Mill Material Balance

Absorption Ability Factor and Bagasse Weight VI-1

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 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 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 without juice in it (fully 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 rf = ----------- ............................................ (11) Vef

Where : Vbf = no-void volume of bagasse exhausted by the feed opening

and : Vef = escribed volume of the feed opening

The absorption ability factor of the delivery opening: Vb r = --------- ................................................... (12) Ved

Where: Vb = no-void volume of bagasse exhausted by the delivery opening

and : Ved = escribed volume 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

Mill Material Balance

Absorption Ability Factor and Bagasse Weight VI-2

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 : rf < 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:

rf @ 1.1

Further to equation (12): Vb r = ------- Ved

Or : Vb = r.Ved ................................................... (13)

If equation (10) and equation (13) combined, then well find:

df - dej -------------- Vf @ r.Ved db - dej df - dej hence : Ved @@ ------------------ Vf .......................... (14) r.db - r.dej

The no-void density of fiber (df) is a little less than the density of cellulose.

According to E. Hugot1), the density of cellulose is 1.55 kg/dm3 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:

1.52 x 152 df = 100 + 0.52 H

... (15)

Whereas : df = no-void density of fiber in kg/dm3

H = ambient humidity in %

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 carried out weekly during the crushing season.

1) Handbook of Cane Sugar Engineering, 1972, page 134

Mill Material Balance

Absorption Ability Factor and Bagasse Weight VI-3

Based on the above description, then the weight of bagasse exhausted by a unit of mill is:

Wb = df.Ved ............................................. (16)

Also : Wb = db.Vb then : db.Vb = df.Ved

We know, that : Vb = r.Ved so : r.db.Ved = df.Ved hence : r.db = df

Substitution of r.db = df to equation (14), well have:

df - dej Ved @@ --------------- Vf ..................................... (14a) 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: (df - dej) df.Vf Wb @ ---------------------- df - r.dej

Because df.Vf = Wf, then: (df - dej) Wb @@ --------------- Wf ..................... (17) df - r.dej Although the work openings known when they were set, but practically the actual average work

openings during operation were not known, especially the operation of mills provided with

hydraulic or spring.

Therefore, if the value of Ved in equation (14a) and the value of Wb 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: df.Ved - (df - dej) Vf r' @@ ------------------------------ ......................... (18) dej.Ved

Hence, the formula for the average bagasse weight of any mill unit (equation 17) becomes: (df - dej) Wb @@ --------------- 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.