XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 3883
feed (cyclone underflow) contains 80.7% greater than 75
microns, and the ball mill discharge contains 71.7% greater
than 75 microns. The circuit CSE at 75 microns is (80.7+
71.7)/2 =76.1% (with rounding errors). The mill contains
solids of an estimated 76.1% plus 75 microns. And 76.1%
of the mill power (76.1% of 9,315 =7,089 kW) is being
used to grind material of a size larger than 75 microns. We
can also see that the rest of the mill power (2,226 kW)
is being expended on already fine product-size material,
minus 75 microns. This represents overgrinding power. In
order to maximize the circuit’s productivity in this regard,
we wish to adjust the classification equipment (pump and
cyclones) performances to maximize CSE (our optimiza-
tion criterion), with steps described later.
The concept of CSE leads to further interesting obser-
vations. CSE is a measure of relative circuit efficiency
because it characterizes the use of available power. But it
is not related to size reduction itself. Does this mean that
there is a separate measure of circuit efficiency related to the
grinding done by the mill’s usefully applied power?
Consider that the rate of production of new minus 75
micron size material by the mill (and also therefore the cir-
cuit) depicted in Appendix A must equal the grinding rate
of plus 75 micron size material in the mill per unit of power
applied to it. As noted above, the applied, or effective, mill
power equals the total mill power multiplied by CSE. For
this (or any) ball mill circuit:
Minus size production rate =Effective mill power
× Mill grinding rate of plus size (1)
And therefore:
Minus size production rate =Total mill power
× CSE × Mill grinding rate of plus size (2)
These values can be readily calculated from plant (survey)
data. The minus size (mill and circuit) production rate
is the circuit tonnage multiplied by the difference in the
percentage of product size material in the circuit product
stream (cyclone overflow) versus that in the ball mill circuit
fresh feed. Total mill power (usually calculated at the pin-
ion) is taken from plant power instruments and the motor
efficiency. As mentioned above, CSE is the average plus size
in the mill feed (cyclone underflow) and the mill discharge.
Given these three, the Mill grinding rate (MGrR) of plus
size can be deduced.
Since the Mill grinding rate (MGrR) will depend not
only on mill operating conditions but also on the ore’s resis-
tance to breakage, this is also measured on the appropriate
survey sample. The most widely used of these is the Bond
Work Index Test, which is conducted on the circuit feed
and provides a standardized measure of ore grindability to
a desired product sizing. We can then deduce, or define, a
relative measure of the mill grinding efficiency (MGrEff)
by taking the ratio of the plant mill grinding rate over the
Bond test mill grinding rate, which is reported by the Bond
test as the ore’s “grindability.” That is:
Mill grinding efficiency Ore grindability
at that size
Mill gringing rate
of plus size
=(3)
Since we have divided the Mill grinding rate by ore grind-
ability, we can balance the right-hand side of Equation 2 by
multiplying by the ore grindability.
Minus size prod uction rate =Total mill power
× CSE × Mill grinding efficiency
× Ore Grindability (4)
This is called the Functional Performance Equation for the
ball milling circuit.
The two distinct efficiencies it reveals highlight that the
circuit equipment performs two different functions: clas-
sification by the pump and cyclones in order to maximize
energy use on the desired plus size material, and size reduc-
tion of the desired plus size material by the ball mill. The
power of a given ball mill is normally maximized by the ball
charge level. Its Mill grinding efficiency (MGeEff) can be
affected by altering the grinding environment, for example,
by choice of ball size, water addition rate, and the mill dis-
charge design.
CSE and MGrEff are the two components of overall
circuit efficiency, a combined, quantitative measure that
can be calculated by isolating the two on one side of the
above equation. Maximizing each of them is the clear opti-
mization objective of performing Functional Performance
Analysis supported by apparent cumulative grinding rates
(ACGR) circuit modeling. Secondary interactions between
them are known to exist. For example, increased creation
of fines within the mill from higher impact breakage with
larger grinding media will naturally decrease CSE. Or, max-
imizing CSE through increased circulating load ratio will
increase mill slurry hold-up while reducing its fines content
and changes to the grinding environment, which may affect
MGrEff. These secondary effects are the topic of ongoing
investigations but are known to be of small enough signifi-
cance not to affect the correct choice of optimization goals
described above.
feed (cyclone underflow) contains 80.7% greater than 75
microns, and the ball mill discharge contains 71.7% greater
than 75 microns. The circuit CSE at 75 microns is (80.7+
71.7)/2 =76.1% (with rounding errors). The mill contains
solids of an estimated 76.1% plus 75 microns. And 76.1%
of the mill power (76.1% of 9,315 =7,089 kW) is being
used to grind material of a size larger than 75 microns. We
can also see that the rest of the mill power (2,226 kW)
is being expended on already fine product-size material,
minus 75 microns. This represents overgrinding power. In
order to maximize the circuit’s productivity in this regard,
we wish to adjust the classification equipment (pump and
cyclones) performances to maximize CSE (our optimiza-
tion criterion), with steps described later.
The concept of CSE leads to further interesting obser-
vations. CSE is a measure of relative circuit efficiency
because it characterizes the use of available power. But it
is not related to size reduction itself. Does this mean that
there is a separate measure of circuit efficiency related to the
grinding done by the mill’s usefully applied power?
Consider that the rate of production of new minus 75
micron size material by the mill (and also therefore the cir-
cuit) depicted in Appendix A must equal the grinding rate
of plus 75 micron size material in the mill per unit of power
applied to it. As noted above, the applied, or effective, mill
power equals the total mill power multiplied by CSE. For
this (or any) ball mill circuit:
Minus size production rate =Effective mill power
× Mill grinding rate of plus size (1)
And therefore:
Minus size production rate =Total mill power
× CSE × Mill grinding rate of plus size (2)
These values can be readily calculated from plant (survey)
data. The minus size (mill and circuit) production rate
is the circuit tonnage multiplied by the difference in the
percentage of product size material in the circuit product
stream (cyclone overflow) versus that in the ball mill circuit
fresh feed. Total mill power (usually calculated at the pin-
ion) is taken from plant power instruments and the motor
efficiency. As mentioned above, CSE is the average plus size
in the mill feed (cyclone underflow) and the mill discharge.
Given these three, the Mill grinding rate (MGrR) of plus
size can be deduced.
Since the Mill grinding rate (MGrR) will depend not
only on mill operating conditions but also on the ore’s resis-
tance to breakage, this is also measured on the appropriate
survey sample. The most widely used of these is the Bond
Work Index Test, which is conducted on the circuit feed
and provides a standardized measure of ore grindability to
a desired product sizing. We can then deduce, or define, a
relative measure of the mill grinding efficiency (MGrEff)
by taking the ratio of the plant mill grinding rate over the
Bond test mill grinding rate, which is reported by the Bond
test as the ore’s “grindability.” That is:
Mill grinding efficiency Ore grindability
at that size
Mill gringing rate
of plus size
=(3)
Since we have divided the Mill grinding rate by ore grind-
ability, we can balance the right-hand side of Equation 2 by
multiplying by the ore grindability.
Minus size prod uction rate =Total mill power
× CSE × Mill grinding efficiency
× Ore Grindability (4)
This is called the Functional Performance Equation for the
ball milling circuit.
The two distinct efficiencies it reveals highlight that the
circuit equipment performs two different functions: clas-
sification by the pump and cyclones in order to maximize
energy use on the desired plus size material, and size reduc-
tion of the desired plus size material by the ball mill. The
power of a given ball mill is normally maximized by the ball
charge level. Its Mill grinding efficiency (MGeEff) can be
affected by altering the grinding environment, for example,
by choice of ball size, water addition rate, and the mill dis-
charge design.
CSE and MGrEff are the two components of overall
circuit efficiency, a combined, quantitative measure that
can be calculated by isolating the two on one side of the
above equation. Maximizing each of them is the clear opti-
mization objective of performing Functional Performance
Analysis supported by apparent cumulative grinding rates
(ACGR) circuit modeling. Secondary interactions between
them are known to exist. For example, increased creation
of fines within the mill from higher impact breakage with
larger grinding media will naturally decrease CSE. Or, max-
imizing CSE through increased circulating load ratio will
increase mill slurry hold-up while reducing its fines content
and changes to the grinding environment, which may affect
MGrEff. These secondary effects are the topic of ongoing
investigations but are known to be of small enough signifi-
cance not to affect the correct choice of optimization goals
described above.