Mäenpää 22. Species Converter Module

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HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-J1 (21)22. Species Converter ModuleSUMMARYComposition conversions, between substance (mineralogy) and elemental analyses, areoften needed in chemical R&D work. The Species Converter module allows you to convertan elemental analysis to a species analysis and vice versa.You can apply weighting of certain species to increase or decrease their amounts in theconverted analysis. Calculations also allow targets to be set on analysis composition toreach a specific weight percentage for selected species. You may also carry out theconversion in G stability order for certain species types.Copyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää22.1.14015-ORC-J2 (21)Converting AnalysesTo convert elemental analyses to species analyses, first you need to enter the Inputanalysis (Fig. 1). Analyses can be typed manually or pasted from e.g. Excel. The species inthe 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%.Fig. 1. Enter the Input analysis in the table.After you have entered the Input analysis, you need to specify the species for the Outputanalysis (Fig. 2) and click Solve to get the converted analysis (Fig. 3). Note that speciescontaining elements which are not present in the input analysis are disregarded in thesolution, with the exceptions of oxygen and hydrogen.Fig. 2. Enter the species for the output analysis.Copyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-J3 (21)Fig. 3. Converted analysis.Along with the converted analysis you may get red values in the Calculated Elementscolumn if the results failed to reach the input elemental analysis based on the Limit set bythe user. The default value for the limit is 99.7. This means that the value of the element willbe colored red in the Calculated Elements if the ratio of the element amount in the outputand input analyses is less than 99.7%1. Note that if the element amount in the outputanalysis is larger than the amount in the input analysis, then the inverse of the ratio is usedin the Limit calculation. You can check the calculated Limit value for each element from theElement Balance dialog (Fig. 4).Ne, totalN e, measured* 100LimitNe,total Total amount of the element in all of the species in output analysisNe,measured Total amount of the element in all of the species in input analysis.Copyright Outotec Oyj 2014(1)

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-J4 (21)Fig. 4. Element Balance. The Limit values for the elements are red if the values are less than theuser-set Limit threshold value.You can try to resolve Limit failures by modifying the species in the output analysis, or youcan add pure elements for elements where the limit failure occurs using Fix ElementBalance (Fig. 5). The added elements will have small weight coefficients by default, so thatthey do not alter the analysis too much.Fig. 5. Fix Element Balance. This will add pure elements to the output analysis to conserve theelemental balance.Analysis conversion also adds the [Others] variable as part of the output analysis. It can beused to include the unknown part of the input analysis. Usually the weight coefficient of thisvariable is low in order to minimize its amount; however, you can adjust the weightCopyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-J5 (21)coefficients at any time to get conversions which better reflect the experimental inputanalyses. The use of weight coefficients is introduced in section 22.2 Analysis weightingand Target calculation.The Residual Error (Fig. 6) at the top of the spreadsheet will indicate the "success" of theoutput analysis solution. The lower the value of the error, the better the solution. The valueis calculated using Equation (2).Fig. 6. Residual Error.Residual ErrorNeNe,measured(2)Ne Total amount of the element in all the output speciesNe, measured Total amount of the element in the input analysisYou can attempt to force the residual error below a set norm value with the Set norm belowthe limit option (Fig. 7). You can set the value in the Norm limit field and click Solve to getthe new conversion with a smaller residual error. Please note that too small norm limits orerrors in the analyses can cause the optimization routine to fail and result in a total wt-%exceeding 100%.Fig. 7. Norm settings can be used to force the residual error below a certain limit. NB! Norm settingscan be used only with solution Methods 1 and 2.The Exact O and H measurement options (Fig. 8) enable you to specify the amounts ofoxygen and hydrogen as the exact amounts entered in the input analysis or as theminimum amounts. If the options are unchecked, you may get an output analysis in whichthe amount of oxygen or hydrogen is larger than that specified in the input analysis. Thiscan be used, for example, when determining a mineralogical composition for an oxidesample for which the metals compositions are known. If Exact O/H is unchecked, thedifference between the measured amount and the calculated amount is not included in theresidual error.Fig. 8. Exact O and H measurement options.The calculated results can be cleared with the Initialize button. Initialization also returns thecalculated elemental composition of the input analysis. This is useful, especially in caseswhere the analysis contains species (Fig. 9).Copyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-J6 (21)Fig. 9. The Initialize button will produce the calculated elemental composition of the input analysis.Copyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää22.2.14015-ORC-J7 (21)Analysis Weighting and Target CalculationThe output analysis can be adjusted with the use of weighting coefficients. You can easilychange the weight coefficient of the species from the Weight Coeff. column (Fig. 2) and recalculate the analysis to obtain different results. The greater the weight coefficient of aspecies is, the greater the amount of included elements will be, in the formation of thespecies in the output analysis.You can also set a Target wt-% value for a species in the analysis (Fig. 2). To use theTarget wt-% feature, enter a target value for a selected species and increase the weightcoefficient of that species to force the conversion towards the target value.The three calculation methods available (Fig. 10) can provide you with alternative solutionsfor analysis conversion. These methods differ from each other in terms of how the solutionis generated and how they enable the weighting to be applied. The methods are presentedbriefly 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 smallamounts in the charts.Fig. 10. Calculation methods and the limit for small measurements.Method 1Method 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 usuallymore analysis adjustment (e.g. Fix Element Balance) than the other two methods in orderfor the solution to reach the element balance limit.Method 2Method 2 allows you to apply weight coefficients only for the species that also have a targetwt-% value. Weight coefficients without target values will be ignored. This method is asimple least squares method with known target values.Method 3Method 3 allows you to apply weight coefficients for species with and without target valuesto a certain extent. The method requires that the number of species in the output list isgreater than the sum of targets and input species, see Equation (3) ([Others] is notconsidered as a species this case). This method is based on the mathematical methodcalled Column scaling. Underdetermined non-negative least squares is used to achieve thesolution.NOutput speciesNTargetsNInput speciesUsually Methods 2 and 3 give a better element balance than Method 1.Copyright Outotec Oyj 2014(3)

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää22.3.14015-ORC-J8 (21)Stability WeightingStability Weighting allows you to form the conversion of specific species types in order ofG 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 indicatedin the Type column (Fig. 2). Note that the species used in Stability Weighting have to existin the HSC Database, in order for them to have a G value.To form the conversion with Stability Weighting, select the correct species type from the topmenu drop-down list (Fig. 11) and set a weighting coefficient value for the stabilityweighting. The coefficient works in a similar way to the weight coefficient in the Targetcalculation, but the weighting is applied to the whole species type. Finally, click Solve tocalculate the results.Fig. 11. Stability weighting and species types.Copyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää22.4.14015-ORC-J9 (21)Example ConversionA mineral sample has the elemental composition shown in Table 1. In addition, the sampleis 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.Element / O32.200MgO0.150Total99.181The elemental analysis of the sample can be copied as the input analysis for theconversion. Next, the output analysis needs to be defined with species that are expected tobe present in the sample (Table 2).Copyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-J10 (21)Table 2. Expected mineral species in the sample and their estimated proportions.SpeciesEstimated S3As2S3Ag2SAuSiO2Al2O3MgOTo promote the target values in the solution, the weight coefficient of three species can beincreased to 10.0 (Fig. 12).Copyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-J11 (21)Fig. 12. Defined input and output analyses. Weight coefficients of the target values have beenincreased to 10.0.A solution calculated with Method 1 for the output analysis is shown in Fig. 13.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 ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-J12 (21)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 ResidualError in this particular example. However, this comparison also shows that the calculatedvalues are closer to the given target values for the results calculated with Method 1. (Notethat 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 (17)).Fig. 14. Conversion results calculated with Method 2.Copyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää22.5.14015-ORC-J13 (21)Description of the Conversion CH,j(AM)O(AM)HpjNCSTjnumber of measured elements excluding oxygen and/or hydrogennumber of compounds to be calculatedmeasured percentage of the i th elementatomic mass of the i th elementmolecular mass of the i th calculated compoundmolecular mass of the i th measured compoundcoefficient of the i th element in the j th calculated compound (e.g. if the i thelement is S and the j th compound is CuFeS2, then the coefficient is 2)coefficient of the i th measured compound in the j th compound (e.g. if the i thmeasured compound is H2O and the j th compound is CaSO4*2H2O, then thiscoefficient is 2. If the i th measured compound is Fe3O4 and the j th compoundis Fe3O4, then this coefficient is 1)coefficient of oxygen in the j th compoundcoefficient of hydrogen in the j th compoundatomic mass of oxygenatomic mass of hydrogencalculated amount of the j th compoundnumber of compounds given in stability order e.g. number of oxides, sulfates,sulfides, carbonates, chlorides or fluoridestarget value of the j th compound1. Calculation of percentages of compounds from the element measurementsCompound measurements may exist. All measured compounds such as oxides (SiO,Al2O3, MgO, CaO,.) are converted back to elements (Si, Al, Mg, Ca, O, ) before thecalculation starts.There are three methods to solve the problem:Method 1The mass balance equations for the elements arei1,., NENC Ci , j ( AM )iMjj 1pjpE iLet matrix B beBi , jLiCi , j ( AM )ii1,.,NEj1,., NCMjCopyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-J14 (21)and vector b bebiLi pEii1,., NEWhereLi10000 if pE iLi1 otherwise15Now the mass balance equations can be written in matrix form:BpbIt is possible, although not very common, that oxygen and/or hydrogen measurementsexist. The measured amounts of these elements can be set as minimum amounts or exactamounts. If the amount of oxygen/hydrogen is considered as an exact amount, NE alsocontains oxygen/hydrogen.If the measured amounts of oxygen and hydrogen are considered as minimum amounts,the equations for oxygen and/or hydrogen areNCCO, j ( AM )OMjj 1NC Cj 1H , j ( AM )HMjpjpEOpjpEHLet matrix E beE1, jE 2, jCO, j ( AM )OMjCH , j ( AM )HMjand vector f bef1pEOf2pEHIf oxygen and/or hydrogen are not measured, the corresponding row(s) of matrix E andvector f are omitted. If O and H measurements are considered as exact amounts, they aretreated as other elements and matrix E and vector f are omitted.Each compound has a given weight wii. Let W be the NC x NC diagonal matrix of theweights. The greater the weight wii, the more we try to create the i th compound. Thedefault value of a weight is 1.Copyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-J15 (21)We might have some known target values for compounds. Usually these target valuescome from mineralogical analysis. Let diagonal matrix D bew ii if Ti is givenDi ,i0 if Ti is not givenDi , j0 ijand vector dw iiTi if Ti is givendi0 if Ti is not givenNow we have to solve the following problem:min Hp h22subject to pWwhere H0 and Epf10100 * B10000 * Dand h100000.100000100 * b10000 * d100000 * 100The condition 100000.100000 p 100000 * 100guarantees that the sum of the percentages of the compounds is 100.Method 2The mass balance equations for the elements arei1,., NENC Ci , j ( AM )iMjj 1pjpE iLet matrix B beBi , jLiCi , j ( AM )ii1,.,NEj1,., NCMjand vector b beCopyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpääbiLi pEii1,., NE14015-ORC-J16 (21)WhereLi10000 if pE iLi1 otherwise15Now we can write the mass balance equations in matrix form:BpbIt is possible, although not very common, that oxygen and/or hydrogen measurementsexist. The measured amounts of these elements can be set as minimum amounts or exactamounts.If the measured amounts of oxygen and hydrogen are considered as minimum amounts,the equations for oxygen and/or hydrogen areNCCO, j ( AM )OMjj 1NC Cj 1H , j ( AM )HMjpjpEOpjpEHLet matrix E beE1, jE 2, jCO, j ( AM )OMjCH , j ( AM )HMjand vector f bef1pEOf2pEHIf oxygen and/or hydrogen are not measured, the corresponding row(s) of matrix E andvector f are omitted. If O and H measurements are considered as exact amounts, they aretreated as other elements and matrix E and vector f are omitted.We might have some known target values for compounds. Usually these target valuescome from mineralogical analysis. Each compound with a given target value has a givenweight wii. Let diagonal matrix D beCopyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-Jw ii if Ti is givenDi ,i0 if Ti is not givenDi , j0 ijand vector dw iiTi if Ti is givendi0 if Ti is not givenNow we have to solve the following problem:min Hp hwhere H22subject to p0 and Ep100 * B10000 * Dfand h100000.100000100 * b10000 * d100000 * 100The condition 100000.100000 p 100000 * 100guarantees that the sum of the percentages of the compounds is 100.Method 3Each compound has a given weight wj. Let W be a diagonal matrix defined asw i if compound i has no target valueW ii1 iftarget value existsThe mass balance equations for the elements arei1,., NENC Cj 1i , j ( AM )iMjpjpE iLet matrix B beCopyright Outotec Oyj 201417 (21)

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpääBi , jWi14015-ORC-J18 (21)Ci , j ( AM )iMji1,., NEj1,., NCand vector b bebipE ii1,., NENow we can write the mass balance equations in matrix form:BpbIt is possible, although not very common, that oxygen and/or hydrogen measurementsexist. The measured amounts of these elements can be set as minimum amounts or exactamounts.If the measured amounts of oxygen and hydrogen are considered as minimum amounts,the equations for oxygen and/or hydrogen areNCCO, j ( AM )OMjj 1NC Cj 1H , j ( AM )HMjpjpEOpjpEHLet matrix E beE1, jWE 2, jWCO, j ( AM )OMjCH , j ( AM )HMjand vector f bef1pEOf2pEHIf oxygen and/or hydrogen are not measured, the corresponding row(s) of matrix E andvector f are omitted. If O and H measurements are considered as exact amounts, they aretreated as other elements and matrix E and the vector f are omitted.We might have some known target values for compounds. Usually these target valuescome from mineralogical analysis. Let matrix D beCopyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-J19 (21)w ii * 0.001 if Ti is givenDi ,i0 if Ti is not givenDi , j0 ijand vector dw ii * 0.001 * Ti if Ti is givendi0 if Ti is not givenNow we have to solve the following problem:min Hp hwhere H22subject to pBDand h1.10 and Epfbd100The solution isp Wp2. Calculation of compounds in order of stabilityStability 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 areconsumed or the amount of compounds exceeds 100%. We now suppose that the numberof compounds NC contains the compounds created in order of stability.Let pS be the vector of amounts of sulfides, sulfates, carbonates, fluorides or chloridescreated in order of stability. Now we can form the mass balance equations as follows:min Hp h22subject to p0.Method 1Wwhere H1100 * B100000.100000and h0100 * b100000 * 100* pS*SCopyright Outotec Oyj 2014

HSC 8 - Species ConverterDecember 10, 2014Research Center, Pori / Jaana Tommiska, LauriMäenpää14015-ORC-J20 (21)Method 2where H100 * B100 * b100000.100000 and h100000 * 100*S* pSB and W as above andSiji0, ith compound in stability orderjth co

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

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