POWER CONSUMPTION EFFECT IN THREE PHASE MIXING

POWER CONSUMPTION EFFECT IN THREE PHASE MIXING

Symposium Series No. 89 POWER CONSUMPTION EFFECT IN THREE PHASE MIXING M. GREAVES * and V. Y. LOH + The power characteristics for three disc turbine...

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Symposium Series No. 89 POWER CONSUMPTION EFFECT IN THREE PHASE MIXING

M. GREAVES * and V. Y. LOH +

The power characteristics for three disc turbine impellers have been investigated over a wide range of solids concentration, particle density and gassing rate. There is generally a decreasing trend for Poq as solids concentration increases. However, at high solids concentrations (X > 20% w/w for resin particles), Pog undergoes a dramatic increase. In the turbulent region, density effect alone does not fully account for the complex interactions taking place in the impeller region. Under very high solids loading conditions (X > 30% w / w ) , unsteady state power response measurements reveal that non-Newtonian properties of the fluid suspension can considerably influence the nature and condition of the impeller gas cavities. The overall decreasing trend of Pog vs X is explained in terms of the rheological­ vi scous effect produced in three phase mixing.

INTRODUCTION The design of stirred vessel processes requires an accurate knowledge of the power consumption effect, particularly to ensure reliability and safety. For scale-up, relationships involving power per unit volume, or alternatively mean rate of energy dissipation (power per unit mass), have achieved a greater measure of success against other criteria. Power dissipation in liquid and gas-liquid systems has been extensively investigated, and to a somewhat lesser extent in the case of solid-liquid systems. For three phase mixing processes, which are very important industrially for many types of polymerisation and hydrogénation reaction, as well as biological fermentation processes, the power dissipation effect is much less well understood, however. This is principally because of the complex hydrodynamic state produced when solid, liquid and gas phases are turbulently agitated together. In this paper, a detailed study is made of the power consumption in a three phase (liquid-solid-gas) mixing process in a stirred vessel. From these results, some interpretations are made concerning the complex interactions taking place between the solid and gas. Effects at very high solids concentrations have been investigated, since changes in fluid rheology can have an important influence on particle * +

University of Bath Food Research Institute

69

Symposium Series No. 89

suspension and gas dispersion. Single phase and two phase mixing results are also included where they serve to aid the understanding of the more complex three phase mixing situation. Until recently, the emphasis in three phase mixing research has been mainly concerned with chemical reaction aspects and the power required to just suspend the solids. Blakeborough and co-workers 1 were the first to investigate the effect of solids concentration. They used paper pulp slurries up to 1% w/w concentration and showed that, at low gassing rates, Pg/P decreased sharply with increasing solids concentration. They attributed this to increased coalescence of gas bubbles, and hence gas hold-up, in the impeller region. Visual observation supported this, since they noticed that the pulp tended to move away from the impeller shaft. Circulation of fluid in the vessel was also considered to be restricted by the presence of solids. They also perceptively identified the role that fluid rheology could have on the gas handling capacity of a turbine impeller. Chapman e,t al2*3 have recently reviewed the most significant contributions in three phase mixing by Arbiter et alh on flotation cells, Quenean et al5 concerned with a nickel leach processing operation and that of Wiedmann et ale on three phase reactors. They concluded that there was no clearly established method of designing a three phase mixing system. Accordingly, they carried out an extensive investigation of the effect that various physical parameters had on the impeller speed requirement and gassed power consymption. They obtained results over a wide range of tank sizes using mainly disc turbine impellers, which they identified as having the most stable operating characteristics compared with other types of impeller. At low solids concentrations, dispersion of gas was not significantly affected by either particle size, or density. Above the minimum suspension speed, N > Nj S g, solids concentration had only a small effect on Pog. However, when tne particles were only partially suspended, so that a 'false bottom' was created causing a reduced impeller clearance, POg decreased very significantly in response to increasing solids concentration. The impeller speed condition for complete dispersion of gas, Nrn was also lower on this account when X > 15% w/w. At Nj S g, small differences in Pog were observed which could not be accounted for solely in terms of the slurry density, thereby indicating a state of particle inhomogeneity. Their results, overall, generally confirm that greater power is required to achieve solids suspension under aerated conditions. The resuspension duty, defined by ANj s = N j s g - N j s , was found to be directly proportional to gassing rate over a wide range of hydrodynamic conditions. A tentative scale-up procedure, relating ANj s to QQ> indicates that the specific power should be maintained constant, or even increased slightly, depending on the gas rate. The small amount of data that is available for three phase systems suggests that Pog is mainly dependent on the state of solids suspension and gas dispersion. As in the gas-liquid mixing case, this implies that the power consumption will be mainly influenced by the conditions prevailing in the impeller region.

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Symposium Series No. 89

EXPERIMENTAL The mixing vessel used for the experiments is shown in Fig 1. Agitation was achieved using three different sizes of disc turbine impeller, having D/T ratios of 0.375, 0.5 and 0.66. The turbines were of standard Rushton dimensions*. A sparger tube of 0.003 m diameter was located 0.02 m below the impeller. The tube was drilled with five 1.2 mm holes, each 12.7 mm apart. All of the equipment in contact with the process fluids was either 316 stainless steel or PTFE. The impeller shaft was driven by a 0.25 h.p. D.C. shunt motor to which a tachogenerator was directly connected, providing a 0-10V output signal. Measurement of the impeller torque was obtained from a strain guage transducer mounted on the shaft. The gas flow rate to the vessel was measured by means of a venturi meter. Data acquisition was carried out using a microcomputer. Filtered air and mains tap water were used for all of the experiments. Three types of solid particles were used. These were polystyrene beads, ion exchange resin (Amberlite IR-l20 supplied by Rohm and Haas Ltd) and lead glass ballotini. The physical properties are given in Table 1. It was not possible to prevent flotation of polystyrene particles when air was. introduced into the suspension, so they were not used for the three phase mixing experiments. *

20:5:4 - d i a m e t e r : b l a d e l e n g t h : b l a d e w i d t h

Particles Polystyrene 'Amberlite' ion exchange resin Lead glass ballotini

Size, d (ym) p

Density, (L (kgm-3f

780 ± 70 1300 ± 100

. 1040 1040

420 ± 80 780 ± 70

1260 1260

275 ± 25 655 ± 55 1300 ± 100

2950 2950 2950

Table 1 Particle Properties

The mixing experiments were carried out at room temperature and atmospheric pressure, using an impeller clearance of C/T = 0.25.

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MINIMUM SUSPENSION SPEED Values of N j s and Nj S g were determined visually in a flaf-bottomed perspex vessel of similar dimensions to the mixing vessel (Fig 1 ) . The sparger unit and impellers were the same as those described previously. A 'Mortiz' L40 mixer unit was used to drive the impellers, but there was no provision for torque measurement. The impeller speed was measured using a stroboscope and the base of the vessel was illuminated by means of a photoflood lamp. Viewing of the particle state was aided by an angled mirror placed beneath the base. The 'justsuspended' condition was judged to have been achieved when none of the particles remained at rest on the tank bottom for more than one or two seconds, as advocated by Zwietering. Values of N j s obtained for the solid-liquid systems were reproducible to within ± 6%, but in the three phase experiments, this deteriorated to ± 10% owing to the increased difficulty in observing the particle motion. The last particles to be suspended were located near the centre of the tank base and also behind the baffles. Ίery large increases in impeller speed were required to suspend glass bai loti ni from these positions. The number of these stationary particles was usually quite small and they were therefore ignored. In any event, it is not expected that this behaviour would occur in the dished vessel. Although Zwietering considered that the shape of the tank base did not affect the suspension speed, Cliff 8 found that, depending oh the impeller clearance, N j s could in fact be higher, or lower, in a flatbottomed tank, compared with a di shed-bottomed vessel. Bohnet and Niesmak 9 also report higher values of N j s with a flat-bottomed tank. The N j s values reported here, therefore, (which have not been corrected), are expected to serve as an indication of the lower limit of operation. Zwietering's expression for estimating N j s is considered to be the most reliable and will be used for comparison. For a disc turbine impeller, Ni enow 1 0 has shown that Zwietering's correlation can be written as: Njs

ex

dp 0.2

Δρ0·45

X °·13 D-2·35

(1)

A linear regression analysis of the solid-liquid data yielded the following relationship: Nj s

-

dp o·1-^ A p 0 - U 2

X

0

·

]

D'2·39

{?.)

with a correlation coefficient of 0.98. This shows good agreement with equation (1), except for the exponent on particle size. Compared with Zwietering's correlation, the data agree within ± 10%. Despite the larger absolute impeller clearance used in these experiments, Zwietering's values tend to be higher at the highest N j s condition. This is hardly surprising, in view of the fact mentioned earlier that small amounts of unsuspended (ballotini) particles behind the baffles were ignored. Prior to Njs» a clear liquid interface existed at the top of the dispersion, but generally, for the most severe operation, with high solids concentration and heavy particles (ballotini), this disappeared when N > N j s . It is also interesting to note that, at high solids concentrations (X > 25%) and comparatively low Reynolds Numbers (Re < 35,000), only particles near the impeller were agitated into 72

Symposium Series No. 89

motion, whilst those further away remained unaffected. This behaviour is analogous to the agitation effect in a viscous nonNewtonian fluid 11 . An increase in impeller speed was required when the solid-liquid suspension was aerated, but at no time did drastic sedimentation of particles occur, as reported by Arbiter14. The variation of Nj S g with QQ as shown in Figs 2 and 3, is slightly non-linear, but essentially linear within a narrower selected range of vvm. For both the ion exchange resin and glass bai loti ni, additional gas loading beyond 1.4 v un appears to have a negligible effect on Nj S g. This suggests that the mechanism responsible for particle sedimentation has achieved its maximum effect, or alternatively, other interactive effects are coming into play. Nevertheless, at lower gas rates, the results demonstrate the damping effect that gas has on the flow and turbulence required for solids suspension. As in the case of the unaerated systems, a slurry-liquid interface was observed, albeit less well defined. The height of this interface depended both on particle density and solids concentration. Aeration appears to aid in producing a more homogeneous dispersion once Nj S g is achieved. At high X and low Reynolds Number, large gas bubbles were seen to escape from the unsuspended bed of solids. It was only after the whole mass of particles began to move at higher impeller speeds that dispersion of gas took place. In addition to gas rate, the effect of particle size, solids concentration, particle density and impeller diameter were investigated. Only Chapman2 has made an extensive study of these effects for three phase mixing. The results are compared in Table 2, where it must be emphasised, the range of physical properties and dimensions investigated was much less extensive than Chapman's, particularly in respect of particle density.

Parameter Exponent

Physical Parameter

Present work

Ap

0.29 - 0.34

0.21 - 0.24

X

0.08 - 0.11

0.08 - 0.15

dp D

0.14 - 0.17

0.12

(-2.28H-2.35)

(-2.30H-2.45)

Table 2 Dependence of N j s g

on

Physical Parameters

73

Chapman

Symposium Series No. 89

With the exception of Δρ, there is good agreement with Chapman's results regarding the dependency of Nj S g on the various parameters, which is similar to that obtained for the solid-liquid systems. Nj S g values are compared in Fig 4 with those obtained by Chapman for the conditions T = 0.56 m, D/T = 0.25 (disc turbine), Δρ = 1480 kgm"3 dp = 206 urn, at Q G = 1.0 vvm. His Nj S g values were adjusted using the rule Nj S g <* T " 0 · 7 2 , suggested by him. Fig 4 shows that there is very reasonable agreement considering the large differences in system geometry and physical properties.

RESULTS AND DISCUSSION Liquid height Only a few studies have been made of the effect of liquid height on power consumption. Weisman et al12 and Arbiter et al13 have suggested that increasing the height above the usual condition, H = T, has little reported that the or no effect. On the other hand, Sverak et allk Reynolds Number corresponding to the start of surface aeration Re$ A , was increased. Fig 5 shows results obtained at two liquid heights for the three sizes of impeller, using a fixed clearance of C/T = 0.25. It is quite clear that surface aeration is delayed by increasing the liquid height for the two larger impellers. As Table 3 shows, increasing H by 25% produces an increase in Re$A of approximately 12 to 30%. Interestingly, there are also changes in the maximum value of the power number, P o m a x .

Po

R e S A x IO-*

max

^"\^ H/T D/T ^\^^

1.00

1.25

1.00

1.25

0.375

4.75

5.50

8.50

8.50

0.500

5.10

5.50

8.00

9.00

0.625

5.00

4.50

7.50

10.00

Table 3 Effect of Liquid Height on P o m a x and R e S A

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For D/T = 0.375 and 0.500, P o m a x increases, but for the largest impeller, it is reduced. It is not clearly understood why the power characteristics should vary in this way, though Brodkey 1 5 has reported that Po could vary between 4.8 and 5.5 in the turbulent region. Also, Brown 1 6 , who measured the power in a production scale fermenter, with H ■·. 1.10 T, found that P o m a x varied between 3.04 and 5.59. Of the three sizes of impeller used, the two larger impellers gave the lowest values of Po m ax· Thus it would appear that D/T can be a significant factor to be considered when H/T > 1, at least in liquid mixing. Detailed gassed power measurements were made using the middle size impeller (D = 0.1016 m ) . A plot of Pog versus F 1 Q produced the now familiar set of curves, with both maxima and minima conditions present. No significant differences were obtained when H/T was reduced to 1.0. This suggests that, when H > T in gas-liquid mixing, the upper circu­ lation loop only extends to one tank diameter. Sol id-Li quid Mixing Power characteristics for the three sizes of impeller are shown in Figs 6 and 7. In these plots, Po and Re are calculated using the properties of the liquid. The effect of particle concentration is clearly evident from the fact that there is a series of curves all wery similar in shape to those obtained for a homogeneous fluid. This therefore confirms the inadequacy of a Po-Re representation based solely on liquid properties. At the highest solids loadings (X = 30% to 5 0 % ) , it is of interest to note that 'laminar' flow mixing appears to persist up to apparently yery high Reynolds Numbers (as evidenced by the -1.0 slope trend of the data). The power plots give the impression therefore, that they have been shifted to the right along the axis. An increase in the effective viscosity of the suspension could be responsible for this. Thus, if a suitable apparent viscosity could be obtained for the solidliquid suspension, then it should be possible to condense all of the data in the 'laminar' range onto a single curve. Numerous correlations have been proposed to try to correlate the effective viscosity in terms of the volumetric concentration of suspended particles. No account is taken of the interaction between particles under hindered settling conditions and, not surprisingly, there is little agreement between them. Thomas 1 7 has managed to reduce the data onto a single curve using extrapolation procedures and there is fair agreement with Rutger's 1 8 average curve, up to about X 1 = 25% v/v, but rapid divergence thereafter at higher concentrations. Jeffrey and Acrivos 1 9 have argued that both Rutgers and Thomas should have considered other factors, such as non-Newtonian flow behaviour, thermal, electrical and van der Waal's forces. Non-Newtonian effects are, of course, yery important at high solids concentrations. Nevertheless, if one examines the average curves of Rutgers and Thomas, for X1 = 25% v/v (which is the upper limit for the present work), they can be approximated fairly well by: p e ff

= ^L (]

+

0-065X 1 )

(3)

where y e ff is the effective viscosity of the solid-liquid suspension. If effective viscosity values are calculated from Equation (3) (for example, y e ff = 0.00263 Nsm" 2 at X1 = 25%, corresponding respectively to X = 30% and 50% for suspension of ion exchange resin and glass ballotini) and used to recalculate the impeller Reynolds Number in 75

Symposium Series No. 89 in Figs 6 and 7, 'laminar' flow mixing still persists up to Re ^ 10 u . It is difficult to conceive that truly laminar flow can exist at such high Reynolds numbers. Certainly, the impeller must experience a high effective viscosity for the apparent 'laminar' trend to be obtained. Now equation (3), which is simply an extension of the original Einstein formula, assumes that all of the solids are uniformly suspended. This is certainly not true for N < N j s . In the case of glass ballotini particularly, the lower portion of the vessel contains a much higher X1 than the assumed mean value. The effective viscosity in this more dense region could therefore be much greater than that predicted from equation (3). Maron et al20*21 who measured \ieff up to X1 = 60% slurry concentration, using capillary and rotational viscometers, found that y e ff could be as high as 0.1 Nsm" 2 . If this were the case, and it is \/ery probably true in view of the high density stratification occurring in the lower part of the tank, then the impeller Reynolds number would be reduced to 30 to 100, which corresponds to the laminar or transitional flow region. Once Nj s is reached, the curves in Figs 6 and 7 closely approximate the turbulent homogeneous fluid curve. However they are displaced vertically, so that higher P o m a x values are achieved as X increases. Now the calculation of Po depends on selecting an appropriate value for the fluid density. To investigate the effect of density variation in the impeller region, the data was subjected to the treatment Droposed by Herringe 22 . The power number is related to an apparent power number Po* by:



=

PIP.

=

p

P

-

(4)

o Pm where p* is the actual density of the suspension and p m is the mean bulk density calculated from: Xp s

+

O -

X

K

<5>

The result is shown in Figs 8 and 9, in which Re is based on the liquid properties. In this form, the data supports the view that the density of the suspension in the impeller zone varies with impeller speed. For N < Nj s , the suspension state is generally not homogeneous (Po*/Po < 1.0). In a number of instances, an impeller speed appreciably higher than Nj S g is needed before Po*/Po approaches unity (p* = p m ) . Three Phase Mixing Low Solids Concentration (X - 30%) As with two phase systems, power consumption in gas-solid-liquid mixing is assumed to be governed primarily by the hydrodynamics in the impeller region. The interaction between the phases is much more complex, but a study of how aeration rate and solids concentration affect Po g should provide some insight. First, if the physical properties of the liquid are used to evaluate Po g , as others have done previously 2 » 6 , a series of curves for each solids concentration is obtained, as shown in Fig 10. At the particular gas rate (QQ = 1.07 vvm), the trends are generally applicable, irrespective of impeller size and solids properties. The decreasing effect on Pog as X increases up to 20%, agrees with Chapman et al3. There is also I relative shift to the right of the minima in these curves for X = 15% and 20%, which corresponds to the Νςη, condition. This is due to the presence of unsuspended solids on the base of the vessel, referred to as a 'false bottom'. At higher concentrations however, when X > 20%, Po q undergoes a dramatic increase, so that 76

Symposium Series No. 89

dispersion of gas is not achieved until much higher impeller speeds. The most likely reason for this sudden increase, is that the impeller is completely immersed in a bed of solid particles, resulting in most of the gas bypassing the impeller. Under these conditions, it is possible that the concentration of solids in the impeller zone is so high, that formation of stable gas cavities is prevented - as witnessed by large fluctuations in the measured torque. The resistance to motion presented by the bed of solids must also be overcome. As the speed of the impeller increases, more particles are suspended, thereby reducing the 'crowding-out' effect in the immediate vicinity of the impeller. Po g values then begin to fall rapidly so that a higher impeller speed is required to disperse the gas. In Fig 10, all of the curves level off as F 1 Q becomes small. There is no distinct maximum to mark the onset of gas recirculation, as there usually is in gas-liquid mixing. This suggests, therefore, that the particles in some way inhibit recirculation of gas bubbles, either directly, or perhaps because the circulation velocity at a given impeller speed is reduced due to increasing apparent viscosity of the fluid suspension. For the reason mentioned previously, pN 3 D 5 is not constant. A more correct approach would be to plot Pog/Po (= Pg/P) against F1Q- This representation should allow a more meaningful examination of any significant effects the presence of solids might have on the gas-liquid hydrodynamics. Figs 11 and 12 are examples of this approach. For the sake of clarity, only data at X = 5% and 30% are shown; the results at other concentrations lie between these two extremes. Although both X and Q G affect Pog/Po in a consistent manner, the value of this ratio is not noticeably altered by the attainment of complete solids suspension. Therefore, density alone does not fully account for the observed trends. Fig 13 presents an overall summary view of these results for the resin and ballotini particles. The effect that aeration rate has on reducing Pog/Po is most pronounced at low Q Q . Whilst there is not a great difference between the gas-liquid curve and that for X = 5%, at QG = 0.36 vvm, there is a relatively large drop in Pog/Po when X is increased to 30%, even when N >> N j s g . This result agrees closely with that obtained by Blakeborough et al , who used a paper pulp slurry.(33) Although they argued that the reduction in Pog/Po was due to higher gas hold up in the vicinity of the impeller, a more accurate description in the light of present understanding of gas-liquid impeller hydrodynamics is that the solid particles enhance the formation of larger gas cavities. On the other hand, Pog/Po is not affected by increase in X when QG = 1.79 vvm. At this high gas rate, large stable cavities are formed in the gas-liquid system. Increasing the concentration of solids under these conditions, therefore, is not expected to significantly affect the size of gas cavity, since the maximum cavity size will already have been reached. The power curves for gas-liquid mixing have been described in detail by Warmoeskerken et al23. Variation of Pog/Po with F 1 Q , is associated with the different stages of cavity growth behind the impeller blades. Thus, the initial drop in power corresponds mainly to the formation of clinging cavities, whereas the levelling off of the curve at high F1 G values reflects the attainment of maximum cavity size. Applying this explanation to the three phase system, at high solids concentrations (X = 30%, Q G = 0.36 and 1.07 vvm in Fig 12), indicates therefore that the 77

Symposium Series No. 89

relative reduction in power is due to the formation of larger gas cavities. High Solids Concentration (40% £ X £ 50%) In this very high concentration range, only glass bai loti ni particles were used. Otherwise, a 40% concentration of resin particles would have produced a near-settled bed of solids, with no clear liquid above it. The power ratio characteristics shown in Fig 13 are quite different from those at lower concentrations. For example, in Fig 14a (QG = 1.07 and 1.79 vvm), Poq does not begin to fall rapidly until a certain impeller speed is reached. Compared with Fig 12b, Pog/Po is now generally much smaller, eg for Q G = 1.79 vvm at Fl ç = 0.015, Pog/Po = 0.35 against a value of 0.55. Therefore, the previous explanation concerning the formation of larger stable gas cavities is not valid for these conditions. It appears that the mechanism of cavity formation and possibly the very nature of the gas cavities themselves, has been altered due to the very high solids loading. In order to obtain further insight into the hydrodynamic effects around the impeller with' these high particle concentrations, a series of unsteady state tests was made. Fig 15 shows the transient power response following a step change in the input gas flow rate (positive and negative). There are two observations to be made. First, it takes approximately 10 seconds for the power to reach its final steady state value. Compared with gas-liquid systems 2 4 , the formation and growth of gas cavities in the gas-liquid-solid systems is a fairly slow process. Secondly, there is the rather strange response to a negative step change in gas flow rate (starting from the steady state value previously attained). Pg(t) - P(o) does not return to zero after the gas is turned off, but remains at the previous steady-state value. The fluctuations in measured torque, normally observed under aerated conditions, are also diminished. Since these fluctuations are associated with the activity of gas flow in the impeller region, these would obviously tend to disappear if QG = 0. Increasing the impeller speed, or leaving the system in operation for a prolonged period (t > 15 minutes), did not alter Pg in any way. Both the longer growth time required to form 'stable gas cavities' and attainment of lower Pg/P values, indicates that when the concentration of solids is very high, the size of cavities which are produced is much larger. It is possible therefore, that all of the six impeller cavities are enjoined together, effectively producing a single large gas bubble. It could be in the form of a "trapped" reservoir of gas beneath the disc of the impeller, or alternatively, the entire impeller may have been enveloped in gas. This would explain why the power did not return to its original ungassed value when the gas was turned off. Overall Considerations The results demonstrate the enormous complexity of the three phase mixing hydrodynamics in the impeller region. Fig 16 shows how Pog/Po varies over the whole range of solids concentration and provides a basis for some rational explanation of the observed effects. Comparison with the power consumption effect in highly viscous liquids (Newtonian and non-Newtonian) reveals that there are some close similarities, particularly regarding the nature of the gas cavities. 78

Symposium Series No. 89

Van't Riet 2 5 found the shape of the cavities in viscous Newtonian liquids to be quite different from those in low viscosity aqueous systems. Yagi and Yoshida 26 and Solomon et al21 who investigated non-Newtonian liquids, found that there was poor dispersion of gas from the impeller because it was rotating in a gas volume or 'cavern', of flattened doughnut-shape. For these systems, Ranade and Ulbrecht 28 have shown that the gassed power only reduces appreciably above a certain Reynolds number, but once achieved, the cavities remain stable, even after the flow of gas has ceased. This insensitivity of the power consumption to gas flow has also been reported by other workers 2 9 » 3 0 . Referring to Fig 16, the variation of Pog/Po with solids concentration is now explained in terms of the rheologicaT-viscous effects produced in three-phase mixing. Region A (0% < X - 30%): A gradual reduction of Pog/Po occurs as the solids concentration increases, which is due to increasing apparent viscosity of the three phase suspension. At the same time, larger stable gas cavities are produced. The increasing viscosity effect is a gradual one - this is supported by Oldshue's 31 work on coal slurries where he found that no large increase in viscosity took place until X exceeded 35% concentration. Weinspach 32 has also shown that, for suspensions up to 25% v/v, the rheology is essentially Newtonian. Regione (40% * X ^ 50%): The three phase suspensions are highly non-Newtonian and there is a large reduction in Pog/Po (this also occurs at lower gas flow rates). Also, the gas cavities remain stable, even when Q Q = 0. Region B (30% < X < 40%): This region, which is reproducible for different size impellers, particle size and gassing rate, is viewed as a discontinuity between regions A a n d c . The reason for this behaviour is not known but it is thought to signify a radical change in the normal process of cavity formation. Thus, the six individual large cavities may have coalesced to form a single large gas bubble, though of smaller dimensions than that formed in region C. CONCLUDING REMARKS For solid-liquid mixing in the turbulent region, Po coincides with the value for a corresponding homogeneous fluid only if a uniform state of particle suspension is achieved. Generally, this requires an impeller speed higher than the minimum suspension speed, N j s . In three phase mixing, the complex interactions occurring between solid particles and gas bubbles in the impeller region have a significant effect on the measured power. It is possible to explain certain features of the three phase power effect by reference to present knowledge on gas-liquid mixing hydrodynamics and rheological properties of solid-liquid suspensions. It is concluded that the size of gas cavities which are formed depends on the effective viscosity of the three phase suspension. At \jery high solids concentrations, the process of cavity formation also appears to be changed. The viscosity effect increases with particle concentration, becoming non-Newtonian at concentrations higher than about 30% w/w. 79

Symposium Series No. 89

SYMBOLS USED dp C D FIQ H N NCD

particle diameter (m) distance of impeller from bottom of vessel (m) impeller diameter (m) flow number, Q Q / N D ^ (dimensionless) height of liquid in vessel (m) impeller speed (s" 1 ) impeller speed at which gas is just dispersed throughout the vessel (s" 1 ) impeller speed at which particles are just suspended off the tank bottom; gassed condition (s" 1 ) impeller power; gassed power (w) power number; gassed power number (dimensionless) maximum value of power number (dimensionless) gas flowrate (m 3 s _ 1 or vvm) Reynolds number; at start of surface aeration (dimensionless) (volumetric flowrate of gas/minute) / (volume of liquid) solids concentration (% w/w) solids concentration (% v/v) liquid density, particle density (kgm~ 3 ) average bulk density (ksnr 3 ) density difference (ps - p u ) (ksnr 3 ) effective viscosity of suspension; liquid viscosity (Nsm~ 2 )

Njs> Njsg P, Pg Po, POg Po max QQ Re, Re$A vvm X XI p£, p s pR Δρ v'eff» ^L

REFERENCES Blakeborough, N. and Sambarmurthy, K. 1964, J. Appi. Ckem. 14,413 Chapman, C M . , 1981, PhD Thesis, University of London Chapman, C M . , Nienow, A.W., Cooke, M. and Middleton, J . C , 1983,

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Design,

61(3), 167

Arbiter, N., Harris, C.C. and Yap, R.F., 1969, Trans AIME 244, 134 Quenau, P.B., Jan, R.J., Rickard, R.S. and Lower, D.F., 1975, Metallurg.

Trans.

6B, 149

Wiedmann, J.A., Steiff, A. and Weinspach, P.M., 1980, Chem. Eng.

Comrn. 6, 245

Zweitering, T.N., 1958, Chem. Eng. Soi. 8, 244 Cliff, M.J., Edwards, M.F. and Chiaeri, I.N., 1981, I. Symposium

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No.64,

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Chem.E.

Bohnet, M. and Niesmak, G., 1980, Ger. Chem. Eng. _3, 57 Nienow, A.W., 1968, Chem. Eng. Sci 21, 1453 Wichterle, K. and Wein, 0., 1981, Int. Chem. Eng.?A_, 116 Weisman, J. and Efferding, L.E., 1960, A.l.Ch.E. Journal (5, 419 Arbiter, N., Harris and Steininger, J., 1964, Trans. AIME, 229, 70 Sverak, S. and Hruby, M. , 1981, Inst. Chem. Eng. 2]_, 519 Brodkey, R.S. in Uhi and Gray (Eds), 1966, Mixing, Academic Press Inc., London, P132 Brown, D.E., 1981, I.Chem.E.

Thomas, D.G., 1965, J. Colloid

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18 19 20

21 22

23

Rutgers, I.R., 1962 Rheological

Acta.

2, 202

Jeffrey, D.J. and Acrivos, A., 1976, AIChE Journal, 2£, 417 Maron, S.H., Madow, B.P. and Krieger, I.M., 1951, J. Colloid Sci, 6>, 584 Maron, S.H. and Fok, S.M., 1955, J. Colloid Sci.]0_, 482 Herringe, R.A., 1979, Proc.

Third

European

Conf. on Mixing

(BHRA)3

199 Warmoeskerken, M.M.C.G., Feijen, J. and Smith, J.M., 1981, I.Chem.E.

Symposium Series

Eng. Sci.

38(11), 1909

No.64> Jl

2k

Greaves, M., Kobbacy, K.A.H. and Millington, G.C., 1983, Chem.

25

Van't Riet, K., 1973, PhD Thesis, Delft University of Technology Yagi, H. and Yoshida, F., 1975, lEC(PDD), 14, 488 Solomon, J., Nienow, A.W. and Pace, G.W., 1981, I.chem.E.

Symvosium

Ranade, V.R. and Ulbrecht, J., 1977, Proc.

Conf.

26

28 29 30 31 32

33

Series

No.643 Al

on Mixing

(BHRA), F6

Taguchi, H. and Miyamoto, S., 1968, Biotech. Edney, H.G.S. and Edwards, M.F. 1976, Trans.

Second European Bioeng. 89 43 Instn. Chem.

Engnrs, j>4, 160 Oldshue, J . Y . , 1980, AIChE Annual Meeting, Chicago, 65e Weinspach, P.M., 1969, Chem. Eng. Tech. 4 ^ , 260 Hamer,G. and B l a k e b o r o u g h , N . , 1963, J . A p p i . C h e m . , 13,517

Postscript to Eqn (4) P Q - power number for homogeneous fluid P Q * - measured apparent power number based on suspension bulk density

81

Symposium Series No. 89

Top Flange Piate

0. 1 5 m

as Sparger

Figure 1

Details of mixing vessel and gas sparging line

82

Symposium Series No. 89

l^Sk 15

p '

x=?oy o



Δ

a



D (n) 0.0762 0.1016 0.1350

^.10 1

00 CD in

''">

- —·

< à

1

A

5 —

L 0.5

n

n

n ■



0 '

Ar

x

|_

1 1.0 QG

ü 1

y -■



ft

1.5

i

2.0

(vvm)

Figure 2 Effect of gassing rate on N j s g (resin particles, dp = 780 pm)

<2

10 L

Figure 3 Effect of gassing rate on NjSg (glass ba^lotini particles, dp = 655 urn) (symbols as in Figure 2) / 83

Symposium Series No. 89

Njsg, Chapman

Figure 4

(s" 1 )

NjSg values compared with those of Chapman2 (QG = 1.0 vvm) Particles •

resin

0

b a l l o t i n i (d p = 275 pm)

(d p = 7S0 urn)

84

Po

h-



Figure 5

3 h"

6

1

/ A



4

J

'



A

Re





A

5

.

A

·

6

7

8

1 J L _i

11

12 13

I I I

01350

Δ

00762

D (m )

\*\\.



01016

10

A ^

a

9

A



■ 1

A



O

I

A

Hrl.OT

A

—o

· ;·■·■·



A



Ητ1·25 Τ

A



x 10"" 4

1L_





Effect of Liquid height on Power Number (X = 0, C/T = 0.25)

3



Ί

Symposium Series No. 89

Symposium Series No. 89

7

1

δ

6



o

5:

i

Î

fi

A

*

1

A

1

Ô

o d X (%)

"js f o r X = 5% X = 30%

— °

3

* * A

* -

L 2

f

1

3

1

5 6 7 8 Re x IO"14 (a) (D = 0.0762 m, resin p a r t i c l e s , d p = 780 pm)

9

6 5

10

^S^

^ 8

,

J 12

T

A

x



4h

f

A

ψ

10 15 20 25 30

_JL_ 1 _ I I I

4

1 T

o 5

A

*

o

s>

Γν A

' Δ

2\~

» N j s for X =5% X =30%

1 2

3

L 4

J

_i.

5

6

1 -

I

1

1

1

7

Ö

9

10

12

J

Re x 1Ü"1· (b) [D = 0.1016m, resin particles, dD = 780 urn, symbols as in ( a ) ] Figure 6

Effect of solids concentration on Power Number 86

15

Symposium Series No. 89

3

k

5

6

7

8

9

10

12

15

Re x 10-* 7 ( e ) [D = 0.1016 m, glass b a l l o t i n i , d p = 655 Mm, symbols as in Figure 6 ( a ) ]

7 —

A

6 A A

5 -

1 o

5

Δ

Δ

S

S ■

0

·

O

·

s0

A

°

·

μ^-^^ 1

k ■

Nj s forX= 10% X=50%

3

I

o

8 5

2

—I

3

J

k

1

5

6

1

7

1

8

1 1 1

9

10

1

12

1

Re x 10-7(b)

[ D = C.135 m, Glass b a l l c t i n i , d p = 1300 ym, symbols as in Fig 6(a) ] Figure 7

Effect of solids concentration on Power Number 87

Symposium Series No. 89

1.1 o 1.0

i





O

-



A Έ

Δ

O

δ ■ O

0.9





o

O

O

O

o

A

A

*S ' ,1 o

A

l

Δ

m

u° 0.Θ "~

o A

X (%) A

Δ

Njs for• x==1C*

A

0.7

0

10



20

Δ

30

A

**0

o

50

O

x=50%

O

1

_. i_.

3

J_ 5

L_

7

J

j

1

11

13

11

13

Re x 1 0 - "

& (a) (glass b a l l o t i n i , d

a?

= 655 um)

0.8

7

8 (b) [ resin p a r t i c l e s , d p Figure 8

9

Re x IO" 4 = 780 um, symbols as i n 8(a) ]

Variation of Power Number r a t i o with Reynolds Number (D = 0.1016 m)

Symposium Series No. 89 1.1

o 1.0

Δ

"

■ O



O

o

S

Δ

Λ

■ Δ

O

o

.

Δ

o?

0.9 —



Nj s for X=10% x=30%

0.8;

I ■ _ . _ !

o.?

5

_i_ 7

J

9

1 11

13

1

Re x IO" * (a) [resin particles, d

= 780 um, D = 0.0762 m, symbols as in Figure S(a)]

1.1

3

5

7

9

11

13

Re x 10-w (b) [glass b a l l o t i n i , d p = 1300 um, D = 0.135 m, symbols as in Figure 8 ( a ) ] Figure 9

Variation of Power Number ratio with Reynolds Number 89

Figure 10

D = 0.1016 m, Q = 1.07 vvm)

Gassed power number against flow number (resin p a r t i c l e s , d p = 780 um,

F1Q χ IO2

Symposium Series No. 89

Symposium Series No. 89

0.9

X = 5%

Arrows i n d i c a t e Nj S g 0.3

4 Φ

X=30%

Q<-, ( w m )

Δ a o

A ■ ·

0.36 1.07 1.79

(

NO S o l i d s

)

0.7

0.6

*^=0.36

vvra

0.5

ο.4Γ

0.3

J

I

I

L

j

I

F1G x 102 (a) (resin p a r t i c l e s , d p = 730 Mm, D = 0.0762 m)

0.9,

(b) [ r e s i n p a r t i c l e s , d p

F U x 10G = 780 pm, D = 0.1016 m, symbols as i n (a) above]

Figure 11 P0g/Po against Flow Number 91

Symposium Series No. 89

o.9h-

o.flL

0.?h-

F1G

(a) [ r e s i n p a r t i c l e s , d

x 102

= 780 μπι, D = 0.135 m, symbols as in Figure 11(a)]

F1C x 102 (b) [glass bal l o t i n i , d p = 655 μπι, D = 0.135 m, symbols as in Figura 11(a) Figure 12

P 0 g /P o against Flow Number 92

Symposium Series No, 89

E

> I-.

ca c I

a

0

d' / 6od

Symposium Series No. 89 1.0 0.9

0.8 0.7

0.6 XrùOi^ X = 50fr

0./.

Q-(

VVmi

Δ



0.36

O



1.07

o



i.79

Arrows mark NiQ a

o. 7 . F1 G x 10£ (a) (glass b a l l o t i n i , d p = 655 urn, D = 0.135 m)

NrZf.O

S

N=5.0 s

-1

:Ì = 5 . 5 s

N=6.0 s - 1

Nr7.0 s 0.3

J

-1 L

F1G x 102

(b) (glass ballotini, d p = 655 μπι, D = 0.135 m, X = 40%) Figure 14

Pnfl /Po against Flow Number y

94



°

?

0

*♦

ο ° ο ο θ

6

ß

io

1

%

(ο)

° 2 ο · ο °

12

0.0

1.07vvm

Qci(t)

ο.°.ο·°·ο.0.. ο· ·ο ο

1.0?vvm

·

Step Pownw.urdü

.

0.0

· .

Step Upwards

Time (a)

Ο

·

dp = 655 Mm, X = 50%, D = 0.135 m, N '= 5 s " 1 )

Figure 15 Transient impeller power response t o a step change i n glas flowrate (glass b a l l o t i n i ,

o

ο

Ο

Γ~ Ο

U

ο ο ο

· · * · · · · · · · . » · ·

H

Symposium Series No. 89

Symposium Series No. 89

X %

Figure 16

Pog/ p 0

a

9 a i n s t solids concentration (glass b a l l o t i n i ,

dp = 655 um, D = 0.1016 m, N = 9.0 s " 1 , QG = 1.07 vvm)

96