HSC Chemistry 7.0 User's Guide
Contents
1. 2009 09006 ORC J Figure 32 Mass balance result copper recovery displayed as a Sankey diagram Figure 33 Press Balance gt gt button to get back to the Balance window Figure 34 Visualizing the goodness values HSC Chemistry 7 0 48 33 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 35 Visualizing Sum of weighted least squares The biggest adjustments considering the standard deviation have been made in the stream CC1 12 0 To visualize the mass balancing result as stream tables select in the menu Flowsheet Create Stream Tables Figure 36 Select the components and items Figure 37 and HSC Sim will create stream tables next to the streams Figure 38 The tables are placed in the Balance layer Reorganize the tables and use Copy Paste or Print to report the result out If you rebalance regenerate the balance tables by selecting Flowsheet Update Stream Tables If you want to freeze the mass balance result in the stream tables i e the values would not change even though the Update Stream Tables were selected select Flowsheet Move Tables into Layer and Inactivate Select the layer give the layer a name and HSC Sim will move the balance tables into the selected layer If you create new Stream Tables they will appear in the Balance layer If continuing the loop Create and Move you can report different mass balancing conditions and cases on one flowsheet Each balance is loca2. RDiff Relative difference between measured and balanced ones Rec Recovery against the Reference Stream Method LS Least Squares NNLS Non negative least squares CLS Constrained Least Squares MinMax MinMax method see Figure 19 Options See figure 20 Component Sum 100 Additional constraint the component sum is 100 Solve Solids tph and assays solves both solids flowrates and assays Assays only uses given flowrates and reconciles assays accordingly Solids Water Balance for solids and water is solved simultaneously Water independently Solids mass balance is solved first followed by water mass balance which does not change any more solids mass balance Figure 18 Balancing Reporting Options When MinMax is checked then the methods are UMM Unconstrained MinMax Chebyshev NMM Non negative MinMax Chebyshev not available in HSC 7 0 CMM Constrained MinMax Chebyshev not available in HSC 7 0 Figure 19 Methods available when MinMax is checked HSC Chemistry 7 0 48 23 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Tolerance Iteration is regarded as converged when this limit is reached Tolerance CLS constraints are min tolerance lt x lt max tolerance Estimate for null standard deviation Value that is used if the standard deviation value is missing or if it is zero max iteration Maximum number of iterations in solving the problem Figure 20 Addit
3. S subflow N sublow B diag B Sub flows are indexed up to 1 S N to avoid linear dependency of equality constraints where the operator diag add matrices subflow B at the diagonal of the matrix B and subflow flow unit flow sublow flow unit F e B HSC Chemistry 7 0 48 50 P Lamberg amp J Tommiska October 12 2009 09006 ORC J 3g sum of sub flows is the total flow E F element chemical tot flow tot flow subflow element chemical flow NS subflow subflow flow N element chemical N flow G F G F 1 _ 1 2 _ _ 1 2f if the option minerals sum 100 is selected the following equations are included S F N ement chemicalel subflow element chemical flow N subflow N flow G E 1 1 100 1 1 _ If equations 2f are included B is 1 1 1 2 S F SRU U S N N N N N to avoid linear dependencies The solution method used is the weighted least squares The equations can be solved without any constraints LS subject to non negativity constraints NNLS and subject to simple bounds MVLS If there are no constraints the minimal maximum norm solution can be calculated LS MinMax 5 48 13 References 1 Golub van Loan Matrix Computations Third edition 1996 2 Markov
4. Sim Particles doc and 46 Sim Particles Examples doc HSC7 allows the user to solve the following mass balance problems Table 1 1 Reconcile measured or estimated component flowrates 1D components The component flowrate has been measured or estimated in some of the process streams Optionally user can give an estimate of the component between the output streams of each unit for the streams where there is no flowrate value The component can be for example total solids flowrate water flowrate copper flowrate etc HSC solves the flowrate of each component and distribution between the output streams of each unit independently 2 Mass balance and reconcile chemical analyses 1D assays The chemical composition of each stream has been analyzed but the flowrates have not been analyzed the flowrate of one feed stream has to be given e g 100 HSC solves the flowrates and reconciles analyses 3 Mass balance minerals in minerals processing circuit 1D Minerals The chemical composition of each stream has been analyzed and mineralogy is known i e the minerals present and their chemical composition are known HSC converts the elemental grades into mineral grades solves total solids flowrates reconciles mineral grades with condition that their sum 100 and converts the mineral grades into balanced elemental grades 4 Mass balance size distribution and water balance 1 5D Size distribution of streams has b
5. surveys on different sheets Rename the Streams sheet by double clicking and typing a new name Then you can generate a new sheet and bring in new data Optionally you can open the file in Excel and organize your data there When ready reopen the file in HSC Sim HSC Chemistry 7 0 48 7 P Lamberg amp J Tommiska October 12 2009 09006 ORC J 48 5 Mass Balance Wizard Once the experimental data is ready in HSC Sim you can start the mass balancing and data reconciliation by pressing Balance and Data Reconciliation gt gt gt gt in the lower right corner of the Experimental Data window Figure 3 Please remember that HSC Sim uses the data of the current spreadsheet Please check that the active sheet is the right one Figure 3 Starting the Mass Balancing and Data Reconciliation Now you are supposed to go through the Wizard with five steps You can skip the wizard by pressing Skip Wizard in any step of the wizard 48 5 1 Step 1 Select Components and Analyses In the first step you can define the components to be selected in the mass balance equation and you define their types Click the second column to change between the selected X and not selected Figure 4 Click the row and you can see the variation of selected element if selected i e the second column has the X in the flowsheet as a Sankey diagram Figure 5 Check the variable type third column If the variable type thi
6. 48 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Equations 2f and 2g are equality constraints The solution method used is the element wise total least squares and m values can be solved without any constraints LS subject to non negativity constraints NNLS and subject to simple bounds MVLS If there are no constraints the minimal maximum norm solution can be calculated LS MinMax 5 1D analyses If 1D analyses are given the balanced analyses are calculated as in 1D Analyses 48 12 3 2D MASS BALANCE Before a 2D mass balance solution 1D or 1 5D mass balance must be solved The results of the 1D or 1 5D solution are used in 2D solution In a 2D solution the sub flows are calculated first and after that the analyses are solved tot flow F 2D sub flows The equations for 2D sub flows solution are 3a mass balance equations for each unit that is not size reducing S NU subflow flow N flow unit flow N subflow reducing size not unit n n unit F e F 1 0 1 1 1 2 Above is the index of ith unit that is not size reducing Units are indexed up to in 1 U N to avoid linear dependency of equality constraints 3b sum of sub flows is the total flow 2 1 1 F tot flow NS subflow subflow flow N flow F F 3c analyses for each unit that is not size reducing S E NU su
7. 48 30 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 29 Page two of the Report Figure 30 Report page three Currently only balanced values Bal are selected to be reported HSC Chemistry 7 0 48 31 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 31 Report page four Items to be reported are selected from the Balance Report options see previous figure where only the balanced values are selected here Meas Bal Dif RDiff and Rec are selected to be visible 48 7 3 Visualizing on the flowsheet A balance result can also be visualized on the flowsheet To display any component and any item measured balanced standard deviation minimum maximum difference relative difference recovery select the corresponding column on the Data Sheet and the Mass Balance window will be minimized and the flowsheet will be shown displaying the selected item in a Sankey diagram Figure 32 To get back to the Balance window use the Balance button Figure 33 To visualize the goodness values from the report please press Visualize in the Report and select between Sum WSSQ sum of weighted least squared DiffSum sum of total differences and RelDiffSum sum of relative differences Figure 34 These figures will help in finding the streams with the biggest adjustments and to fine tune the mass balancing Figure 35 HSC Chemistry 7 0 48 32 P Lamberg amp J Tommiska October 12
8. 7 0 48 37 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 41 Saving Balance file with different name 48 8 3 Saving the result into Assays xls From the menu select File Save Result into Experimental Sheet Analyses xls Figure 42 Give the sheet a name Figure 43 and HSC Sim will copy the balanced values into the sheet and fill in the Source and Destination and calculate recoveries Figure 44 Figure 42 Saving result into Analyses xls Figure 43 Give the sheet a name HSC Chemistry 7 0 48 38 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 44 Balance result Balanced values only in the Experimental Data Analyses xls as a new sheet 48 8 4 Opening mass balance file as an template You can open previously saved mass balance files as templates by selecting File Open Balance File As Template Figure 45 HSC will now take the stream selections error models min max values from the template and then use the measured values of the current data To use this the template data and current mass balance problem should be similar in structure i e the same components assayed in the same streams Figure 45 Opening mass balance file as an template 48 9 Solving Several Cases With HSC Sim it is possible to solve huge number of similar mass balance cases easily in one go This kind of feature is needed when mass balancing e g shift or day assays from a long period s
9. and mass balances particle classes in a way that the balance is in harmony with 1D and 2D balances Table 1 Mass balance cases that can be solved with HSC Sim The red X indicates that data is necessary and defines the case In order to solve the 3D mass balance the particle tracking module of HSC is required This is currently available only for AMIRA P9O Sponsors Assayed or Case estimated values 1D Components 1D Assays 1D Minerals 1 5D 2D Assays 2D Minerals 3D Total stream flowrates X Total solid flowrates X X X X X X X Liquid flowrates X X X X Component flowrates X Component distributions X Solids X X X X X X Bulk chemical compositions X X X X X Minerals and their chemical composition X X X Particle size distribution X X X X Chemical composition of size fractions X X X Particles MLA data X HSC Chemistry 7 0 48 4 P Lamberg amp J Tommiska October 12 2009 09006 ORC J 48 2 Mass balancing steps in HSC 7 The mass balancing steps of HSC 7 are 1 Open HSC Sim and change to Experimental Mode see manual 47 Sim Experimental 2 Draw the flowsheet see manuals 40 Sim Flowsheet and 47 Sim Experimental You can draw all the streams and units HSC will create the mass balance equations according to the available data therefore there is no need to draw the flowsheet for mass balancing only or every time a new flo
10. is called Set also Case can be used and the streams are listed horizontally Figure 47 Changing a Case Set HSC Chemistry 7 0 48 40 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 48 Solving all mass balance cases Figure 49 Give the sheet name in Analyses xls where the results are stored Figure 50 Data 48 10 Solving 2D cases When you have a 2D size by size assay data the procedure in HSC Sim is 1 Organize your data in Analyses xls in a way that for the unsized data the FractionNo is zero FractionNo 0 and the size fractions follow with numbers 1 2 3 Give the Fraction name and Fraction mass percentage Fraction m Figure 51 To initialize select from the menu Create Stream Properties Sheet Horizontal With Multiple Size Fractions Figure 52 2 Solve first the 1D case 3 Change the dimensions to 2D 1D result is now frozen Figure 53 4 Check the conditions and run the mass balance for 2D 5 Study the result report and save The file will have two balance pages 1D and 2D Figure 54 HSC Chemistry 7 0 48 41 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Please note that when changing from 1D to 2D the 1D mass balance is frozen i e it will not be changed 2D data does not need to be complete some streams mass balanced in 1D may be missing analyses and some components may be missing in 2D data For more information see t
11. the Reference stream 48 5 5 Step 5 Check Mass Balance Nodes and Possible Errors In the final 5th step you should check the mass balance nodes and go through the possible errors HSC Sim has found in the raw data Figure 10 Based on the assays available HSC Sim will create mass balance nodes If a stream does not have any measurements then the size of the mass balance node is increased You can check the mass balance node by activating the mass balance node and checking the inputs and outputs of the node on the flowsheet blue is used for input streams of the node red for output streams of the node thick black nodes are streams within the node but cannot be HSC Chemistry 7 0 48 14 P Lamberg amp J Tommiska October 12 2009 09006 ORC J solved directly due to missing data and thin black nodes are not included in the mass balance node See Figures 11 and 12 for examples Figure 10 Fifth step of the Mass Balancing Wizard Check the mass balance nodes and possible errors Errors mean that the assayed values of input streams are out of the range of the output streams see Figure 13 By going through the errors you may find some bad samples that you may even turn off in the mass balancing or you may assign a high sampling error In the same way you may find that some component assay has more errors Again you may end up by turning that component off in mass balancing or then you may assign a high standard deviation for t
12. 09 09006 ORC J a b c d e Figure 8 Error models a Fixed absolute 0 4 b Fixed relative 5 c a b c MIN MAX 5 0 4 1 5 d a b c MIN a b c 5 0 5 2 1 e a b c MAX a b c 5 0 5 2 1 To find out which error model you should use please do some duplicate assays Most laboratories however know their detection limits and relative standard deviations Quite often the standard deviation does not increase any more linearly when reaching the easy assay range see Figure 8c Quite often these types of error models are the most applicable HSC Chemistry 7 0 48 13 P Lamberg amp J Tommiska October 12 2009 09006 ORC J ones i e the ones shown in Figure 8c and 8d Type a b c MIN a b c is the default for assays Figure 8 Avoid mixing the assay error and sampling error You can define the sampling error for each stream individually finally when you have completed steps 1 5 in the Wizard The final standard deviation is the sum of the sampling error and assay error see chapter 48 6 48 5 4 Step 4 Define the Reference Stream In the fourth step you must define the reference stream This is the stream against which the recoveries are calculated Normally this is a feed stream If there are several feed streams you can define only one reference stream in version 7 0 To define the reference stream check the stream in the list box or directly in the flowsheet Figure 9 Step 4 of 5 Define
13. HSC Chemistry 7 0 48 1 P Lamberg amp J Tommiska October 12 2009 09006 ORC J HSC Chemistry 7 0 User s Guide Mass Balancing and Data Reconciliation Pertti Lamberg and Jaana Tommiska Outotec Research Oy Information Service P O Box 69 FIN 28101 PORI FINLAND Fax 358 20 529 3203 Tel 358 20 529 211 E mail hsc outotec com www outotec com hsc HSC Chemistry 7 0 48 2 P Lamberg amp J Tommiska October 12 2009 09006 ORC J 48 MASS BALANCING AND DATA RECONCILIATION 48 1 General Mass balancing is a common practice in metallurgy The mass balance of a circuit is needed for several reasons To estimate the metallurgical performance of the circuit To locate process bottlenecks and for circuit diagnosis To create models of the processing stages To simulate the process The following steps are often required to simulate a process 1 Collecting experimental data experimental work sampling sample preparation assaying 2 Mass balancing and data reconciliation of the experimental data 3 Model building 4 Simulation Currently in HSC you can do all the steps in one program HSC Sim To work with experimental data please see manual 47 HSC Experimental doc for model building see 79 Sim Data Fit doc and for simulations see 40 Sim Flowsheet doc 41 Sim Reactions Example doc 43 Sim Distribution Sample doc 44 Sim Distribution Examples doc 45
14. M W measured water flowrate Pc solids 100 W F F M Pc measured solids M fraction m flow subflow flow F F 100 M M fraction m measurements otherwise unit the from exits flow the unit the enters flow the eunit flow 0 1 1 48 12 1 1D Mass Balance In the 1D mass balance solution solids and water flowrates are solved first After that the 1D analyses are solved The solids and water flowrates can be solved simultaneously or so that the solids flowrates are solved first and after that the water flowrates are solved HSC Chemistry 7 0 48 44 P Lamberg amp J Tommiska October 12 2009 09006 ORC J 1D flowrates The solids flowrate solution first and the water flowrate solution after that The equations for 1D solids flowrate solution are 1a mass balance equations U tot flow N flow unit flow N unit F e F 1 0 1 1 1b analyses E U tot flow M element chemical tot flow N flow unit flow N element chemical N unit F G e F 1 _ 1 0 _ 1 1 1c solids flowrate measurements 1 1 F M tot flow tot flow N flow F F The equations for 1D water flowrate solution are 1d mass balance equations U tot flow N f
15. ass balance nodes available and used Inputs number of input streams available and used Output number of output streams 1D Data 1D mass balance data available and used SF solids flowrate measurements available and used WF water flowrate measurements available and used S solids measurements available and used A assays available and used CF component flowrates available and used 2D Data MF mass flowrates mass proportions 2D A 2D assays Figure 15 Mass Balance Navigator see Figure 14 HSC Chemistry 7 0 48 20 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 16 Data Sheet Above left part of the Data Sheet Below Measured and Balanced columns visible HSC Chemistry 7 0 48 21 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 17 Above Bottom Measured Standard Deviation and Balanced columns visible Below All items are selected to be visible in the Data Sheet Please note that each column is different in color to help its identification HSC Chemistry 7 0 48 22 P Lamberg amp J Tommiska October 12 2009 09006 ORC J gt gt Use for minimizing the Balancing Reporting Options Selector Use to hide or unhide the columns in the Data Sheet Meas Measured values SD Standard Deviation Min Minimum values Max Maximum values Bal Balanced values Diff Absolute difference between balanced and measures
16. avoid linear dependency of equality constraints 2c the flow measurements 1 1 F M tot flow tot flow N flow F F If 1D analyses are given the following equations are included 2d the analyses E U tot flow M element chemical tot flow N flow unit flow N element chemical N unit F G e F 1 _ 1 0 _ 1 1 The equations 2a are equality constraints for the solution The solution method used is the element wise weighted total least squares The weights are standard deviations of the solids flowrate measurements M F the analyses and fraction m M G M M As before the flowrates can be solved without any constraints LS subject to non negativity constraints NNLS and subject to simple bounds MVLS If there are no constraints the minimal maximum norm solution can be calculated LS MinMax 5 The sub flow mass balance Then the m values of sub flows are solved The equations are 2e the fraction m measurements M subflow flow subflow flow M M 2f the mass balance equations SF U tot flow subflow flow N flow unit flow N subflow reducing size not unit N unit F M e F 1 1 0 1 1 2g sum fraction m is a hundred 100 1 SF N i subflow flow M HSC Chemistry 7 0 48
17. ay a year The procedure is as follows In the Assays have as a first column the Case Organize so that each case has the same streams listed Bring in your assays for each case Figure 46 Press the Mass Balancing and Data Reconciliation button Do the Mass Balance Wizard steps as explained in chapter 48 5 From the Case combo box select the case you want to work with first Figure 47 Define the mass balancing conditions probably it would be safer to use NNLS than the LS method Solve the mass balance for the first case and evaluate the result HSC Chemistry 7 0 48 39 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Fine tune if needed and finally when you are happy with the result you may change the case to some other and repeat the balance and fine tuning Finally when studying enough different cases you can select from the menu Tools Solve All Cases Figure 48 Give a name for the new sheet to be placed in Analyses xls file Figure 49 HSC Sim will solve all the cases one by one and report them to the Analyses xls file on the sheet you just named before After finding a solution for all cases HSC will make Experimental Data visible You can complete the mass balance by selecting Identify Streams and Tools Calculate Recoveries Figure 50 Figure 46 Organizing analyses when you have several similar mass balancing cases to be solved The first column
18. bflow flow sublow element chemical flow N flow unit flow N subflow N element chemical reducing size not unit n n unit F G e F 1 1 _ 0 1 _ 1 2 3d fraction m measurements HSC Chemistry 7 0 48 49 P Lamberg amp J Tommiska October 12 2009 09006 ORC J S F tot flow M subflow flow subflow flow N subflow N flow F M F 1 1 100 2 or alternatively 3f flow measurements S F M subflow flow subflow flow N subflow N flow F F 1 1 2 The solution method used is the element wise weighted least squares The equations can be solved without any constraints LS subject to non negativity constraints NNLS and subject to simple bounds MVLS If there are no constraints the minimal maximum norm solution can be calculated LS MinMax 5 2D analyses Let and be G M G E NS F N N 2 matrices The operator vec stacks the columns of a matrix into a vector The equations for the analyses solution are 3f M G vec G vec 3e the mass balance equations for the analyses 0 G B vec where the 1 1 2 S F SRU U S N N N N N matrix B is defined 1 1
19. e window You can change the measured values standard deviation minimum and maximum values To use changed values press Apply and to solve them with new conditions press the Balance button If you are using Min and Max values they become active only in the Constrained Least Squares solution CLS To change from Stream View to Element View in the HSC Mass Balance amp Data Reconciliation Dialog double click on any element visible in the Stream View i e in rows 8 9 10 You can change the element in the combo box located in the bottom part of the window In the Element View you cannot do changes here change back to Stream View or make the changes on the Data Sheet Figure 22 HSC Mass Balance amp Data Reconciliation Dialog Above Stream view Below Element View HSC Chemistry 7 0 48 25 P Lamberg amp J Tommiska October 12 2009 09006 ORC J 48 7 Reporting Tools HSC Sim has a number of reporting tools to study evaluate fine tune and finally report the mass balance solution 48 7 1 Parity Difference and Other Charts To evaluate the mass balance in the Parity Chart i e in an XY diagram where measured is plotted against balanced select from the menu Graphics Parity Chart Figure 23 You will see a plot of the first component Change the component from the Field combo box Figure 24 Figure 23 Drawing a parity chart HSC Chemistry 7 0 48 26 P Lamberg amp J Tommiska Oct
20. ect the stream back Unselecting the stream in mass balancing equals the case where the current stream does not exist in the drawing at all Most commonly you may exclude some streams if you want to balance only part of the circuit you have drawn optional connections in the circuit and those streams are not active in the current mass balancing you are mass balancing only solids in that case you need to make pure liquid water streams inactive Avoid making a stream inactive if you do not have assays of the current stream but you want to mass balance streams both upstream and downstream HSC Chemistry 7 0 48 10 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 6 Excluding mill sump water in mass balancing 48 5 3 Step 3 Define Error Models Each assay and raw data is subject to errors Mass balancing and data reconciliation is meant for adjusting the unreliable values whereas the reliable values should be adjusted only a little if at all Therefore the user has to give a value to how reliable each item of raw data is This is done by defining the Error Model In the Step 3 Wizard window all the components selected in the mass balancing in Step 1 are listed Figure 7 Again the minimum maximum and number of streams with data are listed Activating the row will visualize the component in the Sankey diagram The second column gives the Error Model parameters i e standard deviation the third show
21. een analyzed as well as solids flowrates of some of the streams are known HSC mass balances HSC Chemistry 7 0 48 3 P Lamberg amp J Tommiska October 12 2009 09006 ORC J 5 Mass balance assays and components in 2 or 3 phase systems where the bulk composition is not analyzed 2D Components The component concentrations have been analyzed in different substreams solids liquid gas but the composition of bulk stream is not known The flowrates of different substreams have been measured In some of the units the components may change the substream e g in leaching copper is transformed from a solid to liquid HSC solves flowrates and analyses of each substream 6 Mass balance minerals or chemical assays size by size 2D Assays Chemical composition of the solids has been analyzed they have been sized separated in size fractions and mass proportion and chemical composition of the size fractions has been analyzed If desired HSC converts elemental assays to mineral grades solves first 1D mass balance and uses the 1D mass balance to 7 Mass balance particles MLA assays 3D Particle composition of the streams has been analyzed by size fractions in addition frequently chemical assays has been done on unsize and size by size basis mass proportion of each size fraction has been measured HSC solves first 1D mass balance then 2D mass balance using the 1D solution as constraints HSC classifies particles
22. emicalel element chemical tot flow N flow G E Equations 2b and 2c are the equality constraints for the solution The solution method used is weighted least squares 1 If equations 2c are included in equations 2b the matrix B is 1 1 F U N N to avoid linear dependency of equality constraints As before the analyses can be solved be solved without any constraints LS subject to non negativity constraints NNLS and subject to simple bounds MVLS If there is no constraints minimal maximum norm solution can be calculated LS MinMax 5 48 12 2 1 5 D Mass Balance 1 5D differs from the 1D solution in that the fraction m are solved and that the fraction m measurement are used in the solution of total flows 1 5D differs from 2D in that the analyses are not given and that the number of flows is same as in 1D The total flows mass balance Firstly the total flows are solved The equations are 2a the mass balance equations U tot flow N flow unit flow N unit F e F 1 0 1 1 2b the fraction m measurements HSC Chemistry 7 0 48 47 P Lamberg amp J Tommiska October 12 2009 09006 ORC J SF SRU U tot flow M subflow flow N flow unit flow N subflow N N unit F M e F 1 1 1 0 1 1 Units are indexed up to 1 SRU U N N to
23. he 49 Sim Mass Balance Examples doc manual and the 2D cases there Figure 51 2D data organized in Experimental Data Figure 52 Initializing Stream Properties sheet for multiple size fractions Figure 53 After solving 1D change to 2D HSC Chemistry 7 0 48 42 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 54 2D case solved Please note that when changing from 1D to 2D the 1D mass balance is frozen i e it will not be changed 2D data does not need to be complete some streams mass balanced in 1D may miss some analyses and some components may be missing in 2D data 48 11 Examples See examples in folder HSC7 Flowsheet_MassBalancing Example 1D Components Example 2D Minerals Example Copper Circuit The relevant manual is 49 Sim Mass Balancing Examples doc Please also check the HSC Forum www hsc chemistry com Forum or directly http www hsc chemistry com forum_v3 for updates and new examples HSC Chemistry 7 0 48 43 P Lamberg amp J Tommiska October 12 2009 09006 ORC J 48 12 Math Definitions 1 F N number of flows 1D 2 F N number of flows 2D U N number of units SRU N number of size reducing units SF N number of sub flows E N number of chemical elements G grade of chemical element M G measured grade of chemical element F solids flowrate M F measured solids flowrate W water flowrate
24. he component You can often find errors in components whose grades are low and close to the detection limit HSC Chemistry 7 0 48 15 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 11 Example of a mass balance node 1st Cleaner Input streams are shown as blue streams and output streams as red streams HSC Chemistry 7 0 48 16 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 12 Example of a mass balance case where only three streams have been sampled and assayed and HSC creates only one mass balance node HSC Chemistry 7 0 48 17 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 13 Example of an error Sulfur in the output of the SAG is higher than in both of the input streams 48 6 Mass Balance Window After completing the Mass Balance Wizard steps you will come to the Mass Balance and Data Reconciliation Window Figure 14 On the left hand side you will see the Navigator buttons to navigate between different sub windows In the middle you have the Data Sheet On the right hand side you can see the Balance Report Options To solve the mass balancing problem press the or button The Navigator Figure 15 can be minimized by using the button With the navigator you can navigate between different sub windows which are for redefining some of the issues defined already when using wizards The various controls of the Navigator are shown and explained in F
25. ifferent kinds of mass balance problems When giving the names for the streams use the identical names as in your analysis lists Before proceeding please check the stream connections and check flowsheet for possible errors see manual 47 Sim Experimental 48 4 Organizing the experimental data in HSC When the flowsheet is ready i e all streams are named properly and connections have been checked you can bring in your experimental data The following section will concentrate on how to bring the data for mass balancing and data reconciliation For more information on how to use experimental data in HSC Sim please see manual 47 Sim Experimental The easiest way is to first generate the experimental sheets with HSC Sim Select from the menu Experimental Analyses From the menu select Create Stream Properties Sheet Horizontal optionally you can select Vertical Horizontal with Multiple Size Fractions Horizontal with Multiple Cases Figure 1 HSC Sim will create a sheet named Streams and list all the Streams their Sources and Destinations and generate the standard columns Solids Recovery Total Solids t h FractionNo Fraction name Fraction m and Note Figure 1 Create Stream Properties Sheet using preferentially horizontal data HSC Chemistry 7 0 48 6 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 2 HSC Sim creates a sheet called Streams and lists all the stream
26. igure 15 The Data Sheet Figure 16 shows the mass balancing data in a table Each stream is one row Each component selected in mass balancing is listed from left to right Each component has the following columns from left to right Figure 18 Measured Meas white column Standard deviation SD RSD blue column Minimum Min yellow column Maximum Max pale blue Balanced Bal grey Absolute difference Diff orange Relative difference RDiff pale green HSC Chemistry 7 0 48 18 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Recovery Rec blue The visibility of the columns is controlled on the right hand side in Balance Reporting Options Figure 19 Figure 14 Mass Balancing and Data Reconciliation window Navigator on the left Data Sheet in the middle and Balancing Reporting options on the right To solve a mass balance problem the following mathematical methods are available in the Balance Report Options on the right hand side Least Squares Solution LS Unconstrained MinMax Solution minimizes the maximum difference MinMax and UMM Figure 19 Non negative Least Squares Solution NNLS Constrained Least Squares Solution CLS Mass balance problems are solved in two stages firstly the total mass flowrates are solved and then the assays are reconciled In solving the assays the least squares solution finds the best solution by minimizi
27. ional options Once you hit the or button HSC Sim solves the mass balance problem according to your specifications Running the mass balance will always bring the balanced Bal column visible HSC Sim uses Comment Colors to indicate that the balanced value differs significantly from the measured one Figure 21 Green Comment Symbol indicates that the balance value differs more than 1 standard deviation 1SD from the measured one Yellow Comment Symbol indicates that the difference is greater than 2SD Red Comment Symbol indicates that the difference is greater than 3SD The comment texts shows the difference compared to SD as integers Figure 21 Comment Symbol colors are used to indicate if the balanced value differs significantly from the measured one Green difference gt 1SD Yellow difference gt 2SD red difference gt 3SD true difference shown in comment text The red color in parentheses indicates a negative solution Try to use non negative least squares or constrained least squares solution Double clicking anywhere on the Data Sheet will render HSC Mass Balance amp Data Reconciliation Dialog visible Figure 22 HSC Sim will show the stream which was double HSC Chemistry 7 0 48 24 P Lamberg amp J Tommiska October 12 2009 09006 ORC J clicked in the Data Sheet i e the active row in the Stream View You can change the stream from the Combo Box on the bottom of th
28. low unit flow N unit W e F 1 0 1 1 1e water flowrate measurements 1 1 F M tot flow tot flow N flow W W 1f solids measurements 1 1 100 100 F tot flow M tot flow tot flow M N flow F Pc F W Pc The mass balance equations 1a and 1d are the equality constraints for the solutions The solution method used is the element wise weighted total least squares 2 The weights are standard deviations of the solids flowrate measurements M F the analyses the water flowrate measurements and the solids measurements The flowrates can be M G M W M Pc HSC Chemistry 7 0 48 45 P Lamberg amp J Tommiska October 12 2009 09006 ORC J solved without any constraints LS subject to non negativity constraints NNLS 3 and subject to simple bounds 2 2 1 1 ub W lb ub F lb MVLS 4 If there are no constraints the minimal maximum norm solution can be calculated LS MinMax 5 if only the solids are calculated The solids flowrates and the water flowrates are solved simultaneously The equations are 1g mass balance equations U tot flow N flow unit flow N unit F e F 1 0 1 1 U tot flow N flow unit flow N unit W e F 1 0 1 1 1h s
29. ng the weighted sum of squares That is n i ij ij ij k j s b a WSSQ 1 2 2 1 HSC Chemistry 7 0 48 19 P Lamberg amp J Tommiska October 12 2009 09006 ORC J where j refers to the stream k is the number of streams i refers to the components analyses n is the number of components a is the measured value b is the balanced value and s is standard deviation In the non negative least squares all a s are subject to be non negative In the constrained least squares all a s are subject to be between min and max For more details see the mathematics in chapter 48 12 X You can minimize the Navigator by pressing X See minimized navigator on the right Dimension Select dimension here You should solve 1D before entering into 2D 1 5D is the mass balance problem with particle size distribution Steps 1 Streams Wizard Steps 2 and 4 2 Components Wizard Steps 1 and 3 3 Nodes Wizard Step 5 4 Test Wizard Step 5 5 Conditions Define Sampling Error and individually standard deviations if needed 6 Run Balancing Run the solution for mass balance and data reconciliation problem 7 Report Report the Results lt Table Indicates the number of Units Avl available Used Used Streams number of streams available and used Assayed number of assayed streams available Solved number of solved streams available and used Nodes number of m
30. ober 12 2009 09006 ORC J Figure 24 Parity Chart The difference chart plots the absolute or relative difference against the measured value Figure 25 A cumulative passing chart can be drawn only if the case is 1 5D see examples in manual 49 Mass Balancing Examples The Assays Stacked Bar chart is useful especially when solving the problem where the constraint Component Sum 100 is used Figure 26 HSC Chemistry 7 0 48 27 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 25 Difference chart You can change from an absolute difference to a relative difference in the Y Field combo box HSC Chemistry 7 0 48 28 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 26 Assays Stacked Bar chart 48 7 2 Report Pressing the 7 Report button in the navigator will make the Report spreadsheet visible Figure 27 The report consists of four pages 1 Goodness shows the goodness of the mass balance Figure 28 2 Node Balance reports the balance by mass balance node Figure 29 3 Stream Summary reports the streams horizontally Figure 30 4 StreamsV reports the streams vertically Figure 31 HSC Chemistry 7 0 48 29 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 27 Press Report to make the Report Spreadsheet visible Figure 28 The first page of the Report shows the goodness of the mass balancing HSC Chemistry 7 0
31. olids and water flowrate measurements 1 1 F M tot flow tot flow N flow F F 1 1 F M tot flow tot flow N flow W W 1i solids measurements 1 1 0 100 100 1 F tot flow M tot flow M N flow W Pc F Pc The mass balance equations 1g are equality constraints for the solution The solution method used is the element wise weighted total least squares The weights are standard deviations of the solids flowrate measurements M F the analyses the water flowrate measurements and the solids measurements M G M W M Pc As before the flowrates can be solved be solved without any constraints LS subject to non negativity constraints NNLS and subject to simple bounds MVLS 1D analyses Let and be matrices The operator vec stacks the columns of a matrix into a vector G M G E F N N 1 HSC Chemistry 7 0 48 46 P Lamberg amp J Tommiska October 12 2009 09006 ORC J The equations for the analyses solution are 2a the measurements M G vec G vec 2b the mass balance equations for the analyses 0 G B vec where the 1 F U N N matrix B is defined tot flow flow unit flow unit F e B 2c if the option minerals sum 100 is selected the following equations are included 1 1 _ 1 100 F N ement ch
32. rd column is wrong define the type using the combo box below The options are o Solids flowrate SF o Water flowrate WF o Percent solids weight weight S o Assays A o Fraction mass percentage FM o Fraction name FN will be excluded in mass balancing o Fraction number F will be excluded in mass balancing o Assay of the fraction mass AFM HSC Chemistry 7 0 48 8 P Lamberg amp J Tommiska October 12 2009 09006 ORC J o Component flowrate CF o Component distribution CD o Other O this type will be excluded in the mass balancing The following column gives data minimum Min maximum Max and the number of streams with data NOM If both the minimum and maximum are zero HSC Sim will turn the component to non selected min and max number are yellow and min has a comment both min and max are zero Press for quick information of the window Press Next to proceed to the next step Figure 4 Step 1 HSC Chemistry 7 0 48 9 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 5 Selecting a row will generate a Sankey diagram i e showing the variation of currently selected component in the streams with the thickness of the stream 48 5 2 Step 2 Define Streams to be included in Mass Balancing In the second step you can exclude some of the streams in the mass balance equation Uncheck the stream in the list or click the stream in the flowsheet Click again to sel
33. s their Source and Destination and generates the standard columns Organize your assays in Excel or some other spreadsheet program o row wise each stream is one row o the first column gives the name of the stream o one header row o the name for the first column with stream names must be Stream o the order of the stream can be whatever o some streams can be missing o the following columns gives the experimental data for example assays use syntax element separator method separator unit e g Cu XRF space is separator You can leave method out if you like e g Cu Au ppm o HSC will identify the type of the experimental data from the extension Use ppm or g t for chemical assays e g Cu Use t h tph for flowrates e g Cu tph Use D for distribution e g Cu D Use SD for standard deviation e g Cu SD Use RSD for relative standard deviation e g Cu RDS If you use some other syntax HSC does not recognize the type automatically and you need to specify the type manually Copy and paste the data o Once the data is organized select it in Excel and the Stream cell must be the top left cell and copy to the clipboard o Go the HSC Sim Analyses and select from the menu Edit Paste Special Assays o Save your data file save HSC Sim will create a file named Assays xls in the same folder as the flowsheet see the window title for full path You can have different mass balance cases
34. s the type as listed in Step 1 and the fourth gives the error model The Error Models available are see Figure 8 Error Model Parameters Example Fixed Fixed standard deviation as plain number or fixed relative standard deviation as negative number or in parenthesis 0 1 5 5 X x X 0 x Integer part is the relative standard deviation decimal part is the detection limit 10 1 X 0 1 Given parameter is the relative standard deviation 6 HSC Chemistry 7 0 48 11 P Lamberg amp J Tommiska October 12 2009 09006 ORC J 0 1 is the detection limit 10 X Parameter is the detection limit relative standard deviation is fixed 10 0 05 a b c MIN a b c a is the relative standard deviation b is the detection limit and c is the maximum standard deviation 10 0 01 0 5 a b c MAX a b c a is the relative standard deviation b is the detection limit and c is the minimum standard deviation 10 0 02 0 2 a b c MIN MAX a is the relative standard deviation MIN is minimum standard deviation and MAX is the maximum standard deviation 10 Data Standard deviation is given in data individually for each stream Select the Error Model using the Combo Box and write error model parameters in the text box below Figure 7 Use the Show Graph button to see the error model graphically Figure 8 Figure 7 Step 3 Define the Error Model HSC Chemistry 7 0 48 12 P Lamberg amp J Tommiska October 12 20
35. sky Rastello Premoli Kuhush van Huffel The element wise weighted total least squares problem Computational Statistic amp Data Analysis 50 2006 pp 181 209 3 Lawson Hanson Solving Least Squares Problems 1974 4 Haskell Hanson An Algorithm for Linear Least Squares Problems with Equality and Nonnegativity Constraints Mathematical Programming 21 1981 pp 98 118 5 Barrodale Phillips Algorithm 495 Solution of an Overdetermined System of Linear Equations in the Chebyshev Norm ACM Transactions on Mathematical Software Vol 1 No 3 September 1975 pp 264 270
36. ted in its own layer Figure 36 Creating stream tables HSC Chemistry 7 0 48 34 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 37 Select the components above and items below HSC Chemistry 7 0 48 35 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 38 Mass balance result reported as stream tables on the flowsheet 48 8 Saving Mass Balance 48 8 1 Balance file Each time you exit the mass balance window HSC Sim will save the Balance xls file in the very same folder where the flowsheet file exists The Balance xls file consists of the following pages Figure 39 Data original data used in mass balancing CV error model and standard deviations Units list of units and check for 2D mass balance see the manual 49 Sim Mass Balance Examples xls Conditions mass balance method Balance the Data Sheet If you want to restore the last Balance xls file please select File Restore last Figure 40 HSC Chemistry 7 0 48 36 P Lamberg amp J Tommiska October 12 2009 09006 ORC J Figure 39 Balance xls file Figure 40 Restoring the last Balance file 48 8 2 Save Selecting File Save will let you save the Balance file with a different name The default name is HSCBalance_year_month_day_hours_minutes xls Figure 41 The structure of the file is similar to the Balance xls file see above Figure 39 HSC Chemistry
37. tune your error models and define a sampling error for each stream individually You can select different solution methods least squares MinMax non negative least squares constrained least squares Balanced values are reported with indicator showing if the balanced result deviates from the measured one significantly more than one standard deviation 6 Report the results Mass balance report Visualizing measured balanced standard deviation difference relative difference recovery minimum and maximum values in flowsheet as Sankey diagrams or as stream tables Studying the weighted sum of squares WSSQ on the flowsheet Plotting Parity Charts Plotting Difference Charts HSC Chemistry 7 0 48 5 P Lamberg amp J Tommiska October 12 2009 09006 ORC J 7 Saving the mass balance template Saving the mass balance template to be used later in mass balancing new sample sets from the circuit 48 3 Drawing the flowsheet Basically you draw your flowsheet as you normally do in HSC Sim the only exception is that you should change the mode to the Experimental Mode see manual 47 Sim Experimental For drawing the flowsheet see manuals 40 Sim Flowsheet and 47 Sim Experimental You can draw all the streams and units HSC will create the mass balance equations according to available data therefore there is no need to draw a flowsheet for mass balancing only or every time a new flowsheet for d
38. wsheet for different kinds of mass balance problems When giving the names for the streams use the very same names as in your analysis lists 3 Bring in the experimental data see manual 47 Sim Experimental The data is collected in an Excel file The structure can be horizontal or vertical i e each stream is a row horizontal or a column vertical The name of the stream must match with the drawing There is no need to make a row column for each stream only the one where you have data You can also have extra streams or extra information not be used in mass balancing You can have various data sets place each of them in separate sheets 4 Go through the mass balancing wizard Step 1 HSC identifies the data according to extensions if identification fails you need to tell which type of data you have You can include or exclude part of the data according to your wish Step 2 Define the streams to be included in creating mass balance equations The default is that all streams are included If you want to mass balance only part of the circuit you can just unselect the streams you want to exclude Step 3 Give an error model and standard deviation for each measurement or estimate Step 4 Define the feed stream against which the recovery calculations will be made Step 5 Check the mass balance nodes and possible errors in the data indicated by HSC 5 Run the mass balance You can fine
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