612
V. Skorych et al.
Each unit on the flowsheet formulates and applies a two-dimensional transformation matrix for the particle size distribution.
The screen unit is defined in terms of grade efficiency, which determines a mass
fraction of particles of a certain diameter that leaves the screen through the coarse
outlet. The transformation matrices for coarse T
c and fine T
f output streams are
calculated as:
T
c
i,i = G(x i )
T
f
i,i = 1 − G(x i )
,
(26)
where G(x) is a grade efficiency for particles of size x, calculated according to Plitt’s
model [44].
Selection S(x k ) and breakage B(x k , x i ) functions are used to describe the model
of crusher. S(x k ) determines the mass fraction of particles of size x k , which will be
crushed, while breakage function B(x k , x i ) defines the number of particles of size x i
that get the size of x k after crushing. The transformation laws are calculated as
T i,k =
B(x k , x i ) · S(x k ), i <> k
1 − S(x k ),
i == k
.
(27)
As B(x k , x i ) Vogel’s breakage function [62] was applied, whereas the selection
function S(x k ) was calculated according to King [28].
The source material was described using two interdependent distributed parameters:
• particle size: the main parameter that is calculated directly in all models;
• moisture content: a secondary parameter that is not considered in the models’
equations, but is calculated indirectly by applying transformation matrices.
For simplification, it was assumed that no moisture transfer between particles and
no drying occurs.
From the obtained simulation results (Fig. 17), it can be seen that, despite the fact
that all models were defined to directly calculate only the particle size distribution,
information about the secondary parameter was stored and properly considered in
accordance with the formulated transformation laws. So, for example, at the first
stage of the process (Fig. 17), one can observe a change in particle size (Inlet C—
Milled) due to the operation of the mill. At the same time, the amount of moisture
does not change. After that, the milled wet and small dry particles are mixed and
fed to the next stage. Due to mixing, one can observe a bimodal distribution of
both parameters in the Inlet 2 stream. However, the application of the screen makes
it possible to separate particles by size, while the moisture content is also mainly
distributed between two streams Coarse 2 and Fine 2. Since some initially large wet
particles were crushed in the first mill, and also due to non-ideal separation in the
screen, some mixing of different fractions is observed. At the last stage, the final
V. Skorych et al.
Each unit on the flowsheet formulates and applies a two-dimensional transformation matrix for the particle size distribution.
The screen unit is defined in terms of grade efficiency, which determines a mass
fraction of particles of a certain diameter that leaves the screen through the coarse
outlet. The transformation matrices for coarse T
c and fine T
f output streams are
calculated as:
T
c
i,i = G(x i )
T
f
i,i = 1 − G(x i )
,
(26)
where G(x) is a grade efficiency for particles of size x, calculated according to Plitt’s
model [44].
Selection S(x k ) and breakage B(x k , x i ) functions are used to describe the model
of crusher. S(x k ) determines the mass fraction of particles of size x k , which will be
crushed, while breakage function B(x k , x i ) defines the number of particles of size x i
that get the size of x k after crushing. The transformation laws are calculated as
T i,k =
B(x k , x i ) · S(x k ), i <> k
1 − S(x k ),
i == k
.
(27)
As B(x k , x i ) Vogel’s breakage function [62] was applied, whereas the selection
function S(x k ) was calculated according to King [28].
The source material was described using two interdependent distributed parameters:
• particle size: the main parameter that is calculated directly in all models;
• moisture content: a secondary parameter that is not considered in the models’
equations, but is calculated indirectly by applying transformation matrices.
For simplification, it was assumed that no moisture transfer between particles and
no drying occurs.
From the obtained simulation results (Fig. 17), it can be seen that, despite the fact
that all models were defined to directly calculate only the particle size distribution,
information about the secondary parameter was stored and properly considered in
accordance with the formulated transformation laws. So, for example, at the first
stage of the process (Fig. 17), one can observe a change in particle size (Inlet C—
Milled) due to the operation of the mill. At the same time, the amount of moisture
does not change. After that, the milled wet and small dry particles are mixed and
fed to the next stage. Due to mixing, one can observe a bimodal distribution of
both parameters in the Inlet 2 stream. However, the application of the screen makes
it possible to separate particles by size, while the moisture content is also mainly
distributed between two streams Coarse 2 and Fine 2. Since some initially large wet
particles were crushed in the first mill, and also due to non-ideal separation in the
screen, some mixing of different fractions is observed. At the last stage, the final