Crushing Plant Performance Optimization NZ

8/11/2019 Crushing Plant Performance Optimization NZ

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parameter number. The plant consists of n production units. The production unit has m

variable parameters andpstatic parameters. This forms the input vector xto the system:

{

}1 2

1 2

1,1 1,2 1, 2,1 2,2 2, ,1 ,2 ,

1,1 1,2 1, 2,1 2,2 2, ,1 ,2 ,

, ,..., , , , ..., ,..., , ,..., ,...

..., , ,..., , , ,..., ,..., , ,...,

n

n

m m n n n m

p p n n n p

x x x x x x x x x

y y y y y y y y y

=x

ROCK MATERIAL

As mentioned in the previous section, information about the rock material is transferredbetween the different production unit models and should include all details necessary to

predict production unit performance. Most important is the amount of material and its particle

size distribution, but the Bond work index, moisture content, abrasion index, clay content andso on are also necessary.

ECONOMICS

As stated in the introduction, economics are essential for the optimisation. The whole purpose

of the plant is to earn a profit for its owner by supplying material to the customer. Economiccalculations are necessary in order to evaluate how effectively the plant operates. Predicting

the economic performance of a plant is difficult and an economic model is therefore needed.Two different aspects must be borne in mind when designing such a model; simplicity, so that

the required information can be easily found or calculated and detail, as the model has to be

detailed enough to respond to any changes made in the plant. It was therefore decided to usethe process cost accounting model (Dearden, 1988), which consists of two costs; a fixed Chour

and a variable Cton(x). The main part of these costs have to be calculated manually. The

amount of material passing through the unit is also needed and denoted ( ),rock im x& . The total

production cost per ton Ctot,i(x)for unit iis calculated using the following equation:

( ) ( )( ),

, ,

,

hour i

tot i ton i

rock i

CC Cm

= +x xx&

CUSTOMER DEMANDS

The quality of the products is of great importance, as if they do not fulfil customer demands

they cannot be sold. The optimisation must produce solutions where all products meet thequality demand, the most important of which is the limitation of misplaced particles. A

product with many particles outside the fraction limits cannot be sold, thus it is essential that

the optimisation model can predict this.

OPTIMISATIONTo find the optimal performance of the crushing plant model an optimisation routine isneeded. This routine will with the information generated by the simulation routine the

solutions that will maximise the cost function. The optimisation problem can be classified as

large and discrete. It does not have a large number of parameters but there are a large numberof combinations of setting for the plant. There are a number of different optimisation routines

suited for these types of problems; simulated annealing, tabu search, genetic evolutionary

algorithmsand more. They have all been used to solve optimisation problem similar to this. Inthis work the Probabilistic global search Lausanne(PGSL) has been chosen. This was done

after a selection process where the PGSL algorithm was found to be one of the most suitable


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with the best performance. The selection criteria for the optimisation algorithm are the

following:

The main objective in the selection process was of course a good probability offinding the global optimum.

Good scalability, i.e. the optimisation routine must work without any changes fordifferent number of optimisation parameters.

User independency, i.e. the optimisation routine does not depend on any start guessor optimisation parameter change provided by the user.

Optimisation iterations, number of runs before the optimal solution is found.

CONSTRAINTS

For the optimisation of a crushing plant there are constraints that will restrict the solutionsspace. The type of constraints can be divided into two types. There are constraints that can be

checked without a simulation and those that need a simulation to be carried out. Most

constraints related to production unit adjustment can be checked without performing a

simulation, although model constraints such as feed size restrictions on some units willrequire a simulation, as it will prevent the preceding crusher from running with a large CSS.

All constraints will yield the admissible set of parameter values, which are denoted x.

COST FUNCTION

The cost function used for the optimisation calculates the plant performance during operation.

The aim of the optimisation is to maximise the gross profit. The gross profit is calculated asthe difference between the income from product sales and production cost. To calculate the

income per operating hour for product hthe sales price shand produced amount ( ),rock hm x& are

used. The production cost was derived earlier and the gross profit for product his formed as

the following equation:( ) ( )( ) ( ),h h h init rock hP s C C m= x x x& (1)

The gross profit for the plant is calculated by adding the profit from all products together. The

total gross profit per operating hour will be:

( ) ( )1

q

h

h

P P=

= x x (2)

The statement of the optimisation problem will be to maximise the gross profit subject to all

constraints imposed on the variable parameters x. The statement of the problem is formulated

in the following way:

( )max P

xx

x (3)

The obtained solution *x of the problem represents the most profitable setting of the crushing

plant. This setting will give the global optimum ( )*P x , generating the highest gross profit peroperating hour, provided all products are sold.

EXAMPLE:OPTIMISATION WITH AND WITHOUT PARTICLE SHAPE DEMANDS.

To demonstrate the optimisation method, a three stage crushing plant designed for aggregate

production was studied. The flow sheet is presented in Figure 1.


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Figure 1. Three stage aggregates production plant used in the example. The thicker connection

lines represent conveyors. (Screen shot from the developed software)

Both the primary and secondary crushers operate in an open circuit, while the tertiary crusher

is installed in a closed circuit configuration. In addition to size reduction, the primary stagealso extracts a low quality natural fines product from the feed material, which is most suitable

for applications where the demands on the product are low, for example different types of

land fill, covering or road base. If the feed material contains any moisture the major part willfollow the natural fines product. This will make the rest of the process insensitive to any

moisture in the feed material. The main part of the material processed in this stage is

conveyed to the secondary stage where it is crushed again. The secondary stage is only forsize reduction and no final products are produced. All material is transferred to the tertiary

stage where the high quality final products are made. The tertiary stage also produces a fines

product (0-2 mm) that is considered to be waste. It cannot be sold and is thus transported back

to the quarry where it is deposited.

The selected optimisation parameters are throw and CSS on the secondary and tertiary

crusher. The feed rate of the feeders for the 11-16 mm and 16-22 mm product is also selected

as an optimisation parameter. The aim is to find the value of all optimisation parameters that

will maximise the gross profit of the plant.

The used production unit models are all based on the models used in PlantDesigner (Sandvik).

To these models additional sub-models have been added but the original models has not been


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changed so the prediction of particle shape distribution, capacity and so on remains the same

as the original.

One of these sub-models is a particle shape module that is added to the crusher models. Thismodel was developed by Bengtsson (2006) and predicts the flakiness index for material larger

than 4 mm. The flakiness index is not defined for particles of less than 4 mm. It should also be

noted that the model is still under development. The product flakiness of the rock size pdepends on the average feed sizex , crusher CSS and three constants 1, 2, and3. The

numeric value of the constants depends on the type of crusher and chamber. The following

formula is used to predict flakiness:

( )2 2

22 3 2 312, ,

x xF x CSS p p p x

x CSS CSS

+ + = +

(4)

The particle shape is optimal for particles with the same size as the CSS. The flakiness index

is higher for both larger and smaller particle sizes. An increasing average feed size results in ahigher flakiness index. This is also illustrated in Figure 2.

Flakinessindex[%]

Flakinessindex[%]

Particle size [mm] Particle size [mm]

Increasing CSS

Increasing Feed size x

Figure 2. Illustration of the effect of process parameters on the flakiness index.

As discussed in the introduction, model compatibility is an issue when combining productionunit models. The particle shape model is a good example of why this is so. The model predicts

crusher performance with satisfying accuracy in the example considered. In many plants

where different rock materials are processed, it has been observed that particle shape also

affects screen performance. The screen performance may be fine when processing a rockmaterial that mostly generates cubical material, but when more flaky or elongated material is

processed, it drops significantly and most of the products do not fulfil customer demands.

This implies that, for a full implementation of particle shape prediction, the other productionunit models must be changed so that they both predict product shape and respond correctly to

feed material shape.

To further assist the economic cost calculation, a sub-model for power draw model has been

added to the production unit models (Hulthn, 2004), thus part of the variable costs can beautomatically calculated together with the energy price.

OPERATING CONDITIONS

The plant is assumed to operate in a market where it can expect to sell all of its final products

with the exception of the by-product. The plant is fed with blasted rock defined as granite,

with a particle size distribution denoted medium blasted rock,see the curve in Figure 1. The

hauling capacity of the available trucks limits the feed rate to 270 tonnes per hour.


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Two different optimisations were done to demonstrate the influence of particle shape on the

operation. The first had no demands on particle shape, while in the second, four of theproducts had to fulfil customer shape demands.

In the given exampleall crushers and screens have been assigned a fixed and a variable cost

in accordance with Figure 3. All products are assigned a sales price as well as quality

demands for particle shape and a limited proportion of misplaced particles.

Figure 3. The fixed and variable costs assigned to the different production units. (Screen shot from

the developed software)

A routine to calculate the wear part consumption of the crushers was also implemented, which

estimates the crushing chamber life time, thus allowing the wear part cost to be determined.The installed cone crushers are equipped with a control system that compensates the effect ofmantle wear. This system aims to keep the crusher performance constant with respect to wear.

In the examplethe variable crusher costs were set to zero. The energy and wear part cost was

automatically calculated by the crushing models and no additional variable costs were

assigned.

OPTIMISATION RESULTS

The first optimisation led to the result shown in Figure 4 and Table 2. It maximises plantprofit without activating any shape constraints. As can be seen in the figure, the secondary

crusher was operated with a large CSS. The reduction ratio in the crusher was quite small


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while the capacity was large.There was no need to use a larger throw on the crusher since the

capacity was sufficient. The optimisation algorithm has therefore found the small throw to bethe best. Since a smaller CSS will generate more fines, the crusher was kept as open as

possible. 50 mm is the maximum CSS for this crusher.

Figure 4. Results from the optimisation without any restrictions on particle shape. Note that all

production rate values are average values if nothing else is specified. (Screen shot from the

developed software)

Table 1. Production cost of the final products.

Product Production cost [SEK/ton]2-5 mm

5-8 mm

8-11 mm

11-16 mm

16-22 mm

44.49

44.49

41.38

41.38

41.38


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Table 2 Results from the optimisation without any customer demands for product shape

Parameter Optimal value

Cone Crusher S-type 4800 C

ThrowCSS 25 mm50 mm

Cone Crusher H-type 4800 M

Throw

CSS

28 mm

33 mm

Cone Crusher H-type 4800 MF

Throw

CSS

28 mm

33 mm

Feeder, 11-16 mm 0 tph

Feeder, 16-25 mm 0 tph

At the tertiary stage the crushers are also set with a large CSS, for the same reason as the

secondary crusher, namely to generate as little fines as possible. The CSS of the tertiarycrushers is not limited by the crushers themselves. If a larger CSS were to be selected, more

material would be larger than 22 mm and returned to the crushers. Too much material in theclosed loop is negative, as it generates extra cost. The throw of the tertiary crushers is set

quite low, since they do not require any extra capacity.

The two feeders were set to zero. This is to be expected, as returning the final product to the

plant will not generate more profit. Instead, it will lead to additional costs, as the material willhave to be crushed again, leading to the production of even more fines. The production costs

of the high quality final products are shown in Table 1.The generated gross profit is 14810

SEK/h.

The particle shape constraints were activated for the second optimisation. As seen in Figure 5and Table 3, the results differ from those of the first optimisation. Since no final products are

produced in the secondary crushing stage, the crushers only task is to provide a good feed to

the tertiary crushers. The setting of the secondary crusher is therefore adjusted so that thetertiary crusher can operate with a feed that offers the best trade-off between cost and ability

to generate correctly shaped final products. This is achieved by providing the crusher with the

optimum average feed size x .


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Figure 5. Results from the optimisation with restriction on particle shape. Note that all production

rate values are average values if nothing else is specified. (Screen shot from the developed

software)


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Table 3. Results from the optimisation with the customer demands for product shape. The results

from the previous optimisation is also presented as a reference.

Parameter Optimal value

with shape requirements

Optimal value

without shape requirements

Cone Crusher S-type 4800 C

Throw

CSS

25 mm

43 mm

25 mm

50 mm

Cone Crusher H-type 4800 M

Throw

CSS

32 mm

20 mm

28 mm

33 mm

Cone Crusher H-type 4800 MF

Throw

CSS

32 mm

17 mm

28 mm

33 mm

Feeder, 11-16 mm 16 tph 0 tph

Feeder, 16-25 mm 54 tph 0 tph

The feed material size to the tertiary crushers is one of the most interesting parts of thisoptimisation. Both feeders for the two final products are now used, the reason being to

generate a better feed to the two tertiary crushers. Trials were made with these two feeders

turned off, but the optimisation routine failed to identify any solutions. The main problemseemed to be with the larger products. Unless some of the final products were returned, the

shape of the larger products failed to meet customer demand.

Since a whole range of final products with a good shape are produced, it is important to

operate both tertiary crushers so that the combined product from the two units is optimal. Themix of these products should have good shape over the whole range of sizes. This is normally

achieved by operating the two crushers at different CSSs and is another result of theoptimisation. The left crusher with the slightly coarser M chamber is operated at 20 mm and

yields a good particle shape for the coarser products, while the right crusher with the finer MFchamber is operated with a CSS at 17 mm, which ensures that the finer products are of good

shape. The shape and gradation curves of the two crushers and the mix between them are

presented in Figure 6.


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Figure 6. Product size distribution and flakiness index from H-4800 M and H-4800 MF. Both the

individual crusher production and the mixed product are shown. (Screen shot from the developed

software)

The generated gross profit is 13013 SEK/h this value can be compared to the previous resultof 14810 SEK/h. When doing the comparison one must remember that the prices of all

products have remained the same even though the product quality has been improved. The

production costs of the final products are compared to the previous results in Table 4.

Table 4. Production costs of the final products.

Product Production cost [SEK/ton]

with shape

Production cost [SEK/ton]

without shape

2-5 mm

5-8 mm

8-11 mm

11-16 mm

16-22 mm

49.15

49.15

46.88

46.88

46.88

44.49

44.49

41.38

41.38

41.38

RESULTS

Computer simulation and optimisation can assist the study and improvement of the crushingplant operation. It has been found that it is important to combine both technical and economic

aspects when the plant is studied. This type of combined study is now available by using the

developed methods.

The result from the two cases also show the importance of total plant optimisation. To achieveoptimal plant performance it is not possible to make single machine optimisation. It is

important to study all production units in order to achieve a beneficial adjustment of the plant.

By comparing the two cases this is even more obvious. The setting of the production unitsmust be optimised together in order to find the best solution that both will generate the highestgross profit and ensure that the final products will all fulfil the customer requirements. It is

Flakiness index


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therefore also important to have equipment and plant control system that allow the equipment

to be adjusted.

The developed method is all developed with the aim to be implemented in a computersoftware. The implantation has already started with parts of the developed method

implemented in PlantDesigner. Simulation and optimisation is useful in many situations. In

the design it is useful to be able to do these types of combined economic and technicalcalculations. When the plant has been built and is in operation optimisation is a powerful tool

to determine how to operate the plant in order to meet the current market demand. Finally

simulation and optimisation is useful to educate personnel on all level in the crushing plant.

REFERENCES

Crushing Plant Performance Optimization NZ

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