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Mass transfer in a confined plunging liquid jet bubble column
Chemical Engineering Science 54 (1999) 4981}4990
Mass transfer in a con"ned plunging liquid jet bubble column G. M. Evans *, P. M. Machniewski Department of Chemical Engineering, University of Newcastle, NSW 2308, Australia Department of Chemical and Process Engineering, Warsaw University of Technology, PL-00-645 Warsaw, Poland
Abstract A model of con"ned plunging liquid jet bubble column absorber is formulated and utilized for the interpretation of the experimental data obtained during steady-state absorption of concentrated gaseous CO in water. A strong variability of molar #ux of the gas phase in the contactor was observed and taken into account. Two zones di!ering in mass transfer and mixing characteristics are distinguished within the contactor. Volumetric mass transfer coe$cient in the mixing zone beneath the impingement point, is an order of magnitude greater than in pipe #ow zone and determines the overall performance of the contactor. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Plunging liquid jet; Down#ow bubble column; Mass transfer coe$cient
1. Introduction Con"ned Plunging Liquid Jet systems (CPLJ) have the ability to generate high values of interfacial area per unit volume (Evans, 1990; Evans, Jameson & Atkinson, 1992; Ohkawa, Kawai, Kusabiraki, Sakai & Endoh, 1987; Mao, Evans & Jameson, 1993; BinH , 1993) and o!er an e!ective method for gas}liquid contacting especially for cases when the gaseous component is consumed by a fast reaction in the liquid phase. A schematic of a CPLJ contactor is shown in Fig. 1. A liquid jet ejected from a nozzle plunges into the free surface of the gas}liquid mixture and entrains gas from the headspace. A turbulent region can be distinguished beneath the impingement point where the submerged two-phase jet expands and "nally attaches to the column wall. The region will be called here as the mixing zone. In this zone, the entrained gas is broken into "ne bubbles (sizes in the order of 200 lm were measured by Evans et al. (1992)). A fraction of the entrained gas is recirculated back into the headspace as some bubbles escape from the mixing zone through the free surface. Below the mixing * Corresponding author. Tel.: #61-24921-6180; fax: #61-249216920. This work was carried out during the visit of the second author at The University of Newcastle, Australia. E-mail address: [email protected] (G. M. Evans)
zone, the turbulence level is signi"cantly lower and the #owing liquid steadily transports bubbles down. This region of the contactor will be called here as the pipe #ow zone. When the coalescence of bubbles is not retarded, the coalescence } break-up equilibrium results in bubble sizes signi"cantly higher, in this zone, than that in the mixing zone. In such a case, the bubble sizes are typical of bubbles in ordinary (up-#ow) bubble columns with "ne pore di!users (3}4 mm in tap water). Since CPLJ contactors have been successfully applied for a number of years as #otation units in mineral processing industries (Jameson cell), hydrodynamic properties of these contactors were studied by many authors. Ohkawa, Shiokawa, Sakai and Endoh (1985a), Ohkawa, Shiokawa, Sakai and Imari (1985b), Yamagiwa (1990) and Evans (1990). In gas}water systems, where the coalescence of bubbles is inhibited by the addition of a surfactant the value of gas hold-up as high as 70% is reported (Evans, Jameson & Rielly, 1995). Only a small number of publications are available regarding mass transfer in such contactors. The system similar to that investigated in this work was used by Ohkawa et al. (1987). The authors did not distinguish between the zones of di!erent mass transfer and mixing characteristics in their column. The measured k a values were averaged over the whole two-phase mix* ture volume and were based on the assumption of plug #ow throughout the whole contactor.
0009-2509/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 2 2 1 - 3
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2. Experimental
Fig. 1 . The schematic of the con"ned plunging liquid jet reactor.
Mao et al. (1993) in a similar system (D "51 mm, ! D "5.86 mm, ¸"1.35 m), measured dissolved oxygen , concentration pro"les along the column axis during a steady-state physical absorption of oxygen in water. The authors found that the plug #ow assumption was justi"ed within the pipe #ow region only and assumed the mixing zone as being perfectly mixed. Most of the existing publications dealing with mass transfer in a down#ow loop reactor with self gas-inducing venturi ejector, report average values of k a for the * whole gas}liquid volume in a reactor (ejector#vessel) (Van Dierendonck & Lentritz 1988; Dutta & Raghavan, 1987). Only a few authors investigated mass transfer in gas}liquid ejectors alone (Dirix & van der Wiele 1990; Cramers, Beenackers & van Dierendonck, 1992) and even fewer distinguished the two di!erent zones of the ejector, di!ering in turbulence intensity and mass transfer characteristics (Cramers, Smit, Lenteritz, van Dierendonck & Beenackers, 1993). The results of experimental determination of k a in the * mixing and pipe-#ow zones of a CPLJ bubble column absorber will be presented here. The measurements were performed during a steady-state physical absorption of pure CO in tap water and were accompanied by a con siderable decrease in the gas super"cial velocity due to a high absorption degree, which in#uenced the hydrodynamics of the contactor.
The experimental set-up is shown on Fig. 2. The absorption was carried out in a vertical Perspex column of 51 mm ID, 1.36 m long. Tap water from the bu!er tank supplied the column through 4.7 mm ID nozzle mounted at the top of the column (the nozzle's cylindrical section length was 50 mm). Carbon dioxide of 99.7% purity was fed from a pressurized cylinder. At the beginning of each run the desired gas and liquid #ow rates were set and the peristaltic circulation pump supplying fresh, bubble-free liquid to the sampling point, was turned on. After 2}3 min, when a steady state had been achieved, several liquid samples were collected at various positions of the sampling probe along the PF-zone, starting from the visible `boundarya between the MIX and PF zones, down to the column base. The mixing zone was regarded as a section extending from the free surface of the gas}liquid mixture to the point where the down#ow movement of the mixture is observed to be more or less steady. During each run, the liquid samples (20 ml) collected with a syringe from the sampling point were immediately transferred to 100 ml #asks containing 25 ml 0.1 M NaOH solution and stoppered. After each run concentration of dissolved CO was determined by Winkler type method (i.e. carbonate ions were precipitated by addition of 10 ml 10% BaCl solution and the excess of NaOH was titrated with 0.1 M HCl to phenolophtaleine endpoint). The average gas hold-up in the column was calculated using the headspace pressure from the equation (Eq. (1)) derived from the overall momentum balance around the contactor.
1 4u 1!e " e # e # * . % 2 * * g¸
(1)
In the above formula, e refers to the liquid hold-up * calculated with the assumption of negligible momentum of liquid #owing through the pipe #ow zone (Mao, Ahmed & Jameson, 1991): u u p !p &1.!! , * (2) e " * g¸ go ¸ * Apart from the average gas hold-up, also the hold-up in the pipe #ow zone was measured by means of a manometer attached to the column wall 0.5 m above the free surface of the liquid in the receiver tank (Fig. 2). h #h e " % .$ 0.5 m
(3)
The values of e and e were approximately equal for % % .$ most of the runs and were consistent with the observations of Herbrechtsmeier and Steiner (1978) and Ohkawa et al. (1985a). In the experiments u was varied within , 10}23 m/s and u within 0.06}0.37 m/s. %
G. M. Evans, P. M. Machniewski / Chemical Engineering Science 54 (1999) 4981}4990
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Fig. 2 . Experimental set-up.
3. Mass transfer model A theoretical model has been developed in order to determine the rate of absorption of CO into a liquid phase in a con"ned plunging jet contactor. The model is also used here to determine the volumetric mass transfer coe$cient based on the measured concentration pro"les. The model is based on the de"nition of di!erent hydrodynamic zones, which exist within the CPLJ as illustrated in Fig. 3. Re#ecting the division of the contactor the model is divided into three parts: free jet zone, mixing zone and pipe-#ow zone. The assumptions for each of these zones are: 1. Mass transfer rate to the free liquid jet and to the free surface of the froth is negligible. 2. In the mixing zone, the phases are perfectly mixed and gas is uniformly dispersed in liquid with an average gas void fraction. 3. In the pipe-#ow zone both phases move in a plug #ow manner and gas void fraction is uniform throughout the zone. Additionally, for the interpretation of the experimental concentration pro"les in the CPLJ- bubble column it is
assumed that the desorption (absorption) of inert species from (to) water is negligible. The assumption of perfectly mixed gas and liquid phases in the mixing zone is an approximation of a complex system involving distributions of gas void fraction and interfacial surface area in the upper part of the mixing zone. Given the amount of recirculation created by the jet (Bayly, Rielly, Evans & Hazell, 1992) it seems reasonable to assume, as a "rst approximation, that the concentration gradients are instantaneously removed within the mixing zone. This assumption will be discussed later in the paper. By the de"nition of the mixing zone as one unit, an average volumetric mass transfer coe$cient is assumed to be valid within the whole mixing zone volume. A schematic of the mass transfer model is illustrated in Fig. 3. It shows the various #ows of the gas and liquid phases between the hydrodynamic zones. A gas stream of molar #ow rate, n , and CO concentration, y , enters % the headspace where it is mixed with a gas #ow of, n , and 0 CO concentration, y , which is recirculated from the +'6 mixing zone. The plunging jet entrains, n , amount of gas # from the headspace into the mixing zone where the carbon dioxide is absorbed by the liquid phase. The gas #ow n , and CO concentration, y , passes into the % +'6
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Combining Eqs. (4) and (5), we get Q (c !c ) . (k a) " * +'6 (6) * +'6 < (cH !c ) +'6 +'6 +'6 The average equilibrium liquid CO concentration in the mixing zone cH , is given by the Henry's law equation: +'6 cH "Hy p (7) +'6 +'6 +'6 where p is the average total pressure in the mixing +'6 zone. The Henry's law constant for the system CO }water, was calculated here according to the formula given by Danckwerts and Sharma (1966) and y was +'6 determined from the gas phase CO mass balance: y !a n% !n% +'6. (8) 2 +'6 where a y " " +'6 2 +'6 1!a n 2 +'6 % In the above expression, a is the gas absorption degree, 2 which can also be calculated based on the measured liquid-phase concentration of the dissolved CO : Q (c !c ) . a " * +'6 (9) 2 +'6 n % 3.2. Mass transfer in the pipe-yow zone Based on the assumption of plug #ow in the pipe-#ow zone, the mass balance around a layer of in"nitesimal height (Fig. 3) can be presented as the following system of equations: Total gas phase balance: Fig. 3 . The model of the con"ned plunging liquid jet reactor.
pipe-#ow zone where further carbon dioxide is absorbed into the liquid phase. Eventually, a #ow n , of gas with % CO concentration, y , exits the pipe #ow zone. For the liquid phase, a constant #ow, Q passes * through the reactor. The inlet concentration of dissolved carbon dioxide is c , which increases to c , as gas is +'6 absorbed in the mixing zone, and eventually to c at the end of the pipe #ow zone. 3.1. Mass transfer in the mixing zone The value of the average volumetric mass transfer coe$cient in the mixing zone can be determined based on the CO balance in the liquid phase: Q (c !c )#(Na) < "0. (4) * +'6 +'6 +'6 For negligible gas phase resistance and perfect mixing of the phases, the interphase transfer rate of CO , (Na) +'6 can be expressed as (Na) "(k a) (cH !c ). +'6 * +'6 +'6 +'6
(5)
dN %#Na"0, dx
CO balance in the gas phase: d(N y) % #Na"0, dx CO balance in the liquid phase: dc u !Na"0. * dx
(10)
(11)
(12)
In the above equations, Na is the `locala interfacial mass transfer rate at the level x, averaged over the column crossection. Assuming that pipe-#ow zone is uniform throughout its whole length, Na is given by the following expression: Na"(k a) (Hyp!c) (13) * .$ Eqs. (10)}(12) were simultaneously numerically integrated within the range x"¸ P¸, with the following +'6 initial conditions: at x"¸
N "N , y"y , c"c . (14) +'6 % % +'6 +'6 +'6 The value of (k a) was determined by "tting the pro"le * .$ c(x), resultant from the integration, to the experimental
G. M. Evans, P. M. Machniewski / Chemical Engineering Science 54 (1999) 4981}4990
data using nonlinear regression procedure. The local pressure p in Eq. (13) was calculated, based on the measured gas holdup values, according to p"p !e o (¸!x). * *
(15)
4. Results and discussion 4.1. Concentration proxles in the column Sample concentration pro"les of CO in gas and liquid phases calculated from the "tted model, are shown in the Fig. 4. The deviations from the `plug-#owa model line may indicate some degree of backmixing in the pipe-#ow zone as well as non-uniformity of the two-phase mixture in the pipe #ow zone (i.e. variability of k a along the * pipe-#ow zone). The "gure also shows a local saturation degree of the liquid phase de"ned as LSAT"
c c " . cH Hyp
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4.2. Mass transfer in the mixing zone The measured values of k a for di!erent gas and * +'6 liquid #ow rates are shown in Fig. 6. The results were correlated in a form typical for venturi injectors and gassed stirred tanks as a function of energy dissipated in the mixing zone and gas-feeding rate: (k a) "0.467e u . (17) * +'6 % Energy dissipation rate per unit volume was estimated here based on the relationship developed originally for gas}liquid ejector pumps by Cunningham (1974) and adopted to CPLJ contactors by Evans et al. (1992). o u e " * , [b!2b!b(1#j)#2b(1#j)] 2¸ +'6 F Q where b" , and j" % . F Q ! *
(18)
(16)
At lower feed gas #ow rates (Q /Q (0.8) relatively % * high solubility of CO in water and high values of the volumetric mass transfer coe$cient in the apparatus caused signi"cant consumption (absorption) degree of the gas phase and drop in gas phase CO mole fraction and molar gas #ow rate in the pipe #ow zone (although the whole column was always "lled with bubbles). This phenomenon exhibited itself as a #at concentration pro"le caused by local saturation of the liquid with respect to the gas phase. The e!ect is illustrated on Fig. 5, where the calculated pro"les were very little sensitive to changes in k a value. These e!ects restricted experimental deter* .$ mination of k a for a particular liquid #ow rate, to the * range of gas #ow rates greater than a certain minimum value (Q /Q '0.8). % *
Fig. 4 . CO concentration pro"le in the liquid phase and its saturation degree.
Fig. 5 . Liquid concentration and degree of saturation pro"les when Q /Q (0.8. % *
Fig. 6 . Dependence of the mixing zone volumetric mass transfer coe$cient on gas feed and liquid #ow rates.
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It can be concluded from Eq. (17) that the dependence of k a on energy dissipation rate per unit volume in the * +'6 system investigated here (k a J(e ) ) is weaker * +'6 than, e.g. in ejectors where k aJ(e ) as reported * by the authors cited earlier. In most of these reported cases, the measurements were performed with the aqueous electrolyte solutions used as liquid phase. On the contrary to CO }water system, the coalescence of bubbles is less supported in such systems and the power input is more e!ectively used for the generation of interfacial area. Van't Riet (1979) proposed relationships for the estimation of the volumetric mass transfer coe$cient in gassed stirred vessels, from which it follows that k aJ(e ) for an air}water system and k aJ(e ) * * for solutions where coalescence of bubbles is inhibited. Since u refers to the net gas uptake rate, which is % equal to the di!erence between the gas entrainment rate by the plunging jet and the rate gas escapes from the mixing zone through the free surface, it seems more appropriate to correlate k a either with the actual gas * +'6 entrainment rate u , i.e. the rate gas phase is introduced # into the mixing zone or with the parameters like u and , ¸ , which directly a!ect gas entrainment rate (BinH , 1993; H Evans et al., 1996) and the average energy dissipation rate in the mixing zone. Thus, experimental values of (k a) were also regressed here as a function of nozzle * +'6 velocity and free jet length (see Fig. 7) in the form of the following equation: (k a) "1.175;10\u ¸ . (19) * +'6 , H Statistically, Eq. (19) "ts experimental data better than Eq. (17). The error either of the equations is less than 15%. It is also interesting to note that the dependence of k a on u in Eq. (19) (k aJu ) is in close agreement * +'6 , * , with the results of Dirix & van der Wiele (1990), who measured oxygen desorption rate in the down#ow venturi liquid jet ejector and found that k a in the ejector * (working in the `bubbling regimea) was proportional to Re . , A comparison of the k a values obtained here with * +'6 the results, calculated from the oxygen concentration pro"les obtained by Mao et al. (1993) is also shown in Fig. 7. 4.3. Mass transfer in the pipe-yow zone The volumetric mass transfer coe$cient in the pipe#ow zone, calculated based on the CO concentration pro"le, for each of the examined liquid super"cial velocities and gas uptake rates at the inlet, is shown in Fig. 8. Interpretation of the results on the basis of u is com% plicated by a signi"cant variation of the actual gas velocity within the column caused by the high degree of CO absorption. This explains, why the curves in Fig. 8 can be extrapolated to zero k a values for the non-zero values * .$ of u . %
Fig. 7 . Relation between the volumetric mass transfer coe$cient in the mixing zone and the free jet length.
Fig. 8 . Volumetric mass transfer coe$cient in the pipe #ow zone vs. net gas uptake rate (at the gas inlet).
A di!erent picture (Fig. 9) is revealed when k a is * .$ related to the actual super"cial velocity of the gas entering the pipe-#ow zone (through the MIX/PF boundary). u is calculated by subtracting the amount of gas % +'6 .$ phase absorbed in the mixing zone from u . It can be % observed that the in#uence of the liquid velocity on k a * .$ has almost disappeared and most of the experimental points corresponding to the various liquid #ow rates lay on the same curve. A change in the slope of the functional dependence of k a on u is caused by the de* .$ % +'6 .$ stabilization of the homogeneous, bubbly #ow regime and the development of heterogeneous (or churn-turbulent), and slug #ow regimes at the higher gas #ow rates. The value of u
5 cm/s (Fig. 9) corresponding to % +'6 .$ this transition, is very close to the analogous value in a conventional, up#ow bubble column with a porous gas sparger (4}5 cm/s in air}tap water system, according to Deckwer, 1992).
G. M. Evans, P. M. Machniewski / Chemical Engineering Science 54 (1999) 4981}4990
Fig. 9 . Dependence of the volumetric mass transfer coe$cient in the pipe #ow zone on the actual average velocity of the gas entering this zone.
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Fig. 10 . Average volumetric mass transfer coe$cient for the whole column (solid symbols) and the contribution of the mixing and pipe #ow zones in the values of the coe$cient (open symbols).
The points calculated from Mao's et al. (1993) data (oxygen}water system) are also shown in Fig. 9 and are in fair agreement with the k a values obtained in this * .$ work. The volumetric mass transfer coe$cient averaged over the whole two-phase mixture volume, in the CPLJ bubble column, was calculated according to Eq. (20) and is shown on Fig. 10: ¸ k a #¸ k a .$ * .$. k a " +'6 * +'6 * ¸ #¸ +'6 .$
(20)
The contributions of the two zones in the contactor, in terms of value of this coe$cient are also compared in this chart. It is evident that the contribution of the mixing zone is much more important than that of the pipe-#ow zone, and that it is the mixing zone that mainly determines the performance of the whole contactor. 4.4. Modixcation of the mixing zone model In order to verify the assumption of ideal mixing in the mixing zone the dissolved CO concentration pro"le along the column wall has been measured during the last two runs. The measured pro"les reveal that the treatment of the mixing zone as one, uniform, ideally mixed region is rather rough approximation. The measured pro"les are shown in the Fig. 11. A considerable variation in the liquid concentration pro"le at the wall can be observed, with a minimum situated in the distance of 3.6D from ! the free surface. The minimum most probably corresponds to the reattachment of the submerged expanding jet to the column wall. The distance of 3.6D is in agree! ment with the jest reattachment length (3.5D ) measured ! by Bayly et al. (1992) in a similar geometry and #ow of water containing neutrally buoyant spherical particles of
Fig. 11 . Axial pro"les of dissolved CO concentration at the column wall in the mixing and pipe #ow zones.
0.5}1 mm diameter. The authors found that ¸ /D is 0# ! approximately constant over the wide range of jet to column diameter ratio and jet Reynolds number. As a result of CFD simulation of a con"ned single phase jet the authors obtained ¸ /D +3 which was also 0# ! independent of jet to column diameter ratio and jet Reynolds number. The location of the minimum concentration (anticipated as the mean jet reattachment point) is closer to the free surface than ¸ estimated based on visual observa+'6 tions of the turbulent movements of the two-phase mixture, which apparently extend further down than the mean location of the jet reattachment point. The expanding con"ned jet is unstable in the region of its reattachment to the pipe wall. It #apps from one side of the pipe to the other (Coanda e!ect) causing continuous oscillation of the reattachment location.
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In order to explain the measured wall concentration pro"les, a modi"cation to the previous simple model of the mixing zone had to be introduced. The mixing zone is now subdivided into three di!erent regions shown schematically in Fig. 12. Region (1) is the expanding submerged two-phase jet that entrains #uid from region (2) * the ring surrounding it and discharges into region (3). It is suggested here that the length of the region (1) is determined by the location of the recirculation centre. CFD simulations of single-phase #ow through sudden expansions (Forrester & Evans, 1997) showed that the `eyea of recirculation is usually located at the distance of 0.53¸ from the sudden expansion. Thus, assuming the 0# behaviour of the con"ned two-phase jet as analogous to the single-phase one, the length of region (1) is chosen here as: ¸ "0.53¸ . 0# The entrained gas #ow rate Q can be estimated %# based on the analysis of gas entrainment process by con"ned, plunging liquid jets presented by Evans (1990) and Evans and Jameson (1996). The model predicts gas entrainment rate recognizing two components of the entrained gas stream: `gas "lm entrainmenta and gas contained in the disturbances of free jet surface. In order to utilize this model, an information about the actual free jet characteristics at the impingement point ( jet surface envelope diameter) is necessary. Alternatively, the gas entrainment rate can be calculated according to an empirical correlation for uncon"ned high-speed jets (BinH , 1988, 1993):
¸ Q %#"0.04Fr H (21) H Q D * , valid for nozzles of l/D *10 and jets for which , ¸ ¸ H *100. 0.04Fr H *10, H D D , , The angle of two-phase jet expansion in region (1) is reported in the literature to be smaller than the angle of expansion of single phase submerged jets. Here, the value of a/2"83 was chosen based on the measured value reported by Evans (1990) for similar #ow conditions. Computational modelling shows that velocity distribution in region (1) is analogous to that in free submerged jets (Forrester & Evans, 1997). The #ow rate of the #uid in the region (1) increases due to liquid entrainment from region (2). In the #ow development region of an expanding jet (where the potential core is still present) the #ow
Fig. 12 . Schematic of the modi"ed mixing zone model.
rate can be calculated at the dimensionless distance z from the impingement point (z"x/D ) according to ! (Rajaratnam, 1976):
Q (z) D D Q (z)" * "1#0.083z ! #0.013 z ! Q D D * , , for 0)z)7.577D /D (22) , ! and in the developed #ow region according to (Ricou & Spalding, 1961):
Q (z) D Q (z)" * "2.3752#0.28 z ! !7.577 Q D * , for z'7.577D /D . (23) , ! The constants 2.3752 and 7.577 were chosen here for the sake of continuity of Q within region (1). * Plug #ow is assumed in region (1). Although velocity distribution in the region is Gaussian, the assumption of plug #ow is justi"ed to a certain extent by the `hat-likea lateral distribution of gas void fraction in this region, resulting from merging of two Gaussian peaks `entraineda in the outer boundary of the plunging liquid jet (Van de Donk, 1981). Similar lateral distribution of the dissolved CO concentration is anticipated in region (1). Since the #ow is unstable and the instantaneous #ow patterns are very complicated in regions (2 ) and (3), for the sake of simplicity, these regions are assumed here to be ideally mixed. It has to be pointed out that the turbulence intensity and gas void fraction are much higher in region (3) than in region (2). As a result of these assumptions, the steady-state mass balance of CO in the liquid phase leads to the following system of equations (pure CO in the gas phase was assumed in derivations): Region (1):
dc d ln Q " (c !c )#St (1!c ) dz dz
D F (z)(k a) * , where St " ! (24) Q (z) * St #c < (k a) where St " * , (25) Region (2): c " St #1 Q * St #c (z"¸ /D ) ! Region (3): c " St #1 < (k a) * where St " . (26) Q (z"¸ /D ) * ! The rate of liquid #ow into region (2) is equal to the #ow of liquid entrained by the expanding jet (region (1)). Thus Q "Q (z"¸ /D )!Q . * * ! * In the above equations, the dimensionless liquid concentration is referred to the concentration of saturated solution given by Eq. (7) (i.e. c "c /cH for i"1,2,3). G *G +'6
G. M. Evans, P. M. Machniewski / Chemical Engineering Science 54 (1999) 4981}4990 Table 1 Estimated values of k a in the mixing zone based on the simple and * modi"ed (hybrid) models u "22.25 m/s , u "0.189 m/s *
(k a) } * (1/s)
(k a) * (1/s)
(k a) * +'6 (1/s)
u "0.165 m/s % u "0.188 m/s %
3.14 3.63
0.29 0.5
1.5 1.73
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ous gas spargers. The contribution of the mixing zone in the overall mass transfer characteristics of the whole contactor is much greater than that of pipe #ow zone. A rigorous and detailed modeling of this region of the contactor is vital for the proper design and evaluation of a CPLJ contactor especially as a gas } liquid reactor. With this in mind, a modi"cation of the simple mixing zone model has been suggested and presented here.
Notation The initial condition c (0)"0 for Eq. (22) was applied during the calculations. In order to estimate experimentally the k a values in * regions (1)}(3), apart from the measured liquid concentration pro"le at the column wall, also the concentration pro"le at the column axis is necessary. Gathering these data was not possible with the liquid sampling method used in this work. Since it was not possible to calculate separate values of k a in regions (1) and (3) from the measured wall concen* tration pro"les, apart from (k a) , only a value of (k a) } * * averaged over (1) and (3) was estimated for the two runs by "tting the modi"ed (hybrid) model of the mixing zone to the experimental points. Full utilization of the model in the future will require a better sampling method, which will enable collection of bubbless samples of the liquid phase from region (1). The modelled concentration levels in regions (2) and (3) are shown in Fig. 11. The estimated coe$cients are shown in the Table 1 and compared to the coe$cients averaged over the `apparenta mixing zone volume (equal to ¸ ) F ) estimated previously from the simple model. +'6 ! It also has to be stressed that although the (k a) value * used in the model is averaged over region (1), the energy dissipation rate in this region is highly non-uniform and thus a considerable variation of local k a values has to be * expected within region (1).
5. Conclusions Experimentally determined values of the volumetric mass transfer coe$cient in the mixing zone were an order of magnitude greater than those in the pipe #ow zone and reached 2.5 1/s. A correlation based on energy dissipation rate in the mixing zone and actual gas entrainment rate by the plunging jet as well as correlation based on the free jet velocity and its length, can successfully be used for the determination of k a in the mixing zone. The dependence * of this coe$cient on the energy dissipation in the mixing zone was consistent with the correlation derived based on the measurements conducted in gassed stirred vessels and coalescent liquids. Mass transfer characteristics and hydrodynamics of the pipe #ow zone was found very similar to conventional up#ow bubble columns with por-
a c D F Fr g H k * ¸ ¸ 0# LSAT n N N % p Q R Re ¹ u < x y z
interfacial area per unit volume of the two phase mixture, m/m molar concentration in the liquid phase, mole/m diameter, m, molecular di!usion coe$cient, m/s crossectional area, m Froude number dimensionless gravitational acceleration ("9.806), m/s Henry's law constant, mol/m Pa liquid side mass transfer coe$cient, m/s length, m, froth height, m, (if without any subscripts) distance from free surface to the jet reattachment point, m liquid saturation degree dimensionless (de"ned by Eq. (16)) molar #ow rate of gas, mol/s molar #ux of the component transfered from gas to liquid phase, mol/s m molar #ux of the gas phase, mol/s m pressure, Pa volumetric #ow rate, m/s gas constant ("8.314), J/mol K Reynolds number, dimensionless temperature, K velocity m/s, super"cial velocity (when with ¸ or G subscript), m/s volume, m distance from the free surface of the froth, m mole fraction in the gas phase, dimensionless dimensionless distance from the free surface of the froth, ("x/D ) !
Greek letters a a 0 a 2 e e o
jet spreading angle, degree gas-phase absorption degree, dimensionless gas-phase degree of recirculation from mixing zone to headspace, dimensionless void fraction, dimensionless energy dissipation rate per unit volume, W/m density, kg/m
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G. M. Evans, P. M. Machniewski / Chemical Engineering Science 54 (1999) 4981}4990
Subscripts 0 1,2,3 av C E G HSPC in j ¸ MIX MIX/PF N PF R RE S
ambient conditions, inlet regions in the modi"ed mixing zone model average value column entrainment gas phase in the headspace, in the free jet zone at the inlet free jet liquid phase in the mixing zone referring to the border between the mixing and pipe #ow zones nozzle in the pipe #ow zone recirculation jet reattachment saturation
References Bayly, A. E., Rielly, C. D., Evans, G. M., & Hazell, M. (1992). The rate of expansion of a con"ned, submerged jet. CHEMECA '92, 27}30 September 1992, Canberra, ACT. Australia, 2, 119}125. BinH , A. (1988). Gas entrainment by plunging liquid jets. VDI-Forschungshefte, 648/88, 1}36. BinH , A. (1993). Gas entrainment by plunging liquid jets. Chemical Engineering Science, 48(21), 3585}3630. Cramers, P. H. M. R., Beenackers, A. A. C. M., & van Dierendonck, L. L. (1992). Hydrodynamics and mass transfer characteristics of a loop-venturi reactor with a down#ow liquid jet ejector. Chemical Engineering Science, 47(13/14), 3557}3564. Cramers, P. H. M. R., Smit, L., Leuteritz, G. M., van Dierendonck, L. L., & Beenackers, A. A. C. M. (1993). Hydrodynamics and local mass transfer characteristics of gas}liquid ejectors. Chemical Engineering Journal, 53, 67}73. Cunningham, R. G. (1974). Gas compression with the liquid jet. Journal of Fluids Engineering, 3, 203}215. Danckwerts, P. V., & Sharma, M. M. (1966). The absorption of carbon dioxide into solutions of alkali and amines. The Chemical Engineer, CE244-CE280. Deckwer, W. -D. (1992). Bubble column reactors. Chichester: Wiley.
Dirix, C. A. M. C., & van der Wiele, K. (1990). Mass transfer in jet loop reactors. Chemical Engineering Science, 45(8), 2333}2340. Dutta, N. N., & Raghavan, K. V. (1987). Mass transfer and hydrodynamic characteristics of loop reactors with down#ow liquid jet ejector. Chemical Engineering Journal, 36, 111}121. Evans, G. M. (1990). A study of plunging jet bubble column. Ph.D. thesis, University of Newcastle, Newcastle, Australia. Evans, G. M., Jameson, G. J., & Rielly, C. D. (1995). Hydrodynamics of a plunging liquid jet bubble column. Chemical Engineering Research and Design (Transactions of IChemE), 73 (Part A), 679}684. Evans, G. M., & Jameson, G. J. (1996). Free jet expansion and gas entrainment characteristics of a plunging liquid jet. Experimental Thermal and Fluid Science, 12, 142}149. Evans, G. M., Jameson, G. J., & Atkinson, B. W. (1992). Prediction of the bubble size generated by a plunging liquid jet bubble column. Chemical Engineering Science, 47(13/14), 3265}3272. Forrester, S. E., & Evans, G. M. (1997). Computational modelling study of the hydrodynamics in a sudden expansion-tapered contraction reactor geometry. Chemical Engineering Science, 52, 3773}3785. Herbrechtsmeier, P., & Steiner, R. (1978). Untersuchungen an einem BlasensaK ulen-Abstromreaktor. Chemie-Ingenieur Technik, 50(12), 944}947. Mao, W. P., Ahmed, N., & Jameson, G. J. (1991). Air entrainment in a down#ow bubble column with a plunging liquid jet. 19th Australasian chemical engineering conference CHEMECA 91, Newcastle, 18}20 September. Mao, W. P., Evans, G. M., & Jameson, G. J. (1993). Mass transfer study in plunging jet bubble column, Fifth Australasian heat and mass transfer conference. The University of Queensland, 6}9 December, Paper 63. Ohkawa, A., Kawai, Y., Kusabiraki, D., Sakai, N., & Endoh, K. (1987). Bubble size, interfacial area and volumetric liquid-phase mass transfer coe$cient in down#ow bubble column with gas entrainment by liquid jet. Journal of Chemical Engineering of Japan, 20 (1), 99}101. Ohkawa, A., Shiokawa, Y., Sakai, N., & Endoh, K. (1985a). Gas holdup in down#ow bubble columns with gas entrainment by liquid jet. Journal of Chemical Engineering of Japan, 18(2), 172}174. Ohkawa, A., Shiokawa, Y., Sakai, N., & Imai, H. (1985b). Flow characteristics of down#ow bubble columns with gas entrainment by liquid jet. Journal of Chemical Engineering of Japan, 18(2), 466}469. Rajaratnam, N. (1976). Turbulent jets. Amsterdam: Elsevier. Ricou, F. P., & Spalding, D. B. (1961). Measurements of entrainment by axisymmetrical turbulent jets. Journal of Fluid Mechanics, 11, 21}32. Van de Donk, J. (1981). Water aeration with plunging jets, Ph.D. thesis, Delft University of Technology, Delft, Holland. Van't Riet, K. (1979). Review of measuring methods and results in non-viscous gas}liquid mass transfer in stirred vessels. Industrial & Engineering Chemistry Process Design and Development, 18, 375.
Mass transfer in a con"ned plunging liquid jet bubble column G. M. Evans *, P. M. Machniewski Department of Chemical Engineering, University of Newcastle, NSW 2308, Australia Department of Chemical and Process Engineering, Warsaw University of Technology, PL-00-645 Warsaw, Poland
Abstract A model of con"ned plunging liquid jet bubble column absorber is formulated and utilized for the interpretation of the experimental data obtained during steady-state absorption of concentrated gaseous CO in water. A strong variability of molar #ux of the gas phase in the contactor was observed and taken into account. Two zones di!ering in mass transfer and mixing characteristics are distinguished within the contactor. Volumetric mass transfer coe$cient in the mixing zone beneath the impingement point, is an order of magnitude greater than in pipe #ow zone and determines the overall performance of the contactor. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Plunging liquid jet; Down#ow bubble column; Mass transfer coe$cient
1. Introduction Con"ned Plunging Liquid Jet systems (CPLJ) have the ability to generate high values of interfacial area per unit volume (Evans, 1990; Evans, Jameson & Atkinson, 1992; Ohkawa, Kawai, Kusabiraki, Sakai & Endoh, 1987; Mao, Evans & Jameson, 1993; BinH , 1993) and o!er an e!ective method for gas}liquid contacting especially for cases when the gaseous component is consumed by a fast reaction in the liquid phase. A schematic of a CPLJ contactor is shown in Fig. 1. A liquid jet ejected from a nozzle plunges into the free surface of the gas}liquid mixture and entrains gas from the headspace. A turbulent region can be distinguished beneath the impingement point where the submerged two-phase jet expands and "nally attaches to the column wall. The region will be called here as the mixing zone. In this zone, the entrained gas is broken into "ne bubbles (sizes in the order of 200 lm were measured by Evans et al. (1992)). A fraction of the entrained gas is recirculated back into the headspace as some bubbles escape from the mixing zone through the free surface. Below the mixing * Corresponding author. Tel.: #61-24921-6180; fax: #61-249216920. This work was carried out during the visit of the second author at The University of Newcastle, Australia. E-mail address: [email protected] (G. M. Evans)
zone, the turbulence level is signi"cantly lower and the #owing liquid steadily transports bubbles down. This region of the contactor will be called here as the pipe #ow zone. When the coalescence of bubbles is not retarded, the coalescence } break-up equilibrium results in bubble sizes signi"cantly higher, in this zone, than that in the mixing zone. In such a case, the bubble sizes are typical of bubbles in ordinary (up-#ow) bubble columns with "ne pore di!users (3}4 mm in tap water). Since CPLJ contactors have been successfully applied for a number of years as #otation units in mineral processing industries (Jameson cell), hydrodynamic properties of these contactors were studied by many authors. Ohkawa, Shiokawa, Sakai and Endoh (1985a), Ohkawa, Shiokawa, Sakai and Imari (1985b), Yamagiwa (1990) and Evans (1990). In gas}water systems, where the coalescence of bubbles is inhibited by the addition of a surfactant the value of gas hold-up as high as 70% is reported (Evans, Jameson & Rielly, 1995). Only a small number of publications are available regarding mass transfer in such contactors. The system similar to that investigated in this work was used by Ohkawa et al. (1987). The authors did not distinguish between the zones of di!erent mass transfer and mixing characteristics in their column. The measured k a values were averaged over the whole two-phase mix* ture volume and were based on the assumption of plug #ow throughout the whole contactor.
0009-2509/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 2 2 1 - 3
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2. Experimental
Fig. 1 . The schematic of the con"ned plunging liquid jet reactor.
Mao et al. (1993) in a similar system (D "51 mm, ! D "5.86 mm, ¸"1.35 m), measured dissolved oxygen , concentration pro"les along the column axis during a steady-state physical absorption of oxygen in water. The authors found that the plug #ow assumption was justi"ed within the pipe #ow region only and assumed the mixing zone as being perfectly mixed. Most of the existing publications dealing with mass transfer in a down#ow loop reactor with self gas-inducing venturi ejector, report average values of k a for the * whole gas}liquid volume in a reactor (ejector#vessel) (Van Dierendonck & Lentritz 1988; Dutta & Raghavan, 1987). Only a few authors investigated mass transfer in gas}liquid ejectors alone (Dirix & van der Wiele 1990; Cramers, Beenackers & van Dierendonck, 1992) and even fewer distinguished the two di!erent zones of the ejector, di!ering in turbulence intensity and mass transfer characteristics (Cramers, Smit, Lenteritz, van Dierendonck & Beenackers, 1993). The results of experimental determination of k a in the * mixing and pipe-#ow zones of a CPLJ bubble column absorber will be presented here. The measurements were performed during a steady-state physical absorption of pure CO in tap water and were accompanied by a con siderable decrease in the gas super"cial velocity due to a high absorption degree, which in#uenced the hydrodynamics of the contactor.
The experimental set-up is shown on Fig. 2. The absorption was carried out in a vertical Perspex column of 51 mm ID, 1.36 m long. Tap water from the bu!er tank supplied the column through 4.7 mm ID nozzle mounted at the top of the column (the nozzle's cylindrical section length was 50 mm). Carbon dioxide of 99.7% purity was fed from a pressurized cylinder. At the beginning of each run the desired gas and liquid #ow rates were set and the peristaltic circulation pump supplying fresh, bubble-free liquid to the sampling point, was turned on. After 2}3 min, when a steady state had been achieved, several liquid samples were collected at various positions of the sampling probe along the PF-zone, starting from the visible `boundarya between the MIX and PF zones, down to the column base. The mixing zone was regarded as a section extending from the free surface of the gas}liquid mixture to the point where the down#ow movement of the mixture is observed to be more or less steady. During each run, the liquid samples (20 ml) collected with a syringe from the sampling point were immediately transferred to 100 ml #asks containing 25 ml 0.1 M NaOH solution and stoppered. After each run concentration of dissolved CO was determined by Winkler type method (i.e. carbonate ions were precipitated by addition of 10 ml 10% BaCl solution and the excess of NaOH was titrated with 0.1 M HCl to phenolophtaleine endpoint). The average gas hold-up in the column was calculated using the headspace pressure from the equation (Eq. (1)) derived from the overall momentum balance around the contactor.
1 4u 1!e " e # e # * . % 2 * * g¸
(1)
In the above formula, e refers to the liquid hold-up * calculated with the assumption of negligible momentum of liquid #owing through the pipe #ow zone (Mao, Ahmed & Jameson, 1991): u u p !p &1.!! , * (2) e " * g¸ go ¸ * Apart from the average gas hold-up, also the hold-up in the pipe #ow zone was measured by means of a manometer attached to the column wall 0.5 m above the free surface of the liquid in the receiver tank (Fig. 2). h #h e " % .$ 0.5 m
(3)
The values of e and e were approximately equal for % % .$ most of the runs and were consistent with the observations of Herbrechtsmeier and Steiner (1978) and Ohkawa et al. (1985a). In the experiments u was varied within , 10}23 m/s and u within 0.06}0.37 m/s. %
G. M. Evans, P. M. Machniewski / Chemical Engineering Science 54 (1999) 4981}4990
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Fig. 2 . Experimental set-up.
3. Mass transfer model A theoretical model has been developed in order to determine the rate of absorption of CO into a liquid phase in a con"ned plunging jet contactor. The model is also used here to determine the volumetric mass transfer coe$cient based on the measured concentration pro"les. The model is based on the de"nition of di!erent hydrodynamic zones, which exist within the CPLJ as illustrated in Fig. 3. Re#ecting the division of the contactor the model is divided into three parts: free jet zone, mixing zone and pipe-#ow zone. The assumptions for each of these zones are: 1. Mass transfer rate to the free liquid jet and to the free surface of the froth is negligible. 2. In the mixing zone, the phases are perfectly mixed and gas is uniformly dispersed in liquid with an average gas void fraction. 3. In the pipe-#ow zone both phases move in a plug #ow manner and gas void fraction is uniform throughout the zone. Additionally, for the interpretation of the experimental concentration pro"les in the CPLJ- bubble column it is
assumed that the desorption (absorption) of inert species from (to) water is negligible. The assumption of perfectly mixed gas and liquid phases in the mixing zone is an approximation of a complex system involving distributions of gas void fraction and interfacial surface area in the upper part of the mixing zone. Given the amount of recirculation created by the jet (Bayly, Rielly, Evans & Hazell, 1992) it seems reasonable to assume, as a "rst approximation, that the concentration gradients are instantaneously removed within the mixing zone. This assumption will be discussed later in the paper. By the de"nition of the mixing zone as one unit, an average volumetric mass transfer coe$cient is assumed to be valid within the whole mixing zone volume. A schematic of the mass transfer model is illustrated in Fig. 3. It shows the various #ows of the gas and liquid phases between the hydrodynamic zones. A gas stream of molar #ow rate, n , and CO concentration, y , enters % the headspace where it is mixed with a gas #ow of, n , and 0 CO concentration, y , which is recirculated from the +'6 mixing zone. The plunging jet entrains, n , amount of gas # from the headspace into the mixing zone where the carbon dioxide is absorbed by the liquid phase. The gas #ow n , and CO concentration, y , passes into the % +'6
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Combining Eqs. (4) and (5), we get Q (c !c ) . (k a) " * +'6 (6) * +'6 < (cH !c ) +'6 +'6 +'6 The average equilibrium liquid CO concentration in the mixing zone cH , is given by the Henry's law equation: +'6 cH "Hy p (7) +'6 +'6 +'6 where p is the average total pressure in the mixing +'6 zone. The Henry's law constant for the system CO }water, was calculated here according to the formula given by Danckwerts and Sharma (1966) and y was +'6 determined from the gas phase CO mass balance: y !a n% !n% +'6. (8) 2 +'6 where a y " " +'6 2 +'6 1!a n 2 +'6 % In the above expression, a is the gas absorption degree, 2 which can also be calculated based on the measured liquid-phase concentration of the dissolved CO : Q (c !c ) . a " * +'6 (9) 2 +'6 n % 3.2. Mass transfer in the pipe-yow zone Based on the assumption of plug #ow in the pipe-#ow zone, the mass balance around a layer of in"nitesimal height (Fig. 3) can be presented as the following system of equations: Total gas phase balance: Fig. 3 . The model of the con"ned plunging liquid jet reactor.
pipe-#ow zone where further carbon dioxide is absorbed into the liquid phase. Eventually, a #ow n , of gas with % CO concentration, y , exits the pipe #ow zone. For the liquid phase, a constant #ow, Q passes * through the reactor. The inlet concentration of dissolved carbon dioxide is c , which increases to c , as gas is +'6 absorbed in the mixing zone, and eventually to c at the end of the pipe #ow zone. 3.1. Mass transfer in the mixing zone The value of the average volumetric mass transfer coe$cient in the mixing zone can be determined based on the CO balance in the liquid phase: Q (c !c )#(Na) < "0. (4) * +'6 +'6 +'6 For negligible gas phase resistance and perfect mixing of the phases, the interphase transfer rate of CO , (Na) +'6 can be expressed as (Na) "(k a) (cH !c ). +'6 * +'6 +'6 +'6
(5)
dN %#Na"0, dx
CO balance in the gas phase: d(N y) % #Na"0, dx CO balance in the liquid phase: dc u !Na"0. * dx
(10)
(11)
(12)
In the above equations, Na is the `locala interfacial mass transfer rate at the level x, averaged over the column crossection. Assuming that pipe-#ow zone is uniform throughout its whole length, Na is given by the following expression: Na"(k a) (Hyp!c) (13) * .$ Eqs. (10)}(12) were simultaneously numerically integrated within the range x"¸ P¸, with the following +'6 initial conditions: at x"¸
N "N , y"y , c"c . (14) +'6 % % +'6 +'6 +'6 The value of (k a) was determined by "tting the pro"le * .$ c(x), resultant from the integration, to the experimental
G. M. Evans, P. M. Machniewski / Chemical Engineering Science 54 (1999) 4981}4990
data using nonlinear regression procedure. The local pressure p in Eq. (13) was calculated, based on the measured gas holdup values, according to p"p !e o (¸!x). * *
(15)
4. Results and discussion 4.1. Concentration proxles in the column Sample concentration pro"les of CO in gas and liquid phases calculated from the "tted model, are shown in the Fig. 4. The deviations from the `plug-#owa model line may indicate some degree of backmixing in the pipe-#ow zone as well as non-uniformity of the two-phase mixture in the pipe #ow zone (i.e. variability of k a along the * pipe-#ow zone). The "gure also shows a local saturation degree of the liquid phase de"ned as LSAT"
c c " . cH Hyp
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4.2. Mass transfer in the mixing zone The measured values of k a for di!erent gas and * +'6 liquid #ow rates are shown in Fig. 6. The results were correlated in a form typical for venturi injectors and gassed stirred tanks as a function of energy dissipated in the mixing zone and gas-feeding rate: (k a) "0.467e u . (17) * +'6 % Energy dissipation rate per unit volume was estimated here based on the relationship developed originally for gas}liquid ejector pumps by Cunningham (1974) and adopted to CPLJ contactors by Evans et al. (1992). o u e " * , [b!2b!b(1#j)#2b(1#j)] 2¸ +'6 F Q where b" , and j" % . F Q ! *
(18)
(16)
At lower feed gas #ow rates (Q /Q (0.8) relatively % * high solubility of CO in water and high values of the volumetric mass transfer coe$cient in the apparatus caused signi"cant consumption (absorption) degree of the gas phase and drop in gas phase CO mole fraction and molar gas #ow rate in the pipe #ow zone (although the whole column was always "lled with bubbles). This phenomenon exhibited itself as a #at concentration pro"le caused by local saturation of the liquid with respect to the gas phase. The e!ect is illustrated on Fig. 5, where the calculated pro"les were very little sensitive to changes in k a value. These e!ects restricted experimental deter* .$ mination of k a for a particular liquid #ow rate, to the * range of gas #ow rates greater than a certain minimum value (Q /Q '0.8). % *
Fig. 4 . CO concentration pro"le in the liquid phase and its saturation degree.
Fig. 5 . Liquid concentration and degree of saturation pro"les when Q /Q (0.8. % *
Fig. 6 . Dependence of the mixing zone volumetric mass transfer coe$cient on gas feed and liquid #ow rates.
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It can be concluded from Eq. (17) that the dependence of k a on energy dissipation rate per unit volume in the * +'6 system investigated here (k a J(e ) ) is weaker * +'6 than, e.g. in ejectors where k aJ(e ) as reported * by the authors cited earlier. In most of these reported cases, the measurements were performed with the aqueous electrolyte solutions used as liquid phase. On the contrary to CO }water system, the coalescence of bubbles is less supported in such systems and the power input is more e!ectively used for the generation of interfacial area. Van't Riet (1979) proposed relationships for the estimation of the volumetric mass transfer coe$cient in gassed stirred vessels, from which it follows that k aJ(e ) for an air}water system and k aJ(e ) * * for solutions where coalescence of bubbles is inhibited. Since u refers to the net gas uptake rate, which is % equal to the di!erence between the gas entrainment rate by the plunging jet and the rate gas escapes from the mixing zone through the free surface, it seems more appropriate to correlate k a either with the actual gas * +'6 entrainment rate u , i.e. the rate gas phase is introduced # into the mixing zone or with the parameters like u and , ¸ , which directly a!ect gas entrainment rate (BinH , 1993; H Evans et al., 1996) and the average energy dissipation rate in the mixing zone. Thus, experimental values of (k a) were also regressed here as a function of nozzle * +'6 velocity and free jet length (see Fig. 7) in the form of the following equation: (k a) "1.175;10\u ¸ . (19) * +'6 , H Statistically, Eq. (19) "ts experimental data better than Eq. (17). The error either of the equations is less than 15%. It is also interesting to note that the dependence of k a on u in Eq. (19) (k aJu ) is in close agreement * +'6 , * , with the results of Dirix & van der Wiele (1990), who measured oxygen desorption rate in the down#ow venturi liquid jet ejector and found that k a in the ejector * (working in the `bubbling regimea) was proportional to Re . , A comparison of the k a values obtained here with * +'6 the results, calculated from the oxygen concentration pro"les obtained by Mao et al. (1993) is also shown in Fig. 7. 4.3. Mass transfer in the pipe-yow zone The volumetric mass transfer coe$cient in the pipe#ow zone, calculated based on the CO concentration pro"le, for each of the examined liquid super"cial velocities and gas uptake rates at the inlet, is shown in Fig. 8. Interpretation of the results on the basis of u is com% plicated by a signi"cant variation of the actual gas velocity within the column caused by the high degree of CO absorption. This explains, why the curves in Fig. 8 can be extrapolated to zero k a values for the non-zero values * .$ of u . %
Fig. 7 . Relation between the volumetric mass transfer coe$cient in the mixing zone and the free jet length.
Fig. 8 . Volumetric mass transfer coe$cient in the pipe #ow zone vs. net gas uptake rate (at the gas inlet).
A di!erent picture (Fig. 9) is revealed when k a is * .$ related to the actual super"cial velocity of the gas entering the pipe-#ow zone (through the MIX/PF boundary). u is calculated by subtracting the amount of gas % +'6 .$ phase absorbed in the mixing zone from u . It can be % observed that the in#uence of the liquid velocity on k a * .$ has almost disappeared and most of the experimental points corresponding to the various liquid #ow rates lay on the same curve. A change in the slope of the functional dependence of k a on u is caused by the de* .$ % +'6 .$ stabilization of the homogeneous, bubbly #ow regime and the development of heterogeneous (or churn-turbulent), and slug #ow regimes at the higher gas #ow rates. The value of u
5 cm/s (Fig. 9) corresponding to % +'6 .$ this transition, is very close to the analogous value in a conventional, up#ow bubble column with a porous gas sparger (4}5 cm/s in air}tap water system, according to Deckwer, 1992).
G. M. Evans, P. M. Machniewski / Chemical Engineering Science 54 (1999) 4981}4990
Fig. 9 . Dependence of the volumetric mass transfer coe$cient in the pipe #ow zone on the actual average velocity of the gas entering this zone.
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Fig. 10 . Average volumetric mass transfer coe$cient for the whole column (solid symbols) and the contribution of the mixing and pipe #ow zones in the values of the coe$cient (open symbols).
The points calculated from Mao's et al. (1993) data (oxygen}water system) are also shown in Fig. 9 and are in fair agreement with the k a values obtained in this * .$ work. The volumetric mass transfer coe$cient averaged over the whole two-phase mixture volume, in the CPLJ bubble column, was calculated according to Eq. (20) and is shown on Fig. 10: ¸ k a #¸ k a .$ * .$. k a " +'6 * +'6 * ¸ #¸ +'6 .$
(20)
The contributions of the two zones in the contactor, in terms of value of this coe$cient are also compared in this chart. It is evident that the contribution of the mixing zone is much more important than that of the pipe-#ow zone, and that it is the mixing zone that mainly determines the performance of the whole contactor. 4.4. Modixcation of the mixing zone model In order to verify the assumption of ideal mixing in the mixing zone the dissolved CO concentration pro"le along the column wall has been measured during the last two runs. The measured pro"les reveal that the treatment of the mixing zone as one, uniform, ideally mixed region is rather rough approximation. The measured pro"les are shown in the Fig. 11. A considerable variation in the liquid concentration pro"le at the wall can be observed, with a minimum situated in the distance of 3.6D from ! the free surface. The minimum most probably corresponds to the reattachment of the submerged expanding jet to the column wall. The distance of 3.6D is in agree! ment with the jest reattachment length (3.5D ) measured ! by Bayly et al. (1992) in a similar geometry and #ow of water containing neutrally buoyant spherical particles of
Fig. 11 . Axial pro"les of dissolved CO concentration at the column wall in the mixing and pipe #ow zones.
0.5}1 mm diameter. The authors found that ¸ /D is 0# ! approximately constant over the wide range of jet to column diameter ratio and jet Reynolds number. As a result of CFD simulation of a con"ned single phase jet the authors obtained ¸ /D +3 which was also 0# ! independent of jet to column diameter ratio and jet Reynolds number. The location of the minimum concentration (anticipated as the mean jet reattachment point) is closer to the free surface than ¸ estimated based on visual observa+'6 tions of the turbulent movements of the two-phase mixture, which apparently extend further down than the mean location of the jet reattachment point. The expanding con"ned jet is unstable in the region of its reattachment to the pipe wall. It #apps from one side of the pipe to the other (Coanda e!ect) causing continuous oscillation of the reattachment location.
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In order to explain the measured wall concentration pro"les, a modi"cation to the previous simple model of the mixing zone had to be introduced. The mixing zone is now subdivided into three di!erent regions shown schematically in Fig. 12. Region (1) is the expanding submerged two-phase jet that entrains #uid from region (2) * the ring surrounding it and discharges into region (3). It is suggested here that the length of the region (1) is determined by the location of the recirculation centre. CFD simulations of single-phase #ow through sudden expansions (Forrester & Evans, 1997) showed that the `eyea of recirculation is usually located at the distance of 0.53¸ from the sudden expansion. Thus, assuming the 0# behaviour of the con"ned two-phase jet as analogous to the single-phase one, the length of region (1) is chosen here as: ¸ "0.53¸ . 0# The entrained gas #ow rate Q can be estimated %# based on the analysis of gas entrainment process by con"ned, plunging liquid jets presented by Evans (1990) and Evans and Jameson (1996). The model predicts gas entrainment rate recognizing two components of the entrained gas stream: `gas "lm entrainmenta and gas contained in the disturbances of free jet surface. In order to utilize this model, an information about the actual free jet characteristics at the impingement point ( jet surface envelope diameter) is necessary. Alternatively, the gas entrainment rate can be calculated according to an empirical correlation for uncon"ned high-speed jets (BinH , 1988, 1993):
¸ Q %#"0.04Fr H (21) H Q D * , valid for nozzles of l/D *10 and jets for which , ¸ ¸ H *100. 0.04Fr H *10, H D D , , The angle of two-phase jet expansion in region (1) is reported in the literature to be smaller than the angle of expansion of single phase submerged jets. Here, the value of a/2"83 was chosen based on the measured value reported by Evans (1990) for similar #ow conditions. Computational modelling shows that velocity distribution in region (1) is analogous to that in free submerged jets (Forrester & Evans, 1997). The #ow rate of the #uid in the region (1) increases due to liquid entrainment from region (2). In the #ow development region of an expanding jet (where the potential core is still present) the #ow
Fig. 12 . Schematic of the modi"ed mixing zone model.
rate can be calculated at the dimensionless distance z from the impingement point (z"x/D ) according to ! (Rajaratnam, 1976):
Q (z) D D Q (z)" * "1#0.083z ! #0.013 z ! Q D D * , , for 0)z)7.577D /D (22) , ! and in the developed #ow region according to (Ricou & Spalding, 1961):
Q (z) D Q (z)" * "2.3752#0.28 z ! !7.577 Q D * , for z'7.577D /D . (23) , ! The constants 2.3752 and 7.577 were chosen here for the sake of continuity of Q within region (1). * Plug #ow is assumed in region (1). Although velocity distribution in the region is Gaussian, the assumption of plug #ow is justi"ed to a certain extent by the `hat-likea lateral distribution of gas void fraction in this region, resulting from merging of two Gaussian peaks `entraineda in the outer boundary of the plunging liquid jet (Van de Donk, 1981). Similar lateral distribution of the dissolved CO concentration is anticipated in region (1). Since the #ow is unstable and the instantaneous #ow patterns are very complicated in regions (2 ) and (3), for the sake of simplicity, these regions are assumed here to be ideally mixed. It has to be pointed out that the turbulence intensity and gas void fraction are much higher in region (3) than in region (2). As a result of these assumptions, the steady-state mass balance of CO in the liquid phase leads to the following system of equations (pure CO in the gas phase was assumed in derivations): Region (1):
dc d ln Q " (c !c )#St (1!c ) dz dz
D F (z)(k a) * , where St " ! (24) Q (z) * St #c < (k a) where St " * , (25) Region (2): c " St #1 Q * St #c (z"¸ /D ) ! Region (3): c " St #1 < (k a) * where St " . (26) Q (z"¸ /D ) * ! The rate of liquid #ow into region (2) is equal to the #ow of liquid entrained by the expanding jet (region (1)). Thus Q "Q (z"¸ /D )!Q . * * ! * In the above equations, the dimensionless liquid concentration is referred to the concentration of saturated solution given by Eq. (7) (i.e. c "c /cH for i"1,2,3). G *G +'6
G. M. Evans, P. M. Machniewski / Chemical Engineering Science 54 (1999) 4981}4990 Table 1 Estimated values of k a in the mixing zone based on the simple and * modi"ed (hybrid) models u "22.25 m/s , u "0.189 m/s *
(k a) } * (1/s)
(k a) * (1/s)
(k a) * +'6 (1/s)
u "0.165 m/s % u "0.188 m/s %
3.14 3.63
0.29 0.5
1.5 1.73
4989
ous gas spargers. The contribution of the mixing zone in the overall mass transfer characteristics of the whole contactor is much greater than that of pipe #ow zone. A rigorous and detailed modeling of this region of the contactor is vital for the proper design and evaluation of a CPLJ contactor especially as a gas } liquid reactor. With this in mind, a modi"cation of the simple mixing zone model has been suggested and presented here.
Notation The initial condition c (0)"0 for Eq. (22) was applied during the calculations. In order to estimate experimentally the k a values in * regions (1)}(3), apart from the measured liquid concentration pro"le at the column wall, also the concentration pro"le at the column axis is necessary. Gathering these data was not possible with the liquid sampling method used in this work. Since it was not possible to calculate separate values of k a in regions (1) and (3) from the measured wall concen* tration pro"les, apart from (k a) , only a value of (k a) } * * averaged over (1) and (3) was estimated for the two runs by "tting the modi"ed (hybrid) model of the mixing zone to the experimental points. Full utilization of the model in the future will require a better sampling method, which will enable collection of bubbless samples of the liquid phase from region (1). The modelled concentration levels in regions (2) and (3) are shown in Fig. 11. The estimated coe$cients are shown in the Table 1 and compared to the coe$cients averaged over the `apparenta mixing zone volume (equal to ¸ ) F ) estimated previously from the simple model. +'6 ! It also has to be stressed that although the (k a) value * used in the model is averaged over region (1), the energy dissipation rate in this region is highly non-uniform and thus a considerable variation of local k a values has to be * expected within region (1).
5. Conclusions Experimentally determined values of the volumetric mass transfer coe$cient in the mixing zone were an order of magnitude greater than those in the pipe #ow zone and reached 2.5 1/s. A correlation based on energy dissipation rate in the mixing zone and actual gas entrainment rate by the plunging jet as well as correlation based on the free jet velocity and its length, can successfully be used for the determination of k a in the mixing zone. The dependence * of this coe$cient on the energy dissipation in the mixing zone was consistent with the correlation derived based on the measurements conducted in gassed stirred vessels and coalescent liquids. Mass transfer characteristics and hydrodynamics of the pipe #ow zone was found very similar to conventional up#ow bubble columns with por-
a c D F Fr g H k * ¸ ¸ 0# LSAT n N N % p Q R Re ¹ u < x y z
interfacial area per unit volume of the two phase mixture, m/m molar concentration in the liquid phase, mole/m diameter, m, molecular di!usion coe$cient, m/s crossectional area, m Froude number dimensionless gravitational acceleration ("9.806), m/s Henry's law constant, mol/m Pa liquid side mass transfer coe$cient, m/s length, m, froth height, m, (if without any subscripts) distance from free surface to the jet reattachment point, m liquid saturation degree dimensionless (de"ned by Eq. (16)) molar #ow rate of gas, mol/s molar #ux of the component transfered from gas to liquid phase, mol/s m molar #ux of the gas phase, mol/s m pressure, Pa volumetric #ow rate, m/s gas constant ("8.314), J/mol K Reynolds number, dimensionless temperature, K velocity m/s, super"cial velocity (when with ¸ or G subscript), m/s volume, m distance from the free surface of the froth, m mole fraction in the gas phase, dimensionless dimensionless distance from the free surface of the froth, ("x/D ) !
Greek letters a a 0 a 2 e e o
jet spreading angle, degree gas-phase absorption degree, dimensionless gas-phase degree of recirculation from mixing zone to headspace, dimensionless void fraction, dimensionless energy dissipation rate per unit volume, W/m density, kg/m
4990
G. M. Evans, P. M. Machniewski / Chemical Engineering Science 54 (1999) 4981}4990
Subscripts 0 1,2,3 av C E G HSPC in j ¸ MIX MIX/PF N PF R RE S
ambient conditions, inlet regions in the modi"ed mixing zone model average value column entrainment gas phase in the headspace, in the free jet zone at the inlet free jet liquid phase in the mixing zone referring to the border between the mixing and pipe #ow zones nozzle in the pipe #ow zone recirculation jet reattachment saturation
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