The normal procedure in a crushing plant to study and improve the process is by means of measurements, rules of thumb and visual observations. These tools and methods are inadequate for a more advanced analysis of the complex process that characterises many crushing plants. In order to improve the process, both technical and economic factors must be taken into account. Normal simulation software does not provide sufficient support for such tasks.
The developed optimisation method utilises both technical and economic calculations in order to find the most profitable solution. The aim of the optimisation is to maximise the gross profit of the crushing plant. The gross profit is calculated by subtracting the production costs from the income.
The production cost is calculated using the process accounting method. This method is based on a fixed and variable operating cost for all machines. The production cost of a product is calculated by adding the operating cost of all production units that have been used. This results in a more accurate calculation of the production cost of all products. It is important to be able to calculate the production costs of the products since this, together with the sales price, gives a clear picture of the profitability of different products.
In many crushing plants, the particle shape is an important customer demand. A model that predicts the particle shape of the final products has been developed and implemented. This model predicts the particle shape over the entire gradation produced by a crusher. This allows for the particle shape of the final product to be predicted. The model depends on feed gradation and crusher setting. The optimisation routine will therefore be able to find the best machine parameter settings in the plant. The optimum setting will maximise the gross profit and produce products with the required quality.
From this work, it can be concluded that it is important to be able to adjust the equipment correctly. Viewing the crushing plant as an industrial process clearly shows that it is not the individual machines that need to be optimised. In fact, just optimising a machine will not necessarily be beneficial for the crushing plant. Automating the adjustment of the plant is therefore crucial to ensure that the plant is operating at its peak performance. This is especially important when product demand changes over time.
All methods were developed for use on a standard personal computer. The combination of modelling, simulation and optimisation is useful for design and operation of a crushing plant.
The methods can also be used for education and training purposes. Optimisation generally provides new insights into how to operate the crushing plant process more efficiently.
The performance of a crushing plant is highly dependent on how the production units are configured. Finding the optimal setting of the plant is very difficult without an optimisation tool specially developed for crushing plants.
Today, there are a number of simulation tools on the market. There are some simulation tools with very simple optimisation features. The optimisation that can be conducted is maximisation of one product. This type of optimisation is hard to utilise in most crushing plants since maximisation of one product will not be optimal for the economic situation of the plant. Usually, there is more than one product that is profitable, so maximising one product will decrease the production of other profitable products giving a sub-optimal total production of all products. Since the models used do not take economics into account, the maximisation of one product might also increase the production cost.
Crushing plant layout differs a great deal from site to site. Plants are designed differently due to variation in the type of rock, the use of the products, the size of the quarry, plant history and many other factors. The plant model is formed by connecting the various production unit models to each other. The rock material feed is defined and used as input. In order to optimise the plant, it is necessary to have detailed information about the operating cost of each production unit. Finally, the product demand sequence, desired product quality and product price must be defined.
The plant design comprises a number of different production units. A production unit is defined as a machine or larger arrangement used to move, store, separate or crush material in the crushing plant. A production unit can be a crusher, screen, feeder, storage bin, stockpile or conveyor. Each production unit is represented by a model, which can be used to predict the performance of the individual unit. The models are then connected, which means that the predicted production of a production unit serves as input for the following unit. The crushing plant model forms a grid of production units connected to each other in accordance with the plant layout. Connecting models places demands on the individual unit models.
Besides predicting the performance of the individual machine and the amount of material that will be produced, it must also predict information about the rock material that is of importance for the subsequent units. In other words, it is essential that the models are compatible with each other. There are many individual unit models that are good at predicting the performance of the machine in question, but not well suited for implementation in a crushing plant simulation program. Some types of screen models are a good example of this.
Production units such as crushers, screens and feeders can be configured differently, which changes their performance and thereby crushing plant performance.
Crusher close side setting (CSS) and feed rate on feeders can be changed within minutes and are therefore suitable for production scheduling. Other parameters such as screen media, crusher throw and crusher mantle selection are decided in advance and are not included in the optimisation.
Information about the rock material is transferred between 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 and so on are also necessary.
Economics are essential for optimisation. The whole purpose of the plant is to earn a profit for its owner by supplying material to the customer. Economic calculations 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 use the process cost accounting model.
The quality of the products is of great importance, as if they do not fulfill customer demands they cannot be sold. The optimisation must produce solutions where all products meet the quality 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.
To find the optimal performance of the crushing plant model, an optimisation routine is needed. The optimisation problem can be classified as large and discrete. It does not have a large number of parameters but there are a large number of combinations of settings for the plant. There are a number of different optimisation routines suited for these types of problems: simulated annealing, tabu search, genetic evolutionary algorithms and more. They have all been used to solve optimisation problems. The Probabilistic Global Search Lausanne (PGSL) is also a particularly good optimisation algorithm. The selection criteria for the optimisation algorithms are:
? a good probability of finding the global optimum
? good scalability – the optimisation routine must work without any changes for a different number of optimisation parameters
? user independency – the optimisation routine does not depend on any start guess or optimisation parameter change provided by the user, and
? optimisation iterations (the number of runs before the optimal solution is found).
For the optimisation of a crushing plant, there are constraints that will restrict the solutions space. 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, will require a simulation, as it will prevent the preceding crusher from running with a large CSS.
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 as the difference between the income from product sales and production cost.
The gross profit for the plant is calculated by adding the profit from all products together.
The statement of the optimisation problem will be to maximise the gross profit subject to all constraints. The goal is to find the most profitable setting of the crushing plant, generating the highest gross profit per operating hour, provided all products are sold.
To demonstrate the optimisation method, a three-stage crushing plant designed for aggregate production was studied.
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 stage also 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 will follow 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 for size 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 (0-2mm) 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 11-16mm and 16-22mm 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.
To these models additional sub-models have been added but the original models have not been 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. This model predicts the flakiness index for material larger than 4mm. The flakiness index is not defined for particles of less than 4mm.
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 a higher flakiness index.
Model compatibility is an issue when combining production unit 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 rock material that mostly generates cubical material, but when more flaky or elongated material is processed, it drops significantly and most of the products do not fulfill customer demands.
This implies that, for a full implementation of particle shape prediction, the other production unit 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 has been added to the production unit models, thus part of the variable costs can be automatically calculated together with the energy price.
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 as medium blasted rock. The hauling capacity of the available trucks limits the feed rate to 270 tonnes per hour.
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 the products had to fulfill customer shape demands.
In the given example, all crushers and screens have been assigned a fixed and a variable cost. All products are assigned a sales price as well as quality demands for particle shape and a limited proportion of misplaced particles.
A routine to calculate the wear part consumption of the crushers was also implemented, which estimates the crushing chamber life, thus allowing the wear part cost to be determined.
The installed cone crushers are equipped with a control system that compensates the effect of mantle wear. This system aims to keep the crusher performance constant with respect to wear.
In the example, the 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.
The first optimisation led to the results shown in Table 2. It maximises plant profit without activating any shape constraints. The secondary crusher was operated with a large CSS. The reduction ratio in the crusher was quite small 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 be the best. Since a smaller CSS will generate more fines, the crusher was kept as open as possible. The maximum CSS for this crusher is 50mm.
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 tertiary crushers are not limited by the crushers themselves. If a larger CSS were to be selected, more material would be larger than 22mm and returned to the crushers. Too much material in the closed 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 will have 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 $2550 per hour.
The particle shape constraints were activated for the second optimisation. As seen in Table 3, the results differ from those of the first optimisation. Since no final products are produced in the secondary crushing stage, the crusher’s only task is to provide a good feed to the tertiary crushers. The setting of the secondary crusher is therefore adjusted so that the tertiary 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.
The feed material size to the tertiary crushers is one of the most interesting parts of this optimisation. 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 problem seemed 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. The mix 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 the optimisation. The left crusher with the slightly coarser M chamber is operated at 20mm and yields a good particle shape for the coarser products, while the right crusher with the finer MF chamber is operated with a CSS at 17mm, which ensures that the finer products are of good shape.
The generated gross profit is $2250 per hour, which can be compared to the previous result of $2550 per hour. 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.
Computer simulation and optimisation can assist the study and improvement of the crushing plant 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 shows the importance of total plant optimisation. To achieve optimal 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 units must be optimised together in order to find the best solution that will generate the highest gross profit and ensure that the final products will all fulfill the customer requirements. It is therefore important to have equipment and plant control systems that allow the equipment to be adjusted.
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 technical calculations. 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 levels in the crushing plant.
Per Svedensten is a plant simulation specialist with Sandvik Mining and Construction.