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Simulation of potash rougher flotation Wong, Michael W. K. 1984

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SIMULATION OF POTASH ROUGHER FLOTATION by MICHAEL W.K. WONG B.Sc, Queen's University At Kingston, 1980 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department Of Mining And Mineral Processing Engineering We accept t h i s thesis as conforming to the required standard THE U N I V E , R S 1 T Y \ 6 F BRITISH COLUMBIA September 1984 © Michael W.K. Wong, 1984 In presenting t h i s thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t freely available for reference and study subject to prior agreements between UBC and Potash Corporation of Saskatchewan. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his or her representatives. It is understood that copying or publication of this thesis for f i n a n c i a l gain shall not be allowed without my written permission. Department of Mining And Mineral Processing Engineering The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: 5 September 1984 i i Abstract The rougher f l o t a t i o n behaviour of Potash ore from the Potash Corporation of Saskatchewan was evaluated in both laboratory batch and continuous c e l l s by the use of experimental designs. Data obtained in a l l tests were adjusted s t a t i s t i c a l l y and then used to estimate the parameters of proposed kinetic models. By means of s t a t i s t i c a l and physical significance c r i t e r i a , the Beta d i s t r i b u t i o n model was found to be the best in f i t t i n g kinetic data on a size-by-size basis. The estimated parameters were regressed with the operating variables manipulated in the experimental runs. Ways to enhance the recovery of coarse KC1 p a r t i c l e s were postulated. However, translation of results to a f u l l - s c a l e plant t r i a l depends on matching the mode of operation of the plant ( i . e . whether i t be in rate or equilibrium control) to s h i f t s in the equilibrium recovery and f l o t a t i o n rate that were observed in the laboratory batch tests. The effect of p a r t i c l e size on i n i t i a l f l o t a t i o n rates of KC1 was found to be a maximum at 177 Mm. NaCl (max. at 104 nm) and INSOL (max. at 187 nm) account for poor concentrate grades in the fine size range. F i n a l l y , an empirical scale-up procedure i s proposed to predict large scale continuous data from small batch r e s u l t s . Using model parameter/size relationships, the number of scale-up constants were reduced subs t a n t i a l l y . Table of Contents Abstract i i L i s t of Tables v i L i s t of Figures v i i i Acknowledgement x Chapter I INTRODUCTION .1 Chapter II REVIEW OF FLOTATION MODELS 2 2.1 Model C l a s s i f i c a t i o n 2 2.2 Empirical Models 2 2.3 Probability Models 4 2.4 Kinetic Models 7 2.4.1 B u l l Model 11 2.4.2 The Dis t r i b u t i o n Of Rate Constant Model 14 2.4.3 Lynch Model 16 2.4.4 Chen Model 17 2.5 Summary Of Review Of Models 24 Chapter III EXPERIMENTAL MATERIALS AND PREPARATION PROCEDURES 2 5 3.1 Material Supply 25 3.2 Preparation Of Feed 25 3.3 Preparation Of Saturated Brine 27 3.4 Preparation Of Reagents 27 Chapter IV EXPERIMENTAL DETAILS 29 4.1 Objectives 29 4.2 Small Batch Flotation Tests 29 4.3 Large Batch Flotation Tests 41 4.4 Continuous Flotation Tests 47 Chapter V THE STATISTICAL ADJUSTMENT OF POTASH FLOTATION DATA FOR MASS BALANCES 52 5.1 Adjustment Procedure For Small Batch Flotation Tests 53 5.1.1 Flowsheet C l a r i f i c a t i o n And Symbol Selection ....53 5.1.2 Mass Balance Relations 54 5.1.3 Acquisition Of Raw Data 55 5.1.4 Raw Data Bias Adjustments 55 5.1.5 Selection Of Search Variables 57 5.1.6 Calculation Of Data Points From Search Variables 58 5.1.7 Construction Of Objective Function 59 5.1.8 Choice Of Method To Minimize Objective Function .60 5.1.9 Results Of Data Adjustments 65 5.2 Data Adjustment For Large Batch And Continuous Flo t a t i o n Runs 69 iv Chapter VI DEVELOPMENT OF FLOTATION MODELS 7 5 6.1 Fl o t a t i o n Rate Plots 75 6.2 Model F i t t i n g And Parameter Estimation 75 6.3 Adequacy Of F i t t e d Models 82 Chapter VII CORRELATION BETWEEN MODEL PARAMETERS AND OPERATING VARIABLES 91 7.1 Small Batch Data Correlation 91 7.1.1 Regression Analyses Of Model Parameters 94 7.2 Large Batch Data Correlation 100 Chapter VIII SCALE-UP OF MODEL PARAMETERS 106 8.1 F i t t i n g Model To Data 106 8.2 E f f e c t Of P a r t i c l e Size On Parameters 106 8.3 Correlation Of Coeff i c i e n t s Between Runs 113 Chapter IX SUMMARY AND CONCLUSIONS 118 BIBLIOGRAPHY 120 APPENDICES A APPLICATIONS OF THE CHEN MODEL IN BOTH BATCH AND CONTINUOUS FLOTATION 125 B DEFINITION OF SYMBOLS FOR COMPUTER PROGRAMS 129 C LISTINGS OF PROGRAM DATAD, PRINT1, FORM1, CFORM, AFORM, AND EXAMPLE OUTPUT 137 D DATA ADJUSTMENT PROCEDURE FOR LARGE BATCH FLOTATION RUNS 166 D.1 Data Adjustment Procedure D. 2 L i s t i n g s of Programs DATADL, PRINTL, FORML, AFORML, SIZEFL And Example Output E DATA ADJUSTMENT PROCEDURE FOR CONTINUOUS FLOTATION RUNS 1 99 E. 1 Data Adjustment Procedure V E.2 Li s t i n g s of Programs DATADC, PRINTC, AFORMC, SIZEFC And Example Output F FLOTATION RATE PLOTS FOR ALL RUNS 232 G BULL'S MODEL FITTED TO SMALL BATCH FLOTATION RATE DATA 452 G. 1 Simplex Search Program With Example Output H LYNCH'S MODEL FITTED TO SMALL BATCH FLOTATION RATE DATA 460 H. 1 Simplex Search Program With Example Output I CHEN'S MODEL FITTED TO SMALL BATCH FLOTATION RATE DATA 468 I. 1 Simplex Search Program With Example Output 1.2 Summary Of Model Parameters J CHEN'S MODEL FITTED TO LARGE BATCH FLOTATION RATE DATA 494 J.1 Simplex Search Program With Example Output J.2 Summary of Model Parameters K CHEN'S MODEL FITTED TO CONTINUOUS FLOTATION RATE DATA 506 K.1 Simplex Search Program With Example Output K.2 Summary of Model Parameters v i L i s t of Tables 1. Experimental Runs with Coded Levels for Small Batch Flotation 31 2. Average Results for Seven Flotation Feeds 37 3. A Typical Summary of the Desired Operating Conditions for Run 172 38 4. Raw Data of Run 172 39 5. Corrected Data of Run 172 40 6. Experimental Runs with Coded Levels for Large Batch Flotation 43 7. Desired Operating Conditions for Run 250 45 8. Measured Data of Run 250 46 9. Desired Operating Conditions for Run 302 50 10. Measured Data of Run 302 51 11. Adjusted Data for a Typical Large Batch Run 73 12. Adjusted Data for a Typical Continuous Run 74 13. Flotation Rate Data of Run 172 79 14. Model Parameters for Flotation Rate Data of Run 172 ..81 15. Independent and Dependent Variables for Small Batch Flotation 92 16. Forward Stepwise Regression Results of KC1 for Small Batch Runs .. . . 97 17. Forward Stepwise Regression Results of NaCl for Small Batch Runs 98 18. Forward Stepwise Regression Results of INSOL for Small Batch Runs 99 19. Independent and Dependent Variables for Large Batch Flotation 101 20. Forward Stepwise Regression Results of KC1 for Large Batch Runs 1 02 v i i 21. Forward Stepwise Regression Results of NaCl for Large Batch Runs 103 22. Forward Stepwise Regression Results of INSOL for Large Batch Runs 104 23. Model Parameters for 3 Sets of Center Point F l o t a t i o n Runs 107 24. Dependence of Model Parameters on P a r t i c l e Size 109 v i i i L i s t of Figures 1. C l a s s i f i c a t i o n of the Independent and Dependent Variables in a Flotation Process ( after Lynch(23) ) ..3 2. Diagram of a Bank of n C e l l s 6 3. Two Phase Model of the Flotation Process 6 4. A Gamma Distr i b u t i o n Function of K 15 5. A Beta D i s t r i b u t i o n Function of K 15 6. The Change of Kav With Flotation Time 19 7. Effect of Kav(O) and g on Flotation Rate Curves 23 8. Preparation of Feed for Scrubbing and Desliming 26 9. Small Batch Flotation Flowsheet and Symbols for Mass Balances 34 10. Large Batch Flotation Flowsheet and Symbols for Mass Balances 44 11. Flowsheet for Continuous Rougher Flotation 48 12. Check for Bias Errors on Lc and Lf 56 13. A Step Search on Search Variable S(l) 61 14. Repetitive Quadratic F i t t i n g : 63 15. A Diagram of the Alpha Search 64 16. F i l e Interaction Flowsheet for DATAD .66 17. A General Flow Diagram for Program DATAD ....67 18. Detailed Flowcharts for DATAD 68 19. Adjusted Lf and Lc Values Versus Corrected Lf and Lc .70 20. Adjusted Weight% Retained Points Versus Corrected Weight% Retained points for Concentrate C1 71 21. Adjusted Assays of Size Fractions Versus Corrected Assays of Size Fractions for Concentrate C1 72 22. Fl o t a t i o n Rate Curves for Five Size Fractions of KC1 .76 ix 23. Flotation Rate Curves for Five Size Fractions of NaCl 77 24. Flotation Rate Curves for Five Size Fractions of INSOL 78 25. KC1 Flo t a t i o n Rate Curves F i t t e d by Chen's Model 87 26. INSOL Flo t a t i o n Rate Curves F i t t e d by Chen's Model ...88 27. KC1 Flo t a t i o n Rate Curves of Run 302 89 28. KC1 Flotation Rate Curves of Run 303 90 29. F i t t e d Curves of Kav(0)/Size for KC1 110 30. F i t t e d Curves of Kav(0)/Size for NaCl 111 31. F i t t e d Curves of Kav(0)/Size for INSOL 112 32. F i t t e d Curves of g/Size for KC1 114 33. F i t t e d Curves of g/Size for NaCl 115 34. F i t t e d Curves of g/Size for INSOL 116 X Ac knowledqement The author wishes to express his sincere gratitude to Professor A.L. Mular for his patient guidance, support and encouragement. Assistance and advice from Dr. G.W. Poling, Mr. Allan Richardson, Mr. Ken Armstrong, Mr. Robert Ellwood, Mr. Tracy Bond and Mr. Mike Mular are very much appreciated. Special thanks are also extended to the Potash Corporation of Saskatchewan (PCS) and to the National Science and Engineering Research Council of Canada whose f i n a n c i a l support has made t h i s study possible. Access and use of PCS project reports were invaluable to this study. 1 I . INTRODUCTION In October of 1981, a potash f l o t a t i o n research program was i n i t i a t e d at the UBC mineral processing laboratory. The objective of the program was to simulate potash rougher f l o t a t i o n in the laboratory for subsequent correlation with f u l l scale production units. Samples of potash ore, saturated process brine and f l o t a t i o n reagents from the Potash Corporation of Saskatchewan Cory mine were obtained and three sets of batch and continuous rougher f l o t a t i o n runs were conducted. Experimental designs were constructed for each set of runs so that the effects of operating variables on f l o t a t i o n behaviour could be assessed by means of kinetic models. This thesis describes the simulation methodology employed and demonstrates how the parameters of kinetic models can be u t i l i z e d to evaluate the influence of operating variables on f l o t a t i o n behaviour. An empirical scale-up procedure to predict continuous data from semi-batch results i s discussed. 2 II. REVIEW OF FLOTATION MODELS 2.1 Model C l a s s i f i c a t i o n Mathematical models of the f l o t a t i o n process have been investigated for many years. Generally, they can be placed into one of three categories, namely, Empirical, P r o b a b i l i s t i c and Kinet i c . 2.2 Empirical Models The development of empirical models to represent the f l o t a t i o n process has been described by Faulkner (1) , P i t t (2) and Smith and Lewis (3). E s s e n t i a l l y , the models are obtained from appropriate experimental designs and s t a t i s t i c a l c o rrelations between dependent and independent variables as shown in Fig.1. The s t a t i s t i c a l relationships for these models can be found by normal multiple regression techniques (4). Empirical models often are cheaper to develop in comparison to other types ( i . e . mechanistic, semi-empirical models) provided that the purpose of the models i s c l e a r l y defined for a pa r t i c u l a r plant. However, empirical models do not recognize basic process mechanisms, although some "feed back" may be obtained. Predictions outside the l i m i t s of the data employed to generate an empirical model may be t o t a l l y unreliable. A major disadvantage of an empirical model i s that i t may be inadequate to predict the performance of a large-scale plant from laboratory or p i l o t plant data. 3 Manipulated variables, such as Independent variables Di sturbance va r i a b l e s , such as: -DEGREE OF OXIDATION -MINERAL LIBERATION -SIZE -FLOTATION FEED SIZE DISTRIBUTION -HEAD GRADE -PULP DENSITY -VOLUME FLOWRATE -TEMPERATURE -REAGENT ADDITIONS -AERATION RATE -PULP LEVEL My M2 M3 .... M 3 - > FLOTATION PROCESS <-d, <—d2 <-d3 Dependent variables, such as -FLOWRATE -RECOVERY -GRADE -PULP DENSITY Figure 1 C l a s s i f i c a t i o n of the Independent and Dependent Variables in a F l o t a t i o n Process ( after Lynch(23) ) 4 2.3 Probability Models Schumann (5) considered that the f l o t a t i o n rate of p a r t i c l e s of average size x is related to the overall p r o b a b i l i t y , P(x), of the p a r t i c l e s being sucessfully recovered in the concentrate launder. Assuming that there is no correlation among the individual p r o b a b i l i t i e s for p a r t i c l e s of average size x : P(x) = P(cx) . P(ax) . P(rx) where P(cx), P(ax), P(rx) are the p r o b a b i l i t i e s of successful particle-bubble c o l l i s i o n , adhesion and retention by a i r bubbles of adhered p a r t i c l e s respectively. Tomlinson and Fleming (6) suggested that the last p r o b a b i l i t y P(rx) be replaced by P(ex) and P(fx) P(x) = P(cx) . P(ax) . P(ex) . P(fx) where P(ex) represents the probability of p a r t i c l e s being l e v i t a t e d to the base of the froth column and P(fx) refers to the pr o b a b i l i t y of the p a r t i c l e s being retained in the froth. The pr o b a b i l i t y approach allows recognition of the basic mechanism of the f l o t a t i o n process, such as the pulp and froth phases in each c e l l . Poor recovery of fine sizes of valuable minerals ('\-20nm) may be due to low values for the probability terms P(cx) and P(ax). Unfortunately, the probability terms for the complex g a s - s o i l d - l i q u i d system can hardly be determined for 5 f l o t a t i o n plant simulation. A s i m p l i f i e d probability model was used by K e l s a l l ( 7 ) for continuous f l o t a t i o n c e l l s (Fig.2) n W = W0 (1 - P) (1 ) where W i s the weight of a component in the t a i l i n g from a bank of n continuous c e l l s at steady state, P i s the overall p r o b a b i l i t y of recovery and i s a constant in a bank of c e l l s and W0 i s the weight of the f l o t a t i o n component in the feed to the bank of c e l l s . K e l s a l l showed that the simple form of the pr o b a b i l i t y approach i s similar to a simple f i r s t - o r d e r kinetic model over the f l o t a t i o n components. This treatment was further applied by some investigators (8,9) to i n d u s t r i a l f l o t a t i o n plants. Davis (9) found that while the pr o b a b i l i t y of f l o t a t i o n i s constant for each mineral within an individual stage, the pr o b a b i l i t y decreased for a l l components in the scavenger and increased for the cleaner c e l l s . The most obvious weakness of the s i m p l i f i e d p r o b a b i l i t y approach i s that plug flow properties are assumed in each c e l l and no allowance i s made for the gradual increase in retention time from c e l l to c e l l . 6 W, FEED W 0(1-P) Y w 0(1-P) n- 1 W 0(1-P) n- 1 w n f Y W 0 (1-P) =w • FINAL TAILS WCP W„ (1-P)P n - 2 n - 1 W 0 (1-P) P W 0 (1-P) P Figure 2 - Diagram of a Bank of n C e l l s K i s the rate constant P for concentration transfer from pulp to froth Q 0C 0 FEED M V C f f f K K M V C t t t Q C * f f CONCENTRATE K is the rate constant d for concentration transfer from frot h to pulp Q C -> t t TAILINGS where M, V, C and Q are mass, volume, concentration and volume flow rate resspectively Subscripts o, f, t refer to feed, froth and t a i l i n g respectively Figure 3 - Two Phase Model of the Flot a t i o n Process 7 2.4 Kinetic Models The "chemical analogy" kinetic approach can be traced to many early authors, including Zuniga (10), Beloglazov (11), Grunder and Kadar (12), and Sutherland (13). They proposed that the kinetic model for semi-batch f l o t a t i o n be written as a f i r s t - o r d e r rate process: dC — = -K.C (2) dt where C i s the concentration of so l i d s with i d e n t i c a l f l o t a t i o n properties in the pulp expressed as mass/unit volume of pulp, K is the f l o t a t i o n rate constant, t i m e - 1 , and t i s the f l o t a t i o n time. In other words, p a r t i c l e s with i d e n t i c a l f l o t a t i o n properties are recovered into the concentrate launder at a rate proportional to the concentration of those p a r t i c l e s in the pulp. Integration of equation (2) gives C(t) = C 0 . exp(-K.t) (3) where C 0 stands for the i n i t i a l concentration of s o l i d s with i d e n t i c a l f l o t a t i o n properties in the pulp of a semi-batch c e l l . The f r a c t i o n a l recovery of those p a r t i c l e s at time t i s C(t) R(t) = 1 -C 0 8 R(t) = 1 - exp(-K.t) (4) Since some apparently floatable species may remain in the c e l l even after a prolonged f l o t a t i o n time, a l i m i t i n g recovery R°° may be incorporated in equation (4). Like the probability equation, the f l o t a t i o n rate constant K can be seen as the product of several p r o b a b i l i t i e s concerning bubble-particle c o l l i s i o n , attachment and detachment, aggregate entry from pulp into froth and return from froth to pulp and removal from froth as concentrate. These factors c l e a r l y contribute to the magnitude of the o v e r a l l f l o t a t i o n rate, although an understanding of process mechanism i s not provided by expressing the f l o t a t i o n rate constant as the o v e r a l l p r o b a b i l i t y of consecutive events. In fact, the f l o t a t i o n rate c o e f f i c i e n t can be mathmatically proved to be synonymous to P in equation (1) by expanding equation (3) : R(t) = R°° (1 - exp(-K.t) ) (5) C = C 0 exp(-K.t) K 2 K3 = C 0 (1 - K + — - — + ) 2! 3! t If K2, K3 and higher order terms become small t C = C 0 (1 " K) The above equation shows the s i m i l a r i t y between parameters W and 9 C, n and t, and K and P. In their development both equations assume plug flow conditions for the f l o t a t i o n c e l l . The recovery of a mineral in a continuous f l o t a t i o n c e l l i s closely related to the residence time d i s t r i b u t i o n , E ( t ) , of p a r t i c l e s in the -pulp which depends on the' type of mixing c h a r a c t e r i s t i c s . Several workers (14, 15, 16) showed that the pulp volume of most f l o t a t i o n c e l l s can be reasonably well represented as a perfectly mixed system. Thus for a component i with rate constant K, in a perfectly mixed continuous c e l l , the steady state flow-rate of the component in the t a i l i n g is T: = F j /°°exp(-K. .t) E(t)dt (6) 0 1 where E(t) = (1 /t9) .exp(-t/8) for a perfect mixer, 6 is the nominal retention time in the c e l l ( c e l l volume/volumetric flowrate of t a i l i n g ) , and Fj = the flowrate of the component i ' in the feed. The f i n a l integrated form of equation (6) yields F i T. = 1 1 + Kj e Hence, the f r a c t i o n a l recovery R of the component i is given by Tj Kj d R j = 1 - —- = (7) F j 1 + Kj e This expression is v a l i d for any floatable species and for any feed rate within the l i m i t s of satisfactory operation of a 10 perfectly mixed continuous c e l l . To account for the l i m i t i n g recovery R°°, equation (7) may be rewritten as R I = R j 0 0 (K j 6)/( 1 + Kj 9) (8) or 1 Rj = R|» (1 - ) 1 + K, 6 Another type of kinetic model was postulated by Arbiter and Harris (17) to allow for the existence of pulp and froth phases ( i . e . a two-phase model). They considered the c e l l contents to be partitioned between two perfectly mixed phases as shown in Fig.3, page 6. In this model, two f i r s t - o r d e r rate constants are used to describe the two-directional transfer of material between pulp and froth. However, this treatment has been rejected by several researchers (15, 16, 18) on the basis that the rate constant of f l o t a t i o n p a r t i c l e s from the froth back into the pulp i s negligible because of high froth removal rates. Apart from the models mentioned previously, there are additional kinetic models which are considered herein for the simulation of potash rougher f l o t a t i o n . It is shown in the following section that the development of these models is based on equation (4) for the semi-batch process and on equation (7) for the continuous f l o t a t i o n c e l l . 11 2.4.1 Bull Model Bull (19) evaluated a simple kinetic model by making the following assumptions: (1) The f l o t a t i o n process follows a f i r s t order rate equation (2) A l l c e l l s in a bank are perfect mixers and are i d e n t i c a l with respect to volume (3) The f l o t a t i o n rate c o e f f i c i e n t K is constant throughout any single operation ( i . e . roughing). It has been previously shown that the f r a c t i o n a l recovery in a continuous f l o t a t i o n c e l l is given by R = Roo (-K8 (9) 1 + Kt9 If there are N perfectly mixed c e l l s operating continuously in series, the f r a c t i o n a l recovery of the i t h p a r t i c l e type in each individual c e l l based on the feed to the f i r s t c e l l can be expressed as: K; 0< 1 » R . < 1 ' = R . (• I I 00 1 + Ki e < 1 > K= e ( 2 ) R / 2 ' = ( R i o o - R j < 1 > ) ( 1 + Kj Bl 2 ' •) n - 1 K; 8 < n ) 2 R ; ( J ' ) ( -=1 1 + K; 8 ( n ) 12 where the superscript refers to the c e l l number. Thus the t o t a l recovery of the i t h p a r t i c l e type from a n bank of n c e l l s would be Z R ; ( i ' J=1 1 It should be noted that the retention time of the pulp i s gradually increased from c e l l to c e l l because of the removal of material in each concentrate ( i . e . 0 ( n> > #<n-i> > 0< 2 ' > 0< 1 ' ). The retention times in the f i r s t and the l a s t c e l l s can be estimated as follows: 0<i) ^ v/F & 0<n' = V/T where V = the volume of the c e l l F = the volumetric feed rate to the bank of c e l l s T = the volume flow rate of the t a i l i n g from the bank of c e l l s F ^ T for the f i r s t c e l l Thus the retention times in other c e l l s are obtained by li n e a r i n t e r p o l a t i o n of a simple 6 versus c e l l number graph. In potash rougher f l o t a t i o n , a bank of c e l l s can be characterized by a matrix of f l o t a t i o n rate constants Kjj r e f l e c t i n g p a r t i c l e f l o a t a b i l i t i e s . ' The matrix can be i l l u s t r a t e d as follows: K, 1 K 2 , K 2 2  K 3 1 1 3 K s i ^ S 2 K sm where s i s the number of narrow size fractions and m is the number of minerals ( i . e . KC1, NaCl and INSOL). Each f l o t a t i o n rate constant in the matrix can be found from search methods by minimizing the following objective function: A 2 O.F. = I W • (R . - R , ) (10) i=1 ' ' ' A where Rj and R- are the measured and calculated recoveries of the i t h p a r t i c l e type in a bank of c e l l s respectively, and Wj is the weighting factor sometimes inversely proportional to the estimated error variance associated with the determination of the average measured recovery Rj. This treatment requires mineral assays in each screen size fraction for parameter estimation. The model was successfully f i t t e d by Cheng (20) to Brenda Mines f l o t a t i o n c i r c u i t data. 14 2.4.2 The Distribution Of Rate Constant Model The results of semi-batch and continuous tests under normal conditions of free . f l o t a t i o n have been analyzed by many investigators (13, 15, 16, 21, 22). In most cases, a p l o t 1 of log C(t)/C 0 versus t shows substantial curvature which suggests that the p a r t i c l e s in the pulp possess a continuous d i s t r i b u t i o n of f i r s t order rate constants. Thus the integrated form of the rate equation for a semi-batch c e l l becomes C(t) = C 0 X°°exp(-K.t) f(K,0) dk o where f(K,0) represents a continuous d i s t r i b u t i o n of rate constants in the f l o t a t i o n feed. To account for the heterogeneity of p a r t i c l e s found in f l o t a t i o n pulps, Imaizumi and Inoue (15) developed a graphical procedure to determine the d i s t r i b u t i o n function of rate constants from the f l o t a t i o n rate curves. Woodburn and Loveday (16) postulated that the f l o t a t i o n rate constant d i s t r i b u t i o n could be represented by a gamma function as shown in Fig.4. For a semi-batch f l o t a t i o n process, the f r a c t i o n a l recovery is -Kt R(t) = 1 - / f (K,0) e dK (11) 1 This is known as the f l o t a t i o n rate plot where C(t)/C 0=1-R(t). The plot has been considered as a useful tool for f l o t a t i o n rates evaluation. Rate Constant (K) 4 - A Gamma D i s t r i b u t i o n Function of K 1 q-1 f ( x ) = X p " X ( l - x ) ( p - l ) l ( q - 1 ) - ' w h e r e p a n d q a r e p o s i t i v e c o n s t a n t s *». K av K max / f(x) dx = 1 f1 f(x) x dx = X av re 5 - A Beta D i s t r i b u t i o n Function of K 1 6 b a + 1 a -bK where f(K,0) = . K . e which is a gamma a! d i s t r i b u t i o n function. a and b are the constants. a+1 Integration of equation (11) gives R = 1 - (b/(b+t)) 2.4.3 Lynch Model Lynch et. a l . (23) found that rougher f l o t a t i o n results can be characterized by a discrete bimodal d i s t r i b u t i o n . The model involves three parameters which recognize the existence of fas t -and slow- floa t i n g components in the ore. For semi-batch f l o t a t i o n , the rate equation of the discrete bimodal di s t r i b u t i o n i s given by C(t) = (1 - <p) exp(-K ft) + <t> exp(-K st) Co where <t> i s the slow-floating fraction with rate constant Ks, ( 1 - 0 ) is the f a s t - f l o a t i n g fraction with rate constant' Kf . In a perfectly mixed continuous c e l l , the steady state flow-rate of a mineral in the t a i l i n g is 1 1 (1 - </>)( ) + 0( ) 1 + Kf 6 1 + K s0 where d is the average residence time in the c e l l . 1 7 Lynch's model i s a reasonable representation of the rougher f l o t a t i o n process, but is inadequate in assuming 100% floatable material. It would seem sensible to incorporate the l i m i t i n g recovery, R», into the above equations. Thus the f r a c t i o n a l recovery of a valuable -mineral becomes -K.t ~^s*~ f° r a semi-batch (R» - 0 ) 0 - e ) + 0(1 - e ) f l o t a t a i o n . and (R« - 0 ) ( ) + 0 ( ) for a continuous 1 + K f0 1 + K s0 f l o t a t i o n c e l l . After modification, the model has four c u r v e - f i t t i n g parameters (R°°, 0 , Kf, K s) and each can be assigned some degree of physical significance. 2.4.4 Chen Model Recently Chen and Mular (24,45,46) have shown that the d i s t r i b u t i o n of the f l o t a t i o n rate constants can be described by, a Beta function. From semi-batch data, the Beta d i s t r i b u t i o n was obtained by the graphical method of Imaizumi and Inoue (15). The Beta d i s t r i b u t i o n function to represent the rate constant d i s t r i b u t i o n in the f l o t a t i o n feed is given by (Fig.5, page 15) P-1 q-1 X O-X) (P+q-1)! f(X) = , 0 < X < 1 (p-1)! (q-1)! = 0 otherwise 18 where X = K/Kmax P and q a r e p o s i t i v e c o n s t a n t s and a r e r e l a t e d t o t h e mean (M) and v a r i a n c e (o2) a s f o l l o w s : P Kav p.q M = = Xav = and a2 = P+q Kmax ( P + q ) 2 (P+q+1) where Kav and Kmax a r e t h e mean v a l u e and t h e maximum v a l u e o f t h e f l o t a t i o n r a t e c o n s t a n t d i s t r i b u t i o n r e s p e c t i v e l y . M o d e l d e v e l o p m e n t i s b a s e d on t h e a s s u m p t i o n t h a t e a c h p a r t i c l e c h a r a c t e r i z e d by a r a t e c o n s t a n t K {0 < K < Kmax) l e a v e s t h e c e l l a c c o r d i n g t o f i r s t o r d e r k i n e t i c s . Thus t h e a v e r a g e v a l u e o f K i n a s e m i - b a t c h c e l l a t t i m e t ( F i g . 6 ) i s w r i t t e n a s K m a x d Jn K f ( K , t ) dK = -g / K f ( K , t ) dK d t d K a v ( t ) d t = -g K a v ( t ) (12) where g i s a c o n s t a n t . The i n t e g r a t e d f o r m o f e q u a t i o n (12) i s - g t K a v ( t ) = K a v ( 0 ) e (13) E q u a t i o n (13) i n d i c a t e s t h a t t h e mean v a l u e o f K c h a n g e s e x p o n e n t i a l l y a t a r a t e g w i t h r e s p e c t t o f l o t a t i o n t i m e . K (0) av K av, (MIN ) K ( O av 1 av I \ 1 ; - • o t t TIME(MIN) Figure 6 - The Change of K a v With F l o t a t i o n Time ( after Chen and Mular (24) ) 20 The B e t a d i s t r i b u t i o n f u n c t i o n c a n be a p p l i e d t o b o t h (a) b a t c h and (b) c o n t i n u o u s f l o t a t i o n . (a) I n s e m i - b a t c h f l o t a t i o n , t h e f r a c t i o n a l r e c o v e r y o f m i n e r a l A i s - K t R A ( t ) = 1 - e (14) s i n c e K t c a n be r e p l a c e d by K a v ( t ) d t , e q u a t i o n (14) becomes - f j K a v ( t ) d t R A ( t ) = 1 - e 0 -/ Kav (0 ) e d t = 1 - e 0 .(15) I n t e g r a t i n g e q u a t i o n (15) g i v e s - g t -Kav (0) (1 - e ) R A ( t ) = 1 - e x p ( ) (16) 9 Once Kav (0 ) a n d g a r e d e t e r m i n e d , t h e l i m i t i n g r e c o v e r y a f t e r i n f i n i t e f l o t a t i o n t i m e , R ( c o ) , c a n be e s t i m a t e d a s f o l l o w s : 1 R A ( » ) = 1 - : f o r g > 0 e x p ( K a v ( 0 ) / g ) o r R a ( C O ) = 100% f o r g < 0 21 (b) For a bank of n continuous c e l l s , the f r a c t i o n a l recovery of mineral A from c e l l No. 1 i s 1 + f T l Kav(t)dt o the f r a c t i o n a l recovery from c e l l No. 2 with respect to the feed to the f i r s t c e l l of a bank of c e l l s in series i s : 1 R A 2 = (1 " R A l ) ( l " j ) 1 + / 2 Kav(t)dt s i m i l a r l y , 1 R A 3 = (1 - R A I - R A 2 ) ( 1 - 7 ) 1 + / 3 Kav(t)dt and 1 R A N = ( 1 - R A 1 - R A 2 • • • • - R A ( n - 1 ) ) ( 1 "" j ) 1 + f n Rav(t)dt T n - 1 where T i s the cumulative f l o t a t i o n time ( i . e . T 3 - T 2 = the retention time of pulp in c e l l No.3). It can be shown that the t o t a l recovery of mineral A from a bank of n c e l l s (See Appendix A) i s n 1 £ R = 1 " — :  1 - 1 Ai n Kav(O) -g ' l t, -gt. n {1 + ( )(e j = 0 J ) ( 1 - e ' )} 1=1 „ where t| i s the retention time of pulp in the i t h c e l l . 22 The above models require the determination of Kav(O) and g for each mineral i f the mineral recoveries are of major concern or for each size fraction of the minerals i f the relevant s i z e -by-size rate data are studied. The best values of the model parameters are obtained by minimizing the objective function shown in equation (10), page 13. Mathematical relationships between model parameters and p r i n c i p a l operating variables can be found either by di r e c t searches or standard regression methods. The major features of t h i s model are i l l u s t r a t e d in Fig.7, where Kav(0) represents the slopes of the f l o t a t i o n rate curves at i n i t i a l f l o t a t i o n times. The behaviour shown in curve 1 (+ve g) i s t y p i c a l of that observed in rougher and scavenger f l o t a t i o n and can be a l t e r n a t i v e l y modelled by a combination of two f i r s t - o r d e r rate processes representing fast and slow f l o a t i n g fractions of a mineral ( i . e . Lynch model). The behaviour shown in curve 2 (small g) can be equally well modelled by a f i r s t - o r d e r rate process ( i . e . Bull model). Typical behaviour observed in cleaner f l o t a t i o n i s shown in curve 3 (g<0), where the rate of recovery of mineral increases with increasing f l o t a t i o n time, which i s in contrast to the behaviour observed in the roughers and scavengers ( i . e . Curve 1 and 2) . Therefore the 0 d i s t r i b u t i o n model i s r e l a t i v e l y f l e x i b l e with two basic parameters and can be used to describe cleaner f l o t a t i o n behaviour which i s not allowed for in the Bull and Lynch models. 23 ************** Kav<0>= 1 Kav<Q>= 1 Kav<0)= 1 CHEN .00001 •l MODEL C a l c . R i n -C a l c . Rin= C a l c . Rin= 63.21 'A SOLID LINE 100 'A DOTTED LINE 100 'A DASHED LINE CD ( J \ +-> ( J 01 .V , - \*s. - V X K \ .2 V — — 1 \ * % — — \ — — V V V \ '% \ \ • i i i i i i i i i \ \ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 'l t 1 1 1 1 II I 1 1 1 I ! 1 1 1 V.I 1 1 t 0 2 3 T i m e , m i n u t e s NOTE : CCO'CCO) = FRRCTI ON OF fl MINERAL REMAINING IN fl CELL AFTER FLOTATION TIME t <i.e. 1-«< t > ) Figure 7 - Effect of Kav(O) and g on Flotation Rate Curves 24 2.5 Summary Of Review Of Models Various approaches to the development of mathematical models of the f l o t a t i o n process have been reviewed. Three kinetic models are proposed to simulate potash rougher f l o t a t i o n , because they introduce some "mechanism" and have been f i t t e d successfully by other investigators to f l o t a t i o n plant data. 25 I I I . EXPERIMENTAL MATERIALS AND PREPARATION PROCEDURES Experimental materials employed for this study, along with corresponding preparation procedures (49), are detailed in sections below. 3.1 Material Supply Potash ore from the Potash Corporation of Saskatchewan Cory Mine, located just west of Saskatoon, Saskatchewan, was shipped to the UBC mineral processing laboratory along with f l o t a t i o n reagents and saturated brine taken from the Cory f l o t a t i o n c i r c u i t . The ore has two soluble chlorides, namely, NaCl in the form of h a l i t e and KC1 in the form of s y l v i t e . For p r a c t i c a l purposes other components which include clays, oxides, carbonates etc., are water insoluble (INSOL). 3.2 Preparation Of Feed The procedure used to prepare coarse and fine fractions of Cory ore for scrubbing and desliming i s shown in Fig.8. Feed ore was reduced by 3-stage crushing to e s s e n t i a l l y minus 8 mesh as the s y l v i t e in this ore was lib e r a t e d at 10 mesh. Coarse (-8+28 mesh) and fine (-28+150 mesh) fractions were produced by means of a Gilson screen. Each f r a c t i o n was thoroughly mixed and stored in p l a s t i c bags. 26 Cory Raw Ore JAW CRUSHER -1.5" r GYRATORY CRUSHER k -1 2mm r TERTIARY CONE CRUSHER -4mm r +8 mesh -8+28 mesh As Coarse Fraction 3 DECK GILSON SCREEN -28+150 mesh -150 mesh For BRINE preparation i f desired. As Fine Fraction Figure 8 - Preparation of Feed for Scrubbing and Desliming 27 3.3 Preparation Of Saturated Brine Saturated brines were prepared either from potash ore or from saturated brine drums shipped from Cory. From ore : A calculated amount of either raw ore or screen undersize (-150 mesh) was placed in a large p l a s t i c can. The can was f i l l e d to within 15 inches of the top with warm water. The contents were agitated and s u f f i c i e n t material added to bring the s p e c i f i c gravity to 1.24. The slimes were allowed to set t l e out overnight. Brine temperature was adjusted by means of a heating element, while a mixture of KC1 + NaCl was added to saturate the warm solution. Clear brine was decanted as necessary for use. From Brine Drum : An a i r l i n e would be inserted at the top of a drum. The a i r dispersed and mixed the cr y s t a l s s e t t l e d out on the tank bottom. A resistance heater was then inserted to warm the brine to about 35°C with the compressed a i r turned on. After c r y s t a l s had been dissolved, brine was transferred to p l a s t i c p a i l s . Solids were allowed to s e t t l e out and clear brine was decanted for use in subsequent f l o t a t i o n t e s t s . 3.4 Preparation Of Reagents Potash f l o t a t i o n reagents used in thi s study consisted of Armeen TD ( c o l l e c t o r ) , MRL-154 guar gum (slime-depressant), process o i l 904 (extender), and MIBC (frother). Preparation methods for the f i r s t two reagents are as outlined below: Collector : Amine c o l l e c t o r i s comprised of a 3.3% amine 28 chloride aqueous solution in the proportions 4.8 gm of amine, 1.8 gm of HC1 and 193.4 gm of water. To prepare the mixture: (1) Heat water to about 70°C. (2) With vigorous s t i r r i n g , add 4.8 gm of amine and 1.8 gm of HC1 simultaneously. (3) Cover the container and agitate the solution for approximately 30 minutes. (4) Maintain temperature during a g i t a t i o n . (5) Keep covered during storage. Depressant : Depressant i s a 0.3% aqueous solution in the proportions 1.5 gm of quar gum, 2.5 gm of water and 473.5 gm of brine. The solution i s prepared 24 hours prior to a f l o t a t i o n t e s t . 29 IV. EXPERIMENTAL DETAILS Experimental d e t a i l s relevant to this study (49,50,51,52,53) are summarized in the sections that follow. 4.1 Objectives The purpose of the experimental investigation i s to test whether kinetic models can be used to (1) Simulate potash rougher f l o t a t i o n in batch and continuous c e l l s . (2) Evaluate the effect of important process variables on size-by-size f l o t a t i o n behaviour. (3) Correlate batch data with continuous f l o t a t i o n results by means of scale-up factors. Small batch 2 , large batch 3 and continuous rougher f l o t a t i o n tests were conducted. These are discussed separately. 4.2 Small Batch Flotation Tests Preliminary f l o t a t i o n experiments were performed to develop a sat i s f a c t o r y test procedure and to obtain approximate magnitudes of the factor levels to be used in subsequent test work. A central composite design was constructed with six factors, namely, V, = amine c o l l e c t o r , lb/ton, V 2 = o i l , lb/ton, V 3 = c e l l % s o l i d s , V„ = f l o t a t i o n pulp temperature, °C, V 5 = 2 with a 2 . 7 - l i t r e Denver D1 Lab. c e l l 3 with a modified 1 0 - l i t r e Sub-A c e l l which is i d e n t i c a l to those used for continuous f l o t a t i o n 30 impeller speed, rpm and V 6 = airflow, 1/min. Coding relations were as follows: = (v, -- . 1 8 ) ( 2 . 378 )/ . 04 x 2 = - ( v 2 -- . 0 15 ) ( 2 . 378 ) / . 0075 x 3 = - ( v 3 -- 4 0 ) ( 2 . 3 7 8 ) / l 0 x„ = = ( v , -- 3 0 ) ( 2 . 378 ) /5 x 5 = = ( v 5 -- 1200) (2 .378)/200 x 6 = - ( v 6 -- . 3 ) ( 2 . 3 7 8 ) / . 3 where X; i s the coded factor l e v e l and V. the corresponding real value. Coded factor units employed were -a, - 1 , 0 , 1, a with a = 2.378. The following table l i s t s actual levels for each factor, where Guar and frother are held constant (.12 and .047 lb/ton r e s p e c t i v e l y ) : -a -1 0 + 1 + a Unit amine 0.12 . 1 55 .18 .205 0.24 (lb/T)* o i l .0075 .0118 .015 .0181 .0225 (lb/T)* % solids 30 35.8 40 44.2 50 temperature 25 27.9 30 32. 1 35 °C speed 1000 1115.9 1 200 1284.1 1400 R.P.M. a i r 0 .174 .3 .426 .6 1/min. *Note that a l l reagent consumptions are expressed as pounds of reagent per short ton of ore (abbreviated as lb/T) to be consistent with plant practice. To convert to Kg/MT multiply by .5 . Table 1 shows the design in coded units. The f a c t o r i a l part i s a 2 j " 1 f r a c t i o n a l design of resolution V with factor X 6 confounded with the interaction X ^ ^ X ^ . Center point runs 31 are useful for several reasons, a main one being to estimate error variance. Table 1 - Experimental Runs with Coded Levels for Small Batch Flotation Run No. coded# (design run) x, x2 x3 x« x5 x6 198 1 -1 -1 -•, -! -1 _ ! 1 93 2 +1 -1 -1 - 1 -1 +1 220 3 -1 +1 -1 - 1 -1 +1 184, 238 4 +1 +1 -1 - 1 -1 -1 216 5 -1 -1 +1 -1 -1 +1 188 6 +1 -1 +1 - 1 -1 -1 178 7 -1 +1 +1 - 1 -1 -1 183 8 +1 +1 +1 - 1 -1 +1 1 73 9 -1 -1 - 1 +1 -1 +1 208 1 0 +1 -1 -1 +1 -1 -1 206 1 1 -1 +1 -1 +1 -1 - 1 179 1 2 +1 +1 -1 +1 » -1 +1 192 1 3 -1 -1 +1 +1 -1 -1 175 1 4 +1 -1 +1 +1 -1 +1 231 15 -1 +1 +1 +1 -1 +1 199 16 +1 +1 +1 +1 -1 -1 223 1 7 -1 -1 -1 -1 +1 +1 1 97 18 +1 -1 -1 -1 +1 -1 218, 228 19 -1 +1 -1 - 1 +1 -1 214 20 +1 +1 -1 -1 +1 +1 1 96 21 -1 -1 +1 - 1 +1 -1 180 22 +1 -1 + 1 -1 +1 +1 212 23 -1 +1 +1 -1 +1 +1 204 24 +1 +1 +1 - i +1 -1 195 25 -1 -1 -1 +1 +1 -1 200 26 +1 -1 -1 +1 +1 +1 190 27 -1 +1 -1 +1 +1 +1 187 28 +1 +1 -1 +1 +1 -1 203 29 -1 -1 +1 +1 +1 +1 213 30 +1 -1 +1 +1 +1 -1 209 31 -1 +1 +.1 +1 +1 -1 174 32 +1 +1 +1 +1 +1 +1 continued... 32 Table 1 continued... Run No. coded# (design run) x, x2 x3 x« x5 x6 181 33 ~a 0 0 0 0 0 202 34 + a 0 0 0 0 0 186 35 0 -a 0 0 0 0 217, 224 36 0 + a 0 0 0 0 210 37 0 0 -a 0 0 0 201 38 0 0 + a 0 0 0 185 39 0 0 0 -a 0 0 222 40 0 0 0 + a 0 0 219 41 0 0 0 0 -a 0 21 1 42 0 0 0 0 +a 0 177 43 0 0 0 0 0 -a 205 44 0 0 0 0 0 +a 172 45 0 0 0 0 0 0 191 46 0 0 0 0 0 0 221 47 0 0 0 0 0 0 207 48 0 0 0 0 0 0 215 49 0 0 0 0 0 0 182 50 0 0 0 0 0 0 1 94 51 0 0 0 0 0 0 1 76 52 0 0 0 0 0 0 234 53 0 0 0 0 0 0 236 54 0 0 0 0 0 0 237 55 0 0 0 0 0 0 33 General steps (Fig.9) employed for the design runs include (a) Scrubbing and De-sliming coarse and fine fractions (b) Reagentizing (c) Frother Conditioning and F l o t a t i o n . a. Scrubbing and Desliming : The procedure employed for the coarse fracti o n was as follows, (1) Scrub the coarse fracti o n in saturated brine of desired temperature at 60% solids in a p l a s t i c container for 5 minutes with an agitator. (2) Deslime in batches with brine on a 65 mesh screen mounted on a vibrating screen shaker, u n t i l the discharge" brine i s clea r . Save the discharge brine to estimate slime content. (3) Transfer the sol i d s from the screen to a p l a s t i c container. Mix the contents and take a sample for assay. (4) Adjust to 65% sol i d s with brine at the desired temperature in preparation for reagentizing. The procedure employed for the fines f r a c t i o n i s somewhat similar, except that a 150 mesh screen i s used instead of a 65 mesh screen. In addition, deslimed fines are adjusted to 60% solids for reagentizing at the desired temperature. b. Reagentizing : Reagent temperature and concentrations added are shown below REAGENT CONCENTRATION TEMPERATURE °C ARMEEN TD 3.3% solution 66 GUAR(MRL 154) 0.3% solution 25 PROCESS OIL as received 45 MIBC FROTHER as received 25 34 Fines fracti o n W1 scrubbing and desliming -•Lf / slimes loss (-150 M) W1 Lf Wa, a 1 , a_2, a_3 fines samples & assays reagentizing and conditioning Wf = Wl-Lf-Wa F = Wf+Wo Y(I,6) X(I+25,J) 20 sec. Cl Y T l ,1) X(I,J) f rother/ condition 20 sec Coarse Fraction W2 I scrubbing and desliming Lc, slime loss (-65 M) W2 - Lc Wb, b_1_, b2, b3 coarse samples & assays reagent iz ing and conditioning Wo = W2-Lc-Wb T Y(I f5) X(I+25,J) 20 sec. 60 sec C2 | T l ,2) X(l+5,J) C3 YTl,3) X(I+10,J) C4 YTl,4) X(I+15,J) Note: measured data points are underlined Figure 9 - Small Batch Flotation Flowsheet and Symbols for Mass Balances 35 To reagentize the coarse f r a c t i o n , (1) Add 40% of the t o t a l depressant required to the deslimed coarse f r a c t i o n . (2) Condition for 3 minutes. (3) Add the desired amount of amine and process o i l , and condition for another 1.5 minutes. (4) Transfer the contents into the c e l l . To condition the fines f r a c t i o n , (1) Add 60% of the t o t a l depressant required to the deslimed fines f r a c t i o n . (2) Condition for 3 minutes. (3) Transfer the contents into the c e l l . c. Frother Conditioning and Flotation : To condition and f l o a t , (1) Add MIBC frother . Then add brine of a desired temperature to bring the pulp l e v e l to within 1/2" of the c e l l l i p . (2) Turn on the impeller with the a i r valve turned off and condition for 2 minutes at 1200 RPM. (3) At the end of 2 minutes, set the impeller to the required speed and turn on a i r as necessary. (4) Skim the froth and maintain the pulp l e v e l in a consistent manner. (5) Four concentrates are c o l l e c t e d at 20, 40, 60 and 120 seconds for f l o t a t i o n rate studies. A t o t a l of 58 batch f l o t a t i o n runs, with a Denver D-1 lab c e l l of 2.7 1 capacity, were conducted in random order according to the design (Table.1). However, samples of f l o t a t i o n feed just prior to f l o t a t i o n in the c e l l were d i f f i c u l t to obtain. 36 Since the batch of ore employed for the runs had been c a r e f u l l y blended and mixed, seven independent runs were performed up to the point where a i r should have been introduced for f l o t a t i o n . Rather than f l o a t , each feed was f i l t e r e d , screened, and assayed. Results are shown in Table 2 in raw form. The average feed size analysis and the average assays are assumed to be representative of each f l o t a t i o n feed for a given run. The screening procedure for samples of feeds, concentrates and t a i l i n g i s based on the report by Hickie and Hoist, PCS  Report on Metallurgical Procedures (55), with methanol substituted for trichlorethane. Screens of interest were 8 mesh, 14 mesh, 28 mesh, 48 mesh, 100 mesh and -100 mesh, although samples were screened in a nest that varied by the square root of 2 r a t i o from 8 mesh down. Assay procedures have been described (44). B r i e f l y , s p e c i f i c ion electrodes were employed for KC1 and NaCl determinations. It should be noted that, after assays were complete for a l l runs, the analyst discovered that pipettes used to prepare c a l i b r a t i o n solutions were in error by a constant amount. Consequently, the following was employed to correct assays: Feed: %KCl(corr) = .99545(%KC1(raw)) Con: %NaCl(corr) = 1.0035(%NaCl(raw)) T a i l : %KCl(corr) = .98400(%KCL(raw)) Table 3 shows a t y p i c a l summary of desired operating conditions for run 172. The . raw data and corrected data for the corresponding run are given in Tables 4 and 5 respectively. 37 Table 2 - Average Results for Seven Flotation Feeds % Retained on Size Size, Mesh 14 28 48 100 -100 14.52 20.75 32.48 22.20 10.05 13.34 21.53 30.89 23.44 10.80 15.41 20.25 31.17 22.87 10.30 14.62 21.29 31.33 22.98 9.78 13.11 21.42 31.08 23.84 10.55 11.54 22.94 32.52 23.72 •9.28 10.15 23.30 33.41 23.25 9.89 Ave. 13.24 21.64 31.84 23.19 10.09 %KC1 14 36.9 35.8 37.7 38.5 34.2 33.8 35.1 36.00 28 41.7 40.1 42.2 40.9 40.3 40.1 39.4 40.67 48 42.2 42.9 41.9 42.7 42.9 41.8 41.0 42.20 100 41.7 40.3 41.2 •41.5 40.4 40.7 39.0 40.69 100 43.7 47.7 46.2 45.5 48.5 .49.4 48.8 47.11 %NaCl 14 62.6 64.2 62.0 61.1 63.9 65.1 64.6 63.37 28 59.5 59.6 57.6 58.3 57.7 58.8 60.1 58.80 48 59.0 57.2 57.8 56,8 56.4 57.3 58.0 57.47 100 58.8 59.4 58.2 58.2 58.2 58.6 59.4 58.69 100 57.6 52.2 53.4 56.0 48.6 48.8 48.8 52.20 %INS0L 14 28 48 100 -100 1.18 1.11 1.11 1.13 1.14 1.12 1.06 1.121 1.08 0.87 0.90 0.87 0.89 0.82 0.80 0.886 0.77 0^.86 0.70 0.75 0.77 0.77 0.74 0.766 0.84 1.00 0.87 0.91 0.82 0.89 0.85 0.880 1.73 2.26 1.93 1.91 1.69 1.80 1.97 1.899 38 Table 3 - A Typical Summary of the Desired Operating Conditions for Run 172 **»»*+ R U N ( ! ( 1 7 2 CODED* 45 DATE: OCT. 27 /82 *********** F l o t a t i o n Machine : DENVER DI , 2.7 L i t r e s ' T y p e ' " o f " " p o t a s h " ' 6 r e • • • • . « . » . . » y Q - n e g r e .^ .So] 1 d s i n t he ...Flotation C e 11 : 40 Temperature of t h i s Run : 30 Deg. C WeTght "of" Desi'imed'bre " : 1 5 7 9 -2 "gm »**•**»****•*•*•**»*•*** scrubbing at 60% Solids ************************ fract.ipn Solid[...(grnj) Brine[..(.93.). ..„ T.9.*S.1. T.J.rofLi.™iPJL Coarse 754.8 503.2 1258 5 Fines 1256.7 837.8 2094.5 _ 5_ T o t a l 2 0 l " i ' " . " 5 ~ " ! ' . '*'** Conditioning Coarse at 65% Solid s and Fines at 60% Solids *** T.r.?.9.$J.?.n. 5.9.?..?.!?.. i.9.™). „ .B.C..,..n..e....(9!?.i!._ 1.9.*.?..? .. Coarse 631.7 340.1 971.8 Fines 947.5 631.7 1579.2 ft*************************.**** Reagentjz l.ng the ...Coarse _FrectJjon. Reagent lb/T g/Kg gram c.c. Time (min) Gua'r"''('40%)" o"."l 2 o " . " 6 " E ~ 1 " " " 'b"."4'83E'-'l '"" " 16.1 3 ARMEEN TD 0.18 0.9E-1 O.181 5.5 1.5 f o r Amine Oi 1 (*9p.4) Pi.15E-1 0...7.5E-2 P.;._151E-J. .^.L-.2...P£.ops and O i l combined • •..*-,.***»,*.»******»*•**»,* Reagent 1 z 1 ng the F;jnes; FractJon.***. Reagent lb/T g/Kg gram c.c. Time (min) Guar" " ( 6 6 % ) 6 " . " " 1 2 o " . " 6 " E ' - " i - " o " . ' 7 2 4 E - ' l 24"i" " 3 *»«»*************+**»«#•***+**+• F r o t h e r Conditioning 1n the C e l l ********************** Reagent I.b/I 9 / . K . S . 9 r . a . . m . _ . J ? £ . 9 P . S . -...I.?.?6...!™.1..",.} M I B C 0.47E-1 0.235E-1 0.473E-1 9.5 2 *»»».*»*****»•»* F l o t a t i o n Conditions **************** "A'Yr-""!^ "Yow RaHTeT*""""V"V~"""""V**L*""V"."I"I"J"V""""™V"1"6."af'X/Hi'iin" Impeller Speed of the F l o t a t i o n Machine ... 1200 RPM 39 Table 4 - Raw Data of Run 172 » » » • » , » • . » » • • * < B A T C H F L O T A T I O N DATA S H E E T » • * • » * * • * . • » • * » * * * • « • T » • < • i ->•**••»-r»* ( r a w d a t a ) * * * * * * * * * * * * * * * * * * * * R U N * 1 7 2 F a c t o r C o d e d L e v e l L e v e l A m i n e ( l b / T ) 0 0 . 1 8 oil ' ( " i b / T ) 6 6 ' . ' l " 5 E r i " ' / .So l 1d ('/,) O 4 0 T e m p ( D e g . C ) 0 3 0 S p e e d ( R P M ) 0 1 2 0 0 A i r ( L / m i n ) " 0 0 . 3 CODED* 4 5 D A T E : S a m p l e T y p e * C o a r s e ( g m ) F i n e s ( g m ) Raw F e e d " S 1 "i nis's D e s l I m e d S a m p l e s ...P.P.n£?D.l^S.t.?.§ T a i i s G a i n 7 5 4 . 8 " . 1 0 4 . 2 2 8 . 1 1 2 5 G . 7 ~ 2 6 2 ' ' " 3 " 4 1 . 8 O C T . 27/H2 T o t a l (gm] 2 0 1 1 . 5 ' 36G" . 5 € 9 . 9 6 0 2 . 5 " ' t 0 0 0 ' . 5 ~ ' 2 7 . 9 D e s 1 i m e d S a m p l e s A s s a y s * * * * * * * * * * * * * * ' / .Kc l % N a c l •/.Insol F i n e s S a m p l e 3 9 . 7 5 8 . 4 0 . 9 3 C o a r s e S a m p l e . 4 4 . 7 5 3 . 1 1 . 1 * * * » * + » * * * * * » * * > • * » * 5 ^ 2 e A n a l y s e s a n d A s s a y s o f F l o t a t i o n P r o d u c t s * * * * * * * * * * * * * * * * * * * C o n e . 1 M e s h • / . R e t a i n e d •/.Kcl y .N iac l % I n s o l 2 7 0 . 5 gm - 8 + 1 4 1 . 7 8 9 5 . 4 6 . 1 0 . 5 2 - 1 4 + 2 8 1 1 . 2 9 7 . 5 4 . 8 0 . 3 9 - 2 8 + 4 8 3 7 . 9 1 9 6 5 . 9 0 . 4 - 4 8 + 1 0 0 3 3 . 2 4 9 4 . 4 7 . 6 0 . 4 7 - 1 0 0 1 5 . 8 7 9 3 . 3 1 0 . 1 1.0S C o n e . 2 M e s h • / . R e t a i n e d % K c l y , N a c l % I n s o l 1 0 7 . S gm - 8 + 1 4 0 . 3 5 9 4 . 4 6 . 9 0 . 4 - 1 4 + 2 8 7 . 6 9 9 7 4 . 7 0 . 4 - 2 8 + 4 8 4 0 . 3 2 9 5 . 3 6 . 2 0 . 4 5 - 4 8 + 1 0 0 3 4 . 12 9 2 . 6 9 . 1 0 . 4 6 - 1 0 0 1 7 . 5 2 8 8 . 6 1 1 . 8 1 . 0 9 C o n e . 3 M e s h % R e t a l n a d %kc\ % N a c i fcinso'i 1 2 1 . 4 gm - 8 + 1 4 0 . 8 7 9 5 . 3 5 . 7 0 . 5 6 - 1 4 + 2 8 1 6 . 4 5 9 7 4 . 9 0 . 4 5 - 2 3 + 4 8 4 4 . 3 2 9 2 . 1 9 . 1 0 . 5 3 - 4 8 + 1 0 0 2 4 . 8 8 8 2 . 7 . 1 8 . 4 0 . 5 4 - 1 0 0 1 3 . 4 8 7 6 . 7 2 3 . 8 i . 9 6 C o n s . 4 M e s h ^ R e t a i n e d %KC1 % N a c l 7 » I n s o l 1 0 2 . 7 gm - B + 1 4 1 . 5 6 . 9 9 . 8 2 . 9 5 0 . 6 2 - 1 4 + 2 8 3 0 . 5 7 9 8 . 7 4 . 15 0 . 5 - 2 8 + 4 8 4 0 . 9 8 8 . 9 1 1 . 3 - 4 8 + 1 0 0 1 6 . 4 6 7 1 . 8 2 7 . 3 0 . 8 7 - 1 0 0 1 0 . 5 2 6 9 . 3 2 5 . 1 4 . 2 2 T a i 1 s M e s h y . R e t a 1 n e d '/*Kc1 •/.Nad •/. Insol 1 0 0 0 . 5 gm - 8 + 1 4 1 3 . 4 1 2 3 . 2 7 6 t . 12 - 14 + 2 8 2 5 . 0 8 2 0 . 5 7 8 . 2 1 . 0 7 - 2 8 + 4 B 3 0 . 6 9 2 . 8 4 9 3 . 6 1 . 1 1 - 4 3 + 1 0 0 2 1 . 9 9 1 . 8 4 9 5 . 1 1 . 3 1 - 1 0 0 8 . 8 3 2 . 4 7 9 4 2 . 2 7 40 Table 5 - Corrected Data of Run 172 BAT~CH~f ioTATlON DATASHEET ••••••••••••• • ( raw Data I • RUN* 172 COOED* 45 DATE: OCT . 27 /82 Factor Coded Level Level Sample Type Coarse (gm) F1nes (gm) Total (gm) Amine ( lb/T) 0 0. 18 Raw Feed 754 .8 1256.7 2011.5 011 (lb/T j 0 0. 1SE-1 SI lines 104.2 262.3 366.5 •/.Sol Id (X) 0 40 Deslimed Samples 28.1 41.8 69.9 Temp (Oeg.C) 0 30 Concentrates 602.5 Speed <RPM) 0 1200 Tal Is 1000.5 A i r (L/mln) 0 0 . 3 Gain 27.9 XKCl XNacl XInsol F1nes Samp1e 39. 7 58.4 0.93 Coarse Sample 44 .7 S3. 1 1 . 1 F lo tat Ion Cone. 1 Mesh XRetatned XKcl XNacl XInsol 270.5 gm -8*14 1.78 95.4 6.1 0.52 -14+28 11.2 97.S 4.8 0.39 -28*48 37 .91 96 5 .9 0.4 -48*100 33.24 94.4 7.6 0.47 -100 15.87 93.3 « 0 . 1 1 .06 Cone. 2 Mesh XRetaIned XKCl XNacl XInsol 107.9 gm -8*14 0.35 94.4 6 .9 0.4 -14*28 7 .69 97 4.7 0.4 -28*48 40. 32 95.3 6.2 C.45 -48+100 34 . 12 92.6 9. 1 0.46 -100 17.52 88.6 11.8 1 .09 Cone. 3 Mesh XRetaIned %KC1 XNacl XInsol 121.4 gm -8+ 14 O. 87 95.3 5.7 0.56 - 14 + 28 16.45 97 4 .9 0.45 -28*48 44.32 92 . 1 9 . 1 0.53 -48+100 24 .88 82.7 18.4 0.54 -100 13.48 76.7 23.8 1 .96 Cone. 4 Mesh XRetmned XKCl XNacl XInsol 102.7 gm -8+ 14 1 .56 99.8 2 .95 0.62 - 14*28 30.57 98.7 4. 15 0 .5 -2B*48 40.9 88.9 11.3 0 .7 -48*100 16.46 71 .8 27 .3 0.B7 - lOO 10.52 69 . 3 25. 1 4.22 T a i l s Mesh XRetaIned XKCl XNacl XInsol 1000.5 gm -- 8 * 14 13.41 23.2 76 1 . 12 -14+28 25.08 20. 5 78 .2 1 .07 -28*48 30.69 2.84 93.6 1.11 -48+100 21 .99 1 .84 95. 1 1 .31 -100 B.83 2.47 94 2.27 41 4.3 Large Batch Flotation Tests I n i t i a l experiments conducted in a Denver Sub-A 10-Litre c e l l showed that the o v e r a l l recovery was poor. The +14 mesh material would not f l o a t . A r e c i r c u l a t i o n ring similar to one used in the small batch c e l l was judged necessary. Consequently, the sub-A c e l l was equipped with a 15 cm high x 11.5 cm dia. p l a s t i c ring. Recovery was improved. A f r a c t i o n a l f a c t o r i a l design was constructed with four factors, namely, V, = amine c o l l e c t o r , lb/ton; V 2 = c e l l % s o l i d s ; V 3 = impeller speed, rpm and V„ = airflow, 1/min. Coding relations were as follows: X, = (V, - .18)(2.378)/.04 X 2 = (V 2 - 40)(2.378)/l0 X 3 = (V 3 - 1200)(2.378)/200 X„ = (V„ - 7)/4 where X; i s the coded factor l e v e l and V; the corresponding real value. Coded factor units employed were -1, 0, 1. The table below i l l u s t r a t e s actual l e v e l s for each factor, where amount of o i l and pulp temperature are fixed at centre-point values. Table 6 shows the design in coded units. The f a c t o r i a l part i s a 2""1 f r a c t i o n a l design with factor X„ confounded with the interaction X,X 2X 3. -1 0 + 1 Unit amine .155 .18 .205 (lb/T) % s o l i d s 35.8 40 44.2 speed 1115.9 1 200 1284.1 R.P.M. ai r 3 7 1 1 1/min. 42 A t o t a l of twelve batch runs were completed in accord with the design (Table 6). A flowsheet of the f l o t a t i o n procedure is shown in Fig.10. These runs d i f f e r e d from the e a r l i e r set of 58 in that a l l of the feed was pre-scrubbed, de-slimed and stored under brine u n t i l conditioning. The coarse material was drained, weighed wet and then compensated for brine retained. The draining technique did not result in repeatable percent sol i d s values for fine material. Hence fines were pressure f i l t e r e d in fiv e minutes to 88% s o l i d s . The technique was reproducible. The runs also d i f f e r e d in that a feed sample was taken prior to f l o t a t i o n for each run. During f l o t a t i o n , f i v e concentrates were co l l e c t e d at 20, 40, 60, 120 and 210 seconds. Froth was removed by means of paddles rotating at constant v e l o c i t y . Operating conditions and measured raw data for run #250 are shown in Tables 7 and 8 respectively. Large batch f l o t a t i o n runs are intermediate for scale-up purposes ( i . e . small batch, large batch, and continuous f l o t a t i o n ) . They also served as a f a m i l i a r i z a t i o n with the procedures and equipment employed for the continuous tests as discussed in the following section. 43 Table 6 - Experimental Runs with Coded Levels for Large Batch Fl o t a t i o n coded# Run No. (design run) x, x2 x3 x. 251 1 -1 -1 -1 -1 253 2 + 1 -1 -1 + 1 255 3 -1 + 1 -1 + 1 254 4 + 1 + 1 -1 -1 258 5 -1 -1 + 1 + 1 259 6 + 1 -1 + 1 -1 256 7 -1 + 1 + 1 -1 257 8 + 1 + 1 + 1 + 1 260 9 0 0 0 0 261 10 0 0 0 0 250 1 1 0 0 0 0 252* 12 + 1 -1 0 + 1 *Run 252 i s an extra run performed accidentally. 44 deslimed Fines W1 reagentizing and conditioning deslimed Coarse W2 reagentizing and conditioning Wa •+ f T l ,7) X( I+30,J) add frother/ condit ioning T Y(I,6) X d + 25, J ) 20 sec. C1 YTI,1) x d , J ) C2 Yll,2) X(I+5,J) 20 sec. 20 sec. 60 sec. 90 sec. C3 YTl,3) X d + l0,J) C4 Y l l , 4 ) X d + 1 5 , J ) C5 Yll,5) x T l + 2 0 , J ) Note : measured data points are underlined Figure 10 - Large Batch Flotation Flowsheet and Symbols for Mass Balances 45 Table 7 - Desired Operating Conditions for Run 250 * * * * * * * * * * RUN* 250 CODED* 11 DATE: APR. 13 /83 * * * * * * * * * * * * * * * * * * * A Summary Sheet of Information Required For the Batch Test * * * * * * * * Factor Coded Level Level Amine ( i b / f ) 0 0. 18 %So l id (%) 0 40 Speed (RPM) 0 1200 A i r (L/min) 0 7 F l o t a t i o n Machine : Modif ied DENVER SUB A . 10 L i t r e s Type of Potash Ore : PCS Cory Ore •/.Solids in the F lo ta t ion" F e e d : " 40 % by Weight J.e.n?Re.r.?.t.Hr.?..of..PTJne. ...... ?o..peg. ..c Weight of Des1Imed Ore in the Ce l l : 5849.1 gm Des Timed Coarse I F ihes" Rat:io""in" the Ce i l ' : 46/60 .%!?.9.L'.??.?...in...b.°^  ..'^ ....pj?.".?!!* Fract ion Wet Sol id (gm) Br ine (gm) Total (gm) Coarse 2772.3 981 3753.3 " F i n e s 4 " i ' 5 8 " . " 4 " " " ' 1 9 4 0 ' 6 6 0 9 9 " . " 1 * * * * * • * • * * • * * * * * * • * • * • * * * * * * * * Reagentizing the Coarse Fract ion * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Reagent lb/T q/Kq gram c . c . T i me (min) Guar (40%) 0.12 0.6E-1 6.1792 ARMEEN TD 0.18 0.9E-1 0.6719 O i l (#904) 0.15E-1 0.75E-2 0.56E-1 59.7 20.4 11.8 Drops 3 1.5 for Amine and 0 i1 comb i ned * * • • * * • * * * • • • • • * • * * * * * * * * • * * Reagentizing the Fines Fract ion * * * * * * * * * * * * * * * * * * * * * * * * * * * Reagent lb/T g/Kg gram• C . C . Time (min) Guar (60%) 0.12 0.6E-1 0.2688 89.5 3 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Frother Condit ioning in the Cel1 * » * * * * * • • * * * * * * * * * * * * * Reaqent lb/T g/Kg gram Drops Time (min) MIBC 0.47E-1 0.235E-1 0.1754 35. 1 2 * * * * * * * * * * * * * * * * F l o t a t i o n Condit ions * * * * * * * * * * * * * * * * Inipeii 1 e f ' S p e e ^ • • 1200 RPM 46 Table 8 - Measured Data of Run 250 ***** ******** BATCH FLOTATION DATA SHEET ******-******************** ( raw data ) ****** ******* RUN* 250 CODED* 11 DATE: APR. 13 ******************* sj Zg Analyses and Assays of Flotation Products ******************* Cone. 1 Mesh ^Retained y,Kci %Nacl %Insol 615.5 gm -8+14 3.06 95.4 4 . 13 0.47 -14+28 15.23 94 .06 5.56 0.38 -28+48 38.46 91 .62 8 0.38 -48+100 29.66 90.71 8.84 0.45 -100 13.59 91 .08 7.65 1 .27 Cone. 2 Mesh '/.Retained %Kc 1 %Nac1 XInsol 398 gm -8+14 3.91 96.82 2.75 0.43 -14+28 16.41 93.28 6.23 0.49 -28+48 39. 17 90.35 9. 15 0.5 -48+100 28.62 91 . 12 8 .28 0.6 -100 11 .89 90.94 6.87 2. 19 Cone. 3 Mesh ^Retained %Kcl 7nNacl %i nso'i 300.4 gm -8+14 3.99 96.92 2.63 0.45 -14+28 15.24 •94 .54 4.94 0.52 -28+48 37.44 90.68 8.76 0.56 -48+100 30.4 90.94 8.31 0.75 -ioo 12.93 89.43 7.46 3.11 Cone. 4 Mesh %RetaIned %Kcl %Nacl %Insol 440.3 gm -8+14 3. 16 97.4 2. 1 0.5 -14+28 15.44 94.95 4.57 0.48 -28+48 38. 16 91 .53 7.87 0.6 -48+100 29.58 91 .66 7.48 0.86 -100 13.66 89.35 6.53 4. 12 Cone. 5 Mesh ^Retained %Kcl •/.Nacl %Insol 194.3 cjm -8+14 3.99 97 .3 2 . 13 0.57 - 14+28 17.58 95.94 3.54 0.52 -28+48 36.68 93.01 6. 17 0.82 -48+IOO 28.7 92. 19 6.41 1.4 -IOO 13.05 86.58 5.24 8. 18 Ta i i s Mesh ^Retained %Kci %Nacl #"insol 3902.5 gm -e+14 20.46 24.31 75. 14 0.55 -14+28 15.43 8.39 91.12 0. 49 -28+48 27.08 2.15 97 .42 0.43 -48+100 24.82 ! 1 .67 97 .75 0.58 -100 12.21 7.3 90. 19 2.51 Flo. Feed Mesh y=Reta1ned %Kcl %Nacl %Insol -8+14 18.39 30. 19 68 .98 0.83 -14+28 16.9 33 .36 66.04 0.6 -28+48 34 . 55 35.42 64 0.58 -48+100 23.33 32.98 66.06 0.96 -100 6.83 38.25 58.86 2.89 Sample Type Mass(grn) Fines(WI) 3659.4 Coarse(W2) 2439.6 Sampie(Wa) 301 Concentrates 1948.5 Ta i1s 3902 5 Gain 53 47 4.4 Continuous Flotation Tests A flow diagram of the continuous f l o t a t i o n c i r c u i t employed for t h i s investigation i s shown in Fig.11. Warm saturated brine from a constant head tank i s fed by gravity to three locations to maintain the desired pulp density. Coarse s o l i d s , fed manually to a rotary drum conditioner, are mixed with brine and f l o t a t i o n reagents. A steady discharge rate from the fines storage tank to the fines conditioner i s achieved by means of a moyno pump. The conditioned fractions are combined at a junction box where MIBC frother i s added. A bank of three Denver c e l l s , each being i d e n t i c a l to the large batch c e l l , completes the c i r c u i t . Several t r i a l runs performed on the bank of continuous c e l l s were discouraging. The main problem was the i n a b i l i t y to keep sol i d s from s e t t l i n g in the transfer l i n e s between individual c e l l s . This problem was f i n a l l y overcome by closing the a i r valve on the side of each impeller shaft so that more suction was available to induce both f l o t a t i o n pulp and a i r into the c e l l s via their transfer l i n e s and feedpipes. Subsequent f l o t a t i o n tests were performed with factors fixed at center point lev e l s (except a i r ) . Only three of these runs were considered sucessful enough to reach the steady state conditions. These three runs d i f f e r e d from the previous batch tests in that (1) f l o t a t i o n feed was coarser ( i . e . the deslimed coarse/fines r a t i o was 50/50 as opposed to 40/60 in batch runs), (2) no MIBC conditioning time was given, and 48 Storage Tank for Fines Fraction r Moyno Pump r Tank Conditioner for Fines Fraction Frother • Brine Storage Tank Constant Head Tank Gravity Fed Guar TO FINES CONDITIONER REAGENT TANKS Reagents Guar O i l Amine Coarse Soilds Drum Conditioner for Coarse Fraction Fl o t a t i o n C e l l s F i n a l Tai Is Cone.1 Cone.2 Cone.3 Note : A l l soilds were deslimed prior to the continuous f l o t a t i o n t e sts. Figure 11 - Flowsheet for Continuous Rougher Flo t a t i o n 49 (3) the a i r valves were closed. Table 9 shows the desired operating conditions for a t y p i c a l run. Sixteen minutes were required to reach steady state. At the 16-minute mark, one-minute samples of concentrate and half-minute samples of f l o t a t i o n feed and t a i l s were taken. The measured flowrates, size and assay analyses of the run i s shown Table 10. More complete d e t a i l s of continuous operation and equipment are available in the report to PCS (51) with some modifications as herein described. 50 Table 9 - Desired Operating Conditions for Run 302 * * * * * * * * * * RUN*1 302 C O D E D * 1 D A T E : J U N . 23 /83 * * " * * * * * * * * A S u m m a r y S h e e t o f I n f o r m a t i o n R e q u i r e d F o r t h e C o n t i n u o u s F l o t a t i o n T e s t * * * * * * * * * * * * * * * * F a c t o r C o d e d L e v e l A m i n e ( l b / T ) 0 L e v e l O . 18 ' / S o l i d (%) O F l o t a t i o n M a c h i n e s 40 M o d i f i e d D E N V E R SUB A . . . .J0 . . . L ' t r e s / C e l 1.. T y p e o f P o t a s h O r e % S o f i d s ' i n t h e ' F l o t a t i o n F e e d I?.^ p?.r.?*yc.?...?.L..!:.!?.I"i ..Pu.n P C S C o r y O r e '"4'6'%'by''w'f'Vgh't' 30 . p e g . - c M a s s F l o w o f D e s l t m e d O r e t o t h e C e l l s 5 8 4 9 . 1 g m / m i n D e s l I m e d C o a r s e / F i n e s R a t i o t o t h e C e l l s : 50/50 % S o l i d s i n b o t h D e s l i m e d C o a r s e a n d F i n e s F e e d : 8 8 % .***...?.9. n3.i.^ - - ... F r a c t i o n W e t S o l i d ( g m / m i n ) B r i n e ( c . c . / m i n ) T o t a l ( c . c . / m i n ) • B r i n e ( c . c . / m i n ) C o a r s e F i n e s 3 3 2 3 . 3 3 3 2 3 . 3 9 4 8 . 3 1 2 5 0 . 7 2 7 3 2 . 2 3 0 3 4 . 6 4 0 7 2 . 1 *********** ************* R e a g e n t i z i n g t h e C o a r s e F r a c t i o n * * * * * * * * * * * * * * * * * * * * * * ! c.'c7/m i n t i m e ( m i n ) 5 6 . 7 3 R e a g e n t l b / t G u a r ( 4 0 % ) 0 . 1 2 g / K g 0 . 6 E - 1 g m / m i n 0 . 1 7 0 1 A R M E E N T D 0 . 18 O i l ( / / 9 0 4 ) 0 . 1 5 E - 1 0 . 9 E - 1 O . 7 5 E - 2 0 . 6 3 7 8 0 . 5 3 2 E - 1 1 9 . 3 1 1 . 2 D r o p s 1 . 5 f o r A m i n e a n d O i l c o m b i n e d * * * * * * * * * * * * * * * * R e a g e n t i z i n g t h e F i n e s F r a c t i o n *************************** t i m e ' ( m i r i ) 3 R e a g e n t V b / ' f G u a r ( 6 0 % ) 0 . 1 2 0 . 6 E - 1 gm/m i ri 0 . 2 5 5 1 " c .c7/miri 8 5 A * * * * * * * * * * * * * * * * * * * * * : p r o t h e r C o n d i t i o n i n g p r i o r t o F l c i t a t i o n . . * * . * . * * * . * " . * * R e a g e n t l b / T S / K g g m / m i n c . c . / m i n M I B C O ' . ' 4 7 ' e - i 6 7 2 3 5 E - 1 ' 6 7 1 6 6 5 6 7 1 6 6 5 T i m e ( m i n ) * * * * T * * * * * * * * * * * F l o t a t i o n C o n d i t i o n s * * * * * * * * * * * * * * * * I m p e l l e r S p e e d o f t h e F l o t a t i o n M a c h i n e . . . ! ? o d _ R £ M _ _ 51 Table 10 - Measured Data of Run 302 DATE: JUN. 23 /83 of F lo ta t ion RUN* 302 CODED* 1 Analyses and Assays Cone. 1 Mesn •/.Retained %Kcl •/.Nad %Insol 985 gm/min -8+ 14 1 .08 96 .52 3.09 0. 39 - 14*28 17 .28 96 .62 2 9 9 0.39 -28*48 42 53 94 .73 4.81 0.46 -48*100 28.76 94 04 5 .46 0 .5 - 1O0 10.35 90. 15 6 .46 1 .39 Cone. 2 Mesh •^Retained %Kcl %Nacl %InSOl Sample Type S lu r r y (gtn/mln) 520.5 gm/roin _ . • -8*14 15.54 96.95 2.44 0.61 Cone. 1 -14*28 36.68 93.68 5 . 44 0.88 Cone. 2 1040.3 -28+48 24 .94 87.31 1 1 .42 1 .27 Cone. 3 332 -48+100 13.37 86. 49 1 1 .92 1 .59 T a l l *3 1117 1 -100 9.47 67.75 20.54 11.71 F l o . Feed 14093.4 Cone. 3 Mesh %Retalned %Kcl •/.Nac 1 %Insol Gam 148.3 96.9 gn/mtn 0.78 -8*14 20.5 97 .58 1 .64 -14*28 33.86 94.01 4.51 1 .48 -28*48 17.49 84 .85 13. 12 2.03 -48*100 10.97 83.35 13.7 2.95 - 100 17 . 18 49.02 22.73 28.25 T a i l #3 Mesh ^Retained %KC 1 %Nac 1 %lnsol Sample Type Sol Ids (gm/min) 3739.8 g m A i i n -6+14 30. 17 22.94 76.01 1 .05 Cone. 1 985 -14+28 21 .68 5.25 93.77 0.98 Cone. 2 520.5 -28+48 24 .96 1 .86 97.2 0.94 Cone. 3 96 9 -48+ 100 16.89 3.81 95. 17 1 .02 T a l l "3 37 39.8 -100 6 .3 6.2 90. 1 3.7 F l o . Feed 5195 F l o . Feed Mesh y.Retained %Kcl y.Nac 1 %lnsol Ga in 147.2 5 195 gm/m In -8*14 21 .81 36 .83 61 .87 i . 3 -14+28 21 .23 37 .72 6 1 1 7 1 11 -28*48 26.73 38 57 60.33 1.1 -48+1O0 2 1.23 37 .91 60:77 1.32 -100 9 39.57 65.22 5.21 Ta11 » 1 Mesh XRetalned %Kcl y.Nnc 1 %lnsoi -8+14 28 . 12 30.78 68 .03 1 . 19 - 14 + 28 23.08 26.24 72.77 0.99 -28+48 24 .82 14 . 36 84 .63 1 .01 -48+ 100 17 .32 13.63 85. 15 1 .22 -100 6.66 16.47 77 44 6.09 T a l l #2 Mesh %Retained y.Kci %Nac 1 %Insol -8+14 29 . 3 29.32 69.62 1 .06 -14+28 20.91 10.04 88 . 84 1. 12 -28+48 24 .66 3.04 95. 08 1 08 -48+1O0 18.24 5 . 55 93 . 23 1 .22 - 100 6.89 8.21 86.76 5 .03 52 V. THE STATISTICAL ADJUSTMENT OF POTASH FLOTATION DATA FOR MASS BALANCES The development of models that describe potash f l o t a t i o n depends upon the determination of mass balances acceptable for model building . For t h i s purpose, data generated from laboratory batch/continuous f l o t a t i o n of potash, where tests must approximate plant operation, are subject to a variety of errors. Major errors arise because of: (1) p r e c i p i t a t i o n of aqueous KCl/NaCl in saturated pulps during conditioning , f l o t a t i o n , sample transfer and f i l t r a t i o n of samples. This may occur because pulp temperatures are d i f f i c u l t to maintain. (2) dissolution of KCl/NaCl p a r t i c l e s in unsaturated pulps during conditioning, f l o t a t i o n , sample transfer and f i l t r a t i o n of samples. This may occur during fluctuations in the temperature of brine solutions employed for various purposes. (3) the i n a b i l i t y for operators to exactly duplicate a given f l o t a t i o n t e s t . (4) mechanical degradation of KCl/NaCl p a r t i c l e s during conditioning, f l o t a t i o n and laboratory screening of samples. Mular (1979) has reviewed s t a t i s t i c a l techniques to adjust metallurgical data in the presence of error. Several of the techniques have been generalized (Weigel, 1972; Laguitton, 1982) and employed in the base metals industries. 53 The purpose of this chapter i s to describe the procedure employed to adjust potash rougher f l o t a t i o n data obtained from laboratory batch/continuous t e s t s . The methodology has been reported recently (43). 5.1 Adjustment Procedure For Small Batch Flotation Tests The procedure involves flowsheet c l a r i f i c a t i o n and symbol selection, the establishment of mass balance relationships, the acquisition of raw data, raw data bias adjustments , the selection of search variables, the c a l c u l a t i o n of data points from search variables, construction of an objective function, choice of a d i r e c t search method to minimize the objective function and an assessment of r e s u l t s . 5.1.1 Flowsheet C l a r i f i c a t i o n And Symbol Selection A flowsheet of the potash f l o t a t i o n procedure of interest i s i l l u s t r a t e d in F i g . 9, page 34. Symbols that define corresponding measured data are shown below. Measured Data Point Solids loss in fines slime Solids loss in coarse slime Solids in de-slimed fines sample Solids in de-slimed coarse sample Solids in 1st concentrate solids in 2nd concentrate Solids in 3rd contcentrate solids in 4th contcentrate Solids in t a i l s KC1 in sample of de-slimed coarse INSOL in sample of de-slimed coarse KC1 in sample of de-slimed fines INSOL in sample of de-slimed fines NaCl in sample of de-slimed corase NaCl in sample of de-slimed fines Weight % retained on size I for C l * 1 = 1,5 Weight % retained on size I for C2 Standard Symbol Unit Deviation Lf = m(1) g S(1) Lc = m(2) g S(2) Wa = m(3) g S(3) Wc = m(4) g S(4) C1 = m(5) g S(5) C2 = m(6) g S(6) C3 = m(7) g S(7) C4 = m(8) g S(8) T = mT9) g S(9) b1 = m(10) % S(10) b3 = m(11) % S (1 1 ) a 1 = m (1 2) % S(12) a3 = m(13) % S( 1 3) b2 = m(14) % S( 14) a2 = m(15) % S( 15) YTI , 1 T % S(I , 1 ) Y(I,2) % S(I,2) 54 Weight % retained on size I for C3 Y( 1,3) % S 1,3) Weight % retained on size I for C4 Y( 1,4) % S 1,4) Weight % retained on size I for T Y( 1,5) % S 1,5) Weight % retained on size I for F** Y( 1,6) % S 1,6) Size I mineral J in CI***, 1 = 1,5 i— 1 i X( I , J) % s I , J) Size I mineral J in C2 J — 1 , o X( 1+5,J) % s 1+5,J) Size I of mineral J in C3 X< 1+10,J) % s 1+10,J) Size I of mineral J in C4 X( 1+15,J) % s 11 +1 5 , J) Size I of mineral J in T X< 1+20,J) % s (1+20,J) Size I of mineral J in f l o t a t i o n XI 1+25,J) % s (I+ 25-, J) feed F** *I=1,5 represents -8+14M, -14+28M, -28+48M, -48+l00Mand -100M respectively **weight % on size and assays of size fractions of F from 7 independent feeds ***refers to KCl, NaCl and INSOL respectively for J; Note: X(I,J)=Xij etc. 5.1.2 Mass Balance Relations Mass balance relationships that must be s a t i s f i e d in Fig.9 are: W1 + W2 = Lf + Lc + Wa + Wb + C1 + C2 + C3 + C4 + T F = C1 + C2 + C3 + C4 + T F*Y(I,6) = C1*Y(I,1) + C2*Y(I,2) + C3*Y(I,3) + C4*Y(I,4) + T*Y(I,5) Y(1,J) + Y(2,J) + Y(3,J) + Y(4,J) + Y(5,J) = 100 1 = 1 ,4 J=1 ,6 F*Y(I,6)*X(I+25,J) = C1*Y(I,1)*X(I,J) + C2*Y(I,2)*X(I+5,J)+ C3*Y(I,3)*X(I+10,J) + C4*Y(I,4)*X(I+15,J)+ T*Y(I,5)*X(I+25,J) 1=1,5 J=1 and 3 X(I , 1 ) + X(I,2) + X(I,3) = 100 X(I+5,1) + X(I+5,2) + X(I+5,3) = 100 X(I+10,1) + X(I+10,2) + X(I+10,3) = 100 X(I+15,1) + X(I+15,2) + X(I+15,3) = 100 X(I+20,1) + X(l+20,2) + X(l+20,3) = 100 X(I+25,1) + X(I+25,2) + X(I+25,3) = 100 1 = 1 = 1 = 1 = 1 = 1 = ,5 ,5 ,5 ,5 ,5 ,5 Wf = W1 - Lf - Wa Wo = W2 - Lc - Wb 55 b2 = 100 - b1 - b3 a2 = 100 - a1 - a3 5 Wf*a1-+ Wo*b1 = F* I (Y(I,6)*X(I+25,1)) Wf*a3 + Wo*b3 = F* | (Y(I,6)*X(l+25,3)) wT and W2 are exact values (see Figure 9, page 34) 5.1.3 Acquisition Of Raw Data The description of raw data c o l l e c t i o n for the small batch tests can be found in section 4.2. 5.1.4 Raw Data Bias Adjustments Raw data obtained for runs prior to corrections are given in a report to PCS (54). Pipette error correction must be made as explained previously (page 36). In addition, to reduce error variances, certain assays were corrected as follows (44) : Feed: %NaCl(corr) = 100 - %KCl(corr) - %INSOL(raw) Con: %KCl(corr) = 100 - %NaCl(corr) - %INSOL(raw) T a i l : %NaCl(corr) = 100 - %KCl(corr) - %INSOL(raw) When the above corrections were made, the data were scanned for obvious bias error. Measured Lf + measured Lc were plotted against W1 +• W2 - Wa - Wb - C1 - C2 - C3 - C4 - T. These points should f a l l on a straight line that passes through the or i g i n with unit slope. The graph is shown in Fig. 12. Clearly bias is indicated and the bias depends upon temperature. On the average, Lf and Lc have increased in weight, probably because of a f a l l in brine temperature during the f i l t r a t i o n / d e s l i m i n g step. By f i t t i n g straight lines to the data with unit slopes, intercepts may be used to correct Lf and Lc as follows: 56 o Check for the bias of slimes weights I I I I l I ' ' I l I L_g,—! J 1 _ / 7 o CO IT) IS Oj _ cn P7 pi to CO 0 o 1 CO T CO o CO j_ CM in CO ^ • CD 0 Low Temp Runs /' S + + Med Temp Runs +^  / ^ / / o o High Temp Runs © / / / Low Temp Reg. Line / ^ / Med Temp Reg. Lime/' / High Temp Reg. Litfe All Temp Reg. Lirie / V " , & / + + /**/'/ ///•Vi + + + + c v H 1 1 1 1 1 1 1 I I I I 1 I I 1 200.0 232.5 265.0 297.5 330.0 362.5 395.0 427.5 460.0 Wl+W2-Wa-Wb-Cl-C2-C3-C4-T Figure 12 - Check for "Bias Errors on Lc and Lf 57 Lf(corr) = Lf(raw) - .75(18.622) Lc(corr) = Lc(raw) - .25(18.622) low temperature data Lf(corr) = Lf(raw) - .75(30.0295) Lc(corr) = Lc(raw) - .25(30.0295) medium temperature data Lf(corr) = Lf(raw) - .75(52.962) Lc(corr) = Lc(raw) - .25(52.962) high temperature data .The m u l t i p l i e r 0.75 appears, because 3/4 of the t o t a l wash brine was associated with Lf and 1/4 with Lc. Raw data were corrected for pipette errors, to reduce error variances and to eliminate bias as detected above. A second set of data were thus generated and referred to as the corrected data set. The corrected data set i s available in the report to PCS (54). Bias corrections to f l o t a t i o n feeds were not attempted, because size analyses/assays were not determined for each feed (an average was used as discussed previously). 5.1.5 Selection Of Search Variables Search variables are the minimum number of variables that are necessary to determine mass balances (Fig.9). Their selection i s a r b i t r a r y . With 138 variables involved in 58 independent equations, there must be 138 minus 58 or 80 search variables. The following were selected: Lf, Lc, Wa, Wb, b1, b3, C1, C2, C3, C4, Y ( I , D , Y(1,2), Y(I,3), Y(I,4), Y d,5), with 1=1,2,3,4, and X(I,1), X(I+5,1), X(I+10,1), X(I+15,1), 5-8 X(I+20,1), X(I,3), X(l+5,3), X(I+10,3), X(I+15,3), X(l+20,3) with 1=1,2,3,4,5. An alternative set might influence the speed of convergence. 5.1.6 Calculation Of Data Points From Search Variables Data points must be calculated from a suitable combination of search variables for the objective function. Not a l l search variables need be required to calculate a given data point. Thus Lf = Lf, C1 = C1, Lc = Lc , C2 = C2, Wa C3 Wa, C3, Wb = Wb C4 = C4 T = /\ F = Y d Y(5 Sd Y d W1 + W2 - Lf - Lc - Wa - Wb - C1 - C2 - C3* - C4 C1 + C2 + C3 + C4 + T ,J) = Y d , J) 1 = 1 ,4 J=1 ,5 ,J) = 100 - Y(1,J) - Y(2,J) - Y(3,J) - Y(4,J) J=1 ,6 ,J) = X(I,J) 1=1,25 J=1 and 3 Xd ,6) = {C1*Y(I,1) +AC2*Y(I,2) + C3*Y(I,3) + C4*Y(I,4) +T*Y(I,5)}/F 1=1,4 +25,J) = {C1*Y(I,1)*X(I,J) + C2*Y(I,2)*X(I+5,J) + C3*Y(I , 3)*X(I + 1 0 , J) + C4*Yd ,4)*Xd + 15, J) + T*Yd ,5)*X(I+20,J) }/{F*Yd ,6) } 1 = 1,5 J=1 and 3 I ( I %(I i d 2 d /\ bl ,2) = 100 - xd, 1 ) - xd ,3) + 5,2) = 100 - Xd+5,1) - Xd+5,3) + 10,2) = 100 - X(I + 10,1) - X d + 10,3) + 15,2) = 100 - X(I + 15,1) - X d + 15,3) + 20,2) = 100 - X(I+20,1) - Xd+20,3) + 25,2) = 100 - X(I+25,1) - Xd+25,3) = b l , b3 = b3, b2 = 100 = 1,5 = 1,5 = 1,5 = 1,5 = 1,5 = 1,5 b1 - b3 Wo a1 a3 = W2 - Lc - Wb, Wf = W1 {F* L [ Y d , 6)*X(I+25/ 1 ) 3 {F* £ [ Y d f 6)*X(I+25,3) ] - Lf - Wa - Wo*b1}/Wf - Wo*b3}/Wf 59 a2 = 100 - ai - a3 where the symbol ^ means data point calculated from search variables. 5.1.7 Construction Of Objective Function An objective function, OF, must be written to s a t i s f y the least squares c r i t e r i o n in preparation for a minimization routine. Thus OF = i£ 1{R;(m i - f i j J V S , ' } + i j R u (Y;j - Y. • ) 2/S 2 U } + | l J i C R ; j U ; i - X;j ) V S 2 U ) where _ means measured data point, ^ means data point calculated from search variables, the S.2 and S.2. are error variances associated with corresponding data ..points and found from repeat runs and the R- and R;j are r e l i a b i l i t y factors chosen by operators based on their knowledge of performing runs. Now, i f that unique set of search variable values which cause OF to be a minimum is known, then a l l calculated data points would be the adjusted data points for model building purposes. Error variances were estimated from 3 groups of repeat runs, where group 1 consisted of runs 172, 176 and 191, group 2 consisted of runs 182, 194 and 207 and group 3 consisted of runs 215, 221, 234, 236 and 237. Corresponding variances of each group were calculated and then pooled to obtain pooled variance estimates from the relationship: V; = (2V1 ; + 2V2; + 4Vg; )-/8 60 where V; is the pooled variance for each data point i with 8 degrees of freedom. Results of calculations are available in the report to PCS (54). R e l i a b i l i t y factors were chosen by operators based on their knowledge of the r e l i a b i l i t y of each procedure/step involved in a f l o t a t i o n run. Lf and Lc were assigned R values of 1; Y(I,6) 1=1 to 5 and X(I+25,J) 1=1 to 5 and J=1 to 3 were assigned R values of 2 ; Wa, Wb, CI, C2, C3, C4, T, b l , b2, b3, a 1, a2, a3 were assigned R values .of 100; a l l other data points were assigned R values of 20. 5.1.8 Choice Of Method To Minimize Objective Function Non-Derivative strategies to find the unique set of search variables that cause OF to be the minimum value include the direct search methods (Mular, 1970, 1972). These have been u t i l i z e d in a l l phases of model building (Mular and co-workers, 1978). 'With 80 search variables to determine, the search method developed by White (1977) was chosen for simplicity and speed. However, i t was modified s l i g h t l y to avoid d i f f i c u l t i e s with the o r i g i n a l method. The strategy involves three routines, namely, a step search, a repetitive quadratic f i t t i n g and an alpha search. The step search is a one search variable at a time strategy (Coggin, 1973). The SV's (search variables) are assigned starting values and OF i s calculated (point 1, Fig.13). There are 1=1,2,...,80 SV's involved. With I set to 1, SV(1) is varied by multiples of a step, delta, in the directon of decreasing OF (points 1, 3 and 4 in Fi g . 13) u n t i l a minimum OF 61 Figure 13 - A Step Search on Search Variable S(l) 62 is spanned. At this stage a quadratic of the form OF = A + B(SV(1)) + C(SV(1)) 2, where A, B and C are constants, is f i t t e d to points 1, 3 and 4. The value of SV(1) at the minimum, namely SV(1) = -B/(2C), is compared with SV(1) 3. If the difference is not small enough, SV(1), associated with the largest OF. value is replaced with SV(1) . The quadratic is re-f i t t e d to the points SV(1) 3, SV(1) and SV(1) 4 which straddle the minimum more clo s e l y . This repetitive quadratic f i t t i n g continues u n t i l a current SV(1) d i f f e r s from a current f i t t e d point by a small amount. The quadratic minimization procedure is described in Fig.14. Eventually an SV(1) m is found and retained. The step search is then repeated for the next I, 1=2, the quadratic f i t i s repeated, and so on to 1=80. This f i n a l l y results in a column vector, V1, that contains the SV(I) m values for a l l 1=1, 2,....,80 search variables. The step search-quadratic f i t routines are repeated one more time to provide a column vector, V2. Fig.15 shows how V1 is found for two SV's (line A-A and B-B) and how V2 is then found (lines C-C and D-D). Shown in dotted lines are contours of equal objective function values (sum of squares surface, J ) . At this stage, i t may be argued that along the direction vector E-E (Fig.15) a better vector, V, may be found closer to the minimum, where V = V2 + a(V1 - V2). The variable, a, is a parameter whose value is determined by means of the step search-repetitive quadratic f i t routines. a must be constrained such that a l l elements of V are zero or positive. The strategy is referred to herein as the alpha search. Following the a search, 63 J = A + BS + CS A , B , C ARE CONSTANT ^ = B + 2 C S = 0 A T M I N I M U M 2 J = A + BS(l) + C S ( l ) i 2 J 2 = A + B S ( l )2 + CS( l )2 3 EQUATIONS 3 UNKOWNS 2 J 3 = A + BS( l )3 + CS( l )3 (1) FIND A,B,C, FROM SIMULTANEOUS SOLUTION (2) CALCULATE s ( l ) m (3) CALCULATE DIFFERENCES S ( l ) i - S ( l ) m S( l>2 - S ( l ) m S ( l ) 3 - S ( l ) m (4) IF ANY DIFFERENCE IS LESS THAN E-6 THEN STOP. (5) IF NOT, REPLACE LARGEST s(l)± BY s ( l ) m AND GO TO (1). Figure 14 - Repetitive Quadratic F i t t i n g 64 ORDER ALONG A - A TO FIND S ( l ) m , ALONG B " B TO FIND S(2) m l ALONG C-C TO FIND S ( l ) m J ALONG D-D TO FIND S(2) m 2 ALONG E " E TO FIND V ^ ^ - V « V2 + Qm(VI -V2J EFFECT OF VARYING A L P H A ALONG DIRECTION DEFINED BY VI A N D V 2 . TWO S E A R C H V A R I A B L E S . Figure 15 - A Diagram of the Alpha Search 65 a global i t e r a t i o n i s complete. The o v e r - a l l search i s judged to converge, when the OF, as calculated after a global i t e r a t i o n , d i f f e r s within 0.01% of the OF calculated after the preceding global i t e r a t i o n . Fig.16 shows the f i l e i t e r a t i o n flowsheet for the adjustment program c a l l e d DATAD. F i l e WTFAC contain error variances for data points of corresponding runs; F i l e REFAC contains r e l a b i l i t y factors; F i l e ROFL i s the corrected data for a corresponding run. F i l e OUT stores answers that are placed in tabular form by PRINT1 and/or by AFORM. Fig.17 i s a general flow diagram for program DATAD. Fig.18 -D1, -D2, -D3, -D4, -D5 are the detailed flowcharts for DATAD. Symbols are defined in APPENDIX B. Program l i s t i n g s are provided in APPENDIX C. Note that AFORM print s results with adjusted data; FORM1 print s a summary of raw data; CFORM print s a summary of corrected data; PRINT1 compares corrected with adjusted data. Typical output from PRINT1, AFORM and CFORM are shown in APPENDIX C. 5.1.9 Results Of Data Adjustments Comparisons between corrected and adjusted data for a l l 58 f l o t a t i o n runs are available in the report to. PCS (54) and in (43) . When measured and adjusted data points are compared, most adjustments are observed to be r e l a t i v e l y small. Data points such as Lf, Lc, Y(I,6) and X(I+25,J) show larger discrepancies. These data points are associated with bias and were assigned low r e l i a b i l i t y factors. 66 DATA FILE "OUT" WRITE READ DATA FILE "ROFL" DATAD PROGRAM READ DATA FILE "WTFAC" READ DATA FILE "REFAC" EXECUTION OF DATAD READ READ READ ^ READ PRINT1 PROGRAM AFORM PROGRAM EXECUTION OF .PRIKTl EXECUTION OF AFORM XEROX 9700 PRINTER Figure 16 - F i l e Interaction Flowsheet for DATAD 67 \ OBJECTIVE FUNCTION EVALUATION •7= SEARCH ROUTINE ( i . e . STEP SEARCH, ALPHA SEARCH, AND REPETITIVE QUADRATIC FITTING) f 5l <-^ T A £ T ^ READ DATA S and 51 are current objective function values of V DETERMINE DETERMINE YES .5k CALL PROGRAM PRINT1 CALL PROGRAM AFORM and respectively. Figure'17 - A General Flow Diagram for Program DATAD Al = 6 Bl = 0.5 B2 = 3 B4 = 0 B5 = Q N = 80 READ DATA 2 DO LOOPS TO GET \j and V 'This is a modified version of the Coggin Routine Figure 18 - Detailed Flowcharts for DATAD 68b D2 cs=o W=l C6=0 R=l \ FOR I = 1 TO N DO LOOP [A8 = A(W) A7 = E(R) [ IF C6 = N -> A7 = -1E4 IF C5 = N •+• AS. = 1E4 B3 = 1 L = N + 1 { D = 0.1 » Bl * Al | \ 1 fiOSUB Cojtgin Knubinc 68c 2 Al = 6 - LO . /A8-S(D V S(L)-A7 V g =V 2 - rS(N + l ) (V 1 -V 2 ) > r CALC. O.F. , S \ r PRINT B5,S1,S, S(L) , |(S-S1)/S| • NO CONVERGENCE CALL "PRINT1" CALL "AFORM" STOP 68d D 4 THE COGGIN ROUTINE BEGINS C20 = 0 C = 1 { SCL) » R(C) ( i . e . Subroutine f o r Step Search and Alpha Search) YES S(L) = A7 + (A8-A7) * E* RETURN YES • YES B3 l,NO 1 CMC. 1 CAir. o P s g| RCC) = RCC-3)/10 YES •91 L S ( U = R f q A16 = R(C) - 6 A16 S ( L ) = A 7 + ( A 8 - A 7 ) * L . _ _ _ e +e CALC. V E R(C)-6 6-R(C) 68e D5 -j FOR J=C-2, TO C ( The Coggin Routine Continued. (i.e. Repetitive Quadratic fitting routine for both Step Search and Alpha Search) DO LOOP NEXT J DI = (TCC-1) - T(C)) * (V(C-2) - vco) - fTfc-2-) - T fo i * rvrr-n - vrc-n J, D2 = (VCC-2) - V(O) * (T (C - l ) 2 - nO2) ~ (V(C-l) -V (O) * (T(C-2)2-TCC)2) |S(L) = T(C-I) ,YES •^S(L) = D2/(2*P1) YES RETURN CftLC. V 0 CALC. O.F. , S TCC) = SCL). VCC) = vcc+i) — YES T(J) = RCJ) . 1 «0 j T(J) = A7 + (A8 - A7), E* j sir< ~ 1 T(C-2) S(L) V(C-2) VCC+1) , T(C-2) = T(C-l) { VCC-2) = VCc-j) TCC) = TCC-1) VCC) = VCC-1) S* = T(C- l ) SCD = T(C- l ) TCC-1) = SCL) vcc-i) = vcc+i) 69 Fig.19 shows adjusted Lf and Lc values versus corresponding corrected Lf and Lc values. Note that data appear randomly scattered about a straight l i n e that passes through the or i g i n with a slope of one. Fig.20 shows the adjusted size d i s t r i b u t i o n points versus the measured size d i s t r i b u t i o n points for f l o t a t i o n concentrate C1. Adjustments are minimal. An analogous plot using assays of size fractions for concentrate C1, shown in Fig.21, shows that adjustments are minimal. Such plots are useful to detect bias errors (56). However, the use of r e l i a b i l i t y factors may di s t o r t conclusions. This i s not the case with either Lf or Lc, because bias was eliminated prior to data adjustment. 5.2 Data Adjustment For Large Batch And Continuous Flotation  Runs The adjustment procedures employed for data acquired from large batch and continuous f l o t a t i o n runs are somewhat similar, except that the raw data need not be corrected prior to s t a t i s t i c a l adjustment. The data adjustment procedures, computer programs and example output are given in APPENDICES D and E. A comparison between measured and adjusted data show that adjustments can be r e l a t i v e l y small. Tables 11 and 12 i l l u s t r a t e the adjusted data for run #250 (a t y p i c a l large batch run) and run #302 (a t y p i c a l continuous run) with calculated recoveries and grades for each size f r a c t i o n . The adjusted data were employed for model building as discussed in the following chapter. 70 o o W. CO Check for the bias of s l imes wts J L i ) I i i l 1 1 I I, i o CO Oi o CV2 O o C6 ox -+-> R5 o CO o o o 0 CD D I f +' + JLc + •f + + - r t f + + CD © CD % CD ngnP CD o e r f * ^ % ° ( 3 CD ° _ C9(jj CD Q 0 0 CD© CD ©a a 0 O G ) CD D CD ° CD Q 1 1 1 1 | — 1 1 1 1 I 1 1 1 1 1 40.0 80.0 120.0 160.0 200.0 240.0 28O.0 320.0 Corrected Data Figure 19 - Adjusted Lf and Lc Values Versus Corrected Lf and Lc 71 C H E C K F O R A C O N S T A N T B I A S I l l I i i i ' I I ! I t 18.75 Corrected Data Figure 20 - Adjusted Weight% Retained Points Versus Corrected Weight% Retained points for Concentrate C1 72 C H E C K F O R A C O N S T A N T B I A S 67.2 88.8 90.4 92.0 93.6 95.2 Measured Data 96.8 9 8 . 4 100.0 Figure 21 - Adjusted Assays of Size Fractions Versus Corrected Assays of Size Fractions for Concentrate C1 BATCH FLOTATION DATA SHEET • ( w i t h a d j u s t e d d a t a ) «•«»•• t •»«••»»»« • RUN* 250 CODED* It A n a l y s e s and Assays of F l o t a t i o n P r o d u c t s y .nccovory • * Cone . 1 Mesh '/.Reta Ined '/.Kcl •/.Nacl •/.Insol •/.Rec. ( K c l ) •/.Roc. ( N a c l ) 594 . 9 gm -8+14 - 14 + 28 4 .07 15. 19 9 5 . 3 9 93 .95 4 . 1 3 5 . 6 6 0 . 4 7 0 . 3 8 1. 13 4. 16 0 . 3 E - 1 0 . 14 0 . 2 2 0 . 6 7 -28+48 -48+100 - 100 39. 18 28.67 12.88 91 .93 89.30 9 0 . 8 5 7 .69 10. 16 7 .05 0 . 3 8 0 . 4 6 1.3 10.49 7 . 4 6 3 . 4 1 0 . 4 8 0 . 4 7 0 . 16 1.74 1.53 1 .96 Cone . 3 9 7 . 1 2 gm Mesh '/.Retained '/.Kcl •/Nacl •/.Insol y.Rec. (Kc l ) •/Rec. ( N a c l ) •/.Rec. ( I n s o l )' -8+ 14 - 14 + 28 -20+48 5.3G 17 .04 39. 10 9G.02 9 3 . 11 9 0 . 5 9 2 .75 6 .39 8.91 0 . 4 3 0 . 5 0 . 5 1.01 3 . 0 8 G .9 0 . 2 E - 1 0 . 12 0 . 37 0 . 18 0 . 6 6 1 .53 -43+100 - 100 28 . 32 10.11 89 .78 9 0 . 1G 9.G 7 .63 0 . 63 2 . 2 •1.94 1.77 0 . 29 0 . B E - 1 1 . 30 1 .73 Cone. 29 1 .9 3 gm Mesh "/.Reta Ined '/.Kcl V.Nac 1 jii nsb i W e e . ( k c i j y.Reo. (Kiaci) yiRoc. ( i n s o l j -8+ 14 4.4 9S.92 2 .63 . 0 . 4 5 0 . 6 1 0 . 1 E - 1 0 . 11 - 14+28 -28+40 -40+100 15 . 15 38 . 23 29 .95 94.51 90.81 89.84 4 .96 8 .62 9 . 3 0 0 . 5 3 0 . 5 6 0 . 7 8 2 . 0 5 4 .9G 3 . 0 5 0 . 6 E - 1 0 . 2 6 0 . 2 2 0 . 4 5 1 . 23 1 . 34 - 100 12 .27 09.32 7 .56 3 . 13 1 .57 0 . 7 E - 1 2 . 19 Cone . 4 Mesh '/.Retained •/.Kcl •/.Nacl y.Insol •/.|!ec. (Kc l ) •/.Rec. (Noel ) •/.Rec. ( I n s o l ) 4 2 5 . 7 gra -8+14 - 14 + 23 3.41 15.42 97 .4 94.9?. 2. 1 4 . 6 0 . 5 0 . 4 8 0 . 6 S 3 . 0 5 0 . 1E- 1 0 . 8 E - 1 0 . 14 0 . 6 2 -28+48 -48+100 - 1 0 0 38 .24 29.32 13.SI 91 .61 90.81 09 .26 7.77 0 .25 G.56 0 . 6 2 0 .94 4 . 18 7 . 3 5 . 5 5 2 . 5 3 0 . 3 4 0 . 2 0 0 . 1 1 .96 2 . 3 4 .74 Cone . 185.3 5 Mesh •/.Rota ined y.Kcl •/Nacl '/.Insol y.Rec. (Kc1 ) •/.Rec. ( N a c l ) •/.Roc. ( I n s o l ) gm -8+14 -14+20 -26+48 4.44 17 .59 37.97 9 7 . 3 95 .93 93.07 2 . 13 3 . 5 5 G.03 0 . 5 7 0 . 5 3 0 . 9 0 . 3 9 1.53 3 .21 0 0 . 3 E - 1 0 . 1 1 0 . 9 E - 1 0 . 3 4 1 .24 -4G+100 - 1 0 0 27 .85 12. 15 9 1 . 6 86 .33 6 . 6 2 5 . 4 5 1.78 0 . 2 2 2 .31 0 . 9 5 6. 9E: - \ 0 . 3 E - 1 1 .8 3 .G2 T a i l s 3925 gm Mesh •/.Rat'aihe'cJ jiKo'l WJa'ci '/Unsoi p e c . Wei} '/.Rec. t 'NacU p e c . ( I n s o l )' -8+14 21.08 23 .83 75 .4 0 . 7 7 9 . 6 5 16.74 12.42 - 14 + 28 -20+40 -48+100 17 .52 3 1 . 79 2 1 . 32 7 .66 2 .2 0 . 9 5 9 i . 74 97 .22 98 . 1 0 . 6 0 . 5 7 0 . 9 5 2. 50 1.35 0 . 3 9 16.93 3 2 . 5 6 2 2 . 0 3 8 . 1 14.01 15.62 - ICO 8 .28 7.04 90 .44 2 .53 O S ' " " 7 . 0 9 16. OG Food 58 19. b'gm ' ' Mo?h %RataIned '/.Kel.., XNacl . J f l n s o l JWoe . . ( K c l ) y.Rec. ( N a c l ) y ,Roc.( I n s o l ) -0+14 - 14 + 20 15.61 16.90 30.32 34 68 .94 65 .44 0 . 7 4 0 . 5 6 13.40 16.45 16.01 17 .35 13. 17 10.84 -20+48 -40+100 - 100 34 .04 23.78 9 . 5 9 35.26 3G. 17 41 .53 64 . 10 6 2 . 9 5 5 5 . 6 9 6.56 0 . 8 9 2 . 7 0 3 4 . 2 1 24 .51 1 1 .35 34 . 12 2 3 . 3 7 0 . 3 4 2 1 . 7 1 2 3 . 9 7 3 0 . 3 1 3 > a <-j. c in rr fD a a w rr O +1 +3 n w n VQ rt> W BJ rr n p-s> c 3 Table 11 continued 73b LI c CO CO CN 01 -— rr • T tncn .in o CN 2 t/i I D vr •cn co cn Z3 G n c# CN — co o tn 0 Q > — * « c a r- — 3 3: w CJ w a 0 c Ul (A — o m a O (. a o — c E c o E c — 0 c o a u. O (/» o a * * UJ X < r- (1 < T3 a CO O TJ CJ «— o z V > • o c* a V o O T r--J < i— t; o _i c a. > X _J ( J TJ < O ca •o O o o O O * u » * »— —. • N — E C fl i< a. — • — w C E —• * TJ - J 0 0) — TJ — * c - a u — o & c E V a -o • 3C • tn ir> 01 w 1 to CJ o U i ID •fl' r-0 I CN tn £  I 54 l o I 3 i o 3 TJ tn u> O 6 CO 01 o o d d ; v ui in • - co O) oi r-CN CI CN • co O o • • — <o m o u o u u CJ o CJ CJ CJ tn tn in vt ei O O O O O CN CN ci-iD cn www.— — W *- CN n T Ul " O a a U O U U O h-.ii. CN CM E" -D'UJ + U M CO: ft o u u o U • QJ; CJ O CI CJ n' tn LI tn ifi O O O O o * o CN CN CN ID Gl * a * o - n n tn * or a L> U U U * * • • jtn o •v m CJ * in X * • * o o ts> T O c» CN cn * * o ui O O) o> r- o * • • "N o Li 0> d IM — * 1 CI v in co «-* 1 o n B I in * • :*/> 1/T w * -* * * • • • • • ; * • : • # • P • O * o o c-•«r to n CN c- c °: c + T m n tn o + CJ r- tn T o UJ CO Ul CO 01 CN CO * M T o O U) <c> CO Cj: 1 in to co 0) u M 1 D tn «3 u 1/1 (0 L.. a L, u,; L. U-U, 0 o: N: 0 N N in t/} X r £ ' o CO u CO a: U O i in m to CO u ! C + o CO C) CD o Ul + u> tn cn Ul UJ CO Ul CO m CN CN tn t_: IN CJ o O m o to t_ IM CN 0 c >—I 1 CJ tn ID co O) 0 —t 1 CN n T b_-o I/} u. v» «— u. CN CN + ut TT IN a CO w n n n o d d o o y u O G 0/ O O O O O CN CN CN lD:G> — CN o T ; I V U O U( . o :ui O M — :uiCO IN T CO CJ -c + UJ CO M CN CJ ^ CN CN tD CN -~- ci CN — + O 01 o CO 1 n o p tn U o o o o 01 a a a a tl 1/1 V) W U) t- o o o o o o CN CN CN ID 01 D o a CN O T Lic: c CJ O U U o . . t . CONTINUOUS FLOTATION DATA S.HEF.T •»*»»• RUN* 302 a-jjusina aata j CODED* 1 size Analyses and Assays of Flotation Products ******** ************* ^Recovery ***•'*"**•*'****•** Cone. 1 Mesh •/Retained •/.Kcl •/Nacl y.Insol 102 1 . t g/mtn -8+14 - 14 + 28 1.02 16.81 96.52 96.62 3.09 2.99 0.39 0.39 0.53 8.79 O. 1E-1 0. 16 0.6E-1 -20+48 -48+100 - too 41 .75 29 .03 11.4 94.73 94 .04 90. 16 4.81 5.44 0.45 0.46 0.52 t .39 21.4 1 14 .78 5.56 0.64 0.5 0.31 2.93 2.29 2.41 Cone. 525. 4 2 cj/m \ n Mesh •/.Rota 1 ned •/Kcl '/.Nacl y.Insol XRoc.(Kcl) XRoc.(Nacl) XRec.(Insol) -0+14 - 14 + 20 -20+40 id. 79 3G.62 24 .29 96.92 93.71 87 . 11 2 ."42"" 5.46 11.66 6765 0.82 1.22 4753 9.56 5.9 T T F I 0.33 0.46 0.86' 2.37 2.33 -40+100 -100 13. 12 9. 18 06.51 67.76 11 .89 20.55 t .6 1 1.69 3. 16 1.73 0.26 0.31 1.64 8.41 Cone. 110.3 3 g/ra t n Mesh '/.Retained '/.Kc 1 XNaci jiinsoi XRec.'(kcij •/.Rec. I'Naci j XRec. (insol)' -8+ 14 21 .65 97.58 1 .64 0.78 1 .24 0. IE-1 0.28 - 14 + 20 -28+48 -48+100 33.24 16.72 11.12 93.99 04 . 84 83.4 4 .49 13. 12 13.65 1 .52 2.04 2.96 1.83 0.83 0.54 0.5E-1 O.OE-1 0.5E-1 O.03 0.G6 0.54 - 100 17 .27 47.41 24.42 20. 17 0.48 0. 14 B.OI Tat 1 #3 Mesh •/Retained 14Kcl •/.Nac 1 y.Insol •/.Rec. (Kcl ) XRoc.(Nacl) XRec.(Insol) 3505. 9 g/mln -0+14 - 14 + 28 29.88 20.61 25.18 5.37 73.62 93.57 1.2 1.06 13.99 2.06 24.03 -21.06 18.7 11.42 -28+48 -48+100 - too 24.72 18.44 6.35 2. IB 4. 12 5.58 96.86 94.73 90.85 0.96 1.15 3.57 1 1.41 0.66 26. 15 19.08 6.3 12.39 11 .09 1 1 .87 Flo. 5162 Feed 3 g/mln Mosh •/.Retained '/.Kc1 XNaci •/.Insol XRec.(Kcl ) XRec.(Nacl) •/.Rec. ( Insol ) -8+14 -14+20 -28+48 22.66 2 1 .76 27 .87 32.7 37.34 30. 19 6G. 16 61.73 60.96 1. 14 0.93 0.85 20.29 22.24 29.14 24. 12 21.6 27.33 19.9 15.62 10.21 -48+100 - 100 19.84 7 .87 36.64 39.14 62.34 55.79 1.62 5.06 IS.9 8.43 19.89 15.56 30.7 Tat 1 4141 #1 7 g/mln Mosh ^Retained •/.kci '/.Nacl '/.InsoV'"- '/Rec. (KciJ ' Xn'ec.rHacU '/.Rec. (insol ) -0+14 20 32. 13 6G.72 1. 15 19.76 24. 11 19.04 - 14 + 28 -20+40 -40+100 22.90 24.45 17.57 2G.65 14 .39 ' 13.26 '72 .32 84.6 05.52 i .03 1.01 1.22 13.45 7.73 5. 12 '2i.44 26.69 19.39 14.62 15.20 13.27 -100 7 10.67 74.79 '6.54 2.87 '6.76 28.29 Tail 3616 #2 3 g/min Mosh y.Rotalnod .'..y.Kci... •/Nacl Xlnsot ,Xnoc. (Kcl )_ Xnec..(Nacl) .„..??°=:..(.![..n.?.p..,J. -0+14 - 14 + 20 29.63 20.99 26.8 9.60 72.02 89.27 1 . 19 1.00 15.23 3.89 24 .04 21.11 18.98 12.26 -20+40 -40+100 - 100 24.47 10.22 6 .60 3.9 5.59 8 . 88 95. 12 93.22 85. Gl 0. 90 1. 10 5.51 1.83 1.95 1.14 26.23 19. 13 6.45 12.95 11 .63 19.00 R U N # 3 0 2 CODED* 1 F a c t o r Coded L e v e l Leve l Sample TVDO So l lds (o/mln) S l u r r v f o / m l n i i isni i i r is Amino ( l b/T ) 0 •/.Sol i d (%) 0 0 . 10 40 C o n c . , 1 102 1.1 Cone. 2 525.4 1697.4 1030.2 CO. 2 Cone. 3 110.3 T a l l #3 3505 .9 F l o . Feed 5 1 6 2 . 8 3 3 1 . 8 11068.S 14135.9 3 3 . 3 3 1 . 7 3 6 . 5 G a i n 6 0 R e t e n t i o n t ime In c o l l 1 1s 1.14 1 min . R e t e n t i o n t ime tn c o l t 2 Is R e t e n t i o n t ime 1n c o l l 3 Is 1 .237 min . 1 .274 min . , < . , . , • • . « . . . . c u m u l a t i v e Weight*/, and Assays fo r C o n c e n t r a t e s »•*••«••••••••* « • « » • « • « * c u r a Rec . f o r Cone . • • • * • » • • • • P r o d u c t Weight*/. Cum.wt'/. •/.Kcl '/.Nacl X Inso l y.Reo. (Kc l ) •/.Rec. ( N a c l ) •/.Rec. f, Inso l ) Cone. 1 19.73 19.7(1 29 .96 9 4 . 3 5 5 .00 0 . 5 7 92.64 6 .31 1.05 51 .08 7 5 . 9 7 1.62 3 .04 0 . 7 24 . 3 Cone . 3 2 . 1<1 T a i l » 3 6 7 . 9 1 F l o . f e e d 100 -N 32 . 1 67 .91 100 92. OG G.54 . 1 . 4 10.28 8 8 . 4 6 1.25 3G.53 G2.17 1.3 8 0 . 8 8 19.12 100 3 . 3 8 9 6 . 6 2 too 3 4 . 5 2 6 5 . 4 8 100 "/.Recovery of SIZE 2 K c l For Each S i z e F r a c t i o n " » * • « » SIZE 3 SIZE 4 SIZE 1 SIZE 5 PRODUCT ( - 0 » 14M) Cone. 1 2 .62 Cone . 2 2 4 . 9 6 i - i4*-28M) 39.54 0 2 . 5 3 ( -28 + 40M) ( -48<- i66i 73.40 : 74 .29 9 3 . 7 2 9 0 . 1 0 ( -100M) 65 .96 86.51 Cone . 3 3 1 . 0 5 9 0 . 75 96 .57 9 2 . 9 1 92 . 19 c u m u l a t i v e '/.Recovery of SIZE 1 PRODUCT (-B+14M) Cot\c. 1 0 . 4 E - 1 SIZE 2 ( -t4+20M) 0 . 7 4 SIZE 3 SIZE 4 (-28+48M) ( -48+100) 2.34 2 .53 SIZE 5 ( -100M) 4.34 Cone. 2 0 . 3 2 Cone . 3 0 . 3 7 2 . 26 2 .49 4 .03 3 .81 4.31 4 . 0 7 8 .71 10.76 SIZE 1 PRODUCT (-0+14M) •/.Recovery of SIZE 2 ( -14+28M) Inso l For Each S l z o F r a c t i o n • » • • • » • • * * • • • • » • SIZE 3 SIZE 4 SIZE 5 (-28+48M) ( -48+100) ( -100M) Cone. 1 0 3 1 Cone. 2 4 .62 Cone. 3 6 . 0 3 6 . 4 2 21 .56 2 6 . 6 9 16.1 14.71 2 8 . 9 25 .27 31.90 28 .74 7 .86 3 5 . 2 5 61 .33 75 VI. DEVELOPMENT OF FLOTATION MODELS 6.1 Flotation Rate Plots To simulate rougher f l o t a t i o n behaviour of each mineral on a size-by-size basis, the adjusted data were plotted in the form of log C(t)/C 0 versus f l o t a t i o n time ( i . e . f l o t a t i o n rate plots with C(t)/C 0= 1 - R(t)). Figures 22, 23 and 24 show the fl o t a t i o n rate curves for KC1, NaCl and INSOL of run #172 where SIZE1, SIZE2, SIZE3, SIZE4 and SIZE5 represent -8+14M, -14+28M, -28+48M, -48+100M and -10OM respectively. The corresponding f l o t a t i o n rate data expressed as R(t) are found in Table 13. Flotation rate plots for a l l runs performed are given in APPENDIX F. 6.2 Model F i t t i n g And Parameter Estimation By means of a direct search method (42), the following models were f i t t e d to the small batch f l o t a t i o n rate data acquired for individual runs: (a) Bull's model with parameters R=> and K i.e. R(t) = R»{1 -exp(-K.t)} (b) Lynch's model with parameters.0, Kf and K s -K ft -K st i.e. R(t) = (1 - 0)(1 - e ) + tf>(1 - e ) (c) Chen's model with parameters Kav(0)and g -gt -Kav(O)(1 - e ) i.e. R(t) = 1 - exp( ) 9 76 F i g u r e 22 - F l o t a t i o n R a t e C u r v e s f o r F i v e S i z e F r a c t i o n s o f KC1 77 U ~ — ^ — 3 1 f ! 1 it * RUN NUMBER: 1?2 Q — S i z e l <> S i z e 2 • 5 i z e 3 A S i z e 4 o S i z e 5 v • " r - ~ 1 — — — =-— — — — — — — — " i i I i i i I i i 1 1 1 1 1 1 ! 1 1 I 1 1 1 1 ! 1 1 1 1 1 1 1 1 1 1 1 1 Q 1 2 3 4 . 5 T i m e , mi n u t e s Figure 23 - Flotation Rate Curves for Five Size Fractions of NaCl 78 r pi A f— — • — - ^ ^ ^ ^ - ^ - - ^ " " i -•• RUN NUMBER: 172 " — S i z e l • S i z e 2 • S i z e 3 A S i z e 4 • — — — S i z e 5 T =-'— — — — — — — — 1111111111 " i i i i i i i i i i * i i i i I i i i u i i i I I i i i i i i i i t i i I t i i i i i i 0 1 2 3 4 5 T i m e , m i n u t e s gure 24 - Flotation Rate Curves for Five Size Fractions of INSOL 79 Table 13 - F l o t a t i o n Rate Data of Run 172 Cumulative %Recovery of KCI in Each Size Fraction Size FLOTATION TIME (Sec.) Fraction 20 40 60 120 -8+14M 1 1 .35 12.37 15.02 19.55 -14+28M 20.66 26.39 40.05 62.41 -28+48M 41.33 59.08 80.04 96.20 -48+100M 52.69 74.19 89.75 97.46 -100M 50.01 71 .66 87.41 97.31 Cumulative %Recovery of NaCl in Each Size Fraction Size FLOTATION TIME (Sec.) Fraction 20 40 60 120 -8+14M 0.29 0.32 0.38 0.44 -14+28M 0.73 0.93 1 .42 2.10 -28+48M 1 .95 2.83 4.41 5.96 -48+100M 2.98 4.45 6.86 8.86 -1 00M 4.71 7.14 1 1 .29 14.19 Cumulative %Recovery of INSOL in Each Size Fraction Size FLOTATION TIME (Sec.) Fraction 20 40 60 120 -8+14M 1 .62 1 .73 2. 13 2.88 -14+28M 3.84 4.92 7.86 13.15 -28+48M 8.98 13.33 19.60 26. 14 -48+100M 11.31 15.90 20.26 • 24.17 -100M 1 3.80 20.07 29.67 43.32 80 The parameters of each model were estimated by minimizing the objective function as shown below: O.F. = .Z W;(R(i) - R(i) ) 2 i =1 ' where R(i) and R(i) are the observed and predicted cumulative recoveries at the i t h f l o t a t i o n time i n t e r v a l . A value of one was assigned to W for a l l i . A l l model parameters were constrained to non-negative values. In Bull's model, R°= was further r e s t r i c t e d between R (4 ) and 100% by the following expression: ( 1 00 - R ( 4 ) ) exp(R°°) Roc* = R (4 ) + . exp(R=°) + e x p ( - R » ) where R=>* i s the transformed R » used in the objective function calculation. Details of direct search computer programs and examples of f i t t e d results for the three models are given in APPENDICES G, H and I. For comparison purposes, the model parameters estimated from t y p i c a l f l o t a t i o n rate data are i l l u s t r a t e d in Table 14 . 81 Table 14 - Models Parameters for Fl o t a t i o n Rate Data of Run 172 Bu l l ' s Model Lynch's Model Chen's Model Rco .(%) K min" 1 4> Kf min" 1 Ks min" 1 Kav(0) min" 1 9 min" 1 KCI -8+14M -14+28M -28+48M -48+1OOM -1 OOM 19.55 87.89 100.00 98.93 99.10 1.81 0.61 1 .50 2.22 2.04 0.88 0.52 0.04 0.03 0.03 0.72 0.96 1.6 2.26 2.09 0.09 0.24 0.40 0.56 0.53 0.385 0.548 1 .502 2.24 2.06 1 .83 0.13 3E-6 0.12 0.102 NaCl -8+14M -14+28M -28+48M -48+100M -100M 71 .62 2.73 7.37 10.52 16.80 0.004 0.73 0.84 0.95 0.97 0.93 0.83 0.79 0.78 0.75 0.01 0.04 0.12 0.18 0.29 0.002 0.005 0.015 0.023 0.036 0.012 0.02 0.062 0.101 0. 165 2.84 0.72 0.81 0.90 0.88 INSOL -8+14M -14+28M -28+48M -48+100M -100M 2.88 23.97 30.87 24.96 56.33 1 .66 0.40 0.95 1 .65 0.73 0.93 0.75 0.71 0.79 0.62 0.098 0.23 0.56 0.72 0.89 0.012 0.029 0.07 0.09 0.11 0.05 0.09 0.3 0.43 0.42 1 .74 0.32 0.78 1 .47 0.43 82 6.3 Adequacy Of F i t t e d Models Some assessment of the adequacy of the f i t t e d models i s necessary. Major c r i t e r i a are the physical significance of the estimated parameters and the residual sum of squares ( i . e . the value of O.F.) (a) B u l l model : The o v e r a l l f i t i s acceptable. However, the estimated values of K f a i l xto represent the rate of recovery at i n i t i a l f l o t a t i o n times and this f a i l u r e becomes more pronounced when R°° i s below 50%. For most runs, the K values associated with low R°° are higher than expected from the corresponding f l o t a t i o n rate curves. This overestimate of K i s probably due to a compensation effect in the equation such that K increases with decreasing R°° regardless of the i n i t i a l slopes of the f l o t a t i o n rate curves. (b) Lynch model : The f i t i s r e l a t i v e l y poor in situations where the f l o t a t i o n rate curves l e v e l off at high values ( i . e . the i n f i n i t e recovery i s low). This may be attributed to the fact that the three-parameter model does not allow for low R°=, such as the recoveries of large p a r t i c l e s of KCI. The incorporation of R<=° into the equation improves the f i t but i t would seem i n e f f i c i e n t to f i t four data points with four c u r v e - f i t t i n g parameters. (c) Chen model : The model f i t s the data reasonably well. On the average, the residual sum of squares per run is the lowest of the three models investigated. The predicted recoveries are well within the error associated with data acquisition and normal process fluctuations. Each f l o t a t i o n rate curve i s 83 quantified by two parameters which possess the following si g n i f i c a n c e : (1) Kav(O) r e f l e c t s the slope of a cumulative recovery vs time curve at short f l o t a t i o n times ( i . e . i n i t i a l f l o t a t i o n rate) . (2) g shows the rate of change in recovery rates. As shown on page 20, g and Kav(0) can be used to calculate R(°°) which follows closely with the trends of the corresponding f l o t a t i o n rate curves measured experimentally. Therefore, of the models f i t t e d to the small batch f l o t a t i o n rate data, the Chen model was judged "best". Page 84, 85, 86 show how well f l o t a t i o n rate.data are predicted by the model for run 172. The corresponding f i t t e d curves (NaCl data are too crowded to plot) are i l l u s t r a t e d in Fig.25 and 26. Likewise, the Chen model was f i t t e d to large batch and continuous f l o t a t i o n rate data. Predictions (see APPENDICES J and K) are generally good, except for the -8+14M and -14+28M size fractions of the continuous f l o t a t i o n rate data. For these two size f r a c t i o n s , the corresponding f l o t a t i o n rate curves are of abnormal shape. 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I £6" £,d' asisnray 09) ^3 < D 3 S 05) £3 ( D S S 0 3 ) 33 <33S Q5) T3 31BS1N33N03 •****•• r * * * * CMsaw 83 + t>T-> ^0-36t»fr9896Z95T'£ =SSJ1 £T89I8£9Z£8 6 50-390896£6I63I * I <0)ABX 85"9-39"£ 10" 11 ZZ"TI-3t>" 6£ " 9£" 95 " 8E ' 3£ " 65" 3 3 N 3 c J 3 d d i a y. a3i3irj3ad asisnray ( " s 0 9 ) f3 ( D a s 0 3 ) £3 ( D a s 0 5 ) 33 ( 3 3 9 03) T3 3iyMiN33N03 (qsaw M + 8-) T 3 Z I S l ^ N yod Ad3A033W 3AIiy"inWn3 ** J * * * * * * * * * * * * * * * * * * * * 3zi s i aaawriN Nny *********************** 9 8 86 *********************** RUN NUMBER IS 172 ************************** ******************** CUMULATIVE RECOVERY FOR Insol ********************* ******************** SIZE 1 (-8+14 Mesh) *********************** CONCENTRATE ADJUSTED PREDICTED 'A DIFFERENCE CI (20 sec) 1.62 1.25 -22.94 C2 <2Q sec) 1.73 1.94 12.21 C3 (20 sec) 2.13 2.33 9.27 C4 (68 sec) 2.88 2.73 -5.15 Kav(O) g 4.96456022311E-82 1.73699052511 RSS= 2.43736244475E-05 * * * * * * * * * * * * * * * * * * * * S I Z E 2 (-14+28 Mesh) *********************** CONCENTRATE ADJUSTED PREDICTED 'A DIFFERENCE CI (20 sec) 3.S4 2.97 -22.69 C2 (20 sec) 4.92 5.56 12.97 C3 (20 sec) 7.86 7.32 -.46 C4 (60 sec) 13.15 13.10 -.49 Kav(0) g .095375823067 .323933274883 RSS= 1.17061S53023E-O4 ******************** SIZE 3 (-28+48 Mesh) *********************** CONCENTRATE ADJUSTED PREDICTED 'A DIFFERENCE CI (20 sec) S.93 8.44 -6.05 C2 (23 sec) 13.33 14.46 8.45 C3 (20 sec) 19.60 18.83 -3.93 C4 (60 sec) 26.14 26.25 .41 Kav(0) g .308180936725 .77798590396 RSS= 2.16943425617E-84 ******************** SIZE 4 (-48+100 Mesh)*********************** CONCENTRATE ADJUSTED PREDICTED 'A DIFFERENCE CI (20 sec) 11.31 10.63 -5.61 C2 (20 sec) 15.90 16.64 4.64 • C3 (20 sec) 20.26 20.09 -.85 C4 (60 sec) 24.17 24.09 -.34 Kav(O) g .423673502419 1.47377373839 RSS= 9.82325075333E-05 ******************** SIZE S (-100 Mesh) *********************** CONCENTRATE ADJUSTED PREDICTED 'A DIFFERENCE CI (20 sec) 13.80 12.32 -10.75 C2 (20 sec) 20.O7 21.75 8.37 C3 (20 sec) 29.67 29.09 -1.94 C4 (60 sec) 43.32 43.29 -.08 Kav(O) g .4233270 75859 .431491569567 RSS= 5.35452374364E-04 87 iT^., 1 ••-.7t~\ RUN NUMBER: 172 " -v. • " n - - l -8+14 M 0 " -14+28 M -. . • " -28+48 M A --48+100 M — —o v< - h t ]•.. -100 f "1 V = ' ' V r V ; ; \ \ — — •\ — — — x x J \ — s \ i x A \ \ \ -11111 i 111 . J 1 1 .1 1 1 1 II W \ I 1 \ l \ 1 ! 1 1 l l l l l l l l l 1 U 1 I.I 1 1 1 01 0 2 3 'T i me , minutes Figure 25 - KCI Flotation Rate Curves F i t t e d by Chen's Model 88 RUN NUMBER: 173 -B +14 M o -14+28 M . . • -28+48 M . . . . A -48+100 M - - o - 1 0 0 M — — v 1 — 01 i i i i i i i i i I i i i i i i i i i i i I i i i ' i i i i i i i i i i i i .i i 0 2 3 T i me, mi nutes Figure 26 - INSOL Flotation Rate Curves F i t t e d by Chen's Model 89 T i me , m i n u t e s Figure 27 - KC1 Flotation Rate Curves of Run 302 90 Figure 28 - KCI Flotation Rate Curves of Run 303 91 VII. CORRELATION BETWEEN MODEL PARAMETERS AND OPERATING VARIABLES 7.1 Small Batch Data Correlation Since each time-recovery p r o f i l e is given by Kav(O) and g, i t i s necessary to find how the variation in operating variables introduced into the f l o t a t i o n system affects the model parameters. Based on the central composite design chosen for the small batch runs, a second-order equation was proposed to establish empirical relationships between model parameters and factors manipulated in the design. Thus, 6 6 6 Y = b 0 + .1 b-X. + .1 b-'X? +.1 b-X.X. 0 1=1 i " i=1 ' i i I,J = 1 u ' J where Y i s the dependent variable ( i . e . a model parameter), X,, X 2, X 3, X„, X 5, X 6 are the independent variables respectively denoting the coded levels of Amine, O i l , c e l l % solids, f l o t a t i o n pulp temperature, impeller speed and airflow, and b's are the regression c o e f f i c i e n t s to be determined ( i . e . up to 28 b's). The above equation includes linear terms to show the main effects of the individual variables, second order terms to show nonlinear effects and to indicate a region of maximum response, and cross product terms to show the interactions between pairs of variables. Table 15 shows the independent and dependent 92 Table 15 - Independent and Dependent Variables for Small Batch Flotation INDEPENDENT VARIABLES Run No. Xi X 2 x 3 X, x 5 x 6 1 98 1 « ! ! ! 1 93 +1 -1 -1 -1 - 1 +1 220 -1 +1 - 1 - 1 - 1 +1 184, 238 +1 +1 -1 -1 -1 -1 216 -1 -1 +1 - 1 - 1 +1 188 +1 - 1 +1 - 1 - 1 - 1 1 78 -1 +1 +1 -1 - 1 -1 183 +1 +1 +1 -1 - 1 +1 1 73 -1 -1 - 1 +1 -1 +1 208 +1 -1 - 1 +1 -1 -1 206 -1 +1 - 1 +1 -1 -1 1 79 +1 +1 -1 +1 -1 +1 1 92 -1 -1 +1 +1 -1 -1 1 75 +1 -1 +1 +1 -1 +1 231 -1 +1 +1 +1 -1 +1 199 +1 +1 +1 +1 -1 -1 223 -1 -1 -1 - 1 +1 +1 1 97 +1 -1 - 1 -1 +1 -1 218, 228 -1 +1 - 1 -1 +1 -1 214 +1 +1 - 1 -1 +1 +1 196 -1 -1 +1 -1 +1 -1 180 +1 -1 +1 -1 +1 +1 212 -1 +1 +1 -1 +1 +1 204 +1 +1 +1 -1 +1 -1 1 95 -1 -1 - 1 +1 +1 -1 200 +1 -1 -1 +1 +1 +1 190 -1 +1 -1 +1 +1 +1 187 +1 +1 -1 +1 +1 -1 203 -1 -1 +1 +1 +1 +1 213 +1 -1 +1 +1 +1 -1 209 -1 +1 +1 +1 +1 -1 1 74 +1 +1 +1 +1 +1 +1 181 -a 0 0 0 0 0 202 + a 0 0 0 0 0 186 0 -a 0 0 0 0 217, 224 0 + a 0 0 0 0 210 0 0 -a 0 0 0 201 0 0 + a 0 0 0 185 0 0 0 -a 0 0 DEPENDENT VARIABLES KCI K(i) ,g(i) , R°°(i) NaCl K ( i ) , g ( i ) , R°°(i) INSOL K ( i ) , g ( i ) , R=>(i) SEE FOOTNOTE(4) continued. . . 93 Table 15 continued. Run No, INDEPENDENT VARIABLES X i X2 X 3 X(, X5 X ( DEPENDENT VARIABLES K C 1 K(i) ,g(i) , R»(i) NaCl K(i) ,g(i) , R»(i) INSOL K ( i ) , g ( i ) , R°°(i) 222 0 0 0 + <x 0 0 219 0 0 0 0 -a 0 21 1 0 0 0 0 + a 0 177 0 0 0 0 0 -a 205 0 0 0 0 0 + a 172 0 0 0 0 0 0 191 0 0 0 0 0 0 221 0 0 0 0 0 0 207 0 0 0 0 0 0 215 0 0 0 0 0 0 182 0 0 0 0 0 0 1 94 0 0 0 0 0 0 176 0 0 0 0 0 0 234 0 0 0 0 0 0 236 0 0 0 0 0 0 237 0 0 0 0 0 0 SEE FOOTNOTE(4) Note: (1) K(i) stands for Kav(0) for size i , i=1,5. (2) g(i) respresents g for size i , i=1,5. (3) R°°(i) refers to R°° calculated from K(i) and g(i) for size i , i = 1 ,5 (4) values of K ( i ) , g(i) and R°°(i) for each run are found in APPENDIX I. 94 variables for small batch runs. Since there are 45 dependent variables involved in each run, 45 regression equations are requi red. 7.1.1 Regression Analyses Of Model Parameters Regression analyses of model parameters with operating variables were performed by means of a Triangular Regression Package program available through the UBC computer l i b r a r y . Various regression methods were tested in an attempt to obtain regression equations of high p r e d i c t a b i l i t y with a minimum number of c o e f f i c i e n t s ( i . e . no. of b's) involved. The Forward Stepwise Regression technique was f i n a l l y chosen to achieve these goals(47). The computational sequence of the stepwise technique i s as follows: (1) Calculate the correlations of a l l the Z's ( i . e . Z,, Z2,...., and Z 2 7 are functions of one or more of the X's as shown in the second-order equation) with Y. (2) Choose the Z most correlated with Y (say Z,) to enter the regression equation. (3) Regress Y on and check i f Z, i s s i g n i f i c a n t ( i . e . check i f the F-probability of Z, < .05). If i t i s not, quit and accept the equation Y = Y as best; otherwise retain Z, and go to (4). (4) Calculate the p a r t i a l c o r r e l a t i o n c o e f f i c i e n t s of the remaining Z's with Y. (5) Select, as the next Z to enter into the regression equation, the one with the highest p a r t i a l c o r r e l a t i o n 95 c o e f f i c i e n t (suppose i t is Z 2) (6) Regress Y on the Z's included in the equation (suppose Y = f(Z,,Z 2) is f i t t e d ) . The improvement in the value of R2, the square of the multiple c o r r e l a t i o n c o e f f i c i e n t , i s printed. (7) A l l the Z's now in the equation are tested for significance. If these are a l l s i g n i f i c a n t , go to (4). Otherwise the nonsignificant Z ( i . e . i t s associated F-proba b i l i t y ^ .05 ) i s eliminated from the regression equation. New regression c o e f f i c i e n t s are then calculated for the remaining Z s t i l l in the equation. (8) The potential Z's not currently in the regression equation are checked for the significance of the contribution each would make i f entered next. The most s i g n i f i c a n t Z at thi s stage, i . e . the one with the smallest F-probability, i s added to the regression equation i f this p r o b a b i l i t y i s less than .05. New regression c o e f f i c i e n t s are then computed. (9) If a l l the potential Z's not yet included in the equation have associated F - p r o b a b i l i t i e s > .05, the stepwise regression process i s complete; otherwise go to (7). In short, the Forward Stepwise Regression process adds only the most s i g n i f i c a n t Z in the equation at the f i r s t step, and allows only the s i g n i f i c a n t Z's to be entered to the equation one at a time. Eventually, when no Z's in the current equation can be rejected and the potential Z's cannot retain a place in the equation, the process stops. As each Z i s added into the 96 regression equation, i t s effect on R2 i s printed. By means of the above process, f o r t y - f i v e regression equations were generated along with residuals plots for the small batch runs. Examination of the residuals indicated most data were highly scattered within a horizontal band. The regression equations and their associated R2 for each size fractions of KCI, NaCl and INSOL are shown in Tables 16, 17 and 18 respectively. In view of the low values of R2 obtained, the regression equations were judged unsatisfactory for predictive purposes. Numerous attempts were then made to est a b l i s h correlations without success. Among these e f f o r t s were the following: (1) attempts to reject o u t l i e r s i d e n t i f i e d from residuals plots. (2) attempts to combine data sets with s i m i l i a r operating variables. (3) attempts to eliminate a l l center-point runs. (4) attempts to eliminate a l l center-point and a runs. (5) attempts to f i x one model parameter as a function of another. (6) attempts to transform model parameters by means of Log and exponential functions. As a result of these unsuccessful attempts, the small batch f l o t a t i o n data are believed to be highly scattered. A major problem with these data arises from the lack of r e p r o d u c i b i l i t y caused by many factors outside the control of the operators. The important factors have been described in CHAPTER 5. 97 Table 16 - Forward Stepwise Regression Results of KCl for Small Batch Runs R 2 KCl .5573 K(1) = .2897 - .0795X, - .1483X2 + .1137X,X2 - .1137X,X„ - .1507X 3X„ - .087X5X6 .6512 g(l) = 1.262 - .739X, - .5659X2 - .28X3 + .3429X,2 + .5256X,X2 - . 55X •)X4 - . 4 9 9 5 X 3 X 4 . 1782 R°°( 1 ) = 37.693 + 13.31X3 + 1 3 . 7 6 6 3 X 3 X 4 .5317 K(2) = .8915 - . 3 5 5 9 X 2 + .2124X6 + .2648X,X2 ~ •335X-|Xij -• • 3 5 8 X 3 X 4 ~ « 2 7 5 X g X g .5660 g(2) = .59 - .2779X, - .2238X2 - .2176X3 + .1425X,2 + .265X^2 - .279X,X4 - . 25X 3X a - . 1877X5X6 .4257 Ro°(2) = 86.293 + 7.9446X, + 8.553X3 - 6.747X5 - 7.0544X,2 - 4.9657X62 .5624 K(3) = 2.068 - . 5 4 X 2 + . 3 5 3 X ^ 2 - .61X,Xft - . 5 3 5 4 X 3 X 4 - .4127X5X6 . 1 427 g(3) = .377 - .1 187X, - . 1415X,Xfl . 1 753 R°°(3) = 97.45 + 2.13X, + 1 . 7 5 1 X 3 .6259 K(4) = 2.78 - ,35X2 + .323X,X2 - .6379X ,X4 + .258X2X3 - . 4 4 4 6 X 3 X 4 - .278X3X6 - . 4 7 4 X 5 X 6 .2065 g(4) = .4658 + . 1 3 7 6 X 3 X 5 - .17X5X6 .2763 R°°(4) = 98.593 + .7972X, + .7795X6 - . 8 5 8 X 3 X 4 + .9045X5X6 .53 K(5) = 2.524 - .248X2 + .262X,X2 - .582X ,X4 + .277X2X3 - . 3 7 X 3 X 4 - . 3 9 X 5 X 6 .1759 g(5) = .4789 - .15X , X4 - .16X5X6 .0813 R°°(5) = 98.422 + .6554X6 98 Table 17 - Forward Stepwise Regression Results of NaCl for Small Batch Runs R2 NaCl .481 9 K(1 ) = .0052 - .0026X2 + .0013X6 + .0016X,X2 - .0019X,X, - .0026X 3X« .655 g(D = 1.8 - .678X, - .848X2 + .296X,2 + .5054X,X2 - ,57X,X, + .4527X2X5 - .4656X3Xa - .4X 3X 6 R°°( 1 ) = 4.8663 .5478 K(2) = .025 - .011X2 + .0063X6 + .008X^2 - . 0 0 8 8 X T X , , - , 01 1 3X3X, - .0076X5X6 .53 g(2) = 1.26 - .326X! - .5X2 - .2477X3 + .344X,X2 - ,439X,X0 - .45X 3X„ . 1772 R°°(2) = 22.1813 + 14.761X2 + 11.193X3 .5368 K(3) = .0749 - .0279X2 + .0177X,X2 " .0243X,X« - .0236X3X4 - .019X5X6 .557 g(3) = 1.375 - .5X2 - .258X3 + .333X!X2 - .4846X1X„ - .4255X3Xa - ,3424X5X6 .1734 R=>(3) = 15.6198 + 9.7277X2 + 9.42X3 .492 K(4) = .089 - .0226X2 + .016X,X2 - .022X,X„ - .0208X 3X„ - ,016X5X6 .3516 g(4) = 1 .39 - .369X2 - .41X,X, R°°(4) = 8.5850 .2877 K(5) = .12 - .022X2 - .0329X 1X„ - .0299X3XX,, - .0267X5X6 .256 g(5) = 1.196 - .227X2 - .398X,X, .2173 R°°(5) = 10.408 + 1.285X,X4 + 2.0182X4X6 99 Table 18 - Forward Stepwise Regression Results of INSOL for Small Batch Runs R2 INSOL .4234 K(1 ) = .0397 - .0234X2 - .0l58X,Xa - .0l90X3X« .618 g(D = 1.45 -.789X, - .693X2 + .369X,2 + . 5 3 8 8 X T X 2 - . 6 X , X 4 - .54X3X,4 . 1 428 R=°( 1 ) = 27.522 + 11 . 9 7 5 7 X 2 + 1 4 . 5 6 5 X 3 X 4 .548 K(2) = .175 - .0689X2 + .0457Xe + .0473X1X2 - .06X,Xfl - .067X3X« - .046X5X6 .566 g(2) = 1 - .32X, - .37X2 - .27X3 + .35X,X2 - . 3 7 X , X 4 - . 3 8 9 7 X 3 X 4 - .294X5X6 .3158 R°°(2) = 38.396 + 12X2 + 14 . 3 5 3 X 3 - 10.288X 5 + 1 3 . 5 7 3 6 X 3 X 4 .519 K(3) = .48 - .169X2 - ,148X,X4 - .1223X3X4 - .092x 5X 6 .5185 g(3) 1.46 - .48X2 + .29X,X2 - .457X,X4 - . 4 0 9 X 3 X 4 - . 3 4 X 5 X 6 .1594 R°°(3) = 34.674 + 6.033X2 + 6.914X 3 .4725 K(4) = .15 + .434X, + .604X,2 .3 g(4) = 1.665 + .317X, - .326X2 + .339X,2 - ,4X,Xa .5576 R»(4) = 19.896 + 9.096X,2 .346 K(5) = .3865 - .0435X2 - .08X,X, - . O 7 X 3 X 4 - .g67X5X6 .3739 g (5 ) = .85 - .258X,X» + . 2 0 4 X 2 X 3 + . 1 7 2 X 3 X 5 - .216X5X6 . 1 523 R~(5 ) = 40.0657 + 4.354X,X4 - 4.4X3X5 100 7 . 2 Large Batch Data Correlation Similar regression techniques were applied to the large batch f l o t a t i o n data. Table 19 l i s t s the independent and dependent variables for t h i s set of data, where X , , X 2 , X 3 and Xi, represent the coded lev e l s of Amine, c e l l % s o l i d s , impeller speed and airflow respectively. The regression results of KCI, NaCl and INSOL are shown in Tables 2 0 , 21 and 2 2 . Based on the regression equations associated with high R2 ( i . e . R2 0 . 8 ) , some useful trends are summarized below: (1) Decreasing impeller speed, X 3 , has two b e n e f i c i a l e f f e c t s : (a) Both the f l o t a t i o n rate and the ultimate recovery of KCI in the - 8 + 1 4 M size f r a c t i o n are increased. (b) The ultimate recovery of KCI in the - 1 4 + 2 8 M size f r a c t i o n i s increased. (2) Decreasing f l o t a t i o n pulp density ( X 2 ) has the following ef fects: (a) The f l o t a t i o n rate of KCI in the - 8 + 1 4 M size f r a c t i o n at lower impeller speed is increased. (b) The ultimate recovery of - 8 + 2 8 M p a r t i c l e s of NaCl i s decreased. (c) The ultimate recovery of INSOL in the - 8 + 1 4 M size f r a c t i o n i s decreased. Whether the above trends are observed in f u l l - s c a l e f l o t a t i o n c e l l s depend on matching the mode of operation of the larger c e l l ( i . e . whether i t be in rate or equilibrium control 101 Table 19 - Independent and Dependent Variables for Large Batch Flotation INDENPENT VARIABLES DEPENDENT VARIABLES KCI NaCl INSOL Run No. x , x 2 x 3 x , K ( i ) , g ( i ) K ( i ) , g ( i ) K ( i ) , g ( i ) , R»(i) , R«(i) , R°°(i) 251 -1 -1 -1 -1 253 + 1 -1 -1 + 1 255 -1 + 1 -1 + 1 254 + 1 + 1 -1 -1 258 -1 -1 + 1 + 1 259 + 1 -1 + 1 -1 SEE FOOTNOTE 4) 256 -1 + 1 + 1 -1 257 + 1 + 1 + 1 + 1 260 0 0 0 0 261 0 0 0 0 250 0 0 0 0 252* + 1 -1 0 + 1 *Run 252 i s an extra run performed accidentally. Note: (1) K(i)stands for Kav(0) for size i , i=1,5. (2) g(i) represents g for size i , i=1,5. (3) R=°(i) refers to R°° calculated from K(i) and g(i) for size i , i = 1 , 5 (4) values of K ( i ) , g(i) and R°°(i) for each run are found in APPENDIX J. 1 0 2 Table 2 0 - Forward Stepwise Regression Results of K C I for Large Batch Runs R 2 K C I . 7 7 9 7 . 8 9 3 1 . 7 3 1 7 K ( 1 ) = . 3 0 9 4 - . 1 1 3 0 X 3 + . 0 7 6 5 X 2 X 3 - . 0 9 8 5 X 3 X T T g(l) = 1 . 0 0 8 - . 3 4 6 X 2 + . 3 0 3 X 3 - . 1 9 9 X 3 X „ R ° ° ( 1 ) = 3 3 . 2 4 7 + 1 4 . 1 2 7 X 2 - 1 9 . 8 3 X 3 . 7 2 5 . 9 4 1 K ( 2 ) = 1 . 0 4 8 4 g ( 2 ) = . 4 4 7 6 - , 1 9 X 2 + . 3 3 9 5 X 3 R ° ° ( 2 ) = 8 8 . 5 3 8 + 7 . 0 9 6 7 X 2 - 1 1 . 1 8 4 X 3 + 6 . 5 6 X T X , , K ( 3 ) = 1 . 3 1 9 7 g ( 3 ) = . 1 7 3 2 R » ( 3 ) = 9 9 . 3 4 1 3 . 3 4 6 K ( 4 ) = 1 . 2 8 g ( 4 ) = . 0 6 6 3 + . 0 6 5 5 X F T R»(4) = 9 9 . 9 6 9 7 . 6 6 5 4 . 8 9 4 6 . 9 3 7 2 K ( 5 ) = 1 . 2 9 + . 2 6 7 6 X 3 - . 1 6 7 7 X 3 X « g ( 5 ) = . 2 6 7 7 - . 0 7 1 6 X 2 + . 1 7 5 4 X 3 - . 0 5 6 3 X ! X 3 R o o ( 5 ) = 9 7 . 5 3 4 + . 8 1 7 9 X 2 - 1 . 1 5 4 X 3 + 1 . 1 6 8 X 3 2 + , 6 5 9 9 X 2 X 3 1 03 Table 21 - Forward Stepwise Regression Results of NaCl for Large Batch Runs R2 NaCl .764 .921 7 K(1) = .0048 + .0018X2 - .0035X3 g(D = 1.582 R»( 1 ) = .261 + . 1 362X2 - .2296X3 + . 1 351Xn 2 .3326 .8901 K(2) = .0276 g(2) = 1 .463 + .29X3 R°=(2) = 2.0379 + ,261X2 - .7554X3 .378 .5816 K(3) = .074 - .0187X3X„ g(3) = 1.3827 R»(3) = 5.274 - 1.0883X3 .6368 K(4) = .0978 g(4) = 1.627 + .47X3 - .37X,X3 R°°(4) =6.0121 .3647 .9478 .6605 K(5) = .097 + .0205X3 g.(5) = 1 .29 + ,3369X3 + , 321 0X3 2 - .21 84X 1X 3 - .267X3Xft R»(5) = 6.2578 + .687X2 + .5832X„ Table 22 - Forward Stepwise Regression Results of INSOL for Large Batch Runs R2 INSOL .6329 .816 .81 35 K(1) = .048 - .0156X3 - .0135X 3X„ g(l) = .98 - .2058X2 + .1923X3 - .1598X,X2 R»(1) = 5.7319 + 2.4845X2 - 3.081X3 .464 .8570 K(2) = .2224 g(2) = .81 - .18X,X2 R=>(2) = 25.4723 + 4.1116X2 - 3.7427X3 .823 .795 .5835 K(3) = .363 + .1295X„ + .14X 3 2 + .167X,X2 - .1026X3X« g(3) = .668 - .248X2 + .2198X3 - . 1 4 6 X , X 3 R»(3) = 44.708 + 7.3633X2 .9569 .348 .4765 K ( 4 ) = .253 + .0788X3 + .0272Xa + ,1X 3 2 - .0769X3X4 g(4) = .5126 - .1689X2 R O D ( 4 ) = 49.5648 + 8.21 17X2 .81 39 .359 .4073 K(5) = .4028 + .145X,2 - .0667X,X3 + .115X2X3 g(5) = .3436 - .1088X2 R»(5) = 70.759 + 9.2576X2 105 as discussed by Klimpel (48) ) to the s h i f t s in R°° and Kav(0) that were observed in the lab batch tests. 106 VIII . SCALE-UP OF MODEL PARAMETERS An important aspect of f l o t a t i o n modelling i s to predict the performance of a large-scale f l o t a t i o n c i r c u i t from small batch data. This depends on accurate scale-up of model parameters from the appropriate f l o t a t i o n data. In this study, f l o t a t i o n rate data obtained from small batch, large batch and continuous "center point" runs were employed. The scale-up procedure i s discussed below. 8.1 F i t t i n g Model To Data By means of a dir e c t search method, the Chen model was f i t t e d simultaneously to each set of "center point" f l o t a t i o n rate data . Search results of the three sets of data are summarized in Table 23. 8.2 Effect Of P a r t i c l e Size On Parameters To minimize the number of scale-up constants, the effect of p a r t i c l e size on model parameters must be known, (a) Kav(O) Versus Size Relationship Based on f l o t a t i o n kinetic studies by King (25) and Woodburn e t . a l . (31), the following rel a t i o n s h i p was assumed to hold for each mineral: 0.5 1 .5 Kav(0) = C*(e/D 2) exp(-e/D 2){l - (D/A) } where C i s a constant. e i s the turbulence parameter and i s related to the 107 T a b l e 23 - M o d e l P a r a m e t e r s f o r 3 S e t s o f C e n t e r P o i n t F l o t a t i o n Runs S.B. RUNS L.B RUNS CONTINUOUS RUNS Kcl *** S i ze 1 < -8+14 M) .211468092315 .232953735965 .689335481368 Si ze 2 < -14+28 M> .6365633333 .96313256259 .75734457205 Si ze 3 C -28+48 M> 1.S07875SS671 1. 13495922573 2.55234421229 Si ze 4 < -48+100 M> 2.65883298471 1.09828036407 3.63331409495 Size 5 < -100 M) 2.41130314145 1.1200S534993 2.42309421293 9 Si ze 1 < -8+14 M) 1.27322329939 1.09104324591 4.68S37340149E--08 Si ze 2 < -14+2S M> .459346552139 .429603385401 8. 10499403420E--03 Si ze 3 < -28+48 M) .274173199719 .105664214155 .147299357933 Si ze 4 -48+100 M) .362322030225 2.46696039471E -83 .753954S5241 Si ze 5 c -100 M) .417453100165 .303473663339 .501187187705 *** Nacl *** Kav<0> S i ze 1 <• -3+14 M> 4.21472197469E-03 3.95523022746E -03 S.7S953780620E--04 Si ze 2 <• -14+23 M) .019269702295 2.41097476235E -02 8.24172127130E--93 Si ze 3 <--28+48 M) .063332601923 6.63212151995E -82 2.6339S318S11E--02 Si ze 4 <• -48+190 M) .034431866632 8.63757341435E' -82 3 . 18447155959E-•02 Size 5 <• -100 M> .182324729233 .036089012511 .052543291207 9 S i ze 1 <--3+14 m 1.92395675654 1.5182S052973 7.42516S14460E-•05 Si ze 2 <--14+28 H> 1.04442837443 1.19733827619 .153915383997 Si ze 3 <--23+48 M> 1.14763265657 1.13236726963 .530354199215 Si ze 4 o -43+100 M> 1.13138364374 1.23673239739 .75479515633 Si ze 5 <--100 M) .8318301279 1.26937365409 .304282212895 *** Insol *** Kav<0> Si ze 1 <-•3+14 ro 3.03619336091E-82 4.62964314299E--92 1.33466029125E-02 S i r e 2 <-•14+28 M> .130141323635 .214553278323 .036174594309 Si ze 3 c-•28 + 43 M) .406314644019 .312116367169 .207591556333 Si ze 4 o •43 + 109 N> .50363749967 .247929130301 .214734339353 Si ze 5 <-•109 N) .347927724617 .310496560367 .219453953975 9 Si ze 1 <-•8+14 M> 1.59223052493 1.02337312211 2.7031924S491E- 10 Si ze 2 <-•14 + 28 M> .754692972485 .74151597712 1.77475933891E-99 Si ze 3 < -•28 + 43 M> 1.22129611294 .523724514915 .459934457269 Si ze 4 <- 4S+10U M) 1.S0327194 .343334376595 .504353232855 Size 5 <- 100 M> .67833591035 .233546328311 4.20OO0243771E-09 108 size, M, at which Kav(0) i s maximum ( i . e . e = 0.5M2). A i s the maximum f l o t a t i o n size (jum). D i s the average p a r t i c l e size (urn) taken as the arithmetic mean of the passing and holding screens in each size range. This equation has a unimodal shape to allow for the poor recoveries observed in both the very small and very large p a r t i c l e size ranges. The "best" values of C, e, and A were estimated by minimizing the sums of squares of the deviation between the predicted and observed Kav(0). Results are summarized in Table 24. Figures 29, 30 and 31 show the observed Kav(0) and the f i t t e d curves of the 3 sets of runs for KCl, NaCl and INSOL respectively. In spite of the scatter in the observed data, the ch a r a c t e r i s t i c unimodal shape i s c l e a r l y indicated. Key findings are: (1) For KCl mineral (Fig. 29), the results of the a l l runs show that the maximum Kav(0) ( i . e . i n i t i a l f l o t a t i o n rate) i s obtained in an intermediate size range ( i . e . about 177 jum) and that the rate decreases on either side of thi s range. The continuous runs appear to have higher Kav(0) values in a l l sizes except the coarse end. This low i n i t i a l f l o t a t i o n rate of coarse p a r t i c l e s i s shown in Figs. 27 and 28, where f l o t a t i o n rate curves of coarse p a r t i c l e s are quite d i f f e r e n t from those observed for batch runs. Differences are attributed to i n s u f f i c i e n t MIBC conditioning time, low aeration rate and coarser feed (See 109 Table 24 - Dependence of Model Parameters on P a r t i c l e Size Small Batch Large Batch Cont inuous Runs Runs Runs Kav(0) c 7 3.3 9.386 e 15696 1 5696 1 5696 KCl A 3500 5000 2017.73 Kav(0) C .2694 .233 . 1229 e 5408 5408 5408 NaCl A 3000 3000 3000 Kav(0) C 1 .3 .9 .665 e 17435 1 7435 1 7435 I N S O L A 2674.2 4000 2750.65 9. a 0 -25.4823 11.3887 -117.0715 a 1 33.4638 -9.9370 143.5791 KCl a 2 -14.2523 2.3945 -57.5626 a 3 1.9968 -.0959 7.5746 a a 0 -61.0858 -12.2439 -49.7066 ai 74.1993 17.1580 56.7193 NaCl a 2 -29.2350 -7.1636 -20.8703 a 3 3.8062 .9807 2.4997 a a 0 -148.0623 1 .0701 -21.1269 a. 173.7868 -1.1314 20.1696 I N S O L ' a 2 -66.4270 .3734 -5.6640 a 3 8.3434 -.0091 .4250 Note : (1) 0.5 1.5 Kav(0) = C*(e/D 2) exp(-e/D 2){l - (D/A) } (2) g = a 0 + a,*log(D) + a 2*{log(D)} 2 + a 3*{log(D)} 3 (3) D i s the average p a r t i c l e size (jum). 110 4 3 . a 3 . 6 3 . 4 3 . 2 3 2 . 8 2 . 6 u 2 . 4 \—' 2 . 2 2 © 1 . 8 •w > 1 . 6 1 . 4 1 . 2 1 . 6 . 6 . 4 . 2 Q - / _i i • i I i \1 • \ S. B. RUNS - A L. B. RUNS -- - o CON. RUNS . 10 10 ° SIZE , MICRONS 10 Figure 29 - F i t t e d Curves of Kav(0)/Size for KCl 111 . 12 . 11 .1 . 0 9 .C8 .07 .08 .05 .04 . 0 3 .G2 .01 \ \ \ 3-> ' • • • I • • • \ O A \ • J_Ll S . B . RUNS A L . B . RUNS - -o CON. RUNS . . . • 10 10 S I Z E , MICRONS i l l i n 10 Figure 30 - F i t t e d Curves of Kav(0)/Size for NaCl 1 12 .6 .55 .5 .45 S . B . RUNS A L . B . RUNS o CON. RUNS . . . • .35 .3 .25 J / h / \ \ \ • \ • \ \ . 15 .1 .05 \ \ \ \ J _ i i • 4 j l • ' 1 I i n * • • i i i 1111 I I f i I i J_U 1 0 10 S I Z E MICRONS 10 Figure 31 - F i t t e d Curves of Kav(0)/Size for INSOL 1 1 3 Section 4.4). (2) As shown in Fig. 30 and 31, the maximum Kav(0) appears at 104 Mm for NaCl and 187 w for INSOL. A high Kav(0) generally gives rise to a high equilibrium recovery for NaCl and INSOL. Therfore, the above effects account for the poor concentrate grade observed in the fine size range. (b) g Versus Size Relationship The following third-order polynomial equation was assumed. to hold for each mineral: g = a 0 + a,*log(D) + a 2*{log(D)} 2 + a 3*{log(D)} 3 where D i s the average p a r t i c l e size (Mm). a 0 / a,, a 2, and a 3 are the regression c o e f f i c i e n t s . The regression c o e f f i c i e n t s , found by the least squares search method, are summarized in Table 24. Figures 32, 33 and 34 show how well the polynomial equation predicts the g data for KCl, NaCl and INSOL respectively. F i t s are judged acceptable. 8.3 Correlation Of Coefficients Between Runs By means of linear regression, the following relationships were established to predict a's between-runs From small batch a's ( i . e . a*) to large i batch a's ( i . e . g of KCl a** = i .5837 - .3312a* i i = 0,3 R2 = .9375 g of NaCl a** = i .3648 + .2215a* i i = 0,3 R2 = .9957 g of INSOL a** = .0216 - .0067a* i = 0,3 R2 = .9950 1 1 4 1.4 1 .3 1.2 1 - 1 1 .9 .6 .7 .6 .5 .4 .3 .2 .1 • A I 5 . B . RUNS L . B . RUNS CON. RUNS 7^ £3 i i • • i • • i - 1 .1.1.1 10 10 J . . J . . . U . L . Q J 3 1 , 1 I S I Z E , MICRONS Figure 32 - F i t t e d Curves of g/Size for KCl 115 2 1.9 1.8 1.7 1.6 1.5 1.4 1.3 o 1.2 Z 1.1 1 .9 D~> . 6 .7 . 6 .5 . 4 .3 .2 • .1 • 0 • 10 -4-• • i i i 1111 2 4 / j •i i i-A J . . i . r j j S . B . RUNS A L . B . RUNS - -o CON. RUNS . . . • ' 11! • i II ] l l l l l l l l l 10 10 S I Z E , MICRONS F i g u r e 33 - F i t t e d C u r v e s o f g / S i z e f o r N a C l 1 1 6 Figure 34 - F i t t e d Curves of g/Size for INSOL 1 1 7 (2) From small batch a's ( i . e . a*) to continuous a's ( i . e . i a * * * ) i g of KCI a * * * — i -1.21 + 4.361a* i ,i=0,3 R2 = .9985 g of NaCl a * * * — i -.445 + .7777a* i ,i=0,3 R2 = .9986 g of INSOL a * * * = i -.549 + .1236a* i ,i=0,3 R2 = .9825 Therefore, 12 scale-up constants ( i . e . 6 for g and 6 for Kav(O)) are employed to predict continuous f l o t a t i o n rate data (or large batch rate data) from small batch results in the v i c i n i t y of center point runs. 118 IX. SUMMARY AND CONCLUSIONS The methodology employed to simulate the rougher f l o t a t i o n of the PCS Cory ore has been described. This includes selection of responses and independent variables, selection of f l o t a t i o n models, a c q u i s i t i o n of raw data, s t a t i s t i c a l adjustment of raw/corrected data, f i t t i n g models to kinetic data, assessing the adequacy of f i t t e d models, cor r e l a t i o n between model parameters and independent variables, and scale-up of model parameters. Three sets of batch and continuous rougher f l o t a t i o n runs were conducted in accord with experimental designs. The f l o t a t i o n behaviour was simulated by proposed kinetic models on a size-by-size basis. The following conclusions were drawn: 1. By means of s t a t i s t i c a l and physical significance c r i t e r i a , the Beta d i s t r i b u t i o n model ( i . e . proposed by Chen and Mular) was found to give the best o v e r a l l f i t to the observed data. This model consists of two basic parameters which possess the following significance: (a) Kav(O) represents the i n i t i a l slope of a cumulative recovery vs time curve. (b) g r e f l e c t s the rate of change in f l o t a t i o n rates. Moreover, Kav(O) and g can be u t i l i z e d to estimate the equilibrium recoveries which are consistent with the corresponding f l o t a t i o n rate curves measured experimentally. 2. The Forward Stepwise Regression technique was employed to regress model parameters with the operating variables 1 19 manipulated in the design runs. Enhancement of recovery of coarse KCI p a r t i c l e s were observed in the large batch tests under some test conditions. Extrapolation to f u l l - s c a l e f l o t a t i o n c e l l s depends on matching the mode of operation of a large c e l l to the s h i f t s in R°° and Kav(O) that were observed in laboratory batch tests. The effect of p a r t i c l e size on i n i t i a l recovery rates of KCI was found to be a maximum at 177 Mm; NaCl (max. at 104 Mm) and INSOL (max. at 187 Mm) account for the poor concentrate grade observed in the fine size range. Due to lack of hydrodynamic data (such as Reynolds number and bubble size d i s t r i b u t i o n in a f l o t a t i o n c e l l ) , an empirical scale-up procedure was employed to predict large scale continuous results from small batch data. The number of scale-up constants were greatly reduced by using model parameter/size relationships. 1 20 BIBLIOGRAPHY 1. Faulkner, B.P., 1966. Computer Control Improves Metallurgy at Tennessee Copper's F l o t a t i o n Plant, Mining  Enginerring , 18, No. 11, p. 53-57. c 2.- P i t t , J.C., 1968. The development of systems for continuous optimal control of f l o t a t i o n plants by computer. Systems Dynamics and Automatic Control in Basic  Industries , (I.F.A.C. Symposium, Sydney), p. 165-171 3. Smith, H.W. and Lewis, C.L., 1969. Computer control experiments at Lake Dufault, Can. I.M.M. B u l l e t i n , 62, no. 682, p. 109-115. 4. Mular, A.L., 1972. Empirical modelling and optimization of mineral processes, Mineral Science and Engineering , 4 No. 3, p. 30-42. 5. Schuhmann, R., 1942. Methods for steady state study of f l o t a t i o n problem, J. Phys. Chem. , 46, p. 891-902. 6. Tomlinson, H.S. and Fleming, M.G., 1965. Flotation rate studies, Mineral Processing, 6th Int. Min. Proc.  Congress , Cannes, p. 563-579 7. R e l s a l l , D.F., 1961. Application of p r o b a b i l i t y in the assessment of f l o t a t i o n systems, Trans. Inst. Min. Met. ,70, p. 191-204. 8. K e l s a l l , D.F. and Stewart, P.S.B., 1971. A c r i t i c a l review of application of models of grinding and f l o t a t i o n , Automatic Control Systems in Mineral Processing Plants , (Symposium Aus. I .M.M. ;: Brisbane) , pi 213-232. ~ 9. Davis, W.J.N., 1964. The development of a mathematical model of the lead f l o t a t i o n c i r c u i t at the Zinc Corporeation Limited, P r o c , Aus. I .M.M. , No. 212, p. 61-89. 10. Zuniga, H.G. The e f f i c i e n c y obtained by f l o t a t i o n i s an exponential function of time. Bol. Minero Soc. Nacl.  Mineria (Chile), Vol. 47, 1935. p. 83-86. 11. Beloglazov, K.F. The kinetics of the f l o t a t i o n process. Tsvet. Metall , No. 9, 1939. p. 70-76. 12. Grunder, W., and Kadur, E. The r e l a t i o n between foam surface and volume in f l o t a t i o n c e l l s . Metall. u. Erz. , Vol. 37, 1940. p. 367-372. 13. Sutherland, K.L. Physical chemistry of f l o t a t i o n Part XI. Kinetics of the f l o t a t i o n process. J. Phys. C o l l o i d 121 Chem. , Vol. 52, 1948, p. 394-425. 14. Jowett, A., 1961. Investigation of residince time of f l u i d in froth f l o t a t i o n c e l l s . B r i t . Chem. Eng. , 6, p. 254-259. 15. Imaizumi, T. and Inour, T., 1963. Kinetic considerations of froth f l o t a t i o n , Proc. 6th Int. Min. Proc. Congress (Cannes), p. 581-593. 16. Woodburn, E.T. and Loveday, B.K., 1965. Effect of variable residence time on performance of a f l o t a t i o n system, J.S. Afr. Inst. Min. Met. , 65, p. 612-628. 17. Arbiter, N. and Harris, C.C., 1962. Flotation kinetics  in Froth Flotation 50th Anniversary Volume (ecL D.W. Fuerstenau) , p~. 21 5-246, (Rocky Mountain Fund Series). 18. Niemi, A., Acta Polytechnica Scandinavica, Chem. Met.  Series 1966, No. 48. 19. B u l l , W.R., 1965. Flotation kinetics and i t s application to the interpretation of plant performance and the design of treatment c i r c u i t s , 8th B r i t i s h Commonwealth Min. Met.  Congress , Melbourne, General P r o c , p. 1113-1124. 20. Cheng, K.K. D i g i t a l simulation of a f l o t a t i o n c i r c u i t . M.Eng. Thesis, University of B.C., 1979. 21. Loveday, B.K. Analysis of froth f l o t a t i o n k i n e t i c s . Trans. Inst. Min. Metall. , Vol. 75, 1966. p. C219-C225. 22. Harris, C.C. and Chakravarti, A., 1970. Semi-batch froth f l o t a t i o n k i n e t i c s ; species d i s t r i b u t i o n analysis, Trans•  A.I.M.E. , 247, p. 162-172. 23. Lynch, A.J., Mineral and Coal Flotation C i r c u i t s : Their  simulation and control , Elsevier Press, New York, 1981. 24. Chen, Z.M. and Mular, A.L., 1982. A study of f l o t a t i o n k i n e t i c s . Nonferrous Metals , Vol. 34, p. 38-42. 25. King, R.P., A p i l o t - p l a n t investigation of a kinetic model for f l o t a t i o n , J . Sth. Afr. Inst. Min. Met. , July, 1978, p. 325-338. 26. King, R.P. Simulation of f l o t a t i o n plants. Trans. Soc.  Min. Engrs. AIME . Vol. 258, 1975 , p. 286-293. 27. King, R.P. A model for the design and control of f l o t a t i o n plants. APPLICATION OF COMPUTER METHODS IN THE MINERAL INDUSTRY. Salamon, M.D.G., and Lancaster, F.J. (eds.) Johannesburg, South African Institute of Mining and 122 Metallurgy , 1973. p. 341-350. 28. King, R.P. and Buchalter, E.M., 1974. A p i l o t plant investigation of a f l o t a t i o n model. Report no. 1573, National Institute for Metallurgy , South A f r i c a . 29. King, R.P., 1976. A p i l o t - p l a n t investigation of a kinetic model for f l o t a t i o n . Report no.1847, National  Institute for Metallurgy , South A f r i c a . 30. Jowett, A. Gangue mineral contamination of froth. Chem.  Engr. , Lond., Vol. 2, No.5. May 1966. p. 330-333. 31. Woodburn, E.T., King, R.P., and Colborn, R.P., The e f f e c t of p a r t i c l e s i z e d d i s t r i b u t i o n on the performance of a phosphate f l o t a t i o n process. Metall. Trans. , Vol. 2, 1971 p. 3163. 32. Moys, M.H., et a l . Estimation of parameters in the distributed-constant f l o t a t i o n model. Johannesburg, National Institute for Metallurgy , Report No.1567, 1973. 33. Woodburn, E.T., 1970 . Mathematical modelling of f l o t a t i o n processes, Mineral Science and Engineering , 2, No. 2, p. 3-17. 34. Mular, A.L. and J.A. Herbst, " D i g i t a l Simulation: An aid for mineral processing plant design", Ch.14 in Mineral  Processing Plant Design , Eds. A.L. Mular and R.B. Bhappu, AIME, Colorado, 1978. 35. Hatch, C , C. Larsen and A.L. Mular, 1982. In A.L. Mular and G. Jergensen (Eds), Design and I n s t a l l a t i o n of  Comminution C i r c u i t s , AIME, Colorado, P. 275-285. 36. Kuester, J.L. and J. Mize, 1973. Optimization  Techniques with Fortran , McGraw-Hill, New York, P. 276-279. 37. Laguitton, D., 1982.. Methodology transfer for the simulation of mineral and coal processing plants. CIM  B u l l e t i n , Vol. 75, p. 166-170. 38. White, J.W., 1977. A useful technique for metallurgical mass balances. Int. J. Mineral Proc. , 4, p. 39-45. 39. Weigel, R.L., 1972. Advances in mineral processing material balances. Can. Metallurgical Quarterly , Vol. 11, p. 413-418. 40. Mular, A.L., 1970. Selection of optimization methods for minerial processing. CIM B u l l e t i n , 63, p. 820-826. 41. Mular, A.L., 1976. In M. C. Fuerstenau (Ed.), F l o t a t i o n 123 , Vol. 2, AIME, Colorado, p. 895-936. 42. Mular, A.L., 1979. In A. Weiss (Ed.), Computer Methods  for the 80's , AIME, Colorado, p. 843-849. 43. M. Wong, R. Ellwood, K. Armstrong and A.L. Mular, "The S t a t i s t i c a l Adjustment of Potash Fl o t a t i o n Data For Mass Balancing", Potash Technology , Pergamon Press, Toronto, 1983, p 637-643. 44. R. Ellwood, M. Wong, K. Armstrong and A.L. Mular, "Assay of Potash Ore With Ion Electrodes", Potash  Technology , Pergamon Press, Toronto, 1983, p 533-541. 45. Chen, Z.M. and Mular, A.L., 1982. The simulation of changing addition water in the f l o t a t i o n c i r c u i t with a simulator. Nonferrous Metals , Vol. 34, p. 47-50. 46. Chen, Z.M. and Mular, A.L., 1983. Optimum option of c e l l arrangement with a continuous f l o t a t i o n model. Nonferrous  Metals , Vol. 35, p. 21-26. 47. Draper, N.R. and Smith, H., Applied Regression Analysis ,John Wiley & Sons, Inc., 1981. 48. Klimpel, R.R., "Selection of Chemical Reagents for Flot a t i o n " , Mineral Processing Plant Design , 2nd edition, eds. Mular, A.L. and Bhappu, R.B., Chapter 45, AIME : New York, 1980, p 907-934. 49. Mular, A.L., et. a l . , Batch F l o t a t i o n of PCS Ore, Report to PCS, Dept. of Mining and Mineral Process Engineering, UBC, June 15, 1982. 50. Mular, A.L., et. a l . , Electrode Determination of KCL and NaCL In Potash Samples, Report to PCS, Dept. of Mining and Mineral Process Engineering, UBC, June 30, 1982. 51. Mular, A.L., et. a l . , Continuous Rougher F l o t a t i o n of PCS Ore, Report to PCS, Dept. of Mining and Mineral Process Engineering, UBC, July 15, 1982. 52. Mular, A.L., et. a l . , Improvement in Batch F l o t a t i o n , Assay, and Data Adjustment For PCS Ore, Report to PCS, Dept. of Mining and Mineral Process Engineering, UBC, August 31, 1982. 53. Mular, A.L., et. a l . , Central Composite Design For PCS Flo t a t i o n , Report to PCS, Dept. of Mining and Mineral Process Engineering, UBC, Nov. 30, 1982. 54. Mular, A.L., et. a l . , F i n a l Report on S t a t i s t i c a l Adjustment of Batch Flotation Data, Report to PCS, Dept. of Mining and Mineral Process Engineering, UBC, March 31, 124 1 983. 55. CORY Mine Internal Report, Potash Corporation of Saskatchewan e n t i t l e d "Metallurgical Procedures" by A.G. HICKIE and H.F. HOLST, November, 1974. 56. Mular, A.L., et. a l . , Mass Balance of A Grinding C i r c u i t , CIM B u l l e t i n , December, 1976. 125 APPENDIX A APPLICATIONS OF THE CHEN MODEL IN BOTH BATCH AND CONTINUOUS FLOTATION t .126 APPENDIX A - APPLICATIONS OF THE CHEN MODEL IN BOTH BATCH AND CONTINUOUS FLOTATION (1) In a semi-batch f l o t a t i o n the f r a c t i o n a l r e c o v e r y of m i n e r a l A i s -Kt R A ( t ) = 1 - e t Since Kt can be r e p l a c e d by J Kav(t) d t , the above o equation becomes R A ( t ) = 1 - e = 1 - e Upon i n t e g r a t i n g R.(t) = 1 - exp(-- f Kav(t) dt o t -9* - f Kav(0)e dt o -gt -Kav(O) ( 1 - e ) (A1) (2) For a bank of n continuous c e l l s the f r a c t i o n a l recovery of mi n e r a l A i s 1 R A I = 1 -1 + f 1 Kav(t) dt 0 R A from the 1 s t c e l l R . , = (1 " R A . ) ( 1 " A2 1 + J 2 Kav(t) dt T, R, from the 2nd c e l l A R (1 R A I R A 2 • • • R A ( n _ 1 ) ) ( l 1 + J n Kav(t) dt T_ . R. from the nth c e l l A where T; i s the cumulative f l o t a t i o n . t i m e to the i t h c e l l J 27 ( i . e . T 3 - T 2 = the retention time of pulp in the 3rd c e l l ) . 1 R A 2 = (1 - RA1 H i " f- — ) 1 + / 2 Kav(t) dt T i 1 1 « ( = ) ( 1 - — 1 + /' Kav(t) dt 1 + Kav(t) dt o V I 1 + f'Kav(t) dt ( 1+J'Kav(t) dt)(1+/ 2Kav(t) dt) O 0 T , The sum of R A 1 and R A 2 i s 1 R A l + ^ A 2 = 1 — j ^ (1+f'Kav dt ) ( 1+f 2Kav dt) O T , Therefore, the t o t a l recovery of mineral A from a, bank of n c e l l s is n 1 .Z R • = 1 - — K = ( A 2 ) 1 = 1 .n (1 + / ' Kav(t) dt) 1=1 "T . I -I T. -gt since /' Kav(t) dt = J* ' Kav(0).e dt T i - . T i - , Kav(O) -gT; , -gT-= (e - e ) g Kav(O) - g n i t- -g .1 t-= (e , = ' e 1 =1 ') / 2 8 Thus, equation (B2) can be rewritten as n X RA: = 1 -n Kav(O) -g 'Z t- ~ g t : > n {1 +( ) ( e ^ ° J M l - e )} 9 where t i s the retention time of pulp in the i t h c e l l and t 0 = 0. 129 APPENDIX B DEFINITION OF SYMBOLS FOR COMPUTER PROGRAMS Dl I 30 B. VARIABLE NAME DEFINITIONS FOR DATA ADJUSTMENT PROGRAM, DATAD Al a constant used to calculate the starting value of alpha A7 lower limit of alpha to' ensure elements of Vg > 0 (i.e. A7 < 0) A8 upper limit of alpha to ensure elements of V g > 0 (i.e. A8> 0) A20 value of alpha calculated from each pair of search variables in Vj and V> (i.e. A20 = - 2 ) V2 - l l A(I) positive values of alpha calculated from each pair of search variables in Vj and Vj? to ensure elements of Vg > 0 BI a constant used to calculated the step size for the alpha search (evaluating V_g) B2 a constant used to calculate the step size for the step search (evaluating Vj and V?) B3 a numerical switch-B3 = 0 for step search and quadratic fitting * B3 = 1 for alpha search and quadratic fitting ** B4 a counter for the number of Vg evaluations B5 a counter for the number of times the objective function has been evaluated C " a counter for the number of. step changes C5 *** a counter for the number of search variables that generates a lower limit for alpha (i.e. alpha < 0) C6 *** a counter for the number of search variables that generates a positive upper limit for alpha C20 a counter of for number of times the Coggin routine has been executed C22 a counter for the number of search variables minimized during evaluation of ^  or Vj D 2 /3/ D step size DI § D2 dummies used to determine the minimum point i n repetitive quadratic f i t t i n g E(I) negative values of alpha calculated from each pair of search variables i n and Vj? to ensure elements of Vg>_ 0 L search variable identification M(I) a vector of measured data (i.e. Lf, Lc, Wa, , a2) Ml(I) a vector of calculated data (i.e. Lf, Lc, Wa, , a2) N total number of search variables Q ( I , 1 ) the vector Q(I,2) the vector Y.2 R(C) a buffer vector used to store values of search variables S current value of the objective function SI objective function value corresponding to the current Vj (i.e. SI i s used i n the convergence criterion) S(I) a vector used to store values of step search variables S(N+1) value of alpha during alpha search T(C) a buffer vector for search variables V(C) a buffer vector for objective function values corresponding to R(C) or T(C) Wl - solids i n fines fraction of fresh feed W2 solids in coarse fraction of fresh feed W(I) weighting factors W1(I) r e l i a b i l i t y factors X(I,J) measured mineralogical size distributions X1(I,J) calculated mineralogical size distributions Y(I,J) measured size distributions Y1(I,J) calculated size distributions * step search and quadratic f i t t i n g evaluate a n d ** alpha search and quadratic f i t t i n g evaluate Vg *** C5 + C6 = N 132 Variable Name Definitions for PRINTl LL(I) string variables used to identify the f i r s t 15 measured and adjusted data M( ) identical to M( ) i n DATAD (i.e. f i r s t measured data) Ml( ) identical to Ml( ) in DATAD (i.e. f i r s t 15 calculated data) w.( ) identical to W( ) i n DATAD Wl( ) :. identical to Wl( ) in DATAD X( ) identical to X( ) i n DATAD XI ( ) identical to XI( ) i n DATAD Y( ) identical to Y( ) i n DATAD Yl( ) > identical to Yl( ) i n DATAD /33 Variable Name Definitions of AFORM Al actual value for amine (lb/T) A2 actual value for o i l (lb/T) A3 actual value for % solids A4 acutal value for temperature (°C) A5 actual value for impeller speed (RPM) A6 actual value for aeration rate (1/min) CI coded level for Amine C2 coded level for o i l C3 coded level for % solids C4 coded level for temperature C5 coded level for impeller speed C6 coded level for aeration rate M(I) f i r s t 15 adjusted data MM(I) string variables used to identify each narrow size fraction Y(I,J) adjusted size distributions X(I,J) adjusted mineralogical size distributions K1(I),N1(I),11(1) % recovery of KCl, NaCl and Insol in each narrow size fraction of Cone. 1 K2(I),N2(I),12(1) % recovery of KCl, NaCl and Insol in each narrow size fraction of Cone. 2 K3(I),N3(I),I3(I) % recovery of KCL, NaCl and Insol i n each narrow size fraction of Cone. 3 K4(I),N4(I),14(1) % recovery of KCl, NaCl and Insol i n each narrow size fraction of Cone. 4 K5(I),N5(I),15(I) % recovery of KCl, NaCl and Insol i n each narrow size fraction of Tails : Y l l ( I ) cumulative size distributions 1 3 4 C1(I,1),C1(I,2),C1(I,3) C2(I >1),C2(I,2),C2(I,3) C3(I,1),C3(I,2),C3(I,3) C4(I,1),C4(I,2),C4(I,3) T(I,1),T(I,2),T(I,3) K11(I),N11(I),111(1) K22(I),N22(I),122(1) K33(I),N33(I),133(1) K44(I),N44(I),144(1) K55(I),N55(I),155(1) PP(I) Mil(I) G(I,1),G(I,2),G(I,3) R(I,1),R(I,2),R(I,3) cumulative %KC1, %NaCl, and % Insol i n the size distribution of Cone. 1 cumulative %KC1, %NaCl and %Insol i n the size distribution of Gone. 2 Cumulative %KC1, %NaCl and %Insol i n the size distribution of Cone. 3 cumulative %KC1, %NaCl and %Insol i n the size distribution of Cone. 4 cumulative %KC1, %NaCl and %Insol i n the size distribution of Tails cumulative % recovery o f KCI, NaCl and Insol i n the size distribution of Cone. 1 cumulative % recovery of•KCI, NaCl and Insol in the size distribution of Cone. 2 cumulative % recovery of KCI, NaCl, and Insol In the size distribution of Cone. 3 cumulative % recovery of KCI, NaCl and Insol in the size distribution of Cone. 4 cumulative % recovery of KCI, NaCl and Insol in the size distribution of T a i l string variables used to identify the flotation products cumulative weight% of the flotation feed cumulative %KC1, %NaCl, and %Insol i n Conc-entrates cumulative % recovery of KCI, NaCl and Insol in concentrates 1 3 5 Variable Name Definitions for FORM! Al - A6 identical to Al - A6 in AFORM CI - C6 identical to CI - C6 i n AFORM MM(I) identical to MM(I) i n AFORM M(I) f i r s t 15 raw data Y(I,J) raw size distributions X(I,J) raw mineralogical size distributions Wl, W2 identical to Wl, W2 in DATAD J, K weights of saturated brine required to scrub coarse and fines fractions respectively G weight of deslimed ore required for a given % solids in the c e l l L, M weights of saturated brine needed to condition coarse and fines .fractions respectively Q, R grams and the equivalent c.c. of amine required i n reagentizing the coarse fraction S, T grams and the equivalent volume of o i l required i n reagentizing the coarse fraction 0, P grams and the equivalent c.c. required in reagentizing the coarse fraction 136 Variable Name Definitions for CFORM MCI) f i r s t 15 corrected data Y(I,J) corrected size distributions X(I,J) corrected mineralogical size distributions The rest of the variables are identical to those i n F0RM1. 1 3 7 APPENDIX C LISTINGS OF PROGRAM DATAD, PRINT1, FORM1, CFORM, AFORM, AND EXAMPLE OUTPUT L i s t i n g o f D A T A D a t 1 2 : 0 2 : 3 4 o n APR 6 , 1 9 8 3 f o r C C i d = U F 0 . P a g e 1 1 10 * T h e M a s s B a l a n c e P r o g r a m i s u s e d t o a d j u s t p o t a s h f l o t a t i o n d a t a 1n a l e a s t s q u a r e s s e n s e . 2 3 4 2 0 * T h e C o m p u t e r P r o g r a m e m p l o y s a S T E P - Q U A D R A T I C - A L P H A s e a r c h w h i c h 1s s i m i l a r 3 0 D I M S ( 8 1 ) , A ( 8 0 ) . E ( 8 0 ) , R ( 9 0 ) . V ( 9 0 ) . T ( 9 0 ) , Q ( 8 0 , 2 ) 4 0 D I M W ( 1 3 5 ) , W 1 ( 1 3 5 ) , M ( 1 5 ) , M 1 ( 2 O ) , Y ( 5 , 6 ) , Y 1 ( 5 , 6 ) , X ( 3 O , 3 ) , X 1 ( 3 0 , 3 ) : " t o t h e m e t h o d o f W h i t e ( 1 9 7 6 ) . 5 6 7 5 0 D A T A 6 , 0 , 0 . 5 , 3 . 0 , 8 0 , 1 2 5 6 . 7 , 7 5 4 . 8 GO * R e a d i n p u t d a t a 7 0 + A1 i s a c o n s t a n t u s e d t o c a l c u l a t e t h e s t a r t i n g v a l u e o f a l p h a 8 9 1 0 8 0 * B i i s a c o n s t a n t u s e d t o c a l c u l a t e t h e s t e p s i z e f o r t h e a l p h a s e a r c h 9 0 * B 2 i s a c o n s t a n t u s e d t o c a l c u l a t e t h e s t e p s i z e f o r t h e s t e p s e a r c h 1 0 0 * 3 4 i s a c o u n t e r f o r t h e n o . o f V g e v a l u a t i o n s 1 1 '•• 12 13 l i b * B 5 i s a c o u n t e r f o r t h e n o . o f t i m e s t h e O . F . h a v e b e e n e v a l u a t e d 1 2 0 R E A D A 1 , B 4 , B 1 , B 2 , B 5 , N , W 1 , W 2 1 3 0 * S e t i n p u t a n d o u t p u t f i l e s 14 15 16 1 4 0 F I L E W T F A C , R O F L 1 7 2 , O U T i 7 2 , R E F A C 1 5 0 B B = " 1 7 2 " 1 6 0 F O R 1=1 TO 1 3 5 • 17 18 19 1 7 0 R E A D F I L E i ,w"( i ) 1 8 0 R E A D F I L E 4 , W 1 ( I ) 1 9 0 N E X T I 2 0 21 2 2 2 0 0 R E S T O R E F I L E 1 2 1 0 R E S T O R E F I L E 4 2 2 0 FOR 1=1 T O 15 2 3 2 4 2 5 2 3 0 R E A D F I L E 2 , M ( I ) 2 4 0 I F I < 9 T H E N : S ( I ) = M ( I ) 2 5 0 N E X T I 2 6 2 7 2 8 2 6 0 FOR J=1 TO 6 2 7 0 FOR 1=1 TO 5 2 8 0 R E A D F I L E 2 , Y ( I , d ) 2 9 3 0 31 2 9 0 I F i < 5 T H E N : I F d « 3 T H E N : S ( 4*j '+ I+4 ) = Y ( I . J )' 3 0 0 N E X T I 3 1 0 N E X T J 3 2 3 3 3 4 3 2 0 MAT R E A D F I L E 2,'x(3Q,3) 3 3 0 R E S T O R E F I L E 2 3 4 0 Z 8 = 0 3 5 3 6 3 7 3 5 0 FOR 1=1 TO 2 5 3 6 0 FOR 0=1 TO 3 S T E P 2 3 7 0 S ( 2 9 + Z 8 ) = X ( I , u ) 3 8 3 9 4 0 3 8 0 Z 8 = Z 8 + 1 3 9 0 N E X T J 4 0 0 N E X T I 4 1 4 2 4 3 4 10 S (7 '9 ' ) = M( i6) 4 2 0 S ( 8 0 ) = M ( 1 1 ) 4 3 0 P R I N T " 1 * * * * * * * R U N / / « . B B . » * * * * * * * i. 4 4 4 5 4 S 4 4 0 * B'3 i s a n u m e r i c a l s w i t c h ( i . e . B 3 = 0 fb" r s t e p s e a r c h , B 3 = i f o r a l p h a 4 5 0 B 3 = 0 4 G 0 * C a l c u l a t e t w o c o l u m n v e c t o r s ( I . e . V 2 a n d V1 ) s e a r c h ) 4 7 4 8 4 9 4 7 0 FDR U=1 TO 2 4 8 0 C 2 2 = 2 0 4 9 0 FOR L=1 TO N 5 0 5 1 5 2 5 0 0 I F L < C 2 2 T H E N 5 3 0 5 1 0 P R I N T " C 2 2 = " ; C 2 2 , " S = " ; S , " B 4 = " ; B 4 , " B 5 = " ; B 5 5 2 0 C 2 2 = C 2 2 + 2 0 5 3 5 4 5 5 5 3 0 I F 3 ( L ) < = l ' E - 6 T H E N 5 7 6 5 4 0 D = . 1 * B 2 * S ( L ) 5 5 0 R ( 1 ) = S ( L ) 5 6 5 7 5 8 5 6 0 G O S U B 1 2 8 0 5 7 0 0 ( L , 3 - U ) = S ( L ) 5 8 0 N E X T L LO CD L i s t i n g o f D A T A D a t 1 2 : 0 2 : 3 4 o n APR 6 , 1 9 8 3 f o r C C 1 d = U F 0 . P a g e 2 5 9 5 9 0 G O S U B 2 3 3 0 6 0 6 1 6 2 6 0 0 S 1 = S . ! 6 1 0 I F B 4 > 3 T H E N 6 3 0 6 2 0 B 2 = . 5 * B 2 6 3 6 4 6 5 6 3 0 N E X T U 6 4 0 * C o n s t r a i n t h e a l p h a v a l u e s t o o b t a i n p o s t l v e e l e m e n t s o f t h e r e s u l t a n t v e c t o r V g 6 5 0 C 5 = 0 6 6 6 7 6 8 6 6 0 C 6 = 0 6 7 0 W=1 6 8 0 R=1 . 6 9 7 0 7 1 6 9 0 F O R 1=1 T O N 7 0 0 I F ( Q ( I , 2 ) - Q ( I , 1 ) ) < > 0 T H E N 7 3 0 7 1 0 A 2 0 = 1 E 6 7 2 7 3 7 4 7 2 0 G O T O 7 4 0 7 3 0 A 2 0 = Q ( I , 2 ) / ( Q ( I , 2 ) - Q ( I . O ) 7 4 0 I F A 2 0 > 0 T H E N 7 9 0 7 5 7 6 7 7 7 5 0 C 5 = C 5 + 1 7 6 0 E ( C 5 ) = A 2 0 7 7 0 I F E ( C 5 ) > E ( R ) T H E N : R=C5 7 8 7 9 8 0 7 8 0 G O T O 8 2 0 . 7 9 0 C 6 = C 6 + 1 8 0 0 A ( C 6 ) = A 2 0 8 1 8 2 8 3 8 1 0 I F A ( C 6 J < A T W ) THEN: W«C6 8 2 0 N E X T I 8 3 0 A 8 = A ( W ) 8 4 8 5 8 6 8 4 0 A 7 = E ( R ) 8 5 0 I F C 6 = N T H E N : A 7 = - 1 E 4 8 6 0 I F C 5 = N T H E N : A 8 = 1 E 4 8 7 8 8 8 9 8 7 0 B 3 = 1 8 8 0 L=N+1 8 9 0 D = . 1 * B 1 * A 1 9 0 9 1 9 2 9 0 0 R ' ( i ) = A 1 9 1 0 G O S U B 1 2 8 0 9 2 0 A 1 5 = ( A 8 - S ( L ) ) / ( S ( L ) - A 7 ) 9 3 9 4 9 5 9 3 0 I F A 1 5 < 0 T H E N : M 5 = A B S ( A 1 5 ) ' 9 4 0 A 1 = G - L 0 G ( S Q R ( A 1 5 ) ) 9 5 0 G O S U B 3 0 9 0 9 6 9 7 9 8 9 6 0 G O S U B 2 3 3 0 9 7 0 P R I N T " B 5 = " ; B 5 , " S 1 = " ; S 1 , " S = " ; S , " | ( S - S 1 ) / S | = " ; A B S ( ( S - S 1 ) / S ) . " S ( L ) = " ; S ( L ) 9 8 0 * C h e c k C o n v e r g e n c e 9 9 1 0 0 101 9 9 0 I F A B S f ( S - S 1 ) / S ) < 1 E - 5 T H E N 1 0 6 0 1 0 0 0 B 4 = B 4 + 1 1 0 1 0 I F B 4 > 2 T H E N 1 0 4 0 1 0 2 1 0 3 1 0 4 i b 2 0 B i = . 2 5 * B ' l 1 0 3 0 * M a x i m u m 4 V g I t e r a t i o n s a l l o w e d 1 0 4 0 I F B 4 = 4 T H E N 1 0 9 0 • ' • 1 0 5 1 0 6 1 0 7 1 0 5 0 GOTO 450 1 0 6 0 P R I N T 1 0 7 0 P R I N T " C O N V E R G E N C E . " , " O B J E C T I V E F U N C T I O N ' " ; S 1 0 8 1 0 9 1 10 1 0 8 0 G O T O 1 1 1 0 . 1 0 9 0 P R I N T 1 1 0 0 P R I N T "NO C O N V E R . A T " ; B 4 ; " I T E R A T I O N S . O B J . F U N C . = " ; S 111 1 1 2 1 13 1 1 1 0 P R I N T 1 1 2 0 FOR 1=1 TO 15 1 1 3 0 W R I T E F I L E 3 , M 1 ( I ) 1 14 1 15 1 1 6 1 1 4 0 N E X T I 1 1 5 0 FOR J = 1 TO 6 1 1 6 0 FOR 1=1 TO 5 L i s t i n g o f D A T A D a t 1 2 : 0 2 : 3 4 o n A P R 6 , 1 9 8 3 f o r CC-1d=4l£0, i P a g e 3 1 1 7 1 1 7 0 W R I T E F I L E 3 , Y 1 ( I , d ) 1 18 1 1 9 1 2 0 1 1 8 0 1 1 9 0 1 2 0 0 N E X T I N E X T J MAT W R I T E F I L E 3 . X 1 121 122 1 2 3 1 2 1 0 1 2 2 0 1 2 3 0 * S a v e t h e a d j u s t e d d a t a f i l e B 7 = C M D ( " % S A V E @ N E @ T 0 U T 1 7 2 @ 0 " ) R E S T O R E F I L E 3 1 2 4 1 2 5 12G 1 2 4 0 1 2 5 0 1 2 5 2 P R I N T " A 1 = " ; A 1 , " B 1 = " ; B1 , . "B2= " ; B 2 , " B 4 = " ; B 4 , " B 5 = " ; B 5 P R I N T " 1 C A L L P R I N T 1 1 2 7 1 2 8 1 2 9 1 2 5 4 1 2 6 0 1 2 7 0 C A L L A F O R M S T O P * S u b r o u t i n e f o r s t e p s e a r c h a n d a l p h a s e a r c h ( I . e . T h e C o g g l n r o u t i n e ) 1 3 0 131 1 3 2 1 2 8 0 1 2 9 0 1 3 0 0 C 2 0 = 0 C=1 I F B 3 = 1 T H E N 1 3 3 0 1 3 3 1 3 4 1 3 5 1 3 1 0 1 3 2 0 1 3 3 0 S('L')=R'(C)' GOTO 1 3 7 0 A 1 6 = R ( C ) - 6 136 1 3 7 1 3 8 1 3 4 0 1 3 5 0 1 3 6 0 I F A 1 6 > 1 6 9 T H E N : A 1 6 = 1 6 9 S ( L ) = A 7 + ( A 8 - A 7 ) * E X P ( A 1 6 ) / ( E X P ( A 1 6 ) + E X P ( - A 1 6 ) ) I F ( A 8 - S ( L ) ) < 1 E - 6 T H E N 3 1 4 0 1 3 9 1 4 0 141 1 3 7 0 1 3 8 0 1 3 9 0 I F R(C)<=6 T H E N 15 4 0 I F B 3 = 0 T H E N 1 4 0 0 G O S U B 3 0 9 0 1 4 2 1 4 3 144 . 1 4 0 0 1 4 1 0 1 4 2 0 G O S U B 2 3 3 0 V ( C ) = S I F C=1 T H E N 2 2 7 0 1 4 5 146 1 4 7 1 4 3 0 1 4 4 0 1 4 5 0 I F V'(c)< = V ( C - i ) T H E N 2 2 7 0 I F C > 2 T H E N 1 7 2 0 * R e v e r s e t h e d i r e c t i o n o f s t e p s e a r c h o r a l p h a s e a r c h 1 4 8 . 1 4 9 1 5 0 1 4 6 0 1 4 7 0 1 4 8 0 T 5 = R ( 2 ) R ( 2 ) = R ( 1 ) R ( 1 ) = T 5 151 152 1 5 3 1 4 9 0 1 5 0 0 1 5 1 0 t 6 = V" (2) V ( 2 ) = V ( 1 ) V ( 1 ) = T 6 154 1 5 5 1 5 6 1 5 2 0 1 5 3 0 1 5 4 0 D = - D / 2 G O T O 2 2 7 0 R ( C ) = R ( C - 1 ) / 1 0 1 5 7 158 1 5 9 1 5 5 0 1 5 6 0 1 5 7 0 I F B 3 = 0 T H E N 1 6 1 0 A 1 6 = R ( C ) - 6 I F A 1 6 > 1 6 9 T H E N : A 1 6 = 1 6 9 1 6 0 161 162 1 5 8 0 1 5 9 0 1 6 0 0 S CC) =A"7+'( A 8 - A 7 ) * E X P (A 16)71EXP ( A 16 ) + E X p ( - A 1 6 l ) G O S U B 3 0 9 0 G O T O 1 6 2 0 ' . 1 6 3 164 1 6 5 1 6 1 0 1 6 2 0 1 6 3 0 STQ=R (C) G O S U B 2 3 3 0 V ( C ) = S 1G6 1 6 7 168 1 6 4 0 1 6 5 0 1 6 6 0 I F V(c)>vTc'-i)' T H E N 1 7 2 0 I F R ( C ) < 1 E - 4 T H E N 2 3 1 0 R ( C - 2 ) = R ( C - 1 ) 1 6 9 1 7 0 171 1 6 7 0 V ( C - 2 ) = V ( C - 1 ) 1 6 8 0 R ( C - 1 ) = R ( C ) . • • 1 6 9 0 V ( C - 1 ) = V ( C ) -172 1 7 3 174 1 7 0 0 1 7 1 0 1 7 2 0 GOTO 1 5 4 0 * R e p e t i t i v e q u a d r a t i c f i t t i n g r o u t i n e f o r b o t h s t e p s e a r c h a n d a l p h a s e a r c h FOR J = C - 2 TO C L i s t i n g o f D A T A D a t 1 2 : 0 2 : 3 4 o n APR 6 , 1 9 8 3 f o r C C 1 d = U F 0 . P a g e 4 1 7 5 1 7 3 0 I F B 3 = 0 T H E N 1 7 8 0 1 7 6 1 7 7 1 7 8 1 7 4 0 1 7 5 0 1 7 6 0 A i ' 6 = R ( ' J ' ) - 6 I F A 1 6 > 1 6 9 T H E N : A 1 6 = 1 6 9 T ( d ) = A 7 + ( A 8 - A 7 ) * E X P ( A 1 6 ; / ( E X P ( A 1 6 ) + E X P ( - A 1 S , ) ) 1 7 9 1 8 0 181 1 7 7 0 1 7 8 0 1 7 9 0 G O T O 1 7 9 0 T ( J ) = R ( J ) N E X T J 1 8 2 1 8 3 1 8 4 1 8 0 0 1 8 1 0 1 8 2 0 D i = ( T ( ' c - l ) - f ' ( C ) j * r v ' ( C - 2 J - V ( C J y - ( f D 2 = ( V ( C - 2 ) - V ( C ) ) * ( T ( C - 1 ) * * 2 - T ( C ) * * 2 ) - ( V ( C - 1 ) - V ( C ) ) * ( T ( C - 2 ) * * 2 - T ( C ) * * 2 ) I F D 1 = 0 T H E N 1 8 4 0 1 8 5 1 8 6 1 8 7 1 8 3 0 1 8 4 0 1 8 5 0 G O T O 1 8 9 0 I F 0 2 0 = 0 T H E N 1 8 7 0 S ( L ) = S 4 1 8 8 1 8 9 1 9 0 1 8 6 0 1 8 7 0 1 8 8 0 G O T O 2 3 1 0 S ( L ) = T ( C - 1 ) G O T O 2 3 1 0 191 1 9 2 1 9 3 1 8 9 0 1 9 0 0 19 10 S(L)=D27 ' (2*D' i ) ' I F B 3 = 0 T H E N 1 9 2 0 G O S U B 3 0 9 0 1 9 4 1 9 5 1 9 6 1 9 2 0 1 9 3 0 1 9 4 0 G O S U B 2 3 3 0 F O R K = C - 2 TO C I F A B S ( S ( L ) - T ( K ) ) < 1 E - 4 T H E N 2 3 1 0 1 9 7 1 9 8 1 9 9 1 9 5 0 1 9 6 0 1 9 7 0 N E X T K V ( C + 1 ) = S I F V ( C + 1 ) > V ( C - 1 ) T H E N 2 1 1 0 200 2 0 1 202 1 9 8 0 1 9 9 0 2 0 0 0 I F S ' ( L ) < f ( C ' - l ) T H E N 2 0 6 0 I F S ( L ) < T ( C ) T H E N 2 0 3 0 T ( C ) = T ( C - 1 ) 2 0 3 2 0 4 2 0 5 2 0 1 0 2 0 2 0 2 0 3 0 V ( C ) = V ( C - 1 ) G O T O 2 0 8 0 T ( C - 2 ) = T ( C - 1 ) . 2 0 6 2 0 7 2 0 8 ' 2 0 4 0 2 0 5 0 2 0 6 0 V ( C - 2 ) = V ( C - i ) ' G O T O 2 0 8 0 I F S ( L ) > T ( C ) T H E N 2 0 3 0 2 0 9 2 1 0 21 1 2 0 7 0 2 0 8 0 2 0 9 0 G O T O 2000 T ( C - 1 ) = S ( L ) V ( C - 1 ) = V ( C + 1 ) 2 1 2 2 1 3 2 1 4 2 1 0 0 2 1 1 0 2 1 2 0 G O T O 2 2 3 0 I F S ( L ) > T ( C - 1 ) T H E N 2 2 1 0 I F S ( L ) > T ( C ) T H E N 2 1 6 0 2 1 5 2 1 6 2 1 7 2 1 3 0 2 1 4 0 2 1 5 0 Y ( C ' - 2 ) = S ( L ) ' V ( C - 2 ) = V ( C + 1 ) G O T O 2 1 8 0 2 1 0 2 1 9 2 2 0 2 1 6 0 2 1 7 0 2 1 8 0 " t C c 7 - s T U V ( C ) = V ( C + 1 ) S 4 = T ( C - 1 ) . , 2 2 1 2 2 2 2 2 3 2 1 9 0 2 2 0 0 2 2 1 0 s ( L ) = t ( c - i ) G O T O 2 2 4 0 I F S ( L ) > T ( C ) T H E N 2 1 3 0 2 2 4 2 2 5 2 2 6 2 2 2 0 2 2 3 0 2 2 4 0 G O T O 2 1 6 0 S 4 = S ( L ) 0 2 0 = 0 2 0 + 1 2 2 7 2 2 8 2 2 9 2 2 5 0 2 2 6 0 2 2 7 0 I F C 2 0 > 5 0 T H E N 2 3 1 0 G O T O 1 8 0 0 C = C+1 2 3 0 2 3 1 2 3 2 2 2 8 0 2 2 9 0 2 3 0 0 R ( c ' } = R ' ( C - i ) + D D = 2*D G O T O 1 3 0 0 L 1 s t 1 n g o f D A T A D a t 1 2 : 0 2 : 3 4 o n A P R 6 , 1 9 8 3 f o r C C 1 d = U F 0 . P a g e 5 2 3 3 2 3 1 0 R E T U R N 2 3 4 2 3 5 2 3 S 2 3 2 0 2 3 3 0 2 3 4 0 * S u b r o u t i n e f o r O b j e c t i v e F u n c t i o n c a l c u l a t i o n Z 1 =0 Z 2 = 0 2 3 7 2 3 3 2 3 9 2 3 5 0 2 3 6 0 2 3 7 0 FOR 0=1 T O 8 M 1 ( d ) = S ( d ) Z 1 = Z 1 + M 1 ( 0 ) 2 4 0 2 4 1 2 4 2 2 3 8 0 I F 0>4 T H E N : Z 2 = Z 2 + M 1 ( 0 ) 2 3 9 0 N E X T 0 2 4 0 0 M 1 ( 9 ) = W 1 + W 2 - Z 1 2 4 3 2 4 4 2 4 5 24 10 2 4 2 0 2 4 3 0 M 1 ( 1 6 ) = M 1 ( 9 ) + Z 2 FOR 0=1 T O 5 FOR 1=1 TO 4 2 4 6 2 4 7 2 4 8 2 4 4 0 2 4 5 0 2 4 6 0 Y 1 ( i , J ) = S ( 4 * 0 + i + 4 ) N E X T I N E X T 0 2 4 9 2 5 0 2 5 1 2 4 7 0 2 4 8 0 2 4 9 0 FOR 1=1 TO 4 Y 1 ( I , 6 ) = ( M 1 ( 5 ) * Y 1 ( I , 1 ) + M 1 ( 6 ) * Y 1 ( I , 2 ) + M 1 ( 7 ) * Y 1 ( I , 3 ) + M 1 ( 8 ) * Y 1 ( I . 4 ) + M 1 ( 9 ) * Y 1 ( I . S ) ) / M 1 ( 1 6 ) N E X T I 2 5 2 2 5 3 2 5 4 2 5 0 0 2 5 1 0 2 5 2 0 FOR 0=1 T O 6 Z 3 = 0 FOR 1=1 TO 4 2 5 5 2 5 S 2 5 7 2 5 3 0 2 5 4 0 2 5 5 0 Z 3 = Z3+"Y"i ' ( l , 'o)' N E X T I Y 1 ( 5 , d ) = 1 0 0 - Z 3 2 5 8 2 5 9 2 6 0 2 5 6 0 2 5 7 0 2 5 8 0 N E X T 0 Z 4 = 0 FOR K=1 T O 5 2 G 1 2 6 2 2 6 3 2 5 9 0 2 6 0 0 2 6 1 0 FOR 1=1 TO 5 Z 5 = 0 FOR 0=1 TO 3 S T E P 2 2 6 4 2 6 5 2 6 6 2 6 2 0 2 S 3 0 2 S 4 0 x H i + 5 * k - 5 , 0 ) ' = S ( 2 9 + Z 4 ) ' Z 5 = Z 5 + X 1 ( I + 5 * K - 5 , 0 ) Z 4 = Z 4 + 1 2 6 7 2 6 8 2 6 9 2 6 5 0 ' 2 6 6 0 2 6 7 0 N E X T 0 X 1 ( I + 5 * K - 5 , 2 ) = 1 0 0 - Z 5 N E X T I 2 7 0 2 7 1 2 7 2 2 6 8 0 2 6 9 0 2 7 0 0 N E X T K FOR 1=1 TO 5 • Z 6 = 0 2 7 3 2 7 4 2 7 5 2 7 1 0 2 7 2 0 2 7 3 0 FOR 0 * 1 T O 3 S T E P 2 X 1 ( I + 2 5 , 0 ) = M 1 ( 5 ) * Y 1 ( I , 1 ) * X 1 ( I , 0 ) + M 1 ( 6 ) * Y 1 ( I , 2 ) * X 1 ( I + 5 , 0 ) + M 1 ( 7 ) * Y 1 ( I , 3 ) * X 1 ( I + 1 0 , 0 ) X1 (1 + 2 5 , 0 ) = ( X 1 ( I + 2 5 , d ) + M 1 ( 8 ) * Y 1 ( 1 , 4 ) *X1(1+15 , 0 ) + M 1 (9 )*Y 1 ( 1 , 5 ) * X 1 ( 1 + 2 0 , 0 ) ) / ( M 1 ( 1 6 ) * Y 1 (1 , 6 ) ) 2 7 5 2 7 7 2 7 8 2 7 4 0 2 7 5 0 2 7 6 0 Z6' = Z S + X i ( i + 2 5 , 0 l N E X T 0 X 1 ( I + 2 5 , 2 ) = 1 0 0 - Z 6 2 7 9 2 8 0 2 8 1 2 7 7 0 2 7 8 0 2 7 9 0 N E X T I M 1 ( 1 0 ) = S ( 7 9 ) M 1 ( 1 1 ) = S ( 8 0 ) 2 8 2 2 8 3 2 8 4 2 8 0 0 M 1 ( 1 7 ) = W 1 - M 1 ( 1 ) - M 1 ( 3 ) 2 8 1 0 M 1 ( 1 8 ) = W 2 - M 1 ( 2 ) - M 1 ( 4 ) 2 8 2 0 FOR 0=1 T O 3 S T E P 2 2 8 5 2 8 6 2 8 7 2 8 3 0 2 8 4 0 2 8 5 0 Z 7 = 0 FOR 1=1 T O 5 Z 7 = Z 7 + X 1 ( 2 5 + 1 , 0 ) * Y 1 ( I , 6 ) / 1 0 0 2 8 8 2 8 9 2 9 0 2 8 6 0 2 8 7 0 2 8 8 0 N E X T I I F 0=1 T H E N : M 1 ( 1 2 ) = ( M 1 ( 1 6 ) * Z 7 - M 1 ( 1 8 ) * M 1 ( 1 0 ) ) / M 1 ( 1 7 ) I F 0 = 3 T H E N : M 1 ( 1 3 ) = ( M 1 ( 1 6 ) + Z 7 - M 1 ( 1 8 ) * M 1 ( 1 1 ) ) / M 1 ( 1 7 ) L i s t i n g o f D A T A D a t 1 2 : 0 2 : 3 4 o n A P R 6, 1 9 8 3 f o r C C 1 O U F 0 . P a g e 6 2 9 1 2 8 9 0 N E X T d 2 9 2 2 9 3 2 9 4 2 9 0 0 2 9 1 0 2 9 2 0 MI ( i 4 ) = i 6o - M 1 ( i d j -MI ( i i j M 1 ( 1 5 ) = 1 0 0 - M 1 ( 1 2 ) - M 1 ( 1 3 ) S = 0 2 9 5 2 9 6 2 9 7 2 9 3 0 2 9 4 0 2 9 5 0 FOR 1=1 TO 15 S = S + W ( I ) * W 1 ( I ) * ( M ( I ) - M 1 ( I ) ) * * 2 . N E X T I 2 9 8 2 9 9 3 0 0 2 9 6 0 2 9 7 0 2 9 8 0 FOR u=1 TO 6 FOR 1=1 TO 5 S = S+W (5*d+10+1) *W 1 ( 5 * d + 1 0+1) * ( Y ( I , d ) - Y 1 ( I , d ) ) * * 2 3 0 1 3 0 2 3 0 3 2 9 9 0 3 0 0 0 3 0 1 0 N E X T I N E X T d FOR 1=1 TO 3 0 3 0 4 3 0 5 3 0 6 3 0 2 0 3 0 3 0 3 0 4 0 FOR d=1 TO 3 S = S + W ( 3 * I + 4 2 + d ) * W 1 ( 3 * I + 4 2 + d ) * ( X ( I , d ) - X 1 ( I , d ) ) * * 2 N E X T d 3 0 7 3 0 8 3 0 9 3 0 5 0 3 0 6 0 3 0 7 0 N E X T I B 5 = B 5 + 1 R E T U R N 3 1 0 3 1 1 3 1 2 3 0 8 0 3 0 9 0 3 1 0 0 * S u b r o u t i n e f o r V g c a l c u l a t i o n FOR 1=1 TO N S ( I ) = 0 ( I , 2 ) + S ( L ) * ( 0 ( I . 1 ) - 0 ( I , 2 ) ) 3 1 3 3 1 4 3 1 5 31 10 3 1 2 0 3 1 3 0 N E X T I R E T U R N . * C h e c k I f O . F . o f V g < O . F . o f V1 1n t h e u M v a M a b l e s e a r c h r o u t i n e 3 1 6 3 17 3 1 8 3 1 4 0 3 1 5 0 3 1 6 0 G O S U B 3 0 9 0 G O S U B 2 3 3 0 I F S < S1 T H E N 2 3 1 0 3 1 9 3 1 7 0 G O T O 1 3 7 0 3 2 0 E n d - 0 f - F 1 l e L i s t i n g o f PR I NT 1 a t 1 4 : 0 5 : 0 2 o n APR 5 , i a t J 3 t o r < j ( j i a = u r u . 1 10.P!M..M.(.1^ 2 2 0 F I L E R 0 F L 1 7 2 , 0 U T 1 7 2 , W T F A C , R E F A C 3 2 5 F I L E L A B E L 4 3 0 A A = " 1 7 2 " 5 5 0 FOR 1=1 TO 1 3 5 6 6 0 R E A D F I L E 3 , W ( I ) 7 7 0 R E A D F I L E 4 , W 1 ( I ) . 3 8 0 N E X T I 9 1 0 9 0 B 9 = C M D ( " % S E T L I N E L E N = 1 3 2 " ) 9 5 B 8 = C M D ( " % S E T C W D = 1 8 " ) 1 1 12 1 0 0 1 10 S = 0 P R I N T " 1 * * * * * * * * * RUN/y " ; A A ; " * * * * * * * * * * * " 13 1 2 0 P R I N T " - D A T A P O I N T " , " M E A S U R E D " , " A D d U S T E D " , " / ^ D I F F E R E N C E " , " W T . * R E L . " , " R E L . F A C T O R " , " C U M U L A T I V E S " 14 1 3 0 15 . 1 4 0 FOR 1=1 T O 15 16 1 5 0 R E A D F I L E 1 , M ( I ) 17 1 6 0 R E A D F I L E 2 , M 1 ( i ) 18 1 7 0 R E A D F I L E 5 . L L ( I ) 19 1 8 0 S-=S + W( I ) * W 1 ( I ) * ( M ( I ) - M 1 ( I ) )**2 2 0 1 9 0 I F i < 1 0 T H E N : M i ( I ) = I N T ( M i ( i j * 16+6.5 j 716 2 1 2 2 2 0 0 2 10 I F I>9 T H E N : M 1 ( I ) = I N T ( M 1 ( I ) * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 P R I N T L L ( I ) , M ( I ) , M 1 ( I ) , ( ( M ( I ) - M 1 ( I ) ) / M ( I ) ) * 1 0 0 , W ( I ) * W 1 ( I ) , W 1 ( I ) , S 2 3 2 2 0 N E X T I 2 4 2 3 0 R E S T O R E F I L E 5 2 5 2 4 0 FOR d=1 TO 6 2 6 2 5 0 FOR 1=1 TO 5 2 7 2 6 0 R E A D F I L E 1 , Y ( I , d ) 2 8 2 7 0 R E A D F I L E 2 , Y 1 ( I , d ) 2 9 3 0 3 1 2 8 0 2 9 0 3 0 0 s=s+w'(5*d+ i o + i ) * w i ('5*0+ i o + i )*( Y ' ( i , d ) - Y i ( i , d ) j * * 2 Y 1 ( I , d ) = I N T ( Y 1 ( I , d ) * 1 0 0 + 0 . 5 ) / l O O P R I N T " Y ( " ; I ; " , " ; 0 ; " ) " , Y ( I , 0 ) . Y 1 ( I , 0 ) , ( ( Y ( I , 0 ) - Y 1 ( I , 0 ) ) / Y ( I , 0 ) ) * 1 0 0 , W ( 5 * 0 + 1 0 + 1 ) * W 1 ( 5 * 0 + 1 0 + 1 ) , W1 ( 5 * d + 1 0 + I ) , S 3 2 3 1 0 N E X T I 3 3 3 2 0 N E X T 0 34 3 3 0 FOR 1=1 TO 3 0 3 5 3 4 0 FOR 0=1 TO 3 3 6 3 5 0 R E A D F I L E 1 , X ( I , d ) ~ 3 7 3 6 0 R E A D F I L E 2 , X 1 ( l , d ) 3 8 3 9 4 0 3 7 0 S = S + W ( 3 * I + 4 2 + d ) * W 1 ( 3 * I + 4 2 + d ) * ( X ( I . d ) - X 1 ( I , d ) ) * * 2 3 8 0 X 1 ( I , d ) = I N T ( X 1 ( I , d ) * 1 0 0 0 + 0 . 5 ) / l 0 0 0 3 9 0 P R I N T " X ( " ; I ; " , " ; J ; " ) " , X ( I , d ) , X 1 ( I , d ) , ( ( X ( I . d ) - X 1 ( I , d ) ) / X ( I , d ) ) * 1 0 0 , W ( 3 * 1 + 4 2 + J ) * W 1 ( 3 * I + 4 2 + d ) , W1 ( 3 * I + 4 2 + d ) , S 4 1 4 0 0 N E X T 0 4 2 4 1 0 N E X T I 4 3 4 1 5 P R I N T " 1 N E X T RUN 0 4 4 4 2 0 R E T U R N 4 5 E n d - O f - F l l e * * * * * * * * * R U N # 1 7 2 * * * * * * * * * * * output from PRINT1 D X T T T U T N T M E A S U R E D ' A D O U ' S T E D ' • • ^ ' ' y . ' D I F F E R E N C E ' ' W T V " ' * " " R E L . " . ' R E L . F A C T O R C U M U L A T I V E " " S " L f Cam ) 2 3 9 . 8 2 3 4 . 8 2 . 0 8 5 0 7 1 0 . 2 5 5 7 3 3 1 E - 2 1 0 . 6 4 5 9 2 2 E - 1 L c (gm) 9 6 . 7 9 9 . 3 - 2 . 6 8 8 7 2 8 0 . 8 8 4 0 5 4 7 E - 2 1 0 . 1 2 3 5 6 2 6 Wa (gm) 4 1 . 8 4 1 . 8 0 . 8 4 9 9 3 1 5 E - 1 4 1 5 . 3 3 7 8 2 1 0 0 0 . 1 2 3 5 8 5 Wb (gm ) 2 8 . 1 2 8 . 1 0 . 1 2 6 4 3 1 1 E - 1 3 6 7 . 4 2 3 3 1 1 0 0 0 . 1 2 3 5 9 2 8 C 1 (gm) 2 7 0 . 5 2 7 2 . 1 - 0 . 5 9 1 4 9 7 2 0 . 2 9 9 0 5 7 4 1 0 0 0 . 9 2 9 8 0 2 4 C 2 (gm) 1 0 7 . 9 1 0 9 . 9 - 1 . 8 5 3 5 6 8 0 . 2 0 5 5 1 2 2 100 - ' 1 . 7 2 4 9 4 7 0 3 (gm ) 1 2 1 . 4 1 2 2 . 1 - 0 . 5 7 6 6 0 6 3 0 . 5 1 5 9 2 4 9 1 0 0 1 . 9 5 9 4 5 9 C 4 (gm) 1 0 2 . 7 1 0 5 . 4 - 2 . 6 2 9 0 1 7 0 . 1 3 9 5 5 9 1 1 0 0 2 . 9 5 7 1 2 1 T a l l (gm) 1 0 0 0 . 5 9 9 8 . 1 0 . 2 3 9 8 8 0 1 0 . 1 1 1 2 8 0 2 1 0 0 3 . 6 0 5 0 0 4 b 1 ( % K c l ) 4 4 . 4 9 7 4 3 . 9 9 3 1 . 1 3 2 6 6 1 5 . 1 2 9 7 9 2 2 0 4 . 9 0 S S 5 7 b 3 ( % i n s o i ) " 1 . 1 1 . 1 1 - 0 . 9 0 9 0 9 0 9 2 8 7 0 . 1 2 6 2 0 5 . 1 8 8 8 6 8 a 1 ( % K c l ) 3 9 . 5 1 9 3 8 . 0 5 7 3 . 6 9 9 4 8 6 2 . 6 5 8 5 1 4 2 0 1 0 . 8 6 9 8 2 a 3 ( ' / . I n s o l ) 0 . 9 3 0 . 9 6 - 3 . 2 2 5 8 0 6 1 4 6 6 . 9 9 3 2 0 1 2 . 2 2 6 2 9 b 2 (•/.Nacl')' 5 4 . 4 0 3 5 4 . 8 9 7 - 0 . 9 0 8 0 3 8 2 • 4 . 9 1 5 1 2 6 2 0 1 3 . 4 2 4 8 4 a 2 ( c / .Nac l ) 5 9 . 5 5 1 6 0 . 9 8 2 - 2 . 4 0 2 9 8 2 , 2 . 7 5 4 1 2 0 1 9 . 0 6 7 7 3 Y( 1 , .1 ) 1 . 7 8 1 . 8 2 - 2 . 2 4 7 1 9 1 ' 2 8 7 . 5 6 9 8 2 0 1 9 . 6 2 7 1 8 Y'( 2 , 1) 1 1 . 2 1 1 . 2 6 - 0 . 5 3 5 7 1 4 3 5 . 9 2 3 7 4 4 2 0 1 9 . 6 5 1 8 5 Y( 3 , 1 ) 3 7 . 9 1 3 7 . 6 8 0 . 6 0 6 7 0 0 1 3 . 9 1 4 9 7 4 2 0 1 9 . 8 6 2 5 3 Y( 4 , 1 ) 3 3 . 2 4 3 3 . 16 0 . 2 4 0 6 7 3 9 3 . 2 3 3 8 2 0 1 9 . 8 8 1 1 8 Y( 5 , 1) 1 5 . 8 7 1 G . 0 7 - 1 . 2 6 0 2 3 9 4 . 7 0 3 6 3 2 2 0 2 0 . 0 6 7 9 3 Y( 1 , 2 ) 0 . 3 5 0 . 4 1 - 1 7 . 1 4 2 8 6 8 6 . 3 0 9 8 2 2 0 2 0 . 3 5 1 5 Y( 2 , 2 ) 7 . 6 9 7 . 7 2 - 0 . 3 9 0 1 1 7 2 . 4 2 8 3 8 4 2 0 2 0 . 3 5 3 8 1 Y'( 3 , 2 ) 4 0 . 3 2 4 0 . 2 3 0 . 2 2 3 2 1 4 3 4 . 9 4 8 8 5 2 2 0 2 0 . 3 9 5 9 3 Y( 4 , 2 ) 3 4 . 12 3 4 . 0 7 0 . 1 4 6 5 4 1 6 4 . 3 3 2 7 3 8 '• 2 0 2 0 . 4 0 4 91 Y( 5 , 2 ) 1 7 . 5 2 1 7 . 5 7 - 0 . 2 8 5 3 8 8 1 5 . 1 7 2 9 2 8 2 0 2 0 . 4 1 7 6 4 T(— 3 ) 0 . 8 7 0 . 9 5 - 9 . 1 9 5 4 0 2 7 5 . 3 0 8 7 6 2 0 2 0 . 8 5 6 6 5 Y( 2 . 3 ) 1 6 . 4 5 1 6 . 6 2 - 1 . 0 3 3 4 3 5 1 . 0 7 1 9 9 8 2 0 2 0 . 8 8 9 3 3 Y( 3 , 3 ) 4 4 . 3 2 4 4 . 1 8 0 . 3 1 5 8 8 4 5 3 . 0 2 2 4 2 2 2 0 2 0 . 9 4 7 4 5 Y ( 4 , 3 ) 2 4 . 8 8 2 4 . 7 7 0 . 4 4 2 1 2 2 2 2 . 2 0 1 2 0 6 2 0 2 0 . 9 7 5 9 5 Y( 5 . 3 ) 1 3 . 4 8 1 3 . 4 8 0 7 . 9 3 1 0 0 6 , 2 0 2 0 . 9 7 5 9 7 Y( 1 . 4 ) 1 . 5 6 1 . 8 2 - 1 6 . 6 6 6 6 7 1 9 . 8 5 1 4 8 2 0 2 2 . 3 3 5 0 5 Y( 2 . 4 ) " 3 0 . 5 7 3 1 . 3 1 ' - 2 . 4 2 0 6 7 4 0 . 2 1 0 1 8 8 6 2 0 2 2 . 4 4 9 3 5 Y( 3 , 4 ) 4 0 . 9 4 0 . 5 3 0 . 9 0 4 6 4 5 5 . 1 . 0 7 1 4 5 4 2 0 2 2 . 5 9 9 9 9 Y( 4 , 4 ) 1 G . 4 6 1 6 . 0 3 2 . 6 1 2 3 9 4 0 . 8 1 2 5 6 5 2 2 0 2 2 . 7 5 1 7 4 y'( 5 , 4 ) 1 0 . 5 2 1 0 . 3 2 1 . 9 0 1 1 4 1 0 . 9 3 9 0 6 3 2 0 2 2 . 7 9 0 0 5 Y( 1 . 5 ) 1 3 . 4 1 1 3 . 7 5 - 2 . 5 3 5 4 2 1 2 . 9 6 4 6 6 2 2 0 2 3 . 1 3 3 7 3 Y( 2 , 5 ) 2 5 . 0 8 2 5 . 4 - 1 . 2 7 5 9 1 7 7 . 8 8 1 5 6 6 2 0 2 3 . 9 4 8 1 3 Y'( 3 , 3 0 . 6 9 3 0 . 6 6 . 2 9 3 2 5 5 1 7 . 2 0 9 2 0 4 2 0 2 4 . 0 0 1 8 2 Y( 4 , 5 ) 2 1 . 9 9 2 1 .77 1 . 0 0 0 4 5 5 2 5 . 8 2 4 7 2 2 0 2 5 . 2 5 7 3 1 Y( 5 , 5 ) 8 . 8 3 8 . 4 7 4 . 0 7 7 0 1 2 5 . 7 8 3 4 4 2 0 2 8 . 5 0 9 1 8 •T(— " 6 ) ' 1 3 . 2 4 9 . 0 7 3 1 . 4 9 5 4 7 0 . 5 7 9 2 4 3 2 2 3 8 . 6 0 4 4 4 Y( 2 , 6 ) 2 1 . 6 4 2 1 . 5 2 . 0 . 5 5 4 5 2 8 7 1 . 6 3 2 0 3 1 2 3 8 . 6 2 7 7 6 Y( 3 , 6 ) 3 1 . 8 4 3 4 . 14 - 7 . 2 2 3 6 1 8 2 . 1 7 1 5 5 2 2 ' ' 5 0 . 1 1 9 9 6 Y( 4 . "e") 2 3 . 19 2 4 . 3 9 - 5 . 1 7 4 6 4 4 6 . 3 2 9 2 1 2 5 9 . 2 4 4 3 6 Y( 5 , 6 ) 1 0 . 0 9 1 0 . 8 8 - 7 . 8 2 9 5 3 4 7 . 7 2 4 2 8 2 6 4 . 1 0 3 2 3 X ( 1 . 1 ) 9 3 . 3 5 9 9 3 . 4 2 5 - O . 7 0 6 9 4 8 4 E - 1 2 . 8 8 7 9 7 4 2 0 6 4 . 1 1 5 7 7 x'( i , 2 ) : 6 . 1 2 1 6 . 0 5 5 . L 6 7 8 2 5 5 2 . 8 7 0 2 2 0 6 4 . 1 2 8 2 6 X ( 1, 3 ) 0 . 5 2 0 . 5 2 . 0 . 2 6 6 8 8 0 5 E - 1 4 1 2 0 6 0 . 3 2 0 6 4 . 1 2 8 3 5 X ( 2 , D 9 4 . 7 9 3 9 4 . 7 9 4 - 0 . 1 0 5 4 9 3 E - 2 1 4 3 . 2 0 3 1 2 0 6 4 . 1 2 8 4 3 X'( ' 2 , " 2 ) ' 4 . 8 1 7 4 . 8 1 6 0 . 2 0 7 5 9 8 1 E - 1 1 3 5 . 5 3 8 7 2 0 6 4 . 1 2 8 4 8 X ( 2 . 3 ) 0 . 3 9 0 . 3 9 0 1 8 7 5 0 2 0 6 4 . 1 2 8 6 2 X ( 3 , 1 ) 9 3 . 6 7 9 9 3 . 6 8 1 - 0 . 2 1 3 4 9 5 E - 2 9 4 . 7 3 6 6 6 2 0 6 4 . 1 2 8 8 6 X ( 3 , "2> 5 . 9 2 1 5 . 9 2 0 . 1 6 8 8 9 0 4 E - 1 9 8 . 4 1 3 4 8 2 0 6 4 . 1 2 8 9 8 X ( 3 , 3 ) 0 . 4 0 . 4 0 2 9 7 0 2 . 9 8 2 0 6 4 . 1 3 5 9 3 X ( 4 , 1 ) 9 1 . 9 0 3 9 1 . 9 1 6 - 0 . 1 4 1 4 5 3 5 E - 1 4 0 . 9 1 5 3 2 0 6 4 . 1 4 2 5 7 XC 4 , 2) 7 .627 7.615 0.1573358 41 .2863 20 64.14891 X( 4 , 3) 0 .47 0 .47 0 .2952721E-14 17416.55 20 64.15104 X( 5....1) 88 .805 8 8 . 8 3 - 0 . 2 8 1 5 1 5 7 E - 1 17.78529 20 64 . 16208 XC 5 , 2) 10.135 10.111 . 0.2368032 19.97758 20 64.17318 X( 5 . 3) 1 .06 1.059 0 .9433962E-1 1985.112 20 \s 64 . 17677 X( 6, 1) 92 .676 92.678 - 0 . 2 1 5 8 0 5 6 E - 2 7.40047 20 64.17681 X( 6 , 2) 6 .924 6 .922 0 .2888504E-1 7.27272 20 64 . 17685 X( G, 3) 0 . 4 0 . 4 0 13172.34 20 64.17685 X( 7 . 1) 94.884 94.884 0 .3744271E-14 104.7461 20 64.17685 X( 7 . 2) 4 .716 4.716 0 100.0605 20 64.17686 ' X( 7 . 3) 0 . 4 0 . 4 0 33707.86 20 64.17687 X( 8 , . 1) 93.328 93 .329 - 0 . 1 0 7 1 4 9 E - 2 56.73998 20 64.17694 X( 8 , 2) 6 .222 6.221 0 .16072E -1 58 .68154 20 64 . 17698 X( 8 , 3 ) . 0 . 4 5 0 . 4 5 0 21621.62 20 64.17875 X( 9 , 1) 90 .408 90 .422 -0 .154853GE-1 14.67671 20 64.1810 X( 9 , 2) 9 . 132 9.118 0.1533071 15.22503 20 64.18489 X( 9 , 3) 0 . 4 6 0 . 4 6 0 .301691E-14 19480.52 20 64.18522 I X( 10. 1) 87 .069 87.084 - 0 . 1 7 2 2 7 7 2 E - 1 13.92853 20 64.18816 XC 10, 2) 1 1.841 11.828 0.109788 15.09763 20 64.19084 X( 10, 3) 1 .09 1 .089 0 .9174312E-1 958.39 20 64.1S227 X( 11, 1) 9 3 . 7 2 93.724 . - 0 . 4 2 6 8 0 3 2 E - 2 11.68001 20 64 . 19243 x'( i i , 2) 5 .72 5.716 0 .6993007E-1 12.17994 20 64.1926 X( 11, 3) 0 . 5 6 0 . 5 6 0 14796.55 20 64.1926 I X( 12, 1) 94 .633 94.634 - 0 . 1 0 5 6 7 1 4 E - 2 96.01892 20 64.19164 X( 12. 2) 4 .917 4.916 0 .203376E-1 99.02G52 20 64.19268 X( 12. 3) 0 . 4 5 0 . 4 5 0 79470.2 20 64.1927 X( 13. 1) 90 .338 90.341 - 0 . 3 3 2 0 8 6 2 E - 2 22.04464 20 64.19292 X'( 13. 2) 9 . 132 9 . 129 0.3285151E-1 22.55666 20 64 . 19312 X( 13, 3) 0 . 5 3 0 . 5 3 0 36253.78 20 64.19469 2.621422 64.20594 X'( 14, 2) 18.464 18.399 0.3520364 2.66636 20 64.21734 X( 14. 3) 0 . 5 4 0 . 5 4 O 18633.54 20 64.21756 , X( 15, 1) 74 .157 74 .323 -0 .2238494 1.004202 20 64.24517 X'( 15, 2) 23 .883 23.721 0.6783067 1.093734 20 64.27334 X( 15, 3) 1 .96 1 .956 0.2040816 275.2042 20 64.27761 I X( 1G, 1 ) 96 .42 96.421 - 0 . 1 0 3 7 1 2 9 E - 2 56.18758 20 64.27769 X'( 16, 2j 2.9G 2.959 0 .3378378E-1 65.01482 20 64.27779 XC 16, 3) 0 . 6 2 0 . 6 2 0 3474.232 20 64.27784 X( 17 ; 1) 95 .335 95.336 - 0 . 1 0 4 8 9 3 3 E - 2 120.4228 20 64.27792 X( 17, 2) 4 . 165 4. 164 0 .240096E-1 143.2085 20 64.27799 X( 17. 3) 0 . 5 0 . 5 0 14634. 15 20 64.2782 X( 18, 1) 87 .96 87 .972 - 0 . 1 3 6 4 2 5 6 E - 1 4.891046 20 64.27887 X( 18, 2) i i , 34 1 1 . 33 6 .88 ' i8342E- i 4.'056'1'G 20 64. 2794' X( 18, 3) 0 . 7 0.G99 0.1428571 4792.332 20 64.28689 X( 19. 1) 71 .734 71,058 -0 .1728G08 0.7745356 20 64.29887 'X'( YQ, 2 ) ' " X( 19, 3) 2*7". 396" . 0 . 8 7 27'. 273 0 .869 • b\4TQS707 . 0.1149425 6.787731 B80.79SS 20 20 64.3100 64.31228 XC 20, 1) 70 .592 70.773 - 0 . 2 5 6 4 0 3 0.6471554 20 64.33359 . X( 20 , 2) 25 .188 25.015 0.686835 0.6330134 20 64.35262 X( 20, 3) 4 . 2 2 4 .212 0.1895735 80.98586 20 , 64.35794 X( 2 1 . 1) 22.829 23.951 • -4 .914801 4.689772 20 70 .2655 . X'( 2 1. i) 76.051 74.919 1.488475 4.621902 20 76.18697 -XC 2 1 , 3) 1.12 1.13 -0 .8928571 3054.212 20 76.46488 . X( 2 2 , 2) 78.758 78.083 0.8570558 1.153407 20 77.5188 X( 2 2 , 3) 1 .07 1.067 0.2803738 5295.G76 20 77.55278 X( 23 , 1) 2 .795 2 .89 - 3 . 3 9 8 9 2 7 4.159585 20 77.59058 XC 2 3 , '2 j 9 6 . 0 9 5 96.006 6\926'i668E-i 4.287402 20 77.62427 X( 2 3 , 3) 1.11 1 . 103 0.630G30G 6396.588 20 77.91124 X( 24 , 1) 1.811 1.841 - 1 . 6 5 6 5 4 3 43.20768 20 77.95048 X ( 2 4 , 2 ) 9 6 . 8 7 9 9 6 . 8 5 1 0 . 2 Q 9 0 2 0 3 E - 1 4 1 . 8 5 1 8 0 2 0 7 7 . 3 3 4 0 5 X ( 2 4 . 3 ) 1 . 3 1 1 . 3 0 3 0 . 1 5 2 6 7 1 8 0 0 7 5 . 3 7 2 0 7 8 . 0 1 0 5 3 X ( 2 5 . 1) 2 . 4 3 2 . 4 6 8 - 1 . 5 6 3 7 8 6 3 8 . 3 G 7 3 2 ; 2 0 7 8 . 0 6 4 7 8 X ( 2 5 , 2 ) 9 5 . 3 9 5 . 2 8 5 0 . 1 5 7 3 9 7 7 E - 1 2 2 . 0 2 5 8 8 ' 2 0 7 8 . 0 6 9 5 8 x( 2 5 , 3 ) 2 . 2 7 2 . 2 4 7 1 . 0 1 3 2 1 6 2 0 0 . 4 5 4 4 •': 2 0 7 8 . 1 7 4 1 4 x< 2 6 , 1) 3 5 . 8 4 2 8 . 0 3 7 2 1 . 7 7 1 7 6 0 . 6 4 1 4 1 6 8 !•! 2 1 1 7 . 2 3 1 3 x( 2 6 , 2 ) G 3 . 0 4 7 0 . 8 6 8 - 1 2 . 4 1 7 5 1 0 . 6 3 5 6 0 2 6 . 2 1 5 6 . 1 7 9 6 x( 2 6 , 3 ) 1 . 12 1 . 0 9 5 2 . 2 3 2 1 4 3 1 5 2 1 . 7 3 9 V 2 • 1 5 7 . 1 0 7 X ( 2 7 , 1 ) 4 0 . 4 9 4 0 . 6 4 9 - 0 . 3 9 2 6 8 9 6 2 . 0 6 8 5 6 2 ': 2 1 5 7 . 1 5 9 x( 2 7 , 2 ) 5 8 . 6 2 5 8 . 4 5 1 0 . 2 8 8 2 9 7 5 1 . 8 2 0 4 5 7 2 1 5 7 . 2 1 1 3 x( 2 7 . 3 ) 0 . 8 9 0 . 9 0 1 - 1 . 2 3 5 9 5 5 2 4 0 ••: 2 1 5 7 . 2 3 8 8 x( 2 8 , 1) 4 2 . 0 1 4 2 . 3 5 - 0 . 8 0 9 3 3 1 1 4 . 1 4 7 2 4 2 2 1 5 7 . 7 1 8 X ( 2 8 . 2 ) 5 7 . 2 3 5 6 . 8 1 9 0 . 7 1 8 1 5 4 8 3 . 8 3 7 9 6 2 2 1 5 8 . 3 6 7 1 x( 2 8 , 3 ) 0 . 7 7 0 . 8 3 1 - 7 . 9 2 2 0 7 8 8 4 6 . 7 7 4 2 ;'• 2 1S1 . 5 5 3 3 X ( 2 9 . 1 ) 4 0 . 5 4 0 . 1 5 7 0 . 8 4 6 9 1 3 6 2 . 4 0 8 2 2 8 ••' 2 161 . 8 3 6 5 x( 2 9 , 2 ) 5 8 . 6 9 5 8 . 8 8 7 - 0 . 3 3 5 6 6 2 2 . G 9 8 1 3 8 2 161 . 9 4 1 2 x( 2 9 , 3 ) ' 0 . 8 0 9 0 . 9 5 6 - 1 8 . 1 7 0 5 8 5 7 . 8 3 5 3 2 ..' 2 1 6 3 . 1 3 1 X ( 3 0 , 1) 4 6 . 9 4 4 . 3 9 5 5 . 3 4 1 1 5 1 0 . 4 7 6 2 3 4 2 1 6 6 . 1 7 8 5 X ( 3 0 , 2 ) 5 1 . 2 7 5 3 . 6 8 8 - 4 . 7 1 6 2 0 8 0 . 4 4 1 2 0 4 2 1 6 3 . 7 5 7 4 X ( 3 0 , 3 ) 1 . 8 3 1 . 9 1 7 - 4 . 7 5 4 0 9 8 2 9 . 8 9 9 6 2 2 1 6 8 . 9 E 3 7 L i s t i n g o f F 0 R M 1 a t 0 9 : 3 7 : 3 3 o n J U L 5 , 1 9 8 3 f o r C C 1 d = N R C M P a g e 1 1 1 0 D I M M ( 2 0 ) , Y ( 5 , 6 ) , X ( 3 0 , 3 ) 2 3 4 2 0 F I L E R 0 F L 1 7 2 3 0 D A T A 1 7 2 , 4 5 , " O C T . 2 7 / 8 2 " 4 0 R E A D A A , B B , C C 5 6 7 5 0 Z 1 = 0 6 0 Z 2 = 0 7 0 FOR 1=1 T O 15 . , 8 9 1 0 8 0 R E A D F I L E 1 , M ( I ) 9 0 I F K 1 0 T H E N : M( I ) = I N T ( M ( I ) * 1 0 + 0 . 5 ) / 1 0 1 0 0 I F I > 9 T H E N : M ( I ) = I N T ( M ( I ) * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 1 1 12 13 1 10 1 2 0 1 3 0 I F K 1 0 T H E N : Z 1 = Z 1 + M ( I ) I F I>4 T H E N : I F I < 9 T H E N : Z 2 = Z 2 + M ( I ) N E X T I 14 15 16 1 4 0 1 5 0 1 6 0 FOR J = 1 TO 6 FOR 1=1 TO 5 R E A D F I L E 1 , Y ( I , J ) 17 18 19 1 7 0 1 8 0 1 9 0 Y ( i , J ) = i N T ( Y ( I , J j * 1 0 0+6 . 5 ) / i 66 N E X T I N E X T J 2 0 21 2 2 2 0 0 2 1 0 2 2 0 FOR 1=1 TO 3 0 FOR J = 1 TO 3 R E A D F I L E 1 , X ( I , J ) 2 3 2 4 2 5 2 3 0 2 4 0 2 5 0 x'(' i , j ) = i NT (x ( i , j j * i 666+6 .5)7 i 666 N E X T J N E X T I 2 6 2 7 2 8 2 6 0 2 7 0 2 8 0 D A T A 0 , 0 , 0 , 0 , 0 , 0 R E A D C1 , C 2 , C 3 , C 4 , C 5 , C 6 A 1 = 0 . 1 8 + C 1 * ( 0 . 2 4 - 0 . 1 8 ) / 2 . 3 7 8 2 9 3 0 31 2 9 0 3 0 0 3 1 0 A 2 = 6 . 6 i ' 5 + C 2 * ( 6 . 6 " 2 2 5 - 6 . 6 i 5 U ' 2 . 3 7 ' 8 A 3 = 0 . 4 + C 3 * ( 0 . 5 - 0 . 4 ) / 2 . 3 7 8 A 4 = 3 0 + C 4 * ( 3 5 - 3 0 ) / 2 . 3 7 8 3 2 3 3 34 3 2 0 3 3 0 3 4 0 A 5 = 1 2 0 0 + C 5 * ( 1 4 0 0 - 1200)'7 '2 . 3 7 8 A 6 = 0 . 3 + C 6 * ( 0 . 6 - 0 . 3 ) / 2 . 3 7 8 G = ( 3 . 3 4 8 * A 3 * 1 0 0 0 ) / ( 1 - 0 . 3 8 * A 3 ) 3 5 3 6 3 7 3 5 0 3 6 0 3 7 0 H = ( G * 6 . 4 + 2 5 ) 7 ( 1 - 6 . 1 3 ) W 2 = I N T ( H * 1 0 + 0 . 5 ) / 1 0 I = ( G * 0 . 6 + 3 9 ) / ( 1 - 0 . 2 1 5 ) 3 8 3 9 . 4 0 3 8 0 3 9 0 4 0 0 w"i = i NT ( i * i '6+6 .5)716 J = H * 0 . 4 / 0 . 6 K = I * 0 . 4 / 0 . 6 4 1 4 2 4 3 4 10 4 2 0 4 3 0 L«G*0. 1476.65 M = G * 0 . 4 0 = A 1 * ( H + I ) / 2 0 0 0 4 4 4 5 4 6 4 4 0 4 5 0 4 6 0 R =676.633 S = A 2 * ( H + I ) / 2 0 0 0 T = I N T ( ( S / . 0 0 4 7 5 ) * 1 0 + . 5 ) / 10 4 7 4 8 4 9 4 7 0 4 8 0 4 9 0 6= . 0 6 * TH+i )* .47 i666 P = 0 / 0 . 0 0 3 A 1 = I N T ( A 1 * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 t 5 0 51 5 2 5 0 0 5 1 0 5 2 0 A 2 = ' i N f ( A 2 * i 6666+6 .5)7 '16666 A 3 = I N T ( A 3 * 1 0 0 0 + 0 . 5 ) / 1 0 A 4 = I N T ( A 4 * 1 0 + 0 . 5 ) / 1 0 5 3 5 4 5 5 tr. n 5 3 0 5 4 0 5 5 0 A 5 = i N T ( " A 5 * i6+6 . '5)7i6 A 6 = I N T ( A 6 * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 B 9 = C M D ( " % S E T L I N E L E N = 1 3 2 " ) o n — r-Vm / » i/ e~ r- -r' r u n _ V i— 11 X 5 6 5 6 0 ' B 8 = CMD( " % S E f "CWD = 16"'') 5 7 5 7 0 P R I N T " 1 * * * * * * * * * * * * * B A T C H F L O T A T I O N D A T A S H E E T * * * * * * * * * * * * * * 5 8 5 8 0 P R I N T " * • * * * • . « • > * • • • * * » * * « * * ( r a w d a t a ) * * * * * * * * * * * * * * * * * * * * " , " RUN// " : A A , "CODED/ ' " : B B . " D A T E : " ; C C L i s t i n g o f FORM 1 a t 0 9 : 3 7 : 3 3 o n J U L 5 , 1 9 8 3 f o r C C i d = N R C M P a g e 2 5 9 5 9 0 P R I N T " 0 F a c t o r " . " C o d e d L e v e l " , " L e v e l " . " ! " , " S a m p l e T y p e " , " C o a r s e ( g m ) " . " F i n e s ( g m ) " . " T o t a l ( g m ) " 6 0 61 6 2 6 0 0 6 1 0 6 2 0 P R I N T " A m i n e ( 1 b / T ) " . C 1 , A 1 P R I N T " O i l ( l b / T ) " , C 2 , A 2 , " " j " . " R a w F e e d " . " " ; W 2 , W 1 . W 1 + W 2 " . " S l i m e s " , " " ; M ( 2 ) , M ( 1 ) , M ( 1 ) + M ( 2 ) 6 3 6 4 6 5 6 3 0 S 4 0 6 5 0 P R i N T " % S o i i d ( % ) " , C 3 . A 3 , " P R I N T " T e m p ( D e g . C ) " . C 4 . A 4 P R I N T " S p e e d ( R P M ) " , C 5 , . A 5 , " , " D e s l i m e d S a m p l e s " , " " ; M ( 4 ) , M ( 3 ) , M ( 3 " | " . " C o n c e n t r a t e s " , " " , " " , Z 2 . • 1 " . " T a i l s " , " " , " " , M ( 9 ) 6 6 6 7 6 8 6 6 0 6 7 0 6 8 0 P R I N T " A i r ( L / m i n ) " , C 6 , A 6 . " | " . " G a i n " , " " , " " . Z 1 - W 1 - W 2 P R I N T " 0 * * * * * * * * * * * * * * D e s l l m e d S a m p l e s A s s a y s * * * * * * * * * * * * * * " P R I N T " " , " % K c l " , " % N a c 1 " . " % I n s o l " 6 9 7 0 71 6 9 0 7 0 0 7 1 0 P R I N T " " , " " , " " . " " P R I N T " F i n e s S a m p l e " , M ( 1 2 ) , M ( 1 5 ) , M ( 1 3 ) P R I N T " C o a r s e S a m p l e " , M ( 1 0 ) , M ( 1 4 ) , M ( 1 1 ) 7 2 7 3 7 4 7 2 0 7 3 0 7 4 0 PR I N T " 6 * * * * * * * * * * * * * * * * * * * s i z e A n a l y s e s a n d A s s a y s o f F l o t a t i o n P r o d u c t s * * * * * * * * * * * * * * * * * * * " P R I N T " O C o n c . 1 " , " M e s h " , " % R e t a 1 n e d " , " % K c l " , ! " "/.Nacl " , " ' / . I n s o l " P R I N T M ( 5 ) ; " g m " , " " , " " , " " , " " 7 5 7 6 7 7 7 5 0 7 6 0 7 7 0 D A T A - 8 + 1 4 , - 1 4 + 2 8 , - 2 8 + 4 8 , - 4 8 + 1 0 0 , - 1 0 0 FOR 1=1 TO 5 R E A D M M ( I ) 7 8 7 9 8 0 7 8 0 7 9 0 8 0 0 P R I N T " " , M M ( i ) , Y ( i . i ) . x ( i , i ) . x ' ( i , 2 ) . x ( r , ' 3 ) N E X T I ! . P R I N T " O C o n c . 2 " , " M e s h " , ' " / . R e t a i n e d " , " % K c l " , " ' / .Nacl " , " ' / . I n s o l " 81 8 2 8 3 8 1 0 8 2 0 8 3 0 P R I N T M ( 6 ) ; " g m " , " " , " " , " " , " " FOR 1=1 TO 5 P R I N T " " , M M ( I ) , Y ( I , 2 ) , X ( I + 5 , 1 ) , X ( I + 5 , 2 ) , X ( I + 5 , 3 ) 8 4 8 5 8 6 8 4 0 8 5 0 8 6 0 N E X T I P R I N T " O C o n c . 3 " , " M e s h " , ' " / . R e t a i n e d " , " % K c l " , " "/.Nacl " , " ' / . I n s o l " P R I N T M ( 7 ) ; " g m " , " " , " " , " " ; " " . " " -8 7 8 8 8 9 8 7 0 8 8 0 8 9 0 FOR 1=1 TO 5 ' ! P R I N T " " , M M ( I ) , Y ( I , 3 ) , X ( I + 1 0 , 1 ) , X ( 1 + 1 0 , 2 ) , X ( 1 + 1 0 . 3 ) N E X T I i 9 0 9 1 9 2 9 0 0 9 1 0 9 2 0 P R I N T " 6 c o n c . 4 " , " M e s h " , r / . R e ' t a i n e d " , " % k c i " , " ' / . N a c l " , ' " / . i n s o i " P R I N T M ( 8 ) ; " g m " , " " , " " , " " , ' " " , " " FOR 1=1 TO 5 9 3 9 4 9 5 9 3 0 9 4 0 9 5 0 P R I N T " " , M M ( I ) , Y ( I , 4 ) , X ( I + 1 5 , i ) , X ( i + 1 5 , 2 ) . X ( 1 + 1 5 , 3 ) N E X T I P R I N T " O T a i l s " , " M e s h " , ' " / R e t a i n e d " , " % K c l " , " % N a c l " , ' " / . I n s o l " 9 6 9 7 9 6 9 6 0 9 7 0 9 8 0 PR I N T M ( 9 ) ; " g m " . " " . " " , " " , " " . " " FOR 1=1 TO 5 P R I N T " " , M M ( I ) , Y ( I , 5 ) , X ( I + 2 0 . 1 ) , X ( 1 + 2 0 , 2 ) . X ( 1 + 2 0 , 3 ) 9 9 1 0 0 101 9 9 0 N E X T I 1 0 0 0 G = I N T ( G * 1 0 + 0 . 5 ) / 1 0 1 0 1 0 H = I N T ( H * 1 0 + 0 . 5 ) / 1 0 1 0 2 1 0 3 1 0 4 1 0 2 0 J = i N ? ( U * 1 0 + 0 . 5 )7'ib 1 0 3 0 K = I N T ( K * 1 0 + 0 . 5 ) / 1 0 1 0 4 0 L = I N T ( L * 1 0 + 0 . 5 ) / 1 0 1 0 5 1 0 6 1 0 7 iosb M = i N T C M * 1 0 + 6 .5 ) ' /T o 1 0 6 0 0 = I N T ( 0 * 1 0 0 0 0 + 0 . 5 ) / 1 0 0 0 0 1 0 7 0 0 = I N T ( 0 * 1 0 0 0 0 + 0 . 5 ) / 1 0 0 0 0 1 0 8 1 0 9 1 10 1 0 8 0 5 = IN f ( s * Tocoo+o. 5 ) / i 6 6 6 6 1 0 9 0 P = I N T ( P * 1 0 + 0 . 5 ) / 1 0 1 1 0 0 R = I N T ( R * 1 0 + 0 . 5 ) / 1 0 111 1 1 1 0 P RI NT " 1 * * * * * * * * * * R U N * " : A A , " C O D E D * " ; B B , ' ' D A T E : '"Yc'C ; " ' ' " * * * * * * * ' * * * ' * " 112 1 1 2 0 P R I N T "o******** A S u m m a r y S h e e t o f I n f o r m a t i o n R e q u i r e d F o r t h e B a t c h T e s t * * * * * * * * " 1 1 3 1 1 3 0 P R I N T " O F l o t a t i o n M a c h i n e : D E N V E R D1 , 2 . 7 L i t r e s " 114 ri'46'''pR'i'Nf ^ V ' " T A ' v " ' Z o n e ' " O r e ' , v ' " 1 1 5 1 1 5 0 P R I N T " 0 " / , S o l i d s i n t h e F l o t a t i o n C e l l : " ; A 3 1 16 1 1 6 0 P R I N T " O T e m p e r a t u r e o f t h i s R u n : " ; A4 ; " P e g . C " L i s t i n g o f FORM 1 a t 0 9 : 3 7 : 3 3 o n - O U L 5 , 1 9 8 3 f o r C C 1 d = N R C M " P a g e 3 1 1 7 1 1 7 0 P R I N T " O W e i g h t o f D e s l i m e d . O r e . i n t h e C e l l : 0 ; " g m " ; ' i " i ' 8 i i 6b PR I NT " - * * : » **'*'***'*'**'*'* *'*'* *'*'** * ' * * ' ' ' s c r u b b l ' n g " a t 6 0 % S o l i d s * * » * * * * • » * • » » * * " » * » * * * * * * • « 1 1 9 1 1 9 0 P R I N T " O F r a c t l o n " , " S o l i d ( g m ) " , " B r i n e ( g m ) " , " T o t a l " , " T i m e ( m i n ) " 1 2 0 1 2 0 0 P R I N T " " , " " , " - — » , " " , " " . ' 1 2 1 1 2 i 6 ' ' p R I N f ' " C o a r s e " ' , ' H , J " , H + d , ' " 5 " " 122 1 2 2 0 P R I N T " F i n e s " , W 1 , K , W 1 + K , " 5 " 1 2 3 1 2 3 0 P R I N T " T o t a l " , H + W 1 ' i ' 2 4 T 2 4 0 ' P R I N T " S o l i d s a n d F i n e ' s a t 6 0 % S o l i d s * * * " 1 2 5 1 2 5 0 P R I N T " O F r a c t i o n " , " S o l i d ( g m ) " , " B r i n e ( g m ) " , " T o t a l " 1 2 6 1 2 6 0 P R I N T " " , " - - - - " . " " , " " i ' 2 7T276'""PR ' l N ' f''"''c ' d ' a '• 1 2 8 1 2 8 0 P R I N T " F i n e s " , I N T ( G * 0 . 6 * 1 0 + 0 . 5 ) / 1 0 , M , I N T ( G * 0 . 6 * 1 0 + 0 . 5 ) / 1 0 + M 1 2 9 12?P P R I N T " - * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * R e a g e n t i z I n g t h e C o a r s e F r a c t l o n . * * * * * * * * * * * * * * * * * * * * * * * * * * * * * " " l 3 0 T 3 0 0 ' P R I ^ 'c'.''cTVl'','':''f'i'm'e"''('m'l'n''r'i-1 3 1 1 3 1 0 P R I N T " " , " " , " " , " " , " " , " " 1 3 2 1 3 2 0 P R I N T " G u a r ( 4 0 % ) " , 0 . 1 2 , 0 . 0 6 , 0 , P , " 3 " 1 3 3 T 3 3 0 P'RINT ^ '•" 134 1 3 4 0 P R I N T " O i l ( # 9 0 4 ) " , A 2 , A 2 / 2 , S , T ; " D r o p s " , " a n d 011 c o m b i n e d " 1 3 5 1 3 5 0 P R I N T " - * * * * * * * * * * * * * * * * * * * * * * * * * * * * R e a g e n t i z i n g t h e F i n e s F r a c t i o n * * * * * * * * * * * * * * * * * * * * * * * * * * * " " i ' 3 6 T 3 ' 6 b ' ' P R I N T ' ' ' " b R e a ^ 1 3 7 1 3 7 0 P R I N T " " , " " , " " , " " , " " , " " 1 3 8 1 3 8 0 P R I N T " G u a r ( 6 0 % ) " ,0.12.0 . 0 6 , I N T(0* 1 . . 5 * 10000+. 5 ) / . 1 p p p O . . I N T.(P* 1 .5*10+ 3." " l 3 9 ^ 3 9 0 P R I N T 11 - * *^ ^^  1 4 0 1 4 0 0 P R I N T " O R e a g e n t " , " l b / T " , " g / K g n , " g r a m " , " D r o p s " , " T i m e ( m i n ) " 141 1 4 1 0 P R I N T " " , " " , " " , " " . " " , " " " i ' 4 2 ! 4 2 0 ' P R I N T ' ^ '2 n 1 4 3 1 4 3P P R I N T " - * * * * * * * * * * * * * * * * F l o t a t i o n C o n d i t i o n s * * * * * * * * * * * * * * * * " " i ' 4 4 T 4 4 b ' ' P ' R ' l N ' f ' " ' " 0 A 7 r ' ' F ' i o ^ 1 4 5 1 4 5 0 P R I N T " O l m p e l l e r S p e e d o f t h e F l o t a t i o n M a c h i n e . . . " ; A 5 ; " R P M " 1 4 6 1 4 6 0 P R I N T "1 D O N E " " i ' 4 7 i ' 4 7 0 ' S T b p 148 E n d - O f - F i l e * * * * * * * * * * * * * B A T C H F L O T A T I O N D A T A S H E E T * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ( d a t a ) * * * * * * * * * * * * * * * * * * * * R U N * 1 7 2 C O D E D * 4 5 D A T E : O C T . 2 7 / 8 2 F a c t o r C o d e d L e v e l L e v e l S a m p l e T y p e C o a r s e (gm)' F i n e s ( g m ) t o t a l ( g m ) A m i n e ( l b / T ) 0 0 . 18 Raw F e e d 7 5 4 . 8 1 2 5 6 . 7 2 0 1 1 . 5 O i l ( i b / T J 0 0 . i ' 5 E - i ' S I i m e s 104 . 2 2 6 2 . 3 3 6 6 . 5 ' / . S o l I d ('/,) 0 4 0 D e s l i m e d S a m p l e s 2 8 . 1 4 1 . 8 6 9 . 9 T e m p ( D e g . C ) 0 3 0 C o n c e n t r a t e s 6 0 2 . 5 S p e e d ( R P M ) 0 1 2 0 0 T a i I s 1 0 0 0 . 5 A i r ( L / m 1 n ) 0 0 . 3 G a 1 n 2 7 . 9 ************** D e s l i m e d S a m p l e s A s s a y s * * * * * * * * * * * * * * % K c l °/ ,Nacl % I n s o 1 F0RM1 output F i n e s S a m p l e 3 9 . 7 5 8 . 4 0 . 9 3 C o a r s e S a m p l e 4 4 . 7 5 3 . 1 1 . 1 ******************* s i z e A n a l y s e s a n d A s s a y s o f F l o t a t i o n P r o d u c t s * * * * * * * * * * * * * * * * * * * C o n e . 1 M e s h " / . R e t a i n e d '/ .Kcl "/.Nacl ' / . I n s o l 2 7 0 . 5 gm - 8 + 1 4 1 . 7 8 9 5 . 4 6 . 1 0 . 5 2 - 1 4 + 2 8 1 1 . 2 9 7 . 5 4 . 8 0 . 3 9 - 2 8 + 4 8 3 7 . 9 1 9 6 5 . 9 0 . 4 - 4 8 + 1 0 0 3 3 . 2 4 9 4 . 4 7 . 6 0 . 4 7 - 1 0 0 15 . 8 7 9 3 . 3 1 0 . 1 1 . 0 6 C o n e . 2 M e s h ' / . R e t a i n e d '/ .Kcl ' / .Nac l ' / . I n s o l 1 0 7 . 9 gm - 8 + 1 4 0 . 3 5 9 4 . 4 6 . 9 0 . 4 - 1 4 + 2 8 7 . 6 9 9 7 4 . 7 0 . 4 - 2 8 + 4 8 4 0 . 3 2 9 5 . 3 6 . 2 0 . 4 5 - 4 8 + 1 0 0 3 4 . 12 9 2 . 6 9 . 1 0 . 4 6 - 1 0 0 1 7 . 5 2 8 8 . 6 1 1 . 8 1 . 0 9 C o n e . 3 M e s h p e t a l n e d '/ .Kcl ' / .Nac l % i h s o l 12 1 . 4 gm - 8 + 1 4 0 . 8 7 9 5 . 3 5 . 7 0 . 5 6 - 14 + 2 8 1 6 . 4 5 9 7 4 . 9 0 . 4 5 - 2 8 + 4 8 4 4 . 3 2 9 2 . 1 9 . 1 0 . 5 3 - 4 8 + 1 0 0 2 4 . 8 8 8 2 , 7 1 8 . 4 0 . 5 4 - 1 0 0 1 3 . 4 8 7 6 . 7 2 3 . 8 1 . 9 6 C o n e . 4 M e s h " / . R e t a i n e d % K c l °/.Nacl % I n s o l 1 0 2 . 7 gm _ _ _ _ - 8 + 1 4 1 . 5 6 9 9 . 8 2 . 9 5 0 . 6 2 - 1 4 + 2 8 3 0 . 5 7 9 8 . 7 4 . 15 0 . 5 i , - 2 8 + 4 8 4 0 . 9 8 8 . 9 1 1 . 3 0 . 7 - 4 8 + 1 0 0 1 6 . 4 6 7 1 . 8 2 7 . 3 0 . 8 7 - 1 0 0 1 0 . 5 2 6 9 . 3 2 5 . 1 4 . 2 2 : . T a 1 l s M e s h ' / . R e t a i n e d '/ .Kcl . ' / .Nac l ' / . I n s o l 1 0 0 0 . 5 gm - 8 + 1 4 1 3 . 4 1 2 3 . 2 7 6 1 . 1 2 - 1 4 + 2 8 2 5 . 0 8 2 0 . 5 7 8 . 2 1 . 0 7 - 2 8 + 4 8 3 0 . 6 9 2 . 8 4 9 3 . 6 1 . 1 1 - 4 8 + 1 0 0 2 1 . 9 9 1 . 8 4 9 5 . 1 1 . 3 1 - 1 0 0 8 . 8 3 . 2 . 4 7 9 4 2 . 2 7 * * * * * * * * * * * RUN// 1 7 2 CODED// 4 5 D A T E : O C T . 2 7 / S 2 * * * * * * * *.***_ * * * * * * * * A S u m m a r y S h e e t o f I n f o r m a t i o n R e q u i r e d F o r t h e B a t c h T e s t * * * * * * * * F l o t a t i o n M a c h i n e D E N V E R DI , 2 . 7 L i t r e s T y p e o f P o t a s h O r e : % S o l 1 d s I n t h e F l o t a t i o n C e l l : ' A? Z o n e O r e 4 0 T e m p e r a t u r e o f t h i s R u n : 3 0 D e g . C W e i g h t o f D e s l i m e d O r e i n t h e C e l l 1 5 7 9 . 2 gm * * * * * * * * * * * * * * * * * * * * * * * * S c r u b b i n g a t 6 0 % S o l i d s * * * * * * * * * * * * * * * * * * * * * * * * F r a c t i o n . S o l i d ( g m ) B r i n e . (gm) T o - t a 1 I.1.m.?....(.m.l.n..L C o a r s e 7 5 4 . 8 5 0 3 . 2 1 2 5 8 5 F i n e s 1 2 5 6 . 7 8 3 7 . 8 2 0 9 4 . 5 5 T o t a l 2 ' 6 T i " . " 5 * * * C o n d i t i o n i n g C o a r s e a t 6 5 % S o l i d s a n d F i n e s a t 6 0 % S o l i d s * * * F r a c t i i o n S o 1 i d ( g m ) ? . P . L n . e . . $.9™.). 1.9.^3.1 C o a r s e 6 3 1 . 7 3 4 0 . 1 9 7 1 . 8 F i n e s 9 4 7 . 5 6 3 1 . 7 1 5 7 9 . 2 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * R e a g e n t i z i n g t h e C o a r s e F r a c t i o n * * * * * * * * * * * * * * * * * * * * * * * * * * * * * R e a g e n t l b / T g / K g g r a m c . c . T i m e ( m m ) ' G u a r " ' ' ( 4 0 % ) 6 7 l 2 6 V 6 E - 1 6 7 4 8 3 E - T i " s " . " i ' 3 A R M E E N T D 0 . 1 8 - 0 . 9 E - 1 0 . 1 8 1 5 . 5 1 . 5 f o r A m i n e O i l ( # 9 0 4 ) 0 . 1 5 E - 1 0 . 7 5 E - 2 0 . 1 5 1 E - 1 3 . 2 D r o p s a n d 0 1 1 c o m b i n e d *****.*********************** Roagentlzihg the Fines Ftaction *************************** R e a g e n t l b / T g / K g g r a m c . c . T i m e ( m i n ) G u a r " T 6 " 6 5 0 6 " . i " 2 6 V 6 E - 1 0 7 7 2 4 E - 1 2 4 " . " i 3 ' * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * F r o t h e r C o n d i t i o n i n g i n t h e C e l l * * * * * * * * * * * * * * * * * * * * * * R e a g e n t lb„/J. g./K.S. 9.!?.?™ PX9P..S. ..T..1.m.?....(.mJ..'lL M I B C 0 . 4 7 E - 1 0 . 2 3 5 E - 1 0 . 4 7 3 E - 1 9 . 5 2 * * * * * * * * * * * * * * * * F l o t a t i o n C o n d i t i o n s * * * * * * * * * * * * * * * * ' A ' f r " F i o w R a t e " oTs'T'/mTri I m p e l l e r S p e e d o f t h e F l o t a t i o n M a c h i n e . . . 1 2 0 0 RPM L i s t i n g o f C F O R M a t 0 9 : 3 7 : 3 5 o n J U L 5, 1 9 8 3 f o r C C 1 d = N R C M P a g e 1 1 1 0 D I M M ( 2 0 ) , Y ( 5 , 6 ) , X ( 3 0 , 3 ) 2 2 0 F I L E R 0 F L 1 7 2 3 3 0 D A T A 1 7 2 , 4 5 , " O C T . 2 7 / 8 2 " 4 4 0 R E A D A A , B B . C C 5 5 0 Z 1 = 0 6 6 0 Z 2 = 0 7 7 0 FOR 1=1 TO 15 8 8 0 R E A D F I L E 1 , M ( ' i ) 9 9 0 I F K 1 0 T H E N : M( I ) = I N T ( M ( I ) * 1 0 + 0 . 5 ) / 1 0 1 0 1 0 0 I F I > 9 T H E N : M ( I ) = 1 N T ( M ( I ) * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 1 1 1 1 0 I F K 1 0 T H E N : Z 1 = Z 1 + M ( I ) 12 1 2 0 I F I > 4 T H E N : I F I < 9 T H E N : Z 2 = Z 2 + M ( I ) 13 1 3 0 N E X T I 14 1 4 0 FOR « J=1 T O 6 15 1 5 0 FOR 1=1 T O 5 16 1 6 0 R E A D F I L E 1 , Y ( I , J ) 17 1 7 0 Y ( i , j ) ' = i N ' t (V ( i ,'J )* ibo+o .5)7i66 18 1 8 0 N E X T I 19 1 9 0 N E X T J 2 0 2 0 0 FOR 1=1 TO 3 0 2 1 2 1 0 FOR J = 1 T O 3 22 2 2 0 R E A D F I L E 1 , X ( I , J ) 2 3 2 3 0 x ' ( i , j ) ' = i N ' f ( x " ( i . J)*id'6b+o .5)7i6bb" 2 4 2 4 0 N E X T J 2 5 2 5 0 N E X T I 2 6 2 6 0 D A T A 0 , 0 , 0 , 0 , 0 , 0 2 7 2 7 0 R E A D C 1 , C 2 , C 3 , C 4 , C 5 , C 6 • 2 8 2 8 0 A 1 = 0 . 1 8 + C 1 * ( 0 . 2 4 - 0 . 1 8 ) / 2 . 3 7 8 2 9 2 9 0 A 2 = 0 . 61 5+C 2 * (6. C 2 2 5 - 0 . 615 )72 . 3 7 8 -3 0 3 0 0 A 3 = 0 . 4 + C 3 * ( 0 . 5 - 0 . 4 ) / 2 . 3 7 8 31 3 1 0 A 4 = 3 0 + C 4 * ( 3 5 - 3 0 ) / 2 . 3 7 8 3 2 3 2 0 A 5 = i 2 b b + C 5 * ( 1 4 0 0 - 1 2 0 0 ) 7 2 . 3 7 8 3 3 3 3 0 A 6 = 0 . 3 + C 6 * ( 0 . 6 - 0 . 3 ) / 2 . 3 7 8 3 4 3 4 0 G = ( 3 . 3 4 8 * A 3 * 1 O 0 0 ) / ( 1 - 0 . 3 8 * A 3 ) 3 5 3 5 0 H = ( G * 6 . 4 ' + 2 5 ) / ( i - 0 . 1 3 ) 3 6 3 6 0 W 2=INT ( H * 1 0 + 0 . 5 ) / 1 0 3 7 3 7 0 I = ( G * 0 . 6 + 3 9 ) / ( 1 - 0 . 2 1 5 ) • 3 8 3 8 0 w i = INT(i* i b + b . 5 ) / i b 3 9 3 9 0 J = H * 0 . 4 / 0 . 6 4 0 4 0 0 K = I * 0 . 4 / 0 . 6 4 1 4 10 L = G * 0 . i ' 4 / 0 . 6 5 4 2 4 2 0 M = G * 0 . 4 4 3 4 3 0 Q = A 1 * ( H + I ) / 2 0 0 0 4 4 4 4 0 R = 0 / 0 . 0 3 3 4 5 4 5 0 S = A 2 * ( H + I ) / 2 0 0 0 4 6 4 6 0 T = I N T ( ( S / . 0 0 4 7 5 ) * 1 0 + . 5 ) / 1 0 4 7 4 7 0 b = . b 6 + ( H + i ) * . 4 7 i b b b 4 8 4 8 0 P = 0 / 0 . 0 0 3 4 9 4 9 0 A 1 = I N T ( A 1 * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 5 0 5 0 0 A 2 =I N T ( A 2 * 10666+6.5)/10000 51 5 1 0 A 3 = I N T ( A 3 * 1 0 0 0 + 0 . 5 ) / 1 0 5 2 5 2 0 A 4 = I N T ( A 4 * 1 0 + 0 . 5 ) / 1 0 5 3 5 3 0 A 5 = i N T ( A 5 * i b + b . 5 ) / i b 5 4 5 4 0 A G = I N T ( A 6 * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 5 5 5 5 0 B 9 = C M D ( " % S E T L I N E L E N = 1 3 2 " ) 5 3 5 6 0 E 8 = CMb(',,%SE'f C W b = 1 6 " ) 57 5 G 5 P R I N T " 1 * * * * * * * * * * * * * B A T C H F L O T A T I O N DATA S H E E T * * * * * 4 * * * * * * * " 50 570 P R I N T " 1 • • * + + « * * * • « « * B A T C H F L O T A T I O N D A T A SHEET *************** L i s t i n g o f C F O R M a t 0 9 : 3 7 : 3 5 o n J U L 5 , 1 9 8 3 f o r C C 1 d = N R C M ' P a g e 2 5 9 5 8 0 P R I N T " * * * * * ( w i t h c o r r e c t e d s i 1 m e s w e i g h t s a n d a s s a y s ) * * * * * " , " RUN* " ; A A , " C O D E D * " ; B B , " D A T E : " ; C C 6 0 6 1 6 2 5 9 0 6 0 0 6 1 0 P R I N T " O F a c t o r " , " C o d e d L e v e P R I N T " " , " P R I N T " A m i n e ( 1 b / T ) " , C 1 , A 1 " , " L e v e l " , " »" 11 _ _ _ _ _ II II " 1 " , " R a w f " . " S a m p l e T y p e " , " C o a r s e ( g m ) " , " F i n e s ( g m ) " , " T o t a l n it _ _ i i n _ _ u n _ _ _ _ _ _ _ _ _ n • ' _ _ _ _ _ " e e d " , " " ; W 2 , W 1 , W 1 + W 2 ( g m ) " _ « . _ _ » ! 6 3 6 4 6 5 6 2 0 6 3 0 6 4 0 P R I N T " 0 1 1 ( l b / T ) " , C 2 , A 2 , " P R I N T " ' / . S o l i d ('/.)" , 0 3 , A 3 , " P R I N T " T e m p ( D e g . C ) " , C 4 ' , A 4 " , " S I i m e s " , " " ; M ( 2 ) , M ( 1 ) , M ( 1 ) + M ( 2 ) " , " D e s l t m e d S a m p l e s " , " " ; M ( 4 ) , M ( 3 ) , M ( 3 "I " . " C o n c e n t r a t e s " , " " , " " , Z 2 6 6 6 7 6 8 6 5 0 6 6 0 6 7 0 P R I N T " S p e e d ( R P M ) " , C 5 , A 5 , " P R I N T " A i r ( L / m i n ) " , C 6 . A 6 , " PR I N T " 0 * * * * * * * * * * * * * * D e s l l r " , " T a i I s " , " " , " " , M ( 9 ) " . " G a i n " , " " , " " . Z 1 - W 1 - W 2 n e d S a m p l e s A s s a y s * * * * * * * * * * * * * * * 6 9 7 0 71 6 8 0 6 9 0 7 0 0 P R I N T " " , " % K c l " , " ' / .Nac l " , ' " / . I n s o l " P R I NT " " " — — — - " " ii ii H P R I N T " F i n e s S a m p l e " , M ( 1 2 ) , M ( 1 5 ) , M ( 1 3 ) 7 2 7 3 7 4 7 1 0 7 2 0 7 3 0 P R I N T " C o a r s e S a m p l e " , M ( 1 0 ) , M ( 1 4 ) , M ( 1 1 ) P R I N T " 0 * * * * * * * * * * * * * * * * * * * S i z e A n a l y s e s a n d A s s a y s o f F l o t a t i o n P r o d u c t s * * * * * * * * * * * * * * * * * * * " P R I N T " 0 C o n c . 1 " , " M e s h " ,• ' " / . R e t a i n e d " , " ° / , K c l " , " % N a c l " , " ' / . I n s o l " ' 7 5 7 6 7 7 7 4 0 7 5 0 7 6 0 P R I N T M ( 5 ) ; " g m " , " " , " " , " D A T A - 8 + 1 4 , - 1 4 + 2 8 , - 2 8 + 4 8 , - 4 8 + 1 0 0 , - 1 0 0 FOR 1=1 TO 5 II II _ _ _ _ _ . l l II _ _ _ _ _ _ II 7 8 7 9 8 0 7 7 0 7 8 0 7 9 0 R E A D MM(l) . ' . P R I N T " . " , M M ( I ) , Y ( I , 1 ) , X ( I , 1 ) , X ( I , 2 ) , X ( I , 3 ) N E X T I 81 8 2 8 3 8 0 0 8 1 0 8 2 0 P R I N T " O C o n c . 2 " , " M e s h " , ' " / R e t a i n e d " , " % k ' c i " , " % N a c i " , " % i n s o l " P R I N T M ( 6 ) ; " g m " , " " , " " , " " , " " , " " FOR 1=1 T O 5 8 4 8 5 8 6 8 3 0 8 4 0 8 5 0 P R I N T " " , M M ( I ) , Y ( I , 2 ) , X ( 1 + 5 , 1 ) , X ( 1 + 5 , 2 ) , X ( I + 5 , 3 ) N E X T I P R I N T " O C o n c . 3 " , " M e s h " , " ' / . R e t a i n e d " , " % K c l " , " ' / .Nac l " . " ' / . I n s o l " 8 7 8 8 8 9 8 6 0 8 7 0 8 8 0 P R I N T M ( 7 ) ; " g m " , " " , 11 " , " " , " " FOR 1=1 TO 5 P R I N T " " , M M ( I ) , Y ( I , 3 ) , X ( I + 1 0 , 1 ) , X ( I + 1 0 , 2 ) , X ( I + 1 0 , 3 ) 9 0 9 1 9 2 8 9 0 9 0 0 9 1 0 N E X T I P R I N T " 0 C o n c . 4 1 1 , " M e s h " , ' " / . R e t a i n e d " , " ° / . K c l " , " ' / . N a c l " , ' " / . I n s o l " P R I N T M ( 8 ) ; " g m " , " " , " " , " " , " " , " " 9 3 9 4 9 5 9 2 0 9 3 0 9 4 0 FOR 1=1 TO 5 P R I N T " " , M M ( I ) , Y ( I , 4 ) N E X T I , X ( I + 1 5 , 1 ) , X ( I + 1 5 , 2 ) , X ( I + 1 5 . 3 ) 9 6 9 7 9 8 9 5 0 9 6 0 9 7 0 P R I N T " O T a i l s " , " M e s h " , ' " / . R e t a 1 n e d " , " ° / . K c l " , " ' / .Nac l " , ' " / . I n s o l " P R I N T M ( 9 ) ; " g m " , " " , " " , " " , " " , " " FOR 1=1 TO 5 9 9 1 0 0 101 9 8 0 P R I N T " " , M M ( I ) , Y ( I 9 9 0 N E X T I 1 0 0 0 G = I N T ( G * 1 0 + 0 . 5 ) / l O , 5 ) , X ( l + 2 0 , l ) , X ( l + 2 0 , 2 ) , X ( l + 2 0 , 3 ) 1 0 2 1 0 3 1 0 4 ioio H=iNffH*T6+6' .5)/iO 1 0 2 0 J = I N T ( J * 1 0 + 0 . 5 ) / 1 0 1 0 3 0 K = I N T ( K * 1 0 + 0 . 5 ) / l 0 • 1 0 5 1 0 6 1 0 7 i64"6 C• iN ? f l > 16+6'. s)7i6 1 0 5 0 M = I N T ( M * 1 0 + 0 . 5 ) / 1 0 1 0 6 0 0 = I N T ( 0 * 1 0 0 0 0 + 0 . 5 ) / 1 0 0 0 0 1 1 0 8 1 0 9 1 10 i 07"6 6=i NT Co* i"666'6+6. 5 ) 7 i 6666 1 0 8 0 S = I N T ( S * 1 0 0 0 0 + 0 . 5 ) / 1 0 0 0 0 1 0 9 0 P = I N T ( P * 1 0 + 0 . 5 ) / 1 0 1 1 1 1 12 1 13 1 1 0 0 R = I N T ( R * 1 0 + 0 . 5 ) / 1 0 1 1 1 0 P R I N T " 1 * * * * * * * * * * R U N * " ; A A , " C O D E D * " ; E B , " D A T E : " ; C C ; " * * * * * * * * * * * * 1 1 2 0 P R I N T »o******** A S u m m a r y S h e e t o f I n f o r m a t i o n R e q u i r e d F o r t h e B a t c h T e s t * * * * * * * * " 114 1 15 1 16 1 1 3 0 P R I N T " O F l o t a t i o n M a c h i n e 1 1 4 0 P R I N T " O T y p e o f P o t a s h O r e 1 1 5 0 P R I N T " O n / . S o l i d s i n t h e F l o t a t i o n C e l l : D E N V E R D1 , 2 . 7 L i t r e s " : ' A ' Z o n e O r e " : " : A 3 L i s t i n g o f C F O R M a t 0 9 : 3 7 : 3 5 o n J U L 5 , 1 9 8 3 f o r C C i d = N R C M P a g e 3 1 1 7 11 GO P R I N T " O T e m p e r a t u r e o f t h i s R u n : " ; A 4 ; " D e g . C " T i 8 T i 7 b ' ' p ' R i N f " ' " 6 w e T ^ v " " . v y Q | " » - g m « 1 1 9 1 1 8 0 P R I N T " - * * * * * * * * * * * * * * * * * * * * * * * * S c r u b b i n g a t 6 0 % S o l i d s * * * * * * * * * * * * * * * * * * * * * * * * * 1 2 0 1 1 9 0 P R I N T " O F r a c t i o n " , " S o l i d ( g m ) " , " B r i n e ( g m ) " , " T o t a l " , " T i m e ( m i n ) " . . . . 1 i ' 2 " i • • _ • • _ V i  1 2 2 1 2 1 0 P R I N T " C o a r s e " , H . u , H + « J , " 5 " 1 2 3 1 2 2 0 P R I N T " F1 n e s " , W1 , K . W1+K,,." 5 " . . 1 2 4 T 2 3 0 ' ' P R l W " " ' ' ' T o t a l ' " V H + W i 1 2 5 1 2 4 0 P R I N T " - * * * C o n d i t i o n i n g C o a r s e a t 6 5 % S o l i d s a n d F i n e s a t 6 0 % S o l i d s * * * " 1 2 6 1 2 5 0 P R I N T " O F r a c t i o n " , " S o l i d ( g m ) " . " B r i n e ( g m ) " , " T o t a l " 1 2 7 Y 2 6 0 P R I N T " 11 - - - - " 1 2 8 1 2 7 0 P R I N T " C o a r s e " . I N T ( G * 0 . 4 * 1 0 + 0 . 5 ) / 1 0 , L , I N T ( G * 0 . 4 * 1 0 + 0 . 5 ) / 1 0 + L 1 2 9 1 2 8 0 PR I NT ". F i n e s " , I N T ( G * 0 . 6*10+0....5J/.10.,, M., I N X ( . G * 0 . . 6 * 10„+0. . .5 . ) / .10^+M i ' 3 0 Y 2 9 0 PR I NT ' " - * * * t h e C o a r s e F r a c t i o n * * * * * * ^ * * * * * * * * * * * * * * * * **•**** '• 131 1 3 0 0 P R I N T " O R e a g e n t " . " l b / T " , " g / K g " , " g r a m " , " c . c . " , " T i m e ( m i n ) " 1 3 2 1 3 1 0 P R I N T " " , " ." , " " , " " , " " , " " 1 3 3 Y 3 2 0 ' ' ' P R ' I ^ 3 " 1 3 4 1 3 3 0 P R I N T " A R M E E N T D " , A 1 , A 1 / 2 , 0 , R , " 1 . 5 f o r A m i n e " 1 3 5 1 3 4 0 P R I N T " O i l ( # 9 0 4 ) " , A 2 , A 2 / 2 , S , T ; " D r o p s " , " a n d O i l c o m b i n e d " i ' 3 ' 6 Y 3 5 O ' ' P R ' I N T " - * * * " * 1 3 7 1 3 6 0 P R I N T " O R e a g e n t " , " l b / T " , " g / K g " . " g r a m " , " c . c . " . " T i m e ( m i n ) " 1 3 8 1 3 7 0 P R I N T " " , " " , " " , " " , " " , " " 1 3 9 Y 3 8 0 T R r N T 3 " 1 4 0 1 3 9 0 P R I N T " - * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * F r o t h e r C o n d i t i o n i n g i n t h e C e l l * * * * * * * * * * * * * * * * * * * * * * 1 1 141 1 4 0 0 P R I N T " O R e a g e n t " , " l b / T " . " g / K g " , " g r a m " , " D r o p s " , " T i m e ( m i n ) " 1 4 2 ^ 4 I 6 " " P R T N T " " , V " -1 4 3 1 4 2 0 P R I N T " M I B C " , 0 . 0 4 7 , 0 . 0 4 7 / 2 . I N T ( 0 . 0 4 7 * ( H + W 1 ) * 1 0 0 0 0 / 2 0 0 0 + 0 . 5 ) / 1 0 0 0 0 . I N T ( 0 . 0 4 7 * ( H + W 1 ) * 1 0 / ( 2 0 0 0 * . 0 0 5 ) + 0 . 5 ) / 1 0 . " 2 11 i ' 4 4 i 4 3 0 P R I N T ' " " - * ' * ' * * * ' * * * * ' * ' * * ' * ' * ' * * 1 4 5 1 4 4 0 P R I N T " O A i r F l o w R a t e " ; A 6 ; " L / m i n " 1 4 6 1 4 5 0 P R I N T " O l m p e l l e r S p e e d o f t h e F l o t a t i o n M a c h i n e . . . " ; A 5 ; n R P M " i ' 4 7 i 4 G 0 ' " P R I N T " " , v ' i ' D O N E " ; : 1 4 8 1 4 7 0 S T O P 1 4 9 E n d - O f - F i l e * * * * * * * * * * * * * B A T C H F L O T A T I O N D A T A S H E E T * * * * * * * * * * * * * * * * * * ( w i t h c o r r e c t e d s l i m e s w e i g h t s a n d a s s a y s ) * * * * * R U N * 1 7 2 C O D E D * 4 5 D A T E : O C T . 2 7 / 8 2 F a c t o r C o d e d L e v e l L e v e l S a m p l e T y p e C o a r s e ( g m ) F i n e s ( g m ) fota'i ( g m ) A m i n e ( l b / T ) 0 0 . 1 8 Raw F e e d 7 5 4 . 8 1 2 5 6 . 7 2 0 1 1 . 5 O i l ( " i b ' / f ) 0 0 . 1 5 E - 1 S I i m e s 9 6 . 7 2 3 9 . 8 3 3 6 . 5 •/.Sol I d ("/.) 0 4 0 D e s l i m e d S a m p l e s 2 8 . 1 4 1 . 8 6 9 . 9 T e m p ( D e g . C ) 0 3 0 • • C o n c e n t r a t e s 6 0 2 . 5 S p e e d ( R P M ) 0 1 2 0 0 T a i 1 s 1 0 0 0 . 5 A i r ( L / m i n ) 0 0 . 3 G a i n - 2 . 1 * * * * * * * * * * * * * * O e s l i m e d S a m p l e s A s s a y s * * * * * * * * * * * * * * % K c l °/ .Nacl % I n s o l F i n e s S a m p l e 3 9 . 5 1 9 5 9 . 5 5 1 0 . 9 3 C o a r s e S a m p l e 4 4 . 4 9 7 5 4 . 4 0 3 1 . 1 CFORM output * * * * * * * * * * * * * * * * * * * s i z e A n a l y s e s a n d A s s a y s o f F l o t a t i o n P r o d u c t s * * * * * * * * * * * * * * * * * * * C o n e . 1 M e s h • / . R e t a i n e d '/ .Kcl ' / .Nac l ' / . I n s o l 2 7 0 . 5 gm - 8 + 1 4 1 . 7 8 9 3 . 3 5 9 6 . 1 2 1 0 . 5 2 - 1 4 + 2 8 1 1 . 2 9 4 . 7 9 3 4 . 8 1 7 0 . 3 9 - 2 8 + 4 8 3 7 . 9 1 9 3 . 6 7 9 5 . 9 2 1 0 . 4 - 4 8 + 1 0 0 3 3 . 2 4 9 1 . 9 0 3 7 . 6 2 7 0 . 4 7 - 1 0 0 1 5 . 8 7 8 8 . 8 0 5 1 0 . 1 3 5 1 . 0 6 C o n e . 2 M e s h " / . R e t a i n e d "/.Kcl "/.Nacl ' / . I n s o l 1 0 7 . 9 gm - 8 + 1 4 0 . 3 5 9 2 . 6 7 6 6 . 9 2 4 0 . 4 - 1 4 + 2 8 7 . 6 9 9 4 . 8 8 4 4 . 7 1 6 0 . 4 - 2 8 + 4 8 " 4 0 . 3 2 9 3 . 3 2 8 6 . 2 2 2 0 . 4 5 - 4 8 + 1 0 0 3 4 . 12 9 0 . 4 0 8 9 . 132 0 . 4 6 - 1 0 0 1 7 . 5 2 8 7 . 0 6 9 1 1 . 8 4 1 1 . 0 9 C o n e . 3 M e s h %R e t a i n e d '/oKci "/.Nacl % ' i n s o ' l 1 2 1 . 4 gm - 8 + 1 4 0 . 8 7 9 3 . 7 2 5 . ; 7 2 0 . 5 6 - 1 4 + 2 8 " 1 6 . 4 5 9 4 . 6 3 3 4 . 9 1 7 0 . 4 5 - 2 8 + 4 8 4 4 . 3 2 9 0 . 3 3 8 9 . 1 3 2 0 . 5 3 , - 4 8 + 1 0 0 2 4 . 8 8 8 0 . 9 9 6 1 8 . 4 6 4 0 . 5 4 - 1 0 0 1 3 . 4 8 7 4 . 1 5 7 2 3 . 8 8 3 1 . 9 6 C o n e . 4 M e s h % R e t a i n e d '/ .Kcl ' / .Nac l ' / . I n s o l 1 0 2 . 7 gm - 8 + 1 4 1 . 5 6 9 6 . 4 2 2 . 9 6 0 . 6 2 - 1 4 + 2 8 3 0 . 5 7 9 5 . 3 3 5 4 . 1G5 0 . 5 - 2 8 + 4 8 4 0 . 9 8 7 . 9 6 1 1 . 3 4 0 . 7 - 4 8 + 1 0 0 1 6 . 4 6 7 1 . 7 3 4 2 7 . 3 9 6 0 . 8 7 - 1 0 0 1 0 . 5 2 7 0 . 5 9 2 2 5 . 1 8 8 4 . 2 2 1 T a i l s M e s h " / . R e t a i n e d '/ .Kcl ' / .Nac l •/.Insol 1 0 0 0 . 5 gm - 8 + 1 4 1 3 . 4 1 2 2 . 8 2 9 7 6 . 0 5 1 1 . 1 2 - 14 + 2 8 2 5 . 0 8 2 0 . 1 7 2 7 8 . 7 5 8 1 . 0 7 - 2 8 + 4 8 3 0 . 6 9 2 . 7 9 5 9 6 . 0 9 5 1 . 1 1 - 4 8 + 1 0 0 2 1 . 9 9 1 . 8 1 1 9 6 . 8 7 9 1 . 3 1 - 1 0 0 8 . 8 3 2 . 4 3 9 5 . 3 2 . 2 7 * * * * * * * * * * R U N * 172 C O D E D * 4 5 D A T E : O C T . 2 7 / 8 2 * * * * * * * * * * * .*.^*****..*...A...S.U.^  F l o t a t i o n M a c h i n e T y p e ' o f P o t a s h O r e % S o l i d s 1 n t h e F l o t a t i o n C e l l : D E N V E R D1 , 2 . 7 L i t r e s " : ' ' A ' Z o n e O r e : 4 0 T e m p e r a t u r e o f t h i s R u n : 3 0 D e g . C W e i g h t o f D e s 1 i m e d O r e i n t h e C e l l : 1 5 7 9 . 2 gm * * * * * * * * * * * * * * * * * * * * * * * * s c r u b b i n g a t 6 0 % S o l i d s * * * * * * * * * * * * * * * * * * * * * * * * F r a c t i o n So.Li<?...:(.9!?.) .n.?..J.g.m.). 1.9.?.?..! .T..1.m.?...lm.?..n.l. C o a r s e 7 5 4 . 8 5 0 3 . 2 1 2 5 8 5 F i n e s 1 2 5 6 . 7 8 3 7 . 8 2 0 9 4 . 5 5 T o t a l 2 0 l ' i " . " 5 ' * * * C o n d i t i o n i n g C o a r s e a t 6 5 % S o l i d s a n d F i n e s a t 6 0 % S o l i d s *.** F r a c t i o n So.)Jd__Jj_m) ?.r.l.n.?...i9m.). T o t a l C o a r s e F 1 n e s 6 3 1 . 7 9 4 7 . 5 3 4 0 . 1 6 3 1 . 7 9 7 1 . 8 1 5 7 9 . 2 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * R e a g e n t i z i n g t h e C o a r s e F r a c t i o n * * * * * * * * * * * * * * * * * * * * * * * * * * * * * R e a g e n t l b / T g / K g g r a m c . c . T i m e ( m i n ) G u a ' r ' ' ' ( 4 ' 6 % ' ) ' 6 7 1 2 A R M E E N T D 0 . 1 8 O i l ( # 9 0 4 ) 0 . 1 5 E - 1 0 . 6 E - 1 0 . 9 E - 1 0 . 7 5 E - 2 0 . 4 8 3 E - 1 1 6 . 1 3 0 . 1 8 1 5 . 5 1 . 5 f o r A m i n e 0 . 15 IE - 1 3.-.2...P.CPP.s. .?.P.^...P..i.}.....9°.m9.1h.ed * * * * * * * * * * * * * * * * * * * * * * * * * * * * R e a g e n t i z i n g t h e F i n e s F r a c t i o n * * * * * * * * * * * * * * * * * * * * * * * * * * * R e a g e n t Guar ' ' ' ' (60%' ) ' ' l b / T ' 6'."i"2" g / K g O'.'6'E-T' g r a m '6V72 ' 4 E - ' i " c . c . ............ T i m e ( m i n ) * * * * * * * * * * * * * * * * * * * * * * * * * * * * + * * * F r o t h e r C o n d i t i o n i n g i n t h e C e l l * * * * * * * * * * * * * * * * * * * * * * R e a g e n t ! ? / . ! . . g / K g g r a m D r o p s M T 1 m e (JUlD.).. M I B C 0 . 4 7 E - 1 0 . 2 3 5 E - 1 0 . 4 7 3 E - 1 9 . 5 * * * * * * * * * * * * * * * * F l o t a t i o n C o n d i t i o n s * * * * * * * * * * * * * * * * A'Tr""F'ibV'¥a"te'"V7rr'.'."'."V'rr.' rrTTrrTTrr^TTTTrro73"u7mTn I m p e l l e r S p e e d o f t h e F l o t a t i o n M a c h i n e . . . 1 2 0 0 RPM L i st i n g o f A F O R M at 0 9 : 3 7 : 3 7 o n J U L 5 , 1 9 8 3 f o r C C i d = N R C M P a g e 1 1 10 D I M M ( 2 0 ) . Y ( 5 . 6 ) , X ( 3 0 , 3 ) 2 3 4 2 0 F I L E 0 U T 1 7 2 3 0 D A T A 1 7 2 , 4 5 , " O C T . 2 7 / 8 2 " 4 0 R E A D A A . B B . C C 5 6 7 5 0 Z 1 = 0 6 0 Z 2 = 0 7 0 Z 3 = 0 ' ' 8 3 1 0 8 0 FOR i = i TO i s 9 0 R E A D F I L E 1 , M ( I ) 1 0 0 I F K 1 0 T H E N : Z 1 = Z 1 + M ( I ) 1 1 12 13 1 1 0 1 2 0 1 3 0 I F I>4 T H E N : I F I < 9 T H E N : Z 2 = Z 2 + M ( I ) I F I > 4 T H E N : I F K 1 0 T H E N : Z 3 = Z 3 + M ( I ) N E X T I 14 15 16 . 1 4 0 1 5 0 1 6 0 FOR J = 1 TO 6 FOR 1=1 T O 5 R E A D F I L E 1,Y ( I , J ) 17 18 19 1 7 0 1 8 0 1 9 0 N E X T I N E X T J FOR 1=1 TO 3 0 i 2 0 21 2 2 2 0 0 2 1 0 2 2 0 FOR J = i TO 3 R E A D F I L E 1 , X ( I , J ) N E X T J 2 3 2 4 2 5 2 3 0 2 4 0 2 5 0 N E X T I D A T A 0 , 0 , 0 , 0 , 0 , 0 R E A D C1 , C 2 , C 3 , C 4 , C 5 , C 6 2 6 2 7 2 8 2 6 0 2 7 0 2 8 0 A 1= 6 . i 8 + C 1 * ( 6 . 2 4 - 6 .18)72 .378 A 2 = 0 . 0 1 5 + C 2 * ( 0 . 0 2 2 5 - 0 . 0 1 5 ) / 2 . 3 7 8 A 3 = 0 . 4 + C 3 * ( 0 . 5 - 0 . 4 ) / 2 . 3 7 8 2 9 3 0 31 2 9 0 3 0 0 3 1 0 A4=36+C4*(35-30)72 .378 A 5 = 1 2 0 0 + C 5 * ( 1 4 0 0 - 1 2 0 0 ) / 2 . 3 7 8 A 6 = 0 . 3 + C 6 * ( 0 . 6 - 0 . 3 ) / 2 . 3 7 8 3 2 3 3 3 4 3 2 0 3 3 0 3 4 0 G = ( 3 . 3 4 8 * A 3 * 1 0 0 0 ) 7 ( i - 6 . 3 8 * A 3 ) H = ( G * 0 . 4 + 2 5 ) / ( 1 - 0 . 1 3 ) W 2 = I N T ( H * 1 0 + 0 . 5 ) / l O 3 5 3 6 3 7 3 5 0 3 6 0 3 7 0 'i = ( G * b . 6 + 3 9 ) / ( 1 - 6 . 2 1 5 ) ' W 1 = I N T ( I * 1 0 + 0 . 5 ) / 1 0 FOR K = 0 TO 5 3 8 3 9 4 0 3 8 0 3 9 0 4 0 0 k i i (k) '=6 K 2 2 ( K ) = 0 K 3 3 ( K ) = 0 41 4 2 4 3 4 1 0 4 2 0 4 3 0 k44(k)=6 K 5 5 ( K ) = 0 N 1 1 ( K ) = 0 4 4 4 5 4 6 4 4 0 4 5 0 4 6 0 N22(k)=6 N 3 3 ( K ) = 0 N 4 4 ( K ) = 0 4 7 4 8 4 9 4 7 0 4 8 0 4 9 0 N55(k)=6 I 1 1 ( K ) = 0 I 2 2 ( K ) = 0 5 0 51 5 2 5 0 0 5 1 0 5 2 0 I33(k)=6 I 4 4 ( K ) = 0 I 5 5 ( K ) = 0 5 3 5 4 5 5 5 3 0 5 4 0 5 5 0 Y i i ( k , i ) = 6 Y 1 1 ( K , 2 ) = 0 Y 1 1 ( K , 3 ) = 0 5 6 5 7 5 8 5 6 0 5 7 0 5 8 0 Y i i ( k , 4 ) =6 Y 1 1 ( K , 5 ) = 0 Y 1 1 ( K , 6 ) = 0 L i S t i n g o f A F O R M a t 0 9 : 3 7 : 3 7 o n U U L 5 , 1 9 8 3 f o r C C i d = NRCM Page 2 5 9 5 9 0 N E X T K 6 0 61 6 2 6 0 0 6 1 0 6 2 0 FOR K=1 TO 5 K 1 ( K ) = M ( 5 ) * Y ( K , 1 ) * X ( K , 1 ) / 1 0 0 0 0 K 1 1 ( K ) = K 1 ( K ) + K 1 1 ( K - 1 ) 6 3 6 4 6 5 6 3 0 6 4 0 6 5 0 Y i i ( k , i j = Y ( k , i ) + Y i i ( k - i , i ) C 1 ( K , 1 ) = M ( 5 ) * Y 1 1 ( K , 1 ) / 1 0 0 C 1 (K , 1 )=K1 1 ( K ) * 1 0 0 / C 1 ('K, 1 ) 6 6 6 7 6 8 6 6 0 6 7 0 6 8 0 k 2 ( k j = M ( 6 J + Y ( k , 2 ) * x ( k + ' 5 , i ) ' / i6600 K 2 2 ( K ) = K 2 ( K ) + K 2 2 ( K - 1 ) Y 1 1 ( K , 2 ) = Y ( K , 2 ) + Y 1 1 ( K - 1 , 2 ) 6 9 7 0 7 1 6 9 0 7 0 0 7 1 0 C 2 ( K , i ) =M('6) *Y i i (k , 2 ) / i66 C 2 ( K , 1 ) = K 2 2 ( K ) * 1 0 0 / C 2 ( K , 1 ) K 3 ( K ) = M ( 7 ) * Y ( K , 3 ) * X ( K + 1 0 , 1 ) / 1 0 0 0 0 7 2 7 3 ' 7 4 7 2 0 7 3 0 7 4 0 k 3 '3 (k) = k 3 (k j +k'3 3 (k - i') Y 1 1 ( K . 3 ) = Y ( K , 3 ) + Y 1 1 ( K - 1 , 3 ) C 3 ( K , 1 ) = M ( 7 ) * Y 1 1 ( K , 3 ) 7 1 0 0 7 5 7 6 7 7 7 5 0 7 6 0 7 7 0 C 3 ( k , i ) = k 3 ' 3 ( k)*i667c3 ( k , i ) K 4 ( K ) = M ( 8 ) * Y ( K , 4 ) * . X ( K + 1 5 , 1 )/10000 K 4 4 ( K ) = K 4 ( K ) + K 4 4 ( K - 1 ) 7 8 7 9 8 0 7 8 0 7 9 0 8 0 0 Y i i ( k . ' 4 ) = Y ( k , 4)+Yi i ( k - i , 4 ) 1 C 4 ( K . 1 ) = M ( 8 ) * Y 1 1 ( K , 4 ) / 1 0 0 C 4 ( K , 1 ) = K 4 4 ( K ) * 1 0 0 / C 4 ( K , 1 ) 81 8 2 8 3 8 1 0 K 5 ( K ) = M ( 9 ) * Y ( K , 5 ) * X ( K + 2 0 , 1 ) / 1 0 0 0 0 8 2 0 K 5 5 ( K ) = K 5 ( K ) + K 5 5 ( K - 1 ) 8 3 0 Y1 1 ( K , 5 ) = Y { K , 5 ) + Y 1 1 ( K - 1 , 5 ) 8 4 8 5 8 6 8 4 0 8 5 0 8 6 0 T ( K , 1 ) = M ( 9 ) * Y 1 1 ( K , 5 ) / 1 0 0 T ( K , 1 ) = K 5 5 ( K ) * 1 0 0 / T ( K , 1 ) N 1 ( K ) = M ( 5 ) * Y ( K , 1 ) * X ( K , 2 ) / 1 0 0 0 0 8 7 8 8 8 9 8 7 0 8 8 0 8 9 0 Ni i (k )=N"i(k)+Ni i ( k - i ' ) C 1 ( K , 2 ) = M ( 5 ) * Y 1 1 ( K . 1 ) / 1 0 0 C 1 ( K . 2 ) = N 1 1 ( K ) * 1 0 0 / C 1 ( K . 2 ) 9 0 91 9 2 9 0 0 9 1 0 9 2 0 N2 (k ) '=M (67 '*Y ' ( k ,2^ ' *x(k^5 \277i6666 N 2 2 ( K ) = N 2 ( K ) + N 2 2 ( K - 1 ) C 2 ( K , 2 ) = M ( G ) * Y 1 1 ( K , 2 ) / 1 0 0 9 3 9 4 9 5 9 3 0 9 4 0 9 5 0 C 2 ( k , 2 ) = N 2 2 ( k ) * i 6 6 / C 2 ( k ' , 2 ) N 3 ( K ) = M ( 7 ) * Y ( K , 3 ) * X ( K + 1 0 , 2 ) / 1 0 0 0 0 N 3 3 ( K ) = N 3 ( K ) + N 3 3 ( K - 1 ) 9 6 9 7 9 8 9 6 0 9 7 0 9 8 0 C 3 ( k , 2 ) = M ( ' 7 ' 5*Yi i ' ( k , 3 ) 7 i 6 6 C 3 ( K , 2 ) = N 3 3 ( K ) * 1 0 0 / C 3 ( K , 2 ) ,l N 4 ( K ) = M ( 8 ) * Y ( K , 4 ) * X ( K + 1 5 , 2 ) / 1 0 0 0 0 9 9 100 101 9 9 0 N 4 4 ( k ) ' = N 4 ( k ) + N 4 4 ' ( k - i ) 1000 C 4 ( K , 2 ) = M ( 8 ) * Y 1 1 ( K , 4 ) / 1 0 0 1010 C 4 ( K , 2 ) = N 4 4 ( K ) * 1 0 0 / C 4 ( K , 2 ) 102 1 0 3 104 1020 N 5 ( k ) = M ' ( 9 ) * Y r k , 5 ) * x r k + ^ ^ 1 0 3 0 N 5 5 ( K ) = N 5 ( K ) + N 5 5 ( K - 1 ) 1 0 4 0 T ( K , 2 ) = M ( 9 ) * Y 1 1 ( K , 5 ) / 1 0 0 1 0 5 106 1 0 7 i '050' t ( X . 2 ) = N 5 5(K ) * i667t'(K . 2 j 1 0 6 0 I 1 ( K ) = M ( 5 ) * Y ( K , 1 ) * X ( K , 3 ) / 1 0 0 0 0 1 0 7 0 I 1 1 ( K ) = I 1 ( K ) + I 1 1 ( K - 1 ) 108 1 0 9 1 10 io'so c ' i ( k . ' 3 ) = M ( 5 ) * Y i iTk, i)/ i6d 1 0 9 0 C 1 ( K , 3 ) = I 1 1 ( K ) * 1 0 0 / C 1 ( K , 3 ) 1100 I 2 ( K ) = M ( 6 ) * Y ( K , 2 ) * X ( K + 5 , 3 ) / 1 0 0 0 0 111 1 12 1 13 i i i 6 i 2 2 TK ) = I2 ( k ) ' + i 2 2 ( k - i ) 1120 C 2 ( K . 3 ) = M ( 6 ) * Y 1 1 ( K , 2 ) / 1 0 0 1 1 3 0 C 2 ( K , 3 ) = I 2 2 ( K ) * 1 0 0 / C 2 ( K , 3 ) 1 14 1 15 1 16 i i 4 6 i 3 ( k ) =M ( 7 ) * Y ( k , 3) * x ( k + i 6 , 3 ) / i 6 6 6 6 1 1 5 0 I 3 3 ( K ) = I 3 ( K ) + I 3 3 ( K - 1 ) 1 1 6 0 C 3 ( K . 3 ) = M ( 7 ) * Y 1 1 ( K , 3 ) / 1 0 0 to L i s t i n g o f A F O R M a t 0 9 : 3 7 : 3 7 o n J U L 5 , 1 9 8 3 f o r C C i d = N R C M P a g e 3 1 1.7 ! i Z 9.„C3 . (K,.3j^ 1 18 1 19 1 2 0 1 1 8 0 i ' 4 ( k)=M ( 8 : j * Y ( K.4 ) * X ( k + 1 5,30 / 1 0 0 0 0 1 1 9 0 I 4 4 ( K ) = I 4 ( K ) + I 4 4 ( K - 1 ) 1 2 0 0 C4 ( K,3)=M ( 8 ) * Y 1 1 ( K,4J/ 1 0 0 121 1 2 2 1 2 3 1 2 1 0 C 4 ( k / 3 ) = i 4 4 ^ ( k ^ * l b W c 4 ( k . 3 ) 1 2 2 0 I 5 ( K ) = M ( 9 ) * Y ( K , 5 ) * X ( K + 2 0 , 3 ) / 1 0 0 0 0 1 2 3 0 I 5 5 ( K ) = I 5 ( K ) + I 5 5 ( K - 1 ) , 1 2 4 1 2 5 1 2 S 1 2 4 0 T ( K,3)=M ( 9 ) * Y 1 1 ( K , 5 ) / 1 0 0 1 2 5 0 T ( K , 3 ) = I 5 5 ( K ) * 1 0 0 / T ( K , 3 ) 1 2 6 0 N E X T K 1 2 7 1 2 7 0 FOR 1=1 TO 5 1 2 8 1 2 9 1 2 8 0 FOR J = 1 TO 3 1 2 9 0 C 1 ( I , J ) = I N T ( C 1 ( I , d ) * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 1 3 0 131 1 3 2 i 3 0 0 C 2 ( I , j j = I N T ' ( C 2 ( I , U j * i'666+0. 5 ) / ' i 66b 1 3 1 0 C 3 ( I , U ) = I N T ( C 3 ( I , J ) * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 1 3 2 0 C 4 ( I , d ) = I N T ( C 4 ( I , u ) * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 1 3 3 134 1 3 3 0 t ( i , u ) = i N T ( f ( i , j ) * i666+6.5 j/i666 1 3 4 0 N E X T 0 ' 1 3 5 1 3 5 0 N E X T I 1 3 6 1 3 7 1 3 8 1 3 6 0 K 5 = k i 1 ( 5 ) + k 2 2 ( 5 ) ' + k ' 3 3 f ' 5 ^ j + K 4 4 ' ( 5 ) + k 5 5 ( 5 ) 1 3 7 0 N 5 = N 1 1 ( 5 ) + N 2 2 ( 5 ) + N 3 3 ( 5 ) + N 4 4 ( 5 ) + N 5 5 ( 5 ) 1 3 8 0 1 5 = 1 1 1 ( 5 ) + I 2 2 ( 5 ) + I 3 3 ( 5 ) + I 4 4 ( 5 ) + I 5 5 ( 5 ) 1 3 9 1 4 0 141 i" 3 9 0 G( i . 1 )=K1 1 ( 5 )/M"( 5 ) 1 4 0 0 R ( 1 , 1 ) = K 1 1 ( 5 ) / K 5 1 4 1 0 G (2 , 1 ).= ( K 1 1 ( 5 ) + K 2 2 ( 5 ) )/(M(5)+M(6) ) 1 4 2 1 4 3 1 4 4 i ' 4 2 0 R ( 2 , 1 ) = ( k i r(5) + k 2 2 ( 5 ) ' ) / k 5 1 4 3 0 G ( 3 , 1 ) = ( K 5 - K 4 4 ( 5 ) - K 5 5 ( 5 ) ) / ( Z 2 - M ( 8 ) ) 1 4 4 0 R ( 3 , 1 ) = ( K 5 - K 4 4 ( 5 ) - K 5 5 ( 5 ) ) / K 5 1 4 5 1 4 6 1 4 7 1 4 5 0 G (4, i ) = ' ( k 5 - k 5 5 ( 5 ) ) / Z 2 1 4 6 0 R ( 4 , 1 ) = ( K 5 - K 5 5 ( 5 ) ) / K 5 1 4 7 0 G ( 5 , 1 ) = K 5 5 ( 5)/M ( 9 ) 148 1 4 9 1 5 0 i ' 4 8 0 R ( 5 . 1 )=k55 ( 5 ) / k 5 1 4 9 0 G ( 6 , 1 ) = K 5 / Z 3 1 5 0 0 R ( 6 , 1 ) = K 5 / K 5 151 1 5 2 1 5 3 '1 5 10 G ( i , 2 ) = N l i ( 5 ) 7 M ( 5 ) 1 5 2 0 R ( 1 , 2 ) = N 1 1 ( 5 ) / N 5 1 5 3 0 G ( 2 , 2 ) = ( N 1 1 ( 5 ) + N 2 2 ( 5))/(M ( 5)+M ( 6 ) ) 154 155-156 1 5 4 0 R ( 2 , 2 ) = ' (Ni i ' ( 5 ) + N 2 ' 2 ( 5 ) ) / N 5 1 5 5 0 G ( 3 , 2 ) = ( N 5 - N 4 4 ( 5 ) - N 5 5 ( 5 ) ) / ( Z 2 - M ( 8 ) ) 1 5 6 0 R ( 3 , 2 ) = ( N 5 - N 4 4 ( 5 ) - N 5 5 ( 5 ) ) / N 5 1 5 7 1 5 8 1 5 9 1 5 7 0 G ( 4 . 2 ) = ' ( N 5 - N 5 5 ( 5 ) ) 7 ' Z 2 1 5 8 0 R ( 4 , 2 ) = ( N 5 - N 5 5 ( 5 ) ) / N 5 1 5 9 0 G ( 5 , 2)=N55 ( 5 ) / M ( 9 ) 1 6 0 161 1 6 2 1 6 0 0 R'{5,2)=N55'(5)7N5 1 6 1 0 G ( 6 , 2 ) = N 5 / Z 3 1 6 2 0 R ( 6 , 2 ) = N 5 / N 5 1 6 3 1 6 4 165 i 6 3 0 G ( i , 3 ) = i i i (5)7M"(5) 1 6 4 0 R( 1 , 3 ) = I 1 1 ( 5 ) / I 5 1 6 5 0 G ( 2 , 3 ) = ( I 1 1 ( 5 ) + I 2 2 ( 5))/(M(5)+M ( 6 ) ) 1 1 6 6 1 6 7 168 1 6 6 0 R ( 2 , 3 ) = ' ( i i r(5^ + i ' 2 ' 2 ' ( 5 ) ) 7 i 5 . 1 6 7 0 G ( 3 , 3 ) = ( I 5 - I 4 4 ( 5 ) - I 5 5 ( 5 ) ) / ( Z 2 - M ( 8 ) ) 1 6 8 0 R ( 3 , 3 ) = ( I 5 - I 4 4 ( 5 ) - I 5 5 ( 5 ) ) / I 5 1 6 9 1 7 0 171 iS'9'6 G (4 ,3 ' ) = ' ( i 5 - i 5 5 ( 5 ) ' ) 7 Z 2 1 7 0 0 R ( 4 , 3 ) = ( I 5 - I 5 5 ( 5 ) ) / I 5 1 7 1 0 G ( 5 , 3 ) = I 5 5 ( 5)/M ( 9 ) 172 1 7 3 174 1 7 2 0 R ( 5 , 3 ) = I 5 5 ( 5 ) / ' i 5 1 7 3 0 G ( 6 , 3 ) = I 5 / Z 3 1 7 4 0 R ( G . 3 ) = I 5 / I 5 L i s t i n g o f A F O R M a t 0 9 : 3 7 : 3 7 o n u U L 5 , 1 9 8 3 f o r C C 1 d = N R C M P a g e 4 1 7 5 1 7 5 0 FOR I = 1 TO G " i ' 7 6 i 7 6 0 " F 0 R " ' j » r " T 0 " 3 ' 1 7 7 1 7 7 0 G ( I , u ) = I N T ( G ( I . d ) * 1 0 0 0 0 0 + 0 . 5 ) / 1 0 0 0 1 7 8 1 7 8 0 R ( I , J)»INT(R(I ,d) .*10000+0.5)/100. ; " i ' 7 9 f 7 9 0 ' ' N E X T ' ' ' d 1 8 0 1 8 0 0 N E X T I 181 1 8 1 0 A 1 = I N T ( A 1 * 1 0 0 0 + 0 . 5 ) / 1 0 D 0 " 1 8 2 1 8 2 0 * * * A " 2 « I N T ( A 2 * i666'6+b. s )7 i6'doo 1 8 3 1 8 3 0 A 3 = I N T ( A 3 * 1 O 0 0 + 0 . 5 ) / 1 O 1 8 4 1 8 4 0 A 4 = I N T ( A 4 * 1 O + O . 5 ) / 1 0 " i ' 8 5 T 8 " 5 0 " ' A " 5 " = ' f N T " ( X 5 " * T 6 + 6 " . " 5 ) 7 l O ' : 1 8 6 1 8 6 0 A 6 = I N T ( A 6 * 1 0 0 0 + 0 . 5 ) / l 0 0 0 1 8 7 1 8 7 0 B 9 = C M D ( " % S E T L I N E L E N = 1 3 2 " ) ; " i ' 8 8 l ' 8 7 5 " ' B 7 ' ^ 1 8 9 1 8 8 0 B 8 = C M D ( " % S E T C W D = 1 G " ) 1 9 0 1 8 9 0 P R I N T " 1 * * * * * * * * * * * * * B A T C H F L O T A T I O N D A T A S H E E T * * * * * * * * * * * * * " " 1 3 1 T 9 " 6 6 " " P R " l N t " " v ' T " ^ ^ 1 9 2 1 9 1 0 P R I N T " * * * * * * * * * * * * * * * ( w i t h a d j u s t e d d a t a ) * * * * * * * * * * * * * * * * " , » " , " R U N * " ; A A , " C O D E D * " ; B B 1 9 3 1 9 2 0 P R I N T " O F a c t o r " , " C o d e d L e v e l " , " L e v e l " , " I " , " S a m p l e T y p e " . " C o a r s e (.gm)" , " F i n e s ( g m ) " , " T o t a l ( g m ) " " i ' 9 4 Y 9 " 3 0 " " p " R " i ' N t ' , " 1 " " - - " - - - - " " " r , ; - " - r ^ 1 9 5 1 9 4 0 P R I N T " A m i n e ( l b / T ) " , C 1 , A 1 , " j " . " R a w F e e d " , " " ; W 2 , W 1 . W 1 + W 2 1 9 6 1 9 5 0 P R I N T " O i l ( 1 b / T ) " , C 2 , A 2 , " I " . " S l i m e s " , " " ; I N T ( M ( 2 ) * 1 0 + 0 . 5 ) / 1 0 , I N T ( M ( 1 ) * 1 0 + 0 . 5 ) / 1 0 . I N T ( ( M ( 1 ) + M ( 2 ) ) * 1 0 + 0 . 5 ) / 1 0 " 1 9 7 T g ' G 6 ' ' ' p R I N t " " " ' ' % s o *'7 «o"esrrmed""5amp"i'es"";""" ' ' ; i 'N 'T ' '^ + 0 . 5 ) / 1 0 198 1 9 7 0 P R I N T " T e m p ( D e g . C ) " , C 4 , A 4 , " j " . " C o n c e n t r a t e s " , " " , " " , I N T ( Z 2 * 1 0 + 0 . 5 ) / 1 0 " 1 9 9 • • ' ' i 9 8 0 " p " R " l N T , r " S p " e ' e ' d "'V""Ta"l*1 s'"","""'ri'NT('M'('9)'* T d + 6 " . " 5 " ) 7 1 0 • 2 0 0 1 9 9 0 P R I N T " A i r ( L / m i n ) " , C G , A 6 , " | " . " G a i n " , " " , " " , I N T ( ( Z 1 - W 1 - W 2 ) * 1 0 + 0 . 5 ) / 1 0 2 0 1 2 0 0 0 P R I N T " 0 * * * * * * * * * * * * * * D e s l i m e d S a m p l e s A s s a y s * * * * * * * * * * * * * * ' • " 2 0 2 2 b " l 6 " " p " R"lNt" , Y • ' 7 ' " ' ' ' % K c i ' ' " V ' " " ' % N a ^ T " 7 ' " % i h s o ' : ' 2 0 3 2 0 2 0 P R I N T " " , " " , " " , " " 2 0 4 2 0 3 0 P R I N T " F i n e s S a m p l e " , I N T ( M ( 1 2 ) * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 , I N T ( M ( 1 5 ) * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 , I N T ( M ( 1 3 ) * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 " 2 0 5 2 b ' 4 b " " P R i N T ' " ' C o a r s e ' S a m p l e 2 0 6 2 0 5 0 FOR 0=1 TO 6 2 0 7 2 0 6 0 FOR I=1 TO 5 " 2 0 8 2 b 7 ' b " Y ( ' r y u ' ) ^ 2 0 9 ; 2 0 8 0 Y 1 1 ( I , J ) = I N T ( Y 1 1 ( I , d ) * 1 0 0 + 0 . 5 ) / 1 0 0 2 1 0 2 0 9 0 N E X T I " 2 i i 2 ' i b b ' N E x T ' u ' ' :  2 1 2 2 1 1 0 P R I N T " 0 * * * * * * * * * * * * * * * * * * * S i z e A n a l y s e s a n d A s s a y s o f F l o t a t i o n P r o d u c t s * * * * * * * * * * * * * * * * * * * * * " / R e c o v e r y * * * * * * * * * * * * * * * * ! ! " 2 1 3 2 r 2 ' b ' ' ' F ' b R ' ' l = ' l ' ' ' T 6 ' ' ' 3 " b 2 1 4 2 1 3 0 FOR 0=1 TO 3 \ • • 2 1 5 2 1 4 0 X ( I , d ) = I N T ( X ( I , d ) * 1 0 0 0 + 0 . 5 ) / 1 0 0 0 " ' 2 1 6 2 ' r 5 b " " N E ' x f ' ' u ' ' : ' 2 1 7 2 1 6 0 N E X T I 2 1 8 2 1 7 0 B 8 = C M D ( " % S E T C W D = 1 4 " ) • • " ' 2 " i ' 9 2 i ' ' 8 b ' ' P R ' f N f " b c ' 6 ' 2 2 0 2 1 9 0 P R I N T I N T (M( 5 ) * 1 0 + 0 . 5 ) / 1 0 : " g m " , " " , " " , " " . " " . " " , " - - - - » , » , » _ — _ Ii " 2 2 1 2 " 2 b b " D A f ' A ' ' ' - 8 T r 4 ' 7 - ' l 4 ' + ' 2 8 ' y \ ' • " 2 2 2 2 2 1 0 FOR 1=1 T O 5 2 2 3 2 2 2 0 R E A D M M ( I ) " 2 2 4 2 2 3 0 2 2 5 2 2 4 0 N 1 ( I ) = I N T ( ( N 1 ( I ) * 1 0 0 / N 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 2 2 6 2 2 5 0 I 1 ( I ) = I N T ( ( I 1 ( I ) * 1 0 0 / 1 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 " 2 2 7 ' 2 2 6 ' b " ' P R i N t " V , ' , ' M M ( I )VY ( I , T) , X 2 2 8 2 2 7 0 N E X T I 2 2 9 2 2 8 0 P R I N T " O C o n c . 2 " , " M e s h " , " ° / . R e t a i n e d " , " % K c l " , " % N a c 1 " , "°/.I n s o 1 " , " % R e c . ( K c 1 ) " . " % R e c . ( N a c 1 ) " , " % R e c . ( I n s o 1 ) " L i s t i n g o f A F O R M a t 0 9 : 3 7 : 3 7 o n J U L 5 , 1 9 8 3 f o r C C i d = N R C M P a g e 5 2 3 0 . 2 2 9 0 . P R I N T . . . I N T 2 3 1 2 3 0 0 FOR 1=1 TO 5 2 3 2 2 3 1 0 K 2 ( I ) = I N T ( ( K 2 ( I)*100 / K 5)*100+0 . 5 ) / l O O 2 3 3 2 3 2 ' 6 ' ' ' N ^ 2 3 4 2 3 3 0 I 2 ( I ) = I N T ( ( I 2 ( I)*100/ l 5)*100+0 . 5)/100 2 3 5 2 3 4 0 P R I N T " " , MM ( I ) , Y ( I | 2 ) , X ( I + 5 , 1 )., X (1 + 5 , 2 ) . X (1 + 5 , 3 ) . K 2 ( I ) , N2 ( I ) . 1 2(1.) ' 2 3 6 2 3 5 ' 6 " N E X T " i . . . 2 3 7 2 3 6 0 P R I N T " O C o n o . 3 " , " M e s h " , "7 .Reta 1 n e d " , " 7 , K c 1 " , " % N a c T ' , " % I n s o l " , " % R e c . ( K c l ) " , " ° / , R e c . ( N a c l ) " , " % R e c . ( I n s o l ) " 23.8 „ . .23..70 . . .P^ 2 3 9 2 3 8 0 FOR 1=1 TO 5 2 4 0 2 3 9 0 K 3 ( I ) = I N T ( ( K 3 ( I ) * 1 0 0 / K 5 ) * 1 0 0+0 . 5 ) / 1 0 0 "24 i 2 4 b 6 ' ' N ' 3 ' ' ( i ' ) ' " = ' l N f " ( ' ( ' N ' 3 2 4 2 2 4 1 0 I 3 ( I ) = I N T ( ( I 3 ( I ) * 1 0 0 / l 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 2 4 3 2 4 2 0 P R I N T " " , M M ( I ) , Y ( I , 3 ) , X ( 1 + 1 0 , 1 ) , X ( 1 + 1 0 , 2 ) . X ( 1 + 1 0 , 3 ) , K 3 ( I ) , N 3 ( I ) , 1 3 ( I ) " 2 4 4 2 4 3 6 ' " N E X T " ' ! 2 4 5 2 4 4 0 P R I N T " O C o n c . 4 " , " M e s h " , " % R e t a i n e d " , " % K c l " , " % N a c 1 " , " % I n s o l " , " % R e c . ( K c 1 ) " , " % R e c . ( N a c l ) " , " % R e c . ( I n s o 1 ) " 2 4 6 2 4 5 0 P R I N T I NT (M ( 8 ) * 10+0. 5 ) / 1 0 ; " g m " , " " , " " , " " . " " . " " . " " 2 4 7 2 4 6 0 FOR I=1 TO 5 2 4 8 2 4 7 0 K 4 ( I ) = I N T ( ( K 4 ( I ) * 1 0 0 / K 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 ' 2 4 9 2 ' 4 ' 8 b ' ' ' ^ 2 5 0 2 4 9 0 I 4 ( I ) = I N T ( ( I 4 ( I ) * 1 0 0 / I 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 2 5 1 2 5 0 0 P R I N T " " , MM( I ) , Y ( I , 4 ) , X ( 1 + 1 5 , 1 ) , X ( 1 + 1 5 , 2 ) , X ( 1 + 1 5 . 3 ) , K 4 ( I ) , N4 ( I ) , 1 4 ( I ) ' 2 5 2 2 5 ' l 6 ' ' N E ' x T " i ' " ' . 2 5 3 2 5 2 0 P R I N T " O T a i l s " , " M e s h " , " % R e t a 1 n e d " , " % K c 1 " , " % N a c l " , " % I n s o l " , " % R e c . ( K c l ) " , " % R e c . ( N a c l ) " . " % R e c . ( I n s o l ) " _ _ 2 5 4 2 5 3 0 P R I N T I N T (M( 9 ) * 1 0 + 0 . 5 ) / 1 0 ; " g m " , " " , " " , " " , " " , " » ( » — » , « - - ^ 2 5 5 2 5 4 0 FOR 1=1 TO 5 2 5 6 2 5 5 0 K 5 ( I ) = I N T ( ( K 5 ( I ) * 1 0 0 / K 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 2 5 7 2 5 6 0 " N 5 T f ) ' ' = ^ 2 5 8 2 5 7 0 1 5 ( 1 ) = I N T ( ( 1 5 ( I ) * 1 0 0 / 1 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 2 5 9 2 5 8 0 P R I N T " " , M M ( I ) , Y ( I , 5 ) , X ( 1 + 2 0 , 1 ) , X ( 1 + 2 0 . 2 ) , X ( 1 + 2 0 , 3 ) , K 5 ( I ) , N 5 ( I ) , 1 5 ( I ) 2 6 0 2 5 ' 9 b " ' ' N E X ' f ' ' T ' ' : ' 2 6 1 2 6 0 0 P R I N T " 1 * * * * * * * * * * * * * B A T C H F L O T A T I O N D A T A S H E E T * * * * * * * * * * * * * " 2 6 2 2 6 1 0 P R I N T " * * * * * * * * * * * * * * * ( w i t h a d j u s t e d d a t a ) * * * * * * * * * * * * * * * * » , « " , " " , " R U N 0 " ; A A , " C O D E D * " ; B B ' 2 6 3 2 6 2 d " P R ' i W * * * * * * ' * * * ' ' ' c ' u ' m u V ^ ^ ^ ® c o v e r y * * * * * * * * * " 2 6 4 2 6 3 0 P R I N T " O C o n c . 1 " , " M e s h " , " ° / o R e t a 1 n e d " , " % K c l " , " % N a c l " , " % I n s o l " , " % R e c . ( K c l ) " , " % R e c . ( N a c l )" , " % R e c . ( I n s o l ) " 2 6 5 2 S 4 6 ' ' P R r N t ' ' l ' N f T M ' ( 5 ' ^ 2 6 6 2 6 5 0 FOR 1=1 TO 5 2 6 7 2 6 6 b ' K Y ' i T H ' = ™ ^ 2 6 8 2 6 7 0 N 1 l ( l ) = I N T ( ( N 1 1 ( I ) * 1 0 0 / N 5 ) * 1 0 0 + 0 . 5 ) / l O O 2 6 9 2 6 8 0 I 1 1 ( I ) = I N T ( ( I 1 1 ( I ) * 1 0 0 / I 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 2 7 0 ' 2 6 9 0 " ' P R ' l ' N T ' " ' " ' ' , ' M M ( i')";'Yi"i"('l ','Ty',''c'n'l VT)7^ ^ •' "" 2 7 1 2 7 0 0 N E X T I 2 7 2 2 7 1 0 P R I N T " 0 C o n c . 2 " , " M e s h " , " % R e t a 1 n e d " , " % K c V \ " % N a c l " , " % I n s o l " , " % R e c . ( K c l ) " , "°/oRec . ( N a c l ) " , " % R e c . ( I n s o l ) " 2 7 3 2 7 2 6 P R I N T 2 7 4 2 7 3 0 FOR 1=1 TO 5 2 7 5 2 7 4 6 K 2 2 r n = ' i N T ' U K 2 ^ ' 2 7 6 2 7 5 0 N 2 2 ( I ) = I N T ( ( N 2 2 ( I ) * 1 0 0 / N 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 ' • . 2 7 7 2 7 6 0 I 2 2 ( I ) = I N T ( ( I 2 2 ( I ) * 1 0 0 / I 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 2 7 8 2 7 ' 7 0 ' ' P ' R T N T " " J f X i i ) ^ 2 7 9 2 7 8 0 N E X T I 2 8 0 2 7 9 0 P R I N T " O C o n c . 3 , " M e s h " , " ' / . R e t a i n e d " , " % K c l " , " °/.Nacl " , " ° / . I n s o l " , " % R e c . ( K c l ) " , " % R e c . ( N a c l ) " , " " / R e c . ( I n s o l ]T ; L i s t i n g o f A F O R M a t 0 9 : 3 7 : 3 7 o n J U L 5 , 1 9 8 3 f o r C C 1 d = N R C M P a g e 2 8 1 2 . 8 0 0 . P R i N T I N T 2 8 2 2 8 1 0 FOR 1=1 T O 5 2 8 3 2 8 2 0 K 3 3 ( I ) = I N T ( ( K 3 3 ( I ) * 1 0 0 / K 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 " 2 8 4 2 8 3 0 " N33')=TN'T" ( ' ( 'N33('I )*T6'6/N5)* 100+6.5)/ i66 2 8 5 2 8 4 0 I 3 3 ( I ) = I N T ( ( I 3 3 ( I ) * 1 0 0 / I 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 2 8 6 2 8 5 0 P R I N T " " , M M ( I ) , Y 1 1 ( I , 3 ) , C 3 ( I , 1 ) , C 3 ( I , 2 ) , C 3 ( I . 3 ) . K 3 3 ( I ) , N 3 3 ( I ) , 1 3 3 ( I ) " 2 8 7 2 8 6 6 " N E X T I " 2 8 8 2 8 7 0 P R I N T " O C o n c . 4 " , " M e s h " , ' " / . R e t a 1 n e d " , " % K c l " , " % N a c l " , ' " / . I n s o l " , ' " / . R e c . ( K c l ) " , " % R e c . ( N a c l ) " . " % R e c . ( I n s o l ) " 2 8 9 2 8 8 0 P R I N T I N T (M( 8 ) * 1 0 + 0 . 5 ) / 1 0 ; " g m " , " - - - - " , " " . " " , " " , " - » , « - - •', " -2 9 0 2 8 9 0 FOR 1=1 T O 5 2 9 1 2 9 0 0 K 4 4 ( I ) = I N T ( ( K 4 4 ( ; i ) * 1 0 0 / K 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 2 9 2 " " 2 9 Vd"N44"(T) «'i'Nf'("(N44 (l")"*"l"co/N5"y*"f6o+6. 5 J/ i00 2 9 3 2 9 2 0 I 4 4 ( I ) = I N T ( ( I 4 4 ( I ) * 1 0 0 / I 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 2 9 4 2 9 3 0 P R I N T " " , M M ( I ) , Y 1 1 ( I , 4 ) , C 4 ( I , 1 ) , C 4 ( I , 2 ) , C 4 ( I , 3 ) , K 4 4 ( I ) , N 4 4 ( I ) . 1 4 4 ( I ) " 2 9 5 2 9 4 d " " N E X T " " l ' " ' " 2 9 6 2 9 5 0 P R I N T " 0 T a 1 l s " , " M e s h " , ' " / R e t a i n e d " , " % K c l " . " % N a c l " , " % I n s o l " , " % R e c . ( K c l ) " , ' " / . R e c . ( N a c l ) " , " % R e c . ( I n s o l ) " 2 9 7 2 9 6 0 P R I N T I N T ( M ( 9 ) * 1 0 + 0 . 5 ) / 1 0 ; " g m " , " " , " " , " " , " . - — II _ _ _ _ _ _ _ _ 2 9 8 2 9 7 0 FOR 1=1 T O 5 2 9 9 2 9 8 0 K 5 5 ( I ) = I N T ( ( K 5 5 ( I ) * 1 0 0 / K 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 " 3 0 0 2 9 9 6 ' ' N 5 5 ' ( ' I ) =1W(J N55"ri"y*"l"6o/N5"y*"l"60+d"/5y/'fC)d 3 0 1 3 0 0 0 I 5 5 ( I ) = I N T ( ( I 5 5 ( I ) * 1 0 0 / I 5 ) * 1 0 0 + 0 . 5 ) / 1 0 0 3 0 2 3 0 1 0 P R I N T " " , M M ( I ) , Y 1 1 ( I , 5 ) , T ( 1 . 1 ) , T ( I , 2 ) , T ( 1 , 3 ) , K 5 5 ( I ) , N 5 5 ( I ) , 1 5 5 ( I ) " 3 0 3 3 0 2 0 N E X T I 3 0 4 3 0 3 0 FOR 1=4 TO 9 3 0 5 3 0 4 0 M 1 1 ( I ) = 0 3 0 7 3 0 6 0 FOR 1=5 TO 9 3 0 8 3 0 7 0 M ( I ) = M ( I ) * 1 0 0 / Z 3 " 3 0 9 3 6 8 o " M ' i T r i ' y = M ( ' i ' y + " M ' r f n " - T ) : " " . 3 1 0 3 0 9 0 M ( I ) = I N T ( M ( I ) * 1 0 0 + 0 . 5 ) / 1 0 0 3 1 1 3 1 0 0 M 1 1 ( I ) = I N T ( M 1 1 ( I ) * 1 0 O + 0 . 5 ) / 1 0 0 3 1 3 3 1 2 0 PRINT"-************** C u m u l a t i v e W e i g h t 0 / , a n d A s s a y s f o r C o n c e n t r a t e s * * * * * * * * * * * * * * * * * * * * * * * * C u m _ R e c f o r C o n e . * * * * * * * * * * " • "314•3j3oTfiiW^¥6aijcTiT'iWeTght??'4',""'Cum'"'w't%'"'V"'%kc'l'"';""%N'a'c"i''"7"%YhsbT''"; '"%'R'e'c''."'(kcl')'"'r 3 1 5 3 1 4 0 P R I N T " " , " " , " " , " " , " " , " " , " " , " " , " " 3 1 6 3 1 5 0 D A T A " C 1 ( 2 0 s e c ) " , " C 2 ( 2 0 s e c ) " , " C 3 ( 2 0 s e c ) " , " C 4 ( 6 0 s e c ) " , " T a 1 1 s " , " F e e d " " 3 i ' 7 3 1 66'"M(" i d y = 1 0 0 • * • ' ; 3 1 8 3 1 7 0 M 1 1 ( 1 0 ) = 1 0 0 3 1 9 3 1 8 0 M 1 1 ( 9 ) = M ( 9 ) " 3 2 0 3 ' i 9 d'"'F ' b'R ' " ' ' i ' = ' T ' ' T 0 ' ' ' 6 3 2 1 3 2 0 0 R E A D P P ( I ) 3 2 2 3 2 1 0 P R I N T P P ( I ) , M ( 1 + 4 ) , M 1 1 ( 1 + 4 ) , G ( 1 , 1 ) . G ( 1 , 2 ) , G ( I , 3 ) , R ( 1 , 1 ) , R ( 1 , 2 ) , R ( 1 , 3 ) ' • " 3 2 3 3 2 ' 2 d " N E X f " l . ' ' . 3 2 4 3 2 3 0 P R I N T " 1 D o n e " 3 2 5 3 2 4 0 S T O P " 3 2 6 E n d - O f ' - F ' T l e " ' ' ' • * * * * * * * * * * * * * B A T C H F L O T A T I O N D A T A S H E E T * * * * * * * * * * * * * * * * * * * * * * * * * * * * ( w i t h a d j u s t e d d a t a ) * * * * * * * * * * * * * * * * R U N * 1 7 2 C O D E D * 4 5 F a c t o r C o d e d L e v e l L e v e l S a m p l e T y p e C o a r s e ( g m ) F i n e s ( g m ) T o t a l ( g m ) A m i n e ( l b / T ) 0 0 . 18 Raw F e e d 7 5 4 . 8 1 2 5 6 . 7 2 0 1 1 . 5 b i i ( i b ' / t ) % S o l i d (%) T e m p ( D e g . C ) 0 0 0 0 . 1 5 E -4 0 3 0 i' ' S I 1 m e s D e s l 1 m e d S a m p l e s C o n c e n t r a t e s 9 9 . 3 2 8 . 1 2 3 4 . 8 4 1 . 8 3 3 4 . 1 6 9 . 9 6 0 9 . 5 S p e e d ( R P M ) A i r ( L / m i n ) 0 0 1 2 0 0 0 . 3 T a i l s G a i n 9 9 8 . 1 0 * * * * * * * * * * * * * * D e s l i m e d °/.Kcl S a m p l e s A s s a y s % N a c l * * * * * * * * * * * * * * % I n s o l AFORM output F i n e s S a m p l e C o a r s e S a m p l e 3 3 . 0 5 7 4 3 . 9 9 3 6 0 . 9 8 2 5 4 . 8 9 7 0 1 9 6 1 1 ******************* s i z e A n a l y s e s a n d A s s a y s o f F l o t a t i o n P r o d u c t s * * * * * * * * * * * * * * * * * * * * * % R e c o v e r y * * * * * * * * * * * * * * * * C o n e . 1 M e s h " / . R e t a i n e d % K c l ' / .Nac l •/.Insol */.Rec, ( K c l ) % R e c . ( N a c l ) •/.Rec . ( I n s o l ) 2 7 2 . 1 gm - 8 + 1 4 - 1 4 + 2 8 1 . 8 2 1 1 . 2 6 9 3 . 4 2 5 9 4 . 7 9 4 6 . 0 5 5 4 . 8 1 6 0 . 5 2 0 . 3 9 0 . 7 1 4 . 4 8 0 . 3 E - 1 0 . 16 0 . 1 6 0 . 7 3 - 2 8 + 4 8 - 4 8 + 1 0 0 - 1 0 0 3 7 . 6 8 3 3 . 16 1 6 . 0 7 9 3 . 6 8 1 9 1 . 9 1 6 8 8 . 8 3 5 . 9 2 7 . 6 1 5 1 0 . 1 1 1 0 . 4 0 . 4 7 1 . 0 5 9 1 4 . 8 1 2 . 7 8 5 . 9 9 0 . 6 4 0 . 7 3 0 . 4 7 2 . 5 2 . 5 9 2 . 8 3 C o n e . 2 1 0 9 . 9 gm M e s h % R e t a i n e d % K c 1 ' / .Nac l •/.Insol ° / . R e c . ( K c l ) ' / .Rec . ( N a c l ) % R e c . ( I n s o l ) - 8 + 1 4 - 1 4 + 2 8 - 2 8 + 4 8 0 . 4 1 7 . 7 2 4 0 . 2 3 9 2 . 6 7 8 9 4 . 8 8 4 9 3 . 3 2 9 6 . 9 2 2 4 . 7 1 6 6 . 2 2 1 0 . 4 0 . 4 0 . 4 5 0 . 6 E - 1 1 . 2 4 6 . 3 6 0 0 . 4 E - 1 0 . 2 9 0 . 1 E - 1 0 . 2 1 1 . 2 1 - 4 8 + 1 0 0 - 1 0 0 3 4 . 0 7 1 7 . 5 7 9 0 . 4 2 2 8 7 . 0 8 4 9 . 1 1 8 1 1 . 8 2 8 0 . 4 6 1 . 0 8 9 5 . 2 2 2 . 5 9 0 . 3 6 0 . 2 4 1 . 0 5 1 . 2 8 C o n e . 3 1 2 2 . 1 gm M e s h % R e t a ' i n e d '/.Kc 1 % N a c l y . i ' n s o i % ' R e c . ( K c l ) ' / .Rec . ( S i a c i ) •/.Rec . ( i n s o l ) - 8 + 1 4 0 . 9 5 9 3 . 7 2 4 5 . 7 1 6 0 . 5 6 0 . 17 0 . 1 E - 1 0 . 4 E - 1 - 1 4 + 2 8 - 2 8 + 4 8 - 4 8 + 1 0 0 1 6 . 6 2 4 4 . 1 8 2 4 . 7 7 9 4 . 6 3 4 9 0 . 3 4 1 8 1 . 0 6 1 4 . 9 1 6 9 . 1 2 9 1 8 . 3 9 9 0 . 4 5 0 . 5 3 . 0 . 5 4 2 . 9 6 . 7 . 5 1 3 . 7 8 0 . 11 0 . 5 2 0 . 5 9 0 . 5 6 1 . 7 4 1 - 1 0 0 1 3 . 4 8 7 4 . 3 2 3 2 3 . 7 2 1 1 . 9 5 6 1 . 8 8 0 . 4 1 i . 9 7 C o n e . 4 M e s h • / . R e t a i n e d '/.KCl ' / .Nac l •/.Insol ' / . R e c . ( K c l ) ' / . R e c . ( N a c l ) •/.Rec. ( I n s o l ) 1 0 5 . 4 gm - 8 + 1 4 - 1 4 + 2 8 1 . 8 2 3 1 . 3 1 9 6 . 4 2 1 9 5 . 3 3 6 2 . 9 5 9 4 . 1 6 4 0 . 6 2 0 . 5 0 . 2 9 4 . 8 5 , 0 . 1 E - 1 0 . 15 0 . 7 E - 1 1 . 0 1 - 2 8 + 4 8 • - 4 8 + 1 0 0 - 1 0 0 4 0 . 5 3 1 6 . 0 3 1 0 . 3 2 8 7 . 9 7 2 7 1 . 8 5 8 7 0 . 7 7 3 1 1 . 3 3 2 7 . 2 7 3 2 5 . 0 1 5 0 . 6 9 9 0 . 8 6 9 4 . 2 1 2 5 . 7 9 1 . 8 7 1 . 19 0 . 5 1 0 . 4 9 0 . 2 9 1 . 8 2 0 . 9 2 . 8 T a i l s 9 9 3 . 1 gm M e s h ' / . R e t a i n e d '/ .Kcl •/.Nacl ' / . I n s o l •/.Rec. ( K c l ) •/.Rec. ( N a d ) °/ .Rec . ( I n s o l ) - 8 + 1 4 - 1 4 + 2 8 - 2 8 + 4 8 1 3 . 7 5 2 5 . 4 3 0 . 6 2 3 . 9 5 1 2 0 . 8 5 2 . 8 9 7 4 . 9 1 9 7 8 . 0 8 3 9 6 . 0 0 6 1 . 1 3 1 . 0 6 7 1 . 1 0 3 5 . 0 6 8 . 1 4 . 1 . 3 6 1 0 . 9 1 . 2 1 . 0 1 3 1 . 1 3 9 . 4 7 1 6 . 5 3 2 0 . 5 8 - 4 8 + 1 0 0 - 1 0 0 21 . 7 7 8 . 4 7 1 . 8 4 1 2 . 4 6 8 9 6 . 8 5 1 9 5 . 2 8 5 1 . 3 0 8 2 . 2 4 7 0 . 6 2 0 . 3 2 2 2 . 3 4 8 . 5 5 1 7 . 3 6 1 1 . 6 1 * * * * * * * * * * * * * * * * * * * * * * *  B A T C H F L O T A T I O N D A T A S H E E T * * * * * * * * * * * * * * * * * ( w i t h a d j u s t e d d a t a ) * * * * * * * * * * * * * * * * R U N * 1 7 2 C O D E D * 4 5 * * * * * * * * C u m u l a t i v e S i z e A n a l y s e s a n d A s s a y s o f F l o t a t i o n P r o d u c t s * * * * * * * * * * * * * * * * * c u m u l a t i v e ° / . R e c o v e r y * * * * * * * * * C o n e . 1 M e s h " / . R e t a i n e d % K c l °/.Nac1 "/ . Inso l ' / . R e c . ( K c 1 ) % R e c . ( N a c l ) '/ .Rec . ( I n s o l ) 2 7 2 . 1 gm - 8 + 1 4 - 1 4 + 2 8 1 . 8 2 13 . 0 9 9 3 . 4 2 5 9 4 . 6 0 3 6 . 0 5 5 4 . 9 8 9 0 . 5 2 0 . 4 0 8 0 . 7 1 5 . 19 0 . 3 E - 1 0 . 1 9 0 . 16 0 . 8 9 - 2 8 + 4 8 - 4 8 + 1 0 0 - 1 0 0 5 0 . 7 7 8 3 . 9 3 1 0 0 ' 9 3 . 9 1 8 ' 9 3 . 1 2 7 9 2 . 4 3 7 5 . 6 8 6 . 4 4 4 7 . 0 3 4 0 . 4 0 2 0 . 4 2 9 0 . 5 3 1 9 . 9 9 3 2 . 7 7 3 8 . 7 6 0 . 8 3 1 . 5 6 2 . 0 3 3 . 3 9 5 . 9 8 8 . 8 C o n e . 2 1 0 9 . 9 gm M e s h % R e t a i n e d °/,Kcl % N a c l ' / . I n s o l •/.Rec. ( K c l ) % R e c . ( N a c l ) y . R e c . ( I n s o l ) -- — — — — — - 8 + 1 4 - 14 + 2 8 - 2 8 + 4 8 0 . 4 1 8 . 1 3 4 8 . 3 6 9 2 . 6 7 8 9 4 . 7 7 4 9 3 . 5 7 2 6 . 9 2 2 4 . 8 2 6 5 . 9 8 7 0 . 4 0 . 4 0 . 4 4 1 0 . 6 E - 1 1 . 3 7 . 6 6 0 0 . 5 E - 1 0 . 3 4 0 . 1 E - 1 0 . 2 2 1 . 4 3 - 4 8 + 1 0 0 - 1 0 0 8 2 . 4 3 1 0 0 9 2 . 2 7 9 1 . 3 5 9 7 . 2 8 1 8 . 0 8 0 . 4 4 9 0 . 5 6 1 1 2 . 8 8 1 5 . 4 7 0 . 7 0 . 9 4 2 . 4 8 3 . 7 7 C o n e . 3 1 2 2 . 1 gm M e s h ' / R e t a i n e d •/.kci % N a c l ' / . I n s o l ' / . R e c . ( K c i ) 07.Rec. ( N a c l ) % R e c . ( I n s o l ) - 8 + 1 4 0 . 9 5 9 3 . 7 2 4 5 . 7 1 6 0 . 5 6 0 . 17 0 . 1 E - 1 0 . 4 E - 1 - 14 + 2 8 - 2 8 + 4 8 - 4 8 + 1 0 0 17 . 5 7 6 1 . 7 5 8 6 . 5 2 9 4 . 5 8 5 9 1 . 5 4 9 8 8 . 5 4 7 4 . 9 5 9 7 . 9 4 3 1 0 . 9 3 6 0 . 4 5 6 0 . 5 0 9 0 . 5 1 8 3 . 1 3 1 0 . 6 3 1 4 . 4 1 0 . 1 1 0 . 6 4 1 . 23 0 . 6 2 . 3 4 3 . 3 4 - 1 0 0 1 0 0 8 3 . 6 2 9 1 2 . 6 5 9 0 . 7 1 2 1 6 . 2 9 1 . 6 4 5 . 3 C o n e . 4 M e s h ' / . R e t a i n e d % K c l "/.Nacl ' / . I n s o l % R e c . ( K c l ) ' / .Rec . ( N a c l ) °/ .Rec . ( I n s o l ) 1 0 5 . 4 gm - 8 + 1 4 - 1 4 + 2 8 1 . 8 2 3 3 . 13 9 6 . 4 2 1 9 5 . 3 9 6 2 . 9 5 9 4 . 0 9 8 0 . 6 2 0 . 5 0 6 0 . 2 9 5 . 1 3 0 . 1 E - 1 0 . 1 5 0 . 7 E - 1 1 . 0 8 - 2 8 + 4 8 - 4 8 + 1 0 0 - 1 0 0 7 3 . 6 5 8 9 . 6 8 1 0 0 9 1 . 3 1 1 8 7 . 8 3 4 8 6 . 0 7 4 8 . 0 7 7 1 1 . 5 0 8 1 2 . 9 0 1 0 . 6 1 2 0 . 6 5 8 1 . 0 2 5 1 0 . 9 2 1 2 . 7 9 1 3 . 9 7 0 . 6 7 1 . 1 5 1 . 4 4 2 . 9 3 . 8 6 . 5 9 T a i l s 9 9 8 . 1 gm M e s h •/.Rata i n e d % K c l °/.Nacl ' / . I n s o l ' / . R e c . ( K c l ) ' / .Rec . ( N a c l ) ' / . R e c . ( I n s o l ) - 8 + 1 4 - 1 4 + 2 8 - 2 8 + 4 8 13 . 7 5 3 9 . 15 6 9 . 7 6 2 3 . 9 5 1 2 1 . 9 3 9 1 3 . 5 8 2 7 4 . 9 1 9 7 6 . 9 7 2 8 5 . 3 2 3 1 . 1 3 1 . 0 3 9 1 . 0 9 5 5 . 0 6 1 3 . 2 1 1 4 . 5 7 1 0 . 9 1 31 . 9 3 6 3 . 0 5 9 . 4 7 2 5 . 9 9 4 6 . 5 7 - 4 8 + 1 0 0 - 1 0 0 91 . 5 3 1 0 0 1 0 . 7 8 9 1 0 . 0 8 4 8 8 . 0 6 5 8 8 . 6 7 7 1 . 146 1 . 2 3 9 1 5 . 1 9 1 5 . 5 1 8 5 . 3 9 9 3 . 9 4 6 ' J . 9 2 7 5 . 5 3 * * * * * * * * * * * * * * c u m u l a t i v e W e i g h t 0 / , a n d A s s a y s f o r C o n c e n t r a t e s * * * * * * * * * * * * * * * * * * * * * * * * C u m . R e c . f o r C o n e . * * * * * * * * * * P r o d u c t W e i g h t 0 / . C u m . w t % % K c l '/ .Nacl % I n s o l % R e c . ( k c i ) % R e c . ( N a c l ) % R e c . ( I n s o l ) C 1 ( 2 0 s e c ) 16 . 9 3 1 6 . 9 3 9 2 . 4 3 7 7 . 0 3 4 0 . 5 3 3 8 . 7 6 2 . 0 3 8 . 8 C 2 ( 2 0 s e c ) ' C 3 ( 2 0 s e c ) C 4 ( S O s e c ) 6 . 8 3 7 . 5 9 6 . 5 5 2 3 . 7 6 3 1 . 3 5 3 7 . 9 9 2 . 1 2 7 9 0 . 7 9 5 8 9 . 9 7 9 7 . 3 3 5 8 . 6 2 4 9 . 3 6 4 0 . 5 3 9 0 . 5 8 1 0 . 6 5 8 5 4 . 2 2 7 0 . 5 2 8 4 . 4 9 , 2 . 9 7 4 . 6 1 6 . 0 6 1 2 . 5 7 1 7 . 8 7 2 4 . 4 7 T a i l s F e e d 6 2 . 0 9 1 0 0 6 2 . 0 9 1 0 0 • 1 0 . 0 8 4 4 0 . 3 7 4 8 8 . 6 7 7 5 8 . 6 0 7 1 . 2 3 9 1 . 0 1 9 1 5 . 5 1 1 0 0 9 3 . 9 4 1 0 0 7 5 . 5 3 1 0 0 CD 166 APPENDIX D DATA ADJUSTMENT PROCEDURE FOR LARGE BATCH FLOTATION RUNS D.1 Data Adjustment Procedure D.2 L i s t i n g s of Programs DATADL, PRINTL, FORML, AFORML, SIZEFL And Example Output 167 1. FLOWSHEET CLARIFICATION AND•SYMBOL SELECTION A flowsheet of the large batch f l o t a t i o n for mass balances i s i l l u s t r a t e d below. (<-deslimed Fines Wl reagen t i z i n g and c o n d i t i o n i n g deslimed Coarse W2 reagentizing and conditioning - 4 -Wa -> xTi ,7) X(l+30,J) add f r o t h e r / c o n d i t i o n i n g 1 ( 1 , 6 ) X(1+25,J) C I YTI , 1) X ( I , J ) . 20 sec. 20 sec. 60 sec. 90 sec. C2 Y(I ,2) X(l+5,J) C3 Y l l , 3 ) X (I + 1 0 , J ) C4 Yl l , 4 ) X(l+15,J) C5 YTl,5) xTl+20,J) Mote : measured data points are underlined 168 Symbols that define corresponding measured data are as follows: Measured Data Point S o l i d s i n fi n e s f r a c t i o n S o l i d s i n coarse f r a c t i o n S o l i d s i n combined deslimed sample S o l i d s i n 1st concentrate S o l i d s i n 2nd concentrate s o l i d s in 3rd concentrate S o l i d s in 4th contcentrate s o l i d s in 5th contcentrate S o l i d s in t a i l s Weight % retented on s i z e I Symbol Wl W2 Wa C± C2 C3 C4 C5 T = mTl) m(2) m(3) m(4) m(5) m(6) m(7) m(8) mT9) Weight Weight Weight Weight Weight Weight Size I Size Size Size Size Size Size I % retained % retained % retained % retained % retained % retained mineral J mineral J of mineral of mineral of mineral of mineral of mineral on s i z e I on s i z e I on s i z e I on siz e I on siz e I on siz e I in CI**, 1 = in C2 J in C3 in C4 in C5 in T in F for CI*, 1 = 1,5 for C2 for C3 for C4 for C5 for T for F 1,5 t,3 J J J J y ( i , i ) 1(1,2) Y ( I,3) Y ( I ,4) Y d ,5) Y(I,6) Y ( I ,7) x d , J ) X(l+5, J ) X ( I +1 0 , J ) X d + 1 5, J ) X ( I+20 , J ) X (I+25,J) X(1+30,J) Unit Standard Deviat ion g S(1) g S(2) g S(3) g S(4) g S(5) g S(6) g S(7) g S(8) g S(9) % S(I,1) % S(I,2) % S(I,3) % S(I,4) % S(I,5) % S(I,6) % S(I,7) % S(I,J) % S(I+5,J) % S (I +1 0 ) % S(I+15,J) % S(I+20,J) % S(I+25,J) % S(I+30,0) *I=1,5 stands for -8+14M, -14+28M, -28+48M, -48+100M and -100M re s p e c t i v e l y **represents KCl, NaCl and INSOL re s p e c t i v e l y for J . 2. MASS BALANCE RELATIONS Mass balance r e l a t i o n s h i p s that must be s a t i s f i e d are : W1 + W2.= Wa + CI + C2 + C3 + C4 + C5 + T F = CI + C2 + C3 + C4 + C5 + T F*Y(I,7) = C1*Y(I,1) + C2*Y(I,2) + C3*Y(l,3) + C4*Y(I,4) + C5*Y(I,5) + T*Y(I,6) 1=1,4 Y(1,J) + Y(2,J) + Y(3,J) + Y(4,J) + Y(5,J) = 100 J=1,7 F*Y(I,7)*X(I+30,J) = C1*Y(I,1)*X(I,J) + C2*Y(I,2)*X(I+5,J)+ C3*Y(I,3)*X(I+10,J) + C4*Y{I,4)*X(I+15,J)+ C5*Y(I,5)*X(I+20,J) + T*Y(I,6)*X(I+25,J) X(I,1) + X(I,2) + X(I,3) = 100 1=1,5 J=1 and 3 1=1,5 J 6 9 X ( l + 5, 1) + X(l+5,2) + X(l+5,3) = 100 1 = 1 ,5 x ( i + i o , 1; 1 + X(I+10,2) + X(I+10,3) = 100 1 = 1 ,5 X(I+15,1] • + X(I+15,2) + X d + 15,3) = 100 1 = 1 ,5 X(I + 20, 1 I + X(I+20,2) + X(l+20,3) = 100 1 = 1 ,5 X(I+25,1: I + X(I+25,2) + X(l+25,3) = 100 1 = 1 ,5 X(l+30, 1 : ) + X(l+30,2) + X(l+30,3) = 100 1 = 1 ,5 3. SELECTION OF SEARCH VARIABLES Search v a r i a b l e s are the minimum number of var i a b l e s that are necessary to determine mass balances. Their s e l e c t i o n i s a r b i t r a r y . With 150 var i a b l e s involved in 58 independent equations, there must be 150 minus 58 or 92 search v a r i a b l e s . The following were selected: W1, W2, Wa, C1, C2, C3, C4, C5, Y(I,1), Y(I,2), Y(I,3), Y(I, 4), Y(1,5), Yd,6) with 1 = 1,2,3,4, and X(I,1), Xd+5,1), X(I + 10,1), X(I + 15,1), X(l+20,1), Xd+25,1), X(I,3), X(l+5,3), X(I+10,3), X(l+15,3), X(l+20,3), X(I+25,3) with 1=1,2,3,4,5. An a l t e r n a t i v e set might influence the speed of convergence. 4. CALCULATION OF DATA POINTS FROM SEARCH VARIABLES Data points must be ca l c u l a t e d from a suitable combination of search v a r i a b l e s for the objective function. Not a l l search va r i a b l e s need be required to ca l c u l a t e a given data point. Thus ; -A /\ A A Wl = W1, W2 = W2, Wa = Wa, C1 = C1 A A . A . A C2 = C2, C3 = C3, C4