Economic Model Essentials

Economic Model Essentials

Economic model showing calculated revenue distribution

In an economic model. the economic values of each block are calculated as a function of its geo-metallurgical attributes by specifying parameters such as:​

• The selling price of any commodity recovered by processing where the recovery is defined as a mathematical expression of the block attributes​

• The unit cost of mining (ore and waste) and the unit cost of processing (ore) including any adjustment factors that apply​

• Ore Dilution and Recovery​

• The unit cost of rehabilitation for waste​

• The additional costs for each unit of commodity

Studio NPVS provides alternative methods for calculating whether blocks are ore as well as optionally allowing for mining cost adjustments per bench​

The following information outlines key information relating to the generation of an Economic Model.

If an economic model run has been started, it can be stopped early using the <ESC> key.

 

Lexicon of terms

• Economic Model

• • Cost Model: Studio NPVS-calculated revenues and costs. The Cost model has up to four dollar fields: Revenue, Processing Cost, Mining Cost and (optionally) Underground Value, that is net block value when mined by the underground method.

  • Profit Model: Imported block net values. The Profit model has one dollar field representing block net values. If you import block values instead of letting NPVS calculate them, you will not be able to run MAO or MFO.

  • Reduced Economic Model: this economic model contains information relating only to the Revenue, Processing Cost, Mining Cost and Value.

  • Full Economic Model: this economic model contains the following data fields; Rock Type, Ore Tonnage, Mass, Product Grades, Recovered Products, Revenue, Processing Cost, Mining Cost and Value.

• Product Recovery: the fraction of product mass recovered by a given processing method. For example, a Mill Au recovery of 0.9 means that 9 grams of gold will be recovered by Mill from blocks containing 10 grams of gold. Product recovery can be defined directly as fraction or as a formula.

• Revenue: total receipts from selling products recovered from a block; accounts for product prices and selling costs.

• Processing Costs: method-specific costs of processing an ore block; a sum of up to three components:

• • Upstream Costs: defined per mass unit of ore (raw material) directly or with a formula.

  • Downstream Costs: defined per unit of recovered product for one or more products.

  • Ore Mining Differential Costs: a difference in mining costs when an ore parcel is mined as ore and the same parcel is mined as waste; Studio NPVS calculates these costs automatically.

• Mining Costs: costs of mining a block as waste.

• Underground Value: revenue less processing and mining costs from a block if mined by underground method; used by Lerchs-Grossmann optimization when underground alternative is considered. To generate underground values, define at least one Underground processing method.

  Processing costs in this case must include mining costs.

• Mining Recovery: the percentage or fraction of ore parcel that reaches the  processing plant; for example, 90% mining recovery means that only 900 tons of 1000 tons parcel reaches the plant. Mining Recovery below 100% has the following consequences:

  • The recovered product mass is reduced.

  • The Revenue and Upstream Processing Costs are reduced.

  • The net block values are reduced.

  • The reported in situ ore tonnages and element grades are unchanged. Multiply the in situ ore tonnages by Mining Recovery factor to obtain tonnages processed.

• Mining Dilution: ratio of rock mass sent to processing plant to ore mass; for example, 5% Mining Dilution gives 1.05 dilution factor meaning that instead of a 1000 ton parcel the plant receives 1050 tons of diluted ore. Above zero Mining Dilution has the following consequences:

• • Unit upstream processing costs increase by dilution percentage; for example $10 cost per ore ton becomes $10.50 cost per ton.

  • Economic cutoff grades increase.

  • If product recoveries are defined as functions of grades, the recoveries are reduced because of grade dilution.

  • The net block values are reduced.

  • Ore tonnages may be reduced owing to higher cutoffs.

    Note that NPVS reports in situ ore; to obtain diluted tonnages multiply in situ ore by the dilution factor.

  • In situ and recovered product mass may be reduced.

• Mining Cost Adjustments (MCAF): block-specific or rock type specific multipliers applied to reference mining costs.

• Processing Cost Adjustments (PCAF): block-specific multipliers applied to processing costs.

• Rehabilitation Costs: costs of dumping unprocessed ore parcel.

• Economic Cutoff: product grade at which revenue from selling the product equals the costs of processing ore containing that product.

• Minimum Cutoff: user-defined parameter; the effective cutoff is set to the greater of two numbers: Minimum Cutoff and Economic Cutoff.

• Maximum Cutoff: user-defined parameter; the effective cutoff is set to the smaller of two numbers: Maximum Cutoff and Economic Cutoff.

Ore tests

The first test listed below is the most often-used. It works equally well for one product as for multiple products; maximizing the revenue from the deposit by selecting the optimum processing method for each rock parcel that is worth processing. The remaining three tests are useful if you wish to control cutoff grades directly by setting minimum cutoff or maximum cutoff. These three tests are equivalent for one product models but quite different for multi-product ones.

• Revenue exceeds Rehabilitation Costs: rock parcel is classified as 'ore' if processing the parcel by at least one method is more profitable, or costs less, than dumping it and paying rehabilitation costs. In the absence of rehabilitation costs, it means that at least one method must yield revenues exceeding processing costs.

• Sum of grades divided by cutoffs greater than 1: the parcel is 'ore' if the sum of product grades divided by product economic cutoffs is greater than 1.

• All grades greater than their cutoffs: the parcel is 'ore' if grades of all products exceed their respective economic cutoffs.

• Any grade greater than its cutoff: the parcel is 'ore' if the grade of just one product exceeds the product economic cutoff.

Economic Cutoff defined

The economic cutoff grades are calculated from the equation:

• revenue per mass unit = processing cost per mass unit

The exact form of this equation depends on how the processing recovery is defined, as a constant fraction or as a function of grade:

Notation

Symbol	Meaning
p	Product price.
s	Selling cost.
r	Product recovery.
r(y)	Product recovery as function of product grade.
d	Mining dilution.
c	Processing cost per mass unit of ore.
a	Processing cost per mass unit of product.
x	Economic cutoff grade in product unit per mass unit.

 

Constant recovery

The equation in the case of constant product recovery is:

(p-s-a)*r*x = d*c

hence;

x = d*c/[(p-s-a)*r]

If the product grade is defined as percentage grade, the reported economic cutoff grade is 100*x.

Variable recovery

If you defined the product recovery (r) and/or processing cost (c) by a formula, the recovery and cost are functions of grade where the grade adjusted for mining dilution is given by x/d. Thus, the cutoff grade equation is

(p-s-a)*r(x/d)*x = d*c(x/d)

This, in general, is a nonlinear equation with respect to x which doesn't yield a simple formula for x and must be solved numerically.

If the product grade is defined as percentage grade, the equation changes to

(p-s-a)*r(100*x/d)*x = d*c(100*x/d)

The reported economic cutoff grade is 100*x.

Actual cutoff versus reported cutoff

Economic cutoffs for all rock types, processing methods and products are reported in economic settings reports. These cutoffs are calculated for a fictitious “reference” ore parcel and do not necessarily match the actual cutoffs used by ore tests which may vary from parcel to parcel for the following reasons:

• Processing costs for a block are modified by location specific processing cost adjustment factor (PCAF).

• Product recoveries and/or processing costs are defined with formulas involving other element grades contained in ore parcels.

• Mining costs are adjusted for benches with different parameters (exit bench or cost rate) for waste and ore.

Mining costs adjustments by bench

How the mining costs are adjusted

The mining costs for a parcel of ore or waste located at bench k are calculated as

• Mining Cost = Reference Mining Cost + (k – Reference Bench) * Incremental Cost Below for all benches below the Reference Bench.

• Mining Cost = Reference Mining Cost + (Reference Bench - k) * Incremental Cost Above for all benches above the Reference Bench.

Different mining costs for waste and ore

The differences between mining costs for waste and processing methods are usually caused by different locations of processing plants, leach pads and waste dumps. These differences may affect cutoff grades and ore tonnages.

For example, suppose that the cost of mining a block as waste is $10, the cost of mining the block as ore is $15, and the value of the ore, if processed, is $4. If ore is processed, the block value is $4-$15=$-11, if ore is treated as waste the block value is $-10, so the block will be classified as waste. However, if both mining costs were identical, say equal to $15, then the block would be classified as ore and have value $-11.

In other words, the differences between mining costs as waste and as ore must be treated as extra processing costs rather than normal mining costs. Economic Model, MAO, and MFO treat these cost differences in this way, which is reflected in the program reports.

Underground mining alternative

For projects for which both open pit and underground mining methods are considered, the economics of underground mining may affect the ultimate open pit.

The ultimate pit in the presence of an underground alternative is obtained by modifying economic block values used for optimization as follows:

• new value = block value when mined above ground - block value when mined underground

To consider an underground alternative you need to define at least one underground processing method for at least one rock type.

The underground methods are used to calculate the block values when mined underground and Pit Optimizer uses these values when calculating the ultimate pit and phases. Note, however, that only the block values when mined in open pit are used for pit statistics, so the true open pit statistics are reported and charted.

Underground mining alternative notes

• Waste parcels are ignored. If block contains waste and ore sub-cells (parcels), only the ore sub-cells are assumed to be mined underground.

• Include all underground mining costs in processing costs. Mining costs are ignored when calculating Block values when mined underground, so you must include all underground mining costs in the processing costs of underground processing methods.

• Some open pit parameters are ignored. The following parameters are ignored for Block values when mined underground calculations:

• • positional mining and processing cost adjustment factors (when imported with the block model)

  • the rock type mining cost adjustment factors

  • mining dilution

  • mining recovery

  • rehabilitation cost.

• Use a different rock type code for selective underground mining. If only some blocks (sub-cells) are considered for underground mining, you should assign a different rock type to these sub-cells and define an underground processing method only for this rock type.

• Pit Optimizer allows for switching off the underground option.

How the Economic Model Generator Works

You can follow the logic of the Economic Model Generator with the Check Values button of Optimization screen's Economic Model group.

More about the Check Values function...

Editing parcel parameters

You can edit parcel rock type and grades anytime after the parcel has been created. For example, in order to edit Parcel 4:

1. Select the cell with the "Parcel 4" label.

2. Choose the Parcel command from the Edit menu.

3. Edit the parameters in the Edit parcel parameters dialog and click OK. All calculations for the parcel and the block will be automatically updated.

Mining costs adjusted by bench

The Economic Settings allow for specifying different mining cost adjustments by bench for ore and waste. This difference may affect the calculations that determine whether it is more profitable to process a given parcel as ore or treat it as waste. To account for this, the difference in cost between mining a parcel as ore and as waste is added to the processing cost and mining costs of all parcels is bench-adjusted as for waste.

Mining costs by volume

If the mining costs are calculated by volume rather than by mass, the costs are evaluated only for entire blocks, not for individual parcels. In this case, neither adjustments by rock type nor by bench can be used. Instead, all adjustments must be defined block by block as MCAF and imported with the block model.

	Related Topics
	Quick Start Import Essentials Pit Optimization Essentials Pushback Essentials Scheduler Essentials MAO Essentials MFO Essentials