CHAPT-09.PDF

Mill Material Balance

The Calculation of Mill Material Balance IX-1

CHAPTER IX

THE CALCULATION OF MILL MATERIAL BALANCE

9.1 Mill Performance Evaluation

As it was mentioned in Chapter I - Introduction, that mill material balance is used as reference

for the evaluation of mill performance. To be able to perform and analyze the mill performance,

some analytical works has to be done for the calculation inputs of mill material balance. Such

analyses for the juice extracted by each mill and the last mill bagasse, besides the other data for

the amount of cane crushed, the total crushing hours, the total mixed juice and the total

imbibition water consumed.

Also the technical specification of each roller in use, the outside and inside diameters, the

groove correction, the average actual roll rotation per hour, the dimension of work openings

when set and the ratio between the feed and delivery work openings as well.

Furthermore, the definitions and the units used have to be agreed consistently. The system used

here is kg/hour for the weight unit, dm3/hour for the volume unit and kg/dm3 for the density.

For an example of mill material balance calculation, the following operational data of a mill

tandem are used using all the formulas derived and described in previous Chapters (using the

average or totaled data obtained from the operation):

Sugar Factory EXAMPLE Mill train 2 CC + 5 MILLS Milling season / year 1977 Period of 15 days, number X (the end) I. MILL ROLLERS IN USE (dimension in mm)

M I L L I II III IV V Outside diameter (Do): top 1,052.0 1,073.0 1,051.0 1,050.0 1,064.0

feed 1,066.8 1,066.8 1,066.8 1,066.8 1,066.8 delivery 1,066.8 1,066.8 1,066.8 1,066.8 1,066.8

Groove correction (k): top 25.0 25.0 15.0 15.0 15.0 feed 25.0 25.0 15.0 15.0 15.0 delivery 25.0 25.0 15.0 15.0 15.0

Mean diameter (Dk): top 1,002.0 1,023.0 1,021.0 1,020.0 1,034.0 feed 1,016.8 1,016.8 1,036.8 1,036.8 1,036.8 delivery 1,016.8 1,016.8 1,036.8 1,036.8 1,036.8

Length of shell L 2,133 2,133 2,133 2,133 2,133 Actual roller rotation/hour rph 268 244 216 191 193 Delivery work opening hd 41.23 36.33 27.79 26.14 24.62 Feed to delivery ratio i 2.20 2.00 2.00 2.00 2.00 Hydraulic pressure ph 180 182 182 206 210 Hydraulic ram dia. d 330 330 330 330 330 Mechanical efficiency h 86 86 86 86 86 Mill roller shaft dia. dp 420 420 420 420 420 Mill roller shell length l 4,220 4,220 4,220 4,220 4,220 Top angle a 78 78 78 78 78 Top roller lift t 6.0 6.0 6.0 6.0 6.0



II. CRUSHING INFORMATION Cane: crushed, total Q 4,351.0 TCD

crushing hours jg 24.00 hours pol pt 10.32 %

brix bt 13.41 %

fiber f 16.07 % cane Mixed juice: gross Wmj 3,718.7 Tons

brix bmj 14.69 % purity HK 77.62 %

correction kmj 1.003076

Imbibition water, total: Wi 843.1 Tons Applied on: bagasse 1 = 0 %

bagasse 2 = 0 %

bagasse 3 = 0 %

bagasse 4 = 100 %

Fiber density, average = 1.60 kg/dm3

III. AVERAGE ANALYSES OF JUICES:

M I L L I II III IV V

Juice: brix bn 17,46 12,48 8,90 5,75 2,94

pol pn 14,05 9,29 6,45 4,06 2,00

First calculate the value of items based on the main formula of mill material balance:

Cane + imbibition water = mixed juice + bagasse

Whereas:

Cane, the total cane crushed, constitutes the crushing capacity; the value known from the

result of weighing, in kg/hour.

Imbibition water, the total water used to dilute sugar in the milling process, the amount

known from the weighing or measurement, in kg/hour.

Mixed juice, the total juice extracted by mill#1 and mill#2 and the amount known as the result

of weighing or measurement after deduction of the dirt content, in kg/hour.

Bagasse is the total residual material of cane after extraction of its juice, in kg/hour.

4,351 x 1000 Cane = 24

= 181,291 kg/hour

Imbibitions water = 35,128 kg/hour Mixed juice = 154,946 kg/hour Bagasse = 181,291 + 35,128 154,946 = 61,473 kg/hour

The next calculation follows the items grouped to each mill unit in the tandem.



The input portion:

Cane for mill#1 or bagasse for the following mills, each containing juice and fiber.

The output portion:

Consist of extracted juice and bagasse, where the bagasse itself containing juice and fiber.

The following form is use for the mill material balance:

Description

Mass kg/hr

%brix

Brix kg/hr

%pol

Pol kg/hr

Density kg/dm3

Volume dm3/hr

Miscellaneous

MILL#1 - Juice - Fiber Total input Extracted juice - Juice - Fiber Total bagasse

..............

..............

Dk = L = n = h = i =

Vedo= Ved =

r = r = m = h' = K =

HKej = kB =


..............

..............

Dk = L = n = h = i =

Vedo= Ved =

r = r = m = h' = K =

HKej = kB =


..............

..............

Dk = L = n = h = i =

Vedo= Ved =

r = r = m = h' = K =

HKej = kB =


..............

..............

Dk = L = n = h = i =

Vedo= Ved =

r = r = m = h' = K =

HKej = kB =

MILL#5 .......... etc. ......

The results of calculation is directly filled up to the above form.



The description and meaning of the abbreviations:

Dk = mean diameter of the top roller, in dm

L = roller / shell length, in dm

n = actual rotation of the top roller per hour during the milling of cane

h = delivery work opening, actually when set

i = ratio of feed and delivery work openings, actually when set

Vedo = the escribed volume of the delivery work opening in dm3/hour, the volume escribed by

the actual height (h) of the delivery opening based on the following formula:

Vedo = p . Dk . L . n . h Ved = the no-void volume of bagasse passing through the delivery opening, in dm3/hour (see

formula 16). Wb Ved = df

r = absorption ability factor (see formula 13). Vb r = Ved

r' = normal absorption ability factor (see formula 18). df . Ved - (df - dej) Vf r' @

dej . Ved m = coefficient of friction for bagasse and the mill roller (cast iron/steel, see also formula 22)

p . Dk . n m = 0,43 - 60 x 1524

h' = the average actual work opening Ved h' =

p . Dk . L . n K = compression ratio / value

Vim K = Ved

Where Vim = no-void volume of incoming material.

HKej = purity of the extracted juice %pol of extracted juice x 100 HKej =

%brix of extracted juice kB = Brix distribution coefficient

Bej . Wim kB = Bim . Wej

Where: Bej = weight of brix in extracted juice

Bim = weight of brix in juice of the input portion

Wim = weight of juice in the input portion

Wej = weight of the extracted juice



Beginning from: MILL #1 The input portion: - Juice = 181,291 29,133 = 152,158 kg/hour - Fiber = 0.1607 x 181,291 = 29,133 kg/hour ------------- Total input (cane) = 181,291 kg/hour

29,133 - The no-void volume of fiber = 1.60 = 18,208 dm3/hour

The weight and no-void volume of fiber calculated above each has its same value for the other

mill unit respectively (the value of Wf and Vf).

Further we calculate:

The weight of Brix in cane = 0.1341 x 181,291 = 24,311 kg/hour The weight of Pol in cane = 0.1032 x 181,291 = 18,709 kg/hour

24,311 x 100 - %brix of juice in cane = 152,158

= 15.98

- The density value obtained from the table x 1.01 = 1.07138 kg/dm3

152,158 - Volume of juice in cane = 1.07138

= 142,020 dm3/hour

- Total volume = 142,020 + 18,208 = 160,228 dm3/hour

18,709 x 100 - %pol juice in cane = 152,158

= 12.30

181,291 - The cane density = 160,228

= 1.13146 kg/dm3

The output portion consist of: a. Extracted Juice:

14.69 - 12.48 - the amount = 154,946 x 17.46 12.48

= 68,761 kg/hour

- %brix known from the analysis = 17.46 - The density value obtained from the table x 1.01 = 1.07788 kg/dm3



68,761 - The volume = 1.07788

= 63,792 dm3/hour

0.1746 x 68,761 - Weight of Brix =

1.003076 = 11,969 kg/hour

0.1405 x 68,761 - Weight of Pol =

1.003076 = 9,631 kg/hour

b. Bagasse: - Juice content = 152,158 68,761 = 83,397 kg/hour - Juice volume = 142,020 63,792 = 78,228 dm3/hour

83,397 - Juice density = 78,228

= 1.06608 kg/dm3

- Bagasse weight = 83,397 + 29,133 = 112,530 kg/hour - Bagasse no-void volume = 78,228 + 18,208 = 96,436 dm3/hour

112,530 - Bagasse density = 96,436

= 1.16689 kg/dm3

- Brix in bagasse juice = 24,311 11,969 = 12,342 kg/hour

12,342 x 100 - %brix of bagasse juice = 83,397

= 14.80

- Pol in bagasse juice = 18,709 9,631 = 9,078 kg/hour

9,078 x 100 - %pol of bagasse juice = 83,397

= 10.89

- Brix in bagasse = Brix in bagasse juice = 12,342 kg/hour

12,342 x 100 - %brix of bagasse = 112,530

= 10.97

- Pol in bagasse = Pol in bagasse juice = 9,078 kg/hour

9,078 x 100 - %pol of bagasse = 112,530

= 8.07

Further well have:

Vedo = 3.14 x 10.02 x 21.33 x 268 x 0.4123 = 74,154 dm3/hour

- No-void volume of bagasse passing through the delivery opening: 112,530 Ved =

1.60 = 70,331 dm3/hour



- The absorption ability factor:

1.60 r = 1.16689

= 1.3712

- The normal absorption ability factor:

1.60 x 70,331 - (1.60 1.07788) x 18,208 r = 1.07788 x 70,331 = 1.3590

- Calculated coefficient of friction: p x 10.02 x 268 m = 0.43 - 60 x 1,524 =

0.3378

- Average of actual delivery work opening:

70,331 h' = 3.14 x 10.02 x 21.33 x 268

= 0.3910 dm

- The compression ratio:

160,228 K = 70,331

= 2.28

- The extracted juice purity:

14.05 x 100 HKej = 17.46

= 80.47 %

- The Brix distribution coefficient:

11,969 x 152,158 kB = 24,311 x 68,761

= 1.089

MILL #2 When the calculation in mill#1 begins with the input portion, then it would be not for mill#2

and the other mills. Here, the calculation starts from the back side (the output portion), first

with:

a. Bagasse: - its weight,

1.60 (1.60 1.05646) x 18,208 Wb2 = 1.60 1.3590 x log 9.81 x 1.05646 =

89,846 kg/hour

- its juice = 89,846 29,133 = 60,713 kg/hour b. The extracted juice: - its weight = 154,946 - 68,761 = 86,185 kg/hour

0.1248 x 86,185 - the Brix = 1.003076

= 10,723 kg/hour

- the density obtained from the table x 1.01 = 1.05646 kg/dm3

86,185 - its volume = 1.05646

= 81,579 dm3/hour



0.0929 x 86,185 - the Pol =

1.003076 = 7,982 kg/hour

c. The input portion: - the juice weight = 60,713 + 86,185 = 146,898 kg/hour - total input = 146,898 + 29,133 = 176,031 kg/hour The juice in the input portion of mill#2 consisting of bagasse juice of mill#1 plus the juice

extracted by mill#3 (the imbibition juice), and so:

- The juice extracted by mill#3 = 146,898 83,397 = 63,501 kg/hour - %brix obtained from the analysis = 8.90 - the density obtained from the table x 1.01 = 1.04191 kg/dm3

63,501 - the volume = 1.04191

= 60,946 dm3/hour

- the Brix = 0.089 x 63,501 = 5,652 kg/hour - the Pol = 0.0645 x 63,501 = 4,096 kg/hour Lets back to juice in the input portion of mill#2: - its volume = 78,228 + 60,946 = 139,174 dm3/hour - the Brix = 12,342 + 5,652 = 17,994 kg/hour

17,994 x 100 - its %brix = 146,898

= 12.25

- the Pol = 9,078 + 4,096 = 13,174 kg/hour

13,174 x 100 - its %pol = 146,898

= 8.97

146,898 - the density = 139,174

= 1.05550 kg/dm3

And back to the total input: - its volume = 139,174 + 18,208 = 157,382 dm3/hour

17,994 x 100 - its %brix = 176,031

= 10.22

13,174 x 100 - its %pol =

176,031 = 7.48



176,031 - its density = 157,382

= 1.11850 kg/dm3

At the bagasse portion: - the volume of bagasse juice = 139,174 81,579 = 57,595 dm3/hour

60,713 - density of bagasse juice = 57,595

= 1.05414 kg/dm3

- the Brix in bagasse juice = 17,994 10,723 = 7,271 kg/hour

7,271 x 100 - %brix of bagasse juice = 60,713

= 11.98

- the Pol of bagasse juice = 13,174 7,982 = 5,192 kg/hour

5,192 x 100 - %pol of bagasse juice = 60,713

= 8.55

- the volume of bagasse = 57,595 + 18,208 = 75,803 dm3/hour - the Brix of bagasse = the Brix of bagasse juice = 7,271 kg/hour

7,271 x 100 - %brix of bagasse = 89,846

= 8.09

- the Pol of bagasse = the Pol of bagasse juice = 5,192 kg/hour

5,192 x 100 - %pol of bagasse = 89,846

= 5.78

89,846 - the density of bagasse = 75,803

= 1.18526 kg/dm3

Further well have: - the escribed volume of the delivery work opening:

Vedo = 3.14 x 10.23 x 21.33 x 244 x 0.3633 = 60,737 dm3/hour - the volume of bagasse passing through the delivery opening:

89,846 Ved = 1.60

= 56,154 dm3/hour

- The absorption ability factor:

75,803 r = 56,154

= 1.3499

- The normal absorption ability factor:

r' = 1.3590 x log 9.81 = 1.3477



- The calculated coefficient of friction: p x 10.23 x244

m = 0.43 - 60 x 1.524 = 0.3443

- The average actual delivery work opening:

56,154 h' = 3.14 x 10.23 x 21.33 x 244

= 0.3359 dm

- The compression ratio:

157,382 K = 56,154

= 2.80

- The extracted juice purity:

9.29 x 100 HKej = 12.48

= 74.44 %

- The Brix distribution coefficient:

10,723 x 146,898 kB = 17,994 x 86,185

= 1.016

The sequence and method of calculation for the ensuing mills are the same as for mill#2. But not

for the last mill, where the weight of bagasse should not be calculated with the same formula as

for the amount of bagasse in mill#2 and the ensuing mills, because the weight of last mill

bagasse already known at the beginning of the calculation.

Further we have to pay attention for the last mill, that the total juice in the input portion is the

sum of bagasse juice contained in the ultimate mill plus the amount of imbibition water applied

to the corresponding bagasse.

If imbibition water applied not only on bagasse before the last mill, then the total juice incoming

to the respective mill also the sum of juice containing the bagasse from the ultimate mill and the

imbibition water applied to the same bagasse.

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CHAPT-09.PDF