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Mathematical model of the SL/RN direct reduction process Venkateswaran, V. 1976

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MATHEMATICAL MODEL OF THE SL/RN DIRECT REDUCTION PROCESS by V. VENKATESWARAN B . E . , I n d i a n I n s t i t u t e o f S c i e n c e , 1972 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF THE R E Q U I R E M E N T S FOR THE DEG R E E OF MASTER OF A P P L I E D S C I E N C E In the D e p a r t m e n t o f METALLURGY We a c c e p t t h i s t h e s i s as c o n f o r m i n g to the r e q u i r e d s t a n d a r d THE U N I V E R S I T Y OF B R I T I S H COLUMBIA A p r i l 1 9 7 6 (c) V. Venkateswaran, 1976 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e 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 , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e H e a d o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f METALLURGY  The U n i v e r s i t y o f B r i t i s h C o l u m b i a 20 75 Wesbrook P l a c e Vancouver, Canada V6T 1W5 ABSTRACT A m a t h e m a t i c a l m o d e l h a s b e e n d e v e l o p e d t o p r e d i c t t h e o p e r a t i n g b e h a v i o u r o f a n SL / R N d i r e c t r e d u c t i o n k i l n f r o m a k n o w l e d g e o f t h e m a i n p r o c e s s v a r i a b l e s . T h e m o d e l i s b a s e d on s t e a d y s t a t e p r i n c i p l e s a n d i s c a p a b l e o f q u a n t i t a -t i v e l y d e s c r i b i n g t h e c o m p l e x c h e m i c a l r e a c t i o n s i n t h e k i l n s u c h a s r e d u c t i o n , B o u d o u a r d r e a c t i o n , c o a l v o l a t i l i z a t i o n a n d c o m b u s t i o n i n t h e f r e e b o a r d t o g e t h e r w i t h t h e m a s s a n d h e a t f l o w s . O u t p u t f r o m t h e m o d e l i s i n t h e f o r m o f a x i a l p r o f i l e s o f g a s , s o l i d s a n d w a l l t e m p e r a t u r e s , a n d c o n c e n t r a -t i o n s i n b o t h t h e g a s a n d t h e s o l i d p h a s e s . R e s u l t s f r o m t h e m o d e l a r e i n g o o d a g r e e m e n t w i t h m e a s u r e m e n t s made on t h e 100 t o n p e r d a y p i l o t k i l n a t t h e S t e e l C o m p a n y o f C a n a d a . T h e i n f l u e n c e o f i m p o r t a n t p r o c e s s v a r i a b l e s s u c h a s t h e t y p e o f c o a l , o r e , d e g r e e o f r e d u c t i o n , t h r o u g h p u t e t c . h a s b e e n e x a m i n e d a n d p r e d i c t i o n s made r e g a r d i n g t h e o p e r a t i o n o f l a r g e c o m m e r c i a l SL/RN k i l n s f o r s p o n g e i r o n p r o d u c t i o n . TABLE OF CONTENTS P a g e A B S T R A C T i i L I S T OF F I G U R E S . . v i L I S T OF T A B L E S x i ACKNOWLEDGMENTS x i i i C h a p t e r 1 I N T R O D U C T I O N 1 1.1 S L / R N P r o c e s s 5 1.2 O t h e r D i r e c t R e d u c t i o n P r o c e s s e s 11 1.3 R e v i e w o f t h e P r e v i o u s Work 15 1.4 S c o p e o f t h e P r e s e n t Work 17 2 DEVEL O P M E N T OF THE M A T H E M A T I C A L MODEL 19 2.1 A s s u m p t i o n s Made i n t h e M o d e l 19 2.2 M a s s a n d H e a t B a l a n c e E q u a t i o n s 21 2.2.1 M a s s B a l a n c e on S o l i d s 23 2.2.2 M a s s B a l a n c e f o r G a s e s 25 2. 2 . 3 H e a t B a l a n c e o n S o l i d s 30 2.2.4 H e a t B a l a n c e o n G a s e s . . . . . 3 2 2 . 2 . 5 H e a t B a l a n c e on W a l l 3 3 i i i C h a p t e r P a g e 2.3 R a t e E x p r e s s i o n s 34 2.3.1 B o u d o u a r d a n d R e d u c t i o n R e a c t i o n R a t e s 34 2.3.2 A i r P r o f i l e i n t h e K i l n . . . . 41 2 . 3 . 3 E v o l u t i o n o f V o l a t i l e s f r o m C o a l 44 2.3.4 D r y i n g o f S o l i d s 44 2 . 3 . 5 C o m b u s t i o n i n t h e F r e e b o a r d . . 46 2 . 3 . 6 C a l c i n a t i o n o f D o l o m i t e . . . . 48 2.4 2.4.1 S p e c i f i c H e a t s o f S o l i d s a n d G a s e s 49 2.4.2 P a r t i a l P r e s s u r e s i n t h e F r e e b o a r d G a s P h a s e . . . . . . 50 2.5 H e a t T r a n s f e r i n R o t a r y K i l n s 50 2.5.1 H e a t T r a n s f e r C o e f f i c i e n t s U s e d i n t h e P r e s e n t M o d e l . . . 54 2 . 5 . 2 A r e a T e r m s f o r H e a t T r a n s f e r . . 63 2.6 N u m e r i c a l P r o c e d u r e U s e d i n t h e M o d e l . . 54 2.7 I n t e r n a l C o n s i s t e n c y o f t h e M o d e l . . . . 69 2.8 S t a r t i n g a n d I n s t a b i l i t y P r o b l e m s . . . . 71 2.9 A d j u s t a b l e P a r a m e t e r s i n t h e M o d e l . . . . 74 3 MODEL C A L C U L A T I O N S AND D I S C U S S I O N 75 3.1 E v a l u a t i o n o f t h e M o d e l 75 3.1.1 E v a l u a t i o n R u n s 76 3.2 P r e d i c t e d I n f l u e n c e o f O p e r a t i n g V a r i a b l e s on K i l n P e r f o r m a n c e 98 i v C h a p t e r P a g e 3.2.1 E f f e c t o f D e g r e e o f R e d u c t i o n A c h i e v e d 99 3.2.2 E f f e c t o f T h r o u g h p u t 104 3.2.3 E f f e c t o f L o w e r C o a l R e a c t i v i t y 104 3.2.4 E f f e c t o f P e l l e t T y p e 114 3.2.5 E f f e c t o f N a t u r a l G a s 114 3.2.6 E f f e c t o f D u s t i n t h e F r e e b o a r d G a s 124 3.2.7 P r e d i c t i o n s f o r t h e G r i f f i t h K i l n 127 3.3 G e n e r a l C o m m e n t s o n t h e S L / R N P r o c e s s . . . 136 4 SUMMARY AND C O N C L U S I O N S 1 4 9 4.1 S u g g e s t i o n s f o r F u t u r e Work 152 R E F E R E N C E S 153 A P P E N D I C E S I S o u r c e L i s t i n g o f C o m p u t e r P r o g r a m m e 156 I I I m p o r t a n t D a t a U s e d i n t h e M o d e l 187 v LIST OF FIGURES F i g u r e P a g e 1 S c h e m a t i c d i a g r a m o f t h e S L / R N p r o c e s s 6 2 S c h e m a t i c d i a g r a m o f t h e s o l i d s t e m p e r a t u r e p r o f i l e i n t h e S L / R N k i l n 9 3 S e c t i o n a l v i e w o f t h e S L / R N k i l n s h o w i n g t h e c o n t r o l v o l u m e 22 4 A i r p r o f i l e f o r a t y p i c a l r u n . 43 i 5 R a t e s o f e v o l u t i o n o f v o l a t i l e s f r o m F o r e s t b u r g c o a l 45 6 R a t e o f m o i s t u r e e v o l u t i o n f r o m F o r e s t b u r g c o a l 47 7 ( a ) C r o s s - s e c t i o n o f t h e k i l n s h o w i n g t h e h e a t t r a n s f e r m o d e s 52 7 ( b ) C r o s s - s e c t i o n o f t h e k i l n s h o w i n g t h e a r e a t e r m s i n v o l v e d i n t h e d i f f e r e n t h e a t t r a n s f e r e q u a t i o n s 52 8 G a s e m i s s i v i t y f o r c a r b o n d i o x i d e ( f r o m P e r r y ( 3 0 ) ) 56 9 Gas e m i s s i v i t y f o r w a t e r v a p o u r ( f r o m P e r r y ( 3 0 ) ) 57 10 C r o s s - s e c t i o n o f t h e r o t a r y k i l n s h o w i n g t h e d i f f e r e n t r a d i u s t e r m s u s e d f o r c a l -c u l a t i n g h e a t l o s s t o s u r r o u n d i n g s 62 v i F i g u r e P a g e 11 F l o w s h e e t o f t h e c o m p u t e r p r o g r a m 66 12 E f f e c t o f s t a r t i n g s o l i d s t e m p e r a t u r e ' on t h e s o l i d s t e m p e r a t u r e p r o f i l e 73 13 A i r p r o f i l e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s 78 14 S o l i d s t e m p e r a t u r e p r o f i l e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s . . . . 79 15 G a s t e m p e r a t u r e p r o f i l e f o r t h e r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s 81 16 I n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s 83 17 R e d u c t i o n p r o f i l e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s 84 18 B o u d o u a r d r e a c t i o n r a t e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s . . . . 86 19 F r e e b o a r d g a s c o m p o s i t i o n f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s . . . . 87 20 I n t e r i o r v i e w o f t h e p i l o t S L / R N k i l n t a k e n f r o m t h e d i s c h a r g e e n d 89 21 A i r p r o f i l e f o r t h e k i l n r u n u s i n g l i g n i t e c o a l a n d G r i f f i t h p e l l e t s 92 22 S o l i d s t e m p e r a t u r e p r o f i l e f o r t h e k i l n r u n u s i n g l i g n i t e c o a l a n d G r i f f i t h p e l l e t s 93 23 G a s t e m p e r a t u r e p r o f i l e f o r t h e k i l n r u n u s i n g l i g n i t e c o a l a n d G r i f f i t h p e l l e t s 94 24 I n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e p r o f i l e s f o r t h e k i l n r u n u s i n g l i g n i t e c o a l a n d G r i f f i t h p e l l e t s 9 5 v i i F i g u r e P a g e 25 R e d u c t i o n p r o f i l e f o r t h e k i l n r u n u s i n g l i g n i t e c o a l a n d G r i f f i t h p e l l e t s 96 26 F r e e b o a r d g a s c o m p o s i t i o n f o r t h e k i l n r u n u s i n g l i g n i t e c o a l a n d G r i f f i t h p e l l e t s 97 27 A i r p r o f i l e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a d e g r e e o f r e d u c t i o n o f 9 5 % 101 28 S o l i d s , g a s , i n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e p r o f i l e s f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a d e g r e e o f r e d u c t i o n o f 9 5 % 102 29 R e d u c t i o n a n d f r e e b o a r d g a s c o m p o s i t i o n p r o f i l e s f o r t h e r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a d e g r e e o f r e d u c t i o n o f 9 5 % 103 3D A i r p r o f i l e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t 106 31 S o l i d s , g a s , i n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e p r o f i l e s f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t 107 32 R e d u c t i o n a n d f r e e b o a r d g a s c o m p o s i t i o n p r o f i l e s f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t . . . 108 33 A i r p r o f i l e f o r t h e k i l n r u n u s i n g a n t h r a c i t e c o a l a n d G r i f f i t h p e l l e t s I l l 34 S o l i d s , g a s , i n n e r w a l l a n d o u t e r t e m p e r a t u r e p r o f i l e s f o r t h e k i l n r u n u s i n g a n t h r a c i t e c o a l a n d G r i f f i t h p e l l e t s 112 v i i i F i g u r e P a g e 35 R e d u c t i o n a n d f r e e b o a r d g a s c o m p o s i t i o n p r o f i l e s f o r t h e k i l n r u n u s i n g a n t h r a c i t e c o a l a n d G r i f f i t h p e l l e t s 113 36 A i r p r o f i l e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d F a l c o n b r i d g e p e l l e t s 116 37 S o l i d s , g a s , i n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e s f o r t h e r u n u s i n g F o r e s t b u r g c o a l a n d F a l c o n b r i d g e p e l l e t s 117 38 R e d u c t i o n a n d f r e e b o a r d c o m p o s i t i o n p r o f i l e s f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d F a l c o n b r i d g e p e l l e t s 118 39 A i r p r o f i l e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h o u t a n y n a t u r a l g a s 121 40 S o l i d s , g a s , i n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e p r o f i l e s f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h o u t a n y n a t u r a 1 g a s 122 41 R e d u c t i o n a n d f r e e b o a r d g a s c o m p o s i t i o n p r o f i l e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h o u t a n y n a t u r a l g a s 123 42 E f f e c t o f t h e e m i s s i v i t y o f g a s on t h e g a s t e m p e r a t u r e 126 43 A i r p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g t h e F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s f o r t h e d e s i g n e d t h r o u g h p u t 129 44 S o l i d s t e m p e r a t u r e p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g t h e F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s f o r t h e d e s i g n e d t h r o u g h p u t 131 45 G a s t e m p e r a t u r e p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g t h e F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s f o r d e s i g n e d t h r o u g h p u t 132 i x F i g u r e P a g e 46 I n n e r w a l l t e m p e r a t u r e p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s f o r d e s i g n e d t h r o u g h p u t 133 47 R e d u c t i o n p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s f o r d e s i g n e d t h r o u g h p u t 134 48 F r e e b o a r d g a s c o m p o s i t i o n p r o f i l e s f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s f o r d e s i g n e d t h r o u g h p u t 135 49 A i r p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t 138 50 S o l i d t e m p e r a t u r e p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t 139 51 Gas t e m p e r a t u r e p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t 140 52 I n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e p r o f i l e s f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t 141 53 R e d u c t i o n p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t 142 54 F r e e b o a r d g a s c o m p o s i t i o n p r o f i l e s f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t 143 55 E f f e c t o f k i l n d i a m e t e r o n t h e A/V r a t i o f o r d i f f e r e n t d e g r e e s o f f i l l 1 4 6 56 E f f e c t o f t h e d e g r e e o f f i l l on t h e A/V r a t i o a n d mean r e t e n t i o n t i m e f o r a k i l n w i t h i d 6m 1 4 7 x L I S T O F T A B L E S T a b l e P a g e 1 R e a c t i v i t y P a r a m e t e r f o r D i f f e r e n t C h a r s 37 2 T y p i c a l D a t a f o r t h e A i r B l o w n i n t o a 35m L o n g S L / R N K i l n 42 3 H e a t T r a n s f e r C o e f f i c i e n t s i n t h e L i t e r a t u r e . . . . 53 4 I n p u t D a t a f o r t h e K i l n Run U s i n g F o r e s t b u r g C o a l a n d G r i f f i t h P e l l e t s 77 5 I n p u t D a t a f o r t h e K i l n Run u s i n g L i g n i t e C o a l a n d G r i f f i t h P e l l e t s . . 91 6 I n p u t D a t a f o r t h e K i l n Run U s i n g F o r e s t b u r g C o a l a n d G r i f f i t h P e l l e t s w i t h a D e g r e e o f R e d u c t i o n o f 95% 100 7 I n p u t D a t a f o r t h e K i l n Run U s i n g F o r e s t b u r g C o a l a n d G r i f f i t h P e l l e t s w i t h a 3 0 % H i g h e r ' T h r o u g h p u t 1 0 5 8 I n p u t D a t a f o r t h e K i l n Run U s i n g A n t h r a c i t e C o a l a n d G r i f f i t h P e l l e t s 1 10 9 I n p u t D a t a f o r t h e K i l n Run U s i n g F o r e s t b u r g C o a l a n d F a l c o n b r i d g e P e l l e t s 115 10 I n p u t D a t a f o r t h e K i l n Run U s i n g F o r e s t b u r g C o a l a n d G r i f f i t h P e l l e t s W i t h o u t a n y N a t u r a l G a s 1 20 x i T a b l e P a g e 11 I n p u t D a t a f o r t h e G r i f f i t h K i l n Run U s i n g F o r e s t b u r g C o a l a n d G r i f f i t h P e l l e t s f o r t h e D e s i g n e d T h r o u g h p u t 128 12 I n p u t D a t a f o r t h e G r i f f i t h K i l n Run U s i n g F o r e s t b u r g C o a l a n d G r i f f i t h P e l l e t s f o r a 3 0 % H i g h e r T h r o u g h p u t 137 x i i ACKNOWLEDGMENTS I w o u l d l i k e t o s i n c e r e l y t h a n k my r e s e a r c h s u p e r -v i s o r D r . K e i t h B r i m a c o m b e , f o r h i s a s s i s t a n c e a n d g u i d a n c e t h r o u g h o u t t h e c o u r s e o f t h i s r e s e a r c h p r o j e c t . T h a n k s a r e a l s o e x t e n d e d t o t h e o t h e r f a c u l t y m e m b e r s o f t h e d e p a r t m e n t a n d f e l l o w g r a d u a t e s t u d e n t s f o r t h e h e l p f u l d i s c u s s i o n s , w i t h s p e c i a l a p p r e c i a t i o n t o Mr. B. P r a b h a k a r . T h e h e l p r e c e i v e d f r o m t h e t e c h n i c a l s t a f f o f t h e d e p a r t m e n t i s v e r y much a p p r e c i a t e d . In a d d i t i o n g r a t i t u t e i s e x p r e s s e d t o t h e S t e e l C o m pany o f C a n a d a f o r t h e f i n a n c i a l s u p p o r t , a n d t o D r . T.R. M e a d o w c r o f t , M r . K. W i l s o n , ' D r . P.C. R h e e , M r . N i c k D a n e l i a k a n d M r . C.W.E. J o h n s o n o f t h e R e s e a r c h C e n t r e , S t e l c o f o r t h e i n v a l u a b l e h e l p p r o v i d e d d u r i n g t h e c o u r s e o f t h i s r e s e a r c h . x i i i C h a p t e r 1 INTRODUCTION T h e SL/RN p r o c e s s i s o n e o f a n u m b e r o f d i r e c t r e d u c t i o n p r o c e s s e s t h a t h a v e b e e n d e s i g n e d t o p r o d u c e s p o n g e i r o n f r o m i r o n o x i d e on a c o m m e r c i a l s c a l e . T h e p r o c e s s h a s b e e n d e v e l o p e d o v e r a p e r i o d o f many y e a r s , i n i t i a l l y b y R e p u b l i c S t e e l a n d t h e N a t i o n a l L e a d C o m p a n y [ 1 ] (RN) a n d m o r e r e c e n t l y by t h e S t e e l C o m p a n y o f C a n a d a L t d . a n d L u r g i [ 2 - 4 ] ( S L ) . A s w i l l be s e e n i n t h e n e x t s e c t i o n i t i s d i s t i n g u i s h e d f r o m t h e o t h e r c o m m e r c i a l d i r e c t r e d u c t i o n p r o c e s s e s by i t s u s e o f s o l i d c o a l a s t h e r e d u c i n g a g e n t , r a t h e r t h a n a g a s e o u s r e d u c t a n t , a n d by i t s u s e o f a r o t a r y k i l n a s t h e r e a c t o r , r a t h e r t h a n a v e r t i c a l s h a f t . When v i e w e d t o g e t h e r , t h e S L / R N a n d o t h e r c o m m e r c i a l d i r e c t r e d u c t i o n p r o c e s s e s a r e s e e n t o o c c u p y an i n c r e a s i n g l y i m p o r t a n t p o s i t i o n i n t h e f u t u r e o f s t e e l m a k i n g . T h i s i s b e c a u s e t h e s p o n g e i r o n p r o d u c t c a n be f e d d i r e c t l y i n t o a n e l e c t r i c a r c f u r n a c e f o r c o n v e r s i o n t o s t e e l . T h i s c o m b i n a -t i o n o f d i r e c t r e d u c t i o n w i t h e l e c t r i c a r c f u r n a c e s t e e l m a k i n g 1 2 i s a t t r a c t i n g c o n s i d e r a b l e a t t e n t i o n a s a n a l t e r n a t i v e t o t h e c o n v e n t i o n a l b l a s t f u r n a c e a n d b a s i c o x y g e n f u r n a c e . T h e h e i g h t e n e d i n t e r e s t i n t h e d i r e c t r e d u c t i o n - e l e c t r i c a r c f u r n a c e r o u t e t o s t e e l m a k i n g i n r e c e n t y e a r s c a n be a t t r i b u t e d t o t h e f o l l o w i n g f a c t o r s [ 5 ] . ( i ) Technological f e a s i b i l i t y : S e v e r a l d i r e c t r e d u c t i o n p r o c e s s e s h a v e o v e r c o m e t h e t e c h n o l o g i c a l u n c e r t a i n t y a s s o c i a t e d w i t h c o m m e r c i a l - s i z e o p e r a t i o n s a n d a r e now i n f u l l p r o d u c t i o n . A t t h e e n d o f 1 9 7 4 d i r e c t r e d u c t i o n p l a n t s w e r e p r o d u c i n g 5.2 m i l l i o n m e t r i c t o n s o f s p o n g e i r o n [ 6 ] . An a d d i -t i o n a l 1 2 . 7 m i l l i o n t o n s o f p r o d u c t i o n c a p a c i t y i s d u e t o be b r o u g h t o n s t r e a m i n t h e n e x t t h r e e t o f o u r y e a r s . ( i i ) Decreasing supply of coking coal: I t i s p r e -d i c t e d t h a t t h e r a p i d g r o w t h i n s t e e l p r o d u c t i o n i f t i e d t o b l a s t f u r n a c e s , w i l l l e a d t o d o u b l e t h e p r e s e n t d e m a n d o n w o r l d s u p p l i e s o f c o k i n g c o a l b y t h e e n d o f t h e c e n t u r y . S i n c e t h e a s s u r e d s u p p l y o f c o k i n g c o a l i s a l r e a d y a m a j o r p r o b l e m w i t h e x i s t i n g s t e e l - m a k i n g c a p a c i t y i t i s l i k e l y t o p r e s e n t an e v e n g r e a t e r d i f f i c u l t y w i t h h i g h e r f u t u r e c a p a c i t y . A l t h o u g h t h e d e v e l o p m e n t o f f o r m e d c o k e p r o c e s s e s m i g h t a l t e r t h i s p i c t u r e , t h e p r e s e n t u n c e r t a i n t y w i t h r e g a r d t o c o k e h a s e n h a n c e d t h e p o s i t i o n o f d i r e c t r e d u c t i o n p r o c e s s e s w h i c h a r e n o t b a s e d on c o k i n g c o a l . I t i s i m p o r t a n t t o n o t e i n t h i s 3 r e s p e c t t h a t p a r t i a l l y r e d u c e d i r o n o x i d e f r o m t i o n p l a n t c a n a l s o be e m p l o y e d a s b u r d e n i n a o p e r a t i o n [ 8 ] . T h i s h a s t h e b e n e f i c i a l e f f e c t p r o d u c t i o n w i t h o u t r e q u i r i n g i n v e s t m e n t i n new c o k e o v e n s . ( i i i ) Advantage of scale: I t i s w e l l known t h a t t h e b l a s t f u r n a c e - BOF r o u t e i s o n l y e c o n o m i c a l o n a l a r g e s c a l e , o f t h e o r d e r o f two m i l l i o n m e t r i c t o n s p e r y e a r [ 6 ] . T h u s i f new s t e e l m a k i n g f a c i l i t i e s a r e p l a n n e d b a s e d on t h i s t e c h n o l o g y , l a r g e c a p a c i t y a n d h i g h c a p i t a l c o s t a r e r e q u i r e d . In t h e c a s e o f c o u n t r i e s w i t h a r e l a t i v e l y l o w d e m a n d f o r s t e e l t h e l a r g e i n c r e a s e i n p r o d u c t i o n o f t e n c a n n o t be j u s t i f i e d o w i n g t o m a r k e t c o n d i t i o n s . T h e d i r e c t r e d u c t i o n - e l e c t r i c a r c f u r n a c e r o u t e on t h e o t h e r h a n d r e q u i r e s a l o w e r c a p i t a l i n v e s t m e n t p e r t o n o f s t e e l i n t h e l o w e r p r o d u c t i o n r a n g e m a k i n g i t m o r e a t t r a c t i v e f o r s m a l l e r m a r k e t s . A l t h o u g h t h e d i r e c t r e d u c t i o n - e l e c t r i c a r c f u r n a c e r o u t e h a s a d v a n t a g e s o f s c a l e a t t h e l o w e r e n d o f t h e c a p a c i t y r a n g e , e c o n o m y o f l a r g e s c a l e o p e r a t i o n i s a l s o b e i n g r e a l i s e d . T h e maximum c a p a c i t y o f a s i n g l e d i r e c t r e d u c t i o n u n i t w h i c h up u n t i l now h a s b e e n 4 0 0 , 0 0 0 m e t r i c t o n s p e r y e a r i s i n c r e a s i n g s t e a d i l y . a d i r e c t r e d u c -b l a s t f u r n a c e o f i n c r e a s i n g f u r n a c e s a n d ( i v ) Improvement in e l e c t r i c arc furnace operation: I n d u s t r i a l t e s t s h a v e s h o w n t h a t t h e f e e d i n g o f s p o n g e i r o n 4 i n t o a n e l e c t r i c a r c f u r n a c e h a s a d v a n t a g e s o v e r s c r a p i r o n f e e d i n g [ 6 , 9 ] . I n t h e f i r s t p l a c e , t h e t a p - t o - t a p t i m e i s d e c r e a s e d , t h e r e b y i n c r e a s i n g . p r o d u c t i v i t y . F u r t h e r m o r e , o w i n g t o i t s l o w t r a m p e l e m e n t c o n t e n t , s p o n g e i r o n c a n be u s e d t o p r o d u c e h i g h e r q u a l i t y s t e e l . I t a l s o a p p e a r s t h a t s p o n g e i r o n f e e d r e d u c e s t h e g a s a n d n o i s e e m i s s i o n f r o m a n e l e c t r i c a r c f u r n a c e a l t h o u g h t h e d u s t e m i s s i o n i n c r e a s e s . A f i n a l a d v a n t a g e o f s p o n g e i r o n l i e s i n i t s a b i l i t y t o be f e d c o n t i n u o u s l y . C o n t i n u o u s f e e d i n g , w h i c h h a s b e e n a c h i e v e d i n p r a c t i c e , p r o v i d e s a b a s i s f o r a u t o m a t i o n o f t h e e l e c t r i c a r c f u r n a c e . T h e " i m p o r t a n t r o l e t h a t d i r e c t r e d u c t i o n i s e x p e c t e d t o p l a y i n t h e f u t u r e o f s t e e l m a k i n g i s r e f l e c t e d i n a r e c e n t p r o j e c t i o n o f w o r l d s t e e l m a k i n g c a p a c i t y [ 1 0 ] . In 1 9 7 3 , t h e w o r l d s t e e l p r o d u c t i o n t o t a l l e d a b o u t 7 0 0 m i l l i o n m e t r i c t o n s p e r y e a r . O f t h i s 8 5 % r e s u l t e d f r o m t h e c o n v e n t i o n a l b l a s t f u r n a c e . I n t h e 1 9 8 0 1 s t h e w o r l d p r o d u c t i o n i s e x p e c t e d t o be c l o s e t o 1 b i l l i o n m e t r i c t o n s p e r y e a r w i t h 2 5 % c o m i n g f r o m t h e e l e c t r i c f u r n a c e . I f t h i s p r o j e c t e d f i g u r e p r o v e s c o r r e c t i t m e a n s t h a t 2 5 % m o r e s t e e l w i l l be made v i a t h e c o k e o v e n - b l a s t f u r n a c e r o u t e w h i l e 1 5 0 % m o r e s t e e l w i l l be p r o d u c e d by t h e e l e c t r i c a r c f u r n a c e . S i n c e s u f f i c i e n t s c r a p may n o t be a v a i l a b l e a t r e a s o n a b l e c o s t t o m e e t t h i s e x p e c t e d d e m a n d a n i n c r e a s i n g a m o u n t o f s p o n g e i r o n w i l l u n d o u b t e d l y be r e q u i r e d by t h e e l e c t r i c a r c f u r n a c e . T h e S L / R N p r o c e s s i s e m e r g i n g a s o n e o f t h e s t r o n g c o n t e n d e r s i n t h e f i e l d o f t h e d i r e c t r e d u c t i o n o f i r o n o r e 5 b e c a u s e o f i t s a b i l i t y t o u s e s o l i d r e d u c t a n t s u c h a s l o w g r a d e c o a l . N a t u r a l l y t h e r e i s c o n s i d e r a b l e i n t e r e s t i n o b t a i n i n g a c l e a r e r u n d e r s t a n d i n g o f t h e p h y s i c a l a n d c h e m i c a l n a t u r e o f t h e p r o c e s s f r o m t h e s t a n d p o i n t o f d e s i g n a n d o p t i m i -s a t i o n . F o r t h i s r e a s o n t h e p r e s e n t s t u d y h a s b e e n u n d e r t a k e n t o m a t h e m a t i c a l l y m o d e l t h e S L / R N p r o c e s s a n d s o r e l a t e i n q u a n t i t a t i v e t e r m s , k i l n p e r f o r m a n c e t o p r o c e s s v a r i a b l e s . 1 .1 S L / R N P r o c e s s I n t h i s s e c t i o n t h e S L / R N p r o c e s s i s d e s c r i b e d i n d e t a i l t o p r o v i d e a c l e a r p i c t u r e o f t h e c h e m i c a l a n d p h y s i c a l p h e n o m e n a v i t a l . t o i t s o p e r a t i o n . T h i s m a t e r i a l i s e s s e n t i a l t o u n d e r s t a n d i n g n o t o n l y t h e p r o c e s s i t s e l f b u t a l s o i t s m a t h e m a t i c a l s i m u l a t i o n w i t h w h i c h t h i s s t u d y i s c o n c e r n e d . T h e SL/RN p r o c e s s p r o d u c e s s p o n g e i r o n by r e d u c t i o n o f i r o n o r e w i t h c o a l i n a r o t a r y k i l n . T h e i m p o r t a n c e o f t h i s p r o c e s s r e s t s i n t h e f a c t t h a t t h e c o a l u s e d c a n be n o n -c o k i n g a n d t h e r e f o r e i n e x p e n s i v e c o m p a r e d t o n a t u r a l g a s u s e d by m o s t o t h e r d i r e c t r e d u c t i o n p r o c e s s e s . I n m o s t p a r t s o f t h e w o r l d n a t u r a l g a s i s a l e s s a t t r a c t i v e r e d u c i n g a g e n t o w i n g t o i t s r e l a t i v e l y h i g h c o s t a n d s c a r c i t y . A s c h e m a t i c d i a g r a m o f t h e S L / R N p r o c e s s i s g i v e n i n F i g . 1. T h e c h a r g e t o t h e SL/RN k i l n c o n s i s t s o f i r o n o x i d e p e l l e t s , c o a l , r e c y c l e d c h a r a n d s o m e t i m e s d o l o m i t e , w h i c h i s a d d e d i f t h e s u l p h u r l e v e l i n t h e c o a l i s h i g h . Gas Cleaning System Ore —&>i Coal -)mite - &x Char -—i> k 'Atmosphere Air/Fuel Gases Solids • IOOO°C 90°C <C5-ige Iron F i g . 1. Schemat ic d iagram of the SL/RN p r o c e s s . 7 S h e l l b u r n e r s a r e p o s i t i o n e d a l o n g t h e l e n g t h o f t h e k i l n a n d a r e s u p p l i e d w i t h a i r b y s h e l l f a n s . P r o v i s i o n i s a l s o made f o r t h e s u p p l y o f n a t u r a l g a s i f r e q u i r e d a s a u x i l i a r y f u e l . I n t h e p r o c e s s t h e s o l i d s a n d g a s e s f l o w i n a c o u n t e r -c u r r e n t f a s h i o n . T h e r o t a r y k i l n i s o p e r a t e d u s u a l l y w i t h a s l i g h t l y p o s i t i v e p r e s s u r e t o p r e v e n t t h e i n t r u s i o n o f u n -r e g u l a t e d a i r . Dams a r e p r o v i d e d a t b o t h e n d s o f t h e k i l n t o c o n t r o l t h e f l o w o f s o l i d s i n t h e m o v i n g b e d . T h e k i l n i s n o r m a l l y o p e r a t e d w i t h 2 5 % f i l l i n g , a s l o p e o f a b o u t 3% a n d a r o t a t i o n a l s p e e d o f 0.3 t o 0.6 r p m . T h e h o t p r o d u c t s c o n -s i s t i n g o f 9 1 - 9 5 % r e d u c e d i r o n 5 u n r e a c t e d c o a l c h a r a n d g a n g u e e x i t t h e k i l n a t a b o u t 1 0 0 0 ° C v i a a t r a n s f e r c h u t e i n t o a r o t a r y c o o l e r . T h e r e t h e p r o d u c t s a r e c o o l e d t o r o u g h l y 9 0 ° C a n d u p o n d i s c h a r g e f r o m t h e c o o l e r a r e m a g n e t i c a l l y s e p a r a t e d i n t o s p o n g e i r o n a n d a n o n - m a g n e t i c t a i l i n g . T h e a m o u n t o f c o a l f e d i n t o t h e k i l n i s a d j u s t e d s u c h t h a t t h e r e i s a l w a y s a s l i g h t e x c e s s o f u n r e a c t e d c a r b o n i n t h e p r o d u c t . T h i s p r o c e d u r e m i n i m i s e s t h e p o s s i b i l i t y t h a t t h e r e d u c e d i r o n c o u l d b e c o m e r e o x i d i s e d b e f o r e e x i t i n g t h e k i l n . T h e u n r e a c t e d c o a l c h a r i s r e c y c l e d a s f e e d b a c k i n t o t h e k i l n . T h e w a s t e g a s e s e x i t i n g t h e k i l n p a s s t h r o u g h a n a f t e r b u r n e r b e f o r e d i s c h a r g i n g i n t o t h e a t m o s p h e r e . L o o k i n g a t t h e p r o c e s s i n m o r e d e t a i l t h e k i l n c o n -v e n i e n t l y c a n be d i v i d e d i n t o two s e c t i o n s : I. P r e h e a t Zone 2 . R e d u c t i o n Z o n e 8 T h i s d i v i s i o n i s m o r e o b v i o u s f r o m F i g . 2 w h e r e a s c h e m a t i c d i a g r a m i s p r o v i d e d t o show t h e s o l i d t e m p e r a t u r e p r o f i l e i n t h e k i l n . I n t h e p r e h e a t z o n e t h e s o l i d s a r e h e a t e d f r o m t h e i r f e e d t e m p e r a t u r e t o t h e t e m p e r a t u r e w h e r e CO r e d u c t i o n c a n p r o c e e d . H e a t i n g i s a c h i e v e d by h e a t t r a n s f e r f r o m t h e h o t f r e e b o a r d g a s e s l e a v i n g t h e r e d u c t i o n z o n e . E x t r a h e a t c a n be t r a n s f e r r e d i n t o t h e s o l i d s b y c o m b u s t i n g n a t u r a l g a s i n t h e p r e h e a t z o n e . I n a d d i t i o n t o h e a t t r a n s f e r t h e f o l l o w i r e a c t i o n s o c c u r i n t h e p r e h e a t z o n e : ( i ) R e m o v a l o f m o i s t u r e p r e s e n t i n t h e c h a r g e ( o r e , c o a l a n d d o l o m i t e ) . ( i i ) C a l c i n a t i o n o f t h e d o l o m i t e i f p r e s e n t . ( i i i ) . R e m o v a l o f v o l a t i l e s f r o m c o a l . ( i v ) P r e - r e d u c t i o n w i t h h y d r o g e n ( i n c o a l ) , i . e . F e 2 0 3 + 3 H 2 = 2 F e + 3 H 2 0 ( ( v ) C o m b u s t i o n i n t h e f r e e b o a r d . T h e l e n g t h o f t h e p r e h e a t z o n e i s u s u a l l y a b o u t 40 t o 5 0 % o f t h e t o t a l l e n g t h o f t h e k i l n . F o r e f f i c i e n t u s e o f t h e r o t a r y k i l n t h i s z o n e s h o u l d b e made a s s m a l l a s p o s s i b l e . A s t h e s o l i d s r e a c h a t e m p e r a t u r e i n e x c e s s o f 9 0 0 ° C t h e c a r b o n g a s i f i c a t i o n r e a c t i o n , m o r e c o m m o n l y known a s t h e B o u d o u a r d r e a c t i o n , s e t s i n . O w i n g t o t h e e n d o t h e r m i c n a t u r e o f t h i s r e a c t i o n t h e t e m p e r a t u r e o f t h e s o l i d s c e a s e s t o r i s e a n y f u r t h e r . T h e t e m p e r a t u r e a t w h i c h t h e s o l i d b e d DISTANCE FROM CHARGE END F i g . 2. S c h e m a t i c d i a g r a m o f t h e s o l i d s t e m p e r a t u r e p r o f i l e i n t h e SL/RN k i l n . 10 s t a b i l i s e s d e p e n d s o n a n u m b e r o f f a c t o r s , t h e m o s t i m p o r t a n t b e i n g t h e r e a c t i v e n a t u r e o f t h e c o a l a n d o r e , a n d t h e h e a t t r a n s f e r r a t e f r o m g a s e s a n d w a l l t o t h e s o l i d s . T h e CO g e n e r a t e d t h r o u g h t h e B o u d o u a r d r e a c t i o n i s u s e d i n t h e r e d u c t i o n o f i r o n o x i d e . T h e s p e c i f i c r e a c t i o n s a r e : An i m p o r t a n t p o i n t t o n o t e i s t h a t t h e g a s e o u s a t m o s p h e r e i n s i d e t h e s o l i d s b e d i s r e d u c i n g i n n a t u r e a s o p p o s e d t o t h e o x i d i s i n g c h a r a c t e r o f t h e f r e e b o a r d g a s . A p a r t o f t h e CO g e n e r a t e d t h r o u g h t h e B o u d o u a r d r e a c t i o n i n t h e s o l i d s b e d a l s o e n t e r s t h e f r e e b o a r d g a s p h a s e . D e p e n d i n g on t h e a v a i l a b i l i t y o f o x y g e n t h i s i s b u r n t on t h e s u r f a c e o f t h e s o l i d s b e d o r a t t h e m o u t h o f t h e a i r t u b e s . V i s u a l o b s e r v a t i o n i n t o t h e d i s c h a r g e e n d o f t h e k i l n h a s i n d i c a t e d t h a t o v e r much o f t h e r e d u c t i o n z o n e t h e f l a m e i s l o c a l i s e d on t h e s u r f a c e o f t h e b e d . T h e c o a l u s e d i n t h e S L /RN k i l n c a n be o f i n f e r i o r r a n k b u t a t t h e same t i m e s h o u l d h a v e t h e f o l l o w i n g p r o p e r t i e s : C 0 2 + C = 2C0 ( 2 ) F e 2 0 3 + CO = 2 F e + 3 C 0 2 ( 3 ) 3 . 4 . 5 . 2 . H i g h r e a c t i v i t y L o w f r e e s w e l l i n g i n d e x L o w caking t e n d e n c y H i g h f i x e d c a r b o n H i g h a s h f u s i o n t e m p e r a t u r e 11 T h e maximum t e m p e r a t u r e a t w h i c h t h e k i l n c a n be o p e r a t e d i s d e p e n d e n t o n t h e a s h f u s i o n t e m p e r a t u r e o f t h e c o a l . I f t h e k i l n i s o p e r a t e d b e y o n d t h i s p o i n t , r i n g i n g ( a c c r e t i o n ) p r o b l e m s c a n d e v e l o p . W i t h t h e l o w r a n k , h i g h l y r e a c t i v e c o a l s t h e b e d i s m a i n t a i n e d a t r o u g h l y 9 5 0 t o 9 7 0 ° C w h i l e , u s i n g h i g h r a n k c o a l w i t h a l o w r e a c t i v i t y s u c h a s a n t h r a c i t e , t h e b e d t e m p e r a t u r e i s h i g h e r , r o u g h 1 y a r o u n d 1 1 0 0 ° C , i f p r o p e r m e t a l l i -s a t i o n i s t o be a c h i e v e d . T h e s p o n g e i r o n p r o d u c t f r o m t h i s p r o c e s s h a s b e e n s u c c e s s f u l l y u s e d a s f e e d t o t h e e l e c t r i c a r c f u r n a c e . I n a d d i t i o n i t i s b e i n g e m p l o y e d i n p l a c e o f s c r a p i r o n f o r t h e c e m e n t a t i o n o f c o p p e r a n d h a s a l s o f o u n d u s e a s c o o l a n t i n t h e B 0 F , a n d as c h a r g e t o t h e b l a s t f u r n a c e . 1 .2 O t h e r D i r e c t R e d u c t i o n P r o c e s s e s A l t h o u g h a r e l a t i v e l y l a r g e n u m b e r o f d i r e c t r e d u c -t i o n p r o c e s s e s h a v e b e e n i n v e s t i g a t e d , o n l y a h a n d f u l h a v e b e e n p r o v e n on t h e s c a l e o f a c o m m e r c i a l o p e r a t i o n . I n o r d e r t o v i e w t h e SL/RN p r o c e s s i n t h e p r o p e r p e r s p e c t i v e t h i s s e c t i o n p r o v i d e s a b r i e f d e s c r i p t i o n o f t h e o t h e r i m p o r t a n t r e d u c t i o n p r o c e s s e s [ 5 , 1 2 - 1 4 ] . HyL Process: T h i s p r o c e s s h a s b e e n i n o p e r a t i o n s i n c e 1 9 5 7 . T h e r e d u c t a n t u s e d h e r e i s a m i x t u r e o f h y d r o g e n a n d c a r b o n m o n o x i d e w h i c h i s g e n e r a t e d b y r e f o r m i n g n a t u r a l 12 g a s i n t h e p r e s e n c e o f a c a t a l y s t . T h e r e d u c t i o n i s c a r r i e d o u t i n a s t a t i c b e d t h r o u g h w h i c h t h e h o t r e d u c i n g g a s e s a r e c i r c u l a t e d . T h e r e d u c t i o n s e c t i o n c o n s i s t s o f f o u r r e a c t o r s w i t h e a c h r e a c t o r b e i n g o p e r a t e d i n t h e f o l l o w i n g s t a g e d s e q u e n c e : ( i ) P r e h e a t i n g o f t h e r a w o r e b y s p e n t r e d u c t i o n g a s e s . ( i i ) R e d u c t i o n o f t h e h e a t e d c h a r g e b y h o t r e d u c i n g g a s . ( i i i ) C o o l i n g o f t h e h o t s p o n g e i r o n b y f r e s h r e d u c i n g g a s w h i c h r e s u l t s a l s o i n t h e h e a t i n g o f t h e r e d u c i n g g a s f o r s t a g e ( i i ) . ( i v ) R e m o v a l o f t h e c h a r g e a n d l o a d i n g w i t h f r e s h o r e . E a c h s e q u e n c e o f o p e r a t i o n t a k e s r o u g h l y t h r e e h o u r s , g i v i n g a t o t a l s o l i d s r e s i d e n c e t i m e o f a b o u t 12 h o u r s . T h e r e d u c t i o n i s c a r r i e d o u t i n a t e m p e r a t u r e r a n g e o f a p p r o x i m a t e l y 8 7 0 t o 1 0 5 0 ° C . T h e r e a r e s i x HyL p l a n t s i n o p e r a t i o n p r e -s e n t l y w i t h a t o t a l i n s t a l l e d c a p a c i t y o f 1.35 m i l l i o n t o n s p e r y e a r . Midvex Process: T h i s p r o c e s s h a s b e e n i n o p e r a t i o n s i n c e 1 9 6 7 . U n l i k e t h e o t h e r r e d u c t i o n p r o c e s s e s i t h a s a c h i e v e d an i m p r e s s i v e d e g r e e o f p o p u l a r i t y i n a r e l a t i v e l y s h o r t t i m e . I n c o n t r a s t t o t h e HyL p r o c e s s w h i c h i s b a s e d on b a t c h o p e r a t i o n , t h e M i d r e x p r o c e s s i s c o n t i n u o u s . T h e r e d u c t i o n p l a n t c o n s i s t s o f two m a i n c o m p o n e n t s : a g a s 1 3 r e f o r m i n g u n i t f o r t h e p r o d u c t i o n o f r e d u c i n g g a s a n d a s h a f t f u r n a c e i n w h i c h i r o n o r e p e l l e t s a r e r e d u c e d t o s p o n g e i r o n . T h e s h a f t f u r n a c e i s e q u i p p e d w i t h s e p a r a t e z o n e s f o r r e d u c -t i o n a n d c o o l i n g , a n d t h e s o l i d s f l o w c o u n t e r - c u r r e n t t o t h e r i s i n g h o t r e d u c i n g g a s e s . I n t h e u p p e r r e d u c t i o n z o n e t h e i n c o m i n g m a t e r i a l i s f i r s t h e a t e d t o a r e a c t i o n t e m p e r a t u r e o f a b o u t 8 0 0 ° C by t h e e x i t i n g r e d u c i n g g a s e s . T h e n o r m a l m e t a l l i s a t i o n a c h i e v e d i n t h i s z o n e i s a r o u n d 92 t o 9 6 % a n d t h e s p o n g e i r o n i s c a r b u r i s e d t o 1 t o 1 . 5 % . T h e s p o n g e i r o n t h e n d e s c e n d s i n t o t h e l o w e r z o n e w h e r e i t i s c o o l e d t o 5 0 ° C b y g a s e s i n a c l o s e d l o o p s y s t e m . T h e s p e n t r e d u c i n g g a s f r o m t h e t o p z o n e c o n t a i n s 6 0 % o f t h e o r i g i n a l c a r b o n m o n o x i d e a n d h y d r o g e n , a n d t w o - t h i r d s i s r e t u r n e d t o t h e r e f o r m e r f o r g e n e r a t i o n o f f r e s h 9 5 % CO-H*. r e d u c i n g g a s . T h e r e s t i s u s e d a s r e f o r m e r f u e l . F o u r p l a n t s a r e i n o p e r a t i o n a n d s e v e r a l m o r e a r e s c h e d u l e d f o r c o m p l e t i o n i n 1 9 7 6 . Arrnco Process: T h i s p r o c e s s h a s b e e n d e v e l o p e d b y Arrn c o o v e r a t e n - y e a r p e r i o d a n d h a s many s i m i l a r f e a t u r e s t o t h e M i d r e x p r o c e s s . T h e Ar r n c o p r o c e s s e m p l o y s a v e r t i c a l s h a f t f u r n a c e w i t h s o l i d s d e s c e n d i n g a g a i n s t r i s i n g g a s e s . H o w e v e r , u n l i k e t h e M i d r e x p r o c e s s w h i c h u s e s a c l o s e d l o o p s y s t e m f o r i t s c o o l i n g g a s e s , t h e c o o l i n g g a s e s i n t h e A r r n c o p r o c e s s a r e n o t w i t h d r a w n s e p a r a t e l y f r o m t h e r e d u c i n g g a s e s b u t i n s t e a d r i s e t o t h e t o p a n d e x i t a l o n g w i t h t h e s p e n t r e d u c i n g g a s . T h e t o p g a s i s s c r u b b e d , c o o l e d a n d s p l i t i n t o 14 two p o r t i o n s . A b o u t 6 0 % b e c o m e s r e f o r m e r f u e l w h i l e t h e r e m a i n d e r i s f u r t h e r c o o l e d , c o m p r e s s e d f o r r e - u s e a s c o o l i n g g a s , a n d a l s o f o r b l e n d i n g w i t h f r e s h r e d u c i n g g a s . T h e A r m c o p l a n t a t H o u s t o n u s e s a s t e a m - m e t h a n e c a t a l y t i c r e f o r m e r t o p r o d u c e t h e r e d u c t a n t f r o m t h e n a t u r a l g a s . O r i g i n a l l y p e b b l e s t o v e r e f o r m i n g was a t t e m p t e d i n t h e i r p i l o t p l a n t , b u t l a t e r i t was d r o p p e d i n p r e f e r e n c e t o a s t e a m - n a t u r a l g a s c a t a l y t i c r e f o r m e r o w i n g t o t h e s i m p l i c i t y o f o p e r a t i o n o f t h e l a t t e r . Purofer Process: T h e p r o c e s s was d e v e l o p e d i n G e r m a n y a n d e m p l o y s a s h a f t f u r n a c e a n d two a l t e r n a t e l y o p e r a t -i n g g a s r e f o r m e r s . One o f t h e r e f o r m e r s c r a c k s n a t u r a l g a s t o r e d u c i n g g a s o f c a r b o n m o n o x i d e a n d h y d r o g e n w h i l e t h e o t h e r i s b e i n g h e a t e d . A f t e r a 40 m i n u t e p e r i o d t h e o p e r a t i o n i s r e v e r s e d . T h e r e f o r m i n g o c c u r s a t a t e m p e r a t u r e o f 1 4 0 0 ° C a n d p r o d u c e s a g a s t h a t i s f r e e o f s o o t a n d c o n t a i n s l e s s t h a n 2% C 0 2 + H 2 0 . T h i s p r o c e s s c a n t o l e r a t e s u l p h u r up t o a l e v e l o f 30 ppm i n t h e n a t u r a l g a s . T h e r a w m a t e r i a l s a r e m o s t l y i n d u r a t e d p e l l e t s o r s i z e d l u m p s o f o r e , a n d w o r k i s i n p r o g r e s s t o i n v e s t i g a t e t h e c h a r g i n g o f g r e e n p e l l e t s . FIOR Process: I n t h i s p r o c e s s h i g h g r a d e i r o n o r e f i n e s a r e r e d u c e d t o s p o n g e i r o n i n a f l u i d i s e d b e d r e a c t o r . T h e r e d u c e d i r o n p a r t i c l e s t h e n a r e n o r m a l l y c o m p a c t e d i n t o a u n i f o r m h i g h d e n s i t y b r i q u e t t e . O r e p r e p a r a t i o n f o r m s an 15 i n t e g r a l p a r t o f t h i s p r o c e s s . T h e r e a c t o r s y s t e m c o n t a i n s m u l t i p l e f l u i d i z e d b e d s t a g e s i n s e r i e s . R e d u c i n g g a s i s p r e p a r e d by o n e o f a n u m b e r o f p r o c e s s e s , e . g . c a t a l y t i c s t e a m r e f o r m i n g , o r p a r t i a l o x i d a t i o n f r o m a v a r i e t y o f h y d r o -c a r b o n f e e d s t o c k s ( n a t u r a l g a s , L P G , n a p h t h a , h e a v y o i l s e t c . ) . T h e p r o d u c t m e t a l l i s a t i o n r a n g e s f r o m 90 t o 9 5 % a n d t h e f i n a l c a r b o n c o n t e n t o f t h e i r o n p r o d u c t r a n g e s f r o m n e a r z e r o t o a s much a s 2%. A p l a n t i s u n d e r c o n s t r u c t i o n i n t h e G u a y a n a r e g i o n o f V e n e z u e l a h a v i n g a c a p a c i t y o f 5 0 0 , 0 0 0 t o n s p e r y e a r . A n u m b e r o f o t h e r d i r e c t r e d u c t i o n p r o c e s s e s a r e u n d e r v a r i o u s s t a g e s o f d e v e l o p m e n t , b u t d u e t o l i m i t a t i o n o f s p a c e c a n n o t be d i s c u s s e d h e r e . 1 .3 R e v i e w o f t h e P r e v i o u s Work T h e r o t a r y k i l n i s a w i d e l y u s e d r e a c t o r i n c h e m i c a l a n d m e t a l l u r g i c a l i n d u s t r i e s . Some o f i t s m o s t i m p o r t a n t u s e s a r e i n c e m e n t p r o d u c t i o n a n d c a l c i n a t i o n . A l t h o u g h t h e r e a c t o r h a s b e e n i n u s e f o r a l o n g t i m e , v e r y l i t t l e w o r k h a s :: b e e n d o n e on i m p o r t a n t a s p e c t s o f i t s o p e r a t i o n , p a r t i c u l a r l y h e a t t r a n s f e r . F o r t h i s r e a s o n t h e d e s i g n a n d s c a l e - u p o f r o t a r y k i l n s i s b a s e d h e a v i l y o n e x p e r i e n c e r a t h e r t h a n on f u n d a m e n t a l p r i n c i p l e s . N e v e r t h e l e s s , t h e f u n d a m e n t a l a p p r o a c h h a s b e e n a t t e m p t e d i n t h e p a s t t h r o u g h t h e f o r m u l a t i o n o f m a t h e m a t i c a l m o d e l s o f r o t a r y k i l n s f o r d i f f e r e n t a p p l i c a t i o n s b u t n o t f o r t h e s p e c i f i c c a s e o f t h e S L / R N p r o c e s s . 16 A l l t h e m a t h e m a t i c a l m o d e l s d e v e l o p e d s o f a r f o r t h e r o t a r y k i l n s a r e b a s e d on p r i n c i p l e s o f m a s s a n d h e a t b a l a n c e s . T h e d i f f e r e n c e s b e t w e e n t h e m o d e l s a r e f o u n d i n t h e t y p e o f a p p l i c a t i o n f o r w h i c h t h e r o t a r y k i l n i s u s e d , e . g . : d r y i n g , c a l c i n a t i o n , c e m e n t p r o d u c t i o n e t c . I m b e r a n d P a s c h k i s [ 1 5 ] w e r e t h e f i r s t t o d e v e l o p a m a t h e m a t i c a l m o d e l o f t h e r o t a r y k i l n , b a s e d on h e a t t r a n s f e r a l o n e , f o r t h e p u r p o s e o f c a l c u l a t i n g t h e l e n g t h o f k i l n r e q u i r e d t o h e a t s o l i d s b y a d e s i r e d a m o u n t . T h e i r m o d e l d i d n o t t a k e i n t o a c c o u n t a n y c h e m i c a l r e a c t i o n s . S a a s [ 1 6 - 1 7 ] h a s d e s c r i b e d a m a t h e m a t i c a l m o d e l f o r r o t a r y k i l n s u s e d i n d r y i n g . A s i n t h e p r e v i o u s c a s e i t d e a l s m a i n l y w i t h h e a t t r a n s f e r b u t t a k e s i n t o a c c o u n t t h e r e m o v a l o f m o i s t u r e f r o m t h e s o l i d s . R i f f a u d et al. [ 1 8 ] m o d e l l e d a r o t a r y k i l n f o r a l u m i n a p r o d u c t i o n . U s i n g b o t h a n a l o g a n d d i g i t a l c o m p u t e r s t h e y w e r e a b l e t o s i m u l a t e s t e a d y s t a t e a n d d y n a m i c c o n d i -t i o n s o f t h e r o t a r y k i l n . S p r a n g [ 1 9 ] d e s c r i b e s a d y n a m i c m o d e l f o r a c e m e n t k i l n . T h o u g h no d a t a was a v a i l a b l e t o c h e c k h i s p r e d i c t e d v a l u e s , he c l a i m s q u a l i t a t i v e a g r e e m e n t b e t w e e n h i s m o d e l a n d t h a t o f an a c t u a l c e m e n t k i l n . R e c e n t l y M a n i t i u s et al. [20] h a v e f o r m u l a t e d a s t e a d y s t a t e m o d e l f o r t h e c a l c i n a t i o n o f b a s i c ammonium a l u m i n i u m s u l p h a t e i n a r o t a r y k i l n . T h e i r m o d e l d o e s n o t i n v o l v e b u r n i n g i n t h e f r e e b o a r d g a s p h a s e o f t h e k i l n b u t t a k e s i n t o a c c o u n t t h e c a r r y o v e r o f d u s t i n t h e g a s p h a s e . T h e r e s u l t s o b t a i n e d f r o m t h e i r m o d e l w e r e shown t o be i n r e a s o n a b l e a g r e e m e n t w i t h m e a s u r e d d a t a . 17 T h e o n l y p u b l i s h e d w o r k on t h e m a t h e m a t i c a l m o d e l l i n g o f r o t a r y k i l n s f o r i r o n o x i d e r e d u c t i o n h a s b e e n t h e w o r k o f W i n g f i e l d et al. [ 2 1 ] , I t i s e s s e n t i a l l y a m a t h e m a t i c a l m o d e l f o r t h e g a s e o u s r e d u c t i o n o f i r o n o x i d e b y h y d r o g e n i n a r o t a r y k i l n . S i n c e t h e y d i d n o t h a v e a n y a c t u a l d a t a w i t h w h i c h t o c o m p a r e t h e i r r e s u l t s , t h e i r m o d e l was o f l i m i t e d u s e . I t s h o u l d be n o t e d a l s o t h a t t h e m o d e l t h e y d e v e l o p e d was p r o n e t o i n s t a b i l i t y p r o b l e m s a n d t h e r e s u l t s t h e y o b t a i n e d f r o m t h e m o d e l , e . g . s o l i d s t e m p e r a t u r e , r e t e n t i o n t i m e , w e r e q u i t e u n r e a l i s t i c f r o m a n o p e r a t i n g v i e w p o i n t . No w o r k h a s s o f a r b e e n r e p o r t e d i n t h e l i t e r a t u r e on t h e m a t h e m a t i c a l m o d e l l i n g o f t h e S L / R N p r o c e s s . 1 .4 S c o p e o f t h e P r e s e n t Work T h e p r e s e n t p r o j e c t was e s t a b l i s h e d i n c o - o p e r a t i o n w i t h t h e S t e e l C o m p a n y o f C a n a d a w i t h t h e s p e c i f i c a i m o f d e v e l o p i n g a m a t h e m a t i c a l m o d e l o f t h e S L / R N p r o c e s s . T h e mode! was t o e m b o dy t h e r a t e e x p r e s s i o n s f o r a l l t h e i m p o r t a n t c h e m i c a l a n d p h y s i c a l p r o c e s s e s o c c u r r i n g i n s i d e a n SL/RN k i l n , i n c l u d i n g t h e B o u d o u a r d r e a c t i o n , i r o n o x i d e r e d u c t i o n , c o a l v o l a t i l i z a t i o n , c o m b u s t i o n , d r y i n g a n d h e a t t r a n s f e r ; a n d t o c a l c u l a t e k i l n p e r f o r m a n c e e x p r e s s e d i n t e r m s o f a x i a l p r o f i l e s o f t e m p e r a t u r e a n d c o n c e n t r a t i o n , a s a f u n c t i o n o f i m p o r t a n t k i l n o p e r a t i n g v a r i a b l e s . An i m p o r t a n t p a r t o f t h e p r o j e c t was t o e v a l u a t e t h e m o d e l by c o m p a r i s o n o f p r e d i c t i o n s t o d a t a o b t a i n e d i n t h e 100 t o n / d a y p i l o t p l a n t a t t h e H i l t o n 18 w o r k s , H a m i l t o n . F i n a l l y t h e m o d e l was t o be u s e d t o p r e d i c t t h e e f f e c t o f o p e r a t i n g v a r i a b l e s i n c l u d i n g t y p e o f c o a l a n d o r e , t h r o u g h p u t a n d d e g r e e o f r e d u c t i o n o n t h e p e r f o r m a n c e o f t h e k i l n . I n a d d i t i o n p a r t i c u l a r a t t e n t i o n was t o be p a i d t o t h e p r o b l e m o f s c a l e - u p o f t h e S L / R N k i l n . C h a p t e r 2 DEVELOPMENT OF THE MATHEMATICAL MODEL T h e m a t h e m a t i c a l m o d e l o f t h e S L / R N p r o c e s s , t h a t i s d e v e l o p e d i n t h i s s e c t i o n , i s b a s e d on f u n d a m e n t a l p r i n c i p l e s o f m a s s a n d h e a t f l o w . , T h e d i f f e r e n t p h y s i c a l a n d c h e m i c a l r e a c t i o n s o c c u r r i n g i n t h e SL/RN p r o c e s s a r e q u a n t i t a t i v e l y d e s c r i b e d t h r o u g h m a t h e m a t i c a l e q u a t i o n s . T h e s o l u t i o n o f t h e s e m a s s a n d h e a t b a l a n c e e q u a t i o n s r e s u l t i n t e m p e r a t u r e p r o f i l e s f o r t h e s o l i d s , g a s a n d w a l l , a n d c o n c e n t r a t i o n p r o f i l e s f o r t h e d i f f e r e n t s p e c i e s a l o n g t h e e n t i r e l e n g t h o f t h e k i l n . T h i s s e c t i o n g i v e s t h e g e n e r a l a s s u m p t i o n s made i n t h e m o d e l , t h e d e v e l o p m e n t o f mass a n d h e a t b a l a n c e e q u a -t i o n s , d e s c r i p t i o n o f t h e v a r i o u s r a t e t e r m s f o l l o w e d by t h e n u m e r i c a l p r o c e d u r e u s e d f o r s o l v i n g t h e e q u a t i o n s . 2.1 A s s u m p t i o n s Made i n t h e M o d e l I n o r d e r t o s i m p l i f y t h e c o m p l e x m a t h e m a t i c a l p r o b l e m o f d e s c r i b i n g t h e S L / R N p r o c e s s a n u m b e r o f a s s u m p t i o n s h a v e b e e n made a n d t h e s e a r e l i s t e d b e l o w . 19 20 1. T h e m a t h e m a t i c a l m o d e l i s d e v e l o p e d f o r q u a s i -s t e a d y s t a t e c o n d i t i o n s , t h a t i s , t h e d e r i v a t i v e o f t h e d e p e n -d e n t v a r i a b l e s w i t h t i m e a r e z e r o a t a l l p o i n t s i n t h e k i l n . 2. T h e s o l i d s a n d g a s e s move i n p l u g f l o w , w h i c h m e ans t h e r e i s no a x i a l m i x i n g . S i n c e t h e S L / R N p r o c e s s e m p l o y s k i l n s t h a t h a v e a l a r g e L/D r a t i o t h i s i s a v a l i d a s s u m p t i o n . 3. H e a t t r a n s f e r by c o n d u c t i o n a n d r a d i a t i o n i n t h e a x i a l d i r e c t i o n i s n e g l i g i b l e r e l a t i v e t o r a d i a l l y d i r e c t e d h e a t t r a n s f e r . T h i s a s s u m p t i o n i s t h o u g h t t o be r e a s o n a b l e s i n c e a x i a l h e a t t r a n s f e r b y b u l k m o t i o n o f g a s e s a n d s o l i d s i s c o n s i d e r a b l y l a r g e r t h a n a x i a l c o n d u c t i o n a n d r a d i a t i o n . 4. T h e r e a r e no r a d i a l t e m p e r a t u r e g r a d i e n t s i n t h e s o l i d s b e d a n d i n t h e f r e e b o a r d g a s p h a s e . T h i s i m p l i e s t h a t t h e s o l i d s a n d g a s e s a r e w e l l m i x e d r a d i a l l y . A s a r e s u l t t h e f r e e b o a r d g a s e s a n d t h e b e d e a c h c a n be c h a r a c t e r i s e d b y a s i n g l e t e m p e r a t u r e a t a g i v e n p o i n t i n t h e k i l n . 5 . T h e d e g r e e o f f i l l o f s o l i d s i s c o n s t a n t t h r o u g h -o u t t h e k i l n . I f d e e m e d n e c e s s a r y i t i s p o s s i b l e t o i n c o r p o r a t e a p o s i t i o n - d e p e n d e n t d e g r e e o f f i l l i n t o t h e m o d e l w i t h o u t a n y d i f f i c u l t y . 6. C o m b u s t i o n i n t h e f r e e b o a r d i s i n s t a n t a n e o u s . H e r e a g a i n i t i s p o s s i b l e t o t a k e i n t o a c c o u n t t h e c a s e o f i n c o m p l e t e c o m b u s t i o n i f d a t a i s a v a i l a b l e on b u r n i n g r a t e s . 21 7. A i r a n d n a t u r a l g a s i n t r o d u c e d i n t o t h e k i l n b u r n e r n o z z l e s a r e c o n s i d e r e d t o be l i n e s o u r c e s . T h i s a p p r o x i m a t i o n i s c l o s e t o t h e r e a l s i t u a t i o n . 8. W i t h i n t h e s o l i d s b e d t h e sum o f p a r t i a l p r e s s u r e s o f CO a n d C 0 2 a r e e q u a l t o o n e a t m o s p h e r e i n t h e r e d u c t i o n z o n e . T h i s i s u s e d i n t h e c a l c u l a t i o n o f t h e v o l u m e t r i c r a t e o f t h e B o u d o u a r d r e a c t i o n . T h e a b o v e - m e n t i o n e d a r e t h e m a j o r a s s u m p t i o n s made i n t h e m o d e l . A few o t h e r m i n o r a s s u m p t i o n s t h a t w e r e n e c e s -s a r y w i l l be i n d i c a t e d i n t h e a p p r o p r i a t e s e c t i o n s i n t h i s c h a p t e r . 2.2 M a s s a n d H e a t B a l a n c e E q u a t i o n s H a v i n g made t h e g e n e r a l a s s u m p t i o n s p r e s e n t e d i n t h e p r e v i o u s s e c t i o n , t h e k i l n was b r o k e n down i n t o t h i n s l i c e s . One s u c h s l i c e , known a s t h e c o n t r o l v o l u m e , i s g i v e n i n F i g . 3. H e a t a n d m a s s b a l a n c e s w e r e p e r f o r m e d o n t h i s c o n t r o l v o l u m e a n d t h e r e s u l t i n g e q u a t i o n s w e r e i n t e g r a t e d o v e r t h e e n t i r e l e n g t h o f t h e k i l n t o y i e l d c o n c e n t r a t i o n p r o f i l e s f o r t h e d i f f e r e n t s p e c i e s ( f r o m t h e m a s s b a l a n c e e q u a t i o n s ) a n d t e m p e r a t u r e p r o f i l e s ( f r o m t h e h e a t b a l a n c e e q u a t i o n s ) . H e r e t h e s o l i d s a n d g a s e s f l o w i n a c o u n t e r - c u r r e n t f a s h i o n a n d t h e d i r e c t i o n i n w h i c h g a s f l o w s i s c o n s i d e r e d p o s i t i v e . F i g . 3. S e c t i o n a l v i e w o f t h e SL/RN k i l n s h o w i n g t h e c o n t r o l v o l u m e . l\3 23 2.2.1 M a s s B a l a n c e on S o l i d s T h e g e n e r a l e q u a t i o n u s e d t o d e s c r i b e t h e mass b a l a n c e o f a n y s p e c i e s i s t h e f o l l o w i n g : Rate o f mass f l o w i n t o the c o n t r o l volume Rate o f mass f l o w o u t o f the c o n t r o l volume Rate o f mass g e n e r a t i o n i n the c o n t r o l volume Rate o f mass consumption i n th e c o n t r o l volume S i n c e t h e m o v i n g b e d o f s o l i d s i s c o m p r i s e d o f t h r e e c o m p o n e n t s ( o r e , c o a l a n d d o l o m i t e ) o n e e n d s up w i t h t h r e e e q u a t i o n s d e s c r i b i n g t h e m a s s b a l a n c e f o r s o l i d s . ( a ) O r e : F o l l o w i n g on f r o m E q . ( 4 ) we o b t a i n f o r t h e o r e , R a t e o f o r e i n = ( G 0 A s ) g 2 - a — cm cm • s R a t e o f o r e o u t = G 0A_ + dG dx dx cm • s cm' R a t e o f g e n e r a t i o n = 0 R a t e o f c o n s u m p t i o n = r . A dx + r . A dx — ^ — Cm r r e d s d r y s 3 J cm 0 s S u b s t i t u t i n g b a c k i n t o E q . ( 4 ) t h e r e s u l t i s 24 • G o A . + G 0A_ + fdG, dx dx A. r r e d A s d x r d r y A s d x T h e n d i v i d i n g t h r o u g h o u t b y A g dx t h e f i n a l e q u a t i o n i s o b t a i n e d dG 0 _ + r dx r e d d r y ( 5 ) w h e r e G 0 i s t h e f l u x o f o r e , g / c m 2 « s A s i s t h e c r o s s s e c t i o n a l a r e a o f s o l i d s , c m 2 r r e d i s t h e v o 1 u m e t r " i c r a t e o f r e d u c t i o n , g / c m 3 « s d r y i s t h e v o 1 u m e t r i c r a t e o f d r y i n g , g / cu r H e r e t h e v o l u m e t r i c g e n e r a t i o n t e r m i s z e r o s i n c e n o t h i n g i s a d d e d on t o t h e o r e . T h e v o l u m e t r i c r a t e t e r m u s e d i n E q . ( 5 ) an d i n t h e o t h e r e q u a t i o n s d e r i v e d h e r e w i l l be d e s c r i b e d i n d e t a i l i n a l a t e r s e c t i o n i n t h i s c h a p t e r . ( b ) C o a l T h e d e r i v a t i o n o f t h e m a s s b a l a n c e e q u a t i o n s f o r c o a l a n d d o l o m i t e a r e t h e same a s f o r o r e . T h e e q u a t i o n f o r c o a l i s d6c 17 = rboud + rdryc + rvolt . ^ w h e r e G c i s t h e f l u x o f c o a l b o u d c r K , i s t h e v o l u m e t r i c r a t e o f B o u d o u a r d r e a c t i o n 25 r d r y c 1 S t h e v o l u m e t r i c r a t e o f d r y i n g r I t i s t h e v o l u m e t r i c r a t e o f r e m o v a l o f v o l a t i l e s f r o m c o a l (c) D o l o m i t e d G d " d x - = r c a l + r d r y d w h e r e G d i s t h e f l u x o f d o l o m i t e r c a l 1 s t n e v o^ u m e t r'' c r a t e o f c a l c i n a t i o n o f d o l o m i t e r d r y d 1 S t n e v o ^ u m e t r i c r a t e o f d r y i n g In e q u a t i o n s ( 5 ) t o ( 7 ) t h e r a t e e x p r e s s i o n s h a v e t o be e v a l u a t e d p e r u n i t v o l u m e o f s o l i d s b e d . 2.2.2 M a s s B a l a n c e f o r G a s e s T h e m a s s b a l a n c e e q u a t i o n s f o r t h e g a s e s a r e o b t a i n e d a g a i n f r o m E q . ( 5 ) w i t h t h e g a s e s h a v i n g a p o s i t i v e f l u x . ( a ) N i t r o g e n R a t e o f n i t r o g e n i n = G „ A . n 9 dG R a t e o f n i t r o g e n o u t = G n A g + ' d x * A g-R a t e o f g e n e r a t i o n = r • A „ dx + r , A d x . na 9 nv g R a t e o f c o n s u m p t i o n = 0. 26 S u b s t i t u t i n g t h e s e v a l u e s i n t o E q . ( 5 ) a n d d i v i d i n g by A g dx t h e f i n a l e q u a t i o n i s dG n - r + r ( 8 ) dx na nv w h e r e G n i s t h e f l u x o f n i t r o g e n A „ i s t h e a r e a o f f r e e b o a r d g a s r n a 1 S t h e v o 1 u m e t r i c r a t e o f g e n e r a t i o n o f n i t r o g e n f r o m a i r s u p p l y r i s t h e v o l u m e t r i c r a t e o f g e n e r a t i o n o f N 2 f r o m v o l a t i l e s i n c o a l ( g ) O x y g e n A s i n t h e c a s e o f n i t r o g e n d G o x " d x - = r o a " r o b ( 9 ) w h e r e G Q x i s t h e f l u x o f o x y g e n r i s t h e v o l u m e t r i c r a t e o f o x y g e n s u p p l y f r o m a i r r Q b i s t h e v o l u m e t r i c r a t e o f o x y g e n u s e d up i n b u r n i n g c o m b u s t i b l e s 27 ( c ) C a r b o n d i o x i d e dG dx C 0 2 b r C 0 2 v r C 0 2 C ( 1 0 ) w h e r e G C Q 2 i s t h e f l u x o f C 0 2 ' C Q . i s t h e v o l u m e t r i c r a t e o f C 0 2 g e n e r a t i o n 2 f r o m c o m b u s t i o n p r o d u c t s r C 0 v 1 S t h e v o 1 u m e t r i c r a t e o f C 0 2 g e n e r a t i o n 2 f r o m v o l a t i l e s i n c o a l r C 0 C i s t n e v o l u m e t r i c r a t e o f CO g e n e r a t i o n 2 f r o m d o l o m i t e c a l c i n a t i o n ( d ) C a r b o n m o n o x i d e dG CO dx r C 0 b e d + r C 0 v - r COb ( 1 1 ) w h e r e G c o i s t h e f 1 u x o f CO r C 0 b e d n's t' ie v o l u r n e t r i c r a t e o f CO g e n e r a t i o n t h r o u g h B o u d o u a r d r e a c t i o n i n t h e b e d COv i s t h e v o l u m e t r i c r a t e o f CO g e n e r a t i o n t h r o u g h v o l a t i l e s i n c o a l COb i s t h e v o l u m e t r i c r a t e o f CO c o n s u m p t i o n t h r o u g h b u r n i n g w i t h o x y g e n ( e ) M e t h a n e dG — ™ = r + r - r dx mv mn mb G m i s t h e f l u x o f m e t h a n e r i s t h e v o l u m e t r i c r a t e o f g e n e r a t i o n o f m e t h a n e f r o m v o l a t i l e s i n c o a l r m n i s t h e v o l u m e t r i c r a t e o f g e n e r a t i o n o f m e t h a n e f r o m v o l a t i l e s i n n a t u r a l g a s s u p p l y mb 1 s t n e v o l u m e t r i c r a t e o f c o n s u m p t i o n t h r o u g h b u r n i n g w i t h o x y g e n ( f ) W a t e r v a p o u r dG w - r + r dx ws wb G w i s t h e f l u x o f w a t e r v a p o u r r i s t h e v o l u m e t r i c r a t e o f g e n e r a t i o n o f w a t e r v a p o u r f r o m d r y i n g s o l i d s r ^ i s t h e v o l u m e t r i c r a t e o f g e n e r a t i o n o f w a t e r v a p o u r f r o m c o m b u s t i o n p r o d u c t s ( g ) P r o p a n e dG _P_ _ r + r - f dx pv pn pb Gp i s t h e f l u x o f p r o p a n e r i s t h e v o l u m e t r i c r a t e o f g e n e r a t i o n o f ^ p r o p a n e f r o m v o l a t i l e s i n c o a l r i s t h e v o l u m e t r i c r a t e o f g e n e r a t i o n o f P p r o p a n e f r o m n a t u r a l g a s s u p p l y r . i s t h e v o l u m e t r i c r a t e o f c o n s u m p t i o n o f P p r o p a n e t h r o u g h b u r n i n g w i t h o x y g e n ( h ) H y d r o g e n dG h dx r h v " r h b G^ i s t h e f l u x o f h y d r o g e n r . i s t h e v o l u m e t r i c r a t e o f . g e n e r a t i o n o f h y d r o g e n f r o m v o l a t i l e s i n c o a l r . , i s t h e v o l u m e t r i c r a t e o f c o n s u m p t i o n o f h y d r o g e n t h r o u g h b u r n i n g w i t h o x y g e n ( i ) E t h a n e dG 6 = r.... + - r dx e v e n e b G g i s t h e f l u x o f e t h a n e re v i s t n e v o l u m e t r i c r a t e o f g e n e r a t i o n o f e t h a n e f r o m v o l a t i l e s i n c o a l r e n i s t h e v o l u m e t r i c r a t e o f g e n e r a t i o n o f e t h a n e f r o m n a t u r a l g a s s u p p l y 30 r , i s t h e v o l u m e t r i c r a t e o f c o n s u m p t i o n o f e e t h a n e t h r o u g h b u r n i n g w i t h o x y g e n I n E q s . ( 8 ) t o ( 1 6 ) a l l t h e r a t e e x p r e s s i o n s a r e c a l c a u l t e d p e r u n i t v o l u m e o f t h e f r e e b o a r d g a s . 2 . 2 . 3 H e a t B a l a n c e o n S o l i d s R e f e r r i n g a g a i n t o t h e c o n t r o l v o l u m e i n F i g . 3, h e a t b a l a n c e s a r e p e r f o r m e d o n t h e s o l i d s i n t h e f o l l o w i n g way. • R a t e o f h e a t i n t o t h e c o n t r o l v o l u m e = - H A . s s R a t e o f h e a t o u t o f t h e c o n t r o l v o l u m e = dH -L"H SA S + " d # * d x ' A s ] -R a t e o f h e a t g e n e r a t i o n = l r S g A s d x . R a t e o f h e a t c o n s u m p t i o n = l^sc A s d*-u n d e r s t e a d y s t a t e c o n d i t i o n s H s A s + dH < "s"s ' "dT H „ A _ + -r-5. • A • dx + lr<.„ A r dx - T r A dx = 0 L s g s L s c s d H q s + y _ y r = o ( 1 7 ) dx L s g L s c w h e r e H $ i s t h e e n t h a l p y c o n t e n t o f s o l i d s , c a l / c m 2 s \r i s t h e s u m m a t i o n o f a l l h e a t g e n e r a t i o n t e r m s S 9 p e r u n i t v o l u m e i n t h e s o l i d s b e d , c a l / c m 3 s 31 £r i s t h e s u m m a t i o n o f a l l h e a t c o n s u m p t i o n t e r m s p e r u n i t v o l u m e o f s o l i d s b e d , c a 1 / c m 3 s F o r t h e t h r e e c o m p o n e n t s i n t h e b e d o f solids G 0 C + G C + G.C , -po c p c d p d j T - T s r a n d d ^ i . d x T s " T r c__ 4£r + c dG dG + C po dx p c dx pd dx T - T r- dC G dC. dC s s s-dT s dx -r dT. G 0 C + G C + G.C po c pc d pd dx ( 1 8 ) s u b s t i t u t i n g t h i s i n E q . ( 1 7 ) dT s dx £ r s c " ^ r s g s r dG dG 11 + C - r ^ + C dG po dx pc dx pd dx G 0C + G C + G.C , po c pc d pd 1 — UO „ UV, fJC 71 - s s s- 1 ( 1 9 ) w h e r e C „ . C , C , a r e t h e s p e c i f i c h e a t s o f o r e , po pc pd r c o a l a n d d o l o m i t e r e s p e c t i v e l y 32 T g i s t h e s o l i d s t e m p e r a t u r e , ° C i s t h e r e f e r e n c e t e m p e r a t u r e , °C 2.2.4 H e a t B a l a n c e on G a s e s I n t h e same m a n n e r a h e a t b a l a n c e o n t h e f r e e b o a r d g a s e s g i v e s , H A 9 9 dH g g ax dx • A + £r n A •dx - T r A d L gg g L g c g x dH dx = J r - Vr gg g c w h e r e H g i s t h e h e a t f l u x o f g a s e s \r i s t h e s u m m a t i o n o f h e a t g e n e r a t i o n t e r m s 99 p e r u n i t v o l u m e o f g a s p h a s e Ir i s t h e s u m m a t i o n o f h e a t c o n s u m p t i o n t e r m s p e r u n i t v o l u m e o f g a s p h a s e H g i n t u r n i s g i v e n by T 9 - T r yc G 1 pg-j 9 i dH dx _9_ = dG i P 9 i dx T 9 --Tr dT dC. pg. dx 4- g . dT i i ( dT yc G 33 w h e r e T g i s t h e g a s t e m p e r a t u r e , °C a n d C p g i s t h e s p e c i f i c h e a t o f a p a r t i c u l a r g a s i s p e c i e s T h e s u m m a t i o n r e p r e s e n t s a l l t h e g a s s p e c i e s d e s c r i b e d i n E q s ( 8 ) t o ( 1 6 ) . S u b s t i t u t i n g E q . ( 2 1 ) i n E q . ( 2 0 ) r e s u l t s i n , dT a dx L gg L gc dG T - T | YC - T ^ -1 9 r j L P g i dx dC. ( 2 2 ) l T 9 - T r pg i 9 i d T g + I C P 9 i G 9 i 2 . 2 . 5 H e a t B a l a n c e o n t h e W a l l I n a d d i t i o n t o t h e t w e l v e m a s s b a l a n c e e q u a t i o n s a n d two h e a t b a l a n c e e q u a t i o n s d e r i v e d a b o v e a n a d d i t i o n a l e q u a t i o n i s o b t a i n e d by p e r f o r m i n g a h e a t b a l a n c e on t h e w a l l u n d e r s t e a d y s t a t e c o n d i t i o n s . H e a t R e c e i v e d ! by t h e w a l l f r o m t h e g a s H e a t t r a n s f e r r e d t o s o l i d s H e a t l o s s f r o m o u t s i d e w a l l t o a t m o s p h e r e = 0 ( 2 3 ) T h e w a l l t e m p e r a t u r e i s n o t known a p r i o r i i n t h e s e c a l c u l a t i o n s b u t c a n be c a l c u l a t e d o n a n i t e r a t i v e s c h e m e . A v a l u e f o r t h e w a l l t e m p e r a t u r e i s f i r s t a s s u m e d a n d a l l h e a t t r a n s f e r r a t e s a r e c a l c u l a t e d . T h e n t h e w a l l t e m p e r a t u r e i s c h e c k e d t o d e t e r m i n e w h e t h e r E q . ( 2 3 ) i s o b e y e d . I f n o t a 34 new w a l l t e m p e r a t u r e i s a s s u m e d a n d t h e e n t i r e p r o c e d u r e r e -p e a t e d u n t i l a s a t i s f a c t o r y b a l a n c e i s o b t a i n e d . In t h e m a t h e -m a t i c a l m o d e l t h e e r r o r a l l o w e d b e t w e e n t h e a s s u m e d a n d c a l -c u l a t e d t e m p e r a t u r e s i s 2 ° C . 2 . 3 R a t e E x p r e s s i o n s T h e d i f f e r e n t v o l u m e t r i c t e r m s u s e d i n t h e m a s s a n d h e a t b a l a n c e e q u a t i o n s a r e d e s c r i b e d i n t h i s s e c t i o n . 2.3.1 B o u d o u a r d a n d R e d u c t i o n R e a c t i o n R a t e s T h e r e d u c t i o n o f i r o n o x i d e i s o n e o f t h e m o s t e x t e n -s i v e l y s t u d i e d s u b j e c t s i n t h e l i t e r a t u r e . A l a r g e n u m b e r o f m o d e l s ( t o p o c h e m i c a l , n o n - t o p o c h e m i c a l , e t c . ) h a v e b e e n p r o p o s e d t o d e s c r i b e t h e r a t e o f r e d u c t i o n . S i n c e t h e s e m o d e l s a r e v e r y c o m p l e x a n d r e q u i r e many p a r a m e t e r v a l u e s l i k e p o r o s i t y , d i f f u s i o n c o e f f i c i e n t s , t o r t u o s i t y e t c . , t h e y a r e a w k w a r d t o u s e i n t h e p r e s e n t m a t h e m a t i c a l m o d e l . M o r e o v e r , when i t c o m e s t o i n d u s t r i a l p r o c e s s l i k e t h e S L / R N , t h e s e m o d e l s a r e o f l i t t l e v a l u e s i n c e t h e p e l l e t s u n d e r g o s p a l l i n g , s w e l l i n g a n d s o m e t i m e s c r a c k i n g . F o r t h e s e r e a s o n s t h e r e d u c t i o n r a t e e m p l o y e d i n t h e p r e s e n t m a t h e m a t i c a l m o d e l i s a s i m p l e f i r s t o r d e r e q u a t i o n s b a s e d on e x p e r i m e n t a l w o r k c a r r i e d o u t by P.C. R h e e [ 2 2 ] a t t h e S t e l c o R e s e a r c h C e n t r e w i t h t h e r a w m a t e r i a l s u s e d i n t h e SL/RN k i l n . T h i s e s s e n t i a l l y f o l l o w s t h e a p p r o a c h o f B o g d a n d y [ 2 3 ] . T h e 35 j u s t i f i c a t i o n f o r u s i n g t h i s m e t h o d l i e s i n t h e f a c t t h a t i t i s a b l e t o g i v e m e a n i n g f u l r e s u l t s . A l t h o u g h t h e r e d u c i n g a g e n t u s e d i n t h e S L / R N p r o c e s s i s c a r b o n i n t h e f o r m o f c o a l , t h e r e d u c t i o n i n v o l v e s a g a s e o u s i n t e r m e d i a t e , c a r b o n m o n o x i d e , a c c o r d i n g t o t h e f a m i l i a r r e a c t i o n s : F e 2 0 3 ( s ) • 3 C 0 ( g ) = 2 F e ( s ) • 3 C 0 z ( g ) ( 2 4 ) C 0 1 ( g ) + C ( s ) - 2 C 0 ( g ) ( 2 5 ) In t h i s way, t h e c a r b o n m o n o x i d e u s e d f o r r e d u c t i o n i s r e p l e n i s h e d by t h e B o u d o u a r d r e a c t i o n . S i n c e t h e c a r b o n g a s i f i c a t i o n r e a c t i o n i s h i g h l y e n d o t h e r m i c i n n a t u r e t h e o v e r a l l r a t e o f r e d u c t i o n s t r o n g l y d e p e n d s on t h e r a t e o f h e a t t r a n s f e r f r o m t h e f r e e b o a r d g a s t o t h e s o l i d s b e d . T h e v o l u m e t r i c r a t e o f c a r b o n c o n s u m p t i o n by t h e B o u d o u a r d r e a c t i o n i s d e s c r i b e d b y , c e f f - C. ., ( b ) ' C 0 2 u c o 2 (26) w h e r e v c i s t h e v o l u m e t r i c r a t e o f c a r b o n g a s i f i c a t i o n , mol C/cm 3s. C C Q i s t h e c o n c e n t r a t i o n o f C 0 2 i n t h e b e d , 2 m o l / c m 3 36 C c o i s t h e e q u i l i b r i u m CO2 c o n c e n t r a t i o n 2 ( b ) f o r t h e B o u d o u a r d r e a c t i o n a t t h e s o l i d s t e m p e r a t u r e a n d : e f f = M c H c e x p E B R T s k ^ w h e r e M c i s t h e c a r b o n d e n s i t y , g C / c m 3 H i s t h e r e a c t i v i t y o f t h e c h a r , c m 3 / g s B ( 2 7 ) i s t h e a c t i v a t i o n e n e r g y f o r t h i s r e a c t i o n , ^ 4 -mol ^ s k ^ s t' ie t e m P e r a t u r e ° f s o l i d s , °K T h e r e a c t i v i t y p a r a m e t e r H c , i n E q . ( 2 7 ) i s c h a r a c t e r i s t i c o f a p a r t i c u l a r t y p e o f c o a l c h a r . T h i s i s a m e a s u r e o f t h e r e a d i n e s s w i t h w h i c h t h e c h a r r e a c t s w i t h c a r b o n d i o x i d e t o p r o d u c e t h e c a r b o n m o n o x i d e r e q u i r e d f o r r e d u c t i o n . T a b l e 1 g i v e s t h e r e a c t i v i t y v a l u e s f o r d i f f e r e n t t y p e s o f c h a r s t h a t h a v e b e e n e v a l u a t e d f o r t h e S L / R N p r o c e s s [ 2 2 ] . T h e a c t i v a t i o n e n e r g y E g u s e d i n E q . ( 2 7 ) i s 86 K c a l / m o l . T h e e q u a t i o n u s e d t o d e s c r i b e t h e r a t e o f r e d u c t i o n i s a s l i g h t m o d i f i c a t i o n o f t h e e q u a t i o n p r o p o s e d b y B o g d a n d y [ 2 3 ] . I n t h e p r e s e n t w o r k t h e t e m p e r a t u r e e f f e c t o f t h e r e -a c t i o n r a t e i s r e p r e s e n t e d by an A r r e h e n i u s t y p e o f e q u a t i o n a s f o l l o w s . 37 T a b l e 1 R e a c t i v i t y P a r a m e t e r s f o r D i f f e r e n t C h a r s * B i t u m i n o u s r a n k S u b - b i t u m i n o u s r a n k C h a r T V D e R e a c t i v i t y R e l a t i v e R e a c t i v i t y H c ( l O " 1 6 ) t o A n t h r a c i t e A n t h r a c i t e . 0 2 6 9 1 E l k h o r n 0.332 2 2 . 4 F o r e s t b u r g * * 5 1 . 9 1 9 3 0 L i g n i t e 5 8 . 3 2 1 6 5 38 v 0 = 4 . 4 8 ( 1 0 - 2 ) A p e x p RT s k 1 - R 'Fe C C 0 2 ( R ) " C C 0 2 c c o 2 W ( 2 8 ) w h e r e v 0 i s t h e r a t e o f o x y g e n r e m o v a l p e r c m 3 p e r s e c o n d A i s t h e p r e - e x p o n e n t i a l c o n s t a n t c h a r a c -p t e r i s t i c o f t h e t y p e o f p e l l e t E R i s t h e a c t i v a t i o n e n e r g y f o r t h e r e d u c t i o n r e a c t i o n M p e i s t h e i r o n c o n c e n t r a t i o n i n t h e b e d i s t h e f r a c t i o n a l r e d u c t i o n 'CO ( R ) i s t l i e e c l u 1 T b r i urn C 0 2 c o n c e n t r a t i o n f o r 2 V t h e r e d u c t i o n r e a c t i o n C o n i s t h e a c t u a l c o n c e n t r a t i o n o f C 0 2 i n t h e b e d ' C 0 2 T h e f r a c t i o n a l d e g r e e o f r e d u c t i o n i s c a l c u l a t e d o n t h e b a s i s o f t h e a m o u n t o f o x y g e n p r e s e n t i n t h e o r e (A v a l u e o f 1.0 c o r r e s p o n d s t o h e m a t i t e c o m p o s i t i o n ) . R e p l a c i n g t h e c o n c e n t r a t i o n t e r m s w i t h p a r t i a l p r e s s u r e s t h e f o l l o w i n g e q u a t i o n s a r e o b t a i n e d . v c = M c H c e x p B RT s k CO C 0 2 ( B ) RT ( 2 9 ) s k 39 Vo = 4 . 4 8 ( 1 0 " 2 ) A e x p P E R 1 R T s k J 1 - R [ P C O , ( R ) - W h e L H C 0 2 ( R ) J T h e p a r t i a l p r e s s u r e o f c a r b o n d i o x i d e i s d e t e r m i n e d f r o m t h e f a c t t h a t u n d e r s t e a d y s t a t e c o n d i t i o n s , v c = v 0 (31 ) T h i s i m p l i e s t h a t o n e c a r b o n a t o m r e m o v e s o n l y o n e o x y g e n a t o m f r o m t h e o r e w h i c h c o r r e s p o n d s t o a maximum c a r b o n c o n -s u m p t i o n . I n a c t u a l p r a c t i c e i t i s f o u n d t h a t t h e h i g h e r t h e r e a c t i v i t y v a l u e , t h e c l o s e r i s t h e c a r b o n c o n s u m p t i o n t o t h i s maximum v a l u e . T h e d i f f e r e n t s t e p s i n v o l v e d i n t h e c a l c u l a t i o n o f t h e v o l u m e t r i c r a t e o f B o u d o u a r d a n d r e d u c t i o n r e a c t i o n s a r e l i s t e d b e l o w . ( i ) F r o m t h e s o l i d s t e m p e r a t u r e , e q u i l i b r i u m c o n -s t a n t s f o r t h e B o u d o u a r d a n d r e d u c t i o n r e a c t i o n s a r e c a l c u l a t e d f r o m t h e f o l l o w i n g e q u a t i o n s ! n K b . z l O 3 6 0 _ t _ 2 0 ^ Z ( 3 2 ) s k w h e r e K f a i s t h e e q u i l i b r i u m c o n s t a n t f o r t h e B o u d o u a r d r e a c t i o n l n K r = 21°-5 . 2 > 5 2 5 ( 3 3 ) s k w h e r e K r i s t h e e q u i l i b r i u m c o n s t a n t f o r t h e r e d u c t i o n r e a c t i o n 40 ( i i ) F r o m t h e e q u i l i b r i u m c o n s t a n t s t h e e q u i l i b r i u m c a r b o n d i o x i d e p a r t i a l p r e s s u r e f o r t h e t w o r e a c t i o n s i s c o m p u t e d . 2 (2 + K.) - ^ 4 K . + K = p p ^ b b /-,„\ P C 0 2 ( B ) " 2 ( 3 4 ) p K C 0 2 ( R ) = 1 + r K ( 3 5 ) E q s . ( 3 4 ) a n d ( 3 5 ) a r e d e r i v e d a s s u m i n g Prn + P.. = 1 i n t h e U U 2 LU s o l i d s b e d . ( i i i ) U s i n g t h e s t e a d y s t a t e c o n d i t i o n , v c = v 0 , t h e p a r t i a l p r e s s u r e o f c a r b o n d i o x i d e i n t h e b e d i s c o m p u t e d . ( i v ) T h e a c t u a l v o l u m e t r i c r a t e s f o r t h e B o u d o u a r d a n d r e d u c t i o n r e a c t i o n s a r e f i n a l l y c a l c u l a t e d . I t s h o u l d be n o t e d t h a t t h e e q u i l i b r i u m p a r t i a l p r e s s u r e o f c a r b o n d i o x i d e , P r j 0 2 ( R ) ' c o r r e s P ° n c ' s t o t h e r e a c t i o n " FeO + CO = Fe + C 0 2 ( 3 6 ) In a d d i t i o n t o r e d u c t i o n r e d u c t i o n by h y d r o g e n i s r e d u c t i o n i s p o s s i b l e i f o f i r o n o x i d e b y c a r b o n m o n o x i d e , a l s o c o n s i d e r e d i n t h e m o d e l . H y d r o g e n t h e c o a l e m p l o y e d f o r r e d u c t i o n h a s a 41 h i g h c o n t e n t o f v o l a t i l e m a t t e r c o n t a i n i n g h y d r o g e n . When h y d r o g e n r e d u c t i o n o c c u r s t h e r a t e o f r e d u c t i o n i n t h e m o d e l i s c o u p l e d t o t h e r a t e o f h y d r o g e n e v o l u t i o n f r o m t h e c o a l . 2.3.2 A i r P r o f i l e i n t h e K i l n T h e a i r p r o f i l e i n t h e k i l n i s p e r h a p s t h e m o s t i m p o r -t a n t o p e r a t i n g p a r a m e t e r u s e d f o r c o n t r o l l i n g t h e f r e e b o a r d g a s t e m p e r a t u r e . In c o n t r a s t t o o t h e r o p e r a t i n g v a r i a b l e s l i k e t h r o u g h p u t , t h e e f f e c t o n k i l n p e r f o r m a n c e o f a c h a n g e i n a i r p r o f i l e i s a l m o s t i n s t a n t a n e o u s . I n o r d e r t o d e t e r m i n e t h e a i r p r o f i l e f o r t h e m o d e l , d a t a p e r t a i n i n g t o t h e a i r r a t e t h r o u g h d i f f e r e n t b u r n e r s i s r e q u i r e d , t o g e t h e r w i t h t h e b u r n e r p o s i t i o n a l o n g t h e l e n g t h o f t h e k i l n . I n t h e m a t h e m a t i c a l m o d e l t h e a i r s u p p l y i s t r e a t e d a s a l i n e s o u r c e . In a d d i t i o n , s i n c e t h e a i r i s b l o w n c o u n t e r - c u r r e n t t o t h e g a s f l o w , a c e r t a i n e x t e n t o f b a c k f l o w i s a l l o w e d . T h i s n e c e s s i t a t e d a s m o o t h e n i n g o f t h e a i r p r o f i l e t o p r e v e n t a n y a b r u p t c h a n g e i n t h e g a s t e m p e r a t u r e s i n t h e f r e e b o a r d . By way o f e x a m p l e , F i g . 4 g i v e s t h e a i r p r o f i l e w h i c h r e s u l t s f r o m t h e a i r d i s t r i -b u t i o n d e s c r i b e d i n T a b l e 2. T h e a r e a u n d e r t h e c u r v e g i v e s t h e t o t a l a i r f e d i n t o t h e k i l n m i n u s t h e a i r b l o w n t h r o u g h t h e e n d b u r n e r w h i c h a p p e a r s a s a n i n i t i a l c o n d i t i o n i n t h e m o d e l . 42 T a b l e 2 T y p i c a l D a t a f o r t h e A i r B l o w n i n t o a 35m L o n g S L / R N K i l n B u r n e r B u r n e r P o s i t i o n A i r B l o w n F r o m C h a r g e E n d (m) c f t / m i n 1 5.48 700 2 8.23 700 3 1 1 . 5 8 700 4 1 4 . 3 2 700 5 1 6 . 1 5 6 9 0 6 1 8 . 8 9 680 7 2 1 . 1 8 6 9 0 8 2 3 . 7 7 690 9 26.51 640 10 2 7 . 7 3 550 END 3 4 - 1 3 300 0 CO F i g - 4. A i r p r o f i l e f o r a t y p i c a l r u n . 44 2 . 3 . 3 E v o l u t i o n o f V o l a t i l e s f r o m C o a l B e c a u s e t h e c o a l e m p l o y e d i n t h e S L / R N p r o c e s s c o n -t a i n s a c o n s i d e r a b l e q u a n t i t y o f v o l a t i l e s , t h e e v o l u t i o n o f v o l a t i l e s f r o m t h e c o a l c o n s t i t u t e s o n e o f t h e i m p o r t a n t r e a c t i o n s i n t h e p r e h e a t z o n e . I n o r d e r t o o b t a i n a n a c c u r a t e p i c t u r e r e g a r d i n g t h e d i f f e r e n t v o l a t i l e c o m p o n e n t s p r e s e n t a n d t h e i r r a t e s o f e v o l u t i o n , a t e s t p r o g r a m m e was e s t a b l i s h e d a t t h e F u e l s R e s e a r c h I n s t i t u t e ( M i n e s B r a n c h ) b y S t e l c o . T h e t e s t s c o n s i s t e d o f h e a t i n g a s a m p l e o f c o a l a t t h e same r a t e a s i t i s h e a t e d i n a n SL/RN k i l n , c o l l e c t i n g t h e g a s e s e v o l v e d a t r e g u l a r i n t e r v a l s a n d a n a l y s i n g t h e m b y m a s s s p e c t r o m e t e r . F i g . 5 s h o w s t h e r e s u l t s o f o n e s u c h t e s t i n v o l v i n g F o r e s t b u r g c o a l ( s u b - b i t u m i n o u s r a n k ) , h e a t e d a t a r a t e o f 9 ° C p e r m i n u t e . I t i s i m p o r t a n t t o n o t e i n F i g . 5 t h a t h y d r o g e n i s e v o l v e d a t a c o n s i d e r a b l e r a t e f r o m 3 6 0 ° C ( 4 0 m i n ) t o 1 0 8 0 ( 1 2 0 m i n ) . S i n c e h y d r o g e n i s c a p a b l e o f r e d u c i n g i r o n o x i d e a t t e m p e r a -t u r e s a s l o w a s 5 0 0 ° C , i t i s r e a s o n a b l e t o e x p e c t some h y d r o g e n r e d u c t i o n o f o r e p e l l e t s i n t h e p r e h e a t z o n e i n a d v a n c e o f CO r e d u c t i o n . As m e n t i o n e d e a r l i e r , t h i s h a s b e e n i n c o r p o r a t e d i n t h e m o d e l . T h e e x p r e s s i o n s f o r t h e r a t e a t w h i c h t h e d i f -f e r e n t v o l a t i l e c o m p o n e n t s a r e r e l e a s e d b y t h e c o a l w e r e a r r i v e d a t by a p p r o x i m a t i n g t h e c u r v e s i n F i g . 5 w i t h p o l y n o m i a l e q u a t i o n s . 2.3.4 D r y i ng o f S o l i d s I n a d d i t i o n t o t h e r e m o v a l o f v o l a t i l e c o m p o n e n t s f r o m c o a l a n o t h e r i m p o r t a n t r e a c t i o n p r o c e e d i n g i n t h e p r e h e a t T r~ 1 1 1— Forestburg coal heated at 9 °C/min 10,000 h Time (min) F i g . 5. R a t e s o f e v o l u t i o n o f v o l a t i l e s f r o m F o r e s t b u r g c o a l . 46 z o n e i s t h e r e m o v a l o f m o i s t u r e f r o m a l l t h r e e s o l i d c o m p o n e n t s : • o r e , c o a l a n d d o l o m i t e . S i n c e t h e o r e a n d d o l o m i t e c o n t a i n a r e l a t i v e l y s m a l l e r a m o u n t o f m o i s t u r e a n d a l s o s i n c e t h e a m o u n t o f d o l o m i t e f e d i s s m a l l , t h e r e m o v a l o f m o i s t u r e f r o m o r e a n d d o l o m i t e i s o f m i n o r i m p o r t a n c e c o m p a r e d t o c o a l . I n t h e c a s e o f o r e a n d d o l o m i t e t h e v o l u m e t r i c r a t e o f m o i s t u r e r e m o v a l i s c o n s i d e r e d c o n s t a n t o v e r a s e l e c t e d r e g i o n o f t h e k i l n . F o r t h e c a s e o f c o a l t h e d r y i n g d a t a u s e d i n t h e m o d e l was b a s e d on t h e t e s t s c o n d u c t e d a t t h e F u e l s R e s e a r c h I n s t i t u t e w h e r e m o i s b u r e was a l s o c o l l e c t e d t o g e t h e r w i t h t h e v o l a t i l e s . F i g . 6 g i v e s t h e r e s u l t s o b t a i n e d f r o m t h e t e s t f o r F o r e s t b u r g c o a l . I t i s c l e a r f r o m F i g . 6 t h a t a c o n s i d e r a b l e a m o u n t o f m o i s t u r e i s e v o l v e d a t t e m p e r a t u r e h i g h e r t h a n 1 0 0 ° C . T h i s m e a n s t h a t a p r o x i m a t e a n a l y s i s c a n n o t be u s e d t o g i v e a n a c c u r a t e v a l u e o f t h e t o t a l m o i s t u r e i n t h e c o a l , s i n c e t h e t e m p e r a t u r e u s e d i s o n l y 104 t o 1 1 0 ° C . T h e c u r v e i n F i g . 6 was a g a i n a p p r o x i m a t e d by a p o l y n o m i a l e q u a t i o n f o r u s e i n t h e m o d e l . 2.3.5 C o m b u s t i o n i n t h e F r e e b o a r d I n o r d e r t o m a i n t a i n t h e s o l i d s b e d a t t h e r e q u i r e d t e m p e r a t u r e i n t h e r e d u c t i o n z o n e , a l a r g e q u a n t i t y o f h e a t h a s t o be t r a n s f e r r e d c o n t i n u o u s l y f r o m t h e f e e b o a r d g a s t o t h e s o l i d s . T h i s i s n e c e s s a r y t o m e e t t h e l a r g e h e a t r e q u i r e m e n t s 47 i — 1 Forestburg Cool Heated at 9°C/min Time (min) F i g . 6 . R a t e o f m o i s t u r e e v o l u t i o n f r o m F o r e s t b u r g c o a l . 48 o f t h e e n d o t h e r m i c B o u d o u a r d r e a c t i o n . T h i s h e a t i s g e n e r a t e d i n t h e f r e e b o a r d a r e a by t h e b u r n i n g o f c o m b u s t i b l e s . I n t h e SL/RN p r o c e s s t h e m a i n c o m b u s t i b l e c o n s t i t u e n t i s c a r b o n m o n o x i d e w h i c h i s r e l e a s e d f r o m t h e b e d a s t h e B o u d o u a r d r e a c t i o n p r o c e e d s . A n o t h e r c o m b u s t i b l e i s n a t u r a l g a s w h i c h i s o f t e n i n j e c t e d i n t h e p r e h e a t z o n e a s a n a u x i l i a r y h e a t s u p p l y . N a t u r a l g a s i n j e c t i o n i s p r a c t i s e d f r e q u e n t l y i n k i l n r u n s i n v o l v i n g c o a l w i t h a h i g h m o i s t u r e c o n t e n t . A s m e n t i o n e d a t t h e b e g i n n i n g o f t h i s c h a p t e r , i t i s a s s u m e d i n t h e m o d e l t h a t i n s t a n t a n e o u s c o m b u s t i o n i s a c h i e v e d i n t h e f r e e b o a r d g a s e s . B e f o r e c a l c u l a t i n g t h e q u a n t i t y o f t h e v a r i o u s c o m b u s t i b l e s b u r n t , h o w e v e r , a c h e c k i s made t o a s s e s s w h e t h e r s u f f i c i e n t o x y g e n i s a v a i l a b l e f o r c o m p l e t e c o m b u s t i o n . I f n o t , b u r n i n g i s a l l o w e d o n l y t o t h e e x t e n t t h a t o x y g e n i s p r e s e n t . T h e h e a t g e n e r a t e d by c o m b u s t i o n i s c o n s i d e r e d t o be a v o l u m e t r i c h e a t s o u r c e w h i c h c i r c u m v e n t s t h e n e e d t o t r e a t f l a m e h e a t t r a n s f e r s e p a r a t e l y . > 2 . 3 . 6 C a l c i n a t i o n o f D o l o m i t e D o l o m i t e i s i n c l u d e d i n t h e c h a r g e t o the^J>L/RN k i l n i f t h e s u l p h u r c o n t e n t o f t h e c o a l i s e x c e s s i v e l y h i g h . T h e d o l o m i t e e s s e n t i a l l y a c t s a s a s c a v e n g e r f o r s u l p h u r a n d p r e v e n t s t h e s u l p h u r c o n t e n t o f t h e s p o n g e i r o n f r o m b e i n g u n a c c e p t a b l y h i g h . D u r i n g h e a t i n g , t h e d o l o m i t e c a l c i n e s by r e l e a s i n g C 0 2 t o t h e f r e e b o a r d g a s . T h e i n f l u e n c e o f t h i s r e a c t i o n on b o t h 49 t h e h e a t a n d m a s s b a l a n c e s o v e r t h e k i l n i s r e l a t i v e l y i n s i g -n i f i c a n t , h o w e v e r , b e c a u s e o f t h e s m a l l q u a n t i t y c h a r g e d . N e v e r t h e l e s s , c a l c i n a t i o n o f t h e d o l o m i t e i s i n c o r p o r a t e d i n t o t h e m o d e l b e i n g a l l o w e d t o p r o c e e d a t a c o n s t a n t r a t e b e t w e e n s e t t e m p e r a t u r e l i m i t s . 2.4.1 S p e c i f i c H e a t s o f S o l i d s a n d G a s e s S i n c e t h e s o l i d s a r e a m i x t u r e o f o r e , c o a l a n d d o l o m i t e , t h e a v e r a g e s p e c i f i c h e a t o f t h e s o l i d s a t a n y t e m p e r a t u r e w i l l d e p e n d o n t h e a v e r a g e s p e c i f i c h e a t s o f t h e i n d i v i d u a l c o m p o n e n t s . I n a d d i t i o n , s i n c e t h e c o m p o s i t i o n o f t h e s e s o l i d c o m p o n e n t s a l s o c h a n g e w i t h p o s i t i o n a l o n g t h e k i l n ( w i t h t e m p e r a t u r e ) i t i s n e c e s s a r y t o c a l c u l a t e t h e c o m p o s i t i o n o f i n d i v i d u a l s o l i d : c o m p o n e n t s b e f o r e v e n t u r i n g i n t o t h e c a l c u l a -t i o n o f t h e s p e c i f i c h e a t s . I t s h o u l d be m e n t i o n e d h e r e t h a t t h e s o l i d c o m p o n e n t s a r e a s s u m e d t o be a m e c h a n c i a l m i x t u r e i n t h e s p e c i f i c h e a t c a l c u l a t i o n s . F o r e x a m p l e , o r e i s a s s u m e d t o be a m i x t u r e o f i r o n o x i d e , g a n g u e a n d m o i s t u r e . H e r e a g a i n t h e s p e c i f i c i r o n o x i d e u s e d i n t h e a b o v e c a l c u l a t i o n s d e p e n d s on t h e d e g r e e o f r e d u c t i o n . T h u s a t t h e b e g i n n i n g o f r e d u c t i o n t h e o x i d e p r e s e n t w i l l be F e 2 0 3 , t h e n a m i x t u r e o f F e 2 0 3 a n d F e 3 G \ f o l l o w e d by t h e s e q u e n c e , F e 3 u \ , a m i x t u r e o f F e 3 G \ + F e O , FeO a n d f i n a l l y a m i x t u r e o f F e O + F e . T h e same p r o c e d u r e i s f o l l o w e d f o r c o a l a n d d o l o m i t e . T h e s p e c i f i c h e a t s o f t h e f r e e b o a r d g a s e s a r e l e s s d i f f i c u l t t o c a l c u l a t e c o m p a r e d t o t h e s o l i d s . T h e a v e r a g e 50 s p e c i f i c h e a t o f t h e g a s e s i s c o m p u t e d f r o m t h e s p e c i f i c h e a t o f i n d i v i d u a l c o m p o n e n t s b a s e d o n t h e r e s p e c t i v e w e i g h t f r a c t i o n s . I n a d d i t i o n t o c a l c u l a t i n g t h e s p e c i f i c h e a t , o n e s h o u l d a l s o c a l c u l a t e t h e d e r i v a t i v e o f t h e s p e c i f i c h e a t w i t h r e s p e c t t o t e m p e r a t u r e . T h i s i s o b v i o u s f r o m E q s . ( 1 9 ) a n d (22), a n d a r i s e s f r o m t h e f a c t t h a t t h e s p e c i f i c h e a t i s a l l o w e d t o v a r y w i t h t e m p e r a t u r e i n t h e c a l c u l a t i o n s . 2.4.2 P a r t i a l P r e s s u r e s i n t h e F r e e b o a r d Gas P h a s e K n o w l e d g e o f t h e p a r t i a l p r e s s u r e s o f t h e i n d i v i d u a l c o m p o n e n t s c o m p r i s i n g t h e f r e e b o a r d g a s p h a s e i s r e q u i r e d f o r t h e c a l c u l a t i o n o f r a d i a t i o n h e a t t r a n s f e r f r o m t h e g a s e s t o s o l i d s a n d i n s i d e w a l l o f t h e k i l n . S i n c e t h e m a s s f l o w r a t e o f t h e i n d i v i d u a l g a s c o m p o n e n t s i s c a l c u l a t e d a t e a c h p o i n t i n t h e k i l n f r o m t h e d i f f e r e n t i a l m a s s b a l a n c e s , t h e p a r t i a l p r e s s u r e i s e a s i l y c o m p u t e d u s i n g t h e c o r r e s p o n d i n g m o l e c u l a r w e i g h t s a n d a s s u m i n g a t o t a l p r e s s u r e o f o n e a t m o s p h e r e . T h i s c a l c u l a t i o n i s r e p e a t e d f o r e a c h s l i c e o f t h e k i l n t o y i e l d a x i a l p r o f i l e s o f p a r t i a l p r e s s u r e s . 2.5 H e a t T r a n s f e r i n R o t a r y K i l n s I n s p i t e o f t h e r o t a r y k i l n b e i n g u s e d i n i n d u s t r i a l o p e r a t i o n s s u c h a s d r y i n g a n d t h e p r o d u c t i o n o f c e m e n t f o r s e v e r a l d e c a d e s , a q u a n t i t a t i v e u n d e r s t a n d i n g o f t h e h e a t 51 t r a n s f e r m e c h a n i s m s i n r o t a r y k i l n s i s s t i l l n o t c l e a r . T h e u n c e r t a i n t y a r i s e s b e c a u s e t h e r e a r e s e v e r a l d i f f e r e n t h e a t t r a n s f e r m o d e s , a l l o f w h i c h a r e i n f l u e n c e d t o a d i f f e r e n t e x t e n t b y t h e k i l n v a r i a b l e s . R e f e r r i n g t o F i g . 7 ( a ) , t h e s e d i f f e r e n t m o d e s c a n be c h a r a c t e r i s e d a s f o l l o w s : ( i ) R a d i a t i o n f r o m g a s t o w a l l ( A 2 ) ( i i ) C o n v e c t i o n f r o m g a s t o w a l l ( A 2 ) ( i i i ) R a d i a t i o n f r o m g a s t o s o l i d s ( A i ) ( i v ) C o n v e c t i o n f r o m g a s t o s o l i d s ( A i ) ( v ) . R a d i a t i o n f r o m e x p o s e d i n n e r w a I I t o s o I i d s ( A i ) ( v i ) C o n d u c t i o n f r o m c o v e r e d w a l l t o s o I i d s ( A 3 ) ( v i i ) H e a t l o s s b y c o n v e c t i o n a n d r a d i a t i o n f r o m k i l n s u r f a c e t o s u r r o u n d . i n g s T h e t e r m s A ! , A 2 a n d A 3 l i s t e d i n p a r e n t h e s i s c o r r e s p o n d t o t h e a r e a s a f f e c t i n g t h e i n d i v i d u a l h e a t t r a n s f e r m o d e s . In t h e l i t e r a t u r e d i f f e r e n t e q u a t i o n s h a v e b e e n u s e d b y i n d i v i d u a l a u t h o r s t o d e s c r i b e t h e c o - e f f i c i e n t s w h i c h g o v e r n t h e h e a t t r a n s f e r r a t e o f t h e d i f f e r e n t m o d e s . T h e s e a r e g i v e n i n T a b l e 3. F r o m t h i s t a b l e i t i s c l e a r t h a t t h e r e i s no u n i f o r m s e t o f e q u a t i o n s t h a t h a v e b e e n e m p l o y e d p r e v i o u s l y . A l s o i n many i n s t a n c e s t h e r e i s no i n d i c a t i o n g i v e n a s t o why a p a r t i c u l a r e q u a t i o n h a s b e e n s e l e c t e d i n p r e f e r e n c e t o a n o t h e r . Radiation Convection Conduction F i g . 7 ( a ) . C r o s s - s e c t i o n o f t h e k i l n s h o w i n g t h e h e a t t r a n s f e r m o d e s . Chord AB A, Arc ADB A 2 Arc ACB A 3 7 ( b ) . C r o s s - s e c t i o n o f t h e k i l n s h o w i n q t h e a r e a t e r m s i n v o l v e d i n t h e d i f f e r e n t h e a t t r a n s f e r e q u a t i o n s . Table. 3 Heat Transfer Coefficients in the Literature Riffaud (18) Sass (16) Wingfield (21) Manitius (20) Lyons (31) Sprang (19) GAS TO SOLIDS CONVECTION GAS TO SOLIDS RADIATION 0.67 0.05 G 0.67 0.05 G ( T 4 - T A ) 8 6 ( T - T ) 8 8 0.023 [ ip_C ] 0 , 4 x " V " 8 . VR De" , Kg x [ — ] ( T 4 - T 4 ) 8 a ( T - T ) g s 17.8(X Di) 0 , 2(V / C ) 0 - 8 8 8 P ( E T 4-aV ) 8 8 8 8 e (T8 -T ) 4 B.T.U hr.ft . F . 2 o E e (T 3 - T 3) g s g a' 4 B.T.U. hr.ft 2 . F a c E g 8 (T 4 - T 4) 8 a ( T „ - T«> 8 s GAS TO WALL CONVECTION 0.05 G 0.67 0.05 G 0.67 same as In gas to solids convec-tion . same as In gas to solids convection 5 B.T.U. hr.ft 2 . F 4 B.T.U. hr.ft . F GAS TO WALL RADIATION INNER WALL TO SOLIDS RADIATION (T 4 - T 4 ) g w ? CT„ - T K ) (T 4 - T* ) (T - T ) o E f (T 4 - T 4 ) 8 w (T - T ) 8 w' (T 4 - T 4 ) (T - T ) (T - T ) g w S (T - T , 8 «) (T 4 - T4) W 8 (T - T ) I I - T ) g w (l-o" )T *-(l-o' )T 4 E e [ 8 w 8 8] , A w , 3 3 w 8 — ' 2o E E W(T +T ) 3 + T 3 ) <l-Voe-« (T - T ) W 8 8 w • (T 4 - T 4) 8 w (T - T ) 8 w' W g W W 8 4 It (T - T ) vi s (T - T„ ) INNER WALL TO SOLIDS (COVERED) 40 B.T.U, hr.ft .F 0.25 G 0.67 148 B.T.U. 2 • hr.ft . F 39.1 B.T.U. 2° hr.ft F 4 B.T.U hr.ft F COMMENTS r c K -thermal conductivity - F L O W R A C E ° F & A A E -emissivity of solid 8 s D^-inner diameter o - Stefan Constant f -correction factor e^-emissivity of gas Eg-comprlsed of emis-sivity of solids and uall v -kinematic viscosity p -density C -specific heat P V^-velocity of gas D -equivalent diameter' 1. In.addition another radiation term is also considered. 2. Lengthy expression from a Russian work. thermal conductivity Di Inner diameter A s a r e a o f c h a r 8 e , surface a absorbtivity of gas S at T v a r e a °' exposed wall » s a absorbtivitv of gas 8 at t h° l+2hosin(p/2) 2*-p 2n-p angle subtended by the solids at the ^ centre. h„ -0.0758 5 4 2.5.1 H e a t T r a n s f e r C o e f f i c i e n t s U s e d i n t h e P r e s e n t M o d e l T h e f o l l o w i n g s e c t i o n d e t a i l s t h e e q u a t i o n s u t i l i s e d i n t h e e v a l u a t i o n o f t h e d i f f e r e n t h e a t t r a n s f e r c o e f f i c i e n t s i n t h e p r e s e n t m o d e l . T h e s e h e a t t r a n s f e r c o e f f i c i e n t s a r e e v a l u a t e d a t e a c h s l i c e a l o n g t h e e n t i r e l e n g t h o f t h e k i l n . 2 .5.1.1 H e a t T r a n s f e r f r o m G a s t o W a l l by R a d i a t i o n or h X "* I T 1 * e T - a T g ,g g, w / ( 3 7 ) gwr TT - T ) 3 v g w' E q . ( 3 7 ) gives the heat transfer coefficient from gas to wall by radiation, where h g w r 1 S t n e n e a t t r a n s f e r c o e f f i c i e n t a i s t h e S t e f a n - B o l t z m a n n c o n s t a n t e i s t h e e m i s s i v i t y o f t h e g a s a t t h e 9 g a s t e m p e r a t u r e a 1 i s t h e a b s o r p t i v i t y o f g a s a t t h e 9 w a l l t e m p e r a t u r e T h e a r e a t e r m t h a t i s u s e d i n c o n n e c t i o n w i t h t h i s h e a t t r a n s f e r c o e f f i c i e n t i s A 2 a s g i v e n i n F i g . 7 ( b ) . S y m m e t r i c a l m o l e c u l e s l i k e N 2 a n d 0 2 do n o t p a r t i c i p a t e i n a n y r a d i a t i v e e x c h a n g e b u t a s y m m e t r i c a l m o l e c u l e s s u c h a s C 0 2 a n d H 2 0 do h a v e c e r t a i n b a n d l e n g t h s o v e r w h i c h t h e y e m i t a n d a b s o r b r a d i a t i o n . McAdams [ 2 4 ] g i v e s a d e t a i l e d p r o c e d u r e f o r c a l c u l a t i n g t h e 55 g a s e m i s s i v i t i e s a n d a b s o r p t i v i t i e s . T h e e m i s s i v i t y o f a n y g a s s p e c i e s p a r t i c i p a t i n g i n r a d i a t i v e h e a t e x c h a n g e d e p e n d s on t h e p a r t i a l p r e s s u r e o f t h a t c o m p o n e n t , t h e t e m p e r a t u r e a n d t h e mean beam l e n g t h . T h e mean beam l e n g t h f o r t h e g a s i s a f u n c -t i o n o f t h e g e o m e t r y o f t h e s y s t e m a n d i n t h i s c a s e d e p e n d s on t h e d i a m e t e r o f t h e r o t a r y k i l n . F i g . 8 s h o w s t h e e m i s s i v i t y f o r C 0 2 f o r d i f f e r e n t v a l u e s o f t h e p r o d u c t o f mean beam l e n g t h (L) a n d p a r t i a l p r e s s u r e o f t h e g a s . F i g . 9 g i v e s t h e e m i s s i v i t y f o r H 2 0 . F o r t h e SL/RN m o d e l t h e c u r v e s i n F i g s . 8 a n d 9 w e r e a p p r o x i m a t e d by p o l y n o m i a l e q u a t i o n s a n d s t o r e d i n t h e c o m p u t e r p r o g r a m . T h e s t e p s i n v o l v e d i n c a l c u l a t i n g t h e e m i s s i v i t y v a l u e s i n t h e m o d e l a r e s u m m a r i s e d b e l o w . ( i ) C a l c u l a t i o n o f t h e p a r t i a l p r e s s u r e o f t h e g a s c o n c e r n e d . ( i i ) S e l e c t i o n o f t h e a p p r o p r i a t e l i n e c o r r e s p o n d i n g t o t h a t p a r t i a l p r e s s u r e . ( i i i ) R e a d i n g o f t h e v a l u e o f e m i s s i v i t y f o r t h e p a r t i c u l a r t e m p e r a t u r e . I f o n e i s c o n s i d e r i n g a m i x t u r e o f H 2 0 a n d C 0 2 a s i n . t h e S L/RN k i l n , t h e t o t a l e m i s s i v i t y o f t h e g a s i s e 9 = £ co2 + £ H 2Q - A E ( 3 8 ) w h e r e i s t h e t o t a l g a s e m i s s i v i t y e C 0 2 i s t h e e m i s s i v i t y c o n t r i b u t i o n f r o m C 0 Z e H 2 0 i s t h e e m i s s i v i t y c o n t r i b u t i o n f r o m H2C1 56 "E 8" 0.02 0.015 { ^ 0.010 0.009 0.008 0.007 0.006 0.005 0.004 0.003 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Absolute temperature, in °R F i g . 8. Gas e m m i s s i v i t y f o r carbon d i o x i d e ( f r o m P e r r y ( 3 0 ) ) 57 Absolute temperature, in °R F i g . 9. Gas ( f r o e m i s s i v i t y f o r m P e r r y ( 3 0 ) ) . w a t e r v a p o u r 58 Ae i s t h e c o r r e c t i o n f a c t o r t o a c c o u n t f o r t h e o v e r l a p p i n g o f t h e two a b s o r p t i o n b a n d s In t h e m o d e l c a l c u l a t i o n s , h o w e v e r , i t was f o u n d t o be u n n e c e s -s a r y t o a p p l y t h e c o r r e c t i o n t e r m a s i t was r e l a t i v e l y n e g l i g i b l e 2 . 5 . 1 . 2 C o n v e c t i o n f r o m G a s t o W a l l T h e h e a t t r a n s f e r c o e f f i c i e n t f r o m g a s t o w a l l by c o n v e c t i o n i s g i v e n b y E q . ( 3 9 ) : h n l l „ = 0 . 0 5 G 0 ' 6 7 ( 39 ) gwc v w h e r e G i s t h e m a s s f l u x o f t h e g a s e s . S i n c e t h e c o n t r i b u t i o n by c o n v e c t i o n t o t h e o v e r a l l h e a t t r a n s f e r r a t e i s r e l a t i v e l y m i n o r , a c h a n g e i n i t s m a g n i t u d e d o e s n o t a f f e c t t h e o v e r a l l h e a t t r a n s f e r r a t e t o a n y a p p r e c i a b l e e x t e n t . T h i s h e a t t r a n s f e r c o e f f i c i e n t h a s i t s maximum v a l u e a t t h e c h a r g e e n d w h e r e t h e m a s s f l u x o f g a s e s i s g r e a t e r . A s m e n t i o n e d e a r l i e r , t h e a r e a t e r m u s e d w i t h t h i s c o e f f i c i e n t i s A 2 . 2 . 5 . 1 . 3 R a d i a t i o n f r o m G a s t o S o l i d s T h e e q u a t i o n d e s c r i b i n g t h i s h e a t t r a n s f e r c o e f f i c i e n t i s s i m i l a r t o t h a t f o r g a s t o w a l l r a d i a t i o n a n d i s g i v e n b e l o w o ( e n T* - a " T ! ) : W V - T J 5 <«> y v g s ' 59 w h e r e h g $ r i s t h e h e a t t r a n s f e r c o e f f i c i e n t a" i s t h e a b s o r p t i v i t y o f t h e g a s a t t h e y s o l i d s t e m p e r a t u r e T h e e m i s s i v i t y a n d a b s o r p t i v i t y c a l c u l a t i o n s a r e p e r f o r m e d i n a m a n n e r i d e n t i c a l t o t h a t g i v e n i n t h e p r e v i o u s s e c t i o n . T h e a r e a t e r m u s e d w i t h t h i s h e a t t r a n s f e r c o e f f i c i e n t i s Ax-2.5.1 .4 C o n v e c t i o n f r o m Gas t o S o l i d s T h e e x p r e s s i o n e m p l o y e d f o r t h i s h e a t t r a n s f e r c o e f f i c i e n t , h „ , i s : g s c h g s c = 0 . 0 5 G 0 ' 6 7 ( 4 1 ) T h e a r e a t e r m u s e d h e r e i s A x . 2 . 5 . 1 . 5 R a d i a t i o n f r o m E x p o s e d W a l l t o S o l i d s T h i s h e a t t r a n s f e r mQ.de, t o g e t h e r w i t h r a d i a t i v e h e a t t r a n s f e r f r o m g a s t o s o l i d s , a c c o u n t f o r r o u g h l y t w o -t h i r d s o f t h e t o t a l h e a t t r a n s f e r r e d t o t h e s o l i d s . T h e g o v e r n -i n g e q u a t i o n f o r r a d i a t i o n f r o m w a l l t o s o l i d s i s g i v e n b y h w s r " f 0 S, E s < T w " Ts» < 4 2> w h e r e h i i c i o i s t h e h e a t t r a n s f e r c o e f f i c i e n t wsr f i s t h e f i l t e r i n g f a c t o r 60 e i s t h e e m i s s i v i t v o f t h e w a l l ( 0 . 9 ) w e s i s t h e e m i s s i v i t y o f t h e s o l i d s ( 1 . 0 ) I t i s n o t c l e a r f r o m t h e l i t e r a t u r e w h a t v a l u e o f f s h o u l d be u s e d i n t h e e q u a t i o n . I n a l l t h e m o d e l c a l c u l a t i o n s p r e s e n t e d i n t h i s w o r k a v a l u e o f 1.0 h a s b e e n u s e d f o r f . T h e a r e a t e r m h e r e i s A i . 2 . 5 . 1 . 6 C o v e r e d W a l l t o S o l i d s T h e m a g n i t u d e o f t h i s h e a t t r a n s f e r c o e f f i c i e n t i s t a k e n t o be f i v e t i m e s t h e m a g n i t u d e o f t h e c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t ( E q . 3 9 ) . T h e a c t u a l h e a t t r a n s f e r m e c h -a n i s m f r o m c o v e r e d w a l l t o s o l i d s w i l l be a m i x t u r e o f a l l t h e t h r e e modes o f h e a t t r a n s f e r . T h e a r e a t e r m e m p l o y e d i n t h i s c a s e i s A 3. 2 . 5 . 1 . 7 H e a t L o s s t o t h e S u r r o u n d i n g s H e a t l o s s f r o m t h e k i l n s h e l l d e p e n d s on t h e t h e r m a l c o n d u c t i v i t y o f t h e r e f r a c t o r y 1 i n i n g e m p l o y e d a n d i t s t h i c k -n e s s . T r e a t i n g t h e p r o b l e m a s h e a t t r a n s f e r t h r o u g h a c o m p o s i t e w a l l a n d n e g l e c t i n g t h e t h e r m a l r e s i s t a n c e o f t h e s t e e l s h e l l t h e o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t c a n be o b t a i n e d a s f o l l o w s : 61 2rrr ( r 2 - r ,) ( r 3 - r2)~ V ' 2 ~ ' 1 I + y I 3 ~ r 2 ; TTKJ ( r x + r 2 ) TTK 2 ( r 3 + r 2 ) h S A 2 Tr r i ( 4 3 ) w h e r e i s t h e o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t • r i ,r 2 ,r 3 ,r i> a r e r a d i u s t e r m s d e s c r i b e d i n F i g . 10 K i , K 2 a r e t h e r m a l c o n d u c t i v i t i e s o f t h e d i f f e r e n t r e f r a c t o r y l a y e r s c o m p r i s i n g t h e l i n i n g h<.^ i s t h e h e a t t r a n s f e r c o e f f i c i e n t f r o m t h e s u r f a c e o f t h e k i l n t o t h e s u r r o u n d i n g s by c o n v e c t i o n a n d r a d i a t i o n . T h e a r e a t e r m u s e d h e r e i s 2-nrk. T h e c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t f r o m t h e k i l n s h e l l t o t h e s u r r o u n d i n g s i s c a l c u l a t e d u s i n g t h e e q u a t i o n h D c K = 0.11 ( 0 . 5 R 2 + G ) P euj r' r 0. 35 ( 4 4 ) a n d t h e r a d i a t i v e c o e f f i c i e n t by t h e s t a n d a r d S t e f a n - B o l t z m a n n e q u a t i o n . -ss ° TT < T s h - 0 ( 4 5 ) w h e r e h c i s t h e c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t D i s t h e o u t s i d e d i a m e t e r o f t h e k i l n K i s t h e t h e r m a l c o n d u c t i v i t y o f a i r G r i s t h e G r a s h o f n u m b e r 10. C r o s s s e c t i o n o f t h e r o t a r y k i l n s h o w i n g t h e d i f f e r e n t r a d i u s t e r m s u s e d f o r c a l c u l a t i n g h e a t l o s s t o s u r r o u n d i n q s . CTl 63 P r i s t h e P r a n d t l n u m b e r e s s i s t h e e m i s s i v i t y o f t h e s t e e l s h e l l T s h i s t h e t e m p e r a t u r e o f t h e s h e l l T i s t h e t e m p e r a t u r e o f t h e a m b i e n t m e d i u m a B e c a u s e t h e s h e l l t e m p e r a t u r e was f o u n d t o be v i r t u a l l y i n d e p e n d e n t o f a x i a l p o s i t i o n , t h e c o e f f i c i e n t h c i s e v a l u a t e d o n l y o n c e f o r a g i v e n r u n . As n o t e d e a r l i e r t h e s h e l l t e m p e r a -t u r e i s n o t known a p r i o r i b u t i s c a l c u l a t e d by t r i a l a n d e r r o r a s s h own i n t h e s e c t i o n c o n c e r n e d w i t h t h e h e a t b a l a n c e on t h e w a l 1 . 2.5.2 A r e a T e r m s f o r H e a t T r a n s f e r I n t h e m o d e l t h e a r e a t e r m s u s e d i n t h e h e a t t r a n s f e r c a l c u l a t i o n s w e r e c o m p u t e d f r o m a k n o w l e d g e o f t h e a n g l e s u b -t e n d e d by t h e s o l i d s . T h i s a n g l e , a , was d e t e r m i n e d f r o m t h e d e g r e e o f f i l l a s f o l l o w s . R e f e r r i n g t o F i g . 7 ( b ) A r e a o f s e c t o r OAB = ^ x T r r i 2 A r e a o f t r i a n g l e OAB = j x r j 2 x s i n a A r e a o f t h e h a t c h e d s e c t i o n = r r r x 2 - i r j 2 s i n a c. TT C r 2 - - j — [ a - s i n a ] 6 4 B u t t h i s i s a l s o t h e d e g r e e o f f i l l , F r 2 s o t h a t TT x r i 2 x F = —^— [ a - s i n a ] o r a = s i n a + 2TTF ( 4 6 ) w h e r e r i i s t h e i n t e r n a l r a d i u s o f t h e r o t a r y k i l n . S i n c e t h i s i s a n i m p l i c i t r e l a t i o n s h i p i n a , i t i s s o l v e d by a n i t e r a t i v e p r o c e d u r e u s i n g t h e N e w t o n - R a p h s o n m e t h o d [ 2 5 ] . T h e i m p o r t a n t a r e a s f o r h e a t f l o w c a l c u l a t i o n s a r e a r c s ACB a n d ADB, a n d c h o r d AB. T h e i r r e s p e c t i v e r e l a t i o n s h i p s t o a a r e g i v e n b e l o w . a r c ACB = 2 T r r x 1 - f-2rr a r c ADB = 2 ^ ^ = r xa ( 4 8 ) ( 4 7 ) c h o r d AB = 2r1 s i n | ( 4 9 ) 2 . 6 N u m e r i c a l P r o c e d u r e U s e d i n t h e M o d e l S i n c e t h e s o l i d s a n d g a s e s f l o w i n a c o u n t e r - c u r r e n t f a s h i o n i n t h e S L / R N k i l n , t h e s o l u t i o n o f t h e d i f f e r e n t i a l E q s . (5) t o ( 1 6 ) , ( 1 9 ) a n d (22) p o s e s some d i f f i c u l t i e s . T h e s o l i d s b o u n d a r y c o n d i t i o n s a r e known a t t h e c h a r g e e n d a n d t h a t o f g a s e s a t t h e d i s c h a r g e e n d . H o w e v e r , i n o r d e r t o s t a r t t h e c o m p u t a t i o n s i t i s n e c e s s a r y t o h a v e t h e i n i t i a l c o n d i t i o n s 65 f o r b o t h s o l i d s a n d g a s e s a t e i t h e r e n d . T h i s l e a d s t o two r o u t e s f o r s o l v i n g t h e m i x e d b o u n d a r y p r o b l e m . A s s u m i n g t h a t t h e e n d c o n d i t i o n s f o r t h e g a s e s a t t h e c h a r g e e n d a r e known t h e c a l c u l a t i o n s c a n be s t a r t e d a t t h e c h a r g e e n d . I n t h e m o d e l t h e c a l c u l a t i o n s w e r e b e g u n a t t h e d i s c h a r g e e n d o w i n g t o t h e c o m p l i c a t e d n a t u r e o f t h e a v a i l a b i l i t y o f o x y g e n f o r c o m b u s -t i o n i n t h e f r e e b o a r d g a s e s . I n o t h e r w o r d s i t was e a s i e r t o f o l l o w t h e g a s e s t h r o u g h t h e k i l n r a t h e r t h a n t h e s o l i d s . A s m e n t i o n e d b e f o r e , t h e w a l l t e m p e r a t u r e i s n o t known b e f o r e h a n d a n d h e n c e n e e d s c a l c u l a t i o n on a n i t e r a t i v e b a s i s . T h e f l o w -s h e e t f o r t h e m a t h e m a t i c a l m o d e l i s g i v e n i n F i g s . 1 1 ( a ) t o ( c ) . f i r s t o r d e r d i f f e r e n t i a l e q u a t i o n s ( 5 ) t o ( 1 6 ) , ( 1 9 ) a n d ( 2 2 ) i s t h e K u t t a - M e r s o n m e t h o d , w h i c h i s o n e o f t h e f o u r t h o r d e r R u n g e - K u t t a m e t h o d s . B r i e f l y s t a t e d , t h e p r o c e d u r e w o r k s a s f o l l o w s . I f A, B, C, D a r e f o u r i n t e r m e d i a t e p o i n t s i n a s i n g l e i n t e g r a t i o n s t e p , h , t h e n t h e c a l c u l a t i o n s p e r f o r m e d a r e T h e s p e c i f i c n u m e r i c a l m e t h o d u s e d f o r s o l v i n g t h e = x B = x 0 ( 5 0 ) (51.) x n = x 0 + h = X i ( 5 2 ) I n t r o d u c i n g t h e s h o r t h a n d n o t a t i o n 66 FLOW SHEET OF THE COMPUTER PROGRAMME START READ INPUT DATA GENERAL CALCULATIONS COMMON FOR THE E N T I R E LENGTH OF THE K I L N I N I T I A L I S E V A R I A B L E S FOR THE DISCHARGE END OF THE ROTARY K I L N AND SET THE SWITCHES CALCULATE THE COMPOSITION OF IRON OXIDE CALCULATE THE S P E C I F I C HEATS OF MATERIALS CALCULATE THE D E R I V A T I V E S OF THE S P E C I F I C HEAT WITH TEMPERATURE CALCULATE THE RATES OF BOUDOUARD REACTION AND REDUCTION REACTIONS CALL THE SUBROUTINE CONTROLLING THE SWITCHES C A L C U U C O M Pos i S O L I I LTE THE NEW rioN OF THE )S C ALCULATE THE DEGREE OF REDUCTION M/ CONTINUED F i g . 1 1 . F l o w s h e e t o f t h e c o m p u t e r p r o g r a m 67 CALCULATE THE RATES OF VOLATILES EVOLUTION FROM COAL CALCULATE THE PARTIAL PRESSURE OF GASES IN THE FREEBOARD CALCULATE THE RATE OF AIR SUPPLY INTO THE KILN i U CALCULATE THE DRYING RATES OF SOLIDS ^ : CALCULATE THE RATE OF BURNING OF COMBUSTIBLES BASED ON OXYGEN AVAILABILITY CALCULATE THE VARIOUS HEATS OF REACTIONS IN THE SOLID AND GAS PHASE VJZ ASSUME AN INNER WALL TEMPERATURE CALCULATE EMISSIVITIESi CALCULATE THE VARIOUS HEAT TRANSFER RATES MODIFY THE INNER WALL TEMPERATURE CONTINUED T CALCULATE THE NEW WALL TEMPERATURE BASED ON HEAT BALANCE ON WALL NOT SATISFIED SATISFIED INTEGRATE THROUGH ONE STEP AND CALCULATE THE NEW VALUES OF THE VARIABLES XL CHECK FOR BOUNDARY CONDITIONS AT THE CHARGE END OF THE KILN YES > CALL PLOT ROUTINE STOP 69 y[ = f ( x z , Y z ) z = 0, A, B, C, D "(53) t h e m e t h o d o f M e r s o n c o n s i s t s o f m a k i n g t h e e v a l u a t i o n s Y A = Y 0 + | Y' ; (54) Y B = Yo + £ ( Y 0 + Y^) (55) Y c = Yo + J L ( Y J + 3Yg) ( 5 6 ) Y D = Y 0 + £ ( Y 0 - 3Yg + 4Y^) (57) • Yi = Yo + | ( Y 0 + 4Y .^ + Y p ) ( 5 8 ) An e s t i m a t e o f t h e t r u n c a t i o n e r r o r i s g i v e n by i i h Y ; -1 h Y B + ± h Y' -1 h Y ; (59) w h i c h i s u s e d t o c o n t r o l t h e s t e p s i z e a u t o m a t i c a l l y . T h e s o u r c e l i s t i n g o f t h e c o m p u t e r p r o g r a m i s g i v e n i n A p p e n d i x I . 2.7 I n t e r n a l C o n s i s t e n c y o f t h e M o d e l In o r d e r t o e n s u r e t h a t t h e c a l c u l a t i o n s p e r f o r m e d u s i n g t h e m o d e l a r e i n t e r n a l l y c o n s i s t e n t , a c h e c k was made on t h e o v e r a l l h e a t a n d m a s s b a l a n c e s . T h e r e s u l t s o f t h e s e b a l a n c e s a r e s h o w n b e l o w f o r a t y p i c a l r u n w i t h F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s . M a s s B a l a n c e  M a s s i n o r e i n c o a l i n N i t r o g e n O x y g e n N a t u r a l g a s T O T A L 2 0 1 0 . 5 g / s 1 3 5 9 . 9 g / s 3 2 8 7 . 4 g / s 9 9 8 . 7 g / s 3 1 - 7 g / s 7 6 8 8 . 2 g / s M a s s o u t s p o n g e i r o n n o n - m e t a l l i e s N i t r o g e n O x y g e n C a r b o n d i o x i de w a t e r v a p o u r T O T A L 1 4 5 6 . 0 g / s 3 4 9 . 3 g / s 3 2 9 4 . 9 g / s 5 9 . 2 g / s 1 7 6 0 . 4 g / s 7 6 7 . 4 g / s 7 6 8 8 . 0 g / s H e a t B a l a n c e R e f e r e n c e t e m p e r a t u r e 2 5 ° C S o l i d s come i n a t 1 7 ° C a n d l e a v e a t 1 0 0 0 ° C G a s e s come i n a t 1 0 ° C a n d l e a v e a t 9 1 3 ° C 71 H e a t i n B u r n i n g CO B u r n i n g v o l a t i l e s i n c o a l 2 0 5 2 K c a l / s 1 0 8 8 K c a l / s B u r n i n g n a t u r a l g a s = R e d u c t i o n w i t h c a r b o n m o n o x i d e T O T A L 379 K c a l / s 67 K c a l / s 3 5 8 6 K c a l / s H e a t o u t B o u d o u a r d R e a c t i o n S e n s i b l e h e a t i n s o l i d s S e n s i b l e h e a t i n g a s e s R e d u c t i o n w i t h h y d r o g e n D r y i n g r e a c t i o n H e a t l o s s t h r o u g h k i l n w a l l T O T A L 1 2 5 2 K c a l / s 2 8 8 K c a l / s 1561 K c a l / s 22 K c a l / s 2 8 9 K c a l / s 126 K c a l / s 3 5 3 8 K c a l / s A s c a n be s e e n , t h e b a l a n c e s c l o s e t o j u s t o v e r 1% w h i c h c l e a r l y d e m o n s t r a t e s t h e i n t e r n a l c o n s i s t e n c y o f t h e m o d e l . 2.8 S t a r t i n g a n d I n s t a b i l i t y P r o b l e m s I t s h o u l d be p o i n t e d o u t t h a t e v e n t h o u g h i t i s p o s s i b l e t o o b t a i n a s t a b l e r u n o n t h e c o m p u t e r f o r a 72 h y p o t h e t i c a l c a s e , i n r e a l i t y i t may be i m p o s s i b l e t o a c h i e v e s u c h a r u n d u e t o o p e r a t i o n a l p r o b l e m s a s s o c i a t e d w i t h t h e p r o c e s s . T h u s i t i s e s s e n t i a l t h a t t h e m o d e l i s u s e d w i t h e x t r e m e c a u t i o n . One o f t h e m o s t c r i t i c a l a s p e c t s i n t h i s r e g a r d i s t h e c h o i c e o f s t a r t i n g t e m p e r a t u r e f o r t h e s o l i d s a t t h e d i s c h a r g e e n d o f t h e k i l n w h i c h a r e n o t known a p r i o r i . T o e x a m i n e t h i s p r o b l e m a s e t o f c o m p u t e r r u n s was u n d e r t a k e n u s i n g c o n d i t i o n s f r o m t h e S L / R N p i l o t k i l n , w i t h d i f f e r e n t s o l i d s e x i t t e m p e r a t u r e s . F i g . 12 g i v e s t h e a x i a l s o l i d t e m p e r a -t u r e p r o f i l e s c a l c u l a t e d f o r t h r e e o f t h e r u n s . A s c a n be s e e n , u s e o f 9 0 0 ° C a n d 1 1 0 0 ° C a s t h e i n i t i a l s o l i d s t e m p e r a t u r e r e s u l t s i n w a v y p r o f i l e s t h a t a r e n o t f o u n d i n r e a l i t y . On t h e o t h e r h a n d , t h e s t a r t i n g t e m p e r a t u r e o f 1 0 0 0 ° C y i e l d s a f l a t p r o f i l e w h i c h i s known t o o b t a i n i n t h e r e d u c t i o n z o n e ( m o r e d e t a i l s c a n be f o u n d i n t h e f o l l o w i n g c h a p t e r ) . On t h e b a s i s o f t h e s h a p e o f t h e s o l i d s t e m p e r a t u r e p r o f i l e , t h e s o l i d s t e m p e r a t u r e c h o s e n a t t h e e x i t w o u l d be 1 0 0 0 ° C . I n d e e d t h i s i s t h e e x i t t e m p e r a t u r e m e a s u r e d f o r t h e s e c o n d i t i o n s . T h i s i n d i c a t e s t h a t e v e n t h o u g h t h e s o l i d s e x i t t e m p e r a t u r e i s n o t known i n a d v a n c e i t c a n be a r r i v e d a t b y t r i a 1 - a n d - e r r o r u s i n g t h e s h a p e o f t h e r e s u l t a n t s o l i d s t e m p e r a t u r e p r o f i l e a s a c r i t e r i o n . A n o t h e r m a j o r p r o b l e m e n c o u n t e r e d i n r u n n i n g t h e m o d e l was i n s t a b i l i t y . F o r c e r t a i n s e t s o f i n p u t d a t a t h e t e m p e r a t u r e o f t h e s o l i d s , f o r e x a m p l e , w o u l d r i s e e x p o n e n t i a l l y t o u n r e a l i s t i c v a l u e s . I t s h o u l d be p o i n t e d o u t t h a t t h i s T 7 0 0 1 1 • J 1—- J _ 0 4 8 !2 IS Distance from Discharge End CO F i g . 12 . E f f e c t on t h e o f s t a r t i n g s o l i d s s o l i d s t e m p e r a t u r e t e m p e r a t u r e p r o f i l e . 74 p r o b l e m d i d n o t a r i s e when o p e r a t i n g d a t a t a k e n f r o m s u c c e s s f u l p i l o t p l a n t t r i a l s w e r e u s e d a s i n p u t . F o r t h i s r e a s o n a n i n s t a b i l i t y was t a k e n a s a n i n d i c a t i o n t h a t t h e i n p u t p a r a m e t e r s f o r t h e r u n i n q u e s t i o n w o u l d r e s u l t i n u n s a t i s f a c t o r y k i l n p e r f o r m a n c e . 2.9 A d j u s t a b l e P a r a m e t e r s i n t h e M o d e l One o f t h e m o s t i m p o r t a n t f e a t u r e s o f t h i s m a t h e -m a t i c a l m o d e l i s t h e r e l a t i v e a b s e n c e o f a d j u s t a b l e p a r a m e t e r s . O n l y o n e a d j u s t a b l e p a r a m e t e r i s e m p l o y e d , n e a r t h e d i s c h a r g e e n d t o a c c o u n t f o r t h e u n k n o w n r a t e o f h e a t t r a n s f e r t o s o l i d p a r t i c l e s r o l l i n g t h r o u g h t h e f l a m e s a t t h e s u r f a c e o f t h e b e d . T h i s p a r a m e t e r was a d j u s t e d s o a s t o y i e l d , f r o m a n u m e r i c a l v i e w p o i n t , a s t a b l e s o l u t i o n . I t i s a p e r m a n e n t f e a t u r e o f t h e m o d e l a n d h a s n o t b e e n f o u n d t o h a v e a s i g n i f i c a n t e f f e c t o n m o d e l r e l i a b i l i t y . C h a p t e r 3 MODEL C A L C U L A T I O N S A N D D I S C U S S I O N 3.1 E v a l u a t i o n o f t h e M o d e l One o f t h e m o s t i m p o r t a n t s t a g e s i n t h e d e v e l o p m e n t o f a m a t h e m a t i c a l m o d e l i s i t s e v a l u a t i o n , m e a s u r e d i n t e r m s o f i t s a b i l i t y t o make p r e d i c t i o n s t h a t a g r e e w i t h r e a l i t y . I n t h e c a s e o f t h e SL/R N p r o c e s s m o d e l , c o n s i d e r a b l e t i m e was s p e n t a t t h i s s t a g e . O p e r a t i n g d a t a f r o m t h e l a r g e SL/RN p i l o t k i l n (35m by 2.1m i d ) l o c a t e d a t t h e S t e l c o H i l t o n w o r k s w e r e p r o c u r e d a n d u s e d a s i n p u t t o t h e m o d e l . T h e o u t p u t f r o m t h e m o d e l , a x i a l t e m p e r a t u r e a n d c o n c e n t r a t i o n p r o f i l e s , w e r e t h e n c o m p a r e d t o m e a s u r e m e n t s made u n d e r t h e same c o n d i t i o n s on t h e p i 1 o t k i 1 n . Two r u n s i n w h i c h t h e c h a r g e c o n s i s t e d o f i n d u r a t e d o x i d e p e l l e t s f r o m t h e G r i f f i t h M i n e w i t h F o r e s t b u r g c o a l ( s u b -b i t u m i n o u s ) a n d l i g n i t e c o a l r e s p e c t i v e l y w e r e s e l e c t e d f o r t h i s p u r p o s e . T h e s e p a r t i c u l a r r u n s w e r e c o n s i d e r e d m o s t s u i t a b l e b e c a u s e o f t h e s t a b l e o p e r a t i n g c o n d i t i o n s a c h i e v e d i n t h e k i l n , a n d a l s o a s a r e s u l t o f t h e p o t e n t i a l i m p o r t a n c e , 75 76 f r o m a C a n a d i a n v i e w p o i n t o f t h e c o a l s u s e d f o r r e d u c t i o n - b o t h c o a l s a r e f r o m W e s t e r n C a n a d a . 3.1.1 E v a l u a t i o n R u n s 3.1.1.1 F o r e s t b u r g C o a l a n d G r i f f i t h P e l l e t s T h e i n p u t p a r a m e t e r s u s e d i n t h i s r u n a r e g i v e n i n T a b l e 4. T h e v a l u e s w h i c h h a v e b e e n t a k e n f r o m S t e l c o r e s e a r c h r e p o r t s [ 2 6 ] a r e a v e r a g e s f r o m a c a m p a i g n l a s t i n g t h r e e w e e k s . T h e a i r p r o f i l e u s e d i n t h i s r u n i s g i v e n i n F i g . 1 3 . T h e a i r p r o f i l e was c a l c u l a t e d f r o m a k n o w l e d g e o f t h e b u r n e r p o s i t i o n s a l o n g t h e k i l n a n d t h e a i r r a t e t h r o u g h i n d i v i d u a l b u r n e r s . T h e a r e a u n d e r t h e c u r v e g i v e s t h e t o t a l a i r r a t e b l o w n i n t o t h e k i l n m i n u s t h e a i r d i s c h a r g e d t h r o u g h t h e e n d - b u r n e r w h i c h i s i n c l u d e d i n t h e i n i t i a l c o n d i t i o n s . U s i n g t h i s a i r p r o f i l e a n d s o l v i n g t h e s e t o f f i r s t o r d e r d i f f e r e n t i a l e q u a t i o n s d e v e l o p e d i n C h a p t e r 2, a x i a l c o n c e n t r a t i o n a n d t e m p e r a t u r e p r o f i l e s f o r t h e v a r i o u s g a s e o u s a n d s o l i d s c o m p o n e n t s w e r e c o m p u t e d . T h e s e a r e p r e s e n t e d i n F i g s . 14 t o 1 9 . F i g . 14 g i v e s t h e s o l i d s t e m p e r a t u r e p r o f i l e c a l c u l a t e d f r o m t h e m o d e l t o g e t h e r w i t h t e m p e r a t u r e s t h a t h a v e b e e n m e a s u r e d i n t h e s o l i d s b e d . F r o m F i g . 14 i t c a n be s e e n t h a t t h e g e n e r a l a g r e e m e n t b e t w e e n c a l c u l a t e d a n d m e a s u r e d t e m p e r a t u r e s i s q u i t e r e a s o n a b l e . T h e s m a l l d i f f e r e n c e b e t w e e n t h e two may a r i s e f r o m o n e o f t h e many a s s u m p t i o n s t h a t h a v e b e e n made i n t h e m o d e l s u c h a s no r a d i a l t e m p e r a t u r e g r a d i e n t s 77 T a b l e 4 I n p u t D a t a f o r t h e K i l n Run U s i n g G r i f f i t h P e l l e t s a n d F o r e s t b u r g C o a l O r e - G r i f f i t h P e l l e t s 1 9 1 . 8 t o n s / d a y C o a l - F o r e s t b u r g ( s u b - b i t u m i n o u s ) A i r ( t o t a l ) N a t u r a l g a s D e g r e e o f r e d u c t i o n ( t o t a l ) H y d r o g e n p r e - r e d u c t i o n E x i t s o l i d s t e m p e r a t u r e 1 2 9 . 9 t o n s / d a y 5 2 4 1 5 f t 3 / t o n o r e 6 7 6 f t 3 / t o n o r e 9 2 % 8% 1 0 0 0 ° C S o l i d s d e g r e e o f f i l l 2 5% 10.0 15.0 20.0 25.0 30.0 DISTANCE FROM CHARGE END (METRES) F i g . 1 3 . A i r p r o f i l e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s . 35.0 40.0 CO 10.0 15.0 DI5TflNCE FROM r 20.0 25.0 30.0 CHARGE END (METRES) 35.0 4CUD F i g . 14. S o l i d s t e m p e r a t u r e p r o f i l e f o r t h e k i l n r u n . u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s . 8 0 i n t h e b e d . On t h e o t h e r h a n d , t h e m e a s u r e m e n t s t h e m s e l v e s , made u n d e r i n d u s t r i a l c o n d i t i o n s w i t h h e a v y d u t y t h e r m o c o u p l e s , may be s l i g h t l y i n e r r o r . W h a t e v e r t h e s o u r c e o f e r r o r , t h e d i s c r e p a n c y b e t w e e n c a l c u l a t e d a n d m e a s u r e d t e m p e r a t u r e s i s n o t t h o u g h t t o be s e r i o u s . F i g . 14 a l s o g i v e s i m p o r t a n t i n f o r m a t i o n r e g a r d i n g t h e k i l n l e n g t h . T h e m o d e l c a l c u l a t e s a v a l u e f o r t h e k i l n l e n g t h o f 30m, w h e r e a s t h e a c t u a l l e n g t h i s 35m. I f o n e t a k e s i n t o a c c o u n t dams a t e i t h e r e n d o f t h e k i l n a n d t h e p o s i t i o n o f t h e c h a r g i n g c h u t e , t h e d i s c r e p a n c y i s o n l y m a r g i n a l l y g r e a t e r t h a n 1 0 % . T h e c a l c u l a t e d g a s t e m p e r a t u r e p r o f i l e i s p l o t t e d i n F i g . 1 5 . I n t h i s c a s e , c o m p a r i s o n w i t h m e a s u r e d t e m p e r a t u r e s i s e x c e e d i n g l y d i f f i c u l t b e c a u s e t h e m e a s u r e m e n t s w e r e made w i t h s h e a t h e d , " r a p i d r e s p o n s e " t h e r m o c o u p l e s , r a t h e r t h a n w i t h s u c t i o n t h e r m o c o u p l e s . I t i s w e l l known t h a t t h e u s e o f a b a r e , n o n - s u c t i o n t h e r m o c o u p l e w i l l r e s u l t i n a g a s t e m p e r a t u r e m e a s u r e m e n t t h a t i s l o w e r t h a n t h e r e a l v a l u e , o w i n g t o r a d i a t i v e e x c h a n g e b e t w e e n t h e t h e r m o c o u p l e a n d t h e w a l l [ 2 7 ] . F o r t h e SL/RN k i l n t h i s e r r o r was c a l c u l a t e d t o be r o u g h l y 1 5 0 - 1 7 0 ° C . In an a t t e m p t t o p r e d i c t t h e g a s t e m p e r a t u r e p r o f i l e t h a t w o u l d be m e a s u r e d by a n o n - s u c t i o n t h e r m o c o u p l e , a c o r r e c t i o n was a p p l i e d a n d t h e l o w e r t e m p e r a t u r e p r o f i l e i n F i g . 15 was o b t a i n e d . H o w e v e r , e v e n w i t h t h i s c o r r e c t i o n t h e m e a s u r e d g a s t e m p e r a t u r e s p r o v e d t o be t o o e r r a t i c t o make a m e a n i n g f u l c o m p a r i s o n p o s s i b l e . T h e o n e p o i n t w h e r e t h e g a s t e m p e r a t u r e was a c c u r a t e l y L D r-. •3. C D X LD LU a ZDr-I— CC DC LU Q_ 2 I Q LU • R R -RE PROFILE Actual a o FG 0.0 ~ l 1 1 1 1 1 5.0 10.0 15.0 20.0 25.0 30.0 DISTANCE FROM CHARGE END (METRES) F i g . 1 5 . G a s t e m p e r a t u r e p r o f i l e f o r t h e r u n u s i n g F o r e s t b u r q c o a l a n d G r i f f i t h p e l l e t s . 35.0 40.0 CO 82 m e a s u r e d , j u s t b e y o n d t h e c h a r g e e n d o f t h e k i l n , y i e l d e d a t e m p e r a t u r e t h a t a g r e e d w e l l w i t h t h e c a l c u l a t e d v a l u e . F i g . 16 g i v e s t h e i n n e r w a l l t e m p e r a t u r e p r o f i l e ( u p p e r c u r v e ) a n d t h e o u t e r s h e l l t e m p e r a t u r e p r o f i l e ( l o w e r c u r v e ) . T h e l a t t e r p r o f i l e a g r e e s c l o s e l y w i t h m e a s u r e m e n t s t h a t h a v e b e e n r e p o r t e d by o p e r a t o r s . A d i r e c t e v a l u a t i o n o f t h e c a l c u l a t e d i n s i d e w a l l t e m p e r a t u r e i s i m p o s s i b l e , h o w e v e r , s i n c e m e a s u r e m e n t s h a v e n o t b e e n m a d e . D e s p i t e t h i s , t h e r e i s some i n d i r e c t e v i d e n c e t h a t t h e i n s i d e w a l l t e m p e r a -t u r e s c a l c u l a t e d a r e r e a s o n a b l e . A s c a n be s e e n f r o m F i g . 1 6 , t h e i n n e r w a l l t e m p e r a t u r e p r o f i l e r e a c h e s a p e a k o v e r a s e c t i o n o f t h e k i l n 12 t o 17m f r o m t h e c h a r g e e n d . T h i s a l s o t u r n s o u t t o be t h e r e g i o n o f t h e k i l n i n w h i c h t h e maximum a c c r e t i o n f o r m a t i o n i s o b s e r v e d . S i n c e , a s e x p l a i n e d i n C h a p t e r 1, a c c r e t i o n s a r e a s s o c i a t e d w i t h h i g h i n n e r w a l l t e m p e r a t u r e s , t h i s c o i n c i d e n c e i s e x p e c t e d i f t h e w a l l t e m p e r a t u r e s c a l c u l a t e d a r e r e a l i s t i c . T h i s r e s u l t i s i m p o r t a n t s i n c e i t a l s o m e a n s t h a t t h e m o d e l c a n be u s e d r e a s o n a b l y t o d e t e r m i n e t h e r e g i o n s o f t h e k i l n i n w h i c h a c c r e t i o n s may p o s e a p o t e n t i a l p r o b l e m . T h e r e d u c t i o n p r o f i l e f o r t h i s r u n i s s h o w n i n F i g . 1 7 . T h e c u r v e i s made up o f two p a r t s , t h e f i r s t c o r r e s p o n d i n g t o h y d r o g e n p r e - r e d u c t i o n a n d t h e s e c o n d t o r e d u c t i o n by CO. A l t h o u g h t h e t r a n s i t i o n f r o m o n e t y p e o f r e d u c t i o n t o t h e o t h e r i s s h o w n t o be a b r u p t , i n r e a l i t y i t w i l l be c o n s i d e r a b l y s m o o t h e r . T h e g e n e r a l f o r m o f t h e CO r e d u c t i o n c u r v e , s h o w i n g 0.0 5.0 T 10.0 15.0 20.0 25.0 30.0 DISTANCE FROM CHARGE END (METRES) 35.0 40.0 CO F i g . 1 6 . I n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s . DISTANCE FROM CHARGE END (METRES) F i g . 1 7 . R e d u c t i o n p r o f i l e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s . 85 a d r o p i n r e d u c t i o n r a t e t o w a r d t h e d i s c h a r g e e n d o f t h e k i l n i s c o n s i s t e n t w i t h t h e g o v e r n i n g r a t e e x p r e s s i o n s . F i g . 18 g i v e s t h e r a t e o f B o u d o u a r d r e a c t i o n a s a f u n c t i o n o f k i l n l e n g t h . T h i s a g a i n s h o w s t h e a p p r e c i a b l e d r o p i n t h e r e a c t i o n r a t e w i t h i n c r e a s e d d e g r e e o f r e d u c t i o n . T h e s u d d e n r i s e i n t h e B o u d o u a r d r e a c t i o n r a t e a t 13m i s a n a r t i f a c t a r i s i n g f r o m t h e way t h e c a l c u l a t i o n s a r e p e r f o r m e d i n t h e m a t h e m a t i c a l m o d e l . I n r e a l i t y , t h e r i s e w i l l b e l e s s i n s t a n -t a n e o u s , b u t n e v e r t h e l e s s r a p i d , a n d s h o u l d n o t c a u s e u n d u e e r r o r . I t i s a l s o i n t e r e s t i n g t o n o t e t h a t t h e p e a k i n t h e f r e e b o a r d g a s t e m p e r a t u r e c o i n c i d e s w i t h t h e r e g i o n w h e r e t h e B o u d o u a r d r e a c t i o n r a t e i s maximum. T h i s i s a n e x p e c t e d r e s u l t s i n c e t h e r a t e o f r e l e a s e o f CO f r o m t h e b e d a n d i t s c o m b u s -t i o n i n t h e f r e e b o a r d s h o u l d a l s o be a maximum a t t h i s p o i n t . T h e a x i a l c o n c e n t r a t i o n p r o f i l e s o f t h e g a s e o u s com-p o u n d s i n t h e f r e e b o a r d , e x p r e s s e d a s p a r t i a l p r e s s u r e s , a r e s h o w n i n F i g . 1 9 . T h e s p e c i e s p l o t t e d h e r e i n c l u d e a l l t h e m a j o r c o n s t i t u e n t s s u c h a s N 2 , 0 2 , C 0 2 , CO a n d H 2 0 . S i n c e i n p i l o t p l a n t r u n s t h e g a s c o m p o s i t i o n was n o t a n a l y s e d a t d i f f e r e n t p o i n t s a l o n g t h e k i l n , t h e o n l y c h e c k t h a t c o u l d be made w i t h t h e c a l c u l a t e d r e s u l t s was t h e w a s t e g a s c o m p o s i t i o n . C l o s e a g r e e m e n t b e t w e e n t h o s e m e a s u r e d a n d c a l c u l a t e d c o m p o s i -t i o n s was o b t a i n e d . One o f t h e m o s t i n t e r e s t i n g p o i n t s t o n o t e i n F i g . 19 i s t h e s l i g h t e x c e s s o f o x y g e n p r e s e n t i n t h e f r e e b o a r d t h r o u g h m o s t o f t h e r e d u c t i o n z o n e . T h e p r e s e n c e o f t h e o x y g e n i s 98 a 88 b e l i e v e d t o be i m p o r t a n t b e c a u s e i t i n d i c a t e s t h a t t h e CO d i s -c h a r g i n g f r o m t h e b e d w i l l be c o m b u s t e d n e a r t h e s u r f a c e o f t h e b e d r a t h e r t h a n a t t h e b u r n e r o r i f i c e . T h e f l a m e s a t t h e b e d s u r f a c e s h o u l d e n h a n c e h e a t t r a n s f e r b a c k t o t h e s o l i d s a n d so a s s i s t i n m a i n t a i n i n g t h e h i g h l y e n d o t h e r m i c B o u d o u a r d r e a c t i o n a t a s a t i s f a c t o r y r a t e . W i t h o u t e x t r a h e a t t r a n s f e r f r o m t h e s u r f a c e f l a m e s , i t i s l i k e l y t h a t t h e b e d t e m p e r a t u r e w o u l d d r o p t o a l o w e r l e v e l w h e r e r a t e s o f r e d u c t i o n a n d c a r b o n g a s i f i c a t i o n w o u l d be u n a c c e p t a b l y l o w r e s u l t i n g i n p o o r m e t a l l i -s a t i o n . F l a m e s c l o s e t o t h e s u r f a c e o f t h e b e d h a v e b e e n o b s e r v e d by k i l n o p e r a t o r s a n d c a n be s e e n i n F i g . 2 0 , w h i c h s h o w s a v i e w o f t h e . i n t e r i o r o f t h e S L / R N p i l o t k i l n . S u mming u p , t h e m a t h e m a t i c a l m o d e l i s a b l e t o s i m u l a t e c l o s e l y r e s u l t s o f t h e p i l o t k i l n t e s t u n d e r t a k e n w i t h F o r e s t b u r g c o a l a n d G r i f f i t h P e l l e t s b a s e d on t h e f o l l o w i n g c o m p a r i s o n s . I . S o l i d s t e m p e r a t u r e 2. S h e l l t e m p e r a t u r e 3 . L e n g t h o f t h e k i In 4. G a s c o m p o s i t i o n a n d g a s t e m p e r a t u r e e x i t i n g t h e k i l n 5. P r e s e n c e o f s u r f a c e f l a m e s i n t h e r e d u c t i o n z o n e 3 . 1 . 1 . 2 L i g n i t e C o a l a n d G r i f f i t h P e l l e t s I n o r d e r t o f u r t h e r t e s t t h e v a l i d i t y o f t h e m o d e l a n o t h e r s e t o f r u n c o n d i t i o n s , c o n d u c t e d o n t h e SL/RN p i l o t F i g . 20. I n t e r i o r v i e w o f t h e p i l o t S L/RN k i l n t a k e n f r o m t h e d i s c h a r g e e n d . 90 k i l n [ 2 8 ] , was s i m u l a t e d u s i n g t h e m o d e l . T h e c o a l e m p l o y e d i n t h i s c a m p a i g n was a l i g n i t e t y p e f r o m S a s k a t c h e w a n . T h e c o m p o s i t i o n o f t h e c o a l i s g i v e n i n A p p e n d i x I I . T h e l i g n i t e c o a l d i f f e r e d s l i g h t l y f r o m t h e F o r e s t b u r g c o a l i n t h a t i t c o n t a i n e d m a r g i n a l l y m o r e w a t e r , l e s s f i x e d c a r b o n a n d w a s a l i t t l e m o r e r e a c t i v e . T h e i n p u t d a t a f o r t h i s r u n a r e p r e -s e n t e d i n T a b l e 5. T h e a i r p r o f i l e f o r t h i s r u n i s g i v e n i n F i g . 2 1 . I t d i f f e r s f r o m t h e p r o f i l e u s e d i n t h e F o r e s t b u r g r u n i n t h a t m o r e a i r i s b l o w n i n t o t h e p r e h e a t z o n e . T h e e x t r a a i r i n t h e l i g n i t e r u n was r e q u i r e d t o c o m b u s t a h i g h e r i n p u t o f n a t u r a l g a s w h i c h was c o n s i d e r e d n e c e s s a r y t o o f f s e t t h e h i g h e r w a t e r c o n t e n t o f t h e c o a l . W i t h o u t t h e a d d i t i o n a l s u p p l y o f n a t u r a l g a s , t h e l a r g e r h e a t r e q u i r e m e n t f o r d r y i n g t h e l i g n i t e c o a l m i g h t h a v e e x t e n d e d t h e l e n g t h o f t h e p r e h e a t z o n e a n d t h u s r e d u c e d t h e maximum a c h i e v a b l e s o l i d s t h r o u g h p u t . T h e a x i a l p r o f i l e s o b t a i n e d f r o m t h e m o d e l a r e p r e -s e n t e d i n F i g s . 2 2 - 2 6 . T h e s e r e s u l t s w e r e e v a l u a t e d i n an i d e n t i c a l m a n n e r t o t h e F o r e s t b u r g r u n . A g a i n i t was f o u n d t h a t t h e m o d e l p r e d i c t i o n s a g r e e d c l o s e l y w i t h a v a i l a b l e e x p e r i m e n t a l m e a s u r e m e n t s . I n p a r t i c u l a r t h e s o l i d s b e d t e m p e r a t u r e p r o f i l e , s h o w n i n F i g . 2 2 , i n d i c a t e d g o o d a g r e e m e n t b e t w e e n m e a s u r e d a n d c a l c u l a t e d v a l u e s . T h e m o s t i m p o r t a n t d i f f e r e n c e b e t w e e n t h e c a l c u l a t e d l i g n i t e a n d F o r e s t b u r g r u n s was t h e s l i g h t l y l o w e r b e d t e m p e r a -t u r e d e t e r m i n e d i n t h e r e d u c t i o n z o n e f o r l i g n i t e ( 9 6 0 ° C a s 91 T a b l e 5 I n p u t D a t a f o r t h e K i l n Run U s i n g L i g n i t e C o a l a n d G r i f f i t h P e l l e t s O r e - G r i f f i t h P e l l e t s 1 7 9 . 8 t o n s / d a y C o a l - L i g n i t e D o l o m i t e A i r ( t o t a l ) N a t u r a l g a s D e g r e e o f r e d u c t i o n ( t o t a l ) H y d r o g e n p r e - r e d u c t i o n E x i t s o l i d s t e m p e r a t u r e S o l i d s d e g r e e o f f i l l 1 3 8 . 5 tons/day 5.5 tons/day 5 4 6 7 5 ftVton ore 1 1 6 0 ft3/ton ore 9 2 % 8% 9 2 5 ° C 2 5% i r 1D.D 15.D DISTANCE FROM zo.o CHARGE 25.0 30.0 END (METRES) 35.D 40. F i g . 21 ... . A i r • p r o f i 1 e f o r t h e k i l n r u n u s i n g l i g n i t e c o a l a n d G r i f f i t h p e l l e t s . 0.0 F i g . 22 5.0 10.0 15.0 20.0 DISTANCE FROM CHARGE S o l i d s t empe ra t u r e p r o f i l e f o r the k i l n p e l l e t s . 25.0 30.0 END (METRES) run u s i n g l i g n i t e coa l 35.0 40. and G r i f f i t h i n r - . '9. CD X U S ' CD LU a ZDr-I — c r LU Q_ 1 cn a 1 1 1 1 1 1 . G f l S ^ P M R E PROFILE 1 \ r-v Actual — Corrected 'i - j L G 0.0 5.0 10.0 15.0 20.0 25.0 30.0 DISTANCE FROM CHARGE END (METRES) 35.0 40.0 F i g . 2 3 . G a s t e m p e r a t u r e p r o f i l e f o r . t h e k i l n r u n u s i n g l i g n i t e c o a l a n d G r i f f i t h p e l l e t s D.D F i g . 2 4 . 5.0 10.0 15.0 2D.0 DISTANCE FROM CHARGE Z5.D 30.0 END (METRES) 35.0 40.0 I n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e p r o f i l e s f o r t h e k i l n r u n u s i n a l i g n i t e c o a l a n d G r i f f i t h p e l l e t s . i r DISTANCE FROM CHARGE END (METRES) g. 2 5 . R e d u c t i o n p r o f i l e f o r t h e k i l n r u n u s i n g l i g n i t e c o a l a n d G r i f f i t h p e l l e t s . o C3 T 0.0 F i g . 26 5.0 F r e e b o a r d p e l l e t s . l 10.0 15.0 DISTANCE FROM ZO.D CHARGE r 25.0 30.0 END (METRES) 35.0 4 0 . g a s c o m p o s i t i o n f o r t h e k i l n r u n u s i n g l i g n i t e c o a l a n d G r i f f i t h 98 c o m p a r e d t o 9 9 0 ° C ) . T h i s r e s u l t i s d i r e c t l y a t t r i b u t a b l e t o t h e h i g h e r r e a c t i v i t y o f t h e l i g n i t e c o a l . A l l o t h e r p o i n t s d i s c u s s e d i n t h e p r e v i o u s s e c t i o n a p p l y e q u a l l y t o t h i s r u n . 3.2 P r e d i c t e d I n f l u e n c e o f O p e r a t i n g V a r i a b l e s o n K i l n P e r f o r m a n c e H a v i n g p a s s e d s u c c e s s f u l l y t h r o u g h t h e e v a l u a t i o n s t a g e , t h e m o d e l was n e x t r u n i n a p r e d i c t i v e mode. T h a t i s , t h e m o d e l was r u n u n d e r a v a r i e t y o f o p e r a t i n g c o n d i t i o n s t h a t h a v e n o t b e e n e x p l o r e d e x p e r i m e n t a l l y o r f u l l y c h a r a c t e r i z e d i n o r d e r t o e x a m i n e t h e i n f l u e n c e o f d i f f e r e n t v a r i a b l e s o n t h e k i l n p e r f o r m a n c e . I n c l u d e d i n t h e l i s t o f v a r i a b l e s i n v e s t i -g a t e d a r e d e g r e e o f r e d u c t i o n a c h i e v e d , t h r o u g h p u t , c o a l r e -a c t i v i t y , p e l l e t r e d u c i b i 1 i t y , n a t u r a l g a s i n j e c t i o n a n d d u s t i n t h e f r e e b o a r d g a s ( t h r o u g h a c h a n g e i n t h e g a s e m i s s i v i t y ) . T h e r e s u l t s o f t h e m o d e l p r e d i c t i o n s a r e p r e s e n t e d i n t h i s s e c t i o n . One o f t h e m a j o r d i f f i c u l t i e s t h a t a r o s e i n t h i s s t a g e o f t h e i n v e s t i g a t i o n was t h e i s o l a t i o n o f t h e e f f e c t o f a s i n g l e v a r i a b l e on t h e k i l n o p e r a t i o n . B e c a u s e t h e p r o c e s s i n v o l v e s c l o s e l y c o u p l e d h e a t a n d m a t e r i a l e x c h a n g e s t e p s i t was f o u n d t o be v i r t u a l l y i m p o s s i b l e t o c h a n g e o n e v a r i a b l e w i t h o u t s e r i o u s l y u p s e t t i n g a s t a b l e k i l n o p e r a t i o n . F o r e x a m p l e , a c h a n g e o f t h r o u g h p u t w i t h o u t a c o r r e s p o n d i n g a d j u s t -m e n t i n t h e a i r p r o f i l e g a v e r i s e t o i n o p e r a b l e p e r f o r m a n c e , e . g . a v e r y l o w b e d t e m p e r a t u r e . F o r t h i s r e a s o n i n many o f 99 t h e c a s e s d i s c u s s e d , o n e o r m o r e v a r i a b l e s may h a v e b e e n c h a n g e d s i m u l t a n e o u s l y . 3.2.1 E f f e c t o f D e g r e e o f R e d u c t i o n A c h i e v e d I n o r d e r t o s t u d y t h e e f f e c t o f a h i g h e r d e g r e e o f r e d u c t i o n a c h i e v e d , a r u n was u n d e r t a k e n w i t h a c h a r g e c o n s i s t i n g o f F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s . T h e i n p u t c o n d i t i o n s f o r t h i s c a s e a r e g i v e n i n T a b l e 6. T h e c o n d i t i o n s a r e i d e n -t i c a l t o t h e p r e v i o u s F o r e s t b u r g r u n e x c e p t f o r t h e h i g h e r d e g r e e o f r e d u c t i o n e f f e c t e d h e r e , 9 5 % . I t s h o u l d b e n o t e d t h a t i n o r d e r t o o b t a i n s t a b l e c o n d i t i o n s i t was n e c e s s a r y t o a l t e r t h e o r i g i n a l a i r p r o f i l e i n t h a t t h e a i r r a t e t h r o u g h t h e e n d b u r n e r was r e d u c e d f r o m 3 0 0 t o 150 c f m . T h e a i r p r o f i l e e m p l o y e d i n t h i s r u n i s g i v e n i n F i g . 2 7 . T h e r e s u l t s c o m p u t e d f r o m t h e m o d e l a r e p r e s e n t e d i n F i g s . 28 a n d 2 9 . I t c a n be s e e n t h a t t h e l e n g t h o f k i l n r e q u i r e d t o a c h i e v e a 9 5 % r e d u c -t i o n i s 32.5m, a s c o m p a r e d t o 30.0m f o r t h e c a s e o f 9 2 % r e d u c -t i o n . I f t h e l e n g t h o f k i l n i s f i x e d t h i s m e a n s t h a t t h e t h r o u g h p u t m u s t be d e c r e a s e d f o r a h i g h e r d e g r e e o f r e d u c t i o n . I t s h o u l d be p o i n t e d o u t t h a t i t i s n o t e c o n o m i c a l t o go t o r e d u c t i o n s much h i g h e r t h a n 9 2 % b e c a u s e t h e r a t e o f r e d u c t i o n d r o p s o f f e x p o n e n t i a l l y w i t h i n c r e a s i n g r e d u c t i o n . I n a d d i t i o n r e d u c t i o n s b e y o n d 9 5 % a r e n o t p r a c t i c a b l e b e c a u s e i t l e a d s t o p r o b l e m s i n p r o c e s s i n g t h e p e l l e t s i n t h e e l e c t r i c a r c f u r n a c e . 1 0 0 T a b l e 6 I n p u t D a t a f o r t h e K i l n Run U s i n g F o r e s t b u r g C o a l a n d G r i f f i t h P e l l e t s w i t h a D e g r e e o f R e d u c t i o n o f 9 5 % O r e - G r i f f i t h P e l l e t s 1 9 1 . 8 t o n s / d a y C o a l - F o r e s t b u r g A i r ( t o t a l ) N a t u r a l g a s D e g r e e o f r e d u c t i o n ( t o t a l ) H y d r o g e n p r e - r e d u c t i o n E x i t s o l i d s t e m p e r a t u r e S o l i d s d e g r e e o f f i l l 1 2 9 . 9 t o n s / d a y 5 2 5 4 0 s c f t / t o f o r e 6 7 6 s c f t / t o f o r e 9 5 % 8% 1 0 0 0 ° C 2 5% o.a F i g . 2 7 . 5.0 T 1U.0 15.0 20.0 25.0 30.0 DISTANCE FROM CHARGE END (METRES) 35.0 40. A i r p r o f i l e f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h d e g r e e o f r e d u c t i o n o f 9 5 % . 0.0 F i g . 28 35.0 40.0 i 1 r 10.0 15.0 20.0 25..? 30. DISTANCE FROM CHARGE END (METRES) S o l i d s , g a s , i n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e p r o f i l e s f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a d e g r e e o f r e d u c t i o n o f 9 5 % . o r o r\3 0.0 PERCENTAGE REDUCTION 20.0 40.0 60.0 J 80.0 _l 100.0 o -s (/) r+ CT c -5 Q o o LO UV T T I ^O.u* 0.2 0.4 0.5 0.F PRRTIRL PRESSURES OF FREE B0RRD GASES 1.0 eo L 1 04 3.2.2 E f f e c t o f T h r o u g h p u t A g a i n t h e o r i g i n a l F o r e s t b u r g r u n h a s b e e n u s e d a s a b a s e c a s e t o e v a l u a t e t h e i n f l u e n c e o f s o l i d s t h r o u g h p u t . T h e d a t a f o r t h i s r u n a r e g i v e n i n T a b l e 7. I n t h e p r e s e n t r u n t h e o r e t h r o u g h p u t h a s b e e n i n c r e a s e d by 3 0 % f r o m 1 9 0 . 8 t o n s / d a y t o 2 4 9 . 4 t o n s / d a y . I n t h i s r u n i t h a s a l s o b e e n n e c e s s a r y t o a l t e r t h e a i r p r o f i l e a s s e e n i n F i g . 3 0 , t o m a i n t a i n s i m i l a r t e m p e r a t u r e c o n d i t i o n s . T h e r e s u l t s o b t a i n e d f r o m t h e m a t h e m a t i c a l m o d e l f o r t h e s e c o n d i t i o n s a r e g i v e n i n F i g s . 31 a n d 3 2 . T h e c a l c u l a t i o n s s h o w e d t h a t t h e i n c r e a s e d t h r o u g h p u t r e s u l t e d i n a n i n c r e a s e o f 5m i n t h e r e d u c t i o n z o n e a n d 1.5m i n t h e p r e h e a t z o n e . T h i s i s a n e x p e c t e d r e s u l t s i n c e t h e t h e r m a l b u r d e n i n t h e r e d u c t i o n z o n e i s much h i g h e r t h a n i n t h e p r e h e a t z o n e b e c a u s e o f t h e e n d o t h e r m i c B o u d o u a r d r e a c t i o n . O t h e r f e a t u r e s o f t h i s r u n l o o k s i m i l a r t o t h e o r i g i n a l F o r e s t b u r g r u n . 3.2.3 E f f e c t o f L o w e r C o a l R e a c t i v i t y A r u n was u n d e r t a k e n t o s t u d y k i l n b e h a v i o u r when t h e c o a l b e i n g c h a r g e d was o f a c o n s i d e r a b l y h i g h e r r a n k , e . g . a n t h r a c i t e c o a l , w h i c h a l s o h a s a c o n s i d e r a b l y l o w e r r e a c t i v i t y v a l u e . R e f e r r i n g b a c k t o T a b l e 1 a n t h r a c i t e c o a l c a n be s e e n t o h a v e a r e a c t i v i t y t h a t i s t h r e e o r d e r s o f m a g n i t u d e l e s s t h a n t h a t o f t h e F o r e s t b u r g ( s u b - b i t u m i n o u s ) c o a l . T h e i n p u t p a r a m e t e r s f o r t h i s r u n a r e l i s t e d i n T a b l e 8 a n d t h e a i r T a b l I n p u t D a t a f o r t h e K i l n Run G r i f f i t h P e l l e t s w i t h a O r e - G r i f f i t h P e l l e t s C o a l - F o r e s t b u r g D o l o n i t e A i r ( t o t a l ) N a t u r a l g a s D e g r e e o f r e d u c t i o n H y d r o g e n p r e - r e d u c t i o n S o l i d s d e g r e e o f f i l l 1 05 7 U s i n g F o r e s t b u r g C o a l a n d 3 0 % H i g h e r T h r o u g h p u t 2 4 9 . 3 6 t o n s / d a y 1 6 8 . 9 6 t o n s / d a y 0.0 5 0 1 0 0 s c f t / t o n o r e 578 s c f t / t o n o r e 9 2 % 8% 2 5 % 0.0 F i g . 30 1D.0 15.0 20.0 25.0 30.0 DISTANCE FROM CHARGE END (METRES) 40.0 o CT) A i r p r o f i l e f o r t h e k i l n 3 0 % h i g h e r t h r o u g h p u t . r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a T 5.0 i 1 1 r 10.0 15.0 20.0 25.0 30.0 DISTANCE FROM CHARGE END (METRES) <o.o F i g . 31 S o l i d s , g a s , i n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e p r o f i l e s f o r t h e k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t . o 1 09 p r o f i l e i s g i v e n i n F i g . 3 3 . T h e r e s u l t s f r o m t h e m o d e l a r e p r e s e n t e d i n F i g s . 34 a n d 3 5 . T h e i r o s t s t r i k i n g f e a t u r e o f t h e m o d e l - p r e d i c t i o n s i s t h e h i g h t e m p e r a t u r e o f t h e s o l i d s b e d i n t h e r e d u c t i o n z o n e ( 1 0 8 0 ° C ) a s c o m p a r e d t o t h e o r i g i n a l F o r e s t b u r g r u n ( 9 9 0 ° C ) . T h i s f i n d i n g a g r e e s w e l l w i t h o b s e r -v a t i o n s made d u r i n g l i m i t e d p i l o t k i l n t r i a l s e m p l o y i n g a n t h r a c i t e c o a l a n d G r i f f i t h p e l l e t s . T h e h i g h s o l i d s t e m p e r a -t u r e i s a d i r e c t c o n s e q u e n c e o f t h e l o w c o a l r e a c t i v i t y , a n d i s r e q u i r e d t o m a i n t a i n t h e B o u d o u a r d r e a c t i o n a t a s u f f i c i e n t l y h i g h r a t e t o e n s u r e r e a s o n a b l e m e t a l l i s a t i o n . A n o t h e r i m p o r t a n t r e s u l t w o r t h n o t i n g i s t h e l e n g t h o f t h e r e d u c t i o n z o n e r e l a -t i v e t o t h e p r e h e a t z o n e . F r o m F i g . 3 4 , t h e r e d u c t i o n z o n e c a n be s e e n t o o c c u p y a much l o n g e r f r a c t i o n o f t h e k i l n ( 2 1 . 5 m ) a s c o m p a r e d t o 17m i n t h e F o r e s t b u r g r u n . T h a t t h e p r e h e a t z o n e i n t h e a n t h r a c i t e c a s e i s s h o r t e r i s a d i r e c t r e s u l t o f a h i g h e r f e e d r a t e o f n a t u r a l g a s . In m a k i n g t h e s e c o m p a r i s o n s i t s h o u l d be b o r n e i n m i n d t h a t t h e maximum a c h i e v a b l e t h r o u g h p u t f o u n d w i t h a n t h r a c i t e c o a l i s c o n s i d e r a b l y l o w e r t h a n i n t h e c a s e o f t h e F o r e s t b u r g c o a l . A g a i n 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 p i l o t k i l n t r i a l s . I t s h o u l d be n o t e d t h a t s i n c e t h e a s h s o f t e n i n g t e m p e r a t u r e [ 1 1 ] o f t h e a n t h r a c i t e c o a l ( 1 2 6 0 ° C ) i s much h i g h e r t h a n t h a t o f F o r e s t b u r g c o a l ( 1 0 4 0 ° C ) , o p e r a t i n g t h e k i l n a t t h e h i g h e r s o l i d s b e d t e m p e r a t u r e i n t h i s c a s e d o e s n o t p o s e a n y a c c r e t i o n p r o b l e m s . no T a b l e 8 I n p u t D a t a f o r t h e K i l n Run U s i n g A n t h r a c i t e C o a l a n d G r i f f i t h P e l l e t s O r e - G r i f f i t h P e l l e t s 1 2 8 . 1 6 t o n s / d a y C o a l - A n t h r a c i t e 6 9 . 1 2 t o n s / d a y D o l o m i t e 4.32 t o n s / d a y A i r ( t o t a l ) 5 6 1 9 0 s c f t / t o n o r e N a t u r a l g a s 2 1 3 5 s c f t / t o n o r e D e g r e e o f r e d u c t i o n ( t o t a l ) 9 2 % H y d r o g e n p r e - r e d u c t i o n 0% S o l i d s d e g r e e o f f i l l 2 0 % 0.0 5.0 T 10.0 15.0 20.0 25.0 30 DISTANCE FROM CHARGE END (METRES) 35.0 40. F i g . 33. A i r p r o f i l e f o r t h e k i l n r u n u s i n q a n t h r a c i t e c o a l a n d G r i f f i t h p e l l e t s . i n - 1 1 • 1 1 1 r F i g . 34. S o l i d s , g a s , i n n e r w a l l a n d o u t e r t e m p e r a -t u r e p r o f i l e s f o r t h e k i l n r u n u s i n g a n t h r a c i t e c o a l a n d G r i f f i t h p e l l e t s . a a o <=> C O F i g . 3 5 . R e d u c t i o n a n d f r e e b o a r d g a s c o m p o s i t i o n p r o f i l e s f o r t h e k i l n r u n u s i n g a n t h r a c t i e c o a l a n d G r i f f i t h p e l l e t s . 114 3.2.4 E f f e c t o f P e l l e t T y p e T h e i n f l u e n c e o f p e l l e t t y p e on k i l n o p e r a t i o n c a n be i n v e s t i g a t e d w i t h t h e m o d e l b y a d j u s t i n g t h e p e l l e t r e d u c i -b i l i t y f a c t o r . I n t h i s r u n , , t h i s p a r a m e t e r was c h a n g e d t o c o r r e s p o n d t o F a l c o n b r i d g e p e l l e t s , w h i c h a r e m o r e e a s i l y r e d u c e d t h a n G r i f f i t h p e l l e t s . D e t a i l s r e g a r d i n g o r e r e d u c i -b i l i t y a r e g i v e n i n A p p e n d i x I I . T h e i n p u t d a t a f o r t h i s r u n a r e p r e s e n t e d i n T a b l e 9. T h e a i r p r o f i l e was a g a i n a d j u s t e d t o g i v e a s t a b l e o p e r a t i o n a s s e e n i n F i g . 3 6 . F i g s . 37 a n d 38 show t h e m o d e l - p r e d i c t e d p r o f i l e s . T h e m o s t i m p o r t a n t f e a t u r e o f t h i s r u n was t h e l o w e r t e m p e r a t u r e o f t h e s o l i d s b e d ( F i g . 3 7 ) c o m p a r e d t o t h e G r i f f i t h p e l l e t s c a s e ( F i g . 1 4 ) . T h i s was a c c o m p a n i e d by a l o w e r p r e d i c t e d l e n g t h o f t h e k i l n ( 2 8 . 5 m ) . O n c e a g a i n , t h i s m e a n s t h a t when o p e r a t i n g w i t h t h i s c h a r g e i t s h o u l d be p o s s i b l e t o i n c r e a s e t h e t h r o u g h p u t i n a k i l n o f f i x e d l e n g t h w h i l e m a i n t a i n i n g a h i g h d e g r e e o f r e d u c t i o n . B e c a u s e o f t h e l o w e r w a l l t e m p e r a t u r e , t h i s w i l l r e s u l t i n s m o o t h e r k i l n o p e r a t i o n w i t h l e s s e r a c c r e t i o n p r o b l e m s . 3.2.5 E f f e c t o f N a t u r a l G a s N a t u r a l g a s i s i n j e c t e d i n t o t h e p r e h e a t z o n e o f t h e SL/RN k i l n a s an a u x i l i a r y h e a t s o u r c e t o e n h a n c e h e a t t r a n s f e r t o t h e s o l i d s . T h e r a t e o f n a t u r a l g a s i n j e c t i o n i n t o t h e k i l n d e p e n d s on t h e t y p e o f c h a r g e e m p l o y e d . I t h a s a l r e a d y b e e n s e e n t h a t a much h i g h e r r a t e o f n a t u r a l g a s was u t i l i z e d i n 115 T a b l e 9 I n p u t D a t a f o r t h e K i l n Run U s i n g F o r e s t b u r g C o a l a n d F a l c o n b r i d g e P e l l e t s O r e - F a l c o n b r i d g e p e l l e t s 1 9 1 . 8 t o n s / d a y C o a l - F o r e s t b u r g 1 2 9 . 9 t o n s / d a y A i r ( t o t a l ) 4 9 3 7 5 s c f t / t o n o r e N a t u r a l g a s 6 7 6 s c f t / t o n o r e D e g r e e o f r e d u c t i o n ( t o t a l ) 9 2 % H y d r o g e n p e r - r e d u c t i o n 8% E x i t s o l i d s t e m p e r a t u r e 9 0 0 ° C S o l i d s d e g r e e o f f i l l in o 10.0 15.0 DISTANCE FROM T 20.0 25.0 30.0 CHARGE END (METRES) 35.0 40.0 F i g . 3 7 . S o l i d s , g a s , i n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e f o r t h e r u n u s i n g F o r e s t b u r g c o a l a n d F a l c o n b r i d g e p e l l e t s . 2-] i i r- 1 1 — r F i g . 3 8 . R e d u c t i o n a n d f r e e b o a r d c o m p o s i t i o n p r o f i l e s f o r t h e k i l n r u n u s i n g F o r e s t b u r q c o a l a n d F a l c o n b r i d g e p e l l e t s . 1 1 9 t h e r u n w i t h a n t h r a c i t e c o a l c o m p a r e d t o t h e F o r e s t b u r g c o a l , e v e n t h o u g h t h e o r e t h r o u g h p u t was s m a l l e r i n t h e f o r m e r c a s e . To s t u d y t h e e f f e c t o f n a t u r a l g a s i n j e c t i o n i n t h e p r e h e a t z o n e , a r u n was made w i t h o u t a n y n a t u r a l g a s , b u t o t h e r w i s e u n d e r i d e n t i c a l c o n d i t i o n s t o t h e o r i g i n a l F o r e s t b u r g r u n i n w h i c h g a s was i n j e c t e d a t a r a t e o f 6 7 6 c f / t o f o r e . T h e i n p u t c o n d i t i o n s f o r t h i s r u n a r e p r e s e n t e d i n T a b l e 1 0 . T h e a i r p r o f i l e i s g i v e n i n F i g . 3 9 . F i g s . 40 a n d 41 show t h e p r e d i c t e d p r o f i l e s f r o m t h e m o d e l . By c o m p a r i s o n w i t h F i g . 14 t h e a b s e n c e o f n a t u r a l g a s i n t h i s r u n c a n be s e e n t o e x t e n d t h e l e n g t h o f t h e p r e h e a t z o n e b y 1.2m a n d a l s o t o d e c r e a s e t h e w a s t e g a s t e m p e r a t u r e t o 7 4 5 ° C . A t t h e same t i m e i t s h o u l d be n o t e d t h a t t h e w a s t e g a s i s r i c h e r i n o x y g e n ( 3 % ) . I f t h e a i r i n p u t t o t h e p r e h e a t z o n e i s r e d u c e d s o t h a t no o x y g e n a p p e a r s i n t h e w a s t e g a s e s , t h a t i s t o r e d u c e t h e t h e r m a l b u r d e n on t h e g a s e s , a h i g h e r w a s t e g a s t e m p e r a t u r e r e s u l t s a n d t h e e f f e c t o f a l a c k o f n a t u r a l g a s c o m b u s t i o n d i m i n i s h e s . T h u s i t i s s e e n t h a t a t t h e l o w g a s r a t e s e m p l o y e d w i t h F o r e s t b u r g c o a l t h e i n j e c t i o n o f n a t u r a l g a s p l a y s a r e l a t i v e l y m i n o r r o l e i n t h e k i l n o p e r a t i o n . A t h i g h e r n a t u r a l g a s r a t e s , s u c h a s w e r e u t i l i z e d w i t h t h e a n t h r a c i t e c o a l , t h e p r e s e n c e o f t h i s h e a t h a s a m o r e s i g n i f i c a n t e f f e c t on h e a t t r a n s f e r i n t h e p r e h e a t z o n e . I t s h o u l d be m e n t i o n e d t h a t t h e c o n c l u s i o n d r a w n a b o v e i s b a s e d on t h e a s s u m p t i o n o f i n s t a n t a n e o u s c o m b u s t i o n i n t h e f r e e b o a r d g a s . H o w e v e r i n t h e e v e n t o f i n c o m p l e t e 120 T a b l e 10 I n p u t D a t a f o r t h e K i l n Run U s i n g F o r e s t b u r g C o a l a n d G r i f f i t h P e l l e t s W i t h o u t A n y N a t u r a l G a s O r e - G r i f f i t h p e l l e t s 1 9 1 . 8 t o n s / d a y C o a l - F o r e s t b u r g A i r ( t o t a l ) N a t u r a l g a s D e g r e e o f r e d u c t i o n ( t o t a l ) H y d r o g e n p r e - r e d u c t i o n E x i t s o l i d s t e m p e r a t u r e S o l i d s d e g r e e o f f i l l 1 2 9 . 9 t o n s / d a y 5 2 9 6 0 s c f t / t o n o r e 9 2 % 1 0 0 0 ° C 2 5% 0.0 F i g . 39 5.0 i — r 10.0 15.0 20.0 25.0 30.0 DISTANCE FROM CHARGE END (METRES) 35.0 40.0 A i r p r o f i l e w i t h o u t a n y f o r t h e n a t u r a l k i l n g a s . r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s a in i | 1 1 1 1 r F i g . 4 0 . S o l i d s , g a s , i n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e . p r o f i 1 e s f o r t h e k i l n r u n u s i n g F o r e s t b u r q c o a l a n d R r i f f i t h . p e l 1 e t s w i t h o u t PERCENTAGE REDUCTION 20.0 40.0 60.0 J JL -n TJ o fD -s Q. n> C to o r + r + cr c O CQ Cu o 3 O a. cu — i -s CU fD 3 fD C L cr o C75 Cu -5 -5 — O L -b -hca _j. QJ r + CO zr O -a O fD 3 — i X J —• o fD CO c+ CO r + _ i . S O — i . 3 r + O -5 C O rl- -h — i * Eu — i 3 fD «< -h 3 O a> -s c+ rt--s 3 " a> fD — i 7T J 3 — i . CU — i CO 3 -s c 3 C CO 3 -Cl 100.0 i T r r °0.0 0.2 0.4 0.6 0.B PARTIAL PRESSURES OF FREE BOARD GASES i.o 1 24 c o m b u s t i o n t h e e f f e c t o f n a t u r a l g a s may be m o r e p r o n o u n c e d i n t h e p r e h e a t z o n e . 3 . 2 . 6 E f f e c t o f D u s t i n t h e F r e e b o a r d G a s One o f t h e p r o b l e m s t h a t g e n e r a l l y a r i s e s i n t h e o p e r a t i o n o f r o t a r y k i l n s , s u c h a s t h e S L / R N k i l n , i s t h e g e n -e r a t i o n o f d u s t d u e t o p a r t i c l e s a b r a d i n g a g a i n s t o n e a n o t h e r i n t h e s o l i d s b e d . T h e d u s t i s c a r r i e d o u t o f t h e k i l n i n t h e f r e e b o a r d g a s , a n d i s i m p o r t a n t , n o t o n l y b e c a u s e i t r e p r e -s e n t s a l o s s o f m a t e r i a l ( a l t h o u g h u s u a l l y m i n o r ) b u t a l s o b e c a u s e i t c a n p r o f o u n d l y i n f l u e n c e h e a t t r a n s f e r f r o m t h e g a s t o t h e k i l n w a l l a n d b e d s u r f a c e b y a l t e r i n g t h e e f f e c t i v e g a s e m i s s i v i t y . T h e e x t e n t t o w h i c h d u s t i s g e n e r a t e d i n t h e S L / R N k i l n i s d i f f i c u l t t o q u a n t i f y p r e c i s e l y f r o m p i l o t p l a n t t r i a l s . H o w e v e r , f r o m p h o t o g r a p h s o f t h e k i l n i n t e r i o r , s u c h a s s h o wn i n F i g . 2 0 , i t i s b e l i e v e d t h a t t h e d u s t l o a d i n g i n t h e f r e e b o a r d g a s i s s m a l l , a t l e a s t i n t h e r e d u c t i o n z o n e . F o r t h i s r e a s o n , t h e f r e e b o a r d g a s h a s b e e n a s s u m e d t o be " n o n -d u s t y " i n a l l t h e m o d e l r u n s r e p o r t e d t o t h i s p o i n t . N e v e r t h e -l e s s , b e c a u s e d u s t c a n be a p o t e n t i a l p r o b l e m , i t was d e c i d e d t o i n v e s t i g a t e i t s i n f l u e n c e on k i l n b e h a v i o u r when t h e c h a r g e c o n s i s t e d o f G r i f f i t h p e l l e t s a n d F o r e s t b u r g c o a l . H o t t e l [ 2 9 ] h a s s u g g e s t e d t h a t f o r e n g i n e e r i n g p u r p o s e s t h e e f f e c t o f d u s t o n g a s e m i s s i v i t y c a n be t a k e n i n t o a c c o u n t b y a d d i n g 0.1 t o t h e n o n - l u m i n o u s g a s e m i s s i v i t y . T h i s a d j u s t m e n t 1 2 5 was made f o r t h e r u n w h o s e i n p u t c o n d i t i o n s a r e g i v e n i n T a b l e 4. T h e f r e e b o a r d g a s t e m p e r a t u r e t h a t r e s u l t e d f r o m t h i s c a l c u -l a t i o n i s p r e s e n t e d i n F i g . 42 t o g e t h e r w i t h t h e p r o f i l e o r i g i n a l l y o b t a i n e d w i t h t h e n o n - d u s t y g a s . I t c a n be s e e n t h a t , a s e x p e c t e d , t h e d u s t y g a s h a s a l o w e r t e m p e r a t u r e , p a r -t i c u l a r l y i n t h e r e d u c t i o n z o n e c o m p a r e d t o t h e n o n - d u s t y g a s . T h a t t h e e f f e c t o f d u s t i s s e e n m o r e i n t h e r e d u c t i o n z o n e t h a n i n t h e p r e h e a t z o n e c a n be a t t r i b u t e d t o two r e a s o n s . ( i ) T h e g a s i n t h e r e d u c t i o n z o n e h a s a l o w e r e m i s s i v i t y ( i n t h e a b s e n c e o f d u s t ) t h a n i n t h e p r e h e a t z o n e o w i n g t o a l a c k o f w a t e r v a p o u r . T h u s t h e a d d i t i o n o f 0.1 t o eg i n c r e a s e s t h e g a s e m i s s i v i t y i n t h e r e d u c t i o n z o n e by a p r o p o r t i o n a t e l y l a r g e r a m o u n t . ( i i ) T h e g a s t e m p e r a t u r e i n t h e r e d u c t i o n z o n e i s c o n s i d e r a b l y h i g h e r t h a n i n t h e p r e h e a t z o n e w i t h t h e r e s u l t t h a t r a d i a n t h e a t t r a n s f e r c o n t r i b u t e s m o r e t o t h e o v e r a l l h e a t f l o w p r o c e s s i n t h e r e d u c t i o n z o n e . A g a i n t h e e f f e c t o f i n c r e a s i n g e g w o u l d be g r e a t e r i n t h e r e d u c t i o n z o n e . T h i s r e s u l t i s i m p o r t a n t f r o m t h e s t a n d p o i n t o f t h e m o d e l . I t means t h a t t h e e f f e c t o f d u s t on h e a t t r a n s f e r i s g r e a t e s t i n t h e r e d u c t i o n z o n e w h e r e t h e f r e e b o a r d g a s h a s i t s l o w e s t v e l o c i t y , a n d i s l e a s t l i k e l y t o p i c k up d u s t f r o m t h e b e d s u r f a c e ( F i g . 2 0 ) . On t h e o t h e r h a n d i n t h e p r e h e a t z o n e w h e r e t h e f r e e b o a r d g a s v e l o c i t y i s r e a c h i n g a maximum v a l u e s o Niat d u s t e n t r a i n -m e n t i s e n h a n c e d , d u s t h a s a r e l a t i v e l y m i n o r e f f e c t o n h e a t t r a n s f e r . T h u s , t h e a s s u m p t i o n o f a n o n - d u s t y g a s i n t h e m o d e l w o u l d a p p e a r t o be q u i t e j u s t i f i a b l e . r 1600 h 1400 h I200h 1000 h 800 h 600 8 0 F i g . 4 2 . 160 240 Distance from Charge End (m) E f f e c t o f t h e e m i s s i v i t y o f q a s on t h e q a s t e m p e r a t u r e . 3 2 0 ro 1 2 7 T h e c h a n g e i n t h e g a s e m i s s i v i t y a l s o r e s u l t e d i n a c h a n g e i n t h e s o l i d s a n d i n n e r w a l l t e m p e r a t u r e . T h e s o l i d s s h o w e d an a v e r a g e d r o p o f a r o u n d 2 0 - 3 0 ° C , w h i l e t h e i n n e r w a l l r e g i s t e r e d a d r o p o f a r o u n d 5 0 - 7 0 ° C . 3.2.7 P r e d i c t i o n s f o r t h e G r i f f i t h K i l n P e r h a p s t h e m o s t i m p o r t a n t i n v e s t i g a t i o n t h a t c a n be u n d e r t a k e n w i t h t h e m a t h e m a t i c a l m o d e l , i s t o s t u d y t h e e f f e c t o f s i z e on k i l n o p e r a t i o n - t h e q u e s t i o n o f s c a l e - u p . I n t h i s r e g a r d , a u n i q u e o p p o r t u n i t y p r e s e n t e d i t s e l f , s i n c e a t t h e same t i m e t h a t t h e m o d e l was b e i n g d e v e l o p e d , S t e l c o was c o n s t r u c t i n g a l a r g e p r o d u c t i o n s i z e k i l n , 125m l o n g b y 6 m i d , a t t h e G r i f f i t h M i n e , R e d L a k e , O n t a r i o . T h e m o d e l t h u s was r u n t o p r e d i c t t h e o p e r a t i n g b e h a v i o u r o f t h i s l a r g e k i l n , u s i n g a s i n p u t p a r a m e t e r s , t h e a n t i c i p a t e d o p e r a t i n g c o n d i t i o n s . T h e r e s u l t s o f two m o d e l r u n s w h e r e t h e f e e d r a t e o f s o l i d s was 1 0 0 % a n d 1 3 0 % o f t h e d e s i g n e d s p e c i f i c a t i o n a r e r e p o r t e d b e l o w . 3.2.7.1 1 0 0 % D e s i g n C a p a c i t y T h e G r i f f i t h k i l n i s r a t e d t o p r o c e s s 72 t o n s / h r o f i r o n o r e p e l l e t s t a k e n f r o m t h e G r i f f i t h M i n e o p e r a t i o n s w i t h F o r e s t b u r g c o a l b e i n g u s e d a s t h e s o l i d r e d u c t a n t . T h e i n p u t v a r i a b l e s e m p l o y e d : i n t h i s r u n a r e p r e s e n t e d i n T a b l e 1 1 . F i g . 43 s h o w s t h e t h e o r e t i c a l a i r p r o f i l e s e l e c t e d f o r t h i s T a b l e 11 I n p u t D a t a f o r t h e G r i f f i t h K i l n Run U s i n g F o r e s t b u r g C o a l a n d G r i f f i t h P e l l e t s f o r t h e D e s i g n e d T h r o u g h p u t O r e - G r i f f i t h p e l l e t s C o a l - F o r e s t b u r g A i r ( t o t a l ) N a t u r a l Gas D e g r e e o f r e d u c t i o n H y d r o g e n p r e - r e d u c t i o n E x i t s o l i d s t e m p e r a t u r e S o l i d s d e g r e e o f f i l l 1 7 2 8 t o n s / d a y 1 1 8 6 t o n s / d a y 4 7 3 9 0 f t 3 / t o n o r e 0 f t 3 / t o n o r e 9 5 % 8% 8 5 0 ° C 2 0 % 43 o IT). a ro. CJ to LU £<? or i 3 GC a cn' a > — N \ 1 1 — 1 1 — a.o 60.0 75.0 DISTANCE FROM CHARGE END (METRES) 90.0 105.0 120.0 F i g . 4 3 . A i r p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g t h e F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s f o r t h e d e s i g n e d t h r o u g h p u t . ro co 130 s e t o f o p e r a t i n g c o n d i t i o n s . T h e r e s u l t s c a l c u l a t e d u s i n g t h e m o d e l a r e p r e s e n t e d i n F i g s . 44 t o 4 8 . F r o m F i g . 4 4 , t h e c o m p u t e d k i l n l e n g t h c a n be s e e n t o be s l i g h t l y o v e r 80m, b u t c o n s i d e r a b l y s h o r t e r t h a n t h e 125m o f t h e a c t u a l k i l n . O f t h e c a l c u l a t e d l e n g t h a b o u t 30m o r 3 7 % i s r e q u i r e d t o p r e h e a t t h e s o l i d s . T h e b e d t e m p e r a t u r e t h r o u g h t h e r e d u c t i o n z o n e i s a r o u n d 9 7 5 ° C . T h e g a s t e m p e r a t u r e p r o f i l e i s q u i t e s i m i l a r t o t h e p r o f i l e i n t h e p i l o t k i l n . T h e w a l l t e m p e r a t u r e i s l o w e r t h a n t h a t c a l c u l a t e d f o r t h e p i l o t k i l n p r e s u m a b l y d u e t o a n a b s e n c e o f i n s u l a t i n g b r i c k i n t h e G r i f f i t h k i l n . T h i s i s a l s o r e s p o n s i b l e f o r t h e h i g h e r s h e l l t e m p e r a t u r e c a l c u l a t e d . I n common w i t h t h e p i l o t k i l n t h e r e i s a n e e d t o m a i n t a i n a s l i g h t e x c e s s o f o x y g e n i n t h e f r e e b o a r d t h r o u g h m o s t o f t h e r e d u c -t i o n z o n e . \ I t s h o u l d be m e n t i o n e d t h a t i n t h e s e c a l c u l a t i o n s i n s t a b i l i t y was a much g r e a t e r p r o b l e m t h a n i n t h e p i l o t k i l n r u n s r e q u i r i n g some e x t e r n a l c o n t r o l on t h e B o u d o u a r d r e a c t i o n r a t e . B a s e d o n e x p e r i e n c e w i t h t h e p i l o t p l a n t r u n s , t h i s s i t u a t i o n may i n d i c a t e t h a t t h e a n t i c i p a t e d s e t o f o p e r a t i n g c o n d i t i o n s w i l l r e s u l t i n p o o r k i l n p e r f o r m a n c e . F u r t h e r d e t a i l e d a n a l y s i s o f t h e c h a r a c t e r i s t i c s o f t h e p i l o t a n d G r i f f i t h k i l n s r e v e a l e d a n i n t e r e s t i n g f a c t . F o r a 2 5 % d e g r e e o f f i l l t h e r a t i o o f s u r f a c e a r e a t o v o l u m e o f t h e s o l i d s b e d p e r u n i t l e n g t h o f t h e G r i f f i t h k i l n i s r o u g h l y o n e - t h i r d t h e v a l u e f o r t h e p i l o t k i l n . T h i s m e a n s t h a t l e s s h e a t p e r u n i t v o l u m e o f b e d c a n be t r a n s f e r r e d t o t h e s o l i d s i n t h e G r i f f i t h k i l n . o i n co F i g . 4 4 . S o l i d s t e m p e r a t u r e p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g t h e F o r e s t b u r g - 1 c o a l a n d G r i f f i t h p e l l e t s f o r t h e d e s i g n e d t h r o u g h p u t . G R S J E E M E E R R T U R E PROFILE ^actual cor r e e f e d i "I 1 1 1 1 30.0 45.0 60.0 75.0 90.0 DISTANCE FROM CHARGE END (METRES) n 105.0 120. 1t ^ H e r r f f J - ^ r 0 f i i ] e / 0 I t h e G r i f f i t h k i l n run u s i n g t h e F o r e s t b u r q 1 a n d G r i f f i t h p e l l e t s f o r d e s i g n e d t h r o u g h p u t . i r 0.0 15.0 30.0 45.0 60.0 DISTANCE FROM CHARGE F i g . 4 6 . I n n e r w a l l t e m p e r a t u r e p r o f i l e f o r t h e c o a l a n d G r i f f i t h p e l l e t s f o r d e s i g n e d 75.0 90.0 105.0 END (METRES) G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g t h r o u g h p u t . 120 a 0.0 15.0 30.0 45.0 60.0 75.0 90.0 105.0 120.0 DISTANCE FROM CHARGE END (METRES! F i g . 4 7 . F r e e b o a r d g a s c o m p o s i t i o n p r o f i l e s f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s f o r d e s i g n e d t h r o u g h p u t . CO l i ! CO cx F i g . 4 8 . F r e e b o a r d g a s c o m p o s i t i o n p r o f i l e s f o r t h e G r i f f i t h k i l n r u n u s i n q F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s f o r d e s i g n e d t h r o u g h p u t . 136 3 . 2 . 7 . 2 1 3 0 % D e s i g n C a p a c i t y T h e f a c t t h a t t h e a c t u a l G r i f f i t h k i l n i s l o n g e r t h a n s e e m s r e q u i r e d f o r i t s d e s i g n e d t h r o u g h p u t l e d t o a n a t t e m p t t o p r e d i c t k i l n p e r f o r m a n c e u s i n g a t h r o u g h p u t w h i c h was 1 3 0 % o f i t s r a t e d - c a p a c i t y . T h e o p e r a t i n g c o n d i t i o n s a s s u m e d w e r e a g a i n c l o s e t o t h e c o n d i t i o n s u s e d i n t h e p i l o t k i l n . T h e i n p u t d a t a f o r t h i s r u n i s g i v e n i n T a b l e 1 2 . T h e t h e o r e t i c a l a i r p r o f i l e u s e d i s s h o wn i n F i g . 49 a n d t h e r e s u l t s f r o m t h e m o d e l c a l c u l a t i o n s i n F i g s . 50 t o 5 4 . T h e s o l i d s t e m p e r a t u r e i n t h e r e d u c t i o n z o n e i s v e r y s i m i l a r t o t h e 1 0 0 % r u n . A s d i s c u s s e d i n t h e p r e c e d i n g c a s e , d u e t o i n s t a b i l i t y p r o b l e m s e n c o u n t e r e d , t h e B o u d o u a r d r e a c t i o n r a t e h a d t o be e x t e r n a l l y c o n t r o l l e d . T h e g a s c o m p o s i t i o n p r o f i l e s a g a i n s h ow t h a t a n e x c e s s o f o x y g e n o v e r m o s t o f t h e r e d u c t i o n z o n e i s i n e v i d e n c e . T h e l e n g t h o f t h e k i l n c a l c u l a t e d f r o m t h e m o d e l f o r t h i s r u n i s 98m. T h u s f r o m t h e s e m o d e l c a l c u l a t i o n s i t i s c l e a r t h a t t h e G r i f f i t h k i l n s h o u l d be a b l e t o h a n d l e t h r o u g h p u t s t h a t a r e h i g h e r t h a n i t s r a t e d c a p a c i t y . 3.3 G e n e r a l C o m m e n t s on t h e S L / R N P r o c e s s H a v i n g e x a m i n e d t h e i n f l u e n c e o f d i f f e r e n t o p e r a t i n g v a r i a b l e s on t h e p e r f o r m a n c e o f t h e S L / R N k i l n i t i s c l e a r t h a t i t i s a c o m p l e x o p e r a t i o n i n v o l v i n g c l o s e l y c o u p l e d h e a t a n d m a s s t r a n s p o r t s t e p s . T h i s i s c o n t r a r y t o t h e r a t h e r s i m p l e p i c t u r e o n e m i g h t h a v e i n i t i a l l y o f s o l i d i r o n o x i d e p e l l e t s 1 37 T a b l e 12 I n p u t D a t a f o r t h e G r i f f i t h K i l n Run U s i n g F o r e s t b u r g C o a l a n d G r i f f i t h P e l l e t s f o r a 3 0 % H i g h e r T h r o u g h p u t O r e - G r i f f i t h p e l l e t s 2 2 4 6 t o n s / d a y C o a l - . F o r e s t b u r g 1 5 4 4 t o n s / d a y A i r ( t o t a l ) 4 6 2 7 0 f t 3 / t o n o r e N a t u r a l g a s 0 f t 3 / t o n o r e H y d r o g e n p r e - r e d u c t i o n 8% E x i t s o l i d s t e m p e r a t u r e 8 5 0 ° C S o l i d s d e g r e e o f f i l l 2 0 % in fM_J F i g . 4 9 . A i r p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t . 0.0 F i g . 50, 15.0 i r 30.0 45.0 60.0 DISTANCE FROM CHARGE 75.0 90.0 END (METRES) 105.0 120.0 Soy* * ! ; ? ? r a t u r ? P r o f i : i e f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r q c o a l a n d G r i f f n t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t . CO to XT. CD X C D L U a LLJO ZDr-r— G C C C L U Q_ 21a L U • nzm. E M P E PROFILE a a ' co r rected 0.0 F i g . 51 15.0 ~1 1 1 30.0 45.0 60.0 DISTANCE FROM CHARGE 75.0 90. END (METRES) 105.0 120.0 -Pa o G a s t e m p e r a t u r e p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t . • • •• 0.0 F i g . 52 15.0 i r 30.0 45.0 60.0 75.0 90.0 DISTANCE FROM CHARGE END (METRES) 105.0 120.0 I n n e r w a l l a n d o u t e r s h e l l t e m p e r a t u r e p r o f i l e s f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t . I I I I I I I I 0.0 15.0 30.0 45.0 60.0 75.0 90.0 105.0 120.0 DISTANCE FROM CHARGE END (METRES) . 5 3 . R e d u c t i o n p r o f i l e f o r t h e G r i f f i t h k i l n r u n u s i n g F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t . 30.0 45.0 DISTANCE FROM 75.0 90.0 CHARGE END (METRES) 105.0 120.0 F i g . 5 4 . F r e e b o a r d g a s c o m p o s i t i o n p r o f i l e s f o r t h e G r i f f i t h k i l n r u n u s i n q F o r e s t b u r q c o a l a n d G r i f f i t h p e l l e t s w i t h a 3 0 % h i g h e r t h r o u g h p u t . oo 144. p a s s i n g t h r o u g h a l o n g t u b e i n t e r a c t i n g c h e m i c a l l y w i t h c o a l a n d e m e r g i n g i n a r e d u c e d s t a t e . I n t h i s c h a p t e r i t h a s b e e n s e e n t h a t t h e b e h a v i o u r o f t h e S L / R N k i l n i s s t r o n g l y i n f l u e n c e d b y t h e t y p e o f c o a l a n d o r e p e l l e t s c o m p r i s i n g t h e c h a r g e , b y t h e a i r p r o f i l e s i m p o s e d a n d by t h e k i l n s i z e . I t w o u l d a l s o s e e m c l e a r f r o m t h i s w o r k t h a t t h e p r e d i c t i o n o f k i l n p e r f o r m a n c e w i t h o u t t h e s e r v i c e s o f a m a t h e m a t i c a l m o d e l , s u c h a s d e v e l o p e d h e r e , i s v i r t u a l l y o u t o f t h e q u e s t i o n . A t t h i s s t a g e o f t h e s t u d y i t i s p o s s i b l e t o d e l i n e a t e some o f t h e m o r e g e n e r a l f e a t u r e s o f k i l n b e h a v i o u r , p a r t i c u l a r l y a s r e g a r d s t h e r a t e l i m i t i n g s t e p s . T h e m o d e l h a s s h o w n t h a t t h e o p e r a t i o n o f t h e k i l n i s e x t r e m e l y s e n s i t i v e t o h e a t f l o w ; c o n d i t i o n s . T h i s i s r e f l e c t e d i n t h e f a c t t h a t t h e a i r p r o f i l e i s t h e m o s t i m p o r t a n t o p e r a t i n g v a r i a b l e b e c a u s e i t a b s o l u t e l y ., . c o n t r o l s t h e g a s t e m p e r a t u r e , t h r o u g h c o m b u s t i o n * a n d i n a d d i t i o n , t h e s o l i d s b e d t e m p e r a t u r e t h r o u g h h e a t t r a n s f e r f r o m t h e g a s . T h e r e i s s t r o n g e v i d e n c e t h e r e f o r e t h a t t h e SL/RN p r o c e s s i s g o v e r n e d i n i t s o p e r a t i o n e s s e n t i a l l y by h e a t t r a n s f e r . T h i s c o n c l u s i o n s e e m s r e a s o n a b l e i f t h e two z o n e s o f t h e k i l n a r e e x a m i n e d s e p a r a t e l y . I n t h e p r e h e a t z o n e , w h i c h h a s t h e m a j o r f u n c t i o n o f i n c r e a s i n g t h e s e n s i b l e h e a t o f t h e : s o l i d s , h e a t t r a n s f e r i s c l e a r l y t h e r a t e c o n t r o l l i n g s t e p . I n t h e r e d u c t i o n z o n e , h e a t t r a n s f e r i s a l s o e x t r e m e l y i m p o r -t a n t b e c a u s e t h e B o u d o u a r d r e a c t i o n i s s o h i g h l y e n d o t h e r m i c i n n a t u r e . I n o r d e r t o m a i n t a i n t h e b e d t e m p e r a t u r e a t a 145 h i g h e r l e v e l a n d e n s u r e f a s t r e a c t i o n r a t e s , h e a t m u s t be s u p p l i e d t o t h e b e d t o m e e t t h e d e m a n d s o f t h e B o u d o u a r d r e a c t i o n . I f h e a t t r a n s f e r i s t h e r a t e c o n t r o l ! i n q s t e p i n t h e S L/RN p r o c e s s i t i s p o s s i b l e t o f u r t h e r s t a t e t h a t , f o r p u r p o s e s o f k i l n d e s i g n a n d o p e r a t i o n , o n e o f t h e m o s t i m p o r -t a n t v a r i a b l e s i s t h e r a t i o o f t h e s u r f a c e o f t h e b e d t o i t s e n c l o s e d v o l u m e . T h e A/V r a t i o h a s b e e n c a l c u l a t e d a s a f u n c t i o n o f d i a m e t e r f o r v a r y i n g d e g r e e s o f f i l l a n d i s s h o w n i n F i g . 5 5 . H e r e i t c a n be s e e n t h a t f o r a g i v e n d i a m e t e r t h e A/V r a t i o i n c r e a s e s w i t h d e c r e a s i n g d e g r e e o f f i l l . A t t h e same t i m e f r o m t h e s c a l e - u p p o i n t o f v i e w , i f t h e d i a m e t e r o f t h e k i l n i s i n c r e a s e d a n d t h e A/V r a t i o i s k e p t c o n s t a n t , t h e p e r c e n t a g e d e g r e e o f f i l l m u s t d e c r e a s e t o m a i n t a i n h e a t t r a n s f e r r a t e s . I t i s n o t p o s s i b l e , h o w e v e r , t o v i e w t h e A/V r a t i o i n s u c h a s i m p l e way. In t h e f i r s t p l a c e , a n i n c r e a s e i n k i l n d i a m e t e r w i l l a l s o r e s u l t i n a n i n c r e a s e i n t h e mean, beam l e n g t h a n d c o n s e q u e n t l y , e m i s s i v i t y o f t h e g a s , t h e r e b y i n c r e a s i n g t h e r a d i a n t h e a t t r a n s f e r r a t e . I n t h e s e c o n d p l a c e t h e A/V r a t i o i t s e l f a f f e c t s t h e r e s i d e n c e t i m e o f s o l i d s i n t h e k i l n . T h i s i s s h o wn i n F i g . 56 f o r t h e 6m i d G r i f f i t h k i l n w h e r e t h e mean r e s i d e n c e t i m e h a s b e e n c a l c u l a t e d u s i n g a v e r a g e s o l i d s t h r o u g h p u t a n d b u l k d e n s i t y , a n d a s s u m i n g p l u g f l o w b e h a v i o u r . I t c a n be s e e n t h a t a n i n c r e a s e i n t h e A/V r a t i o w h i c h i s d e s i r a b l e f r o m a h e a t t r a n s f e r v i e w p o i n t r e s u l t s i n a f a s t e r d e c r e a s e i n t h e r e s i d e n c e t i m e o f s o l i d s • T - a n . ' u n d e s i r a b l e , e f f e c t . i 1 1 r D i a m e t e r , m F i g . 5 5 . E f f e c t o f k i l n d i a m e t e r o n t h e A/V r a t i o f o r d i f f e r e n t d e g r e e s o f f i l l . 147 1 4 8 C l e a r l y a b a l a n c e m u s t be s t r u c k b e t w e e n t h e A/V a n d t h e r e s i d e n c e t i m e t , a n d f o r t h e G r i f f i t h k i l n t h i s may l e a d t o 1 5 % d e g r e e o f f i l l a s b e i n g o p t i m u m . S t r i c t l y s p e a k i n g , t h i s a n a l y s i s , i n v o l v i n g A/V r a t i o a n d r e s i d e n c e t i m e , a p p l i e s o n l y t o t h e p r e h e a t z o n e o f t h e k i l n . T h e s i t u a t i o n i s m o r e c o m p l i c a t e d i n t h e r e d u c t i o n z o n e b e c a u s e t h e A/V r a t i o c a n h a v e a c a t a s t r o p h i c e f f e c t on t h e r a t e s o f t h e B o u d o u a r d a n d r e d u c t i o n r e a c t i o n s . I f t h e A/V r a t i o i s t o o s m a l l ( l a r g e d e g r e e s o f f i l l , l o n g r e s i d e n c e t i m e ) s o t h a t t h e r a t e o f h e a t t r a n s f e r p e r u n i t v o l u m e o f b e d i s l o w , t h e b e d t e m p e r a t u r e may s e e k a l o w v a l u e d u e t o t h e e n d o t h e r m i c B o u d o u a r d r e a c t i o n . I n t h e l i m i t , t h e b e d t e m p e r a t u r e may be s o l o w t h a t t h e r a t e o f r e d u c t i o n i s e f f e c -t i v e l y h a l t e d a n d t h e l e n g t h o f t h e r e d u c t i o n z o n e r e q u i r e d t o a c h i e v e m e t a l l i s a t i o n i n c r e a s e d d r a s t i c a l l y . I n a k i l n o f f i x e d l e n g t h t h i s w o u l d mean e x t r e m e l y p o o r m e t a l l i s a t i o n ^ a n d u n s a t i s f a c t o r y p e r f o r m a n c e . On t h e b a s i s o f t h e a n a l y s i s i t w o u l d a p p e a r t h e k i l n s h o u l d be r u n w i t h a h i g h e r d e g r e e o f f i l l i n t h e p r e h e a t z o n e t h a n i n t h e r e d u c t i o n z o n e . C h a p t e r 4 SUMMARY AND CONCLUSIONS A m a t h e m a t i c a l m o d e l h a s b e e n s u c c e s s f u l l y d e v e l o p e d f o r t h e SL/RN d i r e c t r e d u c t i o n k i l n . T h i s m o d e l , b a s e d o n f u n -d a m e n t a l p r i n c i p l e s o f c o n s e r v a t i o n o f h e a t a n d m a s s , i n c o r -p o r a t e s m a t h e m a t i c a l e x p r e s s i o n s t o q u a n t i t a t i v e l y d e s c r i b e t h e r a t e s o f t h e i m p o r t a n t c h e m i c a l a n d p h y s i c a l p r o c e s s e s . U s i n g o p e r a t i n g v a r i a b l e s a s i n p u t p a r a m e t e r s , t h e m o d e l i s a b l e t o c a l c u l a t e a x i a l t e m p e r a t u r e a n d c o n c e n t r a t i o n p r o f i l e s i n b o t h t h e f r e e b o a r d g a s a n d t h e s o l i d s b e d . T h e a b i l i t y o f t h e m o d e l t o r e l i a b l y p r e d i c t t h e o p e r a t i n g p e r f o r m a n c e o f an SL/RN k i l n h a s b e e n c a r e f u l l y t e s t e d b y c o m p a r i s o n o f m o d e l c a l c u l a t i o n s t o m e a s u r e m e n t s made on a l a r g e p i l o t k i l n a t t h e H i l t o n W o r k s , S t e l c o . T h e m a t h e m a t i c a l m o d e l h a s t h e n b e e n u s e d t o p r e d i c t t h e i n f l u e n c e o f s e v e r a l o p e r a t i n g v a r i b l e s on k i l n b e h a v i o u r on t h e s c a l e o f t h e l a r g e p i l o t k i l n u s i n g i n m o s t c a s e s F o r e s t b u r g c o a l a n d G r i f f i t h p e l l e t s . T h e r e s u l t s o f t h e s e p r e d i c t i o n s c a n be s u m m a r i s e d a s f o l l o w s . 149 150 ( i ) Coal type: I n a g r e e m e n t w i t h m e a s u r e m e n t s , t h e m o d e l h a s sh o w n t h a t t h e b e d t e m p e r a t u r e i s s t r o n g l y a f f e c t e d by t h e r a n k o f c o a l u s e d a s s o l i d r e d u c t a n t , b e i n g h i g h e s t f o r a n t h r a c i t e a n d l o w e s t f o r l i g n i t e . F u r t h e r , i t h a s b e e n d e m o n s t r a t e d t h a t t h e u s e o f a n t h r a c i t e c p a l r e s u l t s i n a r e d u c t i o n i n t h e t h r o u g h p u t o f t h e S L / R N k i l n . ( i i ) P e l l e t type: T h e u s e o f a h i g h l y r e d u c i b l e p e l l e t a s c h a r a c t e r i s e d b y a r e d u c i b i l i t y p a r a m e t e r h a s jthe e f f e c t o f r e d u c i n g t h e b e d t e m p e r a t u r e a n d a t t h e same t i m e i n c r e a s i n g t h e t h r o u g h p u t o f t h e k i l n . ( i i i ) Reduction achieved: I n c r e a s e s i n p e r c e n t r e d u c t i o n f r o m 92 t o 9 5 % g i v e r i s e t o a n 8% i n c r e a s e i n l e n g t h o f k i l n r e q u i r e d . ( i v ) Throughput: An i n c r e a s e o f 3 0 % i n t h e s o l i d s t h r o u g h p u t r e s u l t s i n a 2 2 % i n c r e a s e i n t h e k i l n l e n g t h . A m a j o r f r a c t i o n o f t h i s i n c r e a s e i n l e n g t h i s l o c a l i s e d i n t h e r e d u c t i o n z o n e . ( v ) Dust: T h e p r e s e n c e o f d u s t h a s a p r o f o u n d e f f e c t o n t h e g a s t e m p e r a t u r e p r o f i l e . ( v i ) Natural gas: U s i n g F o r e s t b u r g c o a l , t h e i n f l u e n c e o f n a t u r a l g a s a t a r a t e o f 6 7 6 s c f / t o n o f o r e o n l y m a r g i n a l l y r e d u c e s t h e p r e h e a t z o n e . W i t h a n t h r a c i t e c o a l 1 51 t h e i n j e c t i o n o f n a t u r a l g a s i s s e e n t o p l a y a m o r e i m p o r t a n t r o l e b e c a u s e o f t h e l o n g e r r e d u c t i o n z o n e r e q u i r e d . S c a l e - u p c a l c u l a t i o n s h a v e a l s o b e e n p e r f o r m e d w i t h t h e m a t h e m a t i c a l m o d e l . C o m p u t e r r u n s h a v e b e e n u n d e r t a k e n t o p r e d i c t t h e p e r f o r m a n c e o f t h e new c o m m e r c i a l s i z e S L / R N k i l n a t t h e G r i f f i t h m i n e . T h e s e h a v e s h o w n t h a t t h i s k i l n s h o u l d be c a p a b l e o f e x c e e d i n g t h e d e s i g n e d c a p a c i t y o f 1 2 0 0 t o n s o f s p o n g e i r o n p e r d a y . On t h e b a s i s o f m o d e l p r e d i c t i o n s i t s e e m s c e r t a i n t h a t t h e S L / R N p r o c e s s i s c o n t r o l l e d b y h e a t t r a n s f e r i n t h e k i l n . T h i s m e a n s t h a t o n e o f t h e i m p o r t a n t s c a l e - u p p a r a m e t e r s i n d e s i g n i n g S L / R N k i l n s i s t h e A/V r a t i o o f t h e b e d . It; a l s o c o n f o r m s w i t h t h e f i n d i n g t h a t t h e a i r p r o f i l e i s t h e m o s t c r i t i c a l c o n t r o l v a r i a b l e . 152 4.1 S u g g e s t i o n s f o r F u t u r e Work 1. T h e m o d e l s h o u l d be r e f i n e d a s a n d when b e t t e r d a t a i s a v a i l a b l e o n t h e h e a t t r a n s f e r a s p e c t o f r o t a r y k i l n s . 2. B a s e d o n f u r t h e r c o m p a r i s o n w i t h r e s u l t s f r o m t h e G r i f f i t h k i l n , t h e m o d e l may be u s e d t o s t u d y t h e e f f e c t s o f d i f f e r e n t v a r i a b l e s o n c o m m e r c i a l s c a l e o p e r a t i o n . 3. T h e u s e o f t h e m o d e l a s a b a s i c t o o l i n t h e o p t i m i z a t i o n a n d c o n t r o l o f S L / R N k i l n s may be i n v e s t i g a t e d . R E F E R E N C E S S m i t h , R.P., CEP S y m p o s i u m S e r i e s , V o l u m e 5 9 , Number 4 3 , May, 1 9 6 3 . S i b a k i n , J . G . , P r e s e n t e d a t t h e G e n e r a l M e e t i n g o f A I S I a t New Y o r k , May, 1 9 6 2 . K u r t M e y e r , G u n t e r H e i t m a n n , a n d W o l f g a n g J a n k e , J . M e t a l s , J u n e , 1 9 6 6 , p p . 7 4 8 - 7 5 2 . F r a s e r , M . J . a n d G r i g g , C.R., T h e E n g i n e e r i n g J o u r n a l , J u n e , 1 9 6 5 . P r o c e e d i n g s o f t h e S e v e n t h A n n u a l C o n f e r e n c e o f 1 1 S I a t J o h a n n e s b u r g , S o u t h A f r i c a , 1 9 7 3 . R o l l i n g e r , B., I a n d SM, J a n u a r y , 1 9 7 5 , p p . 1 0 - 1 7 . A l t e r n a t i v e r o u t e s t o S t e e l , P r o c e e d i n g s o f t h e A n n u a l G e n e r a l M e e t i n g o f I r o n a n d S t e e l I n s t i t u t e o f L o n d o n , 1 971 . P e a r c e , F . J . , C a n a d i a n M i n i n g a n d M e t a l l u r g i c a l B u l l e t i n , A p r i l , 1 9 6 4 . S i b a k i n , J . G . , H o o k i n g s , P.H. a n d R o e d e r , G.A., T r a n s . E n g i n e e r i n g I n s t i t u t e o f C a n a d a , V o l . 11 , No. E - l , May, 1 9 6 8 . G r e a v e s , M . J . , E / M J , F e b r u a r y , 1 9 7 5 . M e a d o w c r o f t , T.R., J o h n s o n , C.W.E. a n d W i l s o n , K., C a n a d i a n C o a l C o n f e r e n c e , V i c t o r i a , B . C . , 1 9 7 4 . 1 53 154 B e t r a m , J .M., I r o n a n d S t e e l E n g i n e e r , J u l y , 1 9 7 2 , p p . 3 1 - 4 0 . M i l l e r , J . R . , E / M J , May 1 9 7 2 , p p . 6 8 - 7 6 . M c M a n u s , G . J . , I r o n A g e M e t a l W o r k i n g I n t e r n a t i o n a l , A p r i l , 1 9 7 1 . I m b e r , M. a n d P a s c h k i s , V., I n t . J . H e a t M a s s T r a n s f e r , V o l . 5 , 1 9 62 , p p . 6 2 3 - 6 3 8 . A l l a n S a s s , I a n d EC P r o c e s s D e s i g n a n d D e v e l o p m e n t , V o l . 6, No. 4, O c t o b e r , 1 9 6 7 , p p . 5 3 2 - 5 3 5 . K a i s e r , V .A. a n d L a n e , J.W., I a n d EC P r o c e s s D e s i g n a n d D e v e l o p m e n t , V o l . 7, 1 9 6 8 , p p . 3 1 9 - 3 2 0 . R i f f a u d , J . B . , K o e h r e t , B. a n d C o u p a l , B., B r i t . Chem. E n g . a n d P r o c . T e c h . , V o l . 1 7 , No. 5, May, 1 9 7 2 . S p r a n g , I I I , H.A., A u t o m a t i c a , V o l . 8, 1 9 7 2 , p p . 3 0 9 - 3 2 3 . A n d r z e j M a n i t i u s , Ewa K u r c y u s z , a n d W i e s l a w K a w e c k i , I n d . E n g . Chem. P r o c e s s D e s . D e v e l o p . , V o l . 1 3 , No. 2, 1 9 7 4 , p p . 1 3 2 - 1 4 2 . W i n g f i e l d , S . L . , P r o t h e r o , A . a n d A u l d , J . B . , J . I n s t . F u e l , M a r c h , 1 9 7 4 , p p . 64,-72. S t e l c o R e p o r t s 7 2 0 0 6 1 . v o n B o g d a n d y , L . a n d E n g e l l , H . J . , The Reduction of Iron Ores, S p r i n g e r - V e r l a g , B e r l i n , H e i d e l b e r g , New Y o r k , 1 9 7 1 . M c A d a m s , W.H., Heat Transmission, 3 r d E d . , M c G r a w - H i l l , New Y o r k , N. Y., 1 9 5 4 . D o r n , W.S. a n d M c C r a c k e n , D.D., Numerical Methods with Fortran IV Case Studies, J o h n W i l e y & S o n s , I n c . , New Y o r k , 1 9 7 2 . S t e l c o r e p o r t s 7 4 0 0 4 1 , 7 3 0 0 8 5 . 155 2 7 . K r e i c h , F . , Principles of Heat Transfer, 2 n d E d . , I n t . T e x t B o o k C o m p a n y , 1 9 6 9 . 2 8 . S t e l c o R e p o r t s 7 2 0 1 6 1 . 2 9 . H o t t e l , H.C. a n d S a r o f i m , A . F . , Radiative Transfer. M c G r a w - H i l l B o o k C o . , 1 9 6 7 . 3 0 . P e r r y , R.H. a n d C h i l t o n , C.H., C h e m i c a l E n g i n e e r s H a n d b o o k , F i f t h E d i t i o n , M c G r a w H i l l B o o k C o m p a n y , 1 9 7 3 . 3 1 . L y o n s , J.W., M i n . H.S., P a r i s o t , P . E . a n d P a u l , J . F . , I & EC P r o c e s s D e s i g n a n d D e v e l o p m e n t , V o l . 1, No . 1 , J a n u a r y 1 9 6 2 . A P P E N D I X I SOURCE LISTING OF THE COMPUTER PROGRAM 156 1 5 7 rj ********************************************************************** c c ***** MATHEMATICAL MODELLING OF SL/BN PROCESS c ***** FOE THE DIRECT REDUCTION OF IRON OXIDE ****** c ***** I N THE ROTARY KILN ****** C r * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C NOMENCLATURE C RATE OF INPUT CHARGE C ORE FEED RATE IN TONS/HR ORE C COAL FEED RATE IN TONS/HR REDC C DOLOMITE FEED RATE IN TONS/HR — DOLL C AIR FEED RATE (END) SCFM — - A I R C C ANALYSIS OF FEED MATERIAL C C ORE ANALYSIS IN PERCENT — FEED (3) C FEED{1)= HAEMATITE C FEED (2)=MOISTURE C FEED(3)=GANGUE C C GANGUE ANALYSIS FROM ORE GANGO (5) C GANGO(1)=SILICA C GANGO(2)=ALUMINA C GANGO(3)=SODIUM OXIDE C GANGO(4)=CAO 1 C GANGO(5)=MGO C C COAL ANALYSIS COAL (12) C COAL (1)=FIXED CARBON C COAL (2)= WATER C COAL (3) =METHANE C COAL (4)=ETHANE C COAL (5)=CARBON MONOXIDE C COAL(6)=HYDROGEN C COAL(7)=OXYGEN C COAL (8) =NITROGEN C COAL(9)=ASH C COAL (10)=SULPHUH C COAL(11)=CARBONDIOXIDE C COAL (12) =PROPANE C C ANALYSIS OF ASH FROM COAL AASH (6) C AASH (1)=SILICA C AASH (2)=ALUMINA C AASH (3)=SODIUM OXIDE C AASH(4)=FEO C AASH(5)=CAO C AASH(6)=MGO C C ANALYSIS OF DOLOMITE FLUX (5) C FLUX (1)=CAC03 C FLUX (2) =MGC03 C FLUX(3)=GANG0E C FLUX(4)=MOISTURE C C ANALYSIS OF ASH IN DOLOMITE GANGF (5) C GANGF (1)=SILICA C GANGF {2) = ALU MIN A 1 5 g C GANGF(3)=SODIUM OXIDE C GANGF(tl) =FEO C ANALYSIS OF AIR C MOIST-IBS OF WATER PER 100 SCF —-RMOIS C C VOLUME OF NATURAL GAS IN SCFM VGAS C GAS (1)=METHANE C GAS (2) =ETHANE C. GAS (3) =PROPANE C C CHARACTERISTICS OF THE KILN C LENGTH CF THE KILN IN CMS RLEN C DIAMETER OF THE KILN CMS' DIAM C DEGREE OF FILL FRACTION FILL C C TEAPERATURE OF AIR TAIR C PERCENT DEGREE OF METALLISATION AMET C RETENTION TIME OF SOLIDS RTME C THE EMISSIVITY VALUES FOR GASES ARE DESCRIBED THROUGH C POLYNOMIAL EQUATIONS C RATES OF VOLATILES REMOVAL FROM COAL ALSO DESCRIBED C WITH THE HELP OF POLYNOMIAL EQUATIONS C TEMPERATURE OF NATURAL GAS TNAT C C INSULATION FOR THE KILN RX(3),RK(3) C RX (I)=THICKNESS OF INSULATION C RK (I)=THERMAL CONDUCTIVITY OF THE MATERIAL C THE CHARACTERISTICS OF COAL AND ORE ARE INCORPORATED C IN THE SUBROUTINE EOUD C IMPLICIT REAL*8 (A-H,C-Z) EXTERNAL FUNC DIMENSION Y (15) ,F (15) ,T (15) ,S (15) ,G (15) ,DUSTC (4) DIMENSION AX(30) ,AY(30) ,AZ(30) ,AM(30) DIMENSION RD (100) ,RBD (100) , RVHD (100) ,RVCOD(100) ,RVMD (100) DIMENSION BATD (100) ,C02D (100) ,RND (100) ,ROD (100),SHD (100) DIMENSION COD(100) ,HD{100) ,RATD(100) ,BP(11) DIMENSION RS (12) DIMENSION TSD (100) ,TWD(100) ,TGD (100) ,DIST (100) , AIRD (100) ,TCD (100) LOGICAL SSCHB,SWCHV,SHCHM,SWCHR,SWCC,PINrPAN COMMON/SH/SWCH LOGICAL SWCH,SW2 COMMON/ANDY/XG (30) , YG (30) / ZG (30) COMMON/DISTAN/BP COMMON/PARAM/TSD,TWD,TGD,TCD,DIST,AIRD COMMON/CL/CLFX,UTME COMMON/PARAM1/RD,RBD,RVHD,RVCOD,RVMD,SHD COMMON/PARAM2/WATD,C02D,RND,ROD,COD,HD,RATD COHMON/COAD/FEED(3),GANGO(5) COMMON/CFAD/FLUX(4),GANGF(5) COMMON/CCAD/COAL(12) ,AASH (6) COMMON/ADJUST/PARI,PAR2,REDP,BURN,TLEN COMMON/COMM/BLEN,D(14),ALEN,OXY COMMON/DCPS/DCPORE,DCPCOA,DCPDOL COMMON/HNEW/TOTNI,TOTCO,TOTCD,TOTET,TOTPR,TOTHY COMMON/CPS/CPOPE,CPCOAL,CPDOL COMMON/BANG/CVGS,RAGS,CVGW,RAGW,CDWS,RAWS COMMON/PRESS/PPR(9) C0MM0N/PCLY/P(11,25) ,Q(11,32) COMM0N/SPECY/FEO,FE2O3,FE3O4,FS COMHON/DUSTS/ODUST,CDUST,ADUST,DL1,DL2 COMMQN/RDUSTS/RODT,RCDT,RADT COMMON/EMISS/EMIS,ABSS,ABSW COMMQN/ARC/CHORD,ARCA,ARCB,ARCC COMMON/RPAR/EL,DIAM COMMON/SWITCH/PIN,PAN COMMON/AREAS/AW,AS,AG COMMON/GASHTR/GCVS,GRS,GCVa,GRH,GSWT,RHVM COMMON/HTCOEF/HCVGSC,HRGSC,HRHSC,HCWSC,HCVGWC,HRGWC,HCVSAC COMMON/HTRFER/HCVS,HRGS,HRl-JS,HCWS„HRST COMKON/TEMP/T8AL,TBALN COMMON/THICK/RX (3) , RK (3) , AIDIA COMMON/COMBR/RBCO,RBH,REM,ABE,BBP,RBO COMMGN/DRYR/OEED,BOLOD,BOLOC COMMCN/FROD/RPC02,RPH20 COMMON/CFLUX/FLUXO,FLUXB COMMON/THriCH/S'tfCHB,SBCHV,SWCHM,SWCHR,SHCC CO MMCN/BGRE/RHBO,RHVOL,RHDO,R HDRY,RHPED,EHBG,R FSB COMMON/FILE/GH(11,9) COMMON/HYC/CETH,CPRO COMMON/LAST/AIR,RHOIS,VGAS,GAS(3) ,N1,N2 COMMON/EEACT/HFORM(30) COMMON/CPST/AX,AY,AZ COMMON/BUD/RC,RO,RC02,RCO,RCB COMMON/DEGR/RMAS,RMETH,RCOONT,RiATER,RCHECK COMHCN/VCLT/RVH,RVC0,RVCO2,RVM,RVE,RVP,RVN,RVT, BHO,RCM COMMCN/DELT/EINT COMMON/CAMG/FACT COMMON/MISSED/ROXYT,ROXYN,TOTFE COMMON/RATES/.RNIT,RMOI,RME,RET,RPR,ROX,BHGAS COMMON/AMBI/TAIR,TNAT COMMON/MISSIN/ARED,AOLOD,AOLOC NAMELIST/LISTA/ORE,REDC,BOLL,AIR NAMELIST/LISTB/FEED,GANGO NAMELIST/LISTC/CQAL,AASH NAMELIST/LISTD/FLUX,GANGF NAMELIST/LISTE/BMOIS,TAIR,TNAT,VG&S,AHET,RTME,N1, N2 NA MELIST/LISTF/RX,RK NAMELIST/LISTG/RLEN,DIAM,FILL NAMELIST/L1STH/PAR1,PAR2,BURN,TLEN,REDP NAMELIST/LISTI/DOST,DI1,DL2,DUSTC C READING INPUT DATA FOR THE PROGRAM READ(5,10)ORE,REDC,DOLL,AIR READ (5,10) (FEED (I) ,1=1,3) READ(5,10) (GANGO (I) ,1=1,5) READ(5,10) (COAL(I) ,1=1,12) READ (5, 10) (AASH (I) ,1=1,6) READ(5,10) (FLUX (I) ,1=1,4) READ(5, 10) (GANGF(I) ,1=1,4) READ(5,10)RMOIS SEAD(5,10) (GAS (I) ,1=1,3) HEAD(5,10)8D0R,BDCL,BEDL READ(5,10) (RX(I) ,1=1,3) READ (5,10) (RK (I) ,1=1,3) READ(5,10)TAIR,TNAT 10 FORMAT(8G10.4) READ(5,10)VGAS,N1,N2 READ(5,10)AMET. I BEAD (5, 10)RTME READ (5,10)RLEN,DIAM,FILL 160 CALL FREAD(5,•REAL... •,PAR 1,PAR2,CORN,TLES,REDP) READ(5,10)AMAXL READ (5, 10) DUST,DL1 ,DL2, (DUSTC (I) ,1=1,3) READ (5,10) TSIN C READ COEFFTENTS OF SPECIFIC HEAT DO 15 1=1,25 READ (5, 10) AX (I) ,AY(I) ,AZ(I) ,AM(I) XG (T)=AX (I) /AM (I) YG (I) = AY (I)/AM (I) ZG (I)=AZ (I)/AM (I) 15 CONTINUE C READ STANDARD HEATS OF FORMATIONS DO 25 1=1,25 READ (5,31) HFORM (I) 31 FORMAT (F10.4) 25 CONTINUE READ (5,33) NUMB 33 FORMAT (11) C POLYNOMIAL COEFFICIENTS FOR DESCRIBING EMISSIVITY OF C02 DO 50 J=1,25 READ (4) (P(I,J) ,1=1,11) 50 CONTINUE C POLYNOMIAL COEFFICIENTS FOR DESCRIBING EMISSIVITY OF H20 DO 56 J=1,32 READ (4) (Q(I, J) ,1=1,11) 56 CONTINUE C COEFFIENTS OF THE POLYNOMIAL FOR THE REMOVAL OF VOLATILES C FROM COAL DO 30 K=1,7 HEAD (8) (GH (I,K) ,1=1,11) 30 CONTINUE WRITE(6,LISTA) WRITE(6,LISTB) WRITE(6,LISTC) WRITE(6,LISTD) WRITE(6,LISTE) WRITE(6,LISTF) WRITE (6,LISTG) WRITE (6,LISTH) WRITE(6,LISTI) C CALCULATION OF AREAS OCCUPIED BY GAS AND SOLIDS AS= (3. 1416*DIAH*DIAM/4.)*FILL AG= (3. 1416*DIAM*DIAH/4.)* (1.-FILL) CALL ANGLE (FILL,ALPHA) C CALCULATION OF DIFFERENT ARC LENGTHS CHORD=DIAM*DSIN(ALPHA/2.) ARCA=3.1416*DIAM*(1.- (ALPHA/ (2. *3. 1416) ) ) ARC8=3„1416+DIAM-ARCA C CALCULATION OF THE EFFECTIVE BEAMLENGTH FOR RADIATION RAD=DIAM/2. EL=0.9* (RAD+RAD*DCOS(ALPHA/2.)) AW=AS+AG ARCC=ARCA+ARCB PIN=.TRUE. PAN=.TRUE. TERM=454./(AS*3600.) ODUST=DUST*DUSTC(1) *TERM CDUST=DUST*DUSTC(2) *TERM ADUST=DUST*DOSTC (3) *TERM Ri1AS = ORE*2000. *454./(3600. *AS) OCOAL=BEDC*20Q0.*454./(3600.*AS) 1 6 1 ODOL=DCLL*2000.*454./(3600.*AS) ALEN=10.0 H«LOSS=0.0 RMETH=0.0 HWATER=0.0 RCOUNT=OCCAL*COAL(3) TOTNI=OCCAL*COAL(8) TOTCQ=CCCAL*COAL (5) TQTCD=OCCAL*COAL (1 1) TOTET=GCCAL*COAL (4) TOTPR=OCOAL*COAL(12) TOTHY=CCCAL*COAL(6) ROXYT=BBAS*0.3*FEED(1) ROXYN=ROXYT-(ROXYT*AMET) IOIF£=RMAS*FEED (1)*0.7 FLUXD=CDCL FLUXO=RMAS AR ED— FLO XO* FEE D (2) / (B1E"N*0. 5) AOLOD=FLUXD*FLUX(4) /(RLEN*0.5) AOLO=FLUXD*FLUX(1)*44./100.084FL0XD*FLUX(2) *44./84.32 AOLOC=ACLO/(BLEN*0. 333) SWCHV=.FALSE. SWCHR=.FALSE. SWCHM=.FALSE. SWCH=.TRUE, SHCC=.TB0E. SW2=.TB0E. FLUXO=BHAS CLFX=OCOAL FLUXD=ODOL CETH=CLFX*COAL(4)/(RLEN*0.333) CPRO=CL FX*COAL(12)/(RLEN*0 .333) FACT=FLUX (1) /FLUX (2) CALL AIRE (10. , ASK) GLEN=BP (N1) -BP (N2) VGAS=VGAS*0.472/(GLEN*AG) C INITIALISING VALUES OF THE DEPENDENT VARIABLES C ATT HE DISCHARGE END OF THE KILN Y (1) =BMAS- (FEED (2) *RMAS+AMET*RMAS*F£ED(1) *0. 3) -ODUST CCCN=RMAS*FEED(1)*0.3*AMET*REDP*12./16. CCON=CCCN+CCON*BURN Y (2) =OCOAL- (OCOAL* (COAL (2) +COAL (3) +COAL (4) +COAL (5) +COAL (6) +COAL (7) 1+CCAL(8)+COAL(11)+COAL (12)))-CCON-ADUST-CDUST Y (3) =ODCL- (ODOL*FLUX (4) +0DOL*FLUX(1) * (44./10 0.) +ODOL*FLUX (2) * (44./ 184,32)) N=14 DO 60 1=4,12 Y (I) =0.0 bO CONTINUE Y (4) =AIR*0.472*0.79*2 8./(AG*22. 4)> Y (5)= AIE*0.472*0.21*32./ (AG*22.4) Y(13)=TSIN Y(14)=20. DO 70 1=1,14 D(I)=Y (I) 70 CONTINUE RCHECK=CCOAL*COAL(2) U T fl E=R T M E/'B L E N SWCH'B=. TRUE, ANALYSIS CF THE SOLIDS AT THE DISCHARGE END SOBi:=aflftS*FEED (1) - H M A S * A H E I * F E E D(1) *0.3 -ODUST SOG=R!1AS*F2EC (3) FEED(2)=0,0 FEED (1)= S O R E / (SORE+SOG) FEED (3)= SCG/ (SORE + SOG) S.FC=OCGAL*COAL (1) -CCON-CDUST CSAS-=OCCAL*COAL (9) -ADUST CSUL=OCCAL*COAL(10) CSTO=SFC-+CSAS+CSUL COAL(1)=SFC/CSTO DO 220 1=2,8 COAL (I) =0.0 0 CONTINUE COAL (9)=CSAS/CSTO COAL(10)=CSUL/CSTO COAL(11)=0.0 COAL (12) =0.0 SCAG^FLUX ( 1 ) * O D O L * ( 1 . - (U4 . / 1 0 0 . ) ) SMGO=FLUX (2) *ODOL* (1. - (4 4 . / 8 4. 3 2) ) IF (OBO L . EQ. 0.0) GO TO 230 SDG=FLUX (3) *OD01 SGT-SCAC+SMGC+SDG F^UX (1)=SCAO/SGX F L U X (2) =SJ3GO/SGT FLUX (3) =SDG/SGT FLUX (4) =0.0 CONTINUE DIFFL=DL2-DL1 ODUST=ODUST/DIFFL CDUST=CDU5T/DIF?L A DUST= AC UST/DIFFL AIRC=AIR TS=200. RHBOA=0.0 RHVOLA=0.0 RHDO A=0. 0 RHREDA=0.0 HfiSTA=0. 0 RFSBA=0.0 RHEGA=0.0 GSWTA=0. 0 RHGASA=0.0 RhlVMA=0. 0 RHDRYA=0.0 AIBIA=BIAM TWAL=885. CALL PPPESS TW ALN=TWAL CALL H T E A T E CALL WALL (WI.O:SS,TS) TWAL=THALN DIST (1)=0.0 RD (1) =AMET*100. WATD(1)=0.0 C02D (1) =0.0 RND (1) =0.79 KOD ( 1) =0. 21 COD (1) =0.0 H D (1) = 0 . 0 T5D {1) = Y (13) TG D { 1) =Y (14) T al D (1) = T W A L N TCD ( 1) = TW ALN AIBD (1) =0.0 M= 1 E--.001 H=10.0 tf[lIN=0.0 1*H 0 X Y = 1 . - A f l E T W S I T 2 ( 6 , 2 4 0 ) 240 FJHMAT (» 1 « ,45X, • -- R E S U L T S — '////) ALEM=0.0 0 I N I = Y ( 1 ) * A S C I N I = Y (2) *AS DIN.I = Y (3) *AS C A L L HEATS WRIT£{6,630) A LEN , 01 N I , C I NI ,1)1 NI, Y (1 3) , Y ( 1 4 ) , TWAIN , TW AL , OX I , 1HWLOSS X = 0.0 500 C O N T I N U E M--M+ 1 DO 7 50 1=1,5 Z--X + H A L E N = Z RINT=Z-X C A L L O X I D E C A L L HEATS C A L L D ERIV C A L L BCUD C A L L R A T E C A L L P P R F S S C A L L A I R R ( R A I R ) C A L L DRYING C A L L BUSNT C A L L RAPR C A L L HBURN 200 CONTINUE C A L L H I R A T E C A L L WALL(WL0SS,TS) I F ( D A B S ( T W A L N - T W A L ) . L E . 2 . 0 ) G O TO 1400 TtfAL=TWALN GO TO 200 14 00 C O N T I N U E C A L L DRKC (N, X , Z , Y, F , H , HHIN, E , FTJNC ,G , S ,T) HWLOSS=HWLOSS*WLCSS*.RINT AIRC=AIR C+ RI NT *BAIR R H BOA = RH BOA + RHBO * R I N T * AS RHVOLA=BHVOLA+RHVOL*RINT*AS EHDOA=RHCCA+fiHDO*RINT*AS fi tf KE DA = RHR EDA + RH R E D * R I N T * A S HRSTA=HRSTA+HRST*RINT*AS R F S B A = R F S B A + R F S B * R I N T * A S RHEGA=RHBGA+RHBG*RINT*AG GSWTA-GSWTA+GSKT*RINT*AG ft FIG A S A = R H G A S A + E H G A 3 * fiIN T * A G EHVt'l A=H1IVNA + RH VM*RINT*AG RHDRYA=RHDRYA + R'HDRY*.RINT'-*AS I F ( X . G £ . AilAXL) SW2=.FALSE. I F {Y (13) o G B. 1 2 00.) S W 2 = • ." A L S E. ' •'- 164 1? (£ (1 3) . LE. 20. ) SW2 = . FAi.SE. CALL A N AIYS CALL DEGREE CALL CCNTCL DO 610 K=1, 14 D(K)=Y(K) 610 CONTINUE 750 CONTINUE XGK=Y( 1-4)+273. CPN=CP (14,YGK) C PCO = Cr (11,YGK) CPC02-=CP (12, YGK) CPO=CP(13,YGK) WRITE(6,770)CPN , C P C O fCPCQ2,CPO 770 FORMAT(4X,U(F6.4,2X)) IF(NUMB.NE.1)GO TO 666 CALL WRCTE 666 CONTINUE CALL CCRECT(Y (14) ,TWAIN,TC) DO 6 20 J=1,1 RS (J) = Y (J) *AS 52 0 CONTINUE » RITE (6 ,630) ALrtN, (RS(I) ,1=1 ,3) ,Y (13) , Y ( 1 4 ) ,TWALN,TS,TC,OXY,HWLOSS 6 3 0 F OR MAT ( 2 X, F 6 . 1 , 2 X , 3 (? 8. 1, 4 X) , 5 (F6 . I , 3X) , 1 X , F 6. 4 , 4 X , F 8 . 1 /) DJ c 5 0 J=4,12 3S (J) =Y (J) *AG 65 0 CONTINUE WRITE (o ,635) (RS(J) ,J=4,12) ,AI3C 635 FORMAT (2X,10 (F8. 1,4X)/) WUi'E (6, 640) (PPR (I) ,1=1,9) 640 FORMAT(8X,9(F5.2,4X)////) STORING VALUES FOR T H E PLOTS DIST (M) = ALEN TCD (M) =TC TSD(M) =Y (13) TGD (M) = Y (14) 'I D (M) '= T w A L N SdU = TS AIRD (M) •= R A13 RD (M)= (1.-OXY) * 100. R3D(M) =RC*10. ** (5) RVHD (M) =RVH RVCOD(M)=evco R7MD (M) = F:VM n'ATD (M) =PFR (6) C020 (K) = EFR (3) R21D (M)=PFR (1) h JD ( M) = PPR (2) COD (M) = PPB (4) E-1D (M)=PPR (9) 66C CONTINUE IF(.NOT.SW2)GO TO 555 GO TO 500 555 CONTINUE WRITE(6,570)RHBOA,SHVCLA,RHDQA,RHREDA,HRSTA,RKDRYA 570 FORM AT {4X,»RHBOA=»,F11. 1,2X, » R H V O L A = » , F 1 1 . 1,2X, 1R HDO A=', 1F11. 1,2X,'RHRED A=',F11. 1, 2 X , *HfiSTA= 1,F11. 1,2X, »R HDRY A=' , F 11 . 1) WRITE(6,58)RFSEA,RHBGA,GSWTA,RHGASA,RHVMA 58 FORMAT ( 3 X , ' R FS D A - 1 , F 1 1 . 1,2X, ' 3HBGA = ' ,1-1 1 . 1.,2X, «G5tfTA= ' , 1 F 1 1 . 1 , 2 X , 1 R H G A S A = ' ,F1 1 . 1 , 2 X , 1 R H V M A f ' , F i l . 1 ) 1 6 5 CALL PLATO (M) i CALL PLCTND (J STOP END ^ **************************** **** ************************************** c C THIS SUBROUTINE CAICULATES THE AVERAGE VALUE CF C DCP/CT FOR ORE, CCAL AND DOLOMITE C .~ ********************************************************************** SUBROUTINE DZEIV IMPLICIT REAL*8 ( A - H , C - Z ) COMKON/ANDY/XG (30) ,YG(30) ,ZG(30) COMHON/DCFS/DCPORE,ECECOA,DCPDOL C 0 M M 0 N / C G M M / R L E • J, D (14) ,ALEN,OXY C J MMCN/CC AD/FEED (3) , GANGO (5) CO i ' i i iON/C F A D / F L U X (4) ,GANGF (5) COMHON/CCAD/COAL(12) ,AASH (6) COMMO N/C FLUY/FLUXO,FL UXD COMMCN/S FE'C Y/F FQ , FE2G 3 , FE304 , FE C AVERAGE DCP OF ORE DT = D (13) +2"73. DCPGAN =GANGO (1) *DCP(3,DT) + G£NGO(2) *DCP(4,DT) +GANGO (3) *DCP(2 2,DT) • 1GANGC (4) *DCP {6, ET) +GANGO (5) *DCP (7,DT) 0CPOX=FE2O3*DCP (1,DT) +FE3C4*DCP (21,DT) + FEC *DC P (9 , DT) + FF;»DCP (8 , DT) DCPw=DCP (23,DT) : DCPOR E= r.CPOX*FEED (1) +CCPS*FEED (2) +DCPGAN'*FEED ( 3 ) C AVERAGE DCP OF COAL DCPA5H=AASH (1) *DCP (3,DT) + A A S H (2) *DGP (4,DI) + AASH (3) *DCP (22,DT) +AASH 1 (4) *DCP (9 r DT) + AASH (5) *DCP (6,DT) + AASH (6) *DCP (7,DT) DCPCOA=CCAL (1) *DCP (2,CT) +COAL (2) *DCP (23, DT) + COAL (3) *DCP (17, DT) +COA 1L (4) *DCP (16,DT) + CCAL (5) *DCP (11, DT) +COAL (6) *DCP { 1 5, DT) +COAL(7) *DCP ( 213,DT) +CCAL(8) *DCP(14,DT) +COAL(9) *DCPASH + COAL (10) *DCP (5,DT) +COAL (1 31) *DCP (12,DT) C AVERAGE DCP OF DOLOMITE IF (FLUXD.EQ.O.0)GO TO 99 1=19 J=20 IF (D ( 1 3 ) . G T . 6 50.) 1 = 6 IF (D (1 3) . G T . 5 0 0 . ) 1 = 7 DCP i)G-GAi'lGF (1) *DCP (3, ET) +GANGF (2) *DCP (4, DT) +GANGF (3) *DCP (22, DT) + GA, 1NG? ( 4 ) *DCP (9 , D T ) DCPDGL=FLUX ( 1) *DCP (I , ET) +FLUX (2) *DCP (J ,DT) + FI.UX (3) *DCFi}G+ FLU X (4) *D 1CP(23,BI) 2ETU3N 99 DCFDCL=0.0 R F.TU;\M END r ********************************************************************** C C * * * * * SUBROUTINE TO CALCULATE THE FRACTIONS OF DIFFERENT C * * * * * OXIDES PRESENT IN THE CHARGE C C *********#*#********#********#* ************************* ************** SUBROUTINE OXIDE IMPLICIT R E A L * 8 ( A - H , C - Z ) COMflCN/CCMM/RLr.N,D(14) , M E N , OXY COMMON/MISSED/POXYT,FCXYN,TOTFF COMMON/SPECY/FEO,FE203,FE304,FE 1 6 6 TERMA=TCTFE. TERMB=ECXYN IF ( O X Y . L T . O . 662) GO TC 40 I F ( O X Y . G T . 0 . 6 6 2 . A N D . O X Y . L E . . 8 8 3 ) G O TO 50 C THE SPECIES PRESENT ARE FE203,FE304 FEO=0.0 F3203=((TERMB/TERMA)-0.382) /0 .0477 FS304=(1.-FE203) FE=0.0 GO TO 100 C THE SPECIES PRESENI ARE FE304 AND FEC 50 FE2O3=0.0 FE304= ( (TERMB/TERMA)-0 .2865) /0 .09 55 FEC=1.-FE304 FE=0.0 GO TC 100 C SPECIES PRESENT ARE FEO AND FE 40 FE2O3=0.0 FE3O4=0.0 FEO=((TERMB/TERMA)/0.2865) F E= 1 . - F E C 100 CONTINUE RETURN END C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C C THIS SUBROUTINE CALCULATES < THE AVERAGE SPECIFIC C HEATS CF ORE, COAI AND DOLOMITE C Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * SUBROUTINE HEATS IMPLICIT REAL*8 ( A - H , C - Z ) COMMON/CCAD/FEED(3) ,GANGO (5) COMMON/CFAD/FLUX(4),GANGF(5) COHHON/CCAD/COAL(12) ,AASH(6) CCMMCN/SPECY/FEO,FE20 3,FE30 4 ,FE COMMON/CCMM/RLEN,D(14),ALEN,OXY COMMON/CFS/CPOBE,CPCOAL,CPDOL COMMON/OFLUX/FLUXO,FLUXD C AVERAGE CP OF ORE TO=D (13) +273. CPGANG = GANGO (1)*CP(3,TO)+GANGO(2)*CP(4,TO)+GANGO(3)*CP(22,TO)+GANG 10(4) *CP (6,TO) +GANGO (5) *CP (7,TC) CPOX = FE203*CP (1,TO)+FE304*CP (21,TO)+FEO*CP(9,TC)+FE*CP(8,TO) CPW = CP (23,TO) CPORE=CPCX*FEED (1)+CPW*FEED(2)+CPGANG*FEED(3) C SPECIFIC HEAT OF COAL TC = D (13)+273. CPAS H= A ASH (1) *CP (3,TC) +AASH (2) *CP (4, TC) +A ASH (3) *CP (2 2,TC) +AASH (4) * 1 CP (1 ,TC) +AASH (5) *CP (6,TC) +AASH (6) *CP (7,TC) CPCOAL=CCAL (1) *CP (2,TC) +COAL (2) *CP (23,TC) +COAL (3) *CP (17,TC) + COAL (4 1) *CP (16,TC) +COAL (5) *CP(11,TC) +COAL(6) *CP (15,TC) + CCAL(7) *CP(13 ,TC) + 2COAL (8) *CP(14 ,TC) +COAL (9) *CPASH+COAL (10) *CP (5,TO) +COAL (11) *CP (12,1 3C) C AVERAGE SPECIFIC HEAT OF DOLOMITE I F ( F L U X D . E Q . 0 . 0 ) G O TO 99 TD=D (13) +273. 1=19 J=20 IP(D(13) .GT.65C.)I=6 I D / IF(D(13) .GT.500.) J=7 CPDG=GANGF (1) *CP (3,TD) +GAUGF (2) *CP (4,TD) +GANGF (3) *CP (22,TD) +GANGF ( 14)*CP(9,TD) CPDOL=FLUX (1) *CP (I,TD) + FLUX (2) *CP(J,TD) +FLDX (3) *CPDG+FLUX (4) *CP (23 1,TD) RETURN 99 CPDOL=0.0 RETURN END (2 ************************************** C C ****CALCULATICN OF HALL TEMPERATURE ****** C Q ********************************************************************** SUBROUTINE WALL (WLCSS,TSUR) IMPLICIT REAL*8 (A-H,C-Z) LOGICAL PIN,PAN COMMON/A SC/CHO ED,ARCA,ARCE,ARCC COMHON/AREAS/AW, AS, AG COMMCN/CCMM/RLEN,D(14),ALEN,OXY COMMON/TFMP/TWAL,TWALN COMMON/HTCOEF/HCVGSC,HRGSC,HRHSC,HCWSC,HCVGWC,HRGWC, HCVWAC COMMON/THICK/RX (3) , RK (3) ,AIDIA COMMON/SWITCH/PIN,PAN IF (. NOT. PAN) GO TO 10 TOUTC=15. TAMBIC=TSUR TDIFF= (TAMBIC-TOUTC)*1.8 HTCON=0.000135*1.69 STEFAN=1.355D-12 TOUTK=TCUTC*273. TAMBK=TAMBIC+273. HTRAD=0.9*STEFAN*(TOUTK**4-TAMBK**4)/(TOUTK-TAMBK) HTSA=HTRAD+HTCON R0=AIDIA/2. R1 = R0+RX (1) R2=R1+BX (2) R3=B2+BX (3) RESA=(B1-B0)/(3.1416*BK (1) * (B1 + R0) ) RESB = ( (E2-B1) / (3. 1416*RK (2) * (R2+R1)) ) RESC=1./(HTSA*2.*3. 1416*R3) HWAOC=1./ (RESA + HESB+RESC) 10 CONTINUE PAN=.FALSE. C CALCULATION OF HEAT LOSS FROM OUTSIDE TO AMBIENT CONDITION C CALCULATION OF WALL TEMPERATURE HGWOC=HCVGWC+HRGWC HWSOC=HRWSC+HCWSC TWALN= (HGWCC*ARCA*D(14) +HRWSC*CHORD*D(13) +HWAOC*TOUTC + 1HCWSC*ABCB*D(13))/(HGWCC*ARCA+HRWSC*CHORD+HWAOC+HCWSC*ARCB) WLOSS=HWAOC*(TWAL-TOUTC) TSUR=HWACC*(TWAL-TOUTC)*RESC+TOUTC RETURN END Q ********************************************************************** C c ***** SUBROUTINE TO CALCULATE THE RATE OF PRODUCTION **** c ***** CF C02 AND H2G FROM BURNING COMBUSTIBLES **** C 168 £ ****************************************** SUBROUTINE E APR IMPLICIT REAL*8 (A-H,0-Z) COMMCN/PROD/EPC02,RPH2O COMMON/CCMBR/RBCO, REH,REM,RBE, RBP,RBO RPCO2=RBCO*44./28.+RBM*4 4./16.+RBE*88./30.+RBP*132./44. RPH2C=RBH*18./2.+RBM*36./16.+RBE*54./30.+RBP*72./44. RETURN END C ********************************************************************** c c ***** SUBROUTINE TO CALCULATE THE RATES CF COMEUSTION *** c ***** OF THE VARIOUS COMBUSTIBLE SPECIES ***** C ********************************************************************** c 90 SUBROUTINE BURNT IMPLICIT REAL*8 (A-H,0-Z) REAL*8 ME CO MMON/CCMM/RLEN, D (14) ,ALEN,OXY COMMON/CCMBR/RBCO,RBH,EEM,RBE,RBP,RBO COMMON/BUD/RC,RO,RC02,RCO,RCB COMMON/RATES/RNIT,RMOI ,RME,RET,RPR,ROX,RHGAS COMMON/AREAS/AM,AS,AG COMMGN/DELT/RINT COMMON/VCLT/RVH,RVCO,RVC02,RVM,RVE,RVP,RVN,RVT,RHO,RCM CONV=AS/AG CO = D (7)+RCO*RINT*CGNV+RVCO*RINT*CONV H2=D(12)+SVH*RINT*CCNV ME=D (8)+RVM*CONV*RINT+RME*RINT ET=D (11) +RVE*CONV*RINT+RET*RINT Pfi=D (10) +RVP*RINT*CONV + RPR*EINT CB=RCB*BINT*CONV OXYG=D (5)+ROX*RINT IF ( (OXYG/32.) .LT. (CB/12.))GO TO 90 OXYG=OXYG-CB*32./12. CHECK TO SEE WHETHER OXYGEN PRESENT IS SUFFICIENT TO BURN CARBON MONOXIDE IF ( (OXYG/16.).LT. (CO/28.))GO TO 100 RBCO=CC OXYG=OXYG-RBCO*16./28. IF ( (OXYG/16.).LT. (H2/2.))GO TO 110 RBH=H2 OXYG=OXYG-RBH*16./2. IF ( (OXYG/64.) .LT. (ME/16.)) GO TO 120 RBM=ME 0XYG=0XYG-RBM*6U./16. IF((OXYG/112.),LT.(ET/30.)) GO TO 130 RBE=ET OXYG=OXYG-RBE*112./130. IF ( (OXYG/160.) .LT. (PR/44.)) GO TO 140 *BP=PR GO TO 999 RC B=OX YG* 1 2. * A G/ (Rl NT * 3 2 . *AS) RBCO=0.0 RBH-=0. 0 RBM=0.0 RBE=0.0 RBP=0. 0 1 6 9 GO TO 9 9 9 100 RBCO=(CXYG/16.) *28. RBH=0.0 EBH=0.0 RBE=0.0 HBP=0. 0 GO TO 9 9 9 110 EBH= (OXYG/16.) * 2 . RBM=0.0 R8E=0.0 RBP=0.0 GO TO 9 9 9 120 RBM=OXYG*16./64. RBE=0.0 RBP=Q.O GO TO 9 9 9 130 RBE=OXYG*30./112. RBP=0.0 GO TO 9 9 9 140 aBP=OXYG*4U. /160 . 9 9 9 CONTINUE RBO=RBCC*16./2 8.+RBH*16./2.+RBM*64./16. +RBE*112./30.+RBP*160 . / 4 4 . RBCO=RECO/RINT RBH=fiBH/RINT RBM=RBM/RINT RBE-=RBE/RINT EBP=RBP/RINT R BO= RBO/RINT RETURN END Q ********************************************************************** C c * * * * * SUBROUTINE TO CALCULATE THE EMISSIVITY CF THE GAS C * * * * * EMISSIVITY VALUES ARE CALCULATED USING THE POLYNOMIAL c * * * * * EQUATIONS CALCULATED BEFOREHAND C Q ********************************************************************** c c c SUBROUTINE EMIT (TG,EM) IMPLICIT BEAL*8 ( A - H , 0 - Z ) COMMON/CCMM/RLEN,D(14),ALEN,OXY COMMON/EPAR/EL,DIAM COMMON / P O L Y / P (11,25) , Q (11,32) COMMON /PBESS/PPR(9) C CALCULATION OF EMISSIVITY FOR CARBONDIOXIDE DIMENSION A (25) ,B (32) DATA A/5., 3 . ,2. , 1 .5, 1 . , 0 . 8 , 0 . 6 , 0 . 4 , 0 . 3 , 0.2, 0 . 1 5 , 0 . 1 , 0 . 0 8 , 0 . 0 6 , 0 . 0 4 1 , 0 . 0 3 , 0 . 0 2 , 0 . 0 1 5 , 0 . 0 1 0 , 0 . 0 0 8 , 0 . 0 0 6 , 0 . 0 0 5 , 0 . 0 0 4 , 0 . 0 0 3 ,0 .00 2/ DATA B / 2 0 . , 1 0 . , 5 . , 3 . , 2 . , 1 . 5 , 1 . 2 , 1 . 0 , 0 . 8 , 0 . 6 , 0 . 5 , 0 . 4 , 0 , 3 , 0 . 2 5 , 0 . 20, 10. 15 ,0 . 12 ,0 . 10 ,0 . 0 8 , 0 . 0 7 , 0 . 0 6 , 0 . 0 5 , 0 . 0 4 , 0 . 0 3 5 , 0 . 0 3 , 0 . 0 2 5 , 0 . 0 2 , 0 . 0 1 25 , 0 . 0 1 2 , 0 . 0 1 , 0 . 0 0 7 , 0 . 0 0 5 / FEL=EL/30.54 TGR=TG EX= (TGR/4500 . )*4 .625 PCL=FEI*FPR (3) I F ( T G R . L T . 5 2 5 . ) G O TO 70 IF ( P C L . G T .5. ) GO TO 50 IF ( P C L . L T . 0 . 0 0 2 ) GO TO 70 DO 55 J= 1,25 JK=J+1 IF (PCI. LE. A (J) .AND.PCI.GT. A (JK) ) GO TO 40 55 CONTINUE 50 WRITE(6,60) 60 FORMAT (1X,'THE VALUE OF PCL EXCEEDS 5 FEET-ATMOSPHERES') CALL EXIT 70 EMCO=0.0 GO TO 101 40 Y = P {1, J) +EX* (P (2,J) +EX* (P (3,J) + EX* (P (4, J) +EX* (P (5, J) + EX* (P (6, J) +EX 1*(P(7,0) + EX*(P(8,J)+ EX*(P (9, J) + EX* (P (10, J) +EX* (P (11, J) ) ) ) ) ) ) ) ) ) ) EMCO = DEXP(2.303* ({Y/4.894)-2.5229)) C EMISSIVITY FCR HATER VAPOUR 101 PCLW = PPR (6) *FEL IF (PCLK . GT. 20. ) GO TO 90 IF (TGR.IT. 525.)GO TO 100 IF (PCLW.LT.0.005) GO TO 100 DO 110 1=1,32 IJ=I+1 IF (PCLW. LE. B (I) . AND.PCLW.GT. B (IJ) ) GO TO 120 110 CONTINUE 90 WBITE(6,130) 130 FORMAT (IX,'THE VALUE OF PCL EXCEEDS 20 FEET ATMOSPHERES *) CALL EXIT 100 EMW=0.0 GO TO 140 120 YW = Q(1,I) +EX*(Q(2,I) +EX*(Q(3,I) + EX*(Q(4,I) + EX*(Q(5,I) +EX* (Q (6,1) +2 1X*(Q(7,I)+EX*(Q(S,I)+EX*(Q(9,I) +EX* (Q (10, I) +EX* (Q (11, I) ) ) ) ) ) ) ) ) ) ) EMW=D£XP (2. 303* ( (YH/4.894) -2. 154 9) ) 140 E M=£ MCC + EM S RETURN END C c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c c C*****FUNCTION SUBROUTINE TO CALCULATE THE SPECIFIC **** C*****HEATS CF INDIVIDUAL COMPONENT **** C Q ********************************************************************** c c FUNCTION CP(I,T) IMPLICIT REAL*8 (A-H,C-Z) COMMON/ANDY/XG(30) , YG (30) ,ZG (30) CP=XG (I) +YG (I) *T/10.**3+ (ZG (I) *10.**5/ (T**2) ) RETURN END Q ********************************************************************** C c ***** FUNCTION SUEROUTINE TO CALCULATE THE DERIVATIVE **** c ***** OF THE SPECIFIC HEATS C Q ********************************************************************** c c FUNCTION DCP(I,T) IMPLICIT REAL*8 (A-H,0-Z) COMMON/ANDY/XG(30),YG(30) ,ZG(30) DCP=YG ( I ) * 10.**(-3)-ZG (I)*2.*10.**5/ (T**3) RETURN 1 7 1 END C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c C*****SUBROUTINE TO CALCULATE THE ANGLE SUBTENDED BY * * * * * C * * * * * S O L I D S AT THE CENTRE * * * * * C C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c c C HERE NEWTON RAPHSON ITERATIVE TECHNIQUE IS USED IN C THE CALCULATIONS SUBROUTINE ANGLE (F,ALPHA) IMPLICIT REAL*8 ( A - H , C - Z ) PI=3.1416 N0IT=6 NIT=1 ANGO=PI/2. TOL=1.E-03 10 ALPHA= ANGO-((DSIN(ANGC) +2.*PI*F-ANG0)/(DCOS(ANGO) -1 . ) ) IF (DABS (ALPHA-ANGO) . L E . T O L ) GO TO 20 ANGO=ALP HA NIT=NIT+1 IF (NIT.LE.NOIT) GO TO 10 WRITE (6,30) 30 FORM AT (1X,* THE NUMBER OF ITERATIONS EXCEEDS 6') CALL EXIT 20 CONTINUE RETURN END Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c c * * * * * SUBROUTINE TO CALCULATE THE RATE OF BOUDOURD * * * * * c * * * * * flNE gATE CF REDUCTION REACTION * * * * * C C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * SUBROUTINE BOUD IMPLICIT REAL*8 ( A - H , C - Z ) LOGICAL SWCHB,SHCHV,SHCHM,SWCHR,SWCC COMMCN/CCMM/RLEN,D(14),ALEN,OXY COMMON/BUD/RC,R0,RCO2,ECO,RCB COMMON/TWITCH/SWCHB,SWCHV,SWCHM,SHCHR,SWCC COMMON/AREAS/AW,AS,AG COMMON/ADJUST/PARI,PAR2,REDP,BURN,TLEN TSK=D(13)+273. IF (. NOT.SWCHB) GO TO 40 8=1.-OXY AMC=0.253 A M F E = 0 . 7 6 3 HC=0.519D18 AP=3.14D-3 TERMA= (-20360./TSK) +20.97 AKB= DEXP (TERMA) TERKB= ( 2 1 0 5 . / T S K ) - 2 . 5 2 5 AKR=DEXP(TERMB) PC020= ( (2. +AKB) -DSQRT (4 . *AKB+AKB**2) ) / 2 . PC02F=AKR/ (AKR + 1.) TERMC=HC*AMC*DEXP ( -86000. / ( 1. 987*TSK) ) / ( 8 2 . * T S K ) TSRMD=0.0448*AMFE*AP*(1 . -R)*DEXP(-7250 . / (1 .987*TSK)) TERME= FCC2F*(TERMD+TEEMC*PC020) TERMF= (TERMD + PC02F*TEEMC) 172 PC02=TERME/TERMF PC0=1.-FCC2 BC=TER MC*(PC02-PC020) *12. R0=TERMD*16.*(PC02F-PCC2) /PC02F RCO=RC*28./12. RC02=0.0 RCB=RC*EURN IF(D(13) . L E . 850.) ECB=C. 0 BETUBN 40 CONTINUE RCO2=0.0 RCO=0.0 RC=0.0 RO=0.0 RCB=0.0 RETURN END Q ***************************************** c c * * * * * SUBROUTINE TO CALCULATE THE PARTIAL PRESSURE CF THE C GASES IN THE FREE EOARE C rj * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c c SUBROUTINE PPRESS IMPLICIT REAL*8 ( A - H , 0 - Z ) DIMENSION PR (9) COMMON /FRESS/PPR(9) CO MMCN/CCMM/RLEN,D(14) ,ALEN,OXY PR (1) = D (4) / 2 8 . PR (2) =D (5) / 3 2 . PR (3) =D (6) / 4 4 . PR (4)=D (7) /28 . PR (5) = D (8) / 1 6 . PR (6) =D (9) / I 8. PR (7) =D (10) / 4 4 . PR(8)=D(11)/30. PR (9)=B (12)/2 . SUMPfi=0.0 DC 10 1=1,9 10 SUMPR=SUMPR*PR(I) DO 20 1=1,9 20 PPR (I) =PB (I) /SUMPR RETURN END C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c c * * * * * CALCULATION OF VARIOUS HEAT TRANSFER TERMS * * * * * * C c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C c SUBRCUTINE HT R ATE IMPLICIT REAL*8 ( A - H , C - Z ) COMHON/ARC/CHORD,ABCA,ARCB,ARCC COMMCN/CCMM/RLEN,D(14),ALEN,OXY COMMCN/PRESS/PPB(9) COMMCN/GASHTR/GCVS,GRS,GCVW,GRH,GSWT,RHVM 1 7 3 COMMCN/EPAR/EL,DIAM COMMON/AREAS/AH,AS,AG COMMON/HTCOEF/HCVGSC,HRGSC,HRWSC,HCWSC,HCVGWC,HRGWC,HCVWAC COMMON/HTRFER/HCVGS,HRGS,HRWS,HCWS,HRST COMMON/TEMP/TWAL,TW ALN COMMON/BANG/CVGS,RAGS,CVGW,RAGW,CDWS,RAWS COMMCN/EMISS/EMI5,AESS,ABSW C HEAT TRANSFER BY CCNVECTICN FROM GAS TO SOLIDS GSFLUX=(D(4) + D (5) +D (6)+D(7) +D(8) + D(9) +D (10)+D (11)+D (1 2) ) * (AG/AW) TKELS=D (13) +273. TKELG=D (14) +273. TKELW=TWAL+273. HCVGSC=0.000135*0.05* ( (GSFLUX/0.0001352)**0.67) HCVGS=HCVGSC* (CHORD/AS) * (D (1 4) -D (13) ) C HEAT TRANSFER BY RADIATION FROM GAS TO SOLIDS SIGHA=1.355D-12 TR ANS= D (13)*1. 8 + 492, T R A N G= D (14) * 1. 8 + 492. TRANW=TWAL*1.8+492. CALL EMIT (TRANG,EMIS) CALL EMIT(TRANS,AESS) EMIS=EMIS+0.0 A8SS=ABSS+.0 HRGSC=SIGMA*(EMIS*TKELG**4-A3SS*TKELS**4) / (TKELG-TKELS) liRGS=HEGSC* (CHORD/AS) * (C (14) -D (13) ) C HEAT TRANSFER FROM WALL TO SOLIDS BY RADIATION FU=0.9 HRWSC=SIGMA*FU*(TKELW**4-TKELS**4)/(TKELW-TKELS) HRWS = HEWSC* (CHORD/AS) * (TWAL-D (13) ) C HEAT TRANSFER BY CONDUCTION FROM WALL TO SOLIDS HCWSC=5.*HCVGSC HCWS=HCWSC* (CHORD/AS) * (TWAL-D (13) ) C HEAT TRANSFER EY CONVECTION GAS TC WALL HCVGWC=HCVGSC C HEAT TRANSFER BY RADIATION GAS TO WALL CALL EMIT (TRANW, ABSW) ABSW=ABSW+0.0 HRGWC=SIGMA*(EMIS*TKELG**4-ABSW*TKELW**4)/(TKELG-TKEL W) C HEAT TRANSFERRED FROM GAS TO SOLIDS BY CONVECTION C AND RADIATION GCVS=HCVGSC*(CHORD/AG)* (D (14) - D (1 3) ) GRS= HRGSC* (CHORD/AG)*(D(14) -D(13) ) C HEAT TRANSFERRED FROM GAS TO WALL BY CONVECTION C AND RADIATION GCVW=HCVGWC* (ARCA/AG) * (D(14)-TWAL) GRW=HRGWC* (ARCA/AG) * (D (14)-TWAL) GSWT=GCVS+GRS+GCVW+GRW CVGS=HCVGS*AS RAGS=HRGS*AS CVGW=GCVW*AG RAGW=GRW*AG CDWS=HCWS*AS RAWS=HRWS*AS RETURN END Q *#*******************************^ c C*****SUBEOUTINE TO CALCULATE THE VOLUMETRIC RATE OF * * * C*****MOISIURE REMOVAL FROM , ORE,DOLOMITE AND VOLUMETRIC * * * C * * * * * R A T E CF CALCINATION OF DOLOMITE 174 c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * . * * * * * c c c SUBROUTINE DRYING I M P L I C I T REAL*8 (A-H,0-Z) LOGICAL SHCHB,SWCHV,SWCHM,SWCHR,S8CC C0MMCN/CCMM/BLEN,D(14),ALEN,OXY COMMON/TWITCH/SWCHB,SMCHV,SWCHM,SWCHB,SWCC COMMGN/DUSTS/ODUST,CODST,ADUST,DL1,DL2 COMMON/SDUSTS/EODT,RCET,RADT COMMCN/DRYR/ORED,DOLOD,DOLOC COMMON/MISSIN/ARED,AOLOB,AOLQC I F (SWCHB)GO TO 50 ORED=ARED DOLQD= AGLOD DOLOC=AOLOC GO TO 999 50 ORED=0.0 DOLOD=C.0 DOLOC=0.0 999 CONTINUE I F (ALEN.GE.DL1.AND.ALEN.LT.DL2)GO TO 500 RODT=0.0 RCDT=0.0 BADT=0.0 RETURN 500 CONTINUE DELTAL=BI2-DL1 RODT=ODUST*2.*(ALEN-DI1)/DELTAL RCDT=CDUST*2.*(ALEN-D11) /DELTAL RABT=ADUST*2.*(ALEN-DL1)/DELTAL RETURN END Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C C ****SUBROUTINE TO CALCULATE THE VOLUMETBIC RATE ******** C ****QF AIR AND NATURAL GAS SUPPLY ********* C C Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * SUBROUTINE AIRR (RAIR) I M P L I C I T REAL*8 (A-H,G-Z) LOGICAL SWCH DIMENSION B P ( 1 1 ) COMMON/HYC/CETH,EPRO COMMON/DISTAN/BP COMMON/CCMM/RLEN,D(14),ALEN,OXY COMM0N/LAST/AIR,RHOIS,VGAS,GAS(3),N1,N2 COMMON/RATES/RNIT,RMOI,BME,RET,RPR,BOX,RRGAS COMMON/AMBI/TAIR,TNAT COMMON/DELI/RINT COMMON/SW/SWCH COMMON/AREAS/AW,AS,AG CALL AIRE (ALEN,AIR) AIR1=AIR ALEN=AIEN+RINT CALL AIRE (ALEN,AIR) AIR2=AIR HAIR- ( A I R 1 + A I B 2 ) / 2 . 175 ALEN=ALEN-RINT AIR=RAIR AIR= (AIR*0.472)/AG RNIT=AIR*28.*0.7 9/22.4 ROX=AIR*32.*0. 21/22. U IF (ALEN. LT.BP (N2) .OB. ALEN.GE. BP (N1) ) GO TO 50 RME=VGAS*16.*GAS(1)/22.4 R3T=VGA S*GAS(2) *30./22.4 RPR=VGAS*GAS(3) *44./22.4 GO TO 99 50 RM£=0.0 RET=0.0 RPR=0.0 GO TO 99 99 RMOI=0.0 HIG H T= 273. TAI=TAIR+273. TNA=TNAT+273. RHGAS=RNIT*ENT(HIGHT,TAI,16)+EOX*ENT (HIGHT,TAI,13)+RM£*ENI (HIGHT, T 1 N A , 1 7) +EET*ENT(HIGHT,TNA,16) +RPR*ENT(HIGHT,TNA,18) RETURN END C C C ****THIS SUBROUTINE CALCULATES THE RATE EXPRESSION FOR ********* C ****VOLATILES AND MOISTURE FROM COAL ***** C Q ********************************************************************** c SUBROUTINE RATE IMPLICIT REAL*8 (A-H,0-Z) DIMENSION Z{7) LOGICAI SWCHB,SHCHV,SSCHM,SWCHR,SWCC COMMCN/VCLT/BVH,RVCO,RVC02,EVM,RVE,RVP,RVN,RVT,RHO,RCM COMMCN/CCMM/ELEN,D(14),ALEN,OXY COMMON/TWITCH/SWCHB,SWCHV,SWCHM,SHCHR,SWCC COMMON/CL/CLFX,UTME COMMON/HYC/CETH,CPRO COMMON/RNEW/TOTNI,TOTCO,TOTCD,TOTET,TOTPR,TOTHY COMMON/FILE/GH(11,9) COMMON/DELT/RINT COMMCN/DEGR/RMAS,RMETH,RCCUNT,RWATEfi,RCHECK IF (.NOI.SHCC) GO TO 190 ACN=0.0 ACO=0.0 ACD=0.0 A£T=0.0 APR=0. 0 AHY=0.0 SWCC=.FALSE. 190 CONTINUE A=((3500.-ALEN)*.091428)-25. AB=A/20. AM = D(13)/(9.*10.) IF (. NOT. SHCHV) GO TO 50 IF(D(13).LT.250.)GO TO 50 DO 10 1=1,5 2 (I) =GH (1,1) + AB* (GH (2,1) +AB* (GH (3,1) +AB* (GH (4,1) + AB* (GH (5,1) +AB* (G 1 H (6,1) + AB* (GH (7,1) +AB* (GH (8,1) +AB* (GH (9,1) +AB* (GH (10 ,1) + AE* (GH (11 , 2 1 ) ) ) ) ) ) ) ) ) ) ) 10 CONTINUE IF(D(13) .LE.250.) Z (1) =0.0 IF(D(13) .LE.250.)Z(2)=0.0 IF (D (13) .LE. 310.) Z (3) =0.0 IF(D(13) .LE.360.) Z (U) =0.0 I F (D (1 3) .LE.4 50.) Z (5) =0.0 WRITE(6,15)ALEN,D(13) ,CLFX,UTME, (Z (I) ,1=1,5) 5 FORMAT (1X,9 (E12. 5,2X) ) RVH=D£XP (2. 303* (Z (4) /2„) )*1.D-6*CLFX*UTME RVCO=DEXP (2. 303* (Z (2) /2.) ) * 1. D-6*CLFX*OTME RVC02=DEXP(2. 303*( Z ( 1 ) / 2 . ) ) * 1.D-6*CLFX*UTME RVM=DEXP (2.303* ( Z ( 3 ) / 2 . ) ) * 1.D-6*CLFX*UTME RVN=DEXP (2. 303*(Z(5)/2.))*1.D-6*CLFX*UTME RHO=RVH* (16./2.) RVE=CETH RVP=CP,RO IF (.NOT.SWCHR) GO TO 20 RVH=0.0 GO TO 60 20 CONTINUE RHO=0.0 GO TO 60 50 EVH=0.0 RVCO=0.0 RHO=0.0 RVCO2=0. 0 RVM=0.0 RVE=0.0 RVP=0.0 RVN=0.0 RVT=0.0 60 IF (. NOT.SWCHM) GO TO 80 IF (AM. IT. 1.75) GO TO 80 DO 70 M=6,7 Z (M) =GH (1,M) +AM* (GH (2 , M) + A M* (GH (3 , M) «-AM* (GH (4 , M) + AM* (GH (5,M) +AM* (G 1 H (6, M) +AM* (GH (7,M) +AM*(GH(8,M) +AM* (GH (9,M) + AM* (GH (10,M) + AM* (GH (1 1 , 2 M ) ) ) ) ) ) ) ) ) ) ) 70 CONTINUE M=6 IF (D (13).GE. 360..AND.C(13) .LT.525.)M=7 IF (D (13) .LT. 150. .OR.D (13) .GE.525.) GO TO 80 RCM=Z(M)*0.210D-2*CLFX*DTME GO TO 99 80 RCM=0.0 CONTINUE IF (ACN.GE.TOTNI) SVN = 0.0 IF (ACO.GE.TOTCO) RVCO=0.0 IF (ACD.GE.TOTCD)RVCO2=0.0 IF (AET.GE.TOTET) RVE=0.0 IF (APR.GE.TOTPR) RVP=0.0 IF (AHY.GE.TOTHY) RVH=0.0 ACN=ACN+FVN*RINT ACO = ACQ + RVCO*RINT ACD = ACD • RVC02*RINT AET = AET + RVE*RINT APR = APE + RVP*RINT AHY = AHY + RVH*RINT RVT=RVH+RVCO+RVC02+RVK+RVE+RVF+RVN RETURN END 1 77 C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c C ****SUBBOUIINE TO CONTROL THE SWITCHES IN THE PROGRAM * * * * * * * * C c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c SUBROUTINE CONICL IMPLICIT RE AL*8 ( A - H , C - Z ) COMMON/ABJDST/PAR1,PAR2,REDP,BURN,TLEN CQMMCN/COMM/RLEN,D(14),ALEN,OXY COMMON/TWITCH/SWCHB,SKCHV,SWCHM,SWCHR,SWCC LOGICAL SWCHB,SWCHV,SWCHM,SWCHR,SWCC COMMON/DELT/RINT COMMON/VCLT/RVH,RVCO,BVC02,RVM,RVE,RVP,RVN,RVT,RHO,RCM COMMGN/DEGR/RMAS,RMETH,BCOUNT,RWATER,RCHECK RMETH=RMETH+RVM*RINT RW ATEk=RWATER+RCfi*BINI IF (OXY.GE.REDP) GO TO 10 SWCHB=.TRUE. SWCliV= . FALSE. SWCHR=.FALSE. SWCHM=.FALSE. RETURN 10 SWCHB=.FALSE. SWCHB=.TRUE. IF (OXY.GE.1.)SWCHR = . F A L S E . IF (RMETH. GE. RCOUNT) GO TO 20 SWCHV=.TRUE. GO TC 30 20 SWCHV=.FALSE. 30 IF (RWATFR.GE.RCHECK) GC TO 40 SWCHM=.TEUE. RETURN 40 SWCHM=.FALSE. RETURN END C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C C ****3UEROUTINE TC CALCULATE THE OXYGEN REMAINING * * * * * * * * C * * * * I N THE CEE OXY * * * * * * C Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * SUBROUTINE DEGREE IMPLICIT REAL*8 ( A - H , 0 - Z ) COMMCN/VCLT/RVH,RVCO,RVC02,RVM,RVE,RVP,RVN,RVT,RHO,RCM COMMCN/CCMM/RLEN,D(14),ALEN,OXY CO MMON/HISSED/ROXYT,RCXYN,TOTFE COMMON/DELT/RINT COMMON/BUD/BC,BO,BC02,BCO,RCB ROXYN=ROXYN+BINT*RO+RHO*RINT OXY=ROXYN/ROXYT RETURN END 2 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 3 * * * * * FUNCTION SUBROUTINE TO CALCULATE THE ENTHALPY * * * * * * * * * 2 * * * * * DIFFERENCE BETWEEN TWO DIFFERENT TEMPERATURES * * * * * * * * * * 2 * * * * * CF ANY COMPONENT * * * * * * * * * * ; ********************************************************************* 1 78 FUNCTION ENT (TI,TF,I) IMPLICIT REAL*8 (A-H,0-Z) COMMON/ANEY/XG (30) , YG (30) ,ZG (30) 2NT=XG (I) * (TF-TI) +YG (I) *. 5* (TF**2-TI**2) *10.** (-3) +ZG (I) * ((1 1- (1./TF) ) *1.D5 RETURN END /TI) C ****SUBROGTINE TO CALCULATE NET HEAT GENERATED IN THE ******** c * * * * B E D A N C THE FREE EOAR £ THROUGH DIFFERENT REACTIONS ******* Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * SUBROUTINE HBURN IMPLICIT REAL*8 (A-H,0-Z) DIMENSION AX (30) , AY (30) ,AZ (30) COMMON/COMBR/RBCO,REH,RBM,RBE,RBP,RBO COMMCN/CPST/AX,AY,AZ COMMON/CAMG/FACT COMMON/REACT/HFORM(30) COMMON/DRYR/ORED,D0LCD,D0L0C C0MMCN/BUD/RC,R0,RC02,RC0,RCB COMMON/BCRS/RHBO,RHVOL,RHDO,RHDRY,RHRED, RHBG, RFSB COMMCN/VCLT/RVH,RVCO,RVC02,RVM,RVE,RVP,RVN,RVT,RHO,RCM COMMON/ADJUST/PAR1,PAR2,REDP,BURN,TLEN COMMON/CCMM/RLEN,D(14),ALEN,OXY COMMON/AREAS/AW,AS,AG T=D(13) FAC2=1.0 IF (ALEN.GE.TLEN)GO TO 20 FAC =PAR1- ( (PAR1-PAR2)*ALEN/TLEN) GO TO 30 20 CONTINUE FAC=0.0 30 CONTINUE REAC10=540. REAC11=0.0 R2AC12=-11333. REAC13=-11060. CALL HFUNCT(1. CALL HFUNCT(1. ,1.,12,2.,11,0.,25,T,BEAC1) ,1. , 11, 1.,8,1.,12,I,REAC2) CALL HFUNCT(1.,19,0.,25,1.,6,1. , 12, T , REAC3) CALL HFUNCT(1.,20,0.,25,1.,7,1.,12,T,REAC4) CALL HFUNCT(1.,11,0.5,13,1.,12,0.,25,T,REAC5) CALL HFUNCT (1.,2,1.,13,1.,12,0.,25,T,BEAC6) CALL HFUNCT(1.,17,2.,13,1.,12,2.,24,T,REAC7) CALL HFUNCT (1.,1,3.,15,2.,8,3.,24,T,REAC8) CALL HFUNCT(1.,15,0.5,13,1.,24,0.,25,T,REAC14) REAC9=FACT*REAC3+(1.-FACT)*REAC4 RHBO=(REAC 1/12.) *RC RHRSD= (RFAC2/16.)*RO+RHO*(REAC8/48.) RHDO=(REAC9/44.) *DOLOC KH DRY= REAC10*(ORED + DOLOD + RCM) RHV0L=REAC11*RVT RHCOBB=REC0*(REAC5/28.)*(1.-FAC)+ RCB*(REAC6/12.)*( 11.-FAC2) *AS/AG RHBG=RHCCBB + FBH*(REAC 14/2,)+RBM*(REAC7/16.)+REE*REAC 112 + RBP*RFAC13 1 7 9 RFSB=RBCC*(REAC5/28 . )*FAC*AG/AS+RCB*(REAC6/12 . )*FA 1C2 RETURN END Q ***************************************** C C * * * * T H I S SUBROUTINE CONTAINS THE DIFFERENTIAL EQUATIONS * * * * * * C * * * * THIS IS AN EXTERNAL FUNCTION FOR EKC * * * * * C Q ********************************************************************** c c SUBROUTINE FUNC(X,Y ,F) IMPLICIT REAL*8 ( A - H , 0 - Z ) DIMENSION Y (1) , F (1) COMMON/EDUSTS/RODT,RCDT,RABT COMMON/BUB/RC,RO,RC02,ECO,RCB COMMCN/DRYR/ORED,DOLCE,EOLOC COMMON/VCLT/RVH,RVCO,RVC02,RVM,RVE,EVP,RVN,RVT,RHO,RCM COMMCN/BCRE/RHBC,RHVOI,RHDO,EHDRY,RHRED,RHBG,RFSB COMMON/RATES/RNIT,£MOI,RME,RET,RPR,ROX,RHGAS COMMON/CCMBR/RBCO,RBH,REM,RBE,RBP,RBO COMMON/CCMM/BLEN,D (14) ,OXY,ALEN COMMON/HTRFER/HCVGS,HRGS,HBWS,HCWS,HBST COMMCN/PRCD/RPC02,RPH2O COMMON/AEEAS/AH,AS,AG CO MM ON/CO AD/FEED (3) ,GANGO (5) COMMON/CFAD/FLUX (4) ,GANGF (5) COMMON/CCAD/COAL (12) , A A S H (6) COMMON/CES/CPORE,CPCOAL,CPDOL COMMON/DCPS/DCPORE,DCFCOA,DCPDOL COMMON/GASHTE/GCVS,GES,GCVW,GRW,GSHT,EHVM CONV=AS/AG HRST=HCVGS+HRGS+HR¥S+HCWS C EQUATIONS DESCRIBING THE MASS BALANCE T2=D (1 3) +273. T1=273. RHVM=RVN*C0NV*ENT(T1,T2,14)+(RVCO2+DOLOC)*CONV* 1£NT(T1 ,T2,12) + (RCO+EVCC) *CONV*ENT(T1,T2 ,11) + (ORED + 2DOLOD+RCM) *CONV*ENT(T1,T2,24)+EVH*CONV*ENT(T1,T2,15) 3+RVM*CCNV*ENT(T1,T2 ,17)+BCB*CONV*ENT(T1,T2 ,12)*44 . /12 . 4+ RHO*ENT ( T 1 , T 2 , 2 4 ) * ( 1 8 . / 1 6 . ) F(1) =CRED+RO + RHO + RODT F (2)=RC+FCM+RVT+ECB+RCDT+RADT+RHO*2./16. F (3)=DCLCD+DOLOC F (4) =RNIT+RVN*CONV F(5) =ROX-REO-RCE*32.*CONV/12. F(6)=RVCC2*CCNV+EPC02+DCLOC*CONV+RCB*CONV*44./12. F(7) =RCO*CCNV+BVCO*CONV-RBCO F(8)=RVM*CONV+RME-RBM F(9) =RPH2C+RMOI+(ORED + DOLOD + RCM) *CCNV+RHO*CONV*18./16. CONV=AS/AG F (10)=RPR+RVP*CONV-BEP F (12) = RVH*CONV-EBH CALL HEATS F(11)=RVE*CONV-EBE+RET CALL DERIV C EQUATIONS DESCRIBING THE HEAT BALANCES C TQLD=D (14)+273. 180 F(13)= ( (EHBO+RHVOL+RHEO+RHDRY+RHRED-HRST+RFSB)- (Y (13)* (F (1)*CPORE I + F (2) *CECOAL+F (3) *CPDOL) ) )/( (Y(1) *DCPORE+Y (2) *DCPCOA+Y (3) +DCPDOL) 2*Y (13) + (CPORE*Y (1)+CPCOAL*Y (2)+CPDOL*Y (3) )) PRGDCP=Y<4) *DCP(14,TOLD) + Y(5) *DCP (13, TOLD) +Y (6) *DCP (12,TOLD) +Y (7) * 5DCP (11,TOLD) + Y (8) *DCP (17,TOLD) +Y (9) *DCP (24,TOLD) + Y (10) *DCP(18,TOLD 2) +Y (11) *DCP (16,TOLD) + Y (12) *DCP (15,TOLD) PRCPDG=CF(14,TOLD) *F (4) +CP(13,TOLD) *F (5) +CP (12,TOLD) *F(6) +CP (1 1 ,TC 1LD) *F(7) +CP (17,TOLD) *F (8) +CP (24,TOLD) *F (9) +CP (18,TOLD) *F (10) +CP (16 2,TOLD) *F (11) +CP (15,TOLD) *F (12) PRCPG=Y (4) *CP (14,TOLD) +Y (5) *CP (13,TOLD) + Y (6) *CP (12,TOLD) +Y(7) *CP (1 II ,TOLD) +Y (8) *CP(17,TOLD) +Y (9) *CP(24,TOLD) + Y (10) *CP (18,TOLD) +CP (16, 2TOLD)*Y{11) + Y(12) *CP(15,TOLD) R DHG=RODT*(D(14)-D(13))*CPORE+(RCDT+RADT)*CPCOAL* 1 (D(14) -D (13) ) F(14)=((-RHBG-GSWT+RHGAS+BHVM-RDHG)-Y(14)*PRCPDG)/(PRCPG+PRGDCP* 1Y(14)) RETURN END Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c c ***** SUBROUTINE TO CALCULATE THE COMPOSITION OF SOLIDS ******** C rj ********************************************************************** C SUBROUTINE ANALYS IMPLICIT REAL*8 (A-H,C-Z) COMMCN/CCAD/FEED(3) ,GANGO(5) COMMON/CFAD/FLUX (4) ,GANGF (5) COMMON/EDUSTS/RODT,RCDT,RABT COMMON/CCAD/COAL(12),AASH(6) COMMON/VCLT/RVH,RVCO,RVC02,RVM,RVE,RVP,RVN,RVT,RHO,RCM COMMCN/DRYR/ORED,DOLCE,DOIOC COMMON/BUD/RC,RC,RC02,RCO,BCB COMMCN/COMM/ELEN,D(14) ,ALEN,OXY COMMON/CAMG/FACT COMMON/DELT/RINT C CALCULATION OF THE NEW ORE COMPOSITION HAEM=FEED (1) *D (1)+RO*RINT+RODT*RINT+RHO*RINT OREM=FEED (2) *D (1) +ORED*RINT OREG=FEED (3) *D (1) ORET=HAEM+OREM+OREG FEED (1)=HAEM/OEET FEED (2)=OREM/ORET FEED(3)=CREG/ORET C C CALCULATION OF THE NEW DOLOMITE COMPOSITION CAC=FLUX (1) *D (3) +DOLCC*FACT*RINT MGC=FLUX (2)*D (3)+DOLOC*(1.-FACT)*RINT FG=FLUX (3) *D (3) FM = FLUX (4) *D (3) +DOLOD*RINT FT=CAC+MGC+FG+FM FLUX(1)=CAC/FT FLUX (2) =MGC/FT FLUX(3) = FG/FT FLUX(4)=FM/FT C C CALCULATION OF THE NEW COAL COMPOSITION CFC=COAL (1)*D(2) +RC*RINI+RCDT*5INT+RCB*RINT CFM=COAL (2)*D(2)+RCM*RINT CME=COAL (3)*D(2)+RVM*SINT CET=COAL (4) *D (2) •RVE*RINT CCO=COAL (5) *D{2) +RVCO*RINT CN=COAL (8) *D (2)+RVN*RINT CHY=CCAL (6)*D(2)+RVH*EINT+RHO*RINT*2./16. CO=COAL (7) *D (2) CASH=COAL ( 9 ) *D (2) +RADT*RINT CS=COAI (10) *D (2) CC02=COAL (11) *D (2) +RVC0 2*RINT CPR=COAL (12) *D (2) +RVP*RINT CT=CFC+CFM*CME+CET+CC0+CHY*CC+CN+CASH+CS+CCO2+CPR COAL ( 1 ) =CFC/CT COAL (2) = C F M / C T COAL (3) = C M E / C T COAL (4)=CET/CT COAL (5) = C C O / C T COAL ( 6 ) = C H Y / C T COAL (7)=CO/CT COAL(8)=CN/CT COAL (9)=CASH/CT COAL ( 1 0 ) = C S / C T COAL (1 1) = C C 0 2 / C T COAL ( 1 2 ) = C P R / C T RETURN END C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C * C * SUBROUTINE F O R PRINTING SEVERAL USEFUL VALUES C * Q ************************************** SUBROUTINE WROTE IMPLICIT REAL*8 (A -H,C -Z ) COMMON/BUD/RC,RO, F C 0 2,RCO,RCB COMMON/BANG/CVGS,RAGS,CVGW,RAG«,CDWS,RAWS COMMON/DRYR/ORED,DOLCC,DOLOC COMMON/VCLT/HVH,RVCO,EVC02,RVM,RVE,RVP,RVN,RVT,aHO,ECM COMMCN/ECRE/RHBO,RHVOI,RHDO,RHDRY,RHRED,RHBG, RFSB COMMON/RATES/RNIT,RMOI,RME,RET,RPR,ROX,RHGAS COMMCN/CCMBR/RBCO,REH,REM,RBE,RBP,RBO COMMON/CCMM/RLEN,D(14),ALEN,OXY COMMON/HTCOEF/HCVGSC,HRGSC,HRWSC,HCWSC,HCVGWC,HRGWC,HCVWAC COMMON/CCAD/FEED (3) ,GAMGO(5) COMMON/CFAD/FLUX(4) , G 8 N G F (5) COMMON/CCAD/COAL(12) ,AASH (6) COMMCN/CPS/CPORE,CPCOAL,CPDOL COMMON/DCPS/DCPORE,DCPCOA,DCPDOL COMMCN/SPECY/FEC,FE203,FE304,FE COMMON/EMISS/EMIS,ABSS,ABSW J=6 WRITE (J,5)ALEN 5 FORMAT ( 4 X , * A L E N = , , F 6 . 1 , * CMS') WRITE(J,10)RC,RO,RCB 10 FORMAT (4X,•RC=•,E12.5,2X,«RO=»,E12.5,2X,•RCB=•,E12.5) WRITE (0,20)ORED,DOLOD,DOLOC 2 0 FORMAT (4X,»OEED=•,E12.5,2X,'DOLOD=»,E12.5,2X,•DOLOC= 1,E12 . 5) WRITE(J,30)RVT,RCM,RHC 3 0 FORMAT (4X,•RVT=•,E12.5,2X,'RCM=1,E12. 5,2X,•RHO=• , E12. 5) 1 WRITE(0,40)RHBO,RHVOL,RHDO,RHDRY,RHRED,RHBG,RFSB 4 0 FORMAT(4X,» RHB0=',E12.5,2X,»RHV0L=»,E12.5,2X,*RHDO=»,E12.5,2X, 1'RHDRY=',E12.5/4X,'RHRED=»,E12.5,2X,•RHBG=•,E12.5,2X,'RFSfi=», WRITE(J ,50)RNIT,RMOI,RME,RET,RPR,ROX,RHGAS 50 F O R M A T ( 4 X , « R N I T = • , E 1 2 . 5 , 2 X , ' B M O I = • , E 1 2 . 5 , 2 X , » R M E = • , E 1 2 . 5 , 2 X , 1 , R E T = , , E 1 2 . 5 , 2 X , , R P R = , , E 1 2 . 5 , 2 X , • R O X = 1 , E 1 2 . 5 , 2 X , • R H G A S = • , 2E12.5) WRITE(J ,60)RBCO,BBH,REM,RBE,RBP,BBO 60 FORMAT (4X ,•RBCO=' ,E12 .5 ,2X ,*RBH = « ,E1 2 . 5 , 2 X , 1 R B M = ' , E 1 2 . 5 , 2 X , 1'R BE= ' , E 1 2 . 5 , 2 X , ' R B P = « , E 1 2 . 5 , 2 X , ' R B O = ' , E 1 2 . 5 ) WRITE(J,70) HCVGSC,HRGSC,HBWSC,HCWSC,HCVGWC,HRGWC 70 F O K M A T ( 4 X , • H C V G S C = 1 , E 1 2 . 5 , 2 X , ' H R G S C = ' , E 1 2 . 5 , 2 X , • H R W S C = • , E 1 2 . 5 , 12X, • H C W S C = ' , E 1 2 . 5 , 2 X , • H C V G W C = « , E 1 2 . 5 , 2 X , ' H R G W C = * , E 1 2 . 5 ) WRITE(J,75)CVGS,RAGS,CVGW,RAGW,CDWS,RAWS 75 FORMAT (1X,6E12.5) WRITE(J , 80) (FEED (I) ,1=1,3) 80 F O R M A T ( 4 X , ' O R E ' , 4 X , 3 ( F 5 . 3 , 2 X ) ) WRITE(J,90) (COAL (I) ,1 = 1 , 12) 90 F O R M A T ( 4 X , * C O A L ' , 4 X , 12(F5. 3, 2X)) WRITE ( J , 100) (FLUX (I) ,1=1,4) 100 F O R M A T ( 4 X , » D O L O M I T E * , 4 X , 4 ( F 5 . 3 , 2 X ) ) WRITE ( J , 1 1 0 )CPCRE , C P C C A L,CPDOL 110 F O R M A T ( 4 X , • C P O R E = • , F 6 . 3 , 2 X , ' C P C O A L = « , F 6 . 3 , 2 X , ' C P D O L = » , F 6 . 3 ) WRITE(J,120) DCPORE,DCPCCA,DCPDOL 120 FORMAT ( 4 X , • D C P O R E = • , F 6 . 3 , 2 X , 1 D C P C O A L = • , F 6 . 3 , 2 X , ' D C P D O L = • , F 6 . 3 / / ) WRITE(J ,130)FE 2 C 3 ,F E 3 C 4 ,F £ 0 , F E 130 F O R M A T ( 4 X , • F E 2 0 3 = « , F 4 . 2 , 2 X , » F E 3 0 4 = • , F 4 . 2 , 2 X , • F E O = ' , F 4 . 2 , 2 X 1 , » F E = « , F 4 . 2 ) WRITE (J ,140)EMIS,ABSS,ABSW 140 FORMAT ( 4 X , • E M I S = • , F 5 . 3 , 2 X , • A B S S = » , F 5 . 3 , 2 X , • A B S W = » , F 5 . 3 ) RETURN END Q *************************************************************** C * C * SUBROUTINE TO CALCULATE THE AIR RATE C * Q ************************************************************** SUBROUTINE AIRE(ALENS,AIRS) IMPLICIT REAL*8 ( A - H , 0 - Z ) DIMENSION BD(11) ,BP(11) ,EA(11) ,AA(11) COMMON/SW/SWCH COMMON/DISTAN/BP NAMELIST/TNP/BD,BA LOGICAL SWCH IF (.'NOT. SUCH) GO TO 750 READ(5,710) (BD(I) ,1=1,11) EEAD(5,710) (BA (I) ,1=1 ,11) 710 FORMAT (8F10. 1) A=50. SUM=0.0 DO 720 1=1,11 SUM=SUM + BD ( I ) 720 CONTINUE BP(1)=SUM DO 730 1=2,11 BP (I) =BP (1 -1)-BD (1-1) 730 CONTINUE DO 740 1=1,11 AA (I) =BA (I) /BD (I) 740 CONTINUE WRITE (6,60) (BP (I) ,1=1,11) , (BD (I) ,1=1,11) , ( A A(I) ,1=1,11) 60 FORMAT(1X,11F8.2/) 1 8 3 WRITE (6,TNP) S W C H=.FALSE. 750 CONTINUE IF (ALENS. GT. BP (1) ) GO TO 900 IF(ALENS.IT.BP(1).ANE.AIENS.GE. (BP (2) +A))GO TO 999 755 CONTINUE DO 760 J=2,10 IF (ALHNS.LT. (BP (J)+A) . ANE. ALENS. GE. (BP (J)-A) ) GO TO 780 IF (ALE NS. LT. (BP (J) -A) . ANE. ALENS. GE. (BP (J+1)+A) ) GO TO 790 760 CONTINUE IF(ALENS.IT.(BP(11)+ A).AND.ALENS.GT.(BP(11)-A))GO TO 800 IF(ALENS.LT. (BP(11)-A))GO TO 900 780 AIRS=AA (J- 1) - (AA (J-1) - AA (J) ) * (BP (J) + A-ALENS) / (2. *A) RETURN 790 AIRS = AA (J) RETURN 800 AIRS=AA (10) - (AA (10) -AA (11) ) * (BP (11) + A-ALENS) / (2. *A) RETURN 999 AIRS = AA(1) RETURN 900 AIRS=0.0 RETURN END Q *************************************** c * C * PLOTTING SUBROUTINE C * Q ****************************************************************** SUBROUTINE PLATO (M) IMPLICIT REAL*8 (A-H,C-Z) DIMENSION TSD (100) ,T8E (100) ,TGD (100) ,DIST (100) , AIRD (1 00) , TCD (100) DIMENSION RD (100) ,RBD (100) ,RVHD (100) ,RVCCD(100) ,RVMD (100) DIMENSION WATD (100) ,C02B (100) /END (100) ,ROD (1 00) , SHD (100) DIMENSION COD (100) ,HD (100) , RAID (100) COMMON/PARAM1/RD,RBD,RVHD,RVCOD,RVMD,SHD COMMCN/PAPAM2/WATD,CC2B,RND,RCD,COD,HD,RATD COMMON/PARAM/TSD,TWD,TGE,TCD,DIST,AIRD M=M- 1 RBD (1) = RED (2) " SiiD (1) =SHD (2) XMIN=0.0 YMIN=0.0 DX=5.0 DY=350. DO 10 0=1,K DIST(J) =((DIST(M)-DIST(J))/ (DX*100.))+1.5 TSD (J) = ( (TSD (J) -YMIN) /DY) +2.0 TGD (J) = ( (TGD (J) -YMIN) /DY) +2. TWD (J) = ( (TWD (J) - YMIN) /DY) +2. 0 SHD (J) = ( (SHD (J)-YMIN) /DY) +2.0 TCD (J) = ( (TCD (J) -YMIN) /DY) +2. 0 RD (J) = ( (RD(J) - 0.0) /20.) + 2.0 RBD (J) = ( (RBD (J) -0.) /3.) +2. 0 WAID(J)= ( (WATD (J) -0.0)/0. 2) +2.0 C02D (J) = ( (C02D (J) -0.0)/0.2) +2.0 BSD (J)= ( (RND (J) -0.0) /0. 2) +2.0 ROD(J)= { (ROD (J) -0.0) /0. 2) +2.0 COD (J) = ( (COD (J) -0.0) /0. 2) +2. 0 HD (J) = ( (HD (J) - 0.0) /0. 2) + 2.0 AIRD (J) = AIR D (J) +2. 0 1 0 C O N T I N U E C A L L X A X I S C A L L A X I S ( 1 . 5 , 2 . 0 , ' TEMPERATURE {DEG C ) 1 , 1 9 , 5 . , 9 0 . , Y M I N , D Y ) C A L L S Y M B C L ( 3 . , 6 . , 0 . 2 1 , ' S O L I D TEMPERATURE PROFILE',0 . , 2 5 ) C A L L S I N G (DIST,T S D , M, 1) C A L L P I C T ( 1 2 . , 0 . , - 3 ) X A X I S A X I S ( 1 . 5 , 2 . 0 , ' T E M P E R A T U R E ( D E G C ) • , 1 9 , 5 . , 9 0 . , Y M I N , D Y ) S Y M B O L ( 3 . , 6 . , 0 . 2 1 , ' G A S T E M P E R A T U R E P f i O F I L £ ' , 0 . , 2 3 ) S I N G ( D I S T , T G D , M , 1) S I N G ( D I S T , T C D , M , 1) P I C T ( 1 2 . , 0 . 0 , - 3 ) X A X I S A X I S ( 1 . 5 , 2 . T E M P E R A T U R E ( D E G C ) • , 1 9 , 5 . , 9 0 . , Y M I N , D Y ) S Y M B O L ( 3 . , 6 . , 0 . 2 1 , ' W A L L T E M P E R A T U R E P R O F I L E * , 0 . , 2 4 ) S I N G ( D I S T , T W D , M , 1 ) S I N G ( D I S T , S H D , M , 1 ) P I C T ( 1 2 . , 0 . , - 3 ) X A X I S 184 C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L A X I S ( 1 . 5 , 2 . , 'AIR RATE (SCFM/CM) » , 1 8 , 5 . , 9 0 . , 0 . , 1 . 0 ) S I N G ( D I S T , A I R D , M , 1 ) P L C T ( 1 2 . , 0 . , - 3 ) XAXIS A X I S ( 1 . 5 , 2 . , » P E R C E N T A G E R E D U C T I O N ' , 2 0 , 5 . , 9 0 . , 0 . , 2 0 . ) S I N G ( D I S T , R D , M , 1 ) C A L L C A L L P L C T ( 1 2 . , 0 . , - 3 ) C A L L X A X I S C A L L A X I S ( 1 . 5 , 2 . , ' R A T E O F B O U D O U R D R E A C T I O N (GM C / C . C M / S E C 1) ' , 4 0 , 5 . , 9 0 . , 0 . , 3 . ) C A L L S I N G ( D I S T , R B D , M , 1 ) C A L L P I C T ( 1 2 . , 0 . , - 3 ) C A L L X A X I S C A L L A X I S ( 1 . 5 , 2 . , ' P A R T I A L P R E S S U R E S O F F R E E B O A R D G A S E S ' 1 , 3 7 , 5 . , 9 0 . , 0 . , 0 . 2 ) C A L L S I N G ( D I S T , E N D , M , 1 ) S I N G ( D I S T , C 0 2 D , M , 1 ) S I N G ( D I S T , C O D , M , 1) S I N G ( D I S T , 8 A T D , M , 1 ) S I N G ( D I S T , R O D , M , 1) S I N G ( D I S T , H D , M , 1 ) S Y M B O L ( D I S T ( 5 0 ) , ( W A T D ( 5 0 ) + 0 . 5 ) , 0 . 1 4 , ' H 2 0 • , 0 . , 3) S Y M B O L ( D I S I ( 3 5 ) , ( C 0 2 D ( 3 5 ) + 0 . 5 ) , 0 . 14 , • C O 2 • , 0 . , 3) S Y M B O L ( D I S T ( 3 5 ) , (BHD ( 3 5 ) + 0 . 5) , 0 . 1 4 , » N 2 • , 0 . , 2 ) S Y M B O L ( D I S T (4 0 ) , ( R O D ( 4 0 ) + 0 . 5 ) , 0 . 1 4 , » 0 2 ' , 0 . , 2) S Y M B O L ( D I S T ( 3 0 ) , ( C O D ( 3 0 ) + 0 . 5 ) , 0 . 14 , • C O ' , 0 . , 2 ) S Y M B O L ( D I S T ( 5 5 ) , ( H D ( 5 5 ) + 0 . 5 ) , 0 . 1 4 , ' H 2 » , 0 . , 2 ) C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L C A L L R E T U R N E N D C * S U B R O U T I N E F O R P L O T T I N G A X I S S U B R O U T I N E X A X I S I M P L I C I T E E A L * 8 ( A - H , C - Z ) X M I N = 0 . 0 D X = 5 . 0 C A L L A X I S ( 1 . 5 , 2 . 0 , ' D I S T A N C E F R O M C H A R G E E N D 1 0 . , X M I N , D X ) C A L L P L C T ( 1 . 5 , 7 . 0 , 3 ) C A L L P L C T ( 9 . 5 , 7 . 0 , 2 ) C A L L P L C T ( 9 . 5 , 2 . 0 , 2 ) C A L L P L C T ( 1 . 5 , 2 . 0 , 3 ) R E T U R N ( M E T R E S ) » , - 3 3 , 8 . , 1 8 5 END C * SUBROUTINE TO CONVERT DOUBLE PRECISION TO SINGLE FOR PLOTTING SUBROUTINE SING ( A X , A Y , H , N ) RSAL*8 AX (M) , AY (M) DIMENSION SX (100) , SY (100) DO 10 J= 1 , M SX (J) =SNGL (AX (J) ) SY (J) = SNGL (AY (J) ) 10 CONTINUE CALL LINE (SX,SY,M,N) RETURN END C SUBROUTINE TO CALCULATE HEAT OF REACTION AS A FUNCTION OF TEMP SUBROUTINE H F U N C T ( A , I J , E , J K , C , K L , D , L M , T , R E A C ) IMPLICIT EEAL*8 ( A - H , 0 - Z ) DIMENSION AX (30),AY (30) ,AZ(30) COMM ON/REACT/HFOR.M (30) COMMCN/CPST/AX,AY,AZ T2=T+273. T1=298. TliRM 1= (D*AX (LM) +C*AX (KL) - A * A X (IJ) -B*AX (JK) ) TERM2 = (D*AY(LM) +C*AY (KL)-A*AY ( I J ) - B * A Y ( J K ) ) TEflM3= ( D * A Z (IM) +C*AZ (KL) - A * A Z (IJ) - B * A Z (JK) ) H0= (D+HFORH (LM) +C*HFORM (KL) - A * HFORM (IJ) -B*HFORM (JK) ) BEAC =(T2-T1) *(TERM1+(TERM2*(T2 + T 1 ) / 2 . ) * ( 1 0 . * * (-3)) + 1 (TER83/ (T2*T1) ) * ( 10 . * * (5) ) ) +H0 RETURN END Q ********************************************************************* c C CONVERTING GAS TEMPERATURES TG BARE THERMOCOUPLE VALUE Q ***************************************** SUBROUTINE CORECT(TG,TH,TCN) IMPLICIT REAL*8 ( A - H , C - Z ) CGMKON/HTCOEF/HCVGSC,HRGSC,HRWSC,HCWSC,HCVGWC,HRGWC,HCVWAC C O M M O N / E M I S S / E M I S , A B S S , A B S W ET=0.8 SIGMA=0. 1355D-11 TGK=TG+273. TWK=TW+273. TCO=TGK-20. NOIT=10 N= 1 15 CONTINUE TCOR=1.8*TCO CALL EMIT (TCCR,EMT) F X = ( ( S I G M A * ( ( 1 . + E T ) / 2 . ) * ( E M I S * T G K * * 4 - E M T * T C 0 * * 4 ) ) - (3IGM A* ET* 1 ( .TCO**4-TWK**4)))* (1./HCVGSC) +TGK-TCO F D X = ( ( S I G M A * ( ( 1 . + E T ) / 2 . ) * ( - 4 . * E M T * T C O * * 3 ) ) - ( S I G M A * E T * (4 .*TCO**3) 1))*( 1 . / H C V G S C ) - 1 . TCN=TCC-FX/FDX IF (DABS (TCN-TCO) . L E . 5.) GO TO 99 TCO=TCN I F ( N . G E . N C I T ) G O TO 200 •N=N+1 G O TO 15 99 CONTINUE TCN=TCN-273. RETURN 200 WRITE(6, 110)NOIT 1 8 6 110 FORMAT (1X, 'NO OF ITERATIONS EXCEEDS' ,2X,12) RETURN END A P P E N D I X I I IMPORTANT DATA USED IN THE MODEL C o m p o s i t i o n o f F o r e s t b u r g c o a l F i x e d C a r b o n 4 2 % M o i s t u r e 3 1 % M e t h a n e 4% E t h a n e 0 . 6 % C a r b o n m o n o x i d e 6% H y d r o g e n 1% N i t r o g e n 0 . 6 % A s h 1 0 % S u l p h u r 0 . 3 % C a r b o n d i o x i d e 4 . 0 % P r o p a n e 0 . 5 % C o m p o s i t i o n o f A n t h r a c i t e c o a l F i x e d c a r b o n 7 4 . 6 % W a t e r 7 .4% M e t h a n e 1 . 3 % C a r b o n m o n o x i d e 2% H y d r o g e n 0 . 3 % N i t r o g e n 0 . 2 5 % As h 1 2 . 4 % S u l p h u r 0 . 4 5 % C a r b o n d i o x i d e 1 . 3 % 187 188 C o m p o s i t i o n o f L i g n i t e c o a l F i x e d c a r b o n 3 7 % M o i s t u r e 3 6 % M e t h a n e 3% E t h a n e 0 . 3 % C a r b o n m o n o x i d e 5% H y d r o g e n 1% N i t r o g e n 0 . 6 % A s h 1 0 % S u l p h u r 0 . 3 % C a r b o n d i o x i d e 6.6% P r o p a n e 0 . 2 % C o m p o s i t i o n o f G r i f f i t h p e l l e t s H e m a t i t e 9 5 . 5 % M o s i t u r e 1.4% G a n g u e 3 . 1 % T h e same c o m p o s i t i o n h a s b e e n u s e d f o r F a l c o n b r i d g e p e l l e t s R e d u c i b i l i t y p a r a m e t e r f o r t h e o x i d e p e l l e t s A p f o r G r i f f i t h p e l l e t s = 3 . 1 4 3 ( 1 0 " 3 ) A p f o r F a l c o n b r i d g e p e l l e t s = 6.20 ( I O - 3 ) T h e a c t i v a t i o n e n e r g y E R f o r b o t h p e l l e t s 7 2 5 0 c a l / m o l C a r b o n c o n c e n t r a t i o n i n t h e b e d I r o n c o n c e n t r a t i o n i n t h e b e d M c = 0 . 2 5 3 'Fe 0 . 7 6 3 C o m p o s i t i o n o f N a t u r a l G a s M e t h a n e E t h a n e P r o p a n e 9 6 . 3 % 3 .2% 0 . 5 % P i l o t k i l n d i m e n s i o n s L e n g t h = 3 5 . 0 m I n t e r n a l D i a m e t e r - 2.1 m e t e r s I n n e r r e f r a c t o r y o f 23 cms t h i c k ( w i t h t h e r m a l c o n d u c t i v i t y o f 3.1 x 1 0 " 3 c a l / c m . s e c . °C ) O u t e r r e f r a c t o r y o f 5 cms t h i c k ( w i t h t h e r m a l c o n d u c t i v i t y o f 4 . 9 9 x 1 0 _ l f c a 1 / c m . s e c . °C ) G r i f f i t h k i l n d i m e n s i o n s L e n g t h - 125 m e t r e s I n t e r n a l D i a m e t e r - 6 m e t r e s R e f r a c t o r y 23 cms t h i c k w i t h a t h e r m a l c o n d u c t i v i t y o f 2 . 5 1 4 ( 1 0 " 3 ) c a 1 / c m . s . °C 190 S p e c i f i c H e a t D a t a ' C p = x + y T ( 1 0 - 3 ) + z ( 1 0 + 5 ) T - 2 w h e r e C i s s p e c i f i c h e a t i n c a l / m o l , T, t e m p e r a t u r e i n ° K a n d p x, y , z a r e c o e f f i c i e n t s S u b s t a n c e X y z F e 2 0 3 2 3 . 4 9 1 8 . 6 • -3.5.5 C a r b o n ( g r ) 4.10 1 . 02 - 2 . 1 0 S i l i c a 1 3 . 3 8 3.68 - 3 . 4 5 A l 2 0 3 2 7 . 38 3.08 - 8 . 2 0 S u l p h u r 3.58 6.24 0.0 CaO 1 1 . 8 6 1 .08 -1 . 66 MgO 1 0 . 1 8 1 .74 -1 .48 F e ( r ) 1 .84 4.66 0.0 FeO 1 2 . 3 8 1 .62 - 0 . 3 8 CO 6.79 0.98 -0.11 C 0 2 1 0 . 5 5 2.16 - 2 . 0 4 0 2 7.16 1 .00 -0.4 N 2 6.66 1 .02 0.0 H 2 6.52 0.78 0.12 C H 4 5.65 11 .44 - 0 . 4 6 C a C 0 3 2 4 . 9 8 5.24 - 6 . 2 0 M g C 0 3 1 8 . 6 2 1 3.80 - 4 . 1 6 FeaO,, 21 .88 4 8 . 2 0.0 H 2 0 1 5 . 70 5.40 0.0 H 2 0 ( 1 ) 1 8 . 0 3 0.0 0.0 H 2 ° ( g ) 7.17 2.56 0.08 1 - F r o m M e t a l l u r g i c a l T h e r m o c h e m i s t r y by K u b a s c h e w s k i et a i . , 4 t h E d i t i o n . 

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