Mill Material Balance
CHAPTER VI
ABSORPTION ABILITY FACTOR AND BAGASSE WEIGHT
Bagasse has the character of expanding when leaving the feed work opening, as well as when leaving the delivery work opening in a unit of mill. The expanding character of bagasse has influenced the amount of extracted juice, where part of the juice will be re-absorbed during it passing through each of the work opening. Then it is understood that the no-void volume of bagasse will be greater than the escribed volume of the work opening opening respectively. The ratio between the no-void volume of bagasse and the escribed volume of work opening in the same unit time is called the “ absorption ability factor”, which is symbolized with “ r”. The value is not the same with the value of so called the “ re-absorption re-absorption factor”. The “re-absorption factor ” is the ratio between the no-void volume of bagasse contained with juice and the no-void volume of bagasse bagasse without juice in it (fully dry). dry). The value of re-absorption factor, logically increasing from the ultimate up to the penultimate mills, because bagasse becomes respectively dryer from the first up to the last mill. In fact the milling of cane practiced, bagasse is not freely expanded when pressed by the rollers, the space still limited by the gap / work opening between the two rollers. And that is why the occasion would not the same with the term logically occurred to the re-absorption factor mentioned above. The value of the “absorption ability factor” is decreasing from the first to the ensuing mills. Because this is merely the ability to absorb the juice back, while the occurrence is still limited by the gap of work openings, and is not the absorption in a free space (atmospheric condition). We can write the absorption ability factor occurred in feed opening: Vbf ............……………………….…............................... ............. (11) rf = -------- ............……………………….….................. Vef
Where
:
and
:
V bf = no-void volume of bagasse bagasse exhausted exhausted by the feed opening Vef = escribed volume of the feed opening
The absorption ability factor of the delivery opening: Vb r = ----- ..........................…………………….......…............. ..........................…………………….......….................. ..... (12) Ved
Where: and :
V b = no-void volume of bagasse exhausted by the delivery opening Ved = escribed volume of of the delivery opening
The space behind the feed opening is still narrow, limited by the top roller surface and the trash plate. Hence the expansion made by the bagasse exhausted by the feed opening is not as free as when exhausted by the delivery opening. The narrow space behind the feed opening limits the
Absorption Ability Factor and Bagasse Weight
VI-1
Mill Material Balance
expansion of bagasse; the ability to absorb back the juice is smaller if compared to the ability of absorption occurred at the delivery opening. With another word, the absorption ability factor of the feed opening is smaller than the absorption ability factor occurred in the delivery opening. Thus
:
r f < r
The value of absorption ability factor for the feed opening is similarly the same for each mill in the tandem. The predicted average value is: r f
1.1
≅
Further to equation (12): r Or
:
V b = --- Ved
Vb = r.Ved ..............................……………………….........….......... ..............................……………………….........…............ .. (13)
If equation (10) and equation (13) combined, then we’ll find: d f - dej ---- V f ≅ r.Ved d b - dej hence :
Ved
df - dej ---- V f ......………………………….........…........... (14) r.db - r.dej
≅
The no-void density of fiber (d f ) is a little less than the density of cellulose. 1) According to E. Hugot , the density of cellulose is 1.55 kg/dm 3 and the density of cane fiber is a little less, that is around 1.52 kg/dm3. For the purpose of calculation the use of empirical formula hereunder, which is based upon the ambient humidity is relevant to define the no-void density of fiber, that is: df
=
1.52 x 152
………………………………………..….… (15)
100 + 0.52 H
Whereas
:
df
= no-void density of fiber in kg/dm
H
= ambient humidity in %
3
Based on the experience made by the writer, the maximum value of the no-void density of fiber or bagasse under pressure could be also calculated by the empirical formula mentioned above. But it is advisable a periodical compression test should be carried out during the season to determine the most appropriate value of the subject density. This compression test is best implemented by self-made hydraulic press, and is ca rried out weekly during the crushing season. 1)
Handbook of Cane Sugar Engineering, 1972, page 134
Absorption Ability Factor and Bagasse Weight
VI-2
Mill Material Balance
Based on the above description, then the weight of bagasse exhausted by a unit of mill is: Wb = df .Ved .………………………….......................... .………………………….....................................…....... ...........…....... (16)
Also
:
W b = d b .V b then : d b.V b = df .Ved We know, that : V b = r.Ved so
:
r.d b .Ved = df .Ved hence : r.d b = df Substitution of r.d b = df to equation (14), we’ll have: Ved
≅
df - dej .................……………………….................... ....... (14a) -- Vf .................………………………............. df - r.dej
Substitution of this equation to the equation (16), resulting a general formula to calculate the weight of bagasse exhausted by a unit of mill: W b
(df - dej) df .Vf ------- df - r.d ej
≅
Because df .Vf = = W f , then: (df - dej) --- W f …………………………………........…............. (17) df - r.dej Although the work openings known when they were set, but practically the actual average work Wb
≅
openings during operation were not known, especially the operation of mills provided with hydraulic or spring. Therefore, if the value of V ed in equation (14a) and the value of W b in equation (17), each constitute the average value for the unit, then the inherent value of absorption ability factor constitutes the normal value for the respective mill. And that means we could write the formula of the normal absorption ability factor for any mill in the tandem: r'
df .Ved - (df - dej) Vf ------ ..................………………………....... (18) dej.Ved
≅
Hence, the formula for the average bagasse weight of any mill unit (equation 17) becomes: Wb
(df - dej) ---- Wf .........……....………………………….............. (17a) df - r'.dej
≅
The normal value of absorption ability factor for any mill unit in the tandem (n) is a little smaller than the normal value occurred in the ultimate mill (n-1). It experienced approximately equals to the logarithmic of the mass value, or r'n = r'n-1 . log 9.81.
Absorption Ability Factor and Bagasse Weight
VI-3
