By Alexandre Ouellet, President, **SimWell**

NOTE: This article was originally published by Rockwell in the Arena Newsletter.

A mine and its associated ore processing plant are typical environments where simulation provides important benefits. Simulation is used in these plants to address many important business considerations:

**Major Investments****Strategic Decisions which have a major impact on project profitability****Understanding Interdependent and Complex Systems**- Wait times at key resources
- Stockpiles and tank limitations
- Headings availability at a given time
- Traffic in the mine
- Variability in the data
- Equipment availability (failures, preventive maintenance, redundancy)
- Operator availability (limited HR, schedules, operator specialties, absenteeism)
- Ore properties (type of ore, grade of ore)
- Operation times
- Weather factors

## Transporting the Ore with Trucks –> Discrete System

A mine is a system which can be modelled very well using Discrete Event Simulation. For example, in the ore transport operations, the sequence goes something like the following (this is obviously a simplification, but it is the basis of any trucks and shovels model):

- The truck moves towards the shovel
- Waits for its turn to get loaded
- Gets loaded
- Moves towards the crusher
- Waits for its turn to unload
- Unloads in the crusher
- Goes back to the shovel

These operations represent a typical discrete system where entities (trucks) go through a process and Seize-Delay-Release resources (shovels and dump hopper pockets).

## Ore Processing – Continuous System

However, mining simulation projects are not limited to the mining operations themselves. It is just as important to be able to model the **ore processing operations** accurately.

The ore processing plant is more a continuous system than a discrete system. For the rest of this article, let’s assume the following basic process.

## Strategies to Model Ore Processing Plants and Continuous Systems

An ore processing plant is not discrete, but rather continuous. In Arena, it is possible to represent a flow of ore on a conveyor in a continuous manner. It is also possible to discretize the flow, as suggested by Franzese and al. (2007). Here is a comparative analysis of the three methods:

- Discrete Mass – one entity = 1 unit of mass
- Discrete Time – one entity = mass moved during one unit of time
- Continuous – using the Flow Process Template

**Discrete Mass**

With this method, the continuous flow of ore on the conveyor is represented using discrete entities, whereas the entity is equal to a predefined unit of mass of ore (for example: 1 entity = 1 ton). As shown in the graphs below, the smaller the reference mass is, the closer the model will get to a continuous behavior. The higher the mass, the less precise the simulation is. Therefore, one might want to choose the smallest possible reference unit, in order to obtain the most precise results. The issue is that the smaller the reference mass is, the higher the number of unique events will be. Hence, the model will be longer to execute. A slow model means more tedious verification and validation work. Moreover, the cost of running several scenarios increases which may force the analyst to reduce the number of scenarios to be run or increase the duration of the project. It is thus important to choose a reference unit which will be a good compromise between precision and model performance. That unit depends on the total volume of mass moved within the simulated timeframe, the required precision of the model and the type of decision that needs to be made.

**Discrete Time**

This method is similar to the previous one. The flow of ore is represented in a discrete manner, whereas an entity corresponds to the mass transferred within a certain time. (for example: 1 entity = the mass transferred during one minute). Analogically, the shorter the time unit chosen is, the closer we are to running a continuous model. Of course, a longer time unit means lower precision. Also, the shorter the time unit is, the costlier the simulation will be in terms of computer execution time.

**Continuous**

Il is possible to model the transport of ore on conveyors in a continuous manner in **Arena**, using the tools provided in the **Flow Process Template**. If one models the Hopper-Crusher-Conveyor-StockPile sequence shown in above picture, the hopper and stockpile are represented by **Tanks**. Each dump hopper pocket is represented as a **Regulator**. When the truck arrives and starts dumping into the hopper, it seizes a **Regulator**, then **Flows** in the **Tank** until the quantity of ore in the truck is emptied and, finally, **Releases** the **Regulator**. The conveyor is represented as a **Flow** between an **Output-Regulator** of the hopper and an **Input-Regulator** of the stockpile. Below is a picture of the Arena Logic. Please contact us if you wish to receive this model.

The crusher does not need to be represented by a piece of equipment as it is in series with the Hopper and it does not have accumulation within it. If the crusher is in maintenance, then the flow rate out of the Hopper can simply be **Regulated** (Assigned) to Zero. There is not always accumulation before every piece of equipment within a process. If one needs to model a process that add or remove mass, then it can be modelled as a tank with no accumulation and within which the inflow will always be maintained equal to the outflow.

The advantages of using the **Flow Process Template** are:

- No loss of precision due to discretization
- Model execution speed: transferring 100 tons from the hopper to the stockpile generates only 2 events: start and end of the flow

These advantages come with a cost which can be more or less expensive, depending on the application. Indeed, between discrete and continuous, we lose the concept of entity. The entity can be crucial if we must be able to track attributes of the ore precisely (ore grade, for example). We must also live with the assumption that the length of the conveyor is negligible in our system. The assumption is usually acceptable with continuous conveyors, since the sequence of events at the end of the conveyor is the same as at the start of the conveyor. This is even more the case for plants which run 24/7 or plants where conveyors don’t get emptied at the end of a shift.

## Discrete vs Continuous Methods

Choosing a modeling method depends on the system which needs to be modelled.

If we must track the attributes of the ore precisely, it is preferable to opt for discrete methods. Other factors could also lead us to choose a discrete method. For example, repairing a conveyor after a failure might depend on the quantity of ore travelling on it.

If, on the other hand, it is not necessary to track attributes of the ore or if the level of precision required for the ore characteristics is less important than the precision required for the mass, then it should be preferable to use the tools from the **Flow Process Template**, since they improve the model execution time.

## Learning More About the Flow Process Template

To learn more about the Flow Process Template, you can, of course, get some professional training or a coaching session with SimWell. If you prefer to teach yourself, I suggest you look at the “Coal loading” example provided with the **Arena software**. You can find that example in the following path, on your computer: C:UsersPublicDocumentsRockwell SoftwareArenaExamplesFlowProcess

This model created by Rockwell demonstrates in a simple context the complete range of tools from the **Flow Process Template**.