Mill Material Balance
CHAPTER I X
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, dm 3/hour for the volume unit and kg/dm 3 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 Mill train Milling season / year Period of 15 days, number
EXAMPLE 2 CC + 5 MILLS 1977 X (the end)
I. MILL ROLLERS IN USE (dimension in mm) mm) MILL I Outside diameter (Do): top 1,052.0 feed 1,066.8 delivery 1,066.8 Groove correction (k): top 25.0 feed 25.0 delivery 25.0 Mean diameter (Dk): top 1,002.0 feed 1,016.8 delivery 1,016.8 Length of shell L 2,133 Actual roller rotation/hour rph 268 Delivery work opening hd 41.23 Feed to delivery ratio i 2.20 Hydraulic pressure ph 180 Hydraulic ram dia. d 330 η Mechanical efficiency 86 Mill roller shaft dia. dp 420 Mill roller shell length l 4,220 Top angle 78 α Top roller lift t 6.0
The Calculation of Mill Material Balance
II 1,073.0 1,066.8 1,066.8 25.0 25.0 25.0 1,023.0 1,016.8 1,016.8 2,133 244 36.33 2.00 182 330 86 420 4,220 78 6.0
III 1,051.0 1,066.8 1,066.8 15.0 15.0 15.0 1,021.0 1,036.8 1,036.8 2,133 216 27.79 2.00 182 330 86 420 4,220 78 6. 0 6.0
IV 1,050.0 1,066.8 1,066.8 15.0 15.0 15.0 1,020.0 1,036.8 1,036.8 2,133 191 26.14 2.00 206 330 86 420 4,220 78 6.0
V 1,064.0 1,066.8 1,066.8 15.0 15.0 15.0 1,034.0 1,036.8 1,036.8 2,133 193 24.62 2.00 210 330 86 420 4,220 78 6.0
IX-1
Mill Material Balance
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
Imbibition water, total:
1.003076
Wi
Applied on:
843.1 Tons
bagasse 1 =
0 %
bagasse 2 =
0 %
bagasse 3 =
0 %
bagasse 4 =
100 % 1.60 kg/dm3
Fiber density, average = III. AVERAGE ANALYSES OF JUICES: MILL Juice:
I
II
III
IV
V
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 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.
Cane
=
4,351 x 1000
=
181,291 kg/hour
Imbibitions water
=
35,128 kg/hour
Mixed juice
=
154,946 kg/hour
=
61,473 kg/hour
24
Bagasse
=
181,291 + 35,128 – 154,946
The next calculation follows the items grouped to each mill unit in the tandem.
The Calculation of Mill Material Balance
IX-2
Mill Material Balance
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 MILL#1 - Juice - Fiber Total input Extracted juice - Juice - Fiber Total bagasse
Mass kg/hr
%brix
Brix kg/hr
%pol
……… ……… ……… ……… ……… ……… ………
……… ……… ……… ……… ……… ……… ………
……..… ……..… ……..… ……..… ……..… ……..… …….….
……… ……… ……… ……… ……… ……… ………
…..… …..… …..… …..… …..… …..… ……..
……… ……… ……… ……… ……… ……… ………
………… Dk = ………… L = ………… n = ………… h = ………… i = ………… Vedo= ………… Ved =
r = r’ = µ = h' = K = HKej = kB =
MILL#2 - Juice - Fiber Total input Extracted juice - Juice - Fiber Total bagasse
……… ……… ……… ……… ……… ……… ………
……… ……… ……… ……… ……… ……… ………
……..… ……..… ……..… ……..… ……..… ……..… …….….
……… ……… ……… ……… ……… ……… ………
…..… …..… …..… …..… …..… …..… ……..
……… ……… ……… ……… ……… ……… ………
………… Dk = ………… L = ………… n = ………… h = ………… i = ………… Vedo= ………… Ved =
r = r’ = µ = h' = K = HKej = kB =
MILL#3 - Juice - Fiber Total input Extracted juice - Juice - Fiber Total bagasse
……… ……… ……… ……… ……… ……… ………
……… ……… ……… ……… ……… ……… ………
……..… ……..… ……..… ……..… ……..… ……..… …….….
……… ……… ……… ……… ……… ……… ………
…..… …..… …..… …..… …..… …..… ……..
……… ……… ……… ……… ……… ……… ………
………… Dk = ………… L = ………… n = ………… h = ………… i = ………… Vedo= ………… Ved =
r = r’ = µ = h' = K = HKej = kB =
……… ……… ……… ……… ……… ……… ………
……… ……… ……… ……… ……… ……… ………
……..… ……..… ……..… ……..… ……..… ……..… …….….
……… ……… ……… ……… ……… ……… ………
…..… …..… …..… …..… …..… …..… ……..
……… ……… ……… ……… ……… ……… ………
………… Dk = ………… L = ………… n = ………… h = ………… i = ………… Vedo= ………… Ved =
r = r’ = µ = h' = K = HKej = kB =
MILL#4 - Juice - Fiber Total input Extracted juice - Juice - Fiber Total bagasse MILL#5 .......... etc. ......
Pol Density Volume kg/hr kg/dm3 dm3/hr
Miscellaneous
The results of calculation is directly filled up to the above form.
The Calculation of Mill Material Balance
IX-3
Mill Material Balance
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 3
Vedo = the escribed volume of the delivery deli very work opening in dm /hour, the volume escribed by the actual height (h) of the delivery opening based on the following formula: Vedo = π . Dk . L . n . h Ved = the no-void volume of bagasse passing through through the delivery opening, in dm 3/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
µ
= coefficient of friction for bagasse and the mill roller (cast iron/steel, see also formula 22) π . Dk . n µ = 0,43 60 x 1524
h'
= the average actual work opening Ved h' = π . 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
The Calculation of Mill Material Balance
IX-4
Mill Material Balance
Beginning from: MILL#1 The input portion: - Juice
=
181,291 – 29,133
=
- Fiber
=
0.1607 x 181,291
=
=
29,133 1.60
=
Total input (cane) - The no-void volume of fiber
152,158 kg/hour
29,133 kg/hour ------------= 181,291 kg/hour 18,208 dm 3/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 W f 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
- %brix of juice in cane
=
24,311 x 100 152,158
=
- The density value obtained from the table x 1.01
15.98
=
1.07138 kg/dm 3
- Volume of juice in cane
=
152,158 1.07138
=
142,020 dm 3/hour
- Total volume
=
142,020 + 18,208
=
160,228 dm 3/hour
- %pol juice in cane
=
18,709 x 100 152,158
=
- The cane density
=
181,291 160,228
=
1.13146 kg/dm 3
14.69 - 12.48 17.46 – 12.48
=
68,761 kg/hour
12.30
The output portion consist of: a. Extracted Juice: - the amount
= 154,946 x
- %brix known from the analysis
=
- The density value obtained from the table x 1.01
=
The Calculation of Mill Material Balance
17.46 1.07788 kg/dm 3
IX-5
Mill Material Balance
- The volume
=
68,761 1.07788
=
63,792 dm3/hour
- Weight of Brix
=
0.1746 x 68,761 1.003076
=
11,969 kg/hour
- Weight of Pol
=
0.1405 x 68,761 1.003076
=
9,631 kg/hour
- Juice content
=
152,158 – 68,761
=
83,397 kg/hour
- Juice volume
=
142,020 – 63,792
=
78,228 dm 3/hour
- Juice density
=
83,397 78,228
=
1.06608 kg/dm 3
- Bagasse weight - Bagasse no-void volume
= =
83,397 + 29,133 78,228 + 18,208
= =
112,530 kg/hour 96,436 dm 3/hour
- Bagasse density
=
112,530 96,436
=
1.16689 kg/dm 3
- Brix in bagasse juice
=
24,311 – 11,969
=
12,342 kg/hour
- %brix of bagasse juice
=
12,342 x 100 83,397
=
14.80
- Pol in bagasse juice
=
18,709 – 9,631
=
9,078 kg/hour
- %pol of bagasse juice
=
9,078 x 100 83,397
=
10.89
- Brix in bagasse
=
Brix in bagasse juice
=
- %brix of bagasse
=
12,342 x 100 112,530
=
10.97
- Pol in bagasse
=
Pol in bagasse juice
=
9,078 kg/hour
- %pol of bagasse
=
9,078 x 100 112,530
=
b. Bagasse:
12,342 kg/hour
8.07
Further we’ll have: Vedo = 3.14 x 10.02 x 21.33 x 268 x 0.4123 = - No-void volume of bagasse passing through the delivery opening: 112,530 Ved = 1.60
The Calculation of Mill Material Balance
=
74,154 dm 3/hour 3
70,331 dm /hour
IX-6
Mill Material Balance
- The absorption ability factor: 1.60 1.16689
r =
- The normal absorption ability factor: 1.60 x 70,331 - (1.60 – 1.07788) x 18,208 r’ = 1.07788 x 70,331
=
1.3712
=
1.3590
=
0.3378
0.3910 dm
- Calculated coefficient of friction: µ
π x
10.02 x 268 60 x 1,524
= 0.43 -
- Average of actual delivery work opening: h' =
70,331 3.14 x 10.02 x 21.33 x 268
=
K =
160,228 70,331
=
14.05 x 100 17.46
=
80.47 %
11,969 x 152,158 24,311 x 68,761
=
1.089
- The compression ratio: 2.28
- The extracted juice purity: HKej = - The Brix distribution coefficient: kB = 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, Wb2 =
1.60 (1.60 – 1.05646) x 18,208 1.60 – 1.3590 x log 9.81 x 1.05646
- its juice b. The extracted juice: - its weight - the Brix
The Calculation of Mill Material Balance
89,846 kg/hour
=
89,846 – 29,133
=
60,713 kg/hour
=
154,946 - 68,761
=
86,185 kg/hour
=
0.1248 x 86,185 1.003076
=
10,723 kg/hour
=
1.05646 kg/dm 3
- the density obtained from the table x 1.01 - its volume
=
=
86,185 1.05646
=
81,579 dm3/hour
IX-7
Mill Material Balance
=
0.0929 x 86,185 1.003076
=
7,982 kg/hour
- the juice weight
=
60,713 + 86,185
=
146,898 kg/hour
- total input
=
146,898 + 29,133
=
176,031 kg/hour
- the Pol c. The input input portion: portion:
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
=
- %brix obtained from the analysis
=
- the density obtained from the table x 1.01
=
63,501 kg/hour 8.90 1.04191 kg/dm 3
- the volume
=
63,501 1.04191
=
- the Brix
=
0.089 x 63,501
=
5,652
kg/hour
- the Pol
=
0.0645 x 63,501
=
4,096
kg/hour
60,946 dm3/hour
Lets back to juice in the input portion of mill #2: - its volume
=
78,228 + 60,946
=
139,174 dm 3/hour
- the Brix
=
12,342 + 5,652
=
17,994 kg/hour
- its %brix
=
17,994 x 100 146,898
=
- the Pol
=
9,078 + 4,096
=
- its %pol
=
13,174 x 100 146,898
=
- the density
=
146,898 139,174
=
1.05550 kg/dm3
- its volume
=
139,174 + 18,208
=
157,382 dm 3/hour
- its %brix
=
17,994 x 100 176,031
=
10.22
- its %pol
=
13,174 x 100 176,031
=
7.48
12.25 13,174 kg/hour 8.97
And back to the total input:
The Calculation of Mill Material Balance
IX-8
Mill Material Balance
=
176,031 157,382
=
- the volume of bagasse juice
=
139,174 – 81,579
=
- density of bagasse juice
=
60,713 57,595
=
1.05414 kg/dm3
- the Brix in bagasse juice
=
17,994 – 10,723
=
7,271 kg/hour
- %brix of bagasse juice
=
7,271 x 100 60,713
=
11.98
- the Pol of bagasse juice
=
13,174 – 7,982
=
5,192 kg/hour
- %pol of bagasse juice
=
5,192 x 100 60,713
=
8.55
- the volume of bagasse
=
57,595 + 18,208
=
75,803
- the Brix of bagasse
=
the Brix of bagasse juice
=
- %brix of bagasse
=
7,271 x 100 89,846
=
- the Pol of bagasse
=
the Pol of bagasse juice
=
- %pol of bagasse
=
5,192 x 100 89,846
=
- the density of bagasse
=
89,846 75,803
=
- its density
1.11850 kg/dm3
At the bagasse portion: 57,595
dm3/hour
dm3/hour
7,271 kg/hour 8.09 5,192 kg/hour 5.78 1.18526 kg/dm3
Further we’ll have: - the escribed volume of the delivery work opening: Vedo = 3.14 x 10.23 x 21.33 x 244 x 0.3633 = - the volume of bagasse passing through the delivery opening: 89,846 Ved = 1.60
3
60,737 dm /hour
3
=
56,154 dm /hour
75,803 56,154
=
1.3499
1.3590 x log 9.81
=
1.3477
- The absorption ability factor: r = - The normal absorption ability factor: r' =
The Calculation of Mill Material Balance
IX-9
Mill Material Balance
- The calculated coefficient of friction: µ
=
π x 10.23 x244
0.43 -
60 x 1.524
=
0.3443
h' =
56,154 3.14 x 10.23 x 21.33 x 244
=
0.3359 dm
K =
157,382 56,154
=
9.29 x 100 12.48
=
74.44 %
10,723 x 146,898 17,994 x 86,185
=
1.016
- The average actual delivery work opening:
- The compression ratio: 2.80
- The extracted juice purity: HKej = - The Brix distribution coefficient: kB =
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 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.
The Calculation of Mill Material Balance
IX-10
