Chemical Engineering Design Project - Potash Production - The Design of a Rod Mill
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Transcript of Chemical Engineering Design Project - Potash Production - The Design of a Rod Mill
Rod Mill Design For Potash Processing by Lincoln Smith is licensed under
a Creative Commons Attribution 3.0 Unported License.
The design of a rod mill for a potash processing plant at Boulby, UK is described, including
operating principals, sizings and other equipment design considerations. The design process
is gone through in a stepwise manner in order to make the design process clear. A single mill
with internal diameter of 3.2 metres is chosen for the process.
Rod Mill design for
potash processing
Lincoln Smith
935495
UNIVERSITY OF BIRMINGHAM
Chemical Engineering Design Project
Contents
1. Size Reduction .......................................................................................................................................................... 4
2. Description ................................................................................................................................................................ 5
2.1 Rod Mills ........................................................................................................................................................... 5
2.1.1 Rod Mills vs Ball Mills ........................................................................................................................ 5
2.1.2 Operating principle ............................................................................................................................. 5
2.1.3 Design Considerations ....................................................................................................................... 6
2.2 Rod Mill Components .................................................................................................................................. 7
2.3 Discharge Arrangement .............................................................................................................................. 9
3 Particle Sizes .......................................................................................................................................................... 10
3.1 Size Distributions ....................................................................................................................................... 10
3.2 Mean Diameters .......................................................................................................................................... 11
4 Mill Design .............................................................................................................................................................. 12
4.1 Mill Sizing ...................................................................................................................................................... 12
4.1.1 Mill Sizing by Power Requirement ............................................................................................ 12
4.1.2 Mill Power Correction Factors .................................................................................................... 13
4.1.3 Mill Sizing by Residence Time ..................................................................................................... 13
4.2 Number of Lifters ....................................................................................................................................... 13
4.3 Rod Mill Charge ........................................................................................................................................... 13
4.3.1 Rod Volume ......................................................................................................................................... 13
4.3.2 Rod Size ................................................................................................................................................ 14
4.3.3 Number of Rods ................................................................................................................................. 15
4.4 Speed ............................................................................................................................................................... 15
4.4.1 Critical Speed ...................................................................................................................................... 15
4.4.2 Operating Mill Speed ....................................................................................................................... 16
5 Auxiliary Equipment ........................................................................................................................................... 16
5.1 Motor Size ...................................................................................................................................................... 16
5.2 Piping .............................................................................................................................................................. 17
5.3 Hydrocyclones ............................................................................................................................................. 17
6 Control Strategy .................................................................................................................................................... 18
6.1 P & ID Explanation ..................................................................................................................................... 18
6.2 Startup / Shutdown ................................................................................................................................... 19
7 Control Implementation .................................................................................................................................... 19
7.1 Ball Mill Level Control .............................................................................................................................. 20
7.2 Rotation Speed Control ............................................................................................................................ 20
Page 3 of 44
7.3 Residence Time ........................................................................................................................................... 21
7.4 Operator Interaction ................................................................................................................................. 21
8 Hazards .................................................................................................................................................................... 21
8.1 Noise ................................................................................................................................................................ 21
8.2 Dust Exposure .............................................................................................................................................. 21
8.3 Static Electricity .......................................................................................................................................... 21
9 Materials of Construction ................................................................................................................................. 22
9.1 Linings............................................................................................................................................................. 22
9.2 Pipes ................................................................................................................................................................ 23
10 Costs ..................................................................................................................................................................... 24
10.1 Fixed Costs .................................................................................................................................................... 24
10.2 Operating Costs ........................................................................................................................................... 25
10.2.1 Utility Costs ......................................................................................................................................... 25
10.2.2 Maintenance Costs ........................................................................................................................... 25
11 Conclusion .......................................................................................................................................................... 27
12 References .......................................................................................................................................................... 28
13 Appendicies ....................................................................................................................................................... 31
Appendix A - Mill Process Block Flow Diagram ........................................................................................... 31
Appendix B – Size Reduction Process P & ID ................................................................................................ 32
Appendix C - Particle Size Distributions ......................................................................................................... 33
Appendix D - Visualising Particle Size Distributions ................................................................................. 34
Appendix E – Calculating the crusher power requirement ..................................................................... 34
Appendix F - Energy Requirement / tonne .................................................................................................... 35
Appendix G – Correction Factors ....................................................................................................................... 35
Appendix H – Residence Time and mill Volume .......................................................................................... 36
Appendix I - Using Solver to calculate the mill dimensions .................................................................... 37
Appendix J - Number of Mill Lifters ................................................................................................................... 37
Appendix K – Rod Diameters ............................................................................................................................... 38
Appendix L - Calculating the number of rods required ............................................................................ 39
Appendix M – Motor Sizing ................................................................................................................................... 39
Appendix N - Hydrocyclone Pipe Diameter ................................................................................................... 40
Appendix O - Hydrocyclone Sizing .................................................................................................................... 41
Appendix P – Process Specification Sheet ...................................................................................................... 42
Appendix Q – Plant Wide P & ID ......................................................................................................................... 44
Appendix R – Mechanical Drawings .................................................................................................................. 44
1. Size Reduction
Size reduction is an essential part of the potash production processes. After removing sylvite
ore from the ground a series of crushing operations reduce the size of the rock. The milling
stage (or fines crushing stage) forms the final stage of the size reduction process. The breakup
of the rock liberates the entrained minerals as well as impurities (gangue). This allows
separation in later stages of the process (Gupta, et al, 2006).
Figure 1 – Initial Size reduction process (from initial report)
The majority of the potash process uses saturated brine as a transport fluid. Particles are
transported through the process as a suspension or slurry. Hydrocyclones classify the mill
output by particle size into a fines and coarse stream. These are treated separately in the rest of
the process, forming different products, used for different applications. The mining operation
causes the formation of potash fines, which are more difficult to process than particles with
larger diameters (GoodQuarry, 2011).
In our process, coarse KCl particles are separated by flotation, which are then dewatered in
solid bowl centrifuges and dried in fluidised bed dryers. Some potash is upgraded in size by a
compaction process for use in particular fertiliser products. The small particle sizes in the fines
stream make them unsuitable for direct use as fertilisers. After flotation using a suitable
flotation agent, the fines stream requires heating. A subsequent selective crystallisation process
crystallises potash out of the resulting solution. The stream is then dewatered and dried by
centrifuges and fluidised bed dryers. Suspended particles from waste streams are separated
using centrifuges, and the liquid stream saturated with potash and halite is recycled back into
the process, maximising recovery.
Page 5 of 44
The flotation, centrifugation and particle fluidisation drying stages mentioned, are all dependant
on the particle size of the ore. Particle size is a crucial parameter of the effectiveness of
downstream processes, and size reduction is crucial in ensuring a high quality product.
2. Description
2.1 Rod Mills
2.1.1 Rod Mills vs Ball Mills
Tumbling type mills are used for the grinding of potash rock (Couper, et al, 2010a). Rod mills are
used at the existing site at Boulby (Holyfield, et al, 1998).
The balls in a ball mill have a greater surface area to weight than rod mills, and therefore are
more suited to fine grinding (Couper, et al, 2010a). Extreme fine particles are not easily
separated by froth flotation; therefore a rod mill is more suited to the process.
Figure 2 – Cut away diagram of a typical rod mill
(Metso, 2010)
2.1.2 Operating principle
A rod mill is used for the grinding of rock from particle sizes as large as 25mm to between 2 –
0.1 mm mean particle size (Practical Action, 2010). Tumbling mills use the action of falling
masses to grind particles to appropriate sizes. In a rod mill, rods are used, typically filled to 45%
of the mill volume (Couper, et al, 2010b). These are lifted by the rotating action of the mill before
cascading downwards and causing particle breakup. There are three principal mechanisms for
particle breakup in a ball mill:
Impact breakup, due to the fall of the particles onto the rods
Attrition breakup
Page 6 of 44
Abrasion breakup
(Practical Action, 2010)
2.1.3 Design Considerations
To withstand the abrasive forces of the rock and severe impacts, as it is grinds rock to smaller
sizes, the lining of the mill must be carefully selected. For this reason, they are commonly
manufactured from manganese or chrome-molybdenum steels (Metso, 2010), however other
linings are available.
The speed of rotation is a function of the diameter. They commonly spin between 20 and 30 rpm.
The motor used to drive the mill commonly spins at 150 – 250 rpm (ie. low speed motors are
used to drive the mill) (Kanda, 2007).
To avoid the problems associated with dust formation, saturated brine solution is added.
Practical Action identifies dust formation and subsequent inhalation as the “most serious long
term threat from minerals processing.” (Practical Action, 2010) The sylvite ore at the Boulby
mine contains 38 potash and 51% common rock salt and 11% of other insoluble materials
which must be removed in the purification process (Rowson , 2010), or 38% KCl, 50% NaCl, 12%
insoluble’s (Holyfield, 1995). These can be liberated once the particle sizes are smaller than
1mm (Holyfield, 1995). The feed of sylvite ore slurry is controlled as the mill must be contain the
correct level of slurry for effective & efficient grinding to occur.
Classifiers are used to select over, and undersized particles so that they can either be recycled
back into the mill or passed into different parts of the process. Hydrocyclones are most suitable
for classification (over screens and sieves) due their history of use in size reduction circuits.
Their ability to accept particle sizes between 40 and 400 microns makes them particularly
suited to classifying the product from a rod mill, which produces particle sizes between 10 and
200 microns. The mill needs to be carefully chosen, as it is factors such as its size and operation
conditions which ultimately controls the particle sizes of the potash ore.
Page 7 of 44
2.2 Rod Mill Components
Table 1 and Figure 3 show and describe the main components of a rod mill.
Figure 3
No. Part Description
1 Bearing Supports the load of the rotating section and allows it to turn freely.
2 Mill shell Section where grinding takes place. It takes the form or a cylindrical steel shell with a replaceable inner lining.
Man-holes on the body are beneficial for cleaning the steel balls, replacing the liners and repairing the machine.
The thickness is approximately 1/100th of the length.
3 Drive Transfers energy from the motor and gearbox, into the rotational energy of the ball mill. Two principal ways exist to do this:
Rubber rollers - rotate around the outside of the entire length of the mill shell
Gear and pinion – large gear on one end of the mill is driven by a pinion, connected to the gearbox.
To maximize lifetime, this should be reversible so both flanks of the gear teeth can be used. (FLSmidth Minerals, 2008)
4 Motor Transfers electrical energy into kinetic energy to power
1
2 3
4 5 6
7
8
9
10
11
Page 8 of 44
the mill.
The large power requirements of the mills require high power, reliable, efficient, low speed, motors. AC synchronous motors fit this requirement. Where the power requirements are high, two motors and drive systems may need to be used. (GE Motors, 2008)
5 Clutch & Gearbox Allows the motor and gearbox to be engaged and disengaged with the drive system.
Air clutch systems are commonly used. (GE Motors, 2008) Ball mills require a high starting torque to accelerate their contents. (Agrawal, 2001) The clutch is required to deliver the power at the correct rate such that it does not damage the motor.
6 Lubrication System To protect the bearing and drive mechanism, allow it to move freely, minimising wear and damage.
Lubrication can be supplied in three ways
Oil mist system Grease Circulating oil
If lubrication to the bearings stops working, the mill must shut down to prevent it from damage.
7 Inlet To control the feed into the mill shell.
8 Discharge Outlet To control the outlet from the mill, and retain any material requiring further grinding.
9 Lining Helps with the abrasion of the potash rock, and protects the mill shell from wear. Linings need to be replaced regularly due to erosion of the material. (see section 3.5)
10 Charge Rod charge, cause particle break-up by cascading down the sides of the mill. Rods have a practical maximum length of 6 metres. Longer rods bend causing undesirable tangling of the charge (Gupta, et al, 2006)
11 Lifters Part of the lining, used to lift the mill charge and prevent slip on the walls of the mill. There are a variety of lifter designs available.
Table 1
(Zoneding, 2009)
Page 9 of 44
2.3 Discharge Arrangement
There are several different arrangements for discharging the milled ore slurry from the mill shell. The discharge arrangement must allow the grinding media to be retained within the mill, while discharging ground potash ore particles. Figure 4 shows the possible arrangements: trunnion overflow discharge, diaphragm or grate discharge, end peripheral discharge, center peripheral discharge. Trunnion overflow discharge and diaphragm or grate discharge are the most popular (Metso, 2010). In the mill in our potash production process, the simplicity of the trunnion overflow discharge mill makes it the most suitable.
In grate or diaphragm discharge, a slotted full diameter grate with a lifters, convey milled from the bottom of the mill, beyond the diaphragm to the discharge opening. In overflow discharge a gradient forms between the feed inlet and discharge openings. A reverse rotating screw retains larger particles and the rod charge inside the mill. (Metso Minerals - Ball mill, 2010)
Trunnion Overflow Discharge
Diaphram / Grate Discharge
Center Peripheral Discharge
End Peripheral Discharge
Feed
Discharge
Feed
Feed
Feed
Discharge
Discharge
Feed
Discharge
Figure 4
Adapted from: (Metso Minerals, 2010, Rod Mills) & (Gupta et al, 2006)
Page 10 of 44
3 Particle Sizes
It is important to investigate the particle sizes because this helps define the reduction ratios
required for the design. The reduction ratio is the ratio of the initial particle size to final particle
size (Zhang, 1998), and needs to be considered when designing the mill. The run of mine ore is
not delivered to the plant as a mono-modal distribution. Instead the size of the ore takes the
form of a size distribution. The particle sizes of the feed ore and output products are given in the
design brief.
3.1 Size Distributions
Histograms shown in figures 5 and 6 represent the particle size distributions shown in appendix
C.
Figure 5 – Run of mine ore particle size histogram
Figure 6 – Mill output size histogram
The crushing & milling operations need to take the input distribution (figure 5) and transform it
into the output distribution (figure 6). The output feed consists of fine and course streams.
These data has been averaged, assuming 15% fines and 85% course, to obtain a single mill
output size distribution for use in design calculations.
Distribution data is given as mesh passing sizes (the proportion of the feed passes through
different sizes of classification screen.) A maximum particle size is assumed.
Run of mine ore 50mm (50000 μm)
Mill output 2mm (2000 μm)
Table 2 – Assumed Maximum Particle Sizes
Tumbling mills accept feeds with maximum sizes not greater than 25mm. (Gupta, 2006) The
purpose of the primary gyratory crusher is to reduce the particle size to below 2500 μm.
There are two methods which could be used to determine the distribution of the mill input.
Assume a constant reduction ratio and reduce all particle sizes by this amount.
-0.010%
0.000%
0.010%
0.020%
0.030%
0.040%
0.050%
0 10000 20000 30000 40000 50000
frac
tio
n /
μm
Size / microns -0.05%
0.00%
0.05%
0.10%
0.15%
0.20%
0 500 1000 1500 2000
Frac
tio
n /
Mic
ron
Particle Size / Microns
Page 11 of 44
Assume screening takes place, and only particles greater that 25mm are crushed in the
gyratory crusher.
A screening process before the gyratory crusher is more suitable. This method ensures energy is
not wasted by milling particles too small as the rod mill input distribution would have a smaller
standard deviation than the run of mine ore.
Figure 7 – Rod Mill Input Size Distribution Histogram
The feed is screened at 2350 μm. Particle sizes larger than this are reduced. Gyratory crushers
have a reduction ratio of between 3:1 and 10:1. The geometric mean of these numbers, 5.5:1, is
used. This gives the size distribution histogram given in figure 7 as the feed input to the mill.
Alternative ways of showing these particle size distributions are given in appendix D.
3.2 Mean Diameters
There are several important average sizes which are important for the mill design:
Sauter mean diameter
d80 passing diameter
d50 passing diameter
Table 3 – Mean Particle Sizes
The d80 is found from reading from the particle cumulative distribution. The sauter mean
diameter is calculated as follows:
0.00%
0.02%
0.04%
0.06%
0.08%
0.10%
0.12%
0.14%
0 500 1000 1500 2000 2500
Frac
tio
n /
mic
ron
Size / microns
Particle Diameters (given in microns)
Run of mine ore Mill Input Mill Output
d32 7473 324 222
d80 35500 1380 620
Page 12 of 44
Where f is the fraction of particles of a particular particle diameter, d.
This diameter was used to calculate the reduction ratio needed in the mill.
From these calculations, a reduction ratio of 1.46 : 1 is required to mill the ore to the desired
size.
4 Mill Design
4.1 Mill Sizing
4.1.1 Mill Sizing by Power Requirement
The size of the crusher is essentially determined by the power required for the crushing process.
Bond’s Law determines the energy required for grinding.
Equation 1
(Holdich, 2002) (Kanda, 2007)
Where :
Wi = Material Work Index
do = d80 diameter of material entering the mill
di = d80 required diameter of material leaving the mill.
Appendix E shows how this equation is used to calculate the design power requirement of the
crusher of 535kW. Once a safety factor of 10% has been applied, the design power is 589 kW.
This is not consistent with Cohen, 2005, who suggests that 10 – 20 kWh per tonne is required for
grinding. A design power of 589 kW represents an energy requirement of 1.15 kWh / kg (See
Appendix F). The soft nature of the potash rock makes these low energy requirements a
reflection of the reality of the situation.
Ideally, the largest and most efficient crushers should be used to keep costs low. Large diameter
crushers have very high starting torque and hence the motors require large starting currents to
start them moving. (Agrawal, 2001) For this reason, multiple trains of crushers should be
considered.
A single crusher, with a power rating of 630 kW could be used, or two separate rod mill trains,
each with a power rating of 380 kW (MegaIndustry ,2011). The capacities of the mills are
determined by the residence time of the particles in the mill. Two mills might allow room for
expansion in capacity, however for simplicity of design, one mill will be chosen.
This power of mill has an internal diameter of 3.2m and a length of 3.6 metres. For the purposes
of my design, this mill will be chosen.
A sensitivity analysis of the power requirement to work index identifies that the power
requirement is a linear function of the potash ore work index. Different sources quote different
values for the work index, and the work index of the mine ore is likely to vary as different
Page 13 of 44
deposits are found in the mine. The linear relationship means that as long as suitable power
adjustment factors are applied, as above, the rod mill should be able to handle changes in
hardness of rock as required.
4.1.2 Mill Power Correction Factors
The mill power calculated in section 4.1.1, calculates power requirements from the original mill
used to derive this empirical equation. Correction factors can be applied to the mill power, using
the mill dimensions selected. Appendix G shows that the total correction factor which needs to
be applied is 2.2. A simple method of adjusting the mill size for the correction factor calculated
is to double the number of mills.
4.1.3 Mill Sizing by Residence Time
An alternative method of sizing the mill, involves discovering the residence time, the average
time a particle spends in the mill, and using the known volumetric flow rate to calculate the size.
The residence time in a rod mill can be measured using a radioactive tracer. A study on a ball
mill in Chili by Yianatos with dimentions of 3.05m diameter by 4.24m, observed the mean
residence time to be 108 seconds. This mill has a volume of 30.8 m3 (Yianatos, 2005). The
volume of the mill selected above has a total volume of 28.95m3; therefore a residence time of
108 seconds is likely to be a good order of magnitude estimate for the residence time in the
selected mill.
Appendix H shows how a residence time of 71 seconds has been calculated for the selected mill.
Conversely, the mill size can be calculated assuming a residence time of 108 seconds. This gives
a mill volume of 45m3.
A rule of thumb for the ratio of length to diameter in a rod mill is that the length is 1.5 times the
diameter (Couper et al, 2010b). Using Excel’s Solver, as shown in appendix I shows that the mill
would have a diameter of 3.4 m and a length of 5.1 m.
4.2 Number of Lifters
The number of lifters used to raise the balls in the ball mill is given by Gupta, et al, 2010.
Equation 2
Where D is the mill diameter.
The calculation in appendix J, shows that 21 lifters are required in the ball mill and these will be
48 cm apart. The length of these lifters must be greater than half the radius of the balls to allow
them to be lifted above the horizontal.
4.3 Rod Mill Charge
4.3.1 Rod Volume
The rods in a rod mill usually occupy 45% of the internal volume of the mill (Gupta, et al, 2006).
The mill is filled with rock and the action of the mill charge rods cause particle break up. Over
Page 14 of 44
filling the ball mill can cause a cushioning effect which absorbs the impact of the rods. Under
filling causes excessive rod-to-rod contact, slowing the breakage rate.
Ideally, the rods should sit in parallel alignment. In practice, accumulation of particles near the
feed causes the rod charge to become mal-aligned, as shown in figure 6. This is actually an
advantage because this spacing at the feed end preferentially grinds larger particles, resulting in
a narrow size range. (Couper, et al, 2010a) The density of the slurry (solid concentration) affects
the rod charge and must be carefully controlled (Gupta, et al, 2006).
Slurry
Rods
Feed
Discharge
Rotary actionof mill
Greater wear of rods here
Figure 8 – Alignment of rods in the mill
4.3.2 Rod Size
The rods in the mill are 152 mm shorter than the length of the mill (Gupta, et al, 2006). For the
mill length of 3.6 meters, the rods should be 3.448 m long. This allows room for the rods to fall
in the mill, whilst remaining parallel to other rods.
The initial rod diameter is related to the diameter of the mill by equation 2.
Equation 3
Where:
F80 = d80 = feed 80% passing diameter
D = inside diameter of the mill (2.2m)
Wi = work index (~8 kWh / tonne for potash ore)
= solids density
= fraction of the critical speed
(Gupta, et al, 2006)
Mill diameters vary between 1.6 m and 6.6m (FLSmidth, 2011). Rod mills are often bought ‘off
the shelf’ and as such come in fixed sizes. The rod charge is also available in fixed diameters,
bought off-the-shelf. Typical rod diameters vary between 25 mm and 150 mm (Couper, et al,
2010). A range of rod diameters is often chosen, to allow smaller rods to fill the voids between
larger rods as shown in figure 11, increasing the mill efficiency.
Page 15 of 44
Analysis of this empirical equation found in academic literature has found that it does not give
mill or rod diameters which are used in practice or consistent with sources in the literature
which suggest rod diameters sizes should be between 25 and 150 mm, as shown in appendix K.
A more suitable method is to leave the rod sizing to the manufacturer, who will have more
experience with rod selection.
75 mm rods
25 mm rods (filling voids)
Rotary action of rod mill
Figure 9 – Varying rod diameters in a rod mill
The RAEng statement of ethical principles state that engineers should “perform services only in
areas of current competence.” (RAEng, 2009) Accurate rod sizing is outside my level of current
competence and should be left to another engineer. This being said, the rods could be assumed
to lie in the size range given above, and rod sizes of 25mm and 75mm could be used due to the
relative soft nature of the potash ore.
4.3.3 Number of Rods
The volume of the mill is 28.9 m3. A 45% rod mill charge volume is assumed; therefore the rods
will occupy 13 m3. The packing of the rods is not 100% efficient, and voids will form in between
the rods. For straight, cylindrical rods, packing can be assumed to be 75 – 90% efficient. Based
on these assumptions the volume occupied by the rods will be between 9.8 and 11.7 m3. This
calculation is shown in Appendix L
Based on the mill volume, a suitable number of rods for the mill is 700. The mass of this rod
charge will be 82 tonnes. This is approximately the weight of the rest of the mill (WeirMinerals,
2007).
4.4 Speed
4.4.1 Critical Speed
The critical speed is the speed at which the rotational centrifugal force overcomes the gravity
force acting on the balls and mill charge, causing the rods to stick to the outside of the mill wall
rather than cascading. Grinding action is reduced or stopped (Gupta, et al, 2006).
The critical speed of a ball mill is given by an empirical equation (equation 3).
Page 16 of 44
Figure 10
For a mill diameter of 3.2 metres, the critical speed is 24 rpm. As the mill diameter decreases,
the critical speed increases and vice versa.
Figure 11
4.4.2 Operating Mill Speed
A rule of thumb suggests that rod mills should operate at 50 – 65% of the critical speed. This is
between 12 and 16 rpm.
5 Auxiliary Equipment
5.1 Motor Size
An AC synchronous motor will be used to deliver power to the mill. During normal operation,
the motor is required overcome the frictional forces in the bearings. The motor should be sized
for the maximum power draw required rather than the mill power requirement of 630 kW.
Maximum power will be drawn when the motor is starting up. To size a motor, the torque and
rotational speed of the motor need to be known (Oriental Motor U.S.A. Corp, 2000). The mill
torque is related to the inertia of the mill (I) by equation 4.
Equation 4
Where: Torque
time (seconds)
Angular momentum vector
0
5
10
15
20
25
30
35
40
45
1.2 1.8 2.4 3 3.6
Cri
tica
l Sp
ee
d /
rp
m
Mill Diameter / m
Variation of Critical Speed with Mill Diameter
Page 17 of 44
The angular momentum vector is a function of the inertial forces on the mill and the rotational
speed (angular velocity) as in equation 5
Equation 5
The inertia can be calculated by equation 6. The inertia is a function of mass of material at the
edge of the mill (M) and the distance from the centre.
Equation 6
The mill motor should be sized to operate up to the critical speed of the mill. This is 24 rpm. At
this speed, maximum power is required. At the critical speed, the rods will be pressed against
the exterior of the mill. The radius from the centre to the rods is required to find the inertia of
the rotating mill. Appendix M shows the calculation steps showing how a motor size of 50 000
kW is required.
5.2 Piping
Slurry must be pumped to hydrocyclones at a velocity of 2 m s-1 to 3 m s-1, to prevent particles
from settling. Higher than this and excessive wear occurs (Arterburn, 2010). This is the velocity
which the pump must achieve. The internal pipe diameter of the pipe to the hydrocyclone can be
specified using this information.
A pipe with internal diameter of between 6 and 7 cm will be suitable for providing the required
flow rate. This has been calculated by knowing the required flow rate, as well as an empirical
pipe sizing equation given in chapter 5.5 of Coulson & Richardson (Sinnott, 2009c) (see
appendix N). As long as the internal diameter lies within this range, the specific pipe can be
chosen from pipe manufacturer data sheets.
5.3 Hydrocyclones
Hydrocyclones classify the stream into fines and coarse according to the specific weight of the
particles .They require a solids concentration of 30% by mass for efficient operation without
increasing operation pressures (Abulnaga, 2002). The most important slurry property for
hydrocyclone separation is the volumetric slurry density.
The mass balance for the process section is shown in table 4. Only the total flow rates are
shown as this section of the process only involves particle sizes and not compositions.
Flow-Rate Tonnes / day Tonnes / hour
Ore Input 12217 509
Saturated Brine added 12217 509
Total Mill Throughput 24434 1018
Coarse 22789 865
Fines 3665 153
Table 4
The solids concentration by mass is 50%, and is 35% by volume.
Page 18 of 44
The hydrocyclone can be sized according to the method described by Arterburn. The
calculations are shown in appendix O and the results shown in table 5.
Table 5
Hydrocyclone Internal Diameter 0.35 m
Number of Hydrocyclone Units 5
Area of Inlet
Length of Vortex Finder 0.12 m
Length of cylindrical Section 0.35 m
Minimum Orifice Size at apex 0.125 m
Cone Angle 13o
Height of cone 0.76 m
Image from (Sinnott, 2009)
6 Control Strategy
6.1 P & ID Explanation
The P & ID for the crushing and milling process is shown in appendix B. This is a working
document and will need to be adapted as the plant design progresses. It has been adapted from
the block flow diagram in appendix A, which shows major equipment and processes needed to
transport materials. This was used for completing hazard study 2.
A conveyor is used to transport the ore from the mine to the primary gyratory crusher. This
passes a screen to ensure large material does not enter the ball mill. A tank is used to mix the
particulate solids and liquid streams. To ensure the correct amount of saturated brine is added,
the flow of solids must be measured from the ore and recycle streams.
The resulting slurry from the mixing tank is fed into the ball mill. Two methods are available to
do this:
A centrifugal pump
Feed under gravity
Minimising the number of components keeps the design simple, less expensive, and makes the
design intrinsically safer. These principles underpin my mill design. Therefore the slurry should
be fed under gravity.
The level of the slurry inside the ball mill is controlled by varying the input and output flow
rates. The speed of the motor is maintained constant to ensure optimum operation. After
120
350
350
760
Page 19 of 44
scrubbing, three hydrocyclones remove separate fines from coarse streams. The low reduction
ratio of the ball mill and presence of a recycle streams from downstream process, makes the
mill suitable to operate in an open loop system; that is one without recycle of coarse particles.
The most suitable actuated valve for all pipelines is a Globe valve, because they allow accurate
control of flow rate of liquid streams (Sinnott et al, 2009a).
The attrition scrubbing operation removes insoluble slimes, allowing them to settle on the
bottom of the tank for removal.
6.2 Startup / Shutdown
The large starting torques required to start the motor, mean it will be easier to start the mill
when empty of slurry. Operating the mill when the slurry is not present could cause excessive
wear damage to mill components, therefore the mill will be rotated at a speed at which the rods
do not cascade, but simply rotate in the mill. This is likely to be between 10 – 30% of the critical
speed, or 3 – 7 rpm.
Once at this speed, slurry will be discharged from the storage vessel and into the mill. As this
happens the mill speed will be increased until it reaches its operating speed of between 12 and
16 rpm. Table 6 illustrates these steps.
Start-up Procedure
1 Close all valves
2 Start primary crushing circuit
3 Allow brine storage tank to fill
Start mill motor - allow to reach 10 - 30% of critical speed
4 Open mill inlet valve
5 Wait until the mill reaches 45% capacity
6 Open outlet valve and commence automatic control system
Start automatic motor speed adjustment control
Table 6
In the event of emergency process shutdown, the flow to the mill needs to be stopped and the
rotation of the mill needs to be stopped. This is achieved by closing the inlet valve, and cutting
the power to the motor. The inertial forces of the motor is likely to keep it spinning for a
considerable amount of time, therefore it is recommended to use the AC synchronous motor as
a generator, allowing it to act as a brake on the mill.
For normal shutdown operations, the same procedure applies. Process downstream of the mill,
such as scrubbing and hycrocyclone separation can be shut down after the flow to the mill is
shut down. Downstream flows are dependent on the overflow from the mill therefore shutting
down upstream also shuts down downstream classification operations.
7 Control Implementation
Page 20 of 44
An open loop system, without recycle is proposed for the mill. This is for a number of reasons:
Upstream crushing processes are screened.
Downstream flotation separation processes lack an absolute dependence on particle
size, instead simply liberated particles with correct surface chemistry
The bottom product from the coarse flotation circuit is put through an additional mill to
reduce the particle size to ensure all material is liberated.
To design the control strategy for the unit operation, the following need to be considered:
What needs to be controlled?
How and where is it measured?
What is the measured value being compared to?
The mill is responsible for reducing the size of the particles, enabling liberation of the minerals
by downstream processes. Ultimately it is the particle size of the output which needs to be
controlled. In practice this particle size takes the form of a distribution as shown in figure 5.
Recycle streams make off-line control unnecessary for this section of the potash process and a
fully on-line control system is proposed.
A number of variables affects the particle size output of the ball mill:
Controlled Variables
Mill motor speed (as a fraction of the critical speed)
Input flow rate
Uncontrolled Variables
Actual diameter of the milling rods (will be less than initial diameter due to wear)
Number of rods in the mill
Residence time inside the mill
7.1 Ball Mill Level Control
It is difficult to measure the level inside the ball mill as the contents are always rotating. The
correct level in the mill due will be maintained due to the overflow outlet. An appropriate
control solution is to use a negative feedback control loop to control the input to the mill, and
measure the tank output to ensure flow rate into equals the flow rate out of the ball mill.
The flow rate of the stream can be measured using a pressure differential based flow meter such
as an orifice plate or a venturi flow meter. An orifice plate flow meter will be more suitable
because of their reduced cost and size compared to venturi flow meters (Yoder, 1998). This flow
sensor is connected to valve V-3 on the P & ID in appendix B.
7.2 Rotation Speed Control
The inertial forces of the ball mill make changing rotational speed highly energy intensive. A
better control strategy for ball mill speed is to monitor the speed of rotation. The rotation speed
may vary with constant motor power output due to changes of the mill charge, flow rates and
Page 21 of 44
slurry densities. Therefore the rotational speed of the mill should be measured and power
delivered to the motor to varied, in order to keep the rotation speed constant.
7.3 Residence Time
The residence time of the mill is a property of the mill itself, the main parameters being the
distance from inlet to outlet (mill length) as well as the slurry flow rate (higher flow rates will
decrease the residence time of a particle in the mill.)
7.4 Operator Interaction
A distributed control system is used to control the plant. This is inherently safe as it minimises
operator control and responsibility. Manual valves add extra complexity to the process, and add
extra plant items with the potential to go wrong. The globe valves chosen have the ability to be
opened or closed manually if required. Operators will need to evaluate sensor readings respond
by making any adjustments to set points. They have responsibility to adjust set points to ensure
the process is operating efficiently and economically as well as responding appropriately to any
fluctuations in the potash price. They have the responsibility to evaluate the mill wear, and
schedule periods of plant maintenance.
8 Hazards
Hazard study 2 identified several important design considerations. The most significant
hazardous events are noise from the mill, electric fires caused by static charge build up, and
chronic exposure to sylvite dust.
8.1 Noise
An exclusion zone will be implemented around the rod mill. Rod mills can produce noise as loud
as 100 decibels (WeirMinerals, 2007). For this reason a 5 metre exclusion zone around the
equipment will be used when in operation. The exclusion zone will also prevent people from
accessing the rotating parts when in operation.
Mill linings will be chosen which provide a noise damping action.
8.2 Dust Exposure
The Control of Substances Hazardous to Health (COSHH) regulations apply if personal
exposures of sylvite dust exceed 10 mg m-3
eight-hour TWA (total inhalable dust) (HSE, 1998)
The eight-hour TWA limit is a time weighted average (TWA) whereby exposures in a 24 hour
period are treated as a single uniform exposure for 8 hours. (HSE, 2004). Exposure can cause
possible reduced lung function. All dry processes will be completely enclosed. This includes the
conveyors which transport material into the mixing tank, E-5 on the P & ID in Appendix B.
8.3 Static Electricity
Page 22 of 44
Static electricity is generated by the moving parts of the rod mill, as well as by flowing liquids.
Employees working around the ball mill can also be sources of static electricity. A copper wire
connecting the part of the machine where static charge builds up to a water pipe will prevent
the build-up of static charge. However, the mill shell rotates and is insulated by the lubrication
fluid around the bearings making grounding more difficult.
A partial solution to this problem is to humidify the air surrounding the rod mill, allowing
charges to leak off the mill. This would help reduce the risk, as well as providing a better
working environment for operators. (Paul O. Abbe, 2008)
A humidification system, as well as grounding a non-moving component of the mill such as the
motor should prevent the build-up of charge on the mill. The recommendations for controlling
undesirable static electricity laid out in BS 5958-2 should be followed. It states that “charge
separation occurs between the liquid and the internal surface of the pipe, producing
electrostatic charges on both the liquid and the pipe.” It recommends avoiding flammable
atmospheres, achieved by humidifying the air, as well as earthing pipelines and choosing
high conductivity materials of construction. (British Standards Institution, 1991)
9 Materials of Construction
9.1 Linings
An important consideration in mill design is the design of the linings. The internal components
of the mill must be able to cope with the abrasive forces of the potash rock and impact forces
from the rods. Additionally, materials must be resistant to corrosion to withstand the
environment where high concentrations of chloride ions are present. Liner lifetime must be
maximized to keep maintenance costs low, and to prevent catastrophic failure.
Two types of material are commonly used for mill liners: steels and rubbers. The advantages
and disadvantages of steels commonly used for mill linings is given in table 7.
The relative soft nature of the potash ore, means that a high chrome iron is most likely to be the
most suitable lining material if a steel lining is used.
Rubbers suitable for mill linings need to have high tensile strengths (<20MPa), be hard, and able
to be stretched 5 to 6 times its length without damage (Powell, et al, 2006) The rubbers used are
a mixture of natural and synthetic rubbers. The principal advantages of rubber linings are their
noise damping properties as well as corrosion resistance, weight and cost. Different mill
manufacturers have different rubber compositions, such as Metso’s Skega rubber lining. (Metso,
2010)
Composite linings are often used for mill linings to bring together the wear resistance and
abrasive properties of steel with the noise damping and corrosion resistance properties of
rubbers. The two separate materials are fastened together using a chemical bond and a
mechanical attachment to give a secure fastening for the life of the lining. Metal lifter bars can be
used in combination with rubber linings, such as with Metso’s Skega Poly-met lining. (Metso,
2010) (Moller, 2003)
Page 23 of 44
The high concentration of chlorine irons, makes pitting corrosion likely where steels are present
in the mill, therefore the most appropriate mill lining material a rubber one. The linings in the
mill are usually between 65 and 75 mm thick (Gupta, et al, 2006).
Advantages Disadvantages
Austenitic manganese steels (AMS)
Work hardens under stress
Is, tough and can withstand repeated impacts without fracture
Deforms with impact, making solid liners difficult to remove
Low Carbon Chrome Molybdenum Steels
Good wear characteristics Comparatively low impact resistance
High Carbon Chrome Molybdenum Steels
Good wear resistance
Good impact resistance
Nihard Iron High wear resistance
Good abrasive properties
Brittle
High Chrome Irons Very high wear resistance
Good abrasive properties
Chrome Molybdenum White Irons
Excellent wear resistance
Excellent abrasion properties
Higher cost compared to high chrome ions.
Table 7
Adapted from (Powell, et al, 2006)
In the chosen mill, the lining will be 70 mm thick rubber with high chrome iron lifter bars. This
combines the advantages of rubber linings (deforming under impact) with the hardness
advantages of steel.
9.2 Pipes
Mild steel pipelines which is commonly used for a pipeline construction material, cannot be
used to transport the slurry due to corrosion problems. Resistant materials must be used. From
the corrosion chart in Appendix B of Coulson & Richardson volume 6 (Sinnott, et al, 2009b), the
materials listed in table 8 are resistant to sea water:
Aluminium High Nickel Iron
Aluminium Bronze Platinum
Brass Silver
Copper Austenitic Ferricr Stainless Steel
Gunmetal Tantalum
High Silicon Iron Tin
Page 24 of 44
Nickel-Copper Alloys Zirconium
Table 8
A number of other factors play a part in material selection for pipelines, including formability,
tensile strength and costs. Based on prior knowledge of materials, either copper or austenitic
ferricr stainless steel should be used for pipeline construction; however a more thorough
analysis of the benefits of each would be required and checked over with pipeline
manufacturers (Sinnott, et al, 2009).
10 Costs
10.1 Fixed Costs
Equipment costs are determined by the manufacturer.
The equipment cost is essentially a function of the mill size and mill length. Where data is
available, cost estimating equations such as equation 14 given in chapter 6 of Coulson and
Richardson’s chemical engineering design can be used.
Figure 12
(Sinnott, et al, 2009).
Ce = Equipment Cost
a & b= cost constants (given in a data table)
S = Size parameter (for a rod mill this would be the diameter or volume, depending on
the data table used
N = exponent, dependant on equipment type
Matche.com, uses similar formulas to calculate costs of commonly used equipment. A rod mill
diameter of 3.2 metres would have a total cost of $1 350 000 in 2007 (Match.com, 2007).
Updating to 2011 prices using an inflation rate of 4% RPI (BBC, 2010) gives a total cost of $1.58
million , or £972 thousand (XE.com, 2011). This is likely to be a definitive estimate, and accurate
to
Page 25 of 44
Figure 13
Figure 15 shows how rod mill purchased costs vary with mill diameter. In practise not all mill
diameters are available, and accurate equipment costing must be obtained direct from
manufacturers (IChemE, 1988).
More accurate estimates may be obtained by using commercial mill cost estimating software,
such as the CostMine Equipment cost Calculator (InfoMine, 2011).
10.2 Operating Costs
The operating costs for this section can be broken down into two main sections:
Utility Costs
Maintenance Costs
10.2.1 Utility Costs
Utility costs are determined by the power draw of the motor required. The 50 000kW motor,
can be assumed to be operating at low power for most of its operation, say 40%, requiring a
power of 20 000kW.
Electricity for processing plants can cost 5 p/kWh (Rowson, 2010). Assuming operation for 324
days per year, and 24 hours per day, this gives a running cost of £24 000 per day, or £7.7million
per year.
10.2.2 Maintenance Costs
The most significant maintenance cost will be the cost of replacing the mill lining when it wears
down. The conditions of mill linings need to be monitored by evaluating the performance of the
mill as well as by visual inspection at regular intervals. It is recommended that they are replaced
every year. The rubber linings used on this mill are easier and cheaper to replace than steel
linings. Accurate cost information of liners is available direct from manufacturers, however
0
500
1000
1500
2000
2500
1.2 1.8 2.4 3 3.6
Co
st /
$ (
20
07
US
Gu
lf C
oas
t B
asis
)
Tho
usa
nd
s
Mill Diameter / m
Variation of Purchased Rod Mill cost with Mill Diameter
Page 26 of 44
could be assumed to be a fixed percentage of the total mill cost, say 10 – 40%. On this basis the
replacement liners would cost between approximately £100 thousand and £390 thousand.
This does not include the labour costs associated with replacing the mill, or the loss of output,
however this downtime can be included in the 41 days in a year the entire plant will be offline
for maintenance. On this basis, the maintenance costs can be assumed to be the geometric mean,
of approximately £280 thousand.
The total operating costs are approximately £8 million per year,
Page 27 of 44
11 Conclusion
The grinding stage of the potash production process features a single 3.6 m by 3.2 metre
diameter rod mill, capable of processing 510 tonnes of slurry per day. The mill grinds the potash
sylvite ore from an 80% passing size diameter of 1380 microns to an 80% passing size diameter
of 620 microns, allowing the entrained potash mineral to be liberated by downstream flotation
operations. The composite mill lining features 50 mm high chrome iron lifter bars with a 70
mm thick rubber lining, minimising noise in the immediate area surrounding the mill creating a
better working environment for employees.
The 50 000 kW AC synchronous motor provides effective control of mill speeds, and reliable,
smooth startup. A humidification system and grounding of the motor reduces the risk of static
charge build-up on the mill shell. The large electrical power requirement of 20MW, to drive the
motor for the rod mill makes the estimated utility costs £7.7 million per year. Additional costs
are associated with mill maintenance.
The use of ratio control accurately controls the level of slurry in the mill. The grinding system
has the benefits of a simple open loop grinding system due to screening of upstream process
streams to recycle particles larger than 2350 microns (2.3 mm). Classification and separation
into fine and coarse streams is achieved via 5 hydrocyclones, each with a diameter of 35cm.
Page 28 of 44
12 References
Abulnaga, B., 2002. Slurry Systems Handbook, Ch 7-7-3 (Hydrocyclones) McGraw-Hill, ISBN: 0-
07-137508-2, Available via Knovel
Agrawal, K., 2001. Industrial Power Engineering and Applications Handbook, P. 140, Chapter
10.5, General Problems in electric motors and their remedy, Butterworth-Heinemann, ISBN:
978-0-7506-7351-8, Available through ScienceDirect
Arterburn, R., A., 2010, The Sizing and Selection of Hydrocyclones, Accessed: 20/3/2011,
Available at: rockservices.net/83_sizing_select_cyclones.pdf
BBC Business News, 2011. UK Inflation rate rises to 4% in January, Accessed 20/3/2011,
Available at: bbc.co.uk/news/business-12462901
British Standards Institution, 1991. BS5958-2, Control of Undesirable static Electricity
Cohen, H. E. 2000. Communition, Section 2.1, Solid - Solid Separation, Introduction, Ullmann's
Encyclopedia of Industrial Chemistry, Available online via Wiley Online Library
Couper, J. R., Penney, R. W., Fair, J. R., Walas, S. M., 2010a. Chemical Process Equipment -
Selection and Design - 3rd Edition, Chapter 12, Disintegration, Agglomeration, and Size
Separation of Particle Solids, P.365 - 374, Elsevier, Online version available at:
knovel.com/web/portal/browse/display?_EXT_KNOVEL_DISPLAY_bookid=2781&VerticalID=0
Couper, J. R., Penney, R. W., Fair, J. R., Walas, S. M., 2010b. Chapter 0 - Rules of Thumb: Summary
Chemical Process Equipment - Selection and Design - 3rd Edition, Elsevier, Online version
available at:
knovel.com/web/portal/browse/display?_EXT_KNOVEL_DISPLAY_bookid=2781&VerticalID=0
FLSmidth, 2011. Rod Mills – FLSmidth Rod mills are able to grind coarser material than ball
mills, Updated: 14/1/2011, Accessed: 20/3/2011, Available at: flsmidth.com/en-
US/Products/Fertilizer+Minerals/Potash/Grinding/RodMills/RodMills
GE Energy, 2010. Motors Product Line, Accessed: 20/3/2011, Available at: www.ge-
energy.com/prod_serv/products/motors/en/downloads/GEA17491A_MotorLineCard.pdf
GE Motors, 2008. Quadramatic – Large Synchronous SAG and Ball Mill Drive Systems, Accessed:
20/3/2011, Available at: ge-
energy.com/prod_serv/products/motors/en/downloads/deam1043.pdf
GoodQuarry, 2011. Why minimise quarry waste and quarry fines?, Accessed: 20/3/2011,
Available at: goodquarry.com/article.aspx?id=50
Gupta, A., Yan, D.S., 2006. Tubular Rod Mills, Chapter 8, Mineral Processing Design and
Operation, Elsevier, ISBN: 978-0-444-51636-7, Accessed: 26/2/2011, Available online through
ScienceDirect.com at: sciencedirect.com/science/book/9780444516367
Holdich, R., 2002. Fundamentals of Particle Technology, Chapter 11, Crushing and Classification,
Loughbrough, Midland Information Technolgy and Publishing, ISBN: 0-9543881-0-0, Available
free online at: particles.org.uk
Page 29 of 44
Holyfield, G. W., Brown, D. W., 1998. Application of a filter press in the recovery of potash at
Boulby mine, Cleveland Potash Ltd & The University of Nottingham, Available online through
ScienceDirect
HSE, 1998. Health hazards from dusty cargoes during the loading and unloading of ships, HSE
Information Sheet, Accessed: 13/3/2011, Available at: hse.gov.uk/pubns/dis2.pdf
HSE, 2004. Workplace Exposure Limits - Calculation Methods, Health and Safety Executive,
Accessed: 13/3/11, Available at: hse.gov.uk/coshh/calcmethods.pdf
IChemE, 1988. A Guide to Capital Cost Estimating, 3rd Edition, IChemE, ISBN: 0-85295-220-1
InfoMine, 2011. About the mill and mine equipment cost calculator, Accessed: 20/3/11,
Available at: calc2007.costs.infomine.com/about.aspx
Kanda, Y., Kotake N., 2007. Comminution Energy and Evaluation in Fine Grinding, Chapter 12,
Handbook of Powder Technology, Yamagata University, Japan, Available online through
ScienceDirect
Matche.com, 2007, Size Reduction Cost, Accessed: 20/3/2011, Available at:
matche.com/EquipCost/SizeReduction.htm
MegaIndustry, 2011. Zhengzhou Mega Industry Co. Ltd., Rod Mill, Detailed product description
table, Accessed: 20/3/2011, Available at: megaindustry.en.alibaba.com/product/293214379-
209812633/rod_mill.html
Metso, 2010, Rod Mill, Metso Minerals, Accessed: 20/3/2011, Available at: tinyurl.com/6zj574y
Metso, 2010, Mill Linings, Mill Trommels and Trunnion Linings, Metso Minerals, Accessed:
20/3/2011, Available at: tinyurl.com/64tc4zj
Moller, J., 2003. The best of two worlds - A new concept in primary grinding wear protection,
Minerals Engineering, Volume 3, Issues 1-2, Pgs. 221 – 226, Available online through ScienceDirect.
Oriental Motor U.S.A. Corp, 2000. Motor Sizing – With such a wide variety, how do I pick the
right one?, Accessed: 20/3/2011, Available at: charysoftware.com/OM/WP-Motor-Sizing.pdf
Paul O Abbé, 2008. Ball mill Handbook, Accessed: 13/3/11, Available at:
pauloabbe.com/productLines/millingEquipment/ballMillHandbook.html
Powell, M., Smit, I, Radziszewski, P., Cleary, P., Rattray, B., Eriksson, K-G., Schaeffer, L., 2006. The
Selection and Design of Mill Liners, P. 331, Advances in Comminution
Practical Action, 2010. Mineral Processing: Milling, Available through Practical Answers,
Accessed: 20/3/2011, Available at:
practicalaction.org/practicalanswers/product_info.php?products_id=145
RAEng, 2009, Statement of Ethical Principles, Accessed: 6/3/2011, Available at:
raeng.org.uk/societygov/engineeringethics/pdf/Statement_of_Ethical_Principles.pdf
Rowson, 2010. Potash Design Brief, Available online through University of Birmingham VLE
(WebCT)
Sinnott. R., Towler, G., 2009a. Chapeter 5, Valve Seclection, Pgs. 235 - 236, Coulson &
Richardson’s Chemical Engineering Design, 5th Edition, Elsevier, ISBN: 978-0-7506-8551-1
Page 30 of 44
Sinnott. R., Towler, G., 2009b. Appendix B – Corrosion Chart, Coulson & Richardson’s Chemical
Engineering Design, 5th Edition, Elsevier, ISBN: 978-0-7506-8551-1
Sinnott. R., Towler, G., 2009c. Mechanical Design of Piping Systems, Chapter 5.5, Pg. 221,
Coulson & Richardson’s Chemical Engineering Design, 5th Edition, Elsevier, ISBN: 978-0-7506-
8551-1
WeirMinerals, 2007. Vulco – Wear Resistant Linings, Accessed: 20/3/11, Available at:
weirminerals.com/pdf/MLS%20NA0707u%20Mill%20Linings%20bro.pdf
XE.com, 2011. XE Quick Cross Rates (USD – GBP), Accessed: 20/3/2011, Available at:
www.xe.com
Yianatos, J., Bergh, N., Bucarey, R., Rodrı´guez J., Dı´az, F., 2005, The effect of fines recycling on
industrial grinding performance, Minearls Engineering, Ch. 18, Pgs. 1110 – 1115, Available via
ScienceDirect
Zhang, J., 1998. Particle Technology Study Notes, Chapter 3 - Size Reduction, University of
Newcastle Upon Tyne, Accessed: 26/2/2010, Available at:
http://lorien.ncl.ac.uk/ming/particle/cpe124p3.html
Zoneding, 2009. Products-Beneficiation Machine, Zhongding Heavy Duty Machine
Manufacturing Co. Ltd., Accessed: 26/2/2010, Available at: zd-ballmill.com/proinfo/9.html
Cover Photos:
AgroSpace, 2009. Potash Fertiliser Prices continue to go up due to increases in crop yield,
Accessed: 20/3/2011, Available at: agrospace.blogspot.com/2009/01/potash-fertilizer-prices-
continue-to-go.html
BusyTrade.com, 2011. Grinding Steel Rod, Accessed: 20/3/2011, Available at:
a452646120.en.busytrade.com/products/info/1895916/Grinding-Steel-Rod-grinding-Steel-
Bar-rod-Mill-bar-Mill-grin.html
Page 31 of 44
13 Appendicies
Appendix A - Mill Process Block Flow Diagram
Transport to tank
(Conveyor)
Flow from intermediate
crusher (crushed
particulate solids)
Mixing TankSlurry fed under
gravity
Recycled Brine
Solution
Ball Mill Grinding
Stage
Discharge through
grate / overflow
Scrubbing
Pumping to
Flotation Cells
(Coarse & Fines)
Feed Controller
Pumping to
HydrocyclonesHydrocyclones
Recycle from
Coarse
Hydrocyclone
Adapted from (Zhengyuan Powder Engineering Equipment Co. Ltd, 2010)
Page 32 of 44
Appendix B – Size Reduction Process P & ID
E-01
E-06
E-03
E-05
E-04
E-02
M
V-01
E-09
V-03
FIC
E-08
E-10
E-07
V-02
Scrubbing
FT
Run of Mine Ore
Recycled Brine
Classification
FC
FT
FC
FT
SC
ST
Liquid
Discharge
Coarse Flotation
Waste Seperation
& Disposal
Process
KCl Rich Stream
Fines Flotation
Page 33 of 44
Appendix C - Particle Size Distributions
Mill Output
Size / μm Cumulative
Per ent
2000 100%
1180 94%
850 89%
600 79%
20 60%
210 26%
100 5%
Run of Mine Ore
Size / μm Cumulative
Percent
50000 00%
32000 75%
25400 62.7%
9400 3%
4750 43%
2350 39%
1180 22%
850 17%
600 12
500 10%
425 9%
300 7%
2 %
106 3%
75 %
50 2%
30 1%
10 0%
Page 34 of 44
Appendix D - Visualising Particle Size Distributions
Figure 14 - Size Reduction Process Input Cumulative Size Distribution
Figure 15 - Mill Output Cumulative Size Distribution
Figure 16 – Rod mill input Cumulative
Size Distribution
Appendix E – Calculating the crusher power requirement
For potash, the work index is 8.88 kWh / tonne. (Couper, et al, 2010a)
Kanda, et al gives the work index of potash as 8.05 kWh / tonne.
The feed rate is 12217 kg / day, or 510 kg / hr
The power requirement for crushing is approximately
This is 535 kW.
0%
20%
40%
60%
80%
100%
0 10000 20000 30000 40000 50000
Cu
mu
lati
ve P
erc
en
tage
Particle Size / microns
0%
20%
40%
60%
80%
100%
0 500 1000 1500 2000
Cu
mu
lati
ve P
erc
en
tage
Particle Size / microns
0%
20%
40%
60%
80%
100%
0 500 1000 1500 2000 2500
Cu
mu
lati
ve P
erc
en
tage
Particle Size / microns
Page 35 of 44
To ensure the power is sufficient, a safety factor of 10% is applied.
The design power requirement is 589 kW
Appendix F - Energy Requirement / tonne
The energy required for grinding per tonne can be calculated by dividing the power
requirement (or the amount of energy used in kWh in 1 hour) by the flow rate of solids.
Flow rate of solids = 510 tonnes / hour
Energy requirement (from appendix …) = 589 kW
Energy Required per tonne =
Appendix G – Correction Factors
Factor Description Applied? – Yes / No Calculation
F1 Correction for dry grinding
No - Wet Grinding
F2 Correction for wet open circuit grinding in ball mills
No – Rod Mill
F3 Correction for mill diameter
Yes
for D > 3.81 m
Where D is the internal diameter
F4 Correction for oversize feed
No – Applied when:
F5 Correction for fineness of grind
No – Only applied when 80% of product < 75 µm. (Determined from figure 18)
F6 Correction for low reduction ratio
Yes
(section 4.3.2)
D = 3.2 m
F6 is applied when outside the following range:
Page 36 of 44
F7 Correction for low R in ball milling
No – Rod Mill
F8 Correction for feed preparation
Yes – Closed circuit crushing is used to prepare the feed
FT
Appendix H – Residence Time and mill Volume
Total Flowrate (including saturated brine) = 24434 tonnes / day = 283 kg / s
Assume a slurry density of 1500 kg m-3
Assume a 45% charge volume in the mill.
Total mil volumetric flow rate =
Volume required for liquid in mill
Mean residence time =
For a residence time of 108 seconds:
For a charge volume of 45%, Total internal mill volume =
Page 37 of 44
Appendix I - Using Solver to calculate the mill dimensions
Mill Diameter 3.4 m
Mill Length 5.1 m
Mill X-sectional Area 8.9 m2
Mill Volume 45.0 m3
Ratio Mill Length / Diameter 1.5
The following formulas were used in each respective cell:
Solver was used to set the ratio of mill length to diameter to 1.5, whilst changing the mill
diameter.
Appendix J - Number of Mill Lifters
To find the distance these lifters are apart, the circumference is divided by the number of lifters.
Page 38 of 44
Appendix K – Rod Diameters
Table … shows calculated mill diameters based on rod diameters being between 1” and 4.5”
using equation ... and the data below. Only at impractical rod diameters, does the mill diameter
fall within the acceptable range. Table … shows the reverse of this calculation, with mill
diameters varying between 1 and 4 metres to give the rod diameter.
As is shown, the calculated values do not fall within the ranges of mill and rod diameters which
are used in practice.
Table 9
Rod Diameter
mm inches Mill Diameter / m
2.5 0.1 832
6.25 0.25 21
12.5 0.5 1.3
25 1 0.08
37.5 1.5 0.02
50 2 0.005
62.5 2.5 0.002
75 3 0.001
87.5 3.5 0.0006
100 4 0.0003
112.5 4.5 0.0002
Mill Diameter / m Rod Diameter / mm
1 13.4
1.25 12.7
1.5 12.1
1.75 11.7
2 11.3
2.25 11.0
2.5 10.7
2.75 10.4
3 10.2
3.25 10.0
3.5 9.8
3.75 9.6
4 9.5
Table 10
Work Index: 8.88 kWh / tonne
Criticial Speed: 0.7
d80: 1380 μm
Potash density: 1.993 tonnes / m3
Page 39 of 44
Appendix L - Calculating the number of rods required
For the purposes of this calculation, only 75mm diameter rods will be used.
The number of rods is calculated by dividing the volume occupied by the individual rod volume:
Appendix M – Motor Sizing
The mass of material on the outside of the mill must first be found. The internal mill diameter is
known, which allows the distance from the centre axis to the mill charge to be found.
Similar calculations can be done to calculate the volume and masses of the shell and the rubber
lining, shown in table ...
Thickness Volume Dentsity Mass / Tonnes
Shell 20mm 0.76 m3 6
Lining 70mm 2.5 m3 4
Rods 300mm 10.5 m3 82
Total Average = 6655 kg m-3 92 tonnes
Table 11
Page 40 of 44
Assuming a time of 4 minutes from no rotation till full rotational speed:
The mill is powered through a gearing system. The low speed motor will spin between 150 and
250 rpm.
These motor sizes appear appropriate because the large AC synchronous motors available from
General Electric have power ratings between 750 kW and 75 000 kW. A motor with a maximum
power output of 50 000 kW is suggested for the mill (GE Motors, 2010).
Appendix N - Hydrocyclone Pipe Diameter
Method 1
This approximately 8 litres per second. For a flow-rate of 2-3 m s-1,
Upper Bound:
Lower Bound:
The pipe internal diameter must lie between 6 and 7 cm.
Method 2
From Coulson & Richardson’s Chemical Engineering Design, Volume 6 for a stainless steel pipe
with turbulent flow:
Equation 7
(Sinnott, 2009c)
Page 41 of 44
Where:
doptimum is the internal pipe diameter in mm
G is the flowrate in kg / s – 11.7 kg s-1
is the slurry density – assumed to be 1500 kg m-3.
This lies within the range given by method 1 above.
Appendix O - Hydrocyclone Sizing
Method adapted from Arterburn, 2010.
Step 1- Materials Balance on hydrocyclone
Stream Flow-rate
Input Slurry 0.28 kg / s 0.182 m3 s-1
Overflow (fines) – 15% 0.042 kg / s 0.027 m3 s-1
Underflow (coarse) – 85% 0.238 kg / s 0.155 m3 s-1
Step 2 – Calculate D80
From figure 18, in Appendix D, fines can be classified at 425 microns, as 15% of particles lie
below this size. This is the specified micron size. For an efficient separation, 98.8% of particles
should be smaller than the specified micron size, hence the multiplier is 0.54.
Step 3 – Calculating Correction Factors
Where Cv = Volumetric solids concentration = 35%
Where
Page 42 of 44
Step 4 – Calculating D50 (base)
Step 5 – Calculating Hydrocyclone Diameter
From D50 (base), Hy y ’’
Step 6 – Calculate Number of Units required
A 0.35 m diameter hydrocyclone has a flow-rate of 700 US gallons per minute (gpm) or 0.0441
m3 s-1.
Therefore 5 hydrocyclones are required to achieve the separation.
Step 7 – Calculating apex size
Total underflow per unit =
Therefore the apex size is 12.5 cm
The angle at the apex is 13o, therefore the height of the cone can be calculated.
Appendix P – Process Specification Sheet
PREP. BY
CHKD. BY
PROCESS SPECIFICATION APPROVED
SOLIDS DRYING/HEATING/COOLING/MILLING DATE
ISSUE 1 2 3 4
CLIENT N. Rowson PROJECT NO. 1
LOCATION Boulby, North York Moors, UK ITEM NO. E - 01 NO. OFF
PLANT PotentialAsh Potash Plant PDF NO. 1 ELD NO.
SERVICE Milling of Potash Rock SELECTION / AREA Grinding Circuit
ISS DUTY 1018 tonnes / hr SHEET 1 OF 1
MATERIAL HANDLED Saturated Brine
Sylvite Ore – See Appendix C. for composition
SPECIFIC GRAVITY
ANGLE OF REPOSE Not required BULK DENSITY
MAXIMUM LUMP SIZE 2350 microns / 2.3cm
Page 43 of 44
DESIGN BASIS
Input D80 =1380 microns
Output D80= 620 microns
AVERAGE PARTICLE SIZE 273 microns
RATE 24,434 tonnes / day CONTINUOUS/BATCH/INTERMITTENT
Continuious
MOISTURE/VOL
ATILE
COMPONENT
Slurry OPERATING
RANGE
SURGE DESIGN
SLURRY DENSITY 1500 kg / m3
TEMPERATURE INLET Ambient OUTLET Ambient + heat from crushing (minimal)
PRESSURE OPERATING Atmospheric OUTLET Atmospheric
FED FROM Slurry Storage and
mixing tank
Atmospheric (1 atm) DESIGN Atmospheric + 10% = 1.1atm
MATERIALS OF CONSTRUCTION Steel mill shell, Rubber mill lining,
High Chrome Iron Lifters
DISCHARGING TO Hydrocyclone seperators
FIRE / EXPLOSION PROTECTION Grounding Cables. Humidity controlled environment prevents build up of static charge on mill
shell.
FUEL Electricity for motor drive provided by Gas fired CHP Units FLOW RATE 510 tonnes / hour of solids
1018 tonnes / hour slurry
PRINCIPAL
DIMENSIONS (IF
AVAILABLE)
Internal dimensions of mill: 3.6m x 3.2m diameter
See Appendix … for Mechanical Drawings
MOUNTING Steel supports
Mill shell supported by bearings
SAFETY REQUIREMENTS Static Electricity
ANCILLARY EQUIPMENT Slurry Storage Tank & Feed
Overflow discharge grate
Slurry Pump
Hydrocyclone
SPECIFIC
REQUIREMENTS/REMARKS
none
REQUIRED GUARANTEE
Linings: no replacement required before 3 months (6 months is recommended)
Mill Drive & Motor: Same as motor guarantee
Page 44 of 44
Appendix Q – Plant Wide P & ID
Appendix R – Mechanical Drawings