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Taks_2_-_Literature_Interstage_backmixing_in_oscillatory_flow_in_a_baffled_column

Taks_2_-_Literature_Interstage_backmixing_in_oscillatory_flow_in_a_baffled_column

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Unformatted text preview: Chem. Eng. Comm. 189: 1640—1652, 2002 Copyright iii: 2002 Taylor 81 Francis 6 0098~6445I02 $1100 + .00 oct: 10.1080/00936440290123606 Taylor & Francis Yayloi aFranm Croup INTERSTAGE BACKMIXING IN OSCILLATORY FLOW IN A BAFFLED COLUMN MOHD SOBRI TAKRIFF ZUHHINA MASYITHAH Department of Chemical and Process Engineering. Universiti Kebangsaan Malaysia, Bangi, Selangor Darul Ehsan, Malaysia An investigation on oscillatory flow in a baffled column was carried out to determine the effects of various operating parameters on interstage back- mixing. Among parameters studied in this Work were liquid flow rate, liquid viscosity. oscillation frequency and oscillation amplitude. The results of this study indicated [hat the interstage backmiin'ng had a maximum value under nonfiow condition but decreased with liquid flow rate. LDWer backrnixing rate was observed in liquids with higher viscosity. Oscillation frequency and am- plitude are the dominating factors that increase backmix-ing as these factors increase. Keywords: Backmixing; Baffled column; Oscillatory flow; Mixing INTRODUCTION Mixing in laminar flow in a straight tube is controlled by molecular diffusion, which is a very slow mechanism. Under this condition, transfer processes are usually characterized by steep temperature gradients and by large concentration gradients within fluid. Enhancement of mixing in a straight tube is. being actively studied. A technique commonly used to enhance mixing is to operate the equipment in the turbulent regime. A high flow rate is required to achieve turbulent flow, but it results in Received 8 November 2000; in final form 18 June 200]. Address correspondence to Mohd Sobri Takril‘f, Department of Chemical and Process Engineering, Universiti Kebangsaan Malaysia, 43600 Bangi, S'elangor Dani] Eh-san, Malaysia. E—mail: sobriéiiengukmmy 1640 INTERSTAGE BACKMIXING IN OSCILLATORY FLOW 1641 reduction of residence time in the flow system, which is counter— productive to many process objectives. Oscillatory flow in baffled columns has been reported in numerous publications as very promising to enhance mixing in a straight and smooth tube or column (Hewgiil et al., 1993; Mackley, 1987, 1991). Oscillatory flow mixing can be achieved if there is a fully reversing flow around baffle plates. which may be produced either by oscillating the fluid or baffle plates (Mackley, 1991). Oscillatory flow in a baffled tube can be characterized by the oscillatory Reynolds number Rea, which describes the intensity of oscillation applied to the system: ”15“?” (1) I4 The second group that is USed to characterize oscillatory flow is the Strouhal number S, where S, represent a ratio of orifice diameter to oscillation amplitude: Rea = _ D # 471x” S, (2) Efficient mixing can be achieved in Oscillatory flow in a baffled tube when R6,, is greater than 150 (Roberts, 1991). Brunold et a1. (1989) showed that baffle spacing of the order of 1.5 tube diameter and constriction of ratio about 60% is optimal to achieve good mixing in oscillatory condition. The interaction between the sharp edge of the baffle plates and the oscillating fluids is responsible for the improvement in the mixing and transport properties. Flow of liquid around baffle plates in one direction produces vortices behind the plates. These vortices take whatever is near the column’s wall with them. Upon reversing the flow direction the vortices are pushed into the center of the column while new vortices are formed at the same time, and the cycle is repeated. This provides an effective way of moving fluids from the walls to the center of the conduit. Formation and disruption of vortices due to the interaction of fluid and baffles enhance mixing in the space between the two baffles. Application of oscillatory flow in a baffled column produces a certain amount of baekmixing, which is a disadvantage in a continuous system when plug flow is desired. A brief literature review indicated that no work has been carried out to investigate this phenomena in oscillatOry flow in a baffled column. The only related work was by Howes and Mackley (1990), in which they observed that backmixing occurs .in oscillatory flow in baffled column. However, the effects of operating parameters and the magnitude of backmixing were not quantified. The objectives of this work are to quantify the magnitude of backmixing and to investigate the 1642 M. S. TAKRIFF AND 2. MASYITHAH effects of operating parameters on the backmixing. rate in Oscillatory flow- in a baffled column. MATERIALS AND METHODS A schematic of the experimental apparatus is shown in Figure 1. The experiments were carried out in a two—stage baffled column. The height of the column was 282 mm and the diameter was 94 mm. The column made of Perspex, was mounted on a stainless piston sleeve. A pneumatically driven piston mounted at the bottom of the column was used to oscillate the liquid. The range of experimental variables used in this study is presented in Table I. At constant oscillation frequency and amplitude and liquid flow rate, 60mL of 30wt% KCl solution was injected into the exit stage of the liquid phase. Twelve samples were taken from each stage at periodic intervals, The KCl concentration in each sample was determined using an electric-a1 conductivity apparatus. Kmil &.\\_\‘\WI mm an—Cz) .®—> @———> “I‘—£\\ll :1 _a ,4 .’ ‘4 -Hfll—L\\'IKJ ...||::I a] _s._ I! e ‘m.‘\\<_\\:\.‘..\ ". ! L §i§ Figure 1. Schematic of the experimental apparatus. (1) top plate, (2) water inlet, (3) perspex column, (disampling ports, (5) baffle plate, (6) injectioujsampfing parts, ('7) water outlet, (8) pistc‘m, (9) piston bar, (10) Frame. INTERSTAGE BACKMIXING IN OSCILLATORY FLOW 1643 Table 1 Range of Experimental Variables Variable Range of value Liquid flow rate 0.0—1.2 L/min Liquid viscosity 0,001—0.0l kg/m.s Oscillation frequency 0.5—1.0 Hz Oscillation amplitude 7.5—l 5 mm The Ideal Stage with Backmixing (ISB) model (X11, 1994) was employed in this investigation to determine the magnitude of back— mixing“. The ISB model represents backmi-xing using finite difference with the assumption that backtnixing flow occurs between adjacent stages in addition to the net forward flow of liquid. For single-phase flow in absence of chemical reaction, the. mass balance for each com- ponent in j—stagc is given by: dC}: _ , - . V'(E) = (Ff+ Fb)C}-_1 “ (FfthJ + FhJ+IlCl + Fb.j+1C.r‘+I (3) where V is the stage volume, Ff and F}, are forward flow and backmixing flow rates, respectively, and C is concentration. Application of this equation to each individual stage in the. apparatus used for this study gives the following equations. For the first stage: dCl V1? = Fpro + Fsz -'(Ff.1 + Falcz. (4) For the second stage: dC . V27: = (Fla + F001 — (Ffiz + F052” (5) Equations (4) and (5) describe the transient behavior of both stages. Solving these equations for a value of F3, gives the concentrations C1 and C2 with time. The interstage backrnixing rate for a given run was deter- mined by selection of Ft, which provided the best match of the experi— mental result With predicted transient concentration profiles. RESULTS AND DISCUSSION Data Reduction The data obtained from the experiments was analyzed with the ISB model. Differential Equations (4) and (.5) were solved using MatLabfi’ to obtain the concentration profile for each stage with time. An estimated 1644 M. S. TAKHIFF AND 2. MASYITHAH 1 r 1 ' W.i; . 7 r _] | Water {1.001 kglm.s l o Stage1 0-9i Do 3 cm, f 0.33 Hz. to 7.5 mm. :1 Stage 2 Vf 0 cmls, Vb 5.29 cmls . -:- 133 Mgelu CUCO 0.2 _. L 2e 40 so 30 1'00 ' 1'20 Time(5) Figure 2. Temporal profiles of tracer concentration for both stages for zero fiow. value of the backmixing flow rate F}, was chosen until a good match between the experimental concentrations and the concentrations gener— ated from the [SB model was obtained. Stage 1 is the inlet stage and stage 2 is the outlet stage; the KC! solution was always injected into stage 2 throughout the experiments. Figures 2 and 3 present a typical match of the experimental con- centration profiles and the concentration profiles generated from the ISB model for runs without flow and with forward flow, respectively. These figures show that 1813 model successfully predicted the transient behavior of the column and can be used to determine the magnitude of interstage backmixing in oscillatory flew in a baffled column. The assumption of perfect mixing in each stage was reasonable. These figures show that uniform concentration was achieved in both stages after a short period of time. The average difference between the experimental concentrations and the concentration profiles. generated from the ISB model was less than 10% over the range of the experimental data. Zero Flow Experiment Backrnixing experiments under zero flow condition were carried out to establish a basis for comparison with experiments with forward flow. The data collected are plotted against oscillatory Reynolds number Reo in INTERSTAGE BACKMIXING IN OSCILLATORY FLOW 1645 ‘T _ Water 0.001 kg!m.s 0 Stage‘! 0.9L Do 3 cm, f 0.833 Hz, to 1.5 mm, a Stage 2 Vi 1.18 cmls, Vb 4.55 cmls _ {33 Model 0.8, —-- _ CHCO 20 " 4o 60' 30 1-00 1'20 Time{s) Figure 3. Temporal profiles of tracer concentration for both stages with forward flow. .—h M D... 3 cm. vf o llmin, 621<Ren<8858, o.5<s,_<1.5 .Water. 0.001 kglms ‘CMC. 0.006 karma .1. on .Q Backmlxing Velocity, Vb (arms) a: 0 2000 4000 6000 8000 10000 Oscillatory Reynolds Number, Rea Figure 4. Lulerstage backmixing under zero flow. 1646 M. S. TAKHIFF AND 2. MASYITHAH Da 3 cm, Wt) limin, 621<Re°<4429, 0.5<St<1.5 .Watet, 0.001 kgfms ‘CMC, 0.006 kglme Backmlxlng Valoclty,_ Vh(cm1‘s) 0 0.2 0.4 0.6 0.8 ‘l Oscillation Velocity, fo (emis) Figure 5. Effect of liquid viscosity on backmixing rate. Figure 4. This figure shows that backmixing increases linearly with oscillatory Reynolds number. The effect of liquid viscosity on back- mixing was also investigated in this part of the study. The range of liquid viscosity used in this study was 0.001 kg/m.s to 0.01 kg/ 111.5. Figure 5 plots the backmixing velocity versus oscillatory Reynolds number for liquids at different viscosity to illustrate the effects of viscosity on bac'kmixing rate. This figure shows that interstage backmixing is lower in liquids with higher viscosity. In Figure 6 backmixing velocity is plotted against the oscillation velocity or the product of the oscillation amplitude and oscillation fre» quency. This figure shows that backrnixing increased linearly with oscil— lation velocity. As the liquid oscillates back and forth, a certain amount of the liquid ba'ckmixes into the previous stage. At a constant frequency, a longer oscillation amplitude displaced the liquid to a further distance, and liquid at the interstag‘e opening is pushed further into the previous stage, resulting in a greater level of backmixing. While at a constant amplitude, eddies with greater intensity are generated from the interac- tion of the liquid and the edge of the baffle plates for a higher value of the oscillation frequency. As a result a greater amount of liquid at the interstage opening will be pushed into the previous stage and backmixing increases. Figure 6 suggests that the combination of the oscillation amplitude and frequency is the dominating factor that controls back- mixing rate. INTERSTAGE BACKMIXING IN OSCILLATORY FLOW 1647 12 no 3 cm, vf 0 "min. 2214<Reo<3858. o.5<s,<o.99 _\. D . Water, 0.001 kg!m'.s O Backmixlng Velocity, Vbtcmfsj c: 0 0.3 0.6 0.9 1.2 1.5 1.3 Oscillation Velocity, x°*f (cmls) Figure 6. Effect of oscillation amplitude and frequency on backmixing. Experiment with Forward Flow The effects of liquid flow rate on ba‘ckmixing are presented in Figure 7. This figure shows that maximum backmixing occurred under nonflow conditions. The backmixing gradually decreasod with an increase in the liquid flow rate. A similar observation was made by Xu (1994) in his backmixing study in an agitated—compartmented column. Forward flow of liquid from one stage to the next resists the tendency of the liquid from a stage to backmix into a previous one. As the flow rate increases, the resistance increases, resulting in a lower backmixing rate. Backmixing Correlation The results of this study show that backmixing rate is affected by col- umn geometry, liquid physical properties, and operating variables. Backmixing increases with increasing oscillation frequency and oscilla— tion amplitude and decreases with increasing forward flow rate and liquid viscosity. Data collected in this work are correlated with these parameters. Backmixing under zero flow condition is correlated based on the approach used by Lelli et al. (1976) and Magelli et a1. (1986). They correlated the volumetric backmixing flow rate, viscosity, and impeller 1848 M. S. TAKRIFF AND Z. MASYITHAH Water 0.001 kglm.s, Do 4 cm. 0.5<S,<0.99, 4429<Rea<8858 Liq. flow rate: .9.Vf 0 cm/s +Vf 0.4 cmls +Vf 0.93 cmls Backmixing Velocity, Vh(cmls) 0- 2000 4000 6000 8000 10000 Oscillatory Reynolds Number. Re0 Figure 7. Effect of forward flow rate on interstage backmixing. diameter as a function of impeller Reynolds number. Based on the observation made in this work, the following relation is hereby proposed: — 0: R6“ (6) This relation takes into account all the parameters that were identified. to influence backmixing as discussed in the previous paragraphs. Ni and Gough (1997) stated that the baffle geometry is also an important cri- terion that must be considered in the dimensionless parameters that characterize oscillatory flow. The variable (D / Do)'1 is added to Equation (6) to take into account the effect of baffle geometry on backmixing as follows: F59 D n ”D DC Re" (DH) (7) A backmixing parameter (Nbo) is used to represent the left-hand Side of Equation (7): Nae = —— (8) lNTERSTAGE BACKMIXING IN OSCILLATORY FLOW 1649 1 000 100 Water 0.001 kglm.s, VF 0 llmin, — — — 621<Reo<88585t9<DiD¢ <41 0 2000 4000 6000- 8.000 10000 12000 (moot-me... Figure 8. The correlation of- baclcmixing in zero flow. Figure 8 plots N'bu Versus the modified oscillatory Reynolds number. This figure shows that the N50 increases with oscillatory Reynolds number and the value of n that gives the best fit for all of the data is 0.1. The curve fit constant fOr the curve shewn in. Figure 8 is given by: N59 2 —57.364 + 0.14m: _ 6 x 10*“);2 (9) 0.1 where x = Refl (1%) The correlation fits the experimental data well and the regression value (R2) is 0.9484. Comparison between the experimental data and the values given by Equation (9) give an average error of 7% for the entire range of this experiment. A similar approach as used by (Xu, 1994) was. employed to correiate the backrnixing data. under flow condition. He suggested that the ratio of baekmixing velocity (V3,) to hackmixing velocity at zero forward flow (V50). is related to the ratio of forward flow velocity (Vf) to V50 as follows: Vf Vb Woman “0) The (a?) was plotted versus (7%) in Figure 9. This figure shows that the (a?) decreases with (1%). The correlation obtained in the column with 1650 M. S. TAKHIFF AND Z. MASYITHAH 1.0 0.8 0.6 . VbNbo 0.4 0.2 4 Water 0.001 kglms 2214<Reo<8853, 2.35<DID.,<3.13 o_o , i _ 0.0 0.2 0.4 0.6 0.8 1.0 “Who Figure 9. The correlation of ' backmixing in forward flow. forward flow is given in Figure 9. The data in Figure 9 were fitted with the following equation: Z1: 1.0—0.5202(fi) 4.015(3) (11) Van Van The regression value (R2) for the curve .fit was 0.9373, and the average error of cor-relation was less than 5% for the whole range of experi- mental data. CONCLUSIONS Backmixing is significant in oscillatory flow in a baffled column. The magnitude of backrnixing'under zero flow and continuous flow conditions is dominated by amplitude and oscillation frequency. Backmixing was found to increase linearly with an increase in any of these two variables. Backmixing rate in oScillatory flow in a baffled tube also depends on the forward flow rate. The maximum backmixing rate occurs under nonfiow condition. Backmixing. gradually decreased with an increase in the liquid flow rate. Another variable that affects backmixing rate is liquid Visc— osity. The resalt of this study shows that backmixing decreases with liquid viscosity. INTERSTAGE BACKMIXING IN OSCILLATORY FLOW 1651 ACKNOWLEDGMENTS This. research has been carried out with financial support from the Ministry of Science, Technology, and Environment of Malaysia through IRPA grant, 09-02-02-0032, which is gratefully acknowledged. NOTATION Cl KC] concentration at stage I, nunol/L C3 KC] .conCentralion at stage 2, mmol/L 1) column diameter. mm 0., opening diameter, mm f oscillation frequency, Hz Fb volumetric backmixing flow rate, coll/s F} volumetric forward flow rate, ch/s V}, backmixing velocity through the opening, cm/s V; forward liquid velocity through stage divider opening , cm/s V, volume of stage I. em3 V2 volume of stage 2, cm3 x,, oscillation amplitude (center to peak). mm xnf oscillation velocity, cm/ 5 u viscosity, [Kg/111.5 ,0 density, kg/rn3 REFERENCES Brunold, C. R., Harms, J. C. B. and Thompson, J. W. (1989). Experimental observation on flow pattern and energy losses for oscillatory flow in ducts containing sharp edges, Chem. Eng. Sci, 44, 1227—1244. Gutol'l', E. B. (I965). lnterstage mixing in an OldshueRushion liquid~liquid ex~ traction column, AIChE J., 11(4),. 712~715. Hewgill, M. R., Mackley, M. R., Pandit, A. B. and Penn, 3. S. (1993). En- hancement of gas-liquid mass transfer using oscillatory flow in baffle tubes, Chem. Eng. Sci, 48, 799—809. Howes, T. and Mackley, M. R. (1990). Experimental axial dispersion for oscil- latory flow trough a baffled tube, Chem. Eng. Sci, 45, 1349—1358. Ingham, 1., Slater, M. .l. and Re-tamales, J. 0995). Single phase axial mixing studies in pulsed sieve plate liquid»liquid extraction columns, Trans. ICIme, 72(A), 4924196. Lelli, U., Magelli, F. and Pasquali, G- (1976). Multistage mixer columns—a contribution to fluid-dynamic studies, Chem. Eng. Sell, 31, 253—256. Mackley, M. R. (1987). Using oscillatory flow to improve performance, Chem. Eng, Feb. Mackley, M. R. {1991). Process innovation using oscillatory flow within baffled tubes, Trans. IChemE, 69, 197—199. 1652 M. S. TAKHIFF AND Z. MASYITHAH Magelli, F., Fajner, D. and Pasquali, G. U936). Multistage mixer column III, Chem. Eng. Sci, 37, 141—145. Ni, X. and Gough, P. (1997). On the discussion of dimensionless groups gov- erning oscillatory flow in a baffled tube, Chem. Eng. Sci, 52, 3209—3212. Roberts, E. P. L. (1991). The simulation of chaotic advection for application to process engineering, Trans. IChemE, 69, 208+210. Takriff, M. 'S., Penney, W. R. and Fasano, J. B. (1998). Interstage backmixing of an aerated multistage mechanically-agitated, compartmented column, Can. J. Chem. Eng, ‘76, 365—369. Xu, B. C. (1994). Interstage Backmixing in Compartmenred Agitated Columns: Experbuenral Determination and Correlation, PhD. diss., University of Arkansas. ...
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