Dynamic Simulation and Model-based Control System Design for Comminution Circuits - Advanced Control and Supervision of Mineral Processing Plants - page 220

where d is the time delay. This parameter can be estimated by using the length of
the conveyor belt l and its speed v , d v . As depicted in Figure 5.4 both the feed

size distribution and the associated hardness are delayed.

= l /

feed
Flowrate
Size distribution
Hardness

f
f
γ f

out
Flowrate
Size distribution
Hardness

f(t -d)
f (t-d)
γ f (t-d)

Figure 5.4 A conveyor belt

5.4 Dynamic Modeling of Wet Grinding Circuits

The main elements of a grinding circuit are grinding mills, sumps, and hydrocy-
clons. The flow of material considers the water flowrate along the mineral flowrate
with the associated particle size distribution and hardness. In addition, some wet
grinding circuits involving semi-autogenous grinding (SAG) mills will consider
cone crushers.

5.4.1 Ball and Rod Mills

Ball and rod mill models are based on mass balance for material in each size interval,
following the perfect mixing model principle [2]. These equations can be written in
vector form as

d m ( t )

= f ( t )− p ( t )− γ ( t )( φ [ S − BS ] m ( t )+( 1 − φ )[ S − BS ] m ( 0 )), (5.12)

dt

( ) ( )

where f t is the vector of mass fraction of the mill charge, p t is the mass fraction

of the mill product, and φ and ( 1 − φ ) represent the fraction of first and zero order

kinetics assumed. If φ 1it

represents a rod mill [10]. Figure 5.5 depicts the main input and output variables.

= 1, the model represents a ball mill and if 0 < φ <