Species Converter User Manual
Contents
1. After you have entered the Input analysis you need to specify the species for the Output analysis Fig 2 and click Solve to get the converted analysis Fig 3 Note that species containing elements which are not present in the input analysis are disregarded in the solution with the exceptions of oxygen and hydrogen Calculated Target Weight wt o wt o Coeff OU UOI UC UOI OCC UC a Fig 2 Enter the species for the output analysis Copyright Outotec Oyj 2014 Outotec TE Research Center Pori Jaana Tommiska Lauri 14015 ORC J 3 21 Maenpaa Species Converter c 59 amp f Home ia Tools EH o t QZXZBO6 v O9 New Open Save Add Calculation Add Summary Delete Fix Element Initialize Solve Element Charts About Help h Sheet Balance Balance File Workbook Actions Help Oo A B C D E F G H J K Charts 1 Name Residual 3 Input analysis 2 Date Error 2 951 F 3 Author Ni 4 5 6 Calculated Calculated Target Weight Type 7 wt Elements wt wt wt Coeff S 8 100 000 100 000 100 000 0 000 9 Cu 25 000 Cu 25 708 CuS 38 677 1 000 10 S 40 000 S 38 525 Cu2S 0 00E 00 1 000 11 Fe 10 000 Fe 10 000 CuFeS2 0 00E 00 1 000 12 Ni 25 000 Ni 25 768 FeS2 21 481 1 000 Output analysis 13 IU 0 000 NiS 39 841 1 000 x 14 H 0000 Ni3s2 0 00E 00 1 000 NiS 15 Others 2 06E 08 Others 0 00E 00 0 001 16 17 18 19 20 21 22 hd 4 4 gt M Sheeti 42. AM o d M E Cr AM j7 M E and vector f be f pEo h PEy If oxygen and or hydrogen are not measured the corresponding row s of matrix E and vector f are omitted If O and H measurements are considered as exact amounts they are treated as other elements and matrix E and vector f are omitted Each compound has a given weight w Let W be the Nc x Nc diagonal matrix of the weights The greater the weight w the more we try to create the th compound The default value of a weight is 1 Copyright Outotec Oyj 2014 HSC 8 Species Converter utotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 15 21 Maenpaa We might have some known target values for compounds Usually these target values come from mineralogical analysis Let diagonal matrix D be w if T is given D O if T is not given D 0 i2 and vector d W l if T is given l1 O if T is not given Now we have to solve the following problem min Hp h subject to p gt 0 and Ep f Ww 0 where T j and fol 2 10000 D 10000 d 100000 100000 100000 100 The condition i 00000 1 00000 p 100000 100 guarantees that the sum of the percentages of the compounds is 100 Method 2 The mass balance equations for the elements are j 21 Ne Ne C AM Zii pE ya P PE J Let matrix B be C AM B L iil Ji M i 21 Ne 24 Ne and vector b be Copyright
3. Outotec Oyj 2014 Qutotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 16 21 Maenpaa b LjpE i 1 N Where L 10000 ifpE lt 15 L 1 otherwise Now we can write the mass balance equations in matrix form Bp b It is possible although not very common that oxygen and or hydrogen measurements exist The measured amounts of these elements can be set as minimum amounts or exact amounts If the measured amounts of oxygen and hydrogen are considered as minimum amounts the equations for oxygen and or hydrogen are Nc Co j AM o u cp gt pE 2 M P Z PEo Ne Cy AM gt pE M Pj p H Let matrix E be C AM E a Jo j C AM Ee ut u j and vector f be f pEo b PEy If oxygen and or hydrogen are not measured the corresponding row s of matrix E and vector f are omitted If O and H measurements are considered as exact amounts they are treated as other elements and matrix E and vector f are omitted We might have some known target values for compounds Usually these target values come from mineralogical analysis Each compound with a given target value has a given weight w Let diagonal matrix D be Copyright Outotec Oyj 2014 Qutotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 17 21 Maenpaa w if T is given D O0 if T is not given D 0 iz and vector d W l if T is given ii i i O if T is not giv
4. calculated amount of the th compound number of compounds given in stability order e g number of oxides sulfates sulfides carbonates chlorides or fluorides target value of the th compound 1 Calculation of percentages of compounds from the element measurements Compound measurements may exist All measured compounds such as oxides SIO AI2O3 MgO CaO are converted back to elements Si Al Mg Ca O before the calculation starts There are three methods to solve the problem Method 1 The mass balance equations for the elements are i 21 Ne Ne C AM TO es Es i M zs i J Let matrix B be Copyright Outotec Oyj 2014 HSC 8 Species Converter utotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 14 21 Maenpaa and vector b be b LjpE apne Where L 10000 if pE 15 L 1 otherwise Now the mass balance equations can be written in matrix form Bo b It is possible although not very common that oxygen and or hydrogen measurements exist The measured amounts of these elements can be set as minimum amounts or exact amounts If the amount of oxygen hydrogen is considered as an exact amount Ne also contains oxygen hydrogen If the measured amounts of oxygen and hydrogen are considered as minimum amounts the equations for oxygen and or hydrogen are Ne Co AM o gt pE B ow Pi Pro No Cy AM gt pE a M a Let matrix E be _ Co
5. 0 130 As 0 130 Pbs 4 503 4 500 10 000 Ag 0 090 Ag 0 090 Sb253 0 279 Au L OOE 03 Au 1 00E 03 As283 0 213 S102 4 650 Si 2 174 Ag28 0 103 AI203 2 200 Al 1 164 Au 1 00E 03 Mel 0 150 Mg 0 090 sid 4 650 Oo 3 572 AI203 2 200 H 0 000 MeO 0 150 Others 0 802 Others 0 802 Fig 14 Conversion results calculated with Method 2 Copyright Outotec Oyj 2014 Outotec Research Center Pori Jaana Tommiska Lauri 14015 ORC J Maenpaa 22 5 HSC 8 Species Converter December 10 2014 13 21 Description of the Conversion Methods Abbreviations Ne Nc pE AM Mi M Cij M Cj j Coj AM o AM u Dj Nes lj number of measured elements excluding oxygen and or hydrogen number of compounds to be calculated measured percentage of the th element atomic mass of the ith element molecular mass of the th calculated compound molecular mass of the th measured compound coefficient of the i th element in the j th calculated compound e g if the th element is S and the th compound is CuFeS2 then the coefficient is 2 coefficient of the th measured compound in the th compound e g if the th measured compound is H2O and the jth compound is CaSO4 2H20 then this coefficient is 2 If the th measured compound is Fe3O4 and the j th compound is Fe3OA then this coefficient is 1 coefficient of oxygen in the th compound coefficient of hydrogen in the jth compound atomic mass of oxygen atomic mass of hydrogen
6. of the spreadsheet will indicate the success of the output analysis solution The lower the value of the error the better the solution The value is calculated using Equation 2 H Residual Error 0 362 Fig 6 Residual Error Residual Error Y IN No measured 2 Ne Total amount of the element in all the output species Ne measured Otal amount of the element in the input analysis You can attempt to force the residual error below a set norm value with the Set norm below the limit option Fig 7 You can set the value in the Norm limit field and click Solve to get the new conversion with a smaller residual error Please note that too small norm limits or errors in the analyses can cause the optimization routine to fail and result in a total wt exceeding 100 Norm limit 0 0001 Set norm below the limit i Fig 7 Norm settings can be used to force the residual error below a certain limit NB Norm settings can be used only with solution Methods 1 and 2 The Exact O and H measurement options Fig 8 enable you to specify the amounts of oxygen and hydrogen as the exact amounts entered in the input analysis or as the minimum amounts If the options are unchecked you may get an output analysis in which the amount of oxygen or hydrogen is larger than that specified in the input analysis This can be used for example when determining a mineralogical composition for an oxide sample for which the metals compositions are k
7. 4 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 20 21 Maenpaa Method 2 100 B 100 b where H 100000 100000 and h 2 100000 100 A S A ps B and W as above and S 0 ith compound in stability order jth compound j 1 ith compound in stability order jth compound 1 Nes J 1 No The number A may be varied according to how much weight we want to give to the values of vector pS 3 Constrained residual norm It is also possible to solve the following problem for Methods 1 and 2 minw o subject to Bp b lt and l1 1 o 100 and p20 This problem is known as weighted non negative basis pursuit denoising and is described in more detail in Copyright Outotec Oyj 2014 HSC 8 Species Converter Qutotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 21 21 Maenpaa 22 6 References 1 Golub Van Loan Matrix Computations 2 Lawson Hanson Solving Least Squares Problems 3 Tommiska The weighted non negative basis pursuit denoising 4 Escoda Granai Vandergheynst On the Use of A Priori Information for Sparse Signal Approximations Technical Report No 23 2004 Copyright Outotec Oyj 2014
8. 83 0 213 1 000 Sid 4 650 Si 2 174 Ag28 0 103 OO AI203 2 200 AI 1 164 AU 1 00E 03 1 000 M gO 0 150 Mg 0 090 SO 4 650 1 000 0 3 572 AI203 2 200 OOU H 0 000 MgO 0 150 1 000 Others 1 98E 08 Others 0 00E 00 0 00 E Fig 13 Conversion results Please note that the element balance limit is not reached for sulfur copper and iron Copyright Outotec Oyj 2014 HSC 8 Species Converter utotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 12 21 Maenpaa If the results from Fig 13 are compared with the results calculated with Method 2 Fig 14 it can be seen that Method 2 produces a better elemental balance and a smaller Residual Error in this particular example However this comparison also shows that the calculated values are closer to the given target values for the results calculated with Method 1 Note that Method 3 cannot be used in this example because the amount of input species 14 target values 3 is equal to the amount of output species 1 7 Name Example Conversion Residual Date Error 0 017 Author Analysis Calculated Calculated Target Weight Type Elements wt Elements wt o wt o wt Vo Coeff 100 000 79 500 5 32 850 8 32 850 Cus 0 676 Cu 25 700 Cu 25 700 Cu25 5 827 Fe 24 700 Fe 24 717 CuFeS2 59 483 60 000 10 000 Ni 0 550 Mi 0 530 Fes 0 00E 00 Co 0 010 Co 0 010 Fes2 14 210 15 000 10 000 Zn 4 050 Zn 4 050 NiS 0 850 Pb 3 900 Ph 3 900 Cos 0 015 sh 0 200 Sb 0 200 Ans 6 036 As
9. Ei l M 4 Mj Sheeti Kam Fig 4 Element Balance The Limit values for the elements are red if the values are less than the user set Limit threshold value You can try to resolve Limit failures by modifying the species in the output analysis or you can add pure elements for elements where the limit failure occurs using Fix Element Balance Fig 5 The added elements will have small weight coefficients by default so that they do not alter the analysis too much 1 E Initialize Solve Element Charts Balance Actions Calculated Target Weight Type wt o wt s Coeff 100 000 0 000 1 000 1 000 1 000 00 1 000 1 000 0 100 b LOU D LOU QU Fig 5 Fix Element Balance This will add pure elements to the output analysis to conserve the elemental balance Analysis conversion also adds the Others variable as part of the output analysis It can be used to include the unknown part of the input analysis Usually the weight coefficient of this variable is low in order to minimize its amount however you can adjust the weight Copyright Outotec Oyj 2014 HSC 8 Species Converter utotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 5 21 Maenpaa coefficients at any time to get conversions which better reflect the experimental input analyses The use of weight coefficients is introduced in section 22 2 Analysis weighting and Target calculation The Residual Error Fig 6 at the top
10. H L Outotec Fig 3 Converted analysis Along with the converted analysis you may get red values in the Calculated Elements column if the results failed to reach the input elemental analysis based on the Limit set by the user The default value for the limit is 99 7 This means that the value of the element will be colored red in the Calculated Elements if the ratio of the element amount in the output and input analyses is less than 99 7 Note that if the element amount in the output analysis is larger than the amount in the input analysis then the inverse of the ratio is used in the Limit calculation You can check the calculated Limit value for each element from the Element Balance dialog Fig 4 _ ais 490 gt Limit 1 N 1 e measured Ne total otal amount of the element in all of the species in output analysis Ne measured Otal amount of the element in all of the species in input analysis Copyright Outotec Oyj 2014 Outotec S Y Research Center Pori Jaana Tommiska Lauri 14015 ORC J 4 21 M enp Fix Element Initialize Balance Actions Element Balance o X of TS ET x 3 ES Cut Copy Paste Cells ENUGNE 56 0c E EE Elements Cu s Fe Mi 2 nput kg 250 000 400 000 100 000 250 000 3 Output kg 20 0 75 385 247 100 000 257 678 4 Balance kg POS 14 753 0 000 f 678 5 Error 2 830 3 688 0 000 3 071 6 Limit 97 248 96 312 100 000 97 020
11. HSC 8 Species Converter Qutotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 1 21 Maenpaa 22 Species Converter Module Elements iM Cu us M Fe M Ni Species E CuS i Cu2S J CuFeS2 i FeS2 B NiS SUMMARY Composition conversions between substance mineralogy and elemental analyses are often needed in chemical R amp D work The Species Converter module allows you to convert an elemental analysis to a species analysis and vice versa You can apply weighting of certain species to increase or decrease their amounts in the converted analysis Calculations also allow targets to be set on analysis composition to reach a specific weight percentage for selected species You may also carry out the conversion in AG stability order for certain species types Copyright Outotec Oyj 2014 Qutotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J Maenpaa 2 21 22 1 Converting Analyses To convert elemental analyses to species analyses first you need to enter the nput analysis Fig 1 Analyses can be typed manually or pasted from e g Excel The species in the analyses do not have to exist in the HSC Database Please also note that the total wt of the input analysis can be below 100 5 INPUT b Analysis 7 Elements wt o 5 Total 100 000 3 Cu 25 000 10 s 40 000 11 Fe 0 000 12 Ni 25 000 13 Fig 1 Enter the Input analysis in the table
12. Method 3 Method 3 allows you to apply weight coefficients for species with and without target values to a certain extent The method requires that the number of species in the output list is greater than the sum of targets and input species see Equation 3 Others is not considered as a species this case This method is based on the mathematical method called Column scaling Underdetermined non negative least squares is used to achieve the solution N Output species gt N rargets Ninput species 3 Usually Methods 2 and 3 give a better element balance than Method 1 Copyright Outotec Oyj 2014 HSC 8 Species Converter utotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 8 21 Maenpaa 22 3 Stability Weighting Stability Weighting allows you to form the conversion of specific species types in order of AG stability There are currently seven species types that can be used in stability weighting Only one species type can be selected at a time and the recognized species are indicated in the Type column Fig 2 Note that the species used in Stability Weighting have to exist in the HSC Database in order for them to have a AG value To form the conversion with Stability Weighting select the correct species type from the top menu drop down list Fig 11 and set a weighting coefficient value for the stability weighting The coefficient works in a similar way to the weight coefficient in the Target
13. calculation but the weighting is applied to the whole species type Finally click Solve to calculate the results Species type Sulfides Weighting coef 80 Calculated Target Weigh wt wt Coeff cus 3 619 1 000 sulfide cu2s 0 000 1 000 sulfide CuFesS 55 147 1 000 sulfide NiS 41 240 1 000 sulfide Ni352 0 000 1 000 sulfide Others 0 000 0 001 Fig 11 Stability weighting and species types Copyright Outotec Oyj 2014 HSC 8 Species Converter utotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 9 21 Maenpaa 22 4 Example Conversion A mineral sample has the elemental composition shown in Table 1 In addition the sample is known to contain sulfide minerals for which the wt values are 60 chalcopyrite CuFeS2 15 pyrite FeS2 and 4 5 galena PbS Table 1 Elemental composition of a mineral sample m 39e The elemental analysis of the sample can be copied as the input analysis for the conversion Next the output analysis needs to be defined with species that are expected to be present in the sample Table 2 Copyright Outotec Oyj 2014 HSC 8 Species Converter utotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 10 21 Maenpaa Table 2 Expected mineral species in the sample and their estimated proportions Species Estimated Wt CuS Cu2S To promote the target values in the solution the weight coeffici
14. en Now we have to solve the following problem min Hp h subject to p 2 0 and Ep f 100 B 100 b where H 210000 D and h 10000 d 100000 100000 100000 100 The condition I 00000 1 00000 p 100000 100 guarantees that the sum of the percentages of the compounds is 100 Method 3 Each compound has a given weight w Let W be a diagonal matrix defined as w if compound i has no target value W Il 1 if target value exists The mass balance equations for the elements are i 1 N Ne C AM Zii ip DE gt y RBS J Let matrix B be Copyright Outotec Oyj 2014 HSC 8 Species Converter Qutotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 18 21 Maenpaa C AM B W il M i 1 N J 1 No and vector b be b pE i 1 N Now we can write the mass balance equations in matrix form Bo b It is possible although not very common that oxygen and or hydrogen measurements exist The measured amounts of these elements can be set as minimum amounts or exact amounts If the measured amounts of oxygen and hydrogen are considered as minimum amounts the equations for oxygen and or hydrogen are No Ca AM Y Co MIo gt pEo x and vector f be f pEo h PEy If oxygen and or hydrogen are not measured the corresponding row s of matrix E and vector f are omitted If O and H measurements are considered as exact amounts the
15. ent of three species can be increased to 10 0 Fig 12 Copyright Outotec Oyj 2014 HSC 8 Species Converter utotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 11 21 Maenpaa INPUT OUTPUT Analysis Calculated Calculated Target Weight Elements wt Elements wt o wt o Coeff 79 500 s 32 850 Cus QUO Cu 25 700 Cu25 1 000 Fe 24 700 CuFeS2 60 0040 10 000 Ni 0 550 Fes 1 000 Co 0 010 Fe82 15 000 10 000 An 4 050 Mis OU Ph 3 900 CoS 1 000 Sb 0 200 zns 1 000 AS 0 130 PbS 4 500 10 000 AE D OS Sb283 OO Au 00E 03 As253 1 000 SO 4 650 Ag2s i QUO AI203 2 200 Au 1 000 MeO 0 150 SiO2 000 Al203 1 000 MgO 1 000 L Fig 12 Defined input and output analyses Weight coefficients of the target values have been increased to 10 0 A solution calculated with Method 1 for the output analysis is shown in Fig 13 Name Example Conversion Residual Date Error 1 076 Author Analysis Calculated Calculated Target Weight Type Elements wt Elements wt o wt wt Coeff Total 90 181 100 000 S 32 850 33 259 Cus O 00E 00 O00 Cu 25 700 Cu 25 57 Cu28 6 006 1 000 Fe 24 700 Fe 25 239 CuFeS2 59 997 60 000 10 000 Ni 0 550 Ni 0 550 Fes 0 00E 00 1 000 Co 0 010 Co D OTU Fes 14 995 15 000 10 000 Zn 4 050 Zn 4 050 Nis 0 850 O00 Ph 3 900 Pb 3 900 CoS 0 015 1 000 sh 0 200 Sb 0 200 Ans 6 036 O00 As 0 130 As 0 130 PbS 4 503 4 500 10 000 Ag 0 090 Ag 0 090 Sh283 0 279 O00 AU OQE 03 Au 1 00E 03 As2
16. nown If Exact O H is unchecked the difference between the measured amount and the calculated amount is not included in the residual error M Exact Q measurement mE Exact H measurement Fig 8 Exact O and H measurement options The calculated results can be cleared with the nitialize button Initialization also returns the calculated elemental composition of the input analysis This is useful especially in cases where the analysis contains species Fig 9 Copyright Outotec Oyj 2014 HSC 8 Species Converter utotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 6 21 Maenpaa Element Charts Fix Element Initialize Balance Balance Actions Calculated wt Elements 25 000 Cu 10 CuO 25 000 O 15 053 11 25 000 5 10 058 Er 25 000 13 Fig 9 The Initialize button will produce the calculated elemental composition of the input analysis Copyright Outotec Oyj 2014 Qutotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 7 21 Maenpaa 22 2 Analysis Weighting and Target Calculation The output analysis can be adjusted with the use of weighting coefficients You can easily change the weight coefficient of the species from the Weight Coeff column Fig 2 and re calculate the analysis to obtain different results The greater the weight coefficient of a species is the greater the amount of included elements will be in the f
17. ormation of the species in the output analysis You can also set a Target wt value for a species in the analysis Fig 2 To use the Target wt feature enter a target value for a selected species and increase the weight coefficient of that species to force the conversion towards the target value The three calculation methods available Fig 10 can provide you with alternative solutions for analysis conversion These methods differ from each other in terms of how the solution is generated and how they enable the weighting to be applied The methods are presented briefly in the sections below The Small Meas Limit value in the same settings Fig 10 determines the threshold value wt for the species which are considered as small amounts in the charts small Meas Limit 0 5 Method Method 1 Fig 10 Calculation methods and the limit for small measurements Method 1 Method 1 allows you to apply weight coefficients for species with and without target values It also enables the use of all the other calculation options This method requires usually more analysis adjustment e g Fix Element Balance than the other two methods in order for the solution to reach the element balance limit Method 2 Method 2 allows you to apply weight coefficients only for the species that also have a target wt value Weight coefficients without target values will be ignored This method is a simple least squares method with known target values
18. y are treated as other elements and matrix E and the vector f are omitted We might have some known target values for compounds Usually these target values come from mineralogical analysis Let matrix D be Copyright Outotec Oyj 2014 HSC 8 Species Converter utotec December 10 2014 Research Center Pori Jaana Tommiska Lauri 14015 ORC J 19 21 Maenpaa w 0 001 if T is given O0 if T is not given D fs and vector d W 0 001 7 if T is given I O if T is not given Now we have to solve the following problem min Hp h subject to pz 0 and Ep f B b where H D and hid 1 1 100 The solution is p Wp 2 Calculation of compounds in order of stability Stability order calculations are only available if Method 1 or Method 2 is selected Let the stability order of sulfates sulfides carbonates fluorides and chlorides be given First we create the chosen type of compound in order of stability until all elements are consumed or the amount of compounds exceeds 100 We now suppose that the number of compounds Nc contains the compounds created in order of stability Let pS be the vector of amounts of sulfides sulfates carbonates fluorides or chlorides created in order of stability Now we can form the mass balance equations as follows min Hp hl subject to p 20 Method 1 Ww 0 UNT 2 an pepe P 100000 100000 100000 100 A S A pS Copyright Outotec Oyj 2014 Qutotec December 10 201
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