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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 of B r i t i s h Columbia, 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of M i n i n g and M i n e r a l P r o c e s s E n g i n e e r i n g , 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 t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA May 1984 (C) Murray L y t l e , 1984 t In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department o r by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Murray Lytle Mining and Mineral Process Engineering Department o f The U n i v e r s i t y o f B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 March 19, 1984 Date )E-6 (3/81) i i ABSTRACT The r e c e n t economic r e c e s s i o n i n the f r e e market economics of Western 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 western Canadian c o a l p r o d u c e r s . Slower worldwide economic a c t i v i t y has r e d u c e d 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 and c o m p e t i t i o n i n w o r l d c o a l markets has i n c r e a s e d . In r e s p o n s e to t h i s c h a n g i n g economic c l i m a t e , Canadian c o a l 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 o r d e r to r e t a i n t h e i r s h a r e of the w o r l d c o a l market. The Coal Mountain Mine of 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 the mountainous r e g i o n of s o u t h e a s t e r n B r i t i s h C o l u m b i a . The mine c u r r e n t l y t r a n s p o r t s the r u n - o f - m i n e 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 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 the 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 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 to an underground f l u m e , where i t would be conveyed to the p r e p a r a t i o n p l a n t by open ch a n n e l f l o w . An e x p e r i m e n t a l program to measure the t r a n s p o r t of r u n - o f -mine c o a l t h r o u g h a 15.2 c e n t i m e t e r . 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 flume 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 t e s t a p p a r a t u s p r o v i d e d d a t a which was used to 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 the 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 conveyance t h r o u g h a v e r t i c a l , s t e e l l i n e d r a i s e . The p l u g f l o w movement of c o a l t h r o u g h a 300 meter 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 r a i s e i i i was s i m u l a t e d by p a s s i n g 1.5 tonnes 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 tube 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 weight and the p a r t i c l e s i z e d e g r a d a t i o n was r e s t r i c t e d to 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 . A computer program t o model the p r o j e c t economics 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 flume t r a n s p o r t system or a t r u c k t r a n s p o r t system was w r i t t e n . The program was used to 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 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 f r e q u e n c y d i s t r i b u t i o n s , and i i ) 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 economics were d e v e l o p e d f o r the f o l l o w i n g f i v e p r o d u c t i o n and mine development c a s e s : i ) g r a d u a l development of an expanding mine i i ) r a p i d development of an e x p a n d i n g mine i i i ) g r a d u a l development of a new mine i v ) r a p i d development of a new mine 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 mine. In a l l the c a s e s , the flume system 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 than the t r u c k haulage system. i v TABLE OF CONTENTS Page ABSTRACT 1}. LIST OF TABLES x ? n LIST OF FIGURES x l v CHAPTER I: SYNOPSIS 3 A. INTRODUCTION 3 B. SUMMARY 4 1. EXPERIMENTAL PROGRAM 5 a) Run-of-Mine Coal Transport by Open Channel Flow Tests 6 b) Coal Degradation Tests 7 2. ECONOMIC ANALYSIS . 7 CHAPTER II: 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 of Coal Measurement ... 36 e) Elapsed Time Measurement .... 36 f) S p e c i f i c Gravity Measurement . . 36 9. Structure 36 C. EXPERIMENTAL PROCEDURE . . . 36 1. Hydraulic Transport of Coarse Coal . 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 . 47 a) Hydraulic Transport of Raw Coal . 47 b) V e r i f i c a t i o n of the Manning Equation 47 E. INTERPRETATION OF RESULTS 1. Hydraulic Transport of Coarse Coal . 52 a) Dimensional Analysis 52 b) Transport Function 53 c) Prediction of Coarse Coal Transport 57 v i TABLE OF CONTENTS (cont'd) Page 2. Restarting Tests 63 3. V e r i f i c a t i o n of the Manning Equation . 63 F. EXPERIMENTAL ERROR 65 1. Systematic Error 65 a) Flow Rate Measurement 65 b) Depth of Flow Measurement .... 66 c) Flume Slope Measurement 66 d) Weight Measurement 66 e) Elapsed Time Measurement 66 f) Coal S p e c i f i c Gravity Measurement 66 2. RANDOM ERRORS 67 a) Flow Rate Measurement 67 b) Depth of Flow Measurement .... 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 of the Manning Equation 70 G. COMPARISON WITH OTHER RESEARCH 72 1. Ambrose 72 2. Graf and Acaroglu . 75 3. Wilson 77 4. Summary 79 v i i TABLE OF CONTENTS (cont'd) Page H. COMPARISON WITH OPERATING MINES 8 0 1. Westar Mines Ltd 8 0 2. Hansa Hydro Mine 8 2 CHAPTER IV: PARTICLE SIZE DEGRADATION 8 3 A. INTRODUCTION 8 3 B. APPARATUS 8 3 C. PROCEDURE 8 5 D. RESULTS 8 7 CHAPTER V: RUN-OF-MILL FLUME TRANSPORT SYSTEM DESIGN . . A. INTRODUCTION 9 2 B. SURFACE vs UNDERGROUND FLUME TRANSPORT SYSTEM 9 4 C. UNDERGROUND RUN-OF-MINE COAL SLURRY TRANSPORT SYSTEM 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. Au x i l i a r y Manway I l l 9. Ventilation 114 10. Instrumentation 11 11. Service F a c i l i t i e s 115 v i i i TABLE OF CONTENT S (cont'd) Page CHAPTER VI: ESTIMATED CAPITAL AND OPERATING COSTS FOR THE RUN-OF-MINE FLUME TRANSPORT SYSTEM .... 117 A. INTRODUCTION . . . 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 121 8. Ven t i l a t i o n , Instrumentation and Flume Services 121 9. Site Investigation 122 10. Engineering 122 C. OPERATING COSTS FOR THE FLUME TRANSPORT SYSTEM 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 1 2 7 A. INTRODUCTION 1 2 7 i x TABLE OF CONTENTS (cont'd) Page B. CAPITAL AND OPERATING COSTS 128 1. Other Mining 128 2. Other Plant 128 3. Head Office 129 4. O f f - s i t e Coal Transportation .... 129 5. Port Inventory 129 6. Capitalized and Non-capitalized Interest Payments 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 131 1. Coal Loader 131 2. Coal Trucks . 132 C. OPERATING COSTS FOR THE TRUCK TRANSPORT SYSTEM 132 1. Coal Loader 134 2. Coal Trucks 134 CHAPTER IX: ECONOMIC EVALUATION OF FLUME AND TRUCK TRANSPORT OF RUN-OF-MINE COAL .136 A. INTRODUCTION 136 B. COMPARISON OF PRODUCTION AND MINE DEVELOPMENT ALTERNATIVES 137 1. Cases Analyzed 137 2. Analysis of Results 138 3 . Conclusions 161 X TABLE OF CONTENTS (cont'd) Page C. MONTE CARLO RISK STIMULATION I 5 1 1. Analysis of Results 155 D. SENSITIVITY ANALYSIS 155 1. Analysis of Results 156 a) Coal Price 156 b) Wash Plant Yield 158 c) Inflation 158 d) Operating Costs 158 e) Capital Costs 162 f) Underground Construction Costs . 162 g) Truck Operating Hours 162 h) Labour Cost 166 i) Fuel Cost 166 2. CONCLUSIONS 169 E. GENERAL CONCLUSIONS . , 169 CHAPTER X: RECOMMENDATIONS FOR FURTHER RESEARCH INTO RUN-OF-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. FLUME "172 4. COARSE COAL BIN 174 •5. DISCHARGE COLLECTOR TANK 174 x i TABLE OF CONTENTS (cont'd) Page 6. INSTRUMENTATION 174 a) Flowrate Measurement 174 b) Depth of 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 of Return 197 c) S t a t i s t i c a l Results 197 APPENDIX 2: COMPUTER PROGRAM LISTING 198 x i i 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 55 3-6 Measured and Calculated Values f o r 10 V e r i f i c a t i o n Tests 58 3- 7 Calculated and Measured Rate of Coal Transportation 59 4- 1 Coal P a r t i c l e Degradation Test Results 9 0 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 Rock C l a s s i f i c a t i o n using Bienjawski System 1 ° 2 5- 3 Mass Balance o f the Dewatering Plant 113 6- 1 Cost and Production Parameters for Calculating the Flume System Economics 123 8- 1 Cost and Production Parameters for Calculating the Truck System Economics I 3 3 9- 1 Cash Flow Summary f o r Flume Transportation -gradual mine expalsion 139 9-2 Cash Flow Summary for Truck Transportation -gradual mine expansion K 140 9-3 Cash Flow Summaryfor Flume Transportation -rapid mine expansion 141 9-4 Cash Flow Summary f o r Truck Transportation -rapid mine expansion l ^ 2 9-5 Cash Flow Summary for Flume Transportation -gradual new mine development ^ 3 x i i i LIST OF TABLES (cont'd) Table Page 9-6 Cash Flow Summary for Truck Transportation -gradual new mine development 144 9-7 Cash Flow Summary f o r Flume Transportation -rapid new mine development 14E> 9-8 Cash Flow Summary f o r Truck Transportation -rapid new mine development 1^6 9-9 Cash Flow Summary for Flume Transportation -truck replacement 1^7 9-10 Cash Flow Summary f o r Truck Transportation -truck replacement ^ 9-11 Comparison of Project Economics 149 A--1 Data F i l e s f o r Calculating the Flume System Economics 182 A--2 Data F i l e s 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 x i v 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 P a r t i c l e 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 P a r t i c l e 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 G r i z z l y 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 Inf l a t i o n 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 x v i 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 x v i i ACKNOWLEDGEMENT I wish to acknowledge Professor A. J. Reed f o r his unflagging encouragement and desire to be intimately involved in the production of this thesis and to Mr. J . B. Evans f o r making thi s "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 of home to sojourn with me. To them I dedicate this thesis. "Surely there i s a mine for s i l v e r and a place for gold which they refine, 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 of 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 C r o s s s e c t i o n a l a r e a of f l o w B C o e f f i c i e n t of s l u r r y v e l o c i t 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 P i p e d i a m e t e r d P a r t i c l e s i z e d x P e r c e n t of m a t e r i a l p a s s i n g a s i e v e o p e n i n g f 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 and flume s u r f a c e F L Froude Number g A c c e l e r a t i o n due to g r a v i t y k' C o e f f i c i e n t of f l o w energy t r a n s f e r 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 sediment t r a n s p o r t q' S p e c i f i c consumption of water R H y d r a u l i c r a d i u s S S l o p e s j S p e c i f i c g r a v i t y of s o l i d p a r t i c l e s T V o l u m e t r i c r a t e of sediment t r a n s p o r t V Average f l o w v e l o c i t y V c 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 Y Depth of f l u i d f l o w 3 CHAPTER I  SYNOPSIS A. I n t r o d u c t i o n The c o a l s a l e s by w e s t e r n Canadian 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 from the r e c e n t r e c e s s i o n i n the f r e e market economies of Western and T h i r d World c o u n t r i e s . 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 reduced and c o m p e t i t i o n i n world c o a l markets 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 . I t i s v i t a l t h a t Canadian c o a l p r o d u c e r s 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 to r e t a i n t h e i r s h a r e of the 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 of Byron Creek C o l l i e r i e s (1983) L t d . are s i t u a t e d i n the mountains of s o u t h e a s t e r n B r i t i s h C o lumbia. The company produces 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 , to 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 the 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 u n d e r t a k e n to examine the 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 r u n - o f - m i n e c o a l to the 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 to compare t h e s e r e s u l t s w i t h the c u r r e n t t r u c k haulage system of c o a l t r a n s p o r t a t i o n . The proposed 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 flume i n an underground haulage d r i f t . The flume 4 d e l i v e r s the c o a l to a s u r f a c e d e w a t e r i n g p l a n t p r i o r to b e n e f i c i a t i o n i n the p r e p a r a t i o n p l a n t . The o b j e c t i v e s of the 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 the v o l u m e t r i c r a t e of t r a n s p o r t of c o a l p a r t i c l e s l a r g e r than 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 ; i i ) d e t e r m i n e 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 , s t e e l l i n e d r a i s e , and i i i ) d e s i g n a r u n - o f - m i n e c o a l t r a n s p o r t a t i o n system u s i n g open c h a n n e l f l o w and to 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 of an o p e r a t i n g open p i t c o a l 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 to a c h i e v e the 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 to a c c o m p l i s h t h e t h i r d o b j e c t i v e . The c o a l used i n the e x p e r i m e n t s and the 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 the s t a f f of Byron Coal C o l l i e r i e s (1983) L t d . A l t h o u g h the 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, c a p i t a l and o p e r a t i n g c o s t s are not s p e c i f i c and r e p r e s e n t the c o s t s of an average western C a n a d i a n , mountaintop open p i t c o a l mine. B. Summary The s t u d y of f l u i d i z e d sediment t r a n s p o r t has o c c u p i e d the 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 the t h e o r e t i c a l i n v e s t i g a t i o n s . F o r example, r u n - o f - m i n e c o a l has been t r a n s p o r t e d i n open c h a n n e l f l o w s i n c e the t u r n of the l a s t c e n t u r y but o n l y i n the l a s t two decades has t h e r e been a c o n c e r t e d e f f o r t to u n d e r s t a n d the economic advantages of open c h a n n e l 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 i n v e s t i g a t e d phenomenon of sediment t r a n s p o r t by f u l l p i p e f l o w 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 . The s t a f f at underground 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 i n t o open channel t r a n s p o r t of r u n - o f - m i n e c o a l . T h i s work has been s i t e s p e c i f i c but was 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 r e s e a r c h . These underground 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 f l u m e s . The d e f i n i t i o n of " f l u me" f o r the purposes of t h i s t h e s i s has been expanded to be any c o n d u i t , open or c l o s e d , which t r a n s p o r t s f l u i d or f l u i d i z e d s e d iments w i t h a f r e e s u r f a c e . 1. E x p e r i m e n t a l 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 t o p r o v i d e data 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 c o a l 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 t o : i ) d e v e l o p 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 system. i i ) d e t e r m i n e p o t e n t i a l o p e r a t i n g problems i n r e s t a r t i n g the flume system wi t h a bed of c o n s o l i d a t e d c o a l . i i i ) v e r i f y use of the Manning e q u a t i o n t o 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 i v ) measure 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 s l i d i n g t h r o u g h a s t e e l tube i n p l u g f l o w . 6 a) Run-of-Mine Coal T r a n s p o r t by Open Channel Flow T e s t s E x p e r i m e n t a l d a t a f o r r u n - o f - m i n e c o a l t r a n s p o r t a t i o n 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 which conveyed the r u n - o f - m i n e c o a l t h r o u g h a 15.2 c e n t i m e t e r d i a m e t e r 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 s l u r r y . 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 . V a l u e s 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 , i i ) flume s l o p e , i i i ) f l o w depth of the s l u r r y , i v ) weight of r u n - o f - m i n e c o a l t r a n s p o r t e d , v) time t a k e n t o t r a n s p o r t a l l the c o a l t h r o u g h the f l u m e , and v i ) 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 ) h y d r a u l i c r a d i u s , i i ) 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 ) f l o w v e l o c i t y , i v ) 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 , and v) volume c o n c e n t r a t i o n of s o l i d s . These 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 u s i n g d i m e n s i o n a l 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 T r a n s p o r t F u n c t i o n , 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 d i m e n s i o n l e s s r a t i o s . 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 comparing 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 the e x p e r i m e n t a l measurement of c o a r s e c o a l t r a n s p o r t f o r 10 subsequent t e s t s . The flume r e s t a r t t e s t s m o d e l l e d the r e s t a r t i n g of a flume system a f t e r a system shut-down. The t e s t r e s u l t s i n d i c a t e d t h a t the problems a s s o c i a t e d w i t h r e s t a r t i n g the flume system would be m i n o r . 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 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 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 D e g r a d a t i o n T e s t s 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 long 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 . The t e s t was c a r r i e d out by s u s p e n d i n g a column of r u n - o f - m i n e c o a l i n one of the tubes 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 lowered i n t o the empty t u b e , the arrangement of the tubes was s w i t c h e d and the p r o c e s s was r e p e a t e d . In t h i s way, conveyance of c o a l t h r o u g h a 300 meter long 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 t was found 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 l i m i t e d . t o 3 p e r c e n t by weight 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 flume 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 d e s i g n e d 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 to 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 i i ) two v i b r a t i n g g r i z z l i e s to s c r e e n out c o a l p a r t i c l e s l a r g e r than 6.4 c e n t i m e t e r s , 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 convey the c o a l t o an underground main haulage d r i f t , i v ) two s t e e l chambers to r e c e i v e c o a l from the r a i s e s and s l u r r y i t w i t h water, v) a two l i n e , .6 meter d i a m e t e r flume system of 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 s t o convey the c o a l t o the s u r f a c e , and v i ) 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 the 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 s l u r r y 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 p l a n t . 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 t r a n s p o r t system 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 e s t i m a t e d 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 . The 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: i ) waste m i n i n g and mine a d m i n i s t r a t i o n s e r v i c e s , i i ) 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 , i i i ) head o f f i c e o v e r h e a d s , i v ) r a i l t r a n s p o r t to the 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 the ocean t e r m i n a l , and v i ) f i n a n c i n g i n t e r e s t c h a r g e s 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 t r u c k 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 system 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 comparison f o r the flume c o a l t r a n s p o r t system. A computer program, o p e r a t i n g on a HP-9845 computer, was w r i t t e n t o : i ) d e s i g n the r u n - o f - m i n e c o a l t r a n s p o r t system, 9 i i ) g e n e r a t e o p e r a t i n g and c a p i t a l c o s t s f o r the complete m i n i n g p r o j e c t , i i i ) a p p l y a p p r o p r i a t e f e d e r a l and p r o v i n c i a l t a x e s and r o y a l t i e s , i v ) c a l c u l a t e annual net cash 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 i n t e r n a l 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 the p r o j e c t f i n a n c i a l r i s k by c h o o s i n g the i n p u t c o s t and p r o d u c t i o n v a r i a b l e s , i n a Monte C a r l o f a s h i o n , from a skewed 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 . 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 was c o n s t r a i n e d 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 p r e v e n t u n r e a l i s t i c v a l u e s from b e i n g c hosen. By r e p e a t e d l y c a l c u l a t i n g the p r o j e c t economics, a f r e q u e n c y d i s t r i b u t i o n of 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 was d e t e r m i n e d . The p r o j e c t f i n a n c i a l r i s k was a l s o e v a l u a t e d 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 economics to changes i n the f o l l o w i n g 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 v a r i a b l e s : i ) c a p i t a l c o s t s , i i ) o p e r a t i n g c o s t s , i i i ) t r u c k o p e r a t i n g hour r e q u i r e m e n t s , i v ) f u e l c o s t s , v) l a b o u r c o s t s , and v i ) underground c o n s t r u c t i o n c o s t s . The f o l l o w i n g g e n e r a l 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 t e s t e d : i ) i n f l a t i o n r a t e , i i ) c o a l s e l l i n g p r i c e , and 10 i i i ) p r e p a r a t i o n p l a n t y i e l d . The economic c o m p a r i s o n of flume and t r u c k t r a n s p o r t of r u n -of-mine c o a l was e v a l u a t e d by c a l c u l a t i n g 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 f o r the f o l l o w i n g c a s e s : i ) g r a d u a l l y d e v e l o p e d new mine, i i ) g r a d u a l l y d e v e l o p e d mine e x p a n s i o n , i i i ) r a p i d l y d e v e l o p e d new mine, i v ) r a p i d l y d e v e l o p e d mine e x p a n s i o n , and 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 mine. The " g r a d u a l l y d e v e l o p e d " c a s e s 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 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 " c a s e s were at f u l l p r o d u c t i o n i n y e a r 4. The flume c o a l t r a n s p o r t system was e c o n o m i c a l l y s u p e r i o r 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 t r u c k c o a l t r a n s p o r t system i n a l l the c a s e s . I t i s c o n c l u d e d t h a t flume 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 estern Canadian c o a l mine o p e r a t i o n s . CHAPTER II L i t e r a t u r e S e a r c h f o r F l u i d T r a n s p o r t by Open Channel Flow F o r t h o u s a n d s of y e a r s mankind has s t u d i e d and atte m p t e d t o u n d e r s t a n d the p r i n c i p l e s of sediment t r a n s p o r t by open channel f l o w . Rouse and Ince (1980) have t r a c e d the p r o g r e s s i o n o f t h i s u n d e r s t a n d i n g i n the b r o a d e r c o n t e x t o f a h i s t o r i c a l r e v i e w of the s c i e n c e of 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 of man-made water c o n t r o l s t r u c t u r e s are c a n a l s found i n E g y p t . F i v e t h o u s a n d y e a r o l d dom e s t i c plumbing, found i n the 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 advanced. In 1000 B.C., the c i t y of 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 water by a system of aquedu c t s and underground t u n n e l s . The c l a s s i c a l Greeks i n v e s t i g a t e d many a s p e c t s o f h y d r a u l i c s . The e a r l i e s t known e x p r e s s i o n o f 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 fl 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 are remembered f o r t h e i r c i v i l e n g i n e e r i n g s t r u c t u r e s . The w r i t t e n works o f two e n g i n e e r s have s u r v i v e d t o the p r e s e n t . Marcus V i t r u v i u s P o l l i o , s e r v i n g both J u l i u s and Augustus C a e s a r , b u i l t masonry a q u e d u c t s to b r i n g w a t er i n t o Rome from d i s t a n t water s o u r c e s . S e x t u s J u l i u s F r o n t i n u s (40-103 AD) was the Commissioner of Water f o r Rome a t the t u r n o f the f i r s t c e n t u r y A.D. He was r e s p o n s i b l e f o r the d e l i v e r y of f r e s h water to Rome and to 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 M i d d l e , or Dark Ages, from about 400 A.D. to 1500 A.D., produced no advancement i n knowledge about open ch a n n e l f l o w . The a u t h o r i t y of the Roman c h u r c h d i r e c t e d e n e r g i e s toward c o n s t r u c t i o n o f c a t h e d r a l s and m o n a s t e r i e s r a t h e r than p u b l i c water 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 about 1500, was marked by a renewed c u r i o s i t y i n the p h y s i c a l w o r l d and i n c r e a s i n g r e b e l l i o n a g a i n s t e c c l e s i a s t i c c o n t r o l o f l e a r n i n g . Leonardo 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 flumes to i n v e s t i g a t e open ch a n n e l f l o w . He was the f i r s t t o note the v e l o c i t y d i s t r i b u t i o n i n a v o r t e x , the f o r m a t i o n 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 to s t a t e t h a t the fl 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 channel was the same as t h a t i n any o t h e r c r o s s s e c t i o n . T h i s l a t t e r o b s e r v a t i o n , the p r i n c i p l e of c o n t i n u i t y , was noted a f t e r o b s e r v i n g changes i n fl o w v e l o c i t y r e s u l t i n g from changes i n the c r o s s s e c t i o n a l area of fl o w o f r i v e r s and f l u m e s . G u g l i e l m i n i (1655-1710), a u n i v e r s i t y p r o f e s s o r and s u p e r i n t e n d e n t of water f o r the C i t y of B o l o g n a , s t a t e d i n 1697 t h a t t h e tendency f o r f l o w i n g water to i n c r e a s e v e l o c i t y was o f f s e t by the r e s i s t a n c e o f the c h a n n e l . He a l s o made o b s e r v a t i o n s about the s c o u r i n g a c t i o n of water 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 streams t h a t t r a n s p o r t s e d i m e n t . The f i r s t m a t h e m a t i c a l f o r m u l a f o r p r e d i c t i n g f l o w v e l o c i t y i n open c h a n n e l s was proposed by A n t o i n e Chezy (1718-1798) about one hundred 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 d i m e n s i o n s 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 to b r i n g water to 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 the s o u t h . 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 . In t h i s f o r m u l a , "V" i s v e l o c i t y , "R" 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 s l o p e . 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 d e t e r m i n e d by comparing a channel w i t h unknown "C" to one h a v i n g 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 "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 to l i g h t a c e n t u r y l a t e r 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, i n d e p e n d e n t l y proposed r e l a t i o n s h i p s s i m i l a r to C h e z y ' 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 they 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, t h a t p a r t i c l e s i z e i s an i m p o r t a n t v a r i a b l e i n stream sediment t r a n s p o r t . He a l s o noted 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 the c a p a c i t y of a stream to c a r r y s e d i m e n t . 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 channel 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 noted t h a t channel 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 a n a l o g o u s t o f u l l p i p e f l o w . 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 to i n c o r p o r a t e data from the 14 M i s s i s s i p p i r i v e r ( c o l l e c t e d by two American 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 the Bourgogne c a n a l data ( 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 f i r s t to p r opose a roughness c o e f f i c i e n t "n" to a c c o u n t f o r d i f f e r e n t stream bed m a t e r i a l s . T h e i r e q u a t i o n i s ; V = .0015 23 + + 1 n 'RS 1 + (23 + .0015 + n ) s /ir where "n" i s a c o e f f i c i e n t of roughness f o r the channel bed, "S" i s the channel s l o p e and "R" i s the h y d r a u l i c r a d i u s . Manning (1889) proposed a d i m e n s i o n a l 1 y homogeneous r e l a t i o n s h i p o f the form; V = C y g S ( 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 of 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 b a l a n c e s a t m o s p h e r i c p r e s s u r e . 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 propose the r e l a t i o n s h i p which now b e a r s h i s name; V = S i / 2 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 was 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 was adopted f o r i n t e r n a t i o n a l use, i n i t s p r e s e n t form, a t the 1936 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 the U n i v e r s i t y o f C a l i f o r n i a to t e s t the t r a n s p o r t o f sands and 15 g r a v e l s i n t h r e e s i z e s of flumes w i t h a r t i f i c i a l l y roughened beds. The d a t a from t h i s i n v e s t i g a t i o n 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 f l o w v e l o c i t y a t which suspended s e d i m e n t s b e g i n 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 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 and was d e t e r m i n e d by Durand to be; V c = F L Jzgd(si-l) where " s i " i s the s p e c i f i c g r a v i t y o f the 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 f o r c e s to g r a v i t y f o r c e s ( m o d i f i e d Froude Number). I t i s o b t a i n e d from Durand's graph o f Froude Number and p a r t i c l e s i z e f o r v a r y i n g s l u r r y d e n s i t i e s . The r e l a t i o n s h i p does not a p p l y to s e d i m e n t s w i t h a wide range o f p a r t i c l e s i z e s . A 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 e x i s t s f o r sediment t r a n s p o r t by both f u l l p i p e and open ch a n n e l f l o w . A few o f the d i f f e r e n t e q u a t i o n s to p r e d i c t t h i s v e l o c i t y are i n c l u d e d here to g i v e an i n d i c a t i o n o f the v a r i e t y i n m e t h o d o l o g i e s used to c a l c u l a t e 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 . An u n d e r s t a n d i n g o f the c o n c e p t o f 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 i s a l s o i m p o r t a n t i n d e f i n i n g " f l o w r e g i m e s " . D i f f e r e n t f l o w regimes are e s t a b l i s h e d when sediment i s c a r r i e d i n w a t e r . 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 are two d i s t i n c t phases; 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 . As the f l u i d v e l o c i t y i n c r e a s e s or the p a r t i c l e s i z e d e c r e a s e s , the bed o f s o l i d s w i l l b e g i n to move 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 . The s o l i d s and l i q u i d s t i l l 16 e x i s t i n two d i s t i n c t p h a s e s . 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 v e l o c i t y or d e c r e a s e i n p a r t i c l e s i z e some of the sediment w i l l 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 sediment w i l l be c a r r i e d i n the f l u i d and the 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 regimes i s shown g r a p h i c a l l y on F i g u r e 2-1 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 . 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 f l u i d . Ambrose (1953) a t the U n i v e r s i t y of Iowa, was c o n c e r n e d w i t h the problem of sediment b u i l d - u p i n storm sewer sy s t e m s . To model a storm sewer, he used an 18.3 meter 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 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 f l o w . He d e t e r m i n e d a r e l a t i o n s h i p between two d i m e n s i o n l e s s terms; Q and Y/D g2/5 D2 Q s l / 5 ( s i - l ) 2 / 5 where "Q" i s the 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 u n i v e r s a l g r a v i t a t i o n a l c o n s t a n t , "D" i s the flume 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 the 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 . T h i s r e l a t i o n s h i p i s graphed on F i g u r e 2-2 and i s based on the c o n d u i t s l o p e which j u s t p r e v e n t s the suspended s o l i d s from s e t t l i n g out of the w a t e r . His 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 Figure 2-1 Flow regimes are established 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 large p a r t i c l e sizes there i s a s t a t i o n -ary bed of s o l i d s and a moving f l u i d . With increasing flow v e l o c i t y or decreasing p a r t i c l e s i z e , the stationary bed w i l l begin to s l i d e and salt a t e u n t i l a l l the sediment i s i n suspension. If the s o l i d p a r t i c l e s are small enough i t i s possible to form a s l u r r y with a uniform concen-t r a t i o n of sediments. 18 AMBROSE RELATIONSHIP 10| 1 1 i 1 . 1 1 i Y/D Figure 2-2 Ambrose (1953) determined t h i s r e l a t i o n s h i p f o r the transport of sand by open channel flow. It i s based on the conduit shape which ju s t prevents the suspended s o l i d s from s e t t l i n g out of the water. His research indicates that the r a t i o of p a r t i c l e s i z e to flume diam-eter does not a f f e c t the transport of suspended sediment. 19 of p a r t i c l e s i z e to flume 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 o f suspended s e d i m e n t . In 1955, N e w i t t e t a l , d e v e l o p e d a r e l a t i o n s h i p f o r 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 which I n c o r p o r a t e s the s e t t l i n g v e l o c i t y of sediment 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 sediment 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 the 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 not a c c o u n t f o r sediment h a v i n g a wide range of p a r t i c l e s i z e s . These r e s e a r c h e r s proposed 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 a h i n d e r e d s e t t l i n g 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 s e d i m e n t s . The m i n i n g I n d u s t r y was u s i n g open channel f l o w to t r a n s p o r t sediments over 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 p r e s e n t c e n t u r y . 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 meters i n a s h o r t i r o n - l i n e d , wooden f l u m e . In 1925, the S t o c k t o n Mine i n New Z e a l a n d 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 f l u m e . 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 sand-water m i x t u r e f l o w i n g i n a 15.2 c e n t i m e t e r s q u a r e , wooden fl u m e . H i s r e s e a r c h was i n r e s p o n s e to o b s e r v a t i o n s from the m i n i n g i n d u s t r y t h a t " . . . 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 (sand) 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 flumes a t low s l o p e s . " 20 He c o n c l u d e d t h a t the f i n e p a r t i c l e s changed the s l u r r y r h e o l o g y 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 the t r a n s p o r t of 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 p a r a m e t e r s which c o r r e l a t e d a t a f o r both open ch a n n e l and f u l l p i p e f l o w d a t a . The r e l a t i o n s h i p they d e t e r m i n e d i s ; -2 5? *• = 10.39 v ' where $ i s a t r a n s p o r t parameter C v V R and y i s a she a r i n t e n s i t y parameter = ( s ^ - l ) dgg SR " C V " i s the volume c o n c e n t r a t i o n of the s o l i d s and " ^ Q " i s the s c r e e n s i z e which w i l l pass 50 per c e n t o f the sediment p a r t i c l e s . 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 data p o i n t s from G i l b e r t ( 1 9 1 4 ) , Guy e t al (1 9 6 6 ) , A n s l e y (1963) and E i n s l e i n ( 1 9 4 4 ) . Wasp e t al (1970) m o d i f i e d the Durand r e l a t i o n s h i p to a c c o u n t f o r sed i m e n t s w i t h a wide d i s t r i b u t i o n of p a r t i c l e s i z e s . 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 i s ; In 1972, Novak and N a l l u r i compared the a n a l y t i c a l t e c h n i q u e s f o r open channel 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 the same e q u a t i o n s can 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 RELATIONSHIP Figure 2-3 Graf and Acaroglu (1968) developed two dimensionless parameters to c o r r e l a t e 903 data points f o r sediment transport by open channel flow. The hatched area re-presents the scatter of these plotted data values. 22 a p p r o p r i a t e changes i n the e m p i r i c a l l y d e t e r m i n e d e q u a t i o n c o e f f i c i e n t s are made. Klieman (1976) e x p e r i m e n t e d w i t h the open channel t r a n s p o r t 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 . F o r 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 flumes from the mine i n the Andes Mountains to 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 meters 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 flume s l o p e . He c o n c l u d e d t h a t ; i ) 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 f l o w v e l o c i t y i i ) 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 i m p o r t a n t v a r i a b l e s 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 and, i v ) f o r d e s i g n p u r p o s e s , a s o l i d s c o n c e n t r a t i o n o f 50 per 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 meters per second were a p p r o p r i a t e d e s i g n c r i t e r i a f o r t h i s c o p p e r t a i l i n g s t r a n s p o r t system. E x p e r i e n c e w i t h open channel t r a n s p o r t of r u n - o f - m i n e c o a l i n the S o v i e t Union was d e s c r i b e d by Gontov ( 1 9 7 8 ) . 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 c o a l 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 , a t grades as low as 2 per c e n t i n the G i d r o u g a l Mine. The d i a b a s e l i n i n g 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 cha n n e l 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 . S e m i - c i r c u l a r 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 . A f t e r some t e s t i n g of v a r i o u s l i n i n g s , i t was d e t e r m i n e d t h a t u n l i n e d - s t e e l was the most c o s t e f f e c t i v e flume m a t e r i a l . They quote t y p i c a l wear r a t e s o f 7.3 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 tonnes of c o a l t r a n s p o r t e d . T i e n - Y u 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 e x p e r i m e n t s 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 flume c r o s s s e c t i o n and d e v e l o p e d a f o r m u l a 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 . 4 x l 0 - 4 and 0.22 r e s p e c t i v e l y ) and "C w" i s the 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 . 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 conform 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 channel f l o w a t the Hansa-Hydro Mine i n West Germany i s d e s c r i b e d by Kuhn ( 1 9 8 0 ) . 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 meters 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 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 , 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 water to an o p e r a t i n g 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 24 d i s c h a r g e end. F i g u r e 2-4 i n d i c a t e s t h i s s l i p i n a p l o t o f v e l o c i t y v e r s u s s l o p e . Flume d e s i g n a t the Hansa-Hydro Mine i s based on the f o l l o w i n g c r i t e r i a ; i ) v e l o c i t y = 6 m eters per second i i ) c r o s s S e c t i o n a l Area o f Flume = 3 times 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 i v ) 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 c e n t 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 nderground 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 Columbia 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 p a p e r . The a u t h o r s propose 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 l o p e ; S = f l ( s i - 1 ) 100 C s i q l k l + ( s i - 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 flume s u r f a c e , " q l " i s the s p e c i f i c consumption of water and " k 1 " i s the c o e f f i c i e n t o f f l o w energy i m p a r t e d to the c o a l , ( a b o u t 0.61). From t h i s r e l a t i o n s h i p , the volume of water r e q u i r e d t o t r a n s p o r t c o a l a t t h i s p r o p e r t y 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 flume g r a d i e n t s , the r e q u i r e d volume of water i n c r e a s e s r a p i d l y . 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 Froude Number and to a c c o u n t 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 Mine Figure 2-4 Kuhn (1980) described the phenomenon of " s l i p " at the Hansa-Hydro Mine. Kuhn measured the dif 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 coal f o r varying flume slopes. This v e l o c i t y d i f f e r e n c e indicates that i f the supply of water to an operat-ing flume i s cut o f f , the coarse coal w i l l s e t t l e out i n the flume near the discharge end. 26 FLUMING CURVE Figure 2-5 In an unpublished staff paper from Westar Mines Ltd., the authors propose a mechanistic relationship to predict the volume of water required to move coarse coal for a given slope. From this relationship, the volume of water required to transport coal at this property is inversely proportional to the flume slope. 27 The new e q u a t i o n i s ; / z g D ^ - 1) .167 V = 3.116 C c where a l l of the 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 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 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 the r a t e of change of 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 , d e t e r m i n e d 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 d e t e r m i n e d 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 to d e t e r m i n e the optimum s l o p e f o r t r a n s p o r t i n g sediment by open cha n n e l f l o w i n a 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 . 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 maximizes 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 borrowed 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 p i p e f l o w m a i n t a i n i n g 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 are a t work i n open cha 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 the f l o w depth 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 the s o l i d 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. The r e l a t i o n s h i p W i l s o n p r o p o s e d 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 i n m e t e r s . T h i s 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 both bed l o a d and suspended 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 to t h i s r e l a t i o n s h i p are d e f i n e d by two f u r t h e r e q u a t i o n s ; t a n Q = -006 / s - i - l N 0 ' 6 D V TT65 / At g r a d i e n t s below t h i s v a l u e , the sediment w i l l s e t t l e i n t o an immobile bed (homogeneous f l o w ) . / s - , - l \ 0.35 t a n e = 0.43 The sediment 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 (pseudohomogeneous f l o w ) . F i g u r e 2-6 i s a graph o f W i l s o n ' s r e s u l t s f o r sediments h a v i n g a s p e c i f i c g r a v i t y of 2.65. 29 PARTICLE SIZE vs PIPE DIAMETER IO 1 «o° PIPE DIAMETER (m) Figure 2-6 Wilson (1980) developed a computer program to determine the optimum slope for transporting sediment by open channel flow in a pipe of circular cross section. He defined the optimum slope as that slope which maximizes the transport of solids for a given distance of travel. The optimum slope is condi-tional upon the flow depth to pipe diameter ratio being 0:93 and the concentration of solids being 30 percent by volume. 30 CHAPTER I I I E x p e r i m e n t s 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 Flow A. I n t r o d u c t i o n 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 to p r o v i d e 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 s l u r r y t r a n s p o r t system. An e x p e r i m e n t a l a p p a r a t u s to convey c o a l through a 15.2 c e n t i m e t e r 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 i n open channel 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 e x p e r i m e n t s 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 the d e n s i t y o f the r e c i r c u l a t i n g f l u i d . Measurements o f flume s l o p e , depth o f f l u i d f l o w , weight o f 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 f l o w , 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 d i m e n s i o n a l a n a l y s i s , to p r e d i c t the t r a n s p o r t p a r a m e t e r s f o r c o a r s e r u n - o f - m i n e c o a l . i i ) examine problems 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 which 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 channel 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 . 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 program were compared to the 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 . 31 B. A p p a r a t u s 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 flume a p p a r a t u s which conveyed the r u n - o f - m i n e 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 . 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 data 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 equipment 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 the e x p e r i m e n t s was r e c e i v e d from the m i n e s i t e i n p l a s t i c - l i n e d , wooden boxes, 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 than 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 than 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 the e x p e r i m e n t s and the m a t e r i a l l e s s than one m i l l i m e t e r was 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 . 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 not used i n the e x p e r i m e n t s . 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 the 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 the c o a l , c o m p r i s e d of 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 per 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 the c o a r s e c o a l used i n the 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 than 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 meters was used t o p r o v i d e the m o t i v e g r a v i t y head f o r the 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 T E S T APPARATUS Figure 3-1 The experimental data f o r t h i s research program was c o l l e c t e d using a closed loop flume apparatus which conveyed the run-of-mine coal 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 data c o l l e c t e d before, during and a f t e r each run. PARTICLE SIZE DISTRIBUTION 100 O Z CO (J) < Q. # UJ > r-< 3 O PART ICLE 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 ex-periments 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, com-prised 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 spout 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 f l u m e . 3 • Co 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 , gate c o n t r o l l e d d i s c h a r g e o p e n i n g 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 f l u m e . 4 . P_i pe Flume The flume was a 15.2 c e n t i m e t e r 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 c i r c u l a r p i p e , 6.1 meters i n l e n g t h . 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 plank which h e l d i t r i g i d and e n s u r e d a c o n s t a n t p i p e s l o p e . A r u b b e r hose c o n n e c t e d the p i p e flume to the head tank spout and a t 3 meters and 5 meters 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 f l u m e . 5. D e w a t e r i n g S c r e e n A .6 meter by 2.4 meter, low a n g l e , s t a i n l e s s s t e e l d e w a t e r i n g 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 b e i n g r e c i r c u l a t e d t h r o u g h the system. 6 . D i s c h a r g e C o l l e c t o r Tank A 3 meter l o n g by .9 meter wide by .6 meter deep s t e e l 35 tank c o l l e c t e d 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 p r o v i d e d a sump f o r the r e c i r c u l a t i n g pump. 7. Pump and Re t u r n L i n e 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 the f l u i d from the c o l l e c t o r tank to the 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 gate v a l v e s on the r e t u r n l i n e d i r e c t e d the fl o w o f f l u i d to the head tank, back i n t o the c o l l e c t o r tank or th r o u g h two a g i t a t i o n l i n e s . 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 d i a 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 the bottom o f the d i s c h a r g e c o l l e c t o r t a n k . 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 a l o n g t h e i r l e n g t h a l l o w e d r e c i r c u l a t i n g s l u r r y t o spra y o u t , a g i t a t i n g the f l u i d i n the tank and p r e v e n t i n g c o a l p a r t i c l e s from s e t t l i n g . 8 . I n s t r u m e n t a t i o n 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 , magnetic flowmeter i n s t a l l e d on the r i s i n g l e g of the r e t u r n l i n e . An i n d i c a t i n g t o t a l i z e r p r o v i d e d a d i g i t a l d i s p l a y o f the f l u i d f low r a t e i n t e n t h s of a per c e n t o f the c a l i b r a t e d f u l l f l o w . b) 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 me a s u r i n g the d i s t a n c e from the top of the flume to the f l u i d s u r f a c e and 36 s u b t r a c t i n g t h i s from the flume d i a m e t e r . The r u l e r used f o r t h i s purpose 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 to measure the i n c l i n a t i o n of the 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 d e g r e e . 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 timed w i t h a s t o p watch which measured to one hundredth of a second. f ) S p e c i f i c G r a v i t y 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 by w e i g h i n g the 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 , g r a d u a t e d c y l i n d e r s c a l e d i n 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 w e i g h i n g 1 0 l i t e r s o f s l u r r y i n a c a l i b r a t e d b u c k e t . 9. S t r u c t u r e 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. E x p e r i m e n t a l P r o c e d u r e 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 37 t r a n s p o r t t e s t , the system was a l l o w e d t o r e s t a b i l i z e and the data 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 d e t e r m i n e t h e h y d r a u l i c t r a n s p o r t p a r a m e t e r s 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 , i i ) to examine p o t e n t i a l r e s t a r t problems 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 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 f l u m e . 1 • H y d r a u l i c T r a n s p o r t of Coarse Coal The s t e a d y s t a t e f l o w r a t e o f the f l u i d was d e t e r m i n e d and the flume s l o p e was s e t at an a n g l e between 0.5 and 10 per c e n t . The depth of 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 the s u r f a c e o f the f l u i d and m e a s u r i n g the d i s t a n c e to the I n s i d e , top s u r f a c e o f the p i p e . By m i n i m i z i n g the 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 d e v e l o p e d . 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 the w e i g h t of 10 l i t r e s o f water. 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 the b i n gate a t a s t a n d a r d r a t e . The gate was marked and the time taken to uncover the marks as the gate was opened was kept 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 flume 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 the f l u i d s t r e a m . 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 . The 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 which caused 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 the flume w i t h the s l i d i n g bed o f c o a l and when i t passed out of the flume, the t e s t was c o m p l e t e d and the t i m i n g was s t o p p e d . 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 r u n n i n g , 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 low 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 taken a g a i n . 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 g r o u n d - s h e e t . Each t e s t took 20 t o 30 m inutes to c o m p l e t e . R e s t r i c t i o n s 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. R e s t a r t T e s t s 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 taken 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 . The measured we i g h t of c o a r s e c o a l was i n t r o d u c e d i n t o the stream o f water 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 b e h i n d the p l u g . 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 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 t e s t , 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 h o u r s . 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 1n a 15.2 c e n t i m e t e r and a 25 c e n t i m e t e r d i a m e t e r p i p e . 3. 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 of f l o w r a t e , depth o f flow 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 . A new s l o p e 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 r e p e a t e d . A l t h o u g h some e x p e r i m e n t s were run s p e c i f i c a l l y to o b t a i n t h e s e measurements, the data 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. G e n e r a l The d a t a c o l l e c t e d i n the 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 the flume i n d e g r e e s , i i ) 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. g a l l o n s per m i n u t e . 40 i i i ) depth o f f l o w i n i n c h e s , i v ) w e i g h t of c o a r s e c o a l i n pounds, v) d u r a t i o n o f the t e s t i n m i n u t e s , and v i ) s p e c i f i c g r a v i t y of the f l u i d T a b l e 3-1 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 c o n v e r s i o n to SI u n i t s , b) C a l c u l a t e d V a r i a b l e s 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, v a l u e s o f the f o l l o w i n g v a r i a b l e s were c a l c u l a t e d ; i ) i n c l u d e d a n g l e of f l o w i n r a d i a n s , i i ) h y d r a u l i c r a d i u s i n c e n t i m e t e r s , and i i i ) c r o s s s e c t i o n a l a r e a o f f l o w i n square c e n t i m e t e r s . The average f l o w v e l o c i t y i n meters per second, was 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 s e c t i o n a l a r e a o f f l o w . The c o a r s e c o a l t r a n s p o r t r a t e , i n k i l o g r a m s per second, was c a l c u l a t e d by d i v i d i n g the weight 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 volume per c e n t s o l i d s o f the f l u i d was c a l c u l a t e d by the f o r m u l a ; C v = ( 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 o f t h e s e v a r i a b l e s f o r the same 74 e x p e r i m e n t s . The v a l u e s o f t h e s e v a r i a b l e s f o r the flume r e s t a r t t e s t s are shown i n T a b l e 3-3. An average 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 41 MEASURED VALUES FOR EXPERIMENTAL TESTS SLOPE '/, FLOWRATE LPS DEPTH Cm. WEIGHT Kg. TIME Sec SG 1 . 70 17. 56 8. 38 48. 49 10000.00 1 . 00 •J .90 2. 55 2. 79 0. 00 0.00 1 . 00 .3 . 90 8. 50 6. 60 48. 08 10000.00 1 . 00 4 . 90 10. 20 6.10 0. 00 0 . 00 1 . 00 5 . 90 15. 58 6. 60 0. 00 0. 00 1 . 00 6 . 90 21. 24 7. 62 0.00 0.00 1 . 00 7 1 . 00 10. 76 7.11 52. 66 10000.00 1 . 00 8 1 . 00 20. 67 7.37 52. 39 104.00 1.00 9 1. 60 17. 84 7. 37 57. 93 98 . 00 1 . 00 10 1 . 70 11.61 6.10 47. 22 102.00 1 . 00 11 1. 70 1 1. 89 5. 84 0. 00 0. 00 1 . 00 12 1. 70 21.81 7. 37 49. 26 57. 00 1 . 00 13 1. 80 6. 80 4. 57 53. 16 232.00 1 . 00 14 1 . 80 9. 63 6.10 47. 62 180.00 1 . OO 15 2.10 5. 66 4. 06 50. 44 336.OO 1 . 00 16 2.10 9. 63 5. 33 51.12 177.00 1 . 00 17 2.10 9.91 5. 84 56. 1 1 125.OO 1.00 IS 2.10 14. 73 6. 60 48.71 85. 00 1 . 00 19 2.10 15. 29 6. 60 51 . 08 120.00 1.01 20 2.10 15. 29 6. 60 50. 53 131.00 1 . 00 21 2.10 18. 97 7. 1 1 54. 43 90 . 00 1 . OO 22 2.10 19. 54 7.11 52. 35 95. 00 1 . 00 23 2.10 19. 54 7.11 51 . 80 6 1. 00 1 . 00 24 2. 30 12. 46 5. 33 44.17 39. 00 1 . 00 25 2. 30 26. 05 6. 35 48. 40 26. 00 1 . 00 26 2.40 15. 29 6. 35 55. 43 78. 00 1.01 27 2. 60 5. 38 3. 56 0. 00 0 . 00 1 . 00 28 2. 60 6. 80 3.81 52. 39 178.0© 1.00 2 9 2. 60 11.04 5. 33 50. 39 101.00 1 . 00 30 2. 60 13. 59 6. 60 38. 32 66. 00 1 . 00 31 2. 60 15. 29 6.10 0. 00 0. 00 1.00 32 2. 60 18. 12 6. 10 0. 00 0. 00 1 . 00 33 2.60 26. 90 7. 37 0. 00 0. 00 1 . 00 34 3. 00 6. 80 4. 06 51 . 94 117.00 1 . 00 35 3. 00 11. 04 5. 33 52. 39 74. 00 1 . 00 36 3. 00 11. 04 5. 84 56. 89 83. 00 1.01 37 3. 00 12. 74 5. 84 53. 30 49.00 1 . 00 Table 3-1 The data collected in 74 experiments gave values for these measured variables. 42 SLOPE FLOWRATE DEPTH WEIGHT TIME SG LPS Cm. Kg. Sec 38 3. 00 16. 99 6. 60 51. 89 53. 06 1 . OO 39 3. 00 19.54 6.35 52. 57 38. 06 1. OO 4 0 3. 50 5. 95 3. 30 53. 30 64. 60 1 . 06 41 3. 50 7. 36 4. 06 48. 62 76. 06 1 . GO 42 3. 50 5. 95 3. 30 51. 30 112.06 1 . 66 43 3. 50 13. 59 7.11 55. 34 63. 60 1 . 60 44 3. 50 14.16 7. 11 51. 48 68. 60 1 . 60 4 5 3. 50 23. 79 7. 37 48. 90 25. 60 1 . 66 46 5. 60 17. 84 6.10 0. 00 0. 06 1 . OO 4? 5. 60 19. 26 6. 60 0. OO 0. 06 1.00 48 5. 60 24. 64 7. 11 0. 00 0. 06 1 . OO 49 1. 70 2. 27 2. 79 0. 00 6. 06 1 . 04 50 1 . 70 1 1 . 89 5. 84 O. OO 0. 00 1.04 51 1. 70 24. 64 7. 37 0. OO 0.00 1 . 64 52 1 . 70 29. 17 7. 37 0. OO O . 00 1 . 04 1. 70 31. 72 8. 38 0. OO 0 . 00 1 . 64 54 2.10 4.81 4. 06 53. 71 10000.00 1 . 65 55 2.10 17. 56 7.11 56. 43 68. 06 1 . 65 56 2.40 8. 50 5. 08 55. 25 144.GO 1 . 65 5? 2.40 12. 46 5. 33 44. 95 45. GO 1 . 04 58 2.40 16. 43 6. 60 50. 76 62. 00 1 . 65 59 2. 40 19. 54 6. 60 54. 21 55. OO 1.65 60 2.40 22. 66 7.11 43. 72 3 8.00 1 . 65 61 2. 40 24. 36 7.11 39. 54 39. 00 1 . 65 62 3. 00 6.51 3.81 57. 75 138.OO 1 . 65 63 3.50 18.41 6. 35 55. 93 33. 00 1 . 05 64 4. 50 18.41 6.10 52. 89 28. OO 1 . 64 65 5. 20 9. 35 4. 83 54. 93 46. 00 1 . 64 66 6. OO 2. 55 2. 03 0. 00 0. 00 1 . 04 67 6. OO 20. 39 6.10 0. OO 0 . 66 1 . 04 68 6. OO 20. 96 7.11 0. 00 0. 00 1 . 64 69 6. 00 29. 74 6. 60 0. OO 0. 00 1 . 04 70 6.10 17. 84 6. IO 53. 21 24. OO 1 . 04 71 10. 00 4. 53 2. 03 0. 00 0. 00 1 . 04 72 10. 00 19. 82 5. 84 0. 00 0 . OO 1.64 73 10. 00 30. 87 6. 35 O. OO 0. OO 1 . 04 74 10. 00 33. 70 6. 86 0. 00 0. 00 1 . 64 Table 3-1 The data collected in 74 experiments gave values for these measured variables. HYDRAULIC ELEMENTS for DIFFERENT GEOMETRIES AREA ® WETTED PERIM. ® HYD. RADIUS (B) TOP WIDTH (t) HYD. DEPTH ® - = — f ~~ Y i - b by b + 2y by b+2y b y j T ^ (b+zy)y fh+?v1v b+2zy (b+zy)y b+2zy / i b+2y A+z* b+2y / l + z' M' T V 2y 2zy y 2 2y A*zl 2 /l +z< ST7 ^-(6-sin6)D 2 O 6D 2 (sin j 6)D ire - sinei 8 l s i n 1 6 j 2 Figure 3-3 Hydraulic variables f o r these four shapes are calculated according to t h e i r geometries. The cross sectional shape of i n t e r e s t to t h i s re-search i s the c i r c l e . 44 CALCULATED VALUES FOR EXPERIMENTAL TESTS THETfl HYDRAULIC AREA VELOCITY COARSE CV RADIUS TRANSPORT = = = = = = = Rads Cm. S q . C m . M /S ec . K g / S e c . ====== 1 1 . 67 4. 04 102.80 1.71 . OO 0. 00 et . 88 1.70 22. 92 1.11 0.00 0. 00 3 1 . 44 3. 46 75. 77 1. 12 . 00 0.60 4 1 . 37 3. 26 68. 14 1. 56 0. OO 0. 00 Cj 1 . 44 3. 46 75. 77 2. 06 O. OO 0.00 6 1 . 57 3.81 91.21 2. 33 0. 00 0. 00 7 1 . 50 3. 64 83. 47 1 . 29 . 01 0. 00 8 1 . 54 3. 73 87. 34 2. 37 . 50 6. OO 9 1 . 54 3. 73 87. 34 2. 04 . 59 . O l 10 1 . 37 3. 26 68. 14 1 . 70 . 46 O. 00 1 1 1 . 34 3.16 64. 36 1 . 85 0. 00 0. 00 12 1 . 54 3. 73 87. 34 2. 50 . 86 0. 00 13 1 . 16 2.61 46. 03 1. 48 . 23 0. 00 14 1 . 37 3. 26 68. 14 1.41 . 26 O. OO 15 1 . 09 2. 36 3 9.05 1 . 45 . 15 0 . O 0 16 1 • C r 2. 95 56. 96 1 . 69 . 29 0. 00 17 1 . 34 3.16 64.36 1 . 54 . 45 . O l 18 1 . 44 3. 46 75. 77 1 . 94 . 57 .01 19 1 . 44 3.46 75. 77 2. 02 . 43 . 02 20 1 . 44 3.46 75. 77 2. 02 . 39 0. 00 21 1 . 50 3.64 83. 4 7 2. 27 . 60 .01 i! 1 . 50 3. 64 83. 47 2. 34 . 55 .01 1 . 50 3. 64 83. 47 2. 34 . 85 0. 00 24 1 . 27 2. 95 56. 96 2.19 1.13 0. OO 25 1 . 40 3. 36 71. 94 3. 62 1 . 86 0. 00 26 1 . 40 3. 36 71 . 94 2.13 .71 . 02 £. 1 1 .01 2. 1 1 32. 35 1 . 66 O. OO 0. OO 28 1 .05 2. 23 35. 66 1.91 . 29 0. 00 29 1 . 27 2. 95 56. 90 1 . 94 . 50 0.00 30 1 . 44 3. 46 75. 77 1. 79 . 58 .01 31 1 . 37 3. 26 68. 14 2. 24 0. 00 0. 00 1 . 37 3. 26 68. 14 2. 66 0. 00 0. 00 33 1 . 54 3. 73 87.34 3. OS 0. 00 0. oo 34 1 . 69 2. 36 39. 65 1 . 74 . 44 0. OO ~'  Gt 1 . d7 2. 95 56. 96 1 . 94 .71 0. 00 36 1 . 34 3.16 64. 36 1 . 72 . 69 . 02 3 7 1 . 34 3.16 64. 36 1 . 98 1 . 09 .01 Table 3-2 Values of these variables were calculated using the geometric relationships for a c i r c u l a r cross section and the values of the experimentally measured variables. 45 THETA HYDRAULIC RADIUS AREA VELOCITY COARSE TRANSPORT cv Rads Cm. Sq.Cm. M/Sec. Kg/Sec. 38 1. 44 3. 46 75. 77 2. 24 . 98 0. 00 39 1 . 40 3. 36 71. 94 2. 72 1. 38 .01 40 . 97 1. 97 29. 12 2. 04 . 83 .01 41 1 . 09 2. 36 39. 05 1. 89 . 64 0. 00 42 . 97 1 . 97 29. 12 2.04 . 46 0. 00 43 1. 50 3. 64 83. 47 1. 63 . 88 0. 00 44 1. 50 3. 64 83. 47 1. 70 . 76 .01 45 1 . 54 3. 73 87.34 2. 72 1 . 96 0. 00 4 6 1 .37 3. 26 68. 14 2. 62 0. 00 0.00 47 1. 44 3.46 75. 77 2. 54 0. 00 0. 00 48 1 . 50 3. 64 S3. 47 2.95 0. 00 0. 00 49 . 88 1. 70 22. 92 .99 0. 00 . 08 50 1.34 3.16 64. 36 1 . 85 0. 00 . 08 51 1 . 54 3. 73 87.34' 2. 82 0. 00 . 08 52 1 . 54 3. 73 87. 34 3. 34 0 . O O . 08 53 1 . 67 4.04 102.80 3. 09 0. 00 . 08 54 1 . 09 2. 36 39. 05 1 . 23 . 01 . 10 55 1 . 50 3. 64 83. 47 2.10 . 83 . 10 56 1. 23 2. 84 53. 23 1 . 60 . 38 . 10 57 1 . 27 2. 95 56. 90 2.19 1 . 00 . OS 58 1. 44 3.46 75. 77 2. 17 . 82 . 10 59 1 . 44 3. 46 75. 77 2.58 . 99 . 10 60 1. 50 3. 64 83. 47 2.71 1.15 . 10 61 1. 50 3. 64 83. 47 2. 92 1.01 . 10 62 1 . 05 2. 23 35. 66 1. 83 . 42 . 10 63 1. 40 3. 36 71. 94 2. 56 1 . 47 . 10 64 1 . 37 3. 26 68. 14 2. 70 1 . 89 . 08 65 1. 20 2. 72 49. 60 1. 88 1.19 . 08 66 . 75 1. 27 14. 46 1. 76 0. 00 . 08 67 1. 37 3. 26 68. 14 2. 99 0. OO . 08 68 1 . 50 3. 64 83. 47 2.51 0. 00 . 08 69 1 . 44 3. 46 75. 77 3. 92 0. 00 . 08 79 1 .37 3. 26 68. 14 2. 62 2.22 . 08 71 . 75 1 . 27 14. 46 3. 13 0. 00 . 08 72 1 . 34 3.16 64. 36 3. 08 0. 00 . 08 7 3 1 . 40 3. 36 71. 94 4. 29 0 . 00 . 08 74 1.47 3. 55 79. 61 4.23 0. 00 . OS Table 3-2 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 for Flume Restart Tests Test Slope Flowrate Depth Weight Time SG % LPS Cm Kg Sec. 1 1.2 3.09 3.44 24.97 554.9 2 1.9 3.09 3.44 23.56 173.24 3 1.9 3.09 3.44 25.41 279.23 4 2.4 3.09 3.19 24.86 78.18 5 2.4 3.09 3.19 25.03 137.53 6 2.4 3.09 3.19 23.87 175.52 7 2.4 3.09 3.19 23.62 129.78 8 1.2 3.09 3.44 24.68 0 9 2.4 3.09 3.19 25.15 276.37 Test Theta Hydraulic Area Velocity Coarse Rads Radius Cm Sq. Cm. M/Sec. Transport 1 .99 3.44 30.85 1.00 .04 2 .99 3.44 30.85 1.00 .14 3 .99 3.44 30.85 1.00 .09 4 .95 3.19 28.35 1.09 .32 5 .95 3.19 28.35 1.09 .18 6 .95. 3.19 28.35 1.09 .14 7 .95 3.19 28.35 1.09 .18 8 .99 3.44 30.85 1.00 0 9 .95 3.19 30.85 1.09 .09 Table 3-3 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 for 5 minutes. The plug was removed and the time taken to remove a l l the coarse coal from the flume was measured. 47 d e t e r m i n e d from the e x p e r i m e n t a l data 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 Newtonian l i q u i d s as measured by a Stormer 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 each of the t h r e e s l u r r y m i x t u r e s are shown p l o t t e d w i t h a d i s t i l l e d water 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. G r a p h i c a l P r e s e n t a t i o n 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 th e s e v a r i a b l e s , e x p e r i m e n t a l data v a l u e s f o r the 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 second, 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 data 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 v e l o c i t y . °) 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 as; 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 "n" 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 m a n u f a c t u r e r ' 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 flow 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 data can be compared to 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 DRY WEIGHT VOLUME SPECIFIC GRAVITY NO. (grams) ( m i l l i l i t r e s ) 1 23.25 16.0 1.45 2 20.06 15.0 1.34 3 29.44 21.0 1.47 4 26.48 15.0 1.77 5 32.61 21.0 1.55 6 27.98 19.0 1.47 7 29.33 20.0 1.48 8 37.18 25.0 1.49 9 21.45 15.0 1.43 10 32.82 20.0 1.64 AVERAGE 28.06 18.6 1.51 Table 3-4 Samples of coal were weighed and then immersed in 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 in subsequent calculations. 49 F i g u r e 3-4 T h e s o l i d l i n e s a r e c o n s i s t e n c y c u r v e s f o r d i s t i l l e d w a t e r a n d t h e d i s c r e t e p o i n t s a r e t h e e x p e r i m e n t a l r e s u l t s f o r s l u r r i e s o f d i f f e r e n t s p e c i f i c g r a v i t i e s . A l l t h r e e s l u r r y m i x t u r e s b e h a v e d a s N e w t o n i a n f l u i d s 50 4 • 1.86 • 1.01 -1.66 • 1.15 • 1.38 • 1.96 • .86 1 •1.26 \ T' 5 •.55/85 i ^.60 \ ••1.00 T - 9 8 \ •83 T-7V82 \ T31 T 6 6 *-57 • 8 3 T.50 \ ^.58 • 44 • 0 • .46 V69 T.76 v • a s T- 8 8 . T.45 ^ 1-01 ^ •. 23 ,. *o > T.26 1 5 • 0 "V • 0 • 0 • 1.89 • .64 v 1.19 RAW COAL TRANSPORT (kg/sec) 1 2 3 4 5 T 1 1 1 r S L O P E (%) gure 3-5 This presentation of the data defines the limits of slope and velocity below which no coal was transported and supports the intuitive knowledge that coarse coal transport w i l l in-crease with increasing slope and f l u i d velocity. 51 VELOCITY v s DEPTH OF FLOW ^REGRESSION 1 2 3 4 5 6 7 8 9 10 11 12 DEPTH OF FLOW (CM) Figure 3-6 The experimental data i s compared to the Manning equation p r e d i c t i o n f o r a constant slope of 2.1. The regression curve to f i t the experimental data was v e l o c i t y = .4 ( d e p t h ) , 8 G . The discrepancy between the experimental v e l o c i t y was due to eit h e r experimental error or the un-s u i t a b i l i t y of the Manning equation. 52 the 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 the 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 e x p e r i m e n t a l d a t a r e s u l t i n g i n t h e e q u a t i o n ; Rfi 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 and the p r e d i c t e d v e l o c i t y was due to 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 the 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 Coal 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 e x p e r i m e n t s was to d e t e r m i n e 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 system. 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 , which 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 from a d i m e n s i o n a l a n a l y s i s o f the e x p e r i m e n t a l r e s u l t s . a) D i m e n s i o n a l A n a l y s i s A c c o r d i n g to B i n d e r ( 1 9 7 3 ) ; " D i m e n s i o n a l a n a l y s i s i s a u s e f u l t o o l f o r o r g a n i z i n g , 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 too complex f o r a t h e o r e t i c a l s o l u t i o n . " D i m e n s i o n l e s s groups are found 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 a r e 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) are 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) v e l o c i t y V LT-1 i i ) h y d r a u l i c r a d i u s R L i i i ) f l o w r a t e Q LT-3 i v ) g r a v i t y g LT-2 v/ s l ope s -v i ) s l u r r y s p e c i f i c g r a v i t y -v i i ) c o a r s e c o a l t r a n s p o r t T MT-1 The d i m e n s i o n l e s s groups a r e : parameter 1 = /V" D 7 T R flow parameter = parameter 2 =yy^5~ transport parameter = R 2 / 5 g l / 2 s - 3 Qs1 The e x p e r i m e n t a l d a t a were used to c a l c u l a t e v a l u e s f o r t h e s e g r o u p s . The v a l u e s f o r each r a t i o were then p l o t t e d a g a i n s t the v a l u e s f o r each o f the o t h e r d i m e n s i o n l e s s r a t i o s to 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 v e r s u s f l o w parameter was the o n l y p l o t which showed a s y s t e m a t i c c o r r e l a t i o n . The o t h e r c o m b i n a t i o n s o f d i m e n s i o n l e s s r a t i o s r e s u l t e d i n w i d e l y s c a t t e r e d , u n c o r r e l a t e d g r a p h s , b) T r a n s p o r t F u n c t i o n The exponents o f the 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 the f l o w and t r a n s p o r t p a r a m e t e r s . The v a l u e s o f the pa r a m e t e r s were p l o t t e d to 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 the c o m b i n a t i o n o f s p e c i f i c g r a v i t y and s l o p e exponents which r e s u l t e d i n the 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 us 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 the s l o p e v a l u e s were r a i s e d to the power o f 0.3 and the 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 to the power o f 0. T a b l e 3-5 l i s t s the c a l c u l a t e d v a l u e s o f the two m o d i f i e d r a t i o s ; flow parameter = R2/5 g l / 2 $.3 transport parameter = R2 g2/5 T l / 5 The t r a n s p o r t parameter measures 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 flow 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 p a r ameter 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 the flume s l o p e . The pa r a m e t e r s are p l o t t e d a g a i n s t each o t h e r on F i g u r e 3-7 and are f i t t e d by*a power law r e g r e s s i o n e q u a t i o n ; T r a n s p o r t P arameter = 3.57 (Flow P a r a m e t e r ) • 6 7 By r e o r g a n i z i n g the v a r i a b l e s , a 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 o f c o a r s e c o a l was d e v e l o p e d ; Q .0017 Q' 55 FLOW AND TRANSPORT PARAMETER VALUES D A T A FLOW T R A N S P O R T N U M B E R P A R A M E T E R P A R A M E T E R 1 8 24.60 29. 55 2 9 18. 44 24. 70 3 10 16.41 22. OO 4 12 22. 13 27. 98 5 13 16.60 23. 28 6 14 13. 38 20. 41 7 15 16.89 25. 71 8 16 16.47 24. 58 9 17 14. 24 20. 14 10 18 16. 90 23. 81 11 19 17. 55 26.24 12 20 17.55 26. 77 13 21 19.16 27. 40 14 22 19. 73 28. 75 15 23 19. 73 26. 36 16 24 20. 75 24. 20 1? 25 31.21 35. 21 18 26 18. 09 25. 06 19 28 21. 82 36. 10 20 29 17. 72 25. 27 21 30 14. 63 21. 92 22 34 18.21 £4. 84 23 35 16. 98 23. 57 24 36 14. 25 £0. 62 25 37 16.45 21.69 26 38 17.52 24. 69 27 39 21.61 28. 02 28 40 23. 84 27. 4 4 29 41 18. 84 25. Ol 30 42 23. 84 30.93 31 43 1 1 . 77 18.22 32 44 12. 26 19. 55 33 45 19. 44 25. 92 34 55 17. 73 23. 80 35 56 15. 38 £2.13 36 57 20.48 24. 8£ 37 58 18.11 24. 73 38 59 21 . 54 £8. 35 39 60 21 . 98 28. 77 40 61 23. 62 31.71 41 62 20. 03 26. 89 42 63 19. 44 26. 07 43 64 19.43 26. 33 44 65 14. 87 21 . 07 45 70 17. 19 24.72 Table 3-5 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 •V35 V S 30 M da. 25 oc UJ UJ S 1 < cc < a 20 FLOW PARAMETER oc -o a. tn z < oc 15 TRANSPORT PARAMETER = 3.57(Fl_0W PARAMETER) 67 10 10 1 — FLOW 15 PARAMETER 20 —I— 25 30 — i gSR^S" 3 Figure 3 -7 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 the transport and flow parameters was obtained when the slope term was raised to the .3 power. The transport parameter measures the r e l a t i v e e f f e c t s of the volumetric flow of f l u i d and transport of coarse c o a l . The flow parameter measures the r e l a t i v e e f f e c t s of the volu-metric flow rate and the flume slope. 57 T h i s e q u a t i o n , or 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 o f c o a r s e c o a l per u n i t o f t i m e . 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 ) i i ) f l u i d v e l o c i t y (1.0 to 4.3 meters per second) i i i ) f l u i d f l o w depth to flume d i a m e t e r r a t i o (0.13 t o 0.55) i v ) flume roughness c o e f f i c i e n t (n = .008) v) flume c r o s s - s e c t i o n ( c i r c u l a r ) 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 because i t can be kept 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 Froude Number c o n s t a n t 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 ; V l - _V2_ 7gD~i /gD~2 where "D" 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 , to 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 v a l u e s . 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 the r a t i o of i n e r t i a l f o r c e s to g r a v i t y f o r c e s i s kept c o n s t a n t f o r the model to p r o t o t y p e s c a l e 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 SLOPE FLOWRATE DEPTH WEIGHT TIME SG LPS Cm. Kg. Sec 1 l.OO 14.73 6.60 53.30 171.00 1 .OO 2 1.70 16.71 7.37 47.85 73.OO 1.00 3 2."IO 12.46 6.35 52.16 122.00 l.OO 4 2.30 18.69 6.10 46.58 ; 28.00 1.00 5 2.60 15.86 6.60 50.53 62.0O l.OO 6 3.50 11.33 6.35 56.57 56.OO 1.01 7 6.10 17.84 6.10 53.48 24.OO 1.00 8 2.40 1O.20 5.08 43.13 52.OO 1.05 9 2.40 17.56 6.35 45.35 36.OO 1.04 10 3.00 14.44 6.10 56.30 57.OO 1.05 THETR HYDRAULIC AREA VELOCITY COARSE CV Pads RADIUS TRANSPORT Cm. S q.Cm. M-'Sec . Kg-'Sec . 1 1 . 44 3. 46 75. 77 1 . 94 .31 0 . O O 2 1 . 54 3. 73 87. 34 1.91 . 66 0. OO 3 1 . 40 3. 36 71 . 94 1 . 73 . 43 O. 00 4 1 . 37 3. 26 68. 14 2. 74 1 . 66 0. 00 tr 1 . 44 3. 46 75. 77 2. 09 . 82 0. OO 6 1 . 40 3. 36 71 . 94 1 . 57 1.01 . 02 7 1 . 37 3. 26 68. 14 2. 62 2. 23 0. 00 3 1 . 23 2. 84 53. 23 1 . 92 . 83 . 10 9 1 . 40 3. 36 71.94 2. 44 1. 26 . 08 10 1 . 37 3. 26 68. 14 2.12 . 99 . 10 Table 3-6 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 for the 10 tests. 59 CALCULATED AND MEASURED RATE OF COAL TRANSPORTATION TRANSPORT IS IN UNITS OF C u . C m . / S e c . DATA CALCULATED EXPERIMENTAL NUMBER TRANSPORT TRANSPORT 1 192.21 207.80 2 356.19 437.00 3 320. 17 285.05 4 724.55 1109.06 5 565.45 543.34 6 455.23 673.43 7 1778.23 1485.59 8 347.81 552.95 9 648. 12 839.90 10 614.39 658.43 Table 3-7 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 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 f o r t h e s e ten t e s t s . The maximum d i f f e r e n c e between the two r e s u l t s was 59.0 per c e n t w i t h a mean d i f f e r e n c e of 16.2 per c e n t . T h i s i n d i c a t e s t h a t the t r a n s p o r t f u n c t i o n i s a v a l i d r e l a t i o n s h i p t o p r e d i c t the t r a n s p o r t o f c o a r s e c o a l w i t h i n 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 can 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 the da t a p o i n t s and the 45 degree l i n e i s p r o p o r t i o n a l t o 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 . 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 i s o - t r a n s p o r t p l o t . 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 c o n s t a n t t r a n s p o r t of c o a r s e c o a l ( i n u n i t s o f c u b i c c e n t i m e t e r s p e r s e c o n d ) . The i s o - t r a n s p o r t l i n e s are c a l c u l a t e d by f i x i n g the v a l u e s of f l o w depth and c o a r s e c o a l t r a n s p o r t i n the 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 the s l o p e and v e l o c i t y t o change. F i g u r e 3-9 shows a f a m i l y of 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 depth 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 of f o u r o f the t e n v e r i f i c a t i o n t e s t s , which were c a l c u l a t e d u s i n g a f l o w depth of 6.35 c e n t i m e t e r s are 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 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 d e m o n s t 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 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 c o a r s e c o a l . 61 CALCULATED vs EXPERIMENTAL COARSE COAL TRANSPORT IN K I L O G R A M S PER S E C O N D / 1 2 E X P E R I M E N T A L Figure 3 - 8 The experimental and c a l c u l a t e d rates of coarse coal transport are p l o t t e d against each other. The distance between the data points and the 4 5 degree s o l i d l i n e i s proportional to the d i f f e r e n c e between the predicted and experimental r e s u l t s . The dashed l i n e s represent a d i f f e r e n c e of plus and minus 20 percent from the 45 degree l i n e . 62 C O A L ISO-TRANSPORT CURVES D E P T H O F FL0W=6.35 C M . 1 -1 2 S L O P E % Figure 3-9 The iso-transport curves represent l i n e s o f constant coarse coal transport. They are calculated by f i x i n g the flow depth and coarse coal transport i n the Transport Function and allowing the slope and v e l o c i t y to change. The s i m i l a r i t y of the experimental and calculated r e s u l t s demonstrate the accuracy of the Transport Function i n pre d i c t i n g the transportation of coarse c o a l . 63 2. R e s t a r t i n g T e s t s The p o t e n t i a l f o r o p e r a t i n g problems e n c o u n t e r e d i n 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 e x p e r i m e n t s . The e x p e r i m e n t a l r e s u l t s d e m o n s t r a t e 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 hours 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 problem f o r an i n d u s t r i a l s c a l e system i f the r u l e s o f d i m e n s i o n a l s i m i l a r i t y a r e f o l l o w e d . That 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 or equal 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 Froude 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 systems the same. 3. 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 to d e t e r m i n e 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 : . R2/3 ,1/2 n 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 f l o w 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 are 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 or 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 AND MANNING FLUID VELOCITY 10 20 30 40 50 60 70 80 90 100 R A N G E O F D I F F E R E N C E % Figure 3-10 The difference between the experimentally determined flow velocities and the flow velocities calculated by the Manning equation are presented on this cumulative difference plot. This graph demonstrates that, of 84 tests, 80 percent of the experimental velocities are within plus or minus 30 percent of the Manning pre-dictions. 65 I t i s c o n c l u d e d t h a t use o f the Manning e q u a t i o n to 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 v e r i f i e d by the e x p e r i m e n t a l d a t a . F. EXPERIMENTAL ERROR A l l e x p e r i m e n t s are s u b j e c t t o e r r o r s from a v a r i e t y of s o u r c e s . Some are 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 e x p e r i m e n t a l r e s u l t i n the same d i r e c t i o n and magnitude. 1. S y s t e m a t i c 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 the same magnitude and the same s i g n f o r the same g i v e n 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 c u m u l a t i v e , i t i s i m p o r t a n t to d e t e c t and e l i m i n a t e them. P o t e n t i a l s o u r c e s o f s y s t e m a t i c e r r o r i n the c o a l t r a n s p o r t e x p e r i m e n t s were h a n d l e d i n d i f f e r e n t ways, a) Flow Rate Measurement The m a g n e t i c f l o w meter o p e r a t e d i n d e p e n d e n t l y o f f l u i d t e m p e r a t u r e , 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 t e m p e r a t u r e . The pump i n l e t was k e p t submerged to 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 the pump and i n t r o d u c i n g a i r b u b b l e s i n t o the f l o w o f f l u i d . B u b bles i n the fl o w o f f l u i d would cause 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 meter r e a d i n g s t a k e n i n 40 seconds i n d i c a t e d t h a t a i r b u b b l e s were not a problem. 66 b) Depth of Flow Measurement The s u r f a c e t e n s i o n of the water c a u s e d the depth of f l o w v a l u e to be too h i g h . T h i s was c o r r e c t e d by a d d i n g the meniscous h e i g h t (1/16 i n c h e s ) to the measurement of d i s t a n c e from the f l u i d s u r f a c e to the top o f the 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 l e v e l a t t a c h e d t o a c a l i b r a t e d compass. To e n s u r e a c c u r a c y , the 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 to s e t the p o s i t i o n o f the z e r o degree r e a d i n g . d) Weight 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 to t e m p e r a t u r e s beyond a normal o p e r a t i n g range of 15 deg r e e s t o 35 degrees C e l s i u s . V a l i d r e a d i n g s were taken by k e e p i n g the 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 r a n g e . The a c c u r a c y of the 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 the s c a l e s w i t h a known q u a n t i t y o f water. 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 the passage o f a h y d r a u l i c jump out of the f l u m e . T h i s assessment was s u b j e c t t o the e x p e r i e n c e of the o b s e r v e r . To reduce the e f f e c t of 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 the 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 the time k e e p e r . D i s a g r e e m e n t s were h a n d l e d by u s i n g the average of the two o b s e r v a t i o n s . f ) Coal 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 to 67 measure t h e i r volume. Care was taken to remove a l l a i r bu 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 the top or bottom o f the meniscous t o f i n d the 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 r e p e a t e d measurements of the same q u a n t i t y . The magnitude o f t h e measurement i s t h e mean r e s p o n s e p l u s or minus the c a l c u l a t e d e r r o r . Some of the me a s u r i n g i n s t r u m e n t s used i n the c o a l t r a n s p o r t e x p e r i m e n t s had a m a n u f a c t u r e r ' s s t a t e d a c c u r a c y . The random e r r o r s of the 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 the r e s u l t s of r e p e a t e d r e a d i n g s . a) Flow Rate Measurement The f l o w meter 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 the mean v a l u e o f 30 to 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 the 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 the mean. b) Depth o f Flow Measurement The d i s t a n c e t o the f l u i d s u r f a c e was measured 8 to 10 times f o r each t e s t and an a c c u r a c y o f p l u s or 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 the d i a m e t e r o f the f l u m e . The e r r o r i n me a s u r i n g the 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 the depth 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 .1 d e g r e e . The measurement e r r o r was h a l f o f t h i s or .09 per c e n t s l o p e . d) 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 r e f o r e , the measurement e r r o r was 1 ounce. 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 r s e c o a l w e i g h t was the r o o t mean square or 2.24 o u n c e s . 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 the 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 t h a t 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 . The e q u i l i b r i u m , 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 r u n - o f - m i n e c o a l has been d e t e r m i n e d by the mine owners to be 5 per c e n t . 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 r u n - o f - m i n e c o a l 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 to be 6.7 per c e n t . The e r r o r due to the s c a l e r e a d i n g i s s m a l l r e l a t i v e to 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 to be 1 s e c o n d . The c u m u l a t i v e e f f e c t 69 o f t h e s e e r r o r s 1s the r o o t mean square v a l u e , or 1.4 seconds f o r each t e s t . f ) 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 to weigh the c o a l p a r t i c l e s was a c c u r a t e to two de 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 the 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 . U s i n g the minimum measured w e i g h t o f 15.94 grams and the minimum volume o f 10.0 c u b i c c e n t i m e t e r s , the 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 the E x p e r i m e n t a l R e s u l t s The e f f e c t s o f e r r o r s on the e x p e r i m e n t a l r e s u l t s were a n a l y z e d by examining t h e i r e f f e c t on the T r a n s p o r t F u n c t i o n , 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 , the 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 f l o w v e l o c i t y . a) C o a r s e Coal T r a n s p o r t 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 the e r r o r s a s s o c i a t e d w i t h each o f the p e r t i n e n t h y d r a u l i c v a r i a b l e s . The newly c a l c u l a t e d parameter 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 to the 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 to be; p l u s e r r o r : T r a n s p o r t Parameter = 3.45 (Flow P a r a m e t e r ) * 6 7 median: T r a n s p o r t Parameter = 3.57 (Flow P a r a m e t e r ) « 6 7 minus e r r o r : T r a n s p o r t Parameter = 3.75 (Flow P a r a m e t e r ) * 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 the o r i g i n a l t r a n s p o r t f u n c t i o n . The " s t e a d i n e s s " i n 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 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 c o n v e y a n c e . 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 of 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 per c e n t of the e x p 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 as i t p r e d i c t s the h y d r a u l i c conveyance of 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 of c i r c u l a r c r o s s s e c t i o n . 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 the Manning e q u a t i o n and as c a l c u l a t e d from the e x p e r i m e n t a l 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 . The Manning 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 f l o w v e l o c i t y , w i t h i n the 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 or minus 20 per c e n t i n 93 per c e n t o f the t e s t s . The v a l u e o f the r e s i s t a n c e f a c t o r "n" was i t e r a t i v e l y changed 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 CALCULATED vs EXPERIMENTAL COARSE COAL TRANSPORT IN KILOGRAMS PER SECOND 1 2 EXPERIMENTAL Figure 3-11 Errors i n the predicted and experimental coarse coal transport f o r the 10 v a l i d a t i o n t e s t s were calculated and 6 of the predicted values were the same as the ex-perimental values, within the error boundaries. A l l of the predicted values were within 20 percent of the ex-perimental values. This corroborates the accuracy of the Transport Function. 72 p r e d i c t i o n s . 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 m a n u f a c t u r e r s 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 the 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 the 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 c h a n n e l . G. Comparison w i t h o t h e r R e s e a r c h The open channel sediment t r a n s p o r t e x p e r i m e n t s o f Ambrose (1 9 5 3 ) , G r a f and A c a r o g l u (1968), and W i l s o n (1980) are 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 are compared to the c o n c l u s i o n s of t h i s s t u d y . 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 sediment t r a n s p o r t i n open channel p i p e f l o w to d e t e r m i n e d e s i g n p a r a m e t e r s f o r the i n s t a l l a t i o n o f storm sewers. H i s e x p e r i m e n t a l flume was an 18.3 meter 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 conveyed was u n i f o r m l y graded sand, .25 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 m i l l i m e t e r s i n s i z e . 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 f l o w e d t h r o u g h i t u n t i l the sand began to d e p o s i t on the bottom o f the p i p e . 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 r a t i o s ; where "Q s" i s the v o l u m e t r i c f l o w r a t e o f the s o l i d s , "D" i s the 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 are 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 are 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 the 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 the 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 not t e s t i t s a c c u r a c y by a l t e r i n g the 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 s u s p e n s i o n . The c u r r e n t r e s e a r c h used a wide 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 f l o w 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 the t r a n s p o r t o f f i n e c o a l o n l y . 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 was changed to c a l c u l a t e the d i m e n s i o n l e s s r a t i o f o r the c o a l d a t a v a l u e s . A v a l u e o f .06 i n s t e a d o f -.4 was used and the r e s u l t s a r e shown on F i g u r e 3-12 w i t h the o r i g i n a l Ambrose r e l a t i o n s h i p shown by the 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 data f i t the 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 s e d i m e n t t r a n s p o r t a t the p o i n t of i n c i p i e n t d e p o s i t i o n o n l y . Ambrose d i d not t e s 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 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 u s i n g COAL DATA 10 Figure 3-12 The exponent on the s p e c i f i c gravity 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 to 0.06. The coal data, using t h i s modified r e l a t i o n s h i p , has been plotted with the o r i g i n a l Ambrose curve. The good f i t of the coal data suggests that 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 modified to accommodate data using sediments of a d i f f e r e n t density 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 da t a u s i n g sediments of a d i f f e r e n t d e n s i t y . 2. 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; •2.52 10.32 Y " C. V R ~~IT where the t r a n s p o r t p a r a m e t e r , p = X— ^— and /(s-,-1) <" ( s , - l ) d c the s h e a r i n t e n s i t y parameter Y = J50 S R The v a r i a b l e " d 5 0 " r e f e r s to the s c r e e n s i z e , i n m i l l i m e t e r s , which p a s s e s 50 per c e n t o f the m a t e r i a l . The open c h a n n e l f l o w d a t a o f f o u r p r e v i o u s r e s e a r c h e r s , ( G i l b e r t (1914); Guy e t a l (1966); 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 t o c a l c u l a t e the d i m e n s i o n l e s s p a r a m e t e r s which are p l o t t e d on F i g u r e 2-2 on page 21. 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 stream 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 g r a p h . The c o a l t r a n s p o r t d a t a from the 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 the t r a n s p o r t and s h e a r i n t e n s i t y p a r a m e t e r s d e f i n e d above. They are p l o t t e d on F i g u r e 3-4 w i t h 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 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 s h e a r G R A F R E L A T I O N S H I P U S I N G C O A L D A T A 10 1*1 oc UJ I V) • •— • • * = 0 d 5 0 S R • \ • C V V R • i ^ .3 _ I • * • F INE • COARSE v COMBINED « < • • • • w V ress on • c —B „ • a • 1 • • • Q Q — 10 100 1000 TRANSPORT PARAMETER $ Figure 3-13 The coal data are plotted as fine, coarse and combined results to investigate the effect of p a r t i c l e size on the shear intensity and transport parameters. The acceptable f i t of the fine coal data and the poor f i t of the coarse and combined coal data suggests that these parameters are inadequate to model sediment transport for large pa r t i c l e sizes. A different treatment of the pa r t i c l e size terms in the shear intensity and transport para-meters would define a relationship which f i t s a l l of the data more accurately. 77 i n t e n s i t y and t r a n s p o r t p a r a m e t e r s . G r a f and A c a r o g l u ' s r e l a t i o n s h i p u n d e r e s t i m a t e s the da t a f o r the c o a r s e and combined c o a l r e s u l t s b ut the f i n e c o a l r e s u l t s a r e w i t h i n the s c a t t e r o f the o r i g i n a l p l o t . The average p a r t i c l e d i a m e t e r s f o r the 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 c o a r s e c o a l , i i ) 0.65 m i l l i m e t e r s f o r the 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 f o r the combined c o a l . The l a r g e s t p a r t i c l e s used i n the G r a f and A c a r o g l u p l o t were 1.7 m i l l i m e t e r s . The a c c e p t a b l e f i t o f the f i n e c o a l data and the poor f i t of the 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 the shear i n t e n s i t y and t r a n s p o r t p a r a m e t e r s are i n a d e q u a t e to model sediment t r a n s p o r t f o r l a r g e p a r t i c l e s i z e s . The good f i t o f the f i n e c o a l r e s u l t s a l s o s u g g e s t s t h a t the s p e c i f i c g r a v i t y term i s not the 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 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 t r a n s p o r t p a r a m e t e r s 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 da t a more a c c u r a t e l y . 3. 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 , computer a n a l y s i s o f open channel sediment t r a n s p o r t i n a c i r c u l a r c o n d u i t , based on a computer model f o r s l u r r y t r a n s p o r t i n f u l l p i p e f l o w . H i s r e s u l t s are based on the premise 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 the maximum volume of s o l i d s o v e r a s p e c i f i e d d i s t a n c e . T h a t i s ; 78 optimum t r a n s p o r t = maximum P S s 1 C v d QL L tan 0 where P s i s the s p e c i f i c w e i g h t o f the s o l i d , "r " 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 o f the s l u r r y , vd "L" i s the 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 the flume s i ope. W i l s o n s u g g e s t s t h a t a 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 o f about 30 p e r c e n t and a f l u i d f l o w depth o f .93 times the flume d i a m e t e r w i l l d e t e r m i n e the optimum f l o w c o n d i t i o n s . K e e p i n g 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 the 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 p i p e d i a m e t e r s . For h e t e r o g e n e o u s f l o w , W i l s o n p r o p o s e d the f o l l o w i n g e q u a t i o n ; i c _ 7 /s-,-1 \ 1.2 tan 0 = O.ld D J ) where "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 i n m e t e r s . The b o u n d a r i e s to 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 ; .0006 / s n - l \ °- 6 i ) tan 0 = ( i l l ) \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 sediment 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 sediment t r a n s p o r t . 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 er 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 meters b ut the boundary c o n d i t i o n s , which are 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 the 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 . T h i s a m b i g u i t y s u g g e s t s t h a t W i l s o n ' s r e l a t i o n s h i p does not a d e q u a t e l y c o v e r the c a l c u l a t i o n o f an optimum flume s l o p e . Sediment 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 to 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 lower than 27.7 per c e n t , i n the c u r r e n t r e s e a r c h which r a i s e s doubt about the a c c u r a c y o f the 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 not used i n the 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 the open channel t r a n s p o r t of 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 to the s p e c i f i c g r a v i t y term, f i t s the f i n e c o a l d a t a but does not p r e d i c t the t r a n s p o r t of c o a r s e c o a l . 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 c o a l d a t a w i t h i n the s c a t t e r of t h e o r i g i n a l p l o t but does not f i t the c o a r s e and combined c o a l d a t a . 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 to be m o d i f i e d t o i n c o r p o r a t e the 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 s i z e s . 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 e q u a t i o n o f W i l s o n produced ambiguous r e s u l t s when a p p l i e d t o the 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 of 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 . I t 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 w i t h O p e r a t i n g Mines Westar Mines L t d . ( f o r m e r l y B.C. Coal L t d . ) , o p e r a t i n g an underground 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 C olumbia, and the Hansa-Hydro Mine of West Germany have r e s e a r c h e d flume conveyance of f l u i d i z e d c o a r s e c o a l . 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 are r e l a t e d to t h i s r e s e a r c h . 1. Westar Mines 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 propose the f o l l o w i n g r e l a t i o n s h i p t o d e t e r m i n e flume s l o p e ; s = f ( s r l ) 100 [s-.q'k' + ( s r l ) ] where " f " i s the 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 flume s u r f a c e , "q* " i s the s p e c i f i c c onsumption o f water i n c u b i c meters per ton and "k 1 " i s the c o e f f i c i e n t of f l o w energy i m p a r t e d to the c o a l . 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 of water r e q u i r e d to 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 to 8 1 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 flume s l o p e o f 2.5 per c e n t , the s p e c i f i c consumption 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 c u b i c meters per t o n o f s o l i d s . The s p e c i f i c consumption o f water c a l c u l a t e d from the c u r r e n t e x p e r i m e n t a l program, based 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 of 20 per 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 meters of water f o r each t o n o f s o l i d s . I f the e x p e r i m e n t a l t r a n s p o r t of 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 the s p e c i f i c consumption of water, a v a l u e o f 10.9 c u b i c meters per ton o f 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 consumption o f water v a l u e s and t h a t p r e d i c t e d by the f l u m i n g c u r v e are due to the 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 the c o a l p a r t i c l e s , the Westar Mines L t d . e q u a t i o n i s s p e c i f i c t o 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 to 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 the c u r r e n t r e s e a r c h , 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 per c e n t were minus 10 m i l l i m e t e r s . L e s s water i s needed t o move the f i n e c o a l p a r t i c l e s so the 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 the water r e q u i r e m e n t s . The f a c t o r o f 2 d i f f e r e n c e between the s p e c i f i c c onsumption o f water 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 the 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 s m a l l 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 c o a l 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 geometry. 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 the s t a f f a t Westar 8 2 Mines 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 flume m a t e r i a l . The f a i l u r e o f t h i s r e l a t i o n s h i p t o a c c o u n t f o r the 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 which was a c c o u n t e d f o r i n the T r a n s p o r t F u n c t i o n . 2. 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 erground 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 very 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 tonnes of c o a l s l u r r y had p a s s e d t h r o u g h the f l u m e . The p l a s t i c s u r f a c e a l s o p e r m i t t e d a d e c r e a s e i n flume s l o p e t o 8 per c e n t from 12 per c e n t . 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 on page 25. T h i s phenomenon was 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 measurements were t a k e n . 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 bottom of the flume when the water f l o w i s s t o p p e d . Kuhn d i d not d i s c u s s problems i n r e s t a r t i n g the flume but t h i s p o t e n t i a l o p e r a t i n g problem was a d d r e s s e d i n the c u r r e n t r e s e a r c h . 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 c o a l 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 w i t h o u t d i f f i c u l t y . 83 CHAPTER IV  PARTICLE SIZE DEGRADATION A. I n t r o d u c t i o n The t r a n s f e r of 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 , i n p l u g f l o w l e a d s to p a r t i c l e s i z e d e g r a d a t i o n . The o b j e c t i v e of t h i s e x p e r i m e n t a l program was to d e t e r m i n e 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 and p r e d i c t i t s e f f e c t on subsequent c o a l c l e a n i n g p r o c e s s e s . 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 m o d e l l e d i n t h i s e x p e r i m e n t a l program. To reduce t h i s system to 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 , the a p p a r a t u s shown i n F i g u r e 4-1 was b u i l t . B. A p p a r a t u s The a p p a r a t u s c o n s i s t e d o f two, 3 meter l o n g 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 s w i t h a w a l l t h i c k n e s s of 9.5 m i l l i m e t e r s . The f i r s t tube was made of 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 the o t h e r tube was made of 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 l o n g , f l a n g e d 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 . The c l o s e t o l e r a n c e of the ma t i n g ends, as d e t a i l e d on F i g u r e 4-1, d i d not c o n t r i b u t e to p a r t i c l e d e g r a d a t i o n . The i n s i d e w a l l c o n d i t i o n of the tubes 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 rounded weld p r o t r u d i n g 5 m i l l i m e t e r s from the s u r f a c e . COAL SAMPLE TUBE APPARATUS SAMPLING TUBE CUTAWAY VIEW Figure 4-1 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 of two 3 meter long by 75 centimeter diameter s t e e l tubes. The f i r s t tube was made of two, 1.5 meter long flanged s e c t i o n s bolted together (not shown) and the other tube was made of s i x , 30 centimeter long and two, 60 centimeter long flanged sections held together by four compression rods. The mating ends were mechined to a close tolerance. A gasketed coal plug, fastened to a 3 meter long rod supported the column of c o a l . 8 5 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 to a 3 meter l o n g rod s u p p o r t e d the column o f c o a l . A 4.5 tonne 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 the tubes and lower the c o a l . C. P r o c e d u r e 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 the 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 s e c t i o n a t a t i m e . Samples o f c o a l were taken as the tube was 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 at the top o f each s e c t i o n . The p l u g hook was suspended from a s t e e l bar p l a c e d a c r o s s the top of the s t e e l tube to p r e v e n t the c o a l from f a l l i n g out and the c o a l f i l l e d tube was p l a c e d on top o f the empty t u b e . With the 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 overhead c r a n e , the s t e e l bar was removed and the c o a l was dropped i n t o the bottom tube a t the r a t e o f 20 c e n t i m e t e r s per s e c o n d . The s l i n g was removed from the c r a n e and the now empty top tube was p l a c e d on the f l o o r . The s t e e l bar was r e p l a c e d to h o l d the p l u g hook, the c o a l f i l l e d tube was. l i f t e d onto the empty tube and the 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 the s t e e l tubes 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 the l a b o r a t o r y to m i n i m i z e the danger o f the top 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 out to s i m u l a t e the 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 meters of e l e v a t i o n . Figure 4-2 The coal f i l l e d tube was placed on top of the empty tube, the gasketed plug was released from i t s fixed p o s i t i o n and the coal column was lowered into the bottom tube at a rate of 20 centimeters per second by an overhead crane. The p o s i t i o n of the tubes was swapped and the cyc l e was repeated. Plug flow through 300 meters of st e e l l i n e d r a i s e was simulated 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 , s e c t i o n e d tube was taken a p a r t one s e c t i o n a t a t i m e . The c o a l i n the top and bottom 1 meter was d i s c a r d e d due t o the i n f l u e n c e o f end e f f e c t s . Sharpened 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 , 9.5 m i l l i m e t e r s t h i c k and 12 c e n t i m e t e r s deep were d r i v e n i n t o the c o a l . Coal samples, w e i g h i n g 4 k i l o g r a m s , were take n from the 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 o u t s i d e 2 c e n t i m e t e r s 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 c o a l samples were taken from each s e c t i o n of the s t e e l tube and each sample was s i z e d on 4.76 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 m i l l i m e t e r s c r e e n s i z e s . D. R e s u l t s The h e i g h t o f the c o a l column a t the b e g i n n i n g of the e x p e r i m e n t was 2.75 m e t e r s . C o n s o l i d a t i o n and l e a k a g e reduced the c o a l column h e i g h t t o 2.1 meters a t the c o n c l u s i o n o f the t e s t . The 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 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 minus 1.19 m i l l i m e t e r s . At the end o f the c y c l i n g , the w e i g h t of the minus 1.19 m i l l i m e t e r c o a l had i n c r e a s e d t o 35 per c e n t o f the t o t a l c o a l as shown on T a b l e 4-1. T h i s t a b l e a l s o 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 o u t s i d e c i r c u m f e r e n c e of the c o a l column (Sample A ) . There was no i n c r e a s e i n c o a l f i n e s i n the o t h e r two s a m p l i n g l o c a t i o n s w i t h the e x c e p t i o n o f s e c t i o n 3. 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 ectioned tube was taken apart. Sharpened s t e e l r i n g s of d i f f e r e n t diameters were driven i n t o the c o a l . Coal samples, weighing four kilograms were taken from the annular spaces. The outside 2 centimeters of coal were sampled from the circumference of the i n t a c t coal column by slowly 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 p a r t i c l e s were 100 percent minus 65 millimeters p r i o r to the degradation tests. The fraction of coal par t i c l e s f i n e r than 1.19 millimeters was 32 percent. 90 COAL PARTICLE DEGRADATION TEST RESULTS SAMPLE +4.76 mm -4.76 mm to -2.38 mm to -1.19 mm +2.38 mm +1.19 mm % % % % 3A i 42 10 10 38 3B 35 16 12 38 3C 42 13 11 34 Sub-Total 41 12 11 37 HEAD 46 12 11 32 4A 44 9 9 38 4B 43 13 12 32 4C 44 12 12 32 Sub-total 43 11 11 34 HEAD 46 12 11 32 5A 40 4 18 38 5B 44 13 12 30 5C 46 12 11 31 Sub-Total 43 10 14 33 HEAD 46 12 12 32 TOTAL 42 11 12 35 HEAD 46 12 11 32 TABLE 4-1 The degradation of coal took place around the circumference of the coal column (Sample A) and resulted in 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 the b e g i n n i n g of the e x p e r i m e n t . The r a d i a l l i n e s of p a i n t e d c o a l were found unchanged when the c o a l was b e i n g sampled from the s t e e l t u b e . T h i s q u a l i t a t i v e r e s u l t s u g g e s t s t h a t l a t e r a l m i g r a t i o n o f c o a l p a r t i c l e s i s not a phenomenon of 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 , s t e e l l i n e d r a i s e i n p l u g f l o w w i l l not g e n e r a t e c o a l f i n e s d e t r i m e n t a l to subsequent c o a l 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 flume t r a n s p o r t system p r e s e n t e d i n t h i s c h a p t e r 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 t e c h n o l o g y i n i t s d e s i g n . Because the system was p l a n n e d f o r a p a r t i c u l a r mine, some of 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 . An e f f o r t has been made, o t h e r w i s e , 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 e x t e n d 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 c o n d i t i o n s . The unbroken 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 , m e c h a n i c a l l y 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 o v e r s i z e c o a l s c r e e n i n g p l a n t . The p l u s 6.4 c e n t i m e t e r c o a l 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 which i s l o w e r e d through a 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 t o an underground d r i f t . The c o a l i s s l u r r i e d w i t h water and t r a n s p o r t e d t o a d e w a t e r i n g p l a n t t h r o u g h a 61 c e n t i m e t e r 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 . The d e w a t e r i n g p l a n t s c r e e n s and dewaters the c o a l and s t o r e s i t on a 30,000 tonne, l i v e c a p a c i t y , o u t d o o r s t o c k p i l e . The system i s f u l l y automated 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 s c h e m a t i c 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 system i s shown i n F i g u r e 5-1. R e c o g n i t i o n i s g i v e n t o ; i ) Al Bevan and A r t B e r t r a n d who h e l p e d i n u n d e r s t a n d i n g the mine g e o l o g y , 93 SCALPING GRIZZLY DEWATERING STOCKPILE PLANT DESIGN ELEMENTS Figure 5-1 The unbroken, run-of-mine coal is 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 particles are conveyed through a 1 meter diameter steel lined raise to an underground d r i f t . The coal is slurried with water and conveyed to a dewatering plant through a 61 centimeter diameter, high density, poly-ethylene pipe. The dewatered coal is stockpiled and then sent to the wash plant. 94 i i ) B i l l Potma of 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 the 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 ck 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 Underground 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 m i n i n g 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 o f s u f f i c i e n t e l e c t r i c a l power to pump water t o the top o f the mountain. 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 horsepower 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 system and water 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 of the 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 system i n d i c a t e d t h a t i t would be 75 per c e n t o f t h e underground flume system c a p i t a l c o s t . T h i s , combined w i t h the c a p i t a l c o s t 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 out a s u r f a c e flume system f o r economic r e a s o n s . T h i s r e s u l t may not be g e n e r a l f o r e v e r y m i n i n g s i t u a t i o n . C. Underground Run-of-Mine Coal 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 underground r a i s e and flume system t o t r a n s p o r t r u n - o f - m i n e c o a l from the c o a l f a c e to the w a s h p l a n t . the unbroken 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 to 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 to an underground d r i f t t h r o u g h a s t e e l l i n e d r a i s e where i t i s s l u r r i e d and conveyed t h r o u g h a 61 c e n t i m e t e r d i a m e t e r flume to a s u r f a c e d e w a t e r i n g p l a n t . The c o a r s e , 95 dewatered 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 the f i n e c o a l i s s e n t t o the p r e p a r a t i o n p l a n t t h i c k e n e r . 1. Coal L o a d e r and Truck Requirements The i n s i t u c o a l i s dug from the 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 , m e c h a n i c a l l y d r i v e n , r e a r dump t r u c k s . The t r u c k s dump the c o a l i n t o a hopper f e e d i n g 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 . The c o a l s h o v e l p r o d u c t i v i t y of 1,180 tonnes per o p e r a t i n g hour was d e t e r m i n e d from a su r v e y of 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 of 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 of 28.8 k i l o m e t e r s per hour, a t r u c k c a p a c i t y o f 54 tonnes and an average 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 to 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 the 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 the f o l l o w i n g r e l a t i o n s h i p ; O p e r a t i n g hours r e q u i r e d = Tonnes x O p e r a t i n g Hour Year Year Tonnes An o p e r a t i n g hour i s d e f i n e d as the number o f hours per s h i f t t h a t the mach 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 hours t o t o t a l hours i s 0.60 f o r the c o a l l o a d e r and 0.50 f o r the c o a l t r u c k s . 2. Run-of-Mine Coal O v e r s i z e S c a l p i n g The c o a l i s dumped from the 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 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 meter by 2.1 meter 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 ground and the u n d e r s i z e m a t e r i a l p a s s e s over a 2.1 meter by 2.4 meter v i b r a t i n g g r i z z l y . A g a i n , the o v e r s i z e m a t e r i a l drops to the ground and the minus 6.4 c e n t i m e t e r 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. The w e i g h t o f t h i s s ystem, w i t h s u p p o r t i n g s t r u c t u r e , i s a p p r o x i m a t e l y 12.6 t o n n e s . 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 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 hopper w i t h a f r o n t end l o a d e r . M a t e r i a l which c a n n o t be c r u s h e d w i t h the d o z e r i s s e n t to the s p o i l dump. 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 r e q u i r e d . 3. R a i s e P a s s e s The 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 are i n c l i n e d a t 60 d e g r e e s to reduce 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 to c o n n e c t to each r a i s e . 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 machine 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 p r e m a t u r e l y 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 from the f o l l o w i n g p u b l i s h e d r e s e a r c h . K a r a b e l a s (1978) t e s t e d the wear of 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 p i p e t h r o u g h which a sand/water s l u r r y was pumped. He c o n c l u d e d t h a t the r a t e o f wear i s most a f f e c t e d by the s i z e and v e l o c i t y o f sediment p a r t i c l e s and i s unchanged by 97 3 . 2 5 M GRIZZLY SCREENING Figure 5-2 The coal i s dumped from the trucks into a bin feeding a 1 meter wide, elevating conveyor. The coal i s screened at 15.2 centimeters and 6.4 centimeters. The plus 6.4 c e n t i -meter material f a l l s to the ground and the minus 6.4 c e n t i -meter material goes into the r a i s e . The oversize material i s run over by a track dozer and fed back into the screening plant. 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 of s o l i d s . From h i s e x p e r i m e n t s , he p r o p o s e d the f o l l o w i n g r e l a t i o n s h i p ; E = 6.1 d 2 ' 1 5 V 3 , 2 7 where "E" i s the wear r a t e i n m i l l i m e t e r s per y e a r , "dm" i s the w e i g h t mean p a r t i c l e s i z e and "V" i s the average p a r t i c l e v e l o c i t y . Shook e t a l (1981) s t u d i e d the 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 hrough which they pumped a sand water 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 a l 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 meters per second, i i ) 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 of .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 to .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 not show any dependence on p a r t i c l e v e l o c i t y but were s t r o n g l y i n f l u e n c e d by p a r t i c l e s i z e and shape. They p r o p o s e d an e q u a t i o n ; 2 E = E o D o D where "E" i s the wear r a t e i n m i l l i m e t e r s per m i l l i o n tonnes o f s o l i d s , " E 0 " i s the r e f e r e n c e wear r a t e which they measured, " D 0 " i s the r e f e r e n c e p i p e d i a m e t e r of 50 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 o f the p r o p o s e d 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 they measured was 40 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 . 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 the wear r a t e i s c a l c u l a t e d to be .1 m i l l i m e t e r s per m i l l i o n tonnes o f 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 t o n nes o f r u n - o f - m i n e c o a l . T h i s i s c o n s e r v a t i v e e s t i m a t e because 70 per c e n t of the m a t e r i a l g o i n g t h r o u g h the r a i s e s i s c o a l w hich, b e i n g s o f t e r than s t e e l , w i l l not erode the s t e e l l i n i n g . The top o f the c o a l i n the r a i s e s i s kept w i t h i n 15 meters of the 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 to c o a l f a l l i n g i n the r a i s e . To lower the r a i s e a t the c o m p l e t i o n o f each m i n i n g bench, the g r i z z l y s c a l p i n g u n i t i s removed and the rock around the 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 the s t e e l l i n i n g i s f u l l y exposed 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 the r a i s e has been e s t a b l i s h e d . T h i s o p e r a t i o n t a k e s 6 c o n c u r r e n t , 8 hour w o r k i n g s h i f t s to c o m p l e t e . P r o l o n g e d p e r i o d s o f c o l d weather may f r e e z e the c o a l i n th o s e r a i s e s which are not c o n t i n u a l l y b e i n g used. To p r e v e n t t h i s , the top o f the c o a l i s lowe r e d 15 meters down the 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 the r a i s e and warm a i r i s blown i n . I f the c o a l i n the r a i s e does f r e e z e i t i s augered to break up the f r o z e n c o a l and r e t u r n the r a i s e t o u s e f u l s e r v i c e . 4 . Main Haulage D r i f t The main h a u l a g e d r i f t i s the 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 r u n - o f - m i n e c o a l 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 the 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 not 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 the 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 the r e s u l t s o f the two rock 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 . 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 the mine g e o l o g i s t as 65 per c e n t . Three 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 e l s e w h e r e i n the mine. The o r i e n t a t i o n of the d r i f t w i t h r e s p e c t to 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 the j o i n t s are 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 the 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 to w e a t h e r i n g . Both rock mass systems c l a s s i f y the rock as poor. A p p l i c a t i o n o f the rock 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 rock and c o v e r e d 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. T h i s m i n i m i z e s w e a t h e r i n g o f the rock j o i n t s . i i ) Wire mesh i s then b o l t e d o v e r two t h i r d s of the d r i f t 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 a n c h o r e d , f u l l y g r o u t e d , p r e - t e n s i o n e d rock b o l t s . There are 4 b o l t s e v e r y two meters a l o n g the d r i f t . i i i ) Two d r a i n h o l e s , 4 meters l o n g are d r i l l e d e v e r y two meters 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 Rating RQD 65% 65 Jo i n t Sets 3 Orthogonal Sets (J^) 3 Join t Roughness Smooth, planar (JR) 1 J o i n t Alteration unaltered j o i n t walls (JQ) 1 Water Inflow medium inflow (J^) 0.6 Stress Reduction factor clay free shear zones in completed rock 3 Q = RQD_ x J ^ x Jy_ = 4.33 JN JA SRF Equivalent Dimension, D e = 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. 102 ROCK CLASSIFICATION USING BIENIAWSKI SYSTEM Parameter Description Rating .Rock Strength 100 MPa 8 RQD 65% 15 J o i n t Spacing 25mm - 50mm 4 Jo i n t Condition smooth, no gauge, 21mm 20 Ground Water moderate pressure 3 Jo i n t Orientation very unfavourable -12 Total 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 the 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 i n a p p r o p r i a t e to the type o f rock 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 . W e a t h e r i n g o f 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 problem and i s a d e q u a t e l y d e a l t w i t h by the a p p l i c a t i o n o f s h o t -c r e t e . 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 water 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 the d r i f t . The l a r g e number o f d r a i n h o l e s w i l l a d e q u a t e l y h a n d l e water i n f l o w s s u b s e q u e n t t o 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 water 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 the 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 the p r o j e c t e c o n o m i c s . A b e n e f i t o f the underground 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 the p i t a r e a s p r i o r to the commencement o f a c t i v e m i n i n g . The s h o r t e s t r o u t e f o r the main h a u l a g e d r i f t i s to go s t r a i g h t t o the c e n t e r o f the s o u t h e r n m o s t p i t s t a r t i n g a t the s i t e of the 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 the main d r i f t to i n t e r s e c t c o a l r a i s e s which c o n n e c t t o the o t h e r p i t a r e a s . The rock s u p p o r t system 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 the system f o r t h e main h a u l a g e d r i f t . Long s e c t i o n s of the main ha u l a g e d r i f t and the 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 the d r i f t and c r o s s - c u t s a r e the i n d u s t r y s t a n d a r d 3 meters by 3 m e t e r s . T h i s s i z e g u a r a n t e e s ready a c c e s s to the flume and water l i n e s d u r i n g con-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 . 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 the rock s u p p o r t system i s shown on F i g u r e 5-5. 104 PROPOSED ROUTE for MAIN DRIFT 0 meters 5 0 0 gure 5-3 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 at the s i t e of the coal truck dump. A cross c u t i s driven perpendicular 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 500 1790 c o a l -1800 1600 CROSS 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 SECTION OF THE DRIFT Figure 5-5 The cross s e c t i o n a l dimensions of the main d r i f t and cross cuts are the industry standard 3 meters by 3 meters with an arched back. Shotcrete, 50 millimeters thick, i s applied as soon a f t e r b l a s t i n g as possi b l e . Wire mesh i s then bolted over the roof and wall with 3 meter long mechanically anchored, f u l l y grouted, protensioned rock b o l t s . Drain holes, 4 meters long, are d r i l l e d and an addit i o n a l 50 millimeters of shot-crete are sprayed over the 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 speed, 1.5 meter wide by 4.5 meter l o n g pan f e e d e r . T h i s u n i t c o n t r o l s the 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 meter 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 . T h i s i s i l l u s t r a t e d i n F i g u r e 5-6. The s l u r r y chamber d i r e c t s the c o a l s l u r r y i n t o one o f two flumes o r s p l i t s the f l o w i n t o both o f the f l u m e s . 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 the i n p u t r a t e of s o l i d s and the d e n s i t y o f the s l u r r y . The rock chamber i n which the s l u r r y i n g equipment 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 the 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 the s t e e l t a n k s i s the major maintenance problem 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 not b e i n g used. 6 . Flume System The flume 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 the flume t o d i s t r i b u t e the 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 the twin flume main l i n e system and p r o v i d e i n t e r r u p t i o n f r e e s e r v i c e . T h i s d o u b l e s the nominal system 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 the 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 f l o w of c o a l t o t h e w a s h p l a n t . 108 PAN FEEDER FLUME SLURRY CHAMBER PLAN VIEW WATER LINE SECTION VIEW SLURRYING CHAMBER Figure 5-6 The coal i s transferred from the r a i s e to the ste e l s l u r r y i n g tank with a 1.5 meter wide by 4.5 meter long, v a r i a b l e speed pan feeder. Water i s added to the coal i n the 2 meter wide by 1 meter deep by 6 meter long s l u r r y i n g tank and the s l u r r y i s directed into one of two flumes or i s sent to both of the flumes. 109 The s i z e o f the flume was d e t e r m i n e d by an i t e r a t i v e r o u t i n e c o n t a i n e d i n the p r o j e c t e v a l u a t i o n computer program. T h i s r o u t i n e i s based on two p r e m i s e s ; i ) The flume 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 to t h e Froude number as f o l l o w s ; where "V" i s the f l o w v e l o c i t y , "g" i s the g r a v i t a t i o n a l c o n s t a n t and "D" i s the flume 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 the model and o p e r a t i n g systems r e s p e c t i v e l y and i i ) The T r a n s p o r t F u n c t i o n d i s c u s s e d i n C h a p t e r I I I p r e d i c t s the t r a n s p o r t o f c o a r s e r u n - o f - m i n e c o a l 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 f o l l o w i n g r e l a t i o n s h i p ; j _ .0017 Q 5 / 3 S  R5/3 g l / 3 where "T" i s the 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 f l o w r a t e o f the f l u i d . The 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 . The computer program c a l c u l a t e s the 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 flume 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 the d e s i g n p r o d u c t i o n r a t e o f 3.6 m i l l i o n tonnes o f c l e a n c o a l per y e a r . 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 the flume 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 not r e s u l t i n premature flume wear. U s i n g the wear r e l a t i o n s h i p from Shook e t a l ( 1 9 8 1 ) , an e s t i m a t e 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 0 ) , 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 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 10 m i l l i m e t e r s per m i l l i o n tonnes o f s o l i d s . 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 per m i l l i o n tonnes of 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 p i p e . 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 flume w a l l s w i l l t r a n s p o r t 12,000,000 tonnes of r u n - o f - m i n e c o a l b e f o r e 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 to p r o v i d e the volume of water r e q u i r e d t o move the d e s i g n p r o d u c t i o n r a t e of c o a l . 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 water a t maximum d e s i g n p r o d u c t i o n . The pump i s backed 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 a u t o m a t i c a l l y c o n t r o l l e d r e c i r c u l a t i n g system. The water i s pumped to the s l u r r y i n g chambers i n a 46 c e n t i m e t e r d i a m e t e r s t e e l l i n e . 7 . D e w a t e r i n g P l a n t The flume d i s c h a r g e s i n t o a 200 c u b i c meter, a g i t a t e d d i s t r i b u t i o n tank which has a 10 minute surge c a p a c i t y a t the d e s i g n p r o d u c t i o n 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 board to h o l d the c o n t e n t s of the flume system i n the e v e n t of a sudden s h u t down. I l l 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 top 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 the bottom deck s c r e e n s p l u s 6 m i l l i m e t e r c o a l . The s c r e e n o v e r s i z e c o a l i s take n from the d e w a t e r i n g p l a n t to 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 the 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 to 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 to 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 the open s t o c k p i l e . 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 of c o a l f o r the wash p l a n t . The low r e s i d e n c e time and absence o f c o a l f i n e s i n the s t o c k p i l e r e d u c e s the p o t e n t i a l o f problems 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 the 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 t h i c k e n e r . 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 the wash p l a n t and the c l a r i f i e d d e c a n t water i s r e t u r n e d to the flume system head t a n k . 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 the c o a l p r e p a r a t i o n p l a n t proposed by the 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. B e g i n n i n g w i t h a 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 of 25 per c e n t i n the flume d i s c h a r g e , the mass b a l a n c e o f the 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 x IM CONVEYOR -»• TO PLANT FLOW SHEET Figure 5-7 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. 1 1 3 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 i n t o the so u t h e r n m o s t c o a l r a i s e which i s d e v e l o p e d as a 1.8 meter, b o r e d r a i s e . A 1 meter d i a m e t e r s t e e l t u b e , l y i n g on the 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 the r u n - o f - m i n e c o a l and a p r o t e c t e d ladderway i s welded onto the o u t s i d e o f the s t e e l t u b e . To p r e v e n t w e a t h e r i n g o f the r o c k , the r a i s e i s c o a t e d 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 . The a c c e s s i b i l i t y o f the s t e e l c o a l r a i s e a l l o w s measurements of s t e e l l i n e r wear to be made. T h i s p e r m i t s the p r e d i c t i o n 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 t h a t may be r e q u i r e d d u r i n g the l i f e o f t h e r a i s e s . O t h e r 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 the 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 but d i s c o u n t e d due to 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 c o s t s . 9 . V e n t i 1 a t i on F o r c e d v e n t i l a t i o n i s p r o v i d e d to p e r m i t the o p e r a t i o n of a p proved d i e s e l m a i n t e nance machines i n the underground w o r k i n g s . An a i r f l o w o f 250 c u b i c meters per m i n u t e , s u f f i c i e n t t o o p e r a t e a 57 k i l o w a t t d i e s e l machine, i s p r o v i d e d by a 1 meter d i a m e t e r , 18.7 k i l o w a t t e l e c t r i c f a n i n s t a l l e d a t the bottom of 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 the 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 the 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 the top o f the 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 water vapour and d u s t h a z a r d i n the p i t . A u x i l i a r y f a n s i n the main ha u l a g e d r i f t blow f r e s h a i r t h r o u g h 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 o f the flume t r a n s p o r t system a r e 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 the p r e p a r a t i o n p l a n t . 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 the water i n j e c t i o n r a t e and the speed o f the pan f e e d e r . P r e s s u r e s e n s i t i v e p r obes e v e r y 50 meters i n the flume i s o l a t e the l o c a t i o n of p l u g s or b r e a k s i n the l i n e . I f t h i s happens, the i n t e r l o c k e d flume system a u t o m a t i c a l l y s h u t s down and the o p e r a t o r i s a l e r t e d t o the l o c a t i o n and n a t u r e of the problem. With t h i s i n f o r m a t i o n , the s l u r r y f l o w i s t r a n s f e r r e d to the o t h e r flume and the system 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 the top 15 meters o f the 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 to the c o n t r o l room of the 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 c o a l 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 water l i n e c l o s e d , the pump r e c i r c u l a t e s water back i n t o the head t a n k . 1 1 6 11. S e r v i c e F a c i l i t i e s Underground l i g h t i n g , communication and e l e c t r i c a l 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 f a c i l i t i e s . 117 CHAPTER VI  ESTIMATED CAPITAL AND OPERATING COSTS  FOR THE RUN-OF-MINE FLUME TRANSPORT SYSTEM A. I n t r o d u c t i o n T h i s c h a p t e r p r e s e n t s the 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 are e s t i m a t e d i n d i f f e r e n t ways: i ) from equipment s u p p l i e r q u o t a t i o n s , i i ) from i n d u s t r y e x p e r i e n c e w i t h the same equipment and a c t i v i t i e s , i i i ) from summing the c o s t s of i n d i v i d u a l components, and i v ) 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 to e v a l u a t e the p r o j e c t economics 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 the 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 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 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 v a l u e s h i g h e r than the mean more f r e q u e n t l y than v a l u e s lower than the 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 the v a l u e s of "p" and "k" and "X" i s the dependent 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 the mean v a l u e s to 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 . 1 1 8 GAMMA FUNCTION FREQUENCY DISTRIBUTION K = 2 Figure 6-1 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 operating c o s t s . This 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 fu 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 " x /* 6 and i s shown by the curve p = .6 1 1 9 The t o t a l c a p i t a l c o s t f o r the flume t r a n s p o r t a t i o n system, in mid 1983 Canadian d o l l a r s , i s $8,231,900. B. 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 System 1. Coal Loader and Truck Unbroken c o a l at the work f a c e w i l l be dug by a 15 c u b i c 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 . 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 , m e c h a n i c a l l 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 annual c o a l t r u c k and l o a d e r r e q u i r e m e n t s 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 : U n i t o p e r a t i n g hours r e q u i r e d Number of U n i t s = Days Hours .., . ., . Year x "Day— x e f f e c t 1 v e u t i l i z a t i o n I f 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 than .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 i n t e g 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 . New p u r c h a s e s are made o n l y when the r e q u i r e m e n t s f o r an equipment type exceed the e x i s t i n g s u p p l y . The economic 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 economic l i f e of the c o a l t r u c k i s 7 y e a r s . 2. Run-of-Mine Coal O v e r s i z e S c a l p i n g 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 degree 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 g r i z z l i e s . 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 s u p p o r t i n g 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 and minus 30 p e r c e n t . 3. R a i s e P a s s e s The average 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 . The s t e e l r e q u i r e m e n t i s based on the f o r m u l a : l b / m e t e r = 3.28 (D-T) 10.68T where "D" 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 "T" i s the w a l l t h i c k n e s s i n i n c h e s . The 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 meters of r a i s e l i n i n g per hour f o r 3 men, a w e l d i n g machine and a c r a n e at a u n i t c o s t of $150 per hour. T h e r e f o r e , 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 be $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 and minus 10 p e r c e n t . 4. Main Haulage 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 ha 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 underground e x c a v a t i o n 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 p e r c e n t . 1 2 1 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 tank, 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 and minus 30 p e r c e n t . 6. 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 p i p e m a n u f a c t u r e r ' s r e p r e s e n t a t i v e c o n f i r m s , from h i s e x p e r i e n c e , t h a t the i n s t a l l e d flume c o s t w i l l be $120 per meter. The two 10-stage 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 46 c e n t i m e t e r d i a m e t e r water l i n e w i l l be $166 per meter. T h e r e f o r e , the t o t a l flume system 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 p e r c e n t . 7. D e w a t e r i n g P l a n t The c a p i t a l c o s t of the d e w a t e r i n g p l a n t w i l l be $2,135,000 based on the i n d i v i d u a l c o s t s of equipment c o n t a i n e d i n 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 proposed by Mular (1982) was used to c a l c u l a t e t h e s e c o s t s . 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 p e r c e n t . 8. V e n t i l a t i o n , I n s t r u m e n t a t i o n 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 i n s t r u m e n t a t i o n f o r the flume system w i l l c o s t $50,000 and the c o s t of flume s e r v i c e s , i n c l u d i n g underground l i g h t i n g , communications and power w i l l be $30,000. T h e r e f o r e , 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 wit h d e v i a t i o n s of p l u s 30 p e r c e n t and minus 20 p e r c e n t . 9. S i t e I n v e s t i g a t i o n 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 g e o t e c h n i c a l 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 meters 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 p e r c e n t . 10. E n g i n e e r i n g The e n g i n e e r i n g c o s t f o r the flume system d e s i g n w i l l be 5 p e r c e n t of the t o t a l d e s i g n c a p i t a l c o s t . The v a r i a t i o n i n 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 range of v a l u e s f o r each i n d i v i d u a l c a p i t a l c o s t i t e m . C. 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 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 flume 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 o p e r a t i n g time i n a g i v e n time i n t e r v a l . F o r example, i n a time i n t e r v a l of 8 hours, the a c t u a l o p e r a t i n g time 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 l e s s m e c h a n i c a l breakdown (.85) - 51 minutes T o t a l o p e r a t i n g time = 288 minutes 1 2 3 Cost and Production Parameters for Calculating the Flume System Economics Item Average Deviations (X) Cost Plus Minus Coal Loader $210 per hour .15 .10 Coal Truck $101 per hour .15 .10 Gr i z z l y Scalping Unit $55,000 per year .50 .35 Dewatering Plant $0.35 per clean tonne .20 .15 Flume System Services $55,000 per year .50 .35 Table 6-1 The flume run-of-mine coal transport system requires manpower for the coal loader and trucks only. 1 2 4 T h e r e f o r e , i n one 8 hour s h i f t , the number of o p e r a t i n g hours 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 o p e r a t i n g c o s t f o r a p i e c e of equipment 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. _ $ op.hr. y e a r y e a r 1. Coal Loader The computer program c a l c u l a t e s the hours 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 ( t o n n e s 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 per o p e r a t i n g h o u r ) . U s i n g the m a n u f a c t u r e r s ' swing c y c l e i n f o r m a t i o n , the 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 tonnes per o p e r a t i n g hour wi 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 p e r c e n t . 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 per hour wit 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 p e r c e n t . 2. Coal T r u c k s The c o a l t r u c k p r o d u c t i v i t y i s dependent upon the l e n g t h and n a t u r e of the h a u l a g e r o u t e . T h i s changes depending upon which r a i s e i s b e i n g used. The average d i s t a n c e t o each r a i s e w i l l be f i x e d t h r o u g h time and the haulage 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 p r o d u c t i v i t y : Truck C a p a c i t y  P r o d u c t i v i t y = o C D i s t a n c e to r a i s e i ) + f i x e d time (Average Truck Speed) where the " f i x e d t i m e " w i l l be 3.5 minutes and i s the time to l o a d and dump a t r u c k . The t r u c k c a p a c i t y w i l l be 54 tonnes and i t w i l l t r a v e l at an average speed of 28.8 k i l o m e t e r s per hour. 1 2 5 The o p e r a t i n g hours 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 tonnes 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 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 p e r c e n t . 3. Run-of-Mine Coal O v e r s i z e S c a l p i n g 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 time to c l e a r away o v e r -s i z e d m a t e r i a l . 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 equipment, 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 per hour 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 and minus 10 p e r c e n t . 4. Flume System The o p e r a t i n g c o s t f o r the flume system 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 water. 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 to p a t c h areas of h i g h wear at the r a t e of 4 hours of w e l d i n g f o r e v e r y 100,000 tonnes of r u n - o f - m i n e c o a l which passes t h r o u g h the system. 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 the power c o s t p r o f i l e f o r the mine to the k i l o w a t t power r e q u i r e m e n t s 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 i n k i l o w a t t s , "Cv" i s the 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 i n the s l u r r y , "Q" 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 meters per s e c o n d , / 1 2 6 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 . The c o e f f i c i e n t 9.8 i s a c o n v e r s i o n f a c t o r t o o b t a i n k i l o w a t t s . 5. D e w a t e r i n g P l a n t 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 p l a n t , based on i n d u s t r y e x p e r i e n c e 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 , w i l l be $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 p e r c e n t and minus 15 p e r c e n t . The d e w a t e r i n g p l a n t , s i t u a t e d a d j a c e n t to the c o a l 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 by the wash p l a n t o p e r a t o r s and e x t r a manpower i s not r e q u i r e d . 6. 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 flume 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 systems 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 be p l u s 50 p e r c e n t and minus 35 p e r c e n t . 127 CHAPTER VII OTHER ESTIMATED DIRECT MINE OPERATING AND CAPITAL COSTS A. I n t r o d u c t i o n T h i s c h a p t e r d i s c u s s e s the 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 : i ) m i n i n g 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 , i i ) 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 t h e r u n -of-mine c o a l , i i i ) head o f f i c e e x p e n s e s , i v ) o f f - s i t e c o a l t r a n s p o r t a t i o n , v) c l e a n c o a l i n v e n t o r i e s at the deep water p o r t , v i ) 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 are i n d e p e n d e n t of the ty p e of 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 and are the same f o r e v e r y c o a l t r a n s p o r t system b e i n g e v a l u a t e d . The c a p i t a l and o p e r a t i n g c o s t s of r u n - o f - m i n e c o a l t r a n s p o r t are a s m a l l p e r c e n t a g e of the t o t a l mine c a p i t a l and o p e r a t i n g c o s t s . The f i n a n c i n g method w i l l not be i n f l u e n c e d by the c h o i c e of the c o a l t r a n s p o r t system so the i n t e r e s t payments w i l l not change. As w e l l , the waste s t r i p p i n g and p r e p a r a t i o n p l a n t r e q u i r e m e n t s are not a f f e c t e d by the c h o i c e of c o a l t r a n s p o r t system. A p o s s i b l e e x c e p t i o n t o t h i s i s the c a l c u l a t i o n of waste t r u c k r e q u i r e m e n t s f o r an ex p a n d i n g mine. The c o a l t r u c k s i d l e d by a s w i t c h t o a flume t r a n s p o r t system w i l l be i n c l u d e d i n the 1 2 8 waste haul t r u c k f l e e t to r educe subsequent t r u c k r e q u i r e m e n t s and, hence, c a p i t a l c o s t s . B. C a p i t a l and O p e r a t i n g C o s t s 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 r e p r e s e n t a v erages f o r a t y p i c a l C anadian open p i t c o a l mine. They are not 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 e x p e r i e n c e of t h r e e western Canadian c o a l mines. A l l c o s t s are i n mid 1983 C anadian d o l l a r s . 1. Other M i n i n g C o s t s f o r o t h e r m i n i n g f u n c t i o n s such as d r i l l i n g and b l a s t i n g , waste r e m o v a l , road maintenance, mine d r a i n a g e and s p o i l 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 . A l s o i n c l u d e d are a d m i n i s t r a t i o n c o s t s f o r a c c o u n t i n g , p e r s o n n e l , e n g i n e e r i n g , 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 a i d . 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 s e r v i c e 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 equipment. The annual c a p i t a l c o s t s w i l l range from $500,000 to $11,000,000 wit h d e v i a t i o n s of p l u s and minus 25 p e r c e n t . 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 haulage p r o f i l e s and w i l l be from $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 p e r c e n t . 2. 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 l o a d o u t are i n c l u d e d i n t h i s c o s t c e n t e r . 1 2 9 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 two 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 spent e v e r y o t h e r f o l l o w i n g y e a r . 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 and minus 25 p e r c e n t . 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 from $2.50 to $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 p e r c e n t . 3. Head O f f i c e Head o f f i c e expenses i n c l u d e c o s t s f o r m a r k e t i n g , e n g i n e e r i n g s u p p o r t 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 p e r c e n t . 4. O f f - s i t e Coal T r a n s p o r t a t i o n 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 from the mine to the deepwater ocean t e r m i n a l w i l l be $22.00 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 p e r c e n t . 5. P o r t I n v e n t o r y The v a l u e of c l e a n c o a l s t o r e d at the deepwater 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 t h i s i n v e n t o r y are i n c l u d e d i n t h i s i t e m . The economic a n a l y s i s assumed t h e s e c o s t s w i l l be z e r o . 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 These c h a r g e s w i l l be a f u n c t i o n of the f i n a n c i a l s t r u c t u r e o f the c o a l m i n i n g company and f o r the p u r p o s e s of t h i s economic a n a l y s i s are assumed to be z e r o . 1 3 0 CHAPTER V I I I  ESTIMATED CAPITAL AND OPERATING COSTS FOR THE RUN-OF-MINE COAL TRUCK TRANSPORT SYSTEM A. I n t r o d u c t i o n The t r u c k h a u l a g e and t r a n s p o r t system i s c o m p r i s e d of two f u n c t i o n s : 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 exposed c o a l out of the ground and dumps i t i n t o t r u c k s , and i i ) the 108 tonne 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 mountain, to a t r u c k dump l o c a t e d near the c o a l p r e p a r a t i o n p l a n t . The empty t r u c k then r e t u r n s to the c o a l l o a d e r f o r a n o t h e r l o a d . T h i s c h a p t e r p r e s e n t s the 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 t h i s t r a n s p o r t system. 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 equipment s u p p l i e r , q u o t a t i o n s , • i i ) from i n d u s t r y e x p e r i e n c e w i t h the same equipment, 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 economics 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 f r e q u e n c y 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 the v a l u e s of "p" and "k" and "x" i s the dependent 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 C o s t s 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 the t r u c k t r a n s p o r t system are shown on T a b l e 8-1. A l l c o s t s are i n mid 1983 Canadian d o l l a r s . 1. Coal Loader Unbroken c o a l at the working 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 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 p e r c e n t . The number of 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 the f o l l o w i n g r e l a t i o n s h i p : c o a l l o a d e r hours r e q u i r e d Number of l o a d e r s = days hours e f f e c t i v e u t i l i z a t i o n y e a r * 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 the number of hours the 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 the 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 . For example, i f a l o a d e r o n l y produces f o r 4.8 hours in e v e r y 8 hour s h i f t , the 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 the annual p r o d u c t i o n by the p r o d u c t i v i t y of the s h o v e l : Coal l o a d e r hours r e q u i r e d = Annual p r o d u c t i o n ( t o n n e s ) P r o d u c t i v i t y ( t o n n e s per hour) 1 3 2 I f 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 than 0.2, the number of u n i t s i s rounded up to the next h i g h e r i n t e g 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 . New p u r c h a s e s are made o n l y when the r e q u i r e m e n t s f o r c o a l l o a d e r s exceeds the e x i s t i n g s u p p l y . The c o a l l o a d e r s w i l l have an economic l i f e of 10 y e a r s . 2. Coal T r u c k s The c o a l t r u c k s w i l l be 108 tonne 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 w i t h a c a p a c i t y of 77 tonnes and a c o s t of $918,000 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 p e r c e n t . The number of 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 the same manner as the 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 are rounded up or down depending upon the s i z e of the f r a c t i o n a l component. New t r u c k p u r c h a s e s are made when the r e q u i r e m e n t s exceed the a v a i l a b l e s u p p l y and the economic l i f e of the t r u c k s i s 7 y e a r s . C. O p e r a t i n g C o s t s f o r the Truck T r a n s p o r t 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 p arameters f o r the t r u c k t r a n s p o r t system are shown on T a b l e 8-1. The maximum d e v i a t i o n s from t h e s e v a l u e s are a l s o l i s t e d . The d e f i n i t i o n of an o p e r a t i n g hour i s the 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 time l o s t due to s h i f t change, l u n c h , c o f f e e b r e a k s , m e c h a n i c a l f a i l u r e s and time 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 to equipment o p e r a t o r s . 1 3 3 Cost and Production Parameters f o r Calculating the Truck System Economics Item Average Deviations Cost Plus Minus Coal Loader - capital $2,931,500 .15 .10 - operating $210 per hour .15 .10 - productivity 1000 tonnes per hour .10 .25 - u t i l i z a t i o n .65 .10 .15 Coal Truck - capital $918,000 .15 .10 - operating $120 per hour .15 .10 - capacity 77 tonnes .20 .20 - u t i l i z a t i o n .50 .10 .15 - up empty speed 12 k.p.h. .20 .25 - down f u l l speed 28.8 k.p.h. .15 .20 - f l a t haul speed 25 k.p.h. .15 .20 - load and dump time 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 , the t o t a l annual o p e r a t i n g c o s t f o r a p i e c e , or f l e e t , of equipment i s the c o s t per hour t i m e s the annual hours r e q u i r e d : Cost _ Cos t op.hr. Year Op.hr. Year 1. Coal Loader 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 per hour 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 p e r c e n t . The o p e r a t i n g hours r e q u i r e d by the c o a l l o a d e r are c a l c u l a t e d 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 ( t o n n e s 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 per o p e r a t i n g h o u r ) . U s i n g the m a n u f a c t u r e r ' s swing c y c l e i n f o r m a t i o n , the p r o d u c t i v i t y of the c o a l l o a d e r w i l l be 1,000 tonnes per o p e r a t i n g hour w i t h d e v i a t i o n s of p l u s 10 p e r c e n t and minus 15 p e r c e n t . 2. Coal T r u c k s The c o a l t r u c k p r o d u c t i v i t y i s dependent upon the l e n g t h and n a t u r e of the haulage r o u t e which w i l l v a r y a c c o r d i n g to which p i t and which bench i s the s o u r c e of the 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 the f o l l o w i n g r e l a t i o n s h i p : P r o d u c t i v i t y Truck C a p a c i t y  o(B D i s t ) D D i s t (U D i s t ) , f i x e d ( F T p d T D Spd (U Spd) where "B D i s t " i s the average f l a t d i s t a n c e on each bench, "B Spd" i s the average t r u c k speed on the bench, "D D i s t " i s the d i s t a n c e from the edge of the bench to the t r u c k dump, "D Spd" i s the average t r u c k speed d o w n h i l l , "U D i s t " i s the d i s t a n c e from the t r u c k dump back to the bench, "U Spd" i s the average t r u c k speed u p h i l l and " f i x e d " i s the time i n hours t o l o a d and dump 1 3 5 the t r u c k s . The d i s t a n c e s are i n k i l o m e t e r s and the average speeds are i n k i l o m e t e r s per hour. 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 the 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 the 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 the haul a g e speeds, t r u c k c a p a c i t y and f i x e d time are on T a b l e 8-1. The t o t a l o p e r a t i n g hours r e q u i r e d f o r the t r u c k s 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 tonnes of c o a l per y e a r from each bench by the bench p r o d u c t i v i t y f o r the 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 the t r u c k s w i l l be $120.00 per o p e r a t i n g hour 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 p e r c e n t . 1 3 6 CHAPTER IX ECONOMIC EVALUATION OF FLUME AND TRUCK TRANSPORT OF RUN-OF-MINE COAL A. I n t r o d u c t i o n 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 cash f l o w s f o r : i ) T o t a l r e v e n u e , i i ) c o a l t r a n s p o r t o p e r a t i n g c o s t s , i i i ) o t h e r o p e r a t i n g c o s t s i v ) f e d e r a l and p r o v i n c i a l t a x e s and r o y a l t i e s , and v) t o t a l c a p i t a l c o s t s . Using the a n n u a l , a f t e r - t a x net cash f l o w , the p r o j e c t 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 were c a l c u l a t e d . These two economic v a r i a b l e s are the b a s i s f o r the economic e v a l u a t i o n s and comparisons to be' d i s c u s s e d . The computer program was a l s o used to examine p r o j e c t r i s k by e v a l u a t i n g the s e n s i t i v i t y of the economic v a r i a b l e s to changes in i m p o r t a n t cash f l o w v a r i a b l e s . A Monte C a r l o approach was used to s i m u l a t e r i s k by i t e r a t i v e l y and randomly c h o o s i n g i n p u t c o s t and p r o d u c t i o n v a r i a b l e s t o c a l c u l a t e the p r o j e c t cash f l o w s . The p r o j e c t economics were c a l c u l a t e d 150 times t o d e t e r m i n e a f r e q u e n c y d i s t r i b u t i o n f o r t h e 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 . F i v e d i f f e r e n t p r o d u c t i o n r a t e and mine development c a s e s were used t o d e v e l o p p r o j e c t economics f o r mines u s i n g a flume or t r u c k r u n - o f - m i n e c o a l t r a n s p o r t system. The c a s e s examined were: 1 3 7 i ) e x p a n d i n g mine - f a s t development i i ) e x p a n d i n g mine - g r a d u a l development i i i ) new mine - f a s t development i v ) 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 omparison of the flume and t r u c k r u n - o f - m i n e c o a l t r a n s p o r t systems was made by s u b t r a c t i n g the annual net cash f l o w of the t r u c k system from t h a t of the flume system and c a l c u l a t i n g 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 f o r the cash f l o w d i f f e r e n c e s . B. Comparison of P r o d u c t i o n and Mine Development A l t e r n a t i v e s 1. Cases A n a l y z e d Economic a n a l y s e s of 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 ruck 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 i i ) f 1 ume 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 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 i v) f 1 ume 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 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 v i ) f 1 ume 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 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 v i i i ) f 1 ume 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 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 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 flume t r a n s p o r t a t i on system. 1 3 8 The g r a d u a l and r a p i d mine development 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 annual c a p i t a l and o p e r a t i n g c o s t s . The g r a d u a l mine development case 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 of the a n a l y s i s and the r a p i d mine development case 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 of t h e a n a l y s i s. The new mine and ex 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 the p r o d u c t i o n r a t e s were the same e x c e p t f o r y e a r 1 i n the new mine c a s e s i n which no c o a l was p r o d u c e d . The c o a l t r u c k r e p l a c e m e n t 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 c a p i t a l e x p e n d i t u r e s f o r a c o a l p r e p a r a t i o n p l a n t . The p r o d u c t i o n l e v e l expanded m o d e r a t e l y over the 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 the 10 c a s e s , c a l c u l a t e d at the median i n p u t v a r i a b l e v a l u e s , are shown on T a b l e s 9-1 to 9-10. 2. A n a l y s i s of R e s u l t s A summary of 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 the 10 c a s e s i s shown on T a b l e 9-11. The c o m p a r a t i v e economics f o r t r u c k and flume c o a l t r a n s p o r t , f o r each of the mine development 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 the t r u c k t r a n s p o r t net cash f l o w s from the flume t r a n s p o r t net cash f l o w s f o r each y e a r of the a n a l y s i s and f o r each mine development c a s e . 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 t h e s e cash 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 are drawn from t h i s t a b l e : 1 3 9 EXPANDING MINE CASE MEAN VALUES ONLY CASH FLOW SUMH AR' <. a l l amounts FOR FLUME i n c urrent TRANSPORTATION c an ad i an * > 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 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 < a l l amounts i n c u r r e n t C a n a d i a n * > 10 ANNUAL PRODUCTION 3330000 4031000 4644986 4632000 4588680 GROSS REVENUE 188685762 247697628 306475076 327617595 368284059 COAL TRANSPORT COST 3464421 4334276 5210917 5540571 5915385 OTHER OP. COSTS 147346427 177951191 .218565120 234936325 2464434 16 ROYALTY PAYMENT 3962401 5323326 . 6586526 7628810 8163636 FED. INCOME TAX 6235755 11403685 19468865 20994834 28571122 BC INCOME TAX 3135942 6475589 16398159 11201218 15537923 BC MINING TAX 3955911 7559605 9758822 16474625 14533118 TOTAL CAPITAL COST 11636263 14535317 14855463 6364 168 12368373 NET CASH FLOW 8898642 20109640 22431263 30537905 36701092 DISCOUNT , RATE NET PRESENT VALUE VALUE INTERNAL RATE OF RETURN OF RETURN 15. 66 22763883 28. Table 9-1 This i s the cash flow summary f o r the case of a gr 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 production i s i n un i t s of tonnes of raw c o a l . 140 E X P A N D I N G M I N E C A S E MEAN V A L U E S O N L Y C A S H FLOW SUMMARY ( a l l amounts FOR T R U C K T R A N S P O R T A T I ON i n current Canadian S- > A N N U A L P R O D U C T I O N 1 7 7 7 0 0 8 2 4 7 8 0 6 8 2 9 0 5 8 8 8 2 8 8 4 8 8 8 2 7 2 9 9 6 0 G R O S S R E V E N U E 7 7 2 4 6 1 9 8 1 8 7 6 7 7 6 7 4 1 2 9 0 7 2 3 4 8 1 4 6 2 2 9 6 4 4 1 5 1 5 3 9 6 1 7 C O A L T R A N S P O R T COST 2 3 0 7 2 7 6 2 9 1 2 4 3 5 3 7 0 9 2 8 8 3 9 9 2 1 1 6 3 4 6 5 8 4 7 OTHER O P . C O S T S 5 9 1 7 8 5 8 2 8 6 3 5 7 4 9 5 1 6 5 4 5 2 1 6 9 1 2 8 9 8 5 5 8 2 1 1 7 6 9 8 7 9 5 R O Y A L T Y P A Y M E N T 1 5 1 4 8 2 5 2 1 1 6 4 8 2 2 5 2 9 8 1 8 2 9 9 3 5 6 9 3 1 8 2 3 3 2 F E D . INCOME TAX 8 8 8 6 4 3 6 1 7 9 5 BC INCOME TAX 8 8 8 8 1 8 6 9 5 8 5 BC M I N I N G TAX 8 8 8 6 1 1 3 6 4 3 4 T O T A L C A P I T A L COST 2 3 8 6 5 6 8 8 3 9 5 5 9 8 5 3 9 1 6 7 8 1 3 8 6 1 9 5 3 3 1 2 1 0 6 5 1 8 NET C A S H FLOW - 9 5 5 6 6 8 7 - 2 3 2 6 2 5 9 1 8 2 7 3 4 6 1 2 2 3 8 8 4 4 9 1 7 8 3 1 2 C A S H FLOW SUMMARY FOR T R U C K T R A N S P O R T A T I O N < a l l amounts in current Canadian * > 10 A N N U A L P R O D U C T I O N 3 3 3 8 8 6 8 4 8 3 1 6 6 6 4 6 4 4 9 8 6 4 6 3 2 8 6 0 4 5 8 8 6 6 6 G R O S S R E V E N U E ' 1 8 8 6 8 5 7 6 2 2 4 7 6 9 7 6 2 8 3 6 6 4 7 5 8 7 6 3 2 7 8 1 7 5 9 5 3 6 8 2 8 4 6 5 9 C O A L T R A N S P O R T COST 4 5 7 2 4 4 3 6 2 9 8 3 3 7 7 1 6 6 2 5 4 7 6 4 9 8 6 2 6 0 5 5 4 8 8 OTHER O P . C O S T S 1 4 8 5 4 7 1 5 4 1 7 9 4 7 2 1 4 1 2 2 0 4 4 6 9 8 4 2 3 6 9 4 4 3 2 8 2 4 8 5 9 1 7 4 0 R O Y A L T Y P A Y M E N T 3 9 6 2 4 6 1 5 3 2 3 3 2 6 6 5 8 6 5 2 6 7 8 2 8 0 1 8 8 1 6 3 6 3 6 F E D . I N C O M E T A X 5 5 4 8 6 5 9 1 6 7 8 6 8 5 2 1 7 5 1 1 7 2 5 1 9 4 5 6 9 4 7 2 7 3 5 4 4 6 8 BC INCOME TAX 2 7 8 1 2 8 2 5 7 8 6 6 1 9 9 5 6 5 7 2 1 1 6 2 9 4 1 1 6 1 4 7 9 7 4 7 6 BC M I N I N G TAX 2 9 5 5 6 2 8 6 5 5 3 7 6 3 8 6 2 6 2 3 9 9 6 7 9 4 6 9 1 3 3 4 4 1 3 9 T O T A L C A P I T A L COST 1 2 5 6 2 1 4 5 1 6 6 3 2 3 8 8 1 5 4 1 7 8 2 4 1 3 1 9 5 7 5 2 1 5 1 4 4 9 1 2 NET C A S H FLOW , 7 7 5 7 3 3 6 2 2 3 S 8 8 7 1 2 1 2 1 9 7 5 3 2 3 9 6 9 2 3 8 3 4 8 3 2 3 8 8 D I S C O U N T R A T E NET P R E S E N T V A L U E V A L U E I N T E R N A L R A T E OF R E T U R N OF R E T U R N 1 5 . 8 6 1 9 7 8 4 2 1 4 2 8 . 1 6 Table 9-2 This i s the cash flow summary for 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. 1 4 1 EXPAND ING MINE CASE MEAN VALUES ONLY CASH FLOW SUMMARY FOR FLUME TRANSPORTATION C a l l a m o u n t s i n c u r r e n t C a n a d i a n * ') ANNUAL PRODUCTION 1777000 2470000 3336080 GROSS REVENUE 77246190 107677674 147955566 COAL TRANSPORT COST 1755612 2228217 2983832 OTHER OP. COSTS 59170582 85663751 127093831 ROYALTY PAYMENT 1514625 2118482 2899929 FED. INCOME TAX - 0 6 O EC INCOME TAX 0 6 6 BC MINING TAX 6 8 8 TOTAL CAPITAL COST 31176978 39559853 21353925 NET CASH FLOW -16371067 -21824629 -6375951 4644966 235513895 4653655 181967812 4 321369 4688256 2695663 2592313 7459761 28436332 4644966 257343279 44 16766 190569623 5414769• 11168988 538019O 6698721 115634 35 22756847 CASH FLOW SUMMARY FOR FLUME TRANSPORTATION < a l l a m o u n t s - i n c u r r e n t C a n a d i a n $ > 16 ANNUAL PRODUCTION 4644966 4644966 4644966 4644966 4644966 GROSS REVENUE 263191139 235426668 366475676 327928331 372862734 COAL TRANSPORT COST 4535849 4862242 5146266 5447118 5888677 OTHER OP. COSTS 195957767 265652217 218565126 235596617 249467163 ROYALTY PAYMENT 5527614 6134641 6586526 7647583 8263794 FED. INCOME TAX 11968332 18916333 26999494 21965363 28751138 EC INCOME TAX 6841191 10169768 11355498 11845699 15674323 EC MINING TAX 7438825 9567641 16656327 11878826 14718992 TOTAL CAPITAL COST 5639823 2166675 2968165 7788828 22894867 NET CASH FLOW 25298338 28678351 36197746 27164298 27152379 DISCOUNT RATE NET PRESENT VALUE VALUE INTERNAL RATE OF RETURN OF RETURN 15. 86 38659356 3 5 . 63 Table 9-3 This i s the cash flow summary f o r the case of a r a p i d l y expanding mine using a flume system to tr a n s p o r t run-of-mine c o a l . The annual production i s i n unit s of tonnes of raw c o a l . 142 EXPANDING NINE CASE MEAN VALUES ONLY CASH FLOW SUMMARY FOR TRUCK TRANSPORTATION < a l l amounts i n current Canadian * > ANNUAL PRODUCTION 1777000 2470006 3330000 4644966 4644966 GROSS REVENUE 77246196 167677674 147955566 235513895 257843279 COAL TRANSPORT COST 2307276 2912435 3869599 4423867 3966942 OTHER OP. COSTS 59176582 86357495 128129520. 183523092 .192216444 ROYALTY PAYMENT 1514625 2116482 2899929 4821369 5414709 FED . INCOME TAX 0 6 . 6 3946876 16732537 EC INCOME TAX 6 0 6 2263694 4461328 BC MINING TAX 0 0 6 2405175 4930346 TOTAL CAP ITAL COST 23287560 39559853 25898276 7459701 11503435 NET CASH FLOW -9633187 -23262591 • -12781753 26671127 24683545 CASH FLOW SUMMARY FOR TRUCK . TRANSPORTATI ON ( a l l amounts in current Canadian * ) 10 ANNUAL PRODUCTION 4644966 4644966 4644966 4644966 4644960 GROSS REVENUE 263191139 285426668 366475876 327928331 372882734 COAL TRANSPORT COST 4937154 6478838 7166254 7054 163 6675676 OTHER OP. COSTS 197632619 266884360 220446984 237684212 251641846 ROYALTY PAYMENT 5527814 6134641 6586526 7847583 8263794 FED. INCOME TAX 11654328 17668916 19667569 21684884 28663172 BC INCOME TAX 6871546 9374629 16551956 11313952 15236269 BC MINING TAX 6239645 8217395 9358197 16635516 13755457 TOTAL CAPITAL COST 11762363 2188675 2968185 4184212 24841366 NET CASH FLOW 26626539 28761996 29729489 29663875 24985221 DISCOUNT RATE NET PRESENT VALUE VALUE INTERNAL RATE OF RETURN OF RETURN 15. 68 37438395 37 .21 Table 9-4 This 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 production i s i n units of tonnes of raw c o a l . 143 HEW MINE CASE MEflH VALUES ONL'i CASH FLOW SUMMARY FOR FLUME TRANSPORTATI ON ( a l l amounts i n c u r r e n t C a n a d i a n * ) 1 2 3 4 5 ANNUAL PRODUCTION 6 247060O 2905OOO 288406O 2729960 GROSS REVENUE 0 107677674 129072348 146229644 151539617 COAL TRANSPORT COST 0 2223842 2647765 2307284 2801536 OTHER OP. COSTS 0 85603751 104548662 128019915 116134452 ROYALTY PAYMENT 0 2110482 2529313 2993569 3182332 FED . INCOME TAX 0 0 0 0 0 BC INCOME TAX 0 0 6 6 0 BC MINING TAX 0 0 0 6 0 TOTAL CAP ITAL COST 47754573 47239967 7831122 6679667 7266671 NET CASH FLOW -47754573 -295O0368 11515041 5729869 22160633 CASH FLOW SUMMARY FOR FLUME TRANSPORTATION ( a l l amounts i n c u r r e n t C a n a d i a n * > 16 ANNUAL PRODUCTION 3336660 4631086 4644966 4632686 4588660 GROSS REVENUE 188685762 247697628 386475676 327017595 368234659 COAL TRANSPORT COST 3464421 4334276 5218917 5546571 5915385 OTHER OP. COSTS 147346427 177951191 218565128 234936325 246443416 ROYALTY PAYMENT 3962461 5323326 6586526 7828010 8163630 FED. INCOME TAX 3249508 11818956 14682865 19618367 28696951 BC INCOME TAX 1858545 5132138 7821837 16761197 15235745 BC MINING TAX 2296664 6388656 9749779 18869922 14299825 TOTAL CAP ITAL COST 18137153 9397134 19581937 15156853 12368373 NET CASH FLOW 16378644 27351958 24436895 24514351 37768735 DISCOUNT RATE NET PRESENT VALUE VALUE INTERNAL RATE OF RETURN OF RETURN 15. 86 -316148 14. 96 Table 9-5 This i s the cash flow summary for the case of a gradually developed new mine using a flume system to transport run-of-mine coal. The annual production i s in units of tonnes of raw coal. 144 NEW MINE CASE MEAN VALUES ONLY CASH FLOW SUMMARY FOR TRUCK TRANSPORTATION < a l l a m o u n t s i n c u r - r e n t C a n a d i a n * ) 1 3 4 ANNUAL PRODUCTION 0 247O00O 29O5O00 28840O0 2729900 GROSS REVENUE 0 107677674 129072348 146229644 151539617 COAL TRANSPORT COST 0 2912435 37O9208 3992116 3465847 OTHER OP. COSTS 0 86357495 1054521O9 128985582 117098795 ROYALTY PAYMENT 0 2110482 2529818 2993569 3182332 FED. INCOME TAX 0 0 0 0 0 EC INCOME TAX 0 0 0 8 0 BC MINING TAX O 0 0 0 0 TOTAL CAP ITAL COST 41783935 48228102 7831122 6679007 7260671 NET CASH FLOW -41783985 -3193034O 9550092 3579370 20531972 CASH FLOW SUMMARY FOR ' TRUCK TRANSPORTATION ( a l l amounts i n c u r r e n t C a n a d i a n * > 6 7 8 9 10 ANNUAL PRODUCTION 333O0O0 4031O0O 4644900 46320OO 458360O GROSS REVENUE 188685762 247697628 306475O76 327017595 368284059 COAL TRANSPORT COST 4572443 6298337 7166254 70498O2 6O55408 OTHER OP. COSTS 148547154 179472141 220446984 23694 4 328 248591748 ROYALTY PAYMENT 3962401 5323326 6586526 702801O 8163638 FED. INCOME TAX 2579273 1O566702 13539324 16927928 27888588 EC INCOME TAX 0 5348565 7135412 9326879 14627234 BC MINING TAX 0 5987703 8283762 8724730 13057859 TOTAL CAP ITAL COST 11349649 10632380 22873705 14998O60 15144912 NET CASH FLOW 17674842 24018474 203931O9 26017859 35554784 DISCOUNT NET PRESENT VALUE INTERNAL RATE OF RETURN RATE VALUE OF RETURN 15. OO -2422530 1 4 . 1 3 Table 9-6 This i s the cash flow summary f o r the case of a g r a d u a l l y developed new mine using a truck system to haul run-of-mine c o a l . The annual production i s i n u n i t s of tonnes of raw c o a l . 145 HEW HI HE CASE HEAH VALUES ONLY CASH FLOW SUMMARY FOR FLUME .TRANSPORTATION < a l l amounts in c u r r e n t C a n a d i a n * > 1 2 3 4 5 ANNUAL PRODUCTION 0 2478000 3336606 4644906 4644906 GROSS REVENUE 0 187677674 147955566 235513895 257S43279 COAL TRANSPORT COST 6 2223217 2983832 4853655 44 16766 OTHER OP. COSTS 0 85663751 127693831 181967812 190569623 ROYALTY PAYMENT 0 21164 82 2399929 4821369 5414709 FED. INCOME TAX 0 6 0 6 6796972 BC INCOME TAX 0 0 0 6 2694514 BC MINING TAX 0 6 0 6 3341626 TOTAL CAPITAL COST 50445573 46163567 26877233 7459761 11583435 NET CASH FLOW -50445573 -28428343 -5899268 37211958 33111633 CASH FLOW SUMMARY FOR FLUME TRANSPORTATION < a l l amounts i n c u r r e n t C a n a d i a n * > 10 ANNUAL PRODUCTION 4644900 4644906 4644906 4644968 4644960 GROSS REVENUE 263191139 285420668 ' 306475676 327928331 372802734 COAL TRANSPORT COST 4535849 4862242 5146266 5447118 5888677 OTHER OP. COSTS 195957767 205652217 218565120 235598617 249467163 ROYALTY PAYMENT 5527814 6134041 6586526 7647583 8263794 FED. INCOME TAX 11273864 14196742 26522468 ' 22259619 28777798 EC INCOME TAX 5988838 8086598 11365798 12625938 15767653 BC MINING TAX 7458531 9521435 16665983 11247792 14741677 TOTAL CAPITAL COST 5639823 2106675 2968165 4184212 24841366 NET CASH FLOW 26816253 35473318 38654,824. 36125466 251 15812 DISCOUNT 'RATE NET PRESENT VALUE VALUE INTERNAL RATE OF RETURN OF RETURN 15. 86 18743361 26. 94 Table 9-7 This i s the cash flow summary for the case of a rapidly developed new mine using a flume system to transport run-of-mine coal. The annual production i s i n units of tonnes of raw coal. 1 4 6 HEW MI HE CASE MEAN VALUES ONLY CASH FLOW SUMMARY FOR TRUCK TRANSPORTAT I OH < a l l amounts i n c u r r e n t C a n a d i a n * ) 1 2 3 4 5 ANNUAL PRODUCTION O 2470000 3330000 4644900 4644900 GROSS REVENUE 0 107677674 147955566 235513895 257843279 COAL TRANSPORT COST 0 2912435 3809599 4428867 3966942 OTHER OP. COSTS 0 86357495 128129520 183523092 192210444 ROYALTY PAYMENT 0 2110482 2899929 4321369 5414709 FED. INCOME TAX 0 0 0 0 6622741 EC INCOME TAX 0 0 0 O 2528503 EC MINING TAX 0 0 0 O 2686534 TOTAL CAPITAL COST 417746 70 47151702 21109835 8543932 12647299 NET CASH FLOW -417746 70 -30854440 -7993317 34196635 31766108 CASH FLOW SUMMARY FOR TRUCK TRANSPORTATI OH •< a l l amounts i n c u r r e n t C a n a d i a n $ > 10 ANNUAL PRODUCTION 4644900 4644900 4644900 4644900 4644986 GROSS REVENUE 263191139 285428668 366475676 327928331 372882734 COAL TRANSPORT COST 4937154 6478836 7166254 7654 163 6675676 OTHER OP. COSTS 197632619 266864806 228446984 237664212 251641846 ROYALTY PAYMENT 5527614 6134641 6586526 7647583 8263794 FED. INCOME TAX 16755872 13448186 19816929 26916866 27888364 BC INCOME TAX 5244783 7375131 16505662 11211579 15164548 BC MINING TAX 5857875 8291458 9188118 9812852 13561591 TOTAL CAP ITAL COST 5639823 2166675 7655187 5641938 2484 1366 NET CASH FLOW 27596078 34796698 26569415 28645264 25365556 DISCOUNT RATE NET PRESENT VALUE /ALUE INTERNAL RATE OF RETURN OF RETURN 15. 66 18523894 21 .31 Table 9-8 This i s the cash flow summary f o r the case of a r a p i d l y developed new mine using a truck system to haul run-of-mine c o a l . The annual production i s i n u n i t s of tonnes of raw c o a l . 1 4 7 TRUCK REPLRCEM'T CASE MEAN VALUES ONLY CASH FLOW SUMMARY FOR FLUME TRANSPORTATION ( a l l amounts i n c u r r e n t C a n a d i a n * > ANNUAL PRODUCTION 2884800 2729988 3338808 4831668 4644966 GROSS REVENUE 126896678 119667867 146882711 194293679 248293528 COAL TRANSPORT COST 2928694 2424497 2954987 3661189 4491396 OTHER OP. COSTS 113632215 188323581 125485849 156119361 184865817 ROYALTY PAYMENT 2369445 2332553 2863221 3977522 5214164 FED. INCOME TAX 353586 2937252 3168238 8384418 13513858 BC INCOME TAX 8 1693413 1586335 4733234 . 7217167 BC MINING TAX 6 1723799 1515282 4437487 6797214 TOTAL CAPITAL COST 14777463 7493897 9989823 12261972 11361238 NET CASH FLOW -12576668 28815 -1332224 6218584 14392687 CASH FLOW SUMMARY FOR FLUME TRANSPORTATION < a l l amounts i n c u r r e n t C a n a d i a n t > 16 ANNUAL PRODUCTION 4632886 4588688 4649486 4627168 4519666 GROSS REVENUE 262466195 285622968 366771996 326671657 362746674 COAL TRANSPORT COST 4613862 4834828 5131125 5464 125 5733481 OTHER OP. COSTS 195413545 261188316 218776867 232968471 245766465 ROYALTY PAYMENT 5511664 6138383 6592987 7826575 8648871 FED. INCOME TAX 14872647 19238398 28186221 21841816 27734839 BC INCOME TAX 7914659 18396465 16849127 11765729 15084329 BC MINING TAX 7419431 9781653 18171856 11676629 14141559 TOTAL CAPITAL COST 5243583 16697159 8963679 4978181 12364919 NET CASH FLOW 21472683 23955267 26187816 31562731 33895696 DISCOUNT RATE NET PRESENT VALUE VALUE INTERNAL RATE OF RETURN OF RETURN 15. 66 43699653 50. Ii Table 9-9 This i s the cash flow summary for the case of an operating mine replacing i t s coal trucks with a flume system to transport run-of-mine coal. The annual production i s in units of tonnes of raw coal. 1 4 8 TRUCK REPLACEM'T CASE MEAN VALUES ONLY CASH FLOW SUMMARY FOR TRUCK < a l l amounts i n c u r r e n t TRANSPORTATION c an ad i an * ) ANNUAL PRODUCTION 2884900 2729906 3336666 4631006 4644966 GROSS REVENUE 126896676 119667807 146682711 194293679 248293528 COAL TRANSPORT COST 3498358 2993997 3894642 5313268 6016925 OTHER OP. COSTS 113032215 101156636 .126507623 151462433 186445867 ROYALTY PAYMENT 2369445 2332553 2363221 3977522 5214164 FED. INCOME TAX 545786 2788559 2563177 8312474 12718647 EC INCOME TAX 6 1468693 1151994 4335296 6715544 BC MINING TAX 6 1462749 . 1108687 4664334 6326942 TOTAL CAPITAL COST 7627656 16458362 16698334 9611646 12945162 NET CASH FLOW -5583385 -3593681 -2643771 7876719 11916335 CASH FLOW SUMMARY FOR TRUCK TRANSPORTATION < a l l amounts i n c u r r e n t C a n a d i a n * > 16 ANNUAL PRODUCTION 4632666 4588666 4649466 4627166 45.19668 GROSS REVENUE 262466195 285622968 366771998 326671657 362746674 COAL TRANSPORT COST 5863830 5754812 5963205 6879898 6182669 OTHER OP. COSTS 197683746 282942635 228668554 234974358 247876484 ROYALTY PAYMENT 5511664 . 6138388 6592967 7626575 8648871 FED'. INCOME TAX 13656686 186581 16 19144564 28568279 26429491 BC INCOME TAX 7168372 9664933 16261993 16987656 14279727 EC MINING TAX 6728349 9695841 9564373 18348586 13387244 TOTAL CAPITAL COST 16975862 12363339 8963679 9351358 ' 15453687 NET CASH FLOW 15488285 21664489 25688711 .27349756 31696581 DISCOUNT RATE NET PRESENT VALUE VALUE INTERNAL RATE OF RETURN OF RETURN 15. 88 39784930 58. 78 Table 9-10 This i s the cash flow summary f o r the case of an operating mine r e p l a c i n g i t s coal trucks with new coal trucks to haul run-of-mine c o a l . The annual production i s i n u n i t s of tonnes of raw c o a l . COMPARISON OF PROJECT ECONOMICS EXPANDING MINE NEW MINE TRUCK REPLACEMENT GRADUAL DEVELOPMENT FAST DEVELOPMENT GRADUAL DEVELOPMENT FAST DEVELOPMENT Truck Flume » Truck Flume Truck Flume Truck Flume Truck Flume To t a l NPVl($) 19,704,200 22,763,800 37,430,400 38,659,400 -2,422,500 -316,100 18,523,900 18,743,400 39,784,900 43,099,700 P r o j e c t IRR (X) 28.16 28.62 37.21 35.63 14.13 14.90 21.31 20.94 58.78 50.17 Coal NPVl($) 3,059,700 1,229,000 2,106,400 219,500 3,314,700 Transport IRR {%) 33 23 29 16 28 iThe discount rate used i n a l l cases was 15% Table 9-11 The net present value r e s u l t s are higher f o r the flume t r a n s p o r t a t i o n system in a l l the cases. The p r o j e c t i n t e r n a l r a t e of return f o r a flume system i s greater than f o r a truck system when the r a t e of increase of 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 greater f o r the flume system. 1 5 0 i ) The flume t r a n s p o r t system g e n e r a t e s g r e a t e r net p r e s e n t v a l u e s f o r the t o t a l p r o j e c t than the t r u c k t r a n s p o r t system i n a l l of t he c a s e s . i i ) The i n t e r n a l r a t e s of r e t u r n are dependent upon the speed of a t t a i n i n g f u l l p r o d u c t i o n . For the f a s t mine development c a s e s and the t r u c k r e p l a c e m e n t c a s e , the i n t e r n a l r a t e s of r e t u r n f o r the flume system p r o j e c t s were l e s s than t h a t of the t r u c k system p r o j e c t s . i i i ) The p r o j e c t economics were b e t t e r f o r r a p i d mine development c a s e s than f o r g r a d u a l mine development c a s e s . i v ) The e x p a n d i n g mine cas e s were more e c o n o m i c a l l y a t t r a c t i v e than the new mine c a s e s . T h i s was due to the " l o o k f o r w a r d " n a t u r e of the a n a l y s i s . P r i o r c a p i t a l c o s t s were not a c c o u n t e d f o r i n the expanding mine c a s e s . 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 h i g h . v) The economic comparisons of flume t r a n s p o r t v e r s u s t r u c k t r a n s p o r t of r u n - o f - m i n e c o a l show t h a t the net p r e s e n t v a l u e s are p o s i t i v e and the i n t e r n a l r a t e s of r e t u r n are g r e a t e r than the d i s c o u n t r a t e . T h i s means t h a t the flume 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 the t r u c k t r a n s p o r t system. v i ) The economic advantages of flume c o a l t r a n s p o r t are i n c r e a s e d when the mine i s g r a d u a l l y d e v e l o p e d . T h i s i s c o n t r a r y t o the r e s u l t s f o r the t o t a l p r o j e c t economi c s . 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 flume system i s g r e a t e r than f o r a t r u c k system when the r a t e of i n c r e a s e i n the annual cash f l o w s 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. 3. C o n c l u s i o n s A n a l y s i s of the t o t a l mine p r o j e c t economics and c o a l t r a n s p o r t system economics l e a d s t o the c o n c l u s i o n t h a t open chan 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 i s e c o n o m i c a l l y s u p e r i o r to t r u c k t r a n s p o r t . C. Monte C a r l o R i s k S i m u l a t i o n The r i s k i n the t o t a l p r o j e c t economics was s i m u l a t e d by 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 d i s t r i b u t i o n from 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 nsure t h a t the v a l u e s chosen were r e a s o n a b l e . 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 h i g h e r than the mean were chosen more o f t e n than v a l u e s lower than the mean. Thus the s t a t i s t i c a l mode of the r e s u l t i n g 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 f r e q u e n c y 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 . The economic f r e q u e n c y 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 i t e r a t i o n s of c a l c u l a t i n g the p r o j e c t cash f l o w s . H i s t o g r a m s of 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 flume and t r u c k c o a l t r a n s p o r t f o r g r a d u a l new mine development, g r a d u a l mine e x p a n s i o n and t r u c k 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 to 9-3. The a n a l y s i s was c a r r i e d out f o r a g r a d u a l mine development. 1 5 2 GRADUAL MINE EXPANSION Figure 9-1 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 of return f o r the flume system i n d i c a t e s that the rate of inc r e a s e of 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 I I l i ' "T " ) 0 .10 .20 .30 INTERNAL R A T E O F R E T U R N Figure 9-2 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 transport system. 154 TRUCK REPLACEMENT 60n 40-, .2 .4 .6 .8 1.0 I N T E R N A L R A T E O F R E T U R N Figure 9-3 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 of return f o r the flume system i n d i c a t e s that the rate of increase of 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 R e s u l t s The mode of each f r e q u e n c y d i s t r i b u t i o n was lower than the c o r r e s p o n d i n g 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 v a l u e s . The comparable economic 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 t r u c k and f l ume t r a n s p o r t systems 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 economic 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 narrower 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 flume t r a n s p o r t system are n o t e w o r t h y . T h i s i n d i c a t e s t h a t a mine u s i n g a flume c o a l t r a n s p o r t system i s exposed 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 t r a n s p o r t system. D. S e n s i t i v i t y A n a l y s e s 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 the f o l l o w i n g c o a l t r a n s p o r t system v a r i a b l e s was t e s t e d f o r a g r a d u a l l y e x p a n d i n g mine. The v a r i a b l e s are l i s t e d i n o r d e r of d e s c e n d i n g impact on the p r o j e c t economics: i ) c o a l p r i c e , i i ) wash p i ant y i e l d , i i i ) i n f1 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 ) underground 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 ) r e q u i r e d t r u c k o p e r a t i n g h o u r s , v i i i ) l a b o u r c o s t , a n d 156 i x ) f u e l c o s t . 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 e v a l u a t e d f o r mines u s i n g e i t h e r a t r u c k or a flume r u n - o f - m i n e c o a l t r a n s p o r t s ystem. 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 range of p e r c e n t changes 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 d e t e r m i n a t i o n s 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 c u r v e . 1. A n a l y s i s of R e s u l t s The mine economics 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 economics f o r mines u s i n g a flume t r a n s p o r t system 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 economics f o r a l l the. s e n s i t i v i t y a n a l y s e s , a) Coal P r i c e 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 economics f o r both the flume and t r u c k c o a l t r a n s p o r t c a s e s . 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 the p r o j e c t f i n a n c i a l r e t u r n . The v a r i a t i o n i n the flume system 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 from 16.79 to 42.69 p e r c e n t . The net p r e s e n t v a l u e f o r the t r u c k system p r o j e c t ranged 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 p e r c e n t . 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 of 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 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 . The economics of both the flume and t r u c k t r a n s p o r t systems were q u i t e s e n s i t i v e t o t h e s e changes. The l e s s s e n s i t i v e flume p r o j e c t net p r e s e n t v a l u e went from $18,677,500 to $26,947,400. The i n t e r n a l r a t e of r e t u r n was from 26.00 to 31.48 p e r c e n t . The t r u c k system net p r e s e n t v a l u e was 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 from 24.92 to 31.23 p e r c e n t . I n f l a t i o n I n f l a t i o n r a t e changes a f f e c t e d a l l of the c o s t v a r i a b l e s . The i n f l u e n c e of c o a l p r i c e on the p r o j e c t economics overwhelmed the e f f e c t s of changes i n the o t h e r 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 v a r i e d between p l u s and minus 15 p e r c e n t of the median v a l u e . The flume system net p r e s e n t v a l u e went from $20,780,900 and $24,825,900 wit h i n c r e a s i n g i n f l a t i o n . The c o r r e s p o n d i n g changes i n the i n t e r n a l r a t e of r e t u r n were from 27.83 to 29.4 p e r c e n t . The t r u c k t r a n s p o r t system net p r e s e n t v a l u e was 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 v a r i e d between 24.71 and 28.91 p e r c e n t . O p e r a t i n g C o s t s The o p e r a t i n g c o s t s were v a r i e d to p l u s and minus 25 p e r c e n t of the median v a l u e . The net p r e s e n t v a l u e of the flume system p r o j e c t ranged from $24,806,200 to 159 PLANT YIELD r30 FLUME -.04 -.02 0 .02 .04 r-32 •24 -.04 -.02 0 .02 .04 Figure 9-5 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 1 1 1 -.2 -.1 0 .1 .2 Figure 9-6 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 in large changes in the project economics. 161 r-25 23 ^ o -21 > a. z •17 •v. t 1 1 1 r -.2 -.1 0 .1 .2 -.2 -.1 0 .1 .2 OPERATING COST Figure 9-7 The operating costs for a truck run-of-mine coal transport system comprise a larger proportion of the total project operating costs than the flume system operating costs. Therefore, the project economics for a truck transport system are more sensitive fo changes in operating costs. 1 6 2 $20,740,400 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 30.15 to 27.16 p e r c e n t . The t r u c k system net p r e s e n t v a l u e went from $22,253,500 to $16,903,000 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 between 30.23 and 25.92 p e r c e n t . C a p i t a l C o s t s The c o a l t r a n s p o r t system c a p i t a l c o s t s were v a r i e d to p l u s and minus 25 p e r c e n t of the median v a l u e s . The net p r e s e n t v a l u e of the more s e n s i t i v e flume system v a r i e d from $24,259,100 to $21,302,800 and the i n t e r n a l r a t e of r e t u r n ranged from 30.4 to 27.12 p e r c e n t . The t r u c k system net p r e s e n t v a l u e ranged from $20,520,500 to $18,886,500 and the i n t e r n a l r a t e of r e t u r n went from 28.62 to 27.66 p e r c e n t . Underground C o n s t r u c t i o n C o s t s 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 underground opening f o r the flume t r a n s p o r t system was v a r i e d from minus 15 p e r c e n t to 100 p e r c e n t . The net p r e s e n t v a l u e went from $23,234,500 to $19,528,200 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 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 hours 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 to p l u s 25 p e r c e n t of the median v a l u e . The t r u c k t r a n s p o r t economics were s e n s i t i v e to t h e s e changes but the flume t r a n s p o r t economics were e s s e n t i a l l y unchanged. The flume system net p r e s e n t v a l u e ranged from $22,973,400 to $22,198,400 163 -25 ~ ~ — / — o -23 to -21 "—• '— _ - - - > — a. z -19 -17 -2 « -.1 c i ) .1 .2 FLUME TRUCK -.26 -.2 -.1 0 .1 .2 CAPITAL COST Figure 9-8 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 o o 25 23 21 > Q. 19 Z 17 -.15 .2 —| 1.0 U N D E R G R O U N D C O N S T R U C T I O N Figure 9 - 9 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 in good project f i n a n c i a l results. 165 T R U C K HOURS r 2 4 -16 -.2 -.1 0 ,1 .2 r.30 \ \ \ \ v .28 \ 1 1 1 IRR \ \ S \ T R U C K \ N \ \ -XI ^ \ \ \ 1 1 1 I • I < T r--.2 -.1 0 ,1 .2 Figure 9-10 The required annual truck hours for the truck transportation system are greater than for the flume system and so the project economics for the truck system are more sensitive to changes in the required truck hours. 166 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 between 28.82 and 28.16 p e r c e n t . The net p r e s e n t v a l u e of the t r u c k t r a n s p o r t system v a r i e d from $20,407,000 -to $17,887,300 and the i n t e r n a l r a t e of r e t u r n went from 28.70 to 26.67 p e r c e n t . Labour Co s t The l a b o u r c o s t p o r t i o n s of the o p e r a t i n g c o s t s f o r the c o a l t r a n s p o r t system were v a r i e d from 0 to 100 p e r c e n t of the median v a l u e . The net p r e s e n t v a l u e f o r the flume system ranged from $22,763,900 to $20,605,300 and the i n t e r n a l r a t e of r e t u r n was between 28.62 and 27.00 p e r c e n t . The t r u c k system net p r e s e n t v a l u e went from $19,704,200 to $15,484,800 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 between 28.16 and 24.84 p e r c e n t . F u e l C o s t The p r o j e c t economics f o r both the flume and t r u c k c o a l t r a n s p o r t systems were not v e r y s e n s i t i v e to changes i n the c o s t of 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 equipment 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 of the median v a l u e . The net p r e s e n t v a l u e of the flume 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 the f u e l c o s t i n c r e a s e d and the i n t e r n a l r a t e of r e t u r n was between 28.62 and 27.95 p e r c e n t . The t r u c k t r a n s p o r t p r o j e c t net p r e s e n t v a l u e was re d u c e d from $19,704,200 to $17,469,700 and the i n t e r n a l r a t e of r e t u r n went from 28.16 to 26.33 p e r c e n t . 167 Figure 9-11 The truck coal transportation system requires more manpower than the flume system. Therefore, the project economics for the truck system are more sensitive to changes in the cost of labour. 168 o > a. z 25-. 23-2 H 1 H 17H F L U M E — I -.2 -1 1.0 .28-cc 27H T R U C K —1 1.0 FUEL COST Figure 9-12 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. 1 6 9 2. C o n c l u s i o n s The f o l l o w i n g c o n c l u s i o n s are drawn from the s e n s i t i v i t y a n a l y s i s : i ) The flume t r a n s p o r t of 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 t r u c k t r a n s p o r t of r u n - o f - m i n e c o a l . i i ) The flume 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 t o t r u c k t r a n s p o r t of r u n - o f - m i n e c o a l . E. G e n e r a l C o n c l u s i o n s The f o l l o w i n g c o n c l u s i o n s are made from the economic comparisons d e s c r i b e d above: i ) 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 r e t u r n u s i n g a flume system 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 . i i ) 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 to l e s s f i n a n c i a l r i s k by u s i n g a flume system 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 development of the m i n i n g p r o j e c t w i l l i n c r e a s e 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. I n t r o d u c t i o n 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 i n t h i s 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 c o a l i n open cha n n e l f l o w . 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 development 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 s t e p f o r w a r d i n u n d e r s t a n d i n g and u t i l i z i n g the phenomenon of open c h a n n e l sediment t r a n s p o r t . T h i s c h a p t e r 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. Subsequent 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 the 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 be 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 p a r t i c l e s i n 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 a p p a r a t u s to c o n d u c t the 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 i i ) more v a r i a b l e s of i n t e r e s t to be measured. B. 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 F u r t h e r r e s e a r c h i n t o r u n - o f - m i n e c o a l t r a n s p o r t by open chan n e l f l o w s h o u l d extend 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 e x a m i n i n g the i n f l u e n c e of v a r i a b l e s such as: i ) p a r t i c l e s i z e , i i ) p a r t i c l e s p e c i f i c g r a v i t y , i i i ) t r a n s p o r t i n g f l u i d r h e o l o g y , i v ) 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 and v) the roughness 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 m i x t u r e 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 t o i n c o r p o r a t e 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 . The new T r a n s p o r t F u n c t i o n s h o u l d be p r e d i c t i v e of any c o a l sample wi t h a known c o m p o s i t i o n 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 extended 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 and the subsequent 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 . The work of Graf and A c a r o g l u (1968) s h o u l d a l s o be extended 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 roughness c o e f f i c i e n t on the 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 A p p a r a t u s 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 1 7 2 t y p e s of t e s t s c o n d u c t e d . The proposed a p p a r a t u s 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 v a r y i n g s p e c i f i c g r a v i t i e s a c c o r d i n g to the f o l l o w i n g c h a r t : 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 of each of 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 to a l l o w 2 t e s t s per day per m a t e r i a l t y p e . A l l m a t e r i a l s h o u l d be d r i e d o v e r n i g h t t o ensure t h e r e i s no s u r f a c e m o i s t u r e d u r i n g 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 the "sump" to c o n t a i n a l l of the f l u i d i n the 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 of f l u i d d i s c h a r g i n g i n t o the f l u m e . The f r e e water s u r f a c e i n the head tank w i l l be 5 meters above the flume i n t a k e . 3. F1ume The 15 c e n t i m e t e r d i a m e t e r flume w i l l be 15 meters long to e n s u r e t h a t the 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 g r e a t e r r e s i d e n c e time to take measurements. A p i v o t i n g s t e e l beam w i l l be used t o m a i n t a i n a c o n s t a n t flume s l o p e . Two one meter long PROPOSED FLUME TEST APPARATUS HEAD TANK rh-FLOW METER 10m COARSE COAL 61N FLUME L GLASS SECTION STEEL BEAM "XT RETURN LINE 18.5 m : — DEWATERING / SCREEN PUMP Figure 10-1 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 c o l l e c t o r 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 meters and 14 meters from the 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 the flume and to make depth of f l o w measurements. 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 to 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 p i p e . 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 d i a m e t e r 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 , 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 the tank bottom and the d i s c h a r g e l i n e w i l l run out the top of the ta n k . The d e w a t e r i n g s c r e e n w i l l be b u i l t i n t o the d i s c h a r g e c o l l e c t o r tank at a 60 degree a n g l e . S h o r t c i r c u i t i n g of the pump d i s c h a r g e f l u i d w i l l 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 the f l u i d to the d i s c h a r g e c o l l e c t o r tank. 6. I n s t r u m e n t a t i o n a) F Towrate The 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 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 magnetic f l o w meter mounted on the v e r t i c a l head tank d i s c h a r g e l i n e . T h i s w i l l e n s u r e t h a t the f l o w r a t e i n t o the flume i s bein g measured w i t h o u t e n t r a i n e d a i r bub b l e s from the pump. A f l o w c u t t i n g d e v i c e mounted on the flume d i s c h a r g e w i l l be used to c a l i b r a t e the f l o w meter by sampling a weight of f l u i d i n a known time i n t e r v a l . 175 b) Depth of Flow Measurement The depth of 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 flume 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 the flume ends wi t h a l e v e l s u r v e y i n s t r u m e n t . d) Weight Measurements Weight measurements w i l l be made wit 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 t e m p e r a t u r e . D. F u r t h e r O p e r a t i n g T e c h n i q u e I n v e s t i g a t i o n s A more d e t a i l e d assessment of the r u n - o f - m i n e c o a l s c r e e n i n g 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 to 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 the r a i s e to the next 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 f e e d e r . 1 7 6 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 Flow." 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G r a f , W. and A c a r o g l u , E. "Sediment T r a n s p o r t i n Conveyance Systems." 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 (1968). 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 Coal 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 ' R e p o r t ( 1 9 8 3 ) . 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 and S o l u t i o n s . " ASME, Paper No. 80-PET-45 (1 9 8 0 ) . Hanks, R. and S l o a n , D. "A Rheology 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. 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. 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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 Chemical 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 Study i n t o the C o r r e l a t i o n of Sediment Motion i n P i p e and Open Channel Flow." 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 (1980). 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 . " Col 1 i e r y E n g i n e e r i n g ( 1 9 5 9 ) . Westar Mines L t d . S t a f f Paper. W i l b y , B. " T a x a t i o n of Coal 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 Economics Branch ( 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 Flows w i t h a F r e e S u r f a c e . " H y d r o t r a n s p o r t 7 (1980). 179 APPENDIX 1 COMPUTER PROGRAM TO CALCULATE PROJECT ECONOMICS A. I n t r o d u c t i o n The economic a n a l y s i s computer package: 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 i n f o r m a t i o n i i ) d e s i g n s the r u n - o f - m i n e c o a l flume t r a n s p o r t system 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 c o s t s f o r a flume or t r u c k t r a n s p o r t system i v ) 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 t a x e s , v) c a l c u l a t e s the p r o j e c t 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 i ) 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 of the p r o j e c t 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 . A n a l y s i s of f i n a n c i a l r i s k i s i n c o r p o r a t e d i n t o the 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 d i s t r i b u t i o n . 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 to model the s t a t i s t i c a l v a r i a t i o n i n a m i n i n g p r o j e c t . 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 - 1 ' ^ pk ( K - l ) l V where "P" and "K" are .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 element of e i t h e r a flume or t r u c k h a u l a g e system are c a l c u l a t 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 i n t o d e p r e c i a t i o n c l a s s e s i n o r d e r to d e t e r m i n e 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 t a x e s . 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 economics 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 language and o p e r a t e s on a H e w l e t t - P a c k a r d 9845 mi c r o c o m p u t e r . A p p r o x i m a t e l y 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 i t e r a t i o n economic a n a l y s i s t a k e s 20 m i n u t e s . The economic a n a l y s i s package i s c o m p r i s e d of two d i s t i n c t 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 i n f o r m a t i o n ; and i i ) the economic a n a l y s i s program ("MINECO") which c a l c u l a t e s m i n i n g 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 economics. B. 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 flume 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 . The i n f o r m a t i o n 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 r u n n i n g the economic e v a l u a t i o n 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 . A n n u a l , semi-annual or q u a r t e r l y time p e r i o d s are a v a i l a b l e . F o r example, a 10 y e a r 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 p e r i o d s . The u s e r i s then r e q u e s t e d 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 flume t r a n s p o r t . 181 1. Flume T r a n s p o r t Data The d a t a f o r flume t r a n s p o r t i s e n t e r e d i n t o t h r e e a r r a y s . 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 i n f o r m a t i o n 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 from 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 p e r c e n t d e v i a t i o n s u n l e s s s p e c i f i e d o t h e r w i s e . The f i r s t d a t a f i l e f o r the flume t r a n s p o r t d a t a s t o r e s 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 . These 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 second d a t a f i l e . P r i o r knowledge of the number of r a i s e s used 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 the average 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 b a s i s . T h i s f i l e s t o r e s : i ) i n f l a t i o n r a t e s , i i ) r u n - o f - m i n e c o a l p r o d u c t i o n , 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 t r a n s p o r t , i v ) the number of r a i s e s used each y e a r , v) the tonnes 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 v i ) whether the mine i s e xpanding or n o t . T h i s f i l e i s a l s o used i n c a l c u l a t i n g t r u c k t r a n s p o r t e c o n o m i c s . 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 f i l e s i s shown on T a b l e A - l . 182 Data F i l e s f o r C a l c u l a t i n g the Flume System Economics FILE 1 1. C a p i t a l C o s t s c o a l l o a d e r c o a l t r u c k g r i z z l y s c a l p i n g u n i t r a i s e c o n s t r u c t i o n d r i f t c o n s t r u c t i o n pump water l i n e - flume l i n e d e w a t e r i n g p l a n t s i t e i n v e s t i g a t i o n 2. O p e r a t i n g C o s t s c o a l l o a d e r c o a l t r u c k g r i z z l y s c a l p i n g u n i t d e w a t e r i n g p l a n t f 1 ume head o f f i c e expense o f f - s i t e r a i l c l e a n - u p d o z e r c l e a n - u p l o a d e r FILE 2 c o a l l o a d e r p r o d u c t i v i t y c o a l t r u c k c a p a c i t y f l a t haul t r u c k speed d i s t a n c e to r a i s e X c o a l l o a d e r u t i l i z a t i o n c o a l t r u c k u t i l i z a t i o n l o a d and dump time d i s t a n c e to r a i s e Y FILE 3 ( f o r e v e r y p e r i o d i n the a n a l y s i s ) i n f l a t i o n r a t e * a n n u a l p r o d u c t i o n p r e p a r a t i o n p l a n t y i e l d c o a l s e l l i n g p r i c e c a p i t a l c o s t s f o r o t h e r m i n i n g o p e r a t i n g c o s t s f o r o t h e r m i n i n g c a p i t a l c o s t s f o r p r e p a r a t i o n p l a n t o p e r a t i n g c o s t s f o r p r e p a r a t i o n p l a n t days per y e a r • s h i f t s per day c a p i t a l i z e d i n t e r e s t c l e a n c o a l i n v e n t o r y n o n - c a p i t a l i z e d i n t e r e s t • r a i s e s i n use *mine e x p a n s i o n e x p l o r a t i o n * t o n n e s to r a i s e X *tonnes to r a i s e Y Note: items marked w i t h "*" do not r e q u i r e maximum d e v i a t i o n s T a b l e A - l The computer program, "DATFIL"-, prompts the user f o r the i n f o r m a t i o n shown above. The d a t a are s t o r e d to be used i n the economic e v a l u a t i o n program "MINECO". 1 8 3 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 a r r a y s . 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 the 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 the computer s c r e e n and the i n f o r m a t i o n i s e n t e r e d from the k e y b o a r d . Data are r e q u e s t e d as mean and d e v i a t i o n v a l u e s u n l e s s o t h e r w i s e s p e c i f i e d . 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 haulage p a r a m e t e r s 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 f i r s t d a t a f i l e . The second d a t a f i l e s t o r e s p i t c o n f i g u r a t i o n i n f o r m a t i o n f o r 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 , average one way bench haul d i s t a n c e and tonnes of r u n -of-mine c o a l from the bench f o r each p i t and each p e r i o d of the 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 av e r a g e , one way bench haul d i s t a n c e . The t h i r d d a t a f i l e , w i t h annual c o s t and p r o d u c t i o n i n f o r m a t i o n , i s i d e n t i c a l t o the annual c o s t and p r o d u c t i o n i n f o r m a t i o n f i l e f o r the flume t r a n s p o r t d a t a . 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. Economic E v a l u a t i o n Program - "Mineco" The f l o w c h a r t f o r the 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 the i n p u t s r e q u i r e d t h r o u g h -out the f l o w c h a r t and o u t l i n e s the us 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 the 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 of the program i s i n c l u d e d i n A p p e n d i x 2 . 184 Data F i l e s f o r C a l c u l a t i n g the Truck System Economics FILE 1 c o a l l o a d e r c a p i t a l c o s t c o a l l o a d e r o p e r a t i n g c o s t c o a l t r u c k c a p i t a l c o s t c o a l t r u c k o p e r a t i n g c o s t c o a l t r u c k c a p a c i t y c o a l t r u c k u t i l i z a t i o n up loaded speed up empty speed down lo a d e d speed f l a t haul speed c o a l l o a d e r p r o d u c t i v i t y c o a l l o a d e r 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 expense o f f - s i t e r a i l t r a n s p o r t l o a d and dump time FILE 2 Number of p i t s * maximum benches per y e a r f o r any p i t * number of 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 not 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 the user f o r the i n f o r m a t i o n shown above. The d a t a are s t o r e d and then used i n the economic e v a l u a t i o n program "MINECO". 185 COMPUTER PROGRAM FLOWSHEET yes Integrate Frequency D i s t r i b . Input Dat Flume Truck Choose Random Variable Value ^ End Calculate Net Cash Flows Calculate NPV and IRR Print Results Calculate Frequency Histograms Iterate yes Figure A-l 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. 1 8 6 1. Monte 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 The 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 based on f o u r o p e r a t i o n s : i ) choose a p r o b a b i l i t y f r e q u e n c y 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 f u n c t i o n t o c a l c u l a t e a t a b l e of c u m u l a t i v e 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 a c u m u l a t i v e p r o b a b i l i t y i v ) compare the random v a r i a b l e w i t h the 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 v a l u e . T h i s p r o c e s s i s diagrammed on F i g u r e /T-2. P r o b a b i l i t y d a t a f o r s e v e r a l u n i t m i n i n g o p e r a t i o n s i n d i c a t e s the 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 , w i t h a "k" v a l u e of 2, i s a p p r o p r i a t e f o r t h i s s i m u l a t i o n . The gamma f u n c t i o n i s : Y _ 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 of 2 and "p" v a l u e s of .6, .8 and 1.0. A "p" v a l u e of .6 and a "k" v a l u e of 2 i s used i n the computer program. The mean and s t a n d a r d 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 r e s p e c t i v e l y . A Simpson's Rule a l g o r i t h m i n t e g r a t e s the 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 to c a l c u l a t e an a r r a y of p a i r e d v a l u e s ; the dependent v a r i a b l e "x" and the c u m u l a t i v e p r o b a b i l i t y of "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 a c t u a t e d t h r o u g h o u t the computer program to sample f o r c o s t v a l u e s and p r o d u c t i o n p arameters used i n c a l c u l a t i n g the 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 R A N D O M NUMBER H I N T E R P O L A T E —I MONTE CARLO  SIMULATION F i g u r e A-2 The Monte 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 o p e r a t i o n s : i ) c h o o s e a p r o b a b i l i t y f r e q u e n c y 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 t h e d i s t r i b u t i o n f u n c t i o n t o c a l c u l a t e a t a b l e o f c u m u l a t i v e 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 , and i v ) 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 an i n p u t v a r i a b l e v a l u e . 4/ va lue 188 1.0 1 1 2 3 4 5 6 G A M M A FUNCTION CUMULAT IVE FREQUENCY DISTRIBUTION Figure A-3 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 dependent v a r i a b l e , "x", i s i n t e r p o l a t e d and the 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 Y 1.2 * 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 the p r o j e c t economics 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 program. 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 the 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 never more than 20 per c e n t of i t s mean c a p a c i t y . The c o n s t r a i n t s are e n t e r e d as l i m i t s on the range of random numbers g e n e r a t e d . I f the random number g e n e r a t e d f a l l s o u t s i d e the imposed l i m i t s , a new random number i s g e n e r a t e d 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 economics 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 a c c o m p l i s h e d 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 economics 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 a f t e r r e s p o n d i n g 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 , i i ) e n t e r whether the a n a l y s i s i s q u a r t e r l y , s e m i - a n n u a l l y or a n n u a l l y , 1 9 0 i i i ) e n t e r the type of a n a l y s i s to be computed, and i v ) 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 s t o r e d . T h ere 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 flume t r a n s p o r t i i ) e x p a n s i o n of an e x i s t i n g mine u s i n g flume 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 flume t r a n s p o r t i v ) a new mine u s i n g t r u c k t r a n s p o r t v) e x p a n s i o n of an e x i s t i n g mine u s i n g t r u c k t r a n s p o r t v 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 o t h e r t r u c k s . The user 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 xpanding u s i n g a flume c o a l t r a n s p o r t system, the computer w i l l r e q u e s t names f o r a l l the flume and t r u c k t r a n s p o r t d a t a f i l e s . 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 . The number of i t e r a t i o n s w i l l be r e q u e s t e d i f 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 user 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 l o a d e r s . O f t e n i t i s e a s i e r to i n c l u d e the c a p i t a l c o s t s of t h i s equipment w i t h the c o s t s of waste t r u c k s and l o a d e r s . 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 b e g i n n i n g 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 computer. 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 flume r u n - o f - m i n e c o a l 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 e n t e r e d d i r e c t l y , or i i ) 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 systems are c o n s t r u c t e d . The computer d e s i g n e d , 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 subsequent r a i s e azimuth 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 . 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 v a r i a b l e . I f no r a i s e and d r i f t systems are c a l c u l a t e d i n a y e a r , the 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 are used. 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 c o n s t r u c t i o n . A p r a c t i c a l l i m i t of 1500 meters 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 c o n s t r u c t -ion i s charged t o the f o l l o w i n g y e a r . T h i s o p t i o n i s a u t o m a t i c a l l y chosen 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 e v a l u a t i o n . The flume 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 program. 1 9 2 The user i s prompted t o e n t e r the r u n - o f - m i n e c o a l p r o d u c t i o n , the days per y e a r and s h i f t s per day at the 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 of r u n - o f - m i n e c o a l i s i t e r a t i v e l y c a l c u l a t e d f o r d i f f e r e n t flume d i a m e t e r s 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 e q u a l to the 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 the flume i s .44 times the flume d i a m e t e 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 of s o l i d s i s 20 per c e n t , and the 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 of c o a r s e . c o a l i s c a l c u l a t e d from the r e l a t i o n s h i p : j = .0017 Q5/3 S g l / 3 R5/3 where "T" i s the c o a r s e c o a l t r a n s p o r t i n volume per 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 the g r a v i t a t i o n a l c o n s t a n t , "R" i s the h y d r a u l i c r a d i u s , and "S" i s the flume s l o p e . The v a l u e of "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 the f l o w v e l o c i t y and "A" i s the c r o s s s e c t i o n a l a r e a of f l o w . The a r e a i s c a l c u l a t e d from the flume r a d i u s and the c o n s t a n t depth of f l o w and the 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 the d i m e n s i o n l e s s Froude Number: V l = V? /gTJI / W where "V" i s the f l o w v e l o c i t y , "g" i s the g r a v i t a t i o n a l c o n s t a n t and "D" i s the flume 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 the 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 r e s p e c t i v e l y . 1 9 3 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 by 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 , "T", to the f i n e c o a l t r a n s p o r t , ".2Q". T h i s v a l u e 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 d i a m e t e r s and compared to the r e q u i r e d p r o d u c t i o n u n t i l t h e y are e q u a l . 4. C a p i t a l and O p e r a t i n g C o s t s 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 each flume or t r u c k t r a n s p o r t system are c a l c u l a t e d u s i n g the s t o r e d i n p u t d a t a . The r e s u l t s are a c c u m u lated i n t o c a p i t a l and o p e r a t i n g c o s t a r r a y s and the c a p i t a l c o s t s are s e p a r a t e d i n t o d e p r e c i a t i o n c l a s s e s a c c o r d i n g t o the Canada Income Tax A c t . For the c ase of an e x p a n d i n g mine c h a n g i n g to a 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 s f o r a t r u c k 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 flume system i s b e i n g c o n s t r u c t e d . 5. F e d e r a l 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 o r d e r 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 i n v e s t m e n t tax c r e d i t i s c a l c u l a t e d from 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 10 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 educted from t h i s c l a s s . The B r i t i s h Columbia 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 tax 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 they are summarized on T a b l e s A-6 and A-7. 6. P r o j e c t Economics a) Net P r e s e n t V a l u e The p r o j e c t net p r e s e n t v a l u e ' i s ' c a l c u 1 a t e d from the f o l l o w i n g r e l a t i o n s h i p : K NCF. NPV = NPV + i \ . -i=l (1+r) 1 194 FEDERAL INCOME TAX CALCULATION O p e r a t i n g revenue O p e r a t i n g c o s t s O p e r a t i n g P r o f i t I n v e n t o r y a l l o w a n c e F e d e r a l c a p i t a l c o s t a l l o w a n c e s = Income S u b j e c t to Resource A l l o w a n c e F e d e r a l r e s o u r c e a l l o w a n c e Debt i n t e r e s t Canadian e x p l o r a t i o n expense Canadian development expense = Income S u b j e c t to Earned 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 Investment 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 the f e d e r a l income tax p a y a b l e . Investment tax c r e d i t s are a c cumulated on the b a s i s of c l a s s 10 a s s e t s o n l y . 195 B.C. CORPORATION INCOME TAX CALCULATION O p e r a t i n g revenue O p e r a t i n g c o s t s O p e r a t i n g P r o f i t B.C. c o a l r o y a l t y I n v e n t o r y a l l o w a n c e 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 Canadian e x p l o r a t i o n expense Canadian development expense Income S u b j e c t to Earned D e p l e t i o n Earned d e p 1 e t i o n = B.C.•Taxab1e Income x B.C. C o r p o r a t i o n Income Tax Rate (16%) 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 tax p a y a b l e . 1 9 6 B.C. MINING TAX CALCULATION O p e r a t i n g revenue O p e r a t i n g c o s t s O p e r a t i n g P r o f i t B.C. c o a l r o y a l t y I n v e n t o r y a l l o w a n c e 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 anadian e x p l o r a t i o n expense Canadian development 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 (15%) B.C. M i n i n g Tax P a y a b l e T a b l e A-7 The computer program uses t h i s model to c a l c u l a t e the B.C. m i n i n g tax p a y a b l e . 1 9 7 where "NCF" i s the 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 i t e r a t i o n . b) 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 the 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 v a l u e 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. T h i s 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 f o u r s i g n i f i c a n t f i g u r e s . c) S t a t i s t i c a l R e s u l t s 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 to 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 cash 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 ! ******* RE-STORE "MINEC0:H7" ******** 20 ! DRIFT COORDINATES x=6218, y=4196, 2=1599 30 ! R f l l S E l COORDINATES x=5684, y=2623, z=1970 40 ! RAISE2 COORDINATES x=5942, y=3S35, z=1790 50 DEG 60 OPTION EASE 1 70 FIXED 0 80 ! 90 Ss*="N" 100 INPUT "CALCULATE THE ECONOMICS AT THE MEAN VALUES 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 SIMULATION ****** 160 ! ************************************************************************ * 170 ! ISO PRINT L I N C 1 0 ) , " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *******" 190 PRINT " * * * » * COMPUTING CUMULATIVE PROEAEILITIES FOR GAMMA DISTRIBUTION **" 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 STEP .10 270 L i n e = L i n e + l 280 F r s t = l 290 Int=I=0 300 F r s t = 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 IF K = Itmax THEN Hopper 398 PRINT L I N ( 2 ) ,"ERROR IN INTEGRAL EVALUATION, MAXIMUM # OF ITERATIONS EXCE EDED " 408 ' PAUSE 416 Hopper: N = 2M 428 Siz=(Up-Lou>/N 436 X = S i z + L o w 446 Y=2.78*X*EXP<-X/.6> 456 Int=Int+4*Y 466 Darg=Low 476 Up2: Darg=Darg+2*Siz 486 IF Darg<Up THEN Hop2 498 I n t = S i z * I n t ' 3 566 IF 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 THEN Hop4 546 I n t e g r a l ( L i n e , 1 > = U p 556 I n t e g r a l ( L i n e , 2 ) = I n t 566 NEXT Up 576 PRINT LIN<2e> 586 GOTO D a t a _ e n t r y 596 Hop4: I n t o l d = I n t 668 Int=Temp 616 GOTO Upl 200 626 Hop2 : X=Barg 630 Y = 2 . 7 8 * X * E X P ( - X / . 6 ) 640 I n t= In t+2*Y 650 X=Darg+S iz 660 Y = 2 . 7 8 * X * E X P ( - X / . 6 > 670 Int. = In t+4*Y 680 GOTO Up2 690 ! 700 ! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 710 ! * * * * * * * * * * * * * * * * * * * * MONTE CARLO SIMULATION SUBROUTINE * * * * * * * * * * * * * * * 720 ! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 730 ! 740 Random: IF Hi=0 THEN RETURN 750 Hi= ( 1 + H i > * 1 . 2 760 L o = ( l - L o ) * 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 Ra 810 Hi nt er p: Mh i = ( H i - I nt e g r a l ( Ra-1 , 1 ) ) / ( I nt e g r a l ( Ra , 1 ) -1 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 ) 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 Ra 860 L i nt e r p : M 1 o= (Lo-1 nt e g r a l (Ra- 1 , 1 ) ) / ( I nt e g r a l (Ra , 1 ) - I nt e g r a l (Ra- 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 Rand : Rnum=RND 890 IF <Rnur<i>Mhi > OR (RnumCMlo) THEN GOTO Rand 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 nt e g r a l (R i - 1 , 2 ) ) -•' (I nt egr a l (R i , 2 > - I nt e g r a l ( R i - 1 , 2 >) * ( I nt e g r a l ( R i , 1 ^ - I n t e g r a l ( R i - 1 , 1 > > + I n t e g r a l ( R i - 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 >, Cop ( 10, 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 1 2 ( 4 8 ) , B e 1 8 ( 4 6 ) , B c t a x ( 1 1 , 4 8 ) , E d b ( 4 6 ) 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 ( 386 ) , 11 c ( 46 ) , Npvh i s t ( 2, 1 8 ) , Dat a( 42 , 1 8 ) , Sr e f ( 2 , 9 ) 1696 ! 1186 P e r i o d = 1 0 1110 INPUT "ENTER THE NUMBER OF YEARS FOR ECONOMIC ANALYS IS , (1 t o 4 0 ) " , P e r i o d 1 120 ! 1130 Pp=l U 4 0 PRINT L INC8 ) , " ENTER 'A' IF YOU WISH TO DETERMINE THE ECONOMICS QUARTERLY" 1150 PRINT " '2' ' ' ' SEMI-ANNUALLY" 1166 PRINT " ' 1 ' ' ' ANNUALLY" U 7 0 INPUT Pp 1186 PRINT L I N ( 2 6 ) 1196 Pe r i od = Pe r i od/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 C a s e * = " N F " 201 250 PRINT L I N < 1 0 ) , " E N T E R ' N F ' FOR NEW MINE CASE -FLUME" 260 PRINT " ' E F ' FOR EXPANDING MINE CASE " 270 PRINT " ' R F ' FOR TRUCK REPLACEMENT CASE " , L I N O ) 280 PRINT "ENTER " N T ' FOR NEW MINE CASE -TRUCK" 290 PRINT " ' E T ' FOR EXPANDING MINE CASE " 800 PRINT " ' R T ' FOR TRUCK REPLACEMENT CASE " 310 INPUT C a s e * 320 PRINT LIN<20> 330 ! 340 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 350 ! 360 INPUT " ENTER THE TOTAL NUMBER OF RAISES FOR THE MINE 'S L I F E " , N r r 370 DIM F 1 u m e ( 1 0 , 3 ) , F a c t o r ( 9 , 3 > , C o s t ( 1 5 , 6 > 380 ! 390 PRINT L I H ( 1 8 > , " B E SURE TO HAVE A TAPE OR DISK AVA ILABLE TO ENTER DATA 400 D e v * = " : H 7 " 410 INPUT "ENTER THE STORAGE DEVICE TO EE USED <: T14 , : T 15, : H 7 ) " , De-y* 420 MASS STORAGE IS Dec * 430 ! 440 C o s t : INPUT "ENTER THE FILENAME FOR THE FLUME COST INFO (max. 6 c h a r , e* 450 ASSIGN #1 TO F i 1 e*, R<.< 460 A g a i n * = " Y " 470 IF R','=l THEN INPUT "THE F I L E DOES NOT EX I ST , 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 Cos t 500 Down l : FOR J=l TO 15 510 FOR 1=1 TO 6 520 READ tt 1 ; Cos t ( J , I > 530 NEXT I 548 NEXT J 550 ! 560 U p p e r 2 : INPUT "ENTER THE FILENAME FOR THE FACTOR INFO (max. 6 c h a r a d e i 1 e* 570 REDIM F a c t o r ( 7 + N r r , 3 ) 580 ASSIGN tt2 TO F i l e * , R u 590 A g a i n * = " Y " 608 IF Ry=l THEN INPUT "THE F I L E DOES NOT EX I ST , DO YOU WISH TO TRY AGAIN n > " , A g a i n * 610 IF Rc=8 THEN GOTO Down2 620 IF ( A g a i n * = " Y " > OR < A g a i n * ="y"> THEN GOTO Upper2 638 Down2: FOR J=l TO 6+Nrr 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 "ENTER THE FILENAME FOR THE MINE PRODUCTION INFO " . F i l e * 788 REDIM D a t a ( 4 0 + N r r , P e r i o d ) 710 ASSIGN #3 TO F i l e * , R o 728 A g a i n * ="Y" 738 IF Rv=l THEN INPUT "THE F I L E DOES HOT EX I ST , 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 Uppe r3 768 Doun3 : FOR 1=1 TO 40+Nrr 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 1870 1 880 1890 1 900 1910 1920 1930 1940 1950 I960 Y/N> 1970 1980 1990 2000 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 T r u c k _ i n p u t : PRINT L IN ( IO ) DIM T c o s t < 1 0 , 6 ) , T r u c k < I O , 3 ) PRINT " BE SURE TO HAVE R TAPE OR DISK AVAILABLE TO ENTER PATH" D e v t = " : H 7 " INPUT "ENTER THE STORAGE DEVICE TO BE USED < : T 1 4 , : T 1 5 , : H 7 ) " , D e v t MASS STORAGE IS Dev t ! T u p p e r S : INPUT "ENTER THE FILENAME FOR THE TRUCK COST D A T A " , F i l e * ASSIGN #5 TO F i l e t , R v R g a i n t = " Y " IF R'j-l THEN. INPUT " THE F I L E DOES NOT EX I ST , DO YOU WISH TO TRY AGAIN? " , A g a i n t IF Ry=0 THEN GOTO Tdown3 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 Tdown3: FOR 1=1 TO IO FOR J=l TO 6 READ # 5 ; T c o s t ( I , J ) NEXT J NEXT I i T u p p e r 4 : INPUT "ENTER THE FILENAME FOR THE TRUCK PRODUCT I V I T I E S " , F i 1 e * 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 ) I ASSIGN #6 TO F i l e t , R v Aga i n t = " Y " IF Ry=l THEN INPUT " THE F I L E DOES NOT EX I ST , DO YOU WISH TO TRY AGAIN? " , A g a i n t IF Rv = 6 THEN GOTO Tdowri4 IF ( Aga i n t =" Y" ) OR ( A g a i n * = " y " ) THEN GOTO T u p p e r 4 Tdown4: 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 Case*= " 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 CCase$ = " E F " O R CCase#="NF"> OR C C a s e * = " R F " > THEN GOTO S t a g e 2 ! T u p p e r S : INPUT "ENTER THE FILENAME FOR THE MINE PRODUCTION D A T A " , F i l e * RED IM D a t a ( 4 6 , P e r i o d ) ASSIGN #3 TO F i l e t , R v A g a i n t = " Y " IF Rv=l THEN INPUT " THE F I L E DOES NOT EX I ST , DO YOU WISH TO TRY AGAIN? " , A g a i n t 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 L INC20 ) i ! ! ***************************************************** ! * * * * * * * * * * * * * DEVELOP CAP ITAL AND OPERATING COST ARRAYS * * * * * * * * * * * ! * * * * * * * * * * * * * * THIS 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 ) , Fed 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 od+1 ) , C I l O C P e r i od + 1 > REDIM C 1 12CPer i o d + 1 ) , C12 8 C P e r i o d + 1 ) , B e c eCPe r i od+1 ) , Be c d C P e r i od+1> RED IM Be 16 C Per i od+ 1 ) , Be 12 C Pe r i od+ 1 >, Be 28 C Pe r i o d + 1 ) , Edb C Pet- i od > 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 od) 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 2480 2490 2500 2510 2520 2530 2540 2550 2560 YS IS 2570 2580 2590 2600 2610 2620 2630 2640 2650 2660 2678 2680 2698 f < 1 2700 2710 2728 2738 2746 2758 2760 2770 2780 2790 2800 2810 I t e r 23 23: 2840 2858 2868 2878 Coa l * 2888 2898 2988 2918 , C o a l * 2928 2938 2948 2958 2968 2978 2988 2*998 3888 3818 3828 3838 3848 3850 3868 3870 3080 3090 F u e 1 s e n s = L a b s e n s = E x c e s s = T o p s e n s = 0 MAT S r e f=ZER PRINT LIN<.28> ! S e n s * = " N " INPUT "DO WISH TO DO A SENS IT IV ITY ANALYSIS? < Y.-H > " , S e n s * IF S e n s * = " N " THEN GOTO I t e r l ! PRINT LINC 1 8 ) , " T H E S E ARE THE VARIABLES FOR COAL TRANSPORT SENS IT IV ITY ANAL PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT L IN < 2 ) , INPUT "ENTER THE FOR S.j = l TO Sn INPUT "ENTER THE S j ), S r e f (.2, S j ) 1 CAP ITAL COST OF COAL TRANSPORT" 2 OPERATING COST OF COAL TRANSPORT" 3 PREPARATION PLANT Y I E LD " 4 COAL SELL ING PR ICE " 5 INFLATION RATE" 6 FUEL COST" 7 LABOUR COST" 8 RAISE & DRIFT CONSTRUCTION COST" 9 TRUCK PRODUCTIV ITY" NUMBER OF SIMULTANEOUS S ENS IT IV I T I E S TO RUN <1 t. REFERENCE NUMBER <1 t o 9) AND THE CHANGE 20 30 IF S r e f < 1 , S j> = 1 THEN C a p s e n s = S r e f < 2 , S j ) IF S r e f < 1 , S j ) = 2 THEN O p s e n s = S r e f < 2 , S j ) IF S r e f U , S j> = 3 THEN Y I d s e n s = S r e f < 2 , S j ) IF S r e f < 1 , S j ) = 4 THEN Pr i c e s e n s = Sref<•.2,Sj ) IF S r e f <1 , S j ) = 5 THEN I n f s e n s = S r e f < 2 , S j ) 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 ) IF S r e f < 1 , S j ) = 7 THEN L a b s e n s = S r e f ( 2 , S j ) IF S r e f a , S j ) = 8 THEN C o n s e n s = S r e f ( 2 , S j ) IF S r e f < 1 iS j> = 9 THEN T o p s e n s = S r e f ( 2 , S j ) NEXT Sj I t e r 1: I t e r = 1 IF Ss * = " N " THEN INPUT ENTER THE NUMBER OF IF Ss * = " H " THEN 11 e r = 11 e r + 1 IF Ss * = " Y " THEN Iter-=1 ECONOMIC ITERATIONS <r,,.= 14 9 ; PRINT L INC 28) ! C o a l * = " Y " INPUT "ARE COAL TRUCK COSTS INCL. IN OTHER MINING CAP ITAL COSTS? <Y.'N>", IF C o a l * = " N " THEN C o a l = l IF C o a l * = " Y " THEN C o a l = 0 C o a l *=".Y" INPUT "ARE COAL LOADER COSTS INCL. IN OTHER MINING CAPITAL COSTS? < Y-'H > " C o a l * = C o a l *= IF IF ! Tot npy Tot i r r FOR J j M i l l V=l ! MAT MAT MAT MAT MAT MAT MAT MAT MAT " N " " Y " THEN THEN C o a l • C o a l •  = 8 1 TO I t e r 8 Cash=2ER Ccap=ZER Cop=ZER C Iass=ZER Fed tax=ZER Bc t ax = ZER Bcrntax = ZER Cce=ZER Ccd=ZER 204 3100 MAT CI18=2ER 3 H 0 MAT CI 12 = 2ER 3120 MAT C128=2ER 3130 MAT Edb=2ER 3140 MAT Bcce=2ER 3150 MAT Bccd=2ER 3160 MAT BclO=2ER 3170 MAT Bc l2=2ER 3180 MAT Bc28=2ER 3190 MAT Bcedb=2ER 3200 MAT I tc=2ER 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 lume 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 B c _ t a x e s 3300 C a s h < 1 , I i > = Y p r o d ! ANNUAL PRODUCTION 3310 Cash C 2 , I i ) = Y p r o d * Y 1 d * R e v ! GROSS REVENUE 3320 C a s h C 3 , I i > = O p c o s t 1 ! COAL TRANSPORT COST 3330 C a s h C 4 , I i > = 0 p c o s t 2 ! OTHER OPERATING COS 3340 C a s h ( 5 , I i ) = R o y a l t y ! ROYALTY PAYMENTS 3350 C a s h ( 6 , I i > = F e d t a x C 1 3 , I i > ! FEDERAL TAXES PAID 3368 C a s h < 7 , I i > = B c t a x C 1 1 , I i > ! BC TAXES PAID 3378 C a s h < 8 , I i > = B c m t a x C 1 1 , I i > ! BC MINING TAXES PAID 3388 Cash C 9, I i > =Tot a l _ c ap ! TOTAL CAP ITAL COSTS 3396 T e m p t o t = C a s h C 2 , I i > - C a s h < 3 , I i > - C a s h < 4 , I i > - C a s h < 5 , I i > - C a s h C 6 , I i > 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 I i 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 J j 3480 EEEP 3498 GOSUB T a b l e s 3508 IF S s * = " Y " THEN GOTO Newtry 3518 GOSUB S t a t s 3528 GOSUB P l o t l 3538 Neu i t ry : Bb$ = " N " 3548 INPUT "DO YOU HAHT TO RUN THE ECONOMICS AGAIN WITH THIS DATA? ( Y / N ) " , B b t 3550 IF Bb*="Y " THEN GOTO S t a g e 2 3568 END 3570 ! 35SQ ! * * * * * * * * * * * * * * * * * * * * * * * * * * * 3598 ! CONTROLLING STATEMENTS FOR CALCULATING 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 LIHC10> 3680 PRINT "ENTER ' 8 ' IF YOU WISH TO EHTER THE DESIGN D IRECTLY" 3698 PRINT " ' 1 ' IF YOU WISH THE COMPUTER TO DESIGN THE SYSTEM" 3788 PRINT " ' 2 ' IF YOU DO HOT WISH TO CONSTRUCT ANY DRIFTS OR FLUMES" 3718 INPUT Dd 3728 PRINT LIHC28> 3738 IF Dd=8 THEN GOSUB D i r e c t _ i n p u t 3740 IF Dd=l THEN G O S U B ' D r i f t d e s i g n 3756 IF Dd=2 THEN GOTO A v o i d 205 3768 INPUT "ENTER THE MI HE L I F E DESIGN PRODUCTION RATE <RAW M T P Y > " , P r o d 3770 GOSUB F1ume_des i gn 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 DESIGN THE RAISE AND HAULAGE SYSTEM 384 0 ! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 3858 ! 3860 PRINT L I N < 1 0 > , " » * * * * * * * * * * * * * * * * * * * » * * * * * * * * * * * * * * * * * * * * * * * * * " 3878 PRINT " THE DRIFT AND RAISE SYSTEMS ARE BEING DESIGNED" 3880 PRINT " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 3898 Dr-i f t _ d e s i g n : H r r=0 3988 INPUT "ENTER THE NUMBER OF MAIN DRIFT SYSTEMS TO BE CONSTRUCTED THIS PERIO 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 RAISES FROM D R I F T " ; I 3958 INPUT Nr 3968 PRINT L IN<20) 3970 INPUT "ENTER THE COORDINATES OF THE DRIFT OPENING < X , Y , Z ) " , D x , D y , D z 3980 INPUT "ENTER THE FLUME SLOPE <.01 TO . 0 5 ) " , S f 3998 H r r = H r r + N r 4O0O R a i s e : FOR J=A TO Nr+A-1 4010 REDIM A ( H d * N r , 1 1 ) 4020 PRINT LIH< 1 0 ) , "ENTER THE X , Y , Z COORDINATES OF R A I S E " ; . ! 4038 INPUT R x , R y , R z 4040 PRINT L IH<20) 4050 INPUT "ENTER THE RAISE INCLINATION (50 TO 90 D E G R E E S ) " , S r 4068 A C J , l ) = R x 4870 A ( J , 2 ) = R y 403O A c J , 3 ) = R z 4098 A ( J , 4 ) = D x 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) = < B2-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 D i s t = S Q R C C R x - A C J , 7 ) ) ~ 2 + < R y - A < J , 8 ) ) A 2 ) 4188 A<J , 1 1 ) = < R z - A < J , 9 ) ) / S I N ( S r ) ! LEHGTH OF RAISE 4198 R C J , 1 0 ) = Di s t-A< J , 1 1 ) * C O S ( S r ) ! LEHGTH OF DRIFT 420O Temp = A ( J , 9 ) - A < A , 6 ) 4218 IF Ternp-Head>8 THEH Head = Temp 4228 NEXT J 4230 ! 4248 FOR L=l TO Nr*Hd 4250 Dr i f t =Dr i f t +A C L , 1 8 ) +Exc e s s 4266 R a i s e = R a i s e + A < L , 1 1 ) + E x c e s s 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 Advance 4318 O v e r f l o w : E x c e s s = D r i f t - 1 5 0 8 ' P p 4328 D r i f t = 1 5 8 8 ^ P p 4338 PRINT L I H C 1 6 ) , E x c e s s ; " METERS OF DR IFT 'CONSTRUCTION WILL BE DELAYED UHTI L THE HEXT PERIOD" 4348 BEEP 4358 WRIT 2888 4368 PRINT L 1 H ( 2 6 ) 4370 A d v a n c e : HEXT I 4388 A=Nd*Nr+1 4398 X x l : RETURN 4 4 08 ! 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 = R z - D z - T A N < S r ) * X 4460 A < J , ? > = X * < D X - R : K > / 2 + R X 4 4 70 fl<J,8>«*Ry-X*<Ry-DyW 4480 A<J,9>=Y+Dz 4490 A CJ,10>=2 - X 4508 A <J,11>=<Rz-Dz - Y > / S I N(Sr> 4510 M=<Ry-Dy>/<Rx-Dx> 4520 B=Ry-M*Rx 4530 Head=A< J,9>-A<R,6> 4540 N E X T J 4550 ! ! X COORD. OF INTERSECTION ! Y COORD. OF INTERSECTION ! 2 COORD. OF INTERSECTION ! LENGTH OF DRIFT ! LENGTH OF RAISE 4560 ! 4570 4580 4590 4600 D S YEAR 4610 4620 i f t 4630 4640 4650 X 4660 4670 4 630 4690 4700 4710 F 4728 4730 4740 4750 4760 4770 4780 4796 4800 y,Shi f t 4810 Factor ! * ********************************************************************** ! Nd=l i r e c t _ i n p u t : INPUT "ENTER THE NUMBER OF MAIN DRIFTS TO BE CONSTRUCTED THI ",Nd IF Nd=6 THEN GOTO Xx2 INPUT "ENTER THE TOTAL LENGTH OF DRIFT CONSTRUCTION THIS YEAR <METERS>",Dr INPUT "ENTER THE NUMBER OF RAISES CONSTRUCTED THIS YEAR",Mrr INPUT "ENTER THE TOTAL LENGTH OF RAISE CONSTRUCTION THIS YEAR",Raise >;2: RETURN SUB-ROUTINE TO DESIGN AND SIZE THE COMPONENTS OF THE FLUME SYSTEM ume_des i gn:Thet a=1.45 PRINT LIN<10>," **********************************" PRINT " THE FLUME SYSTEM IS BEING DESIGNED" PRINT " ««********************************" N=l Cv=. 2 ! Day=340 Shi ft=3 INPUT "ENTER THE DAYS'YR AND SHIFTS'DAY AT FULL PRODUCTION (340,3)",D; , 75 4 320 4830 4340 4850 4860 INPUT "ENTER THE FLUME SYSTEM EFFECTIVE UTILIZATION < Sf=.025 IF Dd=0 THEN INPUT "ENTER THE FLUME SLOPE C.025>",Sf ! 75>",Factor FOR D = ,4 TO 1, R = D/2 2 STEP .05 4870 Stepl: 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 Fl oui = Vel oc i ty*Area 4920 Transport = < Cv*F 1 ou+. 001 8*F1 o w l .67*Sf* 1OO/(Hrad-1.67*9.82A.33>>* 129666*D ay*Factor 4930 4940 4950 4960 4970 IF ABS(Transport-Prod><10OOO THEN GOTO Jump IF Transport-Prod>0 THEN GOTO Decrement IF N=10 THEN GOTO Jump NEXT D ! 4980 Decrement: D=D-.025/N 4990 H=H+1 50O0 GOTO Stepl 501O Jump: PRINT LIN<20> 5020 RETURN 207 5030 504 0 5050 5060 5070 5030 5690 5100 5110 5120 5130 5140 5150 5160 5170 5180 5190 5200 5210 5220 5230 5240 5250 5268 5270 5288 5290 5380 5310 5320 5330 5340 5358 5 3 6 8 5370 5380 5390 5400 54 18 5420 5438 5448 5458 5468 5470 5430 5490 5500 5510 5520 5530 5540 5558 5560 5578 55S0 5590 5600 5610 5628 5638 5646 5650 5660 5670 5688 5698 *************************** SUE-ROUT I HE TO CALCULATE THE FLUME SYSTEM CAP ITAL COSTS * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Cap_c o s t : T o t a l = T o t a l 2 = T o t a l _ c a p = 6 Yprod=Dat a<4, I O I Day=Data<23 , I O Sh i f t = D a t a < 2 6 , I i > IF Dd = 2 THEH Nrr=Dat a<36, I i > V t e m p = l + D a t a < 1 , I i >*<1+In fsens ) V=V*Vtemp i ******* SHOVEL ******* S h o v e l : Hi= F a c t o r d , 2 ) Lo = Factor-C 1,3) GOSUE Random S p r o d = Fac t o r < 1 , 1 ) * S s / l . 2 S o p h r = Y p r o d / S p r o d ! Hi = F a c t o r < 5 , 2 ) Lo = F a c t o r < : 5 , 3 ) GOSUE Random Sut i 1 = F a c t o r < 5 , 1 )*Ss-'l . 2 Shove l s = Sophr/ ( . '24*Day*Sut i 1 ) I G=Shove1s IF FRACT(G>>.2 THEH G=G+1 Shove l s= IHT<G) IF Coa l=8 THEH Shove 1s = 8 ! Hi =Cost U , 2 ) Lo = Cos t <1,3 ) GOSUE Random Scap = Cos t (1 ,1 >*Ss''l . 2 Ccap < 1 , I i ) = S h o v e 1 s * S c ap* V ! Hi = C o s t ( 2 , 2 ) L o = C o s t ( 2 , 3 ) GOSUE Random C c a p ( 2 , I i ) = F1 ume( I i , 3 ) * C o s t ( 2 , 1 )*Ss--'l . 2*'i IF Coa l=0 THEN C c a p < 2 , I i > = 8 ******* SORT THE CAP ITAL COSTS EY CLASSES ! COAL LOADING UNIT ! TRUCKS ******* ' 1 ' FOR CLASS 16 ASSETS '2' FOR CLASS 12 ASSETS ' 3 ' FOR CLASS 28 ASSETS ' 4 ' FOR CAHAD I AH EXPLORATI OH EXPEHSE ' 5 ' FOR CAHADIRH DEVELOPMENT EXPEHSE So r t : IF Da t a<37 , I O = IF Dat a< 37 , 1 0 = 0 THEH IF Da ta ' ; 37 , I i > = 1 THEH IF ' \ Data 1 : 37 , I O = 1 THEN IF Dat ai. 37 , I i ) = 1 THEH IF D a t a c 3 7 , I O =6 THEN IF Data<37 , I i > = 1 THEN IF | Data ' ; 37 , I O = 1 THEH IF | I i >1 THEH GOTC 2i p Hi = C o s t ( 3 , 2) SHOVELS CI a s s ( 3 , I i ) CI ass.( 1 , I O = C 1 as s < 3, I i ) + C c ap <! 2 = C 1 a s s < 1 , I i >+Ccap<2 I i > I i > ! TRUCK Ecedb = E c e d b + . 3 3 3 * C c a p ( 2 , 1 i 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 6 8 6 8 6070 6686 6890 6160 6118 6120 6138 6146 6156 6168 6178 6186 6198 6260 6210 6228 6230 6248 6250 6268 6276 6280 6 2 9 8 6368 6318 6328 6338 6346 6356 Lo=Cost <3, 3> GOSUB Random C c a p ( 3 , I i >=Cost < 3 , 1 > * S s x i , 2#Hr*V*<1+Capsens> ! GRI: CI a s s ( 3 , I i >=C1ass<3 , I i >+Ccap<3, I i > C1 a s s <1, I i > =C 1 a s s < 1 , I i > +Cc a p ( 3 , I i ) Edb = E d b + . 3 3 3 * C c a p ( 3 , I i > B c e d b = E c e d b + . 3 3 3 * C c a p ( 3 , I i > IF I i a t aC37 , I i > = 1 THEH IF D a t a < 3 7 , I i >=0 THEN IF Da t a<37 , I i > = 1 THEH IF D a t a < 3 7 , I i > = 1 THEH I H i = C o s t < 4 , 2 > Lo = Cos t <4,.3> GOSUB Random Ccap<4 , I i >=Cost k'4, 1 ) * S s / l . 2*Ra i s e *V*< 1 +Consens > * i 1+Capsens> ! RAISES IF H a t a C 3 7 , I i > = 1 THEH C1 ass<2 ,1 i>=C1 a s s < 2 , I i > + C c a p C 4 , I i > I Hi =Cost <5,2 ) L o = C o s t ( 5 , 3 ) GOSUB Random Ccap<5 , I i >=Cost ( 5 , 1 ) * S s / l . 2*<Dr i f t + Exc e s s > *V* 1 .81* ' : 1 +Consens > * < l+Cap; IF IF E x c e s s > 0 THEH Dat. a < 3 7 . I i > = 1 Exc e s s = 0 THEH C l a s s ! DRIFT (. 2, I i > =C 1 a s s (2 , I i > +Cc ap < 5, I i ) H i = C o s t < 6 , 2 ) Lo = Cos t <6, 3) GOSUB Random Temp = Cos t C6, 1 >*Ss-'l . 2 Ki,i=(. l - C v ) * F l o u * H e a d * l . 2 *1088x162 IF Ku<373 THEH C c a p < 6 , I i > = T e m p * V * 2 * C 1 + C a p s e n s > Kw>373 THEH Ccap<6, I i )=<Kw/373>-. 6*Temp*V*2*< 1+Cap: D a t a < 3 7 , I i ) = 1 Dat a>; 37 , I i > =6 D a t a f 3 7 , I i > = 1 D a t a C 3 7 , I i ) = 1 IF IF IF IF IF ! H i =Cost <? ,2 ) Lo = Cos t <7, 3> GOSUB Random Cc ap i7, I i ) = Cos t IF D a t a < 3 7 , I i > = D a t a < 3 7 , I i ) = Da t a<37 , I i > = D a t a < 3 7 , I i > = IF IF IF i Hi =Cost <8,2 ) Lo = Cos t <8,3 ) GOSUB Random C c a p C S , I i > = C o s t IF D a t a C 3 7 , I i > = Dat aC 3 7 , I i Dat aC 3 7 , I i D a t a < 3 7 , I i THEH C1 a s s < 3 , I i > = C 1 a s s < 3 , I i ) + C c a p < 6 THEH CI ass< 1, I i ) = C 1 ass< 1 , I i >+Ccap<:6 THEH Edb = E d b + . 3 3 3 * C c a p < 6 , I i > THEN B c e d b = B c e d b + . 3 3 3 * C c a p < 6 , I i ) 1 ) * S s x l . 2*Dr-i f t *V*< 1+Capsens ) THEN C1 a s s < 3 , I i > =C1 a s s C 3 , I i > +Cc ap < 7 THEH C1 a s s < 1 , I i > = C 1 a s s C 1 , I i > + Ccap<7 THEH E d b = E d b + . 3 3 3 * C c a p < 7 , I i ) THEH B c e d b = B c e d b + . 3 3 3 * C c a p < 7 , I i ) I i I i I i > I i > : 8 , 1 >*Ssx i . 2*Dt-i f t * V * 2 * < 1+Capsens> = 1 >=6 ) = 1 > = 1 THEH THEH THEH THEH C1 a s s ( 3 , I i >=C1ass<3 , I i >+Ccap<8, I i CI a s s < 1 , I i >=C1ass<1 , I i J+CcapCS , I i E d b = E d b + . 3 3 3 * C c a p < 8 , I i > B c e d b = B c e d b + . 3 3 3 * C c a p < 8 , I i > IF IF IF ! Hi =Cost <9,2> L o = C o s t ( 9 , 3 ) GOSUB Random Temp = Cos t <. 9 , 1 > * S sx 1 . 2 Tempi =FT-od^Day.'Fac tor-x24/750 IF T e m p l > . 2 5 THEN Cc ap < 9, I i ) =Temp 1 A . 6*Ternp*V C c a p < 9 , I i >=Temp*V*<1+Capsens) IF Dat a< 37 , I i > = 1 THEN C1 as s C 3, 1 i > = C 1 a s s < 3 , I i > +Cc ap: C 9 , I i > IF D a t a < 3 7 , I i > = 8 THEN CI a s s CI E d b = E d b + . 3 3 3 * C c a p < 9 , I i ) B cedb=Bcedb+. 3 3 3 * C c a p < 9 , I i ':> IF D a t a C 3 7 , I i > = 1 THEH Mi11= N i11+Ccap<9 ! Hi = C o s t ( 1 8 , 2 > Lo = Cos t <16,3> I i )=C1 a s s < 1 , I i > +Cc a p ( 9 , I i I i ) ! PUMP HATER LI HE FLUME ! 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 IF D a t a < 3 7 , I i IF D a t a < 3 7 , I i IF Dat. a < 3 7 , I i IF Da ta t 3 7 , I i ! Hi =Cos t<11 ,2> L o = C o s t < 1 1 , 3 ) GOSUB Random C c a p < 1 1 , I i >=C IF D a t a ( 3 7 , I i IF D a t a ( 3 7 , I i IF B a t a ( 3 7 , I i IF Dat a < 3 7 , I i I FOR J=3 TO 11 T o t a l = T o t a l NEXT J ! C c a p < 1 2 , I i > = . IF D a t a < 3 7 , I i D a t a < 3 7 , I i Dat a< 3 7 , I i D a t a < 3 7 , I i o s t < 10, 1 )*Ss.-'l . 2*V*< 1+Capsens> > = 1 THEN C 1 a s s < 3, I i )=C1 a s s < 3, I i >=0 THEN C I a s s < 1 , I i ) = C 1 a s s C 1 , I i > = 1 THEN E d b = E d b + . 3 3 3 * C c a p < 1 0 , 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 SER'' >+Ccap<IO, I i > ) + C c a p < I O , I i > o s t < 1 1 , 1 > * S s / l . 2 * V * < 1 + C a p s e n s > > = 1 THEN C1 a s s ( 4 , I i ) = C 1 a s s ( 4 , I i > = 0 THEN C l a s s < 1 , I i > = C1 as s < 1, I i > = 1 THEN Edb=Edb+.333*Cc ap<11 , I > = 1 THEN B cedb=Bcedb+ .333*Ccap< + C c a p ( J , I i ) 0 5 * T o t a l > = 1 THEN C1 a s s < 3 , I i )=C1 a s s < 3 , I i >=0 THEN C1 a s s < 1 , I i ) - C 1 a s s < 1 , I i >=1 THEN E d b = E d b + . 3 3 3 * C c a p < 1 2 , I >=1 THEN Bcedb=Bcedb+ .333*Ccap< ) + Ccap<1 1 , I i > ) + C c a p < 1 1 , I i ) i > 1 1 , 1 0 IF IF IF ! > ip : H i = D a t a < 1 2 , I i ) 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 > * S s / 1 . 2 * V IF D a t a < 3 7 , I i IF Da t a t 3 7 , I i IF Dat a<37, Ii IF D a t a < 3 7 , I i ) + C c a p < 1 2 , I i > ) + C c a p < 1 2 , I i > i > 12, I i > >=1 THEN C I a s s < 3 , I i > = C 1 a s s C 3 , I i >=0 THEN C1 as s < 1 , I i ) = C 1 as s (1 , I i >=1 THEN E d b = E d b + . 3 3 3 * C c a p < 1 3 , I >=1 THEN B c s d b = B c e d b + . 3 3 3 * C c a p < >+Ccap<13, >+Ccap<13, i ) 13, I i > I i > I i :> Hi = D a t a C 1 8 , I i L o = D a t a ( 1 9 , I i GOSUB Random C c a p < 1 4 , I i > = D IF D a t a ( 3 7 , I i IF Dat a< 3 7 , I i Edb=Edb+ .333* Bcedb=Bcedb+. IF Dat a ( 2 6 , I i ! Hi = D a t a < 3 9 , I i L o = D a t a C 4 0 , I i GOSUB Random Cc ap < 1 5 , I i > = D IF D a t a C 3 7 , I i IF D a t a C 3 7 , I i IF D a t a C 3 7 , I i IF D a t a < 3 7 , I i ! Hi =Data<28, I i Lo = Dat a < 2 9 , I i GOSUB Random C c a p C 1 6 , I i >=D ! FOR J=l TO 16 Tot a l _ c ap = T NEXT J I C1 a s s i f y: Cc e Ccd< I i >=Ccd< I CI 28<I i>=C128 a t a < 1 7 , I i ) * S s / l . 2 * V > = 1 THEN C1 a s s < 3, I i > =C1 a s s < 3 , I i >=0 THEN C1 a s s < 1 , I i > = C1 a s s <1 , I i Ccap<14 , I O 3 3 3 * C c a p < 1 4 , I O > = 1 THEN Mi 1 1=Mi 1 1 + C c a p ( 1 4 , I i > a t a ( 3 8 , I i > * S s / l . 2 * V > = 1 THEN C1 a s s < 3 , I i )=C1 a s s ( 3 , I i >=0 THEN C l a s s < 1 , I i > = C 1 as s < 1, I i >=1 THEN E d b = E d b + . 3 3 3 * C c a p < 1 5 , I > = 1 THEN B c e d b = B c e d b + . 3 3 3 * C c a p C a t a ( 2 7 , I i > * S s / l . 2 * V ot a l c ap+Cc ap <J, I i ) < I i >=Cce<Ii >+C lass<4 , I i ) i >+C lass<5 , I i > <Ii > + C 1 a s s < 3 , I i > )+CcapC14 , Ii > >+Cc apC14 , I i ) ! S ITE INVEST. ! ENGINEERING OTHER MINING OTHER PLANT ! EXPLORATION >+Ccap<15, I O >+Ccap<: 15, I i > i ) 1 5 , I i > ! C A P . . I N T E R E S T ! TOTAL CAP ITAL ! CUMULATIVE ACCOUNTS FOR ! EACH CAP ITAL COST ! ALLOWANCE CLASS cFED> 210 7 6 2 8 7 0 3 0 7 0 4 0 7 0 5 0 7 0 6 O 7 0 7 0 7 0 8 0 7 0 9 0 7 1 0 0 7 1 1 0 7 1 2 0 7 1 3 0 7 1 4 0 7 1 5 0 7 1 6 0 7 1 7 0 7 1 8 0 7 1 9 0 7 2 0 0 7 2 1 0 7 2 2 0 7 2 3 0 7 2 4 0 7 2 5 0 7 2 6 0 7 2 7 0 7 2 8 0 7 2 9 0 7 3 6 0 7 3 1 6 7 3 2 0 7 3 3 0 7 3 4 0 7 3 5 0 7 3 6 0 7 3 7 0 7 3 8 0 7 3 9 0 7 4 O 0 7 4 10 7 4 2 0 7 4 3 0 7 4 4 6 7 4 5 0 7 4 6 6 7 4 7 0 7 4 8 6 7 4 9 0 7 5 6 6 7 5 1 6 7 5 2 6 7 5 3 6 7 5 4 0 7 5 5 0 7 5 6 8 7 5 7 6 7 5 8 8 7 5 9 6 7 6 6 6 7 6 1 0 7 6 2 8 7 6 3 8 7 6 4 8 7 6 5 6 7 6 6 8 7 6 7 8 C1 12 < I i ) = C 1 1 2 C I i ) + C 1 a s s ( 2 , 1 i ) C 118( : I i > = C 1 1 6 C I i ) + C 1 a s s ( 1 , I i ) E d b ( I i ) = E d b B c e d b ( I i ) = B c e d b B c c e C I i ) = B c c e ( I i ) + C l a s s ( 4 , I i ) B c c d C I i ) = B c c d ( I i ) + C l a s s ( 5 , 1 > Bc 2 8 ( I i ) = B c 2 8 ( I i ) + C l a s s ( 3 , I i ) B e 1 2 C I i ) = B c 1 2 C I i ) + C l a s s ( 2 , I i ) B c I O C I i ) = B c I 0 < I j ) + C l a s s ( 1 , I i ) ! FOR K = l TO 5 T o t a l 2 = T o t a l 2 + C 1 a s s ( K , I i > H E X T K R E T U R N ! ! ***************************; ! F E D T A X D E P L E T I O N B A S E EC TAX D E P L E T I O N B A S E BC C U M U L A T I V E C A P I T A L COST A C C O U N T S ! Y I E L D » S o p h r * V ! S H O V E L C O S T : S U E - R O U T I N E TO C A L C U L A T E THE F L U M E S Y S T E M O P E R A T I N G C O S T S ! O p e r a t i n g : O p c o s t 1 = O p c o s t 2 = 8 ! H i = D a t a < 6 , I i ) L o = D a t a ( 7 , I i ) GOSUB R a n d o m Y 1 d = D a t a ( 5 , I i ) * S s - ' l . 2 * ( 1 + Y 1 d s e n s > ! H i = C o s t ( 1 , 5 ) L o = C o s t ( 1 , 6 ) GOSUE R a n d o m 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 . ! H i =. 5 L o = . 2 5 GOSUE R a n d o m T o p h r = F 1 u m e ( I i , 2 ) * S s ' l . 2 H i = C o s t C 2 , 5 ) L o = C o s t ( 2 , 6 ) 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 ) ! I F C a s e * = " N F " T H E H GOTO O p _ c o s t l I F I i >1 THEH GOTO O p _ c o s t l I F ( 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 ! ' . O p _ c o s t l : H i = C o s t ( 1 5 , 5 ) L o = C o s t ( 1 5 , 6 ) GOSUB R a n d o m L o a d e r = C C o s t ( 1 5 , 4 ) + F u e l s e n s * 1 8 + L a b s e n s * 5 2 ) * S s / 1 . 2 H i = C o s t ( 1 4 , 5 ) L o = C o s t ( 1 4 , 6 ) GOSUB R a n d o m D o z e r * ( C o s t ( 1 4 , 4 > + F u e 1 s e n s * 1 8 + L a b s e n s * 5 2 ) * S s 1 . 2 H i = C o s t ( 3 , 5 ) L o = C o s t ( 3 , 6 ) GOSUB R a n d o m 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 ! G R I Z Z L Y D U M P , ! L O A D E R AHD ! DOZER C O S T S ! Pmpc s t = Y p r o d / 1 6 0 8 0 0 * 4 * 5 0 C o p ( 4 , I i ) = C P m p c s t + K w * C 1 2 * 7 . 1 7 + D a y * F a c t o r * 2 4 * . 8 0 7 4 > > * V ! H i = C o s t ( 9 , 5 > L o = C o s t ( 9 , 6 ) GOSUB R a n d o m 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 ! H i = C o s t ( 1 0 , 5 ) L o = C o s t ( 1 0 , 6 ) ! P U M P I N G COST ! D E W A T E R I N G P L A N T ! C O S T S 211 7680 7690 7700 7710 7720 7730 7740 7750 7760 7776 7780 7790 7800 7810 7820 7830 7840 7850 7860 7870 7880 7890 7900 7910 7920 7930 7940 7950 7960 7970 7980 7990 8000 8010 8026 8030 8040 8656 8060 8676 8686 8696 8166 8116 8126 8136 8146 8156 8166 8176 8180 8190 8200 8216 3220 8236 8240 8256 8266 8276 8286 8296 8360 8316 8 320 8330 ! SERVICE COST ! OTHER MINING ! OTHER PLANT GOSUB Random C o p t 6 , I i ) = C o s t ( 1 0 , 4 > * S s / l . 2*V ! 0 p _ c o s t 2 : FOR C=l TO 6 O p e o s t l = 0 p c o s t 1 + C o p C C , I i >* ( l+0psens> NEXT C I Hi =Dat a<15, I i ) L o = D a t a < 1 6 , I i ) GOSUB Random Cop<7, I i >=Dat aC 14, I i >*Ss/l . 2 *V*Yprod*Y1 d Hi = D a t a < 2 1 , I i ) L o = D a t a < 2 2 , I i ) GOSUB Random P) an t=Da ta<20 , I i > * S s / l . 2*V*Ypr-od*Y 1 d C o p < 8 , I i > = P l a n t - C o p < 5 , I i > ! Hi =Cost <12 ,5 ) Lo=Cos t<12 ,6> GOSUB Random Cop<9, I i >=Cost < 12, 4 > * S s / l . 2*Ypr-od*Y1 d*V i H i = C o s t < 1 3 , 5 ) L o = C o s t < 1 3 , 6 ) GOSUB Random C o p < 1 0 , I i >=Cost <13,4 > * S s / l . 2 * Y p r o d * Y 1 d * V Ra i1=Cop<10 , I i ) I FOR C=7 TO 10 0 p c o s t 2 = 0 p c o s t 2 + Cop<:C, I i > NEXT C ! IF I i >1 THEN GOTO 8030 IF C a s e * = " N F " THEN O p c o s t 1 = 0 p c o s t 2 = 0 RETURN ************************************* ! HEAD OFF ICE ! RAIL SUB-ROUTINE TO CALCULATE THE FEDERAL CORPORATE INCOME TAXES * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * F e d _ t a x e s : Temp = Surn = 0 I H i =Dat a< 3 1 , I i ) Lo = Da ta<32 , I i ) GOSUB Random I n v e n t o r y = B a t a < 3 0 , I i >*Ss.-'l . 2*V ! Hi = D a t a < 9 , I i ) Lo = Dat a < 1 O , I i ) GOSUB Random Rev=Dat a< 8, I i "/ *Ss--' 1 . 2*V* < 1 +Pr i c e s e n s > ! Hi =Data<34, I i ) Lo = Dat a < 3 5 , I i ) GOSUB Random I n t = D a t a < 3 3 , I i > * S s ' l . 2 * V I n c o m e = R e v * Y1 d * Y p r o d * * * * * * i Fedt ax ( 1 , I i ) = I nc ome-Opc o s t 1 -Opc o s t 2 Temp=Fedt ax >'. 1 , I i ) ! IF Temp<.3*C110 < I i > THEN GOTO Jump 1 Temp=Te mp- . 3*C 1 1 0< I i > CI 10= .3*C11O<I i ) C U O U i +1 ) = . 7*C1 10(1 i ) • I n v e n t o r v * . 0 3 212 8340 B a c k l : IF Temp<.3*C128< I i> THEN GOTO Jump2 8350 T e m p 2 8 = . ? * C 1 2 8 ( I i > 8360 Temp=Temp-. 3*C 1 28(1 i > 8370 IF Temp<0 THEN Temp=0 8380 IF Income<Temp28 THEN GOTO Lap i n 8390 ! 8400 IF Temp>Temp2S THEN C I23 = C128<I i > 8410 IF Temp>Temp28 THEN C123(T i+1>=0 8420 IF Temp>Temp23 THEN Temp=Temp-Temp28 8430 IF Temp<Temp28 THEN C128=Temp+.3*C128( I i> 8440 IF Temp<Temp28 THEN C 1 28( I i +1 ) =Temp28-Temp 8450 IF Temp(Temp28 THEN Temp=0 8460 GOTO Back2 8470 ! 8480 L a p i n : IF TempMncome THEN C128=C12S ( I i> 8490 IF TempMncome THEN C128<I i+1 )=0 8500 IF .Temp > I nc ome THEN Temp = Ternp-Income 8510 IF Temp<Income THEN C128 = T e m p + . 3 * C 1 2 8 C I i ) 8520 IF Temp<Income THEN C128 <Ii +1> = Inc ome-Temp 8530 IF Temp<Income THEN Temp=0 8540 ! 8550 B a c k 2 : IF Temp<C112<Ii> THEN GOTO Jump3 8560 Temp = Temp-C112 < I i ) 8570 CI 12 = 0 1 1 2 ( 1 i > 8580 C 1 1 2 ( I i + 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> =C128 ( I i )-Temp 8670 CI 28 = Temp 8680 Temp=0 8690 GOTO Back 2 8700 ! 8710 Junip3: CI 12( I i + 1 )=C) 12( I i )-Temp 8720 CI12=Temp 8730 Temp=0 8740 ! 8750 Jutnp4: F ed t ax ( 2 , I i ) = C1 10 8760 F e d t a x ( 3 , I i ) = C 1 1 2 8770 F e d t a x ( 4 , I i ) = C 1 2 8 S730 F e dt a x ( 5 , I i ) = ( F ed t a x ( 1 , I i ) - C 1 1 0 - C 1 1 2 - C 1 2 8 > * . 7 5 ! RESOURCE ftLLOWRNCE 8790 IF Temp=0 THEN GOTO Jump7 83O0 Temp = F e d t a x ( 5 , I i >-Int 8810 ! 8820 IF Temp<Cce ( I i> THEN GOTO Jump5 8830 Temp=Temp-Cce ( I i> 8840 C c e = C c e ( I i > 8850 C c e ( l i + 1 > = 0 8860 ! 8870 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 C c d = . 3 * C c d ( I i > 890O C c d ( l i + 1 > = 0 8910 GOTO Jump7 8920 ! S930 Jumps: C c e ( I i + 1 > = C c e ( I i > - T e m p 8940 Cce=Temp 8950 Temp=0 8960 GOTO BackS 8970 ! 8980 Jump6: Ccd ( I i + 1> = . 3 * C c d ( I i ) - T e m p 8990 Ccd=Temp 2 1 3 90Q0 Temp=0 9O10 ! 9020 Jump?: Fedt a x ( 6 , I i ) = I nt 9O30 Fedt ax(7, I i ) = Cc d 9040 Fedt ax(8,Ii> = Cc e 9050 ! 9060 Sum=Fedtax(5,Ii>-Int-Ccd-Cce ! RESOURCE PROFIT 9070 IF <Sum<0> OR <Sum=0> THEN GOTO Jump9 9080 IF Sum*.25>Edb THEN GOTO Jump8 9090 IF Surn*.25<Edb THEN Fedt ax ( 9, I i > =. 25*Sum 9100 Edb=Edb-.25*Sum 9116 GOTO Jump 10 9120 JumpS: Fedt ax ( 9,Ii)=Edb 9130 Edb=0 9140 GOTO Jump 10 9150 Jump9: Fedtax<9,Ii >=0 9160 JumpIO: IF <Sum = 0> OR CSum<0> THEN Fedt ax <10,Ii > =0 ! TAXABLE INCOME 9170 IF Sum>e THEN FedtaxC1O,Ii>=Sum-Fedtax(9,Ii> 9180 Fedtax(11,Ii>=FedtaxC1O,Ii>*.36 ! TAX PAYABLE 9190 ! 9200 Itc1=.07*C1ass(1,Ii> 9210 Itc2=15OO0+(FedtaxC11,I I)-150O0)/2 9220 IF Itcl<Itc2 THEN Intax=Itcl 9230 IF Itc l > I t c 2 THEN Intax=Itc2 9240 Itc=Itc+Intax 9250 IF Ii>5 THEN I t c = I t c - I t c ( I i - 5 > 9260 IF Itc<6 THEN Itc=0 9270 ! 9230 IF Fedtax(11, Ii J = 0 THEN GOTO Notax 9298 IF Fedt ax (11 , 1 i X H c THEN GOTO Invest 9300 ! 9318 Fedt ax(12,Ii > = 11 c 9320 Itc=8 9330 Itc( I i >=6 9340 Fedt ax(13, I i > =Fedt ax(11, Ii >-Itc 9358 GOTO Hop-skip 9368 ! 9378 Invest: Fedtax<12,Ii)=Fedtax(11,Ii> 9386 Itc=Itc-Fedtax(12,Ii> 9396 I t c ( I O = Itc 9468 Fedtax(13,Ii>=8 94 16 GOTO Hopskip 9428 ! 9436 Notax: Fedtax(12,Ii> =8 9448 Itc ( I i > = Itc 9456 Fedtax(13,Ii>=6 9466 ! 9476 Hopskip: C118(Ii+1)=C116(Ii+1>-Fedtax(12,Ii> 9486 IF C118(Ii+l><8 THEN C116(Ii+l>=6 9498 Be 18(Ii + 1) = Bc16(Ii +1>-Fedt ax(12,Ii > 9566 IF Bcl0<li + 1><0 THEN B c l 8 ( I i + n=6 9518 ! 9526 IF Fedtax(13,Ii><8 THEN Fedtax(13,Ii > = 6 9536 RETURN 9546 ! 95 56 ! **************************** 9566 ! SUB-ROUTINE TO COMPUTE EC CORPORATE AND MINING INCOME TAXES 9570 ! ********************^^ 9580 ! 9596 Bc_taxes: Ttemp=Sum2=Sum3=8 9686 Royalty=.835*(Income-Rai1) 9616 Be t ax (1 , I i > = I nc ome-Opc ost'l -Ope ost 2-Royal t y-1 nvent c r y * . 63 9626 Be mt ax(1, Ii > = Bc t ax(1, I i ) 9636 ! 9646 Tte(np = Bcmtax( 1, I i > 9656 IF Ttenip< . 3*Bcl0CI i > THEN GOTO Jump 11 214 9660 T t emp=Ttemp- .3*Bc IOC I i > 9670 B e 1 0 = . 3 * B c 1 0 C I i > 9680 B c I O C I i + 1 > = . 7 * B c 1 0 < I i > 9690 ! 9700 Back 11 : IF T t e m p < . 3 * B c 2 8 C I i > THEH GOTO Jump l2 9710 T t e m p 2 8 = . 7 * B c 2 8 < I i ) 9720 Tternp = T t e m p - . 3 * B c 2 8 < I i ) 9730 IF Income<Temp28 THEH GOTO L a p i n S 9740 ! 9750 IF Ttemp>Ttemp28 THEH Bc23 = Bc28C I i >' 9760 IF Ttemp>Ttemp28 THEH Bc28CI i+1>=0 9770 IF Ttemp>Ttemp28 THEH Ttemp=Ttemp-Ttemp28 9780 IF Ttemp<Ttemp28 THEH B c 2 8 = T t e m p + . 3 * B c 2 8 C I i > . 9790 IF Ttemp<Ttemp23 THEH Bc28 ( I i +1 > = T temp28-Ttemp 9800 IF Ttemp<Ttemp23 THEH Ttemp=0 9810 GOTO Back 14 9820 ! 9330 L a p i r i 3 : IF Tt emp> I ncome THEH Bc23 = Bc28< I i > 9840 IF Ttemp>Income THEH Bc28<I i+1>=0 9858 IF Ttemp>Income THEH Ttemp=Ttemp-Income 9868 IF Ttemp<Income THEH B c 2 8 = T t e m p + . 3 * B c 2 8 < I i ) 9878 IF Ttemp<Income THEH Bc28< I i+1 )= Income-T temp 9880 IF Ttemp<Income THEH Ttemp=6 9898 ! 9900 Back 12: IF T t emp<Bc12< I i ) THEH GOTO Jump 13 9916 Tt emp = T t emp-Bc12 <Ii > 9926 Bc12=Bc12<I i> 9938 B c l 2 ( I i + n = 6 9946 ! 9958 Back 13: IF T temp<Bcce<I i > THEH GOTO Jump 14 9966 Ttemp = T t e m p - B c c e C I i > 9978 B c c e = B c c e < I i ) 9988 BcceC I i+1>=8 9998 ! 18808 Back 14: IF T t e m p < . 3 * E c c d < I i ) THEH GOTO JumplS 18816 Tt emp = Tt emp- .3*Bc c d <Ii > 16828 Bccd = B c c d < I i > 16636 B c c d < I i + l ) = 6 18646 GOTO Jump 16 10650 ! 16066 J u m p l l : Bc10< I i + 1>=Bc10<Ii >* .3-Ttemp 10876 Bc lO=Ttemp 16686 Ttemp=8 16896 GOTO Back 11 1O10O ! 1011O Jurnpl2 : Bc28( I i +1 >=Bc2S< I i )-Ttemp 1O120 Bc28=Ttemp 1013O Ttemp=8 16146 GOTO E a c k l 2 10156 ! 10168 J u m p l S : Bc12 CI i +1> = Bc12 < I i>-Tt emp 16176 Bc l2=T temp 18186 Ttemp=6 18196 GOTO Back 13 10286 ! 16218 Jump 14: Bc c e < I i + 1 > = Ec c e < I i ':>-Tt emp 18228 Bcce=Ttemp 16238 Ttemp=8 16240 GOTO B a c k l 4 18258 ! 18268 J u m p l S : B c c d C I i + 1 ) = . 3 * B c c d C I i > - T t e m p 18278 Bccd=Ttemp 18288 Ttemp=6 18298 ! 18380 J u m p l S : B c t a x < 2 , I i ) = B c 1 8 1O310 B c m t a x C 2 , I i ) = B c 1 0 215 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 Bcmtax(3,Ii )=Bc12 Be t ax (4,Ii)=Bc28 Bcmtax(4,Ii)=Bc28 Betax(6,Ii ) = Int Bcmtax(6,Ii ) = Int Betax(7, I i )=Bcce Bcmtax(7,Ii) = Bcce Bctax(8,Ii >=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: Bctax(9,Ii)=Bcedb Bcedb=8 GOTO Jumpl9 Jump 18: Be t ax(9,Ii > =0 Jump 19: IF (Sum2<0) OR (Sum2=0) THEN Ectax(10,Ii IF Sum2>0 THEN Be t ax(10, Ii )=Sum2-Bctax(9,Ii ) Bctax(11,Ii ) = . 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 t * *********************** j THE PROJECT ECONOMICS ! ********* ! 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 PRINT " **************************** INPUT "ENTER THE CORPORATE HURDLE RATE PER ! Jumper 2:Negat i ue=1 Pos i t i ve=.05 P=(Negatiye-Positiwe)/2 C o u n t e r = 1 ! Again: FOR K=l TO Period Np=Np+Cash(10,K)/(1+P)-K IF Counter>l THEN GOTO Jump29 Hpu = Npv + Cash(IO, K)/(1+R)-K Jump29: NEXT K C o u n t e r = C o u n t e r + 1 ! IF AES(Np)<25000 THEN GOTO JumpSO IF Np<0 THEN Negative=P IF Np>0 THEN Positive=P P= (Negat i ue-Pos i t i ve)x2 + Pos i t i ve ! IF Counter MOO THEN PRINT LINC5) IF Counter>100 THEN WAIT 1000 IF Counter)100 THEN GOTO Cont ! IRR ARE BEING COMPUTED' PERIOD (as a dec i ma))",R "ERROR IN NPV CALCULATION' 216 0980 Np=© 0990 GOTO A g a i n 1OO0 JumpSO:Npv < J j ) = Npv 101O I r r< J j>=P 1O20 PRINT L IN<20) 1030 C o n t : RETURN 1040 ! 105O ! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1060 ! CONTROLLING STATEMENTS FOR COMPUTING TRUCK/SHOVEL 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 ) 1 1 1 0 ! 1120 Y p r o d = D a t a < 4 , I i ) 1130 ! 1140 D a y = D a t a < 2 3 , I i ) 1150 Sh i f t = D a t a < 2 6 , I i ) 1 160 Vtemp=l+Data< 1, I i )*< 1 + In f s e n s ) 1170 V=V*Viemp 1180 ! 1190 ! 120O ! * * * * * * * CALCULATE SHOVEL OPERATING AND CAP ITAL 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 Sut i 1 =Tcos t < IO, 4 ) * S s - ' l . 2 1320 Shove 1 s=Sophr/<.24*Dav*Sut i 1 ) 1330 ! 1340 G=Shove l s 1350 IF F R A C T C G X . 2 THEN G = G+1 1360 Shove l s= INT<G) 1370 ! 1380 ! 1390 ! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1400 ! TRUCK AND SHOVEL OPERATING AND CAP ITAL COSTS ARE BEING CALCULATED 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 =Tcos 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 < I i , 3 ) * V 1560 IF C o a l = 0 THEN C c a p < 2 , I i ) = 0 1570 ! 1580 ! 1590 ! * * * * * * * SORT THE CAP ITAL COSTS BY CLASSES * * * * * * * 1600 ! 1616 ! ' 1 ' FOR CLASS 10 ASSETS 1620 ! ' 2 ' FOR CLASS 12 ASSETS 1630 ! ' 3 ' FOR CLASS 28 ASSETS 217 . 1648 .1650 . 1 660 1670 1680 1690 1700 1710 1720 1730 .1740 .1750 1760 1770 1780 1790 1800 1810 1820 .1830 .1340 1850 I860 1870 1880 1890 1900 1910 1920 1 930 1940 1950 I960 1970 1980 . 1990 120OO .2010 2020 2030 2040 12050 12068 12070 2680 2090 2160 12 1 1 © 12120 :130 L2140 !150 ne© L2170 : I s 0 12190 220O 2210 12220 2230 2240 1 2250 i<:260 12278 ?280 i2290 ! IF IF IF IF ! IF IF IF IF ! Hi Lo Hat a':: 3 7 , I i ) D a t a C 3 7 , I i ) Dat aC 37 D a t a t 37 I i > I i > D a t a C 3 7 , I i > Da t a t 3 7 , I i ) D a t a C 3 7 , I i ) D a t a C 3 7 , I i ) = 1 = 0 = 1 = 1 = 1 = 0 = 1 = 1 THEH THEN THEH THEH THEH THEH THEN THEN ' 4 ' FOR CANADIAN EXPLORATION EXPENSE ' 5 ' FOR CANADIAN DEVELOPMENT EXPENSE C1 a s s C 3 , I i > = C1 a s s < 3 , I i > + CcapC 1 , I i ) ! SHOVEL C1 a s s ( 1 , I i > =C1 a s s <1 , I i> + C c a p C 1 , I i > Edb = E d b + . 3 3 3 * C c a p < 1 , I i > B c e d b = E c ? d b + . 3 3 3 * C c a p ( 1 , I i ) 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 > CI a s s a , I i > = C 1 a s s C 1 , I i > + C c a p C 2 , I i > Edb = E d b + . 3 3 3 * C c a p C 2 , I i > B c e d b = B c e d b + . 3 3 3 * C c a p C 2 , I i > D a t a C 1 2 , I i ) D a t a C 1 3 , I i > GOSUB Random C c a p < 3 , I i >=Dat IF D a t a C 3 7 , I i > IF D a t a C 3 7 , I i ) IF D a t a C 3 7 , I i ) IF D a t a C 3 7 , I i ) ! Hi =Da taC18 , I i ) Lo=DataC 19, I i ) GOSUB Random C c a p < 4 , I i ) = D a t IF D a t a C 3 7 , I i ) IF D a t a C 3 7 , I i > Edb=Edb+ .333*C Bc edb = Bc edb+ .3 IF D a t a C 3 7 , I i > I Hi =Da taC39 , I i > Lo = D a t a C 4 0 , I i > GOSUB Random Cc ap C 5, Ii > = Dat IF D a t a C 3 7 , I i ) IF D a t a C 3 7 , I i > IF D a t a C 3 7 , I i ) IF D a t a C 3 7 , I i > iC 1 1 , I i =1 THEH •O THEH = 1 THEH =1 THEH a c 1 7 , I i =1 THEH =0 THEH c ap C 4, I 3*Cc ap 1 THEH aC 38 , I i =1 THEH =0 THEH =1 THEN =1 THEN ) * S s / l . 2 * V 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 > 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 ) Edb = E d b + . 3 3 3 * C c a p ( 3 , I i > B c e d b = B c e d b + . 3 3 3 * C c a p C 3 , I i > > * S s / l . 2 * V 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 ) 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 ) i > ( 4 , I i > Mi 1 1 = M i 1 1 + C c a p C 4 , I i > > 1.2*V C 1 a s s C 3, I i > =C1 a s s C 3 , I i ) + C c a p C 5, C 1 a s s C1, I i > =C1 a s s C 1 , I i >+Cc ap C 5, Edb = E d b + . 3 3 3 * C c a p C 5 , I i > Bcedb = B c « d b + . 3 3 3 * C c a p C 5 , I i.) I i ) I i > Hi = D a t a C 2 3 , I i ) L o = D a t a C 2 9 , I i ) GOSUB Random C c a p C 6 , I i ) = D a t a C 2 7 , I i IF D a t a C 3 7 , I i > = 1 THEN IF D a t a ( 3 7 , I i ) = 0 THEN IF D a t a C 3 7 , I i > = 1 THEH IF D a t a C 3 7 , I i > = 1 THEH > * S s / l . 2 * V C 1 a s s C 3, I i )=C1 a s s C 3, I i > +Ccap C 6, Ii > CI a s s C 1 , I i > = C 1 a s s C 1 , I i >+CcapC6, Ii > Edb = E d b + . 3 3 3 * C c a p C 6 , I i > Bcedb = E c e d b + . 3 3 3 * C c a p C 6 , I i > FOR J= l TO 6 T o t a l _ c a p = T o t a l _ c a p + C c a p C J , I i > HEXT J ! TRUCKS ! OTHER MINING ! OTHER PLANT EXPLORATION ! CAP. INTEREST Cce C I i > + C l a s s C 4 , I i s s C 5, I i > C1 a s s i fy 1: Cc e C I i > C c d C I i ) = C c d C I i >+Cl C 1 28C I i > =C 1 2 8 C I i > +C1 a s s C 3 , I i > CI 12C I i > = C 1 1 2 C I i ) + C l a s s C 2 , I i > C U O C I i ) = C 1 1 0 C I i ) + C l a s s C l , I i > E d b C I i >=Edb B c e d b C I i ) = B c e d b B c c c C I i ) = B c c e C I i > + C l a s s C 4 , I i > B c c d C I i ) = E c c d C I i > + C l a s s C 5 , n B c 2 8 C I i ) = B c 2 8 C I i ) + C l a s s C 3 , I i > B c 1 2 C I i ) = E c 1 2 C I i ) + C l a s s C 2 , I i ) B c 1 0 C I i > = BcISC I i ) + C l a s s C 1 , I i ) ! CUMULATIVE ACCOUNTS FOR ! EACH CAP ITAL COST ! ALLOWANCE CLASS C FED > ! FED TAX DEPLETION BASE BC TAX DEPLETION EASE * * * * * * * * * * * * * * * * * * * * BC CUMULATIVE CAPITAL COST ACCOUNTS 2 1 8 1 2 3 O 0 ! 1 2 3 1 0 FOR. K=l TO 5 1 2 3 2 0 T o t a l = T o t a l + C 1 a s s C K , I i ) 1 2 3 3 0 N E X T K 1 2 3 4 0 ! 1 2 3 5 0 ! * * * * * * * O P E R A T I N G C O S T S * * * * * * * 1 2 3 6 0 ! 1 2 3 7 0 O p c o s t l = O p c o s t 2 = 0 1 2 3 8 0 ! 1 2 3 9 0 H i = D a t a < 6 , I i > 1 2 4 0 0 L o = D a t a < 7 , I i > 1 2 4 1 0 GOSUB R a n d o m 1 2 4 2 0 Y l d = D a t a < 5 , I i > * S s / l . 2 * < 1 + Y 1 d s s n s > 1 2 4 3 0 ! 1 2 4 4 0 H i = T c o s t < 1 , 5 > 1 2 4 5 0 L o = T c o s t < 1 , 6 > 1 2 4 6 0 GOSUB R a n d o m 1 2 4 7 0 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 1 2 4 8 0 ! 1 2 4 9 0 H i = . 5 1 2 5 0 0 L o = . 2 5 1 2 5 1 0 GOSUB R a n d o m 1 2 5 2 0 T o p h r = T r u c k < I i , 2 ) * S s / " l . 2 1 2 5 3 0 H i = T c o s t < 2 , 5 > 1 2 5 4 0 L o = T c o s t ( 2 , 6 > 1 2 5 5 0 GOSUB R a n d o m 1 2 5 6 0 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 ? > *Ss .< '1 . 2 * V * T o p h r * < 1 + T o p s e n s > 1 2 5 7 8 C o p < 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 1 2 5 8 0 ! 1 2 5 9 0 H i = D a t a < 1 5 , I i > 1 2 6 0 O L o = D a t a < 1 6 , I i > 1 2 6 1 0 GOSUB R a n d o m ! OTHER M I N I N G I N C L . 1 2 6 2 0 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 1 2 6 3 0 ! 1 2 6 4 0 H i =Dat a < 2 1 , I i > 1 2 6 5 0 L o = D a t a C 2 2 , I i ) 1 2 6 6 0 GOSUB R a n d o m 1 2 6 7 0 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 1 2 6 8 0 ! 1 2 6 9 0 H i = T c o s t < 3 , 5 > 1 2 7 0 8 L o = T c o s t < 3 , 6 > 1 2 7 1 8 GOSUB R a n d o m 1 2 7 2 0 C o p < 6 , I i > = T c o s t < 3 , 4 > * S s / 1 . 2 * V * Y 1 d * Y p r o d ! HEAD O F F I C E 1 2 7 3 0 ! 1 2 7 4 0 H i = T c o s t < 4 , 5 > 1 2 7 5 0 L o = T c o s t < 4 , 6 > 1 2 7 6 0 GOSUB R a n d o m 1 2 7 7 0 C o p < 7 , I i ) = T c o s t ( 4 , 4 > * S s / 1 . 2 * V * Y1 d * Y p r o d ! R A I L 1 2 7 8 0 R a i 1 = C o p ( 7 , I i > 1 2 7 9 0 ! 1 2 8 O 0 FOR C=l TO 3 1 2 8 1 0 O p c o s t l = 0 p c o s t l + C o p < C , I i > * <l+ 0 p s e n s > 1 2 8 2 0 N E X T C 1 2 8 3 0 ! 1 2 8 4 0 FOR C=4 TO 7 1 2 8 5 0 0 p c o s t 2 = 0 p c o s t 2 + C o p < C , I i > 1 2 8 6 0 N E X T C 1 2 8 7 0 ! 1 2 8 8 0 I F I i > l T H E N GOTO T a x 1 2 3 9 0 I F C a s e * * " N T " T H E N O p c o s t 1 = 0 p c o s t 2 = 0 1 2 9 0 0 T a x : GOTO T a x e s 1 2 9 1 0 ! 1 2 9 2 0 ! . 1 2 9 3 0 ! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1 2 9 4 0 ! 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 1 2 9 5 0 ! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 219 2 9 7 O 2980 2990 3000 3010 3020 3030 3040 3O50 3068 3878 3888 3898 3180 3118 3128 3136 3148 3150 3160 3170 31S0 3198 T ION" 3268 T ION" 3216 3226 3238 3246 3258 3260 3278 3 2 8 O 3290 3380 3310 3328 3336 3348 3356 ! Tab 1 e DIM fi fi*< 1 , R*<2, fi * < 3 , A*<4 , fit ( 5 , A*<6 , fi * <: 7, fit<8, A *<9 , A*< 18 REDIM F=16 ! FOR IF IF IF NEXT ! P r i n t IF <C s: DIM fi* U 6 , 1 ) C 26 ] , E* < 1 1 , 1 ) C 28 3 , C* < 1 3 , 1 > [ 26 3 a*C203 1) = " A N N U A L PRODUCT I ON" 1)="GROSS REVENUE" 1 )="C0AL TRANSPORT COST" 1>="0THER OP. COSTS" 1> = "ROYftLTY PAYMENT" 1>="FED. INCOME TAX" 1>="EC INCOME TAX" 1)="BC MINING TAX" 1 )= "T0TAL CAP ITAL COST" , 1 ) = " H E T CASH FLOW" C a s h t 1 8 , 1 8 ) J= l TO 7 1-Per i od-'5<8 THEN REDIM Cash< 18, < J +1 >*5) 1 - P e r i o d ' 5 < 6 THEN GOTO P r i n t l O-Period<-"5>6) OR <1-Pe r i od^5=0 ) THEN GOTO P r i n t l J l : PRINTER IS F a s e * = " N F " ) OR < C a s e * = " E F " ) OR C C a s e * = 'RF" ; ' THEN fia* = " FLUME TRANSPORTA IF C C a s e * = " N T " > OR < C a s e * = " E T " ) OR < C a s e * = " RT " ) THEN fia* = "TRUCK TRANSPORTA E=l Pe r = P e r i od/S IF P e r i o d < 5 THEN P e r = l F IXED O I PRINT LIN<2) a s e * = "NF"'; ' OR CCase*= "NT "> THEN PRINT TAB < 36 > , "NEW MINE CASE " a s e * = " E F " > OR <Case*="ET "> THEN PRINT TAB<27),"EXPANDING MINE CASE " a s e * = " R F " ) OR CCase*="RT") THEN PRINT T A B C 2 6 ) , " T R U C K REPLACEM'T CASE " IF <C IF <C IF <C PRINT T A E U 7 ) , i FOR K=l TO Per PRINT LIH<5) , ' PRINT " PRINT L I N C 1 ) , ' MEAN VALUES ONLY CASH FLOW SUMMARY FOR " ; A a * < a l l amounts i n c u r r e n t C a n a d i a n * )' 3360 3378 PRINT T A B < 2 4 ) ; E ; T A B < 3 6 ) ; E + l ; T A B ( 4 8 ) ; E + 2 ; T A B ( 6 6 ) ; E + 3 ; T f i B < 7 2 ) ; E + 4 PRINT " 3388 3396 3488 ,E+I; 34 18 3428 3436 3448 3456 3466 3478 34S6 3498 3566 TE OF 3510 — " , L I N < 1 ) ! FOR L=l TO 10 PRINT USING " 2 0 f i , 9D, 3X, 9D, 3X, 9D, 3X, 9D , 3X, 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 PRINTER IS 16 PRINT L INC 1 ) , " PRESS ' C O N T ' " PAUSE PRINTER IS F NEXT K PRINT L INC2) , " RETURN" PRINT " RATE DISCOUNT NET PRESENT VALUE VALUE INTERNAL Rfi OF RETURN 3520 PRINT L I N O ) 3530 PR I NT 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 3540 ! 220 IF Sr-ef ( 1 , S j > = IF S r e f < l , S j ) = IF S r e f a , S j ) = IF S r e f < l , S j ) = 1 THEH PRINT TAB (25 ) ii THEH PRINT TAB<25) 3 THEH PRINT TABC25) 4 THEH PRINT TAB (25 ) 5 THEH PRINT TAB (25 ) 6 THEH PRINT TAB (25 ) —f 1 THEH PRINT TAB (25 ) 8 THEH PRINT TAB (25 ) 9 THEH PRINT TAE<25) ( 2 , S j ) IF S r e f ( l , S HEXT S j F IXED 0 ! H r d c p y : INPUT "ENTER ' O ' IF YOU WISH A HARDCOPY OF THE R E S U L T S " , F IF F=0 THEN GOTO P r i n t l PRINTER IS 16 RETURN 3550 IF S e r i s *= "N " THEH GOTO H r d c p y 3560 PRINT L IN(2> 3570 FOR Sj = l TO 8 3580 F IXED 3 3600 S j > 3610 3620 3630 3640 3650 3660 S r e f 3670 e f ( 2 , 3680 3690 370O 3710 3720 3730 3740 3750 3760 3770 3788 3790 3388 3818 3828 3838 3848 3858 3S60 3870 3888 3898 3988 3918 3928 3938 3940 3958 3968 3976 3988 3998 4888 4618 4628 4638 4646 4856 4868 4676 4886 4090 4168 4116 4 126 4 1 36 4146 COAL PRICE S E N S I T I V I T Y " INFLATION SENS IT IV ITY* FUEL COST S E N S I T I V I T Y " , " L A B O U R COST S E N S I T I V I T Y ' ';sref " ; S r e f < ' ; S r e f (2 S r e f < 2 , S re f < -ef C 'U/G CONSTRUCT I OH COST SENS IT IV ITY 'TRUCK PRODUCTIVITY S E N S I T I V I T Y " ********************************** SUBROUTINE TO CALCULATE FREQUENCY HISTOGRAMS * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * S t a t s : Haxnpv=l M i nnpv =10000000088 Max i r r = 8 M i n i r r = 1 ! FOR A=l TO I t e r IF Hp'.-'< A) >Maxnpv THEH Haxnp v = Hp v ( A ) IF Hpv( A X M i nnpu THEH Mi nnpv = Npv C A) IF I r r ( A ) > M a x i r r THEH M a x i r r = I r r ( A ) IF I r r ( A X M i ni r r THEH M i n i r r = I r r ( A ) HEXT A i I nt e r vnpv= ( Maxnpc-M i nnpc ) •-' 16 I n t e r u i r r = ( M a x i r r - M i ni r r ) / 1 6 Max=Maxl=6 T e m p n p v = Mi n n p v + I n t e r v n p v Tempi r r = Mi ni r r + I n t e r v i r r I 1 o = M i n i r r H 1 o = M i n n p u I FOR A=l TO 18 Count=6 FOR B=l TO I t e r IF N p v ( B X N 1 o THEH St at jump IF H p v < B)> T e m p n pc THEH S t a t jump Count =Count +1 IF Max<Count THEH Max=Count St at j ump : HEXT B I Npvhi s t ( 1, A ) = T e m p n p v - 1 n t e r v n p v / 2 Npvhi s t ( 2 , A )=Count N1 o = T e m p n p v T e m p n p v = T e m p n p v + I n t e r v n p v HEXT A i * * * * * * * * 221 14150 14160 14170 14 180 14 190 14200 14210 14220 14230 14 240 14250 14260 14270 14280 14290 14300 14310 14320 14330 14340 14350 14360 ] 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 FOR A=l TO 10 Count = 0 FOR B=l TO I t e r IF I r r < B X I l o THEN S t a t j u m p l IF I I T <B)>Tempi I T THEN S t a t j u m p l Count =Count +1 IF Max1<Count THEN Max l=Count S t a t j u m p l : NEXT B I r r h i s t < 1 , A ) = Temp i r r - I n t e r v i r r / 2 I r r h i s t ( 2 , A ) = C o u n t I 1o = Temp i r r Temp i r r = Tempi r r + I n t e r v i r r NEXT A ! RETURN I SUBROUTINE TO PLOT THE HISTOGRAMS * * * * * * * * * * * * * * * * * *******************< ************************* o t 1 : D I M T e x t 1 * [ 2 5 ] , T e x t 2 * [ 1 0 ] , T e x t 3 * C 3 0 ] , T e x t 4 * C 2 0 ] , T e x t 5 * [ 3 0 ] , T e x t 6 * [30 PRINT LINC 20) F IXED O Tex t 1* = "NET PRESENT VALUE" Text 2$="FREQUENCY" Text3*=" HISTOGRAM OF" Text .4* = "HET PRESENT VALUES" Tex t 5* = " INTERNAL RATES OF RETURN" Text 6* ="INTERNAL RATE OF RETURN" T e x t ? * = " < x $ 1 , 0 0 0 , 000 V ! Repnpw: EXIT GRAPHICS PLOTTER IS "GRAPHICS" PRINT L I N O 5 ) , " T H E MAXIMUM FREQUENCY IS","Max PRINT " THE MINIMUM NET PRESENT VALUE I S " ; M i n n p v PRINT "THE MAXIMUM NET PRESENT VALUE I S " ; M a x n p v INPUT "ENTER THE MAXIMUM FREQUENCY VALUE FOR THE NPV P L 0 T " , T m a x INPUT "ENTER THE MINIMUM VALUE FOR THE NPV PLOT ( i n mi 11 i o n s ) " , T m i n n p v INPUT "ENTER THE MAXIMUM VALUE FOR THE NPV PLOT ( i n m i 1 1 i oris) " , Tmaxnpv PRINT L INC20) I DEG GRAPHICS LOCATE 2 0 , 1 1 0 , 0 , 8 0 FRAME CS I2E 3 LORG 1 MOVE 4 8 , 5 LABEL T e x t l * CS I2E 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 * CS I2E 3 LDIR 90 LORG 5 MOVE 2 5 , 4 0 LABEL T e x t 2 $ CS I2E 3 LOCATE 3 3 , 1 0 0 , 1 3 , 6 5 222 14800 SCfiLE T m i n n p w , T m a x n p v , 0 , T m a x 14810 LAXES ( Tmaxnpv-Tm i nnp v > / 1 0, Tmax '5 , Tm i nnpv , 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 H c * = " N " 14880 INPUT "DO YOU WANT A HARDCOPY? ( Y / N ) " , H e * 14890 IF H c * = " Y " THEN DUMP GRAPHICS 14900 R e p * = " N " 14910 INPUT "DO YOU WISH TO TRY AGAIN? < Y / N ) " , R e p * 14920 IF R e p * = " Y " THEN GOTO Repnpv 14930 EX IT GRAPHICS 14940 ! 14950 Repirr-I F IXED 2 14960 PLOTTER IS "GRAPHICS" 14970 PRINT L I N C 1 5 ) , " T H E MAXIMUM FREQUENCY I S " ; M a x l 14980 PRINT "THE MINIMUM VALUE OF THE IRR IS " ; M i n i m 14990 PRINT "THE MAXIMUM VALUE OF THE IRR I S " ; M a x i m 150OO INPUT "ENTER THE MAXIMUM FREQUENCY VALUE FOR THE IRR P L O T " , T m a x l 15010 INPUT "ENTER THE MINIMUM VALUE FOR THE IRR PLOT ( . x x ) " , T m i n i r r 15O20 INPUT "ENTER THE MAXIMUM VALUE FOR THE IRR PLOT ( . x x ) " , T m a x i r r 15030 PRINT L I H ( 2 0 ) 15O40 ! 15050 GRAPHICS 15O60 DEG 15O70 LOCATE 1 5 , 1 1 0 , 0 , 8 0 15080 FRAME 15090 CS IZE 3 15100 LORG 1 15110 MOVE 4 8 , 5 15120 LABEL T e x t 6 * 15130 CS IZE 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 CS IZE 3 15190 LDIR 90 152O0 LORG 5 15210 MOVE 2 0 , 4 0 15220 LABEL T e x t 2 * 15230 CS IZE 3 15240 LOCATE 3 3 , 1 0 0 , 1 3 , 6 5 15250 SCALE T m i n i r r , T m a x i r r , O , T m a x 1 15260 LAXES (Tmaxi 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 t 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 H e * = " N " 15330 INPUT "DO YOU WANT A HARDCOPY? ( Y / N ) " , H e * 15340 IF H e * = " Y " THEN DUMP GRAPHICS 15350 R e p * = " N " 15360 INPUT "DO YOU WISH TO TRY AGAIN? ( Y / N ) " , R e p * 15370 IF R e p * = " Y " THEN GOTO R e p i r r 15380 EXIT GRAPHICS 15390 RETURN 

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