Aracruz Uses a Dynamic Simulator for Control System ... - Andritz

Drainage velocity ( w ) equation:
⎛ ρ ⎞
∆P ⎜
⎜1−
c⎟
⎝ ρ ⎟
fib ⎠
w = − 2 2 2
S µρ c kZ
Where,
v m
3
dp / dZ = pressure gradient across a mat of thickness Z
S v = specific surface area of the fibers
(m 2 fiber/kg fiber)
µ = viscosity of filtrate (kg/m-s)
ρ = mat density (kg mat/ m 3 mat)
ρ fib = fiber density (kg fiber/ m 3 fiber)
c = consistency of the mat
(kg fiber/kg mat)
w = linear velocity of the filtrate (m/s)
k = Kozeny factor
Assuming that curvature, compared to the thickness, of the mat within the wash zone is small, then the mat
can be modeled as a flat surface. Consider a flat section of mat of thickness Z m , width y , arc length S , as
shown in Figure 5, below.
Consistency equation:
C
B
RZmC A
=
Z + Z C ( R − 1) − w( 1−
C ) dt
m m A A
Figure 5 Flat Mat Surfaces in Wash Zone
Where the new consistency CB at the end of a zone is a function of the consistency CA at the beginning of
the zone. When this calculation is repeated over all N z slices in the zone, we can obtain the consistency
profile over a full wash zone.
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