A hypothesis on the effect of the bubble wake on coalescence in three-phase fluidised beds

Chemical Enginerrirrg Screncr,Vol. 43. No. 8. pp 2207-2213.lU88. Printedin Great Hrltain.

A HYPOTHESIS

ON

THE EFFECT OF THREE-PHASE

000%2509/M $3.0o+fl.Oa Prrganron PrrssVIC

THE BUBBLE WAKE FLUIDISED BEDS

ON

COALESCENCE

IN

by A.C.

van

‘t

Koninklijke/Shell-Laboratorium, Postbus 3003, 1003

Hoog AA

and

L.

van

Amsterdam Amsterdam,

Raam

(Shell Research The Netherlands

B.V.)

ABSTRACT It has been known for quite some time that bubbles ascending in a three-phase fluidised bed may carry upwards in their wake a considerable volume of liquid. This may locally result in a liquid defluidisation can easily velocity insufficient for proper fluidisation of the particles. Local We have explored the postrigger bubble coalescence, which may be undesired for various reasons. sibility of rationalizing the bubble sizes observed in a three-phase fluidised bed that operates in the coalesced bubble flow regime, using information published recently on the relative wake volume of the bubbles at such condiLions. may be stable in a three Very small bubbles are known to be wakeless. These bubbles, therefore, The production of these small phase fluidised bed, provided the solids are properly fluidised. bubbles is postulated to be a potential solution to the coalescence problem. It is suggested that at intermediate bubble sizes and realistic combinations of gas and liquid velocities an unstable region exists, in which either bubble break-up or bubble coalescence has to occur to arrive at a stable situation. The evidence collected so far confirms the expected position of the way of correlating bubble size in upper boundary of the unstable region, and it suggests a simple the coalescing bubble regime. Further experimental work is, however, required. KEYWORDS Three-phase

fluidised I.

bed;

flow

regime;

coalescence;

bubble

wake;

bubble

size

INTRODUCTION

A three-phase fluidised bed can in principle be employed for any process in which a solid catalyst is used in the reaction of a gas with a liquid, in the production of a liquid from a reacting gas phase or in a gas phase reaction in which the liquid is only present to remove the heat of reaction. Examples are the hydrogen treatment of heavy oil fractions and the production of oxygenates or a broad spectrum of hydrocarbons from hydrogenand carbon monoxide-containing synthesis gas. One might also think of biochemical applications in which micro-organisms are immobilised 011 a solid carrier, or ot processes in which the solid phase itself is one of the reactants. In the latter case the geometrical and physical properties of the solids may change significantly during the time the solids reside in the reactor. process is the A major barrier for the application of a three-phase fluidised bed in a commercial well-known rapid coalescence of gas bubbles in such a reactor. The resulting large bubbles will induce top-to-bottom circulation of the reactor contents. This circulation leads to a highly backmixed reactor, and moreover makes scale-up a instead of the often preferred plug flow reactor, time-consuming exercise, as it will in most cases involve testing at a number of intermediate reactor sizes. The increased bubble size may also lead to gas-liquid mass transfer limitation of the rate of reaction, even for moderately fast reactions. It is therefore of importance to investigate the mechanism(s) underlying the coalescence of bubbles in a three-phase fluidiscd bed in order to be able to devise means to reduce the degree of coalescence to an acceptable level. II.

DEVELOPMENT

OF

THE

HYPOTHESIS

In a liquid-solid fluidised bed a minimum of all particles in the bed. At increasing particles increases, i.e. the bed expands.

liquid velocity (Umf) is required liquid velocity, beyond Umf. the

to achieve fluidisation distance between the

Introduction of gas bubbles into a liquid-solid fluidised bed creates extra movement in the bed and could lead to an apparent lowering of the minimum liquid velocity needed for fluidisation (see e.g. Begovich and Watson, 1978). The introduction of gas bubbles, however, also has as a bed is carried upwards consequence that some of the liquid entering at the bottom of the fluidised in the wake of the bubbles and will therefore not contribute to the fluidisation of the particles. In the literature various publications on the wake theory can be found describing the effect of the wake of rising gas bubbles on bed expansion (see e.g. Stewart and Davidson, 1964: Rigby and Capes, 1970; Epstein, 1976).

CiS

4:19-FF

2207

A. C. VAN?

Darton phase, enhance

and Harrison and reported coalescence.

(1975) mentioned the that both an increase

HOOG and L. VAN RAAM

ultimate in gas

G9

situation of defluidisation flow and a decrease in bed

of the expansion

particulate are known

to

Application of the wake theory may be extended by setting up a mass balance for the liquid, assuming the particulate phase to operate aL the minimum fluidisation velocity, to determine the maximum amount of liquid available for the bubble wakes. Any shift in the liquid balance will be reflecuntil a new balance is reached between the amount of liquid ted in a change in the bubble diameter, the amount used for fluidisation and the amount carried upwards by the bubbles. supplied, In the coalesced bubble flow regime, as we will see later, a maximum value for the volume of the bubble wakes corresponds to a minimum value of the mean bubble diameter. So, in this regime, due to coalescence of gas bubbles a larger fraction of the liquid will be available for fluidisation of the and in fact these may provide us with an particles. For very small bubbles this may be different, alternative solution to the coalescence problem in three-phase fluidised beds. is that for stable operation (i.e. at a stable bubble size distribution) of a So, the hypothesis the volume of liquid supplied (by1 - A.V,I), three-phase fluidised bed, corrected for the volume of liquid carried upwards in the wake of the bubbles (k.~$,~ - k.A.Vsg), should be equal to, or larger than, the volume of liquid required for fluidisation of the particles (A.U,f)_corrected for the fraction of the cross-sectional area occupied by the bubbles and their wake (eg + ic.;,). This may be expressed by the following equation:

A

Vsl

- f A Vsg

&

(1

- ig

__ - k eg)A

In this equation we a.ssume the wakes ticles having sufficient inertia. Equation

(1)

may

be

rewritten

of

Umf the

(1) bubbles

to be

free

of

solids.

This

holds

only

for

par-

as:

(2)

For

sufficiently V

- Umf

Sl

small

values

of

i g U mf/%g

equation

(2)

reduces

to:

&,i;

(3)

i7 In 20

the experiments considered for a first test %. Still,

in of

this publication this the ideas,

this simplification is considered to be

leads to acceptable.

errors

the liquid-to-gas volume ratio Equation (3) suggests that, to avoid defluidisation. correction for the volume of liquid needed for fluidisation of fluidised bed, after in which liquid and gas are transported should be larger than or equal to, the ratio rising bubbles. We will call the left-hand side of equation (3) the excess velocity To test the hypothesis expressed in equation (3) we a relation p resented k. Recently Darton (1984; 1985) bubble diameter in the bubble coalescing regime: k - 0.0002

need for

information on the the parameter 1; as

up

to

about

supplied to the the particles, upwards by the ratio.

value of the parameter a function of the mean

d;1.8

(4)

originally based on data obtained with air-water fluidised 550-pm and 775-pm partiThis equation, glass has been verified for air-water fluidised 0.4, 1, 3 and 6 mm diameter cles (Darton; 1984), beads (Darton; 1985). In these experiments the mean bubble diameter exceeded 4 mm. Hence, equation (4) should not be used for bubble diameters less than 4 mm. Information knowledge,

on not

the wakes available

of in

smaller bubbles in the open literature.

three-phase

fluidised

beds

is,

to

the

best

of

our

Very small bubbles behave as rigid spheres. Rigid spheres for which the Reynolds number is below 20, are known to be wakeless, i.e. k = 0 (Clift et al., 1978). We may, therefore, expect very small bubbles in three-phase fluidized beds to be wakeless as well. For such bubbles equation (3) is always satisfied, provided the solids are properly fluidised, i.e. Vsl >, Umf. For intermediate bubble sizes we will attempt to translate information from solid-liquid systems to the situation in a three-phase fluidised bed. Kalra and Uhlherr (1973) published information on the relative wake volume. i.e. the volume of the wake divided by the volume of the particle. as a function of the Reynolds number, for single spherical particles in an undisturbed flow of water. Recently Wasowski and Blasz (1987) published similar results. From the literature on the behaviour of air bubbles in water (see e.g.

Coalescence

G9

in three-phase

fluidised

beds

2209

Clift et al., 1978), we know air bubbles in water to be spherical up to a diameter of about 1 mm. Although the relative wake volume may be smaller due to internal circulation of the bubbles, as a first guess we assume the results of Kalra and Wasowski to be applicable to single gas bubbles in water, provided the diameter is less than 1 mm. For the conversion of the particle Reynolds rumhers into equivalent bubble diameters we used the terminal velocity data for air bubbles in water of Clift et al. (1978). For bubble sizes larger than 1 mm it may be useful to remember the limiting values of the relative wake volume observed by Wasowski and Blasz (1987) viz. a value of about 2.3 for spherical particles and a value of about 4.3 for ellipsoidal particles. For oscillating gas bubbles with internal circulation a lower value of the relative wake volume may be expected. Wasowski and Blasz (1987) provide some information on experiments reported by Subramanian, who showed that for small bubbles the relative wake volume increases from a value of 0.9 at a Reynolds number of 10 to an almost constant value of 1.6-1.7 at a Reynolds number of 200 The information presented above has been collected translation to the air-water in Figure 1, after system. The downwards sloping line on the righthand side has been taken directly from Darton (1985). It represents the relative wake volume for air bubbles in air/water/glass spheres fluidised beds. On the left-hand side we have indicated the information originating from experiments with single solid particles. The dashed lines encompass bubbles having a Reynolds number of 20 at which a wake starts to develop, Kalra's ?_-esuits (after conversion) for equivalent bubble sizes of 0.5-1.0 mm, Wasowski's results (after conversion) for equivalent bubble sizes of 0.8-1.0 mm and the limiting values for spherical and ellipsoidal particles. The position of this barId of information has to be corrected, to an for the effects of internal cirunknown extent, culation of the gas bubbles, oscillation of the gas bubbles and the prese~lce of neighbouril~g gas bubbles or particles in a three-phase fluidised bed. These factors are expected to result in a relative volume of the bubble wake which is smaller than indicated by the band in Figure 1. We have also included a curve representing Subramanian's data. The value of the relative wake volume at low Reynolds numbers is surprisingly high: the value reached at higher Reynolds numbers is more in line with expectations.

10

1

01

00-1

Fig.

1:

Relative volume of bubble wake dcri ved from data on two-phase systems and for three-phase fluidised beds of air/water/glass spheres. (a) Subramanian (from Wasowski and Blasz, 1987) (b) Wasowski and Blasz (1987) (c) Kalra and Uhlherr (1973)

We have postulated earlier that for stable operation of a three-phase fluidised bed, equation (3) has to be satisfied. This implies that if we would plot in Figure 1 experimental values of the excess velocity ratio (Vs._-Umf)/Vsg versus the mean bubble diameter observed in the experiments, the data should be located just above the straight line (for the coalescing bubble regime) OII the curved band, with due consideration for the factors not yet included in the position of the band, in order to satisfy equation (3). Conversely, stable operation of a three-phase fluidised bed will, in general, not be possible for mean bubble diameters within the region bracketed by the curved band and the straight line. The initial bubble size is to a large extent determined by the design and operation of the sparwithin the "unstable region". Shallow three-phase fluidised beds may, ger, and may be located therefore. operate in the "unstable region" due to the fact that coalescence or bubble break-up has not been able to proceed far enough for stable bubble size to be reached. III.

EXPERIMENTAL

We have done some experiments in the coalescing bubble regime for a first teet In the experiments we used: glass spheres of 2.17 mm diameter. These particles a hydrocarbon solvent (SHELLSOL-T). The gas phase was nitrogen.

of the above ideas. were fluidiscd by

set-up consisted of a perspex column Figure 2 shows a diagram of the equipment. The experimental liquid was pumped to the bottom of the of 0.1 m inside diameter and 5 m height. After filtering, by means of a variable speed gear pump. Liquid left COlUmI-t, via a set of calibrated rotameters, vessel. The liquid the column via an overflow at a height of about 3 m and returned to the storage distributor at the bottom of the column was cross-shaped. It was constructed from 12.7 mm diameter stainless steel tubing and contained 96 holes of 0.8 mm diameter at radial distances from the cenat constant liquid load tre of the column equal to approx. 9, 23, 30, 35, 39 and 42 mm, thus aiming per unit of column cross-sectional area. At each radial position and in each arm four holes were drilled, twca on both sides of the arms in a horizontal direction, and two directed downwards at 450 to the horizon, This liquid distributor was positioned at a distance of approx. 20 mm from the bottom of the column. The nitrogen was metered via calibrated rotameters into the bottom of the column. The gas distrifrom 9.5 mm stainless steel tubing. butor was ring-shaped (outer diameter 80 mm) and constructed opposite positions. The distributor Gas was supplied to the bottom of the ring at two radially

A.C.

2210

VAN?

HOOG

and

L. VAN RAAM

G9

contained 16 holes of 0.3 mm diameter directed vertically upwards and was of approx. 75 mm above the liquid distributor to ensure proper fluidisation the position at which the gas was introduced into the column.

positioned at a distance of the particles at

each pressure tapping The perspex column was equipped with pressure tappings at 0.2 m intervals, being connected to transparent plastic tubing filled with the liquid used in the circulation system. These manometric tubes were used to measure the pressure gradient in the column, from which as will be described below. The temperature of the the gas and liquid hold-up were calculated, contents of the column was measured at 0.9 m from the bottom. The height of the expanded bed of solids was determined by visual observation. In corresponding to the height equivalent to the volume culations a small correction, was applied to this bed height. butors,

subsequent calof the distri-

All experiments were carried out with SHELLSOL-T as liquid. SHELLSOL-T is a hydrocarbon solvent 30 ppm antistatic additive approx. boiling between approx. 180 and 210 OC. In the experiments to increase its electrical conductivity and to avoid the genera(ASA-3) was added to the liquid, tion of electrostatic charges. The heading of Table 1 contains the liquid phase properties at 20 OC. In subsequent calculations the liquid phase properties were corrected for the effect_ of variations in temperature by means of simple interpolation formulae. The particle properties used in rhe evaluation of the experimental results are also given in Table 1. The particle size distribution of the glass spheres was very narrow. The average diameter of the glass spheres was determined by weighing a given number of particles and calculating the volume-averaged diameter using the known density of the particles.

2.8-6 4.2--8 4.8-12 6.0-16 9.5-m 8.0-m

h

2.2-6 3.0-7 6.5-10 6.5-12 6.5-20 6.9-30

Fig.

2:

2.3-C 2. s--10 3.2-25

2.2-e 2.5-m 3.5-30

The solids hold-up was obtained from the known of the particles and the visually observed bed volume of the spargers):

The gas and liquid hold-up were metric tubes described before: dP -dz

==g(LJe

gg

+

p141

+

obtained

"pcs)

from

weight height

the

Schematic diagram of experimental equipment. 1 test section, 2 disengagement section, 3 liquid return line, Ir liquid storage vessel, 6 nitrogen supply 5 gear pump, line, 7 safety valve, 8 position of gas and liquid distributor, 9 connection points for manometric tubes, 10. vent.

of solids (corrected

pressure

in the column, for the height

gradient

measured

by

the known density equivalent to the

means

of

the

mano

Coalescence

G9

Individual

values

% +

‘1

+

c*

Eg and

of =

RESULTS

be

calculated

by

fluidised

taking

into

1

During the experiments respect to bubble size coalesced bubble flow, of smaller bubbles. IV.

fl may

in three-phase

beds

account

2211

that: (7)

visual (and a limited number of photographic) observations were made with and flow regime. We will only consider experiments in which we observed i.e. in which large bubbles were seen to be present alongside a narrow range

AND

DISCUSSION

Table 1 summarizes the results of the experiments and subsequent calculations. The minimum fluiin which the pressure disation velocity of the particles was determined in separate experiments, starting from a well-fluidised drop across the bed was measured as a function of liquid velocity, system and slowly decreasing the liquid throughput. The point of minimum fluidisation was assumed to be located at the intersection produced upon extrapolation of the two straight parts of the pressure drop characteristic. In the calculations the value of the minimum fluidisation velocity was corrected for the effect of changes in temperature by recalculation via the Ergun equation using the relevant physical properties and assuming the voidage at minimum fluidisation conditions to be unaffected by temperature. The average gas velocity is the superficial gas velocity corrected for the average pressure in the section of the column for which the pressure gradient has been measured. In the present experiments this section started at 32 or 52 cm from the bottom i.e. well above the gas distributor. The gas, liquid and solids hold-up have been obtained via the procedure described in the previous section. In Figure 3 we present a first test of the ideas outlined in Section II. In this figure we have plotted on the vertical axis the value of the excess velocity ratio (as defined in equation (3)) and on the horizontal axis rhe observed range of bubble diameters. The lower boundary of this ignoring a minority of very small bubbles. The upper boundary range was obtained from photographs, supplemented by visual observations, especial of the range was obtained from the same photographs,

Fig

3:

Comparison of k value according to eq.4 with relation between excess velocity ratio and observed bubble diameters for 2.17 mm glass spheres in SHELLSOL-T.

Fig.

4:

Comparison of data for air/water/ 0.5-0.6 mm sand particles collected by Darton and Harrison (1974) with boundary for coalesced bubble flow regime (solid line) and corm relating equation 9 (dashed line).

my in experiments in which rather large bubbles were produced. We have not attempted to calculate a mean bubble diameter from these observations. In the figure we have incorporated the straight line representing the relative wake volume of the bubbles as a function of the mean bubble diameter (equation (4)). It is comforting to see that a decrease of the exce~e velocity ratio is in general as is suggested by combination of accompanied by an increase in the observed bubble diameters, position of the experimental data is in line equations (3) and (4), and that even the absolute uncertain whether equation (4) is applicable to our hydrocarbon with expectations. It is, however, system. The constant in equation (4) can easily be imagined to be affected by the liquid phase one would expect Tc to be a function of some kind of Reynolds nunproperties. As a matter of fact, her, just as in two-phase systems. This is a point to be investigated in future experiments. Still, the outcome of this first test of our ideas is satisfactory enough to warrant further research in this area.

2212

A.C.VAN'T

and L. VAN

HOOG

RAAM

G9

As an extension of the hypothesis described so far, and on the basis of the reasonable agreement observed with experimental data, we may go one step further and assume the mean bubble size in the coalesced bubble flow regime to be directly related to the excess velocity ratio. Combination of equations (3) and (4) then leads to the following dimensional relation for the mea~l bubble size in the coalesced bubble flow regime: -0.56 (8) It should lue,

the

be

realised

term

between

that

for

brackets

systems

in which

should

be replaced

the

group

by

the

2 U g mf/%g left-hand

has side

a sufficiently of equation

large

va-

(2).

In Figure 4 we have plotted the arithmetic mean values of the bubble chord length measured by Darton and Harrison (1974) in the centre of a 0.229 m diameter column containing air-water fluidised sand particles of 500-600 pm, The solid line represents equation (8). assuming that that the data are located above the solid E(1) = 2 de/3 (Darton, 1985). It is obvious, as expected, to see the excellent correlation of the experimental values of line. It is surprising, however, of the dashed line in this figure can be repreE(1) with the excess velocity ratio. The position sented by the dimensional equation: -0.43 V Sl -"mf ___ (9) v ( sg ) This equation avoids the use of more complex correlations involving for irlstance the bed viscosity, such as proposed by Darton (1985) and describes Darton's experimental data equally well (compare including variation of liquid properties, will be 1985). Further testing, Fig. 15.5 in Darton. to see whether equation (9) can be extended to make it generally applicable to the coanecessary lesced bubble flow regime. E(1)

= 0.0124

CONCLUSIONS Starting from the hypothesis that coalescence in three-phase fluidised beds may be triggered by local defluidisation s.s a result of the liquid carried upwards in the wake of bubbles, and on the basis of the limited experimental information available at this moment we arrive at a number of preliminary conclusions: - Very small wakeless bubbles are expected to be stable in a three-phase fluidised bed. - At realistic combinarions of gas and liquid velocities an unstable range of bubble sizes is exto (almost) wakeless small bubbles or coalescence to larger pected to exist, in which break-up to be having a smaller relarive wake volllme, has to occur for s stable situation bubbles, reached. - A simple way of correlating bubble size in the coalesced bubble flow regime has been proposed, which

should

It will be correctness

be

further

tested

to investigate

fully

clear that further work has to be done of the above preliminary conclusions.

its applicability

co confirm

the underlying

ideas

and

to prove

ROTATION .4 de D E(1)

cross--sectional

mean

bubble

of the

area

nl2

column

diameter

column diameter arithmetic mean

m m

of bubble

chord

length

g H'

gravitational acceleration bed height corrected for volume

taken

by distributors

k

average value of relative volume of bubble in a three-phase fluidised bed pressure Reynolds number of bubble or particle temperature minimum fluidisation velocity

P Re Ll mf 5 V

local sg Sl

w z ES ; g tl es

superficial

superficial

gas velocity

liquid

weight of solids axis1 distance gas hold-up local

value

gas hold-up

liquid

hold-up

solids

hold-up

velocity

in the

column

m

m/s

(- 5

vg@) (= 4,l/A)

wake

for

2 m

a swilrm of bubbles 2

N/U _ OC

4s

m/s m/s kg Ill _

the

Coalescence

G9

density

of

the

gas

density

of

the

liquid

density

of

the

particles

in three-phase

fluidised

beds

2213

phase

pg fl

local (a vl

volumetric

volumetric

liquid

gas

flow

flow

rate

rate

REFERENCES J.M. and J.S. Watson (1978). In J.F. Davidson and D.L. Keairns (Eds.), Fluidization, Begovich, Cambridge University Press, London, p, 190. Proc. 2nd Eng. Found. Conf., and M.E. Weber (1978). Bubbles. Dross and Particles, Academic Press, London. Clift, R., J.R. Grace R.G. (1984). Paper presented at ICHMT Symp. Heat and Mass Transfer in Fixed and Fluidized Darton, Dubrovnik. Beds, R.C. (1985). In J.F. Davidson, D. Harrison and K. Clift (Eds.), Fluidization. 2nd ed., Darton, Academic Press, London, Ch. 15. R.C. and D. Harrison (1974). Multi-chase Flow systems, Vol. I, I. Chem. E. Symposium Darton. Series No. 38, Inst. Chem. Engrs., London, Paper Bl. R.C. and D. Harrison (1975). Chem. Eng. Sci., 30, 581. Darton, N. (1976). Can. J. Chem. Ens., 54, 259. Epstein, T.R. and P.H.T. Uhlherr (1973). Can. J. Chem. Eng., 51, 655. Kalra, G.R. and C.E. Capes (1970). Can. J. Chem. Enc., 48, 343. Rigby, P.S.B. and J.F. Davidson (1964). Chem. Ene. Sci., Is, 319. stewart, T. and E. Blasz (1987). Chem. Inc. Tech., 59, 544. Wasowski,