Digital Solutions to Evaluate Ball Mill

Circuit Recirculating Load and

Performance
Jeremy Hanhiniemi1,2, Jun Heo2
1 - Julius Kruttschnitt Mineral Research Centre, Brisbane, Queensland, Australia
2 - Weir Minerals, Artarmon, NSW, Australia

Corresponding Author: jeremy.hanhiniemi@uqconnect.edu.au

Abstract
The well-known trade-off when aiming to increasing ball mill throughput between capacity benefits
from increasing circuit recirculating load, versus diminishing classification efficiency, is explored in
this paper using digital tools and simulation. Laboratory CAVEX hydrocyclone tests at varying
recirculating loads inform changes in classification performance models. This is coupled with tools to
ensure simulated overflow ball mill performance is realistic. One tool used includes a volume-based
residence time ball mill model to constrain simulations and prevent ‘overfilling’ and a loss of grinding
performance at high recirculating loads. These are then integrated into a ball mill circuit level
process simulation, to explore increasing Warman® Pump and CAVEX® Hydrocyclone capacity within
these limits to achieve higher circuit throughput. Finally, a cash flow model is incorporated to
quantify the economic value generated based on the value of increased throughput versus increased
classification circuit costs from power and pump/hydrocyclone wear parts. This approach was
applied to an example case study site operating at circa 450 milled tons per hour. For this site the
tools estimated an $8M Australian dollar per annum benefit (additional revenue less additional
operating cost) by doubling the pump and hydrocyclone capacity.

Introduction
The closed ball milling circuit is a key part of many minerals processing operations. Recirculating load
is the fraction of mass flowing through the mill divided by the feed throughput, and this has been
found to be a significant consideration in mill circuit performance, and thus the economics of the
operation. This paper will describe a digital tool and methodology that can, once calibrated to a
baseline, be employed to simulate the performance of the circuit a difference recirculating loads.
The goal is to then provide insights into potential improvements in circuit operation or design,
including classification circuit upgrades.

Jankovic and Valery (2013) provided an overview of closed-circuit ball milling. They described how
researchers from the 20’s onwards showed higher recirculating loads produced increase mill
capacity. Finnish researchers in the 70’s then began to explore the impact of different classification
efficiency on this known improvement in capacity with recirculating load, as shown in Figure 1.
Clearly the performance of the classifier must also be considered, as it has a strong influence on
circuit performance.
 Figure 1: Effect of Circulating Load and Classification Efficiency on Milling Circuit Capacity From Hukki (1979)
(Jankovic and Valery, 2013)

Also summarized by Jankovic and Valery was the known deterioration of hydrocyclone efficiency
with increasing recirculating load, as shown in Figure 2. The paper goes on to state that the
countervailing effects of increased production versus decreased classification efficiency with higher
recirculating loads limits the overall production improvement that can be achieved practically.
Regardless, the improvements in production that can be achieved should be evaluated against the
costs required to achieve them, and a methodology to support this will be described below in this
paper.

Figure 2: Effect of Circulating Load on Classification Efficiency From Jankovic and Valery (2013)

McIvor (2014) described a measure for overall ball milling circuit efficiency and productivity called,
“Classification System Efficiency” (CSE). According to McIvor it is calculated by estimating the
average percentage of coarse material in the ball mill, with the cut-off size between coarse and fine
material being generally selected as the cyclone overflow P80 size. The higher the CSE the less mill
power will be employed in overgrinding of fines. McIvor goes on to describe examples of how
increased recirculating load can increase CSE, and overall production of the ball mill circuit. Other
authors have also described the effect of increased recirculating load on reducing specific energy
demand (and thus increased production for a given power) when using P80 based methods
(Sherman, 2015).

Clearly recirculating load is an important consideration in overall ball mill circuit production. This
paper will present a digital tool and methodology to capture the trade-off between improved
throughput in close circuit overflow ball milling, considering deteriorating classification
performance, for the purposes of valuing potential upgrade options of the classification circuit. This
will employ various simulation methods including the JKSimMet® perfect mixing ball mill model, Size
Specific Energy approaches, the Nageswararao hydrocyclone model, ball mill residence time
constraints, and results from experiments on Weir® Cavex® hydrocyclones. The methods employed
will now be described.

Methodology
First the main parts of the digital twin and methodology will be described, then their overall
integration will be described.

Ball Milling
Ball mill performance was modelled using JKSimMet®. However, this modelling is not constrained
with respect to available power versus comminution energy requirements; the power and breakage
models are separate. Unlike the SAG model, there is no filling constraint. Therefore, constraints must
be applied on ball mill operation using SSE as measured from a baseline, and other methods.

The JKSimMet® ball mill model is also not constrained from a volumetric and residence time
perspective. At increasing flow rates and higher recirculating loads the residence time of the slurry in
the ball mill reduces. Transport through the mill charge is believed to become constrained, with
slurry then washing across the charge and less so through it, reducing grinding performance. The mill
‘overfills’, losses power, and grinding performance further drops. Shi (2016) stated that power
modelling cannot offer an effective constraint on this overfilling, as power consumed is little
affected by the overfilling conditions in overflow ball mills. To address this, a minimum residence
time was employed to indicate if the ball mill is at risk of being overloaded. This method developed
by Shi is adopted in this work; the residence time of slurry in the mill is calculated and a minimum of
two minutes for small mills (internal diameter below 5.9 m), and one minute for larger mills (over
5.9 m), is set based on industrial datasets. Below these residence times, the risk of overfilling is
deemed heightened. This approach was coded in this digital tool and is applied as a constraint in the
modelling. The database provided by Shi on residence time, and his calculation procedure are shown
in Figure 3 and Figure 4 respectively.
 Figure 3: Procedure to Calculate Volume-Based Slurry Residence Time in a Ball Mill to Identify Mill Overfilling
Onset From Shi (2016)

Figure 4: Distribution Pattern of The Volume-Based Residence Time in the Database of Industrial Overflow Ball
Mill Surveys From Shi (2016)

A limit on volumetric flow out of the mill is also established, based on the relation derived by Morrell
(2016) from Bernoulli’s equation. This is based on the allowable vertical height between the inlet
invert and the discharge trunnion invert (Δℎ𝐼𝑛𝑣𝑒𝑟𝑡𝑠 ), and the trunnion radius, 𝑅𝑡 , as follows:

𝑄𝑀𝑎𝑥𝐹𝑙𝑜𝑤 = 0.5𝜋𝑅𝑡 𝑔0.5 (0.67Δℎ𝐼𝑛𝑣𝑒𝑟𝑡𝑠 )1.5

Size Specific Energy

The energy and, thus, throughput of grinding circuits are sensitive to fines generation, which is only
loosely represented by P80 approaches. Ballantyne et al. (2015) described the linear relationship
between cumulative energy input and percent of -75 µm material generated that applies over a wide
range of machines, from crushers to ball mills. This - 75 µm material is a proxy for surface area, as
typically 70-80% of the surface area of grinding mill product lies below this size.

Size Specific Energy (SSE) is the inverse of the gradient of the curve produced when cumulative
specific energy (SE) is plotted against cumulative percentage generation of - 75 µm material. SSE can
better capture energy differences in non-parallel feed and product PSDs. As an indication of
comminution circuit efficiency, it can be used to benchmark site results and to determine where
inefficiencies enter the comminution circuit. The shape of this curve is influenced by the size of the
particles comminuted and the energy level in the comminution event. It can also be used to test the
likely validity of simulation results and is used here for this purpose.

Slurry Pumping
Hydrocyclone feed slurry pumps contribute to grinding costs through power, wear parts, and
maintenance costs. Pump shaft power can be estimated through the relationship between pressure,
P, efficiency, 𝛾, and flowrate, Q. This power can be related to consumed electrical power by the
power factor (PF ) (Warman, 2000). In hydrocyclone feed applications, the pressure can be
estimated as the sum of slurry head pressure and cyclone feed pressures. Slurry head pressure can
be estimated as a function of the vertical distance between the slurry sump and cyclone inlet, H,
below (allowing a factor for dynamic losses 𝑑𝐹 ). Example estimates of slurry pump efficiency and PF
of 70% and 80%, respectively, were used (note that motor PF varies with load, but this simplifying
constant value was used). Power calculations are thus:
𝑃𝑄
𝑃𝑜𝑤𝑒𝑟𝑅𝑒𝑎𝑙 = ; 𝑃𝑜𝑤𝑒𝑟𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐 × 𝑃𝐹 = 𝑃𝑜𝑤𝑒𝑟𝑅𝑒𝑎𝑙
𝛾

1000𝑘𝑔
𝑃 = 𝑔 × 𝑆. 𝐺.× × 𝐻 × 𝑑𝐹 + 𝑃𝐻𝑦𝑑𝑟𝑜𝑐𝑦𝑐𝑙𝑜𝑛𝑒
𝑚3

1000𝑘𝑔
[𝑔 × 𝑆. 𝐺.× × 𝐻 × 𝑑𝐹 + 𝑃𝐻𝑦𝑑𝑟𝑜𝑐𝑦𝑐𝑙𝑜𝑛𝑒 ] 𝑄
𝑚3
𝑃𝑜𝑤𝑒𝑟𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐 =
𝛾 × 𝑃𝐹

Wear parts and maintenance costs increase with the number and size of pumps, as does total pump
power, with increasing recirculating load. Cost estimates commensurate with pump size and
application were incorporated (Weir, 2018).

Hydrocyclone Performance
To study the performance of hydrocyclones under varying recirculating loads an experimental
campaign was undertaken at the Weir® Technical Centre using a hydrocyclone testing rig. To study
the effect of size, two models were tested: the CAVEX 150CVX and 250CVX hydrocyclones (150 mm
and 250 mm feed chamber diameter respectively). Different recirculating loads were emulated in
these tests through different mass-splits to overflow and underflow, achieved by varying the spigot
to vortex finder ratios. The hydrocyclones were surveyed by particle size distribution and percentage
solids, and operating conditions reported including feed pressure. Each survey result was mass
balanced, and model fitted to both the single efficiency model, and the Nageswararao hydrocyclone
models (Napier-Munn et al., 1996). The twenty-four tests conducted are summarised in Table 1.

The model fitted parameters, in both the single efficiency and the Nageswararao models, were then
plotted against varying mass splits. It was then assumed that the change in hydrocyclone
performance parameters with varying mass split fractions would also be representative of the
changing performance with varying recirculating loads when the equipment was employed in the
mill circuit.
 Table 1: Summary of the Hydrocyclone Testing Campaign
Hydrocyclone Feed Vortex Spigot Mass Split (U/F Over Pressure
Chamber Diameter (mm) Finder (mm) (mm) O/F Throughput) (kPa)
35 20 124% 108
35 20 143% 206
35 20 158% 319
35 20 167% 397
35 25 181% 94
35 25 212% 200
150 (150CVX)
35 25 237% 335
35 25 249% 410
35 30 274% 107
35 30 317% 182
35 30 373% 308
35 30 397% 372
70 40 95% 91
70 40 98% 200
70 40 101% 150
70 40 108% 300
70 50 141% 91
70 50 155% 196
250 (250CVX)
70 50 148% 146
70 50 167% 291
70 60 231% 86
70 60 244% 150
70 60 249% 180
70 60 267% 269

As expected, cyclone efficiency parameters including α showed deterioration at increasing mass split
fractions (recirculating loads). The α is the sharpness of the cut, a slope based on the plot of the
percentage of feed reporting to the overflow stream (corrected) and the d/d50c (corrected). A
regression was fitted to these results (Figure 5) which produced a good fit in the 150CVX, and a
reasonable fit in the 250CVX if the two outlying tests shown are omitted (R2 was poor otherwise as
listed); it is thought that these two tests may have been erroneously high.
 Model Fitted α (Nageswararao) Versus Recirculating Load (Mass Split
Fraction)
3.0
X
250CVX
2.5 Nages.

2.0 150CVX
Nages.
1.5
α

R² = 0.8732 Power
1.0 (250CVX
Nages.)
0.5 Power
R² = 0.3033 (with outliers) (150CVX
0.0 Nages.)
50% 150% 250% 350% 450%
Fitted Recirculating Load (Mass Split Fraction)
Figure 5: Model Fitted α (Nageswararao) Versus Recirculating Load (Mass Split Fraction)

The α achieved will be a function of many considerations, such as ore type and feed, therefore some
relative relation for the response of α with recirculating load was desired to account for these
changes; the function above was normalising as a multiplier from an arbitrary recirculating load
(taken at 250%). The metallurgist can therefore survey their current operation and multiply out the
likely α at a new operation using this. This relative α multiplier versus recirculating load is shown in
Figure 6. Interestingly, the results of the two different size hydrocyclones was similar, providing
some indication that this approach could be applicable independent of hydrocyclone size.
 α Multiplier Versus Recirculating Load (Nageswararao)
3.0
150CVX:
Multiplier From 250% Rec. Load

2.5
250CVX:
2.0

1.5

1.0

0.5

0.0
50% 100% 150% 200% 250% 300% 350% 400% 450% 500%
Recirculating Load (Mass Split Fraction)

150CVX (Nages.) 250CVX (Nages.)

Figure 6: α Multiplier Versus Recirculating Load (Nageswararao)

There are two methods of increasing the recirculating load, an increase in the feed flow rate given
fixed geometry, and an increase in the spigot over vortex finder diameter fraction. A higher feed rate
is eventually limited by the onset of roping condition and/or the pressure rating of the hydrocyclone.
To allow for even higher recirculating load, a larger spigot is then required. It was found that
JKSimMet® was very sensitive to spigot size, and therefore to constrain performance, a realistic
spigot size must be inputted into simulations. To provide an indication of this, the experimental
results of recirculating load achieved versus spigot over vortex finder diameter fraction were plotted
in Figure 7, as a strong relationship was found to exist. As expected, higher spigot over vortex finder
diameter fractions allowed for higher recirculating loads, and this figure was used as a guide for
determining what minimum spigot diameter was required iteratively with JKSimMet®.
 Recirculating Load (Mass Split Fraction) Versus
Spigot/Vortex Finder Ratio
500%
Recirculating Load
400%
300% 150CVX

200%
250CVX
100%
0%
0.4 0.5 0.6 0.7 0.8 0.9
Spigot/VF Fraction

Figure 7: Recirculating Load (Mass Split Fraction) Versus Spigot/Vortex Finder Ratio

Water percentage split to overflow is also a key consideration in classification performance. A strong
relationship was found between the water mass split to the overflow, and the spigot to vortex finder
fraction, as illustrated in Figure 9 below. A larger spigot for a fixed vortex finder allowed for higher
recirculating load, and reduces the water split percentage to overflow. The result will therefore be a
deterioration of classification efficiency at higher recirculating load, as the amount of entrained fine
particles flowing to the underflow stream will increase. This is shown in Figure 8.

Water Split to Overflow (%) (Nageswararao) Versus Recirculating Load

100%
Watersplit to O/F (%)

90%
250 CVX Nages.
80%

70%
150 CVX Nages.
60%

50%
0% 100% 200% 300% 400% 500%
Recirculating Load (Mass Split Fraction)

Figure 8: Water Split to Overflow (%) (Nageswararao)

It was later demonstrated that the Nageswararao water split was responding similarly to the
experimental results, when the spigot diameter was set consistent with the recirculating load as
described above, supporting the validity of the simulation methodology. The results also showed
that increasing flow rate, given a fixed cyclone geometry and configuration, improved the efficiency
parameters such as alpha and water split percentage, while the d50c cut size is finer, consistent with
literature (Napier-Munn et al., 1996); this is then constrained within a limited feed rate and mass
split.
 150 CVX & 250 CVX Model Fitted Watersplit to Over Flow Versus
Spigot/Vortex Finder Diameter Fraction (Nageswararao)
95%
Model Fitted Water Split to O/F (%)

90%
85%
80% 250 CVX
75% Nages
70%
65%
150 CVX
60% Nages
55%
50%
0.50 0.60 0.70 0.80 0.90
Spigot/Vortex Finder Diameter

Figure 9: Recirculating Load (Mass Split Fraction) Versus Spigot/Vortex Finder Fraction

The final key variable is the corrected D50c: the size at which a particle has equal chance of
reporting to overflow or underflow, excluding that entrained in water. There are well established
methods for determining the drivers of D50c. The Nageswararao model includes spigot and vortex
finder diameters terms in its mathematics, and so D50c would likely have an existing response to
recirculating load through these terms. Hence, existing D50c approaches were employed.

The other model fitted parameters in the Nageswararao model where also examined. The
Capacity Constant KQ0 had no apparent response to recirculating load. The D50 Constant KD0,
Volume Split Constant KV1, and Water Split Constant KW1 did appear to have a response with
recirculating load, from weak to more pronounced, but this was not included in the methodology as
these terms are generally constant for a fixed feed. This may present a future improvement in the
methodology.

Overall Model Structure - Digital Twin Solution

The methods described above were integrated into a single simulation methodology. This method
can be employed at brownfields sites to estimate performance with classification circuit upgrades,
or revised design and operation. The circuit is surveyed and the underlying JKSimMet® models are
model fitted per practice described in literature (Napier-Munn et al., 1996). The extended methods
described above are then applied and coupled with JKSimMet®. The overall architecture of the
digital tool is illustrated in Figure 10. The case study below explains the application of the method.
 Weir® CAVEX® Model

JKSimMet®

Ball Milling Residence

Time and SSE Model

Warman® Slurry Pump Model

Ball Milling Circuit

Financial Model

Figure 10: Architecture of the Digital Tool

Case Study
An open pit gold mine was used as a case study to demonstrate the application of the digital tool.
This site had a closed ball mill circuit, comprised of a single overflow ball mill, Warman® slurry pump,
and a hydrocyclone cluster processing circa 450 dry tons of ore per hour. The site had an existing
mass balanced, model fitted JKSimMet® model based off a survey conducted.

Technical Assessment
Table 2 describes the as-surveyed operation of the circuit (Baseline). The digital tool described in this
paper was then applied through a series of cases with progressively higher throughput and
recirculating loads (Cases 1 to 3). As throughput increased, recirculating load increased. The spigot
diameter was increased so that the recirculating load and corresponding spigot over vortex finder
diameter fraction was consisted per the guidance from experiments and Figure 7; this needed to be
done iteratively within JKSimMet® as these variables are interrelated. The number of operating
cyclones required was also increased, to maintain pressure to a reasonable value while not allowing
it to vary too far from the measured and model fitted operation.

The maximum volumetric throughput and residence time of the ball mill was calculated as described
above. The mill diameter was below 5.9 m; therefore, the minimum volumetric residence time is 2
min. The volumetric flowrate at 2 minutes residence time was calculated at 1650 m3/hr. The
maximum volumetric flowrate constraint was calculated at 4558 m3/hr based on drawings,
indicating the mill reaches residence time constraints before absolute flow capacity limits. Cases run
were thus constrained to within 1650 m3/hr mill throughput.

Case 1 to 2 are showing increased throughput performance. Case 2 operation matches that of the
maximum calculated ball mill volumetric capacity. The SSE remains very close to the original
baseline, supporting the feasibility of this simulated operation. The spigot over vortex finder fraction
is in reasonable agreement to that derived from experimental results (Figure 7) as shown in Figure
11.

Spigot/Vortex Finder Fraction Versus Recirculating Load

500%
Recirculating Load

400% 3
2
300% 1
200%
Baseline Cases
100%
0%
0.40 0.50 0.60 0.70 0.80 0.90
Spigot/Vortex Finder Fraction
Figure 11: Spigot/Vortex Finder Fraction Versus Recirculating Load

The α was manually adjusted iteratively with recirculating load using the ‘α multiplier’ in Figure 6.
Figure 12 and Figure 13 show the simulated deterioration of the classification performance with a
reduced α and reduced water mass split to overflow. The hycrocyclones used in this case study were
not Cavex® but another manufacturer, and in the authors experience Cavex® generally has a higher
(improved) water split percentage to overflow; the water split curve versus recirculating load is
lower in Figure 13 versus the experimental results for the Cavex® in Figure 8. However, the response
is similar in trend and magnitude, supporting the validity of the simulation.
 α Versus Cases and Recirculating Load
6

4
Baseline
3
α

1
2 2 3
Cases
1

0
150% 200% 250% 300% 350% 400% 450%
Recirculating Load

Figure 12: α Versus Cases and Recirculating Load

Hydrocyclone Water Split to O/F Versus Case and

Recirculating Load
Water Split to Over Flow (%)

80
75
70
Baseline
65
60
55 1
Cases 2 3
50
150% 200% 250% 300% 350% 400% 450%
Recirculating Load

Figure 13: Hydrocyclone Water Split to O/F Versus Case and Recirculating Load

Regardless of the deterioration in classification performance, the digital tool indicates that Case 2
operation is feasible, and an extra 10% throughput has been achieved with only minor coarsening of
the final product size as indicated by Figure 14.
 Final Product Particle Size Distribution Versus Case
100
90
80
70 Baseline
% Passing

60 1
50
2
40
30 3
20
10
0
0.01 0.1 1
Size (mm)
Figure 14: Final Product Particle Size Distribution Versus Case

Case 3 is too far from the originally fitted pressure. Its spigot over vortex finder fraction is becoming
too low as compared to Figure 7, and any further increases in this ratio resulted in a rapidly
increasing recirculating load and ball mill volumetric flowrate. This simulation methodology is
showing an accelerating failure of the circuit to accommodate throughput increases over the
baseline of 13% and beyond. It appears that this methodology has successfully been able to indicate
the achievable limit on throughput, where previous methods were poorly constrained. The ball mill
residence time constraint has been exceeded by 10%, indicating the ball mill might be at risk of
being in an overfilled condition. The SSE is also beginning to drop appreciably below the baseline.
Therefore, the methodology presented here is indicating Case 3 operation may not be achievable in
practice, and a maximum throughput increase of between 10-13% would be achievable with a
doubling of the pump and hydrocyclone capacity.
 Table 2: Summary of Ball Mill Circuit Measured and Simulated Operation
Scenario Baseline 1 2 3
Slurry Pump & Cyclone Capacity
0% 156% 191% 204%
Increase (%)
Throughput Increase (%) 0% 5% 10% 13%
OF Solids Mass Rate (t/hr) 441 463 485 498
UF Solids Mass Rate (t/hr) 821 1504 1919 2079
Recirculating Load (%) 186% 325% 396% 417%
Cyclone Diameter - Dc (m) 0.660 0.660 0.660 0.660
Inlet Diameter - Di (m) 0.206 0.206 0.206 0.206
Vortex Finder Diameter - Do (m) 0.257 0.257 0.257 0.257
Spigot Diameter - Du (m) 0.150 0.190 0.200 0.205
Cylinder Length - Lc (m) 0.559 0.559 0.559 0.559
BM and
Cone Angle - Theta (degrees) 20 20 20 20
Hydrocyclone
Operating Pressure (kPa) 62 97 100 115
Operation
Spigot Over Vortex Finder Ratio 0.58 0.74 0.78 0.80
Number of Op. Hydrocyclones 4 6 6 6
Ball Mill Volumetric Flowrate (m3/hr) 629 1285 1700 1822
Ball Mill Volumetric Flowrate Limit
1650 1650 1650 1650
(m3/hr)
Percentage of Ball Mill Volumetric Limit
38% 78% 103% 110%
(%)
Hydrocyclone Water Split to O/F (%) 73 61 56 57
D50 Constant - KD0 9.69E-05 9.69E-05 9.69E-05 9.69E-05
Capacity Constant - KQ0 621.5 621.5 621.5 621.5
Volume Split Constant - KV1 6.77 6.77 6.77 6.77
Water Split Constant - KW1 10.2 10.2 10.2 10.2
Hydrocyclone Sharpness of Efficiency Curve - Alpha
4.91 4.91 4.91 4.91
Parameters (Org.)
Alpha Multiplier 1.26 0.81 0.69 0.67
Revised Alpha 4.91 3.16 2.70 2.59
Initial Dip in Efficiency Curve - Beta 0 0 0 0
Calculated Value Beta* 1 1 1 1
Feed Mass Below 75 µm (%) 35.9 35.9 35.9 35.9
Product Mass Below 75 µm (%) 74.7 73.9 72.3 72.3
New Below 75 µm Material (%) 38.8 37.9 36.3 36.4
SSE
Mill Power (kW) 3147 3149 3149 3149
SSE (kWh/t -75µm) 18.4 17.9 17.9 17.4
Change in SSE From Baseline (%) 2.5% 2.9% 5.5%
Sump Product Flow (m3/hr) 1637 2555 3122 3347
Sump Product SG 1.47 1.47 1.47 1.47
Static Head (m) 20 20 20 20
Pump Details
Pump Efficiency (%) 0.7 0.7 0.7 0.7
Motor Power Factor 0.8 0.8 0.8 0.8
Pump Power (kW) 285 488 602 670

Financial Assessment
The technical assessment undertaken indicated that an increase in throughput of between 10-13%
was feasible, but this required a near doubling of the slurry pump capacity, and an increase in the
number of operating cyclones, which will increase the operating costs of the ball milling circuit. To
analyse if the expected benefits of the additional throughput outweigh the added operating costs a
simple example financial analysis was conducted. All values are expressed in Australia dollars.
Lane (1988) was used to derive the following simple relation for the additional (marginal) revenue
generated per hour over the baseline operation, 𝐶𝑅𝑒𝑣 , as follows:

𝐶𝑅𝑒𝑣 = (𝑝𝑦𝑔̅ − 𝑐𝑂𝑣𝑒𝑟𝑎𝑙𝑙 ) × (𝑇𝐶𝑎𝑠𝑒 − 𝑇𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒 ) ($/ℎ𝑟)

Here 𝑝 is the price of the valuables with marketing costs deducted, 𝑦 is the recovery as a fraction, 𝑔̅
is the average grade as a valuables-to-ore mass ratio, 𝑐𝑂𝑣𝑒𝑟𝑎𝑙𝑙 is the unit cost (expressed by tons
milled) inclusive of all mining, processing, and period costs of the baseline operation, 𝑇𝐶𝑎𝑠𝑒 and
𝑇𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒 is the dry mass throughput milled per hour of the case and baseline respectively.

To determine the overall marginal cash flow generated, the marginal additional costs must be
calculated with upgraded slurry pumping and hydrocyclone capacity above the baseline. The unit
cost of the baseline operation of only the existing pumps and hydrocyclones (on a per ton milled
basis) is calculated, 𝑐𝐶𝑙𝑎𝑠𝑠𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛, 𝐵𝐿 . Similarly, the unit costs of the upgraded pumps and clusters is
calculated, 𝑐𝐶𝑙𝑎𝑠𝑠𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛, 𝐶𝑎𝑠𝑒 . The marginal additional cost of running the upgraded classification
circuit, 𝐶𝐶𝑙𝑎𝑠𝑠𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 , is then:

𝐶𝐶𝑙𝑎𝑠𝑠𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 = 𝑐𝐶𝑙𝑎𝑠𝑠𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛, 𝐶𝑎𝑠𝑒 × 𝑇𝐶𝑎𝑠𝑒 − 𝑐𝐶𝑙𝑎𝑠𝑠𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛, 𝐵𝐿 × 𝑇𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒 ($/ℎ𝑟)

The cash flow generated by an upgrade of the classification circuit, 𝐶𝑈𝑝𝑔𝑟𝑎𝑑𝑒 , is therefore:

𝐶𝑈𝑝𝑔𝑟𝑎𝑑𝑒 = 𝐶𝑅𝑒𝑣 − 𝐶𝐶𝑙𝑎𝑠𝑠𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 ($/ℎ𝑟)

As the change in the product size distribution was small between cases, no change in recovery
between the scenarios was assumed. For illustrative purposes the following was assumed: a
recovery of 80%, 𝑝 was estimated at $60/g of contained gold, an ore grade 𝑔̅ of 1.2 g/ton, an
electrical power cost of $100/MWhr, pump and hydrocyclone wear part lives of six months, and
indicative wear part costs and labour for the scenarios’ pump and hydrocyclone quantities and
selections were used. The overall unit costs of the mining and concentrator operation, 𝑐𝑂𝑣𝑒𝑟𝑎𝑙𝑙 , was
assumed not to change beyond the pumping and hydrocyclones costs above, and a value of $38/ton
milled was assumed for illustrative purposes.

The case study financial results are now presented. The increased recirculating load, and the
increased pump and hydrocyclone capacity, yielded an additional $8M per annum for this
concentrator size, until the technical limit identified by this digital tool was reached. This is
illustrated in Figure 15 and Figure 16.
 Annual Marginal Cash Flow With Classification Upgrade
Versus Recirculating Load
$10 M
$9 M
Marginal Cash Flow ($ P.A.)
$8 M
$7 M
$6 M
$5 M
$4 M
Limit Reached
$3 M
$2 M
$1 M
$M
150% 200% 250% 300% 350% 400% 450%
Recirculating Load

Figure 15: Annual Marginal Cash Flow with Classification Upgrade Versus Recirculating Load

Annual Marginal Cash Flow With Classification Upgrade

Versus Pump/Cluster Capacity
$10 M
$9 M
Marginal Cash Flow ($ P.A.)

$8 M
$7 M
$6 M
Limit Reached

$5 M
$4 M
$3 M
$2 M
$1 M
$M
1500 2000 2500 3000 3500
Pump and Hydrocyclone Cluster Flowrate (m^3/hr)

Figure 16: Annual Marginal Cash Flow with Classification Upgrade Versus Pump/Cluster Capacity

Conclusion
A methodology for modelling closed circuit ball milling circuits with varying recirculating loads has
been presented. This methodology was supported by a campaign of experimental measurements of
hydrocyclone operation at varying mass splits. Further, integration of other ball mill modelling
constraints, such as residence time and SSE, were also incorporated. These additional tools were
integrated iteratively with JKSimMet® modelling. The result was a digital tool capable of estimating
the likely performance of closed-circuit overflow ball milling upgrades with increased classification
circuit capacity and improved insight into when constraints would be reached. This methodology
was demonstrated through application to a case study site. This showed that the method can be
used to assist in identifying where additional slurry pumping and hydrocyclone capacity can improve
financial performance. For this case study the tool estimated an $8M Australian dollar per annum
benefit (additional revenue less additional operating cost) could be realised by doubling the pump
and hydrocyclone capacity.

Acknowledgements
The authors would like to acknowledge the team at the Weir® Technical Centre, Melbourne, for
completion of the extensive experimental survey work conducted on the hydrocyclones. The authors
would also like to acknowledge the work of Echo Wang, Process Engineer at Weir® Minerals for her
assistance in analysis of experimental results.

References
BALLANTYNE, G. R., PEUKERT, W. & POWELL, M. S. 2015. Size specific energy (SSE)-Energy required
to generate minus 75 micron material. International Journal of Mineral Processing, 136, 2-6.
JANKOVIC, A. & VALERY, W. 2013. Closed circuit ball mill – Basics revisited. Minerals Engineering, 43,
148-153.
LANE, K. F. 1988. The economic definition of ore : cut-off grades in theory and practice, Mining
Journal Books.
MCIVOR, R. 2014. Plant performance improvements: using grinding circuit “classification system
effciency”. Minerals Engineering Magazine.
MORRELL, S. 2016. Modelling the influence on power draw of the slurry phase in Autogenous (AG),
Semi-autogenous (SAG) and ball mills. Minerals Engineering, 89, 148-156.
NAPIER-MUNN, T. J., MORRELL, S., MORRISON, R. D. & KOJOVIC, T. 1996. Mineral comminution
circuits : their operation and optimisation, Indooroopilly Brisbane, Julius Kruttschnitt Mineral
Research Centre.
SHERMAN, M. The bonds that can't be broken. SAG Conference, 2015 Vancouver.
SHI, F. 2016. An overfilling indicator for wet overflow ball mills. Minerals Engineering, 95, 146-154.
WARMAN 2000. Warman Slurry Pumping Handbook, Warman International Ltd.
WEIR. 2018. Technical Bulletin 32 Total Ownership Cost Model for Slurry Pumps.