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

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07-137508-2, Available via Knovel

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978-0-7506-7351-8, Available through ScienceDirect

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BBC Business News, 2011. UK Inflation rate rises to 4% in January, Accessed 20/3/2011,

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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

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Couper, J. R., Penney, R. W., Fair, J. R., Walas, S. M., 2010b. Chapter 0 - Rules of Thumb: Summary

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FLSmidth, 2011. Rod Mills – FLSmidth Rod mills are able to grind coarser material than ball

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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-

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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

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Holdich, R., 2002. Fundamentals of Particle Technology, Chapter 11, Crushing and Classification,

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free online at: particles.org.uk

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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

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Information Sheet, Accessed: 13/3/2011, Available at: hse.gov.uk/pubns/dis2.pdf

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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.

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right one?, Accessed: 20/3/2011, Available at: charysoftware.com/OM/WP-Motor-Sizing.pdf

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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,

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Sinnott. R., Towler, G., 2009a. Chapeter 5, Valve Seclection, Pgs. 235 - 236, Coulson &

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Coulson & Richardson’s Chemical Engineering Design, 5th Edition, Elsevier, ISBN: 978-0-7506-

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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