Ind. Eng. Chem. Res. 1993,32,453-457
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Axial Mixing in an Open Turbine Rotating Disk Contactor for a Solid-Liquid-Liquid System Xiaoxiang Chen,' Kuanhong Li, and Yuanfu Su Chemical Engineering Research Center, East China Znstitute of Chemical Technology, Shanghai 200237, China
The experimental study on axial mixing has been carried out in a newly developed solid-liquidliquid contactor, the open turbine rotating disk contactor (OTRDC), using a quartz particles-tap water-kerosene system. The experimental data are treated by using the backflow model, and the correlation for estimating the backflow ratio of each phase have been obtained. It has been found that (1)the solid-phase axial mixing is mainly determined by the column geometries and rotor speed as well as the particle size distribution and (2) in comparison with the liquid-liquid system, the presence of solid particles results in larger continuous-phase but smaller dispersed-phase axial mixing.
Introduction
At the present time, the liquid-liquid (L-L) extraction process is being widely used in the chemical industries. Some important processes which involve solids, such as slurry extraction, solid-liquid-liquid (S-L-L) double decomposition (Zhou et al., 1989), and LEACHEX (a process comprised of leaching and extraction), have also appeared in academic studies and industries. As a consequence, it is necessary to make some improvements in the conventionalextraction contactorsin order to handle the systemswith solidsand increase separation efficiencies. With these ideas in mind, new equipment, an open turbine rotating disk contactor (OTRDC), has been developed in our laboratory. A diagram of the compartment and stirrer of an OTRDC, which is a modified form of the rotating disk contactor (RDC),is illustrated in Figure 1. Three narrow strips are welded with an angle on one side of the rotor, which faces toward the flow direction of the dispersed phase. In recent years, a series of experiments on the performance of OTRDC have been carried out in the 52- and 152-mm-diameter columns. Zhu et al. (1991) first investigated the hydrodynamics, axial mixing,and mass transfer for a L-L system and pointed out that OTRDC has a high efficiency in L-L extraction. Chen et al. (1992) have reported the details of the study on the hydrodynamics and axial mixing for a solid-liquid (S-L) system as well as the hydrodynamics for a S-L-L system. The studied results have shown that OTRDC also appears promising with respect to handling the systems with high solid particle content. At present, therefore, it is thought desirable to undertake a systematic work on axial mixing in OTRDC for a S-L-L system. The effects of column dimensions and operating conditions on the axial mixing were studied. Experimental Section Equipment. The experimental setup is shown in Figure 2. The column dimensions used in the experiments are listed in Table I. The column shell was constructed from two thick-wall Corning glass cylinders of 152-mm diameter and 1OOOmm height. All the column internals were made of stainless steel. The stator rings were fixed by three 5-mm-diameter wires with spacers to form compartments. The rotating disks were fixed on a column shaft of 25-mm diameter which was driven by a variable-speed motor. The central shaft was supported through the bearing which was held 0888-5885/93/2632-0453$04.o0/0
-@ Figure 1. A typical compartment of OTRDC and ita stirrer. 10
Figure 2. Schematicdiagram of experimentalapparatu. 1,OTRDC; 2,3,variable motors; 4,feed screw; 5,mixer; 6,solid separator; 7,8, proportioning pumps; 9,10,Alters; 11,12,tanka of continuous phase; 13,14,tanks of dispersed phase; 15,16,cushioning tanks; 17,rotor speed meter; 18, interface sensor; 19, regulator; 20,control valve; 21, 22,temperature regulators; 23,24,flow rate measuring devices. Table I. Column Dimensions unit D ~ , m m Ds,mm D ~ , m m D ~ , m m HT,mm b,mm N A 152 90 84 25 50 6 35 B 152 90 84 25 75 6 24 C 152 105 84 25 75 6 24
in the middle section of column. The rotor speed was measured and indicated by an electronic digital speed indicator. 0 1993 American Chemical Society
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Figure 4. Actual recording of experimental impulse response (solid phase). d,, 0.225 mm; u,,4.96 mm/s; Ud, 1.65 mm/s; u,, 0.280 mm/ s; NR, 140 rpm.
Model and Data Processing Axial mixing in the OTRDC occurs due to the nonideal flow in which a random movement of fluid is superimposed on the main flow. It alters the true plug flow pattern, tends to decrease the concentration driving force, and impairs the efficiency of the contactor. Therefore, axial mixing in the column is a very important aspect in the scale-up of laboratory apparatus into an industrial-size contactor. The approaches to the problems of axial mixing are usually described by mathematical models. As the OTRDC is partially compartmentalized, the backflow model developed by Sleicher (1960) and Miyauchi (1963) can be used for simulating the column performance. The column is divided into a series of stages interconnected with assumption that each stage is well mixed, and backmixing occurs by mutual entrainment of the phase between stages. In this case the axial mixing in each phase may be evaluated by the interstage backflow ratio f. In unsteady state the backflow model equation can be established by the material balances around stage i. i = 1,2, ...,N (1)
boundary conditions:
c,= CN-1 C i = O , i z l at 8 = 0 where C is the tracer concentration, 8 dimensionless time, i the stage number which starts from top of the column, and N the total stage number. Mecklenburgh and Hartland (1975) derived the general solution of the model equation. u2 = (1 + 2 f ) / N- 2f(l + f>{l[ f / ( l+ f)IN]/N2 (2) where u2 is the standard deviation which can be obtained from the experimentalRTD curves using moment method. Equation 2 can be solved by the Newton method to get the backflow ratio, f . This is easily feasible on a personal computer.
Results and Discussion Solid-PhaseAxial Mixing. The relationship between the residence time of solid particles in the column and
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Figure 7. Correlation of solid-phase axial mixing.
~ (m/s) N ~
Figure 5. Residence time of solid phase in OTRDC. (A)unit, A; d,, 0.184mm; U,,3.31 mm/s; ud, 3.31 mm/s; U,,0.280 mm/s. (A) unit, A; d,, 0.225 mm; U,,3.31mm/s; Ud, 3.31 mm/s; Us, 0.280mm/s. ( 0 )unit, C; d,, 0.225 mm; U,,3.31 mm/s; udt 3.31 mm/s; Us, 0.194 mm/s. (0) unit, C; d,, 0.225mm; U,,5.51 mm/s; ud, 2.76 mm/s; Us, 0.321 mm/s.
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However, with increasing rotor speed the particles can be kept in suspension and pass through the column freely. As a result, the value of fs decreasesrapidly and approaches a constant value. It can be also seen from Figure 6 that the values of fs for the particles of different sizes differ from each other. The upper curve represents the variation of fa with the rotor speed for the quartz particles of a mean diameter d m = 0.225 mm and situates much higher than the curve for d m = 0.184 mm. Therefore, it appears reasonableto say that fine particleswill be easily "fluidized" by the action of rotors. Figure 6 also shows that the superficial velocities of continuous and dispersed phase have no significant influence on the value of fs. It seems that the solid-phaseaxial mixing is determined mainly by column geometriesand the rotor speed as well as the nature and size distribution of the particles. Using an optimization method to correlate more than 60 raw data obtained in the experiments, an empirical expression for the solid-phase backflow ratio fa is established.
where Ut is the terminal settling velocity and comprises the influence of particle size. This equation gives a mean deviation of f15.0%. The comparison of experimental and calculated values is shown in Figure 7. Continuous-Phase Axial Mixing. The existence of solid particles will have a dual effect on the continuousphase axial mixing. On one hand, the interaction between the motions of particles and the continuous phase may result in entrainment of the continuous phase; e.g., the continuous phase may be entrained by the eddies formed in the wakesof particlesor may be carriedwith the particles as films around them, so as to increase the forward mixing in continuous phase. On the other hand, the stirring intensity enhanced by solid particles will increase the backmixing in the continuous phase. Figure 8 shows obviously the difference between the values of fc for the S-L-L system and those for the L-L system. All experimental points of the former are greater than those of the latter because of the influence of solid particles on the fc. Within the experimental range of NR,the value fc for the L-L system changed very little, while that for the S-L-L system increases with increasing rotor speed. From experiments it has been found that fc is dependent not only on the rotor speed and column geometry but also on the values U,,Ud,and Us.Experimental data were treated in a manner similar to that used in the solid-phasemixing.
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N R (rpm) Figure 8. Continuous-phase axial mixing. (A)unit, A; U,,5.51 mm/ s; Ud, 2.76 mm/s; U,,0.321 mm/s. (0) unit, C; U,,4.96 mm/s; ud, 1.65 mm/s; Us, 0.280 mm/s. ( 0 )unit, C; U,,4.96 m d s ; Ud, 1.65 mmis.
200
150
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NR (rP.1 Figure 10. Dispersed-phase axial mixing. (A)u,, 4.96 mm/s; ud, 1.65 mm/s; Us, 0.280 mm/s. (0) U,, 3.31 mm/s; ud, 3.31 mm/s; Us, 0.194 mm/s. (A)U,,4.96 mmis; ud, 1.65 mm/s. ( 0 )U,,3.31 mm/e; ud, 3.31 mm/s. Unit C
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L 'z)
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Figure 9. Correlation of continuous-phase axid mixing.
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Figure 11. Dispersed-phase axial mixing. (0) u,, 3.31 mm/s; Ud, 3.31 mm/s; us,0.321 mm/s. (A)u,, 3.31 mm/s; ud, 3.31 mm/s; u,, 0.194 mm/s.
The backflow ratio f c can be expressed as f, = 38*2(b/HT)1'54[uJ(uc + ud)]o'57[D:NR(1 -hd-
h*)/D+clo.4 (4) Figure 9 givesthe comparison between the experimental data and the calculated values for the S-L-L system. The great majority of experimental points lie between i205% error lines. The line representing the L-L system given by Zhu et al. (1991) is also shown. Dispersed-PhaseAxial Mixing. It is well-known that the dispersed phase comprises a rather wide range of different drop sizes in L-L extraction operations. The large drops pass through the column more rapidly than drops of average size, whereas the small ones reside for a longer time and may be highly backmixed owing to their low inertia. Consequently,there exists a wide distribution of drop residence time. Particularly at high rotor speeds the eddy diffusion will dominate the axial mixing process, since the low inertia of the small drops should cause them to follow the continuous-phase turbulent fluctuations (Strand et al., 1962). From Figure 10 it seems that, at low rotor speeds, the dispersed-phase backflow ratio fd is almost independent of the rotor speed and then drops slightly as the rotor speed further increases. This may be attributed to the observation that the range of drop size becomes even narrower at high rotor speed than at low. This characteristic of OTRDC is in good agreement with the previous study on a L-L system by Zhu et al. (1991). The experiments also reveal that fd decreases with increasing U, (Figure ll),but increases with increasing U, (Figure 10). The explanation for the latter case may be due to high entrainment of small drops at high values of U,. In comparisonwith the L-L system,the dispersed-phase axial mixing of the S-L-L system is apparently small under the same operating conditions (Figures 10 and 12). This
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5
u,/u,=17.18
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DRNRhd ud
Figure 12. Comparison of dispersed-phase axial mixing.
is probably due to the presence of solid particles which enhance stirring intensity and result in a relativelynarrow spectrum of drop size. This also accounta for the experimental results that fd falls as the superficial velocity of solid phase U, increases. From the experimental data the dispersed-phase axial mixing of the S-L-L system may be correlated by the following equation: fd = 16.39(b/HT)0'95[(D)82 - DA2)/DT2]0'44(UcjUs)0'25 x (DRNRhd/ud)-0'15 (5) This correlationgives a mean deviationof f12.7 % ! . Figure 13 shows the comparison of experimental and calculated values. Conclusions As the residence time of solid phase in OTRDC is short, the column can only be considered for the S-L-L double decomposition reaction with a high rate. When quartz particles are used as the solid phase in a S-L-L system,it seem appropriate to use marble particles
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DR = rotor diameter, m DS= stator ring opening, m DT = column diameter, m
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f = backflow ratio h = holdup HT = compartment height, m N = number of compartment NR = rotor speed, rps t(a) = time, s U = velocity, m/s
Ut= terminal settling velocity, m/s
0 = dimensionless time
u2 = standard deviation Subscripts
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id (c.1.)
c = continuous phase d = dispersed phase i = stage number s = solid phase
Figure 13. Correlation of dispersed-phase axial mixing.
Literature Cited
as tracer with the impulse technique to estimate the solidphase axial mixing. However, it should be noted that the model, which treats the behavior of the solid particles as though it were a continuum, is only a rough approximate to the actual behavior. The presence of solid particles will result in larger continuous-phase but smaller dispersed-phase axial mixingsthan for the L-L system. The rotor speed and particle sizedistribution are the predominant factorethat influence the solid phase axial mixing. The backflow ratio for each phase can be correlated by eqs 3,4, and 5, respectively. The variables in these equations were varied in the experimentsexcept column diameter, rotor disk diameter, and strip width.
Chen, X. X.; Wang, H. T.; Li, K. H.; Su, Y.F. Hydrodynamics and Axial Mixing of Liquid-Solid System in Open Turbine Rotating Disc Contactor. J. Chem. Znd. Eng. (China),Engl. Ed. 1992, 7,
Acknowledgment This work was partly supported by the National Science Foundation of China and the Stiftung Volkswagenwerk of Germany. Nomenclat ure b = width of strip, m c = concentration, km0vm3 or % d , = mean diameter of quartz particles, m D A = shaft diameter, m
28-39.
Chen, X. X.; Su, Y. F. Hydrodynamics in Open Turbine Rotating Disc Contactor for Liquid-Liquid-Solid System. Chin. J. Chern. Eng. 1992, in press. Mecklenburgh, J. C.; Hartland, S. The Theory of Backrnixing; Wiley-Interscience: New York, 1975; p 53. Miyauchi,T.; Vermeulen,T. Diffusionand Backflow Models for TwoPhase Axial Dispersion. Znd. Eng. Chem. Fundam. 1963,2,304310.
Sleicher, C. A. Entrainment and Extraction Efficiency of MixerSettlers. AZChE J. 1960,6, 529-630. Strand, C. P.; Olney, R. B.; Ackerman, G. H. Fundamental Aspects of Rotating Disc Contactor Performance. AZChE J. 1962,8,252261.
Zhou, J. Z.; Jiao, L. L.; Su, Y. F. NazHP04 Obtained by Double Decompositionof NaCl and with an Extractant. Znd.Eng. Chem. Res. 1989,28, 1907-1910. Zhu, F.G.; Ni, X. D.; Zhou, Y.C.; Yu, S. C.; Su, Y. F.Study of a Modified Rotating Disc Contactor with Wire Mesh Coalescers. AZChE Symp. Ser. 1984,80,115-123. Zhu,J. W.;Zhang,S.H.;Zhou,X.K.;Chen,X.X.;Su,Y.F.;Vogelpohl, A. Hydrodynamics, Axial Mixing and Mass Transfer in Open Turbine Rotating Disc Contactor (OTRDC). Chem.Eng. Technol. 1991,14, 167-177.
Received for review May 19, 1992 Revised manuscript received November 9, 1992 Accepted November 23, 1992
