Mine Planning Articles

When scheduling a mining operation’s long term production, one of the first questions that comes up is “Where should I send this block?”

Many operations use a predetermined, or economic, cut-off grade. Sometimes this grade is calculated by pit, by phase, or maybe by ore type. It is almost always calculated while looking at a single block of ore and not while looking at the potential interactions between different blocks or at the mine as a whole.

Let’s look at how this practice could be, and almost certainly is, decreasing the overall value of the project.

An economic cut-off grade is generally calculated by comparing the costs and revenue associated with mining and processing a block of material as ore vs the costs of treating it as waste.

This generally entails comparing mining, transportation, and processing costs with the expected revenue generated from the material in question. There could be other costs included in the calculations, but these are the most common.

The major problem with an economic cut-off grade is that it looks at blocks in isolation.

There are other factors that can, and probably do, influence whether a block should be treated as ore or waste that may not be considered in an economic cut-off grade. Two of the most important factors are blending considerations and the delay of processing higher grade ore by processing low grade ore as it is mined.

An economic cut-off grade is, in essence, the minimum percentage of saleable material contained within a block for it to be profitable if processed as ore.

## Blending Considerations Can Create More Value

When we consider blending, it is possible that material below the economic cut-off grade can be sent through processing facilities with a good result: the increased profit from the blended high grade blocks will be greater than the loss of revenue caused by processing the low grade blocks.

Processing material below the economic cut-off grade can sometimes increase the profits of an operation.

The following examples will consider only a few blocks at a time and assume that there is no limit on the total amount we can process.

### Blending to reduce contaminant percentage

If a high grade block has a high level of a particular contaminant and a block below the economic cut-off grade has none of the contaminant, then processing the two together can result in a product that does not get penalized for the contaminant. If the costs associated with processing the uneconomic block are lower than the penalty associated with processing the high grade block on its own, this will yield an increase in total profit.

### Blending to increase product recovery

Similar but distinct to contaminant reduction, blending can be used to increase desirable qualities in a product. There are times when blocks below cut-off grade may have chemical properties that increase the recovery of the other material that it is processed alongside them.

### Blending to lower processing costs

The chemical properties of blocks below cut-off grade can also lower the processing costs of the other material mentioned above. If the costs of processing the uneconomic blocks are lower than the profit generated from the increased recovery or the cost savings from the other material, this will also yield an increase in profit.

### Blending to increase total saleable product

Some mining operations sell their product by mass rather than grade and receive the same price as long as the properties of the material fall within a given range. If you have a block that is at the upper end of the range of acceptable quality then you can blend it with a block that is below the saleable range. As long as the quality of the resultant blend is within the acceptable range, the total material can be sold. This could potentially double the total profit you would have received from selling the individual (unblended) blocks.

### Blending to increase facility throughput

Blending can also affect crusher and mill throughput. If your high grade ore has properties that make it hard to crush, such as high clay content, it may be possible to increase daily mill throughput by blending the high grade ore with material that would normally fall below the cut-off grade. If this low grade material increases mill throughput enough to offset the added costs, additional value can be unlocked by decreasing the total life of mine and bringing profits forward.

## Wasting Economical Material Can Create More Value Too

Yes, you read that correctly – there are cases where treating material above the economic cut-off grade as waste will increase the value of a project. Read on to see how.

If all material that is above the economic cut-off grade is treated as ore and is processed as soon as it is mined, this may lead to the delay of processing high grade ore that is located lower in the deposit. Now you may be asking yourself “Why does this matter?”

By wasting economical but lower grade material, and accessing the higher grade earlier, we have increased the total discounted value of the operation.

### The Discount Rate

For many mines, time is an enemy. Capital has a cost. Initial capital to start a mining operation usually comes in the form of a loan that has structured interest payments. The longer it takes to pay off the loan, the more interest has to be paid, cutting into the value of the project.

A mine also has to consider price volatility, risk, and inflation. Generally, the sooner you can get the material out of the ground, the less these factors will erode the value of the mining project. These factors and others are generally summed up into a discount factor that is applied to the cash flows each year past the project’s start date.

So what exactly does this mean for your operation?

For the following example we will consider an operation without stockpiles. Let’s assume that your operation will make $100 million a year for the next ten years using an economic cut-off grade. After applying a standard discount rate of 10% to the future cash flows, you end up with the discounted cash flow shown below. $100M+91M+83M+75M+68M+62M+56M+52M+47M+42M=676M$ As you can see, our original cash flow that totalled$1 billion over the life of the mine is only valued at $676 million after discounting. Now let’s assume that the same operation will treat some of the low grade material that is above the economic cut-off grade as waste, allowing the high grade material to be accessed sooner. This yields a cash flow of$130 million per year, but for only seven years. This cash flow only totals $910 million prior to discounting, almost$100 million less than our original cash flow, but it is received sooner than in the previous cash flow.

$130M+118M+107M+98M+89M+81M+73M=696M$

After applying the discount factor we see that our new cash flow is worth $696 million,$20 million more than the first cash flow.

## Maximizing the Outcome

Every operation is different and not all of the situations above will apply to your operation, but it’s likely that some of them will. The problem with cut-off grade is that there is no simple equation that can be used to determine whether a block should be treated as ore or waste.

In order to maximize the value of your project, all the interactions between blocks need to be considered. The only way to truly examine all of the possible interactions between blocks is to mathematically model the potential interactions and then optimize the model using an optimization solver like Minemax Scheduler. The solver will look through all options until it finds the destination for each block that will yield the highest value for your mine while respecting equipment capacities, customer requirements, and operational logistics.

So if you’ve set your economic cut-off grade without looking at blending considerations or the discount rate, it may be worthwhile investigating how optimization can uncover that missing value.