Optimum Dig -Line Design

Optimum Dig-line Design

Isaaks & Co. 2013

Topics

1. Case Study

2. The Digger Algorithm.

3. Working With Digger.

4. Features.

5. Applications

6. Conclusions and Recommendations

The Case Study

Dig–line Case Study

This is an actual case study from an open pit gold mine.• Approximately 3.5 million tonnes of material.• Selective mining unit approx. 10 x 10 m.• Client dig-lines designed manually using MineSight.• Optimum dig-lines designed using computer program

Digger.• Both sets of dig-lines were designed using the identical ore

control model.

Dig–line Case Study

Green = Waste

Orange = LG

Red = HG

Magenta = Premium

The Clients Dig-lines

The Ore Control Model

Optimum Dig-lines

Dig–line Case Study Open Pit Gold Mine• Although the 2 sets of dig-lines appear similar, they are significantly

different.• For example, compare the dig-line tonnages by ore type.

• Note, the client dig-lines capture fewer tonnes in the higher grade ore types (Premium and HG).

Dig–line Case Study Open Pit Gold Mine• Next, compare the dig-line $/tonne (grade) by ore type.

• As expected, the $/tonne (grade) of the higher grade ore types within the client’s dig-lines is greater.

Dig–line Case Study Open Pit Gold Mine• Finally, compare the total dig-line revenues by ore type.

• Interestingly, the revenue generated by the optimum dig-lines is greater in the high grade ore types but less in the low grade ore types.

Dig–line Case Study

Open Pit Gold Mine

Dig-line Comparison – Observations and Conclusions• The High Grade and Premium dig-lines designed by the client capture fewer

tonnes than the optimum dig-lines. • This suggests an aversion to include waste or LG material within the High Grade

and Premium ore type dig-lines. • This appears to be a personal bias common amongst conscientious grade

control engineers.• The result can be seen as “high grading the ore control model”.• “High grading” generally results in fewer tonnes with higher grades. But less total

metal is generally recovered!

Dig–line Case Study

Summary of Dig-line Comparisons

5.8% increase in net revenue!

Dig-linesTotal Revenue

(LG+HG+Premium)

Client $ 119,574,769

Optimum $ 126,578,504

Open Pit Gold Mine

A Second Dig-Line ExampleClient Dig-lines Optimum Dig-lines

5.0% revenueincrease

The Algorithm

Digger2020

So, how does Digger2020 work?• Digger2020 uses simulated annealing to design optimum dig-lines.• The dig-lines are optimum in the sense that they minimize the

misclassification of ore types for a given set of loss functions and a minimum mining width constraint.

• ALL misclassification errors cost real dollars. So by minimizing these errors, optimum dig-lines maximize net revenue subject to the given constraints.

Digger2020 Here is an example.

• Ore control model blocks are 2 x 2 m x bench height.• Minimum mining width is 10 m.• Possible destinations are waste, leach pad, or mill.• Which destination yields the most revenue?

Digger2020 Digger answers this question by calculating the dollars lost for each 2 x 2 m OCM block for each destination (process) where the dollar loss is calculated as:

and

• The “Loss Function” is defined by the red text.

$Loss = abs Potential Revenue - Recovered Revenue

$ Revenue = metal price * block grade * process recovery - process break even cost

Digger2020 An Example “Loss Function”

$(W) = revenue generated by

waste process = 0.

$(Lpad) = revenue generated

from Leach pad process.

$(Mill) = revenue generated

from Mill process.

MisclassificationPotential Revenue

Recovered Revenue Penalty

W => Lpad $(W) $(Lpad) 1.0

W => Mill $(W) $(Mill) 1.0

Lpad => W $(Lpad) $(W) 1.0

Lpad => Mill $(Lpad) $(Mill) 1.0

Mill => W $(Mill) $(W) 1.0

Mill => Lpad $(Mill) $(Lpad) 1.0

$ Revenue = metal price * block grade * process recovery - process break even cost

Note the Penalty factor!

Working With Digger

Working With Digger2020 Digger2020 is very easy to use!

Import the optimum dig-lines into MineSight and use as guidelines for the final dig-

line design.Digger2020 is a

small, but complex C++

program.

Working With Digger2020 Digger2020 is very easy to use!

Example input .csv file containing ore control block

model grades. In this example, the current blast

requiring dig-lines is Shot30.Shot99 and Shot25 identify “fringe” ore control blocks that Digger uses to design dig-lines. This minimizes

edge effects.

Working With Digger2020

Digger2020 is very easy to use!

An example of the Digger Control Parameter file.

A note on minimum mining widths. Minimum mining widths can be set to any dimension. They may be horizontally square or rectangular.

Working With Digger2020 Digger2020 is very easy to use!

An example of the optimum polygon file output by

Digger2020.This file is imported into

MineSight for the final dig-line design

Working With Digger2020

Digger2020 is very easy to use!

Another example of optimum dig-lines.

Working With Digger2020

Digger2020 is very easy to use!

An example of the summary statistics put out by

Digger2020.(Lines 1 to 43)

This file is an excellent record for the reconciliation

of mine to mill or mine to resource model tonnes and

grade etc.

Working With Digger2020

Digger2020 is very easy to use!

An example of the summary statistics put out by

Digger2020.(Lines 44 to 90)

Note the Misclassification Summary. The percentage of ore type blocks misclassified in each ore type is provided. These statistics are very useful for the design of penalty factors.

Penalty factors can be used to influence specific misclassification rates. For example, given a hungry mill, one can optimally influence the

selection of non-mill ore types to supplement mill ore type material.

Working With Digger2020

Digger2020 is very easy to use!

An example of the summary statistics put out by Digger2020.

(Lines 91 to 106).In addition to the tonnes and grade for each ore type, the bottom line

shows the in-situ Total Net Worth of the material captured by the dig-lines.

Features

Digger Features

Variable minimum mining widths.

Minimum mining width

16 x 8 m

Digger Features

Variable minimum mining widths.

Minimum mining width 12 x 12 m.Less selectivity =

more dilution.

Digger Features

Variable minimum mining widths.

Minimum mining width 6 x 10 m.This might be feasible if the

shovel is mining along strike.

Digger Features

An example showing the application of penalties to the misclassification of HG and VHG ore types.

The application of the penalties increased the VGH tonnage from 160,625 to 171,100 tonnes (recall

the hungry mill). The average grade dropped from 2.139 to

2.093 g/t .

No PenaltiesPenalty ( HG => VHG ) = 0.5 Penalty ( VHG => HG ) = 1.5

Digger FeaturesDetailed Statistical Summary for Each Run• As you have seen, Digger can generate significantly different sets of dig-

lines by altering a few parameters such as minimum mining width and penalty factors.

• The detailed statistical summary provided by Digger enables one to easily assess and compare dig-line sets obtained by altering the input parameters.

• Thus, as loading equipment changes (due to repair etc.) or as mining progresses from one geologic zone to another, Digger easily enables optimum dig-lines for the situation at hand.

Applications

Digger ApplicationsGrade Control• Digger can be customized to handle as many as 15 different ore types.• Digger also works with rotated ore control models.• Minimum mining widths can be set to any width. The minimum mining width

perpendicular to the shovel dig direction may be different from the minimum mining width parallel to the shovel dig direction.

• The polygon dig-lines output by digger may be imported into MineSight, Vulcan, or Gemcom etc.

• Digger is currently used by Barrick Gold, Newmont Mining, IAM Gold, and Freeport McMoRan.

Digger ApplicationsMine Design -- Example Case Study• Narrow vein type deposit.• Client wished to know recoverable tonnes and grade for various mining

widths (equipment size).• Resource model blocks measured 10 x 5 x 5 ft.

Digger ApplicationsMine Design -- Example Case Study

Scenario 1 – 15 x 10 m minimum mining width (very selective)

Digger ApplicationsMine Design -- Example Case Study

Scenario 2 – 20 x 15 m minimum mining width (less selective).

Digger ApplicationsMine Design -- Example Case Study

Scenario 3 – 30 x 25 m minimum mining width (excessive dilution).

Digger ApplicationsEstimate recoverable reserves as a function of mine design, e.g., equipment size or selectivity, bench height, blast hole drill pattern, blast hole sampling error etc.

1. Generate a (multivariate) conditional simulation of the ore deposit.

2. Validate the simulation.

3. Extract a subset of simulated values on a nominal blast hole pattern.

4. Add blast hole sampling errors etc.

5. Estimate ore control block model grades using the simulated blast hole grades.

6. Run Digger on the simulated ore control block grades.

7. Assess efficiency of mine design (compare in situ simulated reserves to recovered simulated reserves).

Summary and Conclusions

Summary and Recommendations• Experience suggests that sub-optimal dig-line design is one of the largest

sources of revenue loss in an open pit operation, e.g., ore sent to the dump is very costly!

• No matter how skilled your grade control engineers are at dig-line design, they cannot compete with Digger.

• Experience shows Digger will likely increase your net revenue by 2 to 5%.• Digger offers the biggest bang for your buck. Simply purchase a license and

start saving money.• No additional sampling, equipment, geologists or engineers required.• Digger will likely earn it’s keep in 1 or 2 blasts!• Order Digger today – don’t waste another tonne!• email ed@isaaks.com

The end