MINE DESIGN USING SIMULATIONS

Dr. David W.H. Ellis

e-mail address: dwellis@compusmart.ab.ca

Abstract

Mine simulation modeling is a method of duplicating the operation of a mine with a mathematical model. This paper will describe the typical facilities and operation planning questions that can be studied using these models and the problems or shortcuts that occur when simulation is not used. How accurate are they?, How consistent are their results?, What are the proper sizes and numbers of each kind of equipment?, What is the difference between a large fleet of small trucks and a small fleet of large trucks?, Similarly for shovels?, Similarly for crushers?, What is the benefit of a 1 minute reduction in haul times?, What is the benefit in making equipment operate at a more consistent rate?, Is the cost of double dump facilities worth it?, Should breaks be staggered or together?, Should trucks be dedicated to a shovel or free to return to any shovel?, Are there benefits to a surge pile? These are some of the questions that can be answered and will be illustrated with examples. Typical design features that are not given appropriate attention without simulation will be presented.

How accurate are simulation models ?

Validation in simulation modeling is a process of determining (and adjusting the model) how close the model will duplicate actual operational results with actual operating conditions as input to the model. At Syncrude Canada Ltd., the simulation model results for a bucketwheel/conveyor model were different from the actual operating results by less than 1%. Sufficient detail was included in the model to permit this accuracy to be attained.

D.W. Ellis & Associates Ltd. has developed a Shovel, Truck, Crusher, Conveyor mining simulation model (using GPSSH by Wolverine Software Corporation) to demonstrate simulation (and animation) and our capabilities. In this paper, I will present the results of the cases analysed to answer many typical facility and operations planning questions.

The following questions are answered by analysing different cases with this model. Thus the results obtained here are particular to this model. The detailed data in the model would have to be changed to reflect operating conditions and rules in your mine to obtain results relevant to your mine. This paper is intended to demonstrate what is possible. The answers obtained here are not universal truths.

Is A Simulation Model For You?

If you find yourself doing any of the following in your design of a mine, then simulation modeling is for you. You will obtain more accurate results for each case you analyse (in a fraction of the time).

• Use a fixed truck wait time in the shovel or crusher queue.
• Use average idle times for shovels or crushers.
• Use fixed equipment utilizations or availabilities in the analysis.
• Assume linear changes in performance with linear changes in operating characteristics.
• Use average production rates or travel times.
• Do not consider various combinations of equipment in and out of service.
• Ignore opportune maintenance, weather, or seasons.
• Use average spacing and duration of unscheduled downs.
• Ignore complicated parts of your operation;
  • delays to bring equipment into service
  • variable travel times because of congestion in the mine
  • startup inefficiencies
  • effects of hopper size
  • effects of storage sizes
  • opportune maintenance.

The Base Case

The case used as a reference for this study (the base case) has the following features:

• 2 shovels; 4500 tph +/- 200 tph
• 15 trucks; 151 tonnes
• 3 crushers; 3100 tph +/- 200 tph with 350 tonne hoppers
• 1 conveyor; 10000 tph +/- 300 tph
• All equipment is subject to unscheduled failures.
• All equipment is included in the Preventative Maintenance (PM) schedule. For all but the trucks, it consists of a 12 hours complete shutdown and a staggered 12 hours down for each piece of equipment each week. For the trucks, PM of 6 hours, 24 hours and 48 hours is performed after 250, 750 and 1500 operating hours.
• Trucks are subject to 90 minutes of breaks (driver breaks, lunch, fueling, shift changes, etc.) of various kinds per 12 hour shift.
• The number of trucks allocated to a shovel is a function of the shovel rate, truck size, travel times, and unload time. Trucks are dedicated to their shovel. Shovels and trucks are brought into the mine to cover 120% of the requirements of the crushers.
• The average truck travel time from the shovel to the crusher is 4.6 minutes and from the crusher to the shovel is 3.1 minutes. Both vary by +/- .5 minutes (triangular distribution).
• Shovels move (and do not load) for 5 minutes after every 10,000 tonnes loaded.
• If the queue at the crusher is 2 or larger, the trucks unload at a dump pile (this ore is then not used by the model).
• If an unscheduled down for a shovel is less than 30 minutes, the trucks are not released.

How consistent are simulation models ?

Consistency means the ability to get the same results when the same case is run repeatedly. Simulation models use random number generators to seed the occurrence of random events. For example, the time to the next unscheduled failure of a particular piece of equipment is a random event but with a particular distribution. The model would generate a random number and convert it , through this distribution, to the time of the next failure. If the random number generation was started differently from one case to the next, different results would be obtained. For the same case, these differences determine the precision of the model. For good models, the differences are small. The Shovel, Truck, Crusher, Conveyor model was run 10 times for simulations of 1, 2, 4, and 8 years. The standard deviation in the results for each of these durations was 2127.0, 1402.6, 859.6 and 694.6 tonnes/day. These numbers are the variations in the average daily production of 124,066 tonnes/day. Thus 2 standard deviations represent a variation of 3.5%, 2.3%, 1.4% and 1.1%.

In the following, cases are compared to the base case. If the difference in daily production is large enough, we know the change will make a significant difference. The base case average daily production is 124,066 tonnes/day based on an average from 10 cases (8 years). The standard deviation for individual case production is 694.6 tonnes/day. Thus the standard deviation for the average of the 10 cases is this value divided by the square root of 10 or 219.7 tonnes/day. Below we will be interested in the difference between the case results and the base case average production. The variance (the square of the standard deviation) of the difference is the sum of the variances of the 2 factors. Thus the standard deviation of the difference is 728.5 tonnes/day. We will use a one sided test of significance. The multiplying factors for significance at the 95% and 90% levels of confidence are 1.64 and 1.28. Thus if the difference in the 2 cases is larger than 932 tonnes/day, we are 90% confident that the difference is 'significant'. If the difference is larger than 1195 tonnes/day we are 95% confident. Thus we are able to identify significant changes that are a .75% difference (at the 90% confidence level). Results below are marked with an asterisk (*) and colored red when they are significantly different from the base case at the 90% level of confidence.

What is the right size for each of the pieces of equipment in the mine ?

Simulation models themselves cannot completely answer this question. Fortunately, they can give the most difficult to obtain piece of information; the difference in production because of different sized equipment. The charts below show the average daily production for a 10% change in the size of the pieces of equipment in the model. What is left for the analyst is to meld other information such as capital costs, operating costs, and the value of production to determine if the increased investment in the larger equipment is a good one. Note that in practice, the sizes of more that one piece or type of equipment are changed in cases.

From Chart 1, we see the effects of a 10% change in the maximum production rate for the shovel. For a 10% decrease, the total production rate decreases by 9.3% but for a 10% increase, the total production rate increases by only 3.4%; significantly less than 10%. This is partially explained with a later question (Chart 6) that identifies restrictions in the mine. The rest of the explanation is that when the shovels are removed as a restriction,, another part of the production process becomes the restriction before the 10% increase in production can be realized. From other information provided in the case results, note that the working hours (loading, unloading, and traveling) increased by only 3.0%, the total truck idle time was reduced by 4.3%, the wait time in the shovel queues decreased by 33.7% and the wait time in the crusher queues increased by 22.4%. Thus some of the increased time required by the trucks in the mine came from otherwise unproductive time in the mine. Any hand analysis I have ever seen would not have identified this.

As for the shovels, from Chart 2 we see the effect of a 10% change in the maximum operating rate for the crushers. For a 10% decrease, the total production rate decreases by 1.7% but a 10% increase produces a 2.5% increase in production. Again other areas of the mine became a restriction before the 10% increase could be realized or for some of the time, the crushers were not the restriction.

What would be the effect of a 10% change in both the shovel and crusher's maximum operating rate? Chart 3 shows us these effects. Note that in all this testing of the sensitivity of total production rate to the maximum operating rates of equipment, none of the results were 'obvious' before the case was analysed.

These results show the importance of 'balancing' the equipment in the mine.

No significant change was obtained when the maximum capacity of the conveyor was increased by 10% (see Chart 4). As a partial explanation, below we will see that the conveyor is the restriction in the mine only 9% of the time and most of that is because the crusher is down.

Chart 5 shows that another surprise may be that increasing the size of the trucks also produces no significant improvement in production. Again it is because they are not a significant restriction to production (see Chart 6 below). As well it is possible that with the small trucks, 4.6 trucks per shovel are required with 5 actually allocated but with the large trucks, 4.2 are required with 4 allocated. Matching the truck size to the shovel may be important.

As well as the maximum operating rate of the equipment, of interest also is the correct number of pieces of equipment. For trucks this is of particular interest. What is the right number of trucks to use? What is the value of the last truck added to the fleet? Graph 1 shows how the average daily production in the mine changes as the number of trucks in the fleet changes. This information must be combines with other operating considerations, capital and operating costs, and maintenance practices to determine the right number of trucks to have in the fleet.

What is the bottleneck in the mine ?

In the simulation models D.W. Ellis & Associates Ltd. develop, we always include production restriction reports. Two kinds are possible; shutdowns caused by each piece of equipment, and restricted throughput because of each piece of equipment. Chart 6 shows a combination; the production restrictions in the base case.

From this information, it might be tempting to conclude that a 10% increase in the maximum rate for the shovels would lead to a 4.67% increase in production. This would be incorrect because we saw above that production rose only 3.4%.

What is the difference between a large fleet of small trucks and a small fleet of large trucks ? Similarly for shovels ? Similarly for crushers ?

To answer these questions we analysed 3 cases for each. All cases have the same total production capability. However, the cases have the capability broken into different sized pieces. The following charts show the differences in production for the cases.

The 3 cases are: 15 151 tonne trucks, 13 174 tonne trucks, and 10 227 tonne trucks. Note that the same total truck capacity for the larger trucks produced significantly less production (see Chart 7)?. But is the cost of the capacity the same? Can more capacity be purchased for the same costs? Are there other operating considerations; less queue time at the shovels and crushers?

The cases are: 1 9000 tonne shovel, 2 4500 tonne shovels, and 3 3000 tonne shovels. The choice of two 4500 tph shovels was significantly better that either a single larger one or more smaller ones (see Chart 8). It is probably because when it is down, the whole mine is down

The cases are: 1 9300 tonne crusher, 2 4650 tonne crushers, and 3 3100 tonne crushers. A single large crusher is significantly less productive (in this mine, see Chart 9). When the one crusher goes down, all production must stop.

What is the value of a 1 minute reduction in truck haul times ?

The trucks cycle from the shovel to the crusher and back. The travel times were reduced by 1 minute (.6 for the trip to the crusher and .4 for the return trip). Chart 10 shows the production improvements because of these truck operation changes. Are they worth it? Operating costs, production costs, and the cost to make these travel time reduction must be analysed to determine this. Remember that the trucks are the restriction in the mine only 10.2% of the time. However, note that the change in production is significant only for increased haul time.

What is the benefit of making equipment operate at a more consistent rate ?

To my knowledge, the ability to analyse this question is a unique capability of simulation modeling. We know equipment in the mine cannot operate at the exact same rate all the time. Depending on the mine type and location, issues such as weather, ore consistency, and operator differences cause these variations. It is rare for a mine engineer to be able to account for these variations in the analysis of the mine operation using the typical spreadsheet and costing models. What difference does it make? In our Shovel, Truck, Crusher, Conveyor Model, the maximum operating rate for each piece of equipment and the truck travel times are specified as a simple distribution. Throughout the simulation these values are changed subject to the specified distributions. Usually a simple triangular distribution is specified. Chart 11 shows the differences in production when different levels of variation are used. Note that assuming no variation would have predicted production almost 1% larger than what could actually be attained. Thus it is important to know your maximum operating rate variations and use them in your mine planning. The chart also shows that it is of benefit to you to work to reduce the variation in your operating capabilities.

The 4 cases in the chart are:

1) the same maximum operating rates at all times

2) variations in the maximum operating rates for the shovels and crusher of +/- 200 tph, for the conveyor of +/- 300 tph, and truck travel time variations of +/- .5 minutes.

3) as for 2) but with variations of +/-400 tph, +/-600, tph, and +/-1.0 minutes.

4) as for 2) but with variations of +/- 800 tph, +/- 1200 tph, and +/- 2.0 minutes.

Is the cost of a double dump worth it ?

The base case assumes that there is one queue at the crushers and only one truck can unload at a time. Changes to the mine would have to be made to allow 2 trucks to unload at the same time (at different crushers or at the same crusher). Is the capital cost worth it? As mentioned above, the simulation model can only provide part of the answers but the most difficult part. When the double dump case was analysed, Chart 12 shows the average daily production rose from 124066 to 125317 tonnes/day. This improvement is significant. Again the value of the improved production, the cost of the facility, and any changes to operating costs must be analysed.

What are the implications of different hopper sizes for the crushers?

The base case assumes a hopper size of 350 tonnes. Chart 13 shows the impact of hopper size on average daily production for larger hoppers. The improved production is statistically significant but is it worth it? Note that if the unload time for the larger hoppers were to increase because of a larger ramp to the crusher, that change would have to be made as well. It would appear that the larger hopper size has some value. However, would a surge pile near the crushers make the same improvement but at lower costs? The analysis of another case would answer that question. This is exactly the manner in which simulation models are intended to be used. Would the typical hand or spreadsheet analysis even be able to address this question?

Should PM be scheduled together or staggered ?

The benefits to scheduling preventative maintenance together is that operating staff is not needed during the PM time. The benefits to staggering it are that the work load in maintenance is evened and the supply of ore is more uniform. But what are the trade offs? Chart 14 shows the production differences for the base case studied here.

What measures of production performance can be used to evaluate cases?

So far we have been using average daily production as a measure of how good a case is. Virtually any performance measure can be obtained from a simulation case. Above we saw the source of the restriction used and discussed information about truck idle time, and truck time in queues. Chart 15 illustrates the use of truck time (hours per day for all 15 trucks) in the crusher queue to evaluate the hopper size and the double dump.

The above questions are typical of those faced by facility planners (mining or otherwise). Simulation modeling allows these questions to be investigated quickly, with high accuracy, and with great credibility. Other typical issues might be:

Should breaks in the mine be staggered or scheduled together?

Should trucks be dedicated to a shovel or free to return to any shovel? In general, there may be several possible uses for the trucks (overburden, ore) and determining the use of the truck after the completion of each of its activities may have significant value. Dispatch systems allow different levels of information and communication to permit this flexibility. What is value of a dispatch system to you?

Are there benefits to a surge pile beside the crusher? What rules should be used to build it up? What rules should be used to draw it down?

What effect does the operational changes required because of the seasons and weather have on our production?

Will backup equipment help us? What rules do we use to start it up and shut it down?

Is there congestion in the mine? How much delay is it causing? Model different ways to easy it to determine the best changes to make.

How does the downstream processing of the ore affect the mining operation? Should a dump pocket be used as a buffer between the mine and the further processing of the ore? How should it be managed?

Is your truck fleet not homogeneous? How should the different trucks be allocated to shovels and other duties? Are your shovels or crushers different? Is there a benefit to using different sized equipment?

Should a special cleanup shovel be used in the mine to reduce the time used by the loading shovels in performing cleanup?

Are the tasks performed by the trucks interrelated? Should all truck duties be modeled? What should the priorities and allocation rules be for each duty? In particular, should the overburden removal duties be modeled as well?

Is the ore body so complicated that the ore body should be modeled as well?

Should the handling of waste in the ore body be modeled? How should the shovels be allocated to still provide a consistent flow of ore?

Are your maintenance staff and facilities restricting your production? Include them in your simulation model and study the trade off between extra staff and facilities and getting equipment back into service faster.

It is important to think of these simulations as analysing the same month repeatedly and not as simulating 8 years into the future. Long simulations into the future should include the operational changes that would naturally take place.

Because of the very high costs of mining equipment and operating, studying a proposed change before it is implemented will lead to the better use of capital and operational budgets. Being able to evaluate 100 cases in the time to previously evaluate 1 case will result in better mine plans. It will produce a competitive advantage.

D.W. Ellis & Associates Ltd. is a management consulting firm specializing in the management sciences. With 28 years of industry experience in management science, David Ellis has a very good mix of academic knowledge of simulation and practical experience using simulation modeling. He has developed over 40 significant simulation models for various business situations. These include a gas collection system, open pit mining based on shovels and trucks and bucketwheels, oil and gas plant production, steel production, manufacturing and assembly production, water line breaks, computer scheduling, refinery/pipeline system, inventory management, and risk analysis.

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