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UBC Theses and Dissertations

Coal blending model : theory and application of the model Bauer, Edwin Alois 1988

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COAL BLENDING MODEL Theory and Ap p l i c a t i o n of the Model by EDWIN ALOIS BAUER B.A.Sc., The Univ e r s i t y of B r i t i s h Columbia, 19 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Mining and Mineral Process Engineering U n i v e r s i t y of B r i t i s h Columbia We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December 1988 (c)Edwin A l o i s Bauer, 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of ft\'in\rt^ + M; A<*f»\ Prated gnj. The University of British Columbia Vancouver, Canada Date k p r f l 1 L A 1 DE-6 (2/88) Pg i i ABSTRACT Over the p a s t decade , most Western Canadian c o a l mines have been f o r c e d to mine d e p o s i t s c o n t a i n i n g m u l t i p l e seams of c o a l , w i t h v a r y i n g c o a l q u a l i t i e s . T h i s change i n min ing p r a c t i c e has caused c o n s i d e r a b l e c h a l l e n g e s f o r c o a l washery p e r s o n n e l . B l e n d i n g o r homogenizat ion o f these m u l t i p l e seams has been the s t a n d a r d approach i n a t t e m p t i n g to min imize the d i s r u p t i o n to washery o p e r a t i o n s . The purpose o f t h i s r e s e a r c h was to d e v e l o p a method o f q u a n t i f y i n g the e f f e c t s o f a c o n t r o l l e d b l e n d i n g program on p r e p a r a t i o n p l a n t y i e l d , thus p r o v i d i n g a way to o p t i m i z e the b l e n d i n g program w i t h i n the c o n s t r a i n t s o f the min ing program, the p r o c e s s i n g u n i t o p e r a t i o n s , and the f i n a l p r o d u c t q u a l i t y c o n s t r a i n t s . A y i e l d - b a s e d o b j e c t i v e f u n c t i o n c a l l e d the C o a l B l e n d i n g C o e f f i c i e n t was deve loped t o e v a l u a t e the e f f e c t s o f b l e n d i n g on p r e p a r a t i o n p l a n t y i e l d . T h i s f o r m u l a can be d e s c r i b e d as the d i f f e r e n c e i n y i e l d between b l e n d i n g and b a t c h i n g o f the same c o a l s . The C o a l B l e n d i n g C o e f f i c i e n t was then i n c o r p o r a t e d i n t o a c o l l e c t i o n o f e x i s t i n g computer programs c a l l e d the CANMET C o a l Data M a n i p u l a t i o n Programs, and a f t e r some m o d i f i c a t i o n s , the C o a l B l e n d i n g Model was p r o d u c e d . The C o a l P l a n t S i m u l a t i o n program, which i s i n c l u d e d i n the CANMET program, i s the h e a r t o f the model , w h i l e the Pg i i i C o a l B l e n d i n g C o e f f i c i e n t v a l u e s a l l o w the model to rank the b l e n d s . To d a t e , a p p r o x i m a t e l y twenty runs o f the C o a l B l e n d i n g Model have been t r i e d on c o a l s from t h r e e B r i t i s h Columbia c o a l d e p o s i t s . The r e s u l t s range from zero b e n e f i t o f b l e n d i n g f o r s i m i l a r q u a l i t y seams, t o p o t e n t i a l g a i n s o f over f i v e p e r c e n t i n c r e a s e i n y i e l d f o r h i g h l y v a r i e d seam q u a l i t i e s . Most runs produced C o a l B l e n d i n g C o e f f i c i e n t v a l u e s i n excess o f one , which r e p r e s e n t a p o t e n t i a l g a i n i n p r o f i t s o f over t e n m i l l i o n d o l l a r s f o r the Western Canadian c o a l i n d u s t r y . Though these i n i t i a l t r i a l s have been s u c c e s s f u l , f u r t h e r improvements must be made t o the C o a l B l e n d i n g M o d e l , and a c t u a l f i e l d t e s t i n g performed b e f o r e t h i s model would be a v a i l a b l e f o r use w i t h i n the i n d u s t r y . Pg i v TABLE OF CONTENTS PAGE NO. ABSTRACT i i L I S T OF TABLES v i L I S T OF FIGURES v i i ACKNOWLEDGEMENTS v i i i I . INTRODUCTION G e n e r a l 1 S t a t e m e n t o f t h e P r o b l e m 1 Scope o f t h e S t u d y 3 I I . LITERATURE REVIEW I n t r o d u c t i o n t o G r a v i t y S e p a r a t i o n 5 F l o a t - A n d - S i n k A n a l y s i s 10 Method o f A n a l y s i s 13 P l a n t a n d / o r E q u i p m e n t E f f i c i e n c y 17 E f f e c t o f t h e Raw C o a l 18 E f f e c t o f t h e C l e a n i n g U n i t 19 Methods o f Raw C o a l B l e n d i n g : 25 No B l e n d i n g 26 B a t c h i n g 27 H o m o g e n i z a t i o n 29 B l e n d i n g P r i o r To T r e a t m e n t 30 I n - P i t B l e n d i n g 31 Summary 32 P r e p a r a t i o n P l a n t Computer S i m u l a t i o n M o d e l i n g . . . . 33 I I I . DEVELOPMENT OF THE COAL BLENDING MODEL I n t r o d u c t i o n 35 De v e l o p m e n t o f t h e C o a l B l e n d i n g C o e f f i c i e n t 36 C o a l B l e n d i n g Model D e s c r i p t i o n 41 Model I n p u t 45 Model O u t p u t 51 Summary 57 IV. COAL BLENDING MODEL APPLICATION 59 Example P r o b l e m s and D a t a E v a l u a t i o n : 61 Example P r o b l e m One: Two Seam B l e n d 62 Example P r o b l e m Two: T h r e e Seam B l e n d "1" 68 Example P r o b l e m T h r e e : T h r e e Seam B l e n d "2".... 75 TABLE OF CONTENTS ( c o n t i n u e d . . . ) Pg v PAGE NO. V . SUMMARY AND REMARKS 81 V I . REFERENCES 84 V I I . APPENDICES: 87 A . C o a l B l e n d i n g Model Program L i s t i n g s . . . . 88 B . W a s h a b i l i t y Data Used For Example Problems 92 C . C o a l B l e n d i n g Model R e s u l t s : Example Problem O n e . . 101 D . C o a l B l e n d i n g Model R e s u l t s : Example Problem Two 107 E . C o a l B l e n d i n g Model R e s u l t s : Example Problem Three 123 L I S T OF TABLES Pg v i PAGE NO. I . C l a s s i f i c a t i o n o f C o a l s by Rank 7 I I . C u m u l a t i v e F l o a t D a t a 39 I I I . L i s t o f R e q u i r e d I n p u t I n f o r m a t i o n 47 IV. Sample Model I n p u t s 52 V. Sample B a t c h i n g R e s u l t s 55 V I . Sample C o a l B l e n d i n g Model R e s u l t s 56 V I I . C o a l P r o d u c t i o n F o r Example One 66 V I I I . C o a l P r o d u c t i o n F o r Example Two 74 IX. C o a l P r o d u c t i o n F o r Example T h r e e 76 LIST OF FIGURES Pg v i i PAGE NO. 1. Sample W a s h a b i l i t y G r a p h . 11 2. D i s t r i b u t i o n Curve o f a P e r f e c t S e p a r a t i o n a t 1.50 S p e c i f i c G r a v i t y 20 3. I l l u s t r a t i o n o f P r o b a b l e E r r o r (EPM) o f a S e p a r a t i o n a t 1.50 S p e c i f i c G r a v i t y 21 4. I m p e r f e c t i o n as a F u n c t i o n o f P r o b a b l e E r r o r and S p e c i f i c G r a v i t y of S e p a r a t i o n : U n i t e d S t a t e s Bureau o f Mines 24 5. B e n e f i t s o f Raw C o a l Homogenizat ion 28 6. C o a l B l e n d i n g Model Flowsheet 42 7. Two Seam B l e n d Model R e s u l t s : Example One 63 8. Three Seam B l e n d Model R e s u l t s : Example Two C o a l B l e n d i n g C o e f f i c i e n t Contours No. 1 70 9. Three Seam B l e n d Model R e s u l t s : Example Two C o a l B l e n d i n g C o e f f i c i e n t Contours No. 2 71 10. Three Seam B l e n d Model R e s u l t s : Example Two C o a l B l e n d i n g C o e f f i c i e n t Contours No. 3 72 11. Three Seam B l e n d Model R e s u l t s : Example Three C o a l B l e n d i n g C o e f f i c i e n t Contours 77 12. Three Seam B l e n d Model R e s u l t s : Example Three B l e n d i n g F e a s i b i l i t y Zones 78 Pg v i i i ACKNOWLEDGEMENTS I w i s h t o a c k n o w l e d g e and t h a n k t h e f o l l o w i n g p e o p l e and o r g a n i z a t i o n s f o r t h e i r s u p p o r t and en c o u r a g e m e n t : P r o f e s s o r A l l a n H a l l ; U n i v e r s i t y o f B r i t i s h C o l u m b i a Dr. D a v i d O s b o r n e and Tony W a l t e r s ; K i l b o r n E n g i n e e r i n g Tom M i l n e r ; Quinsam C o a l L i m i t e d I a n P a r s o n s ; CANMET C o a l R e s e a r c h L a b o r a t o r y R o s s L e e d e r ; D e n i s o n M i n e s L t d . I a l s o w i s h t o t h a n k my w i f e , Maureen, f o r h e r h e l p , u n d e r s t a n d i n g , and s u p p o r t , f o r w i t h o u t h e r e n c o u r a g e m e n t , t h i s t h e s i s may n e v e r have been c o m p l e t e d . 1 I.INTRODUCTION GENERAL The c o a l m i n i n g i n d u s t r y i s o f s i g n i f i c a n t e c o n o m i c i m p o r t a n c e t o Canada. I n 1984, t h e r e were 12 o p e r a t i n g c o a l p r e p a r a t i o n p l a n t s i n W e s t e r n Canada, a s w e l l a s one i n E a s t e r n Canada, a l l p r o c e s s i n g c o a l f o r e x p o r t (Duncan) ( 1 ) . The p l a n t s r a n g e d i n c a p a c i t y f r o m a p p r o x i m a t e l y 400 t o 2000 t o n n e s p e r h o u r . T o t a l c a p a c i t y i s o v e r 10,500 t o n n e s p e r h o u r o f t r e a t m e n t c a p a c i t y , w h i c h i s i n e x c e s s o f 50 m i l l i o n t o n n e s o f c l e a n c o a l p e r y e a r . STATEMENT OF THE PROBLEM Ten y e a r s ago, t h e m a j o r i t y o f W e s t e r n C a n a d i a n c o a l m ines worked d e p o s i t s c o n s i s t i n g o f one o r two e c o n o m i c a l seams. S i n c e t h e n , t h e c h a n g e s i n o p e r a t i n g and e c o n o m i c c o n d i t i o n s h a v e n e c e s s i t a t e d m u l t i p l e seam m i n i n g , and some m i n e s c u r r e n t l y work up t o t e n s e p a r a t e seams i n a s i n g l e p i t . Even t h o u g h Rocky M o u n t a i n c o a l s have a s i m i l a r r a n k t o t h e c a r b o n i f e r o u s c o a l s o f W e s t e r n E u r o p e and t h e E a s t e r n U n i t e d S t a t e s , t h e i r seam s t r u c t u r e i s v e r y d i f f e r e n t f r o m c o k i n g c o a l The C o a l B l e n d i n g Model Pg 2 d e p o s i t s e l s e w h e r e ( B u t c h e r ) ( 2 ) . The d e v e l o p m e n t o f t h e m o u n t a i n c o a l seams was a c c o m p a n i e d by s e v e r e g e o l o g i c a l d i s t u r b a n c e s w h i c h c a u s e d most o f t h e c o a l seams t o be s h e a r e d and t h e s t r a t a t o become h i g h l y i n c l i n e d , c l o s e l y f o l d e d and r e p e a t e d by o v e r t h r u s t s . M i n i n g t h e s e m u l t i p l e seams r e q u i r e s c o p i n g w i t h t h e s e complex p h y s i c a l c o n d i t i o n s , i n c l u d i n g : v a r i a b l e seam p i t c h and t h i c k n e s s ; r u g g e d , d i v e r s e t o p o g r a p h y ; s u n d r y r o o f and f l o o r s t r a t a ; as w e l l as t h e most i m p o r t a n t v a r i a b l e t o t h e c o a l p r e p a r a t i o n p r o c e s s - - v a r i a b l e c o a l q u a l i t i e s . M u l t i p l e seam m i n i n g , w i t h i t s added c o m p l e x i t i e s , was s i g n i f i c a n t i n t h e l o w e r t h a n e x p e c t e d y i e l d s e x p e r i e n c e d by s e v e r a l W e s t e r n c o a l w a s h e r i e s r e c e n t l y . The c o s t a s s o c i a t e d w i t h low y i e l d s has b e en c a l c u l a t e d by P i c a r d ( 3 ) , who d e t e r m i n e d i n 1985 t h a t , f o r e a c h 1% improvement i n r e c o v e r y t h a t c o u l d be a c h i e v e d w i t h o u t l o s s o f q u a l i t y , t h e C a n a d i a n c o a l m i n i n g i n d u s t r y as a whole w o u l d g a i n $11-13 m i l l i o n p e r y e a r a t t h e c u r r e n t p r i c e s and p r o d u c t i o n r a t e s . P l a n t y i e l d i s a f f e c t e d by a l a r g e v a r i a t i o n i n f e e d q u a l i t y t h a t commonly o c c u r s i n m u l t i s e a m m i n i n g o p e r a t i o n s . T h i s v a r i a t i o n i n c o a l q u a l i t y c a n have d i v e r s e e f f e c t s on t h e d i f f e r e n t u n i t o p e r a t i o n s i n t h e p l a n t , r e s u l t i n g i n a d e c r e a s e o f o v e r a l l The C o a l B l e n d i n g Model Pg 3 p l a n t y i e l d s . B l e n d i n g o r h o m o g e n i z a t i o n methods have been p r o v e n t o h e l p m i n i m i z e t h e v a r i a t i o n s i n p l a n t f e e d , t h u s i m p r o v i n g t h e o v e r a l l p r o d u c t i o n y i e l d . I n W e s t e r n C a n a d i a n c o a l m i n e s , most m u l t i p l e seam m i n e s p r a c t i c e some f o r m o f b l e n d i n g , b u t few o f t h e s e c o a l mines have d e t e r m i n e d how b l e n d i n g a f f e c t s t h e i r w a s h e r y y i e l d . The r e s t have d e v e l o p e d a r b i t r a r y c r i t e r i a f o r b l e n d i n g w h i c h may o r may n o t o p t i m i z e w a s h e r y y i e l d . C o a l mines r e q u i r e a r e l i a b l e method w h i c h c a n be u s e d t o e s t a b l i s h a b l e n d i n g s t r a t e g y f o r t h e l i f e o f t h e mine, t h u s o p t i m i z i n g t h e c l e a n c o a l y i e l d . SCOPE OF THE STUDY The m a i n o b j e c t i v e o f t h i s r e s e a r c h was t o d e v e l o p a method o f e v a l u a t i n g t h e e f f e c t s o f c o n t r o l l e d b l e n d i n g on p r e p a r a t i o n p l a n t e f f i c i e n c y . A c r i t e r i o n f o r e v a l u a t i o n o f t h e r e l a t i v e p l a n t e f f i c i e n c y due t o c o n t r o l l e d b l e n d i n g o f m u l t i p l e seams was d e v e l o p e d and i s c a l l e d t h e C o a l B l e n d i n g C o e f f i c i e n t . Once t h e C o a l B l e n d i n g C o e f f i c i e n t ' s f o r m u l a was d e t e r m i n e d , t h e n e x t s t a g e o f t h e s t u d y was d a t a c o l l e c t i o n . The d a t a c o l l e c t i o n had t o be done i n one o f t h r e e ways: u s i n g a p i l o t p l a n t , an o p e r a t i n g mine, o r a r e l i a b l e p r e p a r a t i o n p l a n t s i m u l a t i o n m o d e l . U n f o r t u n a t e l y , t h e f i r s t two o p t i o n s were n o t a v a i l a b l e due t o t h e t i m e and f i n a n c i a l c o n s t r a i n t s o f t h e s e p r o c e d u r e s . A c o m p u t e r s i m u l a t i o n model was t h e most The C o a l B l e n d i n g Model Pg 4 a p p r o p r i a t e a l t e r n a t i v e . P l a n t s i m u l a t i o n m o d e l i n g was n o t t h e key o b j e c t i v e o f t h e p r o j e c t and, t h e r e f o r e , any number o f r e l i a b l e p l a n t s i m u l a t i o n m o d e l s c o u l d have been s e l e c t e d f o r t h i s r e s e a r c h . The C o a l D a t a M a n i p u l a t i o n Model ( 4 ) , p r o d u c e d by CANMET, was c h o s e n f o r t h e p r o j e c t f o r t h e f o l l o w i n g f o u r main r e a s o n s : 1/ The model was c o m p a t i b l e t o co m p u t e r h a r d w a r e a v a i l a b l e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a f a c i l i t i e s ; 2/ The model was a c c e s s i b l e t o t h e a u t h o r a t U.B.C. f o r r e s e a r c h p u r p o s e s ; 3/ The model was w r i t t e n i n a m o d i f i e d b a s i c l a n g u a g e f a m i l i a r t o t h e a u t h o r ; and 4/ The model i s u s e r - f r i e n d l y and s i m p l e t o r u n . The C o a l B l e n d i n g Model Pg 5 The a c h i e v e m e n t o f t h e f o l l o w i n g s u b - o b j e c t i v e s a l s o f o r m e d p a r t o f t h i s p r o j e c t : a) To d e v e l o p a b e t t e r u n d e r s t a n d i n g o f t h e e f f e c t s o f raw c o a l b l e n d i n g on p r e p a r a t i o n p l a n t y i e l d . b) To i n v e s t i g a t e t h e u t i l i t y o f i n - p i t b l e n d i n g , f o r W e s t e r n C a n a d i a n c o a l m i n e s . c ) To d e v e l o p i n - p i t b l e n d i n g c r i t e r i a t o g i v e t h e maximum amount o f p r o d u c t i o n f l e x i b i l i t y , w h i l e s a t i s f y i n g p r e p a r a t i o n p l a n t n e e d s , and m i n i m i z i n g t h e c a p a c i t y r e q u i r e d f o r raw c o a l s t o c k p i l e s . d) To i m p r o v e p r e p a r a t i o n p l a n t y i e l d s , t h u s r e d u c i n g c o a l w a s t a g e and i m p r o v i n g p r o f i t s . I I . LITERATURE REVIEW INTRODUCTION TO GRAVITY SEPARATION G e o l o g i c a l l y , c o a l i s a metamorphosed s e d i m e n t a r y r o c k c o n t a i n i n g a m i x t u r e o f c o n s t i t u e n t s w h i c h n o t o n l y v a r y among d i f f e r e n t c o a l s , b u t a l s o v a r y w i t h i n a p a r t i c u l a r seam. T h i s The C o a l B l e n d i n g Model Pg 6 h e t e r o g e n e o u s m a t e r i a l c o n t a i n s c o m b u s t i b l e o r g a n i c m i n e r a l s and i n o r g a n i c m i n e r a l m a t t e r , f o r m e d e s s e n t i a l l y f r o m p l a n t r e m a i n s p r e s e r v e d f r o m c o m p l e t e d e c a y i n a f a v o r a b l e e n v i r o n m e n t , and l a t e r a l t e r e d by v a r i o u s c h e m i c a l and p h y s i c a l a c t i o n s . C o a l i s , t h e r e f o r e , any m i x t u r e o f h y d r o c a r b o n s w i t h i n t r i n s i c and e x t r a n e o u s o r g a n i c and i n o r g a n i c i m p u r i t i e s . The f o r m a t i o n o f c o a l b e g i n s w i t h t h e c o n v e r s i o n o f d e c a y i n g v e g e t a t i o n i n t o p e a t . " C o a l " i s a t e r m w h i c h c o v e r s t h e d i f f e r e n t s t a g e s o f c o a l i f i c a t i o n f r o m brown c o a l , t o l i g n i t e , t o s u b - b i t u m i n o u s c o a l , b i t u m i n o u s c o a l and on t o a n t h r a c i t e . E a c h o f t h e s e s t a g e s i s i n d i c a t e d by t h e d e g r e e o f c o n v e r s i o n o f t h e d e c a y i n g v e g e t a t i o n . The c o n v e r s i o n i s an o n g o i n g c h a n g e i n t h e r a t i o o f v o l a t i l e m a t e r i a l t o f i x e d c a r b o n s . V o l a t i l e m a t t e r i s t h e component o f t h e c o a l e x c l u s i v e o f m o i s t u r e t h a t i s d r i v e n o f f when t h e c o a l i s h e a t e d . T h e r e f o r e , t h e h i g h e r t h e f i x e d c a r b o n c o n t e n t , t h e g r e a t e r t h e d e g r e e o f c o n v e r s i o n . A method f o r t h e s t a n d a r d c l a s s i f i c a t i o n o f A m e r i c a n c o a l and i t s d e g r e e o f c o n v e r s i o n , o r " r a n k " , has been d e v e l o p e d by t h e A m e r i c a n S o c i e t y f o r T e s t i n g and M a t e r i a l s . T h i s method o f r a t i n g c o a l by r a n k i s b a s e d on c h e m i c a l a n a l y s e s and s p e c i f i c p h y s i c a l t e s t s t h a t measure t h e i n c r e a s i n g r e s p o n s e o f c o a l t o p r e s s u r e a n d / o r h e a t (metamorphism). T h i s p r o g r e s s i v e r e s p o n s e TABLE I . CLASSIFICATION OF COAL BY RANK * Claw Qronp Fixed Carbon Limits, % (Dry Mineral-Matter-Free Basla) Equal or. . Greater Less Than Than Volatile Mat-ter Limits, % (Dry, Min-eral-Matter- . Free Basis) Equal or Greater Less Than Than Calorific Value Limits, Btu per L b (Moist,' Mineral-Matter-Free Basis) Equal or Greater Than Less Than Agglomerating Character I. Anthracitic 1. Mcta-authracite 2. Anthracite 3. Semianthracite • 98 92 86 98 92 2 8 14 Nonagglomerating II. Bituminous 1. Low-volatile bituminous coal 2. Medium-volatile bitumi-nous coal 3. High-volatile A bitu-minous coal 4. High-volatile B bitu-minous coal 5. High-volatile C bitu-. minous coal 78 69 86 78 69 14 22 31 31 14,000 <  13,000 * [11,500 110,500 14,000 13,000 11,500 Commonly ag-glomerating * Agglomerating III. Subbituminous 1. 2. 3. Subbituminous A coal Subbituminous B coal Subbituminous C coal 10,500 9,500 8,300 11,500* 10,500 9,500 ' Nonagglomerating IV; Lignitic 1. 2. Lignite A Lignite B 6,300 8,300 6,300. * From: American Society for Testing and Materials, D 388. ° This classification does not include a few coals, principally nonbanded varieties, which have unusual physical and chemical prop-erties and which come within the limits of fixed carbon or calorific value of the high-volatile bituminous and subbituminous ranks. AU of these coals either contain less than 48% dry, mineral-matter-free fixed carbon or have more than 15,500 moist, mineral-matter-free Btu per lb. B Moist refers to coal containing its natural inherent moisture but not including visible water on the surface of the coal. e If agglomerating, classify in low-volatile group of the bituminous class. <* Coals having 69% or more fixed carbon on the dry, mineral-matter-free basis shall be classified according to fixed carbon, regard-less of calorific value. 'It is recognized that there may be nonagglomerating varieties in these groups of the bituminous class, and there are notable exceptions in high-volatile C bituminous group. The Coal Blending Model Pg 8 i s indicated i n an ongoing coal series that ranges from l i g n i t e through the various ranks of bituminous coal through to anthracite and meta-anthracite, as shown in Table I. The rank of coal i s an i n d i c a t i o n of the p o s i t i o n of a coal i n r e l a t i o n to other coals i n the c o a l i f i c a t i o n s e r i e s . In summary, the coal's rank shows i t s maturity i n terms of general physical and chemical properties. According to Jack A. Simon, i n Elements of P r a c t i c a l Coal  Mining(5): "In determination of rank of coal, mineral matter i s excluded from the analysis, as i t i n no way r e f l e c t s the degree of metamorphism of the coa l . In the higher ranks of coal, moisture i s generally low and i s excluded i n determination of rank. In the lower-rank coals, where moisture i s considered to be a fundamental property of the coal, moisture i s included i n the analysis on which rank i s based.... The highest rank of coal, as shown i n Table I, i s meta-anthracie. Coal of t h i s rank i s r e l a t i v e l y rare and resembles, both chemically and p h y s i c a l l y , the mineral graphite (pure carbon). Meta-anthracite has been described from a number of l o c a l i t i e s i n the world, commonly associated with ingneous intrusions. It has also been described from Precambrian rocks and i s The C o a l B l e n d i n g Model Pg 9 b e l i e v e d to be d e r i v e d from a l g a l or f u n g a l a c c u m u l a t i o n s . M e t a - a n t h r a c i t e has been mined c o m m e r c i a l l y i n Rhode I s l a n d . " The purpose o f a c o a l p r e p a r a t i o n p l a n t i s t o upgrade the q u a l i t y o f the r u n - o f - m i n e (ROM) c o a l . In m i n i n g , ROM c o a l i s the p r o d u c t t h a t i s produced a t the c o a l f a c e , w h i l e c l e a n c o a l d e s c r i b e s the c o a l a f t e r i t has been upgraded by s c r e e n i n g , heavy media s e p a r a t i o n , f l o t a t i o n o r by any o t h e r means. In c o a l c l e a n i n g , the s e p a r a t i o n o f the o r g a n i c m i n e r a l s from the extraneous i n o r g a n i c i m p u r i t i e s i s a c h i e v e d by e x p l o i t i n g some d i f f e r e n c e s i n p r o p e r t i e s . For g r a v i t y s e p a r a t i n g d e v i c e s , the p r i n c i p a l m i n e r a l p r o p e r t y used f o r s e p a r a t i o n i s i t s s p e c i f i c g r a v i t y . C o n s e q u e n t l y , the s p e c i f i c g r a v i t i e s o f the i m p u r i t i e s a s s o c i a t e d w i t h c o a l have p r i m a r y i m p o r t a n c e . The s p e c i f i c g r a v i t y o f a body i s the r a t i o o f the weight o f the body i n a i r and the weight o f an equa l volume of water . The s p e c i f i c g r a v i t y o f c o a l can v a r y between 1.25 and 1 .7 , due to d i f f e r e n c e s i n rank and m o i s t u r e , and i n the methods used t o de termine s p e c i f i c g r a v i t y . The s p e c i f i c g r a v i t y o f c l e a n c o a l i n c r e a s e s w i t h the change i n rank from l i g n i t e to a n t h r a c i t e . Other components b e i n g e q u a l , the denser i m p u r i t i e s can be removed i n the c l e a n i n g o p e r a t i o n more e a s i l y than can the l i g h t e r i m p u r i t i e s , which approach i n d e n s i t y the c o a l from which they a r e b e i n g s e p a r a t e d . The C o a l B l e n d i n g Model Pg 10 FLOAT-AND-SINK ANALYSIS To determine s p e c i f i c g r a v i t y d i s t r i b u t i o n , more commonly c a l l e d the w a s h a b i l i t y c h a r a c t e r i s t i c s , o f the ROM c o a l , the p r e p a r a t i o n eng i neer must p e r f o r m a f l o a t - a n d - s i n k t e s t . I n i t i a l l y , a s i z e a n a l y s i s o f the ROM c o a l from the seam i n q u e s t i o n must be p e r f o r m e d . The d e s i r e d s i z e f r a c t i o n s of the c o a l a r e then p l a c e d i n a bath c o n t a i n i n g a l i q u i d o f a known s p e c i f i c g r a v i t y . The c o a l t h a t f l o a t s w i l l then have a s p e c i f i c g r a v i t y which i s l e s s than the l i q u i d i n the b a t h , and the m a t e r i a l t h a t s i n k s w i l l have a s p e c i f i c g r a v i t y g r e a t e r than t h a t o f the b a t h . By s t a r t i n g w i t h the s p e c i f i c g r a v i t y l e v e l l e a s t expec ted ( n o r m a l l y 1 . 3 ) , and i n c r e a s i n g the s p e c i f i c g r a v i t y o f the bath by s m a l l i n c r e m e n t s , a s p e c i f i c g r a v i t y d i s t r i b u t i o n o f the ROM c o a l can be o b t a i n e d . The next s t e p i s t o de termine the ash ( i n o r g a n i c m a t e r i a l ) c o n t e n t o f each f l o a t taken from the f l o a t - a n d - s i n k t e s t . For b i tuminous and a n t h r a c i t e c o a l s , the percentage o f f l o a t (or s i n k ) on a s e l e c t e d s p e c i f i c - g r a v i t y bath i s used t o c o n t r o l the ash c o n t e n t o f c l e a n e d c o a l sh ipments . In o r d e r t o upgrade a c o a l i n the most p r o f i t a b l e way, a c a r e f u l s tudy of the The Coal Blending Model Pg 11 i i i i i I I i i i 2.2 2.1 2 .0 1.9 l . B 1.7 1.6 l . S 1.4 1 . 3 < RELRT3VE D E N S I T Y Legend: 1. ) 2. ) 3 . ) 4. ) 5. ) Cumulative f l o a t s Elementary ash curve Cumulative sinks Relative density d i s t r i b u t i o n curve +/- 0.1 Relative density curve Figure 1. Sample Washability Graph* •(Produced using the CANMET Coal Data Manipulation Program) The C o a l B l e n d i n g Model Pg 12 w a s h a b i l i t y c h a r a c t e r i s t i c s i s r e q u i r e d . F l o a t - a n d - s i n k a n a l y s i s p r o v i d e s t h e n e c e s s a r y i n d i c a t i o n s o f b o t h t h e d e g r e e o f d i f f i c u l t y i n w a s h i n g t h e c o a l , and t h e e f f e c t i v e n e s s o f t h e washer i t s e l f . F o r d a y - t o - d a y p l a n t c o n t r o l , f l o a t - a n d - s i n k s e p a r a t i o n s a r e needed on t h e w a s h i n g p r o d u c t s a t t h e s e p a r a t i o n d e n s i t y i n e f f e c t a t t h o s e t i m e s . Once t h e f l o a t - a n d - s i n k d e t e r m i n a t i o n i s c o m p l e t e d , t h e p r o c e s s e n g i n e e r c a n d e v e l o p a w a s h a b i l i t y c u r v e l i k e t h e one p r o d u c e d u s i n g CANMET's C o a l D a t a M a n i p u l a t i o n p r o g r a m ( 4 ) , shown i n F i g u r e 1 . The f i v e c u r v e s r e p r e s e n t e d on t h i s Sample W a s h a b i l i t y g r a p h ( L e o n a r d and M i t c h e l l ) (6) a r e a s f o l l o w s : i ) The c u m u l a t i v e f l o a t s c u r v e (No. 1 on L e g e n d o f F i g u r e 1) i s t h e c u r v e o b t a i n e d by p l o t t i n g t h e c u m u l a t i v e y i e l d o f t h e f l o a t s a t e a c h r e l a t i v e d e n s i t y a g a i n s t t h e mean a s h c o n t e n t o f t h e t o t a l f l o a t s a t t h a t d e n s i t y . T h i s c u r v e shows t h e r e l a t i o n s h i p between c u m u l a t i v e y i e l d o f t h e f l o a t s and a s h c o n t e n t . i i ) The e l e m e n t a r y a s h c u r v e (No. 2 on L e g e n d o f F i g u r e 1) i n d i c a t e s t h e h i g h e s t a s h c o n t e n t o f a p a r t i c l e l i k e l y t o be f o u n d i n any p a r t i c u l a r y i e l d o f f l o a t s . The shape o f t h e c u r v e i s an i n d i c a t i o n o f t h e e a s e o r d i f f i c u l t y o f c l e a n i n g a p a r t i c u l a r c o a l . The c l o s e r t h e c u r v e a p p r o x i m a t e s t h e shape o f The C o a l B l e n d i n g Model Pg 13 t h e l e t t e r ' L', t h e e a s i e r t h e c o a l i s t o c l e a n . i i i ) The c u m u l a t i v e s i n k c u r v e (No. 3 on L e g e n d o f F i g u r e 1) i s a p l o t o f t h e c u m u l a t i v e y i e l d o f s i n k s a t e a c h r e l a t i v e d e n s i t y a g a i n s t t h e mean a s h o f t h e t o t a l s i n k s a t t h a t d e n s i t y . i v ) The r e l a t i v e d e n s i t y d i s t r i b u t i o n c u r v e (No. 4 on L e g e n d o f F i g u r e 1 ) , sometimes c a l l e d t h e " d e n s i m e t r i c o r s p e c i f i c g r a v i t y c u r v e " , shows t h e r e l a t i o n s h i p between t h e r e l a t i v e d e n s i t y and t h e t h e o r e t i c a l y i e l d f o r t h e g i v e n s i z e f r a c t i o n and c o a l seam. v) The +/- Q . l r e l a t i v e d e n s i t y c u r v e (No.5 on L e g e n d o f F i g u r e 1 ) , o r " d i f f i c u l t y c u r v e " , p r o v i d e s an i n d i c a t i o n o f t h e d i f f i c u l t y o f s e p a r a t i o n by g i v i n g a d i r e c t r e l a t i o n s h i p between n e a r - d e n s i t y m a t e r i a l and t h e a s h c o n t e n t . METHOD OF ANALYSIS Run o f Mine (ROM) c o a l d o e s n o t c o n t a i n a m i x t u r e o f p u r e c o n s t i t u e n t s . The s h a l e s , s a n d s t o n e s , and c l a y s a r e i n t e r m i x e d w i t h low g r a d e c o a l and t h e c a r b o n a c e o u s m a t e r i a l i s l a c e d w i t h m i n e r a l i m p u r i t i e s . T h e r e f o r e , c o a l w i l l c o n t a i n m a t e r i a l a t The Coal Blending Model Pg 14 a l l s p e c i f i c g r a v i t i e s between the l i g h t e s t and heaviest pieces. Even so, the shale and p y r i t e w i l l f a l l to the bottom of a container f i l l e d with water more rapidly than coal . For example, i f the water i s given a pulsating motion by compressed a i r , causing the water to move up and down, the heavy impurities w i l l be kept at the bottom and the coal at the top where i t can be recovered. In addition, the s p e c i f i c gravity of the water i s sometimes adjusted to the s p e c i f i c gravity of the coal by the use of heavy media to e f f e c t a separation of the coal and i t s impurities. The weight and s p e c i f i c gravity of coal depends upon the amount and kind of mineral matter or ash that i t contains. It also depends on the coal's compactness or porosity and i t s carbon content. A higher ash content gives higher s p e c i f i c gravity. S i m i l a r l y , a change i n s p e c i f i c gravity i s exhibited with a i r - d r i e d coal i n comparison to "fresh" or moisture-saturated c o a l . The s p e c i f i c gravity of a coal a f f e c t s i t s burning qu a l i t y ; the lower the s p e c i f i c gravity, the better the i g n i t i o n properties i n each individual c o a l . In addition, coal of a given rank has a higher apparent s p e c i f i c gravity when wet than when dry. Commercially pure coal, that i s coal containing only i n t r i n s i c impurities, has a s p e c i f i c gravity ranging generally The C o a l B l e n d i n g Model Pg 15 f r o m 1.2 t o 1.7, t h o u g h m o s t l y below 1.4 i n o r d i n a r y p r a c t i c e f o r b i t u m i n o u s c o a l . A n t h r a c i t e c o a l o f t h e same p u r i t y may be up t o 1.7. S h a l e , s a n d s t o n e and c a l c s p a r have s p e c i f i c g r a v i t i e s r a n g i n g f r o m 2.3 t o 2.7, w h i l e p y r i t e h as a s p e c i f i c g r a v i t y o f a b o u t 5. The d i f f e r e n c e i n s p e c i f i c g r a v i t y between p u r e c o a l and t h e s e i m p u r i t i e s , i n a f r e e s t a t e , i s s u f f i c i e n t t o e n a b l e an a l m o s t c o m p l e t e s e p a r a t i o n t o be a c h i e v e d f a i r l y e a s i l y . The c h a r a c t e r i s t i c s o f t h e e x t r a n e o u s i m p u r i t i e s a r e o f g r e a t i m p o r t a n c e , e s p e c i a l l y w i t h r e g a r d t o w h e t h e r t h e y a r e f r e e , i n t e r w o v e n o r c l o s e l y i n t e r s t r a t i f i e d w i t h t h e c o a l s u b s t a n c e i n e x t r e m e l y t h i n l a y e r s , i . e . bone c o a l . Such f i n e l y s t r a t i f i e d e x t r a n e o u s i m p u r i t i e s may a p p r o x i m a t e t o i n t r i n s i c i m p u r i t i e s f o r , a l t h o u g h t h e y a r e c a p a b l e o f b e i n g s e p a r a t e d f r o m t h e c o a l s u b s t a n c e , s u c h s e p a r a t i o n w o u l d r e q u i r e t h e r e d u c t i o n o f t h e whole mass o f c o a l t o a v e r y f i n e s t a t e . S u ch f i n e p a r t i c l e s w o u l d n o t be amenable t o e c o n o m i c methods o f t r e a t m e n t . T h e r e f o r e , a s t h e s e f i n e l y d i v i d e d i m p u r i t i e s a r e i n t i m a t e l y i n t e r m i x e d w i t h t h e c o a l s u b s t a n c e and c a n n o t be s e p a r a t e d f r o m i t by p h y s i c a l means, t h e r e i s an e c o n o m i c minimum a s h c o n t e n t t o w h i c h c o a l c a n be c l e a n e d , d e p e n d i n g upon t h e i n t r i n s i c a s h c o n t e n t ( w h i c h f o r any c o a l i s s e l d o m l e s s t h a n 1 % ) . The u s u a l a v e r a g e o f t h e p u r e s t c o a l i s between 2 and 3% a s h c o n t e n t . G e n e r a l l y s p e a k i n g , t h e s p e c i f i c The C o a l B l e n d i n g Model Pg 16 g r a v i t y i n c r e a s e s i n p r o p o r t i o n t o t h e i m p u r i t y c o n t e n t , and i n t h e same way f o r m s a c o n t i n u o u s r a n g e between t h e two e x t r e m e s . The s p e c i f i c g r a v i t y a n a l y s i s must be p r e c e d e d by a s i z e a n a l y s i s o f t h e raw c o a l . As t h e i m p u r i t i e s o f a c o a l v a r y b o t h i n d i f f e r e n t seams and i n d i f f e r e n t s i z e r a n g e s o f t h e same seam, e a c h s i z e r a n g e must be examined s e p a r a t e l y . I t i s a l s o more c o n v e n i e n t and more a c c u r a t e t o c o n d u c t t h e s p e c i f i c g r a v i t y a n a l y s i s on c l o s e l y s i z e d m a t e r i a l - - a maximum s i z e r a t i o o f 2:1 f o r e a c h f r a c t i o n i s a d v i s a b l e . I n most c a s e s , i t i s u n n e c e s s a r y t o e x t e n d t h e u p p e r s i z e l i m i t a bove 6 i n c h e s . F o r c o a l s a m p l e s , t h e t e s t i s u s u a l l y commenced u s i n g a l i q u i d o f S.G. 1.3, and r e p e a t e d w i t h l i q u i d s o f p r o g r e s s i v e l y i n c r e a s i n g s p e c i f i c g r a v i t i e s , t h e s i n k s i n e a c h c a s e p a s s i n g on t o t h e n e x t l i q u i d o f h i g h e r s p e c i f i c g r a v i t y . The f l o a t i n g m a t e r i a l w h i c h i n t e r m e d i a t e d i n S.G. between t h e l i q u i d i n w h i c h i t f l o a t e d and t h e p r e v i o u s l i q u i d , i s k e p t s e p a r a t e . The v a r i o u s s p e c i f i c g r a v i t y f r a c t i o n s a r e w e i g h e d and t h e n s u c c e s s i v e l y c r u s h e d and r e d u c e d t o g i v e a r e p r e s e n t a t i v e sample f o r a n a l y s i s . U s u a l l y , t h e s p e c i f i c g r a v i t y i n c r e m e n t s s h o u l d be t a k e n a s 0.05 between 1.3 and 1.5 S.G., and t h e n 0.1 up t o 2.0 S.G. i n t h e i n i t i a l a n a l y s i s . The C o a l B l e n d i n g Model Pg 17 The f l o a t - a n d - s i n k t e s t i s commenced a t e i t h e r t h e h i g h e s t o r l o w e s t d e n s i t y o f c o a l c o a r s e r t h a n 0.5 mm (28 mesh) and as a g e n e r a l p r i n c i p l e , t h e d e n s i t y c h o s e n s h o u l d a l l o w as much o f t h e sample as p o s s i b l e t o be removed i n t h e f i r s t s t a g e s , f o r example, d i s c a r d s h o u l d be i n i t i a l l y f l o a t e d a t t h e h i g h e s t d e n s i t y u s e d , w i t h c l e a n and raw c o a l a t t h e l o w e s t d e n s i t i e s . PLANT AND/OR EQUIPMENT EFFICIENCY The o v e r a l l p e r f o r m a n c e o f a c o a l p r e p a r a t i o n o p e r a t i o n i s i n f l u e n c e d by t h r e e f a c t o r s : t h e raw c o a l c h a r a c t e r i s t i c s , t h e i n h e r e n t c h a r a c t e r i s t i c s o f t h e c l e a n i n g u n i t , and t h e m a r k e t c o n s i d e r a t i o n s . Y a n c e y and G e e r ( 7 ) , and W a l t e r s , Ramani and S t e f a n k o (8) f e e l t h a t an e f f i c i e n c y c o e f f i c i e n t w h i c h r e l a t e s t h e s e t h r e e f a c t o r s w o u l d d i r e c t l y measure t h e l o s s o f s a l e a b l e c o a l and, t h e r e f o r e , w o u l d be o f g r e a t e s t p r a c t i c a l v a l u e . A t t h e p r e s e n t t i m e , however, no commonly a c c e p t e d e f f i c i e n c y c o e f f i c i e n t l i n k i n g a l l t h r e e f a c t o r s e x i s t s . T h e r e a r e some a c c e p t e d e f f i c i e n c y c r i t e r i a r e l a t i n g t h e e f f e c t o f t h e c o a l on t h e c l e a n i n g u n i t . The f o l l o w i n g d i s c u s s i o n w i l l be l i m i t e d t o t h e e f f i c i e n c y o f a s p e c i f i c g r a v i t y s e p a r a t i o n . The C o a l B l e n d i n g Model Pg 18 EFFECT OF THE RAW COAL O r g a n i c e f f i c i e n c y i s t h e c r i t e r i o n most commonly u s e d t o d e s c r i b e t h e p l a n t p e r f o r m a n c e . To some e x t e n t , t h i s e f f i c i e n c y i s d e p e n d e n t on t h e c o a l t y p e b e i n g p r o c e s s e d . The o r g a n i c e f f i c i e n c y f o r m u l a e x p r e s s e s t h e y i e l d o f washed c o a l as a p e r c e n t a g e o f t h e y i e l d o f f l o a t c o a l ( d e t e r m i n e d by t h e w a s h i n g a n a l y s i s o f t h e f e e d ) . F o r example: O r g a n i c E f f i c i e n c y = A c t u a l Y i e l d o f Washed C o a l X 100 T h e o r e t i c a l Y i e l d a t t h e Same A s h As n o t e d by A.D. W a l t e r s , e t a l ( 8 ) , t h e r e a r e some p r o b l e m s w i t h t h i s f o r m u l a : 1. F r i a b l e c o a l w i l l d e g r a d e d u r i n g t h e c l e a n i n g p r o c e s s . T h e r e f o r e , t h e t h e o r e t i c a l y i e l d d e t e r m i n e d by an a n a l y s i s o f t h e f e e d c a n n o t a l w a y s be u s e d i n t h i s f o r m u l a . One w o u l d have t o r e c o n s t i t u t e t h e m i l l f e e d f r o m t h e f l o a t - a n d - s i n k a n a l y s i s o f t h e washed c o a l and d i s c a r d m a t e r i a l . 2. A l o n g w i t h e f f i c i e n c y , a s h r e d u c t i o n must a l s o be c o n s i d e r e d . I f an a s h c o n t e n t o f 10% were d e s i r e d , and t h e r e s u l t a n t p r o d u c t was 11%, w i t h an o r g a n i c e f f i c i e n c y The C o a l B l e n d i n g Model Pg 19 o f 95%, t h e n t h e p r o c e s s has n o t p r o v e n t o be e f f i c i e n t , d e s p i t e t h e r e p o r t s o f h i g h e f f i c i e n c y . 3. O r g a n i c e f f i c i e n c y i s a l s o i n f l u e n c e d by t h e s p e c i f i c g r a v i t y o f s e p a r a t i o n and t h e i n h e r e n t c h a r a c t e r i s t i c s o f t h e c l e a n i n g u n i t . T h e r e f o r e , c a u t i o n s h o u l d be e x e r c i s e d when a t t e m p t i n g t o u s e o r g a n i c e f f i c i e n c y t o compare c l e a n i n g u n i t s t r e a t i n g c o a l s o f d i f f e r e n t d e n s i t y c o m p o s i t i o n s o r o p e r a t i n g a t 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 o f s e p a r a t i o n . EFFECT OF THE CLEANING UNIT The most w i d e l y a c c e p t e d c r i t e r i o n f o r m e a s u r i n g t h e e f f i c i e n c y o f c o a l p r e p a r a t i o n g r a v i t y s e p a r a t i o n c l e a n i n g u n i t s i s t h e p a r t i t i o n c u r v e , a l s o known as t h e "Tromp c u r v e " , " e r r o r c u r v e " , " d i s t r i b u t i o n c u r v e " , o r " r e c o v e r y c u r v e " . Most c o m p u t e r m o d e l s u s e t h e p a r t i t i o n c u r v e t o s i m u l a t e t h e o p e r a t i o n o f a g r a v i t y s e p a r a t i o n c l e a n i n g u n i t . Tromp d e f i n e d t h e p a r t i t i o n ( d i s t r i b u t i o n ) c u r v e a s : 'the c o n t i n u o u s f u n c t i o n t h a t r e s u l t s when t h e r a t i o o f washed c o a l o r r e j e c t s t o raw c o a l i n an i n f i n i t e s i m a l i n c r e m e n t o f g r a v i t y i s e n t e r e d a s t h e o r d i n a t e a g a i n s t t h a t same g r a v i t y a s a b s c i s s a ' ( K i n d i g e t a l ) (9) . The Coal Blending Model Pg 20 ui u UJ a.' x o T 1.2 1.4 A. 1.6 1.8 SPECIFIC ! GRAVITY 2.0 i SEPARATING GRAVITY Figure 2. D i s t r i b u t i o n Curve of a Perfect Separation at 1.50 S p e c i f i c Gravity The Coal Blending Model Pg 21 SEPARATING GRAVITY Figure 3. I l l u s t r a t i o n of Probable Error (EPM) of a Separation at 1.50 S p e c i f i c Gravity The C o a l B l e n d i n g Model Pg 22 The p e r f e c t s e p a r a t i o n w o u l d o c c u r when a l l p a r t i c l e s o f p u r e , 100% c o a l w o u l d r e p o r t t o t h e c l e a n c o a l , and t h e r e j e c t s w o u l d c o n t a i n no t r a c e o f h y d r o c a r b o n s . The p a r t i t i o n c u r v e f o r t h i s w o u l d l o o k l i k e F i g u r e 2. I n r e a l i t y , t h i s i s n e v e r t h e c a s e , t h u s a t y p i c a l p a r t i t i o n c u r v e a l w a y s shows some m i s p l a c e d m a t e r i a l , as shown i n F i g u r e 3. T h i s d i v e r g e n c e o f t h e c u r v e f r o m t h e p e r f e c t s e p a r a t i o n c u r v e g i v e s a measure o f t h e e f f i c i e n c y o f t h e c l e a n i n g u n i t . T h r e e c r i t e r i a have been d e v e l o p e d f o r m e a s u r i n g t h e d e g r e e o f m i s p l a c e m e n t : E r r o r A r e a , P r o b a b l e E r r o r , and I m p e r f e c t i o n . 1) E r r o r A r e a : The e r r o r a r e a i s t h e a r e a between t h e c u r v e and a v e r t i c a l l i n e drawn t h r o u g h t h e s e p a r a t i n g s p e c i f i c g r a v i t y . T h i s i n t e g r a t e d a r e a u n d e r t h e e f f e c t e d s e c t i o n o f t h e c u r v e c a n be m e a s u r e d and t h e n compared w i t h a s t a n d a r d t o p r o v i d e a d e g r e e o f t h e e f f i c i e n c y o f t h e p r o c e s s . The f o l l o w i n g i s t h e c o n v e n t i o n f o r d e t e r m i n i n g e f f i c i e n c y u s i n g t h i s method: AREA DEGREE OF EFFICIENCY A = 0 P e r f e c t E x c e l l e n t 0 < A < 30 30 < A < 50 50 < A < 100 Good F a i r P o o r A > 0 The C o a l B l e n d i n g Model Pg 23 2) P r o b a b l e E r r o r ( E c a r t P r o b a b l e Moyen): T h i s e f f i c i e n c y r a t i n g i s d e f i n e d a s one h a l f t h e d i f f e r e n c e between t h e r e l a t i v e d e n s i t i e s c o r r e s p o n d i n g t o t h e 75 % and 25 % o r d i n a t e s , a s shown i n t h e p a r t i t i o n c u r v e ( F i g u r e 3 ) . F o r example: d25 - d75 2 The s t e e p e r t h e p a r t i t i o n c u r v e , t h e l o w e r t h e p r o b a b l e e r r o r . A low p r o b a b l e e r r o r d e s i g n a t e s a s h a r p s e p a r a t i o n , w h i l e a l a r g e p r o b a b l e e r r o r d e n o t e s a p o o r e r s e p a r a t i o n . P r o b a b l e e r r o r as a measure o f p e r f o r m a n c e o f a c l e a n i n g u n i t has two m a j o r d r a w b a c k s . F i r s t , t h e " t a i l s " o f t h e c u r v e a r e n o t a d e q u a t e l y d e s c r i b e d and s e c o n d , t h e c a l c u l a t i o n i s n o t i n d e p e n d e n t o f t h e s p e c i f i c g r a v i t y o f t h e s e p a r a t i o n . 3) I m p e r f e c t i o n : To d e v e l o p a c r i t e r i o n o f e f f i c i e n c y w h i c h w o u l d be i n d e p e n d e n t o f t h e s p e c i f i c g r a v i t y o f t h e s e p a r a t i o n , t h e F r e n c h r e s e a r c h o r g a n i z a t i o n , C h e r c h a r (Cheradame e t a l ) ( 1 0 ) , d e v e l o p e d t h e c o n c e p t o f " i m p e r f e c t i o n " . The Coal Blending Model Pg 24 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 S P E C I F I C G R A V I T Y O F S E P A R A T I O N ( T H E P O I N T S P L O T T E D A R E F R O M T E S T S C A R R I E D O U T O N F O U R B I T U M I N O U S W A S H E R S ) Figure 4. Imperfection as a Function of Probable Error and S p e c i f i c Gravity of Separation: United States Bureau of Mines The C o a l B l e n d i n g Model Pg 25 I m p e r f e c t i o n , f o r w h i c h t h e symbol I i s u s e d , i s d e f i n e d a s : I = P r o b a b l e E r r o r / s p e c i f i c g r a v i t y o f s e p a r a t i o n ( f o r d e n s e medium) I = P r o b a b l e E r r o r / s p e c i f i c g r a v i t y o f s e p a r a t i o n - 1 ( f o r j i g s ) C h e r c h a r c l a i m e d t h a t i m p e r f e c t i o n was a c o n s t a n t f o r a p a r t i c u l a r c l e a n i n g u n i t , b u t p r a c t i c a l e x p e r i e n c e has shown t h a t t h e r e i s a s l i g h t c h ange i n i m p e r f e c t i o n w i t h c h a n g e s i n t h e s p e c i f i c g r a v i t y o f s e p a r a t i o n . 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 4, w h i c h shows t h e r e l a t i o n s h i p between p r o b a b l e e r r o r , i m p e r f e c t i o n and s p e c i f i c g r a v i t y o f s e p a r a t i o n . T h e s e r e s u l t s were o b t a i n e d f r o m t e s t s p e r f o r m e d by t h e U.S. B u r e a u o f M i n e s on f o u r b i t u m i n o u s w a s h e r s (Hudy, J r . J.) ( 1 1 ) . METHODS OF RAW COAL BLENDING B l e n d i n g o r h o m o g e n i z a t i o n s y s t e m s a r e commonly employed i n o r d e r t o c ompensate f o r v a r i a t i o n s i n s i z e d i s t r i b u t i o n , m o i s t u r e c o n t e n t , c o a l w a s h a b i l i t y and q u a l i t y p a r a m e t e r s s u c h a s a s h , h e a t and s u l f u r c o n t e n t s . The E u r o p e a n s d e v e l o p e d much The C o a l B l e n d i n g Model Pg 26 o f t h e t e c h n o l o g y t h r o u g h n e c e s s i t y , s i n c e t h e raw c o a l f e e d t o most o f t h e i r l a r g e c o a l w a s h e r i e s c a n v a r y w i d e l y i n c h a r a c t e r i s t i c s f r o m h o u r t o h o u r . Today, managers o f c o a l m i n e s c a n c h o o s e n o t t o b l e n d , t o b a t c h p a r t i c u l a r c o a l s , o r t o s e l e c t one o f s e v e r a l a v a i l a b l e b l e n d i n g o p t i o n s . The m a j o r b l e n d i n g o p t i o n s a r e : a) H o m o g e n i z a t i o n b) B l e n d i n g p r i o r t o t r e a t m e n t i n t h e p l a n t c) I n - p i t b l e n d i n g d) Any c o m b i n a t i o n o f t h e above No B l e n d i n g : A mine t h a t c h o o s e s n o t t o b l e n d c o a l s i m p l i f i e s t h e mine p l a n n i n g p r o c e s s , w h i l e m i n i m i z i n g i t s r e q u i r e d ROM c o a l s t o c k p i l e s . T h i s o p t i o n i s l e a s t e x p e n s i v e , and i s b e s t s u i t e d t o m ines m i n i n g o n l y one homogeneous seam o r mines w i t h c o a l seams h a v i n g s i m i l a r w a s h a b i l i t y c u r v e s o r p h y s i c a l p r o p e r t i e s . C o a l mines f i t t i n g i n t o t h i s c a t e g o r y w i l l d e r i v e no b e n e f i t f r o m d e t e r m i n i n g t h e C o a l B l e n d i n g C o e f f i c i e n t o r f r o m any o t h e r b l e n d i n g m o d e l s . A l l b l e n d i n g t h e o r i e s e x p l o i t d i f f e r e n c e s i n t h e w a s h a b i l i t y d a t a o r p h y s i c a l p r o p e r t i e s , so when t h e r e a r e no d i f f e r e n c e s i n t h e ROM c o a l , t h e i d e a l m i l l f e e d i s o b t a i n e d . The b e s t b l e n d i n g o r h o m o g e n i z a t i o n p l a n s a l w a y s s t r i v e t o w a r d , b u t n e v e r a c h i e v e t h i s g o a l . The C o a l B l e n d i n g Model Pg 27 B a t c h i n g : The term ' b a t c h i n g ' i s n o r m a l l y used to d e s c r i b e a u n i t o p e r a t i o n which i s not c o n t i n u o u s . In c o a l p r e p a r a t i o n t e r m i n o l o g y , b a t c h i n g o f t e n r e f e r s to the p r o c e s s e s o f p u r p o s e f u l l y c l e a n i n g o n l y one q u a l i t y or type o f c o a l a t a t i m e . Some Western Canadian c o a l p l a n t s have p r a c t i c e d t h i s form of o p e r a t i o n f o r y e a r s . A t f i r s t g l a n c e , t h i s would seem t o be an i d e a l way of o p e r a t i n g . The f eed f o r each run would be s i m i l a r i n q u a l i t y , which s h o u l d a l l o w f o r f i n e - t u n i n g o f p r o c e s s equipment . However, b a t c h i n g does have i t s c o m p l i c a t i o n s . F i r s t l y , p r e - p l a n t s t o c k p i l e s a r e r e q u i r e d f o r each q u a l i t y o f c o a l b e i n g mined . S e c o n d l y , i f a l l the p r o d u c t s a r e not c l e a n e d t o the same q u a l i t y ( i . e . s i m i l a r a s h , s u l f u r , F . S . I . , e t c . c o n t e n t s ) , then e i t h e r the d i f f e r e n t c o a l s must each be s o l d s e p a r a t e l y , o r a p o s t - p l a n t b l e n d i n g f a c i l i t y as w e l l as more c o a l s t o r a g e / s t o c k p i l i n g would be r e q u i r e d . When b a t c h i n g i s r e f e r r e d to i n t h i s p a p e r , the term w i l l s p e c i f i c a l l y r e f e r t o the o p e r a t i o n o f c l e a n i n g each c o a l to the same ash c o n t e n t . Some p o s t - b l e n d i n g would be n e c e s s a r y i f the o t h e r c o a l p r o p e r t i e s v a r i e d g r e a t l y . Figure. 5 Benefits of Raw Coal Homogenization* *(Ruhrkohl A.G.) The C o a l B l e n d i n g Model Pg 29 H o m o g e n i z a t i o n : H o m o g e n i z a t i o n , o r m i x i n g , i s e f f e c t i v e when a l a r g e number o f seams o r m i n i n g l o c a t i o n s a r e worked. The raw c o a l f r o m a v a r i e t y o f p r e v i o u s l y s e l e c t e d work f a c e s a r e s t o c k p i l e d on an "as come" b a s i s , u s u a l l y by means o f s p r e a d e r s , o r s t a c k e r s . Once t h e pad i s f u l l , t h e ROM c o a l i s r e c l a i m e d u s i n g a b u c k e t wheel o r draw p o i n t s , i n s u c h a manner a s t o g i v e t h e b e s t p o s s i b l e mix o f t h e d e p o s i t e d c o a l . S u c c e s s f u l a p p l i c a t i o n s a r e i n u s e i n E u r o p e a n m u l t i p l e seam c o a l o p e r a t i o n s , b u t t h e s e r e q u i r e e x p e n s i v e s t o c k p i l e s and b l e n d i n g p ads [ B e t h e & Koch ( 1 2 ) , K u b i t z a ( 1 3 ) , O s b o r n e & W a l t e r s ( 1 4 ) 1 . F i g u r e 5 i l l u s t r a t e s t h e b e f o r e and a f t e r h o m o g e n i z a t i o n e f f e c t s on t h e a s h c o n t e n t o f m i l l f e e d s a m p l e s . B e f o r e h o m o g e n i z a t i o n , t h e m i l l f e e d a s h c o n t e n t was h i g h l y v a r i a b l e , r a n g i n g f r o m a low o f 26%, t o a h i g h o f 42%. A v a r y i n g a s h c o n t e n t i n m i l l f e e d w i l l d i r e c t l y a f f e c t t h e q u a l i t y o f t h e f i n a l p r o d u c t . F o r t u n a t e l y f o r t h o s e m ines w i t h a v a r y i n g f e e d q u a l i t y , t h e c o a l c l e a n i n g p r o c e s s d o e s p e r f o r m c o n s i d e r a b l e h o m o g e n i z a t i o n ( L a z o r i n , S o l o s h e n k o , S l e s a r e v , L i t m a n o v i c h , M i l y u t i n , and C h e r n o v a ) ( 1 5 ) , t h u s p r o d u c i n g a f i n a l p r o d u c t w i t h much l e s s f l u c t u a t i o n t h a n t h e o r i g i n a l f e e d . A f t e r h o m o g e n i z a t i o n , t h e m i l l f e e d and f i n a l p r o d u c t s b o t h r e v e a l s m a l l e r amounts o f v a r i a t i o n . The Coal Blending Model Pg 30 A c c o r d i n g to Salama (16) , L a z o r i n e t a l (15) , and Abbott (17 ) , as w e l l as the m a j o r i t y of other authors of c o a l b l e n d i n g papers, the b e n e f i t s of a c o n s i s t e n t feed are t h a t homogenization of ROM c o a l s decreases the l o s s e s of c o a l to t a i l i n g s , thus improving the washery recovery and y i e l d . Homogenization i s an e x c e l l e n t t o o l f o r p r e - a v e r a g i n g c o a l s from many f a c e s , though the q u a l i t y of the f i n a l product i s s t i l l dependent upon the q u a l i t i e s and q u a n t i t i e s of each component i n the b l e n d . B l e n d i n g P r i o r t o Treatment: Bl e n d i n g p r i o r t o treatment or p r e - p l a n t b l e n d i n g i n v o l v e s the combining of c o a l s a t known or assumed q u a l i t i e s i n predetermined q u a n t i t i e s . A l l b l e n d i n g models r e q u i r e t h a t the q u a l i t y of c o a l seams i s known, as w e l l as having some form of c o n t r o l over the q u a n t i t i e s r e c e i v e d from each seam. T h e r e f o r e , mines which blend p r i o r t o the p l a n t s i t e are i d e a l l y s u i t e d t o take advantage of b l e n d i n g s t r a t e g i e s , i n c l u d i n g the r e s u l t s from the Coal Blending C o e f f i c i e n t model. A p a r t i c u l a r problem with b l e n d i n g i s t h a t e i t h e r a l a r g e c a p i t a l expenditure i s r e q u i r e d f o r s i l o s or b l e n d i n g pads, or the c o a l must be rehandled, thereby i n c r e a s i n g the The C o a l B l e n d i n g Model Pg 31 o p e r a t i n g c o s t s and p r o d u c i n g more f i n e s . I n e i t h e r c a s e , t h e n e c e s s a r y l a r g e s t o c k p i l e s d e l a y c o a l s a l e s and t a k e up v a l u a b l e s p a c e . B l e n d i n g p r i o r t o t r e a t m e n t w o u l d be t h e b l e n d i n g method p r e f e r r e d by most p r e p a r a t i o n p l a n t managers, b u t t h e i n c r e a s e d s p a c e and c a p i t a l r e q u i r e m e n t s o f t h e s y s t e m o f t e n work a g a i n s t t h e a c c e p t a n c e o f t h i s method. I n - P i t B l e n d i n g : As t h e name i m p l i e s , i n - p i t b l e n d i n g i s p e r f o r m e d a t t h e m i n i n g s t a g e . The o b j e c t i v e o f t h i s b l e n d i n g i s t o a c h i e v e a v e r y r o u g h m i x t u r e o f seams. T y p i c a l l y , t h i s method i n v o l v e s b l e n d i n g by t r u c k l o a d : 3 t r u c k l o a d s o f seam A t o 1 t r u c k l o a d o f seam D, f o r example. Even i n t h e b e s t s i t u a t i o n s , c o n t r o l i s u s u a l l y v e r y p o o r , and i s s u b j e c t t o m i n i n g s c h e d u l e s , t h e w e a t h e r , and m e c h a n i c a l b reakdowns. The t r u c k s i z e s a r e commonly 100 m e t r i c t o n n e s o r l a r g e r . A l t h o u g h m i x i n g i n t h e c r u s h e r o r r o t a r y b r e a k e r d o e s o c c u r , as w e l l a s i n t h e s t o c k p i l e s o r s i l o s , t h e f e e d q u a l i t y f l u c t u a t e s a c c o r d i n g t o t h e i n d i v i d u a l seam q u a l i t i e s . A s e c o n d p r o b l e m w i t h t h e " b l e n d i n g by t r u c k l o a d " method i s t h a t t h e t r u c k s r a r e l y a r r i v e a t an e v e n d i s t r i b u t i o n . A 3 and 1 r a t i o t o o o f t e n becomes a 9 and 3 r a t i o . A computer d i s p a t c h s y s t e m , a s w e l l as t h e u s e o f s m a l l s t o c k p i l e s , has i m p r o v e d t h e f e e d The C o a l B l e n d i n g Model Pg 32 d i s t r i b u t i o n but has not overcome the t y p i c a l m i n i n g problems o f equipment breakdown or shor tages o f exposed c o a l . When these c o n d i t i o n s o c c u r , i n - p i t b l e n d i n g i s r e a d i l y d i s r e g a r d e d f o r the sake of o u t p u t , and the ROM c o a l becomes whatever type i s a v a i l a b l e . On i t s own, i n - p i t b l e n d i n g i s n o r m a l l y not e f f e c t i v e enough t o produce a c o n s i s t e n t m i l l f e e d , y e t i s s t i l l a much b e t t e r p r o c e s s than no b l e n d i n g . When combined w i t h a homogeniza t ion program, i n - p i t b l e n d i n g can be a v e r y e f f e c t i v e method. SUMMARY In t o d a y ' s age o f m u l t i p l e seam m i n i n g , most mines have been f o r c e d t o e i t h e r b l e n d , homogenize o r b a t c h t h e i r p l a n t f e e d . For Western Canadian open p i t c o a l mines , the t r a d i t i o n a l c h o i c e has been between b a t c h i n g and b l e n d i n g . Homogenizat ion i s t r a d i t i o n a l l y used i n underground o p e r a t i o n s where 10 o r more f a c e s are mined a t once , making s c h e d u l i n g a lmost i m p o s s i b l e . The C o a l B l e n d i n g C o e f f i c i e n t , d e s c r i b e d l a t e r i n t h i s t h e s i s , can be used to compare the e f f i c i e n c i e s o f b l e n d i n g v e r s u s b a t c h i n g , where a l l the batched c o a l i s c l e a n e d to the same ash c o n t e n t l e v e l . In f a c t , the c o e f f i c i e n t i s d e f i n e d as The C o a l B l e n d i n g Model Pg 33 t h e d i f f e r e n c e i n y i e l d between b l e n d i n g and b a t c h i n g t h e same c o a l s , c l e a n e d t o t h e same a s h l e v e l , p r o c e s s e d by t h e same p l a n t u s i n g t h e same p r o c e s s s t r a t e g y . PREPARATION PLANT COMPUTER SIMULATION MODELING E a r l y c o m p u t e r a p p l i c a t i o n s i n c o a l p r e p a r a t i o n were b a s i c d a t a h a n d l i n g r o u t i n e s . However, i n t h e l a t e f i f t i e s and e a r l y s i x t i e s , t h e u s e o f o p e r a t i o n s r e s e a r c h t e c h n i q u e s and computer s i m u l a t i o n m o d e l s s t a r t e d t o become v e r y p o p u l a r . Charmbury and L o v e l l ( 1 8 ) ; K i n d i g , L u c k i e , and L o v e l l ( 9 ) ; B r o o k e s and Whitmore ( 1 9 ) ; Humphreys, L e o n a r d and B u t t e r w o r t h ( 2 0 ) ; and A b s i l , K e u i n g , and Meerman (21) were among t h e e a r l y p i o n e e r s i n c o a l p r o c e s s c omputer m o d e l i n g . They h e l p e d d e v e l o p t h e computer model f r o m a s i m p l e d a t a b a s e m a n i p u l a t i o n p r o g r a m t o a p l a n t s i m u l a t i o n model c a p a b l e o f e s t i m a t i n g t h e p l a n t y i e l d and a s h c o n t e n t o f t h e c l e a n c o a l . S i n c e t h e e a r l y s e v e n t i e s , much t i m e has been s p e n t p e r f e c t i n g t h e e a r l y c o m p u t e r model c o n c e p t s . CANMET d e v e l o p e d a s u i t e o f p r o g r a m s c a l l e d t h e " C o a l D a t a M a n i p u l a t i o n P r o g r a m s " (4) a s w e l l a s t h e i r "Spock P r o g r a m s " , and t h e U.S. D e p a r t m e n t o f E n e r g y (22) r e c e n t l y r e l e a s e d a new p r e p a r a t i o n p l a n t s i m u l a t o r . T h e s e p r o g r a m s , w h i c h a r e t h e a c c u m u l a t i o n o f t e n s o f t h o u s a n d s o f h o u r s o f programming and r e s e a r c h , a r e The C o a l B l e n d i n g Model Pg 34 c a p a b l e o f p r e d i c t i n g t h e p e r f o r m a n c e o f a p l a n t , and o f o p t i m i z i n g t h e y i e l d a t a s p e c i f i e d a s h c o n t e n t o f c l e a n c o a l f o r a g i v e n c o a l t y p e . The t r a d i t i o n a l u s e s o f computer s i m u l a t i o n p r o g r a m s as o u t l i n e d by Rong and Lyman (23) a r e as f o l l o w s : (1) I n t h e d e s i g n s t a g e : - t o d e t e r m i n e t h e o p t i m a l t e c h n o l o g i c a l scheme by c o m p a r i n g s e v e r a l a l t e r n a t i v e f l o w s h e e t s ; - t o o p t i m i z e t h e f e e d s i z e r a n g e f o r e a c h s e p a r a t o r i n t h e f l o w s h e e t ; - t o p r o d u c e d e t a i l e d e s t i m a t e s o f o p e r a t i o n c o n d i t i o n s f o r t h e p l a n t . (2) F o r a new p l a n t a t s t a r t u p : - t o e s t i m a t e t h e p e r f o r m a n c e o f s e p a r a t o r s and e n t i r e p l a n t s a t any o p e r a t i n g c u t p o i n t , i n c o n s i d e r a b l e d e t a i l ; - t o p r e d i c t t h e o p t i m a l a s h c o n t e n t o f c l e a n c o a l i n e a c h s e p a r a t o r ( o r e a c h c o a l f e e d g r o u p ) when t h e mass f r a c t i o n o f c o a l washed i n e a c h ( s e p a r a t o r o r e a c h c o a l f e e d g r o u p ) and t h e a s h c o n t e n t o f f i n a l c l e a n c o a l a r e s p e c i f i e d . < 3) F o r an o p e r a t i n g p l a n t : - t o d e t e r m i n e t h e o p t i m a l o p e r a t i n g c u t p o i n t s o f a l l s e p a r a t o r s so a s t o m a x i m i z e y i e l d a t a s p e c i f i e d a s h c o n t e n t o f f i n a l c l e a n c o a l ; - t o i n v e s t i g a t e s e n s i t i v i t y t o o p e r a t i n g p a r a m e t e r s o r t o l o c a t e b o t t l e n e c k s i n t h e p l a n t . Modern s i m u l a t i o n and o p t i m i z a t i o n p r o g r a m s a r e a l l c a p a b l e o f p e r f o r m i n g t h e above f u n c t i o n s , and w i t h some m o d i f i c a t i o n s and i m a g i n a t i o n , t h e s e p r o g r a m s c a n be g e n u i n e l y u s e f u l t o o l s f o r s o l v i n g many o t h e r c o a l p r e p a r a t i o n p r o b l e m s . F o r example, t o c a l c u l a t e t h e c o a l b l e n d i n g c o e f f i c i e n t and d e v e l o p t h e m o d el, a modern c o a l p l a n t s i m u l a t i o n model i s The C o a l B l e n d i n g Model Pg 35 r e q u i r e d t o d e t e r m i n e t h e q u a l i t y o f c l e a n c o a l g i v e n t h e q u a l i t y o f t h e ROM c o a l and o p e r a t i n g c o n s t r a i n t s . Modern w a s h e r y computer s i m u l a t o r s a l l o w e v e r y o n e , f r o m r e s e a r c h e r s t o p l a n t managers, an o p p o r t u n i t y t o s i m u l a t e t h e h y p o t h e s e s w i t h o u t i n c u r r i n g t h e h i g h e x p e n s e s and t h e t i m e r e q u i r e d t o t e s t o u t t h e i r t h e o r i e s u s i n g o p e r a t i n g o r p i l o t p l a n t s . Once t h e i d e a s have been p r o v e n i n t h e s i m u l a t i o n , t h e n t h e y c a n be examined u n d e r a c t u a l o p e r a t i n g c o n d i t i o n s . I I I . DEVELOPMENT OF THE COAL BLENDING MODEL INTRODUCTION The i n i t i a l o b j e c t i v e o f t h i s s t u d y was t o d e v e l o p a method o f e v a l u a t i n g t h e e f f e c t s o f c o n t r o l l e d b l e n d i n g on p r e p a r a t i o n p l a n t e f f i c i e n c y . The l a c k o f s u c h a method has been o f m a j o r c o n c e r n t o p r o c e s s e n g i n e e r s . Many a g r e e d w i t h S a l a m a ' s (16) t h o u g h t s : " . . . i t i s n a t u r a l t o e x p e c t t h a t w i de f e e d v a r i a t i o n c a n c a u s e a d i v e r s e e f f e c t on t h e o p e r a t i o n o f d i f f e r e n t u n i t s i n any c o a l c l e a n i n g f a c i l i t y and w i l l r e s u l t i n d e c r e a s e d o v e r a l l y i e l d ". W h i l e some m i n i n g e n g i n e e r s s t i l l f e e l t h a t a c o n t r o l l e d p l a n t f e e d i s n o t n e c e s s a r y , o t h e r s w o u l d l i k e t o f i n d a way t o q u a n t i f y t h e e f f e c t s o f The C o a l B l e n d i n g Model Pg 36 c o n t r o l l e d b l e n d i n g . T h i s c o a l b l e n d i n g model i s a f i r s t a t t e m p t a t d e v e l o p i n g s u c h a method. DEVELOPMENT OF THE COAL BLENDING COEFFICIENT C o a l p r e p a r a t i o n e n g i n e e r s a r e i n t e r e s t e d i n d e t e r m i n i n g how e f f e c t i v e l y a p l a n t c a n p r o c e s s a g i v e n c o a l t y p e . T h i s p r o j e c t was c o n c e r n e d w i t h how e f f e c t i v e l y t h e a c t u a l c o a l b l e n d s f r o m a g i v e n c o a l d e p o s i t and o p e r a t i o n c a n be p r o c e s s e d by a p l a n t c o n f i g u r a t i o n . B e c a u s e a company i s f i n a n c i a l l y c o m m i t t e d t o i t s e x i s t i n g p l a n t and may n o t have f i n a n c e s t o r e m o d e l n o r may t h e p r o d u c t i o n r e q u i r e m e n t s p e r m i t r e m o d e l l i n g , p r o c e s s i n g e f f e c t i v e n e s s i s a m a j o r c o n s i d e r a t i o n f o r e x i s t i n g p l a n t s . T h e r e f o r e t h i s model f i t s t h e c o a l t o t h e p l a n t , n o t t h e p l a n t t o t h e c o a l . The o b j e c t i v e o f t h e c o a l b l e n d i n g model i s t o o p t i m i z e t h e c l e a n c o a l y i e l d w i t h o u t s a c r i f i c i n g c l e a n c o a l q u a l i t y o r i m p o s i n g t i g h t p r o d u c t i o n c o n s t r a i n t s on t h e mine o r p l a n t . A m a t h e m a t i c a l f o r m u l a , t h e C o a l B l e n d i n g C o e f f i c i e n t , was d e v e l o p e d w i t h i t s o b j e c t i v e f u n c t i o n t o o p t i m i z e t h e c l e a n c o a l y i e l d . The C o a l B l e n d i n g C o e f f i c i e n t i s a y i e l d - b a s e d r a t i o b e c a u s e y i e l d m a x i m i z a t i o n , d e f i n e d a s t h e a c t u a l o u t p u t d i v i d e d by t h e optimum o r i d e a l o u t p u t , w i t h o u t s a c r i f i c e o f The C o a l B l e n d i n g Model Pg 37 f i n a l p r o d u c t q u a l i t y , p r o d u c e s i n c r e a s e d p r o f i t s , t h u s i s t h e m a j o r o b j e c t i v e o f a l l c o a l m i n e s . The C o a l B l e n d i n g C o e f f i c i e n t compares b a t c h i n g t o b l e n d i n g o f t h e same c o a l s . M a t h e m a t i c a l l y , t h e C o a l B l e n d i n g C o e f f i c i e n t i s t h e d i f f e r e n c e between t h e p l a n t y i e l d a t a s e t c l e a n c o a l a s h f o r a p a r t i c u l a r b l e n d and t h e y i e l d w h i c h w o u l d be o b t a i n e d were e a c h seam washed s e p a r a t e l y t o t h e same a s h and i n t h e same p r o p o r t i o n s a s f o r t h e b l e n d . The m a t h e m a t i c a l r e p r e s e n t a t i o n i s a s f o l l o w s : Z = BY-) [~~! ( A i * W i i * Y i i ) L--1 j=l where: Z = c o a l b l e n d i n g c o e f f i c i e n t BY = t h e b l e n d y i e l d (%) n = number o f seams t r e a t e d m = number o f s i z e f r a c t i o n s t r e a t e d A i = The p e r c e n t a g e mass o f t h e seam i n t h e b l e n d W i j = P r o p o r t i o n o f t h e s i z e f r a c t i o n ( j ) i n t h e s e a m ( i ) Y i j = Mass y i e l d p r o p o r t i o n o f s i z e f r a c t i o n ( j ) i n s e a m ( i ) Page 89 o f A p p e n d i x A l i s t s t h e a c t u a l C o a l B l e n d i n g C o e f f i c i e n t p r o g r a m . L i n e 3800 i s t h e o b j e c t i v e f u n c t i o n f o r t h e C o a l B l e n d i n g M o d e l . The v a l u e o f t h e C o a l B l e n d i n g C o e f f i c i e n t i n d i c a t e s t h e e f f e c t i v e n e s s o f b l e n d i n g . A h i g h v a l u e s u g g e s t s t h a t a c o n t r o l l e d b l e n d i n g p r o g r a m c o u l d i m p r o v e o v e r a l l p l a n t y i e l d , w h i l e a low o r n e g a t i v e v a l u e s u g g e s t s t h a t b a t c h i n g w o u l d be as good as o r more e f f e c t i v e t h a n b l e n d i n g . The m a g n i t u d e o f t h e C o a l B l e n d i n g C o e f f i c i e n t i s a d i r e c t i n d i c a t i o n o f t h e e x p e c t e d i n c r e a s e i n y i e l d due t o b l e n d i n g v e r s u s b a t c h i n g . The C o a l B l e n d i n g Model Pg 38 I n an o p e r a t i n g w a s h e r y , t h e m a g n i t u d e o f t h e C o a l B l e n d i n g C o e f f i c i e n t r e a l i z e d f r o m any b a t c h i n g v e r s u s b l e n d i n g t e s t s p e r f o r m e d w o u l d be d e p e n d e n t on a complex f u n c t i o n o f t h e w a s h a b i l i t y c h a r a c t e r i s t i c s o f e a c h seam, t h e m i n i n g t e c h n i q u e u s e d , t h e e f f i c i e n c y o f t h e c l e a n i n g u n i t s , and t h e f i n a l q u a l i t y s p e c i f i c a t i o n s . Most c o a l p r e p a r a t i o n p l a n t s i m u l a t i o n m o d e l s o n l y t a k e i n t o a c c o u n t t h e c o a l seam c h a r a c t e r i s t i c s , t h e o r e t i c a l e q u i p m e n t y i e l d s b a s e d on t h e i r t y p i c a l d i s t r i b u t i o n c u r v e s f o r s t a n d a r d s i z e d i s t r i b u t i o n s , and f i n a l q u a l i t y s p e c i f i c a t i o n s . E q u i p m e n t o p e r a t i o n p r o b l e m s t h a t c o u l d a f f e c t t h e shape o f t h e d i s t r i b u t i o n c u r v e s , s u c h as o p e r a t i o n o v e r t h e c a p a c i t y o f e q u i p m e n t , f l o w s u r g e s , o r e x c e p t i o n a l l y c l e a n c o a l , a r e n o t n o r m a l l y b u i l t i n t o c o a l p l a n t s i m u l a t i o n m o d e l s ( L e o n a r d & L e o n a r d ) ( 2 4 ) . T h e s e o p e r a t i n g p r o b l e m s c a n o f t e n be t h e d i f f e r e n c e between t h e r e s u l t s o b t a i n e d by a p r e p a r a t i o n p l a n t model and a c t u a l p l a n t r e s u l t s . The t r u e t h e o r e t i c a l y i e l d f o r a g i v e n p l a n t f e e d c a n be d e t e r m i n e d f r o m t h e c o a l ' s w a s h a b i l i t y c u r v e . A p o s i t i v e v a l u e f o r t h e C o a l B l e n d i n g C o e f f i c i e n t c a n be o b t a i n e d f r o m t h e w a s h a b i l i t y d a t a o f b l e n d e d seams. The f o l l o w i n g example p r o b l e m was c h o s e n t o d e m o n s t r a t e t h e p o s s i b i l i t y o f an i n c r e a s e i n t h e C o a l B l e n d i n g C o e f f i c i e n t due s t r i c t l y t o t h e w a s h a b i l i t y e f f e c t . C o n s i d e r two seams w i t h w a s h a b i l i t y The C o a l B l e n d i n g Model Pg 39 c h a r a c t e r i s t i c s a s i n A p p e n d i x B, p a g e s 95 (Seam 2) and 96 (Seam 1 ) . The c u m u l a t i v e f l o a t d a t a f o r t h e s e seams and a 60:40 b l e n d a r e shown i n T a b l e I I . TABLE I I . CUMULATIVE FLOAT DATA RELATIVE SEAM 1 SEAM 2 BLEND 60:40 DENSITY MASS ASH MASS ASH MASS ASH FRACTIONS % % % % % % FLOAT 1.30 31.98 3.54 5.95 3.93 21.57 3.59 1.30 1.40 69.95 5.69 46.18 8.16 60.44 6.44 1.40 1.50 77.39 6.86 61.13 10.77 70.89 8.21 1.50 1.60 80.07 7.54 66.38 12.48 74.59 9.30 1.60 1.70 82.00 8.21 69.50 13.85 77.00 10.25 1.70 1.80 83.38 8.78 72.53 15.48 79.04 11.24 1.80 SINK 100.00 20.16 100.00 33.54 100.00 25.51 The seams, b l e n d r a t i o , and f i n a l p r o d u c t a s h c o n t e n t were c h o s e n t o s i m p l i f y t h e m a t h e m a t i c s and m i n i m i z e t h e amount o f e r r o r i n t r o d u c e d i n t o t h e p r o b l e m by t r y i n g t o i n t e r p r e t v a l u e s between d a t a p o i n t s . From T a b l e I I , t h e mass p e r c e n t o f seam 1 o b t a i n a b l e a t t h e d e s i r e d a s h o f 8.21 w o u l d be 82.00 p e r c e n t . The mass p e r c e n t o f seam 2 w o u l d be s l i g h t l y g r e a t e r t h a n 46.18 p e r c e n t . T a k i n g t h e w o r s t s c e n a r i o , t h e maximum e x p e c t e d y i e l d a t 8.21 p e r c e n t a s h w o u l d be 46.65 p e r c e n t . The b l e n d y i e l d a c c o r d i n g t o t h e w a s h a b i l i t y d a t a i s 70.89 p e r c e n t . The C o a l B l e n d i n g C o e f f i c i e n t f o r t h i s example w o u l d be as f o l l o w s : C.B.C.= 70.89 - (0.6 * 82.00 + 0.4 * 46.65) = 70.89 - 67.86 = 3.03 The C o a l B l e n d i n g Model Pg 40 The o t h e r i m p o r t a n t e f f e c t on t h e v a l u e o f t h e C o a l B l e n d i n g Model i s t h e t h e o r e t i c a l p e r f o r m a n c e o f t h e c l e a n i n g e q u i p m e n t . A t any s e p a r a t i n g g r a v i t y , t h e t h e o r e t i c a l y i e l d and q u a l i t y must be c o n v e r t e d t o a p r a c t i c a l v a l u e by means o f a d i s t r i b u t i o n c u r v e . Most m o d e l s b a s e p e r f o r m a n c e on s t a n d a r d o r a v e r a g e d i s t r i b u t i o n c u r v e s f o r e a c h c l e a n i n g u n i t , b u t e v e n t h e s e s t a n d a r d c u r v e s a r e n o t o f a f i x e d f o r m b u t v a r y f o r d i f f e r e n t s e p a r a t i n g g r a v i t i e s and p a r t i c l e s i z e s . D e p e n d i n g on r e q u i r e d s e p a r a t i o n g r a v i t i e s o f t h e b a t c h e d seams and t h e b l e n d e d seam, an i n c r e a s e o r d e c r e a s e i n t h e C o a l B l e n d i n g C o e f f i c i e n t c a n be r e a l i z e d a f t e r t h e t h e o r e t i c a l y i e l d s a r e c o n v e r t e d i n t o p r a c t i c a l y i e l d s by u s i n g c l e a n i n g e q u i p m e n t d i s t r i b u t i o n c u r v e s . The C o a l B l e n d i n g Model Pg 41 COAL BLENDING MODEL DESCRIPTION The C o a l B l e n d i n g Model i s a c o l l e c t i o n o f c o mputer p r o g r a m s - - some a r e d e v e l o p e d e s p e c i a l l y f o r t h i s p r o j e c t , and o t h e r s a r e a v a i l a b l e c o m m e r c i a l l y . A s i m p l i f i e d f l o w s h e e t f o r t h e C o a l B l e n d i n g C o e f f i c i e n t Model i s shown i n F i g u r e 6. The C o a l P l a n t S i m u l a t i o n p r o g r a m i s t h e l a r g e s t and most c o m p l i c a t e d p a r t o f t h e e n t i r e m o d e l . Most modern C o a l P l a n t S i m u l a t i o n Model p r o g r a m s , a s p r e v i o u s l y d i s c u s s e d on p a g e s 33 t o 35, a r e s u i t a b l e f o r i n c o r p o r a t i o n i n t o t h i s model and a r e c o m m e r c i a l l y a v a i l a b l e . The s i m u l a t i o n model t h a t i s b e s t a b l e t o model t h e e x i s t i n g p l a n t and p r o d u c e f i n a l r e s u l t s c l o s e s t t o a c t u a l r e s u l t s s h o u l d be c h o s e n . T h i s i s a m a t t e r o f c o m p a r i n g model r e s u l t s w i t h a c t u a l f i e l d r e s u l t s f o r d i f f e r e n t t y p e s o f c o a l . The c h o s e n s i m u l a t i o n model w i l l t h e n d e t e r m i n e t h e f o r m a t o f d a t a i n p u t / o u t p u t . The W a s h a b i l i t y D a t a I n p u t and S t o r a g e r o u t i n e i s n o r m a l l y a v a i l a b l e a s p a r t o f t h e C o a l P l a n t S i m u l a t o r p a c k a g e . T h i s p r o g r a m t a k e s t h e w a s h a b i l i t y d a t a f o r e a c h seam and s t o r e s t h e d a t a i n a f o r m a t t h a t c a n be r e a d by t h e b l e n d i n g and p l a n t s i m u l a t i o n r o u t i n e s . The d a t a f o r e a c h s i z e f r a c t i o n and f l o a t - s i n k d e n s i t y o f e a c h seam i s e n t e r e d a t t h i s p o i n t . The Coal Blending Model Pg 42 CANMET WASHABILITY DATA INPUT PROGRAM STORE WASHABILITY DATA FILES TO DISK] INPUT MODEL AND BLENDING CONSTRAINTS (Appendix A, Pg ?1) > f RETRIEVE WASHABILITY DATA FILES f BLEND GENERATOR PROGRAM (Appendix A, Pg 90) > PRINT RESULTS V Next Blend CANMET WASHABILITY DATA COMBINE PROGRAM CANMET PLANT SIMULATION PROGRAM Consti Chi raint eck N COAL BLENDING COEFICIENT GENERATING PROGRAM (Appendix A, Pg 89) SORT AND STORE MODEL RESULTS (Appendix A, Pg 8?) Figure 6. S i m p l i f i e d Flowsheet The Coal Blending Model For The C o a l B l e n d i n g Model Pg 43 The B l e n d G e n e r a t o r Program, as t h e name i m p l i e s , g e n e r a t e s b l e n d i n g r a t i o s f o r t h e c o a l seam q u a l i t y b l e n d i n g r o u t i n e . T h i s p r o g r a m was d e s i g n e d t o p r o d u c e a l l p o s s i b l e r a t i o s w i t h i n t h e g i v e n c o n s t r a i n t s , a t t h e g i v e n s t e p s i z e . I f two seams were t o be r u n t h r o u g h t h e model w i t h a l l p o s s i b l c o m b i n a t i o n s t r i e d a t a s t e p s i z e o f 10, e l e v e n c o m b i n a t i o n s w o u l d be g e n e r a t e d : COMB. 1 2 3 4 5 6 7 8 9 10 11 SEAM A 0 10 20 30 40 50 60 70 80 90 100 SEAM B 100 90 80 70 60 50 40 30 20 10 0 As t h e s t e p s i z e i s d e c r e a s e d and t h e number o f seams a r e i n c r e a s e d , t h e r e q u i r e d number o f r u n s i s d r a m a t i c a l l y i n c r e a s e d . F o r a l l p o s s i b l e c o m b i n a t i o n s u s i n g t h r e e seams an a s t e p s i z e o f f i v e , t w e n t y - o n e f a c t o r i a l r u n s , o r 231 r u n s w o u l d be r e q u i r e d . The B l e n d G e n e r a t o r i s n o t a s t a n d a r d f e a t u r e o f most s i m u l a t i o n p a c k a g e s , and t h e r e f o r e must be w r i t t e n on s i t e . The l i s t i n g f o r t h e B l e n d G e n e r a t o r Program, w r i t t e n i n H e w l e t t P a c k a r d B a s i c f o r t h e CANMET D a t a M a n i p u l a t i o n P a c k a g e , i s g i v e n i n A p p e n d i x A, page 90. The C o a l B l e n d i n g Model Pg 44 The C o a l Seam Q u a l i t y B l e n d i n g r o u t i n e i s d e s i g n e d t o c ombine w a s h a b i l i t y d a t a f r o m f i l e s , t h e n s t o r e t h e s e r e s u l t s on a d i s k f o r f u t u r e u s e . T h i s r o u t i n e c r e a t e s a new w a s h a b i l i t y c u r v e by c o m b i n i n g w a s h a b i l i t y d a t a f r o m t h e seams b e i n g c o m b i n e d . The p r o g r a m t h e n c o m b i n e s t h e d a t a by u s i n g t h e r a t i o s o f e a c h seam i n t h e d e s i r e d b l e n d . The way i n w h i c h t h i s p r o c e s s works i s d e m o n s t r a t e d i n t h e f o l l o w i n g example, i n w h i c h t h e d e s i r e d b l e n d b e i n g s o u g h t i s 40% seam A, 60% seam B: % o f seam A i n t h e f i r s t w a s h a b i l i t y r a n g e i s 5 % % o f seam B i n t h e f i r s t w a s h a b i l i t y r a n g e i s 10% % o f B l e n d i n t h e f i r s t w a s h a b i l i t y r a n g e i s (.4*5)+(.6*10)=8% The p r o c e s s i s r e p e a t e d f o r a l l w a s h a b i l i t y r a n g e s , t h u s c r e a t i n g a new s e t o f w a s h a b i l i t y d a t a . The n e x t r o u t i n e i n t h e model i s t h e C o n s t r a i n t C h e c k i n g p r o g r a m . T h i s r o u t i n e s i m p l y compares t h e f i n a l c o a l q u a l i t y w i t h t h e i n i t i a l q u a l i t y c o n s t r a i n t s . I f t h e f i n a l p r o d u c t f a i l s t o meet t h e i n p u t q u a l i t y c o n s t r a i n t s , t h e n t h e n e x t b l e n d i n t h e s e q u e n c e i s t r i e d . I f t h e f i n a l p r o d u c t f a l l s w i t h i n t h e s p e c i f i e d c o n s t r a i n t s , t h e C o a l B l e n d i n g C o e f f i c i e n t i s t h e n c a l c u l a t e d f o r t h e b l e n d i n q u e s t i o n . A l l t h e d e s i r e d i n f o r m a t i o n i s s t o r e d f o r f u t u r e p r i n t i n g . The n e x t r u n i s The C o a l B l e n d i n g Model Pg 45 t h e n g e n e r a t e d . Once a l l t h e p o s s i b l e b l e n d s have been a t t e m p t e d , t h e s t o r e d r e s u l t s a r e t h e n r a n k e d by t h e i r c o a l b l e n d i n g c o e f f i c i e n t v a l u e s , and p r i n t e d i n d e s c e n d i n g o r d e r . The s o r t i n g p r o g r a m i s l i s t e d i n A p p e n d i x A, page 89. MODEL INPUT The i n t e r a c t i v e i n p u t r o u t i n e f o r t h e CANMET C o a l D a t a M a n i p u l a t i o n p r o g r a m p r o m p t s t h e u s e r when i n p u t i s r e q u i r e d . T h i s f e a t u r e i s s l o w e r t h a n a p r o g r a m u s i n g a d a t a f i l e , b u t i m p r o v e s t h e e a s e o f u s e . The H e w l e t t P a c k a r d programming r e q u i r e s c o n v e r s i o n i n t o m a c h i n e c o d e f o r e a c h r u n , and t h i s i n c r e a s e s t h e t i m e r e q u i r e d t o r u n t h e p r o g r a m . The l i s t i n g f o r t h e Model I n p u t and W a s h a b i l i t y D a t a l o a d i n g p r o g r a m i s g i v e n i n A p p e n d i x A, page 91. T h r e e t y p e s o f i n p u t i n f o r m a t i o n a r e r e q u i r e d t o r u n t h e mo d e l . The f i r s t i s t h e w a s h a b i l i t y d a t a o f e a c h seam i n v o l v e d i n t h e b l e n d i n g p r o c e s s , w h i l e t h e s e c o n d i s t h e model c o n s t r a i n t s , and t h e t h i r d i s t h e b l e n d g e n e r a t i n g c o n s t r a i n t s . A summary o f t h e i n p u t r e q u i r e m e n t s i s shown i n T a b l e I I I . The a c c u r a c y and t h e d e t a i l o f t h e w a s h a b i l i t y d a t a i s c r i t i c a l t o t h e a c c u r a c y o f t h e model r e s u l t s . A t l e a s t s e v e n The C o a l B l e n d i n g Model Pg 46 f l o a t - s i n k d e n s i t y d a t a p o i n t s a r e r e q u i r e d f o r t h e v a r i o u s s i z e f r a c t i o n s i n o r d e r t o e n s u r e r e s u l t s o f r e a s o n a b l e a c c u r a c y . The CANMET D a t a M a n i p u l a t i o n p r o g r a m w i l l a c c e p t up t o t w e n t y f l o a t - s i n k r e l a t i v e d e n s i t y d a t a p o i n t s . The a c c u r a c y o f t h e P l a n t S i m u l a t i o n Model c a n be d i r e c t l y a f f e c t e d by t h e q u a n t i t y o f d a t a p o i n t s , t h e r e f o r e t h e more d a t a p o i n t s , e s p e c i a l l y a t t h e t a i l ends o f t h e d i s t r i b u t i o n c u r v e , t h e g r e a t e r t h e a c c u r a c y o f t h e f i n a l r e s u l t s . I f t h e s e d a t a p o i n t s a r e u n a v a i l a b l e , t h e model must i n t e r p o l a t e between t h e a v a i l a b l e d a t a p o i n t s and e s t i m a t e t h e a c t u a l shape o f t h e d i s t r i b u t i o n c u r v e [A.D. W a l t e r s , e t a l ( 8 ) ; R.X. Rong and G . J . Lyman ( 2 3 ) ; A. J o w e t t ( 2 5 ) ] . The C o a l B l e n d i n g Model Pg 47 TABLE I I I . L I S T OF REQUIRED INPUT INFORMATION 1. WASHABILITY DATA INPUT - F l o a t - s i n k r e s u l t s f o r e a c h s i z e f r a c t i o n o f e a c h seam. -Weight p e r c e n t a g e o f e a c h s i z e f r a c t i o n . - S u l f u r , c a l o r i f i c v a l u e s a n d / o r m o i s t u r e c o n t e n t s f o r e a c h f l o a t - s i n k f r a c t i o n . 2. MODEL CONSTRAINTS -Number o f seams -Number o f s i z e f r a c t i o n s - W a s h a b i l i t y d a t a f i l e names - R e q u i r e d c l e a n c o a l a s h - C l e a n c o a l s u l f u r r a n g e - O p t i o n r a n g e s -Minimum a c c e p t a b l e y i e l d - C l e a n i n g e q u i p m e n t ' s r e l a t i v e d e n s i t y o p e r a t i n g r a n g e - P l a n t s i m u l a t i o n p r o g r a m s e t - u p 3. BLEND SELECTION INPUT - P e r c e n t i l e r a n g e s o f e a c h seam a l l o w e d i n t h e b l e n d - S t e p s i z e f o r t h e r u n The C o a l B l e n d i n g Model Pg 48 The CANMET C o a l D a t a M a n i p u l a t i o n b l e n d i n g p r o g r a m r e q u i r e s a l l w a s h a b i l i t y d a t a s u b f i l e s t o c o n t a i n t h e same number o f f l o a t - s i n k c u t s w i t h mass %, a s h %, and t h e same s u l p h u r , B.T.U., a n d / o r m o i s t u r e o p t i o n s . When f i l e s c o n t a i n i n g u n e q u a l d a t a p o i n t s must be u s e d , t h e y must be m o d i f i e d t o c o n t a i n i d e n t i c a l numbers o f d a t a p o i n t s and o p t i o n v a l u e s . The s e c o n d s e t o f i n p u t , a s o u t l i n e d i n T a b l e I I I , i s t h e Model C o n s t r a i n t s . T h i s i n p u t s e t s up t h e amount o f d a t a f i l e s p a c e r e q u i r e d , c o n t r o l s c o u n t e r s i n t h e d i f f e r e n t p r o g r a m s , and s e t s q u a l i t y s p e c i f i c a t i o n s f o r t h e f i n a l p r o d u c t . I n p u t o f t h e number o f seams, number o f w a s h a b i l i t y s i z e f r a c t i o n s , and t h e name o f w a s h a b i l i t y d a t a f i l e s a r e e s s e n t i a l f o r s e t t i n g up memory s p a c e , l o c a t i n g p r o p e r d a t a f i l e s , and s e t t i n g up c o u n t e r s t h r o u g h o u t t h e C o a l B l e n d i n g M o d e l . The r e q u i r e d c l e a n c o a l a s h i s t h e most i m p o r t a n t c o n s t r a i n t a f f e c t i n g t h e r e s u l t s o f t h e s i m u l a t i o n m o d e l . T h i s v a r i a b l e i s t h e t a r g e t v a l u e f o r t h e s i m u l a t i o n p r o g r a m . The CANMET C o a l D a t a M a n i p u l a t i o n model was s e t up s u c h t h a t e a c h c l e a n i n g u n i t i s c l e a n e d t o t h e same c l e a n c o a l a s h l e v e l . Some e x p e r t s f e e l t h a t f o r o p t i m a l c l e a n i n g p e r f o r m a n c e e a c h c l e a n i n g u n i t s h o u l d c l e a n t o t h e same e l e m e n t a r y a s h l e v e l (R.X. Rong and G . J . Lyman) ( 2 3 ) . T h i s t h e o r y was n o t t e s t e d as The C o a l B l e n d i n g Model Pg 49 p a r t o f t h i s t h e s i s , a s t h e m o d i f i c a t i o n w o u l d have t o be made t o t h e c o a l p l a n t s i m u l a t i o n p r o g r a m . The S u l f u r , B.T.U, C a l o r i f i c V a l u e , and Y i e l d C o n s t r a i n t s do n o t a f f e c t t h e o p e r a t i o n o f t h e p l a n t s i m u l a t i o n model, b u t a r e u s e d as a s e l e c t i o n p r o c e s s . B l e n d s w h i c h f a i l t o meet t h e r e q u i r e d c o n s t r a i n t s a r e n o t s a v e d , t h u s a r e n o t u s e d i n d e t e r m i n i n g t h e b e s t c o a l b l e n d i n g c o e f f i c i e n t v a l u e s . The C l e a n i n g E q u i p m e n t R e l a t i v e D e n s i t y C o n s t r a i n t l i m i t s t h e o p e r a t i n g r a n g e s f o r t h e d i f f e r e n t c l e a n i n g e q u i p m e n t . I f t h e r e q u i r e d r e l a t i v e d e n s i t y t o a c h i e v e t h e d e s i r e d c l e a n c o a l a s h were t o o h i g h o r low, t h e r u n w o u l d be d i s c o n t i n u e d and a new b l e n d t r i e d . The P l a n t S i m u l a t i o n P r ogram must be s e t up t o a t t e m p t t o match t h e o p e r a t i o n o f t h e e x i s t i n g p l a n t t o be m o d e l e d . Some modern s i m u l a t i o n p r o g r a m s a r e v e r y d e t a i l e d . They n o t o n l y have m o d e l s f o r a l l t h e p r o c e s s e q u i p m e n t , b u t a l s o t a k e i n t o a c c o u n t w a t e r a d d i t i o n s . A good model i s s e t up t o match t h e e x i s t i n g p r o c e s s and c o n s i s t e n t l y p r o d u c e s r e s u l t s t h a t match t h e e x i s t i n g p l a n t . The C o a l B l e n d i n g Model Pg 50 The t h i r d t y p e o f i n p u t c o n t r o l s t h e o p e r a t i o n o f t h e B l e n d G e n e r a t i n g R o u t i n e ( o r B l e n d G e n e r a t i o n P r o g r a m ) . The f i r s t s e t o f d a t a i n t h i s r o u t i n e i s t h e P e r c e n t i l e B l e n d i n g Range f o r e a c h seam i n t h e b l e n d . The d e f a u l t f o r t h i s i n p u t i s "0,100", o r a l l p e r c e n t i l e r a t i o s between 0 % and 100 %. T h i s i n p u t a l l o w s t h e programmer t o l i m i t t h e b l e n d i n g r a n g e . L i m i t i n g t h e r a n g e o f b l e n d i n g m i n i m i z e s t h e number o f r u n s r e q u i r e d f o r e a c h t r i a l and s a v e s computer t i m e . The mine p l a n may l i m i t t h e p o s s i b l e b l e n d i n g r a t i o s , o r a more d e t a i l e d s t u d y may be r e q u i r e d u s i n g a t i g h t e r l i m i t on b l e n d i n g r a t i o s . A s e c o n d s e t o f d a t a i n t h e B l e n d G e n e r a t i n g R o u t i n e i s t h e P e r c e n t i l e S t e p S i z e I n c r e m e n t , w h i c h a l s o c o n t r o l s t h e number o f b l e n d s t o be r u n i n one t r i a l . F o r example, i f f o u r seams w i t h t h r e e s i z e f r a c t i o n s were t o be b l e n d e d , w i t h no c o n s t r a i n t s on t h e P e r c e n t i l e B l e n d i n g R a t i o s and u s i n g a u n i t s t e p s i z e , t h e n 4,598,126 d i f f e r e n t b l e n d s w o u l d r e q u i r e e v a l u a t i o n t o c o m p l e t e t h e t r i a l . I f t h e c o n s t r a i n t s a r e s u c h t h a t e a c h b l e n d q u a l i f i e s t o be r u n t h r o u g h t h e m o d el, t h e n t h e p r o g r a m c o u l d t a k e up t o 12 d a y s t o c o m p l e t e u s i n g t h e H e w l e t t P a c k a r d m i c r o c o m p u t e r . A n o r m a l p r o g r a m r u n o f f o u r seams w i t h t h r e e s i z e f r a c t i o n s , u s i n g a s t e p s i z e o f 10, r e q u i r e s a b o u t 30 m i n u t e s f r o m b l e n d s e l e c t i o n i n p u t s u n t i l t h e p r i n t i n g o f r e s u l t s . The C o a l B l e n d i n g Model Pg 51 The B l e n d G e n e r a t i o n P rogram i s d e l i b e r a t e l y d e s i g n e d t o d e t e r m i n e c o a l b l e n d i n g c o e f f i c i e n t v a l u e s f o r d i f f e r e n t b l e n d i n g r a t i o s w i t h i n a f i x e d g r i d p a t t e r n . The g r i d i s c o n t r o l l e d by t h e b l e n d s e l e c t i o n i n p u t , t h e r e f o r e t h e programmer c a n a d j u s t t h e g r i d t o s u i t i m m e d i a t e r e q u i r e m e n t s . T h i s method was c h o s e n o v e r a s i n g l e p o i n t s e a r c h r o u t i n e , a s an i m p r o v e d u n d e r s t a n d i n g o f t h e e f f e c t s o f v a r y i n g b l e n d s on p l a n t y i e l d i s t h u s o b t a i n e d . T h i s i n f o r m a t i o n shows f e a s i b l e b l e n d i n g r e g i o n s , r a t h e r t h a n a s i n g l e p o i n t w h i c h may be i m p r a c t i c a l . MODEL OUTPUT The C o a l B l e n d i n g Model r e q u i r e s a r o u t i n e t o s t o r e t h e r e s u l t s t h a t meets t h e p r e v i o u s l y d i s c u s s e d model c o n s t r a i n t s as e a c h b l e n d i s r u n t h r o u g h t h e p l a n t s i m u l a t i o n p r o g r a m . Once a l l t h e r e q u i r e d b l e n d s have been r u n , a s o r t i n g r o u t i n e r a n k s t h e r e s u l t s i n d e s c e n d i n g o r d e r , w i t h t h e b l e n d h a v i n g t h e h i g h e s t C o a l B l e n d i n g C o e f f i c i e n t l i s t e d f i r s t . T a b l e s IV, V, and V I , when combined, a r e a t y p i c a l c o a l b l e n d i n g model p r i n t o u t . I n t h e f i r s t s e c t i o n o f T a b l e IV, e a c h seam i s a s s i g n e d a Type Number, w h i c h i s u s e d f o r b l e n d i d e n t i f i c a t i o n l a t e r i n t h e p r i n t o u t . E a c h s i z e f r a c t i o n , i t s r e s p e c t i v e c l e a n i n g u n i t t y p e , and t h e w e i g h t p e r c e n t a g e o f t h e t o t a l s ample c o n t a i n e d i n t h e s i z e f r a c t i o n a r e a l s o l i s t e d . TABLE I V . SAMPLE MODEL INPUTS Type # Seam Name Si z e F r a c t i o n C UNIT '/. Weight y. Minimum X Maximum 1 Coal fl +12.7 mm 12.7.X 0.6 mm - 0.6 mm HMB HMC 35.00 48.25 16.75 10 90 2 CoalB +12.7 mm 12.7 X 0.6 mm — 0.6 mm HMB HMC 59.58 32.98 7.68 20 80 3 CoalC +12.7 mm 12.7 X 0.6 mm - 0.6 mm HMB HMC 42.28 47.68 10.20 30 70 4 Coal D +12.7 mm 12.7 X 0.6 mm - 0.6 mm HMB HMC 45.58 43.50 11.88 10 40 Clean Coal fish • S u l f u r minimum a S p e c i f i c G r a v i t y min. The Step S i z e • 8.00 -1.00 1.28 10.86 Maximum * Maximum • 2.40 1.90 The C o a l B l e n d i n g Model Pg 53 The f i n a l two c o l u m n s i n t h e f i r s t s e c t i o n g i v e t h e minimum and maximum p e r c e n t i l e v a l u e s t h a t e a c h seam c a n c o n t r i b u t e t o t h e b l e n d . The s e c o n d s e c t i o n o f T a b l e IV l i s t s some o f t h e i m p o r t a n t o p e r a t i n g c o n s t r a i n t s , i n c l u d i n g t h e T a r g e t C l e a n C o a l A s h , t h e S u l f u r C o n s t r a i n t Range, t h e S p e c i f i c G r a v i t y Range, and t h e B l e n d i n g R a t i o S t e p - s i z e . The t h i r d s e c t i o n o f t h e p r i n t o u t , T a b l e V, l i s t s t h e C l e a n i n g U n i t R e l a t i v e D e n s i t y , Y i e l d and Q u a l i t y R e s u l t s f r o m t h e P l a n t S i m u l a t i o n Model f o r e a c h s i z e f r a c t i o n o f e a c h i n d i v i d u a l seam i n t h e b l e n d a f t e r b e i n g c l e a n e d t o t h e t a r g e t a s h . The o v e r a l l i n d i v i d u a l seam y i e l d , a s h , and s u l f u r c o n t e n t a r e a l s o l i s t e d . The C o a l B l e n d i n g C o e f f i c i e n t i s a l w a y s z e r o f o r t h i s s e c t i o n by i t s d e f i n i t i o n . F o r t h i s s e c t i o n o n l y , i f a c l e a n i n g u n i t i s u n a b l e t o o p e r a t e a t t h e r e q u i r e d r e l a t i v e d e n s i t y t o a c h i e v e t h e t a r g e t a s h , t h e model a c c e p t s t h e p r o d u c t p r o d u c e d a t maximum o r minimum r e l a t i v e d e n s i t y . T a b l e V I , t h e f o u r t h and f i n a l s e c t i o n o f t h i s p r i n t o u t , l i s t s t h e r e s u l t s o f e a c h b l e n d i n t h e same f o r m a t a s f o r t h e i n d i v i d u a l seams. The b l e n d s a r e r a n k e d i n d e s c e n d i n g o r d e r by t h e v a l u e o f t h e i r t o t a l C o a l B l e n d i n g C o e f f i c i e n t s , s t a r t i n g The C o a l B l e n d i n g Model Pg 54 w i t h t h e b l e n d h a v i n g t h e h i g h e s t C o a l B l e n d i n g C o e f f i c i e n t . S i n c e t h e CANMET C o a l D a t a M a n i p u l a t i o n p r o g r a m s d i d n o t have a model f o r f r o t h f l o t a t i o n , a l l -0.6 m i l l i m e t e r f r a c t i o n s were assumed t o c l e a n t o t h e same c l e a n c o a l a s h , and p r o d u c e t h e same y i e l d . The amount t o w h i c h t h i s a s s u m p t i o n w i l l d i s t o r t t h e f i n a l r e s u l t s i s n o t known. TABLE V. SAMPLE BATCHIHG RESULTS tt T 1 : T 2 : T 3 : T 4 S I Z E F R A C T I O N C L E A N I N G U N I T M O D E L S . G . M O D E L Y I E L D M O D E L A S H M O D E L S U L F U R M O D E L F A C T O R 1 0 9 : 8 : 0 : 0 • 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm T O T A L HMB HMC 1 . 5 4 6 1 . 8 9 3 0 . 0 0 0 0 . 0 0 0 7 2 . 12 7 5 . 8 2 8 0 . 0 0 7 5 . 2 3 8 . 0 0 0 7 . 7 2 6 8 . 0 0 0 7 . 8 6 7 . 6 1 3 . 6 2 4 . 6 0 8 . 6 1 6 Z E R O Z E R O Z E R O Z E R O 0:100:0:0 • 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm T O T A L HMB HMC 1 . 3 6 3 1 . 6 7 1 0 . 0 0 0 0 . 0 0 0 3 5 . 3 8 8 1 . 3 0 8 0 . 0 0 5 3 . 8 8 7 . 9 9 7 8 . 0 0 0 8 . 0 0 0 7 . 9 9 9 1 . 2 6 5 1 . 3 8 4 1 . 4 0 0 1 . 3 3 9 Z E R O Z E R O Z E R O Z E R O 0:0:100:0 + 1 2 . ' ? mm 1 2 . 7 X 0 . 6 mm 0 • S ffiin T O T A L HMB HMC 1 . 4 5 1 1 . 5 5 6 0 . 0 0 0 0 . 0 0 0 6 9 . 18 8 5 . 2 1 8 0 . 0 0 7 7 . 9 1 8 . 0 0 1 8 . 0 0 0 8 . 0 0 0 8 . 0 0 0 . 9 4 5 . 9 8 6 . 9 8 0 . 9 2 0 Z E R O Z E R O Z E R O Z E R O 0:0:0:100 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm T O T A L HMB HMC 1 . 4 2 8 1 . 8 9 7 0 . 0 0 0 0 . 0 0 0 8 4 . 5 4 9 2 . 4 9 8 0 . 0 0 8 7 . 5 0 7 . 9 9 9 7 . 4 4 3 8 . 0 0 0 7 . 7 4 4 1 . 9 7 6 2 . 8 0 6 1 . 2 0 0 1 . 9 1 2 Z E R O Z E R O Z E R O Z E R O TABLE VI. SAMPLE COAL BLENDING MODEL RESULTS T i : T 2 : T 3 : T 4 S I Z E F R A C T I O N C L E A N I N G U N I T M O D E L S . G . M O D E L Y I E L D M O D E L A S H M O D E L S U L F U R M O D E L F A C T O R , 1 I O : 5 0 : 3 0 : 10 + 1 2 . 7 nm . 1 2 . 7 X 0 . 6 mm - 0 . 6 mm T O T A L H U B H M C 1 . 4 2 5 1 . 6 4 4 0 . 0 0 0 0 . 0 0 0 5 6 . 6 6 8 3 . 6 5 8 0 . 0 0 6 9 . 6 8 8 . 0 0 0 8 . 0 0 0 8 . 0 0 0 8 . 0 0 0 -i 1 . 2 8 5 1. 179 1. 150 1.-230 5 . 72 . 3 8 0 . 0 0 3 . 0 9 2 19: 4 0 : 3 0 : 28 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm ** Q • 6 flint T O T A L H M B H M C 1 . 4 2 8 1 . 6 6 3 0.000 0.000 6 0 . 6 5 8 5 . 0 4 8 0 . 0 0 7 2 . 5 7 8 . 0 0 0 7 . 9 9 5 8 . 0 0 0 7 . 9 9 8 1. 3 7 2 1 . 2 5 1 1. 130 1 . 2 9 8 4 . 74 . 6 4 0 . 0 0 2 . 6 3 3 10: 4 0 : 4 0 : 10 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm T O T A L H M B H M C 1 . 4 3 0 1 . 6 2 8 0 . 0 0 0 0 . 0 0 0 5 9 . 2 0 8 4 . 0 1 8 0 . 0 0 7 1 . 5 2 7 . 9 9 7 8 . 0 0 0 8 . 0 0 0 7 . 9 9 8 1.25fc i . 'yts 1 . 1 0 0 1. 186 4 . 7 9 . 36 0 . 0 0 2 . 5 4 4 2 0 : 4 0 : 3 0 : 10 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm T O T A L H M B H M C 1 . 4 3 1 1 . 6 6 4 0 . 0 0 0 0.000 5 9 . 10 8 3 . 10 8 0 . 0 0 7 1 . 2 5 7 . 9 9 8 7 . 9 9 6 8 . 0 0 0 7 . 9 9 7 1 . 2 4 2 1 . 1 1 3 1 . 0 7 8 1. 170 4 . 72 . 5 4 0 . 0 0 2 . 5 3 5 10: 3 0 : 3 0 : 30 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm T O T A L H M B H M C 1 . 4 3 0 1 . 6 8 2 0 . 0 0 0 0 . 0 0 0 6 4 . 8 3 8 6 . 2 8 8 0 . 0 0 7 5 . 4 1 7 . 9 9 8 8 . 0 0 0 8 . 0 0 0 7 . 9 9 9 1. 451 1. 321 1. 110 1. 361 3 . 64 . 7 9 0 . 0 0 2 . 10 The C o a l B l e n d i n g Model Pg 57 SUMMARY The C o a l B l e n d i n g Model i s a c o l l e c t i o n o f p r o g r a m s w h i c h e v a l u a t e t h e e f f e c t o f d i f f e r e n t c o a l b l e n d s on o v e r a l l p l a n t y i e l d . The C o a l P l a n t S i m u l a t i o n Program i s t h e h e a r t o f t h e m o d e l , w h i l e t h e C o a l B l e n d i n g C o e f f i c i e n t a l l o w s t h e model t o r a n k t h e r e s u l t s f r o m t h e s i m u l a t i o n p r o g r a m , t h u s f o r m i n g a method f o r t h e e v a l u a t i o n o f c o a l b l e n d i n g . S i n c e e a c h r u n o f t h e s i m u l a t i o n p r o g r a m f a c i l i t a t e s t h o u s a n d s o f c a l c u l a t i o n s , b l e n d s e l e c t i o n i n p u t s , a l t h o u g h n o t r e q u i r e d , a r e u s e f u l f o r c o n t r o l l i n g t h e amount o f d a t a t o be a n a l y z e d . T h i s m i n i m i z e s t h e r e q u i r e d number o f r u n s t h r o u g h t h e C o a l B l e n d i n g M o d e l , t h u s s a v i n g c o m p u t i n g t i m e . C u r r e n t l y , t h e model has o n l y b een t r i e d u s i n g t h e CANMET C o a l D a t a M a n i p u l a t i o n p r o g r a m s a s t h e p l a n t s i m u l a t i o n p r o g r a m . T h i s p r o g r a m i s u s e r - f r i e n d l y , and o n l y a l i m i t e d u n d e r s t a n d i n g o f c omputer o p e r a t i o n s i s r e q u i r e d t o u s e i t , b u t t h e v e r s i o n u s e d l a c k s a model f o r f l o t a t i o n , and d o e s n o t l e n d i t s e l f w e l l t o t h e c o m p l e t e m o d e l i n g o f a w a s h e r y p r o c e s s . O t h e r c u r r e n t s i m u l a t i o n m o d els a r e p e r h a p s b e t t e r s u i t e d f o r a c t u a l f i e l d t e s t i n g . D e s p i t e some o f t h e s h o r t f a l l s o f t h e c u r r e n t m o d e l , t h e C o a l B l e n d i n g Model has shown t h a t t h e e f f e c t s o f b l e n d i n g c a n be q u a n t i f i e d u s i n g t h e C o a l B l e n d i n g The C o a l B l e n d i n g Model Pg 58 C o e f f i c i e n t , and t h a t t h e r e i s p o t e n t i a l f o r an i n c r e a s e i n o v e r a l l p l a n t y i e l d when a c o n t r o l l e d b l e n d i n g p r o g r a m i s f o l l o w e d . The C o a l B l e n d i n g Model Pg 59 IV. COAL BLENDING MODEL APPLICATION The C o a l B l e n d i n g Model i s d e s i g n e d t o a s s i s t i n s o l v i n g c o a l b l e n d i n g p r o b l e m s by p r o v i d i n g t h e d e c i s i o n - m a k e r w i t h a l a r g e i n f o r m a t i o n b a s e on w h i c h t o make d e c i s i o n s . The model s e l e c t s b l e n d c o m b i n a t i o n s w h i c h f i r s t meet t h e g i v e n s u l f u r , a s h and s i z e c o n s t r a i n t s and t h e n p r i o r i t i z e s them f r o m t h e m a g n i t u d e o f t h e i r C o a l B l e n d i n g C o e f f i c i e n t s . T h i s s c r e e n i n g f i l t e r i n g , and r a n k i n g o f p e r t i n e n t b l e n d i n g d a t a a i d s d e c i s i o n - m a k e r s i n s e l e c t i n g t h e b e s t b l e n d i n g s t r a t e g y f o r t h e i r p a r t i c u l a r o p e r a t i o n . The model c a n be u s e d e f f e c t i v e l y f o r b o t h l o n g - and s h o r t - t e r m p l a n n i n g . S h o r t - t e r m u s e s c o u l d i n c l u d e : a) E v a l u a t i n g t h e e f f e c t o f m i n i n g a n o t h e r seam. b) I n v e s t i g a t i n g t h e c o n s e q u e n c e s o f i n t r o d u c i n g a new m i n i n g method w h i c h a l t e r t h e p l a n t f e e d s i z e d i s t r i b u t i o n ( f o r example, r e p l a c i n g s h o v e l s w i t h r i p p e r t r a c t o r - c r a w l e r s i n t h e p i t , o r c h a n g i n g t h b l a s t i n g m e t h o d ) . The C o a l B l e n d i n g Model Pg 60 c) E x p e r i m e n t i n g w i t h e q u i p m e n t c h a n g e s i n t h e m i l l . L o n g - t e r m u s e s c o u l d i n c l u d e : a) D e v e l o p i n g a m i n i n g s c h e d u l e b a s e d on o p t i m i z i n g t h e b e n e f i t s o f ROM c o a l b l e n d i n g . b) D e v e l o p i n g o p t i m u m - s i z e d p r e p l a n t s t o c k p i l e s t o m i n i m i z e r e h a n d l i n g and o p t i m i z e t h e b e n e f i t s o f ROM c o a l b l e n d i n g . To d a t e , t r i a l s u s i n g t h e model have p r o d u c e d c o a l b l e n d i n g c o e f f i c i e n t s f r o m s l i g h t l y n e g a t i v e v a l u e s up t o a 5% i n d i c a t e d y i e l d i mprovement. I n t i g h t l y c o n s t r a i n e d m o d e l s , m o d e r a t e g a i n s o f 2% a r e common. F o r mines w i t h an u n l i m i t e d s u p p l y o f c o a l and no q u a l i t y c o n t r o l c o n s t r a i n t s , o p t i m i z a t i o n o f t h i s c o e f f i c i e n t w o u l d g i v e t h e most e c o n o m i c a l b l e n d f o r a g i v e n p l a n t c o n f i g u r a t i o n , b u t a c t u a l o p e r a t i o n s w i t h r e s o u r c e and q u a l i t y r e s t r i c t i o n s must e v a l u a t e t h e model o u t p u t t o d e t e r m i n e t h e b e s t o p e r a t i n g b l e n d w i t h i n t h e s e l i m i t s . Thus f o r most c o a l m i n e s , t h e b l e n d w i t h t h e h i g h e s t C o a l B l e n d i n g C o e f f i c i e n t i s n o t n e c e s s a r i l y t h e b e s t c h o i c e , b u t t h e i n f o r m a t i o n a v a i l a b l e f r o m t h e C o a l B l e n d i n g Model a l l o w s a s o u n d e c o n o m i c a l a l t e r n a t i v e t o be s e l e c t e d . The C o a l B l e n d i n g Model Pg 61 The d e t e r m i n a t i o n o f a f e a s i b l e b l e n d i n g r a n g e , w i t h i t s optimum v a l u e s , a l l o w s a mine t o s e t a s t a b l e l o n g - t e r m m i n i n g s c h e d u l e w h i c h accommodates t h e p r e p a r a t i o n p l a n t needs w h i l e p r o v i d i n g f o r a c o s t e f f e c t i v e s h o r t - t e r m mine p l a n . EXAMPLE PROBLEMS AND DATA EVALUATION To a s s i s t i n d e s c r i b i n g and e v a l u a t i n g t h e r e s u l t s f r o m t h e C o a l B l e n d i n g M o d e l , t h r e e example p r o b l e m s w i l l be d i s c u s s e d . A l l t h r e e e x a mples were r u n u s i n g t h e t h e same c l e a n i n g e q u i p m e n t , t h e same seam s i z e f r a c t i o n s , and a c t u a l w a s h a b i l i t y d a t a f r o m a c o a l d e p o s i t i n B r i t i s h C o l u m b i a . I n o r d e r t o g e t a c o m p l e t e p i c t u r e o f t h e v a r i a b i l i t y o f C o a l B l e n d i n g C o e f f i c i e n t v a l u e s , no c o n s t r a i n t s were p u t on t h e c l e a n c o a l p r o d u c t , e x c e p t f o r t h e r e q u i r e d t a r g e t a s h . T h e s e e x amples a r e a l s o t y p i c a l o f r e s u l t s o b t a i n e d f o r o t h e r c o a l d e p o s i t s i n B r i t i s h C o l u m b i a . The C o a l P l a n t S i m u l a t i o n p r o g r a m s e t - u p f o r a l l t h r e e example p r o b l e m s c o n s i s t e d o f t h r e e s t a g e c l e a n i n g : a) a h e a v y medium b a t h (HMB) t r e a t i n g t h e p l u s 12.7 mm m a t e r i a l b) a h e a v y medium c y c l o n e (HMC) t r e a t i n g t h e minus 12.7 t o p l u s 0.6 mm f r a c t i o n The C o a l B l e n d i n g Model Pg 62 c) f l o t a t i o n was assumed f o r t h e minus 0.6 mm f r a c t i o n , b u t s i n c e t h e CANMET C o a l D a t a M a n i p u l a t i o n Programs u s e d do n o t have t h e c a p a b i l i t y t o s i m u l a t e a f l o t a t i o n c e l l , an a r b i t r a r y y i e l d was a s s i g n e d f o r e a c h r u n . ( I f t h e a c t u a l y i e l d f o r t h e s e seams were known, t h e n c o r r e c t v a l u e s c o u l d have been u s e d i n t h e c a l c u l a t i o n s . ) The a c t u a l w a s h a b i l i t y d a t a f o r t h e seams u s e d i n t h e example p r o b l e m s i s shown i n A p p e n d i x B. The q u a l i t y o f t h e seams v a r y m o d e r a t e l y , w i t h seams A and D b e i n g v e r y c l e a n , w h i l e seams B and C a r e r e l a t i v e l y d i r t y . Example P r o b l e m One : Two Seam B l e n d T h i s example p r o b l e m e v a l u a t e s t h e b l e n d i n g p o t e n t i a l f o r a p r e p a r a t i o n p l a n t w a s h i n g two seams w i t h m o d e r a t e l y v a r i e d w a s h a b i l i t y p r o p e r t i e s . Seams A and B were c h o s e n f o r t h i s t r i a l , b e c a u s e o f t h e i r d i f f e r e n c e i n w a s h a b i l i t y a n a l y s i s . The assumed i n p i t r e s e r v e f o r t h i s example i s t e n m i l l i o n t o n n e s f o r e a c h seam. The t a r g e t a s h was s e t a t s e v e n p e r c e n t f o r t h e g r a v i t y s e p a r a t i o n c i r c u i t s , w h i l e t h e f l o t a t i o n c i r c u i t was assumed t o p r o d u c e a p r o d u c t c o n t a i n i n g e i g h t p e r c e n t a s h w i t h a y i e l d o f e i g h t y p e r c e n t f o r a l l seams and b l e n d s . A l l p o t e n t i a l b l e n d s were r u n t h r o u g h t h e C o a l B l e n d i n g M o d e l , u s i n g a s t e p - s i z e o f f i v e . The C o a l B l e n d i n g Model Pg 64 The C o a l B l e n d i n g Model p r i n t o u t f o r t h i s example p r o b l e m i s l i s t e d i n A p p e n d i x C. T h i s i n c l u d e s t h e model i n p u t , b a t c h i n g r e s u l t s and a l l t h e p o t e n t i a l t w e n t y - o n e model r e s u l t s . A b l e n d o f 65 p e r c e n t Seam A and 35 p e r c e n t Seam B had t h e h i g h e s t C o a l B l e n d i n g C o e f f i c i e n t o f o v e r f o u r . F i g u r e 7 compares t h e C o a l B l e n d i n g C o e f f i c i e n t v a l u e s t o t h e p e r c e n t a g e o f seam A i n t h e b l e n d . The i n f l e c t i o n p o i n t a t t h e maximum C o a l B l e n d i n g C o e f f i c i e n t i s i m p o r t a n t f o r two r e a s o n s . T h i s p o i n t i s a s s o c i a t e d w i t h t h e b l e n d t h a t g i v e s t h e h i g h e s t i n c r e a s e i n y i e l d o v e r b a t c h i n g . U s i n g t h e y i e l d t o t a l s f o r t h e b a t c h i n g s e c t i o n o f t h e model p r i n t o u t , t h e e x p e c t e d y i e l d f o r seam A w o u l d be 72.1 %, w h i l e seam B w o u l d be c o n s i d e r a b l y l o w e r a t 41.22 %. B a s e d on t h e s e b a t c h i n g r e s u l t s t h e e x p e c t e d a v e r a g e y i e l d o f a b l e n d c o n t a i n i n g 65% seam A and 35% seam B w o u l d be [.65*72.1 + .35*41.2 ], 61.3% compared w i t h t h e a c t u a l C o a l P l a n t S i m u l a t i o n P rogram r e s u l t o f 65.4%. The d i f f e r e n c e between t h e a c t u a l b l e n d i n g r e s u l t s and t h e e x p e c t e d r e s u l t s b a s e d on t h e b a t c h i n g v a l u e s g i v e s t h e v a l u e o f t h e C o a l B l e n d i n g C o e f f i c i e n t f o r t h i s b l e n d . An i n c r e a s e i n y i e l d f r o m 61.3 % t o 65.4 %, f o r a p l a n t c u r r e n t l y p r o d u c i n g one m i l l i o n t o n n e s p e r y e a r w o u l d i n c r e a s e a n n u a l p r o d u c t i o n by 66,880 t o n n e s . T h i s e x t r a p r o d u c t i o n w o u l d come f r o m c o a l t h a t i s c u r r e n t l y b e i n g d i s c a r d e d t o t h e t a i l i n g s . The C o a l B l e n d i n g Model Pg 65 T h i s g a i n c a n o n l y be a c h i e v e d i f t h e p l a n t i n t h i s example were b a t c h i n g p r e v i o u s l y and t h e c o a l r e s e r v e s a l l o w e d f o r c o n s t a n t b l e n d i n g a t 65 % seam A, and 35 % seam B. F o r most c a s e s , a s i s t h e c a s e i n t h i s example, t h e a c t u a l i n - p i t r e s e r v e s w i l l n o t match t h e optimum b l e n d i n g r a t i o . F o r t h e s e c a s e s , t h e i n f l e c t i o n p o i n t a s s o c i a t e d w i t h t h e maximum C o a l B l e n d i n g C o e f f i c i e n t i s s t i l l o f i m p o r t a n c e . The i n f l e c t i o n p o i n t d i v i d e s F i g u r e 7 i n t o two d i s t i n c t s e c t i o n s — zone A and zone B. I n example 1, t h e i n - p i t r e s e r v e r a t i o f a l l s i n t o zone A. To i l l u s t r a t e t h e p o t e n t i a l b e n e f i t s o f b l e n d i n g , and d e m o n s t r a t e t h e i m p o r t a n c e o f t h e i n f l e c t i o n p o i n t , t h r e e f o l l o w i n g b l e n d i n g s c e n a r i o s were i n v e s t i g a t e d . The t o t a l c o a l p r o d u c t i o n f o r e a c h c a s e i s shown i n T a b l e V I I . 1. B a t c h i n g 2. B l e n d i n g a t t h e maximum C o a l B l e n d i n g C o e f f i c i e n t u n t i l seam A i s d e p l e t e d , and t h e n u s i n g up seam B 3. A l w a y s b l e n d i n g a t t h e r a t i o o f t h e i n - p i t r e s e r v e s . The C o a l B l e n d i n g Model Pg 66 TABLE V I I . COAL PRODUCTION FOR EXAMPLE ONE S c e n a r i o T o t a l Tonnes o f C o a l R e c o v e r e d 1 11330000 t o n n e s 2 11960900 t o n n e s 3 11576000 t o n n e s By a d o p t i n g b l e n d i n g S c e n a r i o Number Two, t h i s mine w o u l d be m a x i m i z i n g t h e i r c l e a n c o a l p r o d u c t i o n f o r t h e g i v e n p l a n t c o n f i g u r a t i o n and c l e a n c o a l q u a l i t y c o n s t r a i n t s . T h i s s c e n a r i o t a k e s f u l l a d v a n t a g e o f t h e maximum b e n e f i t s o f b l e n d i n g t h a t a r e a s s o c i a t e d w i t h t h e w a s h e r y c o n f i g u r a t i o n and t h e c o a l seam c h a r a c t e r i s t i c s . S c e n a r i o One, b a t c h i n g , i s t h e b e s t example o f f e e d i n g t h e p r e p a r a t i o n p l a n t b l e n d s f r o m t h e e x t r e m e ends o f z o n e s A and B, t h u s d i s r e g a r d i n g t h e i m p o r t a n c e o f t h e i n f l e c t i o n p o i n t . I t i s n o t c o i n c i d e n c e t h a t S c e n a r i o One a l s o p r o d u c e s t h e l e a s t amount o f t o t a l p r o d u c t i o n . A l t h o u g h m a x i m i z i n g y i e l d i s a l w a y s f o r e m o s t i n t h e mind o f management, t h e C o a l B l e n d i n g Model c a n p r o v i d e some g u i d e l i n e s f o r t h e i n - p i t b l e n d i n g p r o g r a m t h a t w i l l r e c e i v e The C o a l B l e n d i n g Model Pg 67 some b e n e f i t f r o m a b l e n d i n g p r o g r a m , y e t s t i l l a l l o w mine p l a n n e r s some f l e x i b i l i t y i n t h e i r p l a n s . S c e n a r i o F o u r w o u l d p r o d u c e b l e n d s f r o m o n l y one s i d e o r s e c t i o n o f t h e i n f l e c t i o n p o i n t o r a x e s . U s i n g Example One, t h e mine p l a n n e r w o u l d have t o work w i t h b l e n d s i n zone A, as t h e i n - p i t r e s e r v e s f a l l on t h i s s i d e o f t h e i n f l e c t i o n p o i n t . Any b l e n d w o u l d be a c c e p t a b l e as l o n g as t h e b l e n d c o n t a i n e d 65% o r l e s s o f seam A. The r e s u l t s o f s u c h a p r o g r a m w i l l a l w a y s be somewhere between t h o s e o f S c e n a r i o s Two and T h r e e . The s t r a t e g y f o r S c e n a r i o F o u r i s v e r y s i m p l e - - a s l o n g as t h e b l e n d i n g p r o g r a m i s w i t h i n t h e zone t h a t c o n t a i n s t h e i n - p i t r e s e r v e s , t h e m a j o r g a i n s f r o m b l e n d i n g w i l l be r e a l i z e d , w h i l e s t i l l a l l o w i n g t h e f o r some f l e x i b i l i t y by mine p l a n n e r s t o m i n i m i z e m i n i n g c o s t s . T h i s s t r a t e g y w i l l l i k e l y p r o d u c e t h e g r e a t e s t p r o f i t s o v e r a l 1 . F o r two seam b l e n d s , a n o n - l i n e a r g r a p h i n d i c a t e s t h a t an optimum b l e n d i n g s t r a t e g y e x i s t s . I f t h e b r a n c h o f t h e g r a p h , c o n t a i n i n g t h e o v e r a l l i n - p i t b l e n d i n g r a t i o i s c o n c a v e , as i n zone A, t h e n t h e optimum b l e n d i n g s c e n a r i o i s n o r m a l l y b l e n d i n g a t maximum c o a l b l e n d i n g c o e f f i c i e n t u n t i l Seam A i s e x h a u s t e d . I f t h e b r a n c h o f t h e g r a p h i s c o n v e x as i n zone B, t h e n t h e optimum s o l u t i o n i s u s u a l l y b l e n d i n g a t t h e i n - p i t r e s e r v e r a t i o . F o r g r a p h s t h a t have a n e a r l i n e a r b r a n c h , t h r o u g h t h e z one c o n t a i n i n g t h e i n p i t b l e n d i n g r a t i o , t h e r e s u l t s w i l l be The C o a l B l e n d i n g Model Pg 68 i d e n t i c a l f o r c a s e s two and t h r e e . I n f a c t , so l o n g a s t h e b l e n d i n g r a t i o f a l l s w i t h i n t h e p r o p e r zone, t h e f i n a l t o n n e s o f c l e a n c o a l p r o d u c e d w o u l d be i d e n t i c a l . Example P r o b l e m Two: T h r e e Seam B l e n d "1" T h i s example p r o b l e m e v a l u a t e s t h e b l e n d i n g p o t e n t i a l f o r a p r e p a r a t i o n p l a n t w a s h i n g t h r e e seams w i t h m o d e r a t e l y v a r i e d w a s h a b i l i t y p r o p e r t i e s . Seams A, C,and D were c h o s e n f o r t h i s t r i a l , w i t h assumed p r o v e n i n p i t r e s e r v e s o f t w e l v e m i l l i o n t o n n e s f o r seam A, t w e l v e m i l l i o n t o n n e s f o r seam C and s i x t e e n m i l l i o n t o n n e s f o r seam D. The t a r g e t a s h was s e t a t s e v e n and one h a l f p e r c e n t f o r t h e g r a v i t y s e p a r a t i o n c i r c u i t s , w h i l e t h e f l o t a t i o n c i r c u i t was assumed t o p r o d u c e a p r o d u c t c o n t a i n i n g e i g h t p e r c e n t a s h w i t h a y i e l d o f e i g h t y p e r c e n t f o r a l l seams and b l e n d s . A l l p o t e n t i a l b l e n d s were r u n t h r o u g h t h e C o a l B l e n d i n g M o d e l , u s i n g a s t e p - s i z e o f t e n . A r e s t r i c t e d s e c o n d r u n was p e r f o r m e d a t a s t e p s i z e o f f i v e t o d e v e l o p b e t t e r c o n t o u r l i n e s a r o u n d t h e b l e n d w i t h t h e maximum C o a l B l e n d i n g C o e f f i c i e n t . The C o a l B l e n d i n g Model p r i n t o u t f o r t h e f i r s t r u n o f t h i s example p r o b l e m and t h e t o p 14 b l e n d s o f t h e s e c o n d r u n a r e l i s t e d i n A p p e n d i x D. T h i s i n c l u d e s t h e model i n p u t , b a t c h i n g r e s u l t s , s i x t y - t h r e e o f t h e p o t e n t i a l s i x t y - s i x model r e s u l t s The C o a l B l e n d i n g Model Pg 69 f r o m t h e f i r s t r u n , and t h e t o p f o u r t e e n o f two h u n d r e d and t h i r t y - o n e model r e s u l t s f r o m r u n two. F i g u r e s 8, 9 and 10 a r e s i m i l a r g r a p h s o f t h e C o a l B l e n d i n g C o e f f i c i e n t c o n t o u r l i n e s , e x t r a p o l a t e d f r o m a l l d a t a p o i n t s g e n e r a t e d by t h e two r u n s o f t h e C o a l B l e n d i n g M o d e l . The f i r s t g r a p h , F i g u r e 8, compares C o a l B l e n d i n g C o e f f i c i e n t r e s u l t s t o v a r i a t i o n s i n t h e p e r c e n t a g e o f seams A and B i n t h e b l e n d . The c e n t e r l i n e drawn t h r o u g h t h e i n f l e c t i o n p o i n t s o f t h e c o n t o u r l i n e s d i v i d e s t h e g r a p h i n t o two d i s t i n c t s e c t i o n s . As i n t h e f i r s t example, we w i l l c a l l t h e s e z o n e s A and B. F i g u r e s 9 and 10 compare C o a l B l e n d i n g C o e f f i c i e n t r e s u l t s t o v a r i a t i o n s i n t h e p e r c e n t a g e o f seams A and C, and seams C and D r e s p e c t i v e l y . A l l t h r e e g r a p h s p r e s e n t i d e n t i c a l r e s u l t s , b u t f r o m a d i f f e r e n t v i e w . By c o m b i n i n g t h e s e t h r e e f i g u r e s , a t h r e e - d i m e n s i o n a l model c a n be g e n e r a t e d . The r e g i o n w i t h i n t h e c o n t o u r l i n e t h a t i n d i c a t e s a C o a l B l e n d i n g C o e f f i c i e n t o f 4.5 r e p r e s e n t s t h e h i g h e s t y i e l d i mprovement o v e r b a t c h i n g . A b l e n d o f 20:15:65 o f seams A, C, and D r e s p e c t i v e l y p r o d u c e d t h e h i g h e s t C o a l B l e n d i n g C o e f f i c i e n t o f 4.51. As n o t e d i n Example P r o b l e m One, t h e maximum C o a l B l e n d i n g C o e f f i c i e n t v a l u e i s i m p o r t a n t , b u t i s n o t n e c e s s a r i l y an optimum o p e r a t i n g p o i n t . Percentage of Seam A i n the Blend Figure 8. Three Seam Model Results: Example Two Coal Blending Coefficient Contours No. 1 £ © 90. 0 10 30 50 70 Percentage of Seam A i n the Blend Figure 9. Three Seam Model Results: Example Two Coal Blending Coefficient Contours No. 2 90. fl 0 V A: 1.0 70 a • r l fl 0 w o 0 to a 0 o 0 au 50. 30 10 0 fO ZONE B 30 50 cr A O o tt n s a. H-B 09 X O a n 4.5 70 Percentage of Seam D i n the Blend F i g u r e 1 0 . Three Seam Model R e s u l t s : Example Two Coal B l e n d i n g C o e f f i c i e n t Contours Ho. 3 99 to The C o a l B l e n d i n g Model Pg 73 c o n f i r m t h i s s t a t e m e n t . The C o a l B l e n d i n g C o e f f i c i e n t v a l u e s f o r a two seam b l e n d a t t h i s t a r g e t a s h and u s i n g t h e d e s c r i b e d u n i t o p e r a t i o n s c o m b i n i n g seams A and C a r e a l l z e r o o r s l i g h t l y n e g a t i v e . T h e r e f o r e , seams A and C c o u l d be c o n s i d e r e d a s one seam, t h u s s i m p l i f y i n g t h i s p r o b l e m down t o a two seam b l e n d . As i n Example One, t h e f o l l o w i n g t h r e e s c e n a r i o s , shown i n T a b l e V I I I , a r e e v a l u a t e d i n Example Two t o d e t e r m i n e t h e t o t a l p r o d u c t i o n f o r e a c h c a s e : 1. B a t c h i n g 2. B l e n d i n g a t t h e optimum C o a l B l e n d i n g C o e f f i c i e n t f o r as l o n g a s p o s s i b l e , and t h e n b a t c h i n g 3. B l e n d i n g a t t h e i n - p i t seam r a t i o . The r e l a t i v e l y s t r a i g h t c o n t o u r l i n e s f o u n d i n F i g u r e s 8, 9 and 10 i n d i c a t e t h a t seams A and C have s i m i l a r w a s h a b i l i t y p r o p e r t i e s , t h u s t h e r e i s no a d v a n a t a g e t o b l e n d i n g t h e s e two seams, a s d e m o n s t r a t e d i n r u n s numbered 58 t h r o u g h 63 on page 118 i n A p p e n d i x D. The C o a l B l e n d i n g Model Pg 74 TABLE V I I I . COAL PRODUCTION FOR EXAMPLE TWO S c e n a r i o B l e n d T o t a l Tonnes o f C o a l R e c o v e r e d 1. B a t c h i n g 30462000 t o n n e s 2. 20:15:65 00:100:00 100:00:00 TOTAL 20015000 t o n n e s 6299000 t o n n e s 5257000 t o n n e s 31571000 t o n n e s 3. 30:30:40 31688000 t o n n e s Of t h e above t h r e e s c e n a r i o s , number T h r e e gave t h e h i g h e s t t o t a l p r o d u c t i o n . S c e n a r i o One, b a t c h i n g , was a g a i n t h e w o r s t c h o i c e . O t h e r c o m b i n a t i o n s c a n be e a s i l y e v a l u a t e d u s i n g t h e same method a s i n t h e example p r o b l e m s . The C o a l B l e n d i n g Model Example P r o b l e m T h r e e : T h r e e Seam B l e n d "2" Pg 75 T h i s example p r o b l e m u s e s Seams A, B, C t o f o r m a t h r e e seam b l e n d . The t a r g e t a s h and f l o t a t i o n p r o d u c t a s h a r e b o t h s e t a t n i n e p e r c e n t . As i n Example Two, two r u n s were p e r f o r m e d , t h e f i r s t u s i n g a s t e p - s i z e o f t e n and t h e s e c o n d u s i n g a s t e p - s i z e o f f i v e . The C o a l B l e n d i n g Model p r i n t o u t f o r t h e s e c o n d r u n u s i n g a s t e p - s i z e o f f i v e i s i n A p p e n d i x E. T h i s p r i n t o u t i n c l u d e s t h e model i n p u t , b a t c h i n g r e s u l t s and n i n e t y - e i g h t o f t h e p o t e n t i a l two h u n d r e d and t h i r t y - o n e model r e s u l t s . F i g u r e 11 i s a g r a p h o f t h e C o a l B l e n d i n g C o e f f i c i e n t c o n t o u r l i n e s e x t r a p o l a t e d f r o m a l l d a t a p o i n t s g e n e r a t e d by t h e two r u n s o f t h e C o a l B l e n d i n g M o d e l . The r e g i o n w i t h i n t h e u n i t c o n t o u r l i n e r e p r e s e n t s t h o s e b l e n d s w h i c h g i v e t h e h i g h e s t y i e l d improvement o v e r b a t c h i n g . A b l e n d o f 40:25:35 o f seams A, B, and C r e s p e c t i v e l y p r o d u c e d t h e h i g h e s t c o a l b l e n d i n g c o e f f i c i e n t o f 1.15. As i n Examples One and Two, t h e f o l l o w i n g t h r e e s c e n a r i o s w i l l be e xamined: 1. B a t c h i n g 2. B l e n d i n g a t t h e optimum C o a l B l e n d i n g C o e f f i c i e n t f o r as l o n g a s p o s s i b l e , and t h e n f o r m i n g a two seam b l e n d and f i n a l l y a s i n g l e seam. 3. B l e n d i n g a t t h e i n - p i t seam r a t i o . The C o a l B l e n d i n g Model Pg 76 TABLE IX. COAL PRODUCTION FOR EXAMPLE THREE S c e n a r i o B l e n d T o t a l Tonnes o f C o a l R e c o v e r e d 1. B a t c h i n g 30224400 t o n n e s 2. 40:25:35 60:00:40 100:00:00 TOTAL 24419200 t o n n e s 1558000 t o n n e s 4599600 t o n n e s 30576800 t o n n e s 3. 50:20:30 30604000 t o n n e s The c o n t o u r l i n e s have a f a i r l y r e g u l a r p a t t e r n and s p a c i n g w h i c h i n d i c a t e s t h a t t h e r e i s l i t t l e t o g a i n by j u g g l i n g b l e n d i n g r a t i o s . T h i s r e s u l t i s c o n f i r m e d by t h e c l o s e r e s u l t s i n T a b l e IX between S c e n a r i o s Two and T h r e e . To c o m p l e t e t h e a n a l y s i s o f optimum b l e n d i n g e f f e c t s , a f e a s i b l e zone b a s e d on a c c e p t a b l e s u l f u r c o n t e n t , c a l o r i f i c v a l u e s , a n d / o r y i e l d i s d e t e r m i n e d . F o r t h i s example, o n l y two c o n s t r a i n t s w i l l be c o n s i d e r e d : S u l f u r and Minimum Y i e l d . 10 30 50 70 Percentage of Seam A i n the Blend Figure 11. Three Seam Model Results: Example Three Coal Blending Coefficient Contours 90 NON-FEASIBLE ZONE FEASIBLE ZONE AQZ3 Percentage of Seam A i n the Blend FEASIBLE ZONE B^g Figure 12. Three Sean Model Results: Example Three ^ Blending F e a s i b i l i t y Zones ^ The C o a l B l e n d i n g Model Pg 79 The c l e a n c o a l s u l f u r c o n t e n t was s e t t o be between 1.0 and 1.2 p e r c e n t w h i l e a p l a n t y i e l d o f o v e r 72 p e r c e n t was r e q u i r e d . U s i n g t h e i n f o r m a t i o n g e n e r a t e d by t h e S i m u l a t i o n Model (shown i n A p p e n d i x E ) , t h e c o n s t r a i n i n g b o u n d a r i e s c a n be drawn on a g r a p h o r one c a n t a k e a d v a n t a g e o f a b u i l t i n f u n c t i o n o f t h e p r o g r a m w h i c h i g n o r e s a l l C o a l B l e n d i n g C o e f f i c i e n t v a l u e s w h i c h do n o t meet t h e d e s i r e d c o n s t r a i n t s . P l o t t i n g t h e c o n s t r a i n t s on a g r a p h g i v e s a f i n a l r e s u l t s i m i l a r t o F i g u r e 12. The f e a s i b l e zone o u t l i n e d by t h e c o n s t r a i n i n g p h y s i c a l p r o p e r t i e s i s s p l i t i n two by t h e p r i m a r y a x i s g e n e r a t e d by t h e i n f l e c t i o n p o i n t s o f t h e C o a l B l e n d i n g C o e f f i c i e n t c o n t o u r s . S i n c e t h e r e s u l t s f r o m T a b l e IX i n d i c a t e t h a t S c e n a r i o s Two and T h r e e p r o d u c e a l m o s t t h e same r e s u l t s , t h i s t h r e e seam example i s s i m i l a r t o a two seam example w i t h s t r a i g h t b r a n c h e s . Under t h e s e c i r c u m s t a n c e s , t h e z o n e s o u t l i n e d on F i g u r e 12 s h o u l d be c o n s i d e r e d a s p o t e n t i a l l y f e a s i b l e b l e n d i n g z o n e s . T h e r e f o r e , any b l e n d i n g p r o g r a m u s i n g b l e n d s f r o m o n l y one zone w i l l be s u c c e s s f u l . I n c o n t r a s t , b l e n d s s e l e c t e d f r o m o p p o s i t e s i d e s o f t h e p r i m a r y a x i s r e p r e s e n t a l o s s i n p o t e n t i a l l y r e c o v e r a b l e c l e a n c o a l . T h i s d o e s n o t mean t h a t a c o n s i s t e n t f e e d b l e n d i s n o t r e q u i r e d , b u t r a t h e r t h a t t h e c o n s i s t e n t p l a n t f e e d r a t i o s be s e l e c t e d f r o m w i t h i n t h e same f e a s i b l e b l e n d i n g s u b z o n e . The C o a l B l e n d i n g Model Pg 80 Whenever p o s s i b l e , t h e s e c o n d a r y a x i s s h o u l d a l s o be t a k e n i n t o c o n s i d e r a t i o n . The s e c o n d a r y a x i s d i v i d e s t h e z o n e s c r e a t e d by t h e p r i m a r y a x i s i n t o two s e c t i o n s . The f u n c t i o n o f t h e s e c o n d a r y a x i s i s s i m i l a r t o t h a t o f t h e p r i m a r y a x i s , e x c e p t t h a t l e s s p o t e n t i a l b e n e f i t o c c u r s when l i m i t i n g t h e b l e n d i n g p r o g r a m t o o n l y one s i d e o f one z o n e . I f t h e i n - p i t r e s e r v e s , l o c a t e d i n zone B, were t o c o n t a i n an abundance o f seams B and C and a s h o r t a g e o f Seam A, t o o b t a i n a good b l e n d i n g p r o g r a m w i t h maximum f l e x i b i l i t y w o u l d r e q u i r e t h a t t h e w a s hery f e e d b l e n d s be l i m i t e d t o b l e n d s i n zone B t h a t a r e on t h e l e f t s i d e o f t h e s e c o n d a r y a x i s . F o r t h e i n v e r s e c a s e o f an abundance o f seam A, and a s h o r t a g e o f seam B and seam C, t h e b l e n d i n g zone w o u l d t h e n be l i m i t e d t o t h e more c o n f i n e d a r e a t o t h e r i g h t o f t h e s e c o n d a r y a x i s i n zone B. Example T h r e e d e m o n s t r a t e s a c a s e where t h e optimum b l e n d c a n be c o n s i d e r e d t o be any b l e n d f r o m w i t h i n a b l e n d i n g zone t h a t i s d e f i n e d by t h e C o a l B l e n d i n g C o e f f i c i e n t a x i s and t h e q u a l i t y c o n s t r a i n t s . T h i s example l e n d s i t s e l f w e l l t o an i n - p i t b l e n d i n g p r o g r a m , t h u s e l i m i n a t i n g t h e need f o r l a r g e s t o c k p i l e s . The C o a l B l e n d i n g Model Pg 81 V. SUMMARY AND REMARKS The s c h e d u l i n g o f p r o d u c t i o n i n m u l t i p l e seam c o a l m i n i n g c o m p l i c a t e s t h e p l a n n i n g p r o c e s s , o f t e n c a u s i n g c o n f l i c t s b etween t h e m i n i n g p r o d u c t i o n r e q u i r e m e n t s and t h e p r e p a r a t i o n p l a n t f e e d n e e d s . F a c t o r s s u c h as s u l f u r c o n t e n t s , c a l o r i f i c v a l u e s , s i z e d i s t r i b u t i o n s , a s h c o n t e n t s , and c l e a n c o a l r e c o v e r y must a l l be c o n s i d e r e d i n mine s c h e d u l i n g i f an i n - p i t b l e n d i n g p r o g r a m i s t o be s u c c e s s f u l and r e d u c t i o n o f s t o c k p i l e s i z e s i s t o be a c h i e v e d . The C o a l B l e n d i n g Model p r e s e n t e d i n t h i s t h e s i s q u a n t i f i e s t h e e f f e c t s o f a c o n t r o l l e d b l e n d i n g p r o g r a m on p r e p a r a t i o n p l a n t y i e l d , t h u s p r o v i d i n g a method t o o p t i m i z e t h e b l e n d i n g p r o g r a m w i t h i n t h e c o n s t r a i n t s o f t h e m i n i n g p r o g r a m , t h e w a s h e r y u n i t o p e r a t i o n s , and t h e f i n a l p r o d u c t q u a l i t y . The model d o e s n o t a l w a y s p r o d u c e a s i n g l e optimum b l e n d i n g s t r a t e g y . F o r c o a l s w i t h s i m i l a r w a s h a b i l i t y c h a r a c t e r i s t i c s , t h e r e i s o f t e n no b e n e f i t t o b l e n d i n g . I n t h i s c a s e , t h e two c o a l seams c a n be t r e a t e d as one seam f o r t h e p u r p o s e o f b l e n d i n g . I n some c a s e s , t h e r e i s a f e a s i b l e zone o f b l e n d i n g r a t i o s . T h i s s c e n a r i o l e n d s i t s e l f w e l l t o i n - p i t b l e n d i n g , s i n c e t h e mine p l a n n e r s c a n t a k e f u l l The C o a l B l e n d i n g Model Pg 82 a d v a n t a g e o f t h e e n t i r e b l e n d i n g zone when d e v e l o p i n g t h e mine p l a n . I f a c o n s i s t e n t b l e n d w i t h i n t h e f e a s i b l e zone i s a b l e t o be m a i n t a i n e d f o r a t l e a s t a week, t h e mine c a n have an e f f e c t i v e i n - p i t b l e n d i n g p r o g r a m . The l o n g e r a c o n s i s t e n t b l e n d i s m a i n t a i n e d , t h e g r e a t e r w i l l be t h e p l a n t ' s e f f i c i e n c y , w i t h a d d i t i o n a l f a c t o r s w i t h i n t h e p l a n t l e a d i n g t o e v e n f u r t h e r i m p r o v e m e n t s . S i n g l e optimum s o l u t i o n s a r e a l s o a p o s s i b i l i t y . An e v a l u a t i o n o f t h e model r e s u l t s w i l l d e t e r m i n e t h e b e s t s t r a t e g y . C o a l m i n e s w i t h l a r g e , u n p r o v e n r e s e r v e s may w i s h t o s e l e c t t h e b l e n d w i t h t h e h i g h e s t C o a l B l e n d i n g C o e f f i c i e n t , and t r y t o m a i n t a i n t h a t b l e n d w i t h i n new r e s e r v e s . The C o a l B l e n d i n g Model w i l l n o t s e l e c t an optimum b l e n d i n g p r o g r a m f o r t h e u s e r , b u t w i l l p r o v i d e a means o f e v a l u a t i n g d i f f e r e n t b l e n d s , t h u s a l l o w i n g f o r t h e s e l e c t i o n o f a most a p p r o p r i a t e b l e n d i n g p r o g r a m f o r a mine. F o r t h o s e c a s e s where a b l e n d i n g p r o g r a m p r o v e d u s e f u l , i m p r o v e m e n t s i n c o a l y i e l d o f g r e a t e r t h a n 1% were o b t a i n e d i n most c a s e s . T h i s r e p r e s e n t s a p o t e n t i a l e x t r a p r o f i t o f 11 t o 13 m i l l i o n d o l l a r s f o r t h e W e s t e r n C a n a d i a n c o a l i n d u s t r y . The C o a l B l e n d i n g Model Pg 83 Some d i f f i c u l t i e s may a r i s e i n e v a l u a t i n g r e s u l t s f o r p r o g r a m r u n s i n v o l v i n g more t h a n f o u r seams. T h i s i s b e c a u s e g r a p h i c a l i n t e r p r e t a t i o n s c a n n o t be o b t a i n e d f o r s u c h b l e n d s , w h i c h t h e r e f o r e r e q u i r e g r e a t e r i n t e r p r e t i v e s k i l l s f r o m t h e u s e r . I t i s recommended t h a t b l e n d s o f o n l y t h r e e and f o u r seams be u s e d i n i t i a l l y u n t i l a d a t a b a s e o f C o a l B l e n d i n g C o e f f i c i e n t s i s d e v e l o p e d f o r t h e mine. T h i s w i l l e n a b l e t h e u s e r t o make an a c c u r a t e e v a l u a t i o n o f t h e co m p u t e r r e s u l t s and t h e n p r o c e e d t o e v a l u a t e b l e n d s o f f i v e and more seams, b a s e d on t h e e x p e r i e n c e g a i n e d . The p r e s e n t model r e q u i r e s f u r t h e r i mprovements and t e s t i n g b e f o r e i t i s s u i t a b l e f o r g e n e r a l u s e , a l t h o u g h t h e c o n c e p t o f t h e C o a l B l e n d i n g C o e f f i c i e n t has p r o v e n t o be a p o t e n t i a l t o o l f o r improvement o f t h e o v e r a l l e f f e c t i v e n e s s o f seam b l e n d i n g p r o g r a m s . I n i t i a l t r i a l s have p r o v e n most p r o m i s i n g , b u t more work, w i t h t h e c o o p e r a t i o n o f a c t i v e c o a l m i n e s , i s r e q u i r e d t o p r o v e t h e m e r i t s o f t h e C o a l B l e n d i n g C o e f f i c i e n t . The C o a l B l e n d i n g Model Pg 84 REFERENCES 1. 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O s b o r n e D.G., and W a l t e r s A.D., " D e s i g n C r i t e r i a f o r Canada's E x p o r t C o a l P r e p a r a t i o n P l a n t s " , 8 7 t h A n n u a l  G e n e r a l M e e t i n g o f CIM 1985, A p r i l 21-25, 1985, V a n c o u v e r , B.C. P a p e r 89, p p l 3 - 1 4 . 15. L a z o r i n A . I . , S o l o s h e n k o V.S., S l e s a r e v (DGI) V.V., L i t m a n o v i c h I.M., M i l y u t i n O.M. and C h e r n o v a V.A. ( Y a s i n o v k a Coke W o r k s ) , " A v e r a g i n g o f C o a l i n t h e C l e a n i n g P r o c e s s " , Coke C h e m i s t r y , No. 10, pp. 16-18, A l l e r t o n P r e s s , I n c , 1979. 16. Salama A . I . , " Y i e l d M a x i m i z a t i o n i n C o a l B l e n d i n g " , X I n t e r n a t i o n a l C o a l P r e p a r a t i o n C o n g r e s s , Edmonton, Canada, 1986. pp 196-216 17. A b b o t t J . , "The O p t i m i z a t i o n Of P r o c e s s P a r a m e t e r s To M a x i m i s e t h e P r o f i t a b i l i t y From A Three-Component B l e n d " , A u s t r a l i a n C o a l P r e p a r a t i o n C o n f e r e n c e , 1 s t , N e w c a s t l e , NSW, A u s t r a l i a , A p r i l 1981, pp. 87-105 18. Charmbury H.B. and L o v e l l H.L., "Computer E v a l u a t i o n o f C o a l P r e p a r a t i o n W a s h a b i l i t y D a t a " , M e c h a n i z a t i o n , 24, No. 4, 57, A p r i l 1962, No. 5, 47, May 1962. The C o a l B l e n d i n g Model Pg 86 REFERENCES ( c o n t ' d . . . ) 19. B r o o k e s G.F. and Whitmore R.L., "An A p p l i c a t i o n o f t h e D i g i t a l Computer t o C o a l P r e p a r a t i o n " , C o a l P r e p a r a t i o n , 95, May/June 1966. 20. Humphreys K.K., L e o n a r d J.W. and B u t t e r w o r t h J.A., "Computer Program P e r f o r m s C o m p l e t e C o a l W a s h a b i l i t y A n a l y s i s " , C o a l Age, 76, 101, J u l y 1971. 21. A b s i l J.H., K e u n i n g W. and Meerman P.G., " P r e d i c t i o n o f Washery P l a n t P e r f o r m a n c e by D a t a P r o c e s s i n g " , 5 t h  I n t e r n a t i o n a l C o a l P r e p a r a t i o n C o n g r e s s , P i t t s b u r g h , F4, 381. 22. C o a l P r e p a r a t i o n P l a n t S i m u l a t i o n M o d e l ; a c omputer model by U.S. E n e r g y , M i n e s , and R e s o u r c e s , 1986. 23. Rong R.X. and Lyman G . J . , " C o m p u t a t i o n a l T e c h n i q u e s f o r C o a l Washery O p t i m i z a t i o n - P a r a l l e l G r a v i t y and F r o t h S e p a r a t i o n " , C o a l P r e p a r a t i o n , 2: 51-67; ( 1 9 8 5 ) . 24. L e o n a r d , IV, J o s e p h W. and L e o n a r d , J o s e p h W., "Use o f P a r t i t i o n (Tromp) C u r v e s f o r D i a g n o s i n g P e r f o r m a n c e P r o b l e m s i n O p e r a t i o n a l C o a l C l e a n i n g E q u i p m e n t " , S o c i e t y  o f M i n i n g E n g i n e e r s o f AIME, T r a n s a c t i o n s V o l . 270, 1848--1850, ( 1 9 8 2 ) . 25. J o w e t t , A l a n , An A p p r a i s a l o f P a r t i t i o n C u r v e s f o r C o a l - c l e a n i n g P r o c e s s e s " , I n t e r n a t i o n a l J o u r n a l o f M i n e r a l  P r o c e s s i n g , 16: 75-95, E l s e v i e r S c i e n c e P u b l i s h e r s B.V., Amsterdam ( 1 9 8 6 ) . The C o a l B l e n d i n g Model Pg 87 APPENDICES The C o a l B l e n d i n g Model APPENDIX A: C o a l B l e n d i n g Model P r o g r a m L i s t i n g s COAL BLENDING COEFFICIENT PROGRAM 3780 PROGRAM TO CALCULATE THE C.B.C 3798 FOR R»l TO,8 s 3791 Sun_b1tnd-8 ~ 3792 FOR 1-1 TO Z 3793 3um_blend»Sum b1end+B1end(I,R> 3794 Model<1,R,5>-Model<1,R,5>+Blend<I, R>*Re*ultsCI,R,1> 3795 NEXT I 3796 Model < 1,R,5>«Model < 1, R, 1X-"Model (1, R, 5>/Su* i_bl end 3797 NEXT R 3798 R-8 s+1 3888 Model <l,R,5>«Mode1 <'l,R, 1 >-<11 *Results< 1, R,i>+Jj*Results<2,R, l>+Kk*Result$<3,R, l>tLl*ResuHs<4,R, 1>>/188 SORTING AND STORING PROGRAM 3828 Ta b l e < l , l > « H 3838 T a b l e d , 2 > - J J 3848 Table<l,3>-Kk 3838 T a b l e d , 4>-Ll 3868 FOR R-188 TO 2 STEP -1 3878 Sum table-TableCR,1>+Table<R,2>+Table<R, 3)+fable<R,4> 3888 IF (Model <l,4,3XModel <R,4,5>> AND <Sum_ _tab,U=180> THEN GOTO Ex i t k 3898 FOR Sz-1 TO S s+1 3988 Table<R+l,Sz>»Table<R,Sz> 3918 Table<R,Sz>«Table<1,Sz> 3928 FOR Rz»l TO 5 3938 Model<R+l,Sz,Rz>»Model<R,Sz,Rz) 3948 Model<R,Sz,Rz>»Model<l,Sz,Rz> 3958 NEXT Rz 3968 NEXT Sz 3978 NEXT R BLEND GENERATOR PROGRAM H cr n 2330 PRINT "Input, Minimum and Maximum X of seam"; I; " i n the nd" 2340 INPUT fltnlnU >,flmax< I) 2350 P»P+flm1n<I) 2360 IF P>10O THEN E r r o r 10 2370 NEXT I .2380 INPUT "What i s the step s i z e f o r t h i s run.",Step s i z e 2390 FOR Ii-flmin<l> TO flmax<1> STEP S t e p _ s i z e 2400 FOR Jj-Rmin<2> TO Rmax<2> STEP S t e p _ s i z e 2410 FOR Kk«flmin<3> TO fimax<3> STEP Step s i z e 2420 FOR L1»Rmin<4> TO flmax<4> STEP Step s i z e 2430 IF I1+Jj>lO0 THEN E x i t i 2440 IF Ii+JJ+Kk>10O THEN E x i t j 2450 IF Ii+Jj+Kk+Ll>180 THEN Exitk 2460 Sum blend-Ii+Jj+Kk+Ll 2470 IF Sum blend<°100-Step s i z e THEN E x i t i 2488 FOR I«l TO S s 2490 Blend(l,I)-n 2500 Blend<2, D - J J 2510 Blend<3, D-kk 2520 BUnd(4, I >-Ll 2530 NEXT I 3980 Exi 11: NEXT LI 3990 E x i t k : NEXT Kk 4O00 Exi t j : NEXT J j 4010 E x i t i : NEXT I i b l e o o ft s a a » x o p. ro « o MODEL IHPUT PROGRAM 1480 INPUT "How many se t s of data do you wish to blend (max 4; Oef au l t 3>",Z 1498 INPUT "How many s i z e s f r a c t i o n s do you wish to work with? Def a u l t 3",S_s 1588 ~* INPUT "What Is the name of the coarsest s i z e f r a c t i o n ? Defaul t +28 MESH",Size_na*e$<l> FOR 1-2 TO S INPUT "What Is the name of the next f i n e r s i z e f r a c t i o n ? " , S i z NEXT I INPUT "How many s i z e f r a c t i o n s do you have w a s h a b i l i t y data f INPUT "What i s , t h e r e q u i r e d c l e a n coal ash;Default 9.5 ?",fish 1518 1520 e hamet(I) 1530 1540 or? Default 2",D 1550 _ c M t 1560 Input the min. & max.a 1owable 1 evel s of Clean coal Sulf u r ( D e f a u l t i s . 6 , 1 . 8 ) ? " , S u l f _ m i n , S u l f _ m a x 1570 INPUT "Input the min.8. max. allowable SECIFIC GRAVITY levels<D e f a u l t i s 1.3,1.89)?",Sg m1n,Sg_max 1388 1598 1591 1618 1628 e*<Count) 1720 1730 1740 Ion ";Size_name*<R) 1750 esu1ts(Flag<l),R,1> 1780 ults<Flag(l>,R,2> 1790 Results<F1ag(l>,R,3) 1800 1818 Flag<l),R,5> FOR Count-1 TO Z Tota l - 8 F l a g U ) - C o u n t ' CfiLL Get_fs_data<D> INPUT "What would you l i k e to c a l l t h i s coal type?",Coal_nam IF D-S THEN GOTO Next_count FOR R-D+l TO S_s PRINT "Please input data f o r Type ";Flag<l>;" S i z e f r a c t INPUT "The expected y i e l d f o r t h i s s i z e f r a c t i o n i s ? " , R INPUT "The expected ash f o r t h i s s i z e f r a c t i o n i s ? " , R e s INPUT "The expected s u l f u r f o r t h i s s i z e f r a c t i o n i s ? " , IF R-S_s THEN GOTO Calc_wt INPUT "The weight X of t h i s s i z e f r a c t i o n i s ?",Results< The C o a l B l e n d i n g Model Pg 92 APPENDIX B: W a s h a b i l i t y D a t a Used F o r Example P r o b l e m s The C o a l B l e n d i n g M odel Pg •< Q fl M X m < tn w • Vi CN —l • • Vi X o M Vi o X m * t-J <•fll ai BE Ob o o M H H ac M U o <j < M M OS H CO Oh OS < o SB Bd Oi CO N o M BS vs •o 3 £ O c CO • f l <fl TS u i CO <E (A <A CO .c lA <fl e CO <E (A lA « co on h- a', r-- cm oo in VO © co * N M * 'fl ij) N N K (0 i i ffi t ^ r>- on © co <3 CO IN- Cf» CM CO ~« CO CM CJ vo vo r^ - r-© CO CO CM © CO CM © IO CO IN- VO CM ON © cm © on in co © CO rt CM CM CM CM co © co vo in oo in in vo vo vo Is- cm CO CO CO © CS © CM in © vo © in. cm in. © CM in CO cr» IN-CO VO IN- © CJN ON 00 CM n © © |Nw © © * vo cm t r- © © IN- ON © T } - VO © © -H CO VO CO CO in vo vo cm on in © © © —< *-< in r^ . in f N . co © co on on CO CM —• OO ON © n n >n * n - n — cm co r>-N Cs — CM IN. -~ CM * C\ 'O CO CO o> N f4 S f N --I « <H 1.^  © © © © © © J£ (A 00 m vo |N- © c c y o CO •> ••-*> 1 i i i i i 1 lA u • » .— C ffl IT) © © © © © © C O CO m vo |Nw © C£ a Lu — WASHABILITY ANALYSIS: SEAM A SIZE FRACTION: 12.7 X 0.6 mm PROPORTION OF RAW COAL: 48Z R e 1 a t i ve D e n s i t y F r a c t i o n s E l e m e n t a r y d a t a C u m u l a t i v e d a t a F l o a t S i nk M a s s X A s h . y. s y. M a s s 'A A s h X s y. M a s s y. A s h y. s y. F l o a t - 1.30 42.67 3.46 0.44 42.67 3.46 0.44 100.00 24. 12 0.95 1.30 - 1.40 22.88 f. 30 0.63 65.55 4.88 8.51 57.33 39.49 1.33 1.40 - 1.50 4.89 18.24 1.84 70.44 5.73 0.54 34.45 60.87 1.39 1.50 - 1.60 1.98 25.83 1.48 72.42 6.28 0.57 29.56 67.92 1.92 -1.60 - 1.70 1.70 35.85 1.67 74. 12 6. 94 0.59 27.58 78.94 1.95 1.70 - 1.80 1.65 43.74 1.73 75.77 7.74 0.62 25.88 73.30 1.97 1.80 - S i n k 24.23 75.31 1.99 100.80 24. 12 0.95 24.23 75. 31 1.99 WASHABILITY ANALYSIS: SEAM B SIZE FRACTION: 150 X 12.7 B D PROPORTION OF RAW COAL: 601 Relat ive Dens i t y Frac t i ons Elementary data Cumulative data F l o a t Sink Mass 'A Ash V. s y. Mass '4 Ash 'A- s y. Mass 'A Ash y. s y. F l o a t - 1.30 5.95 3.93 0.70 5.95 J 3.93 0.70 100.00 33.54 1.79 1.30 - 1.40 40.23 8. 78 1.37 46. 18 8. 16 1.28 94.05 35.41 1 .86 1.40 - 1.50 14.95 18.83 3.67 61. 13 10.77 1.87 53.82 55.32 2.23 1.50/- t.60 5.25 32.-45 3.86 66.38 12.48 2.02 38.87 69.35 1.68 1.60/- 1.70 3. 12 43.03 5.37 69.58 13.85 2. 18 33.62 75. 11 1. 34 1.70/ - 1.80 3.03 52.87 2.61 72.53 15.48 2. 19 30.50 78.39 0.93 1.80 - Sink 27.4? 81.21 8. 74 180.00 33.54 1.79 27. 47 81.21 0. 74 WASHABILITY ANALYSIS: SEAM B SIZE FRACTION: 12.7 X 0.6 an PROPORTION OF RAW COAL: 3 3 Z C u m u 1 at i ve d a t a R e l a t i v e E l e m e n t a r y d a t a D e n s i t y F r a c t i o n s F l o a t S i n k M a s s fish y. s y. M a s s X fish y. s y. M a s s 'A fish y. S y. F l o a t - 1 . 3 0 3 1 . 9 8 3 . 5 4 0 . 6 9 3 1 . 9 8 3 . 3 4 8 . 6 9 1 0 0 . 0 0 2 0 . 16 1 . 8 5 1 . 3 0 - 1 . 4 0 3 7 . 9 7 7 . 5 8 1 . 3 1 6 9 . 9 5 5 . 6 9 1 . 0 3 6 8 . 0 2 2 7 . 9 8 2 . 3 9 1 . 4 0 - 1 . 5 0 7 . 4 4 1 7 . 8 5 3 . 0 7 7 7 . 3 9 6 . 8 6 1. 2 2 3 0 . 0 5 5 3 . 8 6 3 . 7 5 1 . 5 0 1 . 6 0 2 . 6 8 2 7 . 3 8 4 . 2 7 8 8 . 0 7 7 . 5 4 1 . 3 2 2 2 . 6 1 6 5 . 7 1 3 . 9 8 1 . 6 0 / - 1 . 7 0 1 . 7 0 / - 1 . 8 0 1 . 9 3 3 5 . 8 4 5 . 0 9 8 2 . 8 8 8 . 2 1 1 . 4 1 1 9 . 9 3 7 8 . 8 7 3 . 9 4 1 . 3 8 4 2 . 9 7 4 . 8 6 8 3 . 3 8 8 . 7 8 1 . 4 7 1 8 . 0 0 7 4 . 6 3 3 . 8 2 1 . 8 0 / - S i n k 1 6 . 6 2 7 7 . 2 6 3 . 7 3 1 0 0 . 0 0 2 8 . 16 1 . 8 5 1 6 . 6 2 7 7 . 2 6 3 . 7 3 WASHABILITY ANALYSIS: SEAM aC SIZE FRACTION: 150 X 12.7 mn PROPORTION OF RAW COAL: 421 R e 1 a t i v e D e n s i t y F r a c t i o n s E l e m e n t a r y d a t a C u m u l a t i v e d a t a F l o a t S i n k - M a s s \ fish 'K S X M a s s 'A fish y. s y. M a s s '< fish y. s y. F l o a t - 1 . 3 0 2 7 . 4 0 4 . 3 2 0 . 7 9 2 7 . 4 0 4 . 3 2 0 . 7 9 1 0 0 . 0 0 1 9 . 5 6 1 . 0 6 1 . 3 0 - 1 . 4 0 3 6 . 2 3 8 . 8 8 1 . 0 7 6 3 . 6 3 6 . 9 2 0 . 9 5 7 2 . 6 0 2 5 . 3 2 1 . 1 6 1 . 4 0 - 1 . 5 0 1 0 . 6 0 2 8 . 2 8 0 . 8 9 7 4 . 2 3 8 . 8 2 0 . 9 4 3 6 . 3 7 4 1 . 6 9 1 . 2 6 1 . 5 0 - 1 . 6 0 7 . 7 2 3 1 . 6 8 0 . 7 7 8 1 . 9 5 1 0 . 9 8 0 . 9 2 2 5 . 7 7 5 0 . 4 9 1 . 4 1 1 . 6 0 - 1 . 7 0 4 . 9 7 4 1 . 6 9 0 . 6 4 8 6 . 9 2 1 2 . 7 3 0 . 9 1 1 8 . 0 5 5 8 . 5 4 1 . 6 8 1 . 7 0 - 1 . 8 0 3 . 2 4 5 0 . 7 7 1 . 1 7 9 0 . 1 6 1 4 . 1 0 0 . 9 2 1 3 . 0 8 6 4 . 9 4 2 . 0 8 1 . 8 0 - S i n k 9 . 8 4 6 9 . 6 1 2 . 3 8 1 0 0 . 0 0 1 9 . 5 6 1 . 0 6 9 . 8 4 6 9 . 6 1 2 . 3 8 WASHABILITY ANALYSIS: SEAM C SIZE FRACTION: 12.7 X 0.6 na PROPORTION OF RAH COAL: 48Z R e 1 a t i v e D e n s i t y F r a c t i o n s E l e m e n t a r y d a t a C u m u l a t i v e d a t a F l o a t S i n k M a s s 'A fish v. S v. M a s s '/. A s h '/. s y. M a s s 'A fish y. s y. F l o a t - 1 . 3 9 4 7 . 2 2 . 3 . 7 3 8 . 7 5 4 7 . 2 2 3 . 7 3 8 . 7 5 1 0 0 . 0 0 1 4 . 8 1 1. 16 1 . 3 0 - 1 . 4 0 2 7 . 3 8 9 . 11 1 . 8 1 7 4 . 5 2 5 . 7 0 8 . 8 5 5 2 . 7 8 2 4 . 7 2 1 . 5 2 1 . 4 0 - 1 . 5 0 8 . 6 5 2 1 . 2 6 1 . 2 8 8 3 . 17 7 . 3 2 0 . 8 9 2 5 . 4 8 4 1 . 4 4 2 . 07 1 . 5 0 - 1 . 6 0 4 . 1 9 3 1 . 2 4 1 . 4 2 8 7 . 3 6 8 . 4 7 0 . 9 2 1 6 . 8 3 5 1 . 8 1 2 . 4 7 1 . 6 0 - 1 . 7 0 2 . 8 4 3 9 . 6 6 1 . 8 7 9 0 . 2 0 9 . 4 5 0 . 9 5 1 2 . 6 4 5 8 . 6 2 2 . 8 2 1 . 7 0 - 1 . 8 0 2 . 1 8 4 7 . 2 5 2 . 8 4 9 2 . 3 8 1 8 . 3 1 0 . 9 7 9 . 8 0 6 4 . 1 2 3. 10 1 . 8 0 - S i n k 7 . 7 8 6 8 . 7 2 3 . 3 9 1 0 0 . 0 0 1 4 . 8 1 1. 16 7. 7 0 6 8 . 7 2 3 . 3 9 H tr A CS o CB M A a a a M X o A R e l a t i v e D e n s i t y F r a c t " i o n s E l e m e n t a r y d a t a C u t n u l a t i v e d a t a F1 o a t S i n k M a s s '4 R s h V. s y. M a s s '4 fish y. s y. M a s s 'K fish X s y. F l o a t - 1 . 3 0 1 7 . 2 3 3 . 8 2 1 . 3 3 1 7 . 2 3 3 . 8 2 1 . 3 3 1 0 0 . 0 0 1 1 . 8 9 2 . 8 9 1 . 3 0 - 1 . 4 0 6 6 . 0 3 8 . 8 6 2 . 11 8 3 . 2 6 7 . 8 2 1 . 9 5 8 2 . 7 7 1 3 . 5 8 3 . 2 1 1 . 4 0 - 1 . 5 0 8 . 8 1 1 8 . 17 3 . 3 1 9 1 . 2 7 8 . 7 3 2 . 0 9 1 6 . 7 4 3 2 . 18 7 . 5 7 1 . 5 0 - 1 . 6 0 2 . 0 6 2 5 . 9 7 5 . 4 6 9 3 . 3 3 9 . 11 2 . 1 6 8 . 7 3 4 5 . 8 3 1 1 . 2 9 1 . 6 0 - 1 . 7 9 1 . 1 2 3 5 . 8 9 5 . 9 5 9 4 . 4 5 9 . 4 2 2 . 2 1 6 . 6 7 5 8 . 9 1 1 3 . 0 9 1 . 7 0 - 1 . 8 0 0 . 8 9 4 6 . 2 6 7 . 1 8 9 5 . 3 4 9 . 7 7 2 . 2 5 5 . 5 5 5 3 . 9 4 1 4 . 5 4 1 . 8 0 - S i n k 4 . 6 6 5 5 . 4 1 1 5 . 9 4 1 0 0 . 0 0 1 1 . 8 9 2 . 8 9 4 . 6 6 55.41 1 5 . 9 4 WASHABILITY ANALYSIS: SEAM D SIZE FRACTION: 150 X 12 .7 mm PROPORTION OF RAW COAL: 461 00 VO WASHABILITY ANALYSIS: SEAN D SIZE FRACTION: 12.7 X 0.6 B B PROPORTION OF RAW COAL: 441 Relat iwe Densi ty Frac t i ons Elementary data C u m u l a t i v e d a t a Fl oat Sink Mass V. Ash V. S Mass 'A Ash y. S X Mass X Ash y. s y. F l o a t - 1.30 41. 17 3.32 1.28 41. 17 3.32 1.28 100.00 12.81 2.46 1.30 - 1.40 40.77 7.33 2.01 81.94 5.32 1.6*4 58. 83 18.09 3.29 1.40 - 1.50 6.26 17.66 3.81 88.28 6. 19 1.80 18.06 42.38 6. 17 1.50 - 1.60 1.88 27.51 4.78 98.00 6.62 1.86 11.88 55.50 7. 42 1.60 - 1.70 1.46 34.86 5. 10 91.46 7.07 1.91 10. 00 60.53 7. 90 1.70 - 1.80 0.99 43.05 5.24 92.45 7.45 1.94 8.54 64.92 8.38 1.80 - S i n k 7.55 67.79 8.79 100.00 12.01 2.46 7.55 67.79 8.79 The C o a l B l e n d i n g Model Pg 101 APPENDIX C: C o a l B l e n d i n g Model R e s u l t s : Example P r o b l e m One The C o a l B l e n d i n g Model Pg 102 '3 £ •»- C0 CO X CD CD fl) £ 3 CO CO C 2: •\" • » CO IO IO CO CO CO cn CO CO is- in CT. CO • • • • • • 0) IO CO CO CM |N-CO •* IO CO •V o o ZZ zz z: zc I X X X O c o £ £ -r- £ £ *> u CO fl) £ * £ • c £ £ £ CO £ u. £ £ Iv. X X <u • CO • CO N CM > CM (N. • ^~ a CO • CO co + CM + CM 1 TA 1 £ fl) £ fl) Ol CC CO .— .— fl) A) o o o o *t (V .-* CM 1-CO CO 1- CO CM CM II II £ £ 3 3 £ £ X X fl) fl) ZZ zz CO CO CO CO CO CO CM CO IN- CO ^ IO c £ II II >. II X £ (rt 3 CC £ fl) ~ O £ O • c C 3 fl) <~ Cu — — 3 O CO > to fl) Isl i. — U CO u a. <^ — CO u 0i CU a. x co t-SIZE CLEANING MODEL MODEL MODEL MODEL MODEL T l : T2 FRACTION UNIT S . G . YIELD ASH SULFUR FACTOR 100: 0 +12.7 mm HMB 1. 453 65. 43 7. 000 . 590 ZERO 12.7 X 0.6 mm HMC 1. 704 74. 14 6. 999 . 595 ZERO - 0.6 mm 0. 000 80. 00 8. 080 . 600 ZERO TOTAL 0. 000 72.08 7. 185 .594 ZERO 0:100 +12.7 mm HMB 1. 337 16.24 7. 003 1 . 124 ZERO 12.7 X 0.6 mm HMC 1.519 77.45 7. 000 1. 242 ZERO - 0.6 mm 0. 008 80. 00 8.800 1.200 ZERO TOTAL 0. 000 41. 22 7. 148 1.209 ZERO 1 6 5 : 35 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .379 1 . 6 5 1 0 . 000 0 . 000 5 1 . 1 0 7 5 . 27 8 0 . 00 6 5 . 38 7 . 002 7 . 000 8 . 0 0 0 7 . 136 . 8 7 1 . 368 . 8 1 0 . 8 3 6 9 . 04 . 24 0 . 00 4 . 1 1 2 7 0 : 30 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 401 1 . 6 6 2 0 . 000 0 . 000 5 3 . 70 7 5 . 17 8 0 . 00 6 6 . 75 6 . 998 7 . 005 8 . 060 7 . 1 4 1 . 847 . 774 . 780 . 8 6 6 8 . 79 . 27 0 . 00 3 . 93 3 7 5 : 25 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .419 1. 671 0 . 000 0 . 000 5 5 . 65 7 4 . 98 8 0 . 08 6 7 . 75 6 . 9 9 9 6 . 9 9 9 8 . 606 7 . 144 . 8 2 3 . 750 . 756 . 780 7 . 79 . 22 6 . 88 3 . 39 4 6 0 : 40 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 368 1. 641 0 . 000 0 . 000 4 5 . 43 7 5 . 44 8 6 . 00 6 2 . 59 7 . 661 7 . 606 8 . 680 7 . 131 . 894 . 8 3 9 . 846 . 8 6 4 6 . 05 . 25 6 . 66 2 . 86 5 8 0 ! 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 425 1. 679 0 . 008 0 . 000 5 7 . 29 7 4 . 80 8 6 . 00 6 8 . 59 6 . 997 6 . 997 8 . 6 8 0 7 . 147 . 788 . 7 1 6 . 726 . 745 6 . 3 3 . 17 8 . 66 2 . 68 6 8 5 : 15 + 1 2 . 7 mm 1 2 . 7 X 8 . 6 mm - 8 . 6 mm TOTAL HMB HMC 1.431 1. 686 0 . 000 0 . 000 5 9 . 05 7 4 . 63 8 0 . 60 6 9 . 43 6 . 999 7 . 660 8 . 000 7 . 154 . 752 . 6 8 3 . 696 . 7 1 1 4 . 3 1 . 13 0 . 66 1. 93 7 5 5 : 45 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 363 1. 632 0 . 000 0 . 000 4 0 . 78 7 5 . 58 8 0 . 00 6 6 . 12 7 . 802 7 . 006 8 . 006 7 . 127 . 9 2 6 . 873 . 8 7 6 . 894 3 . 92 . 25 6 . 60 1. 93 8 9 0 : 10 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .437 1 .693 0 . 000 0 . 000 6 1 . 02 7 4 . 48 8 0 . 00 ' 7 0 . 3 1 7 . 000 7 . 0 0 0 8 . 0 0 0 7 . 158 . 7 1 0 . 6 5 4 . 6 6 0 . 676 3 . 28 . 10 0 . 00 1 .32 9 $0, 50 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 358 1. 622 0 . 000 0 . 000 3 6 . 8 5 7 5 . 74 8 0 . 00 5 7 . 8 8 7 . 0 0 1 7 . 0 0 0 8 . 0 0 0 7 . 122 . 945 . 9 0 3 . 900 . 9 2 3 2 . 36 . 25 0 . 00 1. 23 10 4 5 : 55 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .355 1 .612 0 . 000 0 . 000 3 3 . 59 7 5 . 8 9 8 0 . 00 5 5 . 87 7 . 0 0 0 6 . 999 8 . 000 7 . 117 . 970 . 9 3 9 . 930 . 95-3 1. 36 . 24 0 . 00 . 76 11 9 5 : 5 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 m m TOTAL HMB HMC 1 .443 1. 699 0 . 000 0 . 000 6 3 . 06 7 4 . 3 0 8 0 . 00 7 1 . 1 6 6 . 9 9 5 7 . 0 8 0 8 . 000 7 . 161 . 655 . 627 . 630 . 6 3 8 1. 57 . 85 0 . 00 . 63 12 4 0 : 60 + 1 2 . 7 mm . 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 351 1. 603 0 . 000 0 . 000 3 0 . 6 7 7 6 . 85 8 0 . 0 0 5 3 . 94 6 . 998 6 . 999 8 . 0 0 0 7 . 1 1 1 . 988 . 9 7 4 . 9 6 0 . 9 7 9 . 58 . 2 3 0 . 00 . 38 13 3 5 : 65 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 3 4 9 1 . 5 9 4 0 . 000 0 . 000 2 8 . 17 7 6 . 2 1 8 0 . 00 5 2 . 15 7 . 000 7 . 000 8 . 000 7 . 108 1. 0 0 5 1 . 005 . 990 1 . 0 0 3 . 10 . 2 1 0 . 80 . 13 14 3 0 : 70 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1.347 1. 584 0 . 000 0 . 000 2 6 . 01 7 6 . 38 8 0 . 00 5 0 . 4 8 7 . 002 7 . 000 8 . 000 7 . 104 1 . 8 2 4 1 . 040 1 . 020 1. 029 - . 13 . 20 0 . 80 . 0 1 15 188: 0 +12.7 mm HMB 1. 453 65. 43 7. 000 . 590 - . 04 12.7 X 0.6 mm HMC 1.704 74. 14 6. 999 . 595 - . 0 0 - 0 .6 mm 0. 000 80. 00 8.000 . 600 0. 00 TOTAL 0. 000 72. 08 7. 167 . 594 0.00 16 0:100 +12.7 mm HMB 1.337 16. 24 7.003 1. 124 0. 00 12.7 X 0.6 mm HMC 1.519 77. 45 7. 000 1.242 . 00 - 0.6 mm 0. 000 80. 00 8. 000 1 . 200 0. 00 TOTAL 0. 000 41. 22 7. 078 1. 169 0. 00 17 5: 95 +12.7 mm HMB 1.339 17.51 7. 000 1. 109 - . 2 0 12.7 X 0.6 mm HMC 1.530 77. 25 7. 800 1.210 . 04 - 0 .6 mm 0. 000 80. 00 8. 000 1. 170 0. 00 TOTAL 0. 000 42. 66 7. 088 1. 148 - . 1 0 18 25: 75 +12.7 mm . HMB 1.345 23. 91 6. 999 1. 040 - . 3 8 12.7 X 0.6 mm HMC 1.574 76. 53 7. 00k 1. 074 . 16 - 0.6 mm 0. 000 80. 00 8. 000 1. 050 0. 00 TOTAL 0. 000 48. 79 7.098 1.054 - . 15 19 20: 80 +12.7 mm HMB 1.343 22. 18 7.002 1. 059 - . 3 6 12.7 X 0.6 mm HMC 1.563 76. 69 7. 000 1. 109 . 12 - 0.6 mm 0. 000 80. 00 8. 000 1 . 080 0. OO TOTAL 0. 000 47. 24 7. 095 1. 079 - . 16 28 15: 85 +12.7 mm HMB 1.341 20. 47 7. 002 1 . 080 - . 3 9 12.7 X 0.6 mm HMC 1.551 76. 86 7.000 1. 142 . 08 - 0.6 mm 0. 000 80. 00 8. 000 1.110 0. 00 TOTAL 0. 000 45. 66 7.091 1. 105 - . 19 21 10: 99 +12.7 mm HMB 1. 340 18. 86 6. 999 1 . 091 - . 3 9 12.7 X 0.6 mm HMC 1.540 77. 04 7. 000 1. 176 . 85 - 0.6 mm 0. 000 88. OO 8. 000 1. 140 0. 00 TOTAL 0.000 44. 10 7. 085 1. 124 - .21 The C o a l B l e n d i n g Model Pg 107 APPENDIX D: C o a l B l e n d i n g Model R e s u l t s : Example P r o b l e m Two The C o a l B l e n d i n g Model Pg 108 5 £ CO CO CO X CD CO CO n> •-t *—* z: .V 3 £ CO CO CO C • f — Z! •\" *> CO in in CO CO CO CO CO CO cn o CM CM CO CM in m CO - r— 0) IO CO CO CM IN- CO in CO CO .—1 T»-.\- - . 1— z o o o z: z: z: z: z: i z I z X X U c o £ £ •w- £ £ £ *> u CO CO CO n) £ • £ • £ • 4. £ CO £ £ CO £ £ CO £ U. £ £ £ X X X (to • CO • CO • CO N CM • CM - CM • -w- • CO • CO • CO co + CM + CM + CM 1 1 1 s fl) z £ fl) 0) cc o CO ,— D n) <* o o o o o o * Of CM CO Q. D>. 1— CO CO rf CO CM CM II II £ £ 3 3 X X fl) fl) z: z: CO CO CO CO in co CM co rs- co co II II i. C 3 fl) U-<v — r - 3 U CO IX II •* > 0> fl) N i . — IJ) CO o Q. <u <*-— CO u Hi OI Q. X CO I-# T 1 . T 2 . T 3 SI2E FRfiCTION CLEANING UNIT MODEL S. G. MODEL YIELD MODEL ASH MODEL SULFUR MODEL FACTOR 180:0:0 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTfiL HMB HMC 1. 483 1 . 782 0. 000 0. 000 69. 53 75. 24 80. OO 74. 04 7. 500 7. 499 8. 000 7. 590 .596 .611 . 680 . 604 ZERO ZERO ZERO ZERO 0:180:0 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTfiL ' HMB HMC 1. 434 1.513 0. 000 0. 000 66. 45 83. 38 80. 00 75. 89 7. 500 7.500 8. 000 7. 554 . 947 . 894 . 900 .914 ZERO ZERO ZERO ZERO 0:0:100 +12.7 mm 12.7 X 0.6 mm - 0 . 6 m m . TOTAL HMB HMC 1. 361 1. 891 0. 000 0. 000 63. 59 92. 42 80. 00 77. 94 7. 503 7. 443 8. 000 7.528 1. 900 1. 949 1. 900 1. 925 ZERO ZERO ZERO ZERO 1 30: 0: 70 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTFIL HMB HMC 1. 384 1. 838 0. 000 0. 000 75. 56 86.98 80. 00 81. 23 7. 561 7. 498 8. 668 7. 563 1.684 1. 569 1.516 1.616 10. 45 . 69 0 . 00 4. 46 2 10: 30: 60 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC '1.389 1 . 651 0. 000 0.000 74. 47 88. 12 80. 00 81. 27 7. 562 7. 564 8. 686 7. 559 1.615 1 . 464 1. 476 1. 536 9. 39 . 38 0. 68 4. 34 3 20: 20: 60 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 484 1. 692 0. 060 0. 000 74. 89 87. 21 80. 00 81 . 08 7. 500 7. 500 8. 006 7. 560 1. 665 K 456 1.448 1. 5.18 9. 56 . 35 0. 66 4. 33 4 30: 10: 60 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.415 1. 739 0. 000 0. 600 75.38 86.20 80. 00 80.87 7. 496 7. 506 8. 000 7. 561 1 . 600 1.452 1.410 1. 509 9. 78 . 22 8 . 00 4.31 5 40: 0: 60 +12.7 mm 12.7 X 0.6 mm - 0 . 6 m m TOTAL HMB HMC 1.421 1.814 0 . 000 0. 000 75. 83 85. 19 80. 00 80. 64 7. 498 7. 497 8. 066 7.564 1.591 1. 445 1 . 388 1. 496 10. 25 . 67 6. 66 4. 26 6 20: 10: 70 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.377 1. 740 0. 686 0. 006 73. 75 88. 00 80. 00 80. 90 7. 501 7. 568 8. 000 7. 561 1. 685 1. 574 1 . 548 1 .618 8. 77 . 23 6. 60 3. 95 7 20: 30: 50 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 420 1 . 652 0. 000 0. 000 74.03 86.36 80.00 80. 37 7. 497 7. 504 8. 000 7. 560 1.513 1.349 1.346 1.417 8. 38 . 39 8. 60 3. 33 8 1 0 : 4 0 ! 50 +12 .7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB . HMC 1 .414 1 .616 0 . 000 0 . 800 7 3 . 70 8 7 . 12 8 0 . 80 8 0 . 53 7 . 496 7 . 588 8 . 888 7 . 555 1 . 5 2 3 1 . 3 5 9 1. 370 1 . 431 3 . 29 . 28 0 . 08 3 . 88 9 0 : 4 0 : 60 +12 .7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .379 1 .613 0 . 000 0 . 000 7 2 . 99 8 8 . 8 9 8 8 . 88 8 0 . 9 2 7 . 498 7 . 588 8. 800 7 . 552 1. 6 2 2 1. 4 7 3 1 . 5 0 0 1. 5 4 2 8 . 17 . 28 0 . 00 3 . 30 10 0 : 5 0 : 50 +12 .7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 404 1 . 591 0 . 000 0 . 000 7 3 . 28 8 7 . 93 8 0 . 00 8 0 . 67 7 . 503 7 . 584 8 . 000 7 . 556 1. 5 3 6 1 . 3 7 3 1. 400 1. 447 8 . 13 . 23 0 . 88 3 . 75 11 3 0 : 2 0 : 50 +12 .7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 423 1 . 6 9 3 0 . 0 0 0 0 . 000 7 4 . 27 8 5 . 4 4 8 0 . 00 8 0 . 10 7 . 496 7 . 500 8. 000 7 . 561 1. 588 1 . 3 2 9 1 . 3 1 8 1 . 3 9 8 8 . 37 . 33 0 . 00 3 . 74 12 4 0 : 1 0 : 50 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 2 7 1. 738 0 . 0 0 0 0 . 000 7 4 . 5 5 8 4 . 45 8 0 . 0 0 7 9 . 81 7 . 5 0 0 7 . 500 3 . 000 7 . 5 6 6 1 . 4 8 7 1 . 3 1 8 1. 288 1 . 3 8 2 8 . 39 . 20 0 . 80 3 . 63 13 5 0 : 0 : 50 +12 .7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .431 1 .806 0 . 000 0 . 000 7 4 . 96 8 3 . 45 8 0 . 00 7 9 . 55 7 . 502 7 . 4 9 9 8 . 080 7 . 5 7 0 1. 4 8 3 1 . 388 1. 258 1. 378 8 . 80 . 06 0 . 00 3 . 57 14 10 : 2 0 : 70 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .374 1 .692 0 . 000 0 . 800 7 2 . 36 8 9 . 8 4 8 0 . 00 8 8 . 78 7 . 498 7 . 5 0 1 8 . 000 7 . 5 5 7 1. 694 1. 575 1. 578 1 . 6 2 6 7 . 63 . 38 8 . 00 3 . 56 a 15 0: 60: 40 +12.7 mm HMB 1.419 72.35 7.497 1 . 438 6. 91 12.7 X 0.6 mm HMC 1 . 569 86.96 7.580 1 . 268 15 - 0.6 mm 0. 008 80.00 8.000 1 .300 0. 06 TOTFIL 0. 000 79.87 7. 551 1 . 345 3. 16 16 10: 50: 40 +12.7 mm HMB 1 . 422 72.52 7. 500 1 . 424 6. 84 12.7 X 0.6 mm HMC 1. 593 86. 19 7.500 1 . 248 25 - 0.6 mm 0. 000 80. 00 8.000 1 .270 6. 00 TOTAL 0. 000 79.65 7.556 •1 . 326 3. 13 17 20: 40: 40 +12.7 mm HMB 1. 425 72. 71 7. 499 1 .410 6. 79 12.7 X 0.6 mm HMC 1 .618 85. 40 7. 500 1 . 233 a 30 1 - 0 .6 mm 0. 000 80.00 8. 000 1 . 240 8. 00 TOTAL 0. 000 79.42 7. 559 1 . 369 3. 63 18 30: 30: 40 +12.7 mm HMB 1. 429 72. 95 7. 503 1 . 397 6. 78 12.7 X 0.6 mm HMC 1 . 655 84.62 7.503 1 .220 a 38 - 0 . 6 mm 0. 000 80. 00 8. 000 1 .210 8. 00 TOTAL 0. 000 79.22 7. 565 1 . 292 3. 07 19 0: 30: 70 +12.7 mm HMB 1.372 70. 88 7. 496 1 . 694 6. 39 12.7 X 0.6 mm HMC 1. 649 89. 92 7. 504 1 . 580 38 - 0 . 6 mm 0. 000 80. 00 8. 000 1 . 600 8. 00 TOTAL 0. 000 80.38 7. 554 1 . 633 3. 86 28 40: 20:, 40 +12.7 mm HMB 1 . 432 73. 17 7. 501 1 . 333 6. 73 12.7 X 0.6 mm HMC 1 . 694 83. 72 7. 500 1 . 265 a 33 - 0.6 mm 0. 000 80. 00 8. 060 1 . 186 6. 00 TOTAL 0. 000 78. 94 7. 566 1 . 274 2. 98 21 50: 10: 40 +12.7 mm HMB. 1 . 435 73. 49 7. 500 1 . 361 6. 77 12.7 X 0.6 mm HMC 1 . 735 82. 73 7. 496 1 . 191 a 19 - 0.6 mm 0. 000 80. 00 8. 000 1 . 156 6. 00 TOTAL 0. 000 78. 66 7. 567 1 . 253 2. 88 o o n s o. H-S W x o a re T3 22 68: 8: 48 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1 . 439 1 . 798 0. 880 8. 000 73. 88 81. 74 80. 00 78. 41 7. 497 7. 493 8. 000 7. 570 1. 349 1 . 173 1. 120 1. 234 7. 13 . 84 8. 80 2.81 23 28: 8: 88 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.370 1.890 0. 000 0 . 000 70. 67 88.79 88. 88 79. 86 7. 503 7. 494 8. 800 7. 559 1. 768 1. 695 1. 640 1. 720 6. 13 . 18 8. 00 2. 70 24 8: 78: 38 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1 . 424 1 . 551 0 . 000 0. 000 71.00 86. 03 80. 00 78. 91 7. 499 7. 500 8. 008 7. 552 1. 332 1. 170 i : 200 1. 243 5. 30 . 18 0. 00 2.41 25 10: 18: 80 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1 . 369 1. 743 0. 000 0. 000 69. 47 89.85 80.00 79. 72 7. 501 7. 500 8. 000 7. 558 1. 767 1. 696 1. 670 1.724 5. 88 . 26 8. 88 2. 38 26 10: 60: 30 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1 . 427 1 . 572 0 . 000 0. 000 71. 17 85.26 80.00 78.69 7. 503 7. 500 8. 000 7. 557 1.311 1 . 153 1. 170 1. 222 5. 22 . 13 0. 08 2. 37 27 20: 50: 30 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1 . 430 1 . 595 0. 000 0. 000 71.30 84. 48 80.00 78. 45 7. 508 7. 508 8. 080 7. 559 1. 297 1. 135 1. 140 1. 203 5.11 . 25 8. 88 2. 32 28 30: 40: 30 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1 . 433 1 . 621 0. 000 0. 000 71. 53 83. 70 80. 00 78. 25 7. 504 7. 500 8. 000 7. 564 1.282 1.115 1.110 1. 183 5. 88 .31 8. 88 2. 38 29 4 0 : 3 0 : 30 + 1 2 . 7 mm 1 2 . 7 X 8 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 3 6 1. 657 0 . 0 0 0 0 . 000 7 1 . 76 8 2 . 93 8 0 . 00 7 8 . 0 4 7 . 502 7 . 503 8 . 800 7 ? 5 6 8 1 . 258 1 . 095 1. 080 1. 159 5. 04 .33 0 . 00 2 . 28 30 5 0 : 2 0 : 30 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 3 9 1 . 694 0 . 000 0 . 000 7 2 . 02 8 2 . 02 8 0 . 00 7 7 . 78 7 . 5 0 0 7 . 497 8. 800 7 . 567 1 . 241 1. 076 1. 050 1. 138 5 . 0 2 . 32 0 . 00 2 . 2 1 31 6 0 : 1 0 : 30 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 4 3 1. 734 0 . 000 0 . 000 7 2 . 35 8 1 . 0 4 8 0 . 00 7 7 . 51 7 . 5 0 2 7 . 496 8 . 000 7 . 571 1 . 2 1 3 L. 057 1 . 020 1 .114 5 . 86 . 18 0 . 00 2 . 12 32 7 0 : 0 : 30 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 448 1 . 7 9 4 0 . 000 0 . 000 7 2 . 76 8 8 . 0 7 8 0 . 0 0 7 7 . 27 7 . 500 7 . 499 8 . 000 7 . 574 1. 2 0 2 1. 038 . 998 1 . 0 9 3 5 . 38 . 84 0 . 00 2 . 0 6 33 0 : 2 0 : 80 + 1 2 . 7 mm 12.7 . X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 3 6 8 1. 690 0 . 000 0 . 000 6 8 . 3 2 9 0 . 86 8 0 . 00 7 9 . 57 7 . 4 9 6 7 . 580 8. 000 7 . 552 1. 764 1 . 697 1. 706 1 . 727 4 . 1 4 . 37 0 . 00 2 . 05 34 0 : 8 0 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 2 8 1. 536 0 . 000 8 . 000 6 9 . 54 8 5 . 13 8 8 . 0 0 7 7 . 92 7 . 499 7 . 5 0 8 8. 000 7 . 551 1 . 2 1 2 1. 077 1 . 100 1. 137 3. 58 . 07 0 . 00 1 . 62 35 18 : 7 0 : 28 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL -HMB HMC 1. 430 1. 5 5 3 0 . 000 0 . 000 6 9 . 65 8 4 . 33 8 8 . 80 7 7 . 6 6 7 . 499 7 . 508 8 . 000 7 . 554 1 . 196 1 . 056 1. 078 1 . 1 1 7 3 . 44 . 10 0 . 00 1 . 55 36 2 0 : 6 0 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 3 3 1 . 5 7 5 0 . 000 0 . 000 6 9 . 81 8 3 . 5 6 8 0 . 0 0 7 7 . 45 7 . 500 7 . 5 0 8 8 . 0 0 0 7 . 5 5 8 1. 171 1 . 0 3 3 1. 040 1 .091 3 . 35 . 18 8 . 88 1 .52 37 3 0 : 5 0 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 3 6 1 . 5 9 7 0 . 800 0 . 000 6 9 . 9 7 8 2 . 8 1 8 0 . 0 0 7 7 . 2 4 7 . 5 0 0 7 . 5 0 0 8. 000 7 . 5 6 2 1. 148 1 . 0 1 0 1 . 0 1 0 1 . 0 6 7 3 . 24 . 26 8 . 80 1. 50 38 4 0 : 4 0 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 3 9 1 . 6 2 3 0 . 000 0 . 000 7 0 . 20 8 2 . 04 8 0 . 0 0 7 7 . 0 4 7 . 5 0 2 7 . 500 8 . 0 0 0 7 . 5 6 6 1. 129 . 998 . 9 8 0 1. 844 3 . 1 9 . 32 0 . 00 1. 48 39 5 0 : 3 0 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL . HMB HMC 1. 4 4 3 1 . 6 5 9 0 . 0 0 0 0 . 0 0 0 7 0 . 4 1 8 1 . 29 8 0 . 0 0 7 6 . 84 7 . 4 9 9 7 . 5 0 3 8 . 000 7 . 569 1. 104 . 9 6 9 . 950 1 . 020 3 . 13 . 4 1 0 . 00 1 .47 48 6 0 : 2 0 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 447 1 . 6 9 5 0 . 8 8 8 0 . 000 7 0 . 76 8 0 . 3 6 8 0 . 00 7 6 . 61 7 . 504 7 . 499 8 . 0 0 0 7 . 5 7 3 1. 078 . 9 4 8 . 920 . 9 9 4 3 . 17 . 38 8 . 00 1. 42 41 7 0 : 1 0 : 28 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 453 1. 7 3 3 0 . 000 0 . 000 7 1 . 17 7 9 . 3 8 8 0 . 0 0 7 6 . 3 7 7 . 5 0 0 7 . 4 9 9 8 . 0 0 0 7 . 574 1. 051 . 9 2 2 . 890 .966 3 . 28 . 16 0 . 00 1. 37 42 8 0 : 0 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 459 1 . 7 8 9 0 . 000 0 . 0 0 0 7 1 . 70 7 8 . 4 2 8 0 . 0 0 7 6 . 17 7 . 5 8 0 7 . 4 9 9 8 . 000 7 . 578 1. 031 . 988 . 8 6 8 . 9 4 2 3 . 65 . 82 8 . 0 0 1. 36 43 io: 0: 90 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.365 1. 890 0. 000 8. 000 66. 72 90. 58 80. 00 78.75 7.500 7.472 8 . 0 0 0 7. 546 1.832 1.819 1.778 1.819 2. 66 . 05 0 . 00 1. 20 44 e: 10 : 90 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.364 1.745 0 . 000 0. 000 66.02 91. 73 80. 00 78. 84 7. 501 7.500 8. 800 7. 555 1. 831 1.819 1. 888 1. 822 2. 17 . 28 0 . 0 0 1 . 10 45 o: 9 0 : 10 +12.7 mm 12.7 X 0 .6 mm - 0.6 mm TOTAL HMB HMC 1.431 1.523 0. 000 0. 000 68.01 84. 24 80. 00 76.90 7. 498 7.500 8 . 0 0 0 7. 551 1 . 883 .932 1 . 000 1. 029 1 . 79 . 03 0 . 00 .81 46 10: 80: IO +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.433 1. 539 0. 000 0 . 000 68.07 83. 47 80. 00 76. 65 7. 500 7. 500 8. 880 7. 554 1. 061 . 953 .970 1 . 002 1 . 60 . 09 0 . 00 . 74 47 20: 78: 18 +12.7 mm 12.7 X 0.6 mm - 8.6 mm TOTAL HMB HMC 1. 436 1.556 0. 000 0. 000 63. 25 82.70 80. 00 76. 45 7. 500 7. 500 8. 000 7. 558 1. 038 .932 . 940 . 977 1.51 . 15 8. 00 . 72 48 30: 60: 10 +12.7 mm 12.7 X 8.6 mm - 8.6 mm TOTAL HMB HMC 1.439 1.577 8. 000 0 . 000 68.39 81 . 92 80. 00 76. 22 7. 504 7. 500 8. 000 7. 563 1.011 .903 .910 . 950 1. 38 . 28 0 . 00 . 69 49 60: 30: 10 +12.7 mm 12.7 X 8.6 mm - 8.6 mm TOTAL HMB HMC 1 .451 1.660 0. 000 0 . 0 0 0 69. 07 79. 64 80. OO 75. 66 7. 583 7. 583 8. 808 7. 574 . 920 . 836 . 820 . 366 1.19 . 39 0 . 08 . 67 The C o a l B l e n d i n g Model Pg 117 ID CD CD CO 00 CD CO rt CO CD CO co *—« CD in CM 'v0 CD Tf T-4 CD CD CD CD CD CD CO CD CD CO CM 00 CD CO CM CM CD CO CM CO CD CO rt TH CD co CD CD CD CD CD CD CD CD T-H CD T-H CD T-H CD CD T-H CD i CD CD 1 CD CD ON CD IV CO CD CO CO •M- CD CD CD rv -rH rv CD CD CO T-H CD rt IV CD IV CM in 00 rv in in in ON rv 00 CO CM ON T"H ON CO CO 00 CO T-H ON T-H CD CD rt ON CD T-H CO rv IV rv CO CO 00 CO CO ON CO CO iv CO 03 rv rv CO in CO CO CO ON CO ON ON CD C N CD CD CD CD CD CO CD CD CD •vi- CD CO CD CO T-H CD CD CO CD ON CD 00 CS CD CD T-t CD 0"* CD CO CD CD CD CO CD CD CD ce CD CD CD rv CD CD CD rv CD ON CD CO CD CD CD in in •st CD i n in m CD in in m CD i n tn m CD i n m LO CD in in rt CD in i n in CD i n rv CO rv (V IV CO rv IV IV CO rv rv IV CO rv IV rv CO IV IV IV CO IV IV iv CO rv T-H CD cr. 0N CD CO CO CO CD co •vt CD in CO 00 CD in 00 rt CD rt i n CO CD ON CO CO CD CD IV rt CD CO in TH CD CD rt rv CD rt ON IV CD CM i n CM CD CD •st CO CD CO CD CO CD i n 00 CD CD in CO T-H CD CO C N CO CD in ON IV CD in ON in CD Ti- CO CO CD i n |V CO IV CO CO CO IV CO CO CO rv CO iv CO IV CO IV CO rv CO iv CO r- CO CO CO rv CD m CD CD CO m CD CD CM ON CD CD CO m CD CD CO co CD CD 00 CM CD es Tf CO CD CD IV 00 CD CD rt CM CD CD rt ON CD CD m ON CD CD co CO CD CD CO CO CD CD co -—i CD CD rt IV CD CD CO CD CD Tl" in CD CD CO CD CD Tj- rv CD CD Tt IV CD CD rt in CD CD' T-H r« CD CD T-H T-H CD CD r4 CD CD T-H CD CD T-H CD CD TH CD CD T-H T-H CD CD m u m o o o o o o z: z: z: z: z. z: z: z: z: z: z: z: X X X X X X X X X X X X X X £ £ £ £ £ £ £ £ £ £ £ £ CO CO CO CO CO CO CO £ m £ • £ • • £ > £ • £ • £ CD £ £ CD £ £ CD £ £ CD £ £ CD £ £ CD £ £ CD £ £ £ £ £ £ £ £ rv X _J rv X _J IV X _ l IV X _ i IV X _ l rv X _ l IV X _J • CO cc • CO cc « CO CC > CO cc > CO CC • CO CC > CO cc CM rv • 1- CM IV 1- CM IV m 1— CM rv • « 1- CM IV • I— CM iv • 1- CM rv > 1— T-H CD o TH • CD o • CD o —* • CD o T-H CD o T-H • CD o T-l • CD o + CM 1— + CM 1— + CM t— + CM 1- + CM 1- + CM 1— + CM I— T-H 1 T-H I T-H 1 T-H 1 T-H 1 T-H 1 T-H 1 (9 CD CD CD CD CD OD * H T-H *-H T-H mm a B mu #_ •mm CD CD CD CD CD CD CD in CM T-H CD « , , CD CD CD CD CD CD CD ON i n rt IV CO CD T-H CD —« CM CO rt in CO i n i n i n in i n in i n 57 8 : 8 : 1 8 8 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HUB HMC 1.361 1 . 8 9 0 0 . 000 0 . 000 6 3 . 59 9 2 . 42 88-. 88 7 7 . 9 3 7 . 5 0 3 7 . 4 4 3 8 . 0 0 0 7 . 5 3 2 1 . 9 0 0 1 . 9 4 3 1. 900 1 . 9 1 9 . 8 8 - . 0 1 0 . 88 - . 0 0 58 1 8 : 9 8 : 0 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .436 1 .526 0 . 000 0 . 000 6 6 . 53 8 2 . 59 8 8 . 88 7 5 . 65 7 . 5 0 0 7 . 5 0 0 8 . 800 7 . 554 . 9 1 8 . 868 . 870 . 889 - . 2 2 . 04 0 . 80 - . 8 5 59 9 0 : 1 0 : 0 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .473 1. 733 0 . 000 0 . 000 6 8 . 74 7 6 . 28 8 0 . 00 7 4 . 15 7 . 501 7 . 5 0 3 8 . 800 7 . 5 8 2 . 639 . 6 4 8 . 6 3 0 . 6*38 - . 4 7 . 16 0 . 00 - . 8 7 68 8 8 : 2 0 : 0 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 8 . 6 mm TOTAL HMB HMC 1 . 466 1. 696 0 . 000 0 . 000 6 8 . 20 7 7 . 14 8 0 . 00 7 4 . 32 7 . 5 0 2 7 . 5 0 5 8 . 8 8 8 7 . 588 . 675 . 677 . 668 . 674 - . 6 6 . 29 O. 88 - . 0 9 61 2 0 : 8 8 : 0 + 1 2 . 7 mm 1 2 . 7 X 8 . 6 mm - 8 . 6 mm TOTAL HMB HMC 1. 439 1. 541 0 . 000 0 . 000 6 6 . 61 81 . 83 8 0 . 0 0 7 5 . 41 7 . 5 8 5 7 . 500 8 . 880 7 . 5 5 9 . 888 . 838 . 8 4 8 . 8 5 9 - . 4 1 . 0 9 0 . 00 - . 1 1 62 7 0 : 3 0 : 0 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .459 1. 661 0 . 000 0 . 000 6 7 . 69 7 3 . 84 8 8 . 00 7 4 . 48 7 . 5 0 O 7 . 5 0 3 8 . 800 7 . 576 . 7 1 6 . 704 . 690 . 707 - . 8 3 . 3 7 0 . 00 - . 1 1 63 3 0 : 7 0 : 0 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 442 1 .553 0 . 000 0 . 000 6 6 . 72 81 . 06 8 0 . 00 7 5 . 19 7 . 500 7 . 580 8 . 000 7 . 561 . 859 . 3 1 2 . 8 1 0 . 831 -.57 . 14 0 . 00 - . 14 Type # Seam Hame S i z e F r a c t i o n C UNIT '/. Weight y. Mini mum y. Maximum 1 Coal fl +12.7 mm 12.7 X 0.6 mm - 0.6"mm HMB HMC 35. 00 48.25 16. 75 0 48 2 CoalC +12.7 mm 12.7 X 0.6 mm - 0 . 6 m m HMB HMC 42. 28 47. 68 18. 28 0 •48 .3 Coal D +12.7 mm 12.7 X 0.6 mm - 0.6 mm HMB HMC 45.58 43. 58 11. 88 50 30 CIean Coal fish = S u l f u r minimum = S p e c i f i c G r a v i t y min. The Step S i z e = 7. 59 0. 00 - 1.20 5. 00 Maximum = Maximum = 2.40 2. 00 # T 1 . T 2 . T 3 SI2E FRACTION CLEANING UNIT MODEL S. G. MODEL YIELD MODEL ASH MODEL SULFUR MODEL FACTOR 100:8:0 +12.7 mm 12.7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 483 1. 782 8. 888 8. 888 69. 53 75. 24 86. 66 74.64 7.586 7.499 8. 866 7. 596 . 596 .611 . 688 . 684 ZERO ZERO ' ZERO ZERO 0 : 1 0 0 : 0 +12.7 mm 12.7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 434 1 .513 0. 000 0. 000 66. 45 83. 38 88. 68 75. 89 7.588 7. 506 8.000 7.554 . 947 . 894 . 968 .914 ZERO ZERO ZERO ZERO 0:0:100 +12.7 mm 12.7 X 0.6 mm - 0 . 6 mm TOTAL HMB HMC 1.361 1 . 891 8. 888 8. 868 63. 59 92.42 86. 66 77. 94 7. 503 7. 443 8. 688 7.528 1. 986 1 .949 1. 988 1. 925 ZERO ZERO ZERO ZERO 1 2 8 : 1 5 : 65 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 387 1 . 7 1 2 0 . 000 0 . 000 7 5 . 17 8 7 . 62 8 6 . 88 8 1 . 3 6 7 . 502 7 . 500 8 . 888 7 . 561 1 . 6 4 7 1 . 5 1 7 1 . 4 9 0 1 . 5 6 9 9 . 93 . 3 1 6 . 60 4 . 5 1 2 3 5 : 0 : 65 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 1 0 1 . 8 2 8 0 . 888 8 . 880 7 5 . 9 8 8 6 . 88 8 6 . 86 8 1 . 06 7 . 5 0 2 7 . 4 9 6 8 . 8 8 6 7 . 564 1. 6 4 3 1. 5 0 5 1. 4 4 5 1. 5 5 5 1 0 . 45 . 08 O. 00 4 . 49 3 2 5 : 1 0 : 65 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 390 1. 739 0 . 000 0 . 000 7 5 . 34 8 7 . 11 8 6 . 80 8 1 . 22 7 . 495 7 . 586 8 . 888 7 . 5 6 8 1. 6 4 5 1 .511 1. 4 7 5 1.56*3 1 0 . 03 . 23 0 . 00 4 . 47 4 3 0 : 0 : 70 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 384 1. 838 0 . 688 8 . 868 7 5 . 50 8 6 . 98 8 8 . 68 8 1 . 23 7 . 5 8 1 7 . 498 8. 868 7 . 5 6 3 1. 6 8 4 1 . 5 6 9 1 . 5 1 0 1 . 6 1 0 1 0 . 24 . 08 8 . 88 4 . 46 5 3 0 : 5 : 65 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 399 1 . 773 8 . 868 6 . 600 7 5 . 57 8 6 . 59 8 8 . 88 8 1 . 18 7 . 499 7 . 499 8. 688 7 . 5 6 3 1. 6 4 4 1 . 5 0 6 1. 4 6 0 1. 5 5 8 1 0 . 1 1 . 16 0 . 60 4 . 44 6 1 5 : 2 0 : 65 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 8 . 6 mm TOTAL HMB HMC 1. 383 1. 692 0 . 000 0 . 000 7 4 . 58 8 8 . 12 8 8 . 68 .81.31 7 . 563 7 . 581 8. 666 7 . 568 1. 6 5 5 1 . 5 1 7 1 . 5 0 5 1 . 5 7 5 9 . 53 • j b 0 . 60 4 . 37 7 2 5 : 15 : 60 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .411 1 . 7 1 3 0 . 000 0 . OOO 7 5 . 18 8 6 . 7 2 8 6 . 00 8 1 . 0 0 7 . 497 7 . 582 8. 000 7 . 5 6 1 1 . 6 0 4 1. 450 1. 425 1 . 5 1 2 9 . 78 . 2 9 0 . 00 4 . 35 8 18 : 3 0 : €0 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 3 8 9 1 .651 8 . 868 8 . 868 7 4 . 47 8 8 . 12 8 8 . 8 6 8 1 . 2 7 7 . 562 7 . 5 8 4 8 . 8 0 0 7 . 5 5 9 1 . 6 1 5 1. 464 1 . 4 7 0 1 . 536 9 . 37 . 33 0 . 00 4 . 34 9 2 0 : 2 0 : 60 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .484 1 . 6 9 2 8 . 888 8 . 868 7 4 . 8 9 8 7 . 2 1 8 0 . 0 0 8 1 . 08 7 . 5 0 0 7 . 5 0 0 8 . 8 8 8 7 . 5 6 0 1. 60S 1. 4 5 6 1. 440 1 . 5 1 8 9 . 53 . 35 0 . 00 4 . 33 18 1 5 : 2 5 : 60 + 1 2 . 7 mm 1 2 . 7 X 0. ; 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 392 1. 672 6 . 868 6 . 8 6 8 7 4 . 62 8 7 . 78 8 8 . 88 8 1 . 16 7 . 4 9 6 7 . 5 0 0 8 . 0 0 0 7 . 557 1 . 6 1 3 1. 457 1. 4 5 5 1. 5 2 4 9 . 38 . 40 0 . 00 4 . 32 11 3 0 : 1 0 : 60 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 1 5 1 .739 8 . 8 8 8 8 . 8 8 8 7 5 . 3 8 8 6 . 28 8 8 . 8 8 8 8 . 8 7 7 . 4 9 6 7 . 5 0 0 8 . 8 8 8 7 . 561 1. 6 6 8 1 . 4 5 2 1 . 4 1 6 1 . 5 6 9 9 . 78 . 2 2 0 . 00 4 . 3 1 12 3 5 : 5 : 60 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .418 1 .771 0 . 000 0 . 000 7 5 . 63 8 5 . 7 8 8 8 . 60 8 8 . 7 7 7 . 501 7 . -499 8 . 000 7 . 5 6 5 1. 591 1. 4 4 6 1 . 3 9 5 1 . 5 0 0 9 . 90 . 15 0 . 00 4 . 38 13 5 : 3 5 : 60 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - O . 6 mm TOTAL HMB HMC 1. 386 1. 631 8 . 688 8 . 860 7 4 . 2 3 8 8 . 51 8 0 . 66 8 1 . 3 1 7 . 505 7 . 5 0 0 8 . 000 7 . 557 1 . 6 1 7 1. 466 1. 4 3 5 1 . 534 9 . 25 . 33 0 . 80 4 . 29 14 4 0 : 0 : 60 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .421 1 .814 8 . 888 0 . 000 7 5 . 83 8 5 . 19 3 8 . 88 8 8 . 64 7 . 498 7 . 497 8 . 000 7 . 564 1. 591 1. 445 1. 336 1. 496 10 . 03 . 07 0 . 00 4 . 26 The C o a l B l e n d i n g Model Pg 123 APPENDIX E: C o a l B l e n d i n g Model R e s u l t s : Example P r o b l e m T h r e e The C o a l B l e n d i n g Model Pg 124 £ 3 £ •r- © CO X CD CO CD <d •Hi •i-i ZZ .V <= 5 £ ••- CD CO CO C - r— ZZ .\" «-> <S in in CO CO CO CO CO CO o> CO CM fv m Cn CO CM CD CM •r-(V in CO co cr> CM |V CM IV CO CO — * m CO •* M- r H .\" J— 1—1 « O m O m CJ ZZ ZZ ZZ zz ZZ X X X X X X o c o £ £ £ •p- £ £ £ «-> u CO CO CD rt) £ £ • £ > i . £ CO £ £ CO £ CO £ . li. £ £ £ |V X |V X iv X Ol • CO • CO • CO N CM IV • CM IN. m CM |V • - r - r l • CO • CO CO co + CM + CM + CM 1 1 r H 1 0> s rt) z £ rt) Ol CC m o to >— r — r — rt) rt) rt) o o o o o o * Of CM CO a. CO CO co cn CM II II x x it) rt) CO CO CO CO CO r f CM CO —i in II II x ii Si £ X £ — C rt) • -0 £ O c C 3 rt) <V-01 — — 3 CJ CO > Ol rt) N c — U CO u Q. • r - Ol — 01 (J Ol Ol a x co t— The C o a l B l e n d i n g M odel Pg 125 cc: _l o LU i - O o o o o o o O o o O o « o 0 . Ct. 0 . ct 0. Cn Ct. cn cm cn oc cn o cc Ul LU LU Ul LU Ul Ul Ul Ul Ul LU LU N rsi N rvi (\l N INI i M f\l N M cn CO t CO CO VO CO VD CD CM CO CM _I LO rt CD CO r- rv CD vo rt CO CO CO VO VO vo vo rt •vr •vt -st ON ON ON ON _ l o —H t «-< -c to CO VO CD cr. CD CO CO CD IO CO CO CO _i z CD CM CD CO CD vo CO CD ON CO CO CO LU to CO h- CO CO CD IV. CO cr> ON CO CO CO « cc O OS IV. CO cr. 00 ON CO CO cr. ON ON CO CO CD VO LO Cr> CO 0> VD IO CD —H _ l (=) IV CD VO CO 00 CD CM VO IV- CD ON LU _ l a LU LO VO CD vo CD CO CO CO rt 00 CO o r-i IV- r-. CO r- IO CO CO VO IV- CO CO CO > fs. co CO co CO CM CD CD 0N rt CD CO _ l • LO CD CD CD CO CTv CD CD CO LO CD CD LU L3 VO OS CO CD •vt CO CO CD LO VO CO CO « O to —« CD CO —H CD CO CD CO -C (J z t—1 1-z l-H m o m o m o cc z E: IC LU I z X z X X _ l O £ £ £ £ Z vo vo co UJ o « £ • £ • ISJ CD £ £ CD £ £ CD £ 1- £ £ £ to u X _J (V- X _J IV. X _J cc « VO cc • CD CC • CO CC Ct. CM rv. • 1- CM |v- 1- CM IV. • 1— u. —4 • CO o • CD o —-4 • CO o + CM 1- + CM t - + CM 1— —-4 1 1 1 CO CO CD CO >> CO CO CO --4 CM CD a. 1- CD CO • • CD • > • > —-i CO CO 1-1 4 0 : 2 5 : 35 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 8 9 1 .898 8 . 888 8 . 8 0 0 6 8 . 14 8 3 . 36 8 6 . 8 8 7 6 . 3 1 9 . 000 8 . 9 8 2 9 . 6 6 6 8 . 9 9 2 1 . 106 . 926 . 9 8 5 1. 0 0 2 1. 49 1. 03 0 . 60 1. 15 2 4 5 : 2 5 : 30 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 8 . 6 mm TOTAL HMB HMC 1 .498 1 .898 8 . 800 0 . 000 6 8 . 25 8 2 . 47 8 6 . 00 7 6 . 0 1 9 . 681 8 . 848 9 . 6 8 6 8 . 9 3 3 1 . 0 9 7 . 9 0 6 . 8 9 8 . 9 8 7 1. 63 . 8 6 8 . 88 1.11 3 3 5 : 3 0 : 35 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 479 1 .827 8 . 880 8 . 8 8 8 6 6 . 55 8 3 . 69 8 8 . 66 7 5 . 57 9 . 001 8 . 998 9 . 686 9 . 888 1. 154 . 9 5 8 . 9 4 5 1 . 6 4 4 1. 36 1. 62 6 . 66 1 . 68 4 3 5 : 2 5 : 40 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .485 1 . 8 8 1 8 . 888 8 . 888 6 8 . 67 8 3 . 95 8 8 . 86 7 6 . 49 9 . 664 8 . 996 9 . 668 9 . 866 1 . 1 1 4 . 9 3 6 . 9 2 8 1 . 6 1 2 1. 46 . 99 6 . 68 1 . 0 7 5 4 0 : 3 0 : 30 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 481 1. 898 8 . 688 8 . 688 6 6 . 6 3 8 2 . 88 8 8 . 88 7 5 . 36 9 . 863 8 . 982 9 . 866 8 . 9 5 9 1. 147 . . 9 4 6 . 9 3 6 1. 031 1 . 4 7 . 9 1 0 . 00 1. 07 6 4 0 : 2 0 : 40 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .508 1 .815 6 . 888 8 . 668 6 9 . 5 2 8 3 . 66 8 6 . 88 7 7 . 16 9 . 0 0 0 8 . 997 9 . OOO 8 . 9 9 8 1 . 0 5 3 . 9 0 2 . 8 8 8 . 9 6 3 1 .33 1 .07 0 . 00 1. 07 7 4 5 : 2 0 : 35 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .514 1 .898 6 . 888 8 . 868 6 9 . 52 8 2 . 96 8 6 . 68 7 6 . 89 9 . 002 8 . 9 3 8 9 . 000 8 . 973 1 . 8 4 3 . 8 8 8 . 8 6 5 . 951 1 .35 1. 04 0 . 66 1. 06 8 4 5 : 3 0 : 25 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .484 1 .390 0 . 000 0 . 000 66.76 8 1 . 9 6 8 0 . 0 0 7 5 . 0 1 9 . 005 8 . 751 9 . 000 8 . 8 9 4 1. 139 . 924 . 9 1 5 1 . 0 1 8 1. 64 . 68 0 . 00 1 .04 9 5 0 : 2 5 : 25 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 508 1 .890 0 . 000 0 . 0 0 0 6 8 . 2 6 8 1 . 58 8 0 . 00 7 5 . 66 9 . 000 8 . 701 9 . 000 8 . 8 6 8 1. 0 8 7 . 8 8 6 . 8 7 5 . 971 1 .66 . 66 0 . 00 1 .03 10 3 5 : 2 0 : 45 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .500 1 .785 0 . 000 0 . 000 6 9 . 5 2 8 4 . 2 1 8 0 . 0 0 7 7 . 3 7 9 . 002 8 . 999 9 . 000 9 . 008 1. 8 6 5 . 9 1 6 . 8 9 5 . 9 7 8 1. 33 . 96 0 . 00 1. 02 11 5 0 : 3 0 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .489 1 .890 0 . 000 0 . 000 6 6 . 8 8 8 1 . 06 8 0 . 00 7 4 . 72 9 . 001 8 . 6 0 5 9 . 000 8 . 829 1. 133 . 9 8 5 . 9 8 8 1 . 0 0 4 1 .79 . 4 8 0 . 00 1 .82 12 3 5 : 3 5 : 30 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 474 1 .890 0 . 000 0 . 000 6 5 . 02 8 3 . 30 8 0 . 0 0 7 4 . 56 9 . 000 8 . 9 5 4 9 . 0 0 0 8 . 981 1. 193 . 9 7 9 . 9 7 0 1. 8 7 6 1. 26 . 95 8 . 8@ 1. 80 13 5 5 : 3 0 : 15 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .497 1 .890 0 . 000 0 . 000 6 6 . 9 8 8 0 . 14 8 0 . 00 7 4 . 40 9 . 001 8 . 455 9 . 000 8 . 7 6 3 1. 126 . 8 8 4 . 8 8 5 . 9 8 9 1. 92 . 25 0 . 00 . 97 14 4 0 : 3 5 : 25 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .476 1. 890 0 . 000 0 . 000 6 5 . 12 3 2 . 37 8 0 . 00 7 4 . 2 6 9 . 001 8 . 884 9 . 000 8 . 9 1 7 1 . 185 . 9 5 9 . 9 5 5 1. 861 1 . 39 . 72 0 . 00 . 96 15 30! 30: 40 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1 .477 1. 788 8. 000 0. 000 66. 45 84. 24 80.00 75. 71 9. 003 8.999 9. 000 9. 001 1. 163 . 972 . 960 1.057 1 . 23 . 88 0. 00 . 96 16 30: 25: 45 +12.7 mm 12.7 X 0.6 mm - O.6 mm TOTAL HMB HMC 1.482 1.775 0. 808 8. 880 67. 93 84. 52 88. 00 76. 64 9. 004 8. 999 9. 000 9. 881 1. 123 . 947 . 935 1. 024 1. 25 . 87 8. 86 . 96 17 30: 20: 50 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1 . 491 1. 762 0. 000 8. 000 69. 48 84. 79 88. 88 77. 57 9. 662 8. 999 9. 668 9. 661 1. 073 . 932 .910 . 991 1.27 . 86 0. 00 . 96 18 30: 35: 35 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 472 1.886 8. 868 0. 688 64.97 83. 98 86. 60 74. 77 9.886 8. 999 9. 668 9. 000 1. 198 .998 . 985 1 . 885 1. 16 . 93 6. 88 . 95 19 50- 20: 30 +12.7 mm 12.7 X 0.6 mm - 8.6 mm TOTAL HMB HMC 1.518 1. 898 8. 686 8. 860 69. 48 82. 08 80. 00 76.51 9.882 8. 790 9. 000 8. 986 1 . 832 . 872 .858 . 936 1. 32 . 83 0 . 08 . 95 28 30: 40: 30 +12.7 mm 12.7 X 8.6 mm - 0.6 mm TOTAL HMB HMC 1.469 1.857 0. 000 0. 000 63. 58 83.69 80.00 73. 84 9.O04 8. 999 9. 006 9. 002 1. 227 1.014 1.010 1.113 1.13 . 94 8. 08 . 95 21 45: Ts:' 48 + 12. 7 'mi*. 12.7 X 0.6 mm - 0.6 mm TOTAL HMB " HMC 1.521 1. 852 0. 808 0. 000 70. 76 83.37 86. 00 77. 70 9. 006 8. 999 9. 660 9.000 991 . 871 . 848 .917 .97 1.15 0. 00 . 94 22 4 5 : 3 5 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 478 1 . 8 9 0 0 . 000 0 . 000 6 5 . 2 0 3 1 . 4 5 8 0 . 00 7 3 . 95 9 . 000 8 . 664 9 . 0 0 0 8 . 857 1. 178 . 940 . 9 4 0 1 . 0 4 7 1 .51 . 5 1 0 . 00 . 92 23 5 5 : 2 5 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .514 1 . 8 9 0 0 . 000 0 . 000 6 8 . 2 2 8 0 . 69 8 0 . 00 7 5 . 2 9 9 . 003 8 . 5 5 9 9 . 0 0 0 8 . 8 0 6 1. 076 . 867 . 860 . 955 1. 65 . 45 0 . 00 . 9 2 24 5 0 : 3 5 : 15 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 480 1 . 8 9 0 0 . 000 0 . 000 6 5 . 37 8 0 . 52 8 0 . 00 7 3 . 6 9 9 . 003 8 . 5 0 4 9 . 888 8 . 7 8 9 1. 174 . 920 . 925 1 .034 1 . 73 . 29 0 . 00 . 92 25 4 0 : 1 5 : 45 +12 .7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .518 1. 797 0 . 000 0 . 000 7 0 . 7 8 8 3 . 93 8 8 . 00 7 7 . 93 9 . 001 8 . 9 9 8 9 . 000 8 . 999 1 . 001 . 8 8 7 . 855 . 931 . 99 1. 05 0 . 00 . 9 1 26 3 5 : 4 0 : 25 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 470 1 .890 0 . 000 0 . 000 6 3 . 60 8 2 . 81 8 0 . 00 7 3 . 54 9 . 000 3 . 866 9 . 000 8 . 944 1. 227 . 9 9 5 . 995 1 . 103 1 . 20 • 77 0 . 00 . 9 1 27 5 5 : 3 5 : 10 +12 .7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 484 1. 890 0 . 000 0 . 000 6 5 . 5 0 7 9 . 6 0 8 0 . 0 0 7 3 . 41 9 . 0 0 5 8 . 346 9 . 0 0 0 8 . 722 1. 168 . 903 . 9 1 0 1. 021 1. 90 . 08 0 . 00 . 90 28 6 0 : 3 0 : 10 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 m m TOTAL HMB HMC 1 . 506 1 . 8 9 0 0 . 000 0 . 000 6 6 . 98 7 9 . 26 8 0 . 80 7 4 . 0 7 8 . 995 8 . 304 9 . 000 8 . 6 9 5 1 . 1 1 7 . 864 . 878 . 974 1 . 96 . 87 0 . 00 . 89 29 2 5 : 3 8 : 45 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 475 1 . 7 6 4 0 . 000 0 . 000 6 6 . 39 8 4 . 83 8 0 . 00 7 5 . 8 9 9 . 000 8 . 999 9 . 000 9 . 0 0 0 1 . 170 . 9 8 1 . 975 1 . 0 6 6 1 . 13 . 78 0 . 00 . 87 30 4 0 : 4 0 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 472 1 . 8 9 0 0 . 0 0 0 0 . 000 6 3 . 68 8 1 . 85 8 0 . 00 7 3 . 23 9 . 000 8 . 7 1 1 9 . 0 0 0 8 . 879 1 . 2 2 0 . 980 . 9 8 0 1 . 091 1. 34 . 54 0 . 00 . 87 31 5 0 : 1 5 : 35 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 5 2 5 1 . 8 9 0 0 . 000 0 . 0 0 0 7 0 . 75 8 2 . 55 8 0 . 00 7 7 . 36 8 . 995 8 . 8 7 8 9 . 000 8 . 942 . 979 . 852 . 825 . 901 . 95 . 9 9 0 . 00 . 86 32 3 5 : 1 5 : 50 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 5 1 4 1 . 7 7 2 0 . 000 0 . 000 7 0 . 77 8 4 . 48 8 0 . 00 7 8 . 14 9 . 002 8 . 999 9 . 000 9 . 0 0 0 1 . 0 1 2 . 8 9 7 . 8 7 0 . 9 4 2 . 98 . 94 0 . 00 . 86 33 2 5 : 4 0 : 35 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 6 7 1. 793 0 . 000 0 . 0 0 0 6 3 . 53 8 4 . 31 8 0 . 00 7 4 . 01 9 . 0 0 1 8 . 999 9 . 000 9 . 000 1 . 2 3 3 1. 0 2 7 1. 0 2 5 1. 124 1. S3 . 84 0. 00 . 86 34 2 5 : 2 5 : 50 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 479 1. 753 0 . 008 8 . 800 6 7 . 84 8 5 . 08 8 0 . OO 7 6 . 80 9 . 001 9 . 008 9 . 000 9 . 008 1 .131 . 961 . 950 1. 036 1 .13 . 76 0 . 80 . 86 35 2 5 : 2 0 : 55 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 436 1. 742 0 . 000 8. 000 6 9 . 36 8 5 . 34 8 0 . 88 7 7 . 73 9 . 004 9 . 008 9 . 008 9 . 002 1. 082 . 941 . 925 1 . 081 1 .14 . 74 0. 00 . 85 36 55: 28: 25 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HUB HMC 1. 522 1. 898 0. 000 8. 000 69. 47 81 . 20 80.00 76. 15 9. 001 8. 652 9. 000 8.844 1. 022 . 852 . 835 .921 1. 32 .62 6. 60 .85 37 25: 35: 48 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.471 1.778 0. 000 0. 000 64. 90 84. 57 80. 00 74. 93 9. 000 8.999 9. 000 8. 999 1.208 1. 004 1 . 006 1. 695 1. 65 .81 0. 06 . 85 38 60: 25: 15 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.519 1. 898 8. 000 0. 000 68. 22 79.88 88. 86 74. 94 9. 002 8. 487 9. 000 8. 738 1 . 869 .846 . 845 . 94*6 1. 67 .25 0. 00 . 83 39 45: 40: 15 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB ' HMC 1. 474 1. 898 8. 000 0. 000 63. 76 86. 91 86. 88 72. 93 9. 004 8. 556 9. 086 8.816 1.215 .959 . 965 1.677 1 . 47 .32 0 . 00 . 83 48 25: 45: 30 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 464 1.813 0. 000 8. 000 62. 14 84.88 86. 88 73.64 8. 998 8. 997 9. 886 . 8 .998 1. 263 1. 853 1.056 1. 154 . 94 . 85 0 . 80 .82 41 30: 45: 25 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 465 1. 898-8. 800 8. 068 62. 13 83. 22 80. 00 72. 78 8. 998 3.914 9. 066 8. 964 1. 258 1. 040 1. 035 1. 144 . 99 . 79 0. 00 . 32 42 30: 15: 55 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 583 1.752 6. 600 0. 000 78. 77 85. 03 80. 00 78. 36 3. 995 9. 066 9. 000 8. 998 1 . 626 . 969 • S 8 5 . 956 . 99 . 33 0 . 68 . 81 The Coal Blending Model Pg 132 T-H CO © © cr. IO © © 00 rv © ON © CO © OT rt ON © 00 CD © © 00 CD © © rv CO T-H © CO OT CO © CO a-. LO © IV CO TH © rv © CO © IV IO © IV Ct. CO © rv TH © © TH © TH © TH © TH © © CO © © rv rt © LO rt CM T-H © © . ON in ON CD CO © cr> CO ON © CO ON (V © OT T"H © CD cr. IV rv CO LO CM CM CO CM in TH IV CO CM © CO © CO in CO CO co 1-1 OT 0* CO CO CO CM © © T-H OJ © © T-H cr. CO CO 00 © ON ON ON CM ON cn © ON CO CO OT TH T-H — CD co © rt cr. ON © T-H © T-H © CD © 00 © ON TH in © 00 T-H CM © ON IV rt © CM CD CO © CO ON IV © ON © rv © © © ON © ON © ON © ON © © © rt cr. rt © 00 CD ON © ON Cr* ON © ON © rv © ON © ON © ON © ON © ON © © IV ON IV © 00 OS CO ON CO CO CO ON CO O- 00 ON OT ON 00 cr. co ON 00 cn CO ON OT ON 00 CO 00 ON 00 T-H CO © CO CO ON © ON T-H IV © ON CO © rv 00 LO © ON © rv © CM m T-H © T-H T4 © © CM CO CO © © CM CM © rt © co © rt 00 IO © LO CO ON © CO iv IV © © CM CO © CO © CO © CM CM CM © CM CM CO © CO © IO © 00 CO ON © CM © TH © IV (V CO CO IV CO CO CO rv CO CO 00 IV IV CO 00 rv IV 00 00 IV CD rv 00 rv iv 00 00 IV _, © © © © © © © CO © © © 00 CD © © T-H CM © © IO © © © 0- © © © CO o. © © CO ON © © CO ON © © CM © © © © CO © © rv ON © © CM ON © © LO CO © © CO © © rt CO © © LO CO © © m IV © © rt CO © © in 00 © © T-H © © T-H T-H © © T-H T-H © © T-H -© © TH T-H © © T-H T-H © © T-H T-H © © m o m o CJ m o n o m o o s: x zz ZZ X ZZ zz IZ zz X zz zz zz X X X X X X i . X X X X X X X £ £ £ £ £ £ £ £ £ £ £ £ £ £ CO CO co CO CO CO CO £ a £ a £ a £ a £ a £ a £ a £ © £ £ © £ £ © £ £ © £ £ © £ £ © £ © £ £ £ £ £ £ £ £ (v X _ l IV X _l IV X _l IV X _i IV X _l IV X _J IV X _1 • CO X a CO X a co X a co X a CD X a CD X a CO X CM IV a f - CM IV a 1— CM rv a h- CM IV a h- CM rv a 1— CM IV a K- CM IV a 1-T-H • © o T-H a © o T-H a © O T-H a © O T-H © o T-H a © O T-. a © o + CM I— + CM t- + CM 1— + CM h- + CM 1— + CM 1— + CM 1-• T-H 1 1 1 1 1 T-H 1 © IO © IO © © © CM CM rt CD T-H CO a. a. a. .a a. © © IO © in © in T-H LO rt T-T T-H rt T-H) .a .a a. m m • a .. © IO LO IO in © in IO CM CO rt CM IO in CO rt LO CO rv CO ON rt rt rt rt rt rt rt 50 2 0 ! 2 5 : 55 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 7 7 1 . 7 3 2 0 . 000 0 . 000 6 7 . 79 8 5 . 63 8 0 . 0 0 7 6 . 98 9 . 005 8 . 9 9 5 9 . 000 9 . 000 1 . 139 . 969 . 965 1 . 0 4 5 1 .06 . 6 2 0 . 0 0 . 77 51 2 0 ! 2 0 : 60 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 8 3 1 . 7 2 4 0 . 0 0 0 0 . 000 6 9 . 28 8 5 . 9 0 8 0 . 0 0 7 7 . 9 0 9 . 0 0 5 9 . 000 9 . 0 0 0 9 . 002 1 .091 . 9 5 2 . 940 1 . 0 1 2 1. 06 . 63 0 . 00 . 76 52 6 0 : 2 0 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 527 1 . 8 9 0 0 . 000 0 . 000 6 9 . 4 7 8 0 . 3 3 8 0 . 00 7 5 . 80 9 . 0 0 0 8 . 5 0 3 9 . 0 0 0 8 . 776 1 .011 . 8 3 3 . 820 . 905 1. 33 . 4 2 0 . 00 • 76 53 4 0 : 4 5 : 15 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 6 8 1 . 8 9 0 0 . 0 0 0 0 . 000 6 2 . 2 8 8 1 . 3 1 8 0 . 0 0 7 2 . 19 9 . 003 8 . 6 1 2 9 . 000 8 . 841 1. 254 1. O02 1 . 005 1. 121 1. 26 . 35 0 . 06 . 76 54 5 5 : 4 0 : 5 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 7 7 1 . 8 9 0 0 . 000 0 . 000 6 3 . 9 3 7 9 . 0 3 8 0 . 0 0 7 2 . 3 3 9 . 0 0 5 8 . 2 4 1 9 . 0 0 0 8 . 683 1 .201 . 9 1 9 . 9 3 5 1. 049 1 . 74 - . 12 0 . 00 . 76 55 2 0 : 3 5 ! 45 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 6 9 1 .754 0 . 000 0 . 000 6 4 . 8 5 8 5 . 15 8 0 . 00 7 5 . 10 9 . 000 9 . 000 9 . 0 0 0 9 . 0 0 0 1 . 2 0 7 1 . 0 1 7 1 . 0 1 5 1. 106 . 96 . 68 0 . 00 . 76 56 2 0 : 4 0 : 40 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .466 1 .766 0 . 000 0 . 000 6 3 . 47 8 4 . 89 8 0 . 0 0 7 4 . 17 8 . 999 8 . 999 9 . 0 0 0 8 . 999 1 .241 1. 036 1. 040 1. 134 . 92 . 7 1 0 . 00 . 75 5? 20: 30: 50 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.473 1.742 0. 000 0. 000 66. 25 85. 40 80. 00 76. 03 9. 000 9. 000 9. 000 9. 000 1. 173 . 991 . 990 1. 075 .97 . 66 0. 00 . 75 58 65: 25: 10 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 523 1. 890 0. 000 0. 000 68. 19 78. 92 80. 00 74. 58 9. 001 8. 253 9. 000 8. 669 1 . 060 . 828 . 830 . 925 1. 67 . 05 0. 00 . 74 59 40: 10: 50 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 524 1. 783 0. 000 0. 000 72. 06 84. 19 80. 00 78. 68 8. 998 8. 999 9. 000 8. 999 . 943 . 865 . 830 . 893 . 59 1. 03 0. 60 . 73 60 20: 45: 35 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB " HMC 1.462 1.781 0. 000 0. 000 62. 11 84. 61 80. 00 73. 21 8. 998 8. 999 9. 000 8. 998 1. 271 1.064 1. 065 1. 165 . 85 . 72 0. 00 . 73 61 20: 50: 30 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.459 1.797 0. 000 0. 000 60. 82 84. 34 80. 00 72. 28 9. 000 8. 998 9. 000 8. 999 1. 293 1.086 1.090 1. 189 . 82 . 76 0. 00 . 73 62 30: 50: 20 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 461 1. 890 0. 000 0. 000 60. 80 82. 70 80. 00 71. 74 8. 998 8. 824 9. 000 8. 928 1. 288 1. 059 1. 060 1. 170 . 93 .61 0. 00 . 72 63 20: 55: 25 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 456 1. 827 0. 000 0. 000 59. 57 84. 84 80. 00 71. 33 9. 003 8. 998 9. 000 9. 001 1. 32b 1.119 1.115 1. 220 . 77 . 78 0. 00 .71 64 4 5 : 4 5 : 10 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTfiL HMB HMC 1 . 4 7 0 1. 898 0 . 000 0 . 000 6 2 . 3 1 8 8 . 36 8 0 . 08 7 1 . 8 8 9 . OOO 8 . 453 9 . 0 0 0 8 . 7 7 4 1. 2 4 5 . 9 8 3 . 9 9 8 1. 186 1 .36 . 14 0 . 00 . 7 1 65 5 5 : 1 0 : 35 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTfiL HMB HMC 1. 535 1 .898 0 . 000 8 . 000 7 2 . 12 8 2 . 16 8 0 . 0 0 7 7 . 86 9 . 0 0 0 8 . 8 2 7 9 . 0 0 0 8 . 9 2 8 . 985 . 828 . 7 8 5 . 849 . 6 1 . 94 0 . 80 . 70 66 2 0 : 1 5 : 65 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTfiL HMB HMC 1. 491 1 . 7 1 7 0 . 000 0 . 008 7 0 . 70 8 6 . 13 8 8 . 88 7 8 . 76 8 . 9 9 5 9 . 884 9 . 000 9 . 888 1. 846 . 9 3 3 . 9 1 5 . 988 . 92 . 6 1 0 . 00 . 69 67 3 5 : 1 0 : 55 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTfiL HMB HMC 1 .521 1. 760 0 . 000 0 . 000 7 2 . 06 8 4 . 72 8 8 . 88 7 8 . 98 9 . 000 9 . 888 9 . 000 9 . 880 . 959 . 888 . 845 . 9 8 8 . 62 . 90 0 . 00 . 69 68 6 0 : 1 5 : 25 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 5 3 3 1. 898 0 . 888 8 . 888 7 8 . 7 8 8 8 . 84 8 8 . 00 7 6 . 65 8 . 9 9 8 8 . 598 9 . 888 8 . 8 1 5 . 9 5 7 . 8 1 6 . 795 . 878 . 98 . 60 0 . 00 . 68 69 15 : 3 5 : 50 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 468 1. 733 0 . 000 0 . 880 6 4 . 84 8 5 . 74 8 0 . 00 7 5 . 29 9 . 882 9 . 888 9 . 000 9 . 081 1 . 2 1 4 1. 021 1 . 0 3 0 1 . 1 1 3 . 98 . 57 0 . 00 . 68 78 2 5 : 5 5 : 20 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1. 457 1. 898 8 . 888 6 . 888 5 9 . 53 8 3 . 16 8 0 . 00 7 1 . 04 9 . 882 8 . 884 9 . 888 8 . 955 1 . 3 1 5 1. 097 1 . 100 1. 206 . 8 1 . 65 8 . 80 . 68 71 35: 50: 15 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.463 1.890 0. 000 0. 000 60. 85 81. 72 80. 00 71.44 8. 998 8. 665 9. 000 8. 863 1. 281 1. 040 1. 045 1 . 157 1.04 . 38 0. 80 . 67 72 50: 5: 45 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.537 1.827 0. 000 0. 000 73. 51 83.37 80. 00 79. 03 9. 003 8.998 9. 000 9. 000 . 858 . 825 . 775 . 831 . 23 1.21 0. 00 . 67 73 15: 30: 55 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.472 1. 723 0. 000 0. 000 66. 22 85. 98 80. 00 76. 21 9. 000 8.999 9. 000 9. 000 1. 179 1 . 005 1 . 005 1. 086 .91 . 54 0. 00 . 67 74 15: 25: 60 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB ' HMC 1. 475 1.716 0. 000 0. 000 67. 65 86. 22 80.00 77. 13 9. 000 9. 002 9. 000 9. 001 1.141 . 981 . 980 1. 053 . 90 . 53 0. 00 . 66 75 15! 50: 35 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 458 1. 769 0''. 000 0. 000 60. 86 84. 95 80. 00 72. 47 9. 001 8. 999 9. 000 9. 000 1. 301 1. 098 1. 105 1. 199 . 78 . 63 0. 00 . 66 76 30: 10: 60 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1 .517 1. 742 0. 000 0. 000 72. 07 85. 27 30. 00 79. 13 9.001 9. 000 9. 000 9. 000 . 972 . 890 . 860 . 921 . 64 . 82 0. 00 . 66 77 65: 20: 15 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.530 1.890 0. 000 0. 000 69. 47 79. 44 80. 00 75. 43 8. 995 8. 356 9. 000 8. 708 1 . 001 .811 . 805 . 888 1. 34 .21 0. 00 . 65 78 15: 45: 40 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.461 1. 755 0. 000 0. 000 62. 10 85. 23 86.86 73. 40 8.998 9. 668 9.886 8.999 1. 276 1.672 1 . 638 1. 173 . 79 .61 6. 60 . 65 79 15: 40: 45 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 464 1.742 0. 000 0.000 63. 42 85. 48 80.00 74. 33 8.997 9.888 9.000 8.999 1 . 248 1 . 848 1.055 1 . 145 . 82 . 57 6. 68 . 65 80 50: 45: 5 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 471 1. 898 8. 888 8. 888 62.33 79. 40 88. 88 71. 56 9. 000 8. 292 9. 000 8. 787 1. 241 . 961 .975 1. 093 1. 44 - . 6 9 8. 86 .65 81 15: 55: 30 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 455 1.784 8. 800 8.800 59. 61 84. 68 88. 60 71.53 9.003 8.999 9. 006 9.681 1. 328 1. 128 1. 130 1.230 . 73 . 66 0 . 00 . 64 82 55: 5: 40 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.541 1. 898 8. 000 8. 000 73.56 82.64 88. 88 78. 73 9. 681 8.915 9.688 8. 966 .843 . 866 . 766 .814 .25 1 . 12 0. 00 . 64 83 15: 20: 65 +12.7 mm 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1.488 1. 709 0. 000 0. 000 69. 14 86.43 86. 66 78. 04 9. 862 8.999 9. 000 9. 666 1 . 899 . 966 . 955 1 . 624 . 90 . 49 8. 00 . 63 84 20: 60: 20 + 12.7 mrn 12.7 X 0.6 mm - 0.6 mm TOTAL HMB HMC 1. 453 1. 898 8. 608 0. 008 58.32 83. 63 86.86 76. 32 9. 008 8. 945 9. 068 8. 979 1 . 341 1 . 142 1 . 148 1 . 243 . 68 . 69 0. 60 . 63 85 6 0 : 1 0 : 36 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 5 4 0 1 .890 0 . 000 0 . 0 0 0 7 2 . 18 8 1 . 33 8 0 . 00 7 7 . 52 9 . 001 8 . 692 9 . 000 8 . 857 . 8 9 5 . 8 0 5 . 770 . 8 3 6 . 65 . 76 0 . 00 . 62 86 4 5 : 5 : 50 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .533 1 . 7 9 2 0 . 000 0 . 000 7 3 . 4 6 8 3 . 91 8 0 . 00 7 9 . 2 4 9 . 0 0 1 8 . 9 9 9 9 . 0 0 0 9 . 000 . 8 7 4 . 8 3 6 . 7 9 0 . 8 4 5 . 22 1.11 0 . 00 . 6 2 87 3 0 : 5 5 : 15 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .458 1 .890 0 . 000 0 . 0 0 0 5 9 . 53 8 2 . 17 8 0 . 00 7 0 . 72 9 . 001 8 . 725 9 . 000 8 . 891 1 . 3 1 5 1. 0 8 3 1 . 0 8 5 1. 198 . 88 . 43 0 . 80 . 62 88 2 5 : 1 0 : 65 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .514 1 .725 0 . 000 0 . 0 0 0 7 2 . 08 8 5 . 8 1 8 0 . 00 7 9 . 35 9 . 001 9 . 000 9 . 000 9 . 001 . 9 8 3 . 9 0 5 . 8 7 5 . 934 . 67 . 70 0 . 00 . 6 2 89 4 0 : 5 6 : 10 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .464 1 .890 0 . 000 0 . 000 6 0 . 83 8 0 . 75 8 0 . 00 7 1 . 1 1 8 . 998 8 . 507 9 . 000 8 . 8 0 0 1. 274 1. 0 2 4 1 . 0 3 0 1. 145 1 . 10 . 16 0 . 00 . 6 1 98 1 5 : 1 5 : 70 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 .487 1 .703 0 . 000 0 . 000 7 0 . 65 8 6 . 65 8 0 . 00 7 8 . 9 4 9 . 0 0 3 8 . 995 9 . 0 0 0 8 ."999 1. 0 5 7 . 9 4 5 . 9 3 0 . 9 9 3 . 87 . 47 0 . 80 . 6 1 91 1 5 : 6 0 : 25 + 1 2 . 7 mm 1 2 . 7 X 0 . 6 mm - 0 . 6 mm TOTAL HMB HMC 1 . 4 5 2 1 .804 0 . 000 0 . 000 5 8 . 35 8 4 . 39 8 0 . 00 7 0 . 5 6 9 . 000 8 . 999 9 . 000 9 . 000 1. 3 4 5 1. 154 1. 155 1. 2 5 3 . 63 . 68 0 . 00 . 60 9 2 6 5 : 1 5 : 2 0 + 1 2 . 7 m m 1 2 . 7 X 0 . 6 m m - 0 . 6 mm T O T A L H M B H M C 1 . 5 3 8 1 . 8 9 0 0 . 0 0 0 0 . 0 0 0 7 0 . 8 3 7 9 . 9 6 8 0 . 0 0 7 6 . 3 0 9 . 0 0 0 8 . 4 5 5 9 . 0 0 0 8 . 7 5 0 . 9 4 1 . 7 9 6 . 7 8 0 . 8 5 2 1 . 0 3 . 3 8 0 . 8 0 . 6 6 9 3 7 0 : 2 0 : 1 8 + 1 2 . 7 m m 1 2 . 7 X 0 . 6 m m - 0 . 6 mm T O T A L H M B H M C 1 . 5 3 5 1 . 8 9 0 0 . 0 0 0 0 . 0 0 8 6 9 . 5 0 7 8 . 5 8 8 0 . 0 0 7 5 . 1 0 8 . 9 9 8 8 . 2 0 5 9 . 0 0 0 8 . 6 4 1 . 9 9 1 . 7 9 6 . 7 9 0 . 8 7 4 1 . 3 8 . 6 2 0 . 0 0 . 5 8 9 4 1 0 : 4 5 : 4 5 + 1 2 . 7 m m 1 2 . 7 X 0 . 6 m m - 0 . 6 m m T O T A L H M B H M C 1 . 4 6 0 1 . 7 3 3 0 . 0 0 8 0 . 0 0 0 6 2 . 1 2 8 5 . 8 4 8 0 . 0 0 7 3 . 5 9 8 . 9 9 9 9 . 0 0 0 9 . 0 0 0 9 . 0 0 0 1 . 2 7 9 1 . 0 8 5 1 . 0 9 5 1 . 1 8 } . 7 5 . 4 9 0 . 6 8 . 5 8 9 5 1 0 : 4 0 : 5 0 + 1 2 . 7 m m 1 2 . 7 X 0 . 6 m m - 0 . 6 m m T O T A L H M B H M C 1 . 4 6 3 1 . 7 2 3 0 . 0 0 0 0 . 0 0 0 6 3 . 4 3 8 6 . 0 7 8 0 . 0 0 7 4 . 5 2 8 . 9 9 7 8 . 9 9 9 9 . 0 0 0 8 . 9 9 8 1 . 2 5 4 1 . 0 6 1 1 . 0 7 0 1 . 1 5 5 . 7 8 . 4 5 0 . 0 6 . 5 8 9 6 1 5 : 6 5 : 2 0 + 1 2 . 7 m m 1 2 . 7 X 0 . 6 m m - 0 . 6 m m T O T A L H M B H M C 1 . 4 4 9 1 . 8 7 9 0 . 0 0 0 0 . 0 0 0 5 7 . 1 6 8 4 . 0 9 8 0 . 0 0 6 9 . 6 0 9 . 0 0 0 8 . 9 9 8 9 . 0 0 0 8 . 9 9 9 1 . 3 7 1 1 . 1 9 0 1 . 1 8 0 1 . 2 8 4 . 5 6 . 7 1 6 . 0 0 . 5 8 9 7 1 0 : 3 5 : 5 5 + 1 2 . 7 m m 1 2 . 7 X 0 . 6 m m - 0 . 6 mm T O T A L H M B H M C 1 . 4 6 6 1 . 7 1 5 0 . 0 0 0 0 . 0 0 0 6 4 . 7 5 8 6 . 3 4 8 0 . 0 0 7 5 . 4 5 8 . 9 9 9 9 . 0 0 1 9 . 0 0 0 9 . 0 0 0 1 . 2 2 2 1 . 0 3 5 1 . 0 4 5 1 . 1 2 5 . 7 8 • 4 5 0 . 0 0 . 5 8 9 8 I © : 5 0 : 4 0 + 1 2 . 7 m m 1 2 . 7 X 0 . 6 m m - 0 . 6 mm T O T A L H M B H M C 1 . 4 5 7 1 . 7 4 4 0 . 0 0 0 0 . 0 0 0 6 0 . 8 6 8 5 . 5 7 8 0 . 0 0 7 2 . 6 5 9 . 0 0 2 9 . 0 0 0 9 . 0 0 0 9 . 0 0 1 1 . 3 0 7 1 . 1 8 9 1 . 1 2 0 1 . 2 0 9 . 7 1 . 5 0 0 . 0 0 . 5 7 

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