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KINETICS, CATALYSIS, AND REACTION ENGINEERING Micromixing Efficiency in a Rotating Packed Bed: Experiments and Simulation Hai-Jian Yang, Guang-Wen Chu, Jian-Wen Zhang, Zhi-Gang Shen, and Jian-Feng Chen* Research Center of the Ministry of Education for High Gravity Engineering and Technology, College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China
Micromixing plays a crucial role in fast chemical reactions. The micromixing efficiency in a rotating packed bed (RPB) was first studied via a throughway method with specially designed RPB structure accompanied by adoption of the iodide-iodate reaction system as index to the micromixing efficiency. With sampling along the radial position, micromixing efficiency in different packing zones of RPB was detected and analyzed and the importance of the inlet region of the RPB on micromixing was experimentally confirmed. The effects of different operating conditions (e.g., rotational speed, liquid flow rates, and reagent concentration) on segregation index (Xs) were also investigated. On the basis of micromixing theory and appropriate assumptions on energy dissipation rate, the micromixing time τm in the RPB was evaluated to reach about 10-4 s, almost equal to what we calculated based on the incorporation model. Compared with other mixing devices, the RPB has a distinct advantage in improving micromixing efficiency, and maybe of many novel applications in the chemical and related industries. Introduction Micromixing (i.e., mixing at the molecular scale) is the last stage of turbulent mixing and consists of the viscous-convective deformation of fluid elements, followed by molecular diffusion. It is believed to play a very important role in the chemical industry when the time scale of the chemical reaction involved is at the same magnitude or smaller than the time scale of the mixing process. Industrial processes, such as crystallization, precipitation, and polymerization, are greatly influenced by micromixing.1-3 In these processes, the reactions may have occurred or been completed before the reactants accomplish homogeneous mixing at the molecular scale (i.e., rapidness of the reactions). Hence, the reactions proceed at an inhomogeneous state. Consequently, conversion, selectivity, particle size distribution, molecular weight distribution, etc., are significantly influenced by micromixing. For exothermic reactions, any imperfect micromixing may induce hot spots and instabilities in the feeding region. This could potentially incur dangers under certain industrial conditions. The rotating packed bed (RPB) reactor is a novel reactor that utilizes centrifugal acceleration to intensify the mixing and mass-transfer processes previously conducted in columns. Process intensification has long been known to be a vital concept and is considered to be one of the fundamental pillars of the chemical engineering domain. The benefits of using RPBs in this context were highlighted about 20 years ago by Ram* To whom correspondence should be addressed. Tel.: +8610-64446466. Fax: +86-10-64434784. E-mail: chenjf@ mail.buct.edu.cn. (J. F. Chen).
shaw.4 Since its emergence, many investigations involving the RPB (e.g., mass transfer,5,6 visual study of liquid distribution,7,8 and liquid holdup9) have been carried out. Besides, RPBs have also been applied to processes such as desorption,10 absorption,11 distillation,12 and ozone oxidation.13 In recent years, there has been an emerging trend toward the applications of the RPB for the synthesis of drug nanoparticles and inorganic nanoparticles.14,15 The first commercial operation of using a RPB reactor for production of CaCO3 nanoparticles (1530 nm in mean size) up to an annual capacity of 10000 tonnes was realized successfully in the year 2000.16 Another commercial application of RPB as a reactor for production of HOCl chemical via a fast separationreaction process by DOW Chemical was reported. These pioneering commercial efforts open up the great potential future for RPB as a novel reactor for specific chemicals and advanced materials as well as nanodrugs. Our previous investigations revealed that the RPB was suitable for the production of nanoparticles because of its advantage of short residence time and intensification of mixing and mass transfer. Theoretically, the production of nanoparticles with uniform particle size distribution by precipitation requires rapid mixing with the characteristic micromixing time less than the characteristic time of nucleation and growth time, τn+g, of the nanoparticles. However, the micromixing mechanism in the RPB has not been well understood. At present, the micromixing time scale in the RPB is rather ambiguous, with no formal theoretical report in the literature. To facilitate the wide use of the RPB as a precipitation or crystallization reactor in synthesizing organic or inorganic nanoscale particles, it is vital to explore the micromixing mechanism and efficiency in the RPB.
10.1021/ie0503646 CCC: $30.25 © 2005 American Chemical Society Published on Web 09/01/2005
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Figure 1. Schematic diagram of rotating packed bed.
In the first part of this article, with the aim of throughway study, a special configuration of RPB was designed to achieve radial sampling. The parallel competing reaction systemsiodide-iodate reaction systems was adopted to measure the micromixing efficiency in the RPB. Furthermore, the characteristic micromixing time of the RPB was evaluated by both the micromixing theory with appropriate assumptions on the energy dissipation rate () and an incorporation model at the base of our experimental results. Experiments Reactor Design for the Throughway Study. From a configuration viewpoint, there are three different regions along the direction of liquid flow in the RPB: inlet region, main body region, and cavum region. The key to rapid mixing is 2-fold: (1) produce a region of high turbulent energy dissipation; (2) ensure that the process streams for mixing pass through the highintensity region.17 In the RPB, the liquids, upon entry into the packing via the liquid distributors, are broken up by the high-speed rotary packing, and are splashed randomly. This violent interaction between the liquids and the packing produces a region of highly turbulent energy dissipation. Hence, the inlet region that lies within the inner radius of the packing is considered a crucial factor in influencing mixing and mass transfer. From there, much of the liquid is captured by the wire packing and forced to attain the same circumferential speed as the rotary packing. Concurrently, the liquid flows in a radial fashion, as a consequence of several forces, especially centrifugal force. To verify the importance of the inlet region, we designed a special RPB that was capable of radial sample extraction (Figure 1). In RPB, 22 sampling tubes (2 in symmetrical position and 11 in each side) were deliberately and carefully laid along the radial direction of the packing. The planform of the sampling tubes in the packing is shown in Figure 2. The angle between 2 of the 11 sampling tubes is 15°. Corresponding strictly to these tubes, 11 angular circular troughs were arranged on the chassis of the RPB to collect the solution for sampling. Hence, we are able to collect samples through the sampling tube at the undersurface of the RPB and analyze them with the spectrophotometer at
Figure 2. Distribution of sampling tubes in the packing (planform).
353 nm. Currently, there has been no report of a similar nature in the literature (i.e., a throughway study on micromixing in the RPB). Typical parameters of the RPB configuration are listed in Table 1. Parallel Competing Reaction System. Due to indistinguishability and instrumental limitations, the experimental methods employed for characterizing micromixing efficiency based on physical phenomena (e.g., optical18 and conductometric19 methods) have been deemed limited. Hence, chemical methods (i.e., chemical reactions as molecular probes) were used to test the micromixing efficiency. A good test reaction should comprise the following criteria: a simple reaction scheme to avoid the analysis of multiple products, ease of analysis of the reaction product, known reaction kinetics, reaction rate faster than the mixing rate, and good sensitivity and reproducibility.20 In 1996, Fournier et al.20 gave a good review on the available chemical measurement methods for assessing micromixing efficiency. The authors also presented a novel parallel competing reaction system. This reaction system consists of the following three chemical reactions.
H2BO3- + H+ S H3BO3
(1)
5I- + IO3- + 6H+ S 3I2 + 3H2O
(2)
I- + I2 S I3-
(3)
The first reaction is quasi-instantaneous. The rate of the Dushman reaction (i.e., reaction 2) is given by
R2 ) k2CI-2CIO3-CH+2
(4)
where k2 depends on the ionic strength µ of the medium such as
µ < 0.166 M, log10(k2) ) 9.28105 - 3.664µ1/2 (5) µ > 0.166 M, log10(k2) ) 8.383 - 1.5112µ1/2 + 0.23689µ (6)
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Table 1. Specification of RPB Used in This Study rotor
packing
inner radius outer radius axial height
30 mm 223 mm 50 mm
material voidage wire cross section
wire mesh 95% 0.021 mm2
The third reaction is an equilibrium reaction and the equilibrium constant can be written as
log10 KB )
555 + 7.355 - 2.575 log10 T T
(7)
where T is the reaction temperature. More details about this reaction system can be found in Rousseaux et al.21 or Guichardon et al.22 In our experiments, a solution A1 that contains H2BO3-, I-, and IO3- and the other solution (H2SO4 solution) A2 are pumped into the RPB through two liquid inlets (Figure 3.). The flow rate of solution A1 ranges from 6 to 9 L/min, and its initial boric acid, iodate, and iodide concentrations are 0.0909, 0.00233, and 0.0116 M respectively. The volumetric flow ratio of A1 and A2 (R) is adjusted to be between 7.2 and 12. Upon entry into the wire packing, the liquids spread outward in a radial fashion, as a consequence of both the centrifugal force and other forces. While in the rotating packing zoon, mixing of the reactant solutions occur, and the above reactions proceed. If micromixing is homogeneous, then almost all of the injected H+ reacts with H2BO3- to form H3BO3. That is to say, reactions 2 and 3 may not occur. Otherwise, the three reactions may all occur. We are able to detect the amount of produced I3- via the use of the spectrophotometer at 353 nm (UV2501PC, Shimadzu corporation, Japan). Here, the segregation index (XS) is defined as
XS )
Y YST
(8)
with
Y)
2(nI2 + nI3-) nH+0
and YST )
6(IO3-)0 6(IO3-)0 + (H2BO3-)0
where Y is the ratio of acid mole number consumed by
Figure 3. Experimental flow diagram.
radial positi on of sampling tubes 1. 2. .... n.
40 mm (40 + 17) mm .... (40 + n × 17) mm
reaction 2 divided by the total acid mole number injected and YST is the value of Y in the total segregation case when the micromixing process is infinitely slow. The value of XS should be 0 < XS < 1. XS ) 0 and XS ) 1 indicate maximum micromixing and total segregation, respectively. Experimental Results and Discussion Distribution of XS at Different Radial Positions. Figure 4 shows that XS decreases sharply in the inlet region. Beyond this, XS becomes almost constant. In the experiments, most of the results exhibit similar trends (i.e., see the latter results). The results indicate that the inlet region of the RPB plays a very important role in the mixing and reaction processes. In the inlet region, the injection flows from the liquid distributor, makes contact with the packing, and is then twisted and broken up by the rotary packing. The interactions are violent as a result of the great relative velocity. Nevertheless, the occurrence of iodine is clearly a sign of insufficient micromixing in the initial wire, and segregation of the reactants happens thereafter. However, micromixing is greatly improved by the RPB packing (i.e., XS decreases down to a very low value about 10-2) after a short distance along the radial direction. The above results have practical applications in the industry, and we now know that the packing has to be of an optimum size (i.e., not too thick). The ability of the packing to intensify the mixing is limited to a specific radial thickness (i.e., 80-100 mm in our experimental conditions). In an industrial setting, via regulating the optimum thickness of the packing, we can reduce both the cost of the packing and the energy consumption (use smaller electric engine). Effect of Rotational Speed on XS. Figure 5 illustrates the distribution of XS along the radial direction at different rotational speeds. It is evident that XS decreases with increasing rotational speed under a specific condition, hence inferring that a larger centrifugal force could enhance micromixing efficiency in
Figure 4. Distribution of XS along the radial position.
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Figure 5. Effect of rotational speed on XS.
Figure 6. Effect of concentration H+ on XS.
the RPB. The reasons for this may be as follows. First, greater relative velocity among all kinds of liquid elements and packing will be affected with an increase in rotational speed. Consequently, vigorous impingement of the liquids will occur, hence resulting in good mixing efficiency. Second, the residence time distribution (RTD) of the liquid will decrease with an increase in rotational speed. From Burn’s visual study,7 we know that the liquid flow in the packing is fan-shaped, hence inferring that it is hard for two liquid elements to collide during the flow in the packing. Most of the collisions between the liquid elements occur when they are captured by the packing. The shorter the RTD, the shorter the time interval needed for the two liquid elements to be captured by the packing. Besides, there will also be an acceleration of both the micromixing rate and coalescence-dispersion frequency of the liquid elements. Effect of Reagent Concentration on XS. Figure 6 gives the distribution of XS along the radial direction at two different acid concentrations. When the acid concentration is improperly selected, the amount of the iodine formed is too small or too high and the optical density may not be in the range of the spectrophotometer scale. Hence, prior to experimentation, we should first select the proper reagent concentrations, in particular, the acid concentration. From the experimental results illustrated in Figure 6, it can be appreciated that XS is sensitive to the reagent concentration. Upon entry into the packing
Figure 7. Effect of liquid flow rates on XS.
space, the liquid stream is fragmentized and dispersed into much smaller entities (i.e., droplets). The reactions take place under varying degrees of reactant segregation. A high acid concentration will mean a higher production of iodine, and hence, a larger XS. After the liquids penetrate deeper into the packing, the variation in XS between the above two conditions is reduced. Eventually, XS tends toward a constant value. This result indicates that the RPB has the distinct advantage of accelerating micromixing. Effect of Liquid Flow Rates on XS. Figure 7 shows the distribution of XS along the radial direction at various liquid flow rates. It can be appreciated that XS decreases slightly with increasing liquid flow rates. For a specific liquid distributor, a higher liquid flow rate induces a higher injecting velocity. That is to say, increasing the liquid flow rate could result in a higher impinging velocity between the liquid elements. Consequently, the micromixing efficiency is enhanced as a result of the increased liquid flow rates. In addition, the residence time distribution (RTD) also decreases with increasing liquid flow rates.23 As analogous to the effect of rotational speed, a shorter RTD will mean an increase in the coalescence-dispersion frequency between the liquid elements and, hence, the micromixing rate. By the way, with the increased liquid flow rates, we were able to collect more samples along the radial direction. In view of the large size of the RPB, the outer sampling trough may gather little or even no sample. Comparison with Other Mixing Devices. Since the advent of the iodide-iodate reaction system, the determination of micromixing efficiency in several kinds of mixing devices has thus been measured via that path. Most of the studies were performed in batch or semibatch reactors, with the segregation indices ranging from 0.1 to 0.7. In 1999, Liu and Lee24 measured the micromixing efficiency in a Couette flow reactor. They found that XS decreased from 0.95 to 0.14 with increasing rotational speeds. Monnier et al.25 studied the micromixing in a continuous flow cell and the enhancement of micromixing by ultrasound. They found that an increase in the ultrasound power could improve the micromixing efficiency (i.e., XS varied from 0.03 to 0.07). With almost the same reactant concentrations and liquid flow ratio, in our experiments, XS in RPB (XS is less 0.03) is lower than that of continuous flow cell enhanced by ultrasound. This indicates that the RPB, with the aid of the centrifugal force, could improve
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micromixing efficiency significantly. Meanwhile, compared with batch or semi-batch reactors, as a continuous mixer or reactor, the large capacity of RPB will further widen its applications in the chemical industry. Micromixing time, τm, is an essential parameter for many micromixing models.26 However, we are unable to calculate τm directly through the segregation index. Here, we will evaluate τm via two indirect methods, micromixing theory together with appropriate assumptions on , and an incorporation model at the base of our experimental results. Determination of Micromixing Time τm. Determination of τm Based on Micromixing Theory, with Assumptions on E. From previous investigations, especially Baldyga et al.’s works,27 we know that τm could be calculated via the formula: τm ) km(ν/)1/2. For our present investigation, we only evaluate an approximate value of τm via this equation. In the experiment, as the solutions are very diluted, their kinematic viscosities, ν, are hence assumed to be approximately equal to the kinematic viscosity of water (i.e., 10-6 m2/s at 25 °C). However, the issue lies with the energy dissipation rate, . The energy dissipation rate in the RPB is very difficult to acquire because of the complexity of the liquid flow. At present, no related reports have been gleaned from existing literature. Hence, on the basis of previous investigations, we approximately evaluate the value of from its definition, coupled with the appropriate assumptions. The results from the visual and theoretical studies of liquid flow in the RPB8,28 revealed that the flow of most liquids in the rotary packing is in the form of “film flow”. Thin film flows have a small relative velocity as they rotate with the packing. We assume that the film flows are affected only by the shearing stress imposed by the rotated packing (i.e., because of the relative velocity). Energy is transferred from the packing to the liquid film through the shearing stress. Force equilibrium on liquid film at r are
dF(r) ) τ(r) dS(r) with dS(r) ) 2πr dr Thus, the elementary power induced by the shearing stress can be written as
dP(r) ) U(r) dF(r)
(9)
where U(r) is the relative velocity between the liquid film and the packing at position r. Furthermore, can be calculated as
(r) )
dP(r) U(r)2πr dr U ) τ(r) ) τ(r) dm Fh2πr dr Fh
(10)
where dm ) F dV with dV ) h × 2πr × dr. The relative velocity between the liquid film and the packing is very small (about 10-1 m2/s magnitude), and the flow is laminar at the referenced coordinate. So
τ(r) ) µ
2πN′r )µ h
U(r) U(r) 2πr )µ h h
2πr
(11)
and 2
(r) )
U(r) U(r) U(r) U(r) τ(r) ) µ )υ 2 Fh Fh h h
(12)
Therefore,
τm ) km(υ/)1/2 ∝
h U(r)
(13)
Guo et al.8 presented a model to calculate the gradient of the liquid film’s relative velocity on the packing wire, via appropriately simplifying the packing configuration and solving the Navier-Stokes equation in the cylindrical coordinate. The relative velocity ranges from 0 to about 0.16 m/s on the packing wire. Here we assume U(r) to be equal to 0.15 m/s, and independent of the radial position, r. On the basis of a visual study, Guo et al.8 also determined the liquid film thickness to be about 10 µm on the wire mesh at all conditions in their study, through image analysis of the difference between the appointed packing zone with and without liquid flow. A few years ago, Basic29 also described the theoretical film thickness for the inertial flow via the following equation:
[
]
1 - (1 - K)1/2 U(r) h ) 2.59 aWg1/2dP1/2 K1/2
(14)
where dP is the characteristic distance over which collisions occur and is generally chosen to be equal to the packing pore size and K is assumed to be a constant with 0 < K < 1 for simplicity. By combining eq 14 and our experimental conditions, we are hence able to evaluate the magnitude of h (i.e., h ) 10-5 m). Based on the above analyses, here we let h ) 10-5 m. As a result, we get
τm ∝
10-5 h ) ∝ 10-4s U(r) 0.15
(15)
Determination of τm through the Incorporation Model. The incorporation model is derived from Villermaux’s earlier works,30,31 coupled with the broad application of the iodide-iodate reaction system. According to this model, a limited fluid, acid in our experiment, is divided into aggregates and progressively invaded by environmental fluid that contains iodide and iodate in a basic medium. Acid aggregates grow by progressively incorporating the surrounding medium where reactions 1 and 2 take place. The characteristic time of incorporation, tm, is assumed to be equal to the micromixing time. The volume of the aggregate grows according to the equation V2 ) V20g(t), where g(t) is the incorporation function with the form
g(t) ) exp(t/τm) or g(t) ) 1 + t/τm The equations of the incorporation model or the concentrations of the j species are given by
dCj 1 dg ) (Cj10 - Cj) + Rj dt g dt
(16)
where subscript 10 is used for the surrounding fluid and Rj is the net production rate of species j for the reaction. We adopt the following nomenclature for conciseness: A ) H2BO3-, B ) H+, C ) I-, D ) IO3-, E ) I2,
Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7735
F ) I3-. Via g(t) ) exp(t/τm), eq 16 can be transformed to
dZ CC10 - Z - 8R2 ) dt τm
(25)
(17)
dU CC10 - U ) - 5R2 dt τm
(26)
From (17), mass-balance equations of the ionic species mentioned above can be written as follows:
dCD CD10 - CD - R2 ) dt τm
(27)
dCj Cj10 - Cj + Rj ) dt τm
dCA CA - R1 )dt τm
(18)
dCB CB )- R1 - 6R2 dt τm
(19)
dCC CC10 - CC - 5R2 - R3 + R4 ) dt τm
(20)
dCD CD10 - CD ) - R2 dt τm
(21)
CE dCE + 3R2 - R3 + R4 )dt τm
(22)
dCF CF )+ R3 - R4 dt τm
(23)
CC2 + (1/KB - Z)CC - U/KB ) 0
(28)
By solving this equation, we get
Z - 1/KB + x(Z - 1/KB)2 + 4U/KB CC ) 2
(29)
Hence
In these equations, the difficulty lies with the treatment of the reaction terms R1, R3, and R4 because reactions 1 and 3 are instantaneous and equilibrium reactions, respectively. Hence, we use the W-Z transformation32 to bypass this problem. We let W ) CB - CA, Z ) CC CE, and U ) CC + CF, for the operations (19) - (18), (20) - (22), and (20) + (23), respectively. Thus, equations 18-23 can be transformed as follows:
W dW )- 6R2 dt τm
The equations (24)-(27) can be easily solved via iterative methods such as the Runge-Kutta method. The initial conditions are W ) CH+0, Z ) 0, U ) 0, and CD ) 0. The iteration ends as the concentration of H+ approaches zero. Otherwise, the calculation of R2 should be carefully handled. Before H+ is completely consumed, we consider CH+ to be equal to its initial value CH+0. For eq 3, KB ) CF/CCCE, CF and CE can be substituted with U - CC and CC - Z. Then we get the second-order equation
(24)
R2 )
(
)
Z - 1/KB + x(Z - 1/KB)2 + 4U/KB CD (30) k2(cH+0) 2 2
2
The incorporation model was used widely to calculate τm in the tank reactors after Fournier et al.’s excellent work.33 Furthermore, some researchers have even extended this model to the continuous reactors (e.g., static mixers and flow cells that have two liquid flow inputs.24,34). In our experiments, we also assumed that the
Figure 8. Relationship of XS and τm in our experimental conditions (incorporation model).
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injected acid lies in an environmental solution and incorporates with them because of the big volumetric ratio (i.e., 7.2 or 12). In fact, the maldistribution of the liquids in the RPB may exist at different levels, and the exact situation and action of different solutions may be very complicated. Here we try to determine τm with this model. In this work, by assuming a series of τm, we can calculate the species’ concentrations correspondingly by (24) - (27) on the basis of our experimental conditions. Furthermore, XS can be derived according to its definition.19 Figure 8 shows such resulted theoretical relationship between XS and τm calculated from the incorporation model at the range of our experimental conditions. Compared with the experimental results, we could observe that τm reaches about 10-4 s, corresponding to the value of XS (i.e., about 10-2) acquired from the experiments. These data are consistent with that estimated from the above micromixing model. Conclusions 1. This work measured the micromixing efficiency in a rotating packed bed on the basis of a parallel competing iodide-iodate reaction system. The “throughway” study on micromixing in the RPB is reported. The results show that XS decreases with an increase in rotational speed and a decrease in H+ concentration. A slight decrease is also observed as the liquid flow rate increases. 2. With sampling along the radial direction, the importance of the inlet region in the RPB is highlighted in our work. Currently, details about the mixing in the inlet region are still hazy, and further investigations are in the pipeline (i.e., via adoption CFD or PIV). 3. Through both micromixing theory with appropriate assumptions on energy dissipation rate in the RPB and an incorporation model, τm is approximately evaluated to be about 10-4 s. Hence, this proves that the RPB possesses far superior micromixing efficiency than many other mixing devices. Acknowledgment This work was supported by the National Natural Science Foundation of China (No. 20236020 and No. 20325621). Nomenclature A ) H2BO3A1 ) reactive solution which contains H2BO3-, I-, and IO3A2 ) H2SO4 solution B ) H+ C ) ICj ) concentration of species j, mol/L Cj0 ) initial concentration of species j, mol/L D ) IO3E ) I2 F ) I3F(r) ) shearing stress in the radial r position, N g(t) ) growth function of incorporation law h ) thickness of liquid film in RPB, m K ) constant k2 ) rate constant of Dushman reaction, mol-4 L4 s-1 KB ) equilibrium constant, L mol-1 km ) constant N ) rotational speed, N/min
N1 ) relative rotational speed between packing and liquid film P(r) ) elementary power induced by the shearing stress in the radial r position, W Rj ) rate of reaction j T ) temperature, K t ) time, s tm ) incorporation time, s U ) CC + CF, mol L-1 U(r) ) relative velocity between packing and liquid film in the radial r position, m/s XS ) segregation index W ) CB - CA, mol L-1 Z ) CC - CE, mol L-1 τm ) characteristic micromixing time, s ) energy dissipation rate, W/kg µ ) ionic strength, mol/L ν ) kinematic viscosities, m2 s-1
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Received for review March 19, 2005 Revised manuscript received June 27, 2005 Accepted July 12, 2005 IE0503646
