Some aspects of magnetically stabilized fluidization

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Some aspects of magnetically stabilized fluidization

Citation for published version (APA):

Geuzens, P. L. (1985). Some aspects of magnetically stabilized fluidization. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR238318

DOI:

10.6100/IR238318

Document status and date: Published: 01/01/1985

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SOME ASPECTS OF

MAGNETICALLY STABILIZED

FLUIDIZATION

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SOME ASPECTS OF MAGNETICALLY STABILIZED FLUIDIZATION

proefschrift

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL EINDHOVEN OP GEZAG VAN DE RECTOR MAGNIFICUS , PROF. DR. F.N. HOOGE , VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE

VAN DEKANEN IN HET OPENBAAK TE VERDEDIGEN OP DINSDAG 3 DECEMBER 1985 TE 16.00 UUR

door

PIERRE LEON GEUZENS

(4)

aan mijn ouders ,

(5)

Dit proefschrift is goedgekeurd door de promotoren

prof. Dr. Ir. D. Thoenes prof. Ir. M. Tels

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CONTENTS

1. Introduetion

2. Magnetically stabilized fluidization description

2.1. Literature review

2.2. Mathematica! stability analysis

phenomenological

2.3. Electromagnetic coil and ferromagnetic particles 2.4. Fluidization characteristics : introductory

experiments 2.5. Discussion

3. Gas flow

3.1. Introduetion

3.2. Equipment and experimental method 3.2.1. Axial mixing

3.2.2. Radial mixing

3.3. Modelling of the mixing process 3.3.1. Axial mixing

3.3.1.1. Axial dispersed plug flow model 3 • .3. 1. 2. Parallel cascades of mixers 3.3.2. Radial mixing

3.3.2.1. Dispersed plug flow model 3.4. Results of mixing experiments

3.4.1. Axial gas mixing (results)

3.4.1.1. Fitting with the axial dispersed plug flow model

3.4.1.2. Fitting with the model of parallel cascades of mixers 3.4.2. Radial gas mixing (results)

3.5. Discussion 3.6. Conclusions Table 3.1. Table 3.2. Table 3.3. Table 3.4. page 5 5 8 14 18 26 29 29 30 30 33 36 36 36 42 44 44 47 48 48 54 57 59 64 65 66 67 68

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Table 3.5. Appendix 3.I. Appendix 3.II.

4. Solids flow 4.1. Introduetion

4.2. The use of phosphorescence as a traeet 4.3. Modelling of solids mixing

4.3.a. Steady light profile in a batch fluidized bed 4.3.b. RTD measurement in a bed with continuous

solids throughput 4.4. Equipment and measuring method

4.4.1. The fluidized bed

4.4.2. The magnetic distributor downcorner (MDD) 4.4.3. Photodiodes

4.5. Results 4.6. Discussion 4.7. Conclusions

5. Gas filtration in a magnetically stabilized bed 5.1. Introduetion

5.2. Survey of gas clean up devices 5.2.1. Bag filters

5.2.2. Electrostatic precipitators 5.2.3. Cyclones

5.2.4. Scrubbers

5.2.5. Granular bed filters

5.3. Theory : gas filtration in a granular bed 5.3.1. Partiele collection in a homogeneous

granular bed

5.3.1a Inertial deposition 5.3.1b Diffusional deposition 5.3.1c Interception

5.3.1d Total efficiency and experimental verification

5.3.2. Partiele collection in a heterogeneously fluidized bed i i 68 69 71 73 73 74 79 79 81 84 84 86 89 90 93 96 97 97 98 98 99 99 100 100 102 103 104 106 107 107 110

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5.4. Experimental system 115

5.4.1. Batch dust collection tests 115

5.4.2. Counter-current dust collection tests 122

5.5. Measurements and results 125

5.5.1. Batch dust collection tests 125

5.5.1.1. Conditions for kinetic measurements 125 5.5.1.2. Dust collection tests at u> ut 128 5.5.1.3. Dust collection tests at u <ut 130 5.5.1.4. Axial dust concentration profile 132

5.5.2. Counter-current dust collection 134

5.6. Factors relevant for practical application 137

5.6.1. Optimization of the granular bed partiele size 137

5.6.2. Influence of temperature and pressure 142

5.7. Conclusions 146 Appendix 5.1. 147 Appendix 5.11. 148 Appendix 5.III. 150 Appendix 5.IV. 152 Symbols 154 References 157 Summary 162 Samenvatting 164 Dankwoord 166 Levensbericht 167

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1. Introduetion

In the process industry a large variety of gas-solid

contacting processas are encountered. There are many

examples of chemical reactions between solids and gases,

the solid is then either a reactant that is consumed, a

reaction product, or a catalyst. There are also many

examples of physical gas-solid processes, such as

adsorption, desorption, drying of porous solids, heat

exchange and filtration. For these various operations

different types of contacting devices are in use. The

most widely used are: fixed beds, moving beds, fluidized

beds, risers, zig zag contactors and solid trickle

flow

columns. Each of these has its own characteristics that

make it especially convenient for specific processes.

The fixed bed is the simplest and generally the cheapest

one to build. It is characterized by a relatively high

solid-gas mass transfer coefficient and by a narrow

residence time distribution in the gas flow. Hence it is

well suited for chemical processes that require a high

degree of conversion, and for physical processes that

require a high number of transfer units.

The fixed bed has a number of specific drawbacks, such as

the relatively high pressure drop and the limited heat

transfer rate to the wall.

The fluidized bed is distinguished from all the other

devices by a superior heat transfer coefficient to the

walls of the vessel. Other advantages are the very high

solid surface area, the mixing of the solid phase,

resulting in a uniform temperature throughout the bed,

the relatively low pressure drop, and the possibility for

continuous feeding and removing of solids.

The major application of the fluidized bed is still the

catalytic cracking process of petroleum. Other large

scale catalytic processes include the oxychlorination of

ethylene to ethylene dichloride. the ammoxidation of

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-1-propylene to acrylonitrile. and the synthesis of melamine

from urea. Other fluidized bed processes that are gaining

importance are the cambustion of coal with simultaneous

adsorption of sulphur dioxide. the dehydrogenation of

heavy oil fractions whereby besides lighter oil fractions

also coke is formed {the "Plexicoker" process) and the

gasificaton of coal.

The greatest drawback of the fluidized bed is the

occurrence of large gas bubbles. resulting in both a wide

residence time distribution and a limited gas-solid mass

transfer. The height of a transfer unit under

conventional operating conditions may be of the order of

one metre. which is surprisingly high considering the

dimensions of particles {less than 0.1 mm}.

When operated under continuous solids throughput

conditions. also the solids mixing can be a serious

drawback.

Por ideal behaviour countercurrent devices should have

plug flow in both phases and a high mass transfer rate

between them. Por countercurrent uses several devices are

described in literature. Hoving beds exhibit a high gas

to partiele transfer rate. The pressure drop is high and

it is difficult to maintain a constant solids flow. In

zigzag contactors. high solids throughputs can be

obtained. which makes them attractive for stripping

purposes of large solid flows.

There are also two modifications of the fluidized bed

that can be used in the countercurrent mode. Compared to

the usual fluidized bed. they result in a better mass

transfer performance while retaining the specific

advantage of solids flow.

There are:

- Multistaged fluidized beds. sometimes constructed with

"downcomers" to allow the solids to flow from one plate

to the next one below it. Also a kind of "dual flow"

trays have been proposed. making use of the magnetic

distributor plate [see Wang Yang. 1982].

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Multistaged fluidized beds are frequently used in

countercuerent adsorption processas and as chemica!

reactors/heat exchangers.

Magnatie stabilization of the fluidized bed. such as

proposed by Rosensweig [1978] and others.

The latter metbod that was first described by Fillipov

[1961] has not yet found any large scale technica!

application, as far as we know.

The principle was studied both theoretically and

experimentally by some Exxon research workers,

[Rosensweig, 1978, 1979, 1981, 1983, Lucchesi. 1979].

The principle of tbis metbod is quite simple:

The fluidized bed is made up of solid particles of which

at least a fraction is magnetically susceptible. A coil

around the vessel creates a magnetic field, usually with

vertical field lines. If the magnetic field is

sufficiently strong. the formation of bubbles is

effectively suppressed. The resulting bed is both "fixed"

(it shows little or no mixing) and "fluidized" (the

solids can be removed continuously). Heat transfer to the

walls is reduced. but both the so·lid and the gas phase

can be passed through the bed in near-plug flow. For the

continuous removal of solids the use of a magnetic

distributor plate is very practical.

This thesis is concerned with an experimental study of

the magnetically stabilized fluidized bed (MSB). with the

intention of demonatrating its specific advantages.

The most obvious advantage is its superior performance as

a mass transfer operation. This would point at two types

of applications:

- Adsorption processes. with countercurrent

so~ids

flow.

- Catalytic reactions, with a high degree of conversion.

Another potentlal application. that was also recognized

by the Exxon workers. is:

- The filtration of very fine dust from gas flows.

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-3-Probably the latter application has the most unique potentials, since the process can be used at high temperatures (e.g. t i l l about

soo

°C) and under high pressures.

The experimental study described in this thesis comprises four subjects:

a phenomenological description of magnetically stabilized fluidization (chapter 2)

- gas flow (axial and radial gas mixing) (chapter 3) solids flow (chapter 4)

gas tiltration in a magnetically stabilized bed (chapter 5).

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CHAPTER 2. MAGNETICALLY STABILIZED FLUIDIZATION: PHENOMENOLOGICAL DESCRIPTION

2.1. Literature review

In the recent past, numbers of authors have reported on the influence of a magnetic field on air fluidized magnetizable solids.

Early accounts on these phenomena were reported by Filippov [1960, 1961] and Kirko and Filippov [1960]. These authors investigated the effect of a longitudinal magnetic field on a suspended layer of ferromagnetic particles.

They worked with gas-solid and liquid-solid fluidized beds in an alternating longitudinal magnetic field.

A sort of phase diagram in co-ordinates of magnetic field strength and flow velocity was proposed, in order to give a clear picture of the different regimes of fluidization. Subsequent workers have reported on the influence that magnetization exerts on pulsations, heat transfer, structure and other characteristics of magnetized and fluidized solids.

Sonoliker et al. [1972] studied the effect of magnetic field on the fluidization of iron dust with air. The partiele sizes were in the range 213-715 ~m. It had been observed that the minimum fluidization velocity increased with increasing field intensity.

The fo~lowing relation was proposed:

H

=

magnetic field applied [ A m-1] umf H and umf

0 are the minimum fluidization veloeities

with or without the magnetic field H respectively.

Since the method for measuring umf was not defined, it can be doubted whether umf or ubp was determined

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-5-(ubp

=

bubbling point velocity).

The authors believe that the magnetic field increases the downward force on the particles and hence there should be an increase in the minimum fluidization velocity for the same partiele size. The Bulgarian researchworkers Ivanov and Shumkov [1972, 1975] particularly investigated the fluidized bed structure under the influence of a magnetic field.

In a bed of ferromagnetic ammonia catalyst particles they studied the local density fluctuations as a function of location in the bed, velocity of the fluidizing agent apd strength of the electromagnetic field imposed upon the bed.

The heterogeneity of the bed was evaluated from the puls-ations in its density with the aid of a capacitance probe. Both for the magnetized and unmagnetized beds, they

distinguished three different density zones over the bed height.

By imposing an electromagnetic field, structural changes are set in which are characterized by a more homogeneous bed structure.

The occasional density fluctuations in the bed are

influenced by the magnetic field in amplitude, frequency and distribution.

With increasing magnetization. the amplitude of the density fluctuations decreases while the frequency increases.

Bologa and Syutkin [1977] estab1ished the forma.tion of pseudopolymerie structures along lines of force in a magnetically stabilized bed, in the case of a

longitudina1 magnetic field.

These structures form channels of reduced resistance in the bed.

They established also a constancy in pressure drop with increasing magnetic fields.

Only for high magnetization a sudden fall in pressure drop was noticed, due to spouting of the fluidized bed.

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In a transverse magnatie field the pressur& drop increases with increasing induction.

Bed uniformity was investigated by recording the pressure drop fluctuations.

With increasing magnetization. a steady decrease in the fluctuation amplitude of the pressure drop was estab-lished.

More recently some research workers of Exxon Research and Engineering Company [Rosensweig. 1979; Lucchesi et al., 1979; Rosensweig et al .• 1981]. picked up the subject again and reported on a number of features of magnetical-ly stabilized fluidized solids.

They applied a uniform magnetic field on a bed of at least partly magnetizable solids, the direction of the field being colinear with the direction of gas flow. At gas veloeities beyond the minimum fluidization veloc-ity, the bed expands without bubbling.

This state of homogeneaus expansion has been termed by Rosensweig "the magnetically stabilized bed" (MSB) [ see figure 2.1].

STAlLE FLUIDIZEDEMULSION BUBBLE

FLOWINPUT FLOWINPUT

fig. 2.1 Comparison of fluidized solids (A) unstabilized

(B) magnetically stabilized souree : Rosensweig 1979

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-7-2.2. Mathematica! stability analysis

In order to be able to give a systematic interpretation

of the phenomenon of magnetic stabilization of the state

of uniform fluidization. Rosensweig and coworkers

execut-ed a mathematica! stability analysis [Rosensweig. 1979:

Rosensweig. Zahn. Lee and Hagan. 1983].

A fluidized bed can be regarded as a two phase flow

sys-tem. The behaviour of this flow system can be described

in equations of continuity and motion.

continuity equations

at d.

at

+ l. V • t !!c 0

continuous phase

dispersed phase

y_

0

and

!!a

are the velocity vector for the gas and

solids phase respectively.

Eguations of motion

Gas phase (mass and viscous terms are ignored)

t

grad P - f

=

0 dispersed phase

(2.1)

(2.2) (2.3) (l-t>Pa.9.- r (2.4)

f

=

fluid partiele interaction

For the unmagnetized situation these equations have a

simple formal salution corresponding to the well known

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state of uniform fluidization. In a number of previous

studies. it bas been shown by methods of hydrodynamic

stability analysis, that the formal solution is unstable

to small perturbations of voldage [Jackson, 1963: Pigford

and Baron, 1965].

For a magnetically stabilized bed the equation of motion

for the solids phase (eq. 2.4) can be extended by a

mag-netic stress tensor.

This tensor speelfles forces of magnetic polarization and

is derived from energy conservation. The magnetic stress

tensor is given by:

T

.m

(2.5)

where

H

magnitude of magnet ie field [A m-

1]

B

magnitude of magnet ie induction [kg

s

-1

c .

-1

Tesla]

-7 -2

permeability constant

llo

41T.l0

kg m

c :

(defining equation)

M •

x.

H M

magnitude of magnetization [A m- 1

1 x

magnetic susceptibility

(2.6)

The magnetic force density

~

is computed on the

assump-tion that the material is ferromagnetica1ly soft so that

Mis colinear with

H

<M x

H •

0).

Under these assumptions

~

is given by:

(2.7)

The set of equations (2.1 to 2.4) extended by the

magnet-ie stress tensor. have a simple salution repreaenting a

steady state of uniform fluidization and uniform

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-9-magnetization. in which any magnatie term is absent. This salution is given by:

( 1-c ₀} p p g (2.8)

porosity in the uniform bed

. .

[

-41

drag coeff1.c1.ent N. s m

According to the well known Carman-Kozény relation. a(c } 0 is given by: ~ d 2 p (2.9)

It appears from (2.8) that the magnetics have no influ-ence on the equilibrium solution.

This is a direct consequence of (2.7) in that magnetic farces arise only as a result of field gradients while in the equilibrium system. the magnatie field is spatially uniform. hence free of magnatie farces.

The stability of the steady state salution against small perturbations can be examined by hydrodynamic stability technique.

With magnetic field applied colinear to the flow field for linearly magnetizable particles with susceptibility x the following linear pDE is obtained for axially prop-agating voidage perturbations.

a

2c

ac

a

2c at 2 + a at + b ax - c ax2 where a g_ u g(J-2 co> b • co (2.10)

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c

1+X ( 1-t 0)

MP magnitude of partiele magnetization [A m-1] Magnetics appears explicitly only in the coefficient c. Local expansion or compression of the bed establishes a magnetic force tending to restore the bed to uniformity. Magnetism exerts no net force on the bed but acts only as an elastic-like restoring force.

By introducing a plane wave disturbance, the propagation of a disturbance can be examined. The condition of neu-tral stability (no propagation and no extinction of the perturbation introduced) is given by the criterion

NmNv b2 1 a2c (2 .11) 2 where Nm PP. u MP 2 'ILO kinatic energy _(2.12) magnetic field energy

1+X(1-t t o 2(1-t o>

voidage function {2.13)

Figure 2.2 gives the prediction of theory for the depen-denee of transition velocity on magnetization of magne-tite bed particles (210-420 'ILm).

Gas superficial velocity is normalized to minimum fluid-ization velocity umf"

From eqs. (2.8) and (2.9) follows:

(2.14)

where 'mf bed porosity at umf

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-11-From this relation values of c

0

may be computed for

given values of u /umf·

For the magnetite particles in our experiments holds:

cmf

0.468 (see §5.6.1)

x

4.85 (see figure

2.6)

Magnetization may be represented non-dimensionally as

p

=

partiele density (kgtm

3 )

p

From eqs.

(2.12).

(2.13) and (2.14) the stabi1ity

crite-rion NmNv

<

1 may be deduced as:

(N

)1/2

V (2.15)

Magnetic stabilization produces a wide range in which the

bed medium is quiescently fluidized and free of bubbles.

This stabilized range exists between minimum fluidization

velocity (umf) and the neutral stability curve (see

figure 2. 2) •

Other interesting conclusions from the stability analysis

of Rosensweig are the following:

- The applied magnetic field is most advantageously

oriented in the direction of the bed axis. i.e. along

the flow direction.

- When the bed particles are highly magnetized the medium

develops a considerable yield stress due to mieroaeale

attraction between particles.

The flowability will be impaired and consequently a

modified description of bed stability and behaviour

will be necessary.

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L c

t

2 o.sL---'----:"---:-1 0 10 20 30 40

...

fig. 2.2. Theoretically calculated fluidization regimes for magnetite particles (Eo was calculated from u by means of the Carman-Ko?.eny relation X was taken constant at 4.85 ( magnetite }

d

c

-13-fig. 2.3.

Spatial magnetic field intensity distribution compared to central magnetic field strength

( coil dimensions

L /d ~ 1 )

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2.3. Electromaqnetic coil and ferromaqnetic particles

To realise a magnetically stabilized fluidized bed as

described by Rosensweig and coworkers. a uniform magnetic

field bas to be applied to a bed of magnetizable solids.

For most of our experiments a simple electromagnetic coil

was designed which could be placed in different kinds of

fluidized beds. The magnetic field intensity on the axis

of an electromagnetic coil can easily be calculated in an

analytica! way [e.g. Alonso

& Finn, p.l09].

In our own simple design the coil diameter and the number

of turns/m were always constant along the coil length.

For a coil of infinite length the magnetic field was then

given by:

H

=

n I

where n

I

number of turns/m

electric current

(2.16}

A simple numerical integration metbod {on Commodore 64}

was developed to calculate the magnetic field intensity

for points out of the axis. In figure 2.3 the vertical

term of the spatlal magnetic field intensity was

normal-ized to the magnetic field intensity in the centre of the

circular coil (H

0).

The plot holds for L /d

=

1 (length/diameter ratio).

c

On the vertical axis a negative deviation was found.

In the central horizontal plane the magnetic field

inten-sity deviates positively from H

0•

In figures 2.4 and 2.5. horizontal and vertical

davia-tions from central magnetic field intensity are plotted

for other Lc/d

0

ratios.

According to these data, and given a desired magnetic

field uniformity. a suited electromagnetic coil can be

designed to any fluidized bed.

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x/d c

1

y/L c 0.1 L /d c c L /d c c

-15-...

10 fig. 2.4. Non-dimensional magnetic field (H/H₀) in the central horizontal plane of an electromagnetic coil as a function of dimensionless radial co-ordinate (x/d ) and c coil di~ensions (L /d ) c c fig. 2.5. Non-dimedsional magnetic field (H/H 0) on the axis of an electromagnetic coil as a function of dimensionless axial co-ordinate (y/d ) and

c coil dimensions (L /d )

(24)

To reach a higher magnetic field uniformity within a

coil. compensating turns can be provided at the coil ends.

Most of our fluidization experiments were carried out in

the same straight coil. The most important

characteris-tics are given in table 2.1.

Table 2.1.

Electromagnetic coil characteristics

length

(L ): c

diameter (d ):

c

n:

0.8

m

0.45 m

825 {number of turns/m}

copper wire diameter:

2.36 mm

stabilized

DC

power supply:

±

1000

VA

mantle tube:

stainless steel

From experiments carried out by Rosensweig [1978] it

appears that an alternating field is not or less

desir-able in preparing the stabilized fluidization.

Another advantage of uniform field is reduction of magnet

power.

The solid magnetizable and fluidizable particles to be

used in an MSB can be all ferromagnetic and ferrimagnetic

substances.

Non-magnetic materials may also be coated and/or contain

dispersed therein solids having the quality of

ferro-magnetism.

Since magnetism is the determining factor the

stabiliza-tion will be negatively influenced by mixing with the

ferromagnetics. a non-magnetic substance.

Arnoldos et al. {1983] mixed ferromagnetic crushed nickel

oxide particles (177-250

~) and non-magnetic silicon

(350-420

~) with each other in different quantities. The

transition velocity at an app1ied field of 4000 A m-

1

decreaeed nearly proportionally with increasing quantity

of inert silicon particles.

One means for determining magnetization M of the

parti-cles in a bed under the influence of a given applied

(25)

mag-netic field is to measure their magmag-netic moment in a

vibrating sample magnetometer.

In a vibrating sample magnetometer the sample material is

placed in a uniform magnetic field.

A dipole moment proportional to the product of the sample

susceptibility times the applied field is induced in the

sample.

If the sample is made to undergo sinusoidal motion, an

electric signal proportional to the magnetic moment can

be induced in suitably located stationary piek-up coils.

In figure 2.6 the vibrating sample magnetometer

measure-ments are presented as a M-H curve. The slope of the M-H

curve is the magnetic susceptibility.

The magnetization measurements are carried out in a

Newport type E model 155 vibrating sample magnetometer.

Figure 2.6 gives the M-H curve for magnetite powder. as

used in most fluidization experiments.

fig. 2.6. Magnetization curve of magnetite particles ( d 32 • 209 )Jm )

t

•oo 300 X m 4.85 .~---~~ 0 100 200 300 H ( kA m-1 )

--

(26)

-17-In the low magnetic field range. the magnetic suscepti-bility of the sample was 4.85.

Magnetite (Fe

3

o

4) is a ferrimagnetic iron ore which was received from Hoogovens. It was used in different partiele size distributions: 0-210. 210-420 and 420-670 microns.

2.4. Fluidization characteristics: introductory experiments

As introductory experiments. number of simple fluidiza-tion experiments werè carried out. For the different fluidization solids used (magnetite and crushed iron in different size ranges) pressure drop curves and bed expansions were established as a tunetion of applied magnetic field.

As an illustration the pressure drop curve for magnetite 210-420 micron (surface mean diameter 312 micron) is given in figure 2.7.

The fluidization experiments were mostly carried out in a bed of 15 cm diameter and about 20 cm high.

As in unmagnetized bubbling fluidized beds, the pressure drop through the MSB equals weight of bed solids per unit area. independent of gas velocity or partiele size.

The pressure drop curve appears to be hardly influenced by the magnetic field applied. Only for high magnetiza-tions in shallow beds a sudden fall in pressure drop was established. due to spouting of the rigid bed.

For higher beds this could not be established. The mini mum fluidization velocity clearly does not change by applying a magnetic field. Beyond umf the bed expands homogeneously as gas flow rate increases.

Transition to the bubbling state of flow occurs at veloc-ity ut (transition velocveloc-ity) and represents the onset of bed instability.

In figure 2.8 the normalized bed height (Lb/Lmf> is plottea against non-dimensional gas velocity (u/umf}

(27)

r

60

50

u ::;:

a

u

30

0.. 0 1-< '"Cl

₂₀

Q) 1-< ;:1 tl) til 10 Q) 1-< 0..

0

fig. 2.7. L /L 1·"' b mf 1.3 UI 1.1 0

•

• _•

_•

•

unstabilized

•

3810 A/m

•

5715 A/m 1)

₂₀

_ll

₄₀

₅₀

₆₀

₇₀

₈₀

₉₀ u ( cm/s )

____.,...

Pressure drop behaviour of a stabilized and an unstabilized bed for 210-420 l.lln magnetitc< particles

2 3

"'

...

-19-partiele size magnet ie ( micron field (A/m)

•

420-670 6500

•

210-420 6500

0 210-420 3250

*

120-210 6500

fig. 2.8. Normalized bed height vs normalized super-ficial gas velocity for magnetite in various sizes and magnetic field strengtbs

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The bed material was always magnetite.

It appears that the bed expansion rises linearly with

increasing gas velocity for all partiele sizes.

Beyond ut the bubbling bed mostly does not further

expand.

The transition from the stabilized bed (MSB) to the

destabilized bed with increasing gas velocity is

charac-terized by the appearance of gas bubbles in the bed.

which can be observed visually.

Nevertheless. a more convenient method is to record the

onset of pressure drop fluctuations over the bed.

Pressure noise analysis gives also interesting

informa-tion about the hydrodynamic behaviour of the fluidized

bed. both in the stabilized and in the bubbling

fluidiza-tion regime.

For two magnetite partiele size distributions (<210

microns and 210-420 microns) the pressure drop

fluctua-tion of the magnetized bed was measured.

The bed diameter was 7.5 cm. The gas distributors were a

porous metal plate (PORAL) for the fine magnetite

parti-cles and a wire screen (68 micron) for the coarser

magne-tite.

For both distributors the pressure drop was miriimal.

The transmitter (PC 87634) was linear within the

measur-ing range.

The pressure noise signal was registered by a Honeywell

probability analyser (model SAI 42 A) and analysed in two

different ways:

- probability density tunetion (AC mode):

- autocorrelation tunetion (AC mode).

The data for both measurements were recorded on punch

tape.

The standara deviation

(o)

of the probability density

functions was plotted against superficial gas velocity

for both bed partiele sizes in figures 2.9a and 2.9b

respectively.

(29)

t

8-oe

=

0 •.-l

...

"'

•.-l > tl) 'tl '1:1

""

"'

'1:1

=

"'

...

til

'

,....

N ~ 0

....

_...

"'

•.-l > <11 'tl '1:1

""

"'

'1:1

=

"'

...

_(1,) 40 30 20 10 0 0 10 20 30 40 10 eo u ( cm/s

..

Standard deviation of the probability density function vs superficiaJ gas velocity ( magnetite 210-420 ~m )

from the left to the right the value of the parameter H is respectively : 0,825,1650,2475,3300,4950,5775 A/m)

10

0

u ( cm/s )

-Standard deviation of the probability density function vs superficial gas velocity ( magnetite < 210 ~m )

(30)

-21-t

u (cm/s) unstable fixed oL---~._----~---~~----~---~---J 2 3 5 H (kA/m)

fig. 2.10.a. Fluidization regimes for rnagnetite 210-420 ~m

I

•

20 unstable u (cm/s) fixed oL---~ ₂ ₃ ₄ _s _e H ( kA/m )

---fig. 2.10.b. Fluidization regimes for rnagnetite < 210 ~m

(31)

The pressure drop fluctuation is shown to be very small

(a < 0.5') until the transition velocity (ut) which

corresponds to the homogeneously expanded bed structure. Beyond ut the curves show particularly for magnetite 210-420 micron, a remarkable parallel path, which suggests a similar bubbling behaviour.

Only the range of homogeneous expansion increases with increasing magnetization.

The intersection of the standard deviation curves from figures 2.9 with the horizontal axis is plotted against magnetic field strength in figures 2.10a and 2.10b respectively.

These figures represent the different fluidization regimes of a magnetized bed.

They are perfectly analogous to the theoretica! predic-tion of Rosensweig (see figure 2.2).

t

2 •

...

1.5 ::·· •

....

_.•.

_..

.

.5

~

•.

:~

i _'

_.

~.; '.:.,

_...

. _,~

_{... ...}

... . 0 .. - _ .... - - .. - --.·~ - - - -·~ .... f"':"

*

.t.• ... .. .: .. ~~

....

""f ... : . .

..

T

fig. 2.11. Graphical determination method of the characteristic pressure fluctuation frequency from the auto-correlation function

(32)

-23-Below the minimum fluidization velocity the pressure drop

across the bed is less than the bed weight per unit area

and the bed is fixed. Above umf the fluidization state

can be divided into two zones. Below the transition

velocity the bed is stabilized. Beyond the transition

velocity the bed shows a bubbling behaviour and

increas-ing pressure drop fluctuations.

The characteristic frequency of the pressure noise signal

(i.e. of the bubble pattern) was determined from the

examination of the autocorrelation function {$xx>

$XX

=

E{X ( t ) . X ( t -"t ) } (2.17)

The autocorrelation function shows a maximum for 1:

₁

• 21:

₁

, 3"t

₁

, etc. where

1:

1 is the specific delay.

l/1:

1 is the specific frequency f.

The graphical determination metbod is illustrated in

figure 2.11.

For some conditions the autocorrelation function was less

obvious and did not show a clear specific frequency.

In figures 2.12a and 2.12b the specific frequency of the

pressure drop fluctuation is plotted against superficial

bubble phase gas velocity (u

0

-ut)

u

₀

-ut

=

ub

=

superficial bubble gas velocity

For both bed partiele sizes and for all magnetic fields.

-1

the specific bubble frequency lies between 2 and 4 s

• There was no significant and consequent effect. neither

of magnetic field nor of the bubble phase gas velocity

(ub) on the measured specific frequency of fluctuations

of pressure drop.

(33)

I N UI I 5r---~

t .

» CJ s:: Ql

g.

3 2

---

....

--

..

__

..

--

....

_--

_..

_--

_...

H

=

0 A/m Ql ,... ~ 01~---L---~~---~ 0 10 20 30 0

t "· ---_. __ ,_

-!·-·

---•

•

3 H 0 A/m 5 10 15 0

-

-·

---·--·--·--·--

--H

=

1650

Alm

1---.

-·..#.

--H 4125 A/m 10 20 30 0 10 20

•

• ---w--.---•

•

• ----

·-30

~--

....

--

-

-.----.--

- -

.

-·

H 1650 A/m H

=

4125

Alm

5 10 15 0 5 10 15

bubble phase gas velocity

fig. 2.12. a. and b. Specific frequency of the pressure drop fluctuati~n vs superficial bubbie phase gas velocity ( magnetite 210-420 pm and magnetite

<

210 pro )

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2.5. Discussion

The different stabilization regimes of a magnetized bed can be recognized very good by recording the pressure drop fluctuations. Comparison between the Rosensweig stability analysis and experiment is made in figure 2.13. It gives the theoretica! and experimental fluidization regimes for magnetite <210 ~m. It appears that theory gives only a rough qualitative prediction of the stabil-ity of a magnetite fluidized bed.

This can be due to different reasans as there are:

- difficulty to measure the magnetic susceptibility of a powder sample at fluidizing porosity.

micro-scale attracting forces between particles at higher magnetization are not included in the stability analysis.

Concerning the behaviour of the bubbling bed. Sadasivan (1979] gives a few empirical relations between magnitude of the maximum pressure drop fluctuations and flow condi-tions in a non-magnetized fluidized bed.

6 = (uo-umf)0.71 or ó =

d~'

212 (2.18) (2.19) where 6 db

magnitude of maximum pressure drop f1uctuation bubble diameter.

In a non-magnetized bed: ub ~ u₀-umf"

Although 6 is a rather arbitrary parameter. in first approximation it can be supposed to be proportional to the standard deviation

a

of the pressure noise signal

(see Sadasivan. 1979). It appears that the standard davi-ation

a

is mainly determined by the superficial bubble velocity of by the bubble diameter.

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t

10r---~~ 5 2 experimental I I

/

I I ; I I ; / ; / " " "theoretical 06_{o~----~1o~--~2~o~--~3o~----4~o~----s~o---&~o·} Fluidization regimes of < 210 wm magnetite particles ; comparison between theory and experiment

Taylor and coworkers [1973) found a more than linear relationship {exponent about 1.3) between pressure noise standard deviation and superficial bubble gas velocity. Their data were obtained from a large scale fluidization experiment of ballotini glass.

For our experiments in a magnetized bed a linear rela-tionship was found between standard deviation

a

and superficial bubble velocity ub.

In spite of the Sadasivan and Taylor relations hold only for non-magnetized fluidized beds, there appears to be a certain agreement with our experiments. From figure 2.9 and equation (2.19) one could derive that the bubble diameter should be independent on magnetic field strength for identical superficial bubble velocity.

Nevertheless. by visual observation one could establish that with increasing magnetization the bubble shape changes considerably.

It changes from the well known. rather flattened bubbles in a normal fluidized bed. via small and very fast

(36)

-27-bubbles, to vertically stretched cavities and real chan-nelling in a strong magnetized bed.

This shape transformation apparently does not influence significantly the pressure noise signal.

The relation between bubble frequency and superficial bubble gas velocity is not very significant. Assuming a constant dense phase expansion, or the bubble diameter. or the bubble frequency will increase at increasing bubble phase gas velocity. Both from the pressure noise standard deviation and from the measured specific fre-quency, the bubble diameter appears to increase. while bubble frequency remains unchanged. This finding is in agreement with earlier investigations in a non-magnetized bed (Sadasivan [1979], Hiby [1967)).

Generally it appears that the bubbling regime of the unstable magnetized bed is quite good comparable with a non-magnetized bubbling bed.

Only for high magnetizations. the bed structure is quite different.

(37)

CHAPTER 3. GAS FLOW

3.1 Introduetion

The magnetic

stabilizati~n of a fluidized bed changes the

bed structure and the flow pattern in the bed. It is

therefore to be expected that the residence time distri

bution in the gas flow and radial mixing are both

affect-ed. Consequently the investigation of the gas flow

through a stabilized bed can give us information about

the bed structure. Furthermore the residence time

distri-bution and the radial gas dispersion are of utmost impor

tance for the overall behaviour of a magnetically

stabi-lized bed as a reactor.

Generally one can say that a good radial gas mixing

af-fects the conversion favourably and that the axial mixing

mostly bas a negative influence.

Knowing the reaction kinetics for a first order reaction

the effect of mixing on the overall conversion is

suffi-ciently demonstratea by the residence time distribution.

The gas flow in a conventional gas-solid fluidized bed is

often described by a so-called two phase model in which a

dense and a bubble phase are distinguished. The dense

phase gas passes through the interstitial spaces between

the solid particles. The bubble phase consists of larger

cavities without solids, which rise up through the bed at

a higher velocity than the interstitial gas. Mass

trans-fer between bubbles and dense phase can be described by

all sorts.of models with varying complexity, from which

the bubble cloud model is the most known.

In any case. the RTD of the gas in a heterogeneously

fluidized bed will be determined by the difference in

linear velocity between bubble and dense phase gas, by

mass transfer between them and also by mixing within both

phases. Also the radial gas dispersion is greatly

deter-mined by the bubbling behaviour.

By magnetic stabilization a homogeneaus expansion can be

(38)

-29-realized within a certain range of gas velocities. The hydrodynamic behaviour of the bed varying with gas velo-city and magnetic field can be expected to influence sig-nificantly also the gas flow through the bed. Until the transition velocity (ut) no bubbles occur. although no certainty is obtained about the homogeneity of the bed structure on smaller scale. Beyond ut the bed begins to behave heterogeneously with a bubble behaviour visibly different from the unstabilized state. The pattern of fluid passage through a reactor can be investigated by the so-called stimulus response technique. This technique imposes a varying tracer gas concentration at the inlet stream and observes the corresponding response at the exit stream of the vessel (section 3.2.1). A suitable model can then be selected to repreaent the real flow which has the same or a similar type of residence time distribution. Because of the large variation in bed structure it was hardly possible to find a model which would describe accurately the real gas flow under all conditions. Because of its wide applicability and simpli-city and also because of the more or less homogeneaus bed structure of an ideal MSB. we have chosen for a simple dispersed plug flow model. which supposes essentially a homogeneaus flow. For the heterogeneaus oircumstance the description with this model is likely to be inaccurate. For the examination of these fluidization states we used also a two phase flow model which consists of a parallel conneetion of two series of mixers (section 3.3.1}. The radial gas dispersion was investigated employing a conti-nuous central tracer point souree and measuring the radi-al concentration profile downstraam (section 3.2.2). 3.2 Eguipment and experimental method

~~~:!_~~!~!-~~~~~~

The equipment used in this study (figure 3.1} consisted of a 15.24 cm I.O. glass column with a 2 cm flexolith

(39)

distributor plate. The whole vessel was placed in the 45 cm diameter magnetic coil mentioned above. The upper part of the column was provided with a vertically movable sort of funnel which fitted close to the column wall. In an excentric position in the funnel an air driven stirrer was provided for creating a CSTR in the empty space above the bed surface in order to average the possible radial concentration gradients of the tracer gas coming out of the bed. The stirrer consisted of a propeller and a tur-bine above each other for creating a circulation profile as shown in figure 3.1. A stroboscape was employed for measuring the stirrer speed. The provision of a CSTR above the bed was necessary because the gas sample was withdrawn in only one central point. The mixing charac-teristics of the CSTR were investigated separately by injecting a very short pulse of tracer gas directly in it and registrating the response. A plot of tn C ~ t

should give a straight line. The averaged residence time of the CSTR determined from the slope of this line may be verified with the volumetrie residence time (V/Q).

By adjusting the height of the funnel and the stirrer speed one could establish for most circumstances a good mixing behaviour within the empty space above the bed without backmixing in the bed itself. Only for low super-ficial gas veloeities it seemed to be difficult to get an ideal mixing behaviour avoiding backmixing through the bed surface.

The path of the input concentration (imperfect pulse) was verified experimentally by withdrawing fluidization gas under the bottom plate. The signal measured in this way was the result of different phenomena such as:

finite opening time of the magnetic valve (0.3 s) mixing in the plenum under the bottom plate and back-mixing in the fluidization gas

- axial dispersion in the sampling tube.

The total effect of these phenomena was expressed in terms of a mixing model. The tracer gas used was ethylene

(40)

-31-I w N I

•

• _•

•

ethylene vacuum FID air hydrogP.n ai.r vacuum

•

ethylene _air

(41)

which was detected by a flame ionization detector (FID). The detector was held at an underpressure of 46 kPa by a Negretti vaive and a buffer vessel. Tracer gas could be withdrawn through a 0.2 mm ID capillar tube. The detector was heated by an I.R.light to avoid condènsation.

Conneetion points were just under the distributor plate and centrally in the empty space beyond the bed. By means of a magnetic valve which was opened during 0.3 second. the tracer gas could be injected in the fluidizing air stream with a constant overpressure of 2 kPa.

The signal of the FID was amplified by means of a Becker electrometer. The output of the electrometer was sampled and punched on paper tape with a frequency of 2Hz by means of a set of Philips pieces of equipment {scanner PM 2460. digital voltmeter PM 2441, printer control unit PM 2465 and tape puncher FACIT 4070). By means of a self designed start system the opening of the magnetic valve was synchronized with the first measurement. which bas the advantage that the zero point of the RTD curve is defined exactly. The data on paper tape are handled afterwards on the university computer {Burroughs 7700). The fluidizing gas was ambient air and the particles used in the tests were magnetite from Hoogovens and pulverized iron (Merck 3800), both in various size ranges.

!~~~~-!!~!!!_!!!!!2

Radial dispersion was measured using a central point souree for tracer gas in the bed and measuring the con-centration profile downstream as originally described by Towle and Sherwood [1939].

The measurements were done in the same glass column but provided with special equipment for central tracer input and an assembly for easy moving the sampling tube in a vertical and horizontal direction (figure 3.2). A copper tube. 3 mm I.D •• ending centrally in the bed. ll cm above the distributor plate. was used to introduce tracer into the bed. The pressure drop over a capillary tube winded

(42)

-33-up in a coil was used to control the tracer flow. The tracer injector velocity was matebed to the local inter-stitial gas velocity for not disturbing the normal flow pattern around the injector tube. Local linear velocity was calculated from gas flow rate and voidage measure-ments. The sampling capillary tube to the FID was enelos-ad in a rigid brass supporting pipe.

An assembly which. is schematically represented in figure 3.3 gave the possibility for positioning the point of the

sampling tube in 7 different radial positions. Vertical positioning was proportional. The point of the sampling tube was protected against clogging by a cotton ball. Mass flow through the detector was held constant by

regu-lating carefully the underpressure of the detection sys-tem.

FID _air

hydrogen

top cover

(43)

Figure 3.4 gives the calibration curve of the detector at

measuring conditions. Tracer gas concentration is

expressedas a volumetrie flow ratio (Qt/Q ). Because of

_. _g

the stochastic character of the mixing process the actual

concentration showed a fluctuation in time. especially

for the more heterogeneous bed conditions. The

concentra-tion was sampled during about 5 minutes

(±

120.000 sam-ples) with a Honeywell probability analyser (model

sai-42A). The probability density function of the actual

concentration signal was punched on paper tape. The time

averaged concentration was calculated from the density

function by means of the univarsity computer.

I

mV 300

fig. 3.4. Calibration curve of the flame ionization detector at measuring conditions

-35-•

(44)

3.3 Modellinq of the mixing process

~:~:~-~~!~!-~!~!~~

Two models were used for attempting to describe the

phys-ical conditions in a MSB. The first one is a

convention-al axiconvention-al dispersion model with only 1 parameter. The

sec-ond one, originally proposed by Himmelblau and Bisschoff

[1968], is a 4 parameter model, consisting of two unequal

parallel series of CSTR's.

~:~:!:!_!-~!~~~~~~~-R!~2-~!-~~!

Assuming that the axial mixing process may be described

in terms of a diffusivity constant DL {axial dispersion

coefficient), the mass balance over the bed section is:

ac +uac

at

ax

0 (3.1)

At the bed entrance a closed boundary condition holds

because there is only convective transport through the

distributor plate:

(3.2)

Experimentally it was shown that the imperfect input

pulse (Cf) could be written as a cascade of n CSTR's and

a dead time (figure 3.5). This is expressed in the

fol-lowing equation:

-t/'t .

(n-1)1 e 1 ( 3. 3)

Where c

0

=

concentration at t•O.

For the bed surface it is less obvious which boundary

condition bas to be used.

(45)

I w ...:I I

B-6---'---

..

- - - ' /

•

• DL

oio

r

I--X=O

x=

L

~--[:J---

eb \ I

•

D

fig. 3.5. a. and b. Schematic representation of the measuring equipment for two different sets of boundary conditions a. : closed boundary b. : open boundary

(46)

bed, which consists of a series of ideally mixed empty spaces between the bed particles. a closed boundary con-dition is logical:

0 (3. 4a)

When the axial mixing is ascribed to a difference in lin-ear gas velocity (sart of parallel circuits of plug flow channels) an open boundary is more logica!.

(3.4b) For these sets of boundary conditions no analytica! solu-tion of equasolu-tion {3.1) is available, when the input is an imperfect pulse.

Salution can be obtained by Laplace transformation, which is a technique whereby a partial differential equation can be converted into an equivalent ordinary differential equation [Jenson. 1977). It is a particularly useful

technique becàuse the boundary conditions are introduced into the equation prior to its solution.

The Laplace transfarm is defined as

f [f(t))

00

Je-st f(t) dt

0

For the derivatives holds:

f(s} f [

d:~t1

.. sf(s) - f(o) 2 f. [ d

f(t~

s 2l'(s) -sf(o) - f ' (o) dt (3.5) {3.6) (3.7}

These properties can be applied to equations (3.2). (3.3}. (3.4a) and (3.4b) resulting for the solution in

(47)

the Laplace domain (see appendix 3.1): - 1 . 1 C ( s)

=

_{k1 exp[Pe L(}

Ï

+ q) z] + _{k2 exp[Pe L(}

Ï -

q) z} ( 3. 8) q p

se

ó "( "(

ë

(3.9} The coefficients k

1 and k2 follow from equations (3.3) and (3.4a) or (3.4b).

The metbod for determining the model parameters may be divided into parameter optimization methods and those using the moments of the response curve.

Because of the cumbereome back transformation of equation (3.8} two dedicated methods are used. namely fitting the transfer function (3.lla or 3.llb) and calculating the moments of the response curve directly from (3.8) accord-ing to Van der Laan [1958].

The transfer function concept is one of the most conva-nient ways of characterizing the dynamic behaviour of a disturbed system.

The transfer tunetion is defined as:

W(s) (3.10)

or the ratio of the Laplace transfarm of the output res-ponse Ce(s) of the system to the Laplace transfarm of the input Cf(s) producing the response.

For the two sets of boundary conditions the transfer function is respectively given by:

2q exp(PeL

<! -

q)] 1 2 l { l+ p ( 1-ó) ) {(

2

+ q) - (

2

-39-q)2 exp[-2PecqJ) ( 3 .lla)

(48)

2q exp(PeL <t - q)]

1 2 1 2 1 1

<ï+q) -(2-q) exp[-2Pe L"q]+(l-ó)p((2+q)-(2-q}exp[-2Pe r.;q]) (3.llb) Figure 3.6 represents the transfer function for a realis-tic value of PeL and ó, and'for closed-closed boundary conditions.

The usefulness of the moments for cases where only the solution in the Laplace domain is known, but not in the time domain, is based on the following proparty of the Laplace transform:

k 1.2.3 ...• (3.12)

From the definition of the moments it follows that:

e

mean residence time (3.13)

(3.14)

Applying equations (3.13) and (3.14) to equation (3.8) leads to the following value for the dimensionless residence time (both cases):

e

=

1 (3.15)

For the varianee of the RTD curve. dimension1ess against

e.

one gets respectively

2

(49)

t

W(s)

1).5

0_{o~---~---~2---',}

se

...

fig. 3.6. Transfer function and best fit for

o

0.9 ( closed-closed boundary conditions )

1

2 (J .9 .3 • 7 .6

.s

==::::::::::---::::".

_--....

,

_{__}

• 4 . 3 . 2 . i 0 -I 10 lO 0 10 l

fig. 3.7. Varianee of the RTD-curve according to equations 3.16.a and 3.16.b

parameter •

o

(50)

2

o2

=

26 (1-6- ;e)(1-exp[-P;_,]) + 1 + 62 - 26 +

~

6

e

(3.16b)

PeL L L

In fiqure (3.7) the varianee of the RTD curve. accordinq to equations (3.16a) and (3.16b} is plotted vs.the Peelet number with 6 as parameter.

3.3.1.2 Parallel cascades of mixers

For a number of circumstances a one dimensional diffusion model gives only a poor description of the reality.

Therefore a model of Himmelblau and Bisschoff [1968] was adopted, which consists of two parallel series of CSTR's

(figure 3.8). By means of this model it must be possible to get an idea about the appearance and importance of short-circuiting of gas by channels or bubbles under cer-tain circumstances. The four parameters by which the model can be described are consequently:

m

ll

fig. 3.8. Schematic representation of the 4-pa.ra.meter model ( two parallel cascades of mixers )

(51)

a. 1:2/'tl = ratio of the residence times

f fraction of the total flow through channel 1

n number of mixers in 1

m number of mixers in 2

'tl residence time of slow gas flow (S)

'(2 residence time of fa st gas flow (S)

It is assumed there is no mass transfer between the two cascades of mixers.

Taking equation (3.1) into account the analytica! solu-tion for two parallel series is:

n n-1 C*(t)=f n _t ___ e-nt/1:1 + (1-f) (n-1)1 n m m-1 m _t ___ e-mt/'t 2 (m-1)! 'tm 2 '(1 (3.17) For the factorials the Stirling approximation for the gamma tunetion is used [Abramowitz. p.257, 1970].

f(z) with U(z) (Z-1)1 139 (3.18) ---'=-''-"'---:-4 • • • ( 3 • 1 9 } 2488320z

An approximating tunetion for the factorials is used because the function has to be defined also for not in-teger values of n and m and furthermore because the tune-tion must be differentiable within the minimizatune-tion procedure.

For C*(S) one finds consequently: C*(S) = f 13n ( !L} 1/2 9 n-1 en( 1-t39} + 21T U(n} (3.20} (1-f) (~)m (m_)1/2 9 m-1 em(1- ~, + a. a. 21T U(m) 't