3692 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
et al., 2014 2016 2018a 2018b 2021 Xie, 2022), and
a crusher model for dynamic performance and real-time
optimization (Evertsson, 1999 Asbjörnsson, et al., 2012
Bhadani, et al., 2021).
In this research, an analytical solution for dynamic
model of tumbling mills has been developed based on the
knowledge of solutions to the first-order nonhomogeneous
linear differential equations. The results from analytical
solutions will be compared to the traditional finite dif-
ference numerical methods using two cases of SAG mill
dynamic operations.
METHODOLOGY
In order to use dynamic simulations for tumbling mills,
some sub-models will be introduced in the following sec-
tions including population mass balance, classification,
transportation, breakage and discharge models. There are
two scenarios are shown in Figure 1a and 1b, with different
sub-models, which will depend on different availability of
plant data.
Dynamic Response Model
A general dynamic response model, as the core of dynamic
simulations for tumbling mills, can provide the mill
response to the change of operating conditions, as shown
in equation 1 (Yu, et al., 2018a). It can also be applied to
a segment of interest inside the mill to consider the input
(feed) and output (product) regarding the segment interac-
tion to the surrounding environment inside the mill.
dt
ds^th
Z th s f $=+^^th ^th (1)
where, s(t) is the content of the mill (or segment) at time t
with matrix form f(t) is the flow rate of feed material with
matrix form Z(t) is a response matrix related to all under-
going classification, transportation, breakage, discharge
and other kinds of events. As a simplification, Z(t) can be
Figure 1. Dynamic response model for tumbling mills with different sub-models
et al., 2014 2016 2018a 2018b 2021 Xie, 2022), and
a crusher model for dynamic performance and real-time
optimization (Evertsson, 1999 Asbjörnsson, et al., 2012
Bhadani, et al., 2021).
In this research, an analytical solution for dynamic
model of tumbling mills has been developed based on the
knowledge of solutions to the first-order nonhomogeneous
linear differential equations. The results from analytical
solutions will be compared to the traditional finite dif-
ference numerical methods using two cases of SAG mill
dynamic operations.
METHODOLOGY
In order to use dynamic simulations for tumbling mills,
some sub-models will be introduced in the following sec-
tions including population mass balance, classification,
transportation, breakage and discharge models. There are
two scenarios are shown in Figure 1a and 1b, with different
sub-models, which will depend on different availability of
plant data.
Dynamic Response Model
A general dynamic response model, as the core of dynamic
simulations for tumbling mills, can provide the mill
response to the change of operating conditions, as shown
in equation 1 (Yu, et al., 2018a). It can also be applied to
a segment of interest inside the mill to consider the input
(feed) and output (product) regarding the segment interac-
tion to the surrounding environment inside the mill.
dt
ds^th
Z th s f $=+^^th ^th (1)
where, s(t) is the content of the mill (or segment) at time t
with matrix form f(t) is the flow rate of feed material with
matrix form Z(t) is a response matrix related to all under-
going classification, transportation, breakage, discharge
and other kinds of events. As a simplification, Z(t) can be
Figure 1. Dynamic response model for tumbling mills with different sub-models