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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 .