Tutorial for Calculating Modal Composition

HSC Chemistry® 6.1 1

Pertti Lamberg June 25, 2007 06120-ORC-T

HSC Sim 6.1 Tutorials – Calculating modal composition of samples using HSC

Geo

Prepared by Pertti Lamberg

Date 25th June 2007

For HSC Chemistry Version 6.1

For HSC Chemistry Modele Geo

Tutorial version Draft 2.0, June 2007

Checked and approved -

Language checked -

Keywords Modal composition, mineralogy, Add-in

Table of Contents Table of Contents...........................................................................................................................1 Introduction ................................................................................................................................................... 1 Example 1 – Simple calculations using Excel and HSC Chemistry Add-In functions ................................. 2 Example 2 – More complicated calculation in Microsoft Excel using matrix functions............................... 7 Example 3 – Simple calculation in HSC Chemistry...................................................................................... 8 Example 4 – Complicated modal calculation. Using the rounds................................................................. 17 Example 5 - Worked example to calculate copper mineralogy based on copper phase analyses – using diagnostic leachings..................................................................................................................................... 19

Introduction.............................................................................................................................................. 19 Data.......................................................................................................................................................... 19 Step-by-step instructions.......................................................................................................................... 20

Introduction HSC Chemistry 6.1 has a special module (HSC Geo) designed to calculate mineral composition of samples using chemical assays. The other way to do it utilizing mineral databases of the HSC Chemistry is to use Excel Add-in functions. This tutorial shows how to use mineralogical Add-in functions in Excel, how to calculate more complicated task in HSC Chemistry, how to utilize diagnostic leaching techniques in mineral quantification and how to update the mineralogical databases. HSC Geo 6.1 includes a calculation module for estimating mineral composition of samples based on chemical assays. The equation solved by the program is:

Gelement,mineral*Gmineral = Gelement



where Gelement,mineral is the matrix including chemical composition of minerals, Gmineral is the vector of mineral grades and Gelement is the grades of elements in a sample, i.e. analysed chemical compositoin of the sample. In the HSC Geo in solving the simultaneous mass balance equations different techniques can be used: 1) least square method, 2) weighed least square, 3) non-negative least squares, 4) weighed non-negative least squares.

Example 1 – Simple calculations using Excel and HSC Chemistry Add-In functions HSC Chemistry 6.1 has an extensive mineral database which can be used in Excel. The first example of this tutorial shows how to start using the Add-in functions of the HSC Chemistry in Microsoft Excel. Figures 1 to 4 how to load the HSC6.XLL.

Figure 1. In Microsoft Excel select Add-Ins on the Tools –menu.



Figure 2. Press Browse.

Figure 3. Browse C:\HSC6\AddIns\HSC6.XLL and press OK.



Figure 4. Press OK.

After loading the HSC6 Add-In you can use the HSC Chemistry Add-in functions in Microsoft Excel. To learn different Add-in functions open files AddInSample.xls, AddInSampleEQ.xls and AddInSample_Minerals.xls in folder C:\HSC6\AddIns (Figure 5 and Figure 6). The general mineralogical Add-in function has a syntax MineralProperty(Mineral,Property) Mineral is the name of the mineral, e.g. pyrite, quartz, kyanite, chrysocolla. Proprety is mineral property, like chemical element (e.g. Cu, Si, O, Na), density, color, code, formula. For example MineralProperty(“Chalcopyrite”,”Cu”) will return copper content of chalcopyrite as wt%. See the example file.



Functions Return Values ArgumentsGeneral Return Value Argument 1 Arg. 2 Arg. 3 Arg. 4 Arg. 5

UNITS(T;E) C and MJ C MJBAL(Equation) H2(g)+O2(g)=H2O(g)qweaH2(g)+O2(g)=H2O(g)SPECIES(DBNo,Position) Ag2WO4 2 200

Species Return Value Argument 1 Arg. 2 Arg. 3 Arg. 4 Arg. 5H(Species;T) -390.593 CO2(g) 100HKG(Species;T) -1.104 FeS 100HNM3 or HCM(Species;T) 0.096 N2(g) 100HLAT(Species;T) 0.000 H2O(l) 25S(Species;T) 636.026 H2O(l) 45435CP(Species;T) 205.166 CH4(a) 100G(Species;T) -47.253 He(g) 100

Reaction equation Return Value Argument 1 Arg. 2 Arg. 3 Arg. 4 Arg. 5H(Equation;T) -485.132 2H2(g) + O2(g) = 2H2O(g) 100HKG(Equation;T) -13.465 2H2(g) + O2(g) = 2H2O(g) 100S(Equation;T) -93.276 2H2(g) + O2(g) = 2H2O(g) 100CP(Equation;T) -19.295 2H2(g) + O2(g) = 2H2O(g) 100G(Equation;T) -450.326 2H2(g) + O2(g) = 2H2O(g) 100K(Equation;T) 1.105E+63 2H2(g) + O2(g) = 2H2O(g) 100

Iteration (reverse) Return Value Argument 1 Arg. 2 Arg. 3 Arg. 4 Arg. 5TATH(Species;H) 5046.97 CO2(g) -93.35TATHKG(Species;H) 1191.85 FeS -0.26TATHNM3 or TATHCM(Species;H) 42.94 N2(g) 0.02TATHLAT(Species;H) 25.00 H2O(l) 0.00TATS(Species;S) -138.85 H2O(l) 20.77TATCP(Species;CP) 137.99 CH4(a) 49.04TATG(Species;G) -204.93 He(g) -11.29

Stream/Flow Return Value Argument 1 Arg. 2 Arg. 3 Arg. 4 Arg. 5STREAMH(Species;Amount;T) 5.723 Fe 1 100FLOWH(Species;Amount;T) Cu 1

Zn 1STREAMHKG(Species;Amount;T) 6.364 Cu(+2a) 21.85 100FLOWHKG(Species;Amount;T) Fe(+2a) 6.72

Zn(+2a) 2STREAMHNM3(Species;Amount;T) 2.187 N2(g) 17.78 100FLOWHNM3(Species;Amount;T) O2(g) 4.79

Ar(g) 0.23STREAMHLAT(Species;Amount;T) 14.060 Cu2S 1 100FLOWHLAT(Species;Amount;T) FeS 1

ZnS 1STREAMS(Species;Amount;T) 200.629 N2(g) 0.78 100FLOWS(Species;Amount;T) O2(g) 0.21

Ar(g) 0.01STREAMCP(Species;Amount;T) 29.252 N2(g) 0.78 100FLOWCP(Species;Amount;T) O2(g) 0.21

Ar(g) 0.01STREAMG(Species;Amount;T) -72.677 N2(g) 0.78 100FLOWG(Species;Amount;T) O2(g) 0.21

Ar(g) 0.01DensityA(Species;Amount;T) 1260.348 NaCl 0.2 50

FeSO4 0.1Densitykg(Species;Amount) 2504.675 NaCl 0.2

FeSO4 0.1DensityNm3(Species;Amount) 2.322 N2(g) 1

SO2(g) 2

Stream/Flow iteration (reverse) Return Value Argument 1 Arg. 2 Arg. 3 Arg. 4 Arg. 5STREAMTH(Species;Amount;H;Tmin;TMax) 100.00 Fe 1 5.72 0 1000FLOWTH(Species;Amount;H;Tmin;TMax) Cu 1

Zn 1STREAMTHKG(Species;Amount;H;TMin;TMax) 100.00 Cu(+2a) 21.85 6.36 0 1000FLOWTHKG(Species;Amount;H;Tmin;TMax) Fe(+2a) 6.72

Zn(+2a) 2STREAMTHNM3(Species;Amount;H;Tmin;TMax) 100.00 N2(g) 17.779049 2.19 0 1000FLOWTHNM3(Species;Amount;H;Tmin;TMax) O2(g) 4.786145

Ar(g) 0.227884STREAMTHLAT(Species;Amount;H;Tmin;TMax) 100.00 Cu2S 1 14.06 0 1000FLOWTHLAT(Species;Amount;H;Tmin;TMax) FeS 1

ZnS 1STREAMTS(Species;Amount;S;Tmin;TMax) 100.00 N2(g) 0.78 200.63 0 1000

Figure 5. File AddInSample.xls in folder C:\HSC6\AddIns lists most of the add-in functions and shows how to use them.



Figure 6. File AddInSample_Mineral.xls in folder C:\HSC6\AddIns lists the Add-in functions related to minerals and shows how to use them.

The first example shows how to use Add-in functions to answer following question: Question: Copper grade of the sample is 3.46 wt% Cu and sulphur grade 14.19 wt%. Sample consists of chalcopyrite, pyrite and quartz. What are the grades of the minerals? The steps are:

1. Create table about minerals and their chemical compositions using MineralProperty – Add-in function

2. Input head grades 3. Write function for chalcopyrite grade (GradeChalcopyrite = 100*GCopper / GCopper,Chalcopyrite) 4. Calculate sulphur carried by chalcopyrite 5. Calculate remaining excess sulphur 6. Calculate pyrite grade from the excess sulphur 7. Calculate quartz (100-others)

You can find the calculations in the file Mineral Conversions HSC.xls provided with this tutorial file.



Figure 7. Create table of minerals and their chemical compositions using MineralProperty –function.

Example 2 – More complicated calculation in Microsoft Excel using matrix functions Example 2 shows how to calculate a slightly more complicated mineralogy in Microsoft Excel using matrix –functions. This is needed because minerals are not stoichiometric pure end-members. The task is to calculated mineral composition of sample consisting of sphalerite, chalcopyrite, pyrrhotite and quartz, and then calculate density of the ore sample grading 1.0% Zn, 3.66% Cu and 6.12% S. Mineral Sphalerite Chalcopyrite Pyrrhotite QuartzCode Sp Ccp Po Qtz Density 4.05 4.2 4.62 2.63 Zn 59.03 0.00 0.10 Cu 0.26 34.626 0.00 S 33.12 34.945 37.60 Fe 7.59 30.429 62.30 Sum 100.00 100.00 100.00 0.00 Zn 1.00 Cu 3.66 S 6.12

1. Create first the table of mineral with chemical composition (a) 2. Create table for sample assays (b) 3. Using function MINVERSE and INDEX create a inverse matrix of the (a) = (c) 4. Multiply matrix (b) and (c) to get a vector of mineral grades (d)

5. To calculate the density on unporous basis use formula ∑=

⎟⎟⎠

⎞⎜⎜⎝

⎛=

N

eral eral

eral

DensityG

SG 1min min

min 100/1



Figure 8. Worked example in Excel.

Example 3 – Simple calculation in HSC Chemistry HSC Geo has a special module designed to calculate mineral composition of samples using chemical assays. To follow this example load file Assays.txt (tab-separated text file with header row and SampleNo column). Once you have saved this file you are ready to continue:

1. Open HSC Geo

2. To open the analysis file select File – Open data from the menu, change the “files of type” to “Tab delimited text (*.txt)” and browse for the Assays.txt. HSC Geo opens the file.

Figure 9. Opening data in HSC Geo.



3. Before continuing the structure has to be identified. This is because you can use various formats in the HSCGeo and the Identify –routine is to make all files compatible. Press “Identify” button for that.

4. HSC Geo identifies the structure and to indicate that window changes. For modal calculations

from each column ELEMENT, METHOD and UNIT should be identified correctly. Check that.

Figure 10. Structure identified.

5. For modal composition calculations press “Modal” button in the left panel.

Figure 11. Press Modal.



6. In the “Quantification – Modal composition” window you have to 1) select data source (if only

one open, then it is automatically selected), 2) define minerals, 3) define elements used in quantification. For defining minerals present press “Edit/Add” button

Figure 12. Going to defining the minerals.

7. HSC Geo uses HSCGeo.mdb database and <MineralChemistry –table for defining minerals. In

this example the minerals of interest are sphalerite, chalcopyrite, galena and pyrite. First write “sph” and all minerals starting with name ‘sph’ will be shown. Select STOICH (stoichiometric) and press Add>> -button to move it to the list of minerals. M/Sp/20 appears in the right list box. Repeat this for chalcopyrite, galena and pyrite. When ready, press OK.



Figure 13. Defining the minerals.

8. Press the “Next >>” button



Figure 14. Minerals defined.

9. In the HSC Geo – Modal Calculations –window move all the minerals to be calculated on the first

round by pressing >> button



Figure 15. Modal calculations window.

Figure 16. Minerals are all calculated on the first round..

10. Click on each available element, Cu, Zn, Pb and S, twice to move the elements in the “Elements” list



Figure 17. Defining the calculation basis.

11. Now you have defined that you are calculating the amount of sphalerite (Sp), chalcopyrite (Ccp),

galena (Gn) and pyrite (Py) using mass balance equations for zinc (Zn/TOT), copper (Cu/TOT), galena (Pb/TOT) and sulphur (S/TOT); all analysed with total method (i.e. all minerals will decompose in the analysis method completely).

12. To calculate, press “Calculate” button



13. Modal composition is available as wt% and by pressing “Graph>>” button, you can visualise the modal composition in bar graph.

Figure 18. Studying the results of the modal calculation.

14. You can copy the result on clipboard, save it as an Excel file or save it in Microsoft Access database.

15. You can fine tune calculation using rounds and different mathematical methods like non-negative

least squares.

16. You may study distribution of any of the elements included in the minerals (not necessarily included in the calculations), study the residual of the calculation, composition of mineral fraction (i.e. selected minerals recalculated to 100%) and bulk composition of samples back calculated from mineral composition. All these are also available in graphical format.



Figure 19. Studying the distribution of sulphur.



Example 4 – Complicated modal calculation. Using the rounds The next example is more complicated. The data is from the Ph.D. thesis of Sergio Vianna and the ore is Cannington Pb-Zn-Ag ore. The task is to calculate mineral composition of three flotation test samples, feed, concentrate and tailing. A total of twelve elements have been analysed, as given in the file Cannington Example and shown in Table below. Stream Ag

ppm Pb % Zn % Fe % S % Cu % Sb % As % SiO2

% CaO

% MgO

% Al2O3

% Feed 692 23.36 16.36 4.41 13.24 0.052 0.080 0.000 35.40 2.04 1.22 0.673Concentrate 1400 44.72 22.13 4.15 18.78 0.071 0.176 0.000 6.74 0.48 0.37 0.154Tail 323 9.86 11.41 4.43 8.55 0.037 0.029 0.025 55.00 2.98 1.77 1.020 The minerals present are: galena, sphalerite, freibergite, boulangerite, chalcopyrite, arsenopyrite, pyrite, quartz, talc, fluorite, garnet, magnetite and others. The steps of the calculation are:

1. Open HSC Geo

2. Open the file Cannington Example.xls

3. Identify the structure

Figure 20. Structure identified.



4. Go to Modal calculations

5. Define the minerals: galena, sphalerite, boulangerite, freibergite, chalcopyrite, arsenopyrite, pyrite, quartz, talc, garnet, fluorite, magnetite and gangue. Whenever available, select minerals from Olympia.

6. Press OK to go back and then press Next>> to enter the calculations

7. You may try several possibilities, but the one which gives a reasonable result is given in a table below

Round Minerals Elements Calculation method 1 Gn

Sp Bou Frb Ccp Apy

Pb Zn Sb Ag Cu As

NNLS

2 Py S NNLS 3 Qtz

Tlc Gar Fl Mgt

Si Mg Al Ca Fe

NNLS

4 Gan 100-others SVD

The result should be like given below.



Stream Gn % Sp % Bou %

Frb %

Ccp %

Apy %

Py % Qtz %

Tlc % Gar %

Fl % Mgt %

Gan %

Total

Feed 27.03 28.86 0.27 0.05 0.15 0.00 0.00 31.82 3.84 3.19 2.46 0.00 2.33 100.00Concentrate 51.69 39.04 0.60 0.11 0.21 0.00 0.00 6.04 1.11 0.00 0.66 0.00 0.53 100.00Tail 11.42 20.13 0.09 0.03 0.11 0.06 0.57 49.72 5.56 4.87 3.57 0.13 3.75 100.00

8. Study the distribution of silver, the composition of the minerals used in calculations, the residual.

9. Test graphics

10. Find the ways to transfer the calculation result to Excel or other reporting tools.

Example 5 - Worked example to calculate copper mineralogy based on copper phase analyses – using diagnostic leachings

Introduction This worked example shows how to estimate the quantities of copper minerals by using the Copper Phase Analysis and HSC Geo.

Data Analyses of the samples are given below. The format should be:

• Data is row-wise • The first column is the unique sample ID • The first row is the header row and the format is element-(space)-method-(space)-unit,

e.g. Cu P1 %, S TOT ppm • There can be extra columns, but HSC Geo can use in the calculation only columns, which

it is capable to identify Sample Cu P1 % Cu P2 % Cu P3 % Cu P4 % Cu PSum

% S LECO

% 4435 0.06 0.01 0.36 0.05 0.48 36.00

53 0.02 0.24 1.13 25.20 26.59 32.70 54 0.00 1.18 7.89 18.20 27.27 31.50 79 0.00 0.95 13.68 0.42 15.05 5.46

541 0.06 4.60 33.70 0.84 39.20 29.60 542 1.19 1.05 6.38 19.00 27.62 29.30 543 0.24 2.55 15.20 13.80 31.79 28.30 545 0.02 0.23 2.12 22.60 24.97 34.50 546 0.10 0.45 2.45 18.70 21.70 37.50 701 0.00 1.10 0.50 0.05 1.66 0.73

1577 0.09 1.62 19.00 1.45 22.16 26.90 2594 0.07 1.05 2.99 0.65 4.76 22.60 4118 0.00 0.00 0.54 21.70 22.24 36.00



Step-by-step instructions 1. Arrange your data in spreadsheet, e.g. Excel, as described above 2. Open HSC Geo 3. Copy your data in Excel to clipboard

4. In the HSC Geo select in the main window select Edit – Paste



5. Data is pasted in the new datasheet window called Data 1

6. Identify the data by pressing ”Structure” button on left (the ”Identify Structure” button on right does the same).

HSC Geo identifies the data structure and indicates that each of the copper assays are correctly identified as Cu, method is P1, P2, P3 and P4 and unit each of them %.



7. For modal calculation press the ”Modal” button on left.

8. In the ”Quantification – Modal composition” –window define the phases, i.e. minerals. Press the ”Add / Edit” –button on right.



9. In the ”Phases” window write the name of the mineral in the Criteria text box and follow the

changes in the database query table below. Select appropriate minearal in the list. In this case select: chalchantite, brochantite, chalcocite, chalcopyrite an pyrite. You may change the order of minerals by pressing Move Up and Move Down –buttons. Once ready press OK to exit the window.



10. Back in the the ”Quantification – Modal composition” window you can check the chemical

composition of minerals by double clicking the mineral. To change the mineral press Add / Edit button and remove the mineral from selected and select the appropriate one. Once ready press Next >> to the calculation window.

11. In the HSC Geo – Modal Calculations –window move minerals to calculations by (1) selecting it in the left list box and (2) pressing > -button. (3) Select appropriate elements by clicking it in the peridic table and (4) by selecting the method in the Element | Method listbox on the right side of the periodic table. (5) Then press ”Element | Method Accepted” to move it to the calculation set-up listbox.

In the current example move all the minerals and select Cu P1, Cu P2, Cu P3, Cu P4 and S.



1

2

3 4

5



12. To calculate press ”Calculate”. The result is presented in a separate ”HSC Geo – Mocal Calculation Results” window. Red colour indicates negative value, and in this case chalchantite is slihtly negative in three samples. To correct that, for the calculation method select non-negative least square (NNLS) for the quantification and press ”Calculate” again.

13. For distribution of copper in the Results- window select Distribution tab and press ”Cu” in the

periodic table. To see the result in graphical format press ”Graph >>>” –button.





Maintaining the database The chemical composition of minerals is stored in the HSCGeo.mdb Microsoft Access Database.

Documents

Tutorial for Calculating Modal Composition