“Mine Optimization” is a key factor of planning stages in all mining processes not only open-pit mining but mineral processing, underground mining. Optimization, also known as mathematical programming, collection of mathematical principles and methods used for solving quantitative problems in many disciplines, including physics, biology, engineering, economics, and business. Because of this commonality, many problems can be formulated and solved by using the unified set of ideas and methods that make up the field of optimization. There is a lot of software to solve optimization problems as an Excel Add-in and one of the most popular solvers is Palisade @Risk software which works in Excel perfectly.
“Evolver is an optimization add-in for Microsoft Excel that uses an innovative genetic algorithm (GA), OptQuest, and linear programming technology to quickly solve virtually any type of problem that can be modeled in Excel. Evolver has a unique ability to arrive at the best overall “global” solution to a problem—solutions traditional solvers typically miss” says Palisade corp. Of course, this is a problem solver and not like “mine optimization” software because in mine optimization there are packs of software and they use the Lerch&Grossman algorithm basically for planning mine production periods with economic block values. My previous posts related mine optimization has software used for this and in this post, we’re talking about different optimization approach for daily optimization calculation in a simple example of mineral processing.
Optimization in Mineral Processing
As mentioned before, this is a daily calculation to help an engineer who wants to know which material and how much of tonnes should feed the plant to achieve optimal feeding rate and production tonnage. In this example, Microsoft Excel and Palisade @Risk Add-in are going to be used to solve the optimization problem. You can find and download the sample excel spreadsheet but you should’ve a trial version of Palisade @Risk.
Scope of Problem
- There are 2 types of ROM material (A and B) to feed to the processing plant,
- Plant maximum feeding capacity is 550 t/day and should be feeding 450 t/day in minimum,
- Feeding rates of ROM materials are important. Mineral processing engineer wants to add less material from the high grade of the ROM ore and more from a low grade of the ROM ore.
- ROM A material should be fed in between “300t<=A<=400t” and ROM B material should be fed in between 150t<=B<=200t.
- The feeding rate should be (A/B) between 1.8<=A/B<1.9.
- The grade of ROM A material is 5-7% and ROM B material is 8-10%.
- The grade of final ore concentrate is 46% and metallurgical recovery is 0.55.
- The aim is to maximize the tonnage of the final product.
Formulation and Excel
In mineral processing concentrate or final product ton can be calculated as below;
C.T. = (FxFGxR)/CTformulation of final product after processing
CT is tonnage of concentrate or final product,
F is the amount of feeding material (ROM A and B as t),
FG is the grade of feeding material,
R is the metallurgical recovery,
CT is the grade of concentrate or final product.
Step 1 – Model Definitions
In the sample excel spreadsheet, changing cells (after optimization) marked as yellow, formulated cells (don’t change or edit them) marked as green and our goal Cell B12 marked as light blue (also it has formulation and do not change it or edit). First, we need to define our model so in Palisade @Risk click to Risk Optimizer or Evolver (if you activated this separately from Palisade Risk) tab and click to “Model Definition”. The model window will open.
In the model window at the top part select these options;
- Optimization Goal: Maximum (Because we want to maximize the amount of the final product in cell B12)
- Cell: B12
Then input the adjustable cell ranges;
- Cell A2 and B2 are our the amount of feeding,
- Cell A7 and B7 are our the grade of feeding.
Then we should input our constraint to Constraints window, simply click Add button and then select the C4 and input the limits then click Add button and add other constraints in Cell2 as shown below. The program automatically will shot it in Formula cell with 1.8<=C4<1.9.
Step 2 – Optimization Settings
In the Evolver tab or in Risk Optimizer click to Settings and Optimizations Settings window will open. You can choose any option you want but in this example click to Trials checkbox and input the value of 10000.
Step 3 – Run Optimization
Now you can click the start button in the Evolver tab to see results. Evolver Progress window will appear on the screen and you can see progress. Also, you see changing values in the cells (A2-B2-A7-B7 and final product cell B12) while progress in running. After the progress, the Evolver Watcher window will open. Click to Optimization Summary checkbox and then click OK to show optimization results. You can reset the adjusted values to original ones by clicking Utilities-Reset option.
Step 4 – Results
As you can see adjustable cells (yellow ones) has changed during optimization progress. Ofcourse, the Cell A7 and B7 haven’t changed because for maximum amount of final product, the system always wants higher grades so optimization used these cells in maximum grade value but you can easily define new constraints to change these ones.