the advantage of aqueous ammonia as solvent includes high loading capacity, less corrosion, no absorbent degradation, and low energy consumption. It is found that thermal energy consumption for CO2 regeneration using the aqua ammonia process could be at least 75% less than if the MEA process is used for CO2 absorption and regeneration. Additionally, the three major acid gases (SO2, NOx and CO2) plus HCl and HF, which may exist in the flue gas, will be captured in the aqua ammonia process simultaneously. A single process to capture all acidic gases is attractive, promising to reduce the total cost and complexity of emission control system. In recent years, many researchers were interested in the fundamental work for the CO2 absorption in aqueous ammonia. The UNIQUAC-Non Random Factor (NRF) model was developed by Pazuki et al14,15 for the NH3−CO2−H2O system to correlate the experimental data reported by Edwards et al.16,17 and Bernardis et al.18 Derks and Versteeg19 studied the kinetics and mechanism of the reaction between CO2 and ammonia in a well-stirred cell reactor. Puxty et al.20 presented their latest kinetics results for a reaction in a wetted-wall column reactor. There was a large amount of work21−24 studying the kinetics and mechanism in depth by contributing more experimental data, and thus robust kinetics constants were fitted and available for the determination of the reaction between CO2 and ammonia.

1. INTRODUCTION The continuously rising demand for energy and increasing emissions of CO2 have become severe challenges for the sustainable development of the world. The main sources of carbon dioxide emissions include power generation, industrial processes, transportation, and residential and commercial buildings.1 Power generation, mainly from the use of coal and natural gas, accounts for about a third of CO2 emissions from fossil fuel use.2 Therefore, the main application of CO2 capture is currently expected to be in power generation. Several technologies of CO2 sequestration for power generation have been developed, including postcombustion capture, oxy combustion, and precombustion capture. It should be noted that only the postcombustion decarbonization based on the mature state of the art chemical solvent absorption process has realized the industrial pilot.3 The absorption process is one of the most common industrial technologies today. Chemical solvent absorption methods are considered as a reliable method for reducing CO2 emissions from fossil fuel power plants.4 The most commonly used absorption solvents are alkanolamines, which were discovered in the late 1920s by Bottoms.5 Among the alkanolamines, the most used solvent is monoethanolamine (MEA) scrubbing. However, the cost to capture CO2 from the flue gas of power plants is very high when using MEA scrubbing.4 It is estimated that the energy penalty from using this solvent for CO2 capture from coal-fired power plants is about 15% to 35%.6,7 In addition, it has several major problems,8−10 including low CO2 loading capacity, slow absorption rate, high equipment corrosion rate, amine degradation by SO2, NO2, HCL, and O2 in the flue gas, etc. In order to improve the above detects, Wolsky et al.11 suggested the need for a new solvent to be discovered. As early as in 1997, Bai and Yeh9 found another route of reducing CO2 emissions from power plants by using ammonia. The performance of the ammonia and MEA solvents for scrubbing CO2 emissions were compared experimentally by © 2014 American Chemical Society

Received: Revised: Accepted: Published: 6185

September 18, 2013 December 23, 2013 March 20, 2014 March 20, 2014 dx.doi.org/10.1021/ie403097h | Ind. Eng. Chem. Res. 2014, 53, 6185−6196

Industrial & Engineering Chemistry Research

Article

Figure 1. Experimental apparatus for CO2 absorption by ammonia.

where KG is the overall mass transfer coefficient, kG and kL are the gas and liquid side mass transfer coefficient, respectively, H is the Henry’s law coefficient, and E is the enhancement factor. The chemical reaction results an enhancement of mass transfer rate. The ratio of such a rate to the rate of absorption without chemical reaction is called the enhancement factor.32 The differential mass balance associated with absorption in a packed column is given by35

There are many different types of chemical equipment developed for gas treating purposes, such as the stirred tank, bubble column, packed column, and tray column. Among them, the packed column is the most widely used. The packed column could be classified into random and structured packed columns. It is considered that the use of structured packing would improve the mass transfer performance in the absorption system.25,26 In comparison with random type, the structured packed column27−30 would be superior in lower pressure drop, lower liquid holdup and higher treatment capacity of gas under fixed overall separation efficiency. The motivation of this study focuses on the mass transfer performance of the CO2 absorption process using structured packing and aqueous ammonia solution as the column internal and absorption solvent, respectively. The performance of the process, presented in terms of the volumetric overall mass transfer coefficient (KGae), was evaluated experimentally under various conditions to investigate the effects of operating variables, including gas flow rate, liquid flow rate, partial pressure of CO2 and ammonia concentration. To allow the mass transfer data to be readily utilized, an empirical KGae correlation for this system was developed. Then simulation for the experiments was made by using the currently developed computational mass transfer model (CMT)31 in order to test the correlation.

uG

(2)

where the effective area for mass transfer between the gas phase and liquid phase ae is considered as another important parameter in the mass transfer process in addition to the mass transfer coefficients.25 Therefore, the expression of absorption rates in terms of volumetric overall mass transfer coefficients (KGae)36 is as follows: 1 K Gae

=

1 H + k Gae EkLae

(3)

In the process of absorption, the variation of the total gas flow rate along the height of the column is little as the volume percentage of the inert gas in gas stream is above 92%. Therefore, it is reasonable to assume that the gas phase velocity uG is unchanged and the liquid phase CO2 concentration or the CO2 partial pressure equilibrium with the liquid y* is zero.35,37−39 The volumetric mass transfer coefficient (KGae) is considered to be constant. Under these conditions, integration of eq 2 over the packed height (Z) yields the following expression for the KGae

2. DETERMINATION OF OVERALL MASS TRASNFER COEFFICIENT According to the two-film model,32−34 the relationships between the overall mass transfer coefficient and the individual-phase coefficients can be given as follows:

1 1 H = + KG kG EkL

dy = (K Gae)(RT )(y* − y) dz

⎞ ⎛y uG CO2,in ⎟ ⎜ K Gae = ln ZRT ⎜⎝ yCO out ⎟⎠ 2,

(1) 6186

(4)

dx.doi.org/10.1021/ie403097h | Ind. Eng. Chem. Res. 2014, 53, 6185−6196


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3. EXPERIMENTAL SECTION The schematic diagram of the experimental system is shown in Figure 1. The absorption experiments were performed in a 2.4 m high and 0.15 m inside diameter column. The total height of packing was 2.0 m, and the filler of the packed column was the novel structure packing with diversion windows, which was developed by Liu et al.40 and was provided by Tianjin Tiandatianjiu Polytron Technologies Inc. To achieve maximum performance, structured packing was place with each layer rotated by 45° with respect to the previous one. The gas phase CO2 concentration was measured by using the infrared CO2 sensor (SenseAir Inc., made in Swedish; model: K33-ICB20%). Auxiliary equipment, such as the liquid feed and storage tanks, gas flowmeter, and liquid rotameter, were used in this work. Before an absorption experiment was carried out, an aqueous ammonia solution was prepared by diluting strong ammonia to the desired concentration and was kept for 1.5 h so as to allow the ammonia concentration to stabilize. After the ammonia solution stabilized, the gas was mixed using two gas flowmeters which controlled the flow rates of CO2 and air, and the mixture gas was introduced through the packed column from its bottom to the top at the desired rates. Meanwhile, the prepared ammonia solution flowed into the top of the column at a given rate so as to mix and react with the CO2 counter-currently. Finally, the gas flowed from the top exit of the column, containing a low CO2 content, and the CO2-rich ammonia solution leaving from the bottom of the column are collected in the storage tank. To ensure the reliability of the experimental results, absorption experiments were operated until steady-state conditions were reached. After that, the gas phase CO2 concentration at each probe position (z = 0, 0.270, 0.835, 1.250, and 2.0 m, respectively, as shown in Figure 1) was measured and recorded using the infrared CO2 sensor. The detailed operating conditions are given in Table 1.

ammonia concentration. Therefore, in this study, under the conditions of high gas flow rate and low ammonia concentration, the gas flow rate only has little effect on the overall mass transfer coefficient as shown in Figure 2. Previous

Figure 2. Effect of gas velocity on KGae. (a) PCO2 = 2.8 kPa, L = 22.4 m3·m−2·h−1, C = 0.36 kmol·m−3; (b) PCO2 = 4.0 kpa, L = 28.4 m3·m−2· h−1, C = 0.36 kmol·m−3.

studies in literature, such as the CO2 absorption into NaOH solution37 and the CO2 absorption into 2-amino-2-methyl-1propanol (AMP) solution, also resulted in a similar trend. It also indicates that the mass transfer process in this case is primarily controlled by the resistance residing in the liquid phase. 4.2. Effect of CO2 Partial Pressure. As seen from Figure 3, the KGae value tends to decrease by ∼20% as the CO2 partial

Table 1. Experimental Conditions for CO2 Absorption by Ammonia experimental parameter

experimental condition

pressure temp (K) feed CO2 concentration (kPa) gas velocity (m·s−1) aqueous ammonia concentration (kmol· m−3) liquid flow rate (m3·m−2·h−1)

atmospheric pressure 300 2.8−8 0.393−0.629 0.27−0.72 20−39

Figure 3. Effect of CO2 partial pressure on KGae. (a) G = 1698 m3· m−2·h−1, L = 22.4 m3·m−2·h−1, C = 0.36 kmol·m−3; (b) G = 1415 m3· m−2·h−1, L = 28.4 m3·m−2·h−1, C = 0.36 kmol·m−3

4. EXPERIMENTAL RESULTS The effects of gas flow rate, CO2 partial pressure, volume flow rate of aqueous ammonia solution, and the aqueous ammonia concentration on the volumetric mass transfer coefficient (KGae) are as follows. 4.1. Effect of Gas Flow Rate. According to the experimental results obtained by Zeng et al.,41,42 the increased gas flow rate may lead to a higher KGae value when the gas flow rate is relative small. This might be due to the reason that a more CO2 is available for absorption under that condition, and thus a higher KGae value could be found. However, as pointed out by many researchers,43,44 the overall mass transfer coefficient is not only dependent upon the gas flow rate, it is also dependent upon the liquid flow rate and the aqueous

pressure increases from 2.8 to 8.0 kPa. According to two-film theory, the mass transfer resistance of the gas phase will decrease with increasing CO2 partial pressure. So a higher value of KGae is expected to be found, since the amount of CO2 that travels from gas phase to the gas−liquid interface is increased as the CO2 partial pressure increases from 2.8 to 8.0 kPa. However, as mentioned before, the mass transfer process in this work is mainly controlled by the resistance of the liquid phase. The decrease in ammonia concentration due to the undertaken absorption leads to a smaller enhancement factor, and then would result in higher mass transfer resistance in the liquid phase. Therefore, the overall result in this case is that the KGae 6187



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enhancement factor as the ammonia concentration increases and thus leads to higher KGae values. Earlier studies, such as the CO2 absorption into AMP solution25 also confirmed that increasing ammonia concentration leads to the increasing KGae.

value moves downward when the CO2 partial pressure increases from 2.8 to 8.0 kPa as shown in Figure 3. 4.3. Effect of Liquid Flow Rate. Figure 4 shows the effect of liquid loading on the overall mass transfer coefficient. It

5. MASS TRANSFER CORRELATION FOR CO2-AMMONIA ABSORPTION USING STRUCTURE PACKING 5.1. Proposed Correlation. As mentioned earlier, the absorption of CO2 into aqueous ammonia is primarily controlled by the resistance in the liquid phase. It is found from experiments that the CO2 partial pressure, volume flow rate of aqueous ammonia solution, and the aqueous ammonia concentration have a significant effect on the volumetric mass transfer coefficient (KGae). In order to determine the relationship between them, variations of KGae are plotted in a logarithmic scale versus the CO2 partial pressure PCO2 and the flow rate of aqueous ammonia solution L as well as the aqueous ammonia concentration C (see Figures 6−8).

Figure 4. Effect of liquid loading on KGae. (a) G = 1698 m3·m−2·h−1, PCO2 =4.0 kpa, C = 0.36 kmol·m−3; (b) G = 1415 m3·m−2·h−1, PCO2 =2.8 kpa, C = 0.36 kmol·m−3; (c) G = 2264 m3·m−2·h−1, PCO2 =4.0 kpa, C = 0.54 kmol·m−3.

could be found from this figure that the increase in liquid loading from 20 m3·m−2·h−1 to 39 m3·m−2·h−1 would lead to a significant increase in the KGae value. Previous studies on CO2 absorption in rotating packed column42,45 and spray tower46,47 have also revealed a similar trend of increasing KGae value with increasing liquid loading. This may be attributed to the following reasons: first, with the liquid flow rate increasing, more liquid would be spread on the packing surface, and this leads to an increase in the gas−liquid interfacial area ae; second, the higher liquid loading also leads to a higher liquid side mass transfer coefficient kL which is directly proportional to the overall coefficient KG in case of liquid-phase controlled mass transfer. 4.4. Effect of Ammonia Concentration. Ammonia concentration also has an important effect on the KGae value. Take the three cases of the present experiments for example as shown in Figure 5, when the ammonia concentration increases from 0.27 kmol·m−3 to 0.63 kmol·m−3, the KGae value increases by nearly 50%. This effect is simply due to the increase in the

Figure 6. KGae in a logarithmic scale versus ln(PCO2). (a) G = 1698 m3· m−2·h−1, L = 22.4 m3·m−2·h−1, C = 0.36 kmol·m−3; (b) G = 1415 m3· m−2·h−1, L = 28.4 m3·m−2·h−1, C = 0.36 kmol·m−3; (c) G = 1698 m3· m−2·h−1, L = 28.4 m3·m−2·h−1, C = 0.72 kmol·m−3; (d) G = 1415 m3· m−2·h−1, L = 38.9 m3·m−2·h−1, C = 0.72 kmol·m−3.

As shown in Figure 6, slopes of the fitted lines for a given operation condition (a, b, c, and d) are practically the same. The averaged value of the exponent is −0.194. Thus, the volumetric mass transfer coefficient KGae appears to be increased approximately as −0.194 power of the CO2 partial pressure PCO2. Similarly, the term of ln(KGae) plotted against ln(L) is shown in Figure 7. As stated by Perry and Green,48 KGae is approximately proportional to L0.5 for the CO2-amine absorption system. Experimental results by Aroonwilas and Tontiwachwuthikul25 also confirmed this phenomenon. However, in this study the exponent of the liquid flow rate L is somewhat lower since the averaged value of the slopes for the fitted lines in Figure 7 is found to be 0.442. It may be due to the experimental error. Figure 8 shows the term of ln(KGae) plotted against ln(C). It is found that the averaged value of the fitted lines is 0.495. Therefore, the correlation between KGae and CO2 partial pressure, volume flow rate of aqueous ammonia solution, and the aqueous ammonia concentration could be expressed as follows:

Figure 5. Effect of ammonia concentration on KGae. (a) G = 2264 m3· m−2·h−1, PCO2 =4.0 kpa, L = 28.4 m3·m−2·h−1; (b) G = 1415 m3·m−2· h−1, PCO2 =2.8 kpa, L = 28.4 m3·m−2·h−1; (c) G = 1698 m3·m−2·h−1, PCO2 =2.8 kpa, L = 38.9 m3·m−2·h−1.

K Gae ∝ L0.442C 0.495PCO2−0.194 6188

(5)



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Figure 7. KGae in a logarithmic scale versus ln(L). (a) G = 1415 m3· m−2·h−1, PCO2 =2.8 kPa, C = 0.36 kmol·m−3; (b) G = 1415 m3·m−2·h−1, PCO2 =2.8 kPa, C = 0.72 kmol·m−3; (c) G = 1415 m3·m−2·h−1, PCO2 =8.0 kPa, C = 0.72 kmol·m−3.

Figure 9. KGae versus L0.442C0.495PCO2−0.194. (a) G = 2264 m3·m−2·h−1, L = 28.4 m3·m−2·h−1, PCO2 = 4.0 kPa; (b) G = 1698 m3·m−2·h−1, L = 38.9 m3·m−2·h−1, PCO2 =2.8 kPa; (c) G = 1415 m3·m−2·h−1, L = 28.4 m3·m−2·h−1, PCO2 =2.8 kPa.

Figure 8. KGae in a logarithmic scale versus ln(C). (a) G = 2264 m3· m−2·h−1, L = 28.4 m3·m−2·h−1, PCO2 = 4.0 kPa; (b) G = 1698 m3·m−2· h−1, L = 38.9 m3·m−2·h−1, PCO2 =2.8 kPa; (c) G = 1415 m3·m−2·h−1, L = 28.4 m3·m−2·h−1, PCO2 =2.8 kPa.

Figure 10. Calculated KGae versus those from experiments.

6. SIMULATION In order to ensure that the correlation proposed for KGae in the present study is suitable for simulating the mass transfer process of CO2 absorption into aqueous ammonia solutions in packed column. A detailed simulation was made by using the currently developed computational mass transfer model (CMT)31 along with the proposed correlation. With the idea of using this model, concentration distributions can be obtained without relying on the empirical Sct number or the experimental dispersion coefficient. Then the simulation results will be compared with the corresponding experimental data. 6.1. Assumptions. (1) The gas phase is incompressible. (2) The absorption process is of steady state. (3) The heat of solution and reaction are all absorbed by the liquid phase, and the temperature change of the gas phase is negligible. This assumption is reasonable, because the gas flow rate is relatively high when compared with the liquid flow rate, and thus the heat transferred from the liquid to the gas phase would only have a little effect on the gas phase. (4) Since successive layers are turned by 45° between each other when installed in columns, the gas flow would change its way periodically from one layer to next layer. For an exact simulation, the packing pattern and the gas−liquid-wall interactions should be taken into account. However, due to the complexity of the structured packing geometry and the limited CPU

From the theoretical viewpoint, KGae is related to the enhancement factor E. Since the pseudo-first-order approximation could be applied for ammonia-CO2 absorption system, the enhancement factor could be assumed to be equaled to the Hatta number.19 The Hatta number could be related to the 0.5 power of the ammonia concentration.42 Thus, we have: K Gae ∝ E = Ha ∝ C 0.5

(6)

It is seen from Figure 8 that the phenomenon is confirmed by the experimental results. The term KGae is plotted against L0.442C0.495PCO2−0.194 as shown in Figure 9. A linear relationship could be found between them, and consequently the following correlation is proposed: K Gae = 0.0767

L0.442C 0.495 PCO2 0.194

(7)

The calculated KGae from eq 7 is plotted against the KGae from the experiments in Figure 10. It is seen from Figure 10 that the KGae calculated from eq 7 is in satisfactory agreement with that from experiments. It should be noted that eq 7 was developed on the basis of laboratory structured packing data. To apply this correlation to the industrial-scale structured packing, a scale-up factor involving packing geometry might be required. 6189



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⎛ kc 2 ⎞1/2 ⎟⎟ Dt = Cc0k ⎜⎜ ⎝ εεc ⎠

resources of calculators, it is hard to run this simulation at the scale of a column. Thus, an assumption should be made that the packed column is considered as successive layers of porous volumes. Layers of packing are considered as a porous media. This assumption is reasonable when the number of packing layers is large.49 Therefore, the gas flow could be considered as axis-symmetric. 6.2. Model Equations. The simplified pseudo gas phase model consists of mass transfer equation set and the accompanied CFD equation sets. 6.2.1. Mass Transfer Equation Set. The different mass transfer equation for the concerned species is as follow: ∂(ρβCu̅ i) ∂ ⎡ ∂C̅ ⎤ = ⎢ρβ(D + Dt ) ⎥ + SC ∂xi ∂xi ⎣ ∂xi ⎦

the constants in eqs 12−14 are51,52 Cc0 = 0.11,

∂(ρβuiuj) ∂xj

= −β

⎞ ∂p ∂ ⎛⎜ μ ∂(ρui) + − ρβui′uj′⎟⎟ + βρg β ⎜ ∂xi ∂xj ⎝ ρ ∂xj ⎠ (16)

where μ represents the molecular viscosity of the gas phase, SF,i is the source term for the momentum equation representing the interaction of the gas and liquid phase, and ui′uj′is the Reynolds stress, for which the Boussinisque’s relation is applied: ⎛ ∂u ∂uj ⎞ ⎟⎟ − 2 δijρk −ρui′uj′ = μt ⎜⎜ i + ∂xi ⎠ 3 ⎝ ∂xj

the total liquid hold-up can be calculated from the correlation reported by Suess and Spiegel50

(17)

where μt is the turbulent viscosity of the gas phase and μt = Cμρ

(11)

where ap is the surface area of the packing per unit volume of the column, L is the liquid flow rate, μL and μL,0 are the liquid viscosity and that at T = 20 °C; the constant c and exponent b are dependent on the liquid flow rate

k2 ε

(18)

To solve eq 18, the standard k−ε model is used as follows: Equation of turbulent kinetic energy k ⎛ ∂u ∂uj ⎞ ∂ui μ ⎞ ∂k ⎤ ∂(ρβkui) ∂ ⎡ ⎛ ⎟ ⎢β ⎜μ + t ⎟ ⎥ + βμt ⎜⎜ i + = ∂xi ⎟⎠ ∂xj ∂xi ∂xi ⎢⎣ ⎝ σk ⎠ ∂xi ⎥⎦ ⎝ ∂xj

−2 −1

c = 0.0169, b = 0.37 for L < 40 m ·m ·h

− ρβε

c = 0.0075, b = 0.59 for L > 40 m 3·m−2·h−1

(19)

Equation of turbulent kinetic energy dissipation ε

D and Dt are the molecular and turbulent mass transfer diffusivity respectively, and SC is the source term of mass transfer of the CO2. The Dt is determined by the c 2 − εc model51,52 which consists of the following equations: Equation of concentration variance c 2 :

∂uj ⎞ μ ⎞ ∂ε ⎤ ∂(ρβεui) ∂ ⎡ ⎛ ε ⎛ ∂u ⎟ ⎢β ⎜μ + t ⎟ ⎥ + C1εβ μt ⎜⎜ i + = ∂xi ⎟⎠ k ⎝ ∂xj ∂xi ∂xi ⎢⎣ ⎝ σε ⎠ ∂xi ⎥⎦ ∂ui ε2 − C2ερβ ∂xi k

⎞ ∂( c 2) ⎤ ∂(ρβ c 2ui) ∂ ⎡ ⎛ Dt ∂C ∂C ⎢ρβ ⎜ + D⎟ ⎥ + 2ρβDt ̅ ̅ = ∂xi ⎢⎣ ⎝ σc ∂xi ∂xi ∂xi ⎠ ∂xi ⎥⎦

(20)

where the constants are53 Cμ = 0.09, Ciε = 1.44, C2ε = 1.92, σk = 1.0, and σε = 1.3. 6.3. Evaluation of Source Terms. The object of the simulation is the structured packed column mentioned in the Experimental Section. In the numerical computation, the model equations should be first discrete into a large number of small finite elements, and the model differential equations are at the same time converted to algebraic form and solved by algebraic method. Thus the empirical correlations can be applied to the discrete elements for evaluating the source term under their specific local conditions, such as velocity and concentration obtained in the course of numerical computation. Such way of using

(12)

Equation of concentration variance dissipation εc ⎡ ⎞ ∂(ε ) ⎤ ∂(ρβεcui) ε ∂C̅ ∂ ⎢ ⎛⎜ Dt = ρβ ⎜ + D⎟⎟ c ⎥ + Cc1ρβDt c2 ∂xi ∂xi ⎢⎣ ⎝ σεc c ∂xi ⎠ ∂xi ⎥⎦ 2

ε εε ∂C̅ − Cc2ρβ c2 − Cc3ρβ c k ∂xi c

(15)

+ SF, i

(10)

− 2ρβεc

σεc = 1.0

Momentum transport equation:

where γ is the porosity of the packed column; h is the volume fraction of liquid phase based on pore space and can be calculated by

3

Cc3 = 0.8,

∂(ρβui) = SC ∂xi

(9)

Ht = ca p0.83Lb(μL /μL,0 )0.25

Cc2 = 2.2,

6.2.2. Fluid Dynamics Equation Set. Conservation equation:

(8)

β = γ(1 − h)

Ht γ

Cc1 = 1.8,

σc = 1.0,

where C̅ is the average mass fraction of CO2 in the gas phase, ρ is the gas phase density, β is the volume fraction of the gas phase and can be determined by

h=

(14)

(13)

Equation for computing Dt 6190



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6.4.4. Axis Conditions. Under the assumption of axially symmetrical, we have ∂Φ/∂y = 0 at the column axis. 6.5. Numerical Procedure. The simulation was performed with the commercial software Fluent 6.3.26 (2D). The model equations were solved numerically with finite volume method. The SIMPLEC algorithm is employed for discretization of momentum equation. The object of the present simulation was the experiment described in the foregoing section. The grid arrangement of the packed column comprised totally 25000 quadrilateral cells. There are 50 nodes at the radial direction and 500 nodes at the axial direction. To ensure that the grid resolution could provide sufficient simulation precision, the packed-column was meshed with the other choice of 100 nodes at the radial direction and 1000 nodes at the axial direction. In Figure 11, the results show

empirical correlation, which has been conventionally applied in CFD, is employed for the computation of the model equations. 6.3.1. Source Term of Species and Total Mass Conservation Equation SC. The source term SC in eqs 8 and 15, representing the net mass sink of the gas due to the CO2 absorbed by the aqueous ammonia solution, are given by the following equation: * − PCO )/3600 SC = K GaeMCO2(PCO 2 2

where MCO2 is the molecular weight of CO2, PCO2 is the partial pressure of CO2 in main body of gas, P*CO2 is the partial pressure of CO2 in equilibrium with the aqueous ammonia solution, and as mentioned above, PCO * 2 is approximately zero,35,37−39 and the overall mass transfer coefficient KGae is determined by the proposed correlation in the section 5.1. 6.3.2. Source Term of Momentum Conservation Equation SF,i. The source term SF,i in eq 16, representing the gas phase flow resistance due to the liquid flowing through the surface of the packing, is related to the pressure drop caused by interaction between the gas and liquid phases. For irrigated packing, the pressure drop Δpt is greater than the dry bed pressure drop and can be calculated by using the correlation reported by Brunazzin and Paglianti.54 Then the source term SF,i can be expressed by SF, i =

Δpt |uslip|

uslip

(21)

where uslip is the slip velocity between gas phase and liquid phase, which is defined by uslip = uL − u (22)

Figure 11. Predicted CO2 mass fraction profiles with different grid nodes. (a) G = 1698 m3·m−2·h−1, L = 28.4 m3·m−2·h−1, C = 0.36 kmol· m−3.

where uL is the average velocity of the liquid. 6.3.3. Evaluation of Other Relevant Terms. The molecular diffusivity DG of CO2 in gas phase was calculated from Bianc’s law and the binary molecular diffusivity was calculated by the empirical correlation reported by Poling et al.55 The gas mixture viscosity μG is calculated by the correlation reported by Perry and Green.56 The viscosity of air and CO2 is obtained from Geankoplis.57 The density of gas mixture ρ and that of pure components are obtained according to the method of Lee and Kesler, which was reported by Perry and Green.56 6.4. Boundary Conditions. 6.4.1. Inlet Condition. The mixture gas is introduced at the bottom of the column, and the inlet conditions for the two sets of model equation are as follows:52,58 U̅ = Uin , εin = 0.09

C̅ = C in ,

that the different of the simulated results is small, which indicates that the numerical accuracy of the present simulation with 50 × 500 nodes is sufficient, and it has very weak improvement on the increasing number grid nodes beyond 50 × 500. 6.6. Simulation Results and Comparison with Experiment Measurements. A total of 66 sets of experiments were carried out for the absorption of CO2 into aqueous ammonia solution. Here, only the simulation results on three sets of the experiments [(a) G = 1698 m3·m−2·h−1, L = 28.4 m3·m−2·h−1, C = 0.36 kmol·m−3; (b) G = 1415 m3·m−2·h−1, L = 22.4 m3·m−2· h−1, C = 0.36 kmol·m−3; (c) G = 1415 m3·m−2·h−1, L = 31.7 m3·m−2·h−1, C = 0.54 kmol·m−3] are used as examples for comparison. 6.6.1. Profiles of the Gas Phase CO2 Concentration. The comparisons of the radial averaged gas phase CO2 mass fraction distribution along the axial direction are shown in Figure 12. The square symbols represent the experiment data, and the solid lines are the simulated results. As seen from the figures, the simulated results are in satisfactory agreement with the experimental measurements. It indicates that the employed computational mass transfer model, along with the overall mass transfer coefficient KGae proposed in this paper, is applicable for the simulation of the absorption process undertaken in the concerned structured packed column. Figure 13 gives the profiles of the CO2 mass fraction along the column. As seen from Figure 13b, the CO2 mass fraction at

k in = 0.003 Uin 2 ,

k in1.5 dH

c in 2 = (0.082 Cin)2 ,

⎛ε ⎞ εc,in = 0.4⎜ in ⎟ c in 2 ⎝ k in ⎠

where dH is the hydraulic diameter of the packing, which can be calculated by dH = 4γ/ap(1 − γ). 6.4.2. Outlet Conditions. The outlet of flow is considered to be fully developed so that zero normal gradients are chosen for all variables except pressure. 6.4.3. Wall Conditions. The no-slip condition of flow is applied to the wall. 6191



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Figure 12. Comparison of the CO2 mass fraction between simulated results and experiment. (a) G = 1698 m3·m−2·h−1, L = 28.4 m3·m−2·h−1, C = 0.36 kmol·m−3; (b) G = 1415 m3·m−2·h−1, L = 22.4 m3·m−2·h−1, C = 0.36 kmol·m−3; (c) G = 1415 m3·m−2·h−1, L = 31.7 m3·m−2·h−1, C = 0.54 kmol· m−3.

15, in which νt is found to be gradually decreased from the inlet (column bottom) to the outlet (column top) with uneven distribution along the radial direction and falls rapidly toward the wall surface. As seen from Figure 14b and Figure 15b, the profiles of Dt and νt along the radial direction at different packed height are varying, so that the simulated Sct (ratio of νt/ Dt) are changing in the whole column. According to the present model, the computed volume-average Dt,av = 8.69 × 10−4 m2· s−1, while the calculated value of the turbulent mass diffusivity by using an empirical Sct number (usually take Sct =0.7) together with volume-averaged turbulent kinematic viscosity νt,av = 1.42 × 10−4 m2·s−1 by the CFD simulation is Dt = 2.03 × 10−4 m2·s−1. It demonstrates that the present model is more rigorous than the conventional method of using a fixed Sct number for modeling the turbulent mass transfer process since the later method is only a rough approximation.

a fixed packed height (z = 0.270, 0.835, and 1.250 m) decreases gradually when approaching to the column wall. Figure 13c gives the profiles of the CO2 mass fraction along axial direction at different radial positions. Difference is clearly seen between the CO2 mass fraction at the column center region and that in vicinity of the column wall. In fact, this tendency was obtained by many simulation works,52,59 and could be attribute to the wall effect. 6.6.2. Profiles of Turbulent Mass Transfer Diffusivity. The contour of the turbulent mass transfer diffusivity for the whole column is shown in Figure 14a, and the profiles of the Dt along the radial direction are given in Figure 14b. It can be seen from Figure 14a that the turbulent mass transfer diffusivity increases when approaching the column top. The variation of diffusivity along the radial direction is shown in Figure 14b, where Dt is seen to be lower at the region around the column wall. It can be explained that the no-slip flow condition applied to the column wall constrains the turbulent intensity at the near wall region, and thus lead to a lower value of Dt. This trend of the Dt profiles at different axial positions are consistent wth the experiments60,61 by using gas trace technique. 6.6.3. Profiles of turbulent kinematic viscosity. Taking experiment run a (G = 1698 m3·m−2·h−1, L = 28.4 m3·m−2·h−1, C = 0.36 kmol·m−3) for example, the contour of the turbulent kinematic viscosity νt for the whole column is shown in Figure

7. CONCLUSIONS The mass transfer performance of the CO2-ammonia system in a column packed with structured packing was investigated. For the experiments, e.g., runs a, b, and c as shown in Figure 12, the mass fraction difference of the gas phase CO2 between the column bottom and the column top is relatively small, which is not very satisfying. This is mainly due to the liquid flow rate 6192



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Figure 13. Profiles of the CO2 mass fraction. (a) G = 1698 m3·m−2·h−1, L = 28.4 m3·m−2·h−1, C = 0.36 kmol·m−3.

Figure 14. Profiles of the turbulent mass transfer diffusivity. (a) G = 1698 m3·m−2·h−1, L = 28.4 m3·m−2·h−1, C = 0.36 kmol·m−3.

liquid flow rate is too high, the experiment could not last enough time for reaching the steady state. Generally speaking,

constraint of the experimental apparatus. As shown in Figure 1, the ammonia solution was not used in a recycling way. If the 6193



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Figure 15. Profiles of the turbulent kinematic viscosity νt. (a) G = 1698 m3·m−2·h−1, L = 28.4 m3·m−2·h−1, C = 0.36 kmol·m−3.

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usage of weak-alkali solution like the ammonia solution as the absorbent commonly needs large liquid spraying density to guarantee the absorption efficiency. However, the experiment may be difficult to reach this aim, because the liquid tank will be too large. This is really a pity, and may be overcome by applying the recycling system or by adding a stripping column in future work. The following major conclusions can be drawn from the present study: (1) The overall mass transfer coefficient (KGae) was evaluated over ranges of main operating parameters, which includes the gas flow rate, liquid flow rate, partial pressure of CO2 and ammonia concentration. The results show that the effect of liquid flow rate, partial pressure of CO2, and ammonia concentration on the overall mass transfer coefficient (KGae) is significant, whereas the gas flow rate only has a little effect. This indicates that the mass transfer process in CO2 absorption into aqueous ammonia solutions is primarily controlled by the resistance residing in the liquid phase. Furthermore, higher liquid loading and concentration of aqueous ammonia solution are beneficial to enhance the KGae value. On the contrary, the KGae value decreases as the CO2 partial pressure increases. (2) An empirical correlation between KGae and the operating variables of liquid flow rate, partial pressure of CO2, liquid CO2 loading, and ammonia concentration was established for CO2 absorption into aqueous ammonia solutions. (3) Simulations were made for the absorption of CO2 into aqueous ammonia solutions by using the currently developed computational mass transfer model along with the proposed correlation for the overall mass transfer coefficient KGae. The simulation results of the gas phase CO2 concentration is found to be in satisfactory agreement with the experimental measurements.

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ACKNOWLEDGMENTS

The authors acknowledge financial support by the National Natural Science Foundation of China (Contract No.21176171) and the National Program on Key Basic Research Project (Contract No.2012CB720500).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +86-22-27404732. Fax: 8622-27404496. Notes

The authors declare no competing financial interest. 6194

NOMENCLATURE ae = effective surface area per unit volume of packed column, m2·m−3 ap = surface area per unit volume of packed column, m2·m−3 C = ammonia concentration, kmol·m−3 C̅ = mean concentration (mass fraction) Cμ, C1ε, C1ε = turbulence model constants for the velocity field Cc0, Cc1, Cc2, Cc3 = turbulence model constants for the concentration field c 2 = concentration variance D = molecular diffusivity, m2·s−1 Dt = turbulent mass diffusivity, m2·s−1 dH = hydraulic diameter of packing, m g = gravity acceleration, m·s−2 E = enhancement factor F = gas flow rate, L·min−1 H = Henry’s constant, kmol·m−3·kpa−1 Ht = total liquid hold-up h = volume fraction of liquid phase KG = overall mass transfer coefficient, kmol·m−2·h−1·kpa−1 kG = gas phase mass transfer coefficient, kmol·m−2·h−1·kpa−1 kL = liquid mass transfer coefficient, m·h−1 k = turbulent kinetic energy, m2·s−2 L = liquid flow rate, m3·m−2·h−1 PCO2 = partial pressure of CO2, kPa r = radial distance from the axis of the column, m Sct = Schmidt number base on turbulent diffusivity (Sct = νt/ Dt) SC = source of interphase mass transfer, kg·m−3·s−1 SF,i = source of interphase momentum transfer, N·m−3 y = mole fraction of CO2 in gas phase u = gas interstitial velocity vector, m·s−1 dx.doi.org/10.1021/ie403097h | Ind. Eng. Chem. Res. 2014, 53, 6185−6196


Article

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ui, uj = gas interstitial velocity in axial and radial direction, m· s−1 u′ = gas fluctuating velocity, m·s−1 uL = average velocity vector of the liquid, m·s−1 uG = superficial velocity of the gas phase, m·h−1 Z = total height of packing in the absorption column, m z = height of packing counted from the bottom of the column, m α = liquid CO2 loading, mol CO2/mol ammonia β = volume fraction of the gas phase γ = local column porosity ε = turbulent dissipation, m2·s−3 εc = turbulent dissipation of the concentration, s−1 δij = Kronecker delta ρ = gas density, kg·m−3 μ, μt = gas molecular and turbulent viscosity, respectively, kg· m−1·s−1 σk, σε, σc, σεc, σt, σεt = turbulence model constants for diffusion of k, ε, c 2 , εc, t 2 , εt Superscripts

* = gas−liquid equilibrium Subscripts

eff = effective G = gas phase in = inlet of the gas L = liquid phase out = outlet of the gas

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Mass Transfer Coefficients for CO2 Absorption into Aqueous Ammonia

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