Mass Transfer Studies in a Rotating Packed Bed with Novel Rotors

Article pubs.acs.org/IECR

Mass Transfer Studies in a Rotating Packed Bed with Novel Rotors: Chemisorption of CO2 Yong Luo,† Guang-Wen Chu,‡ Hai-Kui Zou,‡ Fang Wang,‡ Yang Xiang,‡ Lei Shao,† and Jian-Feng Chen*,†,‡ †

State Key Laboratory of Organic−Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, PR China Research Center of the Ministry of Education for High Gravity Engineering and Technology, Beijing University of Chemical Technology, Beijing 100029, PR China

‡

ABSTRACT: In this work, gas−liquid mass transfer characteristics, such as effective interfacial area (ae) and liquid side mass transfer coefficient (kL), were investigated in a rotating packed bed (RPB) contactor with 5 novel rotors equipped with blades in the packing section and 1 conventional rotor without blades and fully filled with the same packing. The chemisorption of CO2 into a NaOH solution was used to evaluate ae and kL within each rotor of the RPB. The experimental results indicate that the rotors with blades can significantly intensify the mass transfer process at all rotational speeds, over a range of gas−liquid ratios. The mass transfer rate achieved within these novel rotors was between 8% and 68% higher in comparison with the conventional rotor. A model based on the Danckwerts surface renewal theory was developed to calculate the liquid side volumetric mass transfer coefficient (kLae) in the rotor. The experimentally obtained values of kLae are in agreement with model predictions within ±15%.

1. INTRODUCTION A rotating packed bed (RPB) was introduced as a gas−liquid countercurrent contactor to enhance the mass transfer process by Ramshaw1 in 1979. In an RPB, the gravitational field, which drives liquid flow in conventional packed beds, is replaced with a centrifugal field produced by a high speed rotor driven by a motor in a static casing. An RPB can achieve high volumetric mass transfer coefficients with a small volume of the contactor.2 Considerable size and investment reductions make it very desirable for space-limited and plant upgrade applications. Hydrodynamics and mass transfer in RPBs have been widely studied by simulations, experiments, empirical correlations, and mathematical models.3−14 During the last three decades, RPBs have been employed to achieve rapid micromixing,15−17 absorption,18,19 desorption,20 distillation,19,21,22 polymer devolatilization,23 reactive precipitation,24,25 and production of nanoparticles.26,27 The research on RPBs continues due to the potential of significant economic benefits in a variety of applications. A significant phenomenon in an RPB, which requires improved understanding and quantification, is the so-called end effect which occurs in the part of the packing close to the inner edge of the rotor. Evidence suggests that a significant part of the overall mass transfer occurs in that region. The mass transfer accomplished in this end zone can indeed be a multiple of what is achieved in the rest of the rotor. In 1989, Dudukovic et al.6 reported the experimental measurement of the gas−liquid interfacial area in an RPB packed with glass beads and demonstrated that end effect did exist. In order to quantify the exact contribution of the end zone, Guo et al.28 measured the mass transfer coefficient by a physical absorption process with an oxygen−water system in 1996. They divided the RPB into three mass transfer zones: the end zone, the bulk zone (the remaining zone of the rotor), and the cavity zone (the zone between the © XXXX American Chemical Society

outer edge of the rotor and the inner edge of the static casing) and published the detailed results for liquid side volumetric mass transfer coefficient in these three zones as shown in Figure 1. Due

Figure 1. Mass transfer contribution of the three zones in a RPB.

to the obvious end effect, Chen et al.8 proposed a correlation, which took the end effect into consideration, for kLae in a RPB for viscous Newtonian and non-Newtonian liquids. On the basis of the visual observation of the liquid in an RPB at a high gravity level by Zhang,29 Yi et al.13 developed a mathematical model for predicting the mass transfer coefficient. Rajan et al.11 and Agarwal et al.19 described a novel RPB with split packing. It was found that the split RPB increased the tangential slip velocity between the gas and the packing, thus enhancing the mass transfer process in the RPB. The end effect which causes the highest mass transfer efficiency in the end (inner rotor) zone is assumed to occur Received: February 22, 2012 Revised: May 28, 2012 Accepted: June 13, 2012

A

dx.doi.org/10.1021/ie300466f | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

Article

equation with the proper boundary conditions for a semi-infinite medium and first-order reaction, eq 1 leads to

due to the following factors: (1) occurrence of the most violent collisions between incoming liquid jets and packing with maximum relative velocity;7 (2) the strongest gas and liquid interactions because of the maximum gas flux rate across a minimum cross-sectional area of the rotor; (3) the most rapid resupply of fresh liquid from the liquid distributor. In the bulk zone of the rotor, the probability of collision decreases sharply because of the smaller relative velocity, which leads to the decrease of effective interfacial area. These findings suggest that the mass transfer ability is not a linear relation of the radial distance in a RPB. Unlike conventional packed columns, where the height of the mass transfer unit is approximately constant and the designer can reach the desired result by merely increasing the height of the column, this is not the case in an RPB. In industrial scale design of an RPB, attention has been paid to the bulk zone of the mass transfer process to achieve the maximum benefit of the whole rotor. However, very little work, if any, has been conducted to account for the end effects and utilize them to enhance efficiency. Therefore, the main goals of this work are the following: (1) to utilize the observed end effect in some novel rotors equipped with blades, in order to artificially create multi end zones in the rotor and thus enhance the mass transfer process in the so-called bulk zone; (2) to evaluate the effective interfacial area (ae) and liquid side mass transfer coefficient (kL) of these novel rotors. For achieving these goals, the gas−liquid chemisorption with CO2−NaOH was employed to measure ae and kL within the rotor of the RPB. Moreover, a model based on the Danckwerts surface renewal theory was adopted to calculate the liquid side volumetric mass transfer coefficient (kLae) in the rotor. The present work focused on the mass transfer performance in the rotor zone only, induced by the significant spray existing within the internal rotor. Although there was also spray between the outer edge of the rotor and the inner edge of the housing, this was not considered within the scope of the present research but will be separately investigated in the future. Little splashing of liquid was observed in the core (the eye) of the rotor.

Na = kLC I 1 + M

where M = Dk1/kL . Consider a chemical reaction between gas component A and liquid component B as A(g) + b B(l) → P(l)

∫0

∞

SNi e−Sθ dθ

(3)

which is an irreversible first-order reaction in both A and B. The condition for the reaction to be pseudo-first-order is 1+

DA k 2C BL kL

2

−1≪

C BL bCAI

(4)

The absorption rate for this pseudo-first-order reaction can be expressed by eq 2 as NA = kLCAI 1 + M = kLCAI 1 +

When the condition M ≫ 1 is satisfied, can be simplified as RA = NAae ≈ kLaeCAI

DA k 2C BL kL 2

DA k 2C BL kL 2 11,34

(5)

the above equation

= aeCAI DA k 2C BL

(6)

It can be seen from eq 6 that RA, the absorption rate of A per unit volume, is independent of kL. The effective interfacial area (ae) can be calculated from RA values experimentally obtained in the reactor and other parameters from the experiments. When M is smaller than 1, RA is sensitive to both kL and ae.11,34 Then eq 5 can be expressed as follows: RA = NAae = kLaeCAI 1 + M = aeCAI kL 2 + DA k 2C BL (7)

The liquid side mass transfer coefficient (kL) can now be calculated using the ae obtained from eq 6, measured RA in the reactor and other parameters from the experiments. 2.2. Chemical System. The reaction between CO2 and aqueous alkano-amine solutions was introduced by Sharma and Danckwerts36 as a model system for the determination of mass transfer parameters. The absorption of CO2 in NaOH solution has been widely used for determining ae and kL.5,7,11 The reaction can be expressed as follows:

2. THEORY Both physical and chemical methods are employed for measuring the mass transfer parameters in various kinds of reactors.8,9,30−33 Chemical methods have however been preferred for the determination of ae and kL in gas−liquid systems in experimental and theoretical studies.34,35 The reactor model used for the RPB is of plug flow nature, with a varying cross sectional area. The plug flow approach seems justified since little back-mixing of liquid and gas phases occur when they move countercurrently through the rotor. 2.1. Determination of Effective Interfacial Area (ae) and Liquid Side Mass Transfer Coefficient (kL). According to the Danckwerts model,34 a parameter S called renewal frequency was introduced to describe the fraction of the gas−liquid interfacial area which is replenished with the fresh liquid per unit time. Danckwerts pointed out that those liquid elements of the renewed surface had a stationary age distribution which was postulated to be exponential. The rate of absorption into the liquid elements at the surface is the average value of the flux over all the elements of the surface, given by Na =

(2)

2

CO2 + OH− → HCO3− HCO3−

−

+ OH →

CO3−

(8)

+ H 2O

(9)

The above reaction can be treated as a pseudo-first-order reaction when inequality given by eq 10 below is satisfied: 1+

DCO2k 2C NaOH,L kL

2

−1≪

C NaOH,L 2CCO2,I

(10)

The detailed parameters for calculating kL and ae are given in the literature.7,11 In this study, a 1 mol/L NaOH solution and a mixed gas of CO2 and N2 with ∼10 mol % of CO2 were used for measuring ae, while a 0.05 mol/L NaOH solution and a mixed gas of CO2 and N2 with ∼2 mol % of CO2 were used for measuring kL. The above conditions for calculating the values of ae and kL had been used and verified by the literature.7,11 The values of the diffusion coefficient were between 1.32 × 10−9 and 1.95 × 10−9 m2/s, and the values of reaction rate constant were between 3006 and 15 893 m3/(kmol s). Strictly speaking, the values of ae in eq 7

(1)

After applying Laplace transform to the governing partial differential equation (Fick’s second law) and solving the resulting B



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are not rigorously equal to that in eq 6 since different concentrations of NaOH solutions and the CO2/N2 molar ratios can affect effective interfacial areas, hence producing an error in the estimated values of kL. In order to get a good approximation for ae and reduce the calculation error in kL in eq 7, experimental operational parameters such as rotational speeds and gas−liquid ratios were kept the same in each individual experiment accordingly. For example, 600 rpm rotational speed and 60 G/L ratio were used to calculate ae, then 600 rpm rotational speed and 60 G/L ratio were used to calculate kL.

3. EXPERIMENTAL SECTION 3.1. Experimental Apparatus. The basic structure of the RPB used in this study is schematically shown in Figure 2. The

Figure 2. Main structure of the RPB (all of the space inside the RPB, including the packing zones, the blade zones, and the cavity zone, are the mass transfer zones).

RPB consists of a rotor driven by a motor and a static casing with a liquid inlet/outlet, a gas inlet/outlet, and a liquid distributor. The liquid distributor consists of two pipes configured in parallel with the axis, and each pipe has six ⌀ 1 mm nozzles aligned along the length direction. The distance between the nozzles and inner edge of the rotor was about 4 mm. The inner and outer radii of the rotor were 78 mm and 153 mm, respectively, and the axial height of the rotor was 50 mm. The static casing had an inner radius of 248 mm and an axial height of 98 mm. The stainless steel wire mesh was used as packing loaded in the rotor. The mesh piles consisted of some individual fiber of steels and the thickness of piles was about 1.4−1.6 mm. The diameter of each fiber of steel was 0.22 mm. The surface area and porosity of the packing were 500 m2/m3 and 0.96, respectively. The RPB was operated at rotational speeds from 0 to 1440 r/min. Six different rotors were designed and used in this study: five novel rotors with blades and multiple packing sections and one conventional rotor without blades. For the five novel rotors, there are three rings of packing sections separated by two rings of blades as shown in Figure 2. Burns and Ramshaw37 demonstrated visually that the liquid motion became synchronized with the rotor after flowing across the inner circular packing with a radial depth of 10−15 mm. In this study, each packing zone has a radial depth of 15 mm and consists of 8 layers of packing. The first packing zone was loaded close to the packing supports in the inner edge of the rotor and then the first ring of blades was installed close to the first packing zone. Additional concentric packing zones and rings of blades were installed in the same manner. Figure 3a shows the radii of the rotor, the parameters of the blades, and the shape of a blade installed in the rotor. Each blade has a height of 50 mm and a width of 4 mm. The first ring of

Figure 3. Schematic structure of (a) parameters and (b) all the rotors.

blades and the second ring of blades had 36 and 48 pieces of blades, respectively. Each blade was a built as a thick cuboid at positioned at a given angle with respect to the axial direction of the rotor. Figure 3b shows the schematic structure of all the rotors. Rotor 1, the conventional rotor, has no blades and represents the basis for comparison of mass transfer performance with the other 5 rotors, all equipped with blades. The angle between the plane of the blades and the equatorial line of the rotor was the main parameter that was varied within these 5 rotors. The length of the blades with different angles is summarized in the Table 1. 3.2. Experimental Procedure. Figure 4 displays the sketch of the experimental setup. The NaOH solution at 20−30 °C in the range of 40−120 L/h is fed into the RPB from the liquid inlet at the eye of the rotor. The temperature of the solution cannot be ignored, and affects the viscosity, surface tension, reaction rate, etc. The liquid jets generated by the liquid distributor’s nozzles impinge onto the inner edge of the rotor, and once gripping the packing move outward through the rotor as a result of the C



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Table 1. Detail Parameters of the Rotors first ring of the blades no. rotor 1 (no blades) rotor 2 rotor 3 rotor 4 rotor 5 rotor 6

α (deg)

L1 (mm)





0 30 60 30 60

16.00 18.05 26.98 18.05 26.98

second ring of the blades

number of blades

β (deg)

L2 (mm)







36

0 −30 −60 −60 −30

16.00 18.14 27.87 27.87 18.14

number of blades 

48

Figure 5. Potential curve of potentiometric titration.

represent the volume of HCl solution consumed at the first titration end-point and the third titration end-point, respectively. The concentration of NaOH and Na2CO3 with a sample volume of V0 can be expressed by C NaOH =

V − V1 V1 C HCl and C Na 2CO3 = 2 C HCl V0 2V0

(11)

As shown in Figure 2, the values of yCO2,1, yCO2,4, CNaOH,2, CNaOH,3, CNaOH,4, and CNa2CO3,3 can be directly obtained from the above measurements. Haas38 proposed that liquid jets discharged from a small opening at laminar flow conditions (the Reynolds number does not exceed 2000) will tend to break into short lengths, which then form spherical drops. The most probable liquid jets length between break points is about five times the diameter of the jet streams. In this work, the Reynolds number of liquid jets at the nozzle of the liquid distributor is in the 750− 1778 range and liquid jets were regarded as laminar. The distance between the liquid distributor and the inner edge of the rotor was about 4 mm. The diameter of the jet streams at the nozzle was 1 mm. Therefore, liquid jets did not break into liquid droplets before colliding with the first layer packing. Furthermore, the liquid jets from the circular holes in the liquid distributor were tested before the liquid distributor was installed in the RPB, to ensure that liquid jets were not broken into droplets during the distance from the liquid distributor to the inner edge of the rotor. The CO2 absorption into liquid between the nozzles and the inner edge of the rotor was neglected and the values of yCO2,2 were regarded to be approximately equal to yCO2,1. The values of yCO2,3 can be calculated from the values of yCO2,4, CNaOH,3, and CNaOH,4. The values of yCO2,2, yCO2,3, CNaOH,2, CNaOH,3, and CNa2CO3,3 are used for the calculation of ae and kL in the rotor.

Figure 4. Sketch of the experimental setup. (A1) sample analysis at gas outlet; (A4) sample analysis at gas inlet; (B2) sample analysis at liquid inlet; (B3) sample analysis at outer edge of packing; (B4) sample analysis at liquid outlet.

centrifugal force. The liquid holdup is about 0.019−0.037 in the rotor. The mixed gas of CO2 and N2 in the range of 800−12 000 L/h is tangentially introduced into the static casing outside the rotor from the gas inlet, and the gas flows inward through the rotor to exit through the eye of the rotor. The liquid and gas are thus contacted countercurrently in the RPB to complete the mass transfer process. Finally, the gas is evacuated through the gas outlet on the top in the eye of the RPB and the liquid is collected at the wall of the static casing and leaves by the liquid outlet on the bottom of the RPB. The concentrations of CO2 at the gas outlet (A1) and gas inlet (A4) were measured by two infrared gas analyzers. Liquid samples were collected at three locations: the liquid inlet (B2), outer edge of the rotor (B3), and liquid outlet (B4). Compared to our previous sample collector,7 the liquid collector at B3 used in this work was improved and built as a closed hollow cuboid with one side-face having no cover and is capable of collecting the liquid leaving the rotor along the whole axial height of the rotor. The collected liquid samples at B3 are thus more representative and indicative of the packing performance than in previous studies. The liquid samples were analyzed by an Automatic Potentiometric Titrator (Beijing Xianqu Weifeng Technology Development Co., ZDJ-2D). The HCl solution of known concentration was used for titration to determine the concentration of NaOH solution in the collected liquid samples at B2 and the concentration of NaOH and Na2CO3 mixed solution in the collected liquid samples at B3 and B4. The potential curve of a test sample detected by this Automatic Potentiometric Titrator is plotted in Figure 5. V1 and V2

4. RESULTS AND DISCUSSION 4.1. Effective Interfacial Area in the Rotor (ae). Figures 6 and 7 present ae in various rotors used in the RPB. Figure 6 shows the effect of varying the rotational speed and gas−liquid ratio on ae of the 4 rotors: rotor 1 with no blades, and rotors 2−4 with the blade angles of 0° and 30° and 60°, respectively. Figure 6a illustrates that ae increases with increasing rotational speed, indicating that the stronger centrifugal field enhances the effective interfacial area, as expected. Figure 6b shows that ae increases with increasing gas−liquid ratio. Finally, it should be noted that the angle between the blades and the radius of the rotor has a significant effect on ae in rotor 2−4, where ae is seen to increase: ae (rotor 4, angle 60°) > ae (rotor 3, angle 30°) > ae D



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Figure 7. Effect of the (a) rotational speed and (b) gas−liquid ratio on ae in rotors 5 and 6. Figure 6. Effect of the (a) rotational speed and (b) gas−liquid ratio on ae in rotors 1−4.

ae in rotor 5 is larger than in rotor 6 at all rotational speeds and gas−liquid ratios. The gas−liquid contacting area produced in the first ring with blades and the subsequent concentric packing in rotor 5 was notated as A1, the second ring with blades and the subsequent concentric packing in rotor 5 as A2, the first ring with blades and the subsequent concentric packing in rotor 6 as A3, and the second ring with blades and the subsequent concentric packing in rotor 6 as A4. The rotor volume was notated as V and aewas equal to Ai/V. The above results can be expressed as A + A4 A1 + A 2 > 3 (12) V V Since the collisions and the gas−liquid interactions at the second ring with blades and the subsequent concentric packing (at a larger radius, as shown in Figure 3) are more violent than that at the first ring with blades and the subsequent concentric packing, the following inequality can be written by A 2 − A4 > A3 − A1 (13)

(rotor 2, angle 0°) > ae (rotor 1). However, this increasing trend is not witnessed in rotor 6 (with higher blade angles). Further repeat experiments are needed to assess this discrepancy in further detail. Compared with rotor 1 with no blades, the mass transfer was enhanced in rotors 2−4. Since the structure of the first packing zone in the above four rotors is identical, the liquid behavior and mass transfer rate could be regarded as almost the same in them. Thus, it can be inferred that mass transfer is enhanced due to the presence of the rings with blades in rotors 2−4. The relative velocity between the liquid and the packing in the rotor can be defined as the difference vector of the liquid velocity vector and packing velocity vector. A higher relative velocity results in more collisions between the liquid and packing. More collisions generate a larger gas−liquid contacting area from better liquid dispersion. In the channels between the blades, most of the liquid collides with the blades since the blades sweep over the space through which the liquid flows outward in the rotor. The shearing of the liquid at the end of the blades not only can produce a multitude of tiny liquid droplets, leading to the next set of violent collisions with the next packing zone, but can also change the direction of the liquid velocity, resulting again in a high relative velocity between the liquid and packing. Meanwhile, gas flux increases with a decreasing gas flow area in the blade channels, leading to strong interactions of gas and liquid phases. One can now use such end effect to enhance the mass transfer in the so-called bulk zone of the rotors 2−4. In Figure 7, rotor 5 has 30° blades in the first ring and 60° blades in the second ring while rotor 6 has 60° blades in first ring and 30° blades in the second ring. As can be seen from Figure 7,

Then, eq 12 can be obtained. The increment in ae in rotor 5 could be higher than that in the rotor 6. 4.2. Liquid Side Mass Transfer Coefficient in the Rotor (kL). Figures 8 and 9 present the liquid side mass transfer coefficient (kL) in the rotor of the RPB and show the effect of the rotational speed and gas−liquid ratio on kL in the above 6 rotors. Clearly, the blades inside the rotors also have a significant effect on kL, similar to the effect as on ae. Rotor 4 has the highest value of kL, and rotor 1 has the lowest value of kL. It also can be seen that kL increases slightly with increasing rotational speed in Figures 8a and 9a. This was mainly attributed to the reduced liquid side mass transfer resistances of the small liquid droplets and the shortened contacting time. Figures 8b and 9b plot the E



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effect of gas−liquid ratio on the kL. Since a large gas−liquid ratio intensifies the liquid−gas interactions in the blade channels and in packing zones, kL increases with the increasing gas−liquid ratio. Meanwhile the blades inside the rotor might increase the frictional pressure drop, which could enhance the turbulent intensity of both phases, thus expected to increase kL. 4.3. Liquid Side Volumetric Mass Transfer Coefficient in the Rotor (kLae). The liquid side volumetric mass transfer coefficient (kLae) is simply the product of ae with kL from the above experimental results. Since ae increases strongly and kL increases slightly with the increasing rotational speed and gas− liquid ratio, kLae will increase with the operating conditions in the above experiments.

5. MODEL DEVELOPMENT FOR MASS TRANSFER IN THE ROTOR Some researchers have suggested correlations and models for gas−liquid mass transfer in the RPBs.6,10−14 Film flow, pore flow, and droplet flow based on some flow visualizations are the three main liquid forms assumed to exist in the RPBs.28,29,37 In this model, the following assumptions for CO2 absorption in the rotor are used: (1) Based on the Burns and Ramshaw study,37 pore flow was replaced by droplet flow in a high voidage packing in RPBs at a high rotational speed (600−800 r/min). In this study, liquid flow is assumed to consist of liquid droplets in the packing at rotational speeds in excess of 600 r/min. The total gas−liquid contacting area in the packing can be calculated as the total surface area of the liquid droplets. On the basis of previous study of liquid flow on rotating blades and disks for predicting the mass transfer coefficient,5 liquid flow patterns are assumed to consist of liquid droplets in channels formed by blades and liquid films on the blades’ surfaces when the rotational speed was in the range of 600−1400 r/min. Since the liquid film is very thin, the total gas−liquid contacting area can be regarded as the full surface area of liquid droplets and plus the surface area of the blades. (2) Each concentric packing zone consisted of eight layers of the stainless steel mesh, and it is assumed that liquid droplets are renewed every time liquid passes through one layer of the packing rings thus eight renewals occur per packing zone. Liquid droplets in the channels between blades were assumed to be renewed only one time when they flew across the ring consisting of blade channels. (3) Gas behavior, such as the gas flow, gas temperature, gas viscosity, and gas composition has no effect on the shape and flow path of liquid droplets. The liquid phase was dispersed in the gas phase. The model parameters for the calculation are summarized in Table 2. The correlation of liquid holdup εL in an RPB in Table 2 was proposed by Ramshaw39 based on a high-voidage reticulated foam packing which can provide film flow and droplet flow at high accelerations. The above correlation was used to calculate the liquid holdup both in the packing zones and the blades zones. It was assumed that there are n rings of packing zones and m rings of blade zones in the rotor. The average liquid side volumetric mass transfer coefficient in the whole rotor can then be obtained as

Figure 8. Effect of the (a) rotational speed and (b) gas−liquid ratio on kL in rotors 1−4.

Figure 9. Effect of the (a) rotational speed and (b) gas−liquid ratio on kL in rotors 5 and 6.

F



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Table 2. Model Parameters for the Calculation of kLae parameters

in the packing rings

in the blade rings

ref

8

1



Ns

⎛ a ⎞−0.5⎛ u ⎞0.6⎛ υ ⎞0.22 0.039⎜⎜ c ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎝ g0 ⎠ ⎝ u0 ⎠ ⎝ υ0 ⎠

39

u

Lf /εL

18

S

uNs/Δr

12

kL

DCO2S

34

d

⎛ σ ⎞0.5 0.7284⎜ ⎟ ⎝ acρ ⎠

12

εL

δ



ae

6εL d

kLae

ab +

(kLae)p 3

kLae =

⎡ 3υL ⎤1/3 b ⎢ ⎥ ⎣ ac ⎦

∑n = 1 ∫

r2n

r2n − 1

2

■

*Tel.: +86 10 64446466. Fax: +86 10 64434784. E-mail address: [email protected].

5

Notes

The authors declare no competing financial interest.

12

(kLae)b



r2m + 1

r2m

AUTHOR INFORMATION

Corresponding Author

6(εL − δab) d

(kLae)p r dr + ∑m = 1 ∫

contain alternating channels with blades and zones of high voidage packing. The values of kLae predicted by the suggested model are in agreement with the experimental data. Blades with different angles should be designed and evaluated with mass transfer experiments in the future. This should help the designer find the optimum degrees of the blades. It should be pointed out that when high mass transfer efficiency is achieved, the structure of the rotors is more complex than that of the conventional rotor. Future work should also be focused on the simplification of manufacture of such novel rotors.

■

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (No. 21121064, No. 20990221), the National Fundamental Research Program of China (973 Program) (No. 2009CB219903), and the China Scholarship Council (NO. 2011688017). The authors appreciated Professor M.P. Dudukovic’s suggestions which helped them improve this manuscript.

(kLae)b r dr

r

∫r 6 r dr 1

(14)

■

It could be seen that the mass transfer performance in the other two subsections of the packing in the so-called bulk zones was enhanced. Figure 10 is a plot of the predicted data calculated

Figure 10. Comparison of experimental and predicted kLae by eq 14.

from the above model with eq 14 and the experimental data of the liquid side volumetric mass transfer coefficient. It can be seen that the kLae predicted from the model is within ±15% of the experimental data, and therefore, the model is considered capable of providing a fair prediction of kLae.

6. SUMMARY AND CONCLUSIONS On the basis of the enhanced mass transfer due to the end effect phenomena observed in the conventional rotor with a single packing zone, five novel rotors were designed to take advantage of this effect. These rotors consist of concentric rings of packing and rings with blades that alternate. Effective interfacial area and liquid side mass transfer coefficient are larger in the new rotors than that in the conventional rotors. Mass transfer intensification in the five novel rotors is likely due to the larger relative velocity and more energetic gas−liquid interactions in the rotors that G

NOMENCLATURE ac = centrifugal acceleration = rω2 (m/s2) ae = gas−liquid effective interfacial area (m2/m3) ab = surface area of the blades (m2/m3) A1 = gas−liquid contacting area produced in the first ring of blades and the subsequent concentric packing in rotor 5 (m2) A2 = gas−liquid contacting area produced in the second ring of blades and the subsequent concentric packing in rotor 5 (m2) A3 = gas−liquid contacting area produced in the first ring of blades and the subsequent concentric packing in rotor 6 (m2) A4 = gas−liquid contacting area produced in the second ring of blades and the subsequent concentric packing in rotor 6 (m2) b = stoichiometric coefficient of reactant B CAI = concentration of A at gas−liquid interface on the liquid side (kmol/m3) CCO2,I = concentration of dissolved gas CO2 at gas−liquid interface (kmol/m3) CBL = concentration of B in bulk of liquid (kmol/m3) CNaOH = concentration of NaOH in the samples (kmol/m3) CNaOH,L = concentration of NaOH in bulk of liquid (kmol/m3) CNaOH,2 = concentration of NaOH at the liquid inlet (kmol/ m3) CNaOH,3 = concentration of NaOH at the outer edge of the rotor (kmol/m3) CNaOH,4 = concentration of NaOH at the liquid outlet (kmol/ m3) CNa2CO3 = concentration of Na2CO3 in the samples (kmol/m3) CNa2CO3,3 = concentration of Na2CO3 at the outer edge of the rotor (kmol/m3) CNa2CO3,4 = concentration of Na2CO3 at the liquid outlet (kmol/m3) d = diameter of the liquid droplet (m) DA = diffusivity of A (m2/s) DCO2 = diffusivity of dissolved gas CO2 (m2/s) dx.doi.org/10.1021/ie300466f | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX


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g0 = characteristic centrifugal acceleration = 100 (m/s2) G = gas flow rate (m3/s) k2 = second-order rate constant of reaction (m3/(kmol s)) kL = liquid side mass transfer coefficient (m/s) kLae = average liquid side volumetric mass transfer coefficient in the rotor (1/s) (kLae)p = liquid side volumetric mass transfer coefficient in the packing rings (1/s) (kLae)b = liquid side volumetric mass transfer coefficient in the blade rings (1/s) L = liquid volumetric flow rate (m3/s) Lb = liquid volumetric flow rate per unit height on the blade surface (m2/ s) Lf = liquid flux (m3/(m2 s)) N = rotational speed (r/min) Na = rate of absorption per unit area (mol/(m2 s)) NA = rate of absorption A per unit area (mol/(m2 s)) Ni = instant rate of absorption A per unit area (mol/(m2 s)) Ns = number of layers of packing r = radius (m) RA = rate of absorption A per unit volume = NAae (mol/(m3 s)) S = renewal frequency (1/s) u = liquid velocity (m/s) u0 = characteristic liquid velocity = 0.01 (m/s) V = volume of rotor (m3) V0 = volume of sample (mL) V1 = volume of HCl consumed at the first titration end-point (mL) V2 = volume of HCl consumed at the third titration end-point (mL) yCO2,1 = mole ratio of CO2 at the gas outlet (mol %) yCO2,2 = mole ratio of CO2 at the inner edge of the rotor (mol %) yCO2,3 = mole ratio of CO2 at the outer edge of the rotor (mol %) yCO2,4 = mole ratio of CO2 at the gas inlet (mol %)

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Greek Symbols

α = angle (in degrees) between the first ring of blades and the center line of the rotor β = angle (in degrees) between the second ring of blades and the center line of the rotor δ = thickness of liquid films on the blades (m) εL = liquid holdup (m3/ m3) υ = kinematic viscosity of the liquid (m2/s) υ0 = characteristic kinematic viscosity of the liquid = 10 −6 (m2/s) θ = time (s) ρ = density of the liquid (kg/m3) σ = surface tension of the liquid (kg/s2) ω = angular speed (rad/s) Δr = radial thickness of the rings of packing or the blades = 0.015 (m)

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REFERENCES

(1) Ramshaw, C.; Mallinson, R. H. Mass Transfer Process. U.S.

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Mass Transfer Studies in a Rotating Packed Bed with Novel Rotors

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