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A technical and economic evaluation of run-of-mine coal transport by open channel flow Lytle, Murray Bryson 1984

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A TECHNICAL AND ECONOMIC EVALUATION OF RUN-OF-MINE COAL TRANSPORT BY OPEN CHANNEL FLOW by MURRAY BRYSON LYTLE, P.Eng. B . A S c , The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department o f M i n i n g and M i n e r a l P r o c e s s  Engineering,  M i n e r a l Economics We a c c e p t t h i s t h e s i s as c o n f o r m i n g to, the  reauAr  tand ard  THE UNIVERSITY OF BRITISH COLUMBIA May 1984 (C) M u r r a y L y t l e , 1984  t In p r e s e n t i n g requirements  this thesis f o r an  in partial  f u l f i l m e n t of  advanced degree a t  the  University  of  B r i t i s h Columbia, I agree that  the  Library  shall  it  freely available  and  study.  I  for reference  agree that permission for  department or  by  understood that for  f o r extensive copying of  s c h o l a r l y p u r p o s e s may h i s or  her  copying or  f i n a n c i a l gain  be  shall  g r a n t e d by  the  not  be  of  further this  this  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3  a l l o w e d w i t h o u t my  Date  )E-6  (3/81)  March 19,  1984  Process Engineering  Columbia  my  thesis  Murray Lytle  Mining and Mineral  thesis  It i s  permission.  Department o f  make  head o f  representatives. publication  the  written  ii  ABSTRACT The r e c e n t economic o f Western  r e c e s s i o n i n the f r e e market  and T h i r d World c o u n t r i e s has had a n e g a t i v e impact on  c o a l s a l e s by w e s t e r n C a n a d i a n c o a l p r o d u c e r s . economic  economics  Slower  worldwide  a c t i v i t y has r e d u c e d t h e demand f o r m e t a l l u r g i c a l and  t h e r m a l c o a l and c o m p e t i t i o n i n w o r l d c o a l markets In r e s p o n s e t o t h i s c h a n g i n g economic  has i n c r e a s e d .  c l i m a t e , Canadian coal  p r o d u c e r s must make t h e i r m i n i n g o p e r a t i o n s more e f f i c i e n t i n order to r e t a i n t h e i r share of the world c o a l The C o a l M o u n t a i n  Mine o f Byron Creek C o l l i e r i e s (1983) L t d .  i s an open p i t mine i n t h e mountainous B r i t i s h Columbia.  market.  r e g i o n of s o u t h e a s t e r n  The mine c u r r e n t l y t r a n s p o r t s t h e  run-of-mine  c o a l from the o p e r a t i n g p i t s t o the p r e p a r a t i o n p l a n t i n l a r g e , r e a r dump t r u c k s . the economic  The c u r r e n t s t u d y was u n d e r t a k e n t o i n v e s t i g a t e  f e a s i b i l i t y o f t r a n s p o r t i n g the r u n - o f - m i n e c o a l  t h r o u g h near v e r t i c a l , s t e e l l i n e d r a i s e s t o an u n d e r g r o u n d where i t would be c o n v e y e d  flume,  t o t h e p r e p a r a t i o n p l a n t by open c h a n n e l  flow. An e x p e r i m e n t a l program mine c o a l t h r o u g h a 15.2  t o measure the t r a n s p o r t o f r u n - o f -  centimeter.diameter, high d e n s i t y  p o l y e t h y l e n e f l u m e was c a r r i e d o u t .  The r e c i r c u l a t i n g f l u i d  test  a p p a r a t u s p r o v i d e d d a t a which was used t o d e v e l o p an e q u a t i o n to p r e d i c t the r a t e of t r a n s p o r t of c o a r s e c o a l t h r o u g h t h e f l u m e . The e x p e r i m e n t a l program  a l s o measured the d e g r a d a t i o n of  c o a l p a r t i c l e s r e s u l t i n g from p l u g f l o w c o n v e y a n c e vertical, steel lined raise. t h r o u g h a 300 meter  through a  The p l u g f l o w movement of c o a l  l o n g by 1 meter d i a m e t e r s t e e l l i n e d  raise  iii  was s i m u l a t e d by p a s s i n g 1.5 t o n n e s of c o a l t h r o u g h a 3 meter long by 75 c e n t i m e t e r d i a m e t e r s t e e l t u b e 100 t i m e s . The i n c r e a s e i n c o a l f i n e s r e s u l t i n g from t h i s t e s t was 3 p e r c e n t by w e i g h t and t h e p a r t i c l e s i z e d e g r a d a t i o n was  restricted  to the o u t e r 2 c e n t i m e t e r s of t h e c o a l column c i r c u m f e r e n c e . A computer program t o model t h e p r o j e c t e c o n o m i c s f o r an open p i t c o a l mine u s i n g e i t h e r a f l u m e t r a n s p o r t s y s t e m or a t r u c k t r a n s p o r t s y s t e m was w r i t t e n .  The program was used t o model  the p r o j e c t f i n a n c i a l r i s k by: i)  g e n e r a t i n g n e t p r e s e n t v a l u e and i n t e r n a l r a t e o f r e t u r n f r e q u e n c y d i s t r i b u t i o n s , and  ii)  t e s t i n g the s e n s i t i v i t y of the p r o j e c t economics to changes i n s e l e c t e d i n p u t v a r i a b l e s .  Mine p r o j e c t e c o n o m i c s were d e v e l o p e d f o r t h e f o l l o w i n g  five  p r o d u c t i o n and mine d e v e l o p m e n t c a s e s : i)  g r a d u a l d e v e l o p m e n t o f an e x p a n d i n g mine  ii)  r a p i d d e v e l o p m e n t of an e x p a n d i n g mine  i i i ) g r a d u a l d e v e l o p m e n t o f a new  mine  iv)  r a p i d d e v e l o p m e n t of a new  mine  v)  r e p l a c e m e n t o f c o a l t r u c k s f o r an o p e r a t i n g mine.  In a l l the c a s e s , the f l u m e s y s t e m was e c o n o m i c a l l y s u p e r i o r and was s u b j e c t to l e s s f i n a n c i a l r i s k t h a n t h e t r u c k h a u l a g e s y s t e m .  iv  TABLE OF CONTENTS Page ABSTRACT LIST OF TABLES LIST OF FIGURES CHAPTER I:  1 x  }. ?  SYNOPSIS  3  A. INTRODUCTION  3  B. SUMMARY  4  CHAPTER II:  n  xlv  1. EXPERIMENTAL PROGRAM a) Run-of-Mine Coal Transport by Open Channel Flow Tests b) Coal Degradation Tests  5 6 7  2. ECONOMIC ANALYSIS .  7  LITERATURE SEARCH FOR FLUID TRANSPORT BY OPEN CHANNEL FLOW  11  CHAPTER I I I : EXPERIMENTS IN RUN-OF-MINE COAL SLURRY TRANSPORT BY OPEN CHANNEL FLOW  30  A. INTRODUCTION  30  B. APPARATUS  31  1. Coal  31  2. Head Tank  31  3. Coarse Coal Bin  34  4. Pipe Flume  34  5. Dewatering Screen  34  6. Discharge Collector Tank  34  7. Pump and Return Line  .  35  8. Instrumentation and Measurements . .  35  a)  Flow Rate Measurements  35  V  f  -TABLE OF CONTENTS (cont'd) Page c) Slope Movement  36  d) Weight o f Coal Measurement e) Elapsed Time Measurement  ...  36  ....  f) S p e c i f i c Gravity Measurement  36  . .  9. Structure  36  C. EXPERIMENTAL PROCEDURE . . . 1. Hydraulic Transport of Coarse Coal  36 .  37  2. Restart Tests  38  3. Verfication of the Manning Equation .  39  D. PRESENTATION OF THE DATA  39  1. General  39  a) Measured Variables  39  b) Calculated Variables  40  2. Graphical Presentation  E.  36  .  47  a) Hydraulic Transport o f Raw Coal .  47  b) V e r i f i c a t i o n o f the Manning Equation  47  INTERPRETATION OF RESULTS 1. Hydraulic Transport o f Coarse Coal  .  52  a) Dimensional Analysis  52  b) Transport Function  53  c) Prediction o f Coarse Coal Transport  57  vi  TABLE OF CONTENTS (cont'd) Page 2. Restarting Tests  63  3. V e r i f i c a t i o n o f the Manning Equation .  63  F. EXPERIMENTAL ERROR  65  1. Systematic Error  65  a) Flow Rate Measurement b) Depth o f Flow Measurement  65 ....  66  c) Flume Slope Measurement  66  d) Weight Measurement  66  e) Elapsed Time Measurement  66  f)  66  Coal S p e c i f i c Gravity Measurement  2. RANDOM ERRORS  67  a) Flow Rate Measurement b) Depth o f Flow Measurement  67 ....  67  c) Flume Slope  68  d) Weight Measurements  68  e) Elapsed Time Measurement  68  f) Coal S p e c i f i c Gravity Measurement  69  3. EFFECT OF ERRORS ON EXPERIMENTAL RESULTS 69 a) Coarse Coal Transport  69  b) V e r i f i c a t i o n o f the Manning Equation 70 G. COMPARISON WITH OTHER RESEARCH 1. Ambrose 2. Graf and Acaroglu  72 72  .  75  3. Wilson  77  4. Summary  79  vii  TABLE OF CONTENTS (cont'd) Page  H. COMPARISON WITH OPERATING MINES  8 0  1. Westar Mines L t d  8 0  2. Hansa Hydro Mine  82  CHAPTER IV: PARTICLE SIZE DEGRADATION A.  CHAPTER V:  8 3  INTRODUCTION  8 3  B. APPARATUS  8 3  C. PROCEDURE  8 5  D. RESULTS  87  RUN-OF-MILL FLUME TRANSPORT SYSTEM DESIGN . . A.  INTRODUCTION  92  B. SURFACE vs UNDERGROUND FLUME TRANSPORT SYSTEM C. UNDERGROUND RUN-OF-MINE COAL SLURRY TRANSPORT SYSTEM  9 4  94  1. Coal Loader and Truck Requirements .  95  2. Run-of-Mine Coal Oversize Scalping  95  .  3. Raise Passes .  96  4. Main Haulage D r i f t  99  5. Slurrying Chamber  107  6. Flume System  107  7. Dewatering Plant  110  8. A u x i l i a r y Manway  Ill  9. Ventilation  114  10.  Instrumentation  11. Service F a c i l i t i e s  11 115  viii  TABLE OF CONTENT S (cont'd)  Page  CHAPTER VI: ESTIMATED CAPITAL AND OPERATING COSTS FOR THE RUN-OF-MINE FLUME TRANSPORT SYSTEM . . . . A.  INTRODUCTION  117  . . . 117  B. CAPITAL COSTS FOR THE FLUME TRANSPORT SYSTEM  119  1. Coal Loader and Truck .  119  2. Run-of-Mine Oversize Scalping  ....  119  3. Raise Passes  120  4. Main Haulage D r i f t  120  5. Slurrying Chamber  121  6. Flume System  121  7. Dewatering Plant 8. V e n t i l a t i o n , Instrumentation and Flume Services 9. Site Investigation 10. Engineering C. OPERATING COSTS FOR THE FLUME TRANSPORT SYSTEM  121 121 122 122 122  1. Coal Loader  124  2. Coal Trucks  124  3. Run-of-Mine Coal Oversize Scalping . .  125  4. Flume System  125  5. Dewatering Plant  126  6. Flume Services  126  CHAPTER VII: OTHER ESTIMATED DIRECT MINE OPERATING AND CAPITAL COSTS A. INTRODUCTION  1 2 7  1 2  7  ix  TABLE OF CONTENTS (cont'd) B.  CAPITAL AND OPERATING COSTS  Page 128  1. Other Mining  128  2.  Other Plant  128  3.  Head Office  129  4. O f f - s i t e Coal Transportation 5.  ....  Port Inventory  6. Capitalized and Non-capitalized Interest Payments  129 129 129  CHAPTER VIII: ESTIMATED CAPITAL AND OPERATING COSTS FOR THE RUN-OF-MINE COAL TRUCK TRANSPORT SYSTEM  130  A.  INTRODUCTION  130  B.  CAPITAL COSTS FOR THE TRUCK TRANSPORT SYSTEM 1.  C.  CHAPTER IX:  Coal Loader  131  2. Coal Trucks . OPERATING COSTS FOR THE TRUCK TRANSPORT SYSTEM 1. Coal Loader  132  2.  134  Coal Trucks  ECONOMIC EVALUATION OF FLUME AND TRUCK TRANSPORT OF RUN-OF-MINE COAL A. INTRODUCTION B.  131  132 134  .136 136  COMPARISON OF PRODUCTION AND MINE DEVELOPMENT ALTERNATIVES  137  1.  Cases Analyzed  137  2.  Analysis o f Results  138  3.  Conclusions  161  X  TABLE OF CONTENTS (cont'd) C. MONTE CARLO RISK STIMULATION  Page I  1. Analysis o f Results  155  5 1  D. SENSITIVITY ANALYSIS 1. Analysis o f Results  156  a) Coal Price  156  b) Wash Plant Yield  158  c) Inflation  158  d) Operating Costs  158  e)  162  2.  CHAPTER X:  155  Capital Costs  f) Underground Construction Costs .  162  g) Truck Operating Hours  162  h) Labour Cost  166  i)  166  Fuel Cost  CONCLUSIONS  169  E. GENERAL CONCLUSIONS . ,  169  RECOMMENDATIONS FOR FURTHER RESEARCH INTO RUNOF-MINE COAL TRANSPORT BY OPEN CHANNEL FLOW .  170  A.  INTRODUCTION  170  B.  VARIABLES AND RELATIONSHIPS TO STUDY  . .  170  C.  CHANGES TO THE EXPERIMENTAL APPARATUS . .  171  1. MATERIAL TO BE TRANSPORTED  172  2. HEAD TANK  172  3.  "172  FLUME  4. COARSE COAL BIN  174  •5. DISCHARGE COLLECTOR TANK  174  xi  TABLE OF CONTENTS (cont'd) 6.  INSTRUMENTATION  Page 174  a) Flowrate Measurement  174  b) Depth o f Flow Measurement  175  c) Flume Slope Measurement  175  d) Weight Measurement  175  BIBLIOGRAPHY  176  APPENDIX I: COMPUTER PROGRAM TO CALCULATE PROJECT ECONOMICS 179 A. INTRODUCTION  179  B. DATA ENTRY PROGRAM  180  1. Flume'Transport Data  181  2. Truck Transport Data  183  C. ECONOMIC EVALUATION PROGRAM  183  1. Monte Carlo S t a t i s t i c a l Simulation . . 186 2. Data Entry  189  3. Flume Design  191  4. Capital and Operating Costs  193  5. Federal and Provincial Taxes  193  6. Project Economics  193  a) Net Present Value  193  b) Internal Rate o f Return  197  c) S t a t i s t i c a l Results  197  APPENDIX 2: COMPUTER PROGRAM LISTING  198  xii  LIST OF TABLES Table  Page  3-1  Measured Values f o r Experimental Tests  41  3-2  Calculated Values f o r Experimental Tests  44  3-3  Measured and Calculated Values f o r Flume Restart Tests  46  3-4  Experimental Data f o r Coal S p e c i f i c Gravity Determination  48  3-5  Flow and Transport Parameter Values  3-6  Measured and Calculated Values f o r 10 V e r i f i c a t i o n  55  Tests  58  3- 7  Calculated and Measured Rate of Coal Transportation  59  4- 1  Coal Particle Degradation Test Results  90  5- 1  Rock C l a s s i f i c a t i o n using N.G.I. System  101  5-2 5- 3 6- 1  Rock C l a s s i f i c a t i o n using Bienjawski System Mass Balance o f the Dewatering Plant Cost and Production Parameters f o r Calculating the Flume System Economics  1° 113  8- 1 9- 1 9-2  9-4 9-5  123  Cost and Production Parameters for Calculating the Truck System Economics  I  Cash Flow Summary f o r Flume Transportation -gradual mine expalsion  139  3 3  Cash Flow Summary f o r Truck Transportation -gradual mine expansion K  9-3  2  Cash Flow Summaryfor Flume Transportation -rapid mine expansion Cash Flow Summary f o r Truck Transportation -rapid mine expansion Cash Flow Summary f o r Flume Transportation -gradual new mine development  140 141 l ^  2  ^  3  xiii  LIST OF TABLES (cont'd) Table 9-6 9-7 9-8 9-9 9-10  Page Cash Flow Summary f o r Truck Transportation -gradual new mine development  144  Cash Flow Summary f o r Flume Transportation -rapid new mine development  14E>  Cash Flow Summary f o r Truck Transportation -rapid new mine development  1^6  Cash Flow Summary f o r Flume Transportation -truck replacement  1^7  Cash Flow Summary f o r Truck Transportation -truck replacement  ^  9-11  Comparison o f Project Economics  149  A--1  Data F i l e s f o r Calculating the Flume System Economics  182  A--2  Data Files f o r Calculating the Truck System Economics  184  A-•3  Federal Income Tax Calculation  194  A-•4  B. C. Corporation Income Tax Calculation  195  A-•5  B. C. Mining Tax Calculation  196  xiv  LIST OF FIGURES Figure  Page  2-1  Flow Regimes  17  2-2  Ambrose Relationship  18  2-3  Graf Relationship  21  2-4  Material Velocity vs Slope  25  2-5  Fluming Curve  26  2- 6  P a r t i c l e Size vs Pipe Diameter  29  3- 1  Flume Test Apparatus  32  3-2  Particle Size Distribution  33  3-3  Hydraulic Elements for Different Geometries  43  3-4  Slurry Rheology  49  3-5  Raw Coal Transport  50  3-6  Velocity vs Depth of Flow  51  3-7  Transport Parameter vs Flow Parameter  56  3-8  Calculated vs Experimental Coarse Coal Transport  61  3-9  Coal Iso-Transport Curves  62  3-10  Cumulative Difference between Experimental and Manning Fluid Velocity  64  3-11  Calculated vs Experimental Coarse Coal Transport  71  3-12  Ambrose Relationship Using Coal Data  74  3- 13 Graf Relationship Using Coal Data  76  4- 1  Coal Sample Tube Apparatus  84  4-2  Coal P a r t i c l e Degradation Test  86  4-3  Particle Size Degradation Samples  88  XV  LIST OF FIGURES Figure  Page  4- 4  P a r t i c l e Size Distribution  89  5- 1  Design Elements  93  5-2  Grizzly Screening  97  5-3  Proposed Route for Main D r i f t  104  5-4  Long Sections of the Underground Workings  105  5-5  Cross Section of the D r i f t  106  5-6  Slurrying Chamber  108  5- 7  Dewatering Plant Flowsheet  112  6- 1  Gamma Function Frequency Distribution  113  9-1  Gradual Mine Expansion  152  9-2  Gradual New Mine Development  153  9-3  Truck Replacement  154  9-4  Coal Price S e n s i t i v i t y  157  9-5  Plant Yield S e n s i t i v i t y  159  9-6  Inflation S e n s i t i v i t y  160  9-7  Operating Cost S e n s i t i v i t y  161  9-8  Capital Cost S e n s i t i v i t y  163  9-9  Underground Construction S e n s i t i v i t y  164  9-10  Truck Hours S e n s i t i v i t y  165  9-11  Labour Cost S e n s i t i v i t y  167  9- 12  Fuel Cost S e n s i t i v i t y  168  10- 1 Proposed Flume Test Apparatus  173  xvi  LIST OF FIGURES Figure  Page  A-l  Computer Program Flowsheet  185  A-2  Monte Carlo Simulation  187  A-3  Gamma Function Cumulative Frequency Distribution  188  xvii  ACKNOWLEDGEMENT I wish to acknowledge Professor A. J . Reed f o r his unflagging encouragement and desire to be intimately involved in the production o f t h i s thesis and to Mr. J . B. Evans f o r making this "adventure i n higher education" available to me. I express my h e a r t f e l t thanks and love to my wife, Hazel, and children, Tessa and Brennan, who voluntarily l e f t the security and comfort o f home to sojourn with me. To them I dedicate this thesis.  "Surely there i s a mine f o r s i l v e r and a place f o r gold which they r e f i n e , Man put his hand to the f l i n t y rock and overturns mountains by the roots But where shall wisdom be found and where is the place of understanding? And God said to Man, 'Behold, the fear o f the Lord, that i s wisdom.'" Job 28  1  A TECHNICAL AND ECONOMIC EVALUATION OF RUN-OF-MINE COAL TRANSPORT BY OPEN CHANNEL FLOW  2  L i s t of Symbols A  Cross s e c t i o n a l  B  C o e f f i c i e n t of s l u r r y  C  Chezy c o e f f i c i e n t  Cj  C o e f f i c i e n t of s o l i d s c o n c e n t r a t i o n i n a s l u r r y  Cp  Drag c o e f f i c i e n t of a p a r t i c l e  Cv  V o l u m e t r i c c o n c e n t r a t i o n of s o l i d s i n a s l u r r y  C\fj  Weight c o n c e n t r a t i o n of s o l i d s i n a s l u r r y  D  Pipe diameter  d  Particle  d  x  f F  a r e a of f l o w velocity  size  P e r c e n t of m a t e r i a l  passing a sieve  C o e f f i c i e n t of f r i c t i o n between s o l i d p a r t i c l e s flume surface L  F r o u d e Number  g  Acceleration  k'  C o e f f i c i e n t of f l o w e n e r g y  n  Manning F r i c t i o n F a c t o r  Qs  V o l u m e t r i c r a t e of s e d i m e n t  q'  S p e c i f i c c o n s u m p t i o n of water  R  Hydraulic  S  Slope  sj  S p e c i f i c g r a v i t y of s o l i d  T  V o l u m e t r i c r a t e of s e d i m e n t  V  Average flow  V Y  opening  c  due  to  gravity transfer transport  radius  velocity  C r i t i c a l deposition Depth of f l u i d  particles  flow  velocity  transport  and  3  CHAPTER I SYNOPSIS A.  Introduction The c o a l s a l e s by w e s t e r n C a n a d i a n p r o d u c e r s have  been  s e r i o u s l y a f f e c t e d by t h e r e d u c e d w o r l d c o a l market e x p a n s i o n r e s u l t i n g f r o m t h e r e c e n t r e c e s s i o n i n t h e f r e e market of Western and T h i r d World c o u n t r i e s .  economies  The demand f o r  m e t a l l u r g i c a l and t h e r m a l c o a l has been r e d u c e d and c o m p e t i t i o n i n w o r l d c o a l m a r k e t s has i n c r e a s e d as a r e s u l t of s l o w e r w o r l d wide economic a c t i v i t y .  It i s v i t a l that Canadian coal producers  make t h e i r m i n i n g o p e r a t i o n s more e f f i c i e n t i n o r d e r t o r e t a i n t h e i r s h a r e of t h e w o r l d c o a l  market.  The open p i t m i n i n g o p e r a t i o n s o f Byron Creek  Collieries  (1983) L t d . a r e s i t u a t e d i n t h e m o u n t a i n s of s o u t h e a s t e r n B r i t i s h Columbia.  The company p r o d u c e s a t h e r m a l c o a l p r o d u c t which i s  s o l d , p r i m a r i l y , t o O n t a r i o Hydro.  P l a n s f o r a mine e x p a n s i o n  are underway and w i l l be implemented when t h e e x t r a c o a l p r o d u c t i o n has been s o l d under c o n t r a c t .  T h i s c u r r e n t s t u d y was  t o examine t h e economic f e a s i b i l i t y of t r a n s p o r t i n g  undertaken run-of-mine  c o a l t o t h e p r e p a r a t i o n p l a n t by open c h a n n e l f l o w and t o compare t h e s e r e s u l t s w i t h t h e c u r r e n t t r u c k h a u l a g e s y s t e m of c o a l transportation.  The p r o p o s e d t r a n s p o r t system i n v o l v e s c o n v e y i n g  the r u n - o f - m i n e c o a l t h r o u g h near v e r t i c a l r a i s e s t o a c i r c u l a r c r o s s s e c t i o n f l u m e i n an u n d e r g r o u n d h a u l a g e d r i f t .  The f l u m e  4  d e l i v e r s the coal to a surface dewatering plant p r i o r to b e n e f i c i a t i o n i n the preparation plant. The o b j e c t i v e s o f t h e s t u d y were t o : i)  d e v e l o p an e q u a t i o n t o p r e d i c t t h e v o l u m e t r i c r a t e o f t r a n s p o r t o f c o a l p a r t i c l e s l a r g e r t h a n 6.4 m i l l i m e t e r s i n open c h a n n e l f l o w ;  ii)  determine the e x t e n t of p a r t i c l e s i z e d e g r a d a t i o n from c o n v e y i n g c o a l , i n p l u g f l o w , t h r o u g h an i n c l i n e d ,  steel  l i n e d r a i s e , and i i i ) design a run-of-mine coal t r a n s p o r t a t i o n system using open c h a n n e l f l o w and t o make economic c o m p a r i s o n s w i t h the e x i s t i n g t r u c k h a u l a g e system o f an o p e r a t i n g open pit coal  mine.  An e x p e r i m e n t a l program was u n d e r t a k e n t o a c h i e v e t h e f i r s t two o b j e c t i v e s and a computer program was w r i t t e n t o a c c o m p l i s h thethirdobjective. The c o a l used i n t h e e x p e r i m e n t s and t h e mine l a y o u t used i n the economic a n a l y s e s were made a v a i l a b l e by t h e s t a f f o f B y r o n C o a l C o l l i e r i e s (1983) L t d . A l t h o u g h t h e p r o d u c t i o n s c h e d u l e s and g e o l o g i c a l i n f o r m a t i o n were p a t t e r n e d a f t e r t h i s mine,  capital  and o p e r a t i n g c o s t s a r e n o t s p e c i f i c and r e p r e s e n t t h e c o s t s o f an a v e r a g e w e s t e r n C a n a d i a n , m o u n t a i n t o p open p i t c o a l  B.  mine.  Summary The s t u d y o f f l u i d i z e d s e d i m e n t t r a n s p o r t has o c c u p i e d t h e  a t t e n t i o n of e n g i n e e r s f o r thousands of y e a r s .  A p p l i c a t i o n of  5  the p r a c t i c a l a s p e c t s of t h i s s t u d y have o f t e n p r e c e d e d theoretical investigations. been t r a n s p o r t e d  the  F o r example, r u n - o f - m i n e c o a l  i n open c h a n n e l  has  f l o w s i n c e the t u r n of the  c e n t u r y but o n l y i n the l a s t two d e c a d e s has t h e r e been a e f f o r t to u n d e r s t a n d  the e c o n o m i c a d v a n t a g e s of open  sediment t r a n s p o r t .  S t u d i e s i n t o the more e x t e n s i v e l y  last concerted  channel  i n v e s t i g a t e d phenomenon of s e d i m e n t t r a n s p o r t by f u l l p i p e have a l s o a c c e l e r a t e d i n the l a s t 20 to 30 y e a r s .  flow  The s t a f f at  u n d e r g r o u n d c o a l mines have c a r r i e d out most of the r e s e a r c h open c h a n n e l  t r a n s p o r t of r u n - o f - m i n e c o a l .  s i t e s p e c i f i c but was  into  T h i s work has been  u s e f u l i n d i r e c t i n g the c u r r e n t  research.  These u n d e r g r o u n d mines t r a n s p o r t c o a l i n open c o n d u i t s or  flumes.  The d e f i n i t i o n of " f l u m e " f o r the p u r p o s e s of t h i s t h e s i s has been expanded t o be any c o n d u i t , open or c l o s e d , which  transports  f l u i d or f l u i d i z e d s e d i m e n t s w i t h a f r e e s u r f a c e . 1.  Experimental  Program  The o b j e c t i v e of the e x p e r i m e n t a l  program was  to  provide  d a t a to d e t e r m i n e the o p e r a t i n g c o n s t r a i n t s f o r a r u n - o f - m i n e coal s l u r r y t r a n s p o r t system.  The e x p e r i m e n t a l  r e s u l t s were used  to: i)  develop  an e m p i r i c a l r e l a t i o n s h i p to p r e d i c t the r a t e  of c o a l t r a n s p o r t a t i o n i n a f l u m i n g ii)  system.  determine p o t e n t i a l o p e r a t i n g problems in r e s t a r t i n g the f l u m e s y s t e m w i t h a bed of c o n s o l i d a t e d  i i i ) v e r i f y use of the Manning e q u a t i o n  coal.  to p r e d i c t f l u i d  f l o w v e l o c i t y , and iv)  measure the d e g r a d a t i o n through  of c o a l p a r t i c l e s w h i l e  a s t e e l tube i n p l u g  flow.  sliding  6  a)  R u n - o f - M i n e Coal T r a n s p o r t by Open Channel Experimental  data f o r run-of-mine  Flow T e s t s  coal transportation  by open c h a n n e l f l o w were c o l l e c t e d u s i n g an a p p a r a t u s conveyed  the r u n - o f - m i n e  coal through  diameter  flume i n a r e c i r c u l a t i n g c o a l / w a t e r  I n d i v i d u a l experiments  a 15.2  which  centimeter slurry.  were run i n a b a t c h mode w i t h  d a t a c o l l e c t e d b e f o r e , d u r i n g and a f t e r each r u n .  Values  of  the f o l l o w i n g v a r i a b l e s were measured f o r 45 t e s t s : i)  volume f l o w r a t e of the s l u r r y ,  ii)  flume  slope,  i i i ) f l o w depth of the s l u r r y , iv)  weight  v)  time t a k e n t o t r a n s p o r t a l l t h e c o a l t h r o u g h flume,  vi)  of r u n - o f - m i n e  coal transported, the  and  s p e c i f i c g r a v i t y of the s l u r r y .  The f o l l o w i n g v a r i a b l e v a l u e s were c a l c u l a t e d from  the  e x p e r i m e n t a l l y measured v a r i a b l e s : i)  hydraulic radius,  ii)  c r o s s s e c t i o n a l a r e a of f l o w ,  i i i ) flow v e l o c i t y , iv)  volume of s o l i d s t r a n s p o r t e d i n u n i t t i m e ,  v)  volume c o n c e n t r a t i o n of s o l i d s .  and  T h e s e v a r i a b l e s were o r g a n i z e d i n t o u n i t l e s s groups using dimensional  a n a l y s i s and the groups were p l o t t e d a g a i n s t  each o t h e r to f i n d c o r r e l a t i n g p a i r s .  A Transport  Function,  to p r e d i c t the volume of s o l i d s t r a n s p o r t e d i n u n i t t i m e , was d e r i v e d from the s t a t i s t i c a l c o r r e l a t i o n of two of the dimensionless ratios.  The p r e d i c t i v e v a l i d i t y of the  7  T r a n s p o r t F u n c t i o n was v e r i f i e d by c o m p a r i n g  the c a l c u l a t e d  t r a n s p o r t of c o a r s e c o a l w i t h t h e e x p e r i m e n t a l of c o a r s e c o a l t r a n s p o r t f o r 10 s u b s e q u e n t  measurement  tests.  The f l u m e r e s t a r t t e s t s m o d e l l e d t h e r e s t a r t i n g of a f l u m e s y s t e m a f t e r a system shut-down. i n d i c a t e d t h a t t h e problems f l u m e system would be  The t e s t  results  a s s o c i a t e d with r e s t a r t i n g the  minor.  Use of the Manning e q u a t i o n t o p r e d i c t f l o w v e l o c i t i e s was v e r i f i e d by the agreement of t h e e x p e r i m e n t a l l y  determined  f l o w v e l o c i t i e s w i t h the c a l c u l a t e d v e l o c i t i e s , b)  Coal Degradation  Tests  The d e g r a d a t i o n of c o a l p a r t i c l e s , w h i l e moving i n p l u g f l o w t h r o u g h an i n c l i n e d s t e e l r a i s e was m o d e l l e d  i n two, 3  meter l o n g by 76 c e n t i m e t e r d i a m e t e r s t e e l t u b e s . was c a r r i e d out by s u s p e n d i n g  The  a column of r u n - o f - m i n e  test coal  in one of the t u b e s and p l a c i n g the c o a l f i l l e d tube on top of the empty s t e e l t u b e .  The column of c o a l was  i n t o the empty t u b e , the arrangement and the p r o c e s s was r e p e a t e d .  lowered  of the t u b e s was  In t h i s way,  conveyance  c o a l t h r o u g h a 300 meter l o n g s t e e l ' l i n e d r a i s e was I t was f o u n d t h a t p a r t i c l e s i z e d e g r a d a t i o n was p e r c e n t by w e i g h t  switched of  simulated.  limited.to 3  and was r e s t r i c t e d t o the o u t e r 2  c e n t i m e t e r s of the c o a l column c i r c u m f e r e n c e . 2.  Economic A n a l y s i s  A f l u m e t r a n s p o r t system f o r r u n - o f - m i n e  c o a l was  designed  to i n c o r p o r a t e : i)  a s h o v e l and t r u c k o p e r a t i o n t o d i g the c o a l and move i t a c r o s s the m i n i n g bench t o s c r e e n i n g p l a n t s ,  8  ii)  two v i b r a t i n g g r i z z l i e s t o s c r e e n out c o a l l a r g e r t h a n 6.4  particles  centimeters,  i i i ) two, 1 meter d i a m e t e r , s t e e l l i n e d r a i s e s t o c o n v e y t h e c o a l t o an u n d e r g r o u n d main h a u l a g e d r i f t , iv)  two s t e e l chambers t o r e c e i v e c o a l f r o m t h e r a i s e s and s l u r r y i t with water,  v)  a two l i n e , .6 meter d i a m e t e r f l u m e s y s t e m o f h i g h density polyethylene  pipes to convey the coal to the  s u r f a c e , and vi)  a c o a l d e w a t e r i n g p l a n t t o dewater and s t o c k p i l e t h e p l u s .6 m i l l i m e t e r c o a l and t r a n s p o r t a t h i c k e n e d of minus .6 m i l l i m e t e r c o a l t o the p r e p a r a t i o n  The c a p i t a l and o p e r a t i n g c o s t s f o r t h i s c o a l  related activities  plant.  transport  s y s t e m and o t h e r mine o p e r a t i o n r e l a t e d a c t i v i t i e s were to c a l c u l a t e mine p r o j e c t e c o n o m i c s .  slurry  The o t h e r mine  estimated  operation  were:  i)  waste m i n i n g and mine a d m i n i s t r a t i o n  ii)  p r e p a r a t i o n p l a n t and c o a l l o a d o u t ,  services,  i i i ) head o f f i c e o v e r h e a d s , iv)  r a i l t r a n s p o r t t o t h e ocean t e r m i n a l ,  v)  c o a l i n v e n t o r i e s at t h e ocean t e r m i n a l , and  vi)  f i n a n c i n g i n t e r e s t charges  The c a p i t a l and o p e r a t i n g c o s t s f o r a c o n v e n t i o n a l  truck  h a u l a g e r u n - o f - m i n e c o a l t r a n s p o r t s y s t e m were a l s o c a l c u l a t e d to p r o v i d e an economic c o m p a r i s o n f o r the f l u m e c o a l t r a n s p o r t A computer program, o p e r a t i n g on a HP-9845 computer, written to: i)  design the run-of-mine coal t r a n s p o r t  system,  system. was  9  ii)  generate operating  and c a p i t a l c o s t s f o r the  complete  f e d e r a l and p r o v i n c i a l t a x e s  and  mining p r o j e c t , i i i ) apply appropriate royalties, iv)  c a l c u l a t e a n n u a l net c a s h f l o w s ,  and  v)  d e t e r m i n e the p r o j e c t net p r e s e n t  v a l u e and  internal  r a t e of r e t u r n . The program was  w r i t t e n to s t a t i s t i c a l l y e v a l u a t e  f i n a n c i a l r i s k by c h o o s i n g  the  the i n p u t c o s t and p r o d u c t i o n  project  variables,  i n a Monte C a r l o f a s h i o n , f r o m a skewed gamma f u n c t i o n  frequency  distribution.  was  constrained  The random s e l e c t i o n of i n p u t v a r i a b l e s  by user d e f i n e d  l i m i t s on each v a r i a b l e to  u n r e a l i s t i c v a l u e s from b e i n g c h o s e n . the p r o j e c t e c o n o m i c s , a f r e q u e n c y v a l u e and  calculating  d i s t r i b u t i o n of the net  i n t e r n a l r a t e of r e t u r n was  The p r o j e c t f i n a n c i a l r i s k was  By r e p e a t e d l y  also evaluated  r u n - o f - m i n e c o a l t r a n s p o r t system i n p u t capital  ii)  operating  present  determined. by t e s t i n g the  s e n s i t i v i t y of the p r o j e c t e c o n o m i c s to changes i n the i)  prevent  following  variables:  costs, costs,  i i i ) truck operating  hour r e q u i r e m e n t s ,  iv)  fuel  costs,  v)  labour c o s t s ,  vi)  underground c o n s t r u c t i o n  and  The f o l l o w i n g g e n e r a l  costs.  p r o j e c t i n p u t v a r i a b l e s were a l s o  tested: i)  inflation  rate,  ii)  c o a l s e l l i n g p r i c e , and  10  i i i ) preparation plant y i e l d . The e c o n o m i c c o m p a r i s o n of f l u m e and t r u c k t r a n s p o r t of o f - m i n e c o a l was  evaluated  by c a l c u l a t i n g the net p r e s e n t  and i n t e r n a l r a t e of r e t u r n f o r the f o l l o w i n g i)  g r a d u a l l y developed  new  ii)  g r a d u a l l y developed  mine  mine, expansion,  new  iv)  r a p i d l y developed  mine e x p a n s i o n ,  v)  r e p l a c e m e n t of c o a l t r u c k s f o r an o p e r a t i n g " g r a d u a l l y developed"  mine,  cases achieved  and mine.  f u l l production  y e a r 8 of the 10 y e a r a n a l y s i s and the " r a p i d l y d e v e l o p e d " were at f u l l p r o d u c t i o n  in year  in  cases  4.  The f l u m e c o a l t r a n s p o r t s y s t e m was  economically  superior  and r e s u l t e d i n l e s s t o t a l p r o j e c t f i n a n c i a l r i s k than the c o a l t r a n s p o r t s y s t e m i n a l l the It i s concluded  value  cases:  i i i ) r a p i d l y developed  The  run-  truck  cases.  t h a t f l u m e t r a n s p o r t of r u n - o f - m i n e c o a l i s  o p e r a t i o n a l l y and e c o n o m i c a l l y  f e a s i b l e and has the p o t e n t i a l to  improve the e f f i c i e n c y and p r o d u c t i v i t y of w e s t e r n C a n a d i a n c o a l mine  operations.  CHAPTER I I L i t e r a t u r e Search f o r F l u i d Transport  by Open Channel Flow  F o r t h o u s a n d s o f y e a r s mankind has s t u d i e d and a t t e m p t e d t o u n d e r s t a n d t h e p r i n c i p l e s o f s e d i m e n t t r a n s p o r t by open c h a n n e l flow.  Rouse and Ince (1980) have t r a c e d t h e p r o g r e s s i o n  understanding  i n the broader context  of this  of a h i s t o r i c a l review of  the s c i e n c e o f h y d r a u l i c s . The e a r l i e s t i n d i c a t i o n s o f man-made w a t e r c o n t r o l s t r u c t u r e s a r e canals found i n Egypt.  Five thousand year o l d  d o m e s t i c p l u m b i n g , f o u n d i n t h e Indus V a l l e y , a t t e s t s t o a c i v i l i z a t i o n t h a t was r e l a t i v e l y a d v a n c e d .  In 1000 B.C., t h e  c i t y o f J e r u s a l e m was s u p p l i e d w i t h f r e s h w a t e r by a system o f a q u e d u c t s and u n d e r g r o u n d  tunnels.  The c l a s s i c a l G r e e k s i n v e s t i g a t e d many a s p e c t s o f hydraulics.  The e a r l i e s t known e x p r e s s i o n  of the r e l a t i o n s h i p  between v e l o c i t y , c r o s s s e c t i o n a l a r e a and f l o w r a t e i s c o n t a i n e d i n "DIOPTRA", w r i t t e n by Hero sometime b e f o r e 150 B.C. The Romans a r e remembered f o r t h e i r c i v i l structures. the p r e s e n t .  The w r i t t e n works o f two e n g i n e e r s  engineering have s u r v i v e d t o  Marcus V i t r u v i u s P o l l i o , s e r v i n g b o t h J u l i u s and  A u g u s t u s C a e s a r , b u i l t masonry a q u e d u c t s t o b r i n g w a t e r i n t o Rome from d i s t a n t w a t e r s o u r c e s . was  Sextus J u l i u s Frontinus  (40-103 AD)  t h e C o m m i s s i o n e r o f Water f o r Rome a t t h e t u r n o f t h e f i r s t  century  A.D. He was r e s p o n s i b l e f o r t h e d e l i v e r y o f f r e s h water  to Rome and t o o v e r s e e i t s d i s t r i b u t i o n t o p r i v a t e and p u b l i c f a c i l i t i e s t h r o u g h an e l a b o r a t e  system of l e a d p i p e s .  The  12  Middle,  o r Dark A g e s , from a b o u t 400 A.D. t o 1500 A.D., p r o d u c e d  no advancement i n knowledge a b o u t open c h a n n e l f l o w . a u t h o r i t y o f t h e Roman c h u r c h d i r e c t e d e n e r g i e s construction of cathedrals  The  toward  and m o n a s t e r i e s r a t h e r t h a n p u b l i c  w a t e r works p r o j e c t s . The R e n a i s s a n c e p e r i o d , b e g i n n i n g  a t a b o u t 1500, was marked  by a renewed c u r i o s i t y i n t h e p h y s i c a l w o r l d  and i n c r e a s i n g  rebellion against e c c l e s i a s t i c control of learning.  L e o n a r d o da  V i n c i (1452-1519) o b s e r v e d r i v e r s and b u i l t f l u m e s t o i n v e s t i g a t e open c h a n n e l f l o w .  He was t h e f i r s t t o n o t e t h e v e l o c i t y  d i s t r i b u t i o n i n a vortex, the formation  o f eddy c u r r e n t s a t a  sudden f l o w c o n s t r i c t i o n and t o s t a t e t h a t t h e f l o w r a t e a t one c r o s s - s e c t i o n i n a f l o w i n g c h a n n e l was t h e same as t h a t i n any other cross s e c t i o n .  This l a t t e r observation,  c o n t i n u i t y , was n o t e d a f t e r o b s e r v i n g  the p r i n c i p l e of  changes i n flow v e l o c i t y  r e s u l t i n g from c h a n g e s i n t h e c r o s s s e c t i o n a l area o f f l o w o f r i v e r s and f l u m e s . Guglielmini superintendent  ( 1 6 5 5 - 1 7 1 0 ) , a u n i v e r s i t y p r o f e s s o r and  o f w a t e r f o r t h e C i t y o f B o l o g n a , s t a t e d i n 1697  t h a t t h e t e n d e n c y f o r f l o w i n g w a t e r t o i n c r e a s e v e l o c i t y was o f f s e t by t h e r e s i s t a n c e o f t h e c h a n n e l . observations  He a l s o made  a b o u t t h e s c o u r i n g a c t i o n o f w a t e r and d e t e r m i n e d  t h a t an e r o s i o n e q u i l i b r i u m i s a c h i e v e d  by s t r e a m s t h a t  transport  sediment. The  f i r s t mathematical formula  f o r p r e d i c t i n g flow v e l o c i t y  i n open c h a n n e l s was p r o p o s e d by A n t o i n e Chezy (1718-1798) a b o u t one h u n d r e d y e a r s l a t e r .  He was r e s p o n s i b l e f o r d e t e r m i n i n g  the  13  dimensions  and f l o w r a t e o f a p r o p o s e d c a n a l t o b r i n g water  P a r i s from the Y v e t t e R i v e r , 20 k i l o m e t e r s to t h e s o u t h .  to The  p r o j e c t was i n t e r r u p t e d by the F r e n c h R e v o l u t i o n and h i s f o r m u l a V = C /RS was not i n c l u d e d i n the f i n a l r e p o r t . v e l o c i t y , "R"  In t h i s f o r m u l a , "V" i s  i s h y d r a u l i c r a d i u s and "S" i s the c h a n n e l  slope.  The c o e f f i c i e n t , "C", b e i n g s p e c i f i c t o each c h a n n e l , i s determined  by comparing  a c h a n n e l w i t h unknown "C" t o one  s i m i l a r h y d r a u l i c c h a r a c t e r i s t i c s f o r which  having  "C" i s known.  Chezy d i e d u n r e c o g n i z e d f o r h i s c o n t r i b u t i o n and i t wasn't u n t i l Clemens H e r s c h e l b r o u g h t h i s work t o l i g h t a c e n t u r y  later  t h a t Chezy was g i v e n c r e d i t f o r t h i s r e l a t i o n s h i p . E y t e l w e i n , i n 1801,  and T a d i n i , i n 1830,  s i m i l a r to Chezy's.  independently proposed r e l a t i o n s h i p s  They i n c o r r e c t l y c o n c l u d e d t h a t the  c h a n n e l - s p e c i f i c v a r i a b l e , "C", c o u l d be r e p l a c e d by a c o n s t a n t . The c o n s t a n t s t h e y p r o p o s e d were 50 and 50.9, r e s p e c t i v e l y . D u p u i t n o t e d , i n 1865, v a r i a b l e i n stream s e d i m e n t  t h a t p a r t i c l e s i z e i s an transport.  He a l s o noted  important the  r e l a t i o n s h i p between f l o w v e l o c i t y and t h e c a p a c i t y of a stream to c a r r y  sediment.  B a z i n (1865) p u b l i s h e d the r e s u l t s o f e x t e n s i v e open c h a n n e l f l o w t e s t s on a c a n a l d i v e r s i o n a t D i j o n c o n d u c t e d by Henry D'Arcy and h i m s e l f .  He n o t e d t h a t c h a n n e l  roughness  and c r o s s  s e c t i o n a l a r e a o f f l o w a f f e c t r e s i s t a n c e to f l o w i n a manner analogous  to f u l l pipe flow.  In 1869,  two Swiss e n g i n e e r s , G a n g u i l l e t and K u t t e r pub-  l i s h e d the r e s u l t s o f t h e i r e f f o r t s t o i n c o r p o r a t e d a t a from  the  14  Mississippi  r i v e r ( c o l l e c t e d by two A m e r i c a n m i l i t a r y e n g i n e e r s ,  Humphreys and A b b o t t ) , and t h e Bourgogne c a n a l d a t a ( f r o m B a z i n ) i n t o one g e n e r a l e q u a t i o n f o r f l o w v e l o c i t y .  They were the  first  to p r o p o s e a r o u g h n e s s c o e f f i c i e n t "n" t o a c c o u n t f o r d i f f e r e n t s t r e a m bed m a t e r i a l s . Their equation i s ;  .0015  +  23 +  V =  1  n  'RS  1 + (23 + .0015 + s  where "n" i s a c o e f f i c i e n t o f r o u g h n e s s i s the c h a n n e l s l o p e and "R"  n)  /ir  f o r the c h a n n e l bed,  "S"  i s the h y d r a u l i c r a d i u s .  Manning (1889) p r o p o s e d a d i m e n s i o n a l 1 y homogeneous relationship  o f the form; V = C ygS  (R / 1  2  + _;_22_  (R - .15m))  ml/2 where "C" i s a c o e f f i c i e n t which v a r i e s w i t h the n a t u r e o f the f l u i d s u r f a c e and "m"  i s the h e i g h t o f mercury which  atmospheric pressure.  balances  I t i s i n t e r e s t i n g t h a t , a t no t i m e , d i d  Manning p r o p o s e the r e l a t i o n s h i p V = Si/2  which now b e a r s h i s name; R2/3  A c c o r d i n g t o Chow ( 1 9 5 9 ) , the o r i g i n a l Manning r e l a t i o n s h i p p r o g r e s s i v e l y s i m p l i f i e d by a s u c c e s s i o n o f a u t h o r s and adopted f o r i n t e r n a t i o n a l  was  use, i n i t s p r e s e n t form, a t the  World Power C o n f e r e n c e . G i l b e r t (1914) c o n d u c t e d e x t e n s i v e e x p e r i m e n t s a t t h e U n i v e r s i t y o f C a l i f o r n i a t o t e s t the t r a n s p o r t o f sands  was  and  1936  15  gravels beds.  i n three s i z e s of flumes with a r t i f i c i a l l y The d a t a from t h i s i n v e s t i g a t i o n  roughened  has been s u b s e q u e n t l y  used by many r e s e a r c h e r s . Durand (1952) d e v e l o p e d a r e l a t i o n s h i p  to p r e d i c t the flow  v e l o c i t y a t which suspended sediments begin t o s e t t l e i n a p i p e . The  v e l o c i t y has been d e s i g n a t e d t h e c r i t i c a l  deposition  velocity  and was d e t e r m i n e d by Durand t o be; V  =  c  F  Jzgd(si-l)  L  where " s i " i s t h e s p e c i f i c g r a v i t y o f t h e s o l i d p a r t i c l e s and "F|_" i s a d i m e n s i o n l e s s r a t i o o f i n e r t i a l forces  (modified  F r o u d e Number).  forces  to gravity  I t i s o b t a i n e d from Durand's  g r a p h o f F r o u d e Number and p a r t i c l e s i z e f o r v a r y i n g densities.  The r e l a t i o n s h i p  wide r a n g e o f p a r t i c l e A critical  does n o t a p p l y t o s e d i m e n t s w i t h a  sizes.  deposition  v e l o c i t y e x i s t s f o r sediment  by b o t h f u l l p i p e and open c h a n n e l f l o w . i n d i c a t i o n of the variety deposition  the c r i t i c a l  h e r e t o g i v e an  i n m e t h o d o l o g i e s used t o c a l c u l a t e t h e  velocity.  deposition  transport  A few o f t h e d i f f e r e n t  equations to predict t h i s v e l o c i t y are included critical  slurry  An u n d e r s t a n d i n g o f t h e c o n c e p t o f  v e l o c i t y i s also important i n defining  "flow regimes". Different  flow regimes are e s t a b l i s h e d  c a r r i e d i n water.  when s e d i m e n t i s  A t low f l u i d v e l o c i t i e s a n d / o r l a r g e  s i z e s t h e r e a r e two d i s t i n c t p h a s e s ; a s t a t i o n a r y and  a moving f l u i d .  bed o f s o l i d s  As t h e f l u i d v e l o c i t y i n c r e a s e s  p a r t i c l e s i z e d e c r e a s e s , t h e bed o f s o l i d s w i l l e i t h e r by s l i d i n g o r by s a l t a t i o n .  particle  or the  b e g i n t o move  The s o l i d s and l i q u i d  still  16  e x i s t i n two d i s t i n c t p h a s e s . v e l o c i t y or d e c r e a s e  With a c o n t i n u e d i n c r e a s e i n f l o w  i n p a r t i c l e s i z e some o f t h e s e d i m e n t  will  be swept up i n t o the f l u i d and a v e r t i c a l c o n c e n t r a t i o n g r a d i e n t w i l l be e s t a b l i s h e d a c r o s s the c r o s s s e c t i o n o f f l o w .  At a  c e r t a i n f l o w v e l o c i t y and p a r t i c l e s i z e , a l l t h e s e d i m e n t  will  be  c a r r i e d i n the f l u i d and t h e bed of s o l i d s w i l l no l o n g e r e x i s t . The d e f i n i t i o n o f f l o w r e g i m e s  i s shown g r a p h i c a l l y  as a p l o t of f l o w v e l o c i t y v e r s u s p a r t i c l e s i z e .  on F i g u r e  2-1  The c r i t i c a l  d e p o s i t i o n v e l o c i t y as d e f i n e d by Durand i s t h a t v e l o c i t y a t which the s o l i d s j u s t b e g i n t o s e t t l e o u t o f s u s p e n s i o n w i t h the fluid. Ambrose (1953) a t t h e U n i v e r s i t y of Iowa, was the problem  of s e d i m e n t  concerned  b u i l d - u p i n s t o r m sewer s y s t e m s .  model a storm sewer, he used an 18.3 m e t e r l o n g by  with  To  15.2  c e n t i m e t e r d i a m e t e r p i p e to t r a n s p o r t sand p a r t i c l e s i n open channel  flow.  He d e t e r m i n e d  dimensionless  a relationship  2/5  where "Q"  D  2  two  terms; Q  g  between  Q s  and  Y/D  l/5(si-l)2/5  i s t h e v o l u m e t r i c f l o w r a t e o f the f l u i d , "g" i s the  universal gravitational  c o n s t a n t , "D" i s the f l u m e d i a m e t e r ,  "Qs"  i s the v o l u m e t r i c f l o w r a t e o f s o l i d s , " s i " i s t h e s p e c i f i c g r a v i t y of the s o l i d s and "Y" i s the depth o f f l o w . This relationship  i s graphed  on F i g u r e 2-2  and i s based  the c o n d u i t s l o p e w h i c h j u s t p r e v e n t s t h e s u s p e n d e d s o l i d s s e t t l i n g o u t of the w a t e r .  on from  H i s r e s e a r c h i n d i c a t e s t h a t the r a t i o  17  FLOW  REGIMES  FLOW  VELOCITY  F i g u r e 2-1 Flow regimes a r e e s t a b l i s h e d when sediment i s c a r r i e d i n water. At low f l u i d v e l o c i t i e s and/or l a r g e p a r t i c l e s i z e s t h e r e i s a s t a t i o n a r y bed o f s o l i d s and a moving f l u i d . With i n c r e a s i n g f l o w v e l o c i t y o r d e c r e a s i n g p a r t i c l e s i z e , t h e s t a t i o n a r y bed w i l l b e g i n t o s l i d e and s a l t a t e u n t i l a l l the sediment i s i n s u s p e n s i o n . I f t h e s o l i d p a r t i c l e s are small enough i t i s p o s s i b l e t o form a s l u r r y w i t h a u n i f o r m concent r a t i o n o f sediments.  18  AMBROSE  10|  1  1  i  RELATIONSHIP  1  .  1  1  i  Y/D F i g u r e 2-2 Ambrose (1953) determined t h i s r e l a t i o n s h i p f o r t h e t r a n s p o r t o f sand by open channel f l o w . I t i s based on t h e c o n d u i t shape which j u s t p r e v e n t s t h e suspended s o l i d s from s e t t l i n g out o f t h e water. His r e s e a r c h i n d i c a t e s t h a t t h e r a t i o o f p a r t i c l e s i z e t o flume diame t e r does not a f f e c t t h e t r a n s p o r t o f suspended sediment.  19  of p a r t i c l e s i z e to f l u m e d i a m e t e r  does not a f f e c t the t r a n s p o r t  of suspended sediment. In 1955,  Newitt et a l , developed  a r e l a t i o n s h i p f o r the  d e p o s i t i o n v e l o c i t y which I n c o r p o r a t e s  critical  the s e t t l i n g v e l o c i t y of  s e d i m e n t p a r t i c l e s . T h e i r r e l a t i o n s h i p 1s;  where "Cp"  i s the drag c o e f f i c i e n t o f the s e d i m e n t p a r t i c l e s  and the o t h e r v a r i a b l e s are as p r e v i o u s l y d e f i n e d . As w i t h Durand r e l a t i o n s h i p , t h i s e q u a t i o n does n o t a c c o u n t h a v i n g a wide range of p a r t i c l e s i z e s . proposed  These  a d d i n g f i n e p a r t i c l e s to d e v e l o p  c o n d i t i o n and i n c r e a s e the t r a n s p o r t o f The m i n i n g  f o r sediment  researchers  a hindered  settling  sediments.  I n d u s t r y was u s i n g open c h a n n e l  f l o w to t r a n s p o r t  s e d i m e n t s o v e r s i g n i f i c a n t d i s t a n c e s e a r l y i n the century.  the  present  Watson (1959) r e p o r t s t h a t the Montana Coal and Coke  Co., a t A l d r i d g e , Montana, t r a n s p o r t e d c o a l a d i s t a n c e o f 2800 m e t e r s i n a s h o r t i r o n - l i n e d , wooden f l u m e . S t o c k t o n Mine i n New  Zealand  In 1925,  the  t r a n s p o r t e d c o a l a d i s t a n c e o f 9200  meters i n a s i m i l a r l y c o n s t r u c t e d  flume.  A n s l e y (1963) i n v e s t i g a t e d the e f f e c t s of a d d i n g v e r y f i n e sand p a r t i c l e s , ( l e s s than .0074 m i l l i m e t e r s i n d i a m e t e r ) , c a l l e d s l i m e s , to a s a n d - w a t e r m i x t u r e s q u a r e , wooden f l u m e .  f l o w i n g i n a 15.2  H i s r e s e a r c h was  o b s e r v a t i o n s from the m i n i n g  i n response  centimeter to  industry that  " . . . t h e p r o p o r t i o n o f s l i m e s and t a i l i n g s ( s a n d ) are q u i t e c r i t i c a l f o r the s u c c e s s f u l o p e r a t i o n of f l u m e s low s l o p e s . "  at  20  He c o n c l u d e d t h a t t h e f i n e p a r t i c l e s changed t h e s l u r r y  rheology  and t h a t t h e r e i s an optimum s l i m e s c o n c e n t r a t i o n f o r t h e t r a n s p o r t o f sand i n a f l u m e . G r a f and A c a r o g l u (1968) d e v e l o p e d two d i m e n s i o n l e s s parameters  which c o r r e l a t e d a t a f o r b o t h open c h a n n e l and f u l l  pipe flow data.  The r e l a t i o n s h i p t h e y d e t e r m i n e d i s ; *• = 10.39 v  where $ i s a t r a n s p o r t p a r a m e t e r and  -2 5? '  C  y i s a shear i n t e n s i t y parameter  v  V R =  ( s ^ - l ) dgg SR  " C V " i s t h e volume c o n c e n t r a t i o n o f t h e s o l i d s and " ^ Q " i s t h e s c r e e n s i z e which w i l l pass 50 p e r c e n t o f t h e s e d i m e n t particles.  The o t h e r v a r i a b l e s have been d e f i n e d p r e v i o u s l y .  T h i s r e l a t i o n s h i p i s p l o t t e d on F i g u r e 2-3 and uses 903 d a t a p o i n t s from G i l b e r t ( 1 9 1 4 ) , Guy e t a l ( 1 9 6 6 ) , A n s l e y (1963) and Einslein  (1944).  Wasp e t a l (1970) m o d i f i e d t h e Durand r e l a t i o n s h i p t o a c c o u n t f o r s e d i m e n t s w i t h a wide d i s t r i b u t i o n o f p a r t i c l e  sizes.  T h e i r r e l a t i o n s h i p r e s u l t e d from d e s i g n s t u d i e s w i t h s l u r r i e s and is;  In 1972, Novak and N a l l u r i compared t h e a n a l y t i c a l t e c h n i q u e s f o r open c h a n n e l and f u l l p i p e f l o w .  They c o n c l u d e d t h a t t h e same  e q u a t i o n s c a n be used t o a n a l y z e both t y p e s o f f l o w i f  GRAF  F i g u r e 2-3  RELATIONSHIP  Graf and A c a r o g l u (1968) developed two d i m e n s i o n l e s s parameters t o c o r r e l a t e 903 data p o i n t s f o r sediment t r a n s p o r t by open channel f l o w . The hatched a r e a r e presents the s c a t t e r o f these p l o t t e d d a t a v a l u e s .  22  a p p r o p r i a t e c h a n g e s i n the e m p i r i c a l l y d e t e r m i n e d  equation  c o e f f i c i e n t s are made. K l i e m a n (1976) e x p e r i m e n t e d  w i t h the open c h a n n e l  transport  o f t a i l i n g s from the E l T e n i e n t e c o p p e r mine i n C h i l e .  For  40  y e a r s the m a t e r i a l had been t r a n s p o r t e d i n f l u m e s from the mine i n the Andes M o u n t a i n s t o a t a i l i n g dam 60 k i l o m e t e r s d i s t a n t and 2500 m e t e r s l o w e r .  H i s work examined the e f f e c t s o f i n c r e a s i n g  the s o l i d s c o n c e n t r a t i o n and r e d u c i n g the f l u m e s l o p e . concluded i)  He  that; the s o l i d s c o n c e n t r a t i o n has no e f f e c t on  flow  v e l o c i ty ii)  the p a r t i c l e s i z e and p a r t i c l e s i z e d i s t r i b u t i o n a r e importantvariables  i i i ) t h e c r i t i c a l d e p o s i t i o n v e l o c i t y i s i n c r e a s e d as the c o n c e n t r a t i o n of the p a r t i c l e s i s d e c r e a s e d iv)  f o r design purposes,  and,  a s o l i d s c o n c e n t r a t i o n o f 50  c e n t by w e i g h t and a f l o w v e l o c i t y o f 1.2 m e t e r s per second a p p r o p r i a t e design c r i t e r i a f o r t h i s copper  per were  tailings transport  system. Experience  w i t h open c h a n n e l  i n the S o v i e t Union was  t r a n s p o r t of r u n - o f - m i n e c o a l  d e s c r i b e d by Gontov  (1978).  D i a b a s e - l i n e d , t r a p e z o i d a l shaped, s t e e l flumes t r a n s p o r t coal p a r t i c l e s , up to 250 m i l l i m e t e r s i n d i a m e t e r , 2 per c e n t i n the G i d r o u g a l  Mine.  at grades  The d i a b a s e l i n i n g  as low  as  was  r e p o r t e d to g i v e e x c e l l e n t wear c h a r a c t e r i s t i c s . M o i r a and Mase (1979) d e s c r i b e d 15 y e a r s of open f l o w c o a l t r a n s p o r t a t the Sunagawa Mine i n J a p a n .  channel  Semi-circular  23  and c i r c u l a r flume c r o s s s e c t i o n s a r e used to move c o a l a t s l o p e s o f 12 per c e n t to 120 per c e n t . l i n i n g s , i t was  determined  e f f e c t i v e flume m a t e r i a l .  A f t e r some t e s t i n g of v a r i o u s  t h a t u n l i n e d - s t e e l was  They q u o t e t y p i c a l wear r a t e s o f  m i l l i m e t e r s o f s t e e l per m i l l i o n t o n n e s o f c o a l Tien-Yu experiments  the most c o s t 7.3  transported.  and Chu-hung (1980) r e p o r t e d on c o a l t r a n s p o r t and e x p e r i e n c e  a t the Y i a n g Chuang c o l l i e r y i n C h i n a .  They found t h a t the t r a n s p o r t o f c o a l p a r t i c l e s l a r g e r than  50  m i l l i m e t e r s does not depend on the f l u m e c r o s s s e c t i o n and developed  a formula  r e l a t i n g flume s l o p e to s o l i d s c o n c e n t r a t i o n  and f l o w v e l o c i t y ; s = CiCw V  2  + B  R where " C i and "B" are c o e f f i c i e n t s of the s l u r r y ( t y p i c a l l y 4.4xl0-  4  and 0.22  r e s p e c t i v e l y ) and " C "  c o n c e n t r a t i o n o f s o l i d s by w e i g h t .  w  i s the  However, a s t a n d a r d i z e d  flume  s l o p e o f 10% i s used by the mine to c o n f o r m to the d i p o f the c o a l seam. The t r a n s p o r t o f r u n - o f - m i n e c o a l by open c h a n n e l  flow at  the Hansa-Hydro Mine i n West Germany i s d e s c r i b e d by Kuhn  (1980).  P l a s t i c l i n e d , s t e e l f l u m e s , up to 10,000 m e t e r s l o n g , t r a n s p o r t c o a l a t s l o p e s g r e a t e r than 7 per c e n t .  In t e s t s on a p r o t o t y p e  f l u m e , Kuhn measured the d i f f e r e n c e i n v e l o c i t y between the and c o a l f o r v a r y i n g flume s l o p e s .  fluid  T h i s v e l o c i t y d i f f e r e n c e , or  s l i p , i n d i c a t e s t h a t i f the s u p p l y o f w a t e r to an o p e r a t i n g i s c u t o f f , the c o a r s e c o a l w i l l s e t t l e out i n the f l u m e near  flume the  24  d i s c h a r g e end.  F i g u r e 2-4  v e l o c i t y versus  slope.  i n d i c a t e s t h i s s l i p i n a p l o t of  Flume d e s i g n a t the Hansa-Hydro Mine i s b a s e d on following  the  criteria;  i)  v e l o c i t y = 6 m e t e r s per  second  ii)  c r o s s S e c t i o n a l Area o f Flume = 3 t i m e s the f l o w r a t e d i v i d e d by the v e l o c i t y  i i i ) s o l i d s c o n c e n t r a t i o n = 33 per c e n t by w e i g h t iv)  maximum p a r t i c l e s i z e = 250 m i l l i m e t e r s  v)  o p e r a t i n g s l o p e = 11 per  cent  Flume d e s i g n f o r t r a n s p o r t i n g r u n - o f - m i n e c o a l a t the u n d e r g r o u n d o p e r a t i o n s o f Westar Mines L t d . i n B r i t i s h i s d e s c r i b e d i n an u n p u b l i s h e d  s t a f f paper.  the f o l l o w i n g r e l a t i o n s h i p to d e t e r m i n e S =  Columbia  The a u t h o r s  propose  slope;  f l ( s i - 1 ) 100 Csiqlkl + (si-1)]  where " f l " i s the c o e f f i c i e n t o f s l i d i n g f r i c t i o n f o r c o a l on the f l u m e s u r f a c e , " q l " i s the s p e c i f i c c o n s u m p t i o n of w a t e r and " k " 1  i s the c o e f f i c i e n t o f f l o w e n e r g y i m p a r t e d  (about 0.61).  to the c o a l ,  From t h i s r e l a t i o n s h i p , the volume o f w a t e r  r e q u i r e d to t r a n s p o r t coal at t h i s property i s i n v e r s e l y p r o p o r t i o n a l to the s l o p e as shown i n F i g u r e 2-5.  With  d e c r e a s i n g f l u m e g r a d i e n t s , the r e q u i r e d volume o f w a t e r increases rapidly. The Durand/Wasp r e l a t i o n s h i p was  f u r t h e r m o d i f i e d by Hanks  (1980) to e l i m i n a t e the m o d i f i e d F r o u d e Number and to  account  d i r e c t l y f o r the v o l u m e t r i c c o n c e n t r a t i o n o f the s o l i d p a r t i c l e s .  25  MATERIAL  VELOCITY vs  SLOPE Hansa  F i g u r e 2-4  Mine  Kuhn (1980) d e s c r i b e d the phenomenon o f " s l i p " a t the HansaHydro Mine. Kuhn measured the d i f f e r e n c e s i n v e l o c i t y between the f l u i d and c o a l f o r v a r y i n g flume s l o p e s . T h i s v e l o c i t y d i f f e r e n c e i n d i c a t e s t h a t i f the s u p p l y o f water t o an o p e r a t ing flume i s c u t o f f , the c o a r s e c o a l w i l l s e t t l e out i n the flume near the d i s c h a r g e end.  26  FLUMING  Figure 2-5  CURVE  In an unpublished s t a f f paper from Westar Mines Ltd., the authors propose a mechanistic relationship to predict the volume of water required to move coarse coal f o r a given slope. From t h i s r e l a t i o n s h i p , the volume of water required to transport coal at t h i s property i s inversely proportional to the flume slope.  27  The new e q u a t i o n i s ;  .167 V c = 3.116 C  /zgD^  -  1)  where a l l of t h e v a r i a b l e s have been p r e v i o u s l y d e f i n e d . Chaudry and Y e v j e v i c h (1980) s t a t e t h a t t h e c r i t i c a l d e p o s i t i o n v e l o c i t y i s a f f e c t e d by the s i g n ( p o s i t i v e or n e g a t i v e ) o f t h e r a t e of change o f v e l o c i t y . T h a t i s , the c r i t i c a l d e p o s i t i o n v e l o c i t y , determined  by i n c r e a s i n g the f l o w  v e l o c i t y , i s d i f f e r e n t from the c r i t i c a l d e p o s i t i o n v e l o c i t y determined  by d e c r e a s i n g the f l o w v e l o c i t y .  W i l s o n (1980) d e v e l o p e d  a computer program t o d e t e r m i n e  optimum s l o p e f o r t r a n s p o r t i n g s e d i m e n t p i p e of c i r c u l a r c r o s s s e c t i o n .  by open c h a n n e l  the  flow in a  He d e f i n e d the optimum s l o p e as  t h a t s l o p e which m a x i m i z e s the t r a n s p o r t o f s o l i d s f o r a g i v e n d i s t a n c e of t r a v e l .  In d o i n g t h i s , he b o r r o w e d knowledge g a i n e d  from s t u d y i n g s e d i m e n t  t r a n s p o r t i n c l o s e d pipe flow maintaining  t h a t the "...same p h y s i c a l p r o c e s s e s o f f l u i d f r i c t i o n , t u r b u l e n t s u s p e n s i o n and m e c h a n i c a l f r i c t i o n a r e a t work i n open c h a n n e l and c l o s e d p i p e f l o w " . The optimum s l o p e d e f i n e d above i s c o n d i t i o n a l upon t h e f l o w d e p t h to p i p e d i a m e t e r  r a t i o b e i n g 0.93  and t h e  c o n c e n t r a t i o n b e i n g 30 per c e n t by volume.  solid  The r e l a t i o n s h i p  Wilson proposed i s ;  where " t a n 9" i s the optimum s l o p e , "d" i s the p a r t i c l e s i z e i n m i l l i m e t e r s and "D" i s the p i p e d i a m e t e r  in meters.  This  28  r e l a t i o n s h i p i s v a l i d f o r a f l o w regime where t h e r e i s b o t h bed l o a d and s u s p e n d e d l o a d t r a n s p o r t ( h e t e r o g e n e o u s f l o w ) . The boundary c o n d i t i o n s t o t h i s r e l a t i o n s h i p a r e d e f i n e d by two further equations;  tan  Q  -006  =  /s-i-lN ' V TT65 / 0  D  At g r a d i e n t s below t h i s v a l u e , the s e d i m e n t w i l l  6  settle into  an i m m o b i l e bed (homogeneous f l o w ) . / s-,-l\ 0.35 tane  =  0.43  The s e d i m e n t w i l l a l l be suspended a t g r a d i e n t s above t h i s v a l u e r e g a r d l e s s o f p a r t i c l e s i z e or p i p e d i a m e t e r flow).  (pseudohomogeneous  F i g u r e 2-6 i s a g r a p h o f W i l s o n ' s r e s u l t s f o r s e d i m e n t s  h a v i n g a s p e c i f i c g r a v i t y o f 2.65.  29  PARTICLE  SIZE  vs PIPE  IO  1  DIAMETER  «o°  PIPE DIAMETER Figure 2-6  (m)  Wilson (1980) developed a computer program to determine the optimum slope f o r transporting sediment by open channel flow in a pipe of c i r c u l a r cross section. He defined the optimum slope as that slope which maximizes the transport of solids for a given distance of t r a v e l . The optimum slope i s condit i o n a l upon the flow depth to pipe diameter r a t i o being 0:93 and the concentration of solids being 30 percent by volume.  30  CHAPTER I I I Experiments  i_n_ Rjjn-o_f-Mijie J^oal S l u r r y T r a n s p o r t By Open Channel  A.  Flow  Introduction The o b j e c t i v e o f t h i s e x p e r i m e n t a l  program was  d a t a to d e t e r m i n e  the o p e r a t i n g c o n s t r a i n t s f o r a  slurry transport  system.  An e x p e r i m e n t a l centimeter diameter, channel  apparatus  to p r o v i d e run-of-mine  to c o n v e y c o a l t h r o u g h  a  15.2  h i g h d e n s i t y p o l y e t h y l e n e p i p e i n open  f l o w was c o n s t r u c t e d .  The c o a l used i n the  experiments  was between 6 m i l l i m e t e r s and 65 m i l l i m e t e r s i n s i z e .  Coal  p a r t i c l e s l e s s than 1 m i l l i m e t e r i n s i z e were used to v a r y d e n s i t y o f the r e c i r c u l a t i n g  the  fluid.  Measurements o f flume s l o p e , depth o f f l u i d f l o w , w e i g h t c o a l t r a n s p o r t e d , e l a p s e d time f o r c o a l t r a n s p o r t , f l u i d  of  flow,  f l o w r a t e and f l u i d s p e c i f i c g r a v i t y were used t o ; i)  d e v e l o p an e m p i r i c a l T r a n s p o r t F u n c t i o n , u s i n g dimensional parameters  ii)  a n a l y s i s , t o p r e d i c t the t r a n s p o r t f o r coarse run-of-mine  coal.  examine p r o b l e m s a s s o c i a t e d w i t h r e s t a r t i n g a flume system w h i c h c o n t a i n s a bed o f s e t t l e d c o a l , and  i i i ) v e r i f y the use o f the Manning e q u a t i o n to p r e d i c t the average  f l o w v e l o c i t y i n an open c h a n n e l  with a  c i r c u l a r cross section. The r e s u l t s o b t a i n e d from the e x p e r i m e n t a l compared t o t h e f i n d i n g s of o t h e r r e s e a r c h e r s .  program were  31  B.  Apparatus The d a t a were c o l l e c t e d u s i n g a c l o s e d l o o p f l u m e a p p a r a t u s  which conveyed the run-of-mine coal i n a r e c i r c u l a t i n g  fluid.  I n d i v i d u a l e x p e r i m e n t s were run i n a b a t c h mode w i t h d a t a c o l l e c t e d b e f o r e , d u r i n g and a f t e r each r u n .  The e q u i p m e n t used  to c o n d u c t the e x p e r i m e n t s i s shown on F i g u r e 3-1. 1.  Coal The c o a l used i n t h e e x p e r i m e n t s was r e c e i v e d from t h e  m i n e s i t e i n p l a s t i c - l i n e d , wooden b o x e s ,  i t was s c r e e n e d a t 6.4  m i l l i m e t e r s and p i e c e s l a r g e r t h a n 65 m i l l i m e t e r s were d i s c a r d e d . The m a t e r i a l l a r g e r t h a n 6.4 m i l l i m e t e r s was used as c o a r s e c o a l i n t h e e x p e r i m e n t s and t h e m a t e r i a l l e s s t h a n one m i l l i m e t e r used to i n c r e a s e the f l u i d s p e c i f i c g r a v i t y .  was  Coal p a r t i c l e s  between 6.4 m i l l i m e t e r s and 1 m i l l i m e t e r were n o t used i n t h e experiments.  S i z e a n a l y s e s f o r the t o t a l sample, the c o a r s e  f r a c t i o n and t h e f i n e f r a c t i o n a r e shown on F i g u r e 3-2. The ash c o n t e n t o f t h e c o a l , c o m p r i s e d o f s a n d s t o n e , s h a l e and s i l t s t o n e v a r i e d between 25 and 30 p e r c e n t by w e i g h t . V i s u a l i n s p e c t i o n o f t h e c o a r s e c o a l used i n t h e e x p e r i m e n t s r e v e a l e d some ash p a r t i c l e s l a r g e r t h a n 25 m i l l i m e t e r s . 2.  Head Tank A 36 c e n t i m e t e r d i a m e t e r , c y l i n d r i c a l s t e e l tank w i t h a  c a p a c i t y o f 0.25 c u b i c m e t e r s was used t o p r o v i d e t h e m o t i v e g r a v i t y head f o r t h e f l u i d .  A 15.2 c e n t i m e t e r d i a m e t e r b u t t e r f l y  FLUME  F i g u r e 3-1  TEST  APPARATUS  The experimental d a t a f o r t h i s r e s e a r c h program was c o l l e c t e d u s i n g a c l o s e d l o o p flume apparatus which conveyed the run-of-mine c o a l i n a r e c i r c u l a t i n g f l u i d . Individual experiments were run i n batch mode with d a t a c o l l e c t e d b e f o r e , d u r i n g and a f t e r each r u n .  PARTICLE  SIZE  DISTRIBUTION  100  O Z CO (J) <  Q.  # UJ  > r<  3  O  PARTICLE Figure 3-2  The run-of-mine coal particles had a wide distribution of sizes and were 100 percent minus 65 millimeters. Fifty percent of the coarse fraction of coal used in the experiments passed a screen size of 10.1 millimeters and 50 percent of the fine coal fraction passed a screen size of .65 millimeters. The ash content of the coal, comprised of sandstone, siltstone and shale, was between 25 and 30 percent.  34  v a l v e on the tank d i s c h a r g e s p o u t r e g u l a t e d the f l o w of f l u i d i n t o the 3  flume.  •  C o a r s e Coal B i n A .08 c u b i c meter c a p a c i t y , mass f l o w b i n w i t h a 7.6  c e n t i m e t e r by 100 c e n t i m e t e r , g a t e c o n t r o l l e d d i s c h a r g e h e l d the c o a r s e f r a c t i o n of c o a l .  The c o a l was d i s c h a r g e d i n t o  the f l u i d t h r o u g h a l o n g i t u d i n a l s l o t c u t i n t o the 4.  opening  flume.  P_i pe Flume The flume was a 15.2  centimeter diameter,  p o l y e t h y l e n e c i r c u l a r p i p e , 6.1  meters i n l e n g t h .  high density I t was  s t r a p p e d to a 7.5 c e n t i m e t e r t h i c k p l a n k which h e l d i t r i g i d ensured  a constant pipe slope.  A r u b b e r hose c o n n e c t e d  and  the p i p e  flume to the head tank s p o u t and a t 3 m e t e r s and 5 m e t e r s  from  the flume i n l e t , o b s e r v a t i o n p o r t s were c u t i n t o the f l u m e .  The  8 c e n t i m e t e r by 15 c e n t i m e t e r o b s e r v a t i o n p o r t s were o r i e n t e d p a r a l l e l to the l o n g a x i s o f the 5.  Dewatering  flume.  Screen  A .6 m e t e r by 2.4 m e t e r , low a n g l e , s t a i n l e s s s t e e l dewatering  s c r e e n w i t h one m i l l i m e t e r o p e n i n g s  was p l a c e d under  the flume d i s c h a r g e to r e t a i n the c o a r s e c o a l and p r e v e n t i t from being r e c i r c u l a t e d through 6.  the  system.  D i s c h a r g e C o l l e c t o r Tank A 3 m e t e r l o n g by .9 m e t e r wide by .6 meter deep s t e e l  35  tank c o l l e c t e d t h e d e w a t e r i n g  screen underflow  and p r o v i d e d a  sump f o r t h e r e c i r c u l a t i n g pump. 7.  Pump and R e t u r n  Line  A F l y g t model B2125 s u b m e r s i b l e pump w i t h a 10 c e n t i m e t e r d i s c h a r g e , r e t u r n e d t h e f l u i d from t h e c o l l e c t o r tank to t h e head tank v i a a 10 c e n t i m e t e r d i a m e t e r p l a s t i c l i n e . B r a s s g a t e v a l v e s on t h e r e t u r n l i n e d i r e c t e d t h e f l o w o f f l u i d to t h e head t a n k , back i n t o t h e c o l l e c t o r tank o r t h r o u g h two agitation lines. diameter  The  a g i t a t i o n l i n e s were 3.8 c e n t i m e t e r  i r o n p i p e s p l a c e d l o n g i t u d i n a l l y i n t h e bottom o f t h e  discharge c o l l e c t o r tank.  H o l e s d r i l l e d e v e r y 10 c e n t i m e t e r s  along t h e i r length allowed r e c i r c u l a t i n g s l u r r y t o spray o u t , a g i t a t i n g t h e f l u i d i n t h e tank and p r e v e n t i n g c o a l  particles  from s e t t l i n g . 8.  Instrumentation  and Measurements  a)  Flow Rate Measurement The v o l u m e t r i c f l o w r a t e was measured w i t h a F i s c h e r  and P o r t e r , s e l f - z e r o 1 n g , m a g n e t i c  flowmeter  the r i s i n g l e g o f t h e r e t u r n l i n e .  i n s t a l l e d on  An i n d i c a t i n g t o t a l i z e r  provided a d i g i t a l d i s p l a y o f the f l u i d flow r a t e i n tenths of a p e r c e n t o f t h e c a l i b r a t e d f u l l b)  flow.  Depth o f Flow Measurement The depth o f f l u i d f l o w was c a l c u l a t e d by m e a s u r i n g t h e  d i s t a n c e from t h e t o p o f t h e flume t o t h e f l u i d s u r f a c e and  36  subtracting  t h i s from the f l u m e d i a m e t e r .  The r u l e r used  f o r t h i s p u r p o s e was s c a l e d i n s i x t e e n t h s o f an i n c h . c)  S l o p e Measurement A v e r n i e r , p r o p e l l e r compass, used t o measure t h e  i n c l i n a t i o n o f t h e f l u m e , was c a l i b r a t e d 1n t e n t h s o f a degree. d)  Weight o f Coal Measurement The c o a r s e c o a l was weighed w i t h a s p r i n g b a l a n c e  s c a l e d i n two ounce d i v i s i o n s . e)  E l a p s e d Time Measurement Each t e s t was t i m e d w i t h a s t o p watch which measured  to  one h u n d r e d t h o f a s e c o n d . f)  Specific Gravity  Measurements  The s p e c i f i c g r a v i t y o f the c o a r s e c o a l was measured w e i g h i n g t h e c o a l and then m e a s u r i n g i t s volume i n a w a t e r - f i l l e d , graduated c y l i n d e r scaled in 2 m i l l i l i t e r 1ncrements. The s p e c i f i c g r a v i t y o f the s l u r r y was o b t a i n e d by weighing 1 0 l i t e r s of s l u r r y in a c a l i b r a t e d 9.  bucket.  Structure C o n s t r u c t i o n s c a f f o l d i n g , s i t t i n g on j a c k screws  s u p p o r t e d the head tank and f l u m e . C.  Experimental  Procedure  Data v a l u e s were c o l l e c t e d when the f l o w r a t e o f the r e c i r c u l a t i n g f l u i d was s t a b i l i z e d .  A f t e r each c o a r s e c o a l  by  37  t r a n s p o r t t e s t , t h e system was a l l o w e d t o r e s t a b i l i z e and t h e d a t a v a l u e s were c o l l e c t e d a g a i n . E x p e r i m e n t s were c o n d u c t e d ; i)  to determine the h y d r a u l i c t r a n s p o r t parameters f o r r u n - o f - m i n e c o a l 1n a p i p e f l u m e ,  ii)  to examine p o t e n t i a l r e s t a r t p r o b l e m s o f an i n d u s t r i a l flume system  and,  i i 1 ) to v e r i f y use o f the Manning e q u a t i o n f o r p r e d i c t i n g the 1  •  f l o w v e l o c i t y o f f l u i d 1n a c i r c u l a r  flume.  H y d r a u l i c T r a n s p o r t o f C o a r s e Coal The s t e a d y s t a t e f l o w r a t e o f t h e f l u i d was  determined  and the flume s l o p e was s e t a t an a n g l e between 0.5 and 10 per cent. the  The depth o f f l o w was c a l c u l a t e d by h o l d i n g the r u l e r on  s u r f a c e o f t h e f l u i d and m e a s u r i n g the d i s t a n c e t o t h e  I n s i d e , top s u r f a c e o f t h e p i p e .  By m i n i m i z i n g t h e d i s t u r b a n c e  on the f l u i d s u r f a c e c a u s e d by the r u l e r , a s t a n d a r d i z e d method of measurement was  developed.  The s l u r r y s p e c i f i c g r a v i t y was measured by w e i g h i n g a 10 l i t e r sample from the d e w a t e r i n g s c r e e n u n d e r f l o w and d i v i d i n g t h i s by t h e w e i g h t o f 10 l i t r e s o f w a t e r . The c o a r s e c o a l b i n was f i l l e d w i t h a weighed amount o f c o a l which was i n t r o d u c e d i n t o the f l u i d by o p e n i n g t h e b i n g a t e a t a s t a n d a r d r a t e . The g a t e was marked and the time t a k e n to u n c o v e r the marks as the g a t e was opened was k e p t the same.  The  s t a n d a r d i z e d o p e n i n g r a t e p r e v e n t e d the c o a l from b l o c k i n g the f l u m e and m a i n t a i n e d a s t e a d y f e e d i n t o t h e f l u i d  stream.  38  T i m i n g o f the t e s t began s i m u l t a n e o u s l y w i t h the o p e n i n g  of  the b i n and c o n c l u d e d when the l a s t c o a l c l e a r e d the end o f the flume d i s c h a r g e .  The end o f the t e s t was e s t a b l i s h e d by  o b s e r v i n g the f l u i d d i s t u r b a n c e c a u s e d by the c o a r s e c o a l . c o a r s e c o a l was t r a n s p o r t e d as a s l i d i n g bed w h i c h c a u s e d  The an  a b r u p t change i n the f l o w depth and r e s u l t e d 1n a h y d r a u l i c jump. The h y d r a u l i c jump moved down t h e flume w i t h the s l i d i n g bed o f c o a l and when i t p a s s e d out of the f l u m e , the t e s t was and the t i m i n g was  completed  stopped.  At the c o n c l u s i o n o f each t e s t , w i t h the pump s t i l l  running,  the system was a l l o w e d to r e t u r n to s t e a d y s t a t e and measurements of f l o w r a t e , depth of f l o w and s p e c i f i c g r a v i t y were t a k e n again.  The c o a r s e c o a l was a i r - d r i e d o v e r n i g h t on a b l a c k  ground-sheet. Each t e s t took 20 t o 30 m i n u t e s to c o m p l e t e .  Restrictions  1n d r y i n g f a c i l i t i e s and i n the q u a n t i t y o f c o a r s e c o a l l i m i t e d the number of t e s t s per day to e i g h t . 2.  Restart Tests The system was  s t a b i l i z e d and measurements of f l o w  r a t e , depth o f f l o w and flume s l o p e were t a k e n as p r e v i o u s l y o u t l i n e d f o r the t e s t s o f h y d r a u l i c t r a n s p o r t of c o a r s e c o a l .  A  wooden p l u g , which b l o c k e d t w o - t h i r d s of the flume c r o s s s e c t i o n , was put i n the d i s c h a r g e end o f the f l u m e . of c o a r s e c o a l was  The measured  i n t r o d u c e d i n t o the s t r e a m o f w a t e r and  s e t t l e d i n t o a 3.5 meter l o n g by 7.5 c e n t i m e t e r deep bar the p l u g .  weight  A f t e r a l l o w i n g the bar of c o a l to s e t t l e  and  behind  39  c o n s o l i d a t e f o r f i v e m i n u t e s , the p l u g was removed and the time to c l e a r the c o a l out o f the flume was r e c o r d e d .  In one  the c o a l bar was a l l o w e d to c o n s o l i d a t e and dry f o r 48  test, hours.  The pump was r e s t a r t e d and the time t a k e n to c l e a r the flume  was  measured. These t e s t s were c o n d u c t e d centimeter diameter 3.  1n a 15.2  c e n t i m e t e r and a 25  pipe.  V e r i f i c a t i o n o f the Manning E q u a t i o n As 1n the p r e v i o u s two e x p e r i m e n t s ,  the system  was  a l l o w e d to r e a c h s t e a d y s t a t e and measurements o f f l o w r a t e , depth o f f l o w and f l u i d s p e c i f i c g r a v i t y were t a k e n . and/or f l o w r a t e was s e l e c t e d and the p r o c e d u r e was A l t h o u g h some e x p e r i m e n t s  A new  slope  repeated.  were run s p e c i f i c a l l y t o o b t a i n t h e s e  measurements, the d a t a from a l l the e x p e r i m e n t s  was used t o  v e r i f y use of the Manning e q u a t i o n . D.  P r e s e n t a t i o n of the Data 1.  General The d a t a c o l l e c t e d i n t h e e x p e r i m e n t s  gave v a l u e s f o r  measured v a r i a b l e s and were used to c a l c u l a t e v a l u e s f o r o t h e r v a r i a b l e s of i n t e r e s t . a)  Measured V a r i a b l e s The measured v a r i a b l e s were; i)  s l o p e o f t h e flume i n d e g r e e s ,  ii)  v o l u m e t r i c f l o w r a t e of the f l u i d i n U.S. per  minute.  gallons  40  i i i ) depth of flow in iv)  w e i g h t of c o a r s e c o a l i n pounds,  v)  duration  vi)  s p e c i f i c g r a v i t y of the  T a b l e 3-1 b)  inches,  of the t e s t i n m i n u t e s ,  and  fluid  shows the r e s u l t s of 74 e x p e r i m e n t s a f t e r  conversion  to SI  units,  Calculated  Variables  U s i n g the g e o m e t r i c r e l a t i o n s h i p s f o r a c i r c u l a r c r o s s s e c t i o n as shown on F i g u r e 3-3,  values  of the  following  v a r i a b l e s were c a l c u l a t e d ; i)  included  ii)  hydraulic  a n g l e of f l o w i n  radians,  radius in centimeters,  and  i i i ) cross s e c t i o n a l area of flow i n square centimeters. The  a v e r a g e f l o w v e l o c i t y i n m e t e r s per s e c o n d ,  c a l c u l a t e d by d i v i d i n g the f l o w r a t e by the c r o s s a r e a of f l o w .  The c o a r s e c o a l t r a n s p o r t  per s e c o n d , was  C  v  sectional  rate, in kilograms  c a l c u l a t e d by d i v i d i n g the w e i g h t of c o a r s e  c o a l by the t e s t d u r a t i o n . the f l u i d was  was  The volume per c e n t s o l i d s of  c a l c u l a t e d by the  formula;  = ( f l u i d s p e c i f i c g r a v i t y - 1) ( c o a l p a r t i c l e s p e c i f i c g r a v i t y - 1)  T a b l e 3-2  l i s t s the c a l c u l a t e d v a l u e s  the same 74 e x p e r i m e n t s .  The  values  of these v a r i a b l e s of t h e s e v a r i a b l e s  the f l u m e r e s t a r t t e s t s are shown i n T a b l e  3-3.  An a v e r a g e c o a l p a r t i c l e s p e c i f i c g r a v i t y of 1.5  was  for for  41  MEASURED VALUES FOR EXPERIMENTAL TESTS  SLOPE  FLOWRATE LPS  DEPTH Cm.  WEIGHT Kg.  . 70 .90 . 90 . 90 . 90 . 90 1 . 00 1 . 00 1. 60 1 . 70 1. 70 1. 70 1. 80 1 . 80 2.10 2.10 2.10 2.10 2.10 2.10 2.10 2.10 2.10 2. 30 2. 30 2.40 2. 60 2. 60 2. 60 2. 60 2. 60 2. 60 2.60 3. 00 3. 00 3. 00 3. 00  17. 56 2. 55 8. 50 10. 20 15. 58 21. 24 10. 76 20. 67 17. 84 11.61 1 1. 89 21.81 6. 80 9. 63 5. 66 9. 63 9.91 14. 73 15. 29 15. 29 18. 97 19. 54 19. 54 12. 46 26. 05 15. 29 5. 38 6. 80 11.04 13. 59 15. 29 18. 12 26. 90 6. 80 11. 04 11. 04 12. 74  8. 38 2. 79 6. 60 6.10 6. 60 7. 62 7.11 7.37 7. 37 6.10 5. 84 7. 37 4. 57 6.10 4. 06 5. 33 5. 84 6. 60 6. 60 6. 60 7. 1 1 7.11 7.11 5. 33 6. 35 6. 35 3. 56 3.81 5. 33 6. 60 6.10 6. 10 7. 37 4. 06 5. 33 5. 84 5. 84  48. 49 0. 00 48. 08 0. 00 0. 00 0.00 52. 66 52. 39 57. 93 47. 22 0. 00 49. 26 53. 16 47. 62 50. 44 51.12 56. 1 1 48.71 51 . 08 50. 53 54. 43 52. 35 51 . 80 44.17 48. 40 55. 43 0. 00 52. 39 50. 39 38. 32 0. 00 0. 00 0. 00 51 . 94 52. 39 56. 89 53. 30  '/,  1 •J .3  4 5 6 7 8 9 10 11 12 13 14 15 16 17 IS 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37  Table 3-1  TIME Sec  10000.00 0.00 10000.00 0 . 00 0. 00 0.00 10000.00 104.00 98 . 00 102.00 0. 00 57. 00 232.00 180.00 336.OO 177.00 125.OO 85. 00 120.00 131.00 90 . 00 95. 00 6 1. 00 39. 00 26. 00 78. 00 0 . 00 178.0© 101.00 66. 00 0. 00 0. 00 0. 00 117.00 74. 00 83. 00 49.00  SG  1 . 00 1 . 00 1 . 00 1 . 00 1 . 00 1 . 00 1 . 00 1.00 1 . 00 1 . 00 1 . 00 1 . 00 1 . 00 1 . OO 1 . 00 1 . 00 1.00 1 . 00 1.01 1 . 00 1 . OO 1 . 00 1 . 00 1 . 00 1 . 00 1.01 1 . 00 1.00 1 . 00 1 . 00 1.00 1 . 00 1 . 00 1 . 00 1 . 00 1.01 1 . 00  The data collected in 74 experiments gave values f o r these measured variables.  42  SLOPE  38 39 4 0 41 42 43 44 4 5 46 4? 48 49 50 51 52 54 55 56 5? 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74  Table 3-1  3. 00 3. 00 3. 50 3. 50 3. 50 3. 50 3. 50 3. 50 5. 60 5. 60 5. 60 1. 70 1 . 70 1. 70 1 . 70 1. 70 2.10 2.10 2.40 2.40 2.40 2. 40 2.40 2. 40 3. 00 3.50 4. 50 5. 20 6. OO 6. OO 6. OO 6. 00 6.10 10. 00 10. 00 10. 00 10. 00  FLOWRATE LPS  DEPTH Cm.  WEIGHT Kg.  16. 99 19.54 5. 95 7. 36 5. 95 13. 59 14.16 23. 79 17. 84 19. 26 24. 64 2. 27 1 1 . 89 24. 64 29. 17 31. 72 4.81 17. 56 8. 50 12. 46 16. 43 19. 54 22. 66 24. 36 6.51 18.41 18.41 9. 35 2. 55 20. 39 20. 96 29. 74 17. 84 4. 53 19. 82 30. 87 33. 70  6. 60 6.35 3. 30 4. 06 3. 30 7.11 7. 11 7. 37 6.10 6. 60 7. 11 2. 79 5. 84 7. 37 7. 37 8. 38 4. 06 7.11 5. 08 5. 33 6. 60 6. 60 7.11 7.11 3.81 6. 35 6.10 4. 83 2. 03 6.10 7.11 6. 60 6. IO 2. 03 5. 84 6. 35 6. 86  51. 89 52. 57 53. 30 48. 62 51. 30 55. 34 51. 48 48. 90 0. 00 0. OO 0. 00 0. 00 O. OO 0. OO 0. OO 0. OO 53. 71 56. 43 55. 25 44. 95 50. 76 54. 21 43. 72 39. 54 57. 75 55. 93 52. 89 54. 93 0. 00 0. OO 0. 00 0. OO 53. 21 0. 00 0. 00 O. OO 0. 00  TIME Sec  SG  53. 06 38. 06 64. 60 76. 06 112.06 63. 60 68. 60 25. 60 0. 06 0. 06 0. 06 6. 06 0. 00 0.00 O . 00 0 . 00 10000.00 68. 06 144.GO 45. GO 62. 00 55. OO 3 8.00 39. 00 138.OO 33. 00 28. OO 46. 00 0. 00 0 . 66 0. 00 0. 00 24. OO 0. 00 0 . OO 0. OO 0. 00  1 . OO 1. OO 1 . 06 1 . GO 1 . 66 1 . 60 1 . 60 1 . 66 1 . OO 1.00 1 . OO 1 . 04 1.04 1 . 64 1 . 04 1 . 64 1 . 65 1 . 65 1 . 65 1 . 04 1 . 65 1.65 1 . 65 1 . 65 1 . 65 1 . 05 1 . 64 1 . 64 1 . 04 1 . 04 1 . 64 1 . 04 1 . 04 1 . 04 1.64 1 . 04 1 . 64  The data collected i n 74 experiments gave values f o r these measured variables.  HYDRAULIC E L E M E N T S AREA  ® - = — ~~ -  f Y  i  WETTED  HYD. PERIM. RADIUS (B)  ®  by  b + 2y  (b+zy)y  b+2y A+z*  GEOMETRIES TOP WIDTH (t)  by b+2y  HYD. DEPTH ® y  b  b  j  ^  T  fh+?v1v  / i M'  for DIFFERENT  T  V  2y A*z  l  b+2y / l + z'  b+2zy  2y  y  2zy  2 /l z<  2  +  ST7 F i g u r e 3-3  ^-(6-sin6)D O  2  6D 2  (sin  j  (b+zy)y b+2zy  6)D  ire - s i n e i 8lsin 1 6 j 2  H y d r a u l i c v a r i a b l e s f o r t h e s e f o u r shapes a r e c a l c u l a t e d a c c o r d i n g t o t h e i r geometries. The c r o s s s e c t i o n a l shape o f i n t e r e s t t o t h i s r e search i s the c i r c l e .  44  CALCULATED VALUES FOR EXPERIMENTAL TESTS  THETfl Rads = == = = = = 1 et  3 4  Cj  6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 i! 24 25 26  £. 1 28 29 30 31 33 34 ~'  t  G  36 37  Table 3-2  1 . 67 . 88 1 . 44 1 . 37 1 . 44 1 . 57 1 . 50 1 . 54 1 . 54 1 . 37 1 . 34 1 . 54 1 . 16 1 . 37 1 . 09 1• C r 1 . 34 1 . 44 1 . 44 1 . 44 1 . 50 1 . 50 1 . 50 1 . 27 1 . 40 1 . 40 1 .01 1 .05 1 . 27 1 . 44 1 . 37 1 . 37 1 . 54 1 . 69 1 . d7 1 . 34 1 . 34  HYDRAULIC RADIUS Cm.  AREA  4. 04 1.70 3. 46 3. 26 3. 46 3.81 3. 64 3. 73 3. 73 3. 26 3.16 3. 73 2.61 3. 26 2. 36 2. 95 3.16 3. 46 3.46 3.46 3.64 3. 64 3. 64 2. 95 3. 36 3. 36 2. 1 1 2. 23 2. 95 3. 46 3. 26 3. 26 3. 73 2. 36 2. 95 3.16 3.16  102.80 22. 92 75. 77 68. 14 75. 77 91.21 83. 47 87. 34 87. 34 68. 14 64. 36 87. 34 46. 03 68. 14 3 9.05 56. 96 64.36 75. 77 75. 77 75. 77 83. 4 7 83. 47 83. 47 56. 96 71. 94 71 . 94 32. 35 35. 66 56. 90 75. 77 68. 14 68. 14 87.34 39. 65 56. 96 64. 36 64. 36  Sq.Cm.  VELOCITY M/Sec.  1.71 1.11 1. 12 1. 56 2. 06 2. 33 1 . 29 2. 37 2. 04 1 . 70 1 . 85 2. 50 1. 48 1.41 1 . 45 1 . 69 1 . 54 1 . 94 2. 02 2. 02 2. 27 2. 34 2. 34 2.19 3. 62 2.13 1 . 66 1.91 1 . 94 1. 79 2. 24 2. 66 3. OS 1 . 74 1 . 94 1 . 72 1 . 98  COARSE TRANSPORT Kg/Sec.  . OO 0.00 . 00 0. OO O. OO 0. 00 . 01 . 50 . 59 . 46 0. 00 . 86 . 23 . 26 . 15 . 29 . 45 . 57 . 43 . 39 . 60 . 55 . 85 1.13 1 . 86 .71 O. OO . 29 . 50 . 58 0. 00 0. 00 0. 00 . 44 .71 . 69 1 . 09  CV ======  0. 00 0. 00 0.60 0. 00 0.00 0. 00 0. 00 6. OO . Ol O. 00 0. 00 0. 00 0. 00 O. OO 0. O0 0. 00 . Ol .01 . 02 0. 00 .01 .01 0. 00 0. OO 0. 00 . 02 0. OO 0. 00 0.00 .01 0. 00 0. 00 0. oo 0. OO 0. 00 . 02 .01  Values of these variables were calculated using the geometric relationships f o r a c i r c u l a r cross section and the values of the experimentally measured variables.  45  THETA Rads  38 39 40 41 42 43 44 45 4 6 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 79 71 72 73 74  Table 3-2  1. 44 1 . 40 . 97 1 . 09 . 97 1. 50 1. 50 1 . 54 1 .37 1. 44 1 . 50 . 88 1.34 1 . 54 1 . 54 1 . 67 1 . 09 1 . 50 1. 23 1 . 27 1. 44 1 . 44 1. 50 1. 50 1 . 05 1. 40 1 . 37 1. 20 . 75 1. 37 1 . 50 1 . 44 1 .37 . 75 1 . 34 1 . 40 1.47  HYDRAULIC RADIUS Cm.  3. 46 3. 36 1. 97 2. 36 1 . 97 3. 64 3. 64 3. 73 3. 26 3.46 3. 64 1. 70 3.16 3. 73 3. 73 4.04 2. 36 3. 64 2. 84 2. 95 3.46 3. 46 3. 64 3. 64 2. 23 3. 36 3. 26 2. 72 1. 27 3. 26 3. 64 3. 46 3. 26 1 . 27 3.16 3. 36 3. 55  AREA  VELOCITY  Sq.Cm.  M/Sec.  COARSE TRANSPORT Kg/Sec.  75. 77 71. 94 29. 12 39. 05 29. 12 83. 47 83. 47 87.34 68. 14 75. 77 S3. 47 22. 92 64. 36 87.34' 87. 34 102.80 39. 05 83. 47 53. 23 56. 90 75. 77 75. 77 83. 47 83. 47 35. 66 71. 94 68. 14 49. 60 14. 46 68. 14 83. 47 75. 77 68. 14 14. 46 64. 36 71. 94 79. 61  2. 24 2. 72 2. 04 1. 89 2.04 1. 63 1. 70 2. 72 2. 62 2. 54 2.95 .99 1 . 85 2. 82 3. 34 3. 09 1 . 23 2.10 1 . 60 2.19 2. 17 2.58 2.71 2. 92 1. 83 2. 56 2. 70 1. 88 1. 76 2. 99 2.51 3. 92 2. 62 3. 13 3. 08 4. 29 4.23  . 98 1. 38 . 83 . 64 . 46 . 88 . 76 1 . 96 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. OO 0. 00 . 01 . 83 . 38 1 . 00 . 82 . 99 1.15 1.01 . 42 1 . 47 1 . 89 1.19 0. 00 0. OO 0. 00 0. 00 2.22 0. 00 0. 00 0 . 00 0. 00  cv  0. 00 .01 .01 0. 00 0. 00 0. 00 .01 0. 00 0.00 0. 00 0. 00 . 08 . 08 . 08 . 08 . 08 . 10 . 10 . 10 . OS . 10 . 10 . 10 . 10 . 10 . 10 . 08 . 08 . 08 . 08 . 08 . 08 . 08 . 08 . 08 . 08 . OS  Values of these variables were calculated using the geometric relationships f o r a c i r c u l a r cross section and the values of the experimentally measured variables.  46  Measured and Calculated Values f o r Flume Restart Tests  Test  Slope %  Flowrate LPS  Depth Cm  Weight Kg  Time Sec.  1 2 3 4 5 6 7 8 9  1.2 1.9 1.9 2.4 2.4 2.4 2.4 1.2 2.4  3.09 3.09 3.09 3.09 3.09 3.09 3.09 3.09 3.09  3.44 3.44 3.44 3.19 3.19 3.19 3.19 3.44 3.19  24.97 23.56 25.41 24.86 25.03 23.87 23.62 24.68 25.15  554.9 173.24 279.23 78.18 137.53 175.52 129.78 0 276.37  Test  Theta Rads  Hydraulic Radius Cm  Area Sq. Cm.  Velocity M/Sec.  Coarse Transport  1.00 1.00 1.00 1.09 1.09 1.09 1.09 1.00 1.09  .04 .14 .09 .32 .18 .14 .18 0 .09  1 2 3 4 5 6 7 8 9  Table 3-3  .99 .99 .99 .95 .95 .95. .95 .99 .95  3.44 3.44 3.44 3.19 3.19 3.19 3.19 3.44 3.19  30.85 30.85 30.85 28.35 28.35 28.35 28.35 30.85 30.85  SG  A wooden plug was put into the discharge end of the flume and coarse coal was then introduced into the transporting f l u i d . The coarse coal settled into a bar behind the plug and was allowed to consolidate f o r 5 minutes. The plug was removed and the time taken to remove a l l the coarse coal from the flume was measured.  47  determined  from the e x p e r i m e n t a l  d a t a shown on T a b l e 3 - 4 .  The s l u r r y m i x t u r e s were N e w t o n i a n l i q u i d s as measured by a S t o r m e r r o t a t i n g cup v i s c o m e t e r .  C o n s i s t e n c y d a t a f o r e a c h of  the t h r e e s l u r r y m i x t u r e s a r e shown p l o t t e d w i t h a d i s t i l l e d w a t e r c a l i b r a t i o n c u r v e on F i g u r e 3 - 4 . 2.  Graphical Presentation To a i d i n v i s u a l i z i n g the r e l a t i o n s h i p s between t h e s e  v a r i a b l e s , experimental  d a t a v a l u e s f o r t h e 74 t e s t s have been  graphed i n d i f f e r e n t c o n f i g u r a t i o n s . a)  H y d r a u l i c t r a n s p o r t of raw c o a l The c o a r s e c o a l t r a n s p o r t r e s u l t s i n k i l o g r a m s  per  s e c o n d , are p l o t t e d on a f l u i d v e l o c i t y v e r s u s s l o p e c u r v e as shown on F i g u r e 3 - 5 .  T h i s p r e s e n t a t i o n o f the d a t a  d e f i n e s the c o n d i t i o n of no t r a n s p o r t and s u p p o r t s  the  i n t u i t i v e knowledge t h a t c o a r s e c o a l t r a n s p o r t w i l l i n c r e a s e w i t h i n c r e a s i n g s l o p e and f l u i d °)  velocity.  V e r i f i c a t i o n o f the Manning E q u a t i o n The Manning e q u a t i o n i s d e f i n e d a s ; n  where "S" i s the s l o p e , "R"  i s the h y d r a u l i c r a d i u s and  i s a c o e f f i c i e n t o f flume r o u g h n e s s .  The  "n"  manufacturer's  v a l u e of "n" f o r h i g h d e n s i t y p o l y e t h y l e n e i s .008.  By  p l o t t i n g f l u i d v e l o c i t y a g a i n s t depth of f l o w f o r c o n s t a n t s l o p e v a l u e s , the e x p e r i m e n t a l  d a t a can be compared t o the  Manning e q u a t i o n as shown on F i g u r e 3 - 6 .  The s o l i d c u r v e i s  48  EXPERIMENTAL DATA FOR COAL SPECIFIC GRAVITY DETERMINATION  SAMPLE NO.  DRY WEIGHT (grams)  VOLUME (millilitres)  SPECIFIC GRAVITY  2 3 4 5 6 7 8 9 10  23.25 20.06 29.44 26.48 32.61 27.98 29.33 37.18 21.45 32.82  16.0 15.0 21.0 15.0 21.0 19.0 20.0 25.0 15.0 20.0  1.45 1.34 1.47 1.77 1.55 1.47 1.48 1.49 1.43 1.64  AVERAGE  28.06  18.6  1.51  1  Table 3-4  Samples of coal were weighed and then immersed i n a graduated cylinder f i l l e d with water to determine the sample volume. A s p e c i f i c gravity value of 1.5 was used i n subsequent calculations.  49  Figure  3-4  The  solid  water  and  results All  lines the  for  three  are  consistency  discrete  slurries  of  points  curves  are  different  slurry mixtures  behaved  the  for  experimental  specific as  distilled gravities.  Newtonian  fluids  50  4  • 1.86  • 1.01 -1.66 • 1.15  • 1.38  • 1.96  • 1.89  • .86 •1.26  1  \  T  '  •.55/85 ^.60 ••1.00  5  i  \  •83 - V  \  T  \  T66  T31  *-57 •  \  7  T 83  T  9 8  .50 ^.58  • .46  • 0  -  82  T.76  V69  •as  v  T  T.45 •. 23 ,. T.26  • 0  >  1  "V  -  8 8  ^ 1-01  .  ^ *o  v 1.19  • .64  • 44  5  • 0  • 0  RAW C O A L T R A N S P O R T (kg/sec) 1  2  3  4  5  T  1  1  1  r  SLOPE gure 3-5  (%)  This presentation of the data defines the l i m i t s of slope and v e l o c i t y below which no coal was transported and supports the i n t u i t i v e knowledge that coarse coal transport w i l l i n crease with increasing slope and f l u i d v e l o c i t y .  51  VELOCITY  v s DEPTH OF FLOW  ^REGRESSION  1  2  3  4  DEPTH  F i g u r e 3-6  5  OF  6  FLOW  7  8  9  10  11  12  (CM)  The experimental d a t a i s compared t o t h e Manning e q u a t i o n p r e d i c t i o n f o r a c o n s t a n t s l o p e o f 2.1. The r e g r e s s i o n curve t o f i t t h e experimental d a t a was v e l o c i t y = .4 (depth) . The d i s c r e p a n c y between the e x p e r i m e n t a l v e l o c i t y was due t o e i t h e r experimental e r r o r o r the uns u i t a b i l i t y o f the Manning e q u a t i o n . , 8 G  52  t h e Manning e q u a t i o n p r e d i c t i o n o f the f l o w v e l o c i t y and t h e dashed c u r v e i s a power c u r v e r e g r e s s i o n f i t o f the experimental data r e s u l t i n g i n the equation; Rfi  velocity = .4 (depth) The d i s c r e p a n c y between t h e e x p e r i m e n t a l v e l o c i t y  and  the p r e d i c t e d v e l o c i t y was due t o e i t h e r e x p e r i m e n t a l e r r o r or the u n s u i t a b i 1 i t y of t h e Manning e q u a t i o n . E.  INTERPRETATION OF RESULTS 1.  H y d r a u l i c T r a n s p o r t of C o a r s e C o a l The o b j e c t i v e of the c o a r s e c o a l t r a n s p o r t  was t o d e t e r m i n e system.  experiments  o p e r a t i n g c o n s t r a i n t s f o r an i n d u s t r i a l  flume  An e m p i r i c a l l y d e r i v e d t r a n s p o r t f u n c t i o n , w h i c h  p r e d i c t s the v o l u m e t r i c t r a n s p o r t of c o a r s e c o a l per u n i t o f time f o r g i v e n h y d r a u l i c v a r i a b l e s , was d e t e r m i n e d a n a l y s i s o f the e x p e r i m e n t a l a)  Dimensional  results.  Analysis  A c c o r d i n g to B i n d e r "Dimensional  from a d i m e n s i o n a l  (1973);  a n a l y s i s i s a useful tool for organizing,  c o r r e l a t i n g and i n t e r p r e t i n g e x p e r i m e n t a l r e s u l t s i n which the p h y s i c a l phenomena were t o o complex f o r a t h e o r e t i c a l solution." D i m e n s i o n l e s s groups a r e f o u n d by a r r a n g i n g v a r i a b l e s of i n t e r e s t i n t o r a t i o s which are u n i t l e s s .  The r a t i o s a r e  o r g a n i z e d such t h a t , i f p o s s i b l e , the p r i m a r y d i m e n s i o n s  of  l e n g t h ( L ) , mass (M), and time (T) a r e r e p r e s e n t e d i n each group.  53  Four d i m e n s i o n l e s s g r o u p s , u s i n g t h e f o l l o w i n g v a r i a b l e s were e s t a b l i s h e d i n t h i s way:  1)  veloci ty  V  LT-1  ii)  hydraulic radius  R  L  i i i ) flow rate  Q  LT-3  iv)  gravi ty  g  LT-2  v/  s l ope  s  -  vi)  slurry specific gravity  -  v i i ) coarse coal t r a n s p o r t The d i m e n s i o n l e s s parameter 1 = /V"  T  groups a r e : flow parameter =  D  7T  parameter  these groups.  R  R  2 =yy^5~  The e x p e r i m e n t a l  MT-1  transport parameter =  2/5 l/2 -3 g  Qs  s  1  d a t a were used t o c a l c u l a t e v a l u e s f o r  The v a l u e s f o r each r a t i o were t h e n p l o t t e d  a g a i n s t t h e v a l u e s f o r each o f t h e o t h e r d i m e n s i o n l e s s r a t i o s t o i n v e s t i g a t e p o s s i b l e r e l a t i o n s h i p s . The graph o f t r a n s p o r t parameter which  versus flow parameter  showed a s y s t e m a t i c c o r r e l a t i o n .  combinations  was t h e o n l y p l o t The o t h e r  of dimensionless r a t i o s r e s u l t e d i n widely  s c a t t e r e d , u n c o r r e l a t e d graphs, b)  Transport Function The e x p o n e n t s  o f t h e d i m e n s i o n l e s s v a r i a b l e s , flume  54  s l o p e and f l u i d s p e c i f i c g r a v i t y , were i n t e r a c t i v e l y changed to c a l c u l a t e new v a l u e s o f t h e f l o w and t r a n s p o r t parameters.  The v a l u e s o f t h e p a r a m e t e r s  were p l o t t e d t o  o b t a i n c o r r e l a t i o n c o e f f i c i e n t s and t h e c o m b i n a t i o n  of  s p e c i f i c g r a v i t y and s l o p e e x p o n e n t s which r e s u l t e d i n t h e b e s t c o r r e l a t i o n c o e f f i c i e n t was u s e d .  The h i g h e s t  c o r r e l a t i o n c o e f f i c i e n t c a l c u l a t e d by t h i s i t e r a t i v e method was 0.88 and was o b t a i n e d when t h e s l o p e v a l u e s were r a i s e d to t h e power o f 0.3 and t h e s p e c i f i c g r a v i t y v a l u e s were r a i s e d t o t h e power o f 0. T a b l e 3-5 l i s t s t h e c a l c u l a t e d v a l u e s o f t h e two m o d i f i e d ratios; flow parameter = 2/5 l / 2 .3 R  g  $  Q transport parameter = 2 2/5 l / 5 R  g  T  The t r a n s p o r t p a r a m e t e r m e a s u r e s r e l a t i v e e f f e c t s o f t h e v o l u m e t r i c f l o w o f f l u i d and t r a n s p o r t o f c o a r s e c o a l .  The f l o w  parameter measures the r e l a t i v e e f f e c t s of the v o l u m e t r i c r a t e and t h e flume s l o p e .  The p a r a m e t e r s  flow  are p l o t t e d against  each o t h e r on F i g u r e 3-7 and a r e f i t t e d by*a power law r e g r e s s i o n equation; T r a n s p o r t P a r a m e t e r = 3.57 (Flow  Parameter)•  6 7  By r e o r g a n i z i n g t h e v a r i a b l e s , a r e l a t i o n s h i p t o p r e d i c t t h e t r a n s p o r t o f c o a r s e c o a l was .0017 Q'  developed;  55  FLOW AND TRANSPORT PARAMETER VALUES  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1? 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45  Table 3-5  DATA NUMBER  FLOW PARAMETER  TRANSPORT PARAMETER  8 9 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 28 29 30 34 35 36 37 38 39 40 41 42 43 44 45 55 56 57 58 59 60 61 62 63 64 65 70  24.60 18. 44 16.41 22. 13 16.60 13. 38 16.89 16.47 14. 24 16. 90 17. 55 17.55 19.16 19. 73 19. 73 20. 75 31.21 18. 09 21. 82 17. 72 14. 63 18.21 16. 98 14. 25 16.45 17.52 21.61 23. 84 18. 84 23. 84 1 1 . 77 12. 26 19. 44 17. 73 15. 38 20.48 18.11 21 . 54 21 . 98 23. 62 20. 03 19. 44 19.43 14. 87 17. 19  29. 55 24. 70 22. OO 27. 98 23. 28 20. 41 25. 71 24. 58 20. 14 23. 81 26.24 26. 77 27. 40 28. 75 26. 36 24. 20 35. 21 25. 06 36. 10 25. 27 21. 92 £4. 84 23. 57 £0. 62 21.69 24. 69 28. 02 27. 4 4 25. Ol 30.93 18.22 19. 55 25. 92 23. 80 £2.13 24. 8£ 24. 73 £8. 35 28. 77 31.71 26. 89 26. 07 26. 33 21 . 07 24.72  Dimensional analysis of the experimental variables and subsequent graphing of the dimensionless ratios indicated that the unitless transport and flow parameters showed a systematic correlation.  56  TRANSPORT  PARAMETER  VS  •V35  FLOW  PARAMETER  30 M  da. 25 oc UJ UJ  S 1  20  <  cc < a oc -15  o  a. z  TRANSPORT  tn  P A R A M E T E R = 3.57(Fl_0W PARAMETER)  67  <  oc  10  10 1 —  FLOW  Figure 3-7  15 PARAMETER  20  25  —I—  gSR^S"  30  —i  3  The best c o r r e l a t i o n c o e f f i c i e n t between t h e t r a n s p o r t and flow parameters was o b t a i n e d when the s l o p e term was r a i s e d t o t h e . 3 power. The t r a n s p o r t parameter measures t h e r e l a t i v e e f f e c t s o f the v o l u m e t r i c f l o w o f f l u i d and t r a n s p o r t o f c o a r s e c o a l . The f l o w parameter measures the r e l a t i v e e f f e c t s o f the v o l u m e t r i c f l o w r a t e and t h e flume s l o p e .  57  T h i s e q u a t i o n , o r T r a n s p o r t F u n c t i o n p r e d i c t s the v o l u m e t r i c t r a n s p o r t of coarse c o a l per u n i t of time. The v a l i d i t y o f the T r a n s p o r t F u n c t i o n i s c o n s t r a i n e d by the e x p e r i m e n t a l l i m i t a t i o n s o f the f o l l o w i n g v a r i a b l e s : i)  s l o p e (.5 to 10.0  per c e n t )  ii)  f l u i d v e l o c i t y (1.0 t o 4.3 m e t e r s p e r s e c o n d )  i i i ) f l u i d f l o w depth t o flume d i a m e t e r r a t i o (0.13  to  0.55) iv)  flume r o u g h n e s s c o e f f i c i e n t (n =  v)  flume c r o s s - s e c t i o n ( c i r c u l a r )  .008)  The d i a m e t e r o f the flume i s not a c o n s t r a i n t b e c a u s e i t can be k e p t d y n a m i c a l l y s i m i l a r by k e e p i n g the d i m e n s i o n l e s s F r o u d e Number c o n s t a n t a c c o r d i n g t o the f o l l o w i n g r e l a t i o n s h i p ; Vl  7gD~i where "D"  -  _V2_  /gD~2  i s the flume d i a m e t e r and the s u b s c r i p t s "1" and  "2"  r e f e r , r e s p e c t i v e l y , t o the e x p e r i m e n t a l and p r o t o t y p e v a r i a b l e values. T h i s r e l a t i o n s h i p e n s u r e s t h a t t h e r a t i o of i n e r t i a l  forces  to g r a v i t y f o r c e s i s k e p t c o n s t a n t f o r the model t o p r o t o t y p e scale  up. c)  P r e d i c t i o n o f C o a r s e Coal T r a n s p o r t Ten c o a r s e c o a l t r a n s p o r t t e s t s were c a r r i e d out to  check the p r e d i c t i v e a c c u r a c y o f the T r a n s p o r t F u n c t i o n w i t h the e x p e r i m e n t a l c o a r s e c o a l t r a n s p o r t r e s u l t s . T a b l e 3-6  shows v a l u e s o f the measured and c a l c u l a t e d  v a r i a b l e s and T a b l e 3-7 compares the p r e d i c t e d and  58  MEASURED AND CALCULATED VALUES FOR 10 VERIFICATION TESTS  1 2 3 4 5 6 7 8 9 10  SLOPE  FLOWRATE LPS  DEPTH Cm.  WEIGHT Kg.  TIME Sec  l.OO 1.70 2."IO 2.30 2.60 3.50 6.10 2.40 2.40 3.00  14.73 16.71 12.46 18.69 15.86 11.33 17.84 1O.20 17.56 14.44  6.60 7.37 6.35 6.10 6.60 6.35 6.10 5.08 6.35 6.10  53.30 47.85 52.16 46.58 50.53 56.57 53.48 43.13 45.35 56.30  171.00 73.OO 122.00 28.00 62.0O 56.OO 24.OO 52.OO 36.OO 57.OO  THETR  HYDRAULIC RADIUS Cm.  AREA  VELOCITY  Pads  1 2 3 4 tr  6 7 3 9 10  Table 3-6  1. 1. 1. 1. 1. 1. 1. 1. 1. 1.  44 54 40 37 44 40 37 23 40 37  3. 46 3. 73 3. 36 3. 26 3. 46 3. 36 3. 26 2. 84 3. 36 3. 26  ;  S q.Cm.  M-'Sec .  COARSE TRANSPORT Kg-'Sec .  75. 77 87. 34 71 . 94 68. 14 75. 77 71 . 94 68. 14 53. 23 71.94 68. 14  1 . 94 1.91 1 . 73 2. 74 2. 09 1 . 57 2. 62 1 . 92 2. 44 2.12  .31 . 66 . 43 1 . 66 . 82 1.01 2. 23 . 83 1. 26 . 99  SG  1 .OO 1.00 l.OO 1.00 l.OO 1.01 1.00 1.05 1.04 1.05  CV  0. OO 0. OO O. 00 0. 00 0. OO . 02 0. 00 . 10 . 08 . 10  Ten coarse coal transport tests were carried out to check the predictive accuracy of the Transport Function with the experimental coarse coal transport results. These are the measured and calculated values of the hydraulic variables f o r the 10 tests.  59  CALCULATED AND MEASURED RATE OF COAL TRANSPORTATION  TRANSPORT DATA NUMBER  1 2 3 4 5 6 7 8 9 10  Table 3-7  IS  IN UNITS OF  Cu.Cm./Sec.  CALCULATED TRANSPORT  EXPERIMENTAL TRANSPORT  192.21 356.19 320. 17 724.55 565.45 455.23 1778.23 347.81 648. 12 614.39  207.80 437.00 285.05 1109.06 543.34 673.43 1485.59 552.95 839.90 658.43  The rate of transportation predicted by the Transport Function and the experimentally determined rate of transport are shown here. The difference between the two results i s from 4 to 59 percent.  60  experimental coarse coal t r a n s p o r t r e s u l t s f o r these ten tests. 59.0  The maximum d i f f e r e n c e between t h e two r e s u l t s was  p e r c e n t w i t h a mean d i f f e r e n c e o f 16.2 p e r c e n t .  This  indicates that the transport function i s a v a l i d r e l a t i o n s h i p to p r e d i c t the t r a n s p o r t of coarse coal within the c o n s t r a i n t s l i s t e d above. The v a l u e s on T a b l e 3-7 c a n be r e p r e s e n t e d on a graph of p r e d i c t e d v e r s u s e x p e r i m e n t a l t r a n s p o r t o f raw c o a l as shown on F i g u r e 3-8.  The d i s t a n c e between t h e d a t a p o i n t s  and t h e 45 d e g r e e l i n e i s p r o p o r t i o n a l t o t h e d i f f e r e n c e between t h e p r e d i c t e d and e x p e r i m e n t a l r e s u l t s .  A n o t h e r way  of p r e s e n t i n g t h i s i n f o r m a t i o n i s on a c o a r s e c o a l iso-transport plot.  T h i s p l o t i s a graph o f s l o p e v e r s u s  v e l o c i t y f o r constant transport of coarse coal ( i n units of cubic centimeters per second).  The i s o - t r a n s p o r t l i n e s a r e  c a l c u l a t e d by f i x i n g t h e v a l u e s o f f l o w d e p t h and c o a r s e c o a l t r a n s p o r t i n t h e T r a n s p o r t F u n c t i o n and a l l o w i n g t h e s l o p e and v e l o c i t y t o c h a n g e .  F i g u r e 3-9 shows a f a m i l y o f  i s o - t r a n s p o r t c u r v e s f o r a f l o w d e p t h o f 6.35 c e n t i m e t e r s . The e x p e r i m e n t a l t r a n s p o r t v a l u e s o f f o u r o f t h e t e n v e r i f i c a t i o n t e s t s , w h i c h were c a l c u l a t e d u s i n g a f l o w d e p t h o f 6.35 c e n t i m e t e r s a r e a l s o p l o t t e d on F i g u r e 3-9.  The  s i m i l a r i t y o f t h e e x p e r i m e n t a l and c a l c u l a t e d r e s u l t s demonstrates the accuracy of the Transport Function i n p r e d i c t i n g the t r a n s p o r t a t i o n of coarse c o a l .  61  CALCULATED COARSE  vs EXPERIMENTAL  COAL IN  TRANSPORT  KILOGRAMS  PER  SECOND /  1  2  EXPERIMENTAL  Figure 3-8  The e x p e r i m e n t a l and c a l c u l a t e d r a t e s o f c o a r s e c o a l t r a n s p o r t are p l o t t e d a g a i n s t each o t h e r . The d i s t a n c e between the d a t a p o i n t s and the 4 5 degree s o l i d l i n e i s p r o p o r t i o n a l to the d i f f e r e n c e between the p r e d i c t e d and e x p e r i m e n t a l r e s u l t s . The dashed l i n e s r e p r e s e n t a d i f f e r e n c e o f p l u s and minus 20 percent from the 45 degree l i n e .  62  COAL  ISO-TRANSPORT CURVES D E P T H OF  FL0W=6.35 C M .  1 -  1 2 SLOPE  F i g u r e 3-9  %  The i s o - t r a n s p o r t c u r v e s r e p r e s e n t l i n e s o f c o n s t a n t c o a r s e c o a l t r a n s p o r t . They a r e c a l c u l a t e d by f i x i n g the flow depth and c o a r s e c o a l t r a n s p o r t i n t h e T r a n s p o r t F u n c t i o n and a l l o w i n g t h e s l o p e and v e l o c i t y t o change. The s i m i l a r i t y o f the e x p e r i m e n t a l and c a l c u l a t e d r e s u l t s demonstrate t h e a c c u r a c y o f the T r a n s p o r t F u n c t i o n i n p r e d i c t i n g the t r a n s p o r t a t i o n o f coarse c o a l .  63  2.  Restarting Tests The p o t e n t i a l f o r o p e r a t i n g p r o b l e m s  encountered  in  r e s t a r t i n g a flume c o n t a i n i n g s e t t l e d c o a l was t e s t e d i n t h e s e experiments.  The e x p e r i m e n t a l  r e s u l t s demonstrate  t h a t a low  f l o w r a t e i s c a p a b l e o f c l e a r i n g a bar o f s e t t l e d c o a r s e c o a l a t flume s l o p e s of 2.5 per c e n t .  When the c o a l was a l l o w e d t o  s e t t l e and c o n s o l i d a t e f o r f o r t y e i g h t h o u r s the r e s u l t was  the  same. I t i s c o n c l u d e d from t h e s e t e s t s t h a t removing  a  s e t t l e d bar of c o a l from a h i g h d e n s i t y p o l y e t h y l e n e , c i r c u l a r flume w i l l not be a p r o b l e m r u l e s of dimensional  f o r an i n d u s t r i a l s c a l e system  s i m i l a r i t y are f o l l o w e d .  i f the  T h a t i s , the f l o w  v e l o c i t y used i n an o p e r a t i n g system must be g r e a t e r than o r e q u a l to the v e l o c i t y c a l c u l a t e d by k e e p i n g the F r o u d e Number f o r the o p e r a t i n g and e x p e r i m e n t a l 3.  systems  the same.  V e r i f i c a t i o n o f the Manning E q u a t i o n The Manning e q u a t i o n , below, i s a r e l a t i o n s h i p t o  determine  the a v e r a g e f l u i d f l o w v e l o c i t y i n an open c h a n n e l : .  R  2/3  n  ,1/2  The d i f f e r e n c e between the e x p e r i m e n t a l l y d e t e r m i n e d  flow  v e l o c i t i e s and the f l o w v e l o c i t i e s c a l c u l a t e d by the Manning e q u a t i o n a r e p r e s e n t e d on a c u m u l a t i v e d i f f e r e n c e p l o t as shown on F i g u r e 3-10.  T h i s graph d e m o n s t r a t e s  t h a t 80 per c e n t o f the  e x p e r i m e n t a l v e l o c i t i e s a r e w i t h i n p l u s o r minus 30 per c e n t of the Manning e q u a t i o n p r e d i c t i o n s .  64  CUMULATIVE  DIFFERENCE BETWEEN  EXPERIMENTAL FLUID  10  20  MANNING  VELOCITY  30  RANGE  Figure 3-10  AND  40 OF  50  60  70  DIFFERENCE  80  90  100  %  The difference between the experimentally determined flow v e l o c i t i e s and the flow v e l o c i t i e s calculated by the Manning equation are presented on t h i s cumulative difference p l o t . This graph demonstrates that, of 84 tests, 80 percent of the experimental v e l o c i t i e s are within plus or minus 30 percent of the Manning predictions.  65  I t i s c o n c l u d e d t h a t use o f t h e Manning e q u a t i o n t o p r e d i c t f l o w v e l o c i t y i n a flume w i t h a c i r c u l a r c r o s s s e c t i o n i s verified F.  by t h e e x p e r i m e n t a l  data.  EXPERIMENTAL ERROR All experiments  sources.  a r e s u b j e c t t o e r r o r s from a v a r i e t y o f  Some a r e random i n s i g n and a m p l i t u d e and o t h e r s  s y s t e m a t i c a l l y a l t e r the experimental  r e s u l t i n t h e same  d i r e c t i o n and m a g n i t u d e . 1.  Systematic E r r o r s B a r r y (1978) s t a t e s :  "A s y s t e m a t i c e r r o r i s one t h a t  i n v a r i a b l y has t h e same m a g n i t u d e and t h e same s i g n f o r t h e same given c o n d i t i o n s . " Because s y s t e m a t i c e r r o r s are cumulative, i t i s important to d e t e c t and e l i m i n a t e them. Potential sources of systematic e r r o r i n the coal t r a n s p o r t experiments a)  were h a n d l e d i n d i f f e r e n t ways, Flow Rate Measurement  The m a g n e t i c  flow meter operated i n d e p e n d e n t l y o f f l u i d  temperature,  v i s c o s i t y , d e n s i t y and p r e s s u r e and ambient a i r  temperature.  The pump i n l e t was k e p t submerged t o p r e v e n t  v o r t i c e s o f a i r from e n t e r i n g t h e pump and i n t r o d u c i n g a i r bubbles i n t o the flow of f l u i d .  Bubbles  i n the flow of  f l u i d would c a u s e a c o n s i s t e n t l y h i g h f l o w r a t e measurement. The s t a b i l i t y  o f 40 m e t e r r e a d i n g s t a k e n i n 40 s e c o n d s  i n d i c a t e d t h a t a i r b u b b l e s were n o t a p r o b l e m .  66  b)  Depth o f Flow Measurement The s u r f a c e t e n s i o n o f t h e w a t e r c a u s e d t h e d e p t h o f  f l o w v a l u e t o be t o o h i g h . meniscous  T h i s was c o r r e c t e d by a d d i n g t h e  h e i g h t (1/16 i n c h e s ) t o t h e measurement o f  d i s t a n c e from t h e f l u i d s u r f a c e t o t h e t o p o f t h e f l u m e . c)  Flume S l o p e Measurement The v e r n i e r p r o p e l l e r compass was a s p i r i t  a t t a c h e d t o a c a l i b r a t e d compass.  level  To e n s u r e a c c u r a c y , t h e  compass was c a l i b r a t e d w i t h a n o t h e r s p i r i t l e v e l t o s e t t h e p o s i t i o n o f t h e z e r o degree d)  reading.  W e i g h t Measurements The s p r i n g b a l a n c e was s e n s i t i v e t o t e m p e r a t u r e s  a normal Celsius.  o p e r a t i n g range o f 15 d e g r e e s t o 35  beyond  degrees  V a l i d r e a d i n g s were t a k e n by k e e p i n g t h e s c a l e s i n  a shaded a r e a a t a t e m p e r a t u r e  i n t h i s range.  The a c c u r a c y  of t h e r e a d i n g s were v e r i f i e d by c a l i b r a t i n g t h e s c a l e s w i t h a known q u a n t i t y o f w a t e r . e)  E l a p s e d Time Measurement The end o f each c o a r s e c o a l t r a n s p o r t t e s t was  e s t i m a t e d by o b s e r v i n g t h e p a s s a g e o f a h y d r a u l i c jump o u t of t h e f l u m e .  T h i s assessment  of t h e o b s e r v e r .  was s u b j e c t t o t h e e x p e r i e n c e  To r e d u c e t h e e f f e c t o f o b s e r v e r b i a s , two  p e o p l e e s t i m a t e d t h e c o n c l u s i o n o f each t e s t and i n d e p e n d e n t l y a l e r t e d t h e time k e e p e r .  Disagreements  were  h a n d l e d by u s i n g t h e a v e r a g e o f t h e two o b s e r v a t i o n s . f)  C o a l S p e c i f i c G r a v i t y Measurement Coal p a r t i c l e s were p l a c e d i n a g r a d u a t e d c y l i n d e r t o  67  measure t h e i r v o l u m e .  Care was t a k e n t o remove a l l a i r  b u b b l e s and c o n s i s t e n t l y r e a d e i t h e r t h e  t o p o r bottom o f  t h e m e n i s c o u s t o f i n d t h e volume d i f f e r e n c e . 2.  Random E r r o r s Random e r r o r s a r e e s t i m a t e d by making  measurements o f t h e same q u a n t i t y . measurement i s t h e mean r e s p o n s e  repeated  The m a g n i t u d e o f t h e  p l u s o r minus t h e c a l c u l a t e d  error. Some o f t h e m e a s u r i n g experiments  i n s t r u m e n t s used i n t h e c o a l t r a n s p o r t  had a m a n u f a c t u r e r ' s  stated accuracy.  The random  e r r o r s o f t h e o t h e r d e v i c e s were o b t a i n e d by a n a l y z i n g t h e r e s u l t s of repeated a)  readings.  Flow Rate Measurement The f l o w m e t e r d i s p l a y e d a new r e a d i n g e v e r y second so  t h e mean v a l u e o f 30 t o 40 measurements was used f o r each f l o w r a t e d e t e r m i n a t i o n , and t h e e r r o r was based on two s t a n d a r d d e v i a t i o n s from t h e mean. b)  Depth o f Flow Measurement The d i s t a n c e t o t h e f l u i d s u r f a c e was m e a s u r e d 8 t o 10  t i m e s f o r each t e s t and an a c c u r a c y o f p l u s o r minus 3.2 m i l l i m e t e r s was e s t i m a t e d .  The depth o f f l u i d f l o w was  c a l c u l a t e d by s u b t r a c t i n g t h e s e measurements from t h e diameter of the flume.  The e r r o r i n m e a s u r i n g  t h e flume  d i a m e t e r was s m a l l r e l a t i v e t o 3.2 m i l l i m e t e r s so t h i s v a l u e was used as t h e d e p t h o f f l o w e r r o r .  68  c)  Flume S l o p e The r e a d i n g a c c u r a c y o f the compass v e r n i e r was  degree. cent d)  .1  The measurement e r r o r was h a l f o f t h i s o r .09  per  slope. Weight Measurements The s c a l e was c a l i b r a t e d e v e r y 2 ounces and,  t h e measurement e r r o r was 1 o u n c e .  therefore,  The c o a r s e c o a l b i n was  f i l l e d w i t h 5 b u c k e t s of c o a l so the e r r o r i n each c o a l w e i g h t was the r o o t mean s q u a r e or 2.24  coarse  ounces.  E r r o r s due to m o i s t u r e d i f f e r e n c e s i n t h e c o a r s e c o a l used i n the t e s t s were c a l c u l a t e d by assuming  that  the  w e i g h t of m o i s t u r e v a r i e d by p l u s or minus 3 per c e n t . equilibrium,  a i r d r i e d m o i s t u r e c o n t e n t of the  c o a l has been d e t e r m i n e d cent.  The  run-of-mine  by the mine owners t o be 5 p e r  The m o i s t u r e c o n t e n t of the c o a l from the mine i s  assumed to be 8 per c e n t . The c o a r s e c o a l t r a n s p o r t  v a l u e s have not been a l t e r e d  to a c c o u n t f o r t h i s m o i s t u r e as i t w i l l be p r e s e n t i n any run-of-mine  coal t r a n s p o r t  system.  The t o t a l e r r o r e s t i m a t e f o r the c o a r s e c o a l w e i g h t i s c a l c u l a t e d t o be 6.7  per c e n t .  The e r r o r due to the  scale  r e a d i n g i s s m a l l r e l a t i v e t o the m o i s t u r e c o n t e n t e r r o r  and  so i s i g n o r e d . e)  E l a p s e d Time Measurement The e r r o r s a s s o c i a t e d  w i t h s t a r t i n g and s t o p p i n g the  t e s t s were e s t i m a t e d t o be 1 s e c o n d .  The c u m u l a t i v e  effect  69  of t h e s e e r r o r s 1s t h e r o o t mean s q u a r e v a l u e , o r 1.4 seconds f)  f o r each  test.  Coal S p e c i f i c G r a v i t y Measurement The d i g i t a l s c a l e used t o weigh t h e c o a l p a r t i c l e s was  a c c u r a t e t o two d e c i m a l p l a c e s w i t h an e r r o r o f .005 grams. The r e a d i n g a c c u r a c y o f t h e g r a d u a t e d  c y l i n d e r was 2.0  m i l l 1 l 1 t r e s w i t h an e r r o r o f 1.0 m i l l i l i t r e .  Using the  minimum measured w e i g h t o f 15.94 grams and t h e minimum volume o f 10.0 c u b i c c e n t i m e t e r s , t h e maximum e r r o r i s 10 per c e n t . 3.  E f f e c t o f E r r o r s on t h e E x p e r i m e n t a l  Results  The e f f e c t s o f e r r o r s on t h e e x p e r i m e n t a l a n a l y z e d by e x a m i n i n g experimental  t h e i r e f f e c t on t h e T r a n s p o r t F u n c t i o n , t h e  c o a r s e c o a l t r a n s p o r t , t h e Manning f l o w v e l o c i t y and  the e x p e r i m e n t a l a)  r e s u l t s were  flow v e l o c i t y .  C o a r s e Coal  Transport  Minimum and maximum v a l u e s o f t h e d i m e n s i o n l e s s t r a n s p o r t and f l o w p a r a m e t e r s  were c a l c u l a t e d by  i n c o r p o r a t i n g t h e e r r o r s a s s o c i a t e d w i t h each o f t h e pertinent hydraulic variables. The newly c a l c u l a t e d p a r a m e t e r v a l u e s were graphed and power law r e g r e s s i o n c u r v e s were f i t t e d t o t h e d a t a .  These  r e g r e s s i o n e q u a t i o n s were c a l c u l a t e d t o be; plus error:  T r a n s p o r t P a r a m e t e r = 3.45 (Flow  Parameter)*  median:  T r a n s p o r t P a r a m e t e r = 3.57 (Flow  Parameter)«6  minus e r r o r : T r a n s p o r t P a r a m e t e r = 3.75 (Flow  Parameter)*  6 7  7  6 7  70  T r a n s p o r t f u n c t i o n s c a l c u l a t e d from t h e s e e q u a t i o n s p r e d i c t c o a r s e c o a l t r a n s p o r t v a l u e s w i t h i n 23 per c e n t o f t h e original transport function. The " s t e a d i n e s s " i n t h e t r a n s p o r t f u n c t i o n d e t e r m i n a t i o n , t h r o u g h the range o f e x p e r i m e n t a l e r r o r , v a l i d a t e s i t s a c c u r a c y as a p r e d i c t o r o f c o a r s e c o a l conveyance. E r r o r s i n p r e d i c t e d and e x p e r i m e n t a l c o a r s e c o a l t r a n s p o r t f o r the 10 v a l i d a t i o n t e s t s were c a l c u l a t e d and 6 o f the p r e d i c t e d v a l u e s were the same as the e x p e r i m e n t a l v a l u e s , w i t h i n the e r r o r b o u n d a r i e s , as shown on F i g u r e 3-11.  A l l o f the p r e d i c t e d v a l u e s were w i t h i n 20 p e r c e n t  o f the e x p e r i m e n t a l  values.  T h i s c o r r o b o r a t e s the a c c u r a c y o f the T r a n s p o r t F u n c t i o n as i t p r e d i c t s the h y d r a u l i c c o n v e y a n c e o f c o a r s e c o a l i n a h i g h d e n s i t y p o l y e t h y l e n e flume o f c i r c u l a r c r o s s section. b)  V e r i f i c a t i o n o f the Manning E q u a t i o n E r r o r s i n the v e l o c i t y o f f l o w as p r e d i c t e d by t h e  Manning e q u a t i o n and as c a l c u l a t e d from the d a t a were d e t e r m i n e d f o r 84 e x p e r i m e n t s . e q u a t i o n p r e d i c t e d the e x p e r i m e n t a l  experimental  The Manning  flow v e l o c i t y , w i t h i n  t h e e r r o r b o u n d a r i e s , i n 80 per c e n t of the t e s t s and  was  a c c u r a t e t o w i t h i n p l u s o r minus 20 per c e n t i n 93 p e r c e n t o f the t e s t s . The v a l u e o f t h e r e s i s t a n c e f a c t o r "n" was  iteratively  c h a n g e d to t e s t i t s e f f e c t on the Manning e q u a t i o n  71  C A L C U L A T E D vs EXPERIMENTAL COARSE COAL TRANSPORT IN KILOGRAMS  PER  SECOND  1  2  EXPERIMENTAL  F i g u r e 3-11  E r r o r s i n the p r e d i c t e d and experimental c o a r s e c o a l t r a n s p o r t f o r t h e 10 v a l i d a t i o n t e s t s were c a l c u l a t e d and 6 o f the p r e d i c t e d v a l u e s were the same as the exp e r i m e n t a l v a l u e s , w i t h i n the e r r o r b o u n d a r i e s . A l l of the p r e d i c t e d v a l u e s were w i t h i n 20 p e r c e n t o f the exp e r i m e n t a l v a l u e s . T h i s c o r r o b o r a t e s the a c c u r a c y o f the T r a n s p o r t F u n c t i o n .  72  predictions.  These c a l c u l a t i o n s c o n f i r m e d t h a t the  flume  manufacturers  v a l u e o f .008 gave the b e s t c o r r e l a t i o n  between the e x p e r i m e n t a l v e l o c i t i e s and the Manning e q u a t i o n p r e d i c t i ons. I t i s c o n c l u d e d t h a t t h e Manning e q u a t i o n a c c u r a t e l y p r e d i c t s t h e v e l o c i t y o f f l u i d f l o w i n g i n a c i r c u l a r , open channel. G.  Comparison  with other  The open c h a n n e l  Research  sediment t r a n s p o r t experiments  o f Ambrose  ( 1 9 5 3 ) , G r a f and A c a r o g l u ( 1 9 6 8 ) , and W i l s o n (1980) a r e p r e s e n t e d and the r e s u l t s o f t h e i r work a r e compared to the c o n c l u s i o n s of this  study. 1.  Ambrose Ambrose ( 1 9 5 3 ) , w o r k i n g a t the U n i v e r s i t y o f Iowa,  i n v e s t i g a t e d s e d i m e n t t r a n s p o r t i n open c h a n n e l p i p e f l o w to determine  design parameters  f o r t h e i n s t a l l a t i o n o f storm  sewers. His experimental  f l u m e was an 18.3 m e t e r l o n g by  15.2  c e n t i m e t e r d i a m e t e r l u c i t e p i p e mounted on a p i v o t i n g , s t e e l beam.  The m a t e r i a l b e i n g c o n v e y e d  was u n i f o r m l y g r a d e d s a n d ,  m i l l i m e t e r s , .58 m i l l i m e t e r s and 1.62  millimeters in size.  The p i p e s l o p e was g r a d u a l l y d e c r e a s e d as the s l u r r y t h r o u g h i t u n t i l the sand began t o d e p o s i t on the bottom pipe.  .25  flowed o f the  The v a l u e s o f f l u i d f l o w r a t e , p i p e s l o p e , depth o f f l u i d  f l o w and v o l u m e t r i c f l o w r a t e of s o l i d s were then r e c o r d e d  and  73  p l o t t e d as d i m e n s i o n l e s s  where "Q " s  ratios;  i s t h e v o l u m e t r i c f l o w r a t e o f t h e s o l i d s , "D" i s  t h e p i p e d i a m e t e r , "Y" i s t h e depth o f f l u i d f l o w and t h e o t h e r v a r i a b l e s a r e as p r e v i o u s l y d e f i n e d . These r a t i o s a r e p l o t t e d a g a i n s t each o t h e r i n F i g u r e 2-2 on page 18 and i n c l u d e d a t a f o r t h e t h r e e sand g r a i n s i z e s . The s p e c i f i c g r a v i t y c o r r e l a t i o n term, ( - 1 ) 2 / 5  s  w a s  i n c l u d e d by Ambrose on t h e b a s i s o f work done by S h i e l d s ( 1 9 3 6 ) . Ambrose d i d n o t t e s t i t s a c c u r a c y by a l t e r i n g t h e s p e c i f i c g r a v i t y of the sediment  i n any o f h i s t e s t s .  The s l u r r i e s used by Ambrose had a low v o l u m e t r i c s o l i d s c o n c e n t r a t i o n and t h e f l o w regime was pseudohomogeneous w i t h a l l the sediment  i n suspension.  The c u r r e n t r e s e a r c h used a w i d e r  range o f p a r t i c l e s i z e s i n a h e t e r o g e n e o u s  flow regime.  However,  the two e x p e r i m e n t a l r e s u l t s a r e compared by u s i n g a m o d i f i e d Ambrose d i m e n s i o n l e s s r a t i o t o a n a l y z e t h e t r a n s p o r t o f f i n e c o a l only.  The e x p o n e n t  on t h e s p e c i f i c g r a v i t y c o r r e c t i o n term was  changed t o c a l c u l a t e t h e d i m e n s i o n l e s s r a t i o f o r t h e c o a l d a t a values.  A v a l u e o f .06 i n s t e a d o f -.4  was used and t h e r e s u l t s  a r e shown on F i g u r e 3-12 w i t h t h e o r i g i n a l Ambrose r e l a t i o n s h i p shown by t h e c u r v e and t h e c o a l d a t a shown as d i s c r e t e p o i n t s . The c o a l d a t a f i t t h e Ambrose r e l a t i o n s h o p w e l l g i v e n t h a t t h i s r e l a t i o n s h i p r e p r e s e n t s sediment incipient deposition only.  t r a n s p o r t at the p o i n t of  Ambrose d i d n o t t e s t t h e s p e c i f i c  g r a v i t y c o r r e c t i o n term used i n h i s r e l a t i o n s h i p and t h i s  74  AMBROSE  RELATIONSHIP using  COAL  DATA  10  F i g u r e 3-12  The exponent on t h e s p e c i f i c g r a v i t y c o r r e c t i o n term i n Ambrose's r e l a t i o n s h i p has been changed from -.4 t o 0.06. The c o a l d a t a , u s i n g t h i s m o d i f i e d r e l a t i o n s h i p , has been p l o t t e d with the o r i g i n a l Ambrose c u r v e . The good f i t o f the c o a l d a t a suggests t h a t the s p e c i f i c g r a v i t y c o r r e c t i o n term must be m o d i f i e d t o accommodate d a t a u s i n g sediments o f a d i f f e r e n t d e n s i t y from those used by Ambrose.  75  r e s e a r c h i n d i c a t e s t h a t i t must be m o d i f i e d t o accommodate d a t a using sediments 2.  of a d i f f e r e n t d e n s i t y .  G r a f and A c a r o g l u G r a f and A c a r o g l u (1968) p r o p o s e d a t r a n s p o r t  r e l a t i o n s h i p o f the  form; 10.32  where t h e t r a n s p o r t p a r a m e t e r , the shear i n t e n s i t y parameter  Y "•2.52  C. V R p = X— ~~IT^—  and  /(s-,-1) <"  Y=  (s,-l) d 50 S R J c  The v a r i a b l e " d " r e f e r s t o the s c r e e n s i z e , i n 5 0  m i l l i m e t e r s , which p a s s e s 50 p e r c e n t o f the m a t e r i a l .  The open  channel flow data of f o u r previous r e s e a r c h e r s , ( G i l b e r t  (1914);  Guy e t a l ( 1 9 6 6 ) ; A n s l e y ( 1 9 6 3 ) ; and E i n s t e i n ( 1 9 4 4 ) ) , were used to c a l c u l a t e the d i m e n s i o n l e s s parameters F i g u r e 2-2 on page 21.  which a r e p l o t t e d on  Data from 903 e x p e r i m e n t s w i t h l a b o r a t o r y  f l u m e s and s t r e a m c h a n n e l s , t r a n s p o r t i n g sand p a r t i c l e s r a n g i n g i n s i z e from .19 m i l l i m e t e r s t o 1.7 m i l l i m e t e r s , a r e r e p r e s e n t e d on t h i s  graph.  The c o a l t r a n s p o r t d a t a from t h e p r e s e n t r e s e a r c h have been used t o c a l c u l a t e v a l u e s f o r t h e t r a n s p o r t and s h e a r parameters  d e f i n e d above.  intensity  They a r e p l o t t e d on F i g u r e 3-4  with  the c u r v e d e f i n e d by G r a f and A c a r o g l u and r e g r e s s i o n c u r v e f o r the c o a r s e and combined c o a l d a t a . The c o a l d a t a were p l o t t e d as f i n e , c o a r s e and combined r e s u l t s t o i n v e s t i g a t e the e f f e c t o f p a r t i c l e s i z e on the s h e a r  GRAF  RELATIONSHIP  USING  COAL  DATA  • • •—  10  •  1*1  •  0d  * =  \ • • Ii • « <  •  5 0  S R C VR V  *  ••  •  • • v  w  ^ .3 _  FINE COARSE COMBINED  V ress on •  c  oc  —B  „  •  a  UJ I  V)  •  •  1  10 TRANSPORT  Figure 3-13  100 PARAMETER  • • Q  Q—  1000  $  The coal data are p l o t t e d as f i n e , coarse and combined r e s u l t s to i n v e s t i g a t e the e f f e c t o f p a r t i c l e s i z e on the shear i n t e n s i t y and t r a n s p o r t parameters. The acceptable f i t o f the f i n e c o a l data and the poor f i t o f the coarse and combined coal data suggests that these parameters a r e inadequate to model sediment transport f o r large p a r t i c l e s i z e s . A d i f f e r e n t treatment o f the p a r t i c l e s i z e terms i n the shear i n t e n s i t y and transport parameters would d e f i n e a r e l a t i o n s h i p which f i t s a l l o f the data more a c c u r a t e l y .  77  i n t e n s i t y and t r a n s p o r t relationship  parameters.  G r a f and A c a r o g l u ' s  u n d e r e s t i m a t e s t h e d a t a f o r t h e c o a r s e and combined  coal r e s u l t s but the f i n e coal the o r i g i n a l p l o t .  results are within  the s c a t t e r of  The a v e r a g e p a r t i c l e d i a m e t e r s f o r t h e c o a l  d a t a were; i)  10.1 m i l l i m e t e r s  f o r the coarse c o a l ,  ii)  0.65 m i l l i m e t e r s  f o r t h e f i n e c o a l , and  i i i ) 6.1 m i l l i m e t e r s The  coal.  l a r g e s t p a r t i c l e s used i n t h e G r a f and A c a r o g l u  were 1.7 m i l l i m e t e r s . and  f o r t h e combined  plot  The a c c e p t a b l e f i t o f t h e f i n e c o a l  data  t h e poor f i t o f t h e c o a r s e and combined c o a l d a t a s u g g e s t s  t h a t t h e s h e a r i n t e n s i t y and t r a n s p o r t to model s e d i m e n t t r a n s p o r t  parameters are inadequate  for large p a r t i c l e sizes.  The good  f i t of the f i n e coal r e s u l t s also suggests that the s p e c i f i c gravity  term i s n o t t h e d e f i c i e n t v a r i a b l e  and t h a t a d i f f e r e n t  t r e a t m e n t o f t h e p a r t i c l e s i z e terms i n t h e s h e a r i n t e n s i t y and transport  p a r a m e t e r s would d e f i n e  of t h e d a t a more 3.  a relationship  accurately.  W11son W i l s o n (1980) p e r f o r m e d a t h e o r e t i c a l ,  analysis  which f i t s a l l  o f open c h a n n e l s e d i m e n t t r a n s p o r t  computer  in a circular  c o n d u i t , b a s e d on a c o m p u t e r model f o r s l u r r y t r a n s p o r t pipe flow.  H i s r e s u l t s a r e b a s e d on t h e p r e m i s e t h a t t h e r e i s an  optimum s l o p e t o t r a n s p o r t specified That i s ;  in full  distance.  t h e maximum volume o f s o l i d s o v e r a  78  P 1  vd Q L tan 0  s  optimum t r a n s p o r t = maximum  S  C  L  where P i s the s p e c i f i c weight of the s o l i d , " i s the d e l i v e r e d v o l u m e t r i c c o n c e n t r a t i o n of the s l u r r y , s  "r  vd "L" i s t h e s p e c i f i e d t r a n s p o r t d i s t a n c e and " t a n 0 " i s t h e flume s i ope. Wilson suggests that a volumetric s o l i d s c o n c e n t r a t i o n of a b o u t 30 p e r c e n t and a f l u i d f l o w d e p t h o f .93 t i m e s t h e f l u m e d i a m e t e r w i l l d e t e r m i n e t h e optimum f l o w c o n d i t i o n s .  Keeping  t h e s e v a r i a b l e s c o n s t a n t , he i t e r a t i v e l y d e t e r m i n e d t h e optimum s l o p e f o r d i f f e r e n t s o l i d s p e c i f i c g r a v i t i e s , p a r t i c l e s i z e s and pipe diameters. For heterogeneous flow, Wilson proposed the f o l l o w i n g i c _ 7 /s-,-1 \ 1.2 tan 0 = O.ld D )  equation;  J  where "d" i s t h e p a r t i c l e s i z e i n m i l l i m e t e r s and "D" i s the pipe diameter i n meters. The b o u n d a r i e s t o t h i s t r a n s p o r t c o n d i t i o n a r e f i x e d by two f u r t h e r e q u a t i o n s ; i)  tan  0 =  .0006 / s - l \ ° -  6  n  (ill)  \1.65 ' T h i s r e p r e s e n t s a c o n d i t i o n o f no s e d i m e n t t r a n s p o r t . /„ -.\0.35 i i ) tan 0 = 0.42 \1.65 / T h i s r e p r e s e n t s a c o n d i t i o n o f f u l l y suspended transport.  sediment  79  The r e s u l t s o f t h e s e c o m p u t a t i o n s  a r e shown on F i g u r e 3-16  on page 29. The optimum s l o p e e q u a t i o n p r o p o s e d by W i l s o n i s r e s t r i c t e d t o p a r t i c l e s i z e s l e s s than 2.8 m i l l i m e t e r s . An optimum s l o p e o f 131 p e r c e n t was c a l c u l a t e d u s i n g a p a r t i c l e d i a m e t e r o f 6 m i l l i m e t e r s and a p i p e d i a m e t e r o f .15 m e t e r s b u t t h e b o u n d a r y c o n d i t i o n s , which a r e i n d e p e n d e n t  o f p a r t i c l e s i z e , would  i n d i c a t e t h a t t h e optimum s l o p e i s between .02 p e r c e n t and 27.7 per c e n t .  This ambiguity suggests that Wilson's r e l a t i o n s h i p  does n o t a d e q u a t e l y c o v e r t h e c a l c u l a t i o n o f an optimum slope.  flume  S e d i m e n t p a r t i c l e s 6 m i l l i m e t e r s i n s i z e were o b s e r v e d t o  be f u l l y t r a n s p o r t e d a t s l o p e s much l o w e r than 27.7 p e r c e n t , i n the c u r r e n t r e s e a r c h w h i c h r a i s e s doubt about t h e a c c u r a c y o f t h e boundary c o n d i t i o n p r e d i c t i o n s . The l a c k o f e x p e r i m e n t a l v e r i f i c a t i o n f o r W i l s o n ' s r e s u l t s i s a d e f i c i e n c y i n h i s work and h i s r e l a t i o n s h i p was n o t used i n t h e r e s e a r c h . 4.  Summary The r e s u l t s o f Ambrose, G r a f and A c a r o g l u and W i l s o n  were based on t h e open c h a n n e l t r a n s p o r t o f u n i f o r m l y  graded  sands w i t h a maximum p a r t i c l e s i z e o f 1.7 m i l l i m e t e r s .  Ambrose's  r e l a t i o n s h i p , w i t h a m o d i f i c a t i o n t o t h e s p e c i f i c g r a v i t y term, f i t s t h e f i n e c o a l d a t a b u t does n o t p r e d i c t t h e t r a n s p o r t o f coarse coal.  The r e l a t i o n s h i p p r e s e n t e d by G r a f and A c a r o g l u  f i t s the f i n e coal data w i t h i n the s c a t t e r of the o r i g i n a l but does n o t f i t t h e c o a r s e and combined c o a l d a t a .  plot  The p a r t i c l e  s i z e terms i n t h e s h e a r i n t e n s i t y and t r a n s p o r t p a r m e t e r s  need t o  be m o d i f i e d t o i n c o r p o r a t e t h e r e s u l t s f o r l a r g e c o a l p a r t i c l e  80  sizes.  The m a t h e m a t i c a l l y d e t e r m i n e d  equation of Wilson  produced  ambiguous r e s u l t s when a p p l i e d t o t h e c o a l d a t a and the e x p e r i m e n t a l o b s e r v a t i o n s o f t h i s r e s e a r c h d i d not s u p p o r t the use o f h i s r e l a t i o n s h i p . I t i s c o n c l u d e d t h a t the T r a n s p o r t F u n c t i o n , d e t e r m i n e d  from  t h i s s t u d y , i s a s i g n i f i c a n t s t e p f o r w a r d i n the u n d e r s t a n d i n g c o a r s e c o a l t r a n s p o r t i n a flume o f c i r c u l a r c r o s s s e c t i o n .  of  It  b u i l d s on the work of p r e v i o u s r e s e a r c h e r s and p r o v i d e s a d i r e c t i o n f o r f u r t h e r work. H.  Comparison  with O p e r a t i n g Mines  Westar M i n e s L t d . ( f o r m e r l y B.C. underground  Coal L t d . ) , o p e r a t i n g an  h y d r a u l i c c o a l mine i n s o u t h e a s t e r n B r i t i s h  and the Hansa-Hydro Mine o f West Germany have r e s e a r c h e d conveyance  of f l u i d i z e d c o a r s e c o a l .  Columbia, flume  The r e s u l t s of work a t  t h e s e p r o p e r t i e s a r e r e l a t e d to t h i s r e s e a r c h . 1.  Westar M i n e s L t d . The a u t h o r s o f an u n p u b l i s h e d s t a f f r e p o r t p r o p o s e  f o l l o w i n g r e l a t i o n s h i p to determine s  f (s l)  =  r  the  flume s l o p e ;  100  [s-.q'k' + ( s l ) ] r  where " f " i s t h e c o e f f i c i e n t of f r i c t i o n f o r c o a l on the s u r f a c e , "q* " i s the s p e c i f i c c o n s u m p t i o n meters  of water i n c u b i c  per ton and "k " i s the c o e f f i c i e n t of f l o w  i m p a r t e d t o the c o a l .  1  flume  energy  T h i s e q u a t i o n s u g g e s t s t h a t the volume o f  w a t e r r e q u i r e d t o t r a n s p o r t the c o a l i s i n v e r s e l y p r o p o r t i o n a l t o  81  the s l o p e as shown on F i g u r e  3-17.  Assuming a f r i c t i o n c o e f f i c i e n t f o r h i g h d e n s i t y p o l y e t h y l e n e o f 0.27 and a f l u m e s l o p e o f 2.5 p e r c e n t , t h e s p e c i f i c c o n s u m p t i o n o f w a t e r , u s i n g t h i s f o r m u l a i s 5.35  cubic  m e t e r s p e r t o n o f s o l i d s . The s p e c i f i c c o n s u m p t i o n o f w a t e r c a l c u l a t e d from t h e c u r r e n t e x p e r i m e n t a l  program, b a s e d on a  s l u r r y s o l i d s c o n c e n t r a t i o n o f 20 p e r c e n t by volume,  was  c a l c u l a t e d t o be .3 c u b i c m e t e r s o f w a t e r f o r e a c h t o n o f s o l i d s . If the experimental  t r a n s p o r t o f c o a r s e c o a l o n l y i s used to  c a l c u l a t e t h e s p e c i f i c c o n s u m p t i o n o f w a t e r , a v a l u e o f 10.9 c u b i c meters per ton of s o l i d s i s o b t a i n e d .  The d i s c r e p a n c i e s  between the c a l c u l a t e d s p e c i f i c c o n s u m p t i o n o f w a t e r v a l u e s and t h a t p r e d i c t e d by t h e f l u m i n g c u r v e a r e due t o t h e d i f f e r e n c e s i n the s i z e d i s t r i b u t i o n s o f t h e c o a l p a r t i c l e s , the Westar Mines Ltd.  equation  i s s p e c i f i c to the flume t r a n s p o r t a t i o n of  h y d r a u l i c a l l y mined c o a l .  The c o a l p a r t i c l e s , as a r e s u l t , a r e  l a r g e r (up t o 150 m i l l i m e t e r s ) and have a s m a l l e r p r o p o r t i o n o f f i n e p a r t i c l e s . The c o a l p a r t i c l e s used i n t h e c u r r e n t  research,  by c o n t r a s t , were 100 p e r c e n t minus 65 m i l l i m e t e r s and 50 p e r c e n t were minus 10 m i l l i m e t e r s .  L e s s w a t e r i s needed t o move t h e  f i n e c o a l p a r t i c l e s so t h e f l u m i n g c u r v e o v e r e s t i m a t e s t h e w a t e r requirements.  The f a c t o r o f 2 d i f f e r e n c e between t h e s p e c i f i c  c o n s u m p t i o n o f w a t e r f o r c o a r s e c o a l as c a l c u l a t e d by t h e T r a n s p o r t F u n c t i o n and t h a t d e t e r m i n e d from the f l u m i n g c u r v e i s small c o n s i d e r i n g the d i f f e r e n c e s i n coal p a r t i c l e s i z e , flume m a t e r i a l and c r o s s s e c t i o n a l g e o m e t r y . The m e c h a n i s t i c  r e l a t i o n s h i p p r o p o s e d by t h e s t a f f a t Westar  82  M i n e s L t d . , was  used i n t h e c u r r e n t r e s e a r c h to v e r i f y the c h o i c e  o f h i g h d e n s i t y p o l y e t h y l e n e as a s u p e r i o r f l u m e m a t e r i a l . f a i l u r e of t h i s r e l a t i o n s h i p to account  f o r t h e f a c t o r s of  h y d r a u l i c r a d i u s and g r a v i t y i s a s h o r t coming w h i c h accounted 2.  f o r i n the T r a n s p o r t  The  was  Function.  Hansa-Hydro Mine Kuhn (1980) d e s c r i b e s the d e s i g n and o p e r a t i o n o f a  flume system i n an u n d e r g r o u n d c o a l mine i n West Germany.  He  r e p o r t s t h a t the wear c h a r a c t e r i s t i c s o f p l a s t i c l i n e r s i s v e r y f a v o u r a b l e w i t h no change i n w a l l t h i c k n e s s a f t e r 560,000 t o n n e s of c o a l s l u r r y had p a s s e d  through  also permitted a decrease  i n f l u m e s l o p e t o 8 p e r c e n t from  per c e n t .  the f l u m e .  The p l a s t i c  surface 12  In t e s t s w i t h a p r o t o t y p e f l u m e , he measured the  d i f f e r e n c e i n v e l o c i t y between the f l u i d and the c o a l f o r v a r y i n g s l o p e a n g l e s as shown on F i g u r e 2-4 T h i s phenomenon was measurements were t a k e n .  on page 25.  n o t e d i n the c u r r e n t r e s e a r c h but  no  The p r a c t i c a l s i g n i f i c a n c e of t h i s  v e l o c i t y d i f f e r e n c e , or s l i p , i s t h a t a bed o f c o a l w i l l  always  be l e f t i n the b o t t o m o f t h e f l u m e when the w a t e r f l o w i s stopped.  Kuhn d i d not d i s c u s s p r o b l e m s i n r e s t a r t i n g the f l u m e  but t h i s p o t e n t i a l o p e r a t i n g p r o b l e m was a d d r e s s e d research.  i n the c u r r e n t  The r e s t a r t t e s t s d e s c r i b e d above showed t h a t a bed of  coal i n a c i r c u l a r flume i s r e f l u i d i z e d without  difficulty.  83  CHAPTER IV PARTICLE SIZE DEGRADATION A.  Introduction The t r a n s f e r o f c o a l t h r o u g h  an i n c l i n e d , s t e e l l i n e d r a i s e ,  in plug flow leads to p a r t i c l e s i z e degradation. of t h i s e x p e r i m e n t a l  program was t o d e t e r m i n e t h e e x t e n t o f  p a r t i c l e size degradation coal cleaning  The o b j e c t i v e  and p r e d i c t i t s e f f e c t on s u b s e q u e n t  processes.  A 75 c e n t i m e t e r  d i a m e t e r by 300 meter l o n g s t e e l l i n e d  v e r t i c a l r a i s e i s modelled  i n t h i s experimental  program.  To  r e d u c e t h i s system t o a w o r k a b l e , l a b o r a t o r y e x p e r i m e n t , t h e apparatus B.  shown i n F i g u r e 4-1 was b u i l t .  Apparatus The a p p a r a t u s  centimeter  c o n s i s t e d o f two, 3 m e t e r l o n g by 75  d i a m e t e r s t e e l t u b e s w i t h a w a l l t h i c k n e s s o f 9.5  millimeters.  The f i r s t tube was made o f two, 1.5 meter l o n g ,  f l a n g e d s e c t i o n s b o l t e d t o g e t h e r and t h e o t h e r tube was made o f s i x , 30 c e n t i m e t e r  l o n g and two, 60 c e n t i m e t e r  long,  s e c t i o n s h e l d t o g e t h e r by f o u r c o m p r e s s i o n r o d s .  flanged  The c l o s e  t o l e r a n c e o f t h e m a t i n g e n d s , as d e t a i l e d on F i g u r e 4-1, d i d n o t contribute to p a r t i c l e degradation. The i n s i d e w a l l c o n d i t i o n o f t h e t u b e s was smooth w i t h a l i g h t s c a l e o f r u s t and a r o u n d e d w e l d p r o t r u d i n g 5 m i l l i m e t e r s from t h e s u r f a c e .  C O A L SAMPLE  SAMPLING  Figure 4-1  TUBE  TUBE  APPARATUS  CUTAWAY  VIEW  The p a r t i c l e s i z e degradation t e s t apparatus c o n s i s t e d o f two 3 meter long by 75 centimeter diameter steel tubes. The f i r s t tube was made o f two, 1.5 meter long f l a n g e d s e c t i o n s bolted together (not shown) and the other tube was made o f s i x , 30 centimeter long and two, 60 centimeter long flanged s e c t i o n s held together by four compression rods. The mating ends were mechined to a close tolerance. A gasketed coal p l u g , fastened t o a 3 meter long rod supported the column o f c o a l .  85  A g a s k e t e d c o a l p l u g , f a s t e n e d t o a 3 meter l o n g r o d s u p p o r t e d the column o f c o a l .  A 4.5 t o n n e c a p a c i t y o v e r h e a d  c r a n e was used t o l i f t t h e t u b e s and l o w e r t h e c o a l . C.  Procedure The g a s k e t e d p l u g hook was p l a c e d i n s i d e the s e c t i o n e d s t e e l  tube and t h e tube was f i l l e d w i t h minus 65 m i l l i m e t e r c o a l  one  section at a time.  was  Samples o f c o a l were t a k e n as the tube  b e i n g f i l l e d and p a i n t e d p i e c e s o f c o a l were p l a c e d r a d i a l l y a t the  t o p o f each s e c t i o n . The p l u g hook was s u s p e n d e d from a s t e e l bar p l a c e d a c r o s s  the  top o f t h e s t e e l tube to p r e v e n t t h e c o a l from f a l l i n g o u t  and t h e c o a l f i l l e d tube was p l a c e d on t o p o f the empty t u b e . With t h e p l u g hook h e l d by a 3.5 meter l o n g s l i n g from the o v e r h e a d c r a n e , t h e s t e e l b a r was removed  and the c o a l  was  d r o p p e d i n t o t h e bottom t u b e a t t h e r a t e o f 20 c e n t i m e t e r s per second. top  The s l i n g was removed  from t h e c r a n e and the now  tube was p l a c e d on t h e f l o o r .  empty  The s t e e l bar was r e p l a c e d to  h o l d t h e p l u g hook, t h e c o a l f i l l e d tube was. l i f t e d onto the empty t u b e and t h e p r o c e d u r e was r e p e a t e d .  The c y c l i c  t r a n s p o s i t i o n o f t h e s t e e l t u b e s i s diagrammed on F i g u r e 4-2. The e x p e r i m e n t was c o n d u c t e d i n a f l o o r " w e l l c o n n e c t i n g two f l o o r s i n t h e l a b o r a t o r y to m i n i m i z e t h e danger o f t h e t o p heavy, s l e n d e r t u b e s from t o p p l i n g . One hundred c y c l e s , as d e s c r i b e d above were c a r r i e d o u t to s i m u l a t e t h e p l u g f l o w o f r u n - o f - m i n e c o a l t h r o u g h 305 m e t e r s o f elevation.  F i g u r e 4-2  The c o a l f i l l e d tube was p l a c e d on top o f t h e empty tube, the gasketed plug was r e l e a s e d from i t s f i x e d p o s i t i o n and the c o a l column was lowered i n t o the bottom tube a t a r a t e o f 20 c e n t i m e t e r s p e r second by an overhead crane. The p o s i t i o n o f the tubes was swapped and t h e c y c l e was r e p e a t e d . Plug flow through 300 meters o f s t e e l l i n e d r a i s e was s i m u l a t e d i n t h i s way.  87  When the c y c l e s were c o m p l e t e d , the c o a l f i l l e d , t u b e was  t a k e n a p a r t one  and bottom 1 m e t e r was effects.  s e c t i o n at a time.  discarded  sectioned  The c o a l i n the  due t o the i n f l u e n c e o f  end  S h a r p e n e d s t e e l r i n g s of d i f f e r e n t d i a m e t e r s ,  millimeters  t h i c k and 12 c e n t i m e t e r s  coal.  samples, weighing 4 kilograms,  Coal  9.5  deep were d r i v e n i n t o  a n n u l a r s p a c e s as shown on F i g u r e 4.3.  the  were t a k e n from  The o u t s i d e 2  top  the  centimeters  of c o a l were sampled from the c i r c u m f e r e n c e o f the i n t a c t c o a l column by s l o w l y  l i f t i n g the s t e e l s e c t i o n .  Three coal  samples  were t a k e n from each s e c t i o n of the s t e e l tube and e a c h sample was  s i z e d on 4.76  screen D.  m i l l i m e t e r , 2.38  m i l l i m e t e r and 1.19  millimeter  sizes. Results  The h e i g h t of the c o a l column a t the b e g i n n i n g e x p e r i m e n t was  2.75  meters.  the c o a l column h e i g h t t o 2.1 test.  The  Consolidation  of  the  and l e a k a g e r e d u c e d  m e t e r s a t the c o n c l u s i o n  s i z e a n a l y s i s o f the c o a l b e f o r e  of  the  the c y c l i n g , as shown  on F i g u r e 4-4,  i n d i c a t e s t h a t 32 per c e n t of the c o a l by w e i g h t  was  millimeters.  minus 1.19  w e i g h t of the minus 1.19  At the end o f the c y c l i n g , the  m i l l i m e t e r c o a l had i n c r e a s e d  c e n t of the t o t a l c o a l as shown on T a b l e 4-1.  This table  i n d i c a t e s t h a t the a d d i t i o n a l c o a l f i n e s came from the c i r c u m f e r e n c e of the c o a l column (Sample A ) . increase  i n c o a l f i n e s i n the o t h e r two  the e x c e p t i o n  of s e c t i o n 3.  t o 35  T h e r e was  per  also  outside no  sampling l o c a t i o n s with  T h i s anomalous r e s u l t c o u l d be  due  88  PARTICLE  SIZE DEGRADATION  SAMPLES  Figure 4-3  When the c y c l e s were completed, the coal f i l l e d , s e c t i o n e d tube was taken apart. Sharpened s t e e l r i n g s o f d i f f e r e n t diameters were d r i v e n i n t o the c o a l . Coal samples, weighing f o u r kilograms were taken from the annular spaces. The o u t s i d e 2 centimeters of coal were sampled from the circumference o f the i n t a c t coal column by s l o w l y l i f t i n g the s t e e l s e c t i o n .  PARTICLE  SIZE  DISTRIBUTION  Figure 4-4 The coal particles were 100 percent minus 65 millimeters p r i o r to the degradation tests. The fraction of coal particles f i n e r than 1.19 millimeters was 32 percent.  90  COAL PARTICLE DEGRADATION TEST RESULTS  SAMPLE 3A 3B 3C Sub-Total HEAD 4A 4B 4C Sub-total HEAD 5A 5B 5C Sub-Total HEAD TOTAL HEAD  +4.76 mm  -4.76 mm to +2.38 mm  -2.38 mm to +1.19 mm  -1.19 mm  35 42 41 46 44 43 44 43 46 40 44 46 43 46  10 16 13 12 12 9 13 12 11 12 4 13 12 10 12  10 12 11 11 11 9 12 12 11 11 18 12 11 14 12  38 38 34 37 32 38 32 32 34 32 38 30 31 33 32  42 46  11 12  12 11  35 32  % i  42  %  %  %  TABLE 4-1 The degradation of coal took place around the circumference of the coal column (Sample A) and resulted i n a 3 per cent increase i n the minus 1.19 millimeter material. - This increase in fines w i l l not a f f e c t subsequent coal washing processes.  91  to a s l i g h t l y d i f f e r e n t s i z e d i s t r i b u t i o n a t t h e b e g i n n i n g o f t h e experiment. The  r a d i a l l i n e s o f p a i n t e d c o a l were f o u n d unchanged when  the c o a l was b e i n g sampled from t h e s t e e l t u b e .  This  qualitative  r e s u l t suggests that l a t e r a l m i g r a t i o n of coal p a r t i c l e s i s not a phenomenon o f p r a c t i c a l i m p o r t a n c e i f i t even e x i s t s . I t i s c o n c l u d e d t h a t c o n v e y i n g r u n - o f - m i n e c o a l t h r o u g h an i n c l i n e d , steel l i n e d r a i s e i n plug flow w i l l not generate coal f i n e s detrimental to subsequent coal washing p r o c e s s e s .  92  CHAPTER V RUN-OF-MINE COAL FLUME TRANSPORT SYSTEM DESIGN A.  I n t r o d u c t i on  The r u n - o f - m i n e c o a l f l u m e t r a n s p o r t system p r e s e n t e d chapter u t i l i z e s c u r r e n t l y e x i s t i n g technology B e c a u s e the s y s t e m was  planned  in i t s design.  f o r a p a r t i c u l a r mine, some o f the  d e s i g n p a r a m e t e r s are s p e c i f i c t o t h i s p r o p e r t y . been made, o t h e r w i s e ,  in this  An e f f o r t  to g e n e r a l i z e the l a y o u t i n o r d e r to  i t s a p p l i c a t i o n to o t h e r m i n i n g  has extend  conditions.  The u n b r o k e n r u n - o f - m i n e c o a l i s e x c a v a t e d  w i t h a 15 c u b i c  meter c a p a c i t y h y d r a u l i c s h o v e l , l o a d e d i n t o 77 tonne c a p a c i t y , mechanically  d r i v e n , r e a r dump t r u c k s and t r a n s p o r t e d to an  oversize coal screening plant.  The p l u s 6.4  centimeter  p a r t i c l e s are s c a l p e d from the r u n - o f - m i n e c o a l w h i c h i s  coal lowered  through  a 1 meter d i a m e t e r ,  drift.  The c o a l i s s l u r r i e d w i t h w a t e r and t r a n s p o r t e d t o a  dewatering  p l a n t through  polyethylene pipe.  s t e e l l i n e d r a i s e t o an u n d e r g r o u n d  a 61 c e n t i m e t e r d i a m e t e r ,  The d e w a t e r i n g  p l a n t s c r e e n s and d e w a t e r s the  c o a l and s t o r e s i t on a 30,000 t o n n e , stockpile.  high d e n s i t y ,  live capacity,  outdoor  The s y s t e m i s f u l l y a u t o m a t e d and i s c o n t r o l l e d from  the p r e p a r a t i o n p l a n t c o n t r o l room. A schematic  r e p r e s e n t a t i o n o f the r u n - o f - m i n e c o a l flume  t r a n s p o r t s y s t e m i s shown i n F i g u r e Recognition i)  5-1.  i s given to;  Al Bevan and A r t B e r t r a n d who the mine  geology,  helped in  understanding  93  SCALPING  GRIZZLY  DEWATERING STOCKPILE  DESIGN Figure 5-1  PLANT  ELEMENTS  The unbroken, run-of-mine coal i s excavated with a 15 cubic meter capacity hydraulic shovel, loaded into 77 tonne capacity trucks and transported to an oversize coal screening plant. The minus 6.4 centimeter coal p a r t i c l e s are conveyed through a 1 meter diameter steel lined r a i s e to an underground d r i f t . The coal i s s l u r r i e d with water and conveyed to a dewatering plant through a 61 centimeter diameter, high density, polyethylene pipe. The dewatered coal i s stockpiled and then sent to the wash plant.  94  ii)  B i l l Potma o f FMC o f Canada L i m i t e d who p r o v i d e d a p r e l i m i n a r y d e s i g n and c o s t e s t i m a t e o f t h e g r i z z l y s c r e e n i n g u n i t , and  i i i ) D a v i d W o e l l e r and Rimas P a k a l n i s who gave a d v i c e i n f o r m u l a t i n g a r o c k c l a s s i f i c a t i o n and ground s u p p o r t system. B.  S u r f a c e v e r s u s U n d e r g r o u n d Flume T r a n s p o r t System A s u r f a c e flume system i s i n a p p r o p r i a t e f o r t h i s mining  p r o p e r t y because of the u n a v a i l a b i l i t y of s u f f i c i e n t power t o pump w a t e r t o t h e t o p o f t h e m o u n t a i n .  electrical  A pumping  i n s t a l l a t i o n r e q u i r i n g a 5,000 h o r s e p o w e r motor would be r e q u i r e d and e x t e n s i v e c l e a r i n g and base p r e p a r a t i o n f o r a l o n g e r flume s y s t e m and w a t e r r e t u r n l i n e would have t o be u n d e r t a k e n .  A  p r e l i m i n a r y e s t i m a t e o f t h e t o t a l c a p i t a l c o s t f o r a s u r f a c e flume s y s t e m i n d i c a t e d t h a t i t would be 75 p e r c e n t o f t h e u n d e r g r o u n d flume s y s t e m c a p i t a l c o s t .  T h i s , combined w i t h t h e c a p i t a l  cost  f o r an i n c r e a s e d power s u p p l y , r u l e d o u t a s u r f a c e f l u m e s y s t e m f o r economic r e a s o n s .  T h i s r e s u l t may n o t be g e n e r a l f o r e v e r y  mining s i t u a t i o n . C.  Underground  Run-of-Mine  C o a l S l u r r y T r a n s p o r t System  T h i s d e s i g n combines a c o n v e n t i o n a l c o a l l o a d i n g and h a u l i n g o p e r a t i o n w i t h an u n d e r g r o u n d r a i s e and flume s y s t e m t o t r a n s p o r t run-of-mine coal from the coal f a c e to the washplant.  the  u n b r o k e n r u n - o f - m i n e c o a l i s e x c a v a t e d and l o a d e d i n t o 77 tonne t r u c k s and h a u l e d t o a s c r e e n i n g p l a n t .  The s c r e e n e d c o a l i s  t r a n s f e r r e d t o an u n d e r g r o u n d d r i f t t h r o u g h a s t e e l l i n e d where i t i s s l u r r i e d and c o n v e y e d t h r o u g h a 61 c e n t i m e t e r diameter flume to a s u r f a c e dewatering p l a n t .  The c o a r s e ,  raise  95  d e w a t e r e d c o a l i s s t a c k e d on an open c o a l s t o c k p i l e and t h e f i n e coal i s sent t o the preparation p l a n t thickener. 1.  C o a l L o a d e r and T r u c k  Requirements  The i n s i t u c o a l i s dug from t h e seam w i t h a 15 c u b i c meter h y d r a u l i c e x c a v a t o r and l o a d e d i n t o 77 tonne s i z e , d r i v e n , r e a r dump t r u c k s .  mechanically  The t r u c k s dump t h e c o a l i n t o a hopper  feeding the oversize coal s c a l p i n g u n i t .  The c o a l  p r o d u c t i v i t y o f 1,180 t o n n e s p e r o p e r a t i n g hour was  shovel determined  from a s u r v e y o f i n d u s t r y e x p e r i e n c e w i t h t h i s t y p e o f m i n i n g machine.  The t r u c k p r o d u c t i v i t y was c a l c u l a t e d from an  average  tramming speed o f 28.8 k i l o m e t e r s p e r h o u r , a t r u c k c a p a c i t y o f 54 t o n n e s and an a v e r a g e l e v e l haul d i s t a n c e f o r each m i n i n g  bench t o  the n e a r e s t o v e r s i z e s c a l p i n g u n i t . The annual  o p e r a t i n g hours r e q u i r e d f o r t h e c o a l l o a d e r and  t r u c k s i s d e f i n e d by t h e f o l l o w i n g r e l a t i o n s h i p ; Operating  h o u r s r e q u i r e d = Tonnes x O p e r a t i n g  Year  Year  Hour  Tonnes  An o p e r a t i n g hour i s d e f i n e d as t h e number o f h o u r s p e r s h i f t t h a t t h e m a c h i n e r y i s d o i n g p r o d u c t i v e work.  The r a t i o o f  o p e r a t i n g h o u r s t o t o t a l h o u r s i s 0.60 f o r t h e c o a l l o a d e r and 0.50  f o r the coal trucks. 2.  Run-of-Mine Coal O v e r s i z e  Scalping  The c o a l i s dumped from t h e t r u c k s i n t o a b i n f e e d i n g a 1 meter w i d e , e l e v a t i n g b e l t c o n v e y o r  which d i s c h a r g e s onto a 1.5  m e t e r by 2.1 m e t e r v i b r a t i n g g r i z z l y .  The p l u s 15.2 c e n t i m e t e r  96  o v e r - s i z e m a t e r i a l f a l l s t o the g r o u n d and the u n d e r s i z e  material  p a s s e s o v e r a 2.1 meter by 2.4 meter v i b r a t i n g g r i z z l y .  Again,  the o v e r s i z e m a t e r i a l d r o p s to the g r o u n d and the minus centimeter  6.4  u n d e r s i z e m a t e r i a l f a l l s i n t o the s t e e l - l i n e d r a i s e .  T h i s s c r e e n i n g system i s shown on F i g u r e 5-2. system, with supporting  The w e i g h t o f t h i s  s t r u c t u r e , i s approximately  The o v e r s i z e m a t e r i a l i s c r u s h e d  12.6  tonnes.  under the t r e a d s o f a t r a c k  d o z e r and dumped back i n t o the f e e d h o p p e r w i t h a f r o n t end loader.  M a t e r i a l w h i c h c a n n o t be c r u s h e d  to the s p o i l dump.  w i t h the d o z e r i s s e n t  One hour per s h i f t of l o a d e r and d o z e r  time  are r e q u i r e d f o r t h i s t a s k . The mine o p e r a t e s  i n t h r e e p i t s , and two s k i d mounted,  g r i z z l y s c a l p i n g u n i t s are 3.  Raise  required.  Passes  The 1 m e t e r d i a m e t e r ,  s t e e l l i n e d r a i s e s are i n c l i n e d a t 60  d e g r e e s to r e d u c e the c o s t o f d r i f t c o n s t r u c t i o n n e c e s s a r y connect  to each r a i s e .  to  The r a i s e s a r e d r i l l e d and reamed w i t h a  b o r i n g m a c h i n e f o r speed and c o s t e f f e c t i v e n e s s . The 19 m i l l i m e t e r t h i c k s t e e l l i n i n g w i l l not wear prematurely  d u r i n g the p r o j e c t l i f e as c o n c l u d e d  following published Karabelas  research.  (1978) t e s t e d the wear o f b r a s s i n s e r t s i n a  s t a i n l e s s s t e e l pipe through pumped. the s i z e  from the  He c o n c l u d e d  which a s a n d / w a t e r s l u r r y  was  t h a t the r a t e o f wear i s most a f f e c t e d by  and v e l o c i t y o f s e d i m e n t p a r t i c l e s and i s unchanged by  97  3.25  GRIZZLY Figure  M  SCREENING  5-2 The c o a l i s dumped from t h e t r u c k s i n t o a b i n f e e d i n g a 1 meter wide, e l e v a t i n g conveyor. The c o a l i s screened at 15.2 c e n t i m e t e r s and 6.4 c e n t i m e t e r s . The p l u s 6.4 c e n t i meter m a t e r i a l f a l l s t o t h e ground and t h e minus 6.4 c e n t i meter m a t e r i a l goes i n t o t h e r a i s e . The o v e r s i z e m a t e r i a l i s run over by a t r a c k d o z e r and f e d back i n t o t h e s c r e e n i n g p l a n t .  98  the v o l u m e t r i c c o n c e n t r a t i o n o f s o l i d s . proposed the f o l l o w i n g E = 6.1 d ' 2  1 5  From h i s e x p e r i m e n t s , he  relationship; V  3 , 2 7  where "E" i s t h e wear r a t e i n m i l l i m e t e r s p e r y e a r , "dm" i s t h e w e i g h t mean p a r t i c l e s i z e and "V" i s t h e a v e r a g e  particle  veloci ty. Shook e t a l (1981) s t u d i e d t h e wear r a t e s o f s t e e l , a c r y l i c , ABS p l a s t i c , PVC p l a s t i c and h i g h d e n s i t y p o l y e t h y l e n e p l a s t i c p i p e s t h r o u g h which t h e y pumped a sand w a t e r s l u r r y .  They  measured wear r a t e s i n each 50 m i l l i m e t e r d i a m e t e r p i p e o f each m a t e r i al f o r ; i)  f l u i d v e l o c i t i e s from 2.3 t o 4.2 m e t e r s p e r s e c o n d ,  ii)  v o l u m e t r i c s o l i d s c o n c e n t r a t i o n s o f .1 and .2 p e r c e n t , and  i i i ) w e i g h t e d a v e r a g e p a r t i c l e s i z e s from .155 t o .94 mi 1 1 i m e t e r s . U n l i k e K a r a b e l a s , t h e i r wear r a t e r e s u l t s d i d n o t show any dependence on p a r t i c l e v e l o c i t y p a r t i c l e s i z e and shape.  b u t were s t r o n g l y i n f l u e n c e d by  They p r o p o s e d an e q u a t i o n ; D  E =E o  o  2  D  where "E" i s t h e wear r a t e i n m i l l i m e t e r s p e r m i l l i o n t o n n e s o f s o l i d s , " E " i s t h e r e f e r e n c e wear r a t e which t h e y m e a s u r e d , 0  "D " 0  i s t h e r e f e r e n c e p i p e d i a m e t e r o f 50 m i l l i m e t e r s and " D "  is the pipe diameter of the proposed  system.  The maximum s p e c i f i c wear r a t e f o r a s t e e l p i p e t h e y measured was 40 m i l l i m e t e r s p e r m i l l i o n t o n n e s o f s o l i d s .  For a  99  1,000 m i l l i m e t e r d i a m e t e r p i p e t h e wear r a t e i s c a l c u l a t e d t o be .1 m i l l i m e t e r s  per m i l l i o n tonnes of s o l i d s .  At t h i s r a t e , the  19 m i l l i m e t e r t h i c k s t e e l l i n i n g s w i l l l a s t f o r 190 m i l l i o n tonnes of run-of-mine c o a l .  This i s conservative  b e c a u s e 70 p e r c e n t o f t h e m a t e r i a l  estimate  going through the r a i s e s i s  coal which, being s o f t e r than s t e e l , w i l l not erode the s t e e l lining. The t o p o f t h e c o a l i n t h e r a i s e s i s k e p t w i t h i n 15 m e t e r s of t h e s u r f a c e .  T h i s r e d u c e s p a r t i c l e d e g r a d a t i o n due t o c o a l  f a l l i n g i n the r a i s e . To l o w e r t h e r a i s e a t t h e c o m p l e t i o n o f each m i n i n g b e n c h , the g r i z z l y s c a l p i n g u n i t i s removed and t h e r o c k a r o u n d t h e s t e e l l i n i n g i s c a r e f u l l y dug o u t . When t h e s t e e l l i n i n g i s f u l l y e x p o s e d i t i s c u t o f f a t bench l e v e l .  The g r i z z l y s c a l p i n g  u n i t i s r e - i n s t a l l e d when a s u i t a b l e w o r k i n g a r e a around t h e r a i s e has been e s t a b l i s h e d .  This operation  takes 6 concurrent, 8  hour w o r k i n g s h i f t s t o c o m p l e t e . Prolonged periods  o f c o l d weather may f r e e z e t h e c o a l i n  t h o s e r a i s e s which a r e n o t c o n t i n u a l l y b e i n g u s e d .  To p r e v e n t  t h i s , t h e t o p o f t h e c o a l i s l o w e r e d 15 m e t e r s down t h e r a i s e , an i n s u l a t e d cap i s p l a c e d o v e r t h e r a i s e and warm a i r i s blown i n . I f t h e c o a l i n t h e r a i s e does f r e e z e i t i s a u g e r e d t o break up the f r o z e n c o a l and r e t u r n t h e r a i s e t o u s e f u l  service.  4 . Main H a u l a g e D r i f t The main h a u l a g e d r i f t i s t h e most i m p o r t a n t and c a p i t a l i n t e n s i v e element o f the run-of-mine coal t r a n s p o r t  system.  The  100  d e s i g n of the d r i f t i s c o n t i g e n t upon t h e g e o l o g i c a l , h y d r o l o g i c a l and g e o t e c h n i c a l p a r a m e t e r s  of the m i n e s i t e .  A c c u r a t e i n f o r m a t i o n on t h e s e p a r a m e t e r s  does n o t e x i s t f o r the  p u r p o s e of t h i s d e s i g n so rock mass c l a s s i f i c a t i o n s u s i n g t h e B i e n i a w s k i and N.G.I, systems were c o m p i l e d . T a b l e s 5-1 and 5-2  summarize t h e r e s u l t s o f the two  mass c l a s s i f i c a t i o n a s s e s s m e n t s .  rock  The rock q u a l i t y d e s i g n a t i o n  (R.Q.D.) was e s t i m a t e d by t h e mine g e o l o g i s t as 65 p e r c e n t . T h r e e o r t h o g o n a l j o i n t s e t s a r e assumed due t o t h e i r u b i q u i t o u s appearance  elsewhere  i n t h e mine.  The o r i e n t a t i o n of the  drift  w i t h r e s p e c t t o t h e s e j o i n t s e t s i s v e r y u n f a v o r a b l e but t h e j o i n t s a r e c h a r a c t e r i z e d as t i g h t .  The rock t h r o u g h which  d r i f t must pass i s h i g h l y s u s c e p t i b l e t o w e a t h e r i n g . mass systems  c l a s s i f y the rock as  Both  the rock  poor.  A p p l i c a t i o n o f the r o c k mass c l a s s i f i c a t i o n  recommendations  r e s u l t e d i n the f o l l o w i n g d r i f t s u p p o r t d e s i g n ; i)  The d r i f t i s s c a l e d t o remove l o o s e r o c k and  covered  w i t h 50 m i l l i m e t e r s o f s h o t c r e t e as soon as p o s s i b l e a f t e r i t has been opened up.  This minimizes  weathering  of the r o c k j o i n t s . ii)  Wire mesh i s t h e n b o l t e d o v e r two t h i r d s of the r o o f and w a l l s w i t h 3 meter l o n g m e c h a n i c a l l y f u l l y grouted, p r e - t e n s i o n e d rock b o l t s . b o l t s e v e r y two m e t e r s  along the  i i i ) Two d r a i n h o l e s , 4 m e t e r s meters  drift anchored,  There are 4  drift.  long are d r i l l e d every  two  a l o n g the d r i f t and an a d d i t i o n a l 50 m i l l i m e t e r s  101  ROCK CLASSIFICATION USING N.G.I. SYSTEM  Parameter  Description  RQD  65%  J o i n t Sets  3 Orthogonal Sets  Joint Roughness  Smooth, planar  Rating 65 (J^)  3  (JR)  1  J o i n t Alteration  unaltered j o i n t walls (JQ)  1  Water Inflow  medium inflow  0.6  Stress Reduction factor  clay free shear zones in completed rock  (J^)  3  Q = RQD_ x J ^ x Jy_ = 4.33 JN JA SRF Equivalent Dimension, D = Span where ESR =1.6 ESR = 1.9 TABLE 5-1 This analysis characterizes the rock as "poor". The close spacing of the j o i n t s and the weathering nature of the rock suggests a rock support system of rock bolts and shotcrete. e  102  ROCK CLASSIFICATION USING BIENIAWSKI SYSTEM  Parameter  Description  .Rock Strength  100 MPa  RQD  65%  J o i n t Spacing  25mm - 50mm  J o i n t Condition  smooth, no gauge, 21mm  Ground Water  moderate pressure  3  J o i n t Orientation  very unfavourable  -12  Total  Rating 8 15 4 20  38  TABLE 5-2 This analysis characterizes the rock as Class IV or poor. The suggested rock support system i s f u l l y grouted rock bolts, wire mesh and shotcrete.  103  of s h o t c r e t e a r e s p r a y e d o v e r t h e w i r e mesh. The use o f s t e e l s e t s was d i s c o u n t e d as b e i n g to t h e t y p e o f r o c k f a i l u r e t h a t i s l i k e l y t o o c c u r .  inappropriate Weathering  of the c l o s e l y spaced j o i n t s i s c o n s i d e r e d the g r e a t e s t p o t e n t i a l p r o b l e m and i s a d e q u a t e l y  d e a l t w i t h by t h e a p p l i c a t i o n o f s h o t -  crete. L a r g e , u n p r e d i c t e d i n f l o w s o f w a t e r would i n c r e a s e t h e c o s t of c o n s t r u c t i n g t h e d r i f t . adequately  The l a r g e number o f d r a i n h o l e s w i l l  handle water i n f l o w s subsequent to d r i f t c o n s t r u c t i o n .  The p o s s i b i l i t y o f w a t e r i n f l o w s d u r i n g c o n s t r u c t i o n i s h a n d l e d by v a r y i n g t h e u n i t c o n s t r u c t i o n c o s t when d e t e r m i n i n g t h e p r o j e c t economics.  A b e n e f i t o f t h e u n d e r g r o u n d d r i f t system i s  the good p o t e n t i a l f o r d r a i n i n g t h e p i t a r e a s p r i o r t o t h e commencement o f a c t i v e  mining.  The s h o r t e s t r o u t e f o r t h e main h a u l a g e  d r i f t i s t o go  s t r a i g h t to the center of the southernmost p i t s t a r t i n g a t the s i t e o f t h e p r o p o s e d  c o a l t r u c k dump as shown on F i g u r e 5-3.  A c r o s s - c u t i s d r i v e n p e r p e n d i c u l a r t o t h e main d r i f t t o i n t e r s e c t coal r a i s e s which connect  to the other p i t areas.  The  rock s u p p o r t s y s t e m f o r t h e s e c r o s s - c u t s i s i d e n t i c a l t o t h e s y s t e m f o r t h e main h a u l a g e haulage  drift.  Long s e c t i o n s o f t h e main  d r i f t and t h e c r o s s - c u t s a r e shown on F i g u r e s 5-4.  The c r o s s s e c t i o n a l d i m e n s i o n s  o f t h e d r i f t and c r o s s - c u t s  a r e t h e i n d u s t r y s t a n d a r d 3 m e t e r s by 3 m e t e r s . guarantees  This size  r e a d y a c c e s s t o t h e f l u m e and w a t e r l i n e s d u r i n g  s t r u c t i o n , o p e r a t i o n and m a i n t e n a n c e .  con-  A c r o s s s e c t i o n a l view o f  the d r i f t showing t h e r o c k s u p p o r t s y s t e m i s shown on F i g u r e 5-5.  104  PROPOSED ROUTE for MAIN DRIFT  0  gure 5-3  meters  5  0  0  The s h o r t e s t route f o r the main haulage d r i f t i s to go s t r a i g h t to the center of the southernmost p i t s t a r t i n g a t the s i t e o f the coal truck dump. A c r o s s c u t i s driven p e r p e n d i c u l a r to the main d r i f t to i n t e r s e c t the coal r a i s e from the other p i t area.  meters  1790 coal  500  -1800  1600  C R O S S CUT RAISE  SECTION A - A  LONG SECTIONS OF THE UNDERGROUND WORKINGS Figure 5-4  The structural geology of the Byron Creek coal deposit is characterized by intense faulting and folding. The main drift, and crosscut pass through a formation below the coal bearing zone and the raises intersect both faults and coal seams.  106  CROSS  F i g u r e 5-5  SECTION OF THE  DRIFT  The c r o s s s e c t i o n a l dimensions o f t h e main d r i f t and c r o s s c u t s a r e t h e i n d u s t r y standard 3 meters by 3 meters w i t h an arched back. S h o t c r e t e , 50 m i l l i m e t e r s t h i c k , i s a p p l i e d as soon a f t e r b l a s t i n g as p o s s i b l e . Wire mesh i s then b o l t e d o v e r t h e r o o f and w a l l w i t h 3 meter long m e c h a n i c a l l y anchored, f u l l y grouted, p r o t e n s i o n e d rock b o l t s . D r a i n h o l e s , 4 meters l o n g , a r e d r i l l e d and an a d d i t i o n a l 50 m i l l i m e t e r s o f s h o t c r e t e a r e sprayed over t h e mesh.  107  5.  S I u r r y i ng Chamber The c o a l i s drawn from each r a i s e by a v a r i a b l e s p e e d ,  1.5 meter wide by 4.5 meter l o n g pan f e e d e r .  This unit controls  t h e r a t e o f c o a l d e l i v e r y i n t o a 2 meter wide by 1 meter deep by 6 m e t e r l o n g s t e e l tank where i t i s mixed w i t h w a t e r . i l l u s t r a t e d i n F i g u r e 5-6.  This i s  The s l u r r y chamber d i r e c t s t h e c o a l  s l u r r y i n t o one o f two f l u m e s o r s p l i t s the f l o w i n t o b o t h o f t h e flumes.  T h i s d e s i g n o f f e r s good c o n t r o l o v e r t h e i n p u t r a t e o f  s o l i d s and t h e d e n s i t y o f t h e s l u r r y . The r o c k chamber i n w h i c h t h e s l u r r y i n g e q u i p m e n t i s i n s t a l l e d i s shaped and s i z e d r e c o g n i z i n g t h e r e q u i r e m e n t f o r l a r g e maintenance equipment.  R o u t i n e w e l d i n g on t h e s t e e l  tanks  i s t h e major m a i n t e n a n c e p r o b l e m and t h i s w i l l be done whenever a s l u r r y i n g tank i s n o t b e i n g u s e d . 6.  Flume  System  The f l u m e i s a .6 meter d i a m e t e r h i g h d e n s i t y , p o l y e t h y l e n e p i p e w i t h a w a l l t h i c k n e s s o f 18 m i l l i m e t e r s .  The  j o i n t s a r e b u t t f u s e d w i t h f l a n g e s used o n l y t o f a c i l i t a t e t u r n i n g t h e f l u m e t o d i s t r i b u t e t h e wear. Two f l u m e s e x t e n d i n g from each s l u r r y i n g chamber c o n n e c t to t h e t w i n f l u m e main l i n e s y s t e m and p r o v i d e i n t e r r u p t i o n f r e e service.  T h i s d o u b l e s t h e nominal s y s t e m c a p a c i t y and i f a flume  p l u g s or b r e a k s t h e o t h e r l i n e i s a v a i l a b l e t o p r o v i d e an u n i n t e r r u p t e d flow of coal to the washplant.  108  PAN  FLUME  FEEDER SLURRY CHAMBER  PLAN  VIEW  WATER LINE  SECTION  VIEW  SLURRYING F i g u r e 5-6  CHAMBER  The c o a l i s t r a n s f e r r e d from t h e r a i s e t o t h e s t e e l s l u r r y i n g tank w i t h a 1.5 meter wide by 4.5 meter l o n g , v a r i a b l e speed pan f e e d e r . Water i s added t o t h e c o a l i n t h e 2 meter wide by 1 meter deep by 6 meter long s l u r r y i n g tank and t h e s l u r r y i s d i r e c t e d i n t o one o f two flumes o r i s sent t o both o f t h e flumes.  109  The s i z e o f t h e f l u m e was d e t e r m i n e d by an i t e r a t i v e contained  routine  i n t h e p r o j e c t e v a l u a t i o n computer p r o g r a m .  T h i s r o u t i n e i s b a s e d on two p r e m i s e s ; i)  The f l u m e d i a m e t e r i s s c a l e d a c c o r d i n g t o t h e F r o u d e number as f o l l o w s ;  where "V" i s t h e f l o w v e l o c i t y , "g" i s t h e gravitational constant  and "D" i s t h e f l u m e d i a m e t e r .  The s u b s c r i p t s "1" and "2" r e f e r t o t h e model and o p e r a t i n g s y s t e m s r e s p e c t i v e l y and ii)  The T r a n s p o r t  Function discussed in Chapter III  p r e d i c t s the t r a n s p o r t of coarse run-of-mine coal i n a flume of c i r c u l a r c r o s s s e c t i o n a c c o r d i n g to the following relationship; j  _  .0017 Q S 5/3 l / 3 5/3  R  g  where "T" i s t h e v o l u m e t r i c t r a n s p o r t o f c o a r s e c o a l and "Q" i s the v o l u m e t r i c as p r e v i o u s l y  flow r a t e of the f l u i d .  The o t h e r v a r i a b l e s a r e  defined.  The c o m p u t e r program c a l c u l a t e s t h e amount o f r u n - o f - m i n e c o a l t h a t can be t r a n s p o r t e d by a f l u m e o f a g i v e n d i a m e t e r and s l o p e and compares t h i s t o t h e d e s i g n p r o d u c t i o n m i l l i o n tonnes of c l e a n coal per year. density polyethylene  r a t e o f 3.6  The c h o i c e o f h i g h  as t h e f l u m e m a t e r i a l i s c o s t e f f e c t i v e and  110  w i l l n o t r e s u l t i n p r e m a t u r e flume wear. U s i n g t h e wear r e l a t i o n s h i p f r o m Shook e t a l ( 1 9 8 1 ) , an estimate  o f p o t e n t i a l wear was made.  The maximum s p e c i f i c wear  r a t e ( D ) , measured i n a 50 m i l l i m e t e r d i a m e t e r h i g h  density  0  polyethylene solids.  f l u m e , was 10 m i l l i m e t e r s p e r m i l l i o n t o n n e s o f  A wear r a t e o f 1.08 m i l l i m e t e r s o f p i p e p e r m i l l i o n  t o n n e s o f s o l i d s was c a l c u l a t e d f o r a 152 m i l l i m e t e r d i a m e t e r pipe.  F o r a minimum a l l o w a b l e w a l l t h i c k n e s s o f 5 m i l l i m e t e r s ,  the 18 m i l l i m e t e r t h i c k f l u m e w a l l s w i l l t r a n s p o r t 12,000,000 tonnes of run-of-mine coal before r e q u i r i n g t u r n i n g .  A ten  s t a g e , 373 k i l o w a t t , c e n t r i f u g a l pump i s used t o p r o v i d e volume o f w a t e r r e q u i r e d t o move t h e d e s i g n p r o d u c t i o n coal.  the  r a t e of  The pump i s f e d from a 2200 c u b i c meter head tank  which s t o r e s a two hour s u p p l y o f w a t e r a t maximum production.  The pump i s b a c k e d up by a d u p l i c a t e u n i t and i s  p r o t e c t e d by a p r e s s u r e  r e l i e f v a l v e and an  c o n t r o l l e d r e c i r c u l a t i n g system.  Dewatering  automatically  The w a t e r i s pumped t o t h e  s l u r r y i n g chambers i n a 46 c e n t i m e t e r  7.  design  diameter steel l i n e .  Plant  The f l u m e d i s c h a r g e s  i n t o a 200 c u b i c m e t e r ,  agitated  d i s t r i b u t i o n tank which has a 10 m i n u t e s u r g e c a p a c i t y a t the design production  r a t e and a l s o a l l o w s s u f f i c i e n t f r e e b o a r d t o  hold the contents  o f t h e f l u m e s y s t e m i n the e v e n t o f a sudden  s h u t down.  Ill  The d i s c h a r g e from t h i s tank i s s p l i t a c r o s s t h r e e , 2 meter wide by 5 meter l o n g d o u b l e - d e c k , v i b r a t i n g s c r e e n s .  The t o p  deck s e p a r a t e s p l u s 50 m i l l i m e t e r c o a l and t h e bottom  deck  screens plus 6 m i l l i m e t e r coal. The s c r e e n o v e r s i z e c o a l i s t a k e n from t h e d e w a t e r i n g p l a n t t o a 30,000 tonne l i v e c a p a c i t y s t o c k p i l e . The u n d e r f l o w from t h e s c r e e n s i s s e n t t o a 150 c u b i c meter sump, pumped t o a d i s t r i b u t o r tank and d e l i v e r e d i n p a r a l l e l t o s i x , 1.5 meter l o n g by 1.5 meter wide d e w a t e r i n g s c r e e n s .  The  p l u s .595 m i l l i m e t e r s c r e e n o v e r s i z e p r o d u c t i s t r a n s f e r r e d t o a 1.5 meter l o n g by 1 meter wide d e w a t e r i n g s c r e e n and s e n t t o t h e open  stockpile. The f r e e d r a i n i n g c o a l s t o c k p i l e s t o r e s a two day s u p p l y o f  c o a l f o r t h e wash p l a n t .  The low r e s i d e n c e t i m e and a b s e n c e o f  c o a l f i n e s i n t h e s t o c k p i l e r e d u c e s t h e p o t e n t i a l o f p r o b l e m s due to o x i d a t i o n , c o m b u s t i o n , f r e e z i n g and d u s t l o s s . The u n d e r f l o w from t h e d e w a t e r i n g s c r e e n s i s s e n t t o a thickener.  The t h i c k e n e r u n d e r f l o w i s d e l i v e r e d t o t h e wash  p l a n t and t h e c l a r i f i e d d e c a n t w a t e r i s r e t u r n e d t o t h e f l u m e system head  tank.  The d e w a t e r i n g p l a n t i s d e s i g n e d t o i n t e r f a c e w i t h t h e c o a l p r e p a r a t i o n p l a n t p r o p o s e d by t h e m i n i n g company and i s shown s c h e m a t i c a l l y on F i g u r e 5-9.  Beginning with a volumetric s o l i d s  c o n c e n t r a t i o n o f 25 p e r c e n t i n t h e f l u m e d i s c h a r g e , t h e mass b a l a n c e o f t h e d e w a t e r i n g p l a n t i s shown on T a b l e 5-3.  60M  FLOW Figure 5-7  x IM  CONVEYOR  -»• TO PLANT  SHEET  The flume discharges i n t o a surge tank which d i r e c t s the s l u r r y across 3 double deck, v i b r a t i n g screens. The minus 6 m i l l i m e t e r screen undersize product i s sent to 6 dewatering screens. The plus 6 m i l l i m e t e r screen o v e r s i z e product i s sent to the open s t o c k p i l e . The dewatering screens separate the coal at .6 m i l l i m e t e r s . The plus .6 m i l l i m e t e r coal i s sent to another dewatering screen and then to the open s t o c k p i l e . The minus .6 m i l l i m e t e r coal i s sent to the preparation p l a n t thickener.  113  Mass Balance of the Dewatering Plant  1  2  3  4  5  6  7  Tonnes of Solids/hour 750  300  450  302  148  15  287  Tonnes of Water/hour 1997  ' 50  1947  190  1757  180  10  % Solids by Weight  27.3  85.7  19.2  61.4  7.8  7.7  96.6  Slurry s p e c i f i c gravity  1.1  1.40  1.07  1.24  1.03  1.03  1.48  Table 5-3  The run-of-mine coal i s transported through the flume (1) at a s l u r r y s p e c i f i c gravity of 1.1. The dewatered coal from the double deck screens (2) contains 15% moisture and i s sent to the stockpile. The undersize product from the screens (3) is 19 percent solids and i s sent to 6 dewatering screens. The screen overflow (4) i s sent to another dewatering screen. The underflow from the 6 dewatering screens (5) i s sent to the thickener at 8 percent s o l i d s . The oversize product from a l l the dewatering screens (7) is sent to the stockpile. The f i n a l dewatering screen underflow (6) is sent to'the plant thickener.  114  8.  A u x i l i a r y Manway The  a u x i l i a r y manway i s i n c o r p o r a t e d  into the  s o u t h e r n m o s t c o a l r a i s e w h i c h i s d e v e l o p e d as a 1.8 m e t e r , b o r e d raise.  A 1 m e t e r d i a m e t e r s t e e l t u b e , l y i n g on t h e f o o t w a l l o f  the r a i s e t r a n s f e r s  t h e r u n - o f - m i n e c o a l and a  protected  ladderway i s welded onto the o u t s i d e o f the s t e e l tube.  To  p r e v e n t w e a t h e r i n g o f t h e r o c k , t h e r a i s e i s c o a t e d w i t h 50 millimeters The  of  shotcrete.  a c c e s s i b i l i t y of the steel coal r a i s e  measurements o f s t e e l l i n e r wear t o be made. prediction  allows This permits the  and s c h e d u l i n g o f any r a i s e l i n i n g r e p l a c e m e n t s  may be r e q u i r e d  that  during the l i f e of the r a i s e s .  Other a l t e r n a t i v e  d e s i g n s f o r t h e a u x i l i a r y manway r a i s e  which a l l o w e d a c c e s s from o u t s i d e t h e a c t i v e m i n i n g a r e a s , were c o n s i d e r e d b u t d i s c o u n t e d due t o t h e i r r e l a t i v e l y h i g h e r c a p i t a l costs. 9.  V e n t i 1 a t i on Forced v e n t i l a t i o n i s provided to permit the operation  of a p p r o v e d d i e s e l m a i n t e n a n c e m a c h i n e s i n t h e u n d e r g r o u n d workings.  An a i r f l o w o f 250 c u b i c m e t e r s p e r m i n u t e , s u f f i c i e n t  to o p e r a t e a 57 k i l o w a t t d i a m e t e r , 18.7 k i l o w a t t  d i e s e l m a c h i n e , i s p r o v i d e d by a 1 meter e l e c t r i c f a n i n s t a l l e d a t t h e bottom o f  the a u x i l i a r y manway r a i s e .  The v e n t i l a t i n g a i r i s drawn i n  t h r o u g h t h e main h a u l a g e d r i f t o p e n i n g and i s e x h a u s t e d up t h e  115  r a i s e i n t o the open p i t . A c o w l i n g l o c a t e d a t t h e t o p o f t h e r a i s e p r e v e n t s t h e v e n t i l a t i o n e x h a u s t from c r e a t i n g a w a t e r v a p o u r and d u s t h a z a r d i n t h e p i t . A u x i l i a r y f a n s i n the main h a u l a g e d r i f t blow f r e s h a i r through v e n t i l a t i o n t u b i n g i n t o the c r o s s - c u t s . 10 .  I n s t r u m e n t a t i on A l l f u n c t i o n s of the flume t r a n s p o r t system are  m o n i t o r e d and d i r e c t e d from a c o n t r o l room i n t h e p r e p a r a t i o n plant.  The s l u r r y d e n s i t y i s r e g u l a t e d by a u t o m a t i c a l l y  c o n t r o l l i n g t h e w a t e r i n j e c t i o n r a t e and t h e s p e e d o f t h e pan feeder. P r e s s u r e s e n s i t i v e p r o b e s e v e r y 50 m e t e r s i n t h e f l u m e i s o l a t e t h e l o c a t i o n o f p l u g s or b r e a k s i n t h e l i n e .  If this  happens, t h e i n t e r l o c k e d f l u m e s y s t e m a u t o m a t i c a l l y s h u t s down and t h e o p e r a t o r i s a l e r t e d t o t h e l o c a t i o n and n a t u r e o f t h e problem.  With t h i s i n f o r m a t i o n , t h e s l u r r y f l o w i s t r a n s f e r r e d  to t h e o t h e r f l u m e and t h e s y s t e m i s r e s t a r t e d . S i g n a l i n t e r r u p t i o n d e v i c e s i n t h e t o p 15 m e t e r s o f t h e s t e e l r a i s e s send an e l e c t r i c a l s i g n a l t o the c o n t r o l room o f t h e p r e p a r a t i o n p l a n t to i n d i c a t e the coal l e v e l .  I f the l e v e l  drops  below 15 m e t e r s , the pan f e e d e r i s t u r n e d o f f and, a f t e r a d e l a y to c l e a r the flume the water i n j e c t i o n v a l v e i s t u r n e d o f f .  With  the w a t e r l i n e c l o s e d , t h e pump r e c i r c u l a t e s w a t e r back i n t o t h e head t a n k .  116  11.  Service  Facilities  Underground l i g h t i n g ,  c o m m u n i c a t i o n and  power s u p p l y a r e i n c l u d e d as s e r v i c e  facilities.  electrical  117  CHAPTER VI ESTIMATED CAPITAL AND OPERATING COSTS FOR THE RUN-OF-MINE FLUME TRANSPORT SYSTEM A.  Introduction T h i s c h a p t e r p r e s e n t s t h e e s t i m a t e d c a p i t a l and o p e r a t i n g  c o s t s f o r the flume t r a n s p o r t system.  The c o s t s a r e e s t i m a t e d i n  d i f f e r e n t ways: i)  from e q u i p m e n t s u p p l i e r q u o t a t i o n s ,  ii)  from i n d u s t r y e x p e r i e n c e w i t h t h e same e q u i p m e n t and activities,  i i i ) from summing t h e c o s t s o f i n d i v i d u a l components, and iv)  from a p p l y i n g u n i t c o s t s t o c a l c u l a t e d p r o d u c t i v i t i e s .  The computer program w r i t t e n t o e v a l u a t e t h e p r o j e c t i s based on a Monte C a r l o s i m u l a t i o n o f t h e s t a t i s t i c a l in t h e e s t i m a t e d c o s t s .  A gamma f u n c t i o n f r e q u e n c y  economics  variation  distribution,  w i t h a "k" v a l u e o f 2 and a "p" v a l u e o f .6 i s used t o model d e v i a t i o n s i n t h e c a p i t a l and o p e r a t i n g c o s t s .  T h i s skewed  d i s t r i b u t i o n p r e d i c t s v a l u e s h i g h e r than t h e mean more f r e q u e n t l y than v a l u e s lower than t h e mean and i s shown on F i g u r e 6-1. The gamma d i s t r i b u t i o n r e l a t i o n s h i p i s : f(X)  = 2.78 X e-*/.6  where "2.78" i s a c o n s t a n t d e t e r m i n e d  by t h e v a l u e s o f "p" and  "k" and "X" i s t h e d e p e n d e n t v a r i a b l e . The computer program t a k e s u s e r d e f i n e d maximum d e v i a t i o n s from t h e mean v a l u e s t o p r e d i c t v a l u e s f o r each v a r i a b l e .  118  GAMMA FUNCTION FREQUENCY DISTRIBUTION K=  Figure 6-1  2  The gamma f u n c t i o n frequency d i s t r i b u t i o n i s used to model d e v i a t i o n s i n the c a p i t a l and o p e r a t i n g c o s t s . T h i s skewed d i s t r i b u t i o n p r e d i c t s values higher than the mean more f r e q u e n t l y than values lower than the mean. The gamma f u n c t i o n d i s t r i b u t i o n used i n t h i s research i s : f ( x ) = 2.78Xe " * and i s shown by the curve p = .6 x/  6  119  The t o t a l c a p i t a l c o s t f o r the f l u m e t r a n s p o r t a t i o n s y s t e m , in mid 1983  B.  C a n a d i a n d o l l a r s , i s $8,231,900.  C a p i t a l C o s t s f o r the Flume T r a n s p o r t 1.  Coal L o a d e r and  System  Truck  Unbroken c o a l at the work f a c e w i l l be dug by a 15  cubic  meter h y d r a u l i c s h o v e l c o s t i n g $2,931,000 w i t h d e v i a t i o n s of p l u s and minus 10 p e r c e n t . mechanically  The c a p i t a l c o s t f o r a 77 tonne c a p a c i t y ,  d r i v e n r e a r dump t r u c k w i l l be $700,000 w i t h  the  same d e v i a t i o n s . The a n n u a l c o a l t r u c k and  loader requirements  are c a l c u l a t e d  by d i v i d i n g the t o t a l r e q u i r e d o p e r a t i n g hours f o r each t y p e  of  equipment by the a v a i l a b l e o p e r a t i n g hours per y e a r a c c o r d i n g  to  the f o l l o w i n g r e l a t i o n s h i p : Number of U n i t s =  U n i t o p e r a t i n g hours r e q u i r e d Days Hours .., . ., . Year "Day— utilization x  x  e f f e c t 1 v e  If the c a l c u l a t e d f r a c t i o n a l number of u n i t s i s g r e a t e r .2, the number of u n i t s i s i n c r e a s e d t o the next h i g h e r O t h e r w i s e , the f r a c t i o n a l p o r t i o n i s o m i t t e d . made o n l y when the r e q u i r e m e n t s e x i s t i n g supply.  New  than  integer.  p u r c h a s e s are  f o r an equipment type e x c e e d  the  The e c o n o m i c l i f e of the c o a l l o a d e r s i s 10  y e a r s and the e c o n o m i c l i f e of the c o a l t r u c k i s 7 y e a r s . 2.  R u n - o f - M i n e Coal O v e r s i z e  Scalping  The o v e r s i z e s c a l p i n g u n i t s w i l l c o n s i s t of a t r u c k dump b i n , a 15 d e g r e e e l e v a t i n g c o n v e y o r and a s e t of two v i b r a t i n g grizzlies.  The c o s t of the b i n and e l e v a t i n g c o n v e y o r w i l l  be  120  $200,000 and the c o s t of the s c a l p i n g s c r e e n s  and  supporting  s t r u c t u r e w i l l be $80,000, making a t o t a l g r i z z l y s c a l p i n g u n i t c a p i t a l c o s t of $280,000 w i t h d e v i a t i o n s of p l u s 50 p e r c e n t minus 30  and  percent.  3.  Raise  Passes  The a v e r a g e r a i s e b o r i n g c o s t w i l l be $520 per meter based on a c o s t of $440 per meter f o r a 1 meter d i a m e t e r r a i s e and $574 per meter f o r a 1.5 meter d i a m e t e r r a i s e . The c o s t of i n s t a l l i n g the s t e e l r a i s e l i n i n g w i l l be $480 per meter based on a s t e e l p r i c e of $700 per s h o r t t o n . requirement  i s based on the lb/meter  where "D"  formula: = 3.28  (D-T)  10.68T  i s the r a i s e l i n i n g o u t s i d e d i a m e t e r i n i n c h e s and  i s the w a l l t h i c k n e s s The  The s t e e l  "T"  in inches.  l a b o u r c o s t t o i n s t a l l the s t e e l l i n i n g w i l l be $7,400,  based on a p r o d u c t i v i t y of 12 m e t e r s of r a i s e l i n i n g per hour f o r 3 men,  a welding  machine and a c r a n e at a u n i t c o s t of $150  per  hour. Therefore,  the t o t a l c o s t of the r a i s e c o n s t r u c t i o n w i l l  $1,000 per meter w i t h d e v i a t i o n s of p l u s 15 p e r c e n t  be  and minus 10  percent. 4.  Main H a u l a g e D r i f t The c o s t of e x c a v a t i n g  and s u p p o r t i n g  the main h a u l a g e  d r i f t , based on the c o n t r a c t p r i c e s of two r e c e n t excavation  underground  p r o j e c t s , w i l l be $2,250 per meter w i t h d e v i a t i o n s of  p l u s 50 p e r c e n t  and minus 10  percent.  121  5.  S l u r r y i n g Chamber The s l u r r y i n g chamber, c o n s i s t i n g of a 1.5 meter wide  v a r i a b l e speed pan f e e d e r and a 1 meter wide by 6 meter l o n g s t e e l t a n k , w i l l c o s t $65,000 w i t h d e v i a t i o n s of p l u s 50 p e r c e n t minus 30 6.  percent. Flume System The h i g h d e n s i t y p o l y e t h y l e n e  representative confirms, flume c o s t w i l l be $120  pipe manufacturer's  from h i s e x p e r i e n c e , per m e t e r .  t h a t the i n s t a l l e d  The two 1 0 - s t a g e c e n t r i f u g a l  pumps w i l l c o s t $75,000 each and the i n s t a l l e d c o s t of the centimeter  and  d i a m e t e r water l i n e w i l l be $166  per m e t e r .  46  Therefore,  the t o t a l f l u m e s y s t e m c o s t w i l l be $150,000 p l u s $286 per meter of water l i n e with, d e v i a t i o n s of p l u s 15 p e r c e n t  and minus 10  percent. 7.  Dewatering Plant The c a p i t a l c o s t of the d e w a t e r i n g  plant will  $2,135,000 based on the i n d i v i d u a l c o s t s of e q u i p m e n t in the p l a n t .  The c a p i t a l c o s t e s t i m a t i n g t e c h n i q u e  M u l a r (1982) was  used t o c a l c u l a t e t h e s e c o s t s .  from t h i s c a p i t a l c o s t w i l l be p l u s 30 p e r c e n t  The  be contained  proposed  by  deviations  and minus 20  percent. 8.  V e n t i l a t i o n , Instrumentation  and Flume S e r v i c e s  The v e n t i l a t i o n f a n , vent t u b i n g and v e n t i l a t i o n s e a l s w i l l c o s t $20,000.  The  instrumentation  f o r the f l u m e s y s t e m w i l l  c o s t $50,000 and the c o s t of f l u m e s e r v i c e s , i n c l u d i n g u n d e r g r o u n d l i g h t i n g , c o m m u n i c a t i o n s and power w i l l be $30,000.  Therefore,  122  the t o t a l c a p i t a l c o s t f o r t h e s e items w i l l be $100,000 w i t h d e v i a t i o n s of p l u s 30 p e r c e n t 9.  Site  and minus 20  percent.  Investigation  The c o s t of o b t a i n i n g g e o l o g i c a l and  geotechnical  i n f o r m a t i o n on the rock mass t r a v e r s e d by the d r i f t and r a i s e s w i l l be $500,000 based on the c o s t of o b t a i n i n g 3,300 m e t e r s of diamond d r i l l c o r e from s u r f a c e and d r i f t f a c e d r i l l i n g .  The  d e v i a t i o n s from t h i s c a p i t a l c o s t w i l l be p l u s 30 p e r c e n t  and  minus 20  percent.  10.  Engineering The e n g i n e e r i n g  be 5 p e r c e n t  c o s t f o r the f l u m e s y s t e m d e s i g n  of the t o t a l d e s i g n c a p i t a l c o s t .  will  The v a r i a t i o n  in  t h i s v a l u e w i l l be d e t e r m i n e d by the r a n g e of v a l u e s f o r each individual  C.  capital cost  Operating  item.  C o s t s f o r the Flume T r a n s p o r t  System  The o p e r a t i n g c o s t mean and d e v i a t i o n v a l u e s f o r the f l u m e t r a n s p o r t system are shown on T a b l e  6-1.  An o p e r a t i n g hour i s d e f i n e d as the t o t a l a c t u a l time i n a g i v e n t i m e i n t e r v a l . of 8 h o u r s ,  operating  F o r example, i n a t i m e  interval  the a c t u a l o p e r a t i n g t i m e i s c a l c u l a t e d as f o l l o w s :  time i n t e r v a l  i s 8 hours  = 480  minutes  l e s s l u n c h , c o f f e e b r e a k s and s h i f t change  -  72  minutes  l e s s o p e r a t i o n a l e f f i c i e n c y (.83)  -  69  minutes  less mechanical  -  51  minutes  = 288  minutes  breakdown (.85)  T o t a l o p e r a t i n g time  123  Cost and Production Parameters f o r Calculating the Flume System Economics  Item  Average Cost  Coal Loader Coal Truck G r i z z l y Scalping Unit Dewatering Plant Flume System Services  Table 6-1  $210 per hour $101 per hour $55,000 per year $0.35 per clean tonne $55,000 per year  Deviations (X) Plus Minus .15 .15 .50 .20 .50  .10 .10 .35 .15 .35  The flume run-of-mine coal transport system requires manpower for the coal loader and trucks only.  124  Therefore,  i n one 8 hour s h i f t , the number of o p e r a t i n g h o u r s i s  4.8. U s i n g t h i s d e f i n i t i o n , the t o t a l annual  operating cost for a  p i e c e of e q u i p m e n t i s the c o s t per o p e r a t i n g hour t i m e s the  annual  o p e r a t i n g hours r e q u i r e d : 1 op.hr. 1.  op.hr. year  _  $ year  Coal Loader The computer program c a l c u l a t e s the h o u r s r e q u i r e d by  the c o a l l o a d e r by d i v i d i n g the annual  raw c o a l p r o d u c t i o n  per y e a r ) by the c o a l l o a d e r p r o d u c t i v i t y ( t o n n e s hour).  U s i n g the m a n u f a c t u r e r s '  per  operating  swing c y c l e i n f o r m a t i o n ,  p r o d u c t i v i t y f o r the c o a l l o a d e r w i l l be 1,000  Coal  operating  percent.  The o p e r a t i n g c o s t f o r the c o a l l o a d e r w i l l be $210 2.  the  t o n n e s per  hour w i t h d e v i a t i o n s of p l u s 25 p e r c e n t and minus 10 w i t h d e v i a t i o n s of p l u s 15 p e r c e n t and minus 10  (tonnes  per hour  percent.  Trucks  The c o a l t r u c k p r o d u c t i v i t y i s d e p e n d e n t upon the and n a t u r e of the h a u l a g e which r a i s e i s b e i n g u s e d . w i l l be f i x e d t h r o u g h  route.  length  T h i s changes d e p e n d i n g upon  The a v e r a g e d i s t a n c e t o each r a i s e  time and the h a u l a g e  r o u t e w i l l be f l a t .  The f o l l o w i n g r e l a t i o n s h i p i s used to c a l c u l a t e c o a l t r u c k product i v i ty: Truck C a p a c i t y Productivity = o C D i s t a n c e to r a i s e i ) f i x e d time (Average T r u c k Speed) where the " f i x e d t i m e " w i l l be 3.5 m i n u t e s and i s the time +  l o a d and dump a t r u c k .  to  The t r u c k c a p a c i t y w i l l be 54 t o n n e s  i t w i l l t r a v e l at an a v e r a g e speed  of 28.8  and  k i l o m e t e r s per h o u r .  125  The o p e r a t i n g h o u r s r e q u i r e d f o r the t r u c k s i s c a l c u l a t e d  by.  d i v i d i n g the t o t a l t o n n e s g o i n g t o a r a i s e by the p r o d u c t i v i t y of the t r u c k s dumping i n t o t h a t r a i s e . The c o s t per o p e r a t i n g hour f o r the t r u c k s w i l l be $101 d e v i a t i o n s of p l u s 15 p e r c e n t 3.  and minus 10  R u n - o f - M i n e Coal O v e r s i z e  with  percent.  Scalping  The o v e r s i z e c o a l s c a l p i n g u n i t w i l l r e q u i r e 1 hour per s h i f t of r u b b e r - t i r e d l o a d e r and d o z e r t i m e to c l e a r away o v e r sized material.  The o p e r a t i n g c o s t s f o r t h e s e p i e c e s of e q u i p m e n t ,  based on i n d u s t r y e x p e r i e n c e ,  w i l l be $152  and $139  r e s p e c t i v e l y w i t h d e v i a t i o n s of p l u s 15 p e r c e n t  per hour  and minus 10  percent. 4.  Flume System The o p e r a t i n g c o s t f o r the f l u m e s y s t e m w i l l be based  on r e p a i r c o s t s f o r the s l u r r y i n g chambers and pumping c o s t s f o r the c l e a n w a t e r . The s l u r r y i n g chambers w i l l r e q u i r e p e r i o d i c w e l d i n g a r e a s of h i g h wear at the r a t e of 4 hours of w e l d i n g  to  for  100,000 t o n n e s of r u n - o f - m i n e c o a l which p a s s e s t h r o u g h  every the s y s t e m .  The power c o s t f o r the pump i s d e t e r m i n e d by a p p l y i n g power c o s t p r o f i l e f o r the mine t o the k i l o w a t t power  patch  the  requirements  a c c o r d i n g t o the f o l l o w i n g r e l a t i o n s h i p : KW = '9.8(1-Cv) QH where "KW"  i s the t o t a l power r e q u i r e m e n t  the v o l u m e t r i c  solids concentration  i n k i l o w a t t s , "Cv"  i n the s l u r r y , "Q"  is  i s the  v o l u m e t r i c f l o w r a t e of the s l u r r y i n c u b i c m e t e r s per s e c o n d , /  126  and "H"  i s the t o t a l s t a t i c head i n m e t e r s .  is a conversion 5.  f a c t o r to o b t a i n  The c o e f f i c i e n t  kilowatts.  Dewatering Plant The o p e r a t i n g c o s t of the d e w a t e r i n g  industry experience  p l a n t , based on  w i t h p l a n t s of s i m i l a r f l o w s h e e t s ,  will  $0.35 per tonne of c l e a n c o a l w i t h d e v i a t i o n s of p l u s 20 and minus 15  be  percent  percent.  The d e w a t e r i n g  plant, situated adjacent  p r e p a r a t i o n p l a n t w i l l be o p e r a t e d and e x t r a manpower i s not 6.  9.8  to the c o a l  by the wash p l a n t  operators  required.  Flume S e r v i c e s The o p e r a t i n g c o s t f o r the f l u m e s e r v i c e s w i l l be $55,000  per y e a r and w i l l be f o r m a i n t a i n i n g  the v e n t i l a t i o n ,  communication  and power d i s t r i b u t i o n s y s t e m s and c l e a n i n g up s p i l l s from the s l u r r y system.  The d e v i a t i o n s f o r t h i s o p e r a t i n g c o s t w i l l  p l u s 50 p e r c e n t  and minus 35  percent.  be  127  CHAPTER V I I OTHER ESTIMATED DIRECT MINE OPERATING AND CAPITAL COSTS A.  Introduction This chapter  discusses the estimated  c a p i t a l and o p e r a t i n g  costs f o r : i)  mining  f u n c t i o n s o t h e r than d i g g i n g and t r a n s p o r t i n g  the r u n - o f - m i n e c o a l , ii)  p r e p a r a t i o n p l a n t c o s t s o t h e r than d e w a t e r i n g  the run-  of-mine c o a l , i i i ) head o f f i c e e x p e n s e s , iv)  o f f - s i t e coal transportation,  v)  c l e a n c o a l i n v e n t o r i e s a t t h e deep water p o r t ,  vi)  c a p i t a l i z e d i n t e r e s t payments, and  v i i ) n o n - c a p i t a l i z e d i n t e r e s t payments. These c o s t s a r e i n d e p e n d e n t o f t h e t y p e o f t r a n s p o r t s y s t e m f o r r u n - o f - m i n e c o a l and a r e t h e same f o r e v e r y c o a l system being  transport  evaluated.  The c a p i t a l and o p e r a t i n g c o s t s o f r u n - o f - m i n e c o a l are a s m a l l p e r c e n t a g e costs.  transport  o f t h e t o t a l mine c a p i t a l and o p e r a t i n g  The f i n a n c i n g method w i l l n o t be i n f l u e n c e d by t h e c h o i c e  of t h e c o a l t r a n s p o r t s y s t e m so t h e i n t e r e s t payments w i l l n o t change.  As w e l l , t h e waste s t r i p p i n g and p r e p a r a t i o n  requirements system.  a r e n o t a f f e c t e d by t h e c h o i c e o f c o a l  A possible exception  truck requirements  plant transport  t o t h i s i s t h e c a l c u l a t i o n o f waste  f o r an e x p a n d i n g mine.  The c o a l t r u c k s  idled  by a s w i t c h t o a f l u m e t r a n s p o r t s y s t e m w i l l be i n c l u d e d i n t h e  128  waste haul t r u c k f l e e t to r e d u c e s u b s e q u e n t t r u c k and,  hence, c a p i t a l  B.  C a p i t a l and O p e r a t i n g  requirements  costs.  Costs  The v a l u e s f o r the c a p i t a l and o p e r a t i n g c o s t s  represent  a v e r a g e s f o r a t y p i c a l C a n a d i a n open p i t c o a l mine.  They are  s p e c i f i c t o one mine but are t a k e n from the o p e r a t i n g of t h r e e w e s t e r n C a n a d i a n c o a l m i n e s .  not  experience  A l l c o s t s are i n mid  1983  Canadian d o l l a r s . 1.  Other  Mining  Costs f o r other mining  f u n c t i o n s such as d r i l l i n g  b l a s t i n g , waste r e m o v a l , road m a i n t e n a n c e , mine d r a i n a g e p i l e c o n s t r u c t i o n are i n t h i s c o s t c e n t e r . administration costs for accounting,  s u p e r v i s i o n , t r a i n i n g , s a f e t y and f i r s t  and  Also included  personnel,  and spoil  are  engineering,  aid.  The c a p i t a l c o s t s model the r e p l a c e m e n t of m i n i n g  and  equipment o t h e r than r u n - o f - m i n e c o a l t r a n s p o r t e q u i p m e n t .  service The  annual c a p i t a l c o s t s w i l l r a n g e from $500,000 to $11,000,000 w i t h d e v i a t i o n s of p l u s and minus 25  percent.  The o p e r a t i n g c o s t s w i l l r e f l e c t the i n f l u e n c e of annual h a u l a g e p r o f i l e s and w i l l be f r o m $12.80 to $20.00 per tonne of c l e a n c o a l w i t h d e v i a t i o n s of p l u s and minus 15 2.  percent.  Other P l a n t C o s t s f o r c o a l c l e a n i n g , s t o c k p i l i n g and r a i l  are i n c l u d e d i n t h i s c o s t  center.  loadout  129  An expanded p r e p a r a t i o n p l a n t w i l l c o s t $45,000,000 over y e a r s w i t h an a d d i t i o n a l $500,000 b e i n g s p e n t e v e r y o t h e r year.  following  The d e v i a t i o n s f o r t h e s e c a p i t a l c o s t s w i l l be p l u s  minus 25  two  and  percent.  The o p e r a t i n g c o s t s f o r t h i s c o s t c e n t e r w i l l be f r o m $2.50 t o $4.00 per tonne of c l e a n c o a l w i t h d e v i a t i o n s of p l u s and minus 15  percent. 3.  Head O f f i c e Head o f f i c e e x p e n s e s i n c l u d e c o s t s f o r  engineering  support  marketing,  and e x e c u t i v e management and w i l l be  $1.00  per tonne of c l e a n c o a l w i t h d e v i a t i o n s of p l u s and minus 10 percent. 4.  O f f - s i t e Coal  Transportation  The c o s t of t r a n s p o r t i n g c l e a n c o a l f r o m the mine to the d e e p w a t e r ocean t e r m i n a l w i l l be $22.00 per t o n n e of c l e a n c o a l w i t h d e v i a t i o n s of p l u s and minus 15 5.  Port  percent.  Inventory  The v a l u e of c l e a n c o a l s t o r e d at the d e e p w a t e r ocean . t e r m i n a l and the c o s t s of m a i n t a i n i n g in t h i s i t e m .  t h i s i n v e n t o r y are  included  The e c o n o m i c a n a l y s i s assumed t h e s e c o s t s w i l l  be  zero. 6.  C a p i t a l i z e d and N o n - c a p i t a l i z e d  I n t e r e s t Payments  T h e s e c h a r g e s w i l l be a f u n c t i o n of the s t r u c t u r e o f the c o a l m i n i n g  financial  company and f o r the p u r p o s e s of t h i s  e c o n o m i c a n a l y s i s are assumed t o be  zero.  130  CHAPTER V I I I ESTIMATED CAPITAL AND FOR A.  THE  OPERATING COSTS  RUN-OF-MINE COAL TRUCK TRANSPORT SYSTEM  Introduction The t r u c k h a u l a g e and t r a n s p o r t s y s t e m i s c o m p r i s e d of  two  functions: i)  The 15 c u b i c meter c a p a c i t y h y d r a u l i c s h o v e l d i g s  the  e x p o s e d c o a l out of the ground and dumps i t i n t o t r u c k s , and ii)  the 108 t o n n e s i z e , e l e c t r i c a l l y d r i v e n r e a r dump t r u c k s t r a n s p o r t the c o a l from the a c t i v e m i n i n g  a r e a , down  the m o u n t a i n , to a t r u c k dump l o c a t e d near the c o a l preparation plant.  The empty t r u c k then r e t u r n s to the  coal loader f o r another This chapter  presents  load.  the e s t i m a t e d  costs f o r t h i s t r a n s p o r t system.  c a p i t a l and  operating  The c o s t s are e s t i m a t e d  i n the  f o l l o w i n g ways: i)  From e q u i p m e n t s u p p l i e r , q u o t a t i o n s , •  ii)  from i n d u s t r y experience  w i t h the same e q u i p m e n t ,  and  i i i ) from a p p l y i n g u n i t c o s t s to c a l c u l a t e d p r o d u c t i v i t i e s . The computer program w r i t t e n to e v a l u a t e the p r o j e c t e c o n o m i c s i s based on a Monte C a r l o s i m u l a t i o n of the s t a t i s t i c a l v a r i a t i o n i n c a p i t a l and o p e r a t i n g c o s t s .  A gamma f u n c t i o n  frequency  d i s t r i b u t i o n , w i t h a "k" v a l u e of 2 and a "p" v a l u e of .6, i s used to model the c o s t d e v i a t i o n s .  131  The gamma d i s t r i b u t i o n r e l a t i o n s h i p i s : f ( x ) = 2.78 x e-x/.6 where "2.78" i s a c o n s t a n t d e t e r m i n e d  by t h e v a l u e s o f "p" and  "k" and "x" i s t h e d e p e n d e n t v a r i a b l e .  T h i s i s shown g r a p h i c a l l y  on F i g u r e 6-1 on page 118.  B.  C a p i t a l Costs f o r the Truck T r a n s p o r t  System  The c a p i t a l c o s t mean and maximum d e v i a t i o n v a l u e s f o r t h e t r u c k t r a n s p o r t s y s t e m a r e shown on T a b l e 8-1.  A l l costs are i n  mid 1983 C a n a d i a n d o l l a r s . 1.  Coal L o a d e r Unbroken c o a l a t t h e w o r k i n g f a c e w i l l be dug by a 15  c u b i c meter c a p a c i t y h y d r a u l i c s h o v e l which w i l l c o s t $2,931,000 w i t h d e v i a t i o n s o f p l u s 15 p e r c e n t and minus 10 p e r c e n t . The number o f c o a l l o a d e r s r e q u i r e d i s c a l c u l a t e d from t h e following relationship: Number o f l o a d e r s  c o a l l o a d e r hours r e q u i r e d = days hours effective utilization year  *  oTy  x  where " e f f e c t i v e u t i l i z a t i o n " i s t h e number o f hours t h e l o a d e r does p r o d u c t i v e work d i v i d e d by t h e t o t a l hours, a v a i 1 a b l e i n t h a t time p e r i o d .  F o r example, i f a l o a d e r o n l y p r o d u c e s f o r 4.8 hours  in e v e r y 8 hour s h i f t , t h e e f f e c t i v e u t i l i z a t i o n w i l l be .6. The c o a l l o a d e r hours r e q u i r e d i s c a l c u l a t e d by d i v i d i n g t h e annual  p r o d u c t i o n by t h e p r o d u c t i v i t y o f t h e s h o v e l :  Coal loader hours r e q u i r e d  = AP nr no ud au lc t ip vr io td uy c t(itoonn n e s( t opnen re s )hour)  132  If t h e c a l c u l a t e d , f r a c t i o n a l number o f u n i t s i s g r e a t e r than 0.2, t h e number o f u n i t s i s r o u n d e d up t o t h e next integer.  Otherwise, the f r a c t i o n a l p o r t i o n i s omitted.  p u r c h a s e s a r e made o n l y when t h e r e q u i r e m e n t s exceeds the e x i s t i n g supply.  f o r coal  higher New loaders  The c o a l l o a d e r s w i l l have an  economic l i f e o f 10 y e a r s . 2.  Coal  Trucks  The c o a l t r u c k s w i l l be 108 tonne s i z e ,  electrically  d r i v e n , r e a r dump t r u c k s w i t h a c a p a c i t y o f 77 t o n n e s and a c o s t of $918,000 w i t h d e v i a t i o n s o f p l u s 15 p e r c e n t  and minus 10  percent. The number o f t r u c k s r e q u i r e d i s c a l c u l a t e d i n t h e same manner as t h e c o a l s h o v e l s .  The c a l c u l a t e d r e q u i r e m e n t s  a r e rounded up  or down d e p e n d i n g upon t h e s i z e o f t h e f r a c t i o n a l component. t r u c k p u r c h a s e s a r e made when t h e r e q u i r e m e n t s  New  exceed the a v a i l a b l e  s u p p l y and t h e e c o n o m i c l i f e o f t h e t r u c k s i s 7 y e a r s .  C.  Operating  Costs f o r the Truck Transport  System  The o p e r a t i n g c o s t v a l u e s and p r o d u c t i o n t r u c k t r a n s p o r t s y s t e m a r e shown on T a b l e 8-1. d e v i a t i o n s from these values are a l s o  parameters f o r the The maximum  listed.  The d e f i n i t i o n o f an o p e r a t i n g hour i s t h e t o t a l a v a i l a b l e time i n a d i s c r e t e p e r i o d l e s s t i m e l o s t due t o s h i f t change, lunch, c o f f e e breaks, mechanical  f a i l u r e s and t i m e l a g s i n  d i s p a t c h i n g new i n s t r u c t i o n s t o equipment  operators.  133  Cost and Production Parameters f o r Calculating the Truck System Economics  Item  Average Cost  Deviations Plus Minus  Coal Loader - capital - operating - productivity - utilization  $2,931,500 $210 per hour 1000 tonnes per hour .65  .15 .15 .10 .10  .10 .10 .25 .15  Coal Truck - capital - operating - capacity - utilization - up empty speed - down f u l l speed - f l a t haul speed - load and dump time  $918,000 $120 per hour 77 tonnes .50 12 k.p.h. 28.8 k.p.h. 25 k.p.h.  .15 .15 .20 .10 .20 .15 .15  .10 .10 .20 .15 .25 .20 .20  3.75 minutes  .15  .10  Table 8-1  The truck run-of-mine coal transport system uses rear dump trucks to haul coal from the mine to the preparation plant.  9  134  U s i n g t h i s d e f i n i t i o n , t h e t o t a l annual  operating cost f o r a  p i e c e , o r f l e e t , o f e q u i p m e n t i s t h e c o s t p e r hour t i m e s t h e annual hours r e q u i r e d : Cost Year 1.  _  Cost Op.hr.  op.hr. Year  Coal L o a d e r The o p e r a t i n g c o s t f o r t h e c o a l l o a d e r w i l l be $210 p e r  hour w i t h d e v i a t i o n s o f p l u s 15 p e r c e n t and minus 10 p e r c e n t . The o p e r a t i n g h o u r s r e q u i r e d by t h e c o a l l o a d e r a r e c a l c u l a t e d by d i v i d i n g t h e annual  raw c o a l p r o d u c t i o n  the c o a l l o a d e r p r o d u c t i v i t y ( t o n n e s the m a n u f a c t u r e r ' s  ( t o n n e s p e r y e a r ) by  per operating hour).  Using  swing c y c l e i n f o r m a t i o n , t h e p r o d u c t i v i t y o f  the c o a l l o a d e r w i l l be 1,000 t o n n e s p e r o p e r a t i n g hour w i t h d e v i a t i o n s o f p l u s 10 p e r c e n t and minus 15 p e r c e n t . 2.  Coal  Trucks  The c o a l t r u c k p r o d u c t i v i t y i s d e p e n d e n t upon t h e l e n g t h and n a t u r e o f t h e h a u l a g e  r o u t e which w i l l v a r y a c c o r d i n g t o which  p i t and which bench i s t h e s o u r c e o f t h e c o a l . The c o a l t r u c k p r o d u c t i v i t y i s c a l c u l a t e d f o r each bench i n each p i t f o r each y e a r a c c o r d i n g t o t h e f o l l o w i n g r e l a t i o n s h i p : Productivity  o(B D i s t ) (FTpdT  Truck C a p a c i t y D Dist (U D i s t ) , f i x e d  D Spd  (U  Spd)  where "B D i s t " i s t h e a v e r a g e f l a t d i s t a n c e on each b e n c h , "B Spd"  i s t h e a v e r a g e t r u c k speed on t h e bench, "D D i s t " i s t h e  d i s t a n c e from t h e edge o f t h e bench t o t h e t r u c k dump, "D Spd" i s the a v e r a g e t r u c k speed d o w n h i l l , "U D i s t " i s t h e d i s t a n c e  from  the t r u c k dump back t o t h e bench, "U Spd" i s t h e a v e r a g e t r u c k speed  u p h i l l and " f i x e d " i s t h e time i n hours t o l o a d and dump  135  the t r u c k s .  The d i s t a n c e s a r e i n k i l o m e t e r s and t h e a v e r a g e  are i n k i l o m e t e r s p e r h o u r .  speeds  The v a r i a b l e s "D D i s t " and "U D i s t "  are c a l c u l a t e d by d i v i d i n g t h e d i f f e r e n c e i n e l e v a t i o n  between  the bench and t h e t r u c k dump by 8 p e r c e n t . The mean and maximum d e v i a t i o n v a l u e s f o r t h e h a u l a g e s p e e d s , t r u c k c a p a c i t y and f i x e d t i m e a r e on T a b l e 8-1. The t o t a l o p e r a t i n g h o u r s r e q u i r e d f o r t h e t r u c k s a r e c a l c u l a t e d by d i v i d i n g t h e t o t a l t o n n e s o f c o a l p e r y e a r f r o m each bench by t h e bench p r o d u c t i v i t y f o r t h e t r u c k s and summing them up. The o p e r a t i n g c o s t f o r t h e t r u c k s w i l l be $120.00 p e r o p e r a t i n g hour w i t h d e v i a t i o n s o f p l u s 15 p e r c e n t and minus 10 percent.  136  CHAPTER IX ECONOMIC EVALUATION OF FLUME AND TRUCK TRANSPORT OF RUN-OF-MINE COAL A.  Introduction The computer program d e s c r i b e d  i n ' A p p e n d i x 1 was used t o  d e v e l o p annual c a s h f l o w s f o r : i)  Total revenue,  ii)  coal transport operating  i i i ) other operating  costs,  costs  iv)  f e d e r a l and p r o v i n c i a l t a x e s  v)  total capital costs.  Using present  the annual,  and r o y a l t i e s , and  a f t e r - t a x net cash flow, the p r o j e c t net  v a l u e and i n t e r n a l r a t e o f r e t u r n were c a l c u l a t e d .  two economic v a r i a b l e s a r e t h e b a s i s f o r t h e economic  These  evaluations  and c o m p a r i s o n s t o be' d i s c u s s e d . The computer program was a l s o used t o examine p r o j e c t  risk  by e v a l u a t i n g t h e s e n s i t i v i t y o f t h e economic v a r i a b l e s t o changes in i m p o r t a n t  cash flow v a r i a b l e s .  used t o s i m u l a t e  A Monte C a r l o a p p r o a c h was  r i s k by i t e r a t i v e l y and r a n d o m l y c h o o s i n g  c o s t and p r o d u c t i o n  v a r i a b l e s to c a l c u l a t e the p r o j e c t cash  input flows.  The p r o j e c t e c o n o m i c s were c a l c u l a t e d 150 t i m e s t o d e t e r m i n e a frequency  d i s t r i b u t i o n f o r t h e net present  v a l u e and i n t e r n a l  rate of r e t u r n . Five d i f f e r e n t production  r a t e and mine d e v e l o p m e n t c a s e s  were used t o d e v e l o p p r o j e c t e c o n o m i c s f o r mines u s i n g a f l u m e or truck run-of-mine coal t r a n s p o r t system.  The c a s e s examined were:  137  i)  e x p a n d i n g mine - f a s t  ii)  e x p a n d i n g mine - g r a d u a l  i i i ) new mine - f a s t  development development  development  iv)  new mine - g r a d u a l  development  v)  e x i s t i n g mine - t r u c k r e p l a c e m e n t .  A d i r e c t c o m p a r i s o n o f t h e f l u m e and t r u c k r u n - o f - m i n e  coal  t r a n s p o r t systems was made by s u b t r a c t i n g t h e a n n u a l n e t c a s h f l o w o f t h e t r u c k system from t h a t o f t h e f l u m e s y s t e m and c a l c u l a t i n g t h e n e t p r e s e n t v a l u e and i n t e r n a l r a t e o f r e t u r n f o r the cash f l o w d i f f e r e n c e s .  B.  Comparison 1.  o f P r o d u c t i o n and Mine D e v e l o p m e n t A l t e r n a t i v e s  Cases A n a l y z e d Economic  a n a l y s e s o f 10 p r o d u c t i o n and c o a l t r a n s p o r t  a l t e r n a t i v e s were c a r r i e d o u t . These were: i ) T r u c k t r a n s p o r t f o r a g r a d u a l mine e x p a n s i o n  1  t r a n s p o r t f o r a g r a d u a l mine e x p a n s i o n f ume i i i ) t r u c k t r a n s p o r t f o r a r a p i d mine e x p a n s i o n ii)  1  t r a n s p o r t f o r a r a p i d mine e x p a n s i o n f ume v) t r u c k t r a n s p o r t f o r a g r a d u a l l y d e v e l o p e d , new mine  i v)  1  t r a n s p o r t f o r a g r a d u a l l y d e v e l o p e d , new mine f ume v i i ) t r u c k t r a n s p o r t f o r a r a p i d l y d e v e l o p e d , new mine vi)  1  t r a n s p o r t f o r a r a p i d l y d e v e l o p e d , new mine f ume i x) r e p l a c i n g an e x i s t i ng c o a l t r u c k f l e e t w i t h t r u c k s  vi i i)  x) r e p l a c i n g an e x i s t i n g c o a l t r u c k f l e e t w i t h a f l u m e t r a n s p o r t a t ion system.  138  The g r a d u a l and r a p i d mine d e v e l o p m e n t c a s e s had d i f f e r e n t annual c o a l p r o d u c t i o n l e v e l s and c o r r e s p o n d i n g l y d i f f e r e n t c a p i t a l and o p e r a t i n g c o s t s .  annual  The g r a d u a l mine d e v e l o p m e n t c a s e  a c h i e v e d f u l l p r o d u c t i o n i n y e a r 8 o f t h e a n a l y s i s and t h e r a p i d mine d e v e l o p m e n t c a s e r e a c h e d f u l l p r o d u c t i o n i n y e a r 4 o f t h e a n a l y s i s. The new mine and e x p a n d i n g  mine c a s e s had d i f f e r e n t  annual  c a p i t a l c o s t s but t h e p r o d u c t i o n r a t e s were t h e same e x c e p t f o r y e a r 1 i n t h e new mine c a s e s i n which no c o a l was p r o d u c e d . coal truck replacement  The  c a s e s m o d e l l e d an o p e r a t i n g mine w i t h no  capital expenditures f o r a coal preparation plant. l e v e l expanded m o d e r a t e l y  The p r o d u c t i o n  o v e r t h e f i r s t 4 y e a r s of p r o d u c t i o n  a n a l y s i s. The annual cash f l o w s f o r t h e 10 c a s e s , c a l c u l a t e d a t t h e median i n p u t v a r i a b l e v a l u e s , a r e shown on T a b l e s 9-1 t o 9-10. 2.  A n a l y s i s of R e s u l t s A summary o f t h e n e t p r e s e n t v a l u e s and i n t e r n a l r a t e s  of r e t u r n f o r t h e 10 c a s e s i s shown on T a b l e 9-11. economics  The  comparative  f o r t r u c k and f l u m e c o a l t r a n s p o r t , f o r each o f t h e  mine d e v e l o p m e n t c a s e s , i s a l s o shown on T a b l e 9-11.  The  economics  were c a l c u l a t e d by s u b t r a c t i n g t h e t r u c k t r a n s p o r t n e t cash f l o w s from t h e f l u m e t r a n s p o r t n e t c a s h f l o w s f o r each y e a r o f t h e a n a l y s i s and f o r each mine d e v e l o p m e n t c a s e .  The n e t p r e s e n t  v a l u e s and i n t e r n a l r a t e s o f r e t u r n f o r t h e s e c a s h f l o w d i f f e r e n c e s were then c a l c u l a t e d . Some i n t e r e s t i n g o b s e r v a t i o n s a r e drawn from t h i s t a b l e :  139  EXPANDING MINE CASE MEAN VALUES ONLY  CASH FLOW SUMH AR' <.  all  amounts  ANNUAL PRODUCTION 1777000 GROSS REVENUE 77246190 COAL TRANSPORT COST 1755612 OTHER OP. COSTS 59170582 ROYALTY PAYMENT 1514025 FED. INCOME TAX 0 EC INCOME TAX 0 BC MINING TAX 0 TOTAL CAPITAL COST 31176978 NET CASH FLOW -16371007  FOR FLUME TRANSPORTATION i n c u r r e n t c an ad i a n * >  24700O0 107677674 2223842 85603751 2110482  V  35894711 -18155112  29050O0 129072348 2647765 104548602 2529818 0 0 0 10384504 8961659  2884O00 146229644 2807284 128019915 2993569 1057224 0 0 6679007. 4672645  2729900 151539617 2S0153O i16134452 3182332 4371612 2220173 274870O 8674926 11405893  CASH FLOW SUMMARY FOR FLUME TRANSPORTATION < all  amounts  in  current  Canadian  * >  10 ANNUAL PRODUCTION 3330000 GROSS REVENUE 188685762 COAL TRANSPORT COST 3464421 OTHER OP. COSTS 147346427 ROYALTY PAYMENT 3962401 FED. INCOME TAX 6235755 BC INCOME TAX 3135942 BC MINING TAX 3955911 TOTAL CAPITAL COST 11636263 NET CASH FLOW 8898642 DISCOUNT , RATE 15. 66  Table 9-1  4031000 247697628 4334276 177951191 5323326 11403685 6475589 7559605 14535317 20109640  NET PRESENT VALUE 22763883  VALUE  4644986 306475076 5210917 .218565120 . 6586526 19468865 16398159 9758822 14855463 22431263  4632000 327617595 5540571 234936325 7628810 20994834 11201218 16474625 6364 168 30537905  4588680 368284059 5915385 2464434 16 8163636 28571122 15537923 14533118 12368373 36701092  INTERNAL RATE OF RETURN OF RETURN 28.  T h i s i s the cash flow summary f o r the case o f a g r a d u a l l y expanding mine using a flume system to t r a n s p o r t run-of-mine c o a l . The annual p r o d u c t i o n i s i n u n i t s of tonnes of raw coal.  140 EXPANDING MINE CASE MEAN V A L U E S ONLY  CASH  F L O W SUMMARY  ( all  ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER O P . COSTS ROYALTY PAYMENT FED. INCOME TAX BC I N C O M E T A X BC M I N I N G T A X TOTAL C A P I T A L COST N E T C A S H FLOW  1777008 77246198 2307276 59178582 1514825 8 8 8 23865688 -9556687  CASH  FLOW  < all  FOR  amounts i n  TRUCK  current  2478068 187677674 2912435 86357495 2116482 8 8 8 39559853 -23262591  2905888 129072348 3709288 165452169 2529818 8 8 8 9167813 8273461  SUMMARY FOR T R U C K  amounts  T R A N S P O R T A T I ON  C a n a d i a n S- >  in c u r r e n t  2884888 146229644 3992116 128985582 2993569 6 8 6 8619533 2238844  2729960 151539617 3465847 117698795 3182332 4361795 1869585 1136434 12106518 9178312  TRANSPORTATION  Canadian * >  10  ANNUAL PRODUCTION GROSS REVENUE ' COAL TRANSPORT COST OTHER O P . COSTS ROYALTY PAYMENT FED. INCOME TAX BC I N C O M E T A X BC M I N I N G T A X TOTAL C A P I T A L COST N E T C A S H FLOW  DISCOUNT RATE  15. 8 6  Table 9-2  3338868 188685762 4572443 148547154 3962461 5548659 2781282 2955628 12562145 , 7757336  NET  4831666 247697628 6298337 179472141 5323326 16786852 5786619 6553763 16632388 223S8871  PRESENT VALUE  19784214  VALUE  4644986 366475876 7166254 220446984 6586526 17511725 9565721 8626239 15417824 21219753  4632860 327817595 7649862 236944328 7828018 19456947 16294 116 9679469 13195752 23969238  INTERNAL OF  R A T E OF RETURN  4588666 368284659 6055488 248591740 8163636 27354468 14797476 13344 139 15144912 34832388  RETURN  28. 1 6  This i s the cash flow summary f o r the case of a gradually expanding mine using a truck system to haul run-of-mine coal The annual production i s in units of tonnes of raw coal.  141  EXPAND ING MINE C A S E MEAN V A L U E S ONLY  CASH FLOW SUMMARY FOR FLUME C all amounts i n current  ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER OP. COSTS ROYALTY PAYMENT FED. INCOME TAX EC INCOME TAX BC MINING TAX TOTAL C A P I T A L COST NET CASH FLOW  1777000 77246190 1755612 59170582 1514625 - 0 0 6 31176978 -16371067  2470000 107677674 2228217 85663751 2118482 6 6 8 39559853 -21824629  TRANSPORTATION Canadian * ')  3336080 147955566 2983832 127093831 2899929 O 6 8 21353925 -6375951  CASH FLOW SUMMARY FOR FLUME < all amounts- i n c u r r e n t  4644966 235513895 4653655 181967812 4 321369 4688256 2695663 2592313 7459761 28436332  4644966 257343279 44 16766 190569623 5414769• 11168988 538019O 6698721 1 1 5 6 3 4 35 22756847  TRANSPORTATION Canadian $ >  16 ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER OP. COSTS ROYALTY PAYMENT FED. INCOME TAX EC INCOME TAX EC MINING TAX TOTAL C A P I T A L COST NET CASH FLOW  DISCOUNT RATE  15. 86  Table 9-3  4644966 263191139 4535849 195957767 5527614 11968332 6841191 7438825 5639823 25298338  NET  4644966 235426668 4862242 265652217 6134641 18916333 10169768 9567641 2166675 28678351  PRESENT VALUE  38659356  VALUE  4644966 366475676 5146266 218565126 6586526 26999494 11355498 16656327 2968165 36197746  4644966 327928331 5447118 235596617 7647583 21965363 11845699 11878826 7788828 27164298  INTERNAL OF  RATE OF RETURN 35.  4644966 372862734 5888677 249467163 8263794 28751138 15674323 14718992 22894867 27152379  RETURN  63  T h i s i s the cash flow summary f o r the case o f a r a p i d l y expanding mine using a flume system t o t r a n s p o r t run-of-mine c o a l . The annual p r o d u c t i o n i s i n u n i t s o f tonnes o f raw coal.  142  EXPANDING NINE C A S E MEAN V A L U E S ONLY  CASH  FLOW  < all  ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER OP. COSTS ROYALTY PAYMENT FED. INCOME TAX EC INCOME TAX BC MINING TAX TOTAL C A P I T A L COST NET CASH FLOW  SUMMARY  amounts  1777000 77246196 2307276 59176582 1514625 0 6 0 23287560 -9633187  CASH  (  FLOW  all  FOR  2470006 167677674 2912435 86357495 2116482 6 0 0 39559853 -23262591  SUMMARY  amounts  TRUCK  in current  FOR  in  TRANSPORTATION  Canadian * >  3330000 147955566 3869599 128129520. 2899929 . 6 6 6 25898276 • -12781753  4644966 235513895 4423867 183523092 4821369 3946876 2263694 2405175 7459701 26671127  4644966 257843279 3966942 .192216444 5414709 16732537 4461328 4930346 11503435 24683545  TRUCK . T R A N S P O R T A T I ON  current  Canadian * )  10 ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER OP. COSTS ROYALTY PAYMENT FED. INCOME TAX BC INCOME TAX BC MINING TAX TOTAL C A P I T A L COST NET CASH FLOW DISCOUNT RATE 15.  Table 9-4  68  4644966 263191139 4937154 197632619 5527814 11654328 6871546 6239645 11762363 26626539  NET  4644966 285426668 6478838 266884360 6134641 17668916 9374629 8217395 2188675 28761996  PRESENT VALUE  37438395  VALUE  4644966 366475876 7166254 220446984 6586526 19667569 16551956 9358197 2968185 29729489  4644966 327928331 7054 163 237684212 7847583 21684884 11313952 16635516 4184212 29663875  INTERNAL OF  RATE OF RETURN  4644960 372882734 6675676 251641846 8263794 28663172 15236269 13755457 24841366 24985221  RETURN  37.21  T h i s i s the cash flow summary f o r the case of a r a p i d l y expanding mine using a truck system to haul run-of-mine c o a l . The annual p r o d u c t i o n i s i n units of tonnes of raw coal.  143  HEW MINE C A S E MEflH V A L U E S ONL'i  CASH FLOW SUMMARY FOR FLUME ( a l l amounts i n c u r r e n t  ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER OP. COSTS ROYALTY PAYMENT FED. INCOME TAX BC INCOME TAX BC MINING TAX TOTAL C A P I T A L COST NET CASH FLOW  T R A N S P O R T A T I ON Canadian * )  1  2  3  4  5  6 0 0 0 0 0 0 0 47754573 -47754573  247060O 107677674 2223842 85603751 2110482 0 0 0 47239967 -295O0368  2905OOO 129072348 2647765 104548662 2529313 0 6 0 7831122 11515041  288406O 146229644 2307284 128019915 2993569 0 6 6 6679667 5729869  2729960 151539617 2801536 116134452 3182332 0 0 0 7266671 22160633  CASH (  FLOW SUMMARY FOR FLUME all amounts i n c u r r e n t  TRANSPORTATION Canadian * >  16 ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER OP. COSTS ROYALTY PAYMENT FED. INCOME TAX BC INCOME TAX BC MINING TAX TOTAL C A P I T A L COST NET CASH FLOW  DISCOUNT RATE 15.  Table 9-5  86  3336660 188685762 3464421 147346427 3962461 3249508 1858545 2296664 18137153 16378644  NET  4631086 247697628 4334276 177951191 5323326 11818956 5132138 6388656 9397134 27351958  PRESENT VALUE -316148  VALUE  4644966 386475676 5218917 218565128 6586526 14682865 7821837 9749779 19581937 24436895  4632686 327017595 5546571 234936325 7828010 19618367 16761197 18869922 15156853 24514351  INTERNAL OF  RATE OF RETURN  14.  4588660 368234659 5915385 246443416 8163630 28696951 15235745 14299825 12368373 37768735  RETURN  96  This i s the cash flow summary f o r the case of a gradually developed new mine using a flume system to transport run-ofmine coal. The annual production i s in units of tonnes of raw coal.  144  NEW MINE C A S E MEAN V A L U E S ONLY  CASH FLOW SUMMARY FOR TRUCK < all amounts i n cur-rent 1 ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER OP. COSTS ROYALTY PAYMENT FED. INCOME TAX EC INCOME TAX BC MINING TAX TOTAL C A P I T A L COST NET CASH FLOW  0 0 0 0 0 0 0 O 41783935 -41783985  CASH (  ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER OP. COSTS ROYALTY PAYMENT FED. INCOME TAX EC INCOME TAX BC MINING TAX TOTAL C A P I T A L COST NET CASH FLOW DISCOUNT RATE 1 5 . OO  Table 9-6  247O00O 107677674 2912435 86357495 2110482 0 0 0 48228102 -3193034O  TRANSPORTATION Canadian * )  3  4  29O5O00 129072348 37O9208 1054521O9 2529818 0 0 0 7831122 9550092  28840O0 146229644 3992116 128985582 2993569 0 8 0 6679007 3579370  FLOW SUMMARY FOR 'TRUCK a l l amounts in c u r r e n t  TRANSPORTATION Canadian * >  6  7  8  9  333O0O0 188685762 4572443 148547154 3962401 2579273 0 0 11349649 17674842  4031O0O 247697628 6298337 179472141 5323326 1O566702 5348565 5987703 10632380 24018474  4644900 306475O76 7166254 220446984 6586526 13539324 7135412 8283762 22873705 203931O9  46320OO 327017595 70498O2 2 3 6 9 4 4 328 702801O 16927928 9326879 8724730 14998O60 26017859  NET  PRESENT VALUE -2422530  VALUE  2729900 151539617 3465847 117098795 3182332 0 0 0 7260671 20531972  INTERNAL OF  10 458360O 368284059 6O55408 248591748 8163638 27888588 14627234 13057859 15144912 35554784  RATE OF RETURN RETURN 14.13  T h i s i s t h e cash f l o w summary f o r t h e case o f a g r a d u a l l y developed new mine u s i n g a t r u c k system t o haul run-of-mine c o a l . The annual p r o d u c t i o n i s i n u n i t s o f tonnes o f raw c o a l .  145  HEW HI HE CASE HEAH VALUES ONLY  CASH FLOW SUMMARY FOR FLUME .TRANSPORTATION < all  amounts  1 ANNUAL PRODUCTION  0 0 GROSS REVENUE 6 COAL TRANSPORT COST 0 OTHER OP. COSTS 0 ROYALTY PAYMENT 0 FED. INCOME TAX 0 BC INCOME TAX 0 BC MINING TAX 50445573 TOTAL CAPITAL COST -50445573 NET CASH FLOW  in c u r r e n t  Canadian  * >  2  3  4  5  2478000 187677674 2223217 85663751 21164 82 6 0 6 46163567 -28428343  3336606 147955566 2983832 127693831 2399929 0 0 0 26877233 -5899268  4644906 235513895 4853655 181967812 4821369 6 6 6 7459761 37211958  4644906 257S43279 44 16766 190569623 5414709 6796972 2694514 3341626 11583435 33111633  CASH FLOW SUMMARY FOR FLUME TRANSPORTATION < all  amounts  in current  Canadian  * >  10 ANNUAL PRODUCTION 4644900 GROSS REVENUE 263191139 COAL TRANSPORT COST 4535849 OTHER OP. COSTS 195957767 ROYALTY PAYMENT 5527814 FED. INCOME TAX 11273864 EC INCOME TAX 5988838 BC MINING TAX 7458531 TOTAL CAPITAL COST 5639823 NET CASH FLOW 26816253 DISCOUNT 'RATE 15. 86  T a b l e 9-7  4644906 285420668 4862242 205652217 6134041 14196742 8086598 9521435 2106675 35473318  NET PRESENT VALUE 18743361  VALUE  4644906 ' 306475676 5146266 218565120 6586526 26522468 ' 11365798 16665983 2968165 38654,824.  4644968 327928331 5447118 235598617 7647583 22259619 12625938 11247792 4184212 36125466  4644960 372802734 5888677 249467163 8263794 28777798 15767653 14741677 24841366 251 15812  INTERNAL RATE OF RETURN OF RETURN 26. 94  T h i s i s t h e cash flow summary f o r the case o f a r a p i d l y developed new mine u s i n g a flume system t o t r a n s p o r t run-ofmine c o a l . The annual p r o d u c t i o n i s i n u n i t s o f tonnes o f raw c o a l .  146  HEW MI HE C A S E MEAN V A L U E S ONLY  CASH FLOW SUMMARY FOR TRUCK < a l l amounts i n c u r r e n t  ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER O P . COSTS ROYALTY PAYMENT FED. INCOME TAX EC INCOME TAX EC MINING TAX TOTAL C A P I T A L COST NET CASH FLOW  TRANSPORTAT I OH Canadian * )  1  2  3  4  5  O 0 0 0 0 0 0 0 4 1 7 7 4 6 70 - 4 1 7 7 4 6 70  2470000 107677674 2912435 86357495 2110482 0 0 0 47151702 -30854440  3330000 147955566 3809599 128129520 2899929 0 0 0 21109835 -7993317  4644900 235513895 4428867 183523092 4321369 0 O O 8543932 34196635  4644900 257843279 3966942 192210444 5414709 6622741 2528503 2686534 12647299 31766108  CASH FLOW SUMMARY FOR TRUCK •< a l l a m o u n t s i n c u r r e n t  T R A N S P O R T A T I OH Canadian $ >  10 ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER O P . COSTS ROYALTY PAYMENT FED. INCOME TAX BC INCOME TAX BC MINING TAX TOTAL C A P I T A L COST NET CASH FLOW  DISCOUNT RATE  1 5 . 66  Table 9-8  4644900 263191139 4937154 197632619 5527614 16755872 5244783 5857875 5639823 27596078  NET  4644900 285428668 6478836 266864806 6134641 13448186 7375131 8291458 2166675 34796698  PRESENT VALUE 18523894  /ALUE  4644900 366475676 7166254 228446984 6586526 19816929 16505662 9188118 7655187 26569415  4644900 327928331 7 6 5 4 163 237664212 7647583 26916866 11211579 9812852 5641938 28645264  INTERNAL OF  4644986 372882734 6675676 251641846 8263794 27888364 15164548 13561591 2484 1366 25365556  RATE OF RETURN RETURN  21.31  T h i s i s t h e cash f l o w summary f o r t h e case o f a r a p i d l y developed new mine u s i n g a t r u c k system t o haul run-of-mine coal. The annual p r o d u c t i o n i s i n u n i t s o f tonnes o f raw c o a l .  147  TRUCK REPLRCEM'T CASE MEAN VALUES ONLY  CASH FLOW SUMMARY FOR (  all  amounts  ANNUAL PRODUCTION 2884800 GROSS REVENUE 126896678 COAL TRANSPORT COST 2928694 OTHER OP. COSTS 113632215 ROYALTY PAYMENT 2369445 FED. INCOME TAX 353586 BC INCOME TAX 8 BC MINING TAX 6 TOTAL CAPITAL COST 14777463 NET CASH FLOW -12576668  in  FLUME TRANSPORTATION  current  2729988 119667867 2424497 188323581 2332553 2937252 1693413 1723799 7493897 28815  Canadian * >  3338808 146882711 2954987 125485849 2863221 3168238 1586335 1515282 9989823 -1332224  4831668 194293679 3661189 156119361 3977522 8384418 4733234 4437487 12261972 6218584  4644966 248293528 4491396 184865817 5214164 13513858 . 7217167 6797214 11361238 14392687  CASH FLOW SUMMARY FOR FLUME TRANSPORTATION < all  amounts  in  current  Canadian  t >  16 ANNUAL PRODUCTION 4632886 GROSS REVENUE 262466195 COAL TRANSPORT COST 4613862 OTHER OP. COSTS 195413545 ROYALTY PAYMENT 5511664 FED. INCOME TAX 14872647 BC INCOME TAX 7914659 BC MINING TAX 7419431 TOTAL CAPITAL COST 5243583 NET CASH FLOW 21472683 DISCOUNT RATE 15. 66  Table 9-9  4588688 285622968 4834828 261188316 6138383 19238398 18396465 9781653 16697159 23955267  NET PRESENT VALUE 43699653  VALUE  4649486 366771996 5131125 218776867 6592987 28186221 16849127 18171856 8963679 26187816  4627168 326671657 5464 125 232968471 7826575 21841816 11765729 11676629 4978181 31562731  4519666 362746674 5733481 245766465 8648871 27734839 15084329 14141559 12364919 33895696  INTERNAL RATE OF RETURN OF RETURN 50. Ii  T h i s i s the cash flow summary f o r the case o f an o p e r a t i n g mine r e p l a c i n g i t s coal t r u c k s with a flume system to t r a n s p o r t run-of-mine c o a l . The annual p r o d u c t i o n i s i n u n i t s o f tonnes o f raw c o a l .  148  TRUCK R E P L A C E M ' T CASE MEAN V A L U E S ONLY  CASH FLOW SUMMARY FOR TRUCK < a l l amounts i n c u r r e n t  ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER OP. COSTS ROYALTY PAYMENT F E D . INCOME TAX EC INCOME TAX BC MINING TAX TOTAL C A P I T A L COST NET CASH FLOW  2884900 126896676 3498358 113032215 2369445 545786 6 6 7627656 -5583385  2729906 119667807 2993997 101156636 2332553 2788559 1468693 1462749 16458362 -3593681  TRANSPORTATION c an ad i a n * )  3336666 146682711 3894642 .126507623 2363221 2563177 1151994 . 1108687 16698334 -2643771  CASH FLOW SUMMARY FOR TRUCK < a l l amounts i n c u r r e n t  4631006 194293679 5313268 151462433 3977522 8312474 4335296 4664334 9611646 7876719  4644966 248293528 6016925 186445867 5214164 12718647 6715544 6326942 12945162 11916335  TRANSPORTATION Canadian * >  16  ANNUAL PRODUCTION GROSS REVENUE COAL TRANSPORT COST OTHER OP. COSTS ROYALTY PAYMENT FED'. INCOME TAX BC INCOME TAX EC MINING TAX T O T A L C A P I T A L COST NET CASH FLOW  DISCOUNT RATE  15. 88  Table 9-10  4632666 262466195 5863830 197683746 5511664 13656686 7168372 6728349 16975862 15488285  NET  4588666 285622968 5754812 282942635 . 6138388 186581 16 9664933 9695841 12363339 21664489  PRESENT VALUE  39784930  VALUE  4649466 366771998 5963205 228668554 6592967 19144564 16261993 9564373 8963679 25688711  4627166 326671657 6879898 234974358 7626575 28568279 16987656 18348586 9351358 .27349756  INTERNAL OF  RATE OF RETURN  45.19668 362746674 6182669 247876484 8648871 26429491 14279727 13387244 ' 15453687 31696581  RETURN  58. 78  T h i s i s the cash flow summary f o r the case o f an o p e r a t i n g mine r e p l a c i n g i t s coal trucks with new coal trucks t o haul run-of-mine c o a l . The annual production i s i n u n i t s o f tonnes o f raw c o a l .  COMPARISON OF PROJECT ECONOMICS  EXPANDING MINE GRADUAL DEVELOPMENT Truck  FAST DEVELOPMENT  GRADUAL DEVELOPMENT  Flume  Truck  Flume  Truck  Flume  22,763,800  37,430,400  38,659,400  -2,422,500  28.62  37.21  35.63  14.13  »  Total  NPVl($) 19,704,200  Project  IRR (X)  Coal  NPVl($)  Transport IRR {%)  28.16  TRUCK REPLACEMENT  NEW MINE FAST DEVELOPMENT  -316,100 18,523,900 14.90  Flume  Truck  Flume  18,743,400  39,784,900  43,099,700  20.94  58.78  50.17  Truck  21.31  3,059,700  1,229,000  2,106,400  219,500  3,314,700  33  23  29  16  28  iThe discount r a t e used i n a l l cases was 15% Table 9-11  The net present value r e s u l t s a r e higher f o r the flume t r a n s p o r t a t i o n system i n a l l the c a s e s . The p r o j e c t i n t e r n a l r a t e o f return f o r a flume system i s g r e a t e r than f o r a truck system when the r a t e o f i n c r e a s e o f t h e annual cash flows r e l a t i v e t o the i n i t i a l c a p i t a l c o s t s i s g r e a t e r f o r the flume system.  150  i)  The f l u m e t r a n s p o r t s y s t e m g e n e r a t e s  g r e a t e r net present  v a l u e s f o r t h e t o t a l p r o j e c t than t h e t r u c k  transport  system i n a l l of the cases. ii)  The i n t e r n a l r a t e s o f r e t u r n a r e d e p e n d e n t upon t h e speed o f a t t a i n i n g f u l l p r o d u c t i o n .  F o r t h e f a s t mine  d e v e l o p m e n t c a s e s and t h e t r u c k r e p l a c e m e n t c a s e , t h e i n t e r n a l r a t e s o f r e t u r n f o r t h e f l u m e system p r o j e c t s were l e s s than t h a t o f t h e t r u c k s y s t e m p r o j e c t s . i i i ) The p r o j e c t e c o n o m i c s were b e t t e r f o r r a p i d mine d e v e l o p m e n t c a s e s than f o r g r a d u a l mine d e v e l o p m e n t cases. iv)  The e x p a n d i n g mine c a s e s were more a t t r a c t i v e than t h e new mine c a s e s . the " l o o k f o r w a r d "  economically T h i s was due t o  nature of the a n a l y s i s .  c o s t s were not a c c o u n t e d  Prior capital  f o r i n t h e e x p a n d i n g mine  cases.  The i n i t i a l c a p i t a l c o s t s , as a r e s u l t , were not as high. v)  The e c o n o m i c c o m p a r i s o n s o f f l u m e t r a n s p o r t v e r s u s  truck  t r a n s p o r t o f r u n - o f - m i n e c o a l show t h a t t h e n e t p r e s e n t v a l u e s a r e p o s i t i v e and t h e i n t e r n a l r a t e s o f r e t u r n are g r e a t e r than t h e d i s c o u n t r a t e .  T h i s means t h a t  the f l u m e c o a l t r a n s p o r t system r e t u r n s a h i g h e r f i n a n c i a l y i e l d than t h e t r u c k t r a n s p o r t s y s t e m . vi)  The e c o n o m i c a d v a n t a g e s o f flume c o a l t r a n s p o r t a r e i n c r e a s e d when t h e mine i s g r a d u a l l y d e v e l o p e d . is contrary to the r e s u l t s f o r the t o t a l economi c s .  project  This  151  v i i ) The p r o j e c t i n t e r n a l r a t e of r e t u r n f o r a f l u m e system i s g r e a t e r than f o r a t r u c k s y s t e m when the r a t e of i n c r e a s e i n the a n n u a l cash f l o w s r e l a t i v e t o the  initial  c a p i t a l c o s t s i s g r e a t e r f o r the f l u m e s y s t e m . 3.  Conclusions A n a l y s i s of the t o t a l mine p r o j e c t e c o n o m i c s and  coal  t r a n s p o r t s y s t e m e c o n o m i c s l e a d s t o the c o n c l u s i o n t h a t open channel truck C.  t r a n s p o r t of r u n - o f - m i n e c o a l i s e c o n o m i c a l l y  s u p e r i o r to  transport. Monte C a r l o R i s k  Simulation  The r i s k i n the t o t a l p r o j e c t e c o n o m i c s was u s i n g a skewed gamma f u n c t i o n f r e q u e n c y  simulated  by  d i s t r i b u t i o n f r o m which  random v a l u e s of a p a r t i c u l a r c o s t or o p e r a t i n g v a r i a b l e were chosen.  S u i t a b l e c o n s t r a i n t s were p l a c e d on the upper and  lower  l i m i t s of each v a r i a b l e to e n s u r e t h a t the v a l u e s c h o s e n were reasonable.  The skewed d i s t r i b u t i o n e s t a b l i s h e s t h a t v a l u e s  than the mean were c h o s e n more o f t e n than v a l u e s mean.  Thus the s t a t i s t i c a l  lower than  mode of the r e s u l t i n g net  v a l u e and i n t e r n a l r a t e of r e t u r n f r e q u e n c y  higher the  present  d i s t r i b u t i o n s were  lower than the net p r e s e n t v a l u e s and i n t e r n a l r a t e s of r e t u r n c a l c u l a t e d from the median v a r i a b l e v a l u e s . d i s t r i b u t i o n s were d e t e r m i n e d from 150 the p r o j e c t cash f l o w s .  The e c o n o m i c  frequency  i t e r a t i o n s of c a l c u l a t i n g  H i s t o g r a m s of the net p r e s e n t  values  and  i n t e r n a l r a t e s of r e t u r n f o r f l u m e and t r u c k c o a l t r a n s p o r t f o r gradual  new mine d e v e l o p m e n t , g r a d u a l mine e x p a n s i o n  r e p l a c e m e n t c a s e s are shown on F i g u r e s 9-1 was  to 9-3.  c a r r i e d out f o r a g r a d u a l mine d e v e l o p m e n t .  and The  truck analysis  152  GRADUAL  Figure 9-1  MINE  EXPANSION  The flume t r a n s p o r t a t i o n system has a higher average net present value and i s exposed to l e s s f i n a n c i a l r i s k than the truck t r a n s p o r t system. The lower average i n t e r n a l rate o f return f o r the flume system i n d i c a t e s that the rate of i n c r e a s e o f the annual cash flows r e l a t i v e to the i n i t i a l c a p i t a l costs i s not as great f o r the flume system as i t i s f o r the truck system.  153_  GRADUAL NEW MINE DEVELOPMENT 60,  50  60n  50-  40-  ,  I  0  I  i '  l  .10 INTERNAL  Figure 9-2  I  "T  .20 RATE  OF  "  )  .30  RETURN  The flume t r a n s p o r t a t i o n system' has a higher net present value and i s exposed to l e s s f i n a n c i a l r i s k than the truck t r a n s p o r t system.  154  TRUCK  REPLACEMENT  60n  40-,  .2  .4 INTERNAL  Figure 9-3  .6 RATE  .8 OF  1.0  RETURN  The flume t r a n s p o r t a t i o n system has a higher average net present value and i s exposed to l e s s f i n a n c i a l r i s k than the truck t r a n s p o r t system. The lower average i n t e r n a l rate o f r e t u r n f o r the flume system i n d i c a t e s that the rate o f i n c r e a s e o f the annual cash flows r e l a t i v e to the i n i t i a l c a p i t a l costs i s not as great f o r the flume system as i t i s f o r the truck system.  155  1.  A n a l y s i s of  Results  The mode of each f r e q u e n c y the corresponding  d i s t r i b u t i o n was  lower  r e s u l t c a l c u l a t e d at the median v a r i a b l e  The c o m p a r a b l e e c o n o m i c f r e q u e n c y  than values.  d i s t r i b u t i o n s f o r the t r u c k  and  f l u m e t r a n s p o r t s y s t e m s o v e r l a y each o t h e r which i s i n a c c o r d w i t h the s i m i l a r i t y of the e c o n o m i c r e s u l t s noted from T a b l e  9-  11.  The r e l a t i v e l y h i g h e r and n a r r o w e r f r e q u e n c y d i s t r i b u t i o n s f o r the f l u m e t r a n s p o r t s y s t e m are n o t e w o r t h y .  This indicates  t h a t a mine u s i n g a f l u m e c o a l t r a n s p o r t system i s e x p o s e d to lower f i n a n c i a l r i s k than a mine u s i n g a t r u c k c o a l  transport  system.  D.  S e n s i t i v i t y Analyses The s e n s i t i v i t y of the p r o j e c t e c o n o m i c s to changes i n the  f o l l o w i n g c o a l t r a n s p o r t s y s t e m v a r i a b l e s was g r a d u a l l y e x p a n d i n g mine. descending  tested for a  The v a r i a b l e s are l i s t e d i n o r d e r  impact on the p r o j e c t e c o n o m i c s :  i) coal p r i c e , i i ) wash p i ant y i e l d , i i i ) inf1 a t i o n , i v) o p e r a t i ng c o s t , v) c a p i t a l c o s t , v i ) u n d e r g r o u n d d r i f t and r a i s e c o n s t r u c t i o n , v i i ) required truck operating viii)labourcost,and  hours,  of  156  ix) fuel  cost.  The s e n s i t i v i t y of t h e s e v a r i a b l e s was  evaluated  f o r mines  u s i n g e i t h e r a t r u c k or a f l u m e r u n - o f - m i n e c o a l t r a n s p o r t s y s t e m . The net p r e s e n t v a l u e s and i n t e r n a l r a t e s of r e t u r n f o r a r a n g e of p e r c e n t c h a n g e s i n the l i s t e d v a r i a b l e s have been p l o t t e d on F i g u r e s 9-4  to 9-12.  A minimum of f o u r s e n s i t i v i t y  were used to d e f i n e the s l o p e and i n t e r c e p t of each 1.  A n a l y s i s of  determinations curve.  Results  The mine e c o n o m i c s c a l c u l a t e d u s i n g a t r u c k c o a l t r a n s p o r t system were, w i t h the e x c e p t i o n  of c a p i t a l c o s t s , more  s e n s i t i v e t o changes i n the above v a r i a b l e s . The e c o n o m i c s f o r mines u s i n g a f l u m e t r a n s p o r t s y s t e m were c o n s i s t e n t l y s u p e r i o r to the t r u c k t r a n s p o r t mine e c o n o m i c s f o r a l l the. s e n s i t i v i t y a)  Coal  analyses,  Price  The c o a l p r i c e v a r i e d between p l u s and minus 5 p e r c e n t of the median v a l u e and had the most impact on  the  p r o j e c t e c o n o m i c s f o r both the f l u m e and t r u c k c o a l transport cases.  A d e v i a t i o n of o n l y 5 p e r c e n t  was  s u f f i c i e n t t o e i t h e r e l i m i n a t e or d o u b l e t h e p r o j e c t financial return.  The v a r i a t i o n i n the f l u m e s y s t e m  p r o j e c t net p r e s e n t v a l u e was  from $3,492,400 to  $41,230,000 and the i n t e r n a l r a t e of r e t u r n was 16.79  to 42.69 p e r c e n t .  The net p r e s e n t  from  v a l u e f o r the  t r u c k s y s t e m p r o j e c t r a n g e d from $2,252,300 to $39,022,600 and the i n t e r n a l r a t e of r e t u r n v a r i e d from 13.72  to 46.50  percent.  Figure 9-4  The p r o j e c t economics are most s e n s i t i v e to changes i n the coal p r i c e . The economics o f the truck t r a n s p o r t a t i o n case are more s e n s i t i v e to these changes than the flume t r a n s p o r t a t i o n case.  158  Wash P l a n t Y i e l d The wash p l a n t y i e l d was 5 percent  v a r i e d between p l u s and  of the median v a l u e .  minus  The e c o n o m i c s of both  the f l u m e and t r u c k t r a n s p o r t s y s t e m s were q u i t e s e n s i t i v e to these changes. p r o j e c t net p r e s e n t $26,947,400. t o 31.48 was  The  The  less s e n s i t i v e flume  v a l u e went f r o m $18,677,500 t o i n t e r n a l r a t e of r e t u r n was  percent.  f r o m 26.00  The t r u c k s y s t e m net p r e s e n t  value  between $15,295,800 and $23,843,900 and the i n t e r n a l  r a t e of r e t u r n v a r i e d f r o m 24.92 to 31.23  percent.  Inflation I n f l a t i o n r a t e c h a n g e s a f f e c t e d a l l of the variables.  The  cost  i n f l u e n c e of c o a l p r i c e on the  project  e c o n o m i c s overwhelmed the e f f e c t s of changes i n the other v a r i a b l e s .  The  r a t e of i n f l a t i o n was  between p l u s and minus 15 p e r c e n t The f l u m e s y s t e m net p r e s e n t and $24,825,900 w i t h corresponding  of the median  percent.  v a l u e was  The t r u c k  and 28.91  transport  from $18,140,700 to  $21,493,200 and the i n t e r n a l r a t e of r e t u r n  varied  percent.  Costs  The o p e r a t i n g percent  The  changes i n the i n t e r n a l r a t e of r e t u r n  s y s t e m net p r e s e n t  Operating  value.  v a l u e went from $20,780,900  increasing inflation.  were f r o m 27.83 to 29.4  between 24.71  varied  c o s t s were v a r i e d to p l u s and minus 25  of the median v a l u e .  The net p r e s e n t  value  the f l u m e s y s t e m p r o j e c t r a n g e d from $24,806,200 to  of  159  PLANT  YIELD r30  FLUME  -.04  -.02  0  .02  .04  .02  .04  r-32  •24  -.04  Figure 9-5  -.02  0  The project economics are sensitive to small changes in the plant y i e l d . The flume transportation system economics are superior to those of the truck system.  160  INFLATION  -.26  1  -.2  Figure 9-6  1  -.1  1  0  .1  1  .2  Changes in the i n f l a t i o n rate affect a l l of the economic variables. The altered coal price offsets the effects of the other altered variables and results i n large changes i n the project economics.  161  r-25  23  ^  o -21  >  a.  z  •v. •17  -.2t  -.1  -.2  -.1  1  OPERATING  Figure 9-7  0  1  .11  .2r  0  .1  .2  COST  The operating costs f o r a truck comprise a larger proportion of than the flume system operating economics f o r a truck transport changes in operating costs.  run-of-mine coal transport system the total project operating costs costs. Therefore, the project system are more sensitive fo  162  $20,740,400 and t h e i n t e r n a l r a t e o f r e t u r n v a r i e d from 30.15 t o 27.16 p e r c e n t .  The t r u c k s y s t e m n e t p r e s e n t  v a l u e went f r o m $22,253,500 t o $16,903,000 and t h e i n t e r n a l r a t e o f r e t u r n v a r i e d between 30.23 and 25.92 percent. Capital Costs The c o a l t r a n s p o r t s y s t e m c a p i t a l c o s t s were v a r i e d t o p l u s and minus 25 p e r c e n t o f t h e median v a l u e s . The n e t p r e s e n t v a l u e of t h e more s e n s i t i v e f l u m e s y s t e m v a r i e d f r o m $24,259,100 t o $21,302,800 and t h e i n t e r n a l r a t e o f r e t u r n r a n g e d from 30.4 t o 27.12 p e r c e n t .  The  t r u c k s y s t e m n e t p r e s e n t v a l u e r a n g e d from $20,520,500 to $18,886,500 and t h e i n t e r n a l r a t e o f r e t u r n went from 28.62 t o 27.66 p e r c e n t . Underground  C o n s t r u c t i o n Costs  The c o s t o f e x c a v a t i n g and s u p p o r t i n g t h e u n d e r g r o u n d o p e n i n g f o r t h e f l u m e t r a n s p o r t s y s t e m was v a r i e d from minus 15 p e r c e n t t o 100 p e r c e n t .  The n e t p r e s e n t v a l u e  went from $23,234,500 t o $19,528,200 and t h e i n t e r n a l r a t e o f r e t u r n v a r i e d between 29.11 and 25.63 p e r c e n t . T r u c k O p e r a t i n g Hours The t r u c k o p e r a t i n g h o u r s r e q u i r e d f o r c o a l t r a n s p o r t were v a r i e d from minus 10 p e r c e n t t o p l u s 25 p e r c e n t o f the median v a l u e .  The t r u c k t r a n s p o r t e c o n o m i c s were  s e n s i t i v e t o t h e s e c h a n g e s but t h e f l u m e t r a n s p o r t e c o n o m i c s were e s s e n t i a l l y u n c h a n g e d . The f l u m e system net p r e s e n t v a l u e r a n g e d from $22,973,400 t o $22,198,400  163  -25  ~ ~ — / — o to  -23  FLUME  -21 "—• '— _  - --  —  >  a. z  -19  -17  «  -2  -.1  c)  i .1  .2  TRUCK  -.26  -.2  -.1  0  CAPITAL  Figure 9-8  .1  .2  COST  The flume transport system has higher i n i t i a l capital costs than the truck transport system and so the flume project economics are more sensitive to capital cost changes.  164  25  o o  23  21  > Q. Z  19  17  -.15  .2  U N D E R G R O U N D  Figure 9 - 9  —|  1.0  C O N S T R U C T I O N  The capital costs of underground construction apply only to the flume coal transportation system. A doubling of the raise and d r i f t construction costs s t i l l results i n good project financial results.  165  TRUCK  HOURS 24  r  -16  -.2  0  -.1  ,1  .2  r.30  \ \  \ \  v .28 \  \  IRR  \ S  \  TRUCK \  N \ \  -XI  ^ \ \ \  1  Figure 9-10  11 -.2  11  1 -.1  I  •  0  I  <  ,1  T  r.2  The required annual truck hours f o r the truck transportation system are greater than f o r the flume system and so the project economics f o r the truck system are more sensitive to changes in the required truck hours.  166  and t h e i n t e r n a l r a t e o f r e t u r n v a r i e d between 28.82 and 28.16 p e r c e n t .  The n e t p r e s e n t  t r a n s p o r t system v a r i e d from  value of the truck  $20,407,000 -to $17,887,300  and t h e i n t e r n a l r a t e o f r e t u r n went f r o m 28.70 t o 26.67 percent. Labour Cost The  labour cost p o r t i o n s of the operating costs f o r the  c o a l t r a n s p o r t s y s t e m were v a r i e d from 0 t o 100 of t h e median v a l u e .  percent  The n e t p r e s e n t v a l u e f o r t h e  f l u m e s y s t e m r a n g e d from $22,763,900 t o $20,605,300 and the i n t e r n a l r a t e o f r e t u r n was between 28.62 and 27.00 percent.  The t r u c k s y s t e m n e t p r e s e n t  v a l u e went f r o m  $19,704,200 t o $15,484,800 and t h e i n t e r n a l r a t e o f r e t u r n v a r i e d between 28.16 and 24.84 Fuel  percent.  Cost  The p r o j e c t e c o n o m i c s f o r both t h e f l u m e and t r u c k c o a l t r a n s p o r t s y s t e m s were not v e r y s e n s i t i v e t o changes i n the c o s t o f f u e l .  The f u e l c o s t p r o p o r t i o n s  of the  e q u i p m e n t o p e r a t i n g c o s t s were v a r i e d between 0 and 100 p e r c e n t o f t h e median v a l u e .  The n e t p r e s e n t v a l u e o f  the f l u m e t r a n s p o r t p r o j e c t ranged between $22,763,900 and $21,863,700 as t h e f u e l c o s t i n c r e a s e d and t h e i n t e r n a l r a t e o f r e t u r n was between 28.62 and 27.95 percent. was r e d u c e d  The t r u c k t r a n s p o r t p r o j e c t n e t p r e s e n t  f r o m $19,704,200 t o $17,469,700 and t h e  i n t e r n a l r a t e o f r e t u r n went from 28.16 t o 26.33 percent.  value  167  Figure 9-11 The truck coal transportation system requires more manpower than the flume system. Therefore, the project economics f o r the truck system are more sensitive to changes i n the cost of labour.  168  25-.  23-  o  FLUME 2 H  >  a.  z  1H  17H  -1 1.0  —I-  .2  .28-  cc  TRUCK  27H  —1  1.0  FUEL  Figure 9-12  COST  The truck transportation system uses more trucks and requires more fuel than the flume system. Therefore the project economics for the truck coal transport system are more sensitive to changes in the cost of fuel.  169  2.  Conclusions The f o l l o w i n g c o n c l u s i o n s a r e drawn from t h e s e n s i t i v i t y  analysis: i)  The f l u m e t r a n s p o r t o f r u n - o f - m i n e c o a l has l e s s i n h e r e n t f i n a n c i a l r i s k than truck t r a n s p o r t of run-of-mine c o a l .  ii)  The f l u m e t r a n s p o r t of r u n - o f - m i n e c o a l i s e c o n o m i c a l l y s u p e r i o r to truck t r a n s p o r t of run-of-mine c o a l .  E.  General  Conclusions  The f o l l o w i n g c o n c l u s i o n s a r e made from t h e e c o n o m i c comparisons described i)  above:  The m i n i n g p r o j e c t w i l l have a g r e a t e r f i n a n c i a l  return  using a flume system f o r t r a n s p o r t i n g run-of-mine c o a l . ii)  The m i n i n g p r o j e c t w i l l be s u b j e c t t o l e s s f i n a n c i a l r i s k by u s i n g a f l u m e s y s t e m f o r t r a n s p o r t i n g r u n - o f mine c o a l .  i i i ) F a s t d e v e l o p m e n t of t h e m i n i n g p r o j e c t w i l l  increase  the f i n a n c i a l r e t u r n r e g a r d l e s s of the c o a l t r a n s p o r t system used.  170  CHAPTER X RECOMMENDATIONS FOR  FURTHER RESEARCH INTO  RUN-OF-MINE COAL TRANSPORT BY OPEN CHANNEL FLOW A.  Introduction The r e s u l t s of the r e s e a r c h p r e s e n t e d  in this t h e s i s i n d i c a t e  the p o t e n t i a l economic b e n e f i t s of t r a n s p o r t i n g r u n - o f - m i n e in open c h a n n e l f l o w .  coal  L i t t l e p r e v i o u s r e s e a r c h has been done i n  t h i s a r e a and d e v e l o p m e n t of the T r a n s p o r t F u n c t i o n r e p r e s e n t s a s i g n i f i c a n t step forward phenomenon of open c h a n n e l  in understanding sediment  and u t i l i z i n g  the  transport.  T h i s chapter o u t l i n e s recommendations f o r f u r t h e r r e s e a r c h to b u i l d upon t h a t d e s c r i b e d above.  S u b s e q u e n t r e s e a r c h programs  s h o u l d expand the l i s t of v a r i a b l e s b e i n g s t u d i e d to e n a b l e d e r i v a t i o n of an improved  T r a n s p o r t F u n c t i o n which w i l l  a p p l i c a b l e to a l l h e t e r o g e n e o u s  m i x t u r e s of sediment  the  be  p a r t i c l e s in  f l u i d s of d i f f e r i n g r h e o l o g i c a l c h a r a c t e r i s t i c s . A recommended new e x p e r i m e n t a l  apparatus  to c o n d u c t t h e t e s t s  i s p r e s e n t e d to a l l o w : i)  more a c c u r a t e measurement of the v a r i a b l e s of i n t e r e s t and  ii)  B.  more v a r i a b l e s of i n t e r e s t to be m e a s u r e d .  V a r i a b l e s and R e l a t i o n s h i p s t o Study Further research i n t o run-of-mine  c o a l t r a n s p o r t by open  c h a n n e l f l o w s h o u l d e x t e n d the T r a n s p o r t F u n c t i o n r e l a t i o n s h i p by  171  examining  t h e i n f l u e n c e of v a r i a b l e s such  i)  particlesize,  ii)  particle specific gravity,  i i i ) transporting fluid  as:  rheology,  iv)  c r o s s s e c t i o n a l shape of the flume c h a n n e l  v)  the r o u g h n e s s c o e f f i c i e n t of the flume m a t e r i a l .  Run-of-mine c o a l , by n a t u r e , i s a h e t e r o g e n e o u s  and mixture  of  p a r t i c l e s i z e s and d e n s i t i e s . A p r e d i c t i v e r e l a t i o n s h i p , based on the T r a n s p o r t F u n c t i o n , s h o u l d be d e t e r m i n e d the e f f e c t s of t h i s h e t e r o g e n e i t y .  to i n c o r p o r a t e  The new T r a n s p o r t  s h o u l d be p r e d i c t i v e of any c o a l sample w i t h a known  Function composition  of p a r t i c l e s i z e s and d e n s i t i e s . The work of A n s l e y (1963) s h o u l d be e x t e n d e d  by  examining  the i n f l u e n c e of f i n e p a r t i c l e s l i m e s on the f l u i d r h e o l o g y the s u b s e q u e n t  e f f e c t s on c o a r s e p a r t i c l e t r a n s p o r t .  G r a f and A c a r o g l u (1968) s h o u l d a l s o be e x t e n d e d  and  The work of  to improve t h e i r  c o r r e l a t i o n f o r l i g h t e r d e n s i t y and l a r g e r s i z e p a r t i c l e s . The s i g n i f i c a n c e of the flume c r o s s s e c t i o n a l shape and r o u g h n e s s c o e f f i c i e n t on t h e t r a n s p o r t of c o a r s e c o a l s h o u l d  be  examined by u s i n g a c i r c u l a r and a s q u a r e , s t e e l flume as w e l l as a c i r c u l a r h i g h d e n s i t y p o l y e t h y l e n e flume to run the t e s t s .  C.  Changes to the E x p e r i m e n t a l  Apparatus  The recommended changes to the a p p a r a t u s  w i l l e n a b l e more  a c c u r a t e measurement of d a t a and a f f o r d more v a r i a t i o n i n the  172  types of t e s t s conducted.  The p r o p o s e d  apparatus  i s shown on  F i g u r e 10-1. 1.  M a t e r i a l t o be T r a n s p o r t e d The m a t e r i a l t o be t r a n s p o r t e d w i l l be graded  s i z e s of  varying s p e c i f i c g r a v i t i e s according to the f o l l o w i n g chart: P l u s m i l l i m e t e r Minus m i l l i m e t e r S p e c i f i c G r a v i t y 1  2  1.5  4  8  1.5  25  32  1.5  50  60  1.5  1  2  2.65  4  8  2.65  S u f f i c i e n t q u a n t i t i e s o f each o f t h e s e m a t e r i a l s s h o u l d be a v a i l a b l e t o a l l o w 2 t e s t s p e r day p e r m a t e r i a l t y p e . s h o u l d be d r i e d o v e r n i g h t t o e n s u r e  A l l material  t h e r e i s no s u r f a c e  moisture  during subsequent t e s t s . 2.  Head Tank The 2 meter d i a m e t e r  by 1.5 meter deep, c o n i c a l bottom  head tank w i l l be t h e "sump" t o c o n t a i n a l l o f t h e f l u i d i n t h e system and w i l l m a i n t a i n  a c o n s t a n t g r a v i t y head o f f l u i d  d i s c h a r g i n g i n t o the flume.  The f r e e water s u r f a c e i n t h e head  tank w i l l be 5 m e t e r s above t h e f l u m e i n t a k e . 3.  F1ume The 15 c e n t i m e t e r  diameter  flume w i l l be 15 m e t e r s long  to e n s u r e t h a t t h e f l u i d i s f l o w i n g u n i f o r m l y and t o a l l o w r e s i d e n c e time t o take m e a s u r e m e n t s . be used t o m a i n t a i n  greater  A p i v o t i n g s t e e l beam w i l l  a constant flume slope.  Two one meter long  PROPOSED  FLUME  TEST APPARATUS  HEAD TANK rh-FLOW 10m  METER COARSE  C O A L 61N  L  FLUME  STEEL  BEAM  "XT RETURN  LINE  18.5 m  Figure 10-1  GLASS  SECTION /  DEWATERING SCREEN PUMP  :—  The 2 meter diameter by 1.5 meter deep, conical bottom, head tank maintains a 5 meter s t a t i c head of f l u i d above the flume intake. The f l u i d passes through a 10.2 centimeter diameter magnetic flow meter into a 15.2 centimeter diameter by 15 meter long flume supported on a pivoting steel beam. Two, 1 meter long glass viewing sections are placed in the flume at 8 and 14 meters from the flume intake. The coarse coal bin i s welded to a steel section of flume pipe. A 60 degree angle dewatering screen separates the coarse coal in the 1 meter diameter by 2 meter deep discharge collector tank. The slurry i s returned to the head tank by a submersible pump.  174  g l a s s s e c t i o n s , p l a c e d 8 m e t e r s and 14 m e t e r s from t h e flume i n t a k e , w i l l be used t o view f l o w c o n d i t i o n s i n t h e flume and t o make depth o f f l o w m e a s u r e m e n t s . 4.  Coarse Coal B i n The  .08 c u b i c meter c a p a c i t y c o a r s e c o a l b i n w i l l be  welded t o a 15 c e n t i m e t e r d i a m e t e r  by 1 meter l o n g f l a n g e d s t e e l  pipe. 5.  D i s c h a r g e C o l l e c t o r Tank The d i s c h a r g e c o l l e c t o r tank w i l l be a 1 meter  by 2 meter deep c y l i n d r i c a l tank w i t h a g a s k e t e d ,  diameter  b o l t - o n bottom.  The F l y g t s u b m e r s i b l e pump w i l l s i t on t h e tank bottom and t h e d i s c h a r g e l i n e w i l l run out the top of the tank. s c r e e n w i l l be b u i l t degree  angle.  The d e w a t e r i n g  i n t o t h e d i s c h a r g e c o l l e c t o r tank a t a 60  S h o r t c i r c u i t i n g o f t h e pump d i s c h a r g e f l u i d  be p e r m i t t e d t h r o u g h  a v a l v e which r e t u r n s t h e f l u i d t o t h e  discharge collector  tank.  6.  will  Instrumentation a)  F Towrate The v o l u m e t r i c f l o w r a t e o f t h e f l u i d w i l l be  measured by a 10 c e n t i m e t e r d i a m e t e r m a g n e t i c  f l o w meter  mounted on t h e v e r t i c a l head tank d i s c h a r g e l i n e .  This  w i l l e n s u r e t h a t t h e f l o w r a t e i n t o t h e flume i s b e i n g measured w i t h o u t e n t r a i n e d a i r b u b b l e s from t h e pump. A f l o w c u t t i n g d e v i c e mounted on t h e flume  discharge  w i l l be used t o c a l i b r a t e t h e f l o w meter by s a m p l i n g a weight  o f f l u i d i n a known time  interval.  175  b)  Depth o f Flow Measurement The d e p t h o f f l u i d f l o w w i l l be measured w i t h  c a l i b r a t e d p o i n t gauges i n the g l a s s s e c t i o n s of the f1ume. c)  Flume S l o p e Measurement The f l u m e s l o p e w i l l be measured by s u r v e y i n g  t a r g e t s at t h e f l u m e ends w i t h a l e v e l s u r v e y d)  instrument.  Weight Measurements Weight measurements w i l l be made w i t h a more  a c c u r a t e s p r i n g b a l a n c e which  i s kept at a u n i f o r m  temperature.  D.  Further Operating Technique I n v e s t i g a t i o n s A more d e t a i l e d a s s e s s m e n t  p r o c e d u r e s h o u l d be u n d e r t a k e n  of the r u n - o f - m i n e  coal screening  t o o b t a i n an a c c u r a t e  assessment  of the q u a n t i t i e s of o v e r s i z e d m a t e r i a l and an a p p r o p r i a t e t e c h n i q u e t o d i s p o s e of i t . The b l a s t i n g p r a c t i c e s around the r a i s e c o l l a r s h o u l d be d e t a i l e d and a s p e c i f i c o p e r a t i n g p r o c e d u r e t o lower t h e r a i s e t o the n e x t bench s h o u l d be o u t l i n e d . The t r a n s f e r of r u n - o f - m i n e  c o a l from the r a i s e onto the pan  f e e d e r s h o u l d be d e t a i l e d i n o r d e r t o p r e v e n t f l o o d i n g of the feeder.  176  B i b 1 i pgr aph.y Ambrose, H. "The T r a n s p o r t a t i o n of Sand i n P i p e s - F r e e S u r f a c e F l o w . " P r o c . of the 5th H y d r a u l i c s C o n f e r e n c e , S t a t e U n i v e r s i t y of Iowa ( 1 9 5 3 ) . A n s l e y , R. "The E f f e c t of S l i m e s on Open C h a n n e l T r a n s p o r t of F l u i d i z e d S o l i d s . " T r a n s a c t i o n s , E n g i n e e r i n g I n s t i t u t e of Canada 6, No. A-7 ( 1 9 6 2 ) . B a r r y , B.A. E r r o r s i n P r a c t i c a l Measurement i n S c i e n c e , E n g i n e e r i n g , and T e c h n o l o g y John W i l e y and Sons I n c . , p. 10 B i n d e r , R.C. p. 87.  F l u i d M e c h a n i c s , 5th ed.  P r e n t i c e - H a l l , Inc.,  C h a u d r y , H. and Y e v j e v i c h , I. C l o s e d C o n d u i t F l o w . R e s o u r c e s P u b l i c a t i o n s , 1982. Chow, V.T. 1959.  Open Channel H y d r a u l i c s .  1978, 1973,  Water  McGraw H i l l Book Co.  Ltd.,  D a r c y , H. and B a z i n , H. " R e c h e r c h e h y d r a u 1 i q u e s ; I r e p a r t i e , r e c h e r c h e s e x p e r i m e n t a l e s sur l ' e c o u l e m e n t de l ' e a u dans l e s canaux de c o u v e r t s ; 2e p a r t i e , r e c h e r c h e s experimentales r e l a t i v e s aux remous e t a l a p r o p a g a t i o n des ondes," P a r i s (1865) from I n c e , S. and Rouse, H., H i s t o r y of H y d r a u l i c s . 2nd ed. Iowa I n s t i t u t e of H y d r a u l i c s R e s e a r c h , 1980. Durand, R. " B a s i c R e l a t i o n s h i p of the T r a n s p o r t a t i o n of S o l i d s in P i p e s - E x p e r i m e n t a l R e s e a r c h . " International Association of H y d r a u l i c R e s e a r c h - 5th C o n g r e s s ( 1 9 5 3 ) . G a n g u i l l e t , E. a n d K u t t e r , W. " V e r s u c h zur A u f s t e l l u n g e i n e r neven a l l g e m e i n e n f o r m e l f u r d i e g 1 i e c h f o r m i g e Bewegung des Wassers i n C a n a l e n und F l u s s e n , " Z e i t s c h r i f t des O e s t e r r e i c h i s c h e n I n g e n i e u r - und A r c h i t e c t e n - V e r e i n s (1869) from I n c e , S. and Rouse, H., H i s t o r y of H y d r a u l i c s , 2nd ed. Iowa I n s t i t u t e of H y d r a u l i c s R e s e a r c h , 1980. G i l b e r t , K. "The T r a n s p o r t a t i o n of D e b r i s by R u n n i n g Water." U.S. G e o l o g i c a l S u r v e y , P r o f e s s i o n a l P a p e r 86 ( 1 9 1 4 ) . G o n t o r , A. " E x p e r i e n c e i n the C o a l H y d r a u l i c T r a n s p o r t a t i o n ; Use and P e r s p e c t i v e s of i t s d e v e l o p m e n t i n the E n t e r p r i s e s of the G i d r o u g a l A m a l g a m a t i o n . " P r o c . of 3rd I n t e r n a t i o n a l T e c h n i c a l C o n f e r e n c e on S l u r r y T r a n s p o r t a t i o n ( 1 9 7 8 ) . G r a f , W. and A c a r o g l u , E. " S e d i m e n t T r a n s p o r t i n C o n v e y a n c e S y s t e m s . " B u l l e t i n , I n t e r n a t i o n a l A s s o c i a t i o n of S c i e n t i f i c H y d r o l o g y , V o l . 13, No. 2 ( 1 9 6 8 ) .  177  H.N.  H a l v o r s o n C o n s u l t a n t s Ltd.. " F o r e c a s t of C o a l M i n i n g A c t i v i t y to 2002 f o r B.C. Hydro and Power A u t h o r i t y " , C o n s u l t a n t s ' Report (1983).  Hanks, R. " S l u r r y P i p e l i n e H y d r a u l i c s ; P r i n c i p l e s , Problems S o l u t i o n s . " ASME, Paper No. 80-PET-45 ( 1 9 8 0 ) .  and  Hanks, R. and S l o a n , D. "A R h e o l o g y based Model f o r C r i t i c a l D e p o s i t i o n V e l o c i t i e s . " P r o c . of 6th I n t e r n a t i o n a l T e c h n i c a l C o n f e r e n c e on S l u r r y T r a n s p o r t a t i o n (1981)~ I n c e , S. and Rouse, H. H i s t o r y of H y d r a u l i c s , 2nd ed. I n s t i t u t e of H y d r a u l i c s R e s e a r c h , 1980.  Iowa  K a r a b e l a s , A. "An E x p e r i m e n t a l S t u d y of P i p e E r o s i o n by T u r b u l e n t S l u r r y Flow." H y d r o t r a n s p o r t 5 (1978). K l i e m a n , P. " H y d r a u l i c T r a n s p o r t of Copper T a i l i n g s . " Proc. American S o c i e t y of C i v i l E n g i n e e r s , J n l . H y d r a u l i c s D i v . (1976). ~ Kuhn, M. " H y d r a u l i c T r a n s p o r t of S o l i d s i n the M i n i n g Hydrotransport 7 (1980).  Industry."  Manning, R. "Flow of Water i n Open C h a n n e l s . " T r a n s a c t i o n s of the I n s t i t u t i o n of C i v i l E n g i n e e r s of I r e l a n d . V o l . 20 ( 1 8 9 0 ) . M o i r a , H. and Mose, S. " O p e r a t i o n and M a i n t e n a n c e of S l u r r y T r a n s p o r t a t i o n , S y s t e m at H y d r a u l i c C o a l M i n e . " P r o c . of 4th I n t e r n a t i o n a l t e c h n i c a l C o n f e r e n c e on S l u r r y T r a n s p o r t a t i o n ( 1979). M u l a r , A. " M i n i n g and M i n e r a l P r o c e s s i n g Equipment C o s t s and P r e l i m i n a r y C a p i t a l C o s t E s t i m a t i o n s . " CIM S p e c i a l Volume No. 25 ( 1 9 8 2 ) . N e w i t t , D., R i c h a r d s o n , J . , A b b o t t , M. and T u r t l e , D. " H y d r a u l i c C o n v e y i n g of S o l i d s i n H o r i z o n t a l P i p e s . " T r a n s . I n s t i t u t e of C h e m i c a l E n g i n e e r s ( 1 9 5 5 ) . Novak, K. and N a l l u r i , C. "A S t u d y i n t o the C o r r e l a t i o n of S e d i m e n t M o t i o n i n P i p e and Open Channel F l o w . " H y d r o t r a n s p o r t 2 (1972). Shook, C , Haas, D., Husband, W. and S m a l l , M. " R e l a t i v e Wear Rate D e t e r m i n a t i o n s f o r S l u r r y P i p e l i n e s . " J o u r n a l of P i p e ! i n e s 1, 1980. T i e n - Y u , W. and Chu-Lungj M. " E v a l u a t i o n of the C r o s s S e c t i o n and S l o p e of the Channel f o r T r a n s p o r t i n g the O r i g i n a l Coal S l u r r y from H y d r a u l i c Mine A c t i v i t i e s . " P r o c . of 4th C o n f e r e n c e on S l u r r y P i p e l i n i n g ( 1 9 8 0 ) .  178  Wasp, E., Aude, T., Kenny, J . , S e i t e r , R. and J a c q u e s , R. " D e p o s i t i o n V e l o c i t i e s , T r a n s i t i o n V e l o c i t i e s and S p a t i a l D i s t r i b u t i o n of S o l i d s i n S l u r r y P i p e l i n e s . " H y d r o t r a n s p o r t 1 (1970). Watson, W. "Flume T r a n s p o r t of C o a l . " (1959). Westar Mines L t d .  Col 1 i e r y E n g i n e e r i n g  S t a f f Paper.  W i l b y , B. " T a x a t i o n of C o a l M i n i n g P r o j e c t s i n B r i t i s h C o l u m b i a " , B.C. Government R e p o r t , M i n e r a l E c o n o m i c s B r a n c h ( 1 9 8 2 ) . W i l s o n , K. " A n a l y s i s of S l u r r y F l o w s w i t h a F r e e H y d r o t r a n s p o r t 7 (1980).  Surface."  179  APPENDIX 1 COMPUTER PROGRAM TO CALCULATE PROJECT ECONOMICS A.  Introduction The economic a n a l y s i s computer p a c k a g e : i)  i n p u t s and s t o r e s c o s t and p r o d u c t i o n  ii)  designs t h e run-of-mine coal flume t r a n s p o r t  i i i ) c a l c u l a t e s c a p i t a l and o p e r a t i n g truck transport  information system  costs f o r a flume or  system  iv)  c a l c u l a t e s a p p l i c a b l e f e d e r a l and p r o v i n c i a l  v)  c a l c u l a t e s the project net present  taxes,  v a l u e and i n t e r n a l  rate of return, vi)  g e n e r a t e s and p l o t s a f r e q u e n c y h i s t o g r a m o f t h e p r o j e c t net p r e s e n t  value  and i n t e r n a l r a t e o f r e t u r n .  Analysis of f i n a n c i a l r i s k i s incorporated  i n t o t h e program  by s e l e c t i n g p r o d u c t i v i t y and c o s t i n p u t f a c t o r s from a p r o b a b i l i t y distribution.  The Monte C a r l o a l g o r i t h m  samples a gamma f u n c t i o n  f r e q u e n c y d i s t r i b u t i o n t o s e l e c t t h e s e f a c t o r s t o model t h e s t a t i s t i c a l v a r i a t i o n i n a mining project.  The e q u a t i o n  f o r the  gamma d i s t r i b u t i o n i s :  f(x) •  -  i,  X ( K  pk ( K - l ) l  - '^ 1  V  where "P" and "K" a r e .6 and 2 r e s p e c t i v e l y . C a p i t a l and o p e r a t i n g  c o s t s f o r each e l e m e n t o f e i t h e r a  flume o r t r u c k h a u l a g e system a r e c a l c u l a t e d and t h e c a p i t a l are s e p a r a t e d  into depreciation  costs  c l a s s e s i n order to determine the  a p p l i c a b l e f e d e r a l and p r o v i n c i a l  taxes.  180  The net p r e s e n t v a l u e and i n t e r n a l r a t e of r e t u r n of the p r o j e c t e c o n o m i c s are c a l c u l a t e d f o r each i t e r a t i o n of the program. The p r o j e c t r i s k i s a s s e s s e d  by the f r e q u e n c y  d i s t r i b u t i o n of  t h e s e economic c r i t e r i a . The program i s w r i t t e n i n the "BASIC" computer l a n g u a g e operates  on a H e w l e t t - P a c k a r d  9845 m i c r o c o m p u t e r .  and  Approximately  120 k i l o b y t e s of computer memory are r e q u i r e d and a 150  iteration  economic a n a l y s i s t a k e s 20 m i n u t e s . The e c o n o m i c a n a l y s i s p a c k a g e i s c o m p r i s e d of two  distinct  programs: i)  a d a t a e n t r y program ("DATFIL") to e n t e r and s t o r e c o s t and p r o d u c t i o n  ii)  and  the economic a n a l y s i s program ("MINECO") which c a l c u l a t e s mining  B.  information;  c o s t s , a p p l i c a b l e t a x e s and p r o j e c t e c o n o m i c s .  Data E n t r y Program - "DATFIL" The d a t a e n t r y program s t o r e s the c o s t and o p e r a t i n g  parameter  d a t a f o r f l u m e and t r u c k t r a n s p o r t economic e v a l u a t i o n s . information  i s p e r m a n e n t l y s t o r e d on f i l e s f o r r e c a l l when  the economic e v a l u a t i o n  The running  program.  The program r e q u i r e s the number of y e a r s and the number of p e r i o d s per y e a r f o r the economic e v a l u a t i o n . or q u a r t e r l y t i m e p e r i o d s are a v a i l a b l e .  Annual, semi-annual  F o r example, a 10  p r o j e c t c a l c u l a t e d q u a r t e r l y w i l l r e q u i r e d a t a f o r 40 The u s e r i s then r e q u e s t e d flume t r a n s p o r t .  year  periods.  to i n p u t d a t a f o r e i t h e r t r u c k or  181  1.  Flume T r a n s p o r t  Data  The d a t a f o r f l u m e t r a n s p o r t i s e n t e r e d arrays.  into three  The computer p r i n t s a r e q u e s t f o r s p e c i f i c  information  and the a p p r o p r i a t e u n i t s on the s c r e e n and i t i s e n t e r e d the k e y b o a r d .  Data are r e q u e s t e d  as mean v a l u e s and  from  percent  deviations unless s p e c i f i e d otherwise. The f i r s t d a t a f i l e f o r the f l u m e t r a n s p o r t d a t a o p e r a t i n g and c a p i t a l c o s t d a t a .  stores  T h e s e c o s t s do not change on a  p e r i o d i c b a s i s and the o p e r a t i n g c o s t s are e n t e r e d as u n i t c o s t s . P r o d u c t i v i t y and p r o d u c t i o n f a c t o r s are s t o r e d i n the datafile.  P r i o r knowledge of the number of r a i s e s used  second  i n the  flume t r a n s p o r t d e s i g n must be a v a i l a b l e to i n p u t t h e a v e r a g e haul d i s t a n c e to each r a i s e .  The t h i r d d a t a f i l e s t o r e s g e n e r a l  p r o d u c t i o n and c o s t i n f o r m a t i o n on an annual  basis.  This  file  stores: i)  inflation rates,  ii)  run-of-mine coal  production,  i i i ) c o s t s f o r a c t i v i t i e s o t h e r than r u n - o f - m i n e c o a l transport, iv)  the number of r a i s e s used each y e a r ,  v)  the t o n n e s of r u n - o f - m i n e c o a l g o i n g to each r a i s e , and  vi)  whether the mine i s e x p a n d i n g or n o t .  T h i s f i l e i s a l s o used economics.  in c a l c u l a t i n g truck t r a n s p o r t  The s p e c i f i c i n f o r m a t i o n s t o r e d i n each of t h e s e  i s shown on T a b l e A - l .  files  182  Data F i l e s f o r C a l c u l a t i n g t h e Flume System E c o n o m i c s FILE 1 1.  C a p i t a l Costs coal loader coal truck grizzly scalping unit raise construction drift construction pump water l i n e - flume l i n e dewatering plant site investigation  2.  Operating Costs coal loader coal truck grizzly scalping unit dewatering plant f 1 ume head o f f i c e e x p e n s e off-site rail clean-up dozer clean-up loader  FILE 2 coal loader p r o d u c t i v i t y coal truck capacity f l a t haul t r u c k speed distance to r a i s e X  coal loader u t i l i z a t i o n coal truck u t i l i z a t i o n l o a d and dump t i m e distance to r a i s e Y  FILE 3 (for every period i n the a n a l y s i s ) inflation rate *annual production preparation plant yield coal s e l l i n g price c a p i t a l costs f o r other mining operating costs f o r other mining capital costs f o r preparation plant operating costs f o r preparation plant days p e r y e a r Note:  • s h i f t s p e r day capitalized interest clean coal inventory non-capitalized interest • r a i s e s i n use *mine e x p a n s i o n exploration *tonnes to r a i s e X *tonnes to r a i s e Y  items marked w i t h "*" do n o t r e q u i r e maximum d e v i a t i o n s  Table A - l  The computer program, "DATFIL"-, prompts t h e u s e r f o r the i n f o r m a t i o n shown above. The d a t a a r e s t o r e d t o be used i n t h e e c o n o m i c e v a l u a t i o n program "MINECO".  183  2.  Truck T r a n s p o r t  Data  The t r u c k t r a n s p o r t i n f o r m a t i o n i s s t o r e d i n t h r e e arrays.  A r e q u e s t f o r s p e c i f i c i n f o r m a t i o n and t h e a p p r o p r i a t e  u n i t s i s p r i n t e d on t h e computer s c r e e n and t h e i n f o r m a t i o n i s e n t e r e d from t h e k e y b o a r d .  Data a r e r e q u e s t e d  deviation values unless otherwise  as mean and  specified.  C a p i t a l and o p e r a t i n g c o s t s , t r u c k h a u l a g e production f a c t o r s are stored in the f i r s t The second for  data  p a r a m e t e r s and file.  data f i l e stores p i t c o n f i g u r a t i o n information  a s p e c i f i c mine p l a n .  The i n f o r m a t i o n i s s t o r e d as bench  e l e v a t i o n , a v e r a g e one way bench haul d i s t a n c e and t o n n e s o f r u n o f - m i n e c o a l from t h e bench f o r each p i t and each p e r i o d o f t h e economic a n a l y s i s .  The o n l y v a r i a b l e e n t e r e d as a mean and  d e v i a t i o n i s the average,  one way bench haul  The t h i r d d a t a f i l e , w i t h annual i n f o r m a t i o n , i s i d e n t i c a l t o t h e annual  distance.  c o s t and p r o d u c t i o n c o s t and p r o d u c t i o n  information f i l e f o r the flume t r a n s p o r t data. The i n f o r m a t i o n c o n t a i n e d  i n t h e s e d a t a f i l e s i s summarized  on T a b l e A-2.  C.  E c o n o m i c E v a l u a t i o n Program - " M i n e c o " The f l o w c h a r t f o r t h e economic e v a l u a t i o n program i s shown  on F i g u r e A - l .  T h i s s e c t i o n examines t h e i n p u t s r e q u i r e d  through-  out t h e f l o w c h a r t and o u t l i n e s t h e u s e r o p t i o n s a v a i l a b l e w i t h o u t d e t a i l i n g t h e i n d i v i d u a l c a l c u l a t i o n s . A l i s t i n g o f t h e program isincludedinAppendix2.  184  Data F i l e s f o r C a l c u l a t i n g t h e Truck System E c o n o m i c s FILE 1 coal loader capital cost coal loader operating cost coal loader p r o d u c t i v i t y coal loader u t i l i z a t i o n R.O.M. b r e a k e r e l e v a t i o n head o f f i c e e x p e n s e off-site rail transport l o a d and dump time  coal truck c a p i t a l cost coal truck operating cost coal truck capacity coal truck u t i l i z a t i o n up l o a d e d speed up empty speed down l o a d e d speed f l a t haul speed  FILE 2 Number o f p i t s * maximum benches p e r y e a r f o r any p i t * number o f benches f o r p i t X i n y e a r Y* f i r s t bench e l e v a t i o n * r u n - o f - m i n e c o a l s h i p p e d i n y e a r Y* one way f l a t haul d i s t a n c e Note:  items marked "*" do n o t r e q u i r e maximum d e v i a t i o n s  T a b l e A-2  The computer program, "DATFIL", prompts t h e u s e r f o r the i n f o r m a t i o n shown above. The d a t a a r e s t o r e d and then used i n t h e economic e v a l u a t i o n program "MINECO".  185  COMPUTER  PROGRAM  FLOWSHEET  yes  Integrate Frequency Distrib.  Flume  Truck  Input Dat  Choose Random Variable Value  Calculate Net Cash Flows Calculate  Iterate  NPV and IRR  Print Results  Calculate Frequency Histograms  yes ^  Figure A-l  End  The computer program allows the user to choose a Monte Carlo iterative technique to calculate the project economics. A choice of 6 mine development cases is available to select from and sensitivity analyses can be performed on up to 9 variables. The program calculates and displays a frequency histogram for the net present values and internal rates of return calculated for each iteration of the economic evaluation.  186  1.  Monte C a r l o S t a t i s t i c a l The  statistical  Simulation  simulation  r o u t i n e i s based on f o u r  operat ions: i)  choose a p r o b a b i l i t y frequency  distribution function  ii)  integrate the function to c a l c u l a t e a table of  cumulative  probabilities i i i ) c a l c u l a t e a random v a r i a b l e t o r e p r e s e n t  a  cumulative  probability iv)  compare t h e random v a r i a b l e w i t h t h e c u m u l a t i v e p r o b a b i l i t i e s and i n t e r p o l a t e a i n p u t v a r i a b l e  This process  value.  i s diagrammed on F i g u r e /T-2.  P r o b a b i l i t y data f o r several u n i t mining operations the gamma f u n c t i o n f r e q u e n c y is appropriate Y _  indicates  d i s t r i b u t i o n , w i t h a "k" v a l u e o f 2,  f o rthis simulation.  The gamma f u n c t i o n i s :  1 X(K-D-X pk ( K - l ) l P  The r e l a t i o n s h i p i s p l o t t e d on F i g u r e 6-1 on page 118 u s i n g a "k" v a l u e o f 2 and "p" v a l u e s o f .6, .8 and 1.0. A "p" v a l u e of .6 and a "k" v a l u e o f 2 i s used i n t h e computer program. mean and s t a n d a r d  The  d e v i a t i o n f o r t h i s f u n c t i o n i s 1.2 and .85  respecti vely. A Simpson's R u l e a l g o r i t h m frequency  i n t e g r a t e s t h e gamma f u n c t i o n  d i s t r i b u t i o n t o c a l c u l a t e an a r r a y of p a i r e d  the d e p e n d e n t v a r i a b l e "x" and t h e c u m u l a t i v e  values;  p r o b a b i l i t y o f "x"  o c c u r r i n g , as shown on F i g u r e A-3. The Monte C a r l o s u b r o u t i n e  i s actuated  computer program t o sample f o r c o s t v a l u e s  throughout the and p r o d u c t i o n  p a r a m e t e r s used i n c a l c u l a t i n g t h e p r o j e c t e c o n o m i c s .  A random  187  C H O O S E A FREQUENCY DISTRIBUTION  INTEGRATE  GENERATE A RANDOM NUMBER  H  INTERPOLATE  4/ value  —I  MONTE CARLO SIMULATION F i g u r e A-2  The M o n t e C a r l o s t a t i s t i c a l s i m u l a t i o n r o u t i n e i s b a s e d on f o u r operations: i ) choose a p r o b a b i l i t y frequency d i s t r i b u t i o n f u n c t i o n , i i ) i n t e g r a t e the d i s t r i b u t i o n f u n c t i o n to c a l c u l a t e a table of cumulative p r o b a b i l i t i e s , i i i ) c a l c u l a t e a random v a r i a b l e t o r e p r e s e n t t h e c u m u l a t i v e p r o b a b i l i t y o f an e v e n t o c c u r r i n g , a n d i v ) c o m p a r e t h e random v a r i a b l e w i t h t h e c u m u l a t i v e p r o b a b i l i t i e s a n d i n t e r p o l a t e an i n p u t v a r i a b l e v a l u e .  188  1.0 1  1  2  3  GAMMA  4  FUNCTION  FREQUENCY  Figure A-3  5  6  CUMULATIVE DISTRIBUTION  A Simpsons Rule algorithm integrates the gamma function frequency d i s t r i b u t i o n to calculate an array of paired values; the dependent variable "x" and the cumulative probability of "x" occurring. The paired values have been plotted to indicate the shape of the cumulative frequency d i s t r i b u t i o n .  189  number i s g e n e r a t e d  and compared to the a r r a y of p a i r e d v a l u e s .  A p r e c i s e v a l u e of the d e p e n d e n t v a r i a b l e , "x", i s i n t e r p o l a t e d and t h e c o s t or p r o d u c t i o n v a l u e i s c a l c u l a t e d as f o l l o w s : V a l u e = Mean 1.2  Y  *  x  where " v a l u e " i s the c o s t or p r o d u c t i o n v a l u e r e q u i r e d to c a l c u l a t e t h e p r o j e c t e c o n o m i c s and "mean" i s the mean c o s t or p r o d u c t i o n v a l u e i n p u t i n the d a t a e n t r y p r o g r a m . C o n s t r a i n t s are p l a c e d on the v a l u e s of t h e v a r i a b l e s i n o r d e r to p r e v e n t the c a l c u l a t i o n of u n r e a l i s t i c r e s u l t s .  For  example, the c a p a c i t y of a h a u l a g e t r u c k i s n e v e r more t h a n  20  per c e n t of i t s mean c a p a c i t y .  as  The c o n s t r a i n t s are e n t e r e d  l i m i t s on the r a n g e of random numbers g e n e r a t e d . number g e n e r a t e d  I f the random  f a l l s o u t s i d e the imposed l i m i t s , a new  number i s g e n e r a t e d  random  u n t i l an a c c e p t a b l e v a l u e i s o b t a i n e d .  The program c o n t a i n s an o p t i o n t o c a l c u l a t e the p r o j e c t e c o n o m i c s at o n l y the mean v a l u e s of the v a r i a b l e s . T h i s i s accomplished  by f i x i n g the v a l u e of "x" at 1 . 2 .  When the program  i s o p e r a t i n g i n the " s t a t i s t i c a l " mode, the f i n a l i t e r a t i o n of the p r o j e c t e c o n o m i c s i s a u t o m a t i c a l l y c a l c u l a t e d at the v a r i a b l e mean v a l u e s .  T h i s a l l o w s the f i n a l t a b l e of r e s u l t s to d i s p l a y  the most r e p r e s e n t a t i v e cash f l o w v a l u e s . 2.  Data E n t r y The d a t a f i l e s are r e t r i e v e d from permanent s t o r a g e  after responding  to the f o l l o w i n g computer prompts:  i)  E n t e r the number of y e a r s f o r the a n a l y s i s ,  ii)  enter whether the a n a l y s i s i s q u a r t e r l y , or a n n u a l l y ,  semi-annually  190  i i i ) e n t e r the t y p e of a n a l y s i s to be computed, iv)  and  e n t e r the s t o r a g e d e v i c e on which the d a t a are  stored.  T h e r e are s i x economic e v a l u a t i o n c a s e s t h a t are a v a i l a b l e : i)  a new mine u s i n g f l u m e t r a n s p o r t  ii)  expansion  of an e x i s t i n g mine u s i n g f l u m e t r a n s p o r t  i i i ) r e p l a c e m e n t of a c o a l t r u c k f l e e t w i t h f l u m e t r a n s p o r t iv)  a new mine u s i n g t r u c k  transport  v)  expansion  vi)  r e p l a c e m e n t of a c o a l t r u c k f l e e t w i t h o t h e r  of an e x i s t i n g mine u s i n g t r u c k  transport trucks.  The u s e r i s prompted f o r the f i l e names of the r e q u i r e d  data  f i l e s a c c o r d i n g to which e v a l u a t i o n case has been s e l e c t e d .  For  example, i f an e x i s t i n g mine i s e x p a n d i n g u s i n g a f l u m e c o a l t r a n s p o r t s y s t e m , the computer w i l l r e q u e s t names f o r a l l the f l u m e and t r u c k t r a n s p o r t d a t a  files.  P r i o r to s t a r t i n g c a l c u l a t i o n s , the computer prompts f o r more c o n t r o l i n f o r m a t i o n . requested  The number of i t e r a t i o n s w i l l  i f the program i s o p e r a t i n g  be  i n the s t a t i s t i c a l mode.  The u s e r i s prompted f o r i n f o r m a t i o n about the p u r c h a s e of c o a l t r u c k s and  loaders.  Often  i t i s e a s i e r to i n c l u d e the  c o s t s of t h i s e q u i p m e n t w i t h the c o s t s of waste t r u c k s and  capital loaders.  I f t h i s has been done then the computer does not r e c a l c u l a t e the c a p i t a l c o s t s of the c o a l t r u c k s and l o a d e r s .  O t h e r w i s e , the  user i s prompted f o r the number of c o a l t r u c k s a v a i l a b l e at the beginning  of p e r i o d one and the c a p i t a l c o s t s are c a l c u l a t e d by  the c o m p u t e r .  191  3.  Flume  Design  The program o f f e r s 3 o p t i o n s i n d e s i g n i n g the f l u m e run-of-mine coal t r a n s p o r t system: i)  The l e n g t h s of the r a i s e s and d r i f t s are  entered  d i r e c t l y , or ii)  the computer c a l c u l a t e s the l e n g t h of each r a i s e and d r i f t based on i n p u t s u r f a c e i n t e r s e c t i o n c o o r d i n a t e s , or  i i i ) no r a i s e - d r i f t s y s t e m s are The computer d e s i g n e d ,  constructed.  r a i s e - d r i f t system i s c a l c u l a t e d from  user i n p u t n o r t h i n g , e a s t i n g and e l e v a t i o n c o o r d i n a t e s f o r the d r i f t and r a i s e s u r f a c e i n t e r s e c t i o n s . The azimuth  d i r e c t i o n s of  the d r i f t and f i r s t r a i s e c o i n c i d e and a l l s u b s e q u e n t r a i s e d i r e c t i o n s are c a l c u l a t e d p e r p e n d i c u l a r to the d r i f t . and r a i s e i n c l i n a t i o n s are i n d e p e n d e n t l y  The  drift  variable.  I f no r a i s e and d r i f t s y s t e m s are c a l c u l a t e d i n a y e a r , v a l u e s of p r e v i o u s c o m p u t a t i o n s  azimuth  are u s e d .  the  However, the c a p i t a l  c o s t of r a i s e and d r i f t c o n s t r u c t i o n a c c r u e s o n l y to the y e a r of construction.  A p r a c t i c a l l i m i t of 1500 m e t e r s of d r i f t  c o n s t r u c t i o n per y e a r i s imposed and the c o s t of e x c e s s ion  i s charged  t o the f o l l o w i n g y e a r .  construct-  This option is automatically  c h o s e n i f the program i s beyond the f i r s t i t e r a t i o n of the economic evaluation. The f l u m e s i z e and o t h e r h y d r a u l i c v a r i a b l e s such as f l o w r a t e , f l o w v e l o c i t y , h y d r a u l i c r a d i u s and c o a r s e c o a l t r a n s p o r t are c a l c u l a t e d i n the p r o g r a m .  192  The u s e r i s prompted t o e n t e r t h e r u n - o f - m i n e  coal production,  the days p e r y e a r and s h i f t s per day at t h e d e s i g n e d mine c a p a c i t y . The t r a n s p o r t o f r u n - o f - m i n e  coal i s i t e r a t i v e l y calculated f o r  d i f f e r e n t flume diameters u n t i l the c a l c u l a t e d t r a n s p o r t i s equal to t h e r e q u i r e d p r o d u c t i o n . The d e s i g n f l o w depth i n t h e flume i s .44 t i m e s t h e f l u m e d i a m e t e r , t h e v o l u m e t r i c c o n c e n t r a t i o n o f s o l i d s i s 20 p e r c e n t , and t h e c o a l s p e c i f i c . g r a v i t y i s 1.5.  The t r a n s p o r t o f c o a r s e  . c o a l i s c a l c u l a t e d from t h e r e l a t i o n s h i p : j  =  .0017  Q5/3  gl/3  R  S 5/3  where "T" i s t h e c o a r s e c o a l t r a n s p o r t i n volume p e r t i m e , "Q" i s the v o l u m e t r i c f l u i d f l o w r a t e , "g" i s t h e g r a v i t a t i o n a l  constant,  "R" i s t h e h y d r a u l i c r a d i u s , and "S" i s t h e flume s l o p e . The v a l u e o f "Q" i s d e t e r m i n e d  by the r e l a t i o n s h i p :  Q = V A where "V" i s t h e f l o w v e l o c i t y and "A" i s t h e c r o s s s e c t i o n a l area of flow.  The a r e a i s c a l c u l a t e d from t h e flume r a d i u s and  the c o n s t a n t depth o f f l o w and t h e v e l o c i t y i s s c a l e d a c c o r d i n g to t h e d i m e n s i o n l e s s F r o u d e Number: Vl /gTJI  =  V? / W  where "V" i s t h e f l o w v e l o c i t y , "g" i s t h e g r a v i t a t i o n a l and "D" i s t h e f l u m e d i a m e t e r .  The s u b s c r i p t s "1" and "2" r e f e r  to t h e e x p e r i m e n t a l r e s u l t s and f u l l s c a l e p r e d i c t i o n s respecti vely.  constant  193  The t o t a l t r a n s p o r t  of r u n - o f - r n i ne c o a l i s c a l c u l a t e d  a d d i n g the c o a r s e c o a l t r a n s p o r t , ".2Q".  This value  production  u n t i l t h e y are  c a p i t a l and o p e r a t i n g  equal.  c o s t s f o r each f l u m e or  s y s t e m are c a l c u l a t e d u s i n g the s t o r e d  and the c a p i t a l c o s t s are s e p a r a t e d  cost  into depreciation  t o the Canada Income Tax  truck  input data.  r e s u l t s are a c c u m u l a t e d i n t o c a p i t a l and o p e r a t i n g according  transport,  C a p i t a l and O p e r a t i n g C o s t s The  transport  to the f i n e c o a l  i s c a l c u l a t e d f o r d i f f e r e n t flume diameters  and compared t o the r e q u i r e d 4.  "T",  by  The  arrays classes  Act.  For the c a s e of an e x p a n d i n g mine c h a n g i n g t o a f l u m e transport  s y s t e m , the o p e r a t i n g  costs f o r a truck haulage system  are c a l c u l a t e d i n the y e a r t h a t the f l u m e s y s t e m i s  being  constructed. 5.  Federal  and P r o v i n c i a l Taxes  The f e d e r a l and p r o v i n c i a l t a x e s are c a l c u l a t e d i n the order e s t a b l i s h e d  by W i l b y ( 1 9 8 2 ) .  The f e d e r a l income tax  c a l c u l a t i o n i s summarized on T a b l e A-5.  The f e d e r a l  investment  tax c r e d i t i s c a l c u l a t e d f r o m c a p i t a l c o s t a l l o w a n c e c l a s s a s s e t s and tax c r e d i t s c l a i m e d  are a l s o d e d u c t e d from t h i s c l a s s .  The B r i t i s h C o l u m b i a p r o v i n c i a l c o r p o r a t e  and m i n i n g  c a l c u l a t i o n s are s i m i l a r t o the f e d e r a l tax c a l c u l a t i o n and are summarized on T a b l e s A-6 6.  Project  a)  Net P r e s e n t V a l u e The  following  10  and  tax they  A-7.  Economics  p r o j e c t net p r e s e n t  value'is' calcu1ated  relationship: K  NPV = NPV +  i  NCF. \ . -  i=l (1+r)  1  from  the  194  FEDERAL INCOME TAX  CALCULATION  O p e r a t i n g revenue Operating costs Operating P r o f i t  =  Inventory allowance Federal c a p i t a l cost allowances Income S u b j e c t t o R e s o u r c e A l l o w a n c e Federal resource allowance Debt i n t e r e s t C a n a d i a n e x p l o r a t i o n expense C a n a d i a n d e v e l o p m e n t expense  =  Income S u b j e c t t o E a r n e d D e p l e t i o n Earned d e p l e t i o n T a x a b l e Income  x  F e d e r a l Income Tax Rate  (36%)  Tax P a y a b l e I n v e s t m e n t tax c r e d i t Net Tax P a y a b l e  T a b l e A-5  The computer program uses t h i s model t o c a l c u l a t e t h e f e d e r a l income t a x p a y a b l e . I n v e s t m e n t t a x c r e d i t s a r e a c c u m u l a t e d on t h e b a s i s o f c l a s s 10 assets only.  195  B.C. CORPORATION INCOME TAX CALCULATION Operating revenue Operating costs Operating P r o f i t B.C. c o a l r o y a l t y Inventory allowance B.C. c a p i t a l c o s t a l l o w a n c e s I n t e r e s t expense C a n a d i a n e x p l o r a t i o n expense C a n a d i a n d e v e l o p m e n t expense Income S u b j e c t t o E a r n e d D e p l e t i o n Earned dep1etion =  B.C.•Taxab1e  Income  x  B.C. C o r p o r a t i o n Income Tax Rate ( 1 6 % ) B.C. Income Tax P a y a b l e  T a b l e A-6  The computer program uses t h i s model t o c a l c u l a t e the B.C. c o r p o r a t i o n income t a x p a y a b l e .  196  B.C. MINING TAX  CALCULATION  Operating revenue Operating costs Operating  Profit  B.C. c o a l r o y a l t y Inventory allowance B.C. c a p i t a l c o s t a l l o w a n c e s Debt i n t e r e s t C a n a d i a n e x p l o r a t i o n expense C a n a d i a n d e v e l o p m e n t expense Income S u b j e c t to B.C. P r o c e s s i n g A l l o w a n c e B.C. p r o c e s s i n g a l l o w a n c e B.C. M i n i n g T a x a b l e Income x  B.C. M i n i n g Tax Rate B.C. M i n i n g Tax  Table  A-7  (15%)  Payable  The computer program uses t h i s model t o c a l c u l a t e the B.C. m i n i n g t a x p a y a b l e .  197  where "NCF"  i s t h e net cash f l o w , "k" i s the p r o j e c t l i f e i n  y e a r s and " r " i s the d i s c o u n t or c o r p o r a t e h u r d l e r a t e which i s i n p u t at the end of the f i r s t b)  iteration.  I n t e r n a l Rate of R e t u r n The i n t e r n a l r a t e of r e t u r n , by d e f i n i t i o n , i s t h e v a l u e  of " r " which r e s u l t s i n a z e r o net p r e s e n t v a l u e .  The  value  of " r " i s i t e r a t i v e l y changed i n the r e l a t i o n s h i p g i v e n above u n t i l the net p r e s e n t v a l u e i s l e s s than $25,000.  This  0  r e s u l t s i n an i n t e r n a l r a t e of r e t u r n which  i s a c c u r a t e to  four s i g n i f i c a n t f i g u r e s . c)  Statistical  Results  The net p r e s e n t v a l u e and i n t e r n a l r a t e of r e t u r n v a l u e s f o r each i t e r a t i o n are s t o r e d i n an a r r a y and used t o c a l c u l a t e f r e q u e n c y h i s t o g r a m s which are d i s p l a y e d w i t h a t a b l e of c a s h f l o w v a l u e s on the computer s c r e e n .  198  APPENDIX 2  COMPUTER PROGRAM LISTING  199  10 ! ******* R E - S T O R E "MINEC0:H7" ******** 20 ! D R I F T COORDINATES x = 6 2 1 8 , y = 4 1 9 6 , 2=1599 30 ! R f l l S E l COORDINATES x = 5 6 8 4 , y = 2 6 2 3 , z = 1 9 7 0 40 ! R A I S E 2 COORDINATES x = 5 9 4 2 , y = 3 S 3 5 , z = 1 7 9 0 50 DEG 60 OPTION E A S E 1 70 FIXED 0 80 ! 90 Ss*="N" 100 INPUT " C A L C U L A T E THE ECONOMICS AT THE MEAN V A L U E S ONLY? <YVN>",Ss* 1 10 ! 120 DIM I n t e g r a l < 1 6 , 2 ) 130 ! 140 ! *********************************************************************** 150 ! ****** SIMPSON'S RULE SUBROUTINE FOR THE MONTE CARLO S I M U L A T I O N ****** 160 ! ************************************************************************ * 170 ! ISO PRINT L I N C 1 0 ) , " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *******" 190 P R I N T " * * * » * COMPUTING C U M U L A T I V E P R O E A E I L I T I E S FOR GAMMA D I S T R I B U T I O N * * " 200 .PRINT "******************************************************************" 210 ! 220 I n t e g r a l : Low = 6 230 Itmax=28 240 Tol=.O001 250 Line=0 260 FOR Up=.6 TO 2 S T E P .10 270 Line=Line+l 280 Frst=l 290 Int=I=0 300 Frst=l 310 X = Low 320 Y=2.78*X*EXP<-X/.6; 338 Int=Int+Y 340 X = Up 358 Y = 2. 7S*X*EXP':-X/. 6 ) 360 Temp=Int=Int+Y 370 U p l : 1=1+1 380 I F K = I t m a x THEN H o p p e r 398 P R I N T L I N ( 2 ) ,"ERROR IN INTEGRAL E V A L U A T I O N , MAXIMUM # OF I T E R A T I O N S E X C E EDED " 408 ' PAUSE 416 H o p p e r : N = 2M 428 Siz=(Up-Lou>/N 436 X=S i z+Low 446 Y=2.78*X*EXP<-X/.6> 456 Int=Int+4*Y 466 Darg=Low 476 Up2: Darg=Darg+2*Siz 486 IF D a r g < U p THEN Hop2 498 Int=Siz*Int'3 566 I F F r s t = 6 THEN Hop3  510  Fr2t=e  526 GOTO Hop4 530 Hop3: IF A B S ( l n t o l d - I n t ) > = T o l 546 Integral(Line,1>=Up 556 Integral(Line,2)=Int 566 NEXT Up  576  PRINT LIN<2e>  586 596 668 616  GOTO D a t a _ e n t r y Hop4: Intold=Int Int=Temp GOTO U p l  THEN  Hop4  200  626 H o p 2 : X=Barg 630 Y=2.78*X*EXP(-X/.6) 640 Int=Int+2*Y 650 X=Darg+Siz 660 Y=2.78*X*EXP(-X/.6> 670 Int. = I n t + 4 * Y 680 GOTO Up2 690 ! 700 ! ******************************************** 710 ! ******************** MONTE CARLO S I M U L A T I O N S U B R O U T I N E *************** 720 ! ************************************************************************ 730 ! 740 R a n d o m : IF H i = 0 THEN RETURN 750 Hi= ( 1 + H i > * 1 . 2 760 Lo=(l-Lo)*l.2 770 ! 780 FOR Ra=2 TO 35 790 IF I n t e g r a l ( R a , 1 ) > H i THEN H i n t e r p 80O NEXT R a 8 1 0 Hi n t e r p: Mh i = ( H i - I n t e g r a l ( Ra-1 , 1 ) ) / ( I n t e g r a l ( R a , 1 ) -1 nt e g r a l ( R a - 1 , 1 ) ) * ( I nt e gral(Ra,2)-Integral(Ra-1,2))+Integral(Ra-1,2) 820 ! 830 FOR Ra=2 TO 35 840 IF I n t e g r a l ( R a , 1 ) > L o THEN L i n t e r p 850 NEXT R a 860 L i n t e r p : M 1 o= ( L o - 1 nt e g r a l ( R a - 1 , 1 ) ) / ( I nt e g r a l ( R a , 1 ) - I nt e g r a l ( R a - 1 , 1 > ) * ( I nt e g r a l ( R a , 2 > - I n t e g r a l ( R a - 1 , 2 ) ) + I n t e g r a l ( R a - 1 , 2) 870 ! 880 R a n d : Rnum=RND 890 IF <Rnur<i>Mhi > OR ( R n u m C M l o ) THEN GOTO R a n d 900 FOR R i =2 TO 35 910 IF I n t e g r a l ( R i , 2 ) > R n u m THEN GOTO I n t e r p 920 NEXT Ri 930 ! 94 0 I nt e r p : Ss=(Rnurn-I n t e g r a l (R i - 1 , 2 ) ) -•' (I nt e g r a l (R i , 2 > - I nt e g r a l ( R i - 1 , 2 >) * ( I nt e gral(Ri,1^-Integral(Ri-1,1> > + Integral(Ri-1,1> 950 ! 960 IF S s * = " Y " THEN S s = 1 . 2 970 IF J j = I t e r THEN S s = 1 . 2 980 RETURN 990 ! 1000 ! ************************************************************************ 1010 ! ******************** UATA ENTRY SUBROUTINE *************************** 1020 ! ************************************************************************ 1O30 ! 1040 I i a t a _ e n t r y : DIM A ( 2 0 , 1 1 >, Cc ap ( 1 6 , 40 >, C o p ( 1 0 , 40 >, C1 a s s ( 6 , 40 > 1050 DIM C c d ( 4 0 ) , C I 1 O ( 4 0 ) , C 1 1 2 ( 4 0 ) , C I 2 8 C 4 0 ) , F e d t a x ( 1 3 , 4 0 ) , C a s h ( 1 8 , 4 8 ) , C c e ( 4 8 > 1868 DIM B c c e ( 4 8 ) , B c c d ( 4 8 ) , B c 2 3 ( 4 8 ) , B e 12(48),Be 18(46),Bctax(11,48),Edb(46) 1678 DIM Bcmta>:( 1 1, 4 8 ) , B c e d b ( 4 8 ) , I r r h i s t ( 2 , 16) 1636 DIM Np',' ( 368 ) , I r r ( 3 8 6 ) , 11 c ( 46 ) , N p v h i s t ( 2, 1 8 ) , Dat a( 42 , 1 8 ) , Sr e f ( 2 , 9 ) 1696 ! 1186 Period=10 1110 INPUT " E N T E R THE NUMBER OF YEARS FOR ECONOMIC A N A L Y S I S , (1 t o 40)",Period 1 120 ! 1130 Pp=l U40 PRINT L I N C 8 ) , " E N T E R 'A' IF YOU WISH TO DETERMINE THE ECONOMICS Q U A R T E R L Y " 1150 PRINT " '2' ' ' ' SEMI-ANNUALLY" 1166 PRINT " '1' ' ' ANNUALLY" U70 INPUT Pp 1186 PRINT L I N ( 2 6 ) 1196 P e r i od = P e r i o d / F ' p 1266 ! 1210 DIM F i l e * C 1 0 3 1226 REDIM D a t a ( 4 2 , P e r i o d ) 1236 ! 1246 Case*="NF"  201  250 260 270 280 290 800 310 320 330 340 350 360 370 380 390 400 410 420 430 440  PRINT L I N < 1 0 ) , " E N T E R ' N F ' FOR NEW MINE C A S E -FLUME" PRINT " ' E F ' FOR EXPANDING MINE C A S E " PRINT " ' R F ' FOR TRUCK R E P L A C E M E N T C A S E " , L I N O ) PRINT " E N T E R " N T ' FOR NEW MINE C A S E -TRUCK" PRINT " ' E T ' FOR EXPANDING MINE C A S E " PRINT " ' R T ' FOR TRUCK R E P L A C E M E N T C A S E " INPUT C a s e * P R I N T LIN<20> ! IF ( C a s e * = " N T " > OR ( C a s e * = " E T " > OR ( C a s e * = " R T " j THEN GOTO T r u c k _ i n p u t ! INPUT " ENTER THE T O T A L NUMBER OF R A I S E S FOR THE M I N E ' S L I F E " , N r r DIM F 1 u m e ( 1 0 , 3 ) , F a c t o r ( 9 , 3 > , C o s t ( 1 5 , 6 > ! PRINT L I H ( 1 8 > , " B E SURE TO HAVE A T A P E OR D I S K A V A I L A B L E TO ENTER DATA Dev*=":H7" INPUT " E N T E R THE STORAGE D E V I C E TO EE USED <: T14 , : T 1 5 , : H 7 ) " , De-y* MASS STORAGE IS D e c * !  Cost:  INPUT  "ENTER  THE  FILENAME  FOR  THE  FLUME  COST  INFO  (max.  6  char,  e* 450 A S S I G N #1 TO F i 1 e*, R<.< 460 Again*="Y" 470 IF R','=l THEN INPUT " T H E F I L E DOES NOT E X I S T , DO YOU WISH TO TRY AGAIN n >", A g a i n * 480 IF Ru=0 THEN GOTO Downl 490 IF ( A g a i n $ = " Y " > OR < A g a i n * = ' V > THEN GOTO C o s t 500 D o w n l : FOR J = l TO 15 510 FOR 1=1 TO 6 520 READ tt 1 ; C o s t ( J , I > 530 NEXT I 548 NEXT J 550 ! 5 6 0 U p p e r 2 : INPUT " E N T E R THE F I L E N A M E FOR THE FACTOR INFO ( m a x . 6 c h a r a d e i 1 e* 570 REDIM Factor(7+Nrr,3) 580 A S S I G N tt2 TO F i l e * , R u 590 Again*="Y" 608 IF R y = l THEN INPUT " T H E F I L E DOES NOT E X I S T , DO YOU WISH TO TRY AGAIN n>",Again* 610 IF Rc=8 THEN GOTO Down2 620 IF ( A g a i n * = " Y " > OR < A g a i n * ="y"> THEN GOTO U p p e r 2 638 Down2: FOR J = l TO 6 + N r r 648 FOR 1=1 TO 3 658 READ # 2 ; F a c t o r ( J , I > 668 NEXT I 670 . NEXT J 688 ! 690 U p p e r s : INPUT " E N T E R THE F I L E N A M E FOR THE MINE PRODUCTION INFO ".File* 788 REDIM Data(40+Nrr,Period) 710 A S S I G N #3 TO F i l e * , R o 728 A g a i n * ="Y" 738 IF R v = l THEN INPUT " T H E F I L E DOES HOT E X I S T , DO YOU WISH TO TRY AGAIN / n ) " , A g a i n* 748 IF Rv=8 THEN GOTO Down3 750 IF ( A g a i n * = " Y " > OR ( A g a i n * = " y " > THEN GOTO U p p e r 3 768 D o u n 3 : FOR 1=1 TO 4 0 + N r r 770 FOR J = l TO P e r i o d 780 READ # 3 ; D a t a ( I , J > 798 NEXT J 800 NEXT I 818 PRINT L I H ( 2 8 ) 828 IF ( C a s e * = " H F " > OR ( C a s e * = " E F " > OR ( C a s e * = " R F " > THEN GOTO T u p p e r 4 838 GOTO S t a g e 2 848 ! 858 !  202 I860 T r u c k _ i n p u t : PRINT L I N ( I O ) 1870 DIM Tcost<10,6),Truck<IO,3) 1 880 PRINT " BE SURE TO HAVE R T A P E OR DISK A V A I L A B L E TO ENTER P A T H " 1890 Devt=":H7" 1 9 0 0 INPUT " E N T E R THE STORAGE D E V I C E TO BE USED <:T14,:T15,:H7)",Devt 1910 MASS STORAGE IS Devt 1920 ! 1930 T u p p e r S : INPUT " E N T E R THE F I L E N A M E FOR THE TRUCK COST D A T A " , F i l e * 1940 A S S I G N #5 TO F i l e t , R v 1950 Rgaint="Y" I960 IF R'j-l THEN. INPUT " THE F I L E DOES NOT E X I S T , DO YOU WISH TO TRY A G A I N ? Y/N> " , A g a i n t 1970 IF Ry=0 THEN GOTO Tdown3 1980 IF C A g a i r i t = " Y " ) OR ( A g a i n t = " y " ) THEN GOTO T u p p e r S 1990 T d o w n 3 : FOR 1=1 TO IO 2000 FOR J=l TO 6 2610 202O 2030 2040 205O 2060 2070 2686 2696 2166 Y-'H) 2116 2126 2136 2146 2156 2166 2176 2186 2196 2266 2216 2226 2236 2246 2256 Y/N) 2266 2276 2286 2296 2366 2316 2326 2336 2346 2356 2366 2376 2386 2390 2400 2410 od) 24 20 2430 2440 2450 2460 2470  READ # 5 ; T c o s t ( I , J ) NEXT J NEXT I i Tupper4: INPUT " E N T E R THE F I L E N A M E FOR RED IM F l u m e C P e r i o d , 3 ) , T r u c k ( P e r i o d , 3 )  THE  TRUCK  PRODUCT I V I T I E S " , F i 1 e *  I  A S S I G N #6 TO F i l e t , R v Agai nt = " Y " IF Ry=l THEN INPUT " THE F I L E DOES NOT E X I S T , DO YOU WISH TO TRY AGAIN? ", Aga i n t IF Rv = 6 THEN GOTO Tdowri4 IF ( A g a i n t =" Y " ) OR ( A g a i n * = " y " ) THEN GOTO T u p p e r 4 T d o w n 4 : FOR 1=1 TO P e r i o d FOR J=l TO 3 IF ( C a s e t = " E F " ) OR C C a s e t = " N F " ) OR C C a s e * = " RF " > : THEN READ * 6 ; F l u i d e ( I IF C C a s e t = " E T " ) OR ( C a s e t = " N T " ) OR C C a s e t = " R T " > THEN READ # 6 ; T r u c k CI NEXT J NEXT I IF C C a s e $ = " E F " O R C C a s e # = " N F " > OR C C a s e * = " R F " > THEN GOTO S t a g e 2 ! TupperS: INPUT " E N T E R THE F I L E N A M E FOR THE MINE PRODUCTION D A T A " , F i l e * RED IM Data(46,Period) A S S I G N #3 TO F i l e t , R v Againt="Y" IF Rv=l THEN INPUT " THE F I L E DOES NOT E X I S T , DO YOU WISH TO TRY A G A I N ? ",Againt IF Rv = 0 THEN GOTO Tdowr.5 IF C A g a i n t = " Y " ) OR < R g a i n t = " y " ) THEN GOTO T u p p e r S Tdowr.5: FOR 1 = 1 TO 40 FOR J=l TO P e r i o d READ # 3 ; D a t a C I , J ) NEXT J NEXT I PRINT LINC20) i !  ! ***************************************************** ! !  !  ************* **************  D E V E L O P C A P I T A L AND O P E R A T I N G COST ARRAYS T H I S IS THE MAIN PROGRAM CONTROL SEGMENT  *********** **********  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  I  St a g e 2 :  REDIM  Cc a p C 1 6 , P e r i o d > , C o p C 1 0 , P e r i o d ) , C I a s s C 5 , P e r i o d ) , F e d t a x C 1 3 , F  REDIM B e t a x C 1 1 , P e r i o d ) , C c e i P e r i o d + 1 ) , C c d C P e r i o d + 1 ) , C I l O C P e r i od + 1 > REDIM C 1 1 2 C P e r i o d + 1 ) , C 1 2 8 C P e r i o d + 1 ) , B e c e C P e r i o d + 1 ) , B e c d C P e r i od+1> RED IM Be 16 C P e r i od+ 1 ) , Be 12 C P e r i od+ 1 >, Be 28 C P e r i o d + 1 ) , E d b C Pet- i o d > REDIM B c m t a x C 1 1 , P e r i o d ) , B e e d b C P e r i o d ) , C a s h C 1 O , P e r i o d ) RED IM I t c ( P e r i o d ) C ap s e n s = 0 p s e n s = Y1 d s e n s = P r i c e s e n s = I n f s e n s = C o n s e n s = O  203  Fue1sens=Labsens=Exc ess=Topsens=0 2480 MAT S r e f = Z E R 2490 PRINT LIN<.28> 2500 ! 2510 2520 Sens*="N" 2530 INPUT "DO WISH TO DO A S E N S I T I V I T Y A N A L Y S I S ? < Y.-H > " , S e n s * 2540 IF S e n s * = " N " THEN GOTO I t e r l 2550 ! 2560 P R I N T LINC 1 8 ) , " T H E S E ARE THE V A R I A B L E S FOR COAL TRANSPORT S E N S I T I V I T Y ANAL YSIS 2570 PRINT L I N < 2 ) , 1 C A P I T A L COST OF COAL T R A N S P O R T " 2580 PRINT 2 O P E R A T I N G COST OF COAL T R A N S P O R T " 2590 PRINT 3 P R E P A R A T I O N PLANT Y I E L D " 2600 PRINT 4 COAL S E L L I N G P R I C E " 2610 PRINT 5 INFLATION RATE" 2620 PRINT 6 FUEL COST" 2630 PRINT 7 LABOUR C O S T " 2640 PRINT 8 R A I S E & D R I F T CONSTRUCTION COST" 2650 PRINT 9 TRUCK P R O D U C T I V I T Y " 2660 2678 INPUT " E N T E R THE NUMBER OF S I M U L T A N E O U S S E N S I T I V I T I E S TO RUN <1 t. 2680 FOR S.j = l TO Sn 2698 INPUT " E N T E R THE R E F E R E N C E NUMBER <1 t o 9 ) AND THE CHANGE f < 1 S j ), S r e f (.2, S j ) 2700 IF S r e f < 1 , S j > = 1 THEN C a p s e n s = S r e f < 2 , S j ) 2710 IF S r e f < 1 , S j ) = 2 THEN O p s e n s = S r e f < 2 , S j ) 2728 IF S r e f U , S j > = 3 THEN Y I d s e n s = S r e f < 2 , S j ) 2738 IF S r e f < 1 , S j ) = 4 THEN P r i c e s e n s = Sref<•.2,Sj ) 2746 IF S r e f <1 , S j ) = 5 THEN I n f s e n s = S r e f < 2 , S j ) 2758 IF S r e f < 1, S j ) = 6 THEN F u e l s e n s = S r e f ( 2 , S j ) 2760 IF S r e f < 1 , S j ) = 7 THEN L a b s e n s = S r e f ( 2 , S j ) 2770 IF S r e f a , S j ) = 8 THEN C o n s e n s = S r e f ( 2 , S j ) 2780 IF S r e f < 1 i S j > = 9 THEN T o p s e n s = S r e f ( 2 , S j ) 2790 NEXT S j 2800 I t e r 1: Iter = 1 2810 IF Ss * = " N " THEN INPUT ENTER THE NUMBER OF ECONOMIC I T E R A T I O N S <r,,.= 14 9 ; Iter 23 20 IF Ss * = " H " THEN 11 e r = 11 e r + 1 2 3 :30 IF Ss * = " Y " THEN Iter-=1 2840 P R I N T L INC 2 8 ) 2858 ! 2868 Coal*="Y" 2878 INPUT " A R E COAL TRUCK COSTS I N C L . IN OTHER MINING C A P I T A L C O S T S ? <Y.'N>", Coal * 2888 IF C o a l * = " N " THEN C o a l = l 2898 IF C o a l * = " Y " THEN C o a l = 0 2988 C o a l *=".Y" 2918 INPUT " A R E COAL LOADER COSTS I N C L . IN OTHER MINING C A P I T A L C O S T S ? < Y-'H > " , Coal * 2928 IF C o a l * = " N " THEN C o a l • 2938 IF C o a l *= " Y " THEN C o a l •• 2948 ! 2958 Tot npy 2968 Tot i r r = 8 2978 FOR J j 1 TO I t e r 2988 Mill 8 2*998 V=l 3888 ! 3818 MAT C a s h = 2 E R 3828 MAT C c a p = Z E R 3838 MAT Cop=ZER 3848 MAT C I a s s = Z E R 3850 MAT F e d t a x = Z E R 3868 MAT Bc t ax = ZER 3870 MAT Bcrntax = ZER 3080 MAT C c e = Z E R 3090 MAT C c d = Z E R  204  3100 MAT C I 1 8 = 2 E R 3H0 MAT CI 12 = 2ER 3120 MAT C 1 2 8 = 2 E R 3130 MAT Edb=2ER 3140 MAT B c c e = 2 E R 3150 MAT B c c d = 2 E R 3160 MAT B c l O = 2 E R 3170 MAT B c l 2 = 2 E R 3180 MAT B c 2 8 = 2 E R 3190 MAT B c e d b = 2 E R 3200 MAT I t c = 2 E R 3210 ! 3220 RANDOMIZE 3230 ! 3240 FOR I i = l TO P e r i o d 3250 IF I i = l THEH Nd=l 3260 IF C C a s e * = " R F " > OR C C a s e * = " E F " > OR C C a s e f = " N F " > THEH GOTO F l u m e 3278 GOTO T r u c k s h o v e l 3280 T a x e s : GOSUB F e d _ t a x e s 3290 GOSUB Bc_taxes 3300 Cash<1,Ii>=Yprod ! ANNUAL PRODUCTION 3310 Cash C 2,Ii)=Yprod*Y1d*Rev ! GROSS REVENUE 3320 CashC3,Ii>=Opcost1 ! COAL TRANSPORT COST 3330 CashC4,Ii>=0pcost2 ! OTHER O P E R A T I N G COS 3340 Cash(5,Ii)=Royalt y ! ROYALTY PAYMENTS 3350 Cash(6,Ii>=FedtaxC13,Ii> ! FEDERAL TAXES PAID 3368 Cash<7,Ii>=BctaxC11,Ii> ! BC T A X E S P A I D 3378 Cash<8,Ii>=BcmtaxC11,Ii> ! BC MINING T A X E S P A I D 3388 C a s h C 9 , I i > =Tot a l _ c ap ! TOTAL C A P I T A L COSTS 3396 Temptot=CashC2,Ii>-Cash<3,Ii>-Cash<4,Ii >-Cash<5,Ii>-CashC6,Ii > 3408 C a s h C 1 0 , I i > = T e m p t o t - C a s h < 7 , I i > - C a s h C 8 , I i > - C a s h < 9 , I i > ! NET CASH FLOW 34 10 Hd=0 3420 HEXT Ii 3430 GOSUB Hpv 34 4 0 ! 3450 IF S s * = " H " THEH PRINT " ITERATI O H " ; J j ; " O F " ; 1 1 e r ; " C O M P L E T E D " 3460 ! 3478 HEXT Jj 3480 EEEP 3498 GOSUB T a b l e s 3508 IF S s * = " Y " THEN GOTO N e w t r y 3518 GOSUB S t a t s 3528 GOSUB Plotl 3538 N e u i t r y : Bb$ = " N " 3548 INPUT "DO YOU HAHT TO RUN THE ECONOMICS AGAIN WITH T H I S D A T A ? ( Y / N ) " , B b t 3550 IF B b * = " Y " THEN GOTO S t a g e 2 3568 END 3570 ! 35SQ !*************************** 3598 ! C O N T R O L L I N G S T A T E M E N T S FOR C A L C U L A T I N G THE FLUME SYSTEM ECONOMICS 3680 ! ************************************************** 3618 ! 3620 F l u m e : T o t a l = 0 3638 IF Dat ac 3 6 , I i ) > 0 THEN Dd = 2 3640 IF Dat aC 3 6 , I i )>0 THEH GOTO A v o i d 3650 IF J j > l THEH Dd=2 3668 IF J j >1 THEH GOTO A v o i d 3670 PR IHT L I H C 1 0 > 3680 P R I N T " E N T E R ' 8 ' IF YOU WISH TO EHTER THE D E S I G N D I R E C T L Y " 3698 PRINT " ' 1 ' IF YOU WISH THE COMPUTER TO D E S I G N THE S Y S T E M " 3788 PRINT " ' 2 ' IF YOU DO HOT WISH TO CONSTRUCT ANY D R I F T S OR F L U M E S " 3718 INPUT Dd 3728 PRINT L I H C 2 8 > 3738 IF Dd=8 THEN GOSUB D i r e c t _ i n p u t 3740 IF D d = l THEN G O S U B ' D r i f t design 3756 IF Dd=2 THEN GOTO A v o i d  205  3768 INPUT " E N T E R THE MI HE L I F E D E S I G N PRODUCTION RATE <RAW M T P Y > " , P r o d 3770 GOSUB F 1 u m e _ d e s i g n 3788 A v o i d : GOSUB C a p _ c o s t 3790 GOSUB O p e r a t i n g 3S00 GOTO T a x e s 3810 ! 3820 ! ************************************* 3838 ! SUB-ROUTIHE TO D E S I G N THE R A I S E AND HAULAGE S Y S T E M 384 0 ! *************************************** 3858 ! 3860 PRINT L I N < 1 0 > , " »*******************»*************************" 3878 PRINT " THE D R I F T AND R A I S E SYSTEMS ARE B E I N G D E S I G N E D " 3880 PRINT " ************************************************ 3 8 9 8 Dr-i f t _ d e s i g n : Hrr=0 3988 INPUT " E N T E R THE NUMBER OF MAIN D R I F T SYSTEMS TO BE C O N S T R U C T E D T H I S P E R I O D" , Hd 3918 IF Nd=8 THEN GOTO X x l 3920 A=l 3938 FOR 1=1 TO Hd 3940 PRINT L I N < 1 0 ) , " E N T E R THE NUMBER OF R A I S E S FROM D R I F T " ; I 3958 INPUT N r 3968 PRINT LIN<20) 3970 INPUT " E N T E R THE COORDINATES OF THE D R I F T OPENING <X,Y,Z)",Dx,Dy,Dz 3980 INPUT " E N T E R THE FLUME S L O P E <.01 TO . 0 5 ) " , S f 3998 Hrr=Hrr+Nr 4O0O R a i s e : FOR J=A TO Nr+A-1 4010 REDIM A ( H d * N r , 1 1 ) 4020 P R I N T LIH< 1 0 ) , " E N T E R THE X , Y , Z C O O R D I N A T E S OF R A I S E " ; . ! 4038 INPUT Rx,Ry,Rz 4040 PRINT LIH<20) 4050 INPUT " E N T E R THE R A I S E I N C L I N A T I O N ( 5 0 TO 90 D E G R E E S ) " , S r 4068 ACJ,l)=Rx 4870 A(J,2)=Ry 403O AcJ,3)=Rz 4098 A(J,4)=Dx 41O0 A<J,5)=Dy 4118 A O J , 6 ) = Dz 4120 IF J = l THEN GOTO F i r s t _ t i m e 4138 B2=Ry+Rx/M 4140 A J , 7) = < B 2 - B ) / < M+1 - M) ! X COORD. OF INTERSECTION 4150 A<J,8)=M*A(J,7)+B ! Y COORD. OF INTERSECTION 4168 A< J , 9 ) = S f *SQR< <Dx-A< J , 7 ) )'-2+<A< J , 8 )-Dy )'-2 )+Dz ! Z COORDINATE 4178 Dist=SQRCCRx-ACJ,7))~2+<Ry-A<J,8)) 2) 4188 A<J, 1 1 ) = < R z - A < J , 9 ) ) / S I N ( S r ) ! L E H G T H OF R A I S E 4198 R C J , 1 0 ) = Di s t - A < J , 1 1 ) * C O S ( S r ) ! L E H G T H OF D R I F T 420O Temp = A ( J , 9 ) - A < A , 6 ) 4218 IF Ternp-Head>8 THEH H e a d = Temp 4228 NEXT J 4230 ! 4248 FOR L = l TO N r * H d 4250 Dr i f t =Dr i f t +A C L , 1 8 ) +Exc e s s 4266 Raise=Raise+A<L,11)+Excess 4278 NEXT L 4286 ! 4298 IF D r i f t > 1 5 8 0 / P p + 5 8 THEH GOTO O v e r f l o w 4380 GOTO A d v a n c e 4318 O v e r f l o w : Excess=Drift-1508'Pp 4328 Drift=1588^Pp 4338 P R I N T L I H C 1 6 ) , E x c e s s ; " METERS OF D R I F T ' C O N S T R U C T I O N WILL BE D E L A Y E D UHTI L THE HEXT P E R I O D " 4348 BEEP 4358 WRIT 2 8 8 8 4368 PRINT L 1 H ( 2 6 ) 4 3 7 0 A d v a n c e : HEXT I 4388 A=Nd*Nr+1 4 3 9 8 X x l : RETURN 4 4 08 ! A  206  4410 ! ***********************************, 4 4 20 ! 4430 F i r s t _ t i m e : 2 = SQR< (.Rx-Dx>--2 + (Ry-By > "-2) 4440 X=(Sf*Z+Dz-Rz)/<Sf-TfiN<Sr)> 4450 Y=Rz-Dz-TAN<Sr)*X A< J , ? > = X * < D X - R : K > / 2 + R X ! X COORD. OF INTERSECTION 4 4 70 fl<J,8>«*Ry-X*<Ry-DyW ! Y COORD. OF INTERSECTION 4480 A<J,9>=Y+Dz ! 2 COORD. OF INTERSECTION 4490 ACJ,10>=2-X ! LENGTH OF DRIFT 4508 A < J , 1 1 > = < R z - D z - Y > / S I N ( S r > ! LENGTH OF RAISE 4510 M=<Ry-Dy>/<Rx-Dx> 4520 B=Ry-M*Rx 4530 H e a d = A < J,9>-A<R,6> 4540 NEXT J 4550 ! 4560 ! 4570 ! *********************************************************************** 4580 ! 4590 Nd=l 4600 D irect_input: INPUT "ENTER THE NUMBER OF MAIN DRIFTS TO BE CONSTRUCTED THI S YEAR ",Nd 4610 IF Nd=6 THEN GOTO Xx2 4620 INPUT "ENTER THE TOTAL LENGTH OF DRIFT CONSTRUCTION THIS YEAR <METERS>",Dr i ft 4630 INPUT "ENTER THE NUMBER OF RAISES CONSTRUCTED THIS YEAR",Mrr 4640 INPUT "ENTER THE TOTAL LENGTH OF RAISE CONSTRUCTION THIS YEAR",Raise 4650 X >;2: RETURN 4660 4670 4 630 SUB-ROUTINE TO DESIGN AND SIZE THE COMPONENTS OF THE FLUME SYSTEM 4690 4700 4710 F ume_des i gn:Thet a=1.45 4728 PRINT LIN<10>," **********************************" 4730 PRINT " THE FLUME SYSTEM IS BEING DESIGNED" 4740 PRINT " ««********************************" 4750 N=l 4760 Cv=. 2 4770 ! 4780 Day=340 4796 Shi f t = 3 4800 INPUT "ENTER THE DAYS'YR AND SHIFTS'DAY AT FULL PRODUCTION (340,3)",D; y,Shi f t 4810 F a c t o r , 75 4 320 INPUT "ENTER THE FLUME SYSTEM EFFECTIVE UTILIZATION < 5>",Factor 4830 Sf=.025 4340 IF Dd=0 THEN INPUT "ENTER THE FLUME SLOPE C.025>",Sf 4850 ! 4860 FOR D = ,4 TO 1, 2 STEP .05 R = D/2 4870 S t e p l : 4880 Vel oc i ty=<D''. 15)"-. 5*2 4890 Hrad=R/C4*Theta)*<2*Theta-SIN<2*Theta>> 4 900 Area=R"2/2*(2*Theta-SIH<2*Theta> > 4910 F l oui = Vel oc i t y * A r e a 4920 T r a n s p o r t = < Cv*F 1 ou+. 001 8*F1 o w l .67*Sf* 1OO/(Hrad-1.67*9.82 .33>>* 129666*D ay*Factor 4930 IF ABS(Transport-Prod><10OOO THEN GOTO Jump 4940 IF T r a n s p o r t - P r o d > 0 THEN GOTO Decrement 4950 IF N=10 THEN GOTO Jump 4960 NEXT D 4970 ! 4980 Decrement: D=D-.025/N 4990 H=H+1 50O0 GOTO S t e p l 501O Jump: PRINT LIN<20> 5020 RETURN 4460  7  A  207  5030 504 0 *************************** 5050 SUE-ROUT I HE TO C A L C U L A T E THE FLUME S Y S T E M C A P I T A L COSTS 5060 ************************************* 5070 Total=Total2=Total_cap=6 5030 Cap_c o s t : Yprod=Dat a<4, I O 5690 I 5100 5110 Day=Data<23,I O 5120 Shi f t = D a t a < 2 6 , I i > 5130 IF Dd = 2 THEH N r r = D a t a < 3 6 , I i > 5140 Vtemp=l+Data<1,Ii >*<1+Infsens) 5150 V=V*Vtemp 5160 i 5170 SHOVEL ******* ******* 5180 5190 S h o v e l : Hi= F a c t o r d , 2 ) 5200 L o = Factor-C 1 , 3 ) 5210 GOSUE Random 5220 S p r o d = Fac t o r < 1 , 1 ) * S s / l . 2 5230 Sophr=Yprod/Sprod 5240 ! 5250 Hi = F a c t o r < 5 , 2 ) 5268 Lo = F a c t o r < : 5 , 3 ) 5270 GOSUE Random 5288 S u t i 1 = F a c t o r < 5 , 1 )*Ss-'l . 2 5290 Shovel s = Sophr/(.'24*Day*Sut i 1 ) 5380 I 5310 G=Shove1s 5320 IF F R A C T ( G > > . 2 THEH G=G+1 5330 Shovels=IHT<G) 5340 IF C o a l = 8 THEH S h o v e 1s = 8 5358 ! 5368 Hi = C o s t U , 2 ) 5370 Lo = C o s t < 1 , 3 ) 5380 GOSUE Random 5390 S c a p = C o s t ( 1 , 1 >*Ss''l . 2 5400 ! COAL LOADING UNIT Ccap < 1 , I i ) = S h o v e 1 s * S c ap* V 54 18 ! 5420 Hi = C o s t ( 2 , 2 ) 5438 Lo=Cost(2,3) 5448 GOSUE Random 5458 ! TRUCKS C c a p ( 2 , I i ) = F1 ume( I i , 3 ) * C o s t ( 2 , 1 )*Ss--'l . 2*'i 5468 IF C o a l = 0 THEN Ccap<2,Ii>=8 5470 5430 SORT THE C A P I T A L COSTS EY C L A S S E S ******* ******* 5490 5500 5510 ' 1 ' FOR C L A S S 16 A S S E T S 5520 '2' FOR C L A S S 12 A S S E T S 5530 ' 3 ' FOR C L A S S 28 A S S E T S 5540 ' 4 ' FOR CAHAD I AH E X P L O R A T I OH E X P E H S E 5558 ' 5 ' FOR CAHADIRH DEVELOPMENT EXPEHSE 5560 5578 S o r t : SHOVELS IF Data<37, I O = 55S0 IF Dat a< 37 , 1 0 = 0 THEH 5590 IF D a t a ' ; 37 , I i > = 1THEH 5600 IF ' D a t a : 3 7 , I O = 1 THEN \ 5610 5628 IF Dat ai. 37 , I i ) = 1 THEH CI a s s ( 3 , I i ) = C 1 as s < 3, I i ) + C c apI <i! 2> ! TRUCK 5638 IF D a t a c 3 7 , I O =6 THEN CI ass.( 1 , I O= C 1 a s s < 1 , I i >+Ccap<2 I i > 5646 IF D a t a < 3 7 , I i > = 1THEN 5650 IF D a t a ' ; 37 , I O = 1THEH E c e d b = E c e d b + . 3 3 3 * C c a p ( 2 , 1 i 5660 | 5670 IF I i >1 THEH GOTC 2 i p 5688 | 5698 Hi = C o s t ( 3 , 2 ) 1  208  5700 5718 5720 5738 5748 5758 5768 5778 5788 5798 5808 5818 5828 5838 5848 5858 5868 5878 5886 5898 5988 5918 5926 5938 5948 5958 5960 5978 5986 5996 6608 6610 6020 6030 6848 6058 6868 6070 6686 6890 6160 6118 6120 6138 6146 6156 6168 6178 6186 6198 6260 6210 6228 6230 6248 6250 6268 6276 6280 6298 6368 6318 6328 6338 6346 6356  L o = C o s t <3, 3> GOSUB Random C c a p ( 3 , I i >=Cost < 3 , 1 > * S s x i , 2 # H r * V * < 1 + C a p s e n s > ! GRI: IF I i a t a C 3 7 , I i > = 1 THEH CI a s s ( 3 , I i > = C 1 a s s < 3 , I i >+Ccap<3, I i > IF D a t a < 3 7 , I i >=0 THEN C1 a s s <1, I i > =C 1 a s s < 1 , I i > +Cc a p ( 3 , I i ) IF D a t a < 3 7 , I i > = 1 THEH E d b = E d b + . 3 3 3 * C c a p ( 3 , I i > IF D a t a < 3 7 , I i > = 1 THEH B c e d b = E c e d b + . 3 3 3 * C c a p ( 3 , I i > I Hi=Cost<4,2> Lo = C o s t <4,.3> GOSUB Random C c a p < 4 , I i >=Cost k'4, 1 ) * S s / l . 2 * R a i s e * V * < 1 + C o n s e n s > * i 1 + C a p s e n s > ! R A I S E S IF H a t a C 3 7 , I i > = 1 THEH C1 a s s < 2 , 1 i > = C 1 ass<2,Ii>+CcapC4,Ii> I Hi = C o s t < 5 , 2 ) Lo=Cost(5,3) GOSUB Random C c a p < 5 , I i >=Cost ( 5 , 1 ) * S s / l . 2 * < D r i f t + Exc e s s > * V * 1 . 8 1 * ' : 1 + C o n s e n s > * < l + C a p ; IF E x c e s s > 0 THEH Exc e s s = 0 ! DRIFT IF Dat. a < 3 7 . I i > = 1 THEH C l a s s (. 2, I i > =C 1 a s s ( 2 , I i > +Cc ap < 5, I i ) Hi=Cost<6,2) Lo = C o s t <6, 3) GOSUB Random Temp = C o s t C 6 , 1 >*Ss-'l . 2 Ki,i=(. l - C v ) * F l o u * H e a d * l . 2 * 1 0 8 8 x 1 6 2 IF Ku<373 THEH Ccap<6,Ii>=Temp*V*2*C1+Capsens> IF Kw>373 THEH C c a p < 6 , I i ) = < K w / 3 7 3 > - . 6 * T e m p * V * 2 * < 1+Cap: IF D a t a < 3 7 , I i ) = 1 THEH C1 a s s < 3 , I i > = C 1 a s s < 3 , I i ) + C c a p < 6 I i IF Dat a>; 37 , I i > =6 THEH CI a s s < 1, I i ) = C 1 ass< 1 , I i >+Ccap<:6 I i IF D a t a f 3 7 , I i > = 1 THEH E d b = E d b + . 3 3 3 * C c a p < 6 , I i > IF D a t a C 3 7 , I i ) = 1 THEN Bcedb=Bcedb+.333*Ccap<6,Ii) ! H i =Cost <?,2) Lo = C o s t <7, 3> GOSUB Random Cc ap i7, I i ) = C o s t 1 ) * S s x l . 2*Dr-i f t * V * < 1 + C a p s e n s ) IF D a t a < 3 7 , I i > = THEN C1 a s s < 3 , I i > =C1 a s s C 3 , I i > +Cc ap <I 7i > THEH C1 a s s < 1 , I i > = C 1 a s s C 1 , I i > + C c a p < 7I i > IF D a t a < 3 7 , I i ) = IF D a t a < 3 7 , I i > = THEH Edb=Edb+.333*Ccap<7,Ii) IF D a t a < 3 7 , I i > = THEH Bcedb=Bcedb+.333*Ccap<7,Ii) i Hi = C o s t < 8 , 2 ) Lo = C o s t < 8 , 3 ) GOSUB Random C c a p C S , I i > = C o s t : 8 , 1 > * S s x i . 2*Dt-i f t * V * 2 * < 1 + C a p s e n s > IF D a t a C 3 7 , I i >== 1 THEH C1 a s s ( 3 , I i > = C 1 a s s < 3 , I i >+Ccap<8, I i IF Dat aC 3 7 , I i >=6 THEH CI a s s < 1 , I i > = C 1 a s s < 1 , I i J + C c a p C S , I i IF Dat aC 3 7 , I i ) = 1 THEH E d b = E d b + . 3 3 3 * C c a p < 8 , I i > IF D a t a < 3 7 , I i > = 1 THEH B c e d b = B c e d b + . 3 3 3 * C c a p < 8 , I i > ! Hi = C o s t <9,2> Lo=Cost(9,3) GOSUB Random Temp = C o s t <. 9 , 1 > * S s x 1 . 2 T e m p i =FT-od^Day.'Fac t o r - x 2 4 / 7 5 0 IF T e m p l > . 2 5 THEN Cc ap < 9 , I i ) =Temp 1 . 6*Ternp*V C c a p < 9 , I i >=Temp*V*<1+Capsens) 9 , I ap: i > IF Dat a< 37 , I i > = 1 THEN C1 as s C 3, 1 i > = C 1 a s s < 3 , I i >C +Cc IF D a t a < 3 7 , I i > = 8 THEN CI a s s CI I i ) = C 1 a s s < 1 , I i > +Cc a p ( 9 , I i Edb=Edb+.333*Ccap<9,Ii) B c e d b = B c e d b + . 3 3 3 * C c a p < 9 , I i :> ' IF D a t a C 3 7 , I i > = 1 THEH M i 1 1 = N i 1 1 + C c a p < 9 I i ) ! Hi = C o s t ( 1 8 , 2 > Lo = C o s t <16,3>  !  PUMP  HATER  LI HE  FLUME  A  !  DEWATERIHG  PL.  209  6360 6370 6380 6390 640O 6410 6420 6430 6440 6450 6460 6470 64 80 6490 6500 6510 6520 6530 6540 6550 6560 6570 6580 6590 6600 6610 6620 6630 6640 6650 6660 6670 6680 6690 6700 6710 6720 6730 6740 6750 6760 6770 6780 6790 6800 6810 6820 6830 6840 6850 6860 6870 6880 6890 6900 6910 6920 6930 6940 6950 6960 6970 6980 6990 7000  7O10  GOSUB Random C c a p C 1 0 , I i >=C o s t < 1 0 , 1 )*Ss.-'l . 2*V*< 1 + C a p s e n s > IF D a t a < 3 7 , I i > = 1 THEN C 1 a s s < 3, I i ) = C 1 a s s < 3, > +I C i cap<IO,Ii > IF D a t a < 3 7 , I i >=0 THEN CIass<1,Ii)=C1assC1,Ii )+Ccap<IO,Ii > IF Dat. a < 3 7 , I i > = 1 THEN E d b = E d b + . 3 3 3 * C c a p < 1 0 , I i > IF D a t a t 3 7 , I i > = 1 THEN B c e d b = B c e d b + . 3 3 3 * C c a p t I O , I i > !  FLUME  Hi = C o s t < 1 1 , 2 > Lo=Cost<11,3) GOSUB Random C c a p < 1 1 , I i >=C o s t < 1 1 , 1 > * S s / l . 2 * V * < 1 + C a p s e n s > ! SITE IF D a t a ( 3 7 , I i > = 1 THEN C1 a s s ( 4 , I i ) = C 1 a s s ( 4 , I i) + Ccap<1 1 , I i > IF D a t a ( 3 7 , I i > = 0 THEN C l a s s < 1 , I i > = C1 a s s < 1), + Ii C c a p < 1 1 , I i ) IF B a t a ( 3 7 , I i > = 1 THEN E d b = E d b + . 3 3 3 * C c a p < 1 1i ,> I IF Dat a < 3 7 , I i > = 1 THEN B c e d b = B c e d b + . 3 3 3 * C c a p1< 1,10  SER''  INVEST.  I  FOR J=3 TO 11 T o t a l = T o t al + C c a p ( J , I i ) NEXT J ! Ccap<12,Ii > = 0 . 5*Tot al IF D a t a < 3 7 , I i > = 1 THEN C1 a s s < 3 , I i ) = C 1 a s s < 3) + , I iC c a p < 1 2 , I i > IF D a t a < 3 7 , I i >=0 THEN C1 a s s < 1 , I i ) - C 1 a s s < 1 , I i ) + C c a p < 1 2 , I i > IF Dat a< 3 7 , I i >=1 THEN E d b = E d b + . 3 3 3 * C c a p < 1 2 , I i > IF D a t a < 3 7 , I i >=1 THEN B c e d b = B c e d b + . 3 3 3 * C c a p < 1 2 , I i > !  >ip: Hi=Data<12,Ii) Lo = D a t a C 1 3 , I i > GOSUB Random Cc ap < 1 3 , I i ) = D a t a < 1 1 , I i IF D a t a < 3 7 , I i >=1 THEN IF D a t a t 3 7 , I i >=0 THEN IF Dat a < 3 7 , Ii >=1 THEN IF D a t a < 3 7 , I i >=1 THEN  !  > *Ss/1.2*V C I a s s < 3 , I i > = C 1 a s s C 3 , I i >+Ccap<13, I i > C1 a s s < 1 , I i ) = C 1 a s s (1> +, ICi c a p < 1 3 , I i > : Edb=Edb+.333*Ccap<13,I i ) B c s d b = B c e d b + . 3 3 3 * C c a p < 13, Ii >  Hi = D a t a C 1 8 , I i Lo=Data(19,Ii GOSUB Random Ccap<14,Ii > = D ata<17, I i ) * S s / l . 2 * V IF D a t a ( 3 7 , I i > = 1 THEN C1 a s s < 3, I i > =C1 a s s < 3 ), + I i C c a p C 1 4 , Ii > IF Dat a< 3 7 , I i >=0 THEN C1 a s s < 1 , I i > = C1 a s s < 1 , I i>+Cc a p C 1 4 , I i ) Edb=Edb+.333* Ccap<14, I O Bcedb=Bcedb+. 333*Ccap<14, I O IF Dat a ( 2 6 , I i > = 1 THEN Mi 1 1=Mi 1 1 + C c a p ( 1 4 , I i > ! Hi = D a t a < 3 9 , I i Lo=DataC40,Ii GOSUB Random Cc ap < 1 5 , I i > = D a t a ( 3 8 , I i >*Ss/l.2*V ! IF D a t a C 3 7 , I i > = 1 THEN C1 a s s < 3 , I i )=C1 a s s ( 3>, + I iC c a p < 1 5 , I O IF D a t a C 3 7 , I i >=0 THEN C l a s s < 1 , I i > = C 1 a s s < 1>+Ccap<: 15, I i > ,Ii IF D a t a C 3 7 , I i >=1 THEN E d b = E d b + . 3 3 3 * C c a p < 1 5 , I i ) IF D a t a < 3 7 , I i > = 1 THEN B c e d b = B c e d b + . 3 3 3 * C c a p1C 5,Ii > ! Hi = D a t a < 2 8 , I i L o = Dat a < 2 9 , I i GOSUB Random C c a p C 1 6 , I i >=D a t a ( 2 7 , I i ! FOR J = l TO 16 T o t a l _ c ap = T o t a l NEXT J  ENGINEERING  OTHER  MINING  OTHER  PLANT  EXPLORATION  >*Ss/l.2*V  !  c ap+Cc ap < J , I i )  !  CAP..INTEREST  TOTAL  CAPITAL  I  C1 a s s i f y: Cc e < I i > = C c e < I i > + C l a s s < 4 , I i ) C c d < I i >=Ccd< I i > + C l a s s < 5 , I i > CI 2 8 < I i > = C 1 2 8 <Ii > + C 1 a s s < 3 , I i >  ! ! !  C U M U L A T I V E ACCOUNTS FOR EACH C A P I T A L COST ALLOWANCE C L A S S cFED>  210  7628 C1 1 2 < I i ) = C 1 1 2 C I i ) + C 1 a s s ( 2 , 1 i ) 7030 C 118(: I i > = C 1 1 6 C I i ) + C 1 a s s ( 1 , I i ) 7040 Edb( I i ) = E d b FED TAX D E P L E T I O N BASE 7050 B c e d b ( I i )=Bcedb EC T A X D E P L E T I O N B A S E 706O BcceC I i )=Bcce(I i ) + C l a s s ( 4 , I i ) 7070 BccdCIi)=Bccd(Ii)+Class(5,1> BC C U M U L A T I V E CAPITAL 7080 Bc 2 8 ( I i ) = B c 2 8 ( I i ) + C l a s s ( 3 , I i ) COST ACCOUNTS 7090 Be12CIi)=Bc12CIi)+Class(2,Ii) 7100 BcIOC I i ) = B c I 0 < I j ) + C l a s s ( 1 , I i ) 7110 ! 7120 FOR K = l TO 5 7130 Total2 =Total2+C1ass(K,Ii > 7140 HEXT K 7150 RETURN 7160 ! 7170 ! ***************************; 7180 SUE-ROUTINE TO C A L C U L A T E T H E F L U M E S Y S T E M O P E R A T I N G COSTS ! 7190 7200 ! 7210 O p e r a t i n g : Opcost1=Opcost2=8 7220 ! 7230 Hi =Data<6, Ii ) 7240 Lo=Data(7,Ii) 7250 GOSUB R a n d o m 7260 Y 1 d = Dat a( 5 , I i ) * S s - ' l . 2*(1+Y1 d s e n s > ! YIELD 7270 ! 7280 Hi =Cost ( 1 , 5 ) 7290 Lo =C o s t ( 1 , 6 ) 7360 GOSUE R a n d o m 7316 Cop<: 1 , l i ) = < C o s t < l , 4 ) + F u e l s e n s * 4 0 + L a b s e n s * 7 3 > * S s . " 1 . » S o p h r * V ! S H O V E L COST: 7320 ! 7330 H i =. 5 7340 Lo=.25 7350 GOSUE R a n d o m 7360 T o p h r = F1ume ( I i , 2 ) * S s ' l . 2 7370 Hi =Cost C 2 , 5 ) 7380 Lo=Cost(2,6) 7390 C o p C 2 , I i ) = ( C o s t ( 2 , 4 ) + F u e l s e n s * 1 8+L a b s e n s * 5 2 ) * S s - ' 1 . 2 * T o p h r » V # < 1 + T c p s e n s ) 74O0 ! 7 4 10 I F C a s e * = " N F " T H E H GOTO O p _ c o s t l 7420 I F I i >1 T H E H GOTO O p _ c o s t l 7430 IF ( C a s e * = " E F " ) OR C C a s e $ = " R F " ) T H E H GOTO 0 p _ c o s t 2 7446 ! ' . 7450 Op_costl: Hi=Cost(15,5) 7466 Lo=Cost(15,6) 7470 GOSUB R a n d o m 7486 ! G R I Z Z L Y DUMP, Loader=CCost(15,4)+Fuelsens*18+Labsens*52)*Ss/1.2 7490 Hi = C o s t ( 1 4 , 5 ) 7566 Lo=Cost(14,6) 7516 GOSUB R a n d o m ! L O A D E R AHD 7526 ! DOZER COSTS Dozer*(Cost(14,4>+Fue1 sens*18 + L a b s e n s * 5 2 ) * S s 1 . 2 7536 Hi=Cost(3,5) 7540 Lo=Cost(3,6) 7550 GOSUB R a n d o m 7568 C o p ( 3 , I i ) = ( C o s t ( 3 , 4 ) * S s - - ' l . 2 * D a t a ( 3 6 , I i ) + Dai.'*Shi f t * ( L o a d e r + D o z e r ) >*V 7576 ! 7588 ! P U M P I N G COST Pmpc s t = Y p r o d / 1 6 0 8 0 0 * 4 * 5 0 7596 Cop(4,Ii )=CPmpcst+Kw*C12*7.17+Day*Factor*24*.8074>>*V 7666 ! 7610 Hi=Cost(9,5> 7628 Lo=Cost(9,6) 7638 GOSUB R a n d o m 7648 ! DEWATERING PLANT C o p ( 5 , I i ) = C o s t ( 9 , 4 ) * S s - ' 1 . 2 * Y p r o d * Y 1 d*V 7656 ! COSTS ! 7668 Hi = C o s t ( 1 0 , 5 ) 7678 Lo=Cost(10,6)  211  GOSUB Random 7680 C o p t 6 , I i ) = C o s t ( 1 0 , 4 > * S s / l . 2*V 7690 ! 7700 FOR C = l TO 6 7710 0 p _ c o s t 2 : Opeostl=0pcost1+CopCC,Ii >*(l+0psens> 7720 NEXT C 7730 I 7740 7750 Hi =Dat a < 1 5 , I i ) 7760 Lo=Data<16,Ii ) 7776 GOSUB Random 7780 C o p < 7 , I i >=Dat aC 1 4 , I i > * S s / l . 2 * V * Y p r o d * Y 1 d 7790 7800 Hi = D a t a < 2 1 , I i ) 7810 Lo=Data<22,Ii) 7820 GOSUB Random 7830 P) a n t = D a t a < 2 0 , I i > * S s / l . 2 * V * Y p r - o d * Y 1 d 7840 C o p < 8 , I i > = P l a n t - C o p < 5 , Ii > 7850 ! 7860 Hi = C o s t < 1 2 , 5 ) 7870 Lo=Cost<12,6> 7880 GOSUB Random 7890 C o p < 9 , I i >=Cost < 1 2 , 4 > * S s / l . 2*Ypr-od*Y1 d*V 7900 i 7910 Hi=Cost<13,5) 7920 L o=Cost < 1 3, 6 ) 7930 GOSUB Random 7940 C o p < 1 0 , I i >=Cost < 1 3 , 4 > * S s / l . 2 * Y p r o d * Y 1 d * V 7950 Rai1=Cop<10, I i ) 7960 I 7970 FOR C=7 TO 10 7980 0 p c o s t 2 = 0 p c o s t 2 + Cop<:C, I i > 7990 NEXT C ! 8000  !  SERVICE  COST  !  OTHER  MINING  !  OTHER  PLANT  !  HEAD  !  RAIL  OFFICE  IF I i >1 THEN GOTO 8 0 3 0 8010 IF C a s e * = " N F " THEN Opcost1=0pcost2=0 8026 RETURN 8030 8040 8656 ************************************* 8060 S U B - R O U T I N E TO C A L C U L A T E THE F E D E R A L CORPORATE INCOME T A X E S 8676 ************************************************************* ****** i 8686 F e d _ t a x e s : Temp = Surn = 0 8696 I 8166 H i =Dat a< 3 1 , I i ) 8116 Lo = D a t a < 3 2 , I i ) 8126 GOSUB Random 8136 I n v e n t o r y = B a t a < 3 0 , I i >*Ss.-'l . 2*V 8146 ! 8156 Hi = D a t a < 9 , I i ) 8166 Lo = Dat a < 1 O , I i ) 8176 GOSUB Random 8180 R e v = D a t a< 8, I i "/ *Ss--' 1 . 2 * V * < 1 +Pr i c e s e n s > 8190 ! 8200 Hi = D a t a < 3 4 , I i ) 8216 Lo = Dat a < 3 5 , I i ) 3220 GOSUB Random 8236 Int=Data<33,Ii>*Ss'l.2*V 8240 I n c o m e = R e v * Y1 d * Y p r o d 8256 8266 F e d t ax ( 1 , I i ) = I nc ome-Opc o s t 1 -Opc o s • t I2n v e n t o r v * . 0 3 8276 T e m p = F e d t ax >.' 1 , I i ) 8286 ! 8296 8360 IF T e m p < . 3 * C 1 1 0 < I i > THEN GOTO Jump 1 8316 Temp=Te mp- . 3*C 1 1 0< I i > 8 320 CI 1 0 = . 3 * C 1 1 O < I i ) 8330 C U O U i +1 ) = . 7*C1 10(1 i )  212  8340 B a c k l : IF T e m p < . 3 * C 1 2 8 < I i > THEN GOTO Jump2 8350 Temp28=.?*C128(Ii > 8360 T e m p = T e m p - . 3*C 1 2 8 ( 1 i > 8370 IF Temp<0 THEN Temp=0 8380 IF I n c o m e < T e m p 2 8 THEN GOTO L a p i n 8390 ! 8400 IF Temp>Temp2S THEN C I 2 3 = C 1 2 8 < I i > 8410 IF Temp>Temp28 THEN C 1 2 3 ( T i + 1 > = 0 8420 IF Temp>Temp23 THEN Temp=Temp-Temp28 8430 IF Temp<Temp28 THEN C 1 2 8 = T e m p + . 3 * C 1 2 8 ( I i> 8440 IF Temp<Temp28 THEN C 1 2 8 ( I i +1 ) =Temp28-Temp 8450 IF T e m p ( T e m p 2 8 THEN Temp=0 8460 GOTO B a c k 2 8470 ! 8480 L a p i n : IF T e m p M n c o m e THEN C 1 2 8 = C 1 2 S ( I i > 8490 IF T e m p M n c o m e THEN C128<Ii+1)=0 8500 IF .Temp > I nc ome THEN Temp = Ternp-Income 8510 IF T e m p < I n c o m e THEN C 1 2 8 = T e m p + . 3 * C 1 2 8 C I i ) 8520 IF Temp<Income THEN C 1 2 8 <Ii +1> = Inc ome-Temp 8530 IF Temp<Income THEN Temp=0 8540 ! 8550 B a c k 2 : IF T e m p < C 1 1 2 < I i > THEN GOTO Jump3 8560 Temp = T e m p - C 1 1 2 < I i ) 8570 CI 12 = 0 1 1 2 ( 1 i > 8580 C112(Ii+l>=0 8590 GOTO Jutnp4 8600 ! 8610 J u m p l : CI 10( I i +1 > = C U 0 ( I i > * . 3-Temp 8620 CI10=Temp 8630 Temp=8 8640 GOTO B a c k l 8650 ! 8660 Jump2: C 1 2 3 ( I i + 1> = C 1 2 8 ( I i )-Temp 8670 CI 28 = Temp 8680 Temp=0 8690 GOTO B a c k 2 8700 ! 8710 Junip3: CI 12( I i + 1 )=C) 12( I i )-Temp 8720 CI12=Temp 8730 Temp=0 8740 ! 8 7 5 0 Jutnp4: F e d t ax ( 2 , I i ) = C1 10 8760 Fedtax(3,Ii)=C112 8770 Fedtax(4,Ii)=C128 S730 Fedt a x ( 5 , I i ) = (Fedt ax(1,Ii)-C110-C112-C128 > * . 7 5 8790 IF Temp=0 THEN GOTO Jump7 83O0 Temp = F e d t a x ( 5 , I i >-Int 8810 ! 8820 IF T e m p < C c e ( I i > THEN GOTO Jump5 8830 Temp=Temp-Cce(Ii> 8840 Cce=Cce(Ii> 8850 Cce(li+1>=0 8860 ! 8 8 7 0 B a c k S : IF T e m p < . 3 * C c d ( I i > THEN GOTO Jump6 8880 Temp = T e m p - . 3 * C c d ( I i > 8890 Ccd=.3*Ccd( I i > 890O Ccd(li+1>=0 8910 GOTO Jump7 8920 ! S930 Jumps: Cce(Ii+1>=Cce(Ii>-Temp 8940 Cce=Temp 8950 Temp=0 8960 GOTO B a c k S 8970 ! 8980 Jump6: C c d ( I i + 1> = . 3 * C c d ( I i ) - T e m p 8990 Ccd=Temp  ! RESOURCE  ftLLOWRNCE  213  90Q0 9O10 9020 9O30 9040 9050 9060 9070 9080 9090 9100 9116 9120 9130 9140 9150 9160 9170 9180 9190 9200 9210 9220 9230 9240 9250 9260 9270 9230 9298 9300 9318 9320 9330 9340 9358 9368 9378 9386 9396 9468 94 16 9428 9436 9448 9456 9466 9476 9486 9498 9566 9518 9526 9536 9546 95 56 9566 9570 9580 9596 9686 9616 9626 9636 9646 9656  Temp=0 ! Jump?: Fedt a x ( 6 , I i ) = I nt Fedt ax(7, I i ) = Cc d Fedt a x ( 8 , I i > = Cc e ! Sum=Fedtax(5,Ii>-Int-Ccd-Cce ! RESOURCE PROFIT IF <Sum<0> OR <Sum=0> THEN GOTO Jump9 IF Sum*.25>Edb THEN GOTO Jump8 IF Surn*.25<Edb THEN Fedt ax ( 9, I i > =. 25*Sum Edb=Edb-.25*Sum GOTO Jump 10 JumpS: Fedt ax ( 9,Ii)=Edb Edb=0 GOTO Jump 10 Jump9: F e d t a x < 9 , I i >=0 JumpIO: IF <Sum = 0> OR CSum<0> THEN Fedt ax <10,Ii > =0 ! TAXABLE INCOME IF Sum>e THEN FedtaxC1O,Ii>=Sum-Fedtax(9,Ii> Fedtax(11,Ii>=FedtaxC1O,Ii>*.36 ! TAX PAYABLE ! Itc1=.07*C1ass(1,Ii> Itc2=15OO0+(FedtaxC11,II)-150O0)/2 IF I t c l < I t c 2 THEN I n t a x = I t c l IF I t c l > I t c 2 THEN I n t a x = I t c 2 Itc=Itc+Intax IF Ii>5 THEN I t c = I t c - I t c ( I i - 5 > IF Itc<6 THEN Itc=0 ! IF F e d t a x ( 1 1 , Ii J = 0 THEN GOTO Notax IF Fedt ax (11 , 1 i X H c THEN GOTO Invest ! Fedt a x ( 1 2 , I i > = 11 c Itc=8 I t c ( I i >=6 Fedt ax(13, I i > =Fedt ax(11, Ii >-Itc GOTO Hop-skip ! Invest: Fedtax<12,Ii)=Fedtax(11,Ii> Itc=Itc-Fedtax(12,Ii> I t c ( I O = Itc Fedtax(13,Ii>=8 GOTO Hopskip ! Notax: F e d t a x ( 1 2 , I i > =8 Itc ( I i > = Itc Fedtax(13,Ii>=6 ! Hopskip: C118(Ii+1)=C116(Ii+1>-Fedtax(12,Ii> IF C118(Ii+l><8 THEN C116(Ii+l>=6 Be 1 8 ( I i + 1) = B c 1 6 ( I i +1>-Fedt a x ( 1 2 , I i > IF B c l 0 < l i + 1><0 THEN B c l 8 ( I i + n=6 ! IF F e d t a x ( 1 3 , I i > < 8 THEN F e d t a x ( 1 3 , I i > = 6 RETURN ! ! **************************** ! SUB-ROUTINE TO COMPUTE EC CORPORATE AND MINING INCOME TAXES ! ********************^^ ! B c _ t a x e s : Ttemp=Sum2=Sum3=8 Royalty=.835*(Income-Rai1) Be t ax (1 , I i > = I nc ome-Opc ost'l -Ope ost 2-Royal t y-1 nvent c r y * . 63 Be mt ax(1, Ii > = Bc t ax(1, I i ) ! Tte(np = Bcmtax( 1, I i > IF Ttenip< . 3*Bcl0CI i > THEN GOTO Jump 11  214  9660 Ttemp=Ttemp-.3*BcIOC I i > 9670 Be10=.3*Bc10CIi> 9680 BcIOCIi+1>=.7*Bc10<Ii> 9690 ! 9 7 0 0 Back 1 1 : IF T t e m p < . 3 * B c 2 8 C I i > THEH GOTO J u m p l 2 9710 Ttemp28=.7*Bc28<Ii ) 9720 Tternp = T t e m p - . 3 * B c 2 8 < I i ) 9730 IF I n c o m e < T e m p 2 8 THEH GOTO L a p i n S 9740 ! 9750 IF T t e m p > T t e m p 2 8 THEH B c 2 3 = B c 2 8 C I i > ' 9760 IF T t e m p > T t e m p 2 8 THEH B c 2 8 C I i + 1 > = 0 9770 IF T t e m p > T t e m p 2 8 THEH T t e m p = T t e m p - T t e m p 2 8 9780 I F T t e m p < T t e m p 2 8 THEH B c 2 8 = T t e m p + . 3 * B c 2 8 C I i > . 9790 IF T t e m p < T t e m p 2 3 THEH B c 2 8 ( I i +1 > = T t e m p 2 8 - T t e m p 9800 IF T t e m p < T t e m p 2 3 THEH T t e m p = 0 9810 GOTO Back 14 9820 ! 9 3 3 0 L a p i r i 3 : IF T t emp> I ncome THEH B c 2 3 = Bc28< I i > 9840 IF T t e m p > I n c o m e THEH B c 2 8 < I i + 1 > = 0 9858 IF T t e m p > I n c o m e THEH T t e m p = T t e m p - I n c o m e 9868 IF T t e m p < I n c o m e THEH B c 2 8 = T t e m p + . 3 * B c 2 8 < I i ) 9878 I F T t e m p < I n c o m e THEH B c 2 8 < I i + 1 ) = I n c o m e - T t e m p 9880 IF T t e m p < I n c o m e THEH T t e m p = 6 9898 ! 9 9 0 0 Back 1 2 : IF T t e m p < B c 1 2 < I i ) THEH GOTO Jump 13 9916 T t emp = T t e m p - B c 1 2 <Ii > 9926 Bc12=Bc12<Ii> 9938 Bcl2(Ii+n=6 9946 ! 9 9 5 8 Back 1 3 : IF T t e m p < B c c e < I i > THEH GOTO Jump 14 9966 Ttemp = T t e m p - B c c e C I i > 9978 Bcce=Bcce<Ii) 9988 BcceCIi+1>=8 9998 ! 1 8 8 0 8 Back 1 4 : IF T t e m p < . 3 * E c c d < I i ) THEH GOTO J u m p l S 18816 T t emp = T t e m p - . 3 * B c c d < I i > 16828 B c c d = B c c d < I i > 16636 Bccd<Ii+l)=6 18646 GOTO Jump 16 10650 ! 16066 J u m p l l : Bc10< I i + 1 > = B c 1 0 < I i > * . 3 - T t e m p 10876 B c l O = T t e m p 16686 T t e m p = 8 16896 GOTO Back 11 1O10O ! 1011O J u r n p l 2 : B c 2 8 ( I i +1 >=Bc2S< I i ) - T t e m p 1O120 B c 2 8 = T t e m p 1013O T t e m p = 8 1 6 1 4 6 GOTO E a c k l 2 10156 ! 10168 J u m p l S : B c 1 2 C I i +1> = B c 1 2 < I i > - T t emp 16176 B c l 2 = T t e m p 18186 T t e m p = 6 18196 GOTO Back 13 10286 ! 16218 Jump 1 4 : Bc c e < I i + 1 > = Ec c e < I i ':>-Tt emp 18228 B c c e = T t e m p 16238 T t e m p = 8 16240 GOTO B a c k l 4 18258 ! 18268 J u m p l S : BccdCIi+1)=.3*BccdCIi>-Ttemp 18278 B c c d = T t e m p 18288 Ttemp=6 18298 ! 18380 J u m p l S : Bctax<2,Ii)=Bc18 1O310 BcmtaxC2,Ii)=Bc10  215  10320 10330 10340 1O350 10360 16370 10380 1O390 10400 10410 10420 10430 10440 10450 10460 10470 10480 10490 10500 10510 10520 10530 10540 10550 10560 10570 10580 10590 10600 10610 10620 10630 10640 10650 1066O 10670 1068O 10690 10700 10710 10720 1073O 10740 10750 10760 10770 10780 10790 1 0800 10810 10820 1083O 1084O 1035O 1086O 10870 10880 10890 10900 10910 1092O 10930 10940 10950 1096O 10970  Bctax(3,Ii)=Ec12 B c m t a x ( 3 , I i )=Bc12 Be t ax ( 4 , I i ) = B c 2 8 Bcmtax(4,Ii)=Bc28 B e t a x ( 6 , I i ) = Int B c m t a x ( 6 , I i ) = Int B e t a x ( 7 , I i )=Bcce B c m t a x ( 7 , I i ) = Bcce B c t a x ( 8 , I i >=Bccd Bcmtax(8,Ii)=Bccd ! Sum2=Bctax(1,Ii >-Be 10-Bc12-Bc28-Bcce-Becd-I nt IF (Sum2<0) OR (Sum2=0) THEN GOTO Jump 18 IF Sum2x4>Bcedb THEN GOTO Jump 17 IF Sum2-'4<Bcedb THEN Be t ax ( 9, I i > =Sum2 .-'4 Bcedb=Bcedb-Sum2/4 GOTO Jumpl.9 Jumpl7: B c t a x ( 9 , I i ) = B c e d b Bcedb=8 GOTO Jumpl9 Jump 18: Be t a x ( 9 , I i > =0 Jump 19: IF (Sum2<0) OR (Sum2=0) THEN E c t a x ( 1 0 , I i IF Sum2>0 THEN Be t ax(10, I i )=Sum2-Bctax(9,Ii ) B c t a x ( 1 1 , I i ) = . 16*Ectax(IO, I i ) I  Sum3=Bcmtax(1,Ii )-Bc10-Bc12-Bc28-Bccd-Bcce-Int IF Mi 1 1 *. 0S< . 15*Sum3 THEN Bemtax(9, I i ) =Ni 1 1 *. 08 IF Mi 11 *. 08 >. 15*Sum3 THEN Bemtax(9,Ii)=.15*Sum3 Bcmtax<10,Ii)=Sum3-Bcmtax<9,Ii) Be mt. ax C 1 1 , I i ) = M 5*Ec mt ax (1 O, I i ) ! RETURN i  ! TAXABLE  INCOME  ! BC CORPORATE TR>  ! TAXABLE INCOME ! BC MINING TAX  SUB-ROUTINE TO CALCULATE THE PROJECT ECONOMICS  ! !  *********  t************************j  Npv:Npv=Np=0 RED IM N p v ( I t e r ) , I r r ( I t e r ) IF J j M THEN GOTO Jumper2 PRINT L I N ( 3 ) , " ****************** PRINT " THE NET PRESENT VALUE AND IRR ARE BEING COMPUTED' PRINT " **************************** INPUT "ENTER THE CORPORATE HURDLE RATE PER PERIOD (as a dec i ma))",R ! Jumper 2:Negat i ue=1 Pos i t i ve=.05 P=(Negatiye-Positiwe)/2 Count er = 1 !  A g a i n : FOR K=l TO P e r i o d Np=Np+Cash(10,K)/(1+P)-K IF C o u n t e r > l THEN GOTO Jump29 Hpu = Npv + Cash(IO, K)/(1+R)-K Jump29: NEXT K Count er =Count er + 1 !  IF IF IF P= !  AES(Np)<25000 THEN GOTO JumpSO Np<0 THEN Negative=P Np>0 THEN P o s i t i v e = P (Negat i ue-Pos i t i ve)x2 + Pos i t i ve  IF C o u n t e r MOO THEN PRINT LINC5) "ERROR IN NPV IF Counter>100 THEN WAIT 1000 IF C o u n t e r ) 1 0 0 THEN GOTO Cont !  CALCULATION'  216  0 9 8 0 Np=© 0 9 9 0 GOTO A g a i n 1OO0 J u m p S O : N p v < J j ) = Npv 101O I r r < J j > = P 1O20 P R I N T L I N < 2 0 ) 1030 C o n t : RETURN 1040 ! 105O ! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1060 ! C O N T R O L L I N G S T A T E M E N T S FOR COMPUTING T R U C K / S H O V E L HAULAGE ECONOMIC 1070 ! ************************** 108O ! 109O T r u e k s h o v e 1 : T o p h r = T o t a l _ c a p = 0 1100 REDIM C c a p < 6 , P e r i o d ) , C o p < 7 , P e r i o d ) 1110! 1120 Yprod=Data<4,Ii) 1130 ! 1140 Day=Data<23,Ii) 1150 S h i f t = D a t a < 2 6 , I i ) 1 160 V t e m p = l + D a t a < 1, I i )*< 1 + I n f s e n s ) 1170 V = V * V i e m p 1180 ! 1190 ! 120O ! * * * * * * * C A L C U L A T E SHOVEL O P E R A T I N G AND C A P I T A L PARAMETERS * * * * * * * 1210 ! 1220 H i = T c o s t < 5 , 2 ) 1230 L o = T c o s t ( 5 , 3 ) 1240 GOSUB Random 1250 S p r o d = T c o s t <5, 1 ) * S s - ' l . 2 1260 S o p h r = Y p r o d / S p r o d 1270 ! 1280 H i = T c o s t ( 1 0 , 5 ) 1290 L o = T c o s t < I O , 6 ) 1300 GOSUB Random 1310 S u t i 1 = T c o s t < I O , 4 ) * S s - ' l . 2 1320 S h o v e 1 s = S o p h r / < . 2 4 * D a v * S u t i 1 ) 1330 ! 1340 G = S h o v e l s 1350 IF F R A C T C G X . 2 THEN G = G+1 1360 S h o v e l s = I N T < G ) 1370 ! 1380 ! 1390 ! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1400 ! TRUCK AND SHOVEL O P E R A T I N G AND C A P I T A L COSTS ARE B E I N G C A L C U L A T E D 1410 ! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1420 ! 1430 ! 1440 O p c o s t l = O p c o s t 2 = T o t a l = 0 1450 ! 1460 H i = T c o s t < 1 , 2 ) 1470 L o = T c o s t < 1 , 3 ) 1480 GOSUB Random 1490 C c a p < 1 , I i ) = T c o s t < 1 , 1 ) * S s / l . 2 * S h o v e 1 s * V 150O IF C o a l = 8 THEN C c a p C l , I i ) = 0 1510 ! 1520 Hi = T c o s t <'2, 2 ) 1530 L o = T c o s t < 2 , 3 ) 1540 GOSUB Random 1550 C c a p C 2 , I i ) = T c o s t <2,1)*Ss/l.2*Truck <Ii,3)*V 1560 IF C o a l = 0 THEN C c a p < 2 , I i ) = 0 1570 ! 1580 ! 1590 ! ******* SORT THE C A P I T A L COSTS BY C L A S S E S ******* 1600 ! 1616 ! ' 1 ' FOR C L A S S 10 A S S E T S 1620 ! ' 2 ' FOR C L A S S 12 A S S E T S 1630 ! ' 3 ' FOR C L A S S 28 A S S E T S  217  ' 4 ' FOR CANADIAN E X P L O R A T I O N E X P E N S E . 1648 ' 5 ' FOR CANADIAN DEVELOPMENT E X P E N S E .1650 . 1 660! 1670 IF Hat a':: 3 7 , I i ) = 1 THEH C1 a s s C 3 , I i > = C1 a s s < 3 , I i > + C c a p C 1 , I i ) ! SHOVEL 1680 IF D a t a C 3 7 , I i ) = 0 THEN C1 a s s ( 1 , I i > =C1 a s s < 1 , I i > + C c a p C 1 , I i > 1690 IF Dat aC 37 I i >= 1 THEH E d b = E d b + . 3 3 3 * C c a p < 1 , I i > 1700 IF D a t a t 37 I i >= 1 THEH B c e d b = E c ? d b + . 3 3 3 * C c a p ( 1 , I i ) 1710 ! 1720 IF D a t a C 3 7 , I i > = 1 THEH C I a s s < 3 , I i ) = C 1 a s s C 3 , I i > + C c a p C 2 , I i > ! TRUCKS 1730 IF D a t a t 3 7 , I i ) = 0 THEH CI a s s a , I i >=C1assC1,Ii>+CcapC2,Ii > . 1 7 4 0 IF D a t a C 3 7 , I i ) = 1THEN E d b = E d b + . 3 3 3 * C c a p C 2 , I i > . 1 7 5 0 IF D a t a C 3 7 , I i ) = 1 THEN B c e d b = B c e d b + . 3 3 3 * C c a p C 2 , I i > 1760 ! 1770 Hi D a t a C 1 2 , I i ) 1780 Lo D a t a C 1 3 , I i > 1790 GOSUB Random 1800 C c a p < 3 , I i >=Dat iC 1 1 , ) I* iS s / l . 2 * V ! OTHER MINING 1810 IF D a t a C 3 7 , I i > =1 THEH C I a s s C 3 , I i > = C 1 a s s C 3 , I i > + C c a p C 3 , I i > 1820 IF D a t a C 3 7 , I i ) •O THEH CI a s s C 1 , I i ) = C 1 a s s C 1 , I i > + C c a p C 3 , I i ) . 1 8 3 0 IF D a t a C 3 7 , I i ) = 1 THEH E d b = E d b + . 3 3 3 * C c a p ( 3 , I i > . 1 3 4 0 IF D a t a C 3 7 , I i ) =1 THEH B c e d b = B c e d b + . 3 3 3 * C c a p C 3 , I i > 1850 ! I 8 6 0 Hi = D a t a C 1 8 , I i ) 1870 L o = D a t a C 1 9 , I i ) 1880 GOSUB Random 1890 C c a p < 4 , I i ) = D a t a c 1 7 , I i > * S s / l . 2 * V ! OTHER PLANT 1900 IF D a t a C 3 7 , I i ) =1 THEH C1 a s s C 3 , I i > = C 1 a s s C 3 , I i > + C c a p C 4 , I i ) 1910 IF D a t a C 3 7 , I i >=0 THEH C I a s s C 1 , I i > = C 1 a s s C 1 , I i > + C c a p C 4 , I i ) 1920 E d b = E d b + . 3 3 3 * C c ap C 4 , Ii > 1 930Bc e d b = Bc e d b + . 3 3*Cc ap ( 4 , I i > 1940 IF D a t a C 3 7 , I i > 1 THEH Mi 1 1 = M i 1 1 + C c a p C 4 , I i > 1950 I I 9 6 0 Hi = D a t a C 3 9 , I i > 1970 L o = D a t a C 4 0 , I i > 1980 GOSUB Random . 1990 Cc ap C 5, Ii > = Dat aC 3 8 , I i > 1.2*V EXPLORATION 120OO IF D a t a C 3 7 , I i ) =1 THEH C 1 a s s C 3, I i > =C1 a s s C 3 , I i ) + C c a p CI i5,) . 2 0 1 0 IF D a t a C 3 7 , I i > =0 THEH C 1 a s s C 1 , I i > =C1 a s s C 1 , I i >+Cc ap CI 5, i > D a t a C 3 7 , I i ) =1 THEN E d b = E d b + . 3 3 3 * C c a p C 5 , I i > 2 0 2 0 IF 2 0 3 0 IF D a t a C 3 7 , I i > =1 THEN B c e d b = B c « d b + . 3 3 3 * C c a p C 5 , I i.)  2040 12050 Hi = D a t a C 2 3 , I i ) 12068 L o = D a t a C 2 9 , I i ) 12070 GOSUB Random 2680 C c a p C 6 , I i ) = D a t a C 2 7 , I i > * S s / l . 2 * V ! CAP. INTEREST 2090 IF D a t a C 3 7 , I i > = 1 THEN C 1 a s s C 3, I i ) = C 1 a s s C 3, I i > + C c a p C 6 , Ii > 2160 IF D a t a ( 3 7 , I i ) = 0 THEN CI a s s C 1 , I i > = C 1 a s s C 1 , I i > + C c a p C 6 , Ii > 12 1 1IF © D a t a C 3 7 , I i > = 1 THEH E d b = E d b + . 3 3 3 * C c a p C 6 , I i > 12120 IF D a t a C 3 7 , I i > = 1 THEH B c e d b = E c e d b + . 3 3 3 * C c a p C 6 , I i > :130 L2140 FOR J = l TO 6 !150 Total_cap =Total_cap +CcapCJ,Ii > HEXT J L2170 ! C U M U L A T I V E ACCOUNTS FOR : I s 0 C1 a s s i fy 1: Cce C I i > + C l a s s C 4 , Ii Cc e C I i > ! EACH C A P I T A L COST 12190 C c d C I i ) = C c d C I i >+Cl s s C 5, I i > ! ALLOWANCE C L A S S C FED > 220O C 1 28C I i > =C 1 2 8 C I i > +C1 a s s C 3 , I i > 2210 CI 1 2 C I i > = C 1 1 2 C I i ) + C l a s s C 2 , I i > 12220 C U O C I i ) = C 1 1 0 C I i ) + C l a s s C l , I i > ! FED TAX D E P L E T I O N BASE 2 2 3 0 E d b C I i >=Edb BC TAX D E P L E T I O N EASE 2240 B c e d b C I i ) = B c e d b ******************** 1 2 2 5 0B c c c C I i ) = B c c e C I i > + C l a s s C 4 , I i > BC C U M U L A T I V E C A P I T A L i<:260 B c c d C I i ) = E c c d C I i > + C l a s s C 5 , n COST ACCOUNTS 12278 B c 2 8 C I i ) = B c 2 8 C I i ) + C l a s s C 3 , I i > ?280 B c 1 2 C I i ) = E c 1 2 C I i ) + C l a s s C 2 , I i ) i2290 Bc10CIi > = BcISC I i ) + C l a s s C 1 , I i )  ne©  218  123O0 12310 12320 12330 12340 12350 12360 12370 12380 12390 12400 12410 12420 12430 12440 12450 12460 12470 12480 12490 12500 12510 12520 12530 12540 12550 1 2560 12578 12580 12590 1260O 12610 1 2620 12630 12640 12650 12660 12670 12680 12690 12708 12718 12720 12730 12740 12750 12760 12770 12780 12790 128O0 12810 12820 12830 12840 12850 12860 12870 12880 12390 12900 12910 12920 12930 12940 12950  ! FOR. K=l TO 5 Total=Total+C1assCK,Ii) NEXT K ! ! ******* OPERATING COSTS ******* ! Opcostl=Opcost2=0 ! Hi = D a t a < 6 , I i > Lo=Data<7,Ii > GOSUB R a n d o m Y l d = D a t a < 5 , I i >*Ss/l.2*<1+Y1 dssns> ! Hi=Tcost<1,5> Lo=Tcost<1,6> GOSUB R a n d o m C o p U , I i > = < T c o s t < 1 , 4 > + F u e l s e n s * 4 0 + L a b s e n s * 7 3 > *Ss<" 1 . 2 * V * S o p h r - ! C O A L L O A D E R ! Hi=.5 Lo=.25 GOSUB R a n d o m Tophr=Truck <I i , 2)*Ss/"l . 2 Hi=Tcost<2,5> Lo=Tcost(2,6> GOSUB R a n d o m C o p ( 2 , I i ) = < Tc o s t ( 2 , 4 ) + F u e 1 s e n s * 3 0 + L a b s e n s * 5 ? > * S s . < ' 1 . 2 * V * T o p h r * < 1 + T o p s e n s > Cop < 3 , I i ) = ( 5 0 0 0 0 0 + F u e 1 s e n s * 1 9 + L a b s e n s * 5 2 ) * V ! ROAD M A I N T E N A N C E ! Hi = D a t a < 1 5 , I i > Lo =D a t a < 1 6 , I i > GOSUB R a n d o m ! OTHER M I N I N G INCL. C o p (. 4 , I i > : = D a t a< 1 4 , I i > * S s - ' 1 . 2 * Y p r o d * Y 1 d*V ! H i =Dat a < 2 1 , I i > Lo=DataC22,Ii) GOSUB R a n d o m C o p < 5 , I i ) = D a t a< 2 0 , I i > * S s - ' 1 . 2 * V* Y 1 d * Y p r o d ! OTHER P L A N T ! Hi=Tcost<3,5> Lo=Tcost<3,6> GOSUB R a n d o m Cop<6, Ii >=Tcost<3, 4>*Ss/1.2*V*Y1d*Yprod ! HEAD OFFICE ! Hi=Tcost<4,5> Lo=Tcost<4,6> GOSUB R a n d o m Co p < 7 , I i ) =T c o s t ( 4 , 4 > *S s / 1 . 2 *V * Y1d * Yp r o d ! RAIL Rai1=Cop(7,Ii > ! FOR C=l TO 3 O p c o s t l = 0 p c o s t l + C o p < C , I i >*<l+0psens> NEXT C ! F O R C=4 TO 7 0 p c o s t 2 =0 p c o s t 2 +C o p < C , I i > NEXT C ! I F I i > l T H E N GOTO T a x IF C a s e * * " N T " THEN O p c o s t 1 = 0 p c o s t 2 = 0 Tax: GOTO T a x e s ! ! . ! ********************************************************************** ! S U B - R O U T I N E TO P R I N T A T A B L E OF R E S U L T S ! **********************************************************************  219  297O 2980 2990 3000 3010 3020 3030 3040 3O50 3068 3878 3888 3898 3180 3118 3128 3136 3148 3150 3160 3170 31S0 3198 TION" 3268 TION" 3216 3226 3238 3246 3258 3260 3278 328O 3290 3380 3310 3328 3336 3348 3356 3360 3378 3388 3396 3488  ,E+I;  ! T a b 1 se: DIM fi* U 6 , 1 ) C 26 ] , E* < 1 1 , 1 ) C 28 3 , C * < 1 3 , 1 > [ 26 3 DIM fi a * C 2 0 3 fi*< 1 1) , = " A N N U A L PRODUCT I ON" R*<2, 1)="GROSS REVENUE" COST" fi * < 3 1 , ) = " C 0 A L TRANSPORT A * < 4 , 1>="0THER O P . C O S T S " PAYMENT" fit ( 5 ,1> = "ROYftLTY INCOME T A X " A*<6, 1>="FED. fi * <: 7,1>="EC INCOME T A X " fit<8, 1 ) = " B C MINING T A X " A*<9, 1)="T0TAL CAPITAL COST" A*< 18 , 1 ) = " H E T CASH FLOW" REDIM C a s h t 1 8 , 1 8 ) F=16 !  FOR J = l TO 7 IF 1 - P e r i od-'5<8 THEN REDIM C a s h < 1 8 , < J +1 >*5) IF 1 - P e r i o d ' 5 < 6 THEN GOTO P r i n t l OR < 1 - P e r i o d ^ 5 = 0 ) THEN GOTO P r i n t l IF O - P e r i o d < - " 5 > 6 ) NEXT J ! P r i n t l : P R I N T E R IS F IF <C a s e * = " N F " ) OR < C a s e * = " E F " ) OR C C a s e * = ' R F " ; ' THEN fia* = " FLUME IF  C C a s e * = " N T " > OR < C a s e * = " E T " )  OR < C a s e * = " R T " )  TRANSPORTA  THEN fia* = "TRUCK  TRANSPORTA  E=l Per = P e r i od/S IF P e r i o d < 5 THEN FIXED O  Per=l  I  PRINT L I N < 2 ) IF <C a s e * = "NF"';' OR C C a s e * = " N T " > THEN PRINT TAB < 36 > , "NEW MINE C A S E " IF <C a s e * = " E F " > OR < C a s e * = " E T " > THEN PRINT TAB<27),"EXPANDING MINE C A S E " IF <C a s e * = " R F " ) OR CCase*="RT") THEN PRINT T A B C 2 6 ) , " T R U C K REPLACEM'T CASE" PRINT T A E U 7 ) , MEAN V A L U E S ONLY i FOR K = l TO P e r PRINT LIH<5) , ' CASH FLOW SUMMARY FOR " ; A a * PRINT " < a l l amounts i n c u r r e n t C a n a d i a n * )' PRINT L I N C 1 ) , '  —  PRINT PRINT  TAB<24);E;TAB<36);E+l;TAB(48);E+2;TAB(66);E+3;TfiB<72);E+4 " ",LIN<1)  ! FOR L = l TO 10 P R I N T USING " 2 0 f i , 9 D , 3 X , 9 D , 3 X , 9 D , 3 X , 9D , 3 X , 9D " ; fi*<:L, 1 ) , C a s h C L , E ) , Cash< . C a s h C L , E + 2 ) , C a s h C L , E + 3 ) , C a s h ( L , E + 4) NEXT L i E =E+5 P R I N T E R IS 16 P R I N T L INC 1 ) , " P R E S S ' C O N T ' " PAUSE P R I N T E R IS F NEXT K  34 18 3428 3436 3448 3456 3466 3478 34S6 3498 3 5 6 6 PRINT L I N C 2 ) , " TE OF R E T U R N " 3 5 1 0 PRINT " 3520  PRINT  3530 3540  PR I NT !  DISCOUNT RATE  NET P R E S E N T VALUE  VALUE  INTERNAL OF  RETURN  LINO) US ING  " 8 X , D D . D D , 1 2 X , 8 D , 2 4 X , D D . D D " ; R * 1 O O , N p w < 1 1 e r ) , I r r <11 e r ) * 1OO  Rfi  220  3550 3560 3570 3580  IF S e r i s * = " N " THEH GOTO H r d c p y PRINT L I N ( 2 > FOR S j = l TO 8 FIXED 3 1 THEH PRINT T A B ( 2 5 )  3600 Sj > 3610 3620 3630 3640 3650  THEH  PRINT  TAB<25)  3 THEH  PRINT  TABC25)  Sr-ef ( 1 , S j >4 = THEH S r e f < l , S j ) = 5 THEH S r e f a , S j ) = 6 THEH S r e f < l , S j ) = —f THEH  PRINT PRINT PRINT PRINT  TAB(25) COAL P R I C E S E N S I T I V I T Y " TAB(25) INFLATION S E N S I T I V I T Y * TAB(25) F U E L COST S E N S I T I V I T Y " T A B ( 2 5 ) , " L A B O U R COST S E N S I T I V I T Y '  ii  IF IF IF IF  1  ';sref  ";Sref< ' ; S r e f (2 Sref<2, Sref < -ef C  3660 8 THEH P R I N T T A B ( 2 5 ) 'U/G CONSTRUCT I OH COST S E N S I T I V I T Y Sref (2,Sj) 3670 9 THEH P R I N T T A E < 2 5 ) 'TRUCK P R O D U C T I V I T Y S E N S I T I V I T Y " IF Sref(l,S ef (2, 3 6 8 0 HEXT Sj 3690 FIXED 0 370O ! 3710 H r d c p y : INPUT " E N T E R ' O ' IF YOU WISH A HARDCOPY OF THE R E S U L T S " , F 3 7 2 0 IF F=0 THEN GOTO P r i n t l 3 7 3 0 P R I N T E R IS 16 3 7 4 0 RETURN 3750 3760 ********************************** ******** 3770 S U B R O U T I N E TO C A L C U L A T E FREQUENCY HISTOGRAMS 3788 ********************************************************** 3790 3388 S t a t s : Haxnpv=l 3818 M i nnpv =10000000088 3 8 2 8 Max i r r = 8 3838 M i n i r r = 1 3848 ! 3858 FOR A = l TO I t e r 3S60 IF Hp'.-'< A) >Maxnpv THEH H a x n p v = Hp v ( A ) 3870 IF H p v ( A X M i n n p u THEH Mi n n p v = N p v C A ) 3888 IF I r r ( A ) > M a x i r r THEH M a x i r r = I r r ( A ) 3898 IF I r r ( A X M i n i r r THEH M i n i r r = I r r ( A ) 3988 HEXT A 3918 i 3928 I nt e r v n p v = ( M a x n p c - M i n n p c ) •-' 16 3938 I n t e r u i r r = ( M a x i r r - M i ni r r ) / 1 6 3940 Max=Maxl=6 3958 T e m p n p v = Mi n n p v + I n t e r v n p v 3968 T e m p i r r = Mi n i r r + I n t e r v i r r 3976 I 1 o=M i n i r r 3988 H 1 o=M i nnp u 3998 I 4888 FOR A=l TO 18 4618 Count=6 4628 FOR B=l TO I t e r 4638 IF N p v ( B X N 1 o THEH St a t j u m p 4646 IF H p v < B)> T e m p n p c THEH S t a t j u m p 4856 C o u n t = C o u n t +1 4868 IF M a x < C o u n t THEH M a x = C o u n t 4 6 7 6 St a t j u m p : HEXT B I 4886 4090 N p v h i s t ( 1, A ) = T e m p n p v - 1 n t e r v n p v / 2 4168 Npvhi st (2, A)=Count 4116 N1 o = T e m p n p v 4 126 Tempnpv = T empnpv+ I nt er v npv 4 1 36 HEXT A i 4146  221  14150 FOR A = l TO 10 14160 Count = 0 14170 FOR B = l TO I t e r 14 180 IF I r r < B X I l o THEN S t a t j u m p l 14 190 IF I I T <B)>Tempi I T THEN S t a t j u m p l 14200 C o u n t =Count +1 14210 IF M a x 1 < C o u n t THEN M a x l = C o u n t 14220 S t a t j u m p l : NEXT B 14230 14 2 4 0 I r r h i s t < 1 , A ) = Temp i r r - I n t e r v i r r / 2 14250 Irrhi st(2,A)=Count 14260 I 1o = Temp i r r 14270 Temp i r r = Tempi r r + I n t e r v i r r 14280 NEXT A 14290 ! 14300 RETURN 14310 I 14320 ***************** 14330 SUBROUTINE TO PLOT THE HISTOGRAMS 14340 *******************< ************************* 14350 14360 ot1:DIM T e x t 1 * [ 2 5 ] , T e x t 2 * [ 1 0 ] , T e x t 3*C30],Text 4*C20],Text 5*[30],Text 6*[30 ] 14370 14380 14390 1 4400 14410 14420 14430 14440 14450 14460 1 4470 14480 1 4496 14500 14 510 14 520 14530 14540 14550 14560 14570 14530 14590 1 4600 14610 14620 14630 14640 14650 14660 14670 14680 1.4690 14700 14710 14720 14730 14740 14750 14760 14770 14780 14790  PRINT LINC 2 0 ) FIXED O T e x t 1* = "NET PRESENT V A L U E " Text 2$="FREQUENCY" Text3*=" HISTOGRAM O F " T e x t . 4 * = " H E T PRESENT V A L U E S " T e x t 5* = " I N T E R N A L R A T E S OF R E T U R N " T e x t 6 * = " I N T E R N A L RATE OF R E T U R N " T e x t ? * = " < x $ 1 , 0 0 0 , 000 V ! Repnpw: E X I T GRAPHICS P L O T T E R IS " G R A P H I C S " P R I N T L I N O 5 ) , " T H E MAXIMUM FREQUENCY IS","Max PRINT " THE MINIMUM NET PRESENT VALUE IS";Minnpv PRINT " T H E MAXIMUM NET PRESENT VALUE IS";Maxnpv INPUT " E N T E R THE MAXIMUM FREQUENCY VALUE FOR THE NPV P L 0 T " , T m a x INPUT " E N T E R THE MINIMUM VALUE FOR THE NPV PLOT ( i n mi 11 i o n s ) " , T m i n n p v INPUT " E N T E R THE MAXIMUM VALUE FOR THE NPV PLOT ( i n m i 1 1 i oris) " , T m a x n p v PRINT L I N C 2 0 )  I  DEG GRAPHICS LOCATE 2 0 , 1 1 0 , 0 , 8 0 FRAME CSI2E 3 LORG 1 MOVE 4 8 , 5 LABEL T e x t l * CSI2E 4 MOVE 5 0 , 7 0 LABEL T e x t 3 * MOVE 5 0 , 6 5 LABEL T e x t 4 * MOVE 5 3 , 6 0 LABEL T e x t 7 * CSI2E 3 L D I R 90 LORG 5 MOVE 2 5 , 4 0 LABEL Text2$ CSI2E 3 LOCATE 33,100,13,65  222  14800 SCfiLE Tminnpw,Tmaxnpv,0,Tmax 14810 L A X E S ( T m a x n p v - T m i nnp v > / 1 0 , T m a x ' 5 , Tm i n n p v , O , - 1 , 1 14820 ! 14830 FOR 1=1 TO 10 14840 MOVE N p v h i s t ( 1 , I ) / 1 8 0 O 0 0 O , N p v h i s t ( 2 , I ) 14850 LABEL " + " 14860 NEXT I 14370 Hc*="N" 14880 INPUT "DO YOU WANT A HARDCOPY? ( Y / N ) " , H e * 14890 IF H c * = " Y " THEN DUMP G R A P H I C S 14900 Rep*="N" 14910 INPUT "DO YOU WISH TO TRY A G A I N ? < Y / N ) " , R e p * 14920 IF R e p * = " Y " THEN GOTO R e p n p v 14930 E X I T GRAPHICS 14940 ! 14950 Repirr-I FIXED 2 14960 P L O T T E R IS "GRAPHICS" 14970 PRINT L I N C 1 5 ) , " T H E MAXIMUM FREQUENCY I S " ; M a x l 14980 PRINT " T H E MINIMUM V A L U E OF THE IRR IS"; Minim 14990 PRINT " T H E MAXIMUM V A L U E OF THE IRR IS";Maxim 150OO INPUT " E N T E R THE MAXIMUM FREQUENCY V A L U E FOR THE IRR PLOT",Tmaxl 15010 INPUT " E N T E R THE MINIMUM V A L U E FOR THE IRR PLOT (.xx)",Tminirr 15O20 INPUT " E N T E R THE MAXIMUM V A L U E FOR THE IRR PLOT (.xx)",Tmaxirr 15030 PRINT L I H ( 2 0 ) 15O40 ! 15050 GRAPHICS 15O60 DEG 15O70 LOCATE 15,110,0,80 15080 FRAME 15090 CSIZE 3 15100 LORG 1 15110 MOVE 4 8 , 5 15120 LABEL T e x t 6 * 15130 CSIZE 4 15140 MOVE 5 0 , 7 0 15150 LABEL T e x t 3 * 15160 MOVE 4 6 , 6 5 15170 LABEL T e x t 5 * 15180 CSIZE 3 15190 L D I R 90 152O0 LORG 5 15210 MOVE 2 0 , 4 0 15220 LABEL T e x t 2 * 15230 CSIZE 3 15240 LOCATE 33,100,13,65 15250 SCALE Tminirr,Tmaxirr,O,Tmax1 15260 L A X E S ( T m a x i m - T m i n i r r ) / 1 0 , I N T ( T m a x 1 / 5 ) , T m i n i r r , O , - 1,1 15270 ! 15280 FOR J = l TO 10 15290 MOVE I r r h i s t ( 1 , J ) , I m h i s t ( 2 , J) 15300 LABEL " + " 15310 NEXT J 15320 He*="N" 15330 INPUT "DO YOU WANT A HARDCOPY? ( Y / N ) " , H e * 15340 IF H e * = " Y " THEN DUMP G R A P H I C S 15350 Rep*="N" 15360 INPUT "DO YOU WISH TO TRY A G A I N ? ( Y / N ) " , R e p * 15370 IF R e p * = " Y " THEN GOTO R e p i r r 15380 E X I T GRAPHICS 15390 RETURN t  

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