Love, D. J Percolation Behaviour of a Cane Diffuser.

PERCOLATION BEHAVIOUR OF A CANE DIFFUSER

By

D.J. Love and P.W. Rein Huletts Sugar Limited Mount Edgecombe, South Africa

1.

ABSTRACT

The percolation behaviour of a cane diffuser has been investi

gated in both pilot plant and full scale diffusers. A wide range

of factors was investigated and correlations have been developed

from the pilot plant experiments which relate the percolation rate

at which flooding occurs to the bed height, specific surface, mean

particle size and fibre content of the cane. The dispersed plug

flow model was found to fit the results of tracer tests on both the

pilot plant and full scale diffusers, providing measures of the

percolation velocity and the dispersion coefficients.

2.

INTRODUCTION

Flooding is probably the most serious operating problem en

countered in moving bed diffusers. Flooding occurs when more

liquid is sprayed onto the top surface of the bed than is able

to percolate downwards through the bed, and its occurrence causes

a noticeable drop in extraction as the countercurrent extraction

process is destroyed.

However it has been shown9 that high liquid flow

rates through the cane bed are highly desirable, as these condi

tions promote high rates of mass transfer. Ideally then the

diffuser should be operated at all times with liquid flow rates

at a maximum but just slightly below levels at which flooding

occurs. The maximum percolation rate is therefore a very impor

tant operating parameter.

A considerable amount of work has been done on bagasse diffu

sion, and maximum percolation rates were shown to be dependent on

degree of preparation and bed density.9 However,

Payne7 has stated that higher percolation rates should be obtainable

in cane diffusers, due to the less dense beds with a more fibrous

type of preparation. Experience with running a bagasse diffuser

at Empangeni as a cane diffuser for a limited period tended to rein

force these ideas.

However, operation of a cane diffuser at Amatikulu has re

sulted in fibre packing densities ± 20% higher than originally

anticipated, and percolation rates well below expected values,

lower even than obtained in bagasse diffusers.

A program was therefore initiated to investigate the nature

of flooding in a cane diffuser.

3.

Work was concentrated in two areas :

1) Pilot plant plant experiments aimed at establishing the factors

affecting maximum percolation rates and

2) Measurements of percolation behaviour in a full scale diffuser

via tracer testing.

THE NATURE OF PERCOLATION IN A CANE

DIFFUSER

Flooding in a packed bed

Most work on flow through packed beds is in relation to either

single phase fluid flow through packed beds (filters, catalyst

beds, fluidised beds) or countercurrent gas-liquid flow through

packed beds (absorption or distillation columns).

Rein8 developed a correlation for predicting the maximum per

colation rate attainable without flooding, U, in a bagasse diffuser

from the results of pilot plant experiments, as a function of bulk

fibre density D, and specific surface (or fineness) of prepared

cane S :

(1)

The form of this correlation is based on the work of Lavin who

considered single phase flooding as a special case of flooding in

countercurrent gas-liquid flow (i.e. no gas flow).

An alternative approach is to consider flooding as a special

case of single phase flow through a packed bed. By drawing an

analogy between viscous flow in packed beds and viscous flow in

pipes, the well known Kozeny Carman Equation can be derived.

Appendix 1 details the modification of this equation for the

4.

case of flooding percolation rate through a packed bed viz. :

Nomenclature used is listed at the end ot the paper.

This equation is not directly applicable to fibrous beds due

to the presence of static liquid hold-up and, in the case of percola

tion, trapped air . The voidage of a cane bed cannot thus be

simply considered as the volume fraction of the bed unoccupied by

fibre.

Fig. 1 outlines the factors which affect flooding in a cane

diffuser and the mechanism by which this takes place, based on

the Kozeny Carman equation.

Insert Fig. 1

Flow patterns in a pilot plant diffuser

The residence time distribution of liquid flowing through a

packed bed (as measured by tracer tests) has been successfully

modelled by the axially dispersed plug flow model

The differential equation describing tracer dispersion in an

axially dispersed plug flow system is :

where Ez is a dispersion coefficient in the direction of flow. For

plug flow liz = 0, and higher values indicate a greater spread in

residence times. v is the percolation velocity which is dif

ferent from the percolation rate (superficial velocity) due to the

reduced open area for flow in the bed.

The solution to this equation for the concentration of tracer

in the liquid leaving a packed bed of length i when a pulse of

5.

is applied at the inlet to the bbd at time t = 0 is :

The flow model used by Rein8 in work on a pilot plant bagasse

diffuser was that of plug flow with exchange with stagnant regions.

The differential equations describing tracer dispersion under

these conditions are :

6.

Flow patterns in a moving bed diffuser

It has been shown that in a moving bed type diffuser extrac

tion may be increased by increasing the amount of juice recircu

lation. The increased juice recirculation gives higher flow

rates through the bed increasing the liquid solid contact effi

ciency and thus allowing more of the sucrose to be extracted by

washing and less by diffusion. Juice recirculation must how

ever not be increased to the point where flooding occurs as this

drastically reduces extraction.

The use of tracers is a well known method of determining flow

patterns in process equipment and has already been used to in

vestigate flow patterns in moving bed type diffusers. It was

felt however, that the value of these tests would be greatly

enhanced if (1) a rapid method of performing tracer tests with

continuous tracer monitoring could be devised and (2) a mathe

matical model could be derived to analyse the results.

The axially dispersed plug flow model which was investigated

in the pilot plant was extended to a model postulating both

axial and lateral dispersion superimposed on plug flow. Fig. 2

represents the physical situation and the differential equation for

this model in rectangular co-ordinates is :

7.

Appendix 2 shows how the equation is solved and how the

concentrations of tracer from the various diffuser trays are

calculated.

EXPERIMENTAL DETAILS

Pilot plant diffuser tests

A pilot plant diffuser was constructed in which percolation

rates could be measured under controlled conditions. A schematic

diagram of the pilot plant is given in Fig. 3.

Insert Fig. 3

The sample of shredded cane is held in the column which is

0,32 m in diameter and 2,42 m high. The column is provided with

plastic windows down one side so that percolation and thus the

occurrence of flooding could be observed.

Juice flow to the pilot plant diffuser is controlled by a

pneumatic valve operated from a manual loading station. The flow

is measured by an orifice plate and d/p cell. A juice distri

butor is provided at the top of the column to ensure even distri

bution of juice over the surface of the bed. To maintain a con

stant flow for any valve setting, a constant head tank is pro

vided, with excess juice overflowing back to the storage tank.

The temperature of juice in the storage tank is regulated by

thermostatically controlled direct steam injection.

The column is hung from a beam which is counterbalanced by

the dial mechanism of a platform scale. This allows the mass of

liquid held up in the column during operation to be measured.

To perform a test, a consignment of cane was selected and

a sample of sliredded cane was taken from the cane sampling hatch.

The direct cane analysis figures were utilised for the corresponding

consignment.

8.

The pilot plant diffuser column was filled with this cane to

a level selected to give the desired bed height after compaction.

The mass of cane was recorded.

Percolation was started and the bed allowed to compact as

a result of the weight of the juice holdup in the bed and

softening of the fibres with increased temperature. The flow to

the column was manually adjusted to give the maximum flow without

flooding occurring on the surface of the bed. This maximum flow

rate decreased with time as the bed compacted. When the bed had

stabilised, this flow rate was recorded as the maximum percolation

rate, and the bed height was measured.

To perform a tracer test on the pilot plant diffuser, 100 gms

of NaCl was added as a 10% solution to the distributor at the top

of the column. The conductivity of the juice leaving the bottom

of the column was recorded on a chart recorder for 20 mins. During

this time, the juice leaving the column was run to drain to pre

vent any interference from recycled salt.

Cane preparation was varied by altering the speed and/or

clearances in the shredder. Samples were taken for particle size

analysis.

Tracer tests in full scale diffuser

Some initial experiments showed that NaCl could be used for

tracer experiments in a full scale diffuser with conductivity

being used as the measurement technique for monitoring the tracer.

Conductivity probes (Beckman type 414) were placed in the dis

charge lines of three consecutive stage pumps. The probes were

connected to conductivity transmitters (Bekcman Model SM 222) and

recorders to give a permanent record of the tracer peaks appearing

in each tray during a tracer test.

9.

To perform a test, the conductivity meters and recorders were

switched on about 15 minutes before salt addition, to monitor the

natural variations in background conductivity. Approximately

70 kg of NaCl was dissolved in 180 litres of hot water. To start

the test, the salt solution was added rapidly to the last of the

three monitored juice trays (tray R in Fig. 2). The concentra

tion of tracer appearing in each of the three trays was thus auto

matically recorded.

The bed height was measured at the windows at the side of

the diffuser. Bed speed was recorded. In tests at Amatikulu

the feed rate of cane to the diffuser could be measured by a

belt weigher.

PILOT PLANT DIFFUSER TESTS

Due to the large number of factors which can affect percola

tion rates and the complexity of their effects, only some of them

could be investigated quantitatively. One of the factors which

was anticipated to have a substantial effect was cane quality.

Although an analysis of the cane and measurement of tops and

trash was undertaken, these measurable factors do not characterise

cane quality adequately. Therefore all tests were undertaken on

burnt cane consignments, of variety NCo 376. Apart from cane analy

sis, the measurable factors which were varied in a test program to

develop correlations for use in optimising diffuser performance

were bed height and level of cane preparation.

10.

Initial tests were undertakeh to check reproducibility of

the measurements. Sufficient cane was sampled from a single

consignment of cane to allow a test to be duplicated. For the

replicate test, the column was filled to the same level, keeping

the method of packing as consistent as possible. Table 1 shows

good agreement of packing density and percolation rate for the five

duplicate tests performed.

Insert Table 1 .

These tests do not include the effects of any error in the

analysis of the cane as only one sample of cane was analysed for

each set of duplicate tests.

It was not anticipated that wall effects due to the size of

the column would be significant, since the column diameter/

particle size ratio was well over the minimum value of 12 quoted

by Gunn . To check whether there was an effect on either packing

density or percolation rate, a column 0,61 m in diameter was con

structed for comparative tests using duplicate samples of the same

prepared cane. No evidence of any wall effect could be established

A number of other effects were checked qualitatively to deter

mine whether they have a significant effect on percolation rate.

Qualitative investigations.

Packing method

Two variations in the method of packing the pilot plant column

were compared with the normal method in duplicate tests.

Compaction of the cane bed using high initial flows (approxi

mately 3 to 4 times the percolation rate achieved after compaction

of the bed) had no noticeable effect on the percolation rate

achieved after compaction.

11.

Initial tests on filling the column with water from the

bottom before starting percolation (to remove all air from the

bed) indicated that this resulted in an increased percolation

rate after compaction of the bed. This was however not confirmed

by the results of subsequent tests.

Surface tension of juice

Teepol, a detergent, and Sucrapol, a low foaming surface

tension reducer, were tested for their ability to increase perco

lation rate by lowering surface tension of the juice (thus reducing

the quantity of stagnant liquid and air in the bed).

Neither of these products had any effect on percolation rate

when added to the percolating juice after the bed had compacted and

the percolation rate stabilised. Sucrapol was tested in the re

commended concentration range of 9 to 20 p.p.m. whilst Teepol was

tested to the level where foaming became excessive.

Agitation of bed

In an attempt to reduce the bed density at the bottom of the

bed and thereby increase percolation rate, air, water and steam

were injected into the bottom of the bed through the perforated

plate. No effect on percolation rate was measured.

Bagacillo addition to surface of bed

Bagacillo was added to the surface of the cane bed in the

pilot plant diffuser to simulate conditions in the full scale

diffuser.

In a moving bed diffuser pith particles washed out of the

bottom of the cane bed are re-deposited on the surface of the bed.

From measurements of pith content in stage juice in the Amatikulu

diffuser, the quantity of pith deposited on the surface of the

bed (excluding that added with press water) was estimated to be

1,8 kg/m2.

12.

The addition of bagacillo to the pilot plant equivalent to 2,9

kg/m2 caused a reduction in percblation rate of 15%.

pH of juice

The effect of pH on percolation rate in the pilot plant was

investigated both by adding lime after the bed had compacted and

the percolation rate stabilised to check for any decrease in per

colation rate, and by doing duplicate tests at different pH's.

Table 2 gives the results of two tests where lime was added

after the percolation rate had stabilised.

Insert Table 2.

In duplicate tests performed on sub-samples of the same cane

sample, lime was added to the water before starting percolation.

The following results were obtained :

Insert Table 3.

In the tests were lime was added to the surface of the bed

after the percolation rate had stabilised, some compaction of the

bed occurred. It appeared, however, that only the surface

of the bed might be compacting, resulting in a small region of

high density on the surface of the bed. This would cause the re

duction in percolation rate without a significant drop in the over

all bed density.

When lime was used in the duplicate tests, (Table 3) it was

added to the water, before starting percolation. The cane bed

thus compacted evenly without the surface of the bed experiencing

high lime concentrations, as in the other tests. In this test

where lime was used, the bed density was only 2% higher than in

the duplicate without lime, whilst as can be seen from Table 3,

the percolation rate was 33% lower. The effect of lime CpH)

on percolation rate cannot thus be explained by its effect on fibre

packing density alone.

13.

Measurement of cane quality and Cane preparation

To develop numerical correlations for percolation rate it was

necessary to quantify both cane quality and cane preparation.

1) Cane quality

Cane quality, particularly in terms of its effect on percola

tion rate in a diffuser, is difficult to quantify. Normally

cane quality is measured in terms of tops and trash but since

burnt cane of a single variety was used in the tests, tops

and trash were found to be very low and did not vary much

between samples. The percentage of fibre in the cane was found

to correlate well with densities obtained in the cane bed.

Fibre % cane has thus been selected as an arbitrary measure of

cane quality for these tests.

2) Cane preparation

Although the level of preparation of cane is usually measured in

terms of P.I., this applies to the extractability of the cane

and not to its percolation behaviour. Particle size distri

bution, measured by sieve analysis, is a more direct measure

of cane preparation and is also more directly applicable to

the percolation behaviour of the cane.

Since the results of the sieving analysis consist of five points

on a cumulative size distribution curve, they cannot be used

directly for correlating with percolation rate. By numerically

fitting a smooth curve to this cumulative size distribution,

the moments of the distribution (mean, variance and skewness)

and the specific surface of the shredded cane were calculated

(See Appendix 3 ) .

14.

Correlation of percolation testing results

As previously described the equation

has been used as a basis for correlating the results o± the perco

lation tests.

15.

which is significant at the 0.1 % level. This is shown as the

solid line in Fig. 4.

To complete the correlation of percolation rate with the

factors varied in the tests, the dependence of bulk fibre

density (D) on fibre in cane, bed height and level of prepara

tion must be obtained.

Unfortunately the tests for which particle size analyses

are available, only have a small variation in bed height and the

dependence of density on bed height must be correlated separately

by including other results over a wider range of bed height.

From a linear regression, the correlation

was found to be significant at the 0.1 % level, with a = 0,58 and

b = 4,3, despite the fact that these tests included a wide range of

levels of cane preparation.

In linear correlations of bed density with measures of the

particle size distributions, the best correlations were obtained

with the inverse of the mean particle size.

If it is assumed that bed density is inversely related to

mean particle size, with a finite maximum density for infinitely

16.

small particle sizes, the following relationship for density can

be expected :

where M is the mean particle size (mm).

Using the previously determined values of a and b in a

non-linear regression on the results for which particle size

analyses are available yields

c = 26,5

g = 21,2

with a correlation coefficient of 0,998.

Tracer testing in the pilot plant diffuser

To analyse these results, a smooth curve was drawn through the

conductivity trace on the recorder chart and data points read off

this curve, relative to the base-line conductivity.

These data points were used for performing computerised non

linear regressions to fit the flow models to the experimental

results.

Fig. 5 shows the fit of the two flow models viz. axially dispersed

plug flow and plug flow with exchange with stagnant regions,to a

set of experimental data.

Insert Fig. 5

Since a better fit was obtained with the axially dispersed plug

flow model, this model was used in preference to the plug flow

with exchange model.

The results of tracer tests (determined by fitting the model

to the experimental data), are given in Table 4.

Insert Table 4.

17.

The percolation velocities determined from the tracer tests are

larger than the percolation rates (superficial velocities) due to

the reduction in flow area in the bed. The ratio of percolation

rate (U) to percolation velocity (V) is thus a measure of the voi-

dage of the bed i.e. the volume fraction of the bed available to

the flowing liquid.

No correlation is evident between this estimate of bed voidage

and either bed density or mean particle size. However the average

value of the voidage of 0,70 is of interest because the positioning

of sprays in a moving bed type diffuser depends on the percolation

velocity and not the percolation rate.

The axial dispersion coefficient (E7) is a measure of the

amount of mixing in the bed in the direction of fluid flow. Fig. 6

shows how the dispersion coefficient increases with increasing per

colation velocity.

Insert Fig. 6

For comparison with other work on dispersion in packed beds,

the results must be compared in terms of Pcclet and Reynolds numbers

dispersion in a cane bed is far greater than that normally found in

a granular bed.

Liquid holdup in bed

The total liquid holdup in the bed during percolation expressed

as mass of liquid per unit mass of fibre was found to decrease

with increasing bed density (Fig. 7). This is probably due to

the decreased void spaces at higher bed densities although there

Insert Fig. 7

18.

might be some effect resulting from the lower percolation rates

at higher bed densities.

FULL SCALE DIFFUSER TRACER TESTS

A typical conductivity recording during a tracer test on the

full scale diffuser at Amatikulu is shown in Fig. 8.

Insert Fig.8

To analyse these results, smooth curves were drawn through

the conductivity trace on the recorder chart, and data points read

off this curve relative to the base line conductivity.

The equations previously developed from the model of plug flow

with dispersion (see Appendix 2) were fitted to these data points

using a computerised non-linear regression technique.

The fit of the model to the experimental results is shown in

Fig. 9.

Insert Fig. 9

The results obtained by fitting the model to the data from

tracer tests on the Amatikulu diffuser are shown in Tabic 5. The

tests were all performed on stages 5, 6 and 7 of the diffuser which

contains 13 stages.

Insert Table 5.

Although some of these tracer tests were undertaken when flood

ing was not occurring to any great extent, the percolation rates

are still considerably lower than those obtained in the pilot plant,

and lower than the value of 0,26 m/min reported by Payne7 in Hawaii.

The reason for this large discrepancy has not yet been adequate

ly explained. However the effects of bagacillo addition and lime

addition are large enough to explain these differences.

19.

The axial dispersion coefficients calculated for these tests are

significantly higher than those measured in the pilot plant diffuser.

The results show an increase in dispersion with increasing percola

tion velocity which is greater than that found with the pilot plant

results as shown in Fig. 10 below. This can be explained by a more

tortuous bed or a bed which is not uniform across its whole width.

Since bed densities of comparable value have been obtained in the

pilot plant and the diffuser on the same cane, the former is unlikely.

Because of the great width of the Amatikulu diffuser (11 m) , it is

difficult to ensure an even bed across this length, and this could

well account for the increased spread in residence times which the

higher dispersion coefficient implies.

Insert Fig. 10

The deviation from stagewise percolation is in all but one of

the tests, in the form of bypassing rather than recycle. This

indicates that the diffusersprays have been advanced too far to

wards the head end of the diffuser in an attempt to reduce flooding.

Tracer tests were also performed on the Tongaat cane diffuser

for comparison purposes, on stages 4, 5 and 6.

Since in the Tongaat diffuser, juice is added to the top of

the bed from weirs (and not from sprays which effectively cover the

whole surface of the bed) there must be some horizontal percolation

of juice to compensate for the overloading of the bed directly below

the weirs. It is most likely that the direction of the horizontal

percolation of the juice from the point where the juice is added

will be towards the feed end of the diffuser since the bed on the

discharge side of this point has just passed under the weir and

should thus be saturated with juice.

20.

The effect of this horizontal percolation was compensated for

by assuming, in the mathematical model used for analysing the re

sults, that the juice is added over 2,0 m of bed length from below

the weir towards the feed end of the diffuser. From visual ob

servations, the actual length of bed over which the juice is

added from the weir is only about 0,6 m.

The fits of the model to the experimental data, even with this

empirical correction, are not as good as those achieved when ana

lysing the Amatikulu data. The results are tabulated below :

Insert Table 6.

The percolation velocities measured are on average similar to

those measured at Amatikulu although significantly lower values have

been measured at Amatikulu (See Table 5 )

A single sample of shredded cane from Tongaat was analysed

for particle size by the same grading method used for all tests

at Amatikulu. The shredded cane was found to be coarser than any

used in the pilot plant percolation tests.

CONCLUSIONS

A correlation has been developed from the Kozcny Carman equa

tion for flow through packed beds, which correlates percolation

rates with degree of preparation and bulk fibre density. Low bulk

densities and coarse preparation lead to higher maximum percolation

rates. Preparation has a further effect in that it affects bulk

fibre density; a correlation for density in terms of preparation,

bed height and the fibre content of the cane has been produced.

Degree of cane preparation was varied by changing the shredder

speed and the clearance between hammers and anvils. It was not

possible to establish how the shredder should be operated to give

the optimum type of preparation for diffusion, to achieve both a

high degree of fineness and an open bed promoting high percolation

21.

rates. The variance and the skewness of the particle size dis

tribution did not appear to affdct bed density in a consistent way.

Other factors which were investigated included the effects of

method of packing the pilot plant column, surface tension and

agitation of the bed, none of which had a significant effect. The

quantity of bagacillo deposited on the top surface of a diffuser

should not have a substantial effect on the maximum percolation

rate, but the pH of the percolating liquid does have a very signi

ficant effect.

Use has been made of the dispersion model to analyse tracer

tests in the pilot plant column. This yields information on the

actual liquid velocities through the bed. Ratios of applied

liquid percolation rates to actual percolation velocities were

found to average 0,70. In addition dispersion coefficients are

obtained from the model. These indicate that the degree of dis

persion occurring is very much larger than that found in beds of

more conventional packing materials.

Tracer tests have been undertaken in full scale diffusers.

Of interest is the large degree of flow bypassing necessary to

reduce flow rates to a point where flooding is not a problem.

The dispersion model has been applied to these tests as well, and

appears to adequately describe the flow process. Percolation

velocities are on average significantly lower in the full scale

diffusers than those measured in the pilot plant. In addition a

greater degree of dispersion is present, which may be caused by

unevenness in the diffuser bed.

This investigation has provided significant insight into the

flow processes, and the experimental techniques have been used to

optimise diffuser spray positions.

24.

REFERENCES

1. Bird, R.B., W.E. Stewart and E.N. Lightfoot (1960). Transport

phenomena John Wiley New York. 780 p

2. Carslaw U.S. and J.C. Jager (1959). Conduction of heat in

solids Oxford University Press Oxford.

3. Gunn, D.J. (1968). Mixing in packed and fluidised beds Chem.

Engr (London) 219 : 153.

4. Lavin, R.E. (1964). M.S. Thesis Polytechnic Inst, of Brooklyn

5. Levenspiel, 0. (1962). Chemical Reaction Engineering John Wiley

New York. 501 p

6. Matthesius, G. (1977). An investigation of juice flow behaviour

in cane and bagasse diffusers. Proc. ISSCT 16 : 2187 - 2197

8. Rein, P.W. (1972). A study of the cane sugar diffusion process

PhD thesis. Univ. of Natal 330 p.

9. Rein, P.W. (1974). Prediction of the extraction performance of

a diffuscr usinga mathematical model. Proc. ISSCT 15 ;1523-

1537.

10. Van Swaaij, W.P.M., J.C. Charpentier and J. Villermaux (1969).

Residence time distribution in the liquid phase of 'trickle flow

in packed columns. Chem. Eng. Sci. 24 : 1083.

11. Villermaux, J. and W.P.M. Van Swaaij (1969). Modele represen-

tatif de la distribution des temps de sejour dans un reacteur

semi-infini a dispersion axiale avec zones stagnantes. Ap

plication a l'ecoulement ruisselant dans des colonnes d'anneaux

Raschig. Chem. Eng. Sci. 24 : 1097.

APPENDIX 1 . ., 25*

The Kozeny Carman equation

The Kozeny Carman equation is giVen by :

25.

The specific surface of the bed is related to the specific surface

of the particles by :

S b = SD

Thus for constant liquid density and viscosity,

26.

APPENDIX 2.

Solution of two dimensional dispersion

V is the fluid velocity in the Z direction.

The initial conditions for this equation are obtained by considering

the conditions during a tracer test.

At time t = 0, a pulse of tracer is added to the surface of the

bed over a length of bed, T, across the full width of the bed. The

co-ordinates are fixed relative to this point of tracer addition as

shown in Fig. 2.

Under these conditions, the solution to the differential

equation is

At any time t the position of the juice trays B, D and R re

lative to the cane bed are given by :

27.

Tray B

Tray D

Tray R

from

from

from

y = A - Vt

y = A + L - Vt

y = A + 2L - Vt

to

to

to

y = A + L - Vt

y = A + 2L - Vt

y = A + 3L - Vt

The concentration of tracer leaving a tray at time t may be

equated to the average concentration of tracer leaving the cane bed

directly above the tray

By fitting this equation to the results of the tracer tests, es

timates of the percolation velocity v and the dispersion coefficients

Ey , Ez can be obtained.

It can be seen from Fig. 2 that to achieve stagewise percola

tion without recycle or bypassing, the bed must have travelled a

distance A + 1,5L - 0, 5T. For 1001 recycle the bed will have

travelled A + 2,5L - 0,5T and for 100% bypassing the bed will have

travelled A + 0,5L - 0,5T.

.'. the percentage of recycle or bypassing is given by :

where +ve value indicates recycle

-ve value indicates bypassing.

APPENDIX 3

Particle size distribution calculations

The results of a grading test are available as the mass

fraction of particles less than five given sizes. It has been

found that these results can be fitted by a curve of the form :

y = exp (ax3 + bx2 + cx)-1

where y is the mass fraction of particles less than a given

size x.

The frequency distribution of particle sizes is thus given by

The moments of the distribution may be calculated from :

It can be shown that the specific surface of the shredded cane is

given by :

Since it is difficult to estimate the actual volume and surface

shape factors, a relative value for specific surface may be

obtained by arbitrarily setting

A computer program is available to evaluate the moments and the

specific surface when given the points on the cumulative size

distribution curve from the grading analysis.

28.

List of Tables

1. Reproducibility test results

2. Effect of lime addition on percolation rate

3. Effect of lime on percolation rate

4. Results of pilot plant tracer tests

5. Results of tracer tests on Amatikulu diffuser.

6. Results of tracer tests on Tongaat diffuser

29

Table 1 : Reproducibility test results

Bed height (m)

A

0,96

0,81

0,84

1 ,76

1 ,54

B

0,85

0,75

0,75

1 ,71

1 ,54

Bed density (kg fibre/m3 )

A

63,4

69,8

75,7

75,4

62,3

B

65,6

72,9

75,1

75,6

61,6

Percolation rate (m/min)

A

0,23

0,25

0,18

0,18

0,33

B

0,24

0,24

0,18

0,18

0,33

30.

Table 2 : Effect of lime addition on percolation rate

Initial pH

5,3

5,1

pH after lime

addition

7,8

8,6

Percolation rate before lime (m/min)

0,335

0,248

Percolation rate after lime (m/min)

0,147

0,084

Table 3 : Effect of lime on percolation rate

Without lime addition

With lime addition

pH

5,2

7,6

Percolation rate (m/min)

0,200

0,134

31 .

Table 4 : Results of pilot plant tracer tests

Bed height

(m)

1 ,39 1,50 1,70 1 ,58 1,53 1 ,52 1,52 1,45 1,36 1,47 1,13

Mean 1,47

Mean particle size

(mm)

6,44

-5,17

-4,22 5,02 4,79 6,42

--

5,45

5,36

Variance of particle size

(mm )

62,7

-63,3

-45,6 62,6 49,8 6 £,3

-_

55,4

58,4

Fibre in cane

(%)

16,43 14,20 15,86 12,85 14,70 12,90 15,14 10,26 14,76 17,39 14,62

14,5

Packing density

(kg fib/ m3 )

83,1 79,0 82,7 68,0 78,4 72,5 80,7 49,9 63,9 87,6 75,8

74,7

Percolation rate

(m/min)

0,23 0,17 0,15 0,21 0,21 0,24 0,28 0,32 0,21 0,19 0,25

0,22

Percolation velocity

(m/min)

0,31 0,24 0,21 0,29 0,30 0,38 0,40 0,45 0,31 0,29 0,34

0,32

Dispersion coefficient

(m2 /min)

0,037 0,018 0,015 0,024 0,031 0,037 0,045 0,041 0,022 0,031 0,021

0,029

Ratio of percolation velocity to percolation rate

0,74 0,71 0,71 0,72 0,70 0,63 0,70 0,71 0,68 0,66 0,74

0,70

33.

Table 5 : Results of tracer tests on Amatikulu diffuser

Bed height

Cm)

1 ,7 1 ,7 1,7

1.7 1 ,6

1 ,60 1,60 1 ,70 1 ,55 1,70 1 ,60

Mean 1,65

Bed speed

(m/min)

0,70 0,63 0,75 0,62 0,80

0,65 0,63 0,66 0,66 0,70 0,70

Cane throughput

(tons/hr)

-

350 364 373 400 366 468

Percolation Velocity (m/min)

0,17 0,14 0,20 0,28 0,21

0,14 0,17 0,23 0,14 0,20 0,18

0,19

Recycle or

bypass (%) *

-20 3

-33 -100 -48

- 5 -52 -85 -17 -52 -42

Bed density

(kg/fib/

m 3)

-

72,9 78,2 72,1 84,7 66,6 89,9

77,4

Percolation rate

(m/min) ^

0,12 0,10 0,14 0,20 0,15

0,10 0,12 0,16 0,10 0,14 0,13

0,13

^ Assuming 70% voidage

* -ve value indicates bypassing +ve value indicates recycling

34.

Table 6 : Results of tracer tests on Tongaat diffuser

Bed height

(m)

1 ,25

1 ,25

1 ,20

1 ,25

Bed speed (m/min)

1 ,00

1 ,01

1 ,00

1 ,03

Percolation velocity (m/min)

0,22

0,22

0,18

0,18

Recycle * or

bypassing

-45 %

-43 %

-12 90

- 1 %

* -ve values indicate bypassing

List of Figures

Fig. 1. Mechanism of flooding in a cane diffuser.

Fig. 2. Schematic diagram of a moving bed cane diffuser.

Fig. 3. Pilot plant diffuser.

Fig. 4. Dependence of percolation rate on specific surface and bulk density.

Fig. 5. Fit of models to experimental results of a tracer test on the pilot plant diffuser. Bed height 1,46 m, percolation rate 0,206 m/min.

Fig. 6. Axial dispersion coefficients measured in a pilot plant cane diffuser.

Fig. 7. The effect of bulk fibre density on total liquid holdup in a pilot plant cane diffuser. Solid line represents maximum liquid holdup based on a fibre density of 1520 kg/m3

Fig. 8. Typical conductivity record for a tracer test on the Amatikulu diffuser.

Fig. 9. Fit of model to results of a tracer test on the Amatikulu diffuser. Bed height 1,55 m. Bed speed 0,66 m/min.

Fig. 10. Axial dispersion coefficients measured in full scale diffu-sers.

Figure 2 Page 36.

FIGURE 3 Page 37.

Figure 6.

Figure 7

Page 42.

Figure 9. Page 43 .