Trickle flow of dense particles through a fluidized bed of others

Pergamon PII:

Chemi~.l En~Jineerin~j Science~ Vol. 52, No. 4, pp. 553 565. 1997 Copyright ,/~ 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0oo9 2509/97 $17.oo - o.oo

S0009-2509(96)00427-7

Trickle flow of dense particles through a fluidized bed of others L. A. M. van der Wielen,* M. H. H. van Dam and K. Ch. A. M. Luyben Department of Biochemical Engineering, Delft University of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands (Received 12 December 1995: accepted 29 August 19961 Abstract--Dense (or large) particles fall through liquid fluidized beds of light (or small) particles. In this work, a new contactor is described in which continuous, countercurrent transport of dense particles in a stationary, liquid fluidized bed of light particles is exploited to obtain selective and continuous transport of the dense phase. The system is referred to as the 'trickle flow fluidized-bed reactor'. This system is evaluated in its application as a countercurrent adsorptive reactor. By selecting a suitable adsorbent as the dense phase, and a catalyst as the light phase, simultaneous reaction and countercurrent product removal may be achieved within one contactor. For a systematic design and optimization of such an adsorptive trickle flow fluidized-bed reactor, a predictive hydrodynamic model is required. In this work, the relation between the volume fractions and the fluxes of the three phases is investigated. A laboratory scale trickle flow fluidized-bed reactor has been constructed for experimental studies on hold-up and flux. A multi-component transport model to predict the volume fractions, fluxes and operating conditions is developed. The model is validated with the experimental hold-up and flux data from the trickle flow fluidized-bed reactor. To apply this concept as a countercurrent adsorptive reactor, a high countercurrent adsorbent flow, a high hold-up of the dense adsorbent and light catalyst are required, together with a stable operation. Hence, the reactor should operate at a minimum liquid fraction of approximately 50 vol% and a free area fraction of the supporting plate between 0.3 and 0.5. It is demonstrated that the system is very sensitive to the bulk density of the multi-component suspension. At a high hold-up of the dense particles, the bulk density of the bidisperse suspension may increase to a level which causes a complete wash-out of the light particles. Therefore, the difference in density between the light catalyst and dense adsorbent particles should be as small as possible. Copyright ~(? 1997 Elsevier Science Ltd Keywords: Multi-component fluidized bed; trickle flow; hydrodynamics.

INTRODUCTION

Contactors with multiple solid phases Contactors with a binary or multiple solid-fuid system are widely applied in industry. Systems with multiple solid phases can be classified into three categories: 1. particle classifiers, 2. countercurrent contactors with flow stabilization via a structured packing, 3. multi-functional (adsorptive and chromatographic) reactors.

*Corresponding author. Tel.: 31 15 2782361. Fax: 31 15 2782355. E-mail: L.A.M.Vanderwielen@stm. tudelfl.nl.

The first category is perhaps the oldest. The basic concept is that suspensions of particles with a reasonable distribution in density or size show a segregation tendency resulting in a low density, small particle top zone and a high density, large particle bottom zone. Whether the transition from bottom to top zone is gradual or steep depends on the density and size distribution. The phenomenon is often exploited at an industrial scale. Examples are continuous contactors with selective removal of a specified class of solids from mixtures of particles such as those encountered in particle classification systems and continuous crystallization equipment, Vesely et a l. 11991) studied the continuous separation of a binary mixture of solids in a fluidized bed by allowing the 'heavier particles fall through a perforated plate'. They showed this continuous fluidization-separator to have a higher capacity for solids separation than a batchwise arrangement at identical hydrodynamic conditions.

553

554

L.A.M. van der Wielen et al.

Conventional countercurrent fluidized-bed reactors exhibit a large degree of solids and fluid mixing, bypassing of fluid, poor solids distribution and a relatively large pressure drop because the fluidizing medium supports the solid phase. A stationary, inert solid phase may stabilize the flow of the countercurrently moving, active phase. The stabilizing phase can be a randomly dumped packing as indicated by Claus et al. (1976) and Roes (1979a, b} or a structured packing as applied by Verver (1987) and Kiel et al. (1992). These authors used a trickle flow of relatively small particles in a column of rather coarse packing of various types. Verver applied this solid-gas trickle flow system for the catalytic oxidation of hydrogen sulphide to sulphur. The produced sulphur was removed by simultaneous adsorption on the catalyst thus shifting the reaction equilibrium towards the product side. Kiel et al. (1992) investigated in a similar system the continuous, countercurrent non-catalytic adsorption of both sulphur oxides and nitrogen oxides from flue gas by regenerative CuO-on-poroussilica particles. Another variety of the same concept is the use of a stationary phase of magnetic particles to stabilize a countercurrent flow of non-magnetic particles (Chetty and Burns, 1991). A minimum volumetric fraction of magnetic particles of 20% was sufficient to stabilize the bed. Mass transfer efficiencies nearly equal those of packed-bed systems. Cherty and Burns (1991) used a countercurrent flow of non-magnetic affinity-adsorbents to continuously recover proteins from turbid fermentation broths. The last category, multi-functional reactors, employs a binary solid system in which each solid phase has a different function, other than mere flow stabilization. Westerterp and co-workers (Westerterp and Kuczynski, 1987; Kuczynski et al., 1987) used a reactor with a catalytically active packing and a countercurrent flow of product selective adsorbents for the single-passage production of methanol. Berruti et al. (1988) described a fluidized-bed pyrolysis reactor for the thermal conversion of biomass to organic liquid products. In this reactor, fluidized hot sand controls the residence of the light biomass as well as providing good heat transfer properties. In this article, we focus on this last category of multi-functional, adsorptive reactors which are especially suitable for handling turbid liquids such as often encountered in biotechnological applications. Van der Widen et al. (1993, 1995) and van Dam (1991) describe a fluidized-bed reactor which is capable of selective countercurrent transport of a 'heavy' solid phase with retention of the 'lighteff phase in the reactor. The terms heavy and light can be replaced by large and small particles, respectively. The application as an adsorptive reactor is investigated. Then, the segregation tendency of dense particles in fluidized beds of lighter ones is exploited to create a continuous countercurrent flow of heavy adsorbent particles in fluidized systems of lighter gel-type biocatalysts. The bottom section of this reactor contains

•

•

•

/ ° o Oo O o ,

~ o oO

k_'O:ooO o U8O o o OoOA,0 ~o B~%o. o9 o oo.~o "O U 0 u w oo 0OOo~ o O o~O C !°° oo'o~, o'ot o~ uw 0 u 0 u

Io o

0

00"0

OO

oo

C

080 c

b'O

O

b° oO,O,oooooo •

•

TiT Fig. 1. Selective countercurrent adsorbent transport a trickle flow fluidized-bed reactor.

a sieve plate with a conically shaped hole. At some liquid velocity gradient, the lighter phase is retained in the reactor whereas the dense adsorbent particles can pass selectively. We refer to this set-up, which is shown in Fig. 1, as a trickle flow fluidized-bed reactor. A sufficiently selective adsorbent will give an adsorbent flow, containing the product, from the bottom of the reactor. In case of a hydrolysis reaction giving two products, the application of a sufficiently selective adsorbent for one of the products might give an adsorbent flow from the bottom of the reactor containing one product and a liquid flow from the top containing the other product. A similar set-up has independently been described by Davison and Scott (1992) and by Srivastava et al. (1992) for lactic acid production. In conventional batch fermentation of lactic acid, the pH drops due to lactic acid production and the pH in the fermenter is controlled by alkali addition. Davison and Scott (1992) and Srivastava et al. (1992) have supplied fresh adsorbent particles at the top of a lactic acid producing culture of immobilized Lactobacillus delbruekii. By removing the lactic acid by adsorption it seems to be possible to control the pH without alkali addition. Scope q# this work

To predict the performance of a 'trickle flow' contactor in terms of transport rates and hold-ups, an adequate model for a segregating fluidized bed is required. In the following sections, we will extend a model for the relative motion of two fluidized particle species (van der Wielen et al., 1996). The model is used to derive loading and flooding criteria for the cases of single- and multi-component countercurrent fluidized systems. The model is verified experimentally using both literature and original data for segregating systems. Fluxes and hold-ups of the trickle flow fluidized-bed systems are described and

555

Trickle flow of dense particles verified by experiment. In addition, some visual observations on the trickle flow system are discussed.

fraction ~:~ . . 9 fraction e z - " T

THEORY

9

th

A multi-component transport model for a segregating fluidized bed In previous work (van der Wielen et al., 1996), we derived a relation for the relative motion of a single particle in a fluidized bed of other particles. In that case, the characteristic properties of the fluidized bed, such as bulk density and porosity, were completely determined by the 'other' phase. In the case of a continuous, segregating flow of particles in a fluidized bed of others, as demonstrated in Fig. 2, both phases influence the bulk density and liquid phase hold-up. Hence, hold-ups (8) and linear velocities (u) of the liquid (L), light (1) and dense (2) phases are not independent. Analogous to van der Wielen et al. (1996) and following Masliyah (1979), van Duijn and Rietema (1982) and Law et al. (1987), we proceed with a force balance relation for each component i in this multicomponent particle system Fgravity = Fbuoyancy + FLi + 2 Ffr.ij • J

(1)

FL~ is the liquid-particle friction (drag) and Fy,.u is the (frictional) interaction between the various particle species in the system. In general, individual liquid-particle and particle-particle contributions cannot be distinguished but are combined in an overall suspension drag for that component, Fdi. An overview of possible formulations of the friction terms is given by Law et al. (1987). In this work, this friction term is formulated analogously to Foscolo and Gibilaro (1987) and van der Wielen et al. (1996) as Fdi

=

rcd~ T(Pi

-

, Vo [ r L ,,VLil-14.8/,, ~{3.8 ,0"'g

J

(2)

with Vzi being the (linear) slip velocity of component i: (uL - u3. We have neglected the particle particle interaction and thus assume a completely hydrodynamic origin of the drag force. This results in

,0i -- [9 = (,0i -- ,0L) F~L(UL vu.z Ui!] 4"Sm'8L3"8

liquid ~L

UL

Fig. 2 Continuous, segregating flow of dense particles (2) in a fluidized bed of lighter particles (1).

tions in the form of overall mass balance equations to relate particle velocities and hold-ups according to Ji = 8iui

and

~bi= J i A .

(6)

Note that the solids flux Ji will be negative for countercurrent operation. The resulting set of nonlinear equations has been solved numerically. Experimental evidence for the validity of the model in each of these cases was obtained from literature (Lockett and Al-Habbooby, 1973; Law et al., 1987) and from the experimental set-up described below. Countercurrent transport in a fluidized system The single-component form of the model is used to evaluate the flooding conditions of a swarm of particles in countercurrent with a liquid. The following procedure is similar to the work of Mertes and Rhodes (1955a, b) and is a modification of the graphical procedure as outlined by Wallis (1969). However, Mertes and Rhodes (1955a,b) based their relation between the solids-liquid slip velocity at fluidized and terminal conditions on a theoretical model for liquid flow through a cubic arrangement of spherical particles. In this work, the expression for the relative motion of both phases is obtained by substituting eqs (4) and (5) into eq. (3), giving [EL(U_~L Z lli)14"8/n' f;L 3.8 Pi - [9 = 8L(pi - PL) = ( P i - - PC) L vL/~ ]

(3) (7)

The bulk density is determined by the solid and liquid phases present (van Duijn and Rietema, 1982). This results in the following equation for a binary solids system:

Reformulating this into the modified RichardsonZaki equation for a moving solids phase gives

(4)

The magnitude of the solids flux Ji of species i is given by:

[9 = 8L,0L -4- ~:1,01 + 82,02

while the total of the fractions must equal unity: 1 -~- 81. "4- [~1 At- E2"

(5)

The set of eqs (3)-(5) relates the velocities and holdups of the three phases. To solve this set of equations, one requires additional flux (J) or flow rate (q~) rela-

~L(UL - - ui) = ULo - - ~,Lui = V L i ~ L

j,

\(ULo eL

n,

vu~ e~- 1) (1 - 8L)

•

(8)

(9)

Equation (9) is made dimensionless resulting in the following expression for the solids flux relative to the

556

L. A. M. van der Wielen et al. 0.15 -di/VLi ~ 0.10

~0d~ . . - " 0.05

0.00 0.4

Fig. 3. Relation between dimensionless solids flux JI/VLU, and bed porosity. Particles: 1360 kg/m 3, VLU~= 0.0729 m/s, n = 3.19. Each curve is drawn for constant superficial velocity.

co~nt~rcctr~t flow

0.5

0.6

0.7

0.8

Ji -- (ULo/VLi~ ~

e ' ~ - l ) ( 1 - - eL).

1.0

~L

Fig. 4. Dimensionless solids flux J~/vL~, as function of e,L in the countercurrent regime. Particles: 1360kg/m3, VLU~= 0.0729 m/s, n = 3.19. The intersection of dotted and solid curves indicates flooding conditions.

terminal velocity of the particles:

ULi~

0.9

40

(10)

eL

In Fig. 3, the solids flux is plotted as a function of eL for a typical water fluidized system of particles (1360 kg/m 3, vu~ = 0.0729 m/s, n = 3.19; see also Table 1, type III). This figure is equivalent to the 'solids-throughput number'-diagrams of Mertes and Rhodes (1955). The curves in Fig. 3 are drawn for constant liquid flow. Fig. 3 also shows the three main regimes of solids fluid transport: cocurrent downflow, cocurrent upflow (solids lift) and countercurrent flow (shaded region) in which we are interested in this work. Note that the equilibrium fluidized state with a fixed position with respect to the fixed reference plane, corresponds to the Ji/vLi~ = 0-ordinate. When focusing on the countercurrent flow regime, one notices multiple solutions for the bed porosity for a specific solids flux. These solutions correspond to systems with a dilute suspension flowing at a high velocity (high eL-SOlution) and to a dense suspension flowing at a lower, hindered velocity (low eL-SOlution). Mertes and Rhodes define the former system as the P-phase and the latter system as the N-phase. The existence of both phases was shown experimentally by Blanding and Elgin (1942) for countercurrent solid-liquid systems and by Claus et al. (1976) for the countercurrent flow of gas and sand particles over a packing of cylindrical screens. This phenomenon was also observed in our experiments. Both regimes come together at the maximum of the curves. The flooding condition for a countercurrent solid fluid system is defined as the condition at which rejection of particles at the system entrance occurs (Elgin and Foust, 1950). This can be reformulated as the maximum value of Ji/vLg~ for which eq. (10) still has a solution in the relevant variable domain (0 <~ ULO/VLi,~ <~ 1; 2.4 ~< ni ~ 4.8; 0.3 ~< ~:I. ~< 1). The flooding condition is given by the maxima of the curves in Fig. 3. The relation between (ULo/Vu-~) and ~:L at the maximum value of J~/vu~ is obtained by equating its first derivative with respect to eL to zero. This leads to the following implicit relation in the

f =x 4 O3 qO =

8

30

E

20

~0 o 19 >

2

"s, 0 0.00

if) 0

0.02

0.04

0.06

liquid velocity ULo [m/s]

Fig. 5. Maximum solids flux J2 and particle velocity u2 for water fluidized particles at flooding. Particles: 1360 kg/m 3, vLi~ = 0.0729 m/s, n = 3.19. liquid fraction:

ULO =(rtiE L -- n i ÷ l)e~j.

(11)

~)Lic~

Equation (11) can be solved numerically to obtain the implicit function eL(Ut,O/VLU~). Substitution of the thus obtained eL in eq. (10) gives the maximum solids flux as a function of the superficial velocity. Figure 4 shows the countercurrent regime in more detail and the flooding condition is drawn as the thick, dashed line. For convenience, the sedimentation curve, where the solids flux equals the liquid flux ( - Ji = Ut,o), is drawn as the thin, dotted curve. Figure 5 shows solids flux J2 and the solids velocity u2 at flooding for the system of particles indicated before (1360 kg/m 3, VLi~ = 0.0729 m/s, n = 3.19; see also Table 1, type III). In a later section, it will he demonstrated that eqs (10) and (11) also describe the transport rate of solids through the hole of a sieve plate of a trickle flow fluidized-bed reactor. EXPERIMENTAL

SET-U P

Fluidized-bed system The basic experimental set-up has been described earlier (van der Wielen et al., 1990, 1995, 1996) and is

557

Trickle flow of dense particles

I Fc

im

collection point for solids Pc

Fig. 6. Laboratory-scale fluidized-bed system used for trickle flow experiments. Perspex column {1), RTD measurement system (2,3), plate with conical hole (4), dense phase supply (5) and gearless, rotary pump (6).

T IH

IH IHI

\

\

/tl

Fig. 7. One-hole, conical plate constructed from 20 rings for easy off-line adjustment of the free area. Adjustable cone at central axis for on-line control of free area.

shown schematically in Fig. 6. The set-up consists of a 0.75 m Perspex contactor with an internal diameter of 40.3 mm. The system is equipped with a pulseless rotary gear pump, a magneto-inductive flow meter and a pulsation system as described by Vos et al. (1990). The water was recycled through a 200 1 storage vessel.

Plate design For trickle flow experiments, a different plate with one single conical hole was used. Because some flexibility in the free area was required, the plate was constructed of 20 rings, each with a different internal diameter. By adding or omitting rings, the free area of the plate could be varied easily. The internal diameters of the rings ranged from 14.2 to 28.4 mm, allowing a change in free area between 12.4 and 49.5%. Furthermore, we used a smaller, solid cone mounted on a central axis with its tapered side up. The diameter of the bottom part of this cone was slightly smaller than the diameter of the apex of the plate. This allowed the free area to be varied during operation. See Fig. 7 for a more detailed description. The hold-up of two solid phases in the trickle flow bed is determined by placing the solid cone in the apex of the plate and by simultaneously stopping the solids feed to the system. The dense phase hold-up under our experimental conditions was always very low tl-3%). The hold-up measurements were corrected for the hold-up in the buffer zone just above the plate. In our experiments with the trickle flow set-up, we observed a large influence of hole and particle diameter on solids transport. This was probably due to the abrupt change in the hydrodynamical situation at the position of the hole in the conical support plate in combination with a relatively small diameter ratio of the dense particles and the hole. This ratio could be as small as 0.1 for the largest particles and the smallest hole diameters. Particles Particles over a broad range of densities and sizes were used in the experiments. An overview of their

558

L. A. M. van der Wielen et al. Table I. Overview of the average properties of the particles used in this work Composition

d (10 -3 m)

p (kg m -3)

n

vri~ (m/s)

Gelatin based matrix (filler: none) Gelatin based matrix (filler: biomass) Alginate matrix (filler: zeolite powder) Alginate matrix (filler: glass spheres) Alginate matrix (filler: copper powder) Alginate matrix (filler: zinc powder)

1.385

1024

3.59

0.0157

1.3

1100

3.29

0.0333

1.3

1360

3.19

0.0729

1 1.4

1280

3.29

0.0701

I 1.4

1386

3.20

0.0736

1.4 1.6

1594

3.12

0.1207

Series I II Ill 1V V VI

Table 2. Overview of the average properties of the particles used by Lockett and AI-Habbooby (1973) Series

Composition

d(10 3m)

p(kg/m ~)

n

vLi~,(m/s )

LI L2 L3 L4

Glass beads Glass beads Glass beads Glass beads

1.960 1.145 0.975 0.682

2990 2990 2990 2990

3.07 2.97 3.14 3.23

0.270 0.175 0.155 0.106

properties is given in Table 1. Densities were determined by repeated addition of amounts of the particles to a calibrated, water-filled cylinder and by a simultaneous recording of added volume and mass. The densities were determined within 0.5% error. The terminal velocity of the particles was determined from triplicate settling experiments in a 7.8 cm internal diameter, water filled glass cylinder. From the terminal velocity, an equivalent particle diameter d was calculated using Dallavalle's drag correlation (Dallavalle, 1948). Both were used to compute the Richardson and Zaki exponent n of the 'dense' phase. Fluidization characteristics of the 'lighter' phases were obtained from steady-state expansion experiments at various liquid flow rates in the fluidized-bed system described above. The mass flow rates of the dense phase were determined by collecting the dense phase outlet during an interval of time. The superficial volumetric solids fluxes were calculated from mass flow rates using particle density and column area. RESULTS

Model verification using previous experimental results Application of the model to data of Lockett and AI-Habbooby (1973). Lockett and A1-Habbooby (1973) constructed a countercurrent fluidized-bed system capable of transporting binary or multicomponent mixtures of particles. They measured the hold-up and flow rate of each phase and provided a wealth of data. Their particle mixtures were composed of twice

sieved particle fractions of Ballotini with a different size but an identical density. An overview of the average properties of the particles used in their experiments is given in Table 2. The original work supplies data concerning fluid properties, terminal velocity and Richardson and Zaki exponent n of individual fractions and experimental slip velocity-hold-up data for binary mixtures. The velocities of the smaller particles have about the same magnitude as the liquid velocity. The systems investigated by Lockett and A1-Habbooby actually behave as unsupported fluidized beds of the small particles through which the larger particles trickle. We have verified the multicomponent transport model with their data and compared our results with their model. The non-linear set of equations (3)-(6) was solved numerically as indicated earlier. Some results are shown in Figs 8 and 9 for experiments with mixtures of the fractions L1 L4 and L1 L3, respectively. Slip velocities of each of the solid phases with the liquid phase were predicted satisfactorily in the lower range of the solids hold-up (~< 40%). Experimental slip velocities at high solids hold-up of the small and large fractions seem to coincide and tend to the slip velocity curve of the larger particle. The slip velocities of the particle and liquid phases could be predicted rather accurately. The prediction of the particle velocity with respect to a fixed reference plane, which is computed from the slip velocity and the liquid velocity, is only accurate for the larger particles.

559

Trickle flow of dense particles W

0.25

~

particle: ~4 fractions

•

•

=~ 0 . 2 0 -1

0.15

~)

0.10

cz

0.05

0,00 0.4.

0.5

'

'

0.6

0.7

bed

' 0.8

--

O.g

~ .0

porosity

Fig. 8. Slip velocities of particle fractions L1 (O) and L4 IO) in a countercurrent fluidized bed (Lockett and AIHabbooby. 1973). Solid lines are predictions of the multicomponent transport model, eqs (3)-161.

results with various models. They found the model by Masliyah (1979), among others, to give a good predictions of their results (Table 3). The model by Masliyah is very similar to the multicomponent transport model used in this work. The main difference is the exact formulation of the hydrodynamic interaction in the force balance equations, which Masliyah took from Wallis (19691 whereas we took it from Foscolo and Gibilaro 09871. As their experiments were performed at low overall solids hold-ups (~< 16%), the assumption of negligible particle particle friclion, made in both models, seems justified. The overall results of the predictions with the multi-component transport model predictions approximately equal those from the Masliyah model and the accuracy of both models supports the approach taken in this work (Table 3).

0.25 par t bcle fractbon£

# --

•

0.20

0 -I >.

0.15

G o

0.10

g

0.05

L3

• •

o: o j

0.00

i

0.4

0.5

0.6 bed

f° n

0.7

n

i

0.8

0.9

1.0

porosity

Fig. 9. Slip velocities of particle fractions L1 (O) and L3 (C) in a countercurrent ftuidized bed (Lockett and A1Habbooby, 1973). Solid lines are predictions of the multicomponent transport model, eqs (3~6).

Application to the gravity separation experiments by L a w et al. (1987). Law et al. (1987) have studied the gravity separation of bidisperse suspensions containing particles lighter and heavier than the suspending fluid in a vertical tube. The light phase was polystyrene (Pl = 1050 kg/m 3, d~ = 0.241 mm, nl = 5.39, vL~~, = - 1.348 mm/s) and the dense phase was polymethyl methacrylate (P2 = 1186 kg/m 3, d2 = 0.237 ram, n2 = 5.39, vL2,,, = 1.24 ram/s), with a very narrow size distribution. The wall effect is already included in the Richardson and Zaki exponent and in the terminal velocities. The suspending liquid was an aqueous sodium chloride solution ( P L - - l l 2 0 k g / m 3, th. = 1.41 Pa s). They have compared their experimental

Countercurrent transport through a perfi~rated plate Experiments were performed to determine the minimum operation conditions in terms of superficial liquid velocity of the fluidized bed, ULo, in combination with the free area of the supporting plate, at which the particles begin to rain through the hole in the plate. The corresponding liquid velocity in the hole, Ul,o,{fis indicated with u~. The results are shown in Table 4. The terminal velocities are in general higher than the liquid velocities in the hole of the plate. This is probably due to the increased turbulence at the position of the hole. The particles have a similar size, hence a similar wall effect is observed. It resulted in ratios of liquid velocity and terminal velocity of 0.7 for the 12% free area plate and 0.9 for the 19% free area plate. When applying Francis' equation for wall effect (van der Wielen et al., 1996), we obtained correction factors for the wall effect of 0.8 and 0.9, respectively. Nevertheless, it should be noted that the assumption of fully developed laminar flow through the hole is of course violated because of the conical shape of the hole. Visual observations on the trickle.flow system Solids fluxes and corresponding hold-ups of various types of dense particles (II-VI) in steady fluidized beds of lighter ones (l, II) at free areas ranging from 12 to 28% free area have been studied. An overview of

Table 3. A comparison of experimental and theoretical settling velocities of bidisperse systems by Law et al. (1987) and predictions from the multi-component transport model (this work) cI

Law et al. (19871 experiment Law et al. (1987) model this work, eqs (3t-t6)

=

0.08, '~;2 0.08 U~, U2(mm/s)

/~;I= 0.04, ~:2 = 0.08 U~,u2 (mm/'s)

~ = 0.08, ~:2 = 0.04 u t, ~2(mm/s}

0.75, - 0.75

0.86, - 0.77

0.79, - 0.83

0.74. -- 0.70

0.93,

0.75

0.80, - 0.88

0.76. - 0.70

0.92,

0.78

0.85, - 0.86

=

L. A. M. van der Wielen et al.

560

Table 4. Raining velocities of various combinations of types of particles and free area of the plate. Fluidization in tap water at 20°C

Particle type

Free area of plate f

uLo at raining (m,/s)

u* at raining (m/s)

vLi,~ (m/s)

u~/vri,~,

I II IV V VI I 1I III IV V Vl

0.124 0.124 0.119 0.119 0.119 0.194 0.194 0.19 0.19 0.19 0.19

0.00129 0.00325 0.00567 0.00520 0.00873 0.0021 0.0089 0.0124 0.0115 0.0112 0.0180

0.0104 0.0262 0.0476 0.0437 0.0733 0.0106 0.0455 0.0653 0.0605 0.0589 0.0947

0.0157 0.0333 0.0701 0.0736 0.1207 0.0157 0.0333 0.0729 0.0701 0.0736 0.1207

0.66 0.79 0.68 0.59 0.61 0.68 1.37 0.90 0.86 0.80 0.78

the runs as well as the experimental hold-up and flux values for the trickle flow transport for various combinations of particles, free areas of the supporting plate and superficial liquid velocities are given in Table 5. Solids fluxes J2 and solids hold-ups are the averaged values of the indicated multiplicates. Prior to the discussion of the numerical results, some phenomena observed during the trickle flow operation will be reported. Because the raining velocity of the particles was usually lower than the terminal velocity, raining of the light phase was still possible at the lower superficial velocity range. Therefore, the column was operated in such a way that a small, steady-state buffer zone of 1-5 cm of the dense solids phase existed just above the plate. This completely prevented the raining of the light phase and improved the stability of the trickle flow system. The trickle flow system with a stationary bed of the very low density type I particles is very sensitive to buoyancy effects. The slightest increase in bulk density, caused by an increasing hold-up of the dense phase at elevated solids fluxes, caused a dramatic wash-out of the light phase. Although it was possible to operate with all types of dense particles, only operation with type II particles as trickling phase was sufficiently stable (Table 5, runs l-8). All other trickle flow experiments were performed using type II particles as stationary fluidized bed (Table 5, runs 9-30). The capacity of the valves in the bottom part of the column to remove the solids from the system became limiting at higher solids flows ( > 50 ml/min). As these flow rates were the highest encountered in our experiments, it did not interfere with our experiments, but it is an aspect to consider in column design. Elsewhere, we have reported a possible solution other than increasing valve diameter (van der Wielen et al., 1995, 1996). Another important point is the uniform distribution of the solids at the top of the fluidized bed. A non-uniform solids feed may introduce channelling of the dense solids and should be avoided. We placed

a plate with a solid cone, similar to the one depicted in Fig. 7, at the top of the bed. This provided a more uniform solids distribution. At a larger scale, multiple feed points might be a possible solution. Summarizing, Table 5 indicates three main tendencies: 1. a decline of the solids flux at increasing superficial fluid velocity (ULo), 2. an overall very low hold-up of the dense segregating phase, 3. a general increase in dense phase hold-up (E2) at increasing dense solids flux J2 at a fixed superficial liquid velocity.

Trickle flow operation: solids fluxes During the experiments, we maintained a small buffer of dense phase just above the plate to prevent raining of the light phase. Therefore, the flux of the dense phase seems to be limited by the solids flow through the hole of the plate. The experiments indicate that the flow rate of solids through the stationary bed could be increased at the expense of the light phase hold-up. But once the capacity of the hole of the plate is reached, a further increase in the solids flow rate results in an accumulation of dense phase in the buffer zone just above the plate. Hence, it seems that the flux of the dense phase can be described as a mono-component flow of the dense phase through the hole of the plate. Because a constant head of dense phase was provided just above the plate, dense phase transport through the hole is at its maximum and hence at flooding conditions. The solids flux is then described with eqs (10) and (11). Both solids and liquid fluxes are recalculated to the (free area) conditions in the hole of the plate. This is not merely performing a correction for the free area but also incorporating the wall effects encountered in the hole. Therefore, in the simulation of the dense phase fluxes we have used the raining velocities as indicated in Table 4 and we have corrected the Richardson and Zaki exponent n of the dense phase for the wall effect such as

561

Trickle flow of dense particles Table 5. Overview of trickle flow experiments Run no.

Phase (11

Phase (2)

ul,o (mm,'s)

Free area

~:1,

~:z

lab 2ab 3ab 4ab 5ab 6ab 7a b 8ab 9ab 10ab 11 ab 12ab 13ab 14ab 15ab 16ab 17ab 18ab 19ab 20 21 22 23 24abc 25abc 26abc 27abc 28abc 29abcd 30ab

l 1 I I 1 l I I II |I 11 II II II I1 I1 II II I1 11 I! II 11 II 1I II II II II Il

lI I! II lI 11 It lI II V V V IV IV IV V1 VI VI VI VI Ill III III Ill III III II1 III III llI I11

1.44 1.91 2.31 2.70 3.25 4.03 4.81 5.52 8.88 9.67 10.45 9.04 9.90 10.69 9.04 9.82 10.61 11.39 12.17 7.94 7.16 6.38 5.60 11.08 9.51 7.94 6.38 I 1.08 9.51 7.94

0.12 0.12 0.12 0.12 0.19 0.19 0,19 O. 19 0.19 0.19 0.19 0.19 0.19 O.19 0.19 O.19 0.19 O.19 O.19 0.23 0.23 0.23 0.23 0.28 0.28 0.28 0.28 0.28 0.28 0.28

0.514 0.556 0.586 0.612 0.645 0.685 0.719 0.747 I).670 0.687 0.703 0.673 0.692 0.708 0.673 0.690 0.706

0.011 0.0044 0.0028 0.0013 0.0185 0.0111 0.0090 0.0040 0.0012 0.0010 0.0013 0.0045 0.0030 0.0031 0.0051 0.0051 0.0032 0.0022 0.0016 0.0057 0.0094 0.024 0.019 0.0049 0.0044 0.0072 0.011 0.0099 0.017 0.01

2.0

E

\

1.5

'\

\

0.736 0.647 0.627 0.605 0.582 (/.716 0.683 /).647 0.605 (/.716 0.683 (I.647

VI 1.0

•

o

oC-

•

_c

1.0

\ \.

ra,plng m

X

0.5

m q.-

U~ 7D

(ram/s)

0.0407 0.0278 0.0132 0.0066 0.(1806 0.0437 0.0261 0.0082 0.0378 0.0181 0.0088 0.0263 0.0147 0.0081 O. 1549 O.134(1 0.1031 0.0832 0.0671 0.778 0.982 1.2 t 6 1.527 0.823 1.204 1.529 2.001 1.652 1.922 2.943

:'2o:!!"

(D

C

0.722

-- J2

i

iv

0.5

"~"'", ~,-....

•

I

C9

o.o 0.04

0.0 0.00

0.01

liquid

velocity

0.02

for

hole

0.03

[m/s]

I

0.05

l

0.06

liquid v e l o c , t y

for

I

0.07

I

J

0.08

hole [m/s]

Fig. 10. Experimental (markers) and calculated (curves) solids fluxes of the dense phase for runs 1-8 (type II particles, Table 3). Curves from eqs (10) and (11) and Table 1.

Fig. 11. Experimental (markers) and calculated [curves) solids fluxes of the dense phase for runs 9 19 [Table 3). Curves from eqs (10) and (ll); particles: IV(A), V(O) and V](II); data in Table I.

i n d i c a t e d in the original w o r k o f R i c h a r d s o n a n d Zaki (1954). T h e solids flux at a given liquid flux is calc u l a t e d t h r o u g h eqs (101 a n d (11). F i g u r e s 10-12 s h o w t h e e x p e r i m e n t a l a n d p r e d i c t e d solids a n d liquid fluxes in the hole o f the plate for the various runs from

T a b l e 3. N o t e that the values of the (interstitial) liquid velocities in the hole are c o r r e s p o n d i n g l y larger. N o t w i t h s t a n d i n g the fact that the conical s h a p e o f the hole in the plate d o e s n o t p r o v i d e a fully dev e l o p e d l a m i n a r flow, the fluxes o f the d e n s e solid

562

L. A. M. van der Wielen et al. •

2

10,a

o voo ° / /

o

1-8

J

9-11

•

20-30

X

0 c-

/,/"

#24-30

X

10 -~ 10"

10 -3

10 -2

10-'

q3

~2 (model)

0 0.02

0.00

0.04

liquid velocity

0.06

0.08

in hole [mm/s]

Fig. 12. Experimental (markers) and calculated (curves) solids fluxes of the dense phase for the runs 2(~23(O), 24-27(A) and 28-30(m). Curves: eqs (10) and (11) and data from Table 1.

0.8

//// /"

0.7

/" ,,," •

X 0) tO

/ /fl •

0.6 o •,/

/ ,o 0.5 0.5

///

0.6

0.7

o

1-8

•

9-11

•

12-14

•

15-19

•

20-30

0.8

~L(model) Fig. 13. Parityplot of the experimentaldata and simulations of the liquid phase hold-up for runs 1-30 (Table 3). Simulations with the multicomponent transport model, eqs (3)-(6). phases are predicted rather accurately. The largest deviations are encountered for the heaviest particles used (type VI particles, runs 15-19) as shown in Fig. 11. When investigating the sensitivity of the parameters in the model, it showed to be very sensitive to the value of the terminal velocity of the dense phase in the hole of the plate. A (negative) correction of 10-20% in the exact value of the terminal velocity in the hole, which is in the order of the experimental error, was enough to obtain a far better match between experimental values and predictions. This correction was not applied in the Figs 10-12.

Trickle flow operation: hold-up predictions As shown in Table 5, the hold-up of the dense phase is rather low and the bed can be regarded as a single(light) component fluidized bed with a dilute flow of the trickling phase. To investigate whether the multicomponent transport model can adequately predict this phenomenon, we have simulated the hold-up values from Table 5, using the monocomponent flui-

Fig. 14. Parity plot of experimental data and simulated values of the dense phase hold-up for runs 1-30 (Table 3). Simulations are performed with the multicomponent transport model, eqs (3}-(6).

dization characteristics from Table 1. The fluxes of the liquid and the dense solids phases are given in Table 5 as well, and the hold-up values are obtained by numerical solution of the model. The results are shown as the parity plots in Figs 13 and 14 for the volume fraction of liquid and the dense (trickling) solids, respectively. As displayed in Fig. 13, the liquid fraction eL is predicted accurately for runs 1-19. The liquid hold-up for runs 20-30, however, is systematically overestimated. Similarly, the model predicts the hold-ups of the dense phase fairly well for runs 1-19, but overestimates those of runs 20-30. Both effects are of course related, in the sense that an overestimation of the dense solids fractions results in a too high bulk density of the fluidized suspension. Hence, that effect is compensated by wash-out of the light, fluidized phase (phase 1), and thus results in an increase in the liquid fraction. This once more indicates the sensitivity of a fluidization phenomena state to the bulk density of the fluidized bed (van der Widen et al., 1996). In addition, these observations also seem to answer the still controversial question of whether the bulk density or the liquid density determines the buoyancy. The bulk density appears to determine the buoyancy. This is also observed in earlier work (van der Wielen et al., 1996). Furthermore, it underlines that the holdup of the dense phase is very low. DISCUSSION

Reactor loading: minimum superficial liquid velocity Enlargement of the free area of the plate seems to be the best method to increase the operational range of the trickle flow system. But it should be noted that an increase in the free area of the plate increases the solids flux of the dense phase and also raises the lower operation boundary. In this section, we investigate the effect of the free area on the range of operation. The minimum superficial fluid velocity which can be used in the trickle flow system is determined either (a) by raining of the light phase through the hole(s) in

563

Trickle flow of dense particles the plate or (b) by a too high overall solids hold-up of the fluidized bed (too low porosity), In the latter case, no solids transport is possible. The maximum value of the two corresponding superficial fluid velocities determines the lower boundary of the operation regime. The first restriction, raining of the light phase, is given by the terminal velocity of the light phase in the hole of the plate, v*~ ,,.,.The value of v*~ ,~ can be estimated from the (unhindered) terminal velocity of the light phase corrected for the wall effect by the hole using Francis' equation for laminar flow or the correlation by Strom and Kintner for turbulent flow (van der Wielen et al., 1996). When the flow conditions in the hole deviate substantially from those for which the correction is valid, such as in a conical hole, experimental determination of v*~, is more reliable. The minimum superficial liquid velocity is then given by

ULO.min--f[,Ll~,.

(12)

Using eq. (11), the corresponding porosity of the dense solids flux through the hole can be calculated and, using eq. (10), the dense phase flux at minimum superficial liquid velocity is obtained. It should be noted, however, that the presence of a buffer of dense phase just above the plate prevents raining of the light phase and generally improves stability. In that case, the criterium for the minimum fluid velocity will be provided by the minimum fluidization velocity of the light phase. The criterium concerning a too low bed voidage is somewhat more arbitrary. Data from Lockett and A1-Habbooby (1973), which are shown in Figs 8 and 9, suggest a minimum porosity of the fluid bed of 0,5 for independent transport of different solids species. Van der Wielen et al. (1996) indicated a drastic decline of the segregation velocity of a single, dense particle in a fluidized bed of others when approaching the fixed bed porosity (t;~,~ 0.4). For a first estimate and because the dense phase hold-up in the trickle flow fluidized bed is on the average very low, the bed porosity can be computed from the expansion characteristics of the light phase only. Figure 15 indicates the influence of the free area of the plate on the solids flux of type lIl particles in a fluidized bed of type II particles for free area fractions of 0.1, 0.2 and 0.3. The porosity of the fluidized bed of type II particles is shown as the solid, spherical markers whereas the "raining' criterium of the light phase is shown as the fine, dotted curve.

El:feet of the super[icial velocity on the hold-ups For a fixed free area of the plate, only the liquid velocity remains a parameter. Using the multicomponent transport model, we have investigated the changes in hold-up of the solids and liquid phases for a fixed free plate area. In Fig. 16, this is illustrated by calculations for a plate with a free area fraction of 20% and particles II/lII. This corresponds approximately to runs 20-23 (Table 5) which were performed at 23% free area. Again, the decline of the

-f

2.5

1.O \

*

•

•

*

0.8

2.0

• ,,.."

~~ ~

bed porosity

~.,'

1.5

~.o j ~ "

0.6

b

ofraction free a r e a

0.4

~=°

G "0 ¢

0.2 o.o°"5~

°

o.ooo

0.005

'

2 ~ .........." o.o 1o

o.o 15

0.020

0.0 0.025

superficial fluid flux [m/s]

Fig. 15. Influence of free area fraction of plate o11 flux of dense solids. Dotted line : solids flux at raining criterium of light phase: markers: liquid fraction, Simulations for type 111 (dense) particles in fluidized bed of type II dightl.

10 ° m ~L

5

4

10-1

3

10-2

~2

- 10~:,J

10 -~ 10--4

2

2 [rn/s] 1

_

0.005

_

0.010

u~

m/s

0 0.015

Fig. 16. Simulation of hold-ups and superficial dense phase flux with the multi-component transport model for a fixed free area of 20%. Data for type tI/III-particles (Table 1).

flux of the dense solids is shown for an increase in the superficial liquid velocity. The hold-up of both phases also decreases with increasing liquid velocity. The dense phase hold-up shows the highest sensitivity because of the higher liquid flux in the fluidized bed -and hence a lower overall porosity--and because of the reduced solids flux through the hole in the plate. The simulation results of the liquid fraction in the fluidized bed justifies the previous assumption that the dense phase hold-up of the fluidized bed at these low dense phase fluxes is determined to the largest extent by the lighter phase.

E~bct ( f the fi'ee area.jraction on the hold-ups When increasing the free area of the plate, larger fluxes of the denser phase are possible. Note that the limiting case of a free area fraction of unity corresponds to the absence of the light, fluidized phase. In Fig. 17, we have shown the computational results of the flux of the dense phase and the hold-ups of each phase as function of the free area fraction of the plate lbr an arbitrary and fixed superficial velocity of eL2 ~,/10 for type II1 particles. Note that for free area fractions smaller than 15%, no substantial transport of the dense phase is possible. This is also shown in Figs 15 and 17. The trickling countercurrent flow of the dense phase increases to its maximum value (at flooding

L. A. M. van der Wielen et al.

564

7.5

1.00 ..... I f -~~--~ 0.75

5.0

//

-lo'-~J~ tm/~] 2.5

. .. ,

0.50

/

.//-J2 0.25

~2 0.00

O.O

0,0

0.2 free

0.4 area

0.6 fraction

0.8 of

1.o

plate

Fig. 17. Simulation of the hold-ups and dense phase flux as function of the free area fraction for a fixed liquid velocity. ULo/t¥2 ~ = 0.1, data for type II and type III particles (Table 1).

conditions) when approaching a free area fraction of unity. Two cases can be distinguished: the density of the 'dense' phase is equal to that of the light phase (but its diameter larger) or the density is higher than the density of the light phase. In the latter case, the increasing hold-up of the dense phase at the increasing free area leads to an increase in the bulk density of the fluidized bed. Therefore, the hold-up of the dense phase occurs at the expense of the light phase, which is increasingly washed out. Complete wash out of the light phase will occur when the bulk density of the fluidized suspension exceeds the density of the light particle, thus will occur more easily when the density difference of the dense particle and the lighter particle is increasing. This is the case for Fig. 17. Too low free area fractions (approximately smaller than 15%) result in very low flows of the dense phase, whereas too high free area fractions (towards unity) lead to wash-out of the light stationary phase. Obviously, an intermediate range of free area fractions would be optimal. Of course, optimization for a specific system of a particular liquid and a particular bidisperse set of particles is possible using the model presented in this work, but strongly depends on other than hydrodynamic properties of the system (adsorption capacity, reactivity). As a rule of thumb, the lower boundary of the free area fraction could be in the order of 30 area percent. This usually allows a sufficiently high liquid flow to give a fluidized bed of light particles with a porosity of approximately 60%, as is shown in Fig. 15. Bed porosities smaller than 50% will lead to too much friction between the particles. This was also shown by Lockett and A1-Habbooby (1973), will lead to a steep decline of the dense solids flow. This is shown in Fig. 17 for a trickle flow fluidized-bed system with type I1 and type III particles. The upper boundary of the free area fraction could in the order of magnitude of 50-60%. This corresponds to a bed porosity of approximately 80%. The overall liquid hold-up does not change very much upon a further increase of the free area fraction, but the hold-up of lighter phase will decrease significantly. This is also shown in Fig. 17. However, these figures should only be considered as a preliminary estimate.

CONCLUDING REMARKS

In this work, the relations between the volume fractions and fluxes of the liquid, light and dense solid phases in a countercurrent trickle flow reactor have been studied. A predictive hydrodynamic model is verified with experimental data for a range of particle systems, operating conditions and plate configurations. With the application of this trickle flow system as a countercurrent adsorptive reactor in mind (van der Wielen et al., 1995), one can select dense adsorbent particles and light biocatalyst particles. For a countercurrent reactor on this basis, it can be concluded that: • For a high (dense) adsorbent flow, the reactor should be operated at a low superficial liquid velocity. The lower boundary of the superficial liquid velocity is determined by having a high enough liquid fraction to allow the adsorbent transport. This corresponds to a minimum liquid fraction of about 50 vol %. • A too high free area fraction of the perforated plate leads to unstable operation, and a too low free area fraction leads to a low sorbent flow. For stable operation and a high sorbent flow, the free area fraction of the plate should be somewhere between 30 and 50 area percent. • An adequate balance between the densities of the 'light' and 'dense' solids phase is crucial for proper operation. Large differences in solids densities, and especially when the density of the fluidized (light) phase approaches that of the liquid phase, lead either to very low sorbent hold-up in the system (low sorbent flow), or to a wash out of the lighter phase (high sorbent flow). The wash out is caused by the increase of the bulk density due to a high dense phase hold-up. • The densities and the millimeter-range of typical immobilized biocatalyst systems and typical adsorbent materials are such that the system can be operated only at a relatively low adsorbent hold-up. Whether or not this may satisfy the objective of this integrated reacto~separator depends on the substrate flow in the reactor and the adsorbent capability to take up the product. Acknowledgements

The Netherlands Organization for Scientific Research (NWO) is gratefully acknowledged for the financial support. The Mechanical Workshop of the Kluyver Laboratory for Biotechnology is thanked for its technical assistance. NOTATION

A d

f F Ji ULO

area, m 2 particle diameter, m free area fraction of perforated plate force per particle, N flux of species i, m/s Richardson and Zaki exponent of solids i superficial fluid velocity, m/s

Trickle flow of dense particles Ui Vij ULi x

linear velocity of phase i relative to observer, m/s (linear) slip velocity of phase i and j, m/s terminal velocity of species i, m/s

Greek letters rs volumetric fraction of species i p density, kg/m J 0 flow rate, m3/s Subseripts f fluid phase i phase i 0 superficial L, 1, 2 liquid, light and dense solids phase REFERENCES

Berruti, F., Liden, A. G. and Scott, D. S. (1988) Measuring and modelling residence time distribution of low density solids in a fluidized bed reactor of sand particles. Chem. Engng Sci. 43, 739-748. Blanding, F. H. and Elgin, J. C. (1942) Trans. Am. lnstn Chem. Engng 38, 305. Chetty, A. S. and Burns, M. A. (1991) Continuous protein separations in a magnetically stabilized fluidized bed using non-magnetic supports. Biotechnol. Bioengng 38, 963-971. Claus, G., Vergnes, F. and Goff, P. le (1976) Hydrodynamic study of gas and solid flow through a screen-packing. Can. J. Chem. Engng 54, 143. Dallavalle, J. M. (1948) Micromerities: The Technology q]' Fine Particles, 2nd Edn. Pitman, London. Dam, M. H. H. van (1991) Design and modelling of a fluid bed adsorptive reactor with adsorbent trickle flow. M.Sc. Report, Delft University of Technology. Davison, B. H. and Scott, C. D. (1992) A proposed biparticle fluidized bed for lactic acid fermentation and simultaneous adsorption. Biotechnol. Bioengng 39, 365--368. Duijn, G. van and Rietema, K. (1982) Segregation of liquid-fluidized solids. Chem. Engng Sci, 37, 727 -733. Elgin, J. C. and Foust, H. C. (1950) Countercurrent flow of particles through moving continuous fluid. Ind. Engng Chem. 42, 1127. Foscolo, P. U. and Gibilaro, L. G. (1987) Fluid dynamic stability of fluidized suspension: the particle bed model. Chem. Engng Sci. 42, 1489-1500. Kid, J. H. A., Prins, W. and Swaaij, W. P. M. van (1992) Modelling of non-catalytic reactions in a gas-solid trickle flow reactor: dry, regenerative flue gas desulphurization using a silica supported copper oxide sorbent. Chem. Engng Sci. 47, 4271~4286. Kuczynski, M., Oyevaar, M. H., Pieters, R. T. and Westerterp K. R. (lV987) Methanol synthesis in a countercurrent gas solid-solid trickle flow reactor. An experimental study. Chem. En~tng Sci. 42, 1887-1898. Masliyah, J. H. (1979) Hindered settling in a multispecies particle system. Chem. Engng Sci. 34, 1166-1168.

Mertes, T. S. and Rhodes, H. B. (1955a) Liquid-particle behaviour. Part 1. Chem. Engng Prog. 51, 429 432.

565

Mertes, T. S. and Rhodes, H. B. (1955b) Liquid-particle behaviour. Part II. Chem. Engng Prog. 51, 517-522. Law, H.-S., Masliyah, J. H., MacTaggart, R. S. and Nandakumar, K. (1987) Gravity separation of bidisperse suspensions: light and heavy particle species. Chem. Engng Sci. 42, 1527 1538. Lockett, M. J. and A1-Habbooby, H. M. (1973) Differential settling by size of two particle species in a liquid. Trans. lnstn Chem. Engrs 51, 281 292. Protod'yakonov, I. O., Romankov, P. G. and Samsonov, A. G. (1972) Countercurrent adsorption column. J. Appl. Chem. USSR (Engl. transl). 45, 1185 1187. Richardson, J. F. and Zaki, W. N. (1954) Sedimentation and fluidisation. Part 1. Trans. lnstn Chem. Engrs 32, 35-53. Roes, A. W. M. and Swaaij, W. P. M. van (1979a) Hydrodynamic behaviour of a gas-solid packed column at trickle flow. Chem. Engng J. 17, 81 -89. Roes, A. W. M. and Swaaij, W. P. M. van (1979b) Axial dispersion of gas and solid phases in a gas solid packed column at trickle flow. Chem. Engng J. 18, 13 28 Srivastava, A., Roychoudbary, P. K. and Sahai, V. (1992) Extractive lactic acid fermentation using ion-exchange resin. Biotechnol. Bioengnq 39, 607 613. Verver, A. B. and Swaaij, W. P. M. van (1987) The gas solid trickle flow reactor for the catalytic sulphide oxidation: a trickle phase model. Chem. Engng Sci. 42, 435 445. Vesely, V., Hartman, M., Carsky, M. and Svoboda, K. ( 1991 ) Separation of a binary mixture of particles in a fluidized layer by the use of a perforated plate. Int. Chem. En.qng 31, 161 166. Vos, H. J., Houwelingen, C. van, Zomerdijk, M. and Luyben, K. Ch. A. M. (1990) Countercurrent multistage fluidized bed reactor for immobilized biocatalysts. Ili. Hydrodynamic aspects. Biotechnol. Bioengng 36, 387-396. Wallis, G. B. (1969) One Dimensional Two-phase Flow. McGraw-Hill, New York, U.S.A. Westerterp, K. R. and Kuczynski, M. (1987) A model for a countercurrent gas solid solid trickle flow reactor for equilibrium reactions. The methanol synthesis. Chem. Engng Sci. 42, 1871-1885. Wielen, L. A. M. van der, Potters, J. J. M., Straathof, A. J. J. and Luyben, K. Ch. A. M. (1990) Integration of bioconversion and continuous product separation by means of countercurrent adsorption. Chem. Engn,q Sci. 45, 2397 2404. Widen, L. A. M. van der, Straathof, A. J. J. and Luyben, K. Ch. A. M. (1993) Adsorptive and chromatographic bioreactors. In Precision Process Technolo~ly, eds M. P. C. Weijnen and A. A. H. Drinkenburg, pp. 353 379. Kluwer, Dordrecht. Wielen, L. A. M. van der, Diepen, P. J., Straathof, A. J. J. and Luyben, K. Ch. A. M. (1995) Two new countercurrent adsorptive enzyme reactors. Operational conditions for deacylation of penicillin G. Ann. N.Y. Aead. Sci. 750, 482-490. Widen, L. A. M. van der, Dam, M, H. H. van and Luyben, K. Ch. A. M. (1996) On the relative motion of a sphere in a swarm of different spheres. (?hem. Engn,q Sei. 51. 995 1008.