Still about the operation of one unit of mill, let’s back to equation (1):
Or
:
Wim = Wej + W b Wej = Wim - W b
We can also write: Wej
Because
:
and
:
then
:
Also because: and
:
then
:
or
:
W b Wim
= Wim (1 -
)
Wim = dim x Vim W b = d b x V b db.Vb Wej = dim.Vim (1 - -------) ...........………………………............ (4) dim.Vim
Wej = dej x Vej Vej = Vim - V b ------- à (no-void volumes) Wej = dej (Vim - V b ) Vb Wej = dej.Vim (1 - ------) ……………………........…..................... ……………………........…..................... (5) Vim
Further, from equation (4) and (5) we obtain: d b.V b V b dim.Vim (1 - ------) = d ej.Vim (1 - ----) dim.Vim Vim d b.V b dej.V b dim - ---- = d ej - ---- Vim Vim dim - dej
therefore
:
Bagasse Volume
V b = ---- (d b - dej) Vim
db - dej Vim = --- V b ..............………….......... ..............…………........................... ................. (6) dim - dej
V-1
Mill Material Balance
With the same method, we observe equation (2):
or
:
Wim = Wij + W f Wij = Wim - Wf
We can also write: Wij Because
:
and
:
= Wim (1 -
Wf Wim
)
Wim = dim x Vim Wf = df x Vf
and
:
df .Vf Wij = dim.Vim (1 - ---------) .............……………………............ (7) dim.Vim Wij = dij x Vij Vij = Vim - Vf ----à (no-void volumes)
Further, from equation (7) and (8), we find: df .Vf Vf dim.Vim (1 - ------) = d ij.Vim (1 - ----) dim.Vim Vim df .Vf dij.Vf d im - ----- = d ij - ---- Vim Vim And so
:
and
:
Vf dim - dij = ----- (df - dij) Vim df - dij Vim = ----- Vf ..............…………......…........ ..............…………......….............. ...... (9) dim – dij
Then both equation (6) and (9) combined, we find: d b - dej df - dij ---- ---- V b = --- V f dim - dej dim - dij Now observe each value of the densities in this equation, mainly the juice density at the input portion (dij) and the density of extracted juice (d ej).
Bagasse Volume
V-2
Mill Material Balance
5)
When we look the Brix table , e.g. for cane juice of 15,9°Brix, the density is 1,06077 kg/dm
3
compare to juice of mill #1, say = 17,4°Brix, the density is 1,06721 kg/dm 3, which means there is only a different of 0,60%. This value is very small if compared to the different in degrees of Brix, which is about 8,62% (the condition was made by the calculation for mill mass balance, where assumption is made for the Brix degree of juice in the incoming material have the same value of Brix degree with the juice extracted by the respective mill). Based upon the relatively small different of the densities, the writer has the reason why assumption is made for the above equation, that the density of juice in the incoming material (dij) is equals to the density of juice extracted by the respective mill (d ej). Thus
