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Ind. Eng. Chem. Res. 1999, 38, 218-222
Sieve-Tray Extractor Continuous-Phase Mixing R. Bruce Eldridge* and James R. Fair The Separations Research Program, The University of Texas at Austin, Austin, Texas 78712-1062
The continuous-phase-mixing characteristics of a sieve-tray extractor were studied in a specially designed single-stage experimental apparatus. Two chemical systems were studied: toluenewater and n-butanol-water. The degree of continuous-phase axial mixing was determined for various tray geometries and phase flow rates. A predictive model was developed and combined with a point efficiency correlation to yield an overall tray efficiency. The results indicate that the level of continuous-phase mixing does not significantly affect the overall mass-transfer efficiency of an extractor sieve tray. Introduction Separations by liquid-liquid extraction are receiving increased attention because of the potential they hold for the recovery of high-value-added products. Liquidliquid extraction also permits the processing of temperature-sensitive materials, such as biomolecules, at nearambient temperature levels. Rocha et al.1 reported on a series of experiments in a 10.2-cm sieve-tray extractor and developed a masstransfer model based on their observations that the continuous phase was perfectly mixed on each tray. By analogy with gas-liquid contactor behavior, one would anticipate that as the extractor diameter is increased the cross-flowing continuous phase would depart from the perfectly mixed condition. The goal of this work was to determine whether the continuous phase is wellmixed on large-diameter extractor sieve trays and, if not, to develop a model for partial mixing. In this paper a predictive mixing model will be presented which when combined with a mass-transfer model2 can provide a rational method for larger-scale sieve-tray-extractor design. The measurement of continuous-phase mixing on sieve trays has not been reported previously. Angelo and Lightfoot3 considered liquid-liquid system mixing in such a geometry but limited their work to the completely mixed condition. For other types of extractors there has been a significant amount of investigation into mixing behavior, for example, the work of Miyauchi and Vermeulen4 on packed extractors. Preliminary results for sieve-tray mixing have been previously reported by the present authors.5 Background Efficiency Correction Factors. The stagewise masstransfer process for a cross-flow sieve tray can be expressed in terms of the Murphree tray efficiency:
Yn - Yn-1 Emd ) Yn* - Yn-1
(1)
where the Y values refer to the solute mole fraction in the dispersed phase and the Y* term refers to an * To whom correspondence is addressed. Telephone: 512471-7067. Fax: 512-471-1720. E-mail:
[email protected].
Figure 1. Schematic diagram of a single-pass crossflow sieve tray (light phase dispersed).
equilibrium concentration with respect to the continuous phase leaving the tray:
Yn* ) mdc(Xn)
(2)
The extraction efficiency at a point on the tray (Figure 1) is a function of the underlying mass-transfer mechanism. Seibert et al.2 have developed a fundamental model for local extraction efficiency as a function of various operating and physical parameters. Depending on the level of mixing, the value of the Murphree tray efficiency will be equal to or greater than the local efficiency Epd. For a nonperfectly mixed continuous phase, the point efficiency will vary with the location on the tray. For the case of a perfectly mixed continuous phase, Emd ) Epd. For the case of plug flow of the continuous-phase, zero mixing, the efficiency relationship is given by
Emd )
exp(Epdλ) - 1 λ
(3)
For cases that are intermediate between complete mixing and plug flow, a measurement of the departure from ideal flow is necessary. The following approach is based on a direct analogy between the mixing behavior of sieve trays in gas-liquid and in liquid-liquid service. The mixing stage, or mixing pool, model of Gautreaux and O’Connell6 when related to extraction can represent
10.1021/ie980542d CCC: $18.00 © 1999 American Chemical Society Published on Web 12/03/1998
Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 219
Figure 2. Flow diagram of the experimental apparatus.
intermediate cases between complete mixing and plug flow:
Emd )
(1 + λEpd/S)S - 1 λEpd
(4)
where S ) number of perfectly mixed stages on the tray. For plug flow, S ) ∞; for complete mixing, S ) 1. Residence Time Distribution. The residence time distribution (RTD) curve is used extensively to quantify the level of mixing in chemical reactors and masstransfer devices. The curve is typically obtained by using tracer injection techniques. Once obtained, the RTD can be analyzed to determine the extent to which the vessel mixing departs from a plug-flow mixing pattern. The reader is referred to the text of Levenspiel7 for a more detailed discussion of RTD theory. For closed boundary conditions (plug flow into and out of the vessel), the variance of the RTD can be related to the number of perfectly mixed stages in the vessel by
σv2 ) tm2/S
(5)
where S ) number of perfectly mixed stages, tm ) mean residence time of tracer in vessel, and σv2 ) variance of RTD. Thus, if the variance and the mean residence time of the RTD are known, the number of perfectly mixed stages can be readily obtained. Experimental Equipment and Procedure A flow diagram of the experimental unit is shown in Figure 2. Detailed dimensions of the test tray are given in Table 1. The tray cross section (Figure 3) was designed to simulate a slice of a large-diameter commercial extractor. The front and back panels of the extractor were constructed of glass and allowed good visibility of the continuous- and dispersed-phase contacting. The equipment allowed a variety of tray spacings, downcomer dimensions, phase flow rates, and chemical systems to be tested. For the observation and measurement of mixing effects, a pulse dye injection technique was used. Water-
Table 1. Test Tray Dimensions hole diameter (mm) pitch-diameter ratio downcomer area (m2) length of flow path (m) active area (m2) hole area (m2) tray spacing (m) tray width (m)
3.18 2.6 0.0023 0.495 0.0566 0.0057 0.152 or 0.305 0.152
soluble dye was injected into the inlet downcomer with a hypodermic syringe. The dye entered the test tray through the inlet downcomer and was agitated by the dispersed phase. A representative sample of the effluent was passed through a Beckman model 21 MV spectrophotometer. This allowed the variation of dye concentration in the tray effluent to be determined as a function of time. A typical plot obtained from the spectrophotometer is shown in Figure 4. Averaged (Sauter mean) drop sizes were determined by digital analysis of a photograph of a 8 in. × 10 in. zone in the center of the test tray. The mixing pattern was recorded on videotape. The concentration versus time plots, expressed in dimensionless form, yielded the RTD of the dye on the test tray. The variance and mean residence time of the RTD were determined by curve-fitting the concentration profile and were combined through eq 5 to yield the number of perfectly mixed stages on the test tray. The two test systems were toluene-water and n-butanol-water. Properties of these systems are given in Table 2. Toluene-water, with its relatively high interfacial tension, led to larger drops, and n-butanol-water, a low interfacial tension system, produced small drops. Interfacial tensions reported are based on experimental measurements of the two test systems in the absence of solute or dye. The impact of the dye on the interfacial tension was not considered to be significant. Experimental Results Quantitative Results. During the course of the experimentation it was observed that at low dispersedphase superficial velocities a large percentage of the tray holes did not function. The holes passing the dispersed
220 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999
Figure 3. Diagram of the test tray.
Figure 4. Residence time plot. Table 2. Properties of Test Systems (25 °C) density (kg/m3)
interfacial tension (mN/m)
viscosity (mPa s)
system
Fc
Fd
σpure
σexp
µc
µd
toluene-water n-butanol-water
1000 1000
870 865
35.0 2.0
30.0 1.8
1.1 1.1
0.55 2.60
Figure 5. Fraction holes operating versus hole Weber number.
phase were randomly distributed on the tray. The tray was level, and no physical difference in the tray perforations could be observed. The percentage of holes operating was estimated by visual inspection; results are presented in Figure 5, with the percentage of holes operating plotted versus the hole Weber number:
We ) doVo2Fd/σ
(6)
The scatter of the values is to be expected, since multiple observers estimated the number of holes operating, and a group average was determined. The need for NWe g 2 to have all holes active coincides with the finding by Rocha et al.1 that NWe g 2 is necessary for hole jetting operation. This conclusion is also supported by the results of Kumar and Hartland.8 While this Weber number criterion is useful for good design, it does not appear to have an influence on the number of mixing stages. For a constant dispersed-phase flow rate, a reduction in active holes does not materially reduce the population of drops above the tray.
Figure 6. Number of mixing stages for a 30.4-cm tray spacing.
The mixing results of the two systems, for a 30.4-cm tray spacing, are presented in Figure 6. For toluenewater, the number of stages on the test tray approached 1 as the continuous-dispersed velocity ratio approached zero. For n-butanol-water, the continuous phase was totally mixed at all velocity ratios. Tabulation of all run data may be found elsewhere.9 The large scatter ob-
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served in the toluene-water data is typical of mixing experiments which are, by nature, inherently random. Qualitative Results. The n-butanol-water system exhibited large eddy patterns in the continuous phase at all velocity ratios. Because of the low interfacial tension, there was a high density of small drops, giving the tray a foglike appearance. The dye was vigorously agitated as it exited the inlet downcomer. These observations are in agreement with the quantitative results, which indicated that the tray was perfectly mixed. This conforms to the analogy of mixing in bubble columns by high-density gas bubbles. For the toluene-water system, high dispersed-phase rates together with a 30.5-cm tray spacing gave a behavior similar to that of the n-butanol-water system. When the tray spacing was reduced to 15.2 cm, the eddy patterns were much less pronounced. The dye front appeared to travel directly across the tray with a minimum amount of circulation. This behavior was reflected in the larger number of perfectly mixed stages obtained for the lower tray spacing. Model Development and Application Ideally, the degree of mixing should be directly related to the momentum transfer between the drops and the continuous phase. Multiple attempts to produce a rigorous correlation failed to yield a satisfactory agreement with the experimental data. Hopefully, at some point in the future, computational fluid dynamics (CFD) will be able to fully describe the mixing process. Until that time, mixing phenomena will continue to be modeled using an empirical or semiempirical approach. These approaches effectively “smooth out” the inherent randomness of the drop interaction with the continuous phase. The predictive model outlined below produces a satisfactory fit to the data over a range of operating conditions typically found in a commercial extractor. However, as in the case of all empirical models, the model’s accuracy extrapolated to a wider set of operating conditions is unproved. The impact of mass transfer on the mixing process was not addressed by the model. Predictive Model. On the basis of visual observations as well as quantitative results, there appears to be a drop population limit, above which the mixing characteristics of the continuous phase do not change. This limit is influenced by the tray spacing/flow pathlength ratio. The number of perfectly mixed stages per meter of tray length was correlated by three parameters: the height from the tray deck to the coalesced layer (Ht), the tray flow path length (L), and the drop population per volume of tray (Nd). As might be anticipated, the drop population and geometric parameters can be arranged to produce a “perfectly” mixed cell on the tray. Equation 7 presents the mixing index n˜ mix. When the mixing index approaches an upper limit of 220 000 drops/m3, two perfectly mixed stages per meter of path length are obtained (for the present study, with the 0.5-m tray length the tray was completely mixed). The drop population can be readily calculated for drop size and holdup predictions found in extractor masstransfer models.2
n˜ mix ) (Ht/L)(Nd)
(7)
One would expect S to be inversely proportional to tray spacing and directly proportional to the flow path length. Although the path length was not varied in the
Figure 7. Parity plot (30.4- and 15.2-cm tray spacing). Table 3. Case Studies for Point Efficiency Enhancementa TAW case 1
case 2
BSW case 3
case 4
interfacial tension 28 28 1.7 1.7 (mN/m)b flow path length (m) 3.0 3.0 3.0 3.0 hole diameter (mm) 6.4 6.4 6.4 6.4 tray spacing (m) 0.61 0.305 0.61 0.305 drop rise distance (m) 0.56 0.254 0.56 0.254 hole velocity (Vo) (m/s) 0.10 0.10 0.04 0.04 cont. phase velocity 0.03 0.07 0.02 0.05 (Vc) (m/s) drop diameter 8.0 8.0 3.0 3.0 (Sauter) (mm) hole Weber number 3.0 3.0 3.0 3.0 drops/m3 (103) 248 248 4720 4720 extraction factor, λ 1.0 1.0 1.0 1.0 mixing stages/m 6.63 24.2 2.0 2.0 mixing stages 20.0 73.0 6.0 6.0 Epdc 0.143 0.075 0.297 0.195 Emd/Epd (eq 4) 1.07 1.04 1.13 1.13 Emd 0.153 0.078 0.336 0.220 a TAW ) toluene-acetone-water. BSW ) n-butanol-succinic acid-water. All studies were performed at 25 °C with an initial dispersed-phase concentration of 5.0 wt % solute. The masstransfer direction is dispersed to continuous. b Measured value. c E pd was calculated by the method of Seibert et al. (1993). The mass-transfer direction is from the dispersed phase to the continuous phase.
present study, it was retained as a variable based on the analogous behavior of distillation trays.6 The developed model was fitted to the data for n˜ mix values less than 220 000 drops/m3 using a nonlinear curve fit algorithm. The final relationship is
S ) 2L + 0.90(Vc/Vo)0.66L2.5Ht-1.5
(8)
where S ) number of mixing stages, L ) path length (m), Vc ) cross-flow velocity of the continuous phase, based on the area available for flow [an interstitial velocity which takes into account the distance from the tray deck to the coalesced layer, an average tray width, and the area occupied by the cross section of the drops (m/s)], Vo ) linear velocity of the dispersed phase through the holes, based on complete hole activity (m/ s), Ht ) distance from the tray to the coalesced layer of the next tray (m). A parity plot for the model is presented in Figure 7. The model appears to make the transition from low levels of mixing to high levels of mixing fairly well, with 85% of the points falling within 30% error. The degree
222 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999
of scatter is an indication of the inherently random nature of the mixing process. Model Application. With eqs 4 and 8 providing for mixing effects and the Seibert et al. model providing local efficiency data, four example design cases were chosen for analysis. The cases as well as the tabulated results are given in Table 3. Cases 1 and 2 deal with the toluene-acetic acid-water system with different phase flow ratios and tray spacings. Cases 3 and 4 deal with the n-butanol-succinic acid-water system, also at different phase flow ratios and tray spacings. For all cases enhancement of the local efficiency was minimal. For example, even with an estimated 20 stages, case 1 gave only a 7% enhancement of point efficiency because of the inherently low point efficiency of the toluene-acetic acid-water system. Systems with low interfacial tensions produce high densities of small drops, thereby providing relatively high local efficiencies and also high levels of backmixing. Conversely, the high interfacial tension systems are characterized by lower local efficiencies and lower degrees of backmixing. In either the high or low interfacial tension case, the enhancement of the point efficiency is low.
Emd ) Murphree dispersed-phase tray efficiency, fractional Epd ) point dispersed-phase efficiency, fractional Fc ) continuous-phase molar flow rate Fd ) dispersed-phase molar flow rate Ht ) distance from the tray to the coalesced layer above, m L ) tray flow path length, m mdc ) slope of the equilibrium curve Nd ) number of drops per cubic meter Qc ) volumetric flow rate of the continuous phase, m3/s S ) number of perfectly mixed stages on the tray tm ) mean residence time of the tracer on the tray, s Vc ) cross-flow velocity of the continuous phase, based on the area available for flow, m/s ()Qc/Htdavg) Vd ) dispersed-phase velocity based on the tray active area, m/s Vo ) hole velocity of the dispersed phase, based on the total tray hole area, m/s X ) mole fraction of solute in the continuous phase Y ) mole fraction of solute in the dispersed phase Y* ) mole fraction of solute in the dispersed phase, in equilibrium with the continuous-phase ) mole fraction X
Summary and Conclusions
Greek Letters λ ) extraction factor, mdcFd/Fc σv2 ) variance of RTD σ ) interfacial tension, dyn/cm n˜ mix ) mixing index defined by eq 7, drops/m3
An experimental study has been made of the mixing of the continuous phase flowing across a sieve-tray extractor. A predictive algorithm has been developed based on the experimental data. Results obtained from this study indicate that the level of continuous-phase mixing does not impact significantly the overall tray efficiency. Transfer mechanisms that promote high mass transfer also promote high momentum transfer and a high level of continuous-phase mixing. The low local mass-transfer efficiencies for the high interfacial tension system counteract any enhancement gained by the low level of mixing. For the low interfacial tension system, the high level of mixing provides a limited enhancement to the local efficiency. It would appear prudent for tray designers to use the local efficiency as equal to tray efficiency; this would yield a conservative extractor design. As CFD methods become more robust, more rigorous modeling approaches will be possible. Ideally, the momentum transfer from the drop surface to the continuous phase should be rigorously modeled to produce a model based on a rigorous treatment of the system physics. Also, higher level data acquisition techniques, such as continuous monitoring of an operating extractor by X-ray tomography, will yield significantly better mixing data. This combination, along with an enhanced understanding of the mass-transfer phenomena on a tray, will eliminate the uncertainty in sieve-tray-extractor design. Acknowledgment This research was supported by the sponsors of the Separations Research Program at The University of Texas at Austin. Nomenclature ACF ) average cross-flow area for the continuous phase, m2 ()Htdavg) davg ) average diameter of the column, m
Subscripts c ) continuous phase d ) dispersed phase n ) tray n n - 1 ) tray n - 1 (below tray n)
Literature Cited (1) Rocha, J. A.; Humphrey, J. L.; Fair, J. R. Mass Transfer Efficiency of Sieve Tray Extractors Ind. Eng. Chem. Proc. Des. Dev. 1986, 25, 862-871. (2) Seibert, A. F.; Fair, J. R. Mass-Transfer Efficiency of a Large-Scale Sieve Tray Extractor Ind. Eng. Chem. Res. 1993, 32, 2213-2219. (3) Angelo, J. B.; Lightfoot, E. N. Mass Transfer Across Mobile Interfaces AIChE J. 1968, 14, 531-540. (4) Miyauchi, T.; Vermeulen, T. Longitudinal Dispersion in Two-Phase Continuous-Flow Operations Ind. Eng. Chem. Fundam. 1963, 2, 113-126. (5) Eldridge, R. B.; Fair, J. R. Continuous Phase Mixing on Crossflow Extraction Sieve Trays Sep. Sci. Technol. 1987, 22, 1121-1134. (6) Gautreaux, M. F.; O’Connell, H. E. Effect of Length of Liquid Path on Plate Efficiency. Chem. Eng. Prog. 1955, 51, 232-237. (7) Levenspiel, O. Chemical Reaction Engineering, 2nd ed.; John Wiley: New York, 1972. (8) Kumar, A.; Hartland, S. Prediction of drop size produced by multi-orifice distributor. Trans. Inst. Chem. Eng. 1982, 50, 3539. (9) Eldridge, R. B. Mixing Characteristics of a Crossflow Sieve Tray Extractor. Ph.D. Dissertation, The University of Texas at Austin, Austin, TX, Aug 1986.
Received for review August 13, 1998 Revised manuscript received October 13, 1998 Accepted October 13, 1998 IE980542D
