UBC Theses and Dissertations

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UBC Theses and Dissertations

Comparison of two fouling probes Fetissoff, Peter Eugene 1982

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COMPARISON OF TWO FOULING PROBES by P e t e r Eugene F e t i s s o f f B . A . S c , 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 , 1978 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Depar tmen t o f C h e m i c a l E n g i n e e r i n g ) 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 t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA M a r c h , 1982 (c) P e t e r Eugene F e t i s s o f f , 1982 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Cj-|gnA\C&L fcAJG )AlggftlMG The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date frftDL () i q S X DE-6 (3/81) i i ABSTRACT S t u d i e s o f h e a t e x c h a n g e r f o u l i n g a r e c o n v e n i e n t l y c a r r i e d o u t u s i n g s m a l l s c a l e p r o b e s . The p r o l i f e r a t i o n o f p robe d e s i g n s has r a i s e d t he q u e s t i o n o f w h e t h e r r a d i c a l l y d i f f e r e n t p r o b e s g i v e c o m p a r a b l e r e s u l t s . In t h i s w o r k , t h e p e r f o r m a n c e o f two f o u l i n g p r o b e s was compared q u a n t i t a t i v e l y i n an e x p e r i m e n t a l r i g i n w h i c h t h e y were c o n n e c t e d i n p a r a l l e l . A s o l u t i o n o f s t y r e n e i n n - h e p t a n e was c o n t i n u o u s l y c i r c u l a t e d t h r o u g h .the p robe a s s e m b l i e s f o r p e r i o d s r a n g i n g f r o m 12 h o u r s t o 70 h o u r s . S t y r e n e was s e l e c t e d as t h e f o u l a n t s i n c e i t s p o l y m e r i z a t i o n t o p o l y s t y r e n e can be i n i t i a t e d t h e r m a l l y . One o f t h e p r o b e s was a h o t w i r e p robe (HWP), based on t he UOP M o n i r e x F o u l i n g T e s t . The h e a t e d s u r f a c e was p r o v i d e d by a 0 . 1 4 mm d i a m e t e r s t a i n l e s s s t e e l 304 c o i l e d w i r e . I t was p o s i t i o n e d w i t h i n a r e c t a n g u l a r d u c t o f c r o s s - s e c t i o n 40 mm x 13 mm, p e r p e n d i c u l a r t o t he f l u i d f l o w . The s u r f a c e t e m p e r a t u r e o f t h e w i r e was d e t e r m i n e d v i a w i r e r e s i s t a n c e m e a s u r e m e n t s . The o t h e r p robe was t h e P o r t a b l e F o u l i n g R e s e a r c h U n i t ( P F R U ) , d e s i g n e d and m a n u f a c t u r e d by HTRI . The a s s e m b l y was a s t a i n l e s s s t e e l 304 h e a t e r r o d o f 1 0 . 7 4 mm o u t e r d i a m e t e r , s u r r o u n d e d by a 7 / 8 i n . s t a i n l e s s s t e e l 304 t u b e o f 1 9 . 7 4 mm i n n e r d i a m e t e r , t h r o u g h w h i c h t h e f l u i d f l o w s . The r o d was i n t e r n a l l y h e a t e d by a N ich rome e l e c t r i c a l r e s i s t a n c e c o i l p a c k e d i n magnesium o x i d e , w h i c h p r o v i d e d a h e a t e d s e c t i o n 1 0 1 . 6 mm l o n g . The s u r f a c e t e m p e r a t u r e was d e t e r m i n e d u s i n g t h e r m o c o u p l e s imbedded i n t h e w a l l o f t h e r o d , 7 6 . 2 mm f rom the u p s t r e a m end o f t h e h e a t e d s e c t i o n . i i i In t h e c o m p a r a t i v e f o u l i n g t e s t s , t he h e a t f l u x , i n i t i a l s u r f a c e t e m p e r a t u r e , b u l k f l u i d t e m p e r a t u r e , f l u i d c o m p o s i t i o n and t h u s i n i t i a l h e a t t r a n s f e r c o e f f i c i e n t were m a i n t a i n e d e s s e n t i a l l y t he same f o r b o t h p r o b e s . The f l o w r a t e s o f t h e two p r o b e s were r a d i c a l l y d i f f e r e n t , w i t h t u r b u l e n t , h i g h - v e l o c i t y f l o w i n t h e PFRU and l a m i n a r , l o w - v e l o c i t y f l o w i n t he HWP. H o w e v e r , r e s i d e n c e t i m e s o v e r t h e h e a t e d s e c t i o n s were s i m i l a r . c In t w e l v e o f t h e t h i r t e e n r u n s , f o u l i n g was t h e r m a l l y and v i s u a l l y d e t e c t e d on b o t h p r o b e s . N u c l e a t e b o i l i n g o c c u r r e d on t h e p robe s u r f a c e s d u r i n g t h e s e t w e l v e r u n s . In t h e l a s t r u n , under t h e c o n d i t i o n s o f l ow s u r f a c e t e m p e r a t u r e , l ow h e a t f l u x and no b o i l i n g , o n l y t h e HWP e x h i b i t e d f o u l i n g . B o t h p r o b e s e x h i b i t e d s i m i l a r f o u l i n g b e h a v i o u r - an i n d u c t i o n p e r i o d , f o l l o w e d by a r i s e i n t h e f o u l i n g r e s i s t a n c e , w h i c h i n most c a s e s l e v e l l e d o f f t o an a s y m p t o t i c v a l u e . In r u n s a t 11-12% s t y r e n e and h e a t 2 f l u x e s g r e a t e r t h a n 400 KW/m , t h e f o u l i n g r e s i s t a n c e o f t h e P F R U , a f t e r f i r s t l e v e l l i n g o f f , e x h i b i t e d an a b r u p t d e c l i n e . T h i s d e c l i n e was a t t r i b u t e d t o t h e r m a l d e g r a d a t i o n a t t he h i g h s u r f a c e t e m p e r a t u r e s o f t he f o u l e d p r o b e . T h e r e was e v i d e n c e t h a t t h e d e p o s i t s on t h e p r o b e s were no t s o l i d b u t behaved l i k e v i s c o u s f l u i d s . T h i s was n o t u n e x p e c t e d s i n c e s u r f a c e t e m p e r a t u r e s e x c e e d e d t he m e l t i n g p o i n t o f p o l y s t y r e n e . T h u s , t he PFRU' d e p o s i t s con fo rmed t o t h e h y d r o d y n a m i c s o f t h e f l o w , w i t h s t r i a t i o n s i n t h e h e a t e d s e c t i o n d e p o s i t and t h i n " s t r e a m l i n e " d e p o s i t s on t h e n o n - h e a t e d s e c t i o n s . The HWP d e p o s i t a c c u m u l a t e d a t t he u p s t r e a m i v end o f t h e w i r e c o i l i n t h e f o r m o f g l o b u l e s . I n c r e a s i n g t h e f l o w r a t e d e c r e a s e d t h e HWP a s y m p t o t i c f o u l i n g r e s i s t a n c e , bu t had no s i g n i f i c a n t e f f e c t on t he PFRU a s y m p t o t i c f o u l i n g r e s i s t a n c e . The r a t e o f f o u l i n g and t h e a s y m p t o t i c r e s i s t a n c e i n c r e a s e d w i t h t h e s t y r e n e c o n c e n t r a t i o n , however t h e HWP was a f f e c t e d l e s s t h a n t he PFRU. The HWP and PFRU f o u l i n g c u r v e s were no t i d e n t i c a l i n a b s o l u t e t e r m s , b u t on a r u n - t o - r u n b a s i s t h e y p a r a l l e l e d each o t h e r i n t e rms o f i n d u c t i o n t i m e , t he r a t e o f f o u l i n g , and t h e a s y m p t o t i c f o u l i n g r e s i s t a n c e . In te rms o f r e p r o d u c i b i l i t y , s i m p l i c i t y o f c o n s t r u c t i o n and t h e number o f p r o b l e m s , t h e HWP was s u p e r i o r t o t h e PFRU. V TABLE OF CONTENTS Page ABSTRACT i"i L IST OF TABLES x L IST OF FIGURES x i v ACKNOWLEDGEMENTS x v i i 1. INTRODUCTION 1 2 . LITERATURE REVIEW 5 2 . 1 . C a t e g o r i e s o f F o u l i n g 5 2 . 2 . C h a r a c t e r i z a t i o n o f D e p o s i t A c c u m u l a t i o n 5 2 . 3 . F o u l i n g C u r v e s 7 2 . 4 . F a c t o r s A f f e c t i n g F o u l i n g 7 2 . 4 . 1 . E f f e c t o f V e l o c i t y / T u r b u l e n c e / M a s s F low ^ 2 . 4 . 2 . E f f e c t o f T e m p e r a t u r e 9 2 . 4 . 3 . E f f e c t o f S u l p h u r Compounds i n H y d r o c a r b o n F o u l i n g 12 2 . 4 . 4 . E f f e c t o f N i t r o g e n Compounds i n H y d r o c a r b o n F o u l i n g 13 2 . 4 . 5 . E f f e c t o f T r a c e M e t a l s (homogeneous and h e t e r o g e n e o u s ) i n H y d r o c a r b o n F o u l i n g 13 2 . 4 . 6 . E f f e c t o f Oxygen C o n t e n t / D e o x y g e n a t i o n i n H y d r o c a r b o n F o u l i n g 14 2 . 4 . 7 . E f f e c t o f A d d i t i v e s / S u r f a c e C o a t i n g s i n H y d r o c a r b o n F o u l i n g 16 2 . 4 . 8 . E f f e c t o f F l u i d C h e m i s t r y 17 2 . 4 . 9 . E f f e c t o f S u r f a c e C o n d i t i o n / F l o w Geomet ry 18 2 . 5 . Measurement o f D e p o s i t A c c u m u l a t i o n 20 2 . 6 . PFRU and UOP M o n i r e x F o u l i n g P r o b e s - D e t a i l s o f C o n s t r u c t i o n , H y d r o d y n a m i c s , and Hea t T r a n s f e r . 37 2 . 6 . 1 . PFRU F o u l i n g P robe 37 2 . 6 . 2 . UOP M o n i r e x F o u l i n g T e s t 46 v i Page 2 . 7 . F o u l i n g M o d e l s 6 0 2 . 8 . P o l y m e r i z a t i o n K i n e t i c s 65 2 . 9 . B o i l i n g 6 8 3 . SCOPE AND METHOD OF PRESENT WORK 7 2 4 . SELECTION OF WORKING FLUID 7 7 4 . 1 . B a c k g r o u n d 7 7 4 . 2 . P r o p e r t i e s o f S t y r e n e and n -Hep tane 80 4 . 3 . S o l v e n t E f f e c t s 8 5 4 . 4 . P r o p e r t i e s o f P o l y s t y r e n e 8 6 4 . 5 . S t y r e n e P o l y m e r i z a t i o n 8 6 4 . 6 . T e r t i a r y B u t y l C a t e c h o l 92 4 . 7 . R o l e o f Oxygen 94 5 . EXPERIMENTAL APPARATUS 96 5 . 1 . F low Loop 96 5 . 2 . S u p p l y Tank 100 5 . 3 . PFRU T e s t S e c t i o n 102 5 . 4 . HWP T e s t S e c t i o n 107 5 . 5 . C i r c u i t and S a f e t y Components H I 6 . EXPERIMENTAL PROCEDURES 115 6 . 1 . D e t e r m i n a t i o n o f K i n e m a t i c V i s c o s i t y 115 6 . 2 . D e t e r m i n a t i o n o f D e n s i t y 116 6 . 3 . Equ ipmen t C a l i b r a t i o n 118 6 . 3 . 1 . O r i f i c e M e t e r C a l i b r a t i o n 118 v i i Page 6 . 3 . 1 . 1 . PFRU 118 6 . 3 . 1 . 2 . HWP 120 6 . 3 . 2 . T h e r m o c o u p l e s 121 6 . 3 . 3 . D a t a l o g g e r 123 6 . 3 . 4 . W i l s o n P l o t C a l i b r a t i o n o f PFRU T h e r m o c o u p l e s 124 6 . 4 . Removal o f TBC 125 6 . 5 . S o l u t i o n P r e p a r a t i o n 126 6 . 6 . T e m p e r a t u r e P r o f i l e s 127 6 . 6 . 1 . HWP 127 6 . 6 . 2 . PFRU 127 6 . 7 . R e s i s t i v i t y and T e m p e r a t u r e C o e f f i c i e n t o f R e s i s t i v i t y o f S t a i n l e s s S t e e l 304 128 6 . 8 . P r o c e d u r e f o r F o u l i n g Run 128 6 . 9 . C l e a n i n g 134 6 . 1 0 . B o i l i n g E x p e r i m e n t s 134 6 . 1 0 . 1 . V i s u a l E x p e r i m e n t 134 6 . 1 0 . 2 . P robe E x p e r i m e n t s 136 6 . 1 1 . E x p e r i m e n t a l Hea t T r a n s f e r C o r r e l a t i o n s 137 7 . RESULTS AND DISCUSSION 138 7 . 1 . C a l c u l a t i o n Methods 138 7 . 2 . I n i t i a l and O p e r a t i n g C o n d i t i o n s 150 7 . 3 . D e p o s i t A n a l y s i s 152 7 . 4 . B o i l i n g A n a l y s i s 175 7 . 5 . Hea t B a l a n c e 181 7 . 6 . B u l k C o n t a c t T imes 184 7 . 7 . Hea t T r a n s f e r C o e f f i c i e n t C o r r e l a t i o n s 186 7 . 8 . C r i t i c a l R a d i u s 195 v i i i Page 7 . 9 . E f f e c t o f D e p o s i t T h i c k n e s s on F o u l i n g R e s i s t a n c e 197 7 . 1 0 . D i s c u s s i o n o f F o u l i n g C u r v e s 200 7 . 1 0 . 1 . E x p l a n a t i o n o f C u r v e Shape 200 7 . 1 0 . 2 . I n t e r p r e t a t i o n o f F o u l i n g Cu rve A n a l y s i s 205 8 . CONCLUSIONS 209 9 . RECOMMENDATIONS 215 9 . 1 . Equ ipmen t 215 9 . 2 . F u r t h e r Work 216 1 0 . NOMENCLATURE 218 1 1 . REFERENCES 229 APPENDIX I. E r r o r A n a l y s i s 237 1 . 1 . E r r o r i n Power I n p u t s 237 1 . 2 . E r r o r i n S u r f a c e A r e a 242 1 . 2 . 1 . E r r o r i n PFRU S u r f a c e A r e a 242 1 . 2 . 2 . E r r o r i n HWP S u r f a c e A r e a 242 1 . 3 . E r r o r i n Hea t F l u x 243 1 . 4 . E r r o r i n T e m p e r a t u r e 244 1 . 4 . 1 . E r r o r i n T e m p e r a t u r e R e a d i n g s 244 1 . 4 . 2 . E r r o r i n HWP S u r f a c e T e m p e r a t u r e 248 1 . 4 . 3 . E r r o r i n PFRU S u r f a c e T e m p e r a t u r e 250 1 . 4 . 3 . 1 . E r r o r i n k o f S t a i n l e s s S t e e l 304 250 1 . 4 . 3 . 2 . E r r o r i n x 251 1 . 4 . 3 . 2 . 1 . E r r o r i n Run 5 . 252 1 . 4 . 3 . 2 . 2 . E r r o r i n Run 1 252 1 . 4 . 3 . 2 . 3 . E r r o r i n Runs 2 t o 4 253 1 . 4 . 3 . 2 . 4 . E r r o r i n Runs 6 t o 13 258 i x Page 1 . 4 . 3 . 3 . Sample C a l c u l a t i o n o f E r r o r i n PFRU S u r f a c e T e m p e r a t u r e 260 1 . 5 . E r r o r i n F o u l i n g R e s i s t a n c e 261 . , I . 5 . 1 . E r r o r i n PFRU F o u l i n g R e s i s t a n c e 261 I . 5 . 2 . E r r o r i n HWP F o u l i n g R e s i s t a n c e 263 1 . 6 . E r r o r i n I n i t i a l S t y r e n e C o n c e n t r a t i o n 264 1 . 7 . E r r o r i n F l o w R a t e s 266 1 . 7 . 1 . E r r o r i n g 266 1 . 7 . 2 . E r r o r i n A z . 267 1 . 7 . 3 . E r r o r i n ( p m D p ) R - T - 267 1 . 7 . 4 . E r r o r i n p 267 1 . 7 . 5 . E r r o r i n C d 268 1 . 7 . 6 . Sample C a l c u l a t i o n f o r PFRU 270 1 . 7 . 7 . Sample C a l c u l a t i o n f o r HWP 270 APPENDIX I I . T e m p e r a t u r e and V e l o c i t y P r o f i l e s 272 1 1 . 1 . PFRU V e l o c i t y and T e m p e r a t u r e P r o f i l e s 272 1 1 . 2 . HWP V e l o c i t y and T e m p e r a t u r e P r o f i l e s 275 1 1 . 2 . 1 . HWP V e l o c i t y P r o f i l e 275 1 1 . 2 . 2 . HWP T e m p e r a t u r e P r o f i l e 277 APPENDIX I I I . T a b u l a t e d Data and R e s u l t s o f t h e E x p e r i m e n t a l Runs 280 I I I . 1. N o m e n c l a t u r e o f H e a d i n g s 280 1 1 1 . 2 . T a b l e s o f Da ta and R e s u l t s f o r Runs 1 t h r o u g h 13 281 APPENDIX I V . F o u l i n g C u r v e A n a l y s i s 312 APPENDIX V . Computer P rograms 335 X L IST OF TABLES T a b l e Page 1- 1 C o s t s o f F o u l i n g i n P e t r o l e u m R e f i n e r i e s 3 2 - 1 C l a s s i f i c a t i o n o f F o u l i n g Measurement T e c h n i q u e s 21 2 - 2 C o m p a r i s o n o f T e s t D e v i c e s 38. 2 - 3 N u s s e l t Numbers and I n f l u e n c e C o e f f i c i e n t s , T u r b u l e n t F l o w between P a r a l l e l P l a n e s , One S i d e a t C o n s t a n t Hea t R a t e , t h e O t h e r I n s u l a t e d , Thermal E n t r y L e n g t h S o l u t i o n 42 4-1 V a p o r P r e s s u r e o f S t y r e n e / n - H e p t a n e S o l u t i o n 79 4 - 2 P r o p e r t i e s o f S t y r e n e Monomer as a F u n c t i o n o f T e m p e r a t u r e 81 4 - 3 K i n e m a t i c V i s c o s i t y and D e n s i t y o f S t y r e n e / n - H e p t a n e S o l u t i o n s a s a F u n c t i o n o f T e m p e r a t u r e ( i n OF) and C o n c e n t r a t i o n ( i n wt%) 80 4 - 4 P h y s i c a l P r o p e r t i e s o f P u r e S t y r e n e 83 4 - 5 P h y s i c a l P r o p e r t i e s o f n - H e p t a n e 84 4 - 6 P r o p e r t i e s and E q u a t i o n C o n s t a n t s f o r n -Hep tane and S t y r e n e 85 4 - 7 G e n e r a l P h y s i c a l P r o p e r t i e s o f P o l y s t y r e n e 87 4 - 8 P h y s i c a l C o n s t a n t s o f P o l y s t y r e n e 88 4 - 9 P o l y m e r i z a t i o n R a t e and M o l e c u l a r We igh t f o r S t y r e n e a t S e v e r a l T e m p e r a t u r e s o f P o l y m e r i z a t i o n 89 7-1 T y p i c a l D a t a l o g g e r S c a n n i n g Sequence 138 7 -2 C h r o m e l - C o n s t a n t a n The rmocoup le C o n v e r s i o n E q u a t i o n s 140 7 -3 Summary o f I n i t i a l and O p e r a t i n g C o n d i t i o n s 151 7-4 Summary o f D e p o s i t A n a l y s e s 152 7 -5 R e s u l t s o f V i s u a l E x p e r i m e n t t o V e r i f y B o i l i n g 176 7 -6 R e s u l t s o f PFRU Hea t B a l a n c e 182 7 -7 R e s u l t s o f HWP Hea t B a l a n c e 183 xi . T a b l e Page 7 - 8 Summary o f B u l k C o n t a c t Time A n a l y s i s 186 7-9 N u s s e l t Number C o r r e l a t i o n s f r om P a r a l l e l P l a t e Da ta 187 7 -10 Summary o f Heat T r a n s f e r C o e f f i c i e n t C o m p a r i s o n s 188 7-11 Hea t T r a n s f e r C o e f f i c i e n t s C a l c u l a t e d f r o m E q . (2.-50.) and E q , 1(2-53) 190 7 -12 E s t i m a t e o f A c t u a l R f v e r s u s C o n v e n t i o n a l l y C a l c u l a t e d R f 199 7 -13 Hea t T r a n s f e r C o e f f i c i e n t s w h i c h B a l a n c e S u r f a c e A r e a E f f e c t 199 APPENDIX I 1-1 Summary o f C u r r e n t and V o l t a g e E r r o r s 241 1 - 2 D a t a l o g g e r R e a d i n g - T e m p e r a t u r e C o n v e r s i o n E q u a t i o n s 245 1 - 3 S t a n d a r d D e v i a t i o n s o f C o n v e r s i o n E q u a t i o n s 246 1-4 Summary o f T h e r m o c o u p l e Dep ths 251 1 - 5 I n t e r m e d i a t e V a l u e s f o r D e t e r m i n i n g t h e S t a n d a r d D e v i a t i o n o f t h e W i l s o n P l o t I n t e r c e p t , a 255 1 - 6 S t a n d a r d D e v i a t i o n o f t he W i l s o n P l o t I n t e r c e p t , a . 259 I- 7 C o m p a r i s o n o f E x p e r i m e n t a l C^ f o r HWP w i t h E q u a t i o n C^ 269 •APPENDIX I I I I - 1 V e l o c i t y P r o f i l e i n PFRU Annu l us 273 11-2 V e l o c i t y P r o f i l e i n a R e c t a n g u l a r Duc t 276 I I - 3 E x p e r i m e n t a l HWP T e m p e r a t u r e P r o f i l e 279 APPENDIX I I I I I I - l D a t a and R e s u l t s o f Run 1 282 x i i 111-2 Da ta and R e s u l t s o f Run 2 284 111 -3 Da ta and R e s u l t s o f Run 3 287 I I I - 4 Da ta and R e s u l t s o f Run 4 290 111-5 Da ta and R e s u l t s o f Run 5 293 111-6 Da ta and R e s u l t s o f Run 6 295 I I I - 7 Da ta and R e s u l t s o f Run 7 298 I I I - 8 Da ta and R e s u l t s o f Run 8 300 111-9 Da ta and R e s u l t s o f Run 9 302 1 1 1 - 1 0 Da ta and R e s u l t s o f Run 10 304 1 1 1 - 1 1 Data and R e s u l t s o f Run 11 306 1 1 1 - 1 2 Da ta and R e s u l t s o f Run 12 309 111-13 Da ta and R e s u l t s o f Run 13 311 APPENDIX IV IV-1 R e s u l t s o f I n d u c t i o n P e r i o d A n a l y s i s 312 I V - 2 Maximum F o u l i n g Ra te ( i ) based on any two p o i n t s a l o n g r i s e 313 I V - 3 Maximum F o u l i n g Ra te ( i i ) based on 2 p o i n t s , 4 p o i n t s , and 6 p o i n t s a r o u n d t h e i n f l e c t i o n ; p o i n t . 315 I V - 4 Maximum F o u l i n g Ra te ( i i i ) based on t h e K e r n -S e a t o n e q u a t i o n . 317 I V - 5 O v e r a l l A v e r a g e F o u l i n g Ra te ( n o t i n c l u d i n g t h e f l a t p o r t i o n s o f r i s e ) 319 I V - 6 F o u l i n g R i s e T ime 320 I V - 7 A v e r a g e V a l u e o f R f i n P l a t e a u R e g i o n ( a f t e r f o u l i n g r i s e ) 321 I V - 8 L e n g t h o f T ime f o r A s y m p t o t i c / P l a t e a u R e g i o n 322 x i n Page IV -9 , L e n g t h o f D e f o u l i n g T ime 323 I V - 1 0 A v e r a g e V a l u e o f R f i n P l a t e a u R e g i o n ( a f t e r d e f o u l i n g ) 323 IV-11 O v e r a l l A v e r a g e D e f o u l i n g Ra te ( n o t i n c l u d i n g f l a t p o r t i o n s o f d e c l i n e ) 324 I V - 1 2 Maximum D e f o u l i n g Ra te ( i ) based on any two p o i n t s a l o n g d e c l i n e 324 I V - 1 3 Maximum D e f o u l i n g R a t e ( i i ) based on 2 p o i n t s , 4 p o i n t s and 6 p o i n t s a r o u n d t he i n f l e c t i o n p o i n t 325 I V - 1 4 Maximum D e f o u l i n g Ra te ( i i i ) b a s e d on t he K e r n - S e a t o n e q u a t i o n 326 I V - 1 5 L e n g t h o f T ime f o r A s y m p t o t i c / P l a t e a u R e g i o n ( a f t e r d e f o u l i n g ) 327 IV -16 O v e r a l l Maximum and Minimum V a l u e s o f R^ 328 IV -17 E s t i m a t i o n o f U n i f o r m D e p o s i t T h i c k n e s s f r o m t h e F i n a l R f 329 I V - 1 8 E s t i m a t i o n o f U n i f o r m D e p o s i t , . T h i c k n e s s f r om D e p o s i t W e i g h t Measurements 331 I V - 1 9 Summary o f M a x i m u m / A s y m p t o t i c F o u l i n g R e s i s t a n c e s 332 I V - 2 0 Summary o f Maximum F o u l i n g and D e f o u l i n g R a t e s 333 IV-21 S p e c i a l Cases o f Runs 3 and 11 334 x i v L IST OF FIGURES F i g u r e Page 2-1 W a l l T e m p e r a t u r e P r o f i l e i n t h e V i c i n i t y o f T e m p e r a t u r e S e n s o r 41 2 - 2 N u - | f o r F u l l y D e v e l o p e d T u r b u l e n t F low t h r o u g h an Annu l us 47 2 - 3 UOP M o n i r e x F o u l i n g T e s t P r o b e 48 2 - 4 G r a p h i c a l R e s u l t s o f UOP M o n i r e x F o u l i n g T e s t 50 2 - 5 UOP M o n r f e x F o u l i n g T e s t T e m p e r a t u r e C o m p e n s a t i n g C i r c u i t 52 4-1 Thermal P o l y m e r i z a t i o n Da ta f o r V a r i o u s T e m p e r a t u r e s and C o n v e r s i o n s 91 4 - 2 F u n c t i o n a l D e f i n i t i o n s o f t h e Terms I n d u c t i o n P e r i o d , I n h i b i t i o n and R e t a r d a t i o n 95 5 - 1 F l o w D iag ram o f A p p a r a t u s 97 5 -2 O r i f i c e P l a t e s and F l a n g e s 99 5 - 3 I n t e r n a l s and E x t e r n a l s o f S u p p l y Tank 103 5-4 PFRU A s s e m b l y - 104 5 - 5 P h o t o g r a p h s o f PFRU A s s e m b l e y ••_ , 105 5 -6 Hot W i r e P r o b e A s s e m b l y 108 5 -7 P h o t o g r a p h s o f D i s a s s e m b l e d . H o t W i r e P r o b e 109 5 - 8 P h o t o g r a p h s o f A s s e m b l e d Hot W i r e P r o b e 110 5 - 9 C i r c u i t D i a g r a m o f A p p a r a t u s 113 5 - 10 AC/DC C o n v e r s i o n C i r c u i t 114 6 - 1 A p p a r a t u s t o D e t e c t B o i l i n g V i s u a l l y 135 7 - 1 Run 1 F o u l i n g C u r v e 153 7 -2 Run 2 F o u l i n g C u r v e 154 7 - 3 Run 3 F o u l i n g C u r v e 155 XV F i g u r e 7-4 7 -5 7-6 7-7 7 -8 7 -9 7 -10 7-11 7-12 7 -13 7 -14 7 -15 7-16 7 -17 7 -18 7 -19 7 -20 7-21 7 -22 7 -23 Run 4 F o u l i n g C u r v e Run 5 F o u l i n g C u r v e Run 6 F o u l i n g Cu rve Run 7 F o u l i n g Cu rve Run 8 F o u l i n g C u r v e Run 9 F o u l i n g C u r v e Run 10 F o u l i n g Cu rve Run 11 F o u l i n g Cu rve Run 12 F o u l i n g Cu rve Run 13 F o u l i n g C u r v e Low M a g n i f i c a t i o n P h o t o g r a p h s o f the HWP D e p o s i t s H i g h M a g n i f i c a t i o n P h o t o g r a p h s o f t he HWP D e p o s i t s Coked PFRU D e p o s i t G l o b u l a r , D r o p - l i k e D e p o s i t on PFRU S t r e a m l i n e D e p o s i t s on PFRU E f f e c t o f B o i l i n g on D e p o s i t i o n Ups t ream and Downstream Ends o f t h e F o u l e d PFRU Hea ted S e c t i o n D e t a i l e d P h o t o g r a p h s o f PFRU D e p o s i t H e a t T r a n s f e r C o e f f i c i e n t v e r s u s T e m p e r a t u r e D i f f e r e n c e a t C o n s t a n t F l o w R a t e ( B o i l i n g E x p e r i m e n t ) E f f e c t o f D i s s o l v e d A i r on t h e B o i l i n g Cu rve Page 156 157 158 159 160 161 162 163 164 165 167 168 170 170 171 171 172 173 178 179 x v i Page APPENDIX I I II—1 V e l o c i t y and T e m p e r a t u r e P r o f i l e s i n A n n u l a r F l o w 274 APPENDIX V •; V - l P rogram QQ t o D e t e r m i n e F o u l i n g R e s i s t a n c e s 336 V - 2 P rog ram POI t o D e t e r m i n e F l o w R a t e s 341 x v i i ACKNOWLEDGEMENTS I w o u l d l i k e t o t hank D r . A . P . W a t k i n s o n and D r . N. E p s t e i n f o r t h e i r g u i d a n c e and s u p e r v i s i o n * d u r i n g my s t u d i e s on F o u l i n g . S p e c i a l t h a n k s go t o J . B a r a n o w s k i and t h e work shop f o r a s s i s t i n g i n t h e d e s i g n and c o n s t r u c t i o n o f t h e e x p e r i m e n t a l a p p a r a t u s . I am i n d e b t e d t o my p a r e n t s f o r t h e i r l o v e and f i n a n c i a l s u p p o r t , t h r o u g h o u t my s t u d i e s a t UBC. Thanks s h o u l d a l s o go t o H. Lam f o r h i s a s s i s t a n c e i n t he a c q u i s i t i o n o f s e v e r a l p i e c e s o f e q u i p m e n t . 1 1. INTRODUCTION I t i s a w e l l o b s e r v e d phenomenon t h a t d u r i n g o p e r a t i o n , t he p e r f o r m a n c e o f most h e a t e x c h a n g e r s d e t e r i o r a t e s . The d e t e r i o r a t i o n i s due t o t he a c c u m u l a t i o n on t h e h e a t t r a n s f e r s u r f a c e o f a d e p o s i t u s u a l l y o f much l o w e r t h e r m a l c o n d u c t i v i t y t h a n t he m e t a l s u r f a c e . The a c c u m u l a t i o n o f u n d e s i r e d m a t e r i a l on h e a t e x c h a n g e r s u r f a c e s s u c h t h a t t he t h e r m a l r e s i s t a n c e t o h e a t t r a n s f e r i s i n c r e a s e d , has been te rmed " f o u l i n g " . T h e r e have been r a r e c a s e s r e p o r t e d ( e . g ; . S m i t h ( 1 ) ) where f o u l i n g d e c r e a s e s t he t h e r m a l r e s i s t a n c e b e c a u s e t he i n c r e a s e i n t h e r m a l r e s i s t a n c e due t o t he i n s u l a t i n g e f f e c t o f t h e d e p o s i t i s o u t w e i g h e d by a d e c r e a s e i n t h e f l u i d t h e r m a l r e s i s t a n c e due t o a " r o u g h n e s s " e f f e c t o f t he d e p o s i t . D e p e n d i n g on t h e c h e m i s t r y o f p r o c e s s s t r e a m s and t h e f o u l i n g m e c h a n i s m , c r y s t a l s , s e d i m e n t , p o l y m e r s , c o k i n g p r o d u c t ' s , b i o l o g i c a l g r o w t h s , c o r r o s i o n p r o d u c t s , o r a c o m b i n a t i o n o f t h e s e may d e p o s i t . F a c t o r s t h a t a f f e c t f o u l i n g a r e t e m p e r a t u r e - b u l k , s u r f a c e and w a l l , f l o w r a t e , g e o m e t r y , s u r f a c e c o n d i t i o n and m a t e r i a l o f c o n s t r u c t i o n o f t he h e a t e x c h a n g e r , and f l u i d c h e m i s t r y . F o u l i n g i s a c o s t l y p r o b l e m . B e c a u s e t h e f o u l i n g r e s i s t a n c e i s o f t e n o v e r e s t i m a t e d , h e a t exchangers a re d e s i g n e d w i t h e x c e s s s u r f a c e , w h i c h i n c r e a s e s c a p i t a l c o s t s . M a i n t e n a n c e c o s t s i n c r e a s e due t o more f r e q u e n t c l e a n i n g o f t he h e a t e x c h a n g e r s . In some i n s t a n c e s , t h e h e a t e x c h a n g e r t ube b u n d l e s c a n n o t be c l e a n e d o r have been damaged by t h e h i g h s k i n t e m p e r a t u r e s w h i c h r e s u l t f r om f o u l i n g , and t h u s must be r e p l a c e d . Due t o t h e d e c r e a s e d h e a t t r a n s f e r e f f i c i e n c y c a u s e d by 2 f o u l i n g , e x t r a f u e l must be b u r n e d , f o r examp le t o m a i n t a i n r e a c t o r i n l e t t e m p e r a t u r e s . T h i s i n c r e a s e s o p e r a t i n g c o s t s . Pumping c o s t s may a l s o i n c r e a s e due t o t h e r e d u c e d c r o s s - s e c t i o n a l a r e a f o r f l o w , o r due t o d e p o s i t r o u g h n e s s . T a b l e 1-1 t a k e n f r om H a u s l e r (2) shows t h e economic e f f e c t o f f o u l i n g i n p e t r o l e u m r e f i n e r i e s . A c c o r d i n g t o t h i s t a b l e , t h e c o s t s a s s o c i a t e d w i t h r e d u c e d t h r o u g h p u t and c l e a n i n g a r e t he p r i n c i p a l c o s t s o f f o u l i n g . The e x t r a p r o c e s s i n g c o s t s due t o f o u l i n g can be as h i g h as $ 3 7 / 1 0 0 0 b b l i n 1973 U . S . d o l l a r s . .To c o n t r o l f o u l i n g i n h y d r o c a r b o n s y s t e m s , C a n a p a r y (3) s u g g e s t s u s i n g l o w e r t e m p e r a t u r e s and h i g h e r v e l o c i t i e s ; r e d u c i n g u n s a t u r a t e s by e l i m i n a t i n g c r a c k e d s t o c k ; r e d u c i n g s a l t c o n t e n t by e f f i c i e n t d e s a l t i n g ; e l i m i n a t i n g oxygen by i n e r t gas b l a n k e t t i n g and oxygen s t r i p p i n g ; i n h i b i t i n g c o r r o s i o n by u s i n g f i l m - f o r m i n g c o r r o s i o n i n h i b i t o r s ; and i n h i b i t i n g p o l y m e r i z a t i o n by u s i n g s t a b i l i z e r -d i s p e r s a n t a d d i t i v e s . The u s u a l p r a c t i c e t o a c c o u n t f o r t h e e f f e c t o f f o u l i n g i n h e a t e x c h a n g e r d e s i g n i s t o i n c o r p o r a t e f o u l i n g f a c t o r s i n t o t he d e s i g n e q u a t i o n . A = 2 - ( R h : . + K + R f , + R f + + R w ) ( 1 - D M A T " i n o r i r o u t w m T h i s p r o c e d u r e r e s u l t s i n a d d i t i o n a l h e a t t r a n s f e r s u r f a c e a r e a t o accommodate f o u l i n g . R u . and R h can be d e t e r m i n e d f a i r l y a c c u r a t e l y • n o f r om e m p i r i c a l d e s i g n c o r r e l a t i o n s and R w f r om knowledge o f t he m e t a l w a l l t h e r m a l c o n d u c t i v i t y , t h i c k n e s s and g e o m e t r y . The f o u l i n g f a c t o r s come f r om " e x p e r i e n c e - b a s e d " s o u r c e s such as TEMA ( 4 ) . B o t t and W a l k e r (5 ) Fouling in petroleum refineries* Respondents % distribution noting effect on r—of fouling costs—* r-operating time—\ Re* r Se> tfueed Clean* fna. Unit Hone Modr. vera Thrpt ing Crude 25 50 Freheaters 7 8 1 Vacuum tower bottoms 10 5 1 Cokers 95 S Furnaces 1 2 3 Reformers 55 . . Reboiler* 0 2 1 Hydro* 100 desulfuriiers 9 Freheaters 7 6 Furnaces 0 1 0 60 40 Alkytation Freheaters 0 J 0 Reboilers 7 5 4 10 FCC-VRU 90 Freheaters 8 4 4 Compressors 6 S 1 Ethylene Oe-ethanizer 0 0 1 1 1 0 Benzene concentrator 0 0 1 Foly unit 0 0 1 stlmated S/1.0M »M > Anti-ng foulant Savings 25 . . 0-2B-L10 0.15-0.53 0.00*0.45 1270 2J2-3J5 9J5 35 10 2-33-22.00 044-0X0 1.92-20.40 . . 140* *20 1.06*340 U8-5.S5 - . 340-37JO 1.40-2.14 142-38.40 . . . . L23-148 0.59-0.73 0X1-1.14 28X0 'HACE T a b l e 1 - 1 . C o s t s o f F o u l i n g i n P e t r o l e u m R e f i n e r i e s ( t a k e n f r om H a u s l e r ( 2 ) ) 4 p r o d u c e d a t a b l e w h i c h c l e a r l y r e v e a l s how t h e TEMA v a l u e s f a i l t o t a k e i n t o a c c o u n t t h e t i m e - d e p e n d e n c e o f f o u l i n g . K e r n and S e a t o n ( 6 ) , Tabo rek e t a l . (7 ) and S t a r n e r (8) a l l c r i t i c i z e t h e use o f f o u l i n g f a c t o r s , and c i t e s p e c i f i c examp les o f how use o f f o u l i n g f a c t o r s a c t u a l l y i n c r e a s e d t h e e x t e n t o f f o u l i n g . F o u l i n g can be t h o u g h t o f as a m u l t i - v a r i a b l e , comp lex m a s s , momentum and h e a t t r a n s f e r p r o b l e m , c o m p l i c a t e d by p o o r l y u n d e r s t o o d c h e m i c a l k i n e t i c s . Due t o t h e v a r i e t y o f f o u l i n g mechan isms and o p e r a t i n g c o n d i t i o n s , i t i s v i r t u a l l y i m p o s s i b l e t o d e v e l o p a g e n e r a l i z e d e q u a t i o n w h i c h a l l o w s t he p r e d i c t i o n o f t h e r a t e o r e x t e n t o f f o u l i n g . E p s t e i n (9) r e v i e w s s e v e r a l f o u l i n g m o d e l s . The d a t a on w h i c h t h e s e m o d e l s a r e based a r e u s u a l l y o b t a i n e d f r om s m a l l - s c a l e f o u l i n g r i g s e m p l o y i n g v a r i o u s f o u l i n g measurement t e c h n i q u e s . The p u r p o s e o f t h i s t h e s i s i s t o make a q u a n t i t a t i v e c o m p a r i s o n o f t he p e r f o r m a n c e o f two o f t h e s e p r o b e s u n d e r s i m i l a r o p e r a t i n g c o n d i t i o n s . 5 2 . LITERATURE REVIEW 2 . 1 . C a t e g o r i e s o f F o u l i n g A c c o r d i n g t o E p s t e i n ( 9 ) , t h e r e a r e s i x c a t e g o r i e s o f f o u l i n g . 1) P r e c i p i t a t i o n f o u l i n g - t h e p r e c i p i t a t i o n o f d i s s o l v e d s u b s t a n c e s on t he h e a t t r a n s f e r s u r f a c e . The s c a l i n g o f i n v e r s e : s o l u b i l i t y s a l t s such as CaSO^ i s a fo rm o f p r e c i p i t a t i o n f o u l i n g . 2) P a r t i c u l a t e f o u l i n g - t h e a c c u m u l a t i o n o f f i n e l y d i v i d e d s o l i d s s u s p e n d e d i n t h e p r o c e s s f l u i d o n t o t h e h e a t t r a n s f e r s u r f a c e . 3) C h e m i c a l r e a c t i o n f o u l i n g - d e p o s i t s fo rmed a t t he h e a t t r a n s f e r s u r f a c e by c h e m i c a l r e a t i o n s such as p o l y m e r i z a t i o n , i n w h i c h t h e s u r f a c e m a t e r i a l i t s e l f i s no t a r e a c t a n t . 4) C o r r o s i o n f o u l i n g - t h e h e a t t r a n s f e r s u r f a c e i t s e l f r e a c t s t o p r o d u c e c o r r o s i o n p r o d u c t s w h i c h f o u l t h e s u r f a c e and may promote t h e a t t a c h m e n t o f o t h e r f o u l a n t s . 5) B i o l o g i c a l f o u l i n g - t he a t t a c h m e n t o f m a c r o - o r g a n i s m s a n d / o r m i c r o - o r g a n i s m s t o a h e a t t r a n s f e r s u r f a c e , a l o n g w i t h t h e a d h e r e n t s l i m e s o f t e n g e n e r a t e d by t he l a t t e r . 6 ) F r e e z i n g f o u l i n g - s o l i d i f i c a t i o n o f a l i q u i d o r some o f i t s h i g h e r m e l t i n g c o n s t i t u e n t s o n t o a s u b c o o l e d h e a t t r a n s f e r s u r f a c e . 2 . 2 . C h a r a c t e r i z a t i o n o f D e p o s i t A c c u m u l a t i o n T h e r e a r e t h r e e b a s i c methods o f e x p r e s s i n g t h e amount o f d e p o s i t on a h e a t t r a n s f e r s u r f a c e - mass p e r u n i t s u r f a c e a r e a , m; d e p o s i t t h i c k n e s s , x ; and u n i t t h e r m a l f o u l i n g r e s i s t a n c e , R f , ( 9 ) . 6 They a r e i n t e r - r e l a t e d d i f f e r e n t i a l l y as dm = p.rdx = f ) f k f d R ( 2 - 1 ) o r e x p r e s s e d as f o u l i n g r a t e s dR ( 2 - 2 ) A s s u m i n g and a r e i n d e p e n d e n t o f x , t h e n t h e e x p r e s s i o n s i n E q . ( 2 - 1 ) c a n be i n t e g r a t e d t o m = p .pX = p f k f R . p ( 2 - 3 ) T h i s a s s u m p t i o n i s n o t a l w a y s v a l i d . C a s e s have been r e p o r t e d ( 7 , 1 0 , 1 1 ) where t h e d e p o s i t has v a r i e d f r o m a h a r d dense s c a l e o f r e l a t i v e l y h i g h t h e r m a l c o n d u c t i v i t y n e a r t h e h e a t t r a n s f e r s u r f a c e t o a s o f t , p o r o u s m a t e r i a l o f r e l a t i v e l y low t h e r m a l c o n d u c t i v i t y n e a r t h e f l u i d - d e p o s i t i n t e r f a c e . M e e t o r - e t . a T ( 1 1 ) , i n h i s s team g e n e r a t o r s t u d i e s , shows t h a t t h e f o l l o w i n g l a y e r s e x i s t i n t he f o u l i n g d e p o s i t on t h e me ta l s u r f a c e -a c o r r o s i o n i n d u c e d l a y e r ; a s o l i d s i n t e r e d l a y e r ; a g r a i n e d l a y e r ; and a s o o t l a y e r . measurements o f R f o r d R f / d e a r e mos t i m p o r t a n t , ( 9 ) . From the i n t e g r a t e d r e l a t i o n s h i p s o f E q . ( 2 - 3 ) , F o r s t u d i e s o f t h e e f f e c t o f f o u l i n g on h e a t t r a n s f e r e f f i c i e n c y x _ m ( 2 - 4 ) f k f p f k f 7 2 . 3 . F o u l i n g C u r v e s A common method o f e x p l a i n i n g f o u l i n g b e h a v i o u r i s t h r o u g h t he use o f t he c o n c e p t o f two o p p o s i n g m e c h a n i s m s , d e p o s i t i o n and r e m o v a l . De:-p o s i t i o n o f f o u l a n t n o r m a l l y i n c r e a s e s t h e f o u l i n g r e s i s t a n c e w h i l e remova l o f f o u l a n t (e.g,. v i a s h e a r f o r c e s ) n o r m a l l y d e c r e a s e s i t . The most common f o u l i n g c u r v e s where R^ , t h e f o u l i n g r e s i s t a n c e , i s p l o t t e d a g a i n s t t i m e , .are ttie l i n e a r c u r v e s , where t y p i c a l l y t h e r a t e o f d e p o s i t i o n o f f o u l a n t i s much g r e a t e r t h a n t h e r a t e o f r e m o v a l ; t he a s y m p t o t i c c u r v e s , where t y p i c a l l y t h e r a t e o f r emova l o f f o u l a n t has i n c r e a s e d t o t h e p o i n t where i t e q u a l s t h e r a t e o f d e p o s i t i o n ( o r i n t he c a s e o f no remova l m e c h a n i s m , where t h e d e p o s i t i o n r a t e has d e c r e a s e d t o z e r o ) ; and t h e f a l l i n g r a t e c u r v e s , wh i ch r e p r e s e n t t h e t r a n s i t i o n between l i n e a r and a s y m p t o t i c c u r v e s . Many f o u l i n g c u r v e s e x h i b i t a d e l a y p e r i o d where no f o u l i n g i s o b s e r v e d t h e r m a l l y . T h i s p e r i o d i s r e f e r r e d t o as a n u c l e a t i o n , i n d u c t i o n o r i n c u b a t i o n p e r i o d , d e p e n d i n g on t h e t y p e o f f o u l i n g i n v o l v e d . 2 . 4 . F a c t o r s A f f e c t i n g F o u l i n g 2 . 4 . 1 . E f f e c t o f V e l o c i t y / T u r b u l e n c e / M a s s F l o w D e p o s i t i o n may be c o n t r o l l e d by e i t h e r mass d i f f u s i o n o r s u r f a c e r e a c t i o n . In t h e c a s e o f mass d i f f u s i o n , t h e d e p o s i t i o n t e r m can be e x p r e s s e d i n te rms o f the c o n v e o t i v e mass t r a n s f e r c o e f f i c i e n t w h i c h i s dependen t on f l u i d v e l o c i t y . The mass, t r a n s f e r c o e f f i c i e n t i s e x p r e s s e d as K = C l u b 0 - 8 ( 2 - 5 ) 8 F o r mass t r a n s f e r c o n t r o l l e d d e p o s i t i o n , C r i t t e n d e n and K o l a c z k o w s k i (12) a d v o c a t e t he f o l l o w i n g e x p r e s s i o n 0 . 2 , , 0 . 8 f > .<- ' ->A-| a U^ d R x 1.213A-, ;J u d 9 p ( d r 2 x ) 1 ' 8 P f k f C P B C D , ( S c / - 6 7 ( S c D ) 0 - 6 7 -Thus, i f t h e r e were no remova l m e c h a n i s m , t h e r a t e o f f o u l i n g wou ld i n c r e a s e as f l u i d v e l o c i t y i s i n c r e a s e d . The p o s i t i v e e f f e c t o f v e l o c i t y on d e p o s i t i o n r a t e i s o n l y m e a s u r a b l e under c o n d i t i o n s where remova l o f t h e d e p o s i t i s i n s i g n i f i c a n t , e . g . s i f t h e f o u l i h g d e p o s i t i s v e r y t e n a c i o u s o r t he v e l o c i t y i s v e r y l o w . U s i n g v a l u e s o f R e y n o l d s number and w a l l s h e a r s t r e s s f r om Hasson ( 1 3 ) , Hasson e t a l . ( 1 4 ) , and W a t k i n s o n and M a r t i n e z ( 1 5 ) , S u i t o r e t . a l . (16) showed t h a t an a s y m p t o t i c f o u l i n g r e s i s t a n c e does no t o c c u r u n t i l a t h r e s h o l d s h e a r s t r e s s i s e x c e e d e d . T h u s , t he e f f e c t o f v e l o c i t y on t h e remova l p r o c e s s i s b e t t e r c h a r a c t e r i z e d by w a l l s h e a r s t r e s s and ..the m e c h a n i c a l s t r e n g t h o f t h e d e p o s i t . Mos t p a p e r s ( 1 7 , 18) show t h a t f o u l i n g r a t e d e c r e a s e s as f l u i d v e l o c i t y i s i n c r e a s e d , a l t h o u g h Hasson (13) has shown t h a t the o p p o s i t e c a s e can be t r u e . W a t k i n s o n and E p s t e i n (18) g i v e t h e f o l l o w i n g e q u a t i o n f o r gas o i l f o u l i n g : d R f 7 7 6 , 0 0 0 e - 1 2 0 ' 0 0 0 / R g T s ( d e _ ) e = o . " 7 T T 0 7 ( 2 " 7 ) V 9 T h i s e q u a t i o n shows t h a t t h e r e a r e t h r e e e f f e c t s t h a t i n c r e a s e U , 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 , as u ^ , t he b u l k v e l o c i t y , i n c r e a s e s ( 9 ) : ( i ) t h e normal e f f e c t o f u^ i n i n c r e a s i n g h ( i i ) t h e d i r e c t e f f e c t o f u^ i n d e c r e a s i n g d R ^ / d e f r om E q . ( 2 - 7 ) ( i i i ) t h e d e c r e a s e i n T g as a c o n s e q u e n c e o f ( i ) and hence a f u r t h e r d e c r e a s e i n f o u l i n g r a t e by E q . ( 2 - 7 ) . Tabo rek e t a l . (7 ) d e r i v e d an e q u a t i o n f o r R^ , t he a s y m p t o t i c f o u l i n g r e s i s t a n c e : n - E / R n T c : * <S ? P d (n) e ' 9 s -R f = b — where 0<b<2 ( 2 - 8 ) u b * T h u s , R f a l s o a p p e a r s t o have a n e g a t i v e dependence on f l u i d v e l o c i t y . 2 . 4 . 2 . E f f e c t o f T e m p e r a t u r e F o r c h e m i c a l r e a c t i o n c o n t r o l l e d d e p o s i t i o n , the s u r f a c e t e m p e r a t u r e o f t h e d e p o s i t i s t he most i m p o r t a n t p a r a m e t e r and t he d e p o s i t i o n f u n c t i o n t a k e s an A r r h e n i u s f o r m , as shown by t h i s d e p o s i t i o n r a t e e q u a t i o n f r o m Tabo rek e t a l . ( 7 ) : * d = d 3 ( C r ) r e x p ( ^ 7 ^ ' ' ( 2 _ 9 ) E q u a t i o n s ( 2 - 7 ) and ( 2 - 8 ) show a s i m i l a r dependence on s u r f a c e t e m p e r a t u r e . Numerous s t u d i e s ( 1 , 2 , 3 , 7 , 1 0 , 1 6 , 1 7 , 1 8 , 2 2 - 3 4 ) have shown a s t r o n g dependence o f c h e m i c a l r e a c t i o n f o u l i n g on s u r f a c e t e m p e r a t u r e (35) T a y l o r ( 2 3 - 2 9 ) c o n s i s t e n t l y used t e m p e r a t u r e as one o f t he two p a r a m e t e r s i n h i s i n v e s t i g a t i o n s on j e t f u e l h y d r o c a r b o n s . The r a t e o f f o u l i n g 10 n o r m a l l y i n c r e a s e d e x p o n e n t i a l l y w i t h t e m p e r a t u r e , t he a p p a r e n t a c t i v a t i o n e n e r g y v a r y i n g f r o m 5 t o 45 k c a l / g - m o l e . T a y l o r ' s d a t a i n d i c a t e d t h a t t h e d e p o s i t f o r m a t i o n r a t e i n c r e a s e d w i t h i n c r e a s i n g t e m p e r a t u r e u n t i l a s h a r p d e c r e a s e o r l e v e l l i n g o f f p o i n t was r e a c h e d , w h i c h s u b s e q u e n t e x p e r i m e n t s r e v e a l e d was a g e n e r a l ^ p h e n o m e n o n . The t e m p e r a t u r e a t w h i c h t h i s phenomenon o c c u r r e d was d e s i g n a t e d t he " d e p o s i t f o r m a t i o n c u t - o f f t e m p e r a t u r e " ( 2 4 ) . T a y l o r (29) a t t r i b u t e d t h e c u t - o f f i n d e p o s i t f o r m a t i o n t o a r e d u c t i o n i n a u t o x i d a t i o n r e a c t i o n r a t e c a u s e d by a l o w e r i n g o f c o n c e n t r a t i o n o f r e a c t i v e s p e c i e s as t h e s y s t e m p a s s e s f r om l i q u i d phase t o v a p o u r p h a s e . W a t k i n s o n and E p s t e i n (18) showed t h a t t he f o u l i n g r a t e o f gas o i l s i n c r e a s e d s h a r p l y w i t h s u r f a c e t e m p e r a t u r e i n t he range 295°F t o 4 0 0 ° F , w i t h an a v e r a g e a c t i v a t i o n e n e r g y o f 29 k c a l / m o l e . H a u s l e r ( 2 ) , H a u s l e r and T h a l m a y e r (17) and B raun and H a u s l e r ( 2 2 ) , i n t h e i r p e t r o l e u m f o u l i n g r e s u l t s u s i n g t he ho t w i r e t e s t (UOP M o n i r e x F o u l i n g T e s t ) , show t h a t f o u l i n g r a t e g e n e r a l l y i n c r e a s e s w i t h w i r e t e m p e r a t u r e . T h e i r t y p i c a l p l o t o f d R y / d e v e r s u s w i r e t e m p e r a t u r e c o n s i s t e d o f a r e g i o n o f low f o u l i n g r a t e s u n t i l a " b r e a k - t h r o u g h t e m p e r a t u r e " was r e a c h e d , , u p o n w h i c h t h e f o u l i n g r a t e i n c r e a s e d d r a m a t i c a l l y . Be low t h i s b r e a k - t h r o u g h t e m p e r a t u r e , i t was o b s e r v e d i n some r u n s t h a t f o u l i n g r a t e a c t u a l l y d e c r e a s e d w i t h i n c r e a s i n g w i r e t e m p e r a t u r e . T a b o r e k e t a l . (7 ) s t a t e t h a t , unde r c o n s t a n t h e a t f l u x c o n d i t i o n s , t h e i n t e r n a l t e m p e r a t u r e o f t h e d e p o s i t i n c r e a s e s as d e p o s i t i o n p r o g r e s s e s . S i n c e c r y s t a l l i z a t i o n i s a f u n c t i o n o f t e m p e r a t u r e , t h e i n t e r n a l p o r t i o n o f t h e d e p o s i t w i l l undergo a d d i t i o n a l c r y s t a l l i z a t i o n 11 p r o c e s s e s . Such c r y s t a l l i z a t i o n p r o c e s s e s wou ld a f f e c t t h e s t r e n g t h o f t he d e p o s i t and t h e r e b y t h e remova l o f t h e d e p o s i t . T h i s wou ld a l s o a p p l y t o c h e m i c a l r e a c t i o n p r o c e s s e s s u c h as p o l y m e r i z a t i o n . A c c o r d i n g t o S u i t o r e t a l . ( 1 6 ) , t h e t e m p e r a t u r e o f i m p o r t a n c e i n d e p o s i t i o n a r e t h e l i q u i d / b u l k , s u r f a c e and w a l l t e m p e r a t u r e s . F u r t h e r m o r e , t h e t e m p e r a t u r e dependence o f t h e d e p o s i t i o n p r o c e s s i s a f u n c t i o n o f t h e mode o f h e a t i n g . A c c o r d i n g t o F i s c h e r e t a l . ( 2 1 ) , unde r c o n s t a n t h e a t f l u x c o n d i t i o n s , t h e d e p o s i t s u r f a c e t e m p e r a t u r e r e m a i n s c o n s t a n t ( as l o n g as t h e s u r f a c e / f l u i d h e a t t r a n s f e r c o e f f i c i e n t r e m a i n s e q u a l t o t he i n i t i a l , c l e a n h e a t t r a n s f e r c o e f f i c i e n t ) . W i t h f o u l i n g s t reams t h a t a r e n o t s i g n i f i c a n t l y a l t e r e d by a change i n h y d r a u l i c d i a m e t e r o r c h e m i c a l c o m p o s i t i o n , t h e c o n s t a n t h e a t f l u x c o n d i t i o n w i l l r e s u l t i n a u n i f o r m d e p o s i t i o n r a t e . In t h e c a s e o f c o n s t a n t w a l l t e m p e r a t u r e , t he d e p o s i t s u r f a c e t e m p e r a t u r e d e c r e a s e s w i t h i n c r e a s i n g d e p o s i t i o n . T h u s , t he d e p o s i t i o n r a t e w i l l d e c r e a s e w i t h t i m e . As s u r f a c e t e m p e r a t u r e i n c r e a s e s , t h e i n t e r f a c i a l f o u l a n t c o n c e n t r a t i o n ( f o r a c h e m i c a l r e a c t i o n f o u l i n g s y s t e m ) d e c r e a s e s , and t h u s t h e c o n c e n t r a t i o n g r a d i e n t i n c r e a s e s . A c c o r d i n g t o E q . ( 2 - 6 ) , t h e r a t e o f d e p o s i t i o n w o u l d . t h e n i n c r e a s e . In t h e c a s e o f s c a l i n g s y s t e m s , t h e c o n c e n t r a t i o n g r a d i e n t s e t up due t o t h e t e m p e r a t u r e d i f f e r e n c e between t h e s a t u r a t i o n t e m p e r a t u r e in - t he b u l k f l u i d and t he s c a l e s u r f a c e t e m p e r a t u r e , i s t h e d r i v i n g f o r c e f o r mass t r a n s f e r ( 1 6 ) . 12 2 . 4 . 3 . E f f e c t o f S u l p h u r Compounds i n H y d r o c a r b o n F o u l i n g T a y l o r ( 2 3 , 2 7 , 2 8 , 2 9 ) p r o v e d e x p e r i m e n t a l l y t h e c a p a b i l i t y o f v a r i o u s s u l p h u r compounds i n t r a c e l e v e l s t o i n c r e a s e m a r k e d l y t h e r a t e o f d e p o s i t f o r m a t i o n . He doped an o x y g e n a t e d h y d r o c a r b o n w i t h a v a r i e t y o f s u l p h u r compounds (1000 ppm c o n c e n t r a t i o n ) . A s q u a r e r o o t dependence o f d e p o s i t f o r m a t i o n r a t e on t h e r e l a t i v e s u l p h u r l e v e l was o b s e r v e d . T a y l o r (23) e x p l a i n s t h e phenomenon by s t a t i n g t h a t i f a s u l p h u r compound decomposed t o p r o d u c e a s i n g l e a c t i v e f r e e r a d i c a l , and d e p o s i t s were p r o d u c e d v i a a r a d i c a l - r a d i c a l r e c o m b i n a t i o n r e a c t i o n , a s q u a r e r o o t dependence o f f o r m a t i o n r a t e on s u l p h u r l e v e l c o u l d be e x p e c t e d . I t w o u l d a p p e a r t h a t s u l p h u r compounds e i t h e r i n i t i a t e o r c a t a l y z e t h e d e p o s i t i o n p r o c e s s . The d e p o s i t i o n r a t e c o u l d be e x p r e s s e d i n an A r r h e n i u s - t y p e r e l a t i o n (a p l o t o f l o g ( d e p o s i t i o n f o r m a t i o n r a t e ) v e r s u s 1000 /T (deg K) ) , w i t h t h e a p p a r e n t a c t i v a t i o n e n e r g y r a n g i n g f r om 10 t o 20 k c a l / m o l e . On a d e o x y g e n a t e d b a s i s ( 2 3 ) , d e p o s i t i o n r a t e c o u l d n o t be e x p r e s s e d i n an A r r h e n i u s - t y p e r e l a t i o n , b u t t h e r a t e o f d e p o s i t i o n was d e f i n i t e l y i n c r e a s e d by t h e p r e s e n c e o f s u l p h u r compounds. H a u s l e r and T h a l m a y e r (17) examined the s c a l e d e p o s i t e d on t h e i r h o t w i r e f o u l i n g p r o b l e f r o m a p e t r o l e u m r e f i n e r y f e e d s t o c k . They p r o d u c e d X - r a y s c a t t e r p a t t e r n s o f t h e i r d e p o s i t s c a l e f o r i r o n and s u l p h u r w h i c h showed t h a t i r o n s u l f i d e was d i s t r i b u t e d t h r o u g h o u t t h e d e p o s i t . T h i s i n d i c a t e s t h a t t h e r e may be a mechan ism whereby i r o n s u l f i d e can m i g r a t e t h r o u g h a c a r b o n a c e o u s l a y e r and can c o n t i n u e t o p a r t i c i p a t e i n t h e r e a c t i o n s l e a d i n g t o f o u l i n g d e p o s i t s . In t he same p a p e r , H a u s l e r p o s t u l a t e s t h e r e a c t i o n 13 R-SH + Fe FeSH + R- ( 2 - 1 0 ) w h i c h can y i e l d h y d r o c a r b o n r a d i c a l s t h a t may i n i t i a t e p o l y m e r i z a t i o n . 2 . 4 . 4 . E f f e c t o f N i t r o g e n Compounds i n H y d r o c a r b o n F o u l i n g T a y l o r (28) p e r f o r m e d e x p e r i m e n t s i n w h i c h pu re n i t r o g e n compounds were added t o an o x y g e n a t e d h y d r o c a r b o n j e t f u e l a t t h e 1000 ppm n i t r o g e n l e v e l . T h e r e was a s q u a r e r o o t dependence o f d e p o s i t f o r m a t i o n r a t e on r e l a t i v e n i t r o g e n c o n c e n t r a t i o n , w h i c h s u g g e s t e d t h a t n i t r o g e n compounds c o n t r i b u t e t o t h e i n i t i a t i o n s t e p . 2 . 4 . 5 . E f f e c t o f T r a c e M e t a l s (homogeneous and ' h e t e r o g e n e o u s ) i n H y d r o c a r b o n F o u l i n g  M e t a l s , bo th h e t e r o g e n e o u s ( s u r f a c e i n c o n t a c t ) and homogeneous ( d i s s o l v e d i n f l u i d ) , have been shown t o c o n t r i b u t e t o f o u l i n g by c a t a l y z i n g o r i n i t i a t i n g o r g a n i c p o l y m e r f o r m a t i o n . A c c o r d i n g t o B raun and H a u s l e r ( 2 2 ) , a number o f t r a n s i t i o n me ta l i o n s can a c t as c a t a l y s t s • i n t h e a u t o x i d a t i o n i n i t i a t i o n r e a c t i o n : M n + 2 + 0 2 - M n + 3 + ( 0 2 O ~ ( 2 - l l a ) RH + ( 0 2 • • ) " - + ( 0 2 H ) " (2-1 l b ) ( 0 2 H ) " + M n + 3 -y M n + 2 + - 0 2 H ( 2 - l l c ) ( R e g e n e r a t i o n o f c a t a l y s t ) • 0 2 H + RH -> R- + H 2 0 2 (2-1 I d ) C r a w f o r d and M i l l e r (36) g i v e t h e f o l l o w i n g r e a c t i o n s : I n i t i a t i o n M e + + + RH -> M e + + R- + H + ( 2 - 1 2 a ) M e + + + R00H + M e + + R00- + H + ( 2 - 1 2 b ) 14 C a t a l y s t R e g e n e r a t i o n M e + + ROOH -> R0- + M e + + + OH" ( 2 . 1 2 c ) B e s i d e s c a t a l y z i n g p o l y m e r f o r m a t i o n , me ta l c o n t a m i n a t i o n has been shown t o i n c r e a s e oxygen u p t a k e and i n c r e a s e t h e b u l k o f f o u l i n g d e p o s i t s byy p r o v i d i n g a d d i t i o n a l s u r f a c e t o w h i c h p o l y m e r s can a d h e r e ( 3 6 ) . T a y l o r (28) c o n d u c t e d a s e r i e s o f e x p e r i m e n t s f o r b o t h t h e he te rogeneous , and homogeneous e f f e c t s s o f m e t a l . A r r h e n i u s p l o t s f o r f o u l i n g on d i f f e r e n t me ta l s u r f a c e s e x h i b i t e d a p p a r e n t a c t i v a t i o n e n e r g i e s o f 10 k c a l / m o l e , w i t h c o p p e r a p p e a r i n g t o be t h e most d e l e t e r i o u s me ta l s u r f a c e . F o r h y d r o c a r b o n j e t f u e l doped w i t h v a r i o u s me ta l a c e t y l a c e t o n a t e s a t t h e 50 ppm m e t a l l e v e l , t h e a d d i t i o n o f t h e m e t a l a c e t y l a c e t o n a t e s i n c r e a s e d t h e a p p a r e n t a c t i v a t i o n e n e r g y f o r t h e d e p o s i t f o r m a t i o n p r o c e s s f r om 10 t o 25 k c a l / m o l e . T a y l o r f o u n d a s q u a r e r o o t dependence o f d e p o s i t f o r m a t i o n r a t e on t h e r e l a t i v e i r o n c o n c e n t r a t i o n i n t h e doped f u e l and on t h e vanad ium c o n t e n t o f t h e t i t a n i u m m e t a l s u r f a c e s , w h i c h wou ld s u g g e s t t h a t m e t a l s c a t a l y z e o r i n i t i a t e t h e c h a i n r e a c t i o n s o f d e p o s i t f o r m a t i o n . 2 . 4 . 6 . E f f e c t o f Oxygen C o n t e n t / D e o x y g e n a t i o n i n H y d r o c a r b o n F o u l i n g  The e f f e c t o f oxygen on p e t r o l e u m p r o c e s s f o u l i n g i s embod ied i n a u t o x i d a t i o n , a f r e e r a d i c a l mechan ism i n v o l v i n g h y d r o c a r b o n s and oxygen t o y i e l d a l k y l and p e r o x y r a d i c a l s ( 3 7 , 3 8 ) : I n i t i a t i o n RH + Z- + R- + HZ ( 2 - 1 3 a ) C h a i n P r o p a - R- + 0 2 -> R00- ( 2 - 1 3 b ) g a t i o n 15 ROO- + RH •* ROOH + R- ( 2 - 1 3 c ) T e r m i n a t i o n R- + R- -> RR ( 2 - 1 3 d ) ROO- + R- + ROOR ( 2 - 1 3 e ) 2 R 2 C 0 0 - -> 2 R 2 C O - + 0 2 -> R 2 C 0 + R^COH ( 2 - 1 3 f ) The a u t o x i d a t i o n i n i t i a t i o n r e a c t i o n i n v o l v e s a r a d i c a l Z? o f s u f f i c i e n t l y h i g h r e a c t i v i t y t o remove a hyd rogen atom f rom a h y d r o c a r b o n m o l e c u l e ( 2 2 ) . The p r o d u c t s o f t h e a u t o x i d a t i o n c h a i n r e a c t i o n a r e h y d r o p e r o x i d e s , w h i l e t h e c h a i n t e r m i n a t i o n r e s u l t s i n a c i d s , k e t o n e s and a l c o h o l s . e l i m i n a t e d d e p o s i t f o r m a t i o n up t o t e m p e r a t u r e s o f 3 1 5 ° C , i n f i v e o u t o f s i x f u e l s t e s t e d . The e x c e p t i o n was a v e r y p o o r q u a l i t y f u e l . In t he t e m p e r a t u r e range f rom 150°C t o 3 1 5 ° C , a p p a r e n t a c t i v a t i o n e n e r g i e s f o r d e p o s i t f o r m a t i o n f r o m o x y g e n a t e d f u e l s r a n g e d f r om 5 t o 15 k c a l / m o l e , w h i l e v a l u e s f o r d e o x y g e n a t e d f u e l s were l e s s t h a n 5 k c a l / m o l e . A d e o x y g e n a t e d f u e l c o n t i n u e d t o e x h i b i t r e l a t i v e l y l ow d e p o s i t i o n r a t e s u n t i l a b o u t 6 0 0 ° C , The a p p a r e n t a c t i v a t i o n e n e r g y o v e r t h i s t e m p e r a t u r e range (315°C - 600°C) i n c r e a s e d f r om l e s s t h a n 5 k c a l / m o l e t o 40 k c a l / m o l e . F o r o x y g e n a t e d f u e l s , t h e g e n e r a l p a t t e r n was t h a t o f i n c r e a s i n g d e p o s i t f o r m a t i o n r a t e w i t h i n c r e a s i n g t e m p e r a t u r e ; a s h a r p d r o p - o f f i n f o r m a t i o n r a t e i n a t r a n s i t i o n zone c o v e r i n g t h e 350-425°C r a n g e ; f o l l o w e d by i n c r e a s i n g d e p o s i t f o r m a t i o n r a t e w i t h i n c r e a s i n g t e m p e r a t u r e . T a y l o r p o s t u l a t e d M a t . t h e p r i m a r y e f f e c t o f oxygen c o n c e n t r a t i o n on t h e d e p o s i t f o r m a t i o n r a t e o c c u r s a t l o w e r t e m p e r a t u r e s , T a y l o r (24) r e p o r t e d t h a t r i g o r o u s e x c l u s i o n o f oxygen a l m o s t 16 j u s t b e f o r e t h e t r a n s i t i o n z o n e . A t h i g h e r t e m p e r a t u r e s , new h y d r o c a r b o n r e a c t i o n s b e g i n t o assume i m p o r t a n c e and t h e e f f e c t o f d e o x y g e n a t i o n i s n o t as p r o n o u n c e d . B raun and H a u s l e r (22) a l s o showed t h a t o x y g e n a t i n g a h y d r o c a r b o n f u e l d r a m a t i c a l l y i n c r e a s e s t h e f o u l i n g r a t e . 2 . 4 . 7 . E f f e c t o f A d d i t i v e s / S u r f a c e C o a t i n g s i n H y d r o c a r b o n F o u l i n g  H a u s l e r ( 2 ) , H a u s l e r and T h a l m a y e r ( 1 7 ) , and T a y l o r (26) show t h a t a d d i t i v e s and s u r f a c e c o a t i n g s work e f f e c t i v e l y o n l y o v e r s p e c i f i c t e m p e r a t u r e r a n g e s . O u t s i d e t h e s e t e m p e r a t u r e r a n g e s , t h e a d d i t i v e s a n d / o r s u r f a c e c o a t i n g s c o u l d i n c r e a s e r a t h e r t h a n d e c r e a s e f o u l i n g . P a p e r s by C a n a p a r y ( 3 ) , F r a z i e r e t a l . (30) and HaTuska (39) r e v e a l t h a t i n t h e p r o p e r c o n c e n t r a t i o n s , t h e c o r r e c t k i n d o f a d d i t i v e can be v e r y e f f e c t i v e i n r e d u c i n g o r i n h i b i t i n g f o u l i n g . T a y l o r (26) s t u d i e d t h e e f f e c t i v e n e s s o f a n t i o x i d a n t s , r u s t p r e v e n t a t i v e and m e t a l - d e a c t i v a t o r a d d i t i v e s , and o f c o a t i n g a c a t a l y t i c a l a c t i v e m e t a l s u r f a c e w i t h p o l y m e r i c m a t e r i a l s {e;:§, t e f l o n ) , i n r e d u c i n g f o u l i n g o f h y d r o c a r b o n f u e l s , i n t h e t e m p e r a t u r e range o f 2 5 0 - 4 2 5 ° F . He f o u n d t h a t t h e a n t i o x i d a n t s were i n e f f e c t i v e ; t h e r u s t p r e v e n t a t i v e and m e t a l - d e a c t i v a t o r a d d i t i v e s i n c r e a s e d t h e r a t e o f d e p o s i t f o r m a t i o n above 3 5 0 ° F ; and t h e c o a t i n g s i n c r e a s e d t h e r a t e o f d e p o s i t i o n . A t h i g h t e m p e r a t u r e s , t h e r u s t p r e v e n t a t i v e and m e t a l - d e a c t i v a t o r a d d i t i v e s were p r o b a b l y decompos ing t o r a d i c a l f r a g m e n t s a n d / o r f u e l i n s o l u b l e p r o d u c t s : . Emanuel (40) s u g g e s t e d t h a t t h e t e f l o n s u r f a c e c o a t i n g 17 c a t a l y z e d t h e d e c o m p o s i t i o n o f t h e i n t e r m e d i a t e h y d r o p e r o x i d e s t o f r e e r a d i c a l f r a g m e n t s f a s t e r t h a n d i d t h e me ta l s u r f a c e . C a n a p a r y (3) used a s t a b i l i z e r d i s p e r s a n t a d d i t i v e w h i c h s t a b i l i z e s , i n c i p i e n t p o l y m e r -f o r m i n g m a t e r i a l s and p r e v e n t s a g g l o m e r a t i o n o f a l r e a d y f o rmed p o l y m e r s so t h e y r e m a i n s o l u b l e i n t h e h y d r o c a r b o n s t r e a m . Such an a d d i t i v e was f ound t o imp rove h e a t t r a n s f e r by 77% t o 98%. 2 . 4 . 8 . E f f e c t o f F l u i d C h e m i s t r y C a n a p a r y (3) s t a t e s t h a t r e d u c i n g u n s a t u r a t e s by e l i m i n a t i n g c r a c k e d s t o c k w i l l h e l p r e d u c e t h e t e n d e n c y o f h y d r o c a r b o n s t r e a m s t o f o u l . C r a w f o r d and M i l l e r (36 ) make t h e same s t a t e m e n t , a d d i n g t h a t s t r a i g h t run s t o o k s a l s o c o n t r i b u t e t o o r g a n i c f o u l i n g , a l t h o u g h t o a l e s s e r d e g r e e . T a y l o r (25) s t u d i e d t h e d e p o s i t f o r m a t i o n t e n d e n c y o f v a r i o u s pu re h y d r o c a r b o n s and b i n a r y b l e n d s f r o m 200°F t o 450°F i n t h e p r e s e n c e o f a i r . He f o u n d t h a t t h e d e p o s i t f o r m a t i o n t e n d e n c y o f normal p a r a f f i n s i n c r e a s e d w i t h d e c r e a s i n g c a r b o n number . F o r a g i v e n c a r b o n number , b r a n c h e d p a r a f f i n s t e n d t o f o u l more t h a n normal p a r a f f i n s . The p r e s e n c e o f an a r o m a t i c o r naph thene i n a b i n a r y b l e n d w i t h a p a r a f f i n i n h i b i t s d e p o s i t f o r m a t i o n , p a r t i c u l a r l y a t l o w e r c o n c e n t r a t i o n s and t e m p e r a t u r e s . In g e n e r a l , t h e a d d i t i o n o f an o l e f i n t o normal p a r a f f i n s i n c r e a s e s . t h e l e v e l o f d e p o s i t f o r m a t i o n , bu t t h e m a g n i t u d e o f t h e i n c r e a s e v a r i e s m a r k e d l y , d e p e n d i n g on t h e o l e f i n a d d e d . I t was a l s o shown t h a t t h e r e l a t i v e r a t e o f d e p o s i t f o r m a t i o n e s s e n t i a l l y i n c r e a s e s l i n e a r l y w i t h i n c r e a s i n g o l e f i n c o n c e n t r a t i o n . T a y l o r s t a t e s t h a t t h e 18 a d d i t i o n o f an o l e f i n t o a p a r a f f i n - r i c h m i x t u r e i n c r e a s e s t h e r a t e o f a u t o x i d a t i v e d e p o s i t f o r m a t i o n . Mayo (41) s t a t e s t h a t o l e f i n s can e i t h e r r e a c t w i t h oxygen t o f o rm h y d r o p e r o x i d e s i n i t i a l l y v i a a hyd rogen a b s t r a c t i o n m e c h a n i s m , o r t h e y can undergo an a d d i t i o n mechan ism t o f o rm p o l y p e r o x i d e s . F u r t h e r m o r e , t h e r e l a t i v e e f f e c t o f v a r i o u s o l e f i n s on d e p o s i t f o r m a t i o n c l o s e l y p a r a l l e l s t h e i r o b s e r v e d r e a c t i v i t y t owa rd o x i d a t i o n . 2 . 4 . 9 . E f f e c t o f S u r f a c e C o n d i t i o n / F l o w Geometry Tabo rek e t a l . (7 ) s t a t e t h a t s u r f a c e r o u g h n e s s , s i z e and d e n s i t y o f c a v i t i e s w i l l a f f e c t t h e c r y s t a l l i n e n u c l e a t i o n , s e d i m e n t a t i o n and a d h e r e n c e t e n d e n c y o f d e p o s i t s . They d e f i n e a d e p o s i t bond r e s i s t a n c e , R^ , as t h e a d h e s i v e s t r e n g t h o f t h e d e p o s i t p e r u n i t a r e a a t t h e p l a n e o f w e a k e s t a d h e s i o n . They s t a t e t h a t R^ i s a f u n c t i o n o f t h e o r i g i n a l s u r f a c e c h a r a c t e r i s t i c s o n l y i f t h e d e p o s i t - s u r f a c e i n t e r f a c e a d h e s i o n i s weake r t h a n t h e d e p o s i t - i n t e r n a l a d h e s i o n , .which a c c o u n t s f o r t h e f a c t t h a t s p e c i a l l y p r e p a r e d smooth s u r f a c e s r e t a r d f o u l i n g ~. i n some i n s t a n c e s and n o t i n o t h e r s . S u r f a c e c o n d i t i o n has i t s g r e a t e s t e f f e c t i n f o u l i n g i n i t i a t i o n r a t h e r t h a n f o r t h e c o n t i n u e d f o u l i n g p r o c e s s . Tabo rek e t a l . (7 ) a l s o s t a t e t h a t t h e c o n s i d e r a b l e v a r i e t y i n equ ipmen t d e s i g n g e o m e t r i e s and f l o w s y s t e m s w i l l r e s u l t i n a c o n s i d e r a b l e d i f f e r e n c e i n f l o w p a t t e r n s , v e l o c i t y and w a l l t e m p e r a t u r e d i s t r i b u t i o n s , d e g r e e o f t u r b u l e n c e , a b i l i t y t o " s h e d " f o u l i n g d e p o s i t s , e t c . They f u r t h e r s t a t e t h a t h e a t t r a n s f e r equ ipmen t w i t h t h e f o l l o w i n g 19 t y p e s o f f l o w p a t t e r n s may r e a c t t o v a r i o u s t y p e s o f f o u l i n g and o p e r a t i o n a l p a r a m e t e r s i n a d r a s t i c a l l y d i f f e r e n t manner : ( i ) t u b e s i d e and a n n u l a r f l o w . F o r t h e same f l o w v e l o c i t y and w a l l t e m p e r a t u r e , t u b e s i d e and a n n u l a r f l o w behave i d e n t i c a l l y . ( i i ) s h e l l s i d e f l o w , s u b j e c t t o e f f e c t s o f v a r i o u s b a f f l e geomet ry d e s i g n s . S h e l l s i d e f l o w i s c h a r a c t e r i z e d by many l e a k a g e and b y p a s s s t r e a m s , and a r e a s o f w i d e l y v a r y i n g f l o w v e l o c i t y . L a r g e b a f f l e c u t s c r e a t e dead a r e a s o f v i r t u a l l y z e r o f l o w v e l o c i t i e s . S i n c e most f o u l i n g i s v e l o c i t y d e p e n d e n t , f o u l i n g d e p o s i t s w i l l no t be u n i f o r m , and t h u s o n l y o v e r a l l f o u l i n g r e s i s t a n c e s can be used i n s h e l l - s i d e f l o w , ( i i i ) p l a t e and s p i r a l h e a t e x c h a n g e r s . B o t h t y p e s o f e x c h a n g e r s e x h i b i t a h i g h d e g r e e o f t u r b u l e n c e , w h i c h s h o u l d s u p p r e s s f o u l i n g . ( i v ) f l e x i b l e t u b e d e s i g n e.g. . T e f l o n . Due t o t h e f l e x i b i l i t y o f t h e m a t e r i a l , t h e r e i s a t e n d e n c y f o r t h e s e t u b e s t o " s h e d " t h e f o u l i n g d e p o s i t , ( v ) f i n n e d t u b e s . T h e r e i s e v i d e n c e t h a t t h e f o u l i n g p r o c e s s i s l e s s p ronounced on f i n n e d t u b e s t h a n on p l a i n ones ( 4 2 , 4 3 ) . Howeve r , W a t k i n s o n e t a l . (44 ) showed t h a t f o r i n n e r - f i n n e d t u b e s , t h e f o u l i n g r e s i s t a n c e e x c e e d e d p l a i n t u b e v a l u e s , w h i l e f o r s p i r a l l y i n d e n t e d t u b e s , f o u l i n g r e s i s t a n c e s were be low t h e p l a i n t u b e v a l u e s . 20 ( v i ) o t h e r p r o p r i e t a r y d e s i g n s . T a b o r e k e t a l . (7 ) s t a t e t h a t s m a l l p i t s i n t h e s u r f a c e can p r o v i d e i n i t i a l s h e l t e r f r om f l u i d s h e a r f o r c e s and a n c h o r s f o r g r o w i n g c r y s t a l o r p o l y m e r p a r t i c l e s . In p r e d i c t i v e f o u l i n g m o d e l s , s u r f a c e e f f e c t s a r e a c c o u n t e d f o r i n " s t i c k i n g " o r a d h e s i o n p r o b a b i l i t y f u n c t i o n s . S m i t h (1) showed t h a t t u r b u l e n c e p r o m o t e r s d e c r e a s e t h e t h i c k n e s s o f t h e l a m i n a r s u b l a y e r and t h u s i n c r e a s e 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 . S m i t h a l s o o b s e r v e d t h e s o - c a l l e d " r o u g h n e s s e f f e c t " . . The l a m i n a r s u b l a y e r p r e s e n t s t h e m a j o r r e s i s t a n c e t o t h e f l o w o f h e a t f r om t h e w a l l t o t h e t u r b u l e n t c o r e . As d e p o s i t i o n p r o c e e d s , t h e d e p o s i t r o u g h n e s s e l e m e n t s d i s t u r b t h e l a m i n a r s u b l a y e r , c a u s i n g t u r b u l e n c e a d j a c e n t t o t h e w a l l , and t h u s t e n d i n g t o i n c r e a s e 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 . T h i s e f f e c t opposes t h e t e n d e n c y o f 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 t o f a l l due t o t h e l ow t h e r m a l c o n d u c t i v i t y o f t h e d e p o s i t . These two o p p o s i n g t e n d e n c i e s w i l l compete u n t i l t h e t h i c k n e s s o f t he d e p o s i t a p p r o a c h e s and e x c e e d s t h e t h i c k n e s s o f t h e l a m i n a r s u b l a y e r . Hasson (19) and B o t t and Gudmundsson (20) b o t h had f o u l i n g c u r v e s t h a t e x h i b i t e d n e g a t i v e f o u l i n g r e s i s t a n c e s due t o t h e r o u g h n e s s e f f e c t . 2 . 5 . Measurement o f D e p o s i t A c c u m u l a t i o n T h e r e have been numerous f o u l i n g measurement t e c h n i q u e s . A c c o r d i n g t o E p s t e i n ( 9 ) , t h e v a r i o u s t e c h n i q u e s can be c l a s s i f i e d 21 a c c o r d i n g t o t h e g e o m e t r y o f t he f o u l i r i g s u r f a c e , t he t y p e o f h e a t i n g , and t h e method o f m o n i t o r i n g t h e d e p o s i t ( s e e T a b l e 2 - 1 ) . T a b l e 2 - 1 . . C l a s s i f i c a t i o n o f F o u l i n g Measurement T e c h n i q u e s Geomet ry o f F o u l i n g S u r f a c e I n s i d e o f t ube C i r c u l a r c y l i n d e r S p h e r e O u t s i d e o f U - t ube I n s i d e o f U - t ube M e t a l l i c s t r i p P l a t e P o r o u s p l u g W i r e S h e l l s i d e o f h e a t e x c h a n g e r H e l i x W i r e c o i l Type o f H e a t i n g S e n s i b l e f l u i d h e a t i n g C o n d e n s i n g v a p o u r h e a t i n g E l e c t r i c a l r e s i s t a n c e h e a t i n g o f t e s t s e c t i o n i t s e l f I n d i r e c t e l e c t r i c a l h e a t i n g T h e r m o - e l e c t r i c h e a t i n g and c o o l i n g Method o f M o n i t o r i n g D e p o s i t V i s u a l l y By d i r e c t w e i g h i n g By e l e c t r i c a l c o n d u c t a n c e M i c r o s c o p i c a l l y By p r e s s u r e d r o p T h e r m a l l y R a d i o a c t i v e l y E l e c t r o l y t i c a l l y C h e m i c a l l y 22 One o f t h e b e s t - k n o w n l a b o r a t o r y t e s t s f o r a s s e s s i n g the t e n d e n c y o f a h y d r o c a r b o n f u e l t o f o u l i n h e a t - e x c h a n g e equ ipmen t i s t he E r d c o CFR f u e l c o k e r t e s t ( 3 0 ) . O i l i s pumped t h r o u g h an e l e c t r i c a l l y h e a t e d t u b u l a r h e a t e r and t h e n t h r o u g h an e l e c t r i c a l l y h e a t e d p o r o u s me ta l f i l t e r w h i c h i s h e l d a t a t e m p e r a t u r e 100°F h i g h e r t h a n t h a t o f t h e t u b e . The p r e s s u r e d rop a c r o s s t h e f i l t e r i s measured and a f o u l i n g i n d e x i s c a l c u l a t e d f r om a p r e s s u r e d r o p v e r s u s t i m e c u r v e . The ma in d i s a d v a n t a g e o f t h i s t e s t i s t h a t no c o r r e l a t i o n has been e s t a b l i s h e d between t h e p r e s s u r e d rop a c r o s s a p o r o u s m e t a l f i l t e r and t he h e a t t r a n s f e r e f f i c i e n c y o f a h e a t e x c h a n g e r . ( 2 ) . The J e t F u e l Thermal O x i d a t i o n T e s t (JFTOT) o p e r a t e s on t he same g e n e r a l p r i n c i p l e s as t h e E r d c o c o k e r . The p r e h e a t e r t u b e , w h i c h i s h e a t e d by p a s s i n g e l e c t r i c a l c u r r e n t d i r e c t l y t h r o u g h the t ube w a l l , has been m i n i a t u r i z e d , w h i c h p e r m i t s d e t e r m i n a t i o n o f t h e e x t e n t o f f o u l i n g by t h e w e i g h t change o f t h e p r e h e a t e r t u b e , as w e l l as by t he p r e s s u r e drop s a c r o s s t h e t e s t f i l t e r . The p r e h e a t e r t ube t e m p e r a t u r e i s measured by a movab le t h e r m o c o u p l e i n s i d e t he t u b e , w h i c h i s p o s i t i o n e d a t t h e maximum t e m p e r a t u r e p o i n t o f t he t u b e . The p r e h e a t e r t ube d e p o s i t s can be r a t e d by a v i s u a l method as s p e c i f i e d i n ASTM D-1660 a n d / o r by a "Tube D e p o s i t R a t e r " w h i c h u t i l i z e s t h e change i n l i g h t r e f l e c t i o n as a measure o f d e p o s i t q u a n t i t y ( 3 9 , 4 5 , 4 6 ) . The p r o b l e m w i t h t h i s t e s t i s t h e l a c k o f a c o r r e l a t i o n be tween h e a t t r a n s f e r e f f i c i e n c y and t h e d e p o s i t w e i g h t on t h e p r e h e a t e r . MTRI (Hea t T r a n s f e r R e s e a r c h I n c . ) has d e s i g n e d f o u r n o t e -w o r t h y f o u l i n g measurement s y s t e m s ( 2 1 ) . The S t a t i o n a r y F o u l i n g 23 R e s e a r c h U n i t uses i n d i r e c t e l e c t r i c a l h e a t i n g f o r t h r e e p a r a l l e l t e s t s e c t i o n s . Each t e s t s e c t i o n c o n s i s t s o f a heavy w a l l e d t ube w i t h h e a t i n g r o d s p l a c e d i n l o n g i t u d i n a l f l u t e s on t h e o u t e r c i r c u m f e r e n c e and t h e r m o c o u p l e s imbedded i n t h e t ube w a l l a t s e v e n p o i n t s down the l e n g t h o f e a c h t u b e . The e n t i r e a s s e m b l y i s p o t t e d i n h e a t t r a n s f e r c e m e n t . The r a t e o f f o u l i n g i s m o n i t o r e d t h e r m a l l y , i . e . l o c a l f o u l i n g r e s i s t a n c e s a r e measured as a f u n c t i o n o f t i m e . • In t he P o r t a b l e F o u l i n g R e s e a r c h U n i t , f l u i d f l o w s t h r o u g h an a n n u l a r s p a c e , t h e i n n e r s u r f a c e o f w h i c h i s h e a t e d by t h e i n d i r e c t e l e c t r i c a l h e a t i n g o f a r e s i s t a n c e c o i l p a c k e d i n magnesium o x i d e i n s i d e t h e i n n e r t u b e . T h r e e t h e r m o c o u p l e s a r e imbedded i n t h e t ube w a l l n e a r t h e downs t ream end o f the h e a t e d s e c t i o n . Hea t t r a n s f e r c o e f f i c i e n t s a r e d e t e r m i n e d by t e m p e r a t u r e measurements a t a known h e a t f l u x . The T u b e s i d e F o u l i n g R e s e a r c h U n i t measu res f o u l i n g i n s i d e a t u b e w h i c h i s e x t e r n a l l y h e a t e d by a c o n d e n s i n g v a p o u r , u s u a l l y s t e a m . F o u l i n g r e s i s t a n c e s a r e d e t e r m i n e d f r om o v e r a l l measurements o f t e m p e r a t u r e and h e a t f l o w . A d o u b l e j a c k e t d e s i g n i s u s e d , where t h e o u t e r j a c k e t p r e v e n t s h e a t l o s s and a c t s as a d e s u p e r h e a t e r so t h a t t he c o n d e n s i n g v a p o u r i n t h e i n n e r j a c k e t i s a t t h e s a t u r a t i o n t e m p e r a t u r e . The amount o f h e a t t r a n s f e r r e d t o t h e t e s t f l u i d i s d e t e r m i n e d by t h e amount o f v a p o u r c o n d e n s e d i n t h e i n n e r j a c k e t . The S h e l l s i d e F o u l i n g R e s e a r c h U n i t measu res f o u l i n g o f t h e comp lex g e o m e t r i e s f o u n d on t h e s h e l l s i d e o f s h e l l - a n d - t u b e h e a t e x c h a n g e r s . Hot w a t e r is.used as a s e n s i b l e h e a t i n g f l u i d . The u n i t has two t u b u l a r e x c h a n g e r s , e a c h w i t h o v e r 100 t u b e s , and a p l a t e e x c h a n g e r . F o u l i n g r e s i s t a n c e s a r e d e t e r m i n e d by o v e r a l l measurements 24 o f t e m p e r a t u r e and h e a t f l o w . In t h e R e f i n e r y - s t r e a m - f o u l i n g a p p a r a t u s o f C a n a p a r y ( 3 ) , o i l f l o w s t h r o u g h a h e a t e d tube e q u i p p e d w i t h a t h e r m o c o u p l e a d j a c e n t t o t h e t ube w a l l . A w i r e h e a t e r i s wound a r o u n d t he m i c a - c o v e r e d t u b e . VThe a s s e m b l y i s p o t t e d i n h e a t t r a n s f e r c e m e n t . A s i m i l a r u n i t i s d e s c r i b e d by Knudsen ( 4 7 ) . W a t k i n s o n and E p s t e i n (18) used a s y s t e m where f l u i d i s pumped t h r o u g h a t ube h e a t e d by p a s s i n g c u r r e n t d i r e c t l y t h r o u g h t he t u b e w a l l . T h e r m o c o u p l e s a r e s o l d e r e d t o t he o u t s i d e o f t h e tube a t s e v e r a l p o i n t s down t h e l e n g t h o f t he t u b e . In h i s e x p e r i m e n t s , W a t k i n s o n showed t h a t r e c i r c u l a t i o n o f f l u i d t h r o u g h t h e t e s t s e c t i o n d i d n o t s i g n i f i c a n t l y a f f e c t t h e r a t e o f f o u l i n g (due t o t he c o n c e n -t r a t i o n o f t he f o u l a n t i n t h e b u l k f l u i d no t d e c r e a s i n g a p p r e c i a b l y o v e r t h e l e n g t h o f a r u n ) . P r e v i o u s l y , most f o u l i n g measurement t e c h n i q u e s were done on a o n c e - t h r o u g h b a s i s (evg,. E r d c o c o k e r ) . In t he a p p a r a t u s o f C o r l e t t and Knudsen ( 4 8 ) , t h e r e i s a n n u l a r f l o w o f f l u i d between an o u t e r p l e x i g l a s s t ube and a c o n c e n t r i c , t h i n -w a l l e d s t a i n l e s s s t e e l t u b e , w h i c h i s h e a t e d by p a s s a g e o f d i r e c t c u r r e n t t h r o u g h t h e tube w a l l . The h o l l o w c o n c e n t r i c t ube accommodates mov ing t h e r m o c o u p l e s w h i c h a r e h e l d by s p r i n g s a g a i n s t t h e i n n e r w a l l o f t h e t u b e and w h i c h may be moved a x i a l l y and c i r c u m f e r e n t i a l l y as d e s i r e d . 25 In t h e s i n g l e - t u b e h e a t t r a n s f e r r i g o f S m i t h ( 1 ) , f u e l i s pumped t h r o u g h a t u b u l a r t e s t s e c t i o n , h e a t e d by p a s s i n g c u r r e n t d i r e c t l y t h r o u g h t h e t ube w a l l . The h e a t i n p u t t o t h e f u e l i s d e t e r m i n e d f r om the r i s e i n b u l k t e m p e r a t u r e . The e x t e n t o f f o u l i n g i s d e t e r m i n e d by s u r f a c e t e m p e r a t u r e measurements u s i n g t h e r m o c o u p l e s s p o t - w e l d e d t o t h e o u t e r s u r f a c e o f t he t u b e , and p r e s s u r e d rop m e a s u r e m e n t s . W a t k i n s o n e t a l . (44) r e c i r c u l a t e d t he t e s t f l u i d t h r o u g h a c o n d e n s e r w i t h s team on t he s h e l l s i d e . Hea t f l o w i s c a l c u l a t e d by t h e i n c r e a s e i n b u l k t e m p e r a t u r e . The t e s t s e c t i o n c o n t a i n e d an enhanced t u b e and a p l a i n tube mounted i n p a r a l l e l . In t h e a p p a r a t u s o f B u t l e r and McCurdy ( 3 1 ) , o i l i s pumped t h r o u g h a s t e e l c o i l immersed i n a c o n s t a n t t e m p e r a t u r e o i l b a t h . E x t e n t o f f o u l i n g i s . d e t e r m i n e d by t e m p e r a t u r e measurements a t t h e o u t l e t o f t h e c o i l . In t h e K i n e t i c U n i t o f T a y l o r and W a l l a c e ( 2 7 ) , a m i x t u r e o f gas and f u e l f l o w s down a s l i g h t l y i n c l i n e d g l a s s t u b u l a r r e a c t o r . The u n i t has f i v e i n d e p e n d e n t l y r e g u l a t e d , s e p a r a t e r e a c t o r h e a t e r s . The r e a c t o r h e a t e r s a r e c o n t r o l l e d so t h a t t he f u e l e n c o u n t e r s a sequence o f r i s i n g t e m p e r a t u r e zones as i t f l o w s down the r e a c t o r . A t h e r m o c o u p l e i s p o s i t i o n e d i n each h e a t e r z o n e . C a r e f u l l y w e i g h e d m e t a l s t r i p s a r e p o s i t i o n e d i n t h e c e n t e r s e c t i o n o f each z o n e . E x t e n t o f f o u l i n g i s d e t e r m i n e d by the change i n w e i g h t o f t h e s t r i p s . 26 In t h e Advanced K i n e t i c U n i t o f T a y l o r ( 2 3 ) , f u e l i s d e l i v e r e d t o t h e u n i t by h i g h p r e s s u r e n i t r o g e n . F u e l i s p a s s e d t h r o u g h a h e a t e d t u b u l a r r e a c t o r s e c t i o n , c o n s i s t i n g o f a s t a i n l e s s s t e e l 304 tube w h i c h i s c o n t a i n e d i n s i d e o f f o u r i n d i v i d u a l l y c o n t r o l l e d h e a t e r s . The t ube i t s e l f i s c o n t a i n e d i n s i d e o f a t h i c k - w a l l e d p i p e w h i c h has s l o t s m a c h i n e d o u t so as t o h o l d a s e r i e s o f s h e a t h e d t h e r m o c o u p l e s f i r m l y a g a i n s t t h e o u t s i d e w a l l o f t h e t u b e . A f t e r t he t e s t r u n , t he r e a c t o r t ube i s c u t i n t o s i x t e e n s e c t i o n s ( f o u r f o r each r e a c t i o n z o n e ) , exam ined and w e i g h e d . Shah e t a l . (49) p a s s e d p r e h e a t e d f e e d t h r o u g h a t u b u l a r r e a c t o r w h i c h was p o s i t i o n e d i n a f u r n a c e and was h e a t e d by t he f u r n a c e . R e a c t o r t e m p e r a t u r e was measured by t h e r m o c o u p l e s imbedded i n t h e w a l l s o f t h e r e a c t o r . In t h e OTEC f o u l i n g p robe d e v e l o p e d by F e t k o v i c h e t a l . ( 5 0 ) . power i s p e r i o d i c a l l y s u p p l i e d t o a r e s i s t a n c e h e a t e r wound a r o u n d a t h i c k - w a l l e d , j a c k e t i n w h i c h s e v e r a l t h e r m o p i l e s a r e i n s t a l l e d . -Power i s s h u t o f f a f t e r t he t e m p e r a t u r e o f t h e j a c k e t becomes c o n s t a n t . When t h e power i s s h u t o f f , t h e t e m p e r a t u r e o f t he j a c k e t d e c a y s a c c o r d i n g t o - e / r T = (T ) e - ( 2 - 1 4 ) w v w ' o .where x = t i m e c o n s t a n t o f decay f u n c t i o n T = w a l l t e m p e r a t u r e a t t i m e e w (•T w ) b = i n i t i a l w a l l t e m p e r a t u r e e f t i m e 27 T i s p r o p o r t i o n a l t o t h e sum o f t he b i o f o u l i n g r e s i s t a n c e and s e a w a t e r r e s i s t a n c e t o h e a t t r a n s f e r . N o r m a l l y , no power i s s u p p l i e d t o t h e t e s t s e c t i o n bu t f l o w i s m a i n t a i n e d i n t he c i r c u l a r t ube d u r i n g w h i c h t i m e b i o f o u l i n g i s o c c u r r i n g on t h e i n n e r s u r f a c e o f t h e t u b e . In t h e a p p a r a t u s o f M e s s e n g e r ( 5 1 ) , a t h i c k - w a l l e d j a c k e t i s c l amped a r o u n d a c i r c u l a r t u b e . The o u t e r s u r f a c e o f t h e j a c k e t i s an o c t a g o n a l c y l i n d e r . T h e r m o e l e c t r i c d e v i c e s a r e mounted on t he f l a t s u r f a c e o f t h e o c t a g o n . These d e v i c e s can pump h e a t t o o r f r om t h e c e n t e r t ube f r om o r t o h e a t i n g o r c o o l i n g m a n i f o l d s . In t h e s y s t e m o f Freedman e t a l . (52). t h e r e i s a n n u l a r f l o w between an o u t e r g l a s s j a c k e t and an i n n e r h e a t t r a n s f e r t ube f i t t e d w i t h an e l e c t r i c c a r t r i d g e h e a t e r . Water t h e n f l o w s t h r o u g h t h r e e c l e a r p l a s t i c coupon b l o c k s i n w h i c h coupons o r e l e c t r i c a l r e s i s t a n c e m e t e r s a r e f i t t e d . A f t e r t h e r u n , t h e t ube and coupons a r e r e m o v e d , d r i e d and p h o t o g r a p h e d . They a r e t h e n w e i g h e d , c l e a n e d and r e w e i g h e d t o d e t e r m i n e t h e amount o f d e p o s i t i o n and c o r r o s i o n l o s s . In t h e s y s t e m o f M c A l l i s t e r e t a l . (53), c o n d e n s e r t u b e s a r e f i t t e d w i t h a r e m o v a b l e c o n c e n t r i c p i p e j a c k e t t h r o u g h w h i c h ho t w a t e r i s c i r c u l a t e d . In t h e a n n u l u s be tween t h e tube and j a c k e t , a c o p p e r tube c a r r y i n g s team i s c o i l e d f o r t he p u r p o s e o f m a i n t a i n i n g a c o n s t a n t h e a t i n g t e m p e r a t u r e a l o n g t h e l e n g t h o f t h e o u t s i d e o f t h e c o n d e n s e r t u b e . T h i r t e e n such e x c h a n g e r s a r e c o n n e c t e d i n p a r a l l e l . F o u l i n g r e s i s t a n c e s a r e d e t e r m i n e d by o v e r a l l measurements o f t e m p e r a t u r e and h e a t f l o w . 28 Thomas and G r i g u l l (54) r a d i o a c t i v e l y l a b e l l e d m a g n e t i t e w i t h chromium - 51 r a d i o i s o t o p e w h i c h e n a b l e d t h e q u a n t i t a t i v e d e t e r m i n a t i o n o f t he d e p o s i t i o n o f m a g n e t i t e as a f u n c t i o n o f t i m e , f l o w c o n d i t i o n s and h e a t f l u x . The v e r t i c a l h e a t e r i s h e a t e d by p a s s i n g c u r r e n t d i r e c t l y t h r o u g h t h e tube w a l l . The r a t e o f d e p o s i t i o n i s m o n i t o r e d by a v e r t i -c a l l y a d j u s t a b l e s c i n t i l l a t i o n c o u n t e r and r a d i a t i o n m o n i t o r . A r a d i o a c t i v e c o r r o s i o n p r o d u c t s o u r c e and a d e p o s i t i o n s u r f a c e a r e p o s i t i o n e d i n a d e p r e s s i o n i n t h e L u c i t e t e s t c o n d u i t o f K a b e l e and B a r t l e t t ( 5 5 ) , s u c h t h a t t h e y a r e f l u s h w i t h the t e s t c o n d u i t ' s i n n e r s u r f a c e . A f t e r t he r u n , m a s k i n g t a p e i s p l a c e d on t h e d e p o s i t i o n s u r f a c e p a r a l l e l t o t h e f l o w d i r e c t i o n , r e m o v e d , and c o u n t e d on a s c i n t i l l a t i o n d e t e c t o r / c o u n t e r . Two t y p e s o f p r o b e s a r e used by K e r s t ( 5 6 ) . The f i r s t i s a h a i r p i n shaped l e n g t h o f 1 / 4 . i n . s e a m l e s s s t e e l t u b i n g mounted on a p i p e p l u g by means o f c o m p r e s s i o n f i t t i n g s so t h a t i t can be i n s e r t e d i n t o t he f l o w i n g s t r e a m o f a c o o l i n g s y s t e m . Hot f l u i d i s c i r c u l a t e d t h r o u g h t h e t u b e . The s e c o n d i s a m i n i a t u r e s i n g l e tube h e a t e x c h a n g e r o f 1 / 2 i n . s e a m l e s s s t e e l t u b i n g c o n t a i n e d i n a s h e l l made o f s t a n d a r d p i p e f i t t i n g s . Hot f l u i d i s c i r c u l a t e d on t he o u t s i d e o f t h i s t u b e w h i l e w a t e r f l o w s i n s i d e . S c a l e d e p o s i t i o n and c o r r o s i o n l o s s a r e measured q u a n t i t a t i v e l y f o r bo th p r o b e s . The a s s e m b l y o f B o t t and P i n h e i r o (57) c o n s i s t e d o f a d e p o s i t i o n and.a ;. c o o l i n g d u c t s e p a r a t e d by a r e m o v a b l e p l a t e p l a c e d i n a v e r t i c a l p o s i t i o n . The a s s e m b l y s i m u l a t e d a c o u n t e r c u r r e n t " . h e a t . e x c h a n g e r « 29 A t r a v e l l i n g m i c r o s c o p e was used t o measure t he t h i c k n e s s o f t he b i o l o g i c a l f o u l i n g on t h i s d e p o s i t i o n p l a t e . A h e l i c a l geome t r y i s used i n t h e a s s e m b l y o f B a n c h e r o and Gordon ( 5 8 ) . A h e l i c a l g r o o v e i s c u t on t h e e x t e r n a l s u r f a c e o f a c o p p e r c y l i n d e r . On t h e o u t s i d e t h e r e i s a c l o s e - f i t t i n g g l a s s t u b e , t h r o u g h w h i c h t h e s o l u t i o n f l o w i n g i n t h e g r o o v e can be seen and s c a l e d e p o s i t i o n can be f o l l o w e d v i s u a l l y . The s o l u t i o n i s h e a t e d by a c o u n t e r c u r r e n t s t r e a m o f ho t w a t e r unde r p r e s s u r e f l o w i n g i n an i n t e r n a l h e l i x , p r e p a r e d by c u t t i n g a h e l i c a l g r o o v e on t h e e x t e r n a l s u r f a c e o f a s m a l l e r c o p p e r c y l i n d e r and s h r i n k - f i t t i n g i t i n s i d e o f t he s o l u t i o n c y l i n d e r . T h e r m o c o u p l e w e l l s a r e c u t t h r o u g h t h e c y l i n d e r s t o a l l o w t h e r m o c o u p l e s t o measure t h e f l u i d t e m p e r a t u r e o f t h e s o l u t i o n and ho t w a t e r a t v a r i o u s p o i n t s a l o n g t h e i r h e l i c a l p a t h . The P y r o l y t i c C a p s u l e F o u l i n g T e s t o f Benson and M a r t i n i (34) emp loys an e l e c t r i c a l l y h e a t e d , v e r t i c a l s t a i n l e s s s t e e l t ube w h i c h i s i n s e r t e d i n t o t h e c o o l a n t b e i n g t e s t e d . The c a p s u l e o f c o o l a n t i s p r e s s u r i z e d w i t h n i t r o g e n t o p r e v e n t b o i l i n g a t t h e t e s t h e a t e r s u r f a c e . A t h e r m o c o u p l e f o r t he measurement o f t h e h e a t e r t e m p e r a t u r e i s i n s e r t e d i n t o t h e s t a i n l e s s s t e e l t u b e . The c a p s u l e i s s u s p e n d e d i n a s a l t b a t h m a i n t a i n e d a t 6 0 0 ° F . A f t e r t h e r u n , t h e w e i g h t o f t he f i l m d e p o s i t e d on t h e h e a t e r i s m e a s u r e d . In t h e S m a l l P r o b e F o u l i n g T e s t o f B a n c r o f t ( 5 9 ) , c o o l a n t f l o w s o v e r an e l e c t r i c a l l y h e a t e d t u b e . F l o w r a t e i s c a l c u l a t e d by m e a s u r i n g t h e t e m p e r a t u r e r i s e a c r o s s t he t e s t h e a t e r and r e l a t i n g t h i s to t h e power i n p u t . A t h e r m o c o u p l e i s i n s e r t e d w i t h i n t h e t e s t h e a t e r tube, t o 30 d e t e r m i n e h e a t e r s u r f a c e t e m p e r a t u r e . The e x t e n t o f f o u l i n g i s d e t e r m i n e d by r e m o v i n g and w e i g h i n g t he f i l m fo rmed on t he f o u l i n g p robe s u r f a c e and t h e n a n a l y z i n g f o r t h e c o m p o s i t i o n o f t h e f i l m . The same s y s t e m was used by H a t c h e r e t a l . ( 6 0 ) . In t h e s y s t e m d e s c r i b e d by C r a w f o r d and M i l l e r ( 3 6 ) , f e e d i s pumped t h r o u g h an e x c h a n g e r and i s h e a t e d f r o m room t e m p e r a t u r e t o t e m p e r a t u r e s as h i g h as 6 0 0 ° F . The d e p o s i t on t h e h e a t e x c h a n g e r t u b e s r a n g e d f r om a y e l l o w - b r o w n gum o r l i g h t v a r n i s h a t t h e c o o l end o f t h e t ube t o heavy coke a t t h e h o t e n d . The t y p e o f d e p o s i t i s r a t e d v i s u a l l y by a s p e c i f i c f o r m u l a . In t he F o u l i n g E v a l u a t i o n U n i t o f O b e r h o f e r and F u l k s ( 6 1 ) , c o o l i n g w a t e r f l o w i s d i v i d e d i n t o two s t r e a m s . I n j e c t i o n p o r t s a r e p r o v i d e d on each s i d e f o r c h e m i c a l t r e a t m e n t s . Each w a t e r s t r e a m i s p a s s e d o v e r n i n e i n d i v i d u a l h e a t t r a n s f e r s u r f a c e s . The re a r e two t y p e s o f h e a t t r a n s f e r s u r f a c e . The f i r s t i s a tube i n t e r n a l l y h e a t e d by an e l e c t r i c r e s i s t a n c e c a r t r i d g e h e a t e r . Wate r i s pumped t h r o u g h an a n n u l a r s p a c e be tween t h i s h e a t e r t u b e and an o u t e r g l a s s t u b e . The h e a t e r t ube i s w e i g h e d b e f o r e and a f t e r t h e r un f o r d e p o s i t w e i g h t and c o r r o s i o n l o s s . The s e c o n d i s an i m m e r s i o n h e a t e r w i t h a t h e r m o c o u p l e imbedded i n t h e m e t a l s h e a t h . The d e p o s i t i s w e i g h e d and a n a l y z e d . F o u l i n g r e s i s t a n c e s a r e d e t e r m i n e d f r om s u r f a c e t e m p e r a t u r e s a t a known h e a t f l u x . In t h e a p p a r a t u s o f B u r r i l l ( 6 2 ) , t h r e e s t a i n l e s s s t e e l t u b e s a r e c o n n e c t e d i n s e r i e s i n each o f two t e s t s e c t i o n s . The t u b e s a r e h e a t e d by c o n d e n s i n g s team on t he o u t s i d e i n one t e s t s e c t i o n and on t h e : " i n s i d e i n t he o t h e r t e s t s e c t i o n . 31 In t h e t e s t s e c t i o n o f H a r t y and B o t t ( 6 3 ) , an i n s p e c t i o n p l a t e a s s e m b l y i s h o u s e d , w h i c h i s r e m o v a b l e f o r measurement o f b i o f i l m t h i c k -n e s s . F l o w i n t h e t e s t s e c t i o n i s t h r o u g h a r e c t a n g u l a r d u c t c o n s t r u c t e d f rom a b r a s s b l o c k . The b i o f i l m t h i c k n e s s i s d e t e r m i n e d u s i n g t he e l e c t r i c a l c o n d u c t a n c e method d e v e l o p e d by C h a r a c k l i s ( 6 4 ) . I t c o n s i s t s o f a s t e e l n e e d l e mounted on a m i c r o m e t e r c o n n e c t e d t o a c o n d u c t i v i t y c e l l . When t h e n e e d l e i s l o w e r e d t o c o n t a c t w i t h t h e b i o f i l m s u r f a c e , a c u r r e n t i s r e g i s t e r e d and t h e v e r n i e r i s t h e n r e a d . The n e e d l e i s t h e n l o w e r e d u n t i l c o n t a c t i s made w i t h the s u r f a c e o f t he b r a s s p l a t e , where a f u r t h e r d e f l e c t i o n o c c u r s , and a g a i n t he v e r n i e r i s r e a d . The d i f f e r e n c e i n v e r n i e r r e a d i n g s i s e q u a l t o t h e f i l m t h i c k n e s s . The a p p a r a t u s o f N o s e t a n i e t a l . (65) c o n s i s t e d o f two p a r a l l e l c o n d e n s e r s w i t h f o u r c o n d e n s e r t u b e s a r r a n g e d h o r i z o n t a l l y . H e a t i n g o f t h e t u b e s was p r o v i d e d by c o n d e n s i n g s team on t h e s h e l l s i d e o f t h e t u b e s . C a l i b r a t e d t h e r m i s t o r s were used t o measu re t h e c o o l i n g w a t e r and s team t e m p e r a t u r e s . F o u r o r e i g h t t u b e s c o u l d be t e s t e d s i d e by s i d e a g a i n s t each o t h e r under p r a c t i c a l l y i d e n t i c a l o p e r a t i n g c o n d i t i o n s . The P o r t a b l e F o u l i n g U n i t o f Novak (66) uses two p l a t e h e a t e x c h a n g e r s , one f o r t e s t i n g p u r p o s e s and one f o r h e a t r e c o v e r y . The t e s t w a t e r i s pumped t h r o u g h t h e t e s t p l a t e h e a t e x c h a n g e r and i s h e a t e d up by a c i r c u l a t i n g h e a t i n g medium. A f o u l i n g measurement t e c h n i q u e i s d e s c r i b e d by G i l l e s p i e ( 6 7 ) . where a s m a l l r e a c t o r o f t h e t y p e used f o r c a t a l y s t t e s t i n g i s s e t up 32 w i t h s t a i n l e s s s t e e l p a c k i n g . The e x t e n t o f f o u l i n g i s d e t e r m i n e d by m e a s u r i n g t he amount o f d e p o s i t f o rmed on t h e p a c k i n g a f t e r a r u n . A h o t w i r e t e s t i s d e s c r i b e d by H a u s l e r (2) and NACE ( 6 9 ) . A m e t a l w i r e i s h e a t e d i n a h y d r o c a r b o n samp le u n t i l f o u l i n g t a k e s p l a c e on i t s s u r f a c e . The e x t e n t o f f o u l i n g i s d e t e r m i n e d b o t h v i s u a l l y and by a change i n w e i g h t o f t h e w i r e . A s i m i l a r t e s t i s d e s c r i b e d by Anonymous ( 6 8 ) . In t h e M o d i f i e d Hot W i re T e s t o f H a u s l e r ( 2 ) , a p r e - h e a t e d f l u i d i s pumped p a r a l l e l t o an e l e c t r i c a l l y h e a t e d c o i l e d w i r e o f c a r b o n s t e e l , t h r o u g h a s t a i n l e s s s t e e l t u b e . The s u r f a c e t e m p e r a t u r e o f t h e w i r e i s d e t e r m i n e d v i a w i r e r e s i s t a n c e m e a s u r e m e n t s . In a n o t h e r v e r s i o n o f t h e M o d i f i e d Hot W i r e T e s t o f H a u s l e r ( 2 ) , a p r e h e a t e d f l u i d i s pumped p e r p e n d i c u l a r t o an e l e c t r i c a l l y h e a t e d c o i l e d w i r e o f c a r b o n s t e e l , t h r o u g h a d u c t o f r e c t a n g u l a r c r o s s - s e c t i o n . The n o n - u n i f o r m a x i a l f o u l i n g o f t h e c o c u r r e n t f l o w c a s e i s e l i m i n a t e d i n t h i s c r o s s f l o w a r rangemen t . . A g a i n , t he s u r f a c e t e m p e r a t u r e o f t h e w i r e i s d e t e r m i n e d v i a w i r e r e s i s t a n c e m e a s u r e m e n t s . The same t e s t i s d e s c r i b e d by H a u s l e r and T h a l m a y e r (17) and B raun and H a u s l e r ( 2 2 ) , where i t i s r e f e r r e d t o as t he UOP M o n i r e x F o u l i n g T e s t . In t h e G u l f R e s e a r c h C o r p . F o u l i n g T e s t e r d e s c r i b e d by H a u s l e r (2) and NACE ( 6 9 ) , f l u i d i s pumped t h r o u g h a U - t u b e w h i c h i s immersed i n a h e a t e d , f l u i d i z e d sand b a t h . The e x t e n t o f f o u l i n g i s d e t e r m i n e d by t e m p e r a t u r e measurement a t t he o u t l e t o f t h e U - t u b e . 33 An a p p a r a t u s d e s c r i b e d by Knudsen ( 4 7 ) , i s c o m p r i s e d o f a tube w i t h • a t h i c k - w a l l e d j a c k e t c l a m p e d - a r o u n d i t and an e l e c t r i c a l w i r e r e s i s t a n c e h e a t e r mounted on t h e j a c k e t . T e m p e r a t u r e s e n s o r s l o c a t e d i n t h e j a c k e t a r e used t o c a l c u l a t e h e a t t r a n s f e r r a t e p e r u n i t l e n g t h . 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 v a r i a b i l i t y o f t he c o n t a c t r e s i s t a n c e be tween t h e j a c k e t and t h e t a b l e a r e a l l e v i a t e d by p l a c i n g t h e r m a l g r e a s e between t h e two s u r f a c e s . W i t h t h i s a p p a r a t u s , t h e i n s i d e t ube can be removed and d e s t r o y e d f o r v i s u a l o b s e r v a t i o n o f t h e d e p o s i t , w i t h o u t a l s o d e s t r o y i n g t he h e a t e r and t e m p e r a t u r e s e n s o r a s s e m b l y . A vague d e s c r i p t i o n i s g i v e n by Braun and H a u s l e r (22) o f t h e G . E . M i n e x T e s t o f Z e n g e l ( 7 0 ) , where a p r e h e a t e d f e e d i s pumped t h r o u g h a h e a t e d t u b e . The i n l e t and o u t l e t p r e s s u r e s and f l u i d t e m p e r a t u r e s a r e measured a l o n g w i t h t he a v e r a g e w a l l t e m p e r a t u r e , t o g i v e an a v e r a g e h e a t t r a n s f e r c o e f f i c i e n t . The H e a t T r a n s f e r U n i t o f Bachman (71) i s a l s o d e s c r i b e d by B raun e t a l . ( 2 2 ) , where p r e h e a t e d f e e d i s pumped t h r o u g h a s e r i e s o f e i g h t a n n u l a r h e a t i n g t u b e s . As w i t h t he M inex t e s t , an a v e r a g e 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 c a l c u l a t e d . The t u b u l a r t e s t s e c t i o n o f V r a n o s e t a l . (72) i s c l amped w i t h i n a m a s s i v e , t e m p e r a t u r e - r e g u l a t e d c o p p e r b l o c k . T h i n m e t a l s t r i p s a r e h e l d a l o n g t h e t ube a x i s by t h e tube w a l l . A f t e r a r u n , t he d e p o s i t on t h e m e t a l s t r i p s i s w e i g h e d , a n a l y z e d by e l e c t r o n m i c r o p r o b e , and p h o t o g r a p h e d by s c a n n i n g e l e c t r o n m i c r o s c o p e . 34 In t h e c o k i n g a p p a r a t u s . o f Sunderam and F roment ( 7 3 ) , a s m a l l , h o l l o w c y l i n d e r c o n n e c t e d t o t h e arm o f an e l e c t r o b a l a n c e i s s u s p e n d e d i n t h e m i d d l e o f a r e a c t o r . The amount o f coke d e p o s i t e d as a f u n c t i o n o f t i m e can t h e n be d e t e r m i n e d . H i r t and P a l m e r (74) use an i n t e r e s t i n g t e c h n i q u e w h i c h i s b a s e d upon t h e e l e c t r i c a l c o n d u c t i v i t y change o f a r o d upon w h i c h c o k e i s d e p o s i t e d . Cook (75) d e s c r i b e s a t e c h n i q u e t o d e t e r m i n e t h e f o u l i n g t e n d e n c i e s o f i n t e r m e d i a t e p e t r o l e u m d i s t i l l a t e s . A samp le o f t h e d i s t i l l a t e i s h e a t e d ; i t s e l e c t r i c a l c o n d u c t i v i t y i s d e t e r m i n e d ; sample i s c o o l e d ; and i t s e l e c t r i c a l c o n d u c t i v i t y i s a g a i n d e t e r m i n e d . The d i f f e r e n c e between e l e c t r i c a l c o n d u c t i v i t i e s i s a measure o f t he f o u l i n g t e n d e n c y o f t he d i s t i l l a t e . D a j a n i (76) a l s o d e s c r i b e s a t e c h n i q u e t o d e t e r m i n e t he f o u l i n g t e n d e n c i e s o f d i s t i l l a t e s . The d i s t i l l a t e s a r e s t o r e d . The s t r e a m i n g c u r r e n t o f t h e d i s t i l l a t e s u n d e r l a m i n a r f l o w c o n d i t i o n s i s measured a t c e r t a i n i n t e r v a l s d u r i n g s t o r a g e . The m a g n i t u d e o f t h e f l u c t u a t i o n s o f t h e s t r e a m i n g c u r r e n t d u r i n g t h e s t o r a g e p e r i o d i s d e t e r m i n e d . The m a g n i t u d e o f t he f l u c t u a t i o n s i s p r o p o r t i o n a l t o t he f o u l i n g t e n d e n c y o f t h e d i s t i l l a t e . Each t e c h n i q u e has i t s a d v a n t a g e s and d i s a d v a n t a g e s . Me thods w h i c h employ an imbedded t h e r m a l s e n s o r be low t h e f o u l i n g s u r f a c e , d i r e c t l y p r o v i d e i n f o r m a t i o n on and d R ^ / d e , , , w h i c h can be used t o d e t e r m i n e t h e e x t e n t o f f o u l i n g . E p s t e i n (9 ) s t a t e s t h a t l o c a l v a l u e s 35 o f R f and d R f / d e a r e more b a s i c a l l y i n f o r m a t i v e t h a n i n t e g r a l v a l u e s o v e r an e x c h a n g e r , s i n c e t h e y a p p l y t o s p e c i f i c v a l u e s o f h e a t t r a n s f e r w a l l t e m p e r a t u r e T w , s u r f a c e t e m p e r a t u r e T , and b u l k f l u i d t e m p e r a t u r e T ^ . A v e r a g e f o u l i n g r e s i s t a n c e s o v e r t h e t o t a l s u r f a c e o f an e x c h a n g e r a r e s u i t e d t o comp lex g e o m e t r i e s s u c h as s h e l l - a n d - t u b e e x c h a n g e r s , bu t s i g n i f i c a n t e r r o r s can r e s u l t when t h e a r e a , f o u l i n g r e s i s t a n c e , o r h e a t f l u x i s s m a l l . E p s t e i n f u r t h e r s t a t e s t h a t o p e r a t i o n unde r c o n s t a n t h e a t f l u x has t h e a d v a n t a g e o v e r o p e r a t i o n under c o n s t a n t h e a t i n g medium t e m p e r a t u r e , i n t h a t t he l o c a l v a l u e o f R f a t any i n s t a n t can be o b t a i n e d s i m p l y f r o m a know ledge o f h e a t f l u x and r e a d i n g s o f a t h e r m o c o u p l e imbedded i n t h e h e a t t r a n s f e r w a l l . I n d i r e c t methods o f m o n i t o r i n g d e p o s i t s such as v i s u a l o b s e r v a t i o n and p o s t - t e s t measurement o f d e p o s i t t h i c k n e s s and w e i g h t , s u f f e r f r o m t h e d rawback t h a t g r o w t h o f t he f o u l i n g d e p o s i t w i t h t i m e c a n n o t be d e t e r m i n e d q u a n t i t a t i v e l y . Even when t h e s e v a l u e s a r e known as a f u n c t i o n o f t i m e , t h e r e w o u l d be no e s t a b l i s h e d c o r r e l a t i o n be tween p r e s s u r e d r o p a c r o s s f i l t e r , d e p o s i t w e i g h t , d e p o s i t t h i c k n e s s , e t c . and t h e h e a t t r a n s f e r e f f i c i e n c y o f a h e a t e x c h a n g e r . E l e c t r i c a l r e s i s t a n c e h e a t i n g o f t h e t e s t s e c t i o n has t h e d i s a d v a n t a g e o f r e q u i r i n g h i g h e l e c t r i c a l c u r r e n t s . The t e s t s e c t i o n i s l i m i t e d t o m a t e r i a l s o f c o n s t r u c t i o n o f h i g h e l e c t r i c a l r e s i s t a n c e . The h i g h c u r r e n t l i m i t s t h e use o f t h i s h e a t i n g method t o n o n - h a z a r d o u s f l u i d s and can c a u s e i n s t r u m e n t a t i o n p r o b l e m s f o r t h e r m o c o u p l e measurements ( 2 1 ) . I f a l t e r n a t i n g c u r r e n t i s u s e d , t h e n t he AC f r e q u e n c y c o u l d g i v e r i s e t o a m a g n e t i c f i e l d a r o u n d t h e h e a t t r a n s f e r 36 me ta l w h i c h c o u l d i n f l u e n c e p a r t i c l e d e p o s i t i o n on t h e w a l l . O t h e r w i s e , t h i s method c a n be used i n somewhat comp lex g e o m e t r i e s t o h e a t u n i f o r m l y o v e r t h e s u r f a c e and e a s i l y m a i n t a i n c o n s t a n t h e a t f l u x o p e r a t i o n . I n d i r e c t e l e c t r i c a l h e a t i n g o f an a n n u l a r t e s t s e c t i o n v i a a c a r t r i d g e t y p e h e a t e r has t h e a d v a n t a g e s o f c o n s t r u c t i o n , s e l e c t i o n ' o f m a t e r i a l , e a s y remova l o f d e p o s i t a f t e r a t e s t r u n , r e p l a c e m e n t o f the e l e m e n t , u n i f o r m h e a t f l u x , e a s i l y m a i n t a i n e d c o n s t a n t h e a t f l u x . o p e r a t i o n , and p o s s i b l e v i s u a l o b s e r v a t i o n o f t h e f o u l i n g p r o c e s s . H o w e v e r , i t i s e s s e n t i a l l y r e s t r i c t e d t o s i m p l e g e o m e t r i e s ( 4 7 ) . I n d i r e c t e l e c t r i c a l h e a t i n g on t h e o u t s i d e o f a t ube has t h e added d i s a d v a n t a g e s o f no p o s s i b i l i t y o f v i s u a l l y o b s e r v i n g t h e f o u l i n g p r o c e s s d u r i n g a r u n and t h e e x p e n s e and t i m e i n d e s t r o y i n g t he t e s t s e c t i o n t o o b s e r v e t h e d e p o s i t ( 4 7 ) . C o n d e n s i n g v a p o u r h e a t i n g has the a d v a n t a g e o f b e i n g a c o n s t a n t t e m p e r a t u r e h e a t i n g medium o r a s o u r c e o f c o n s t a n t h e a t f l u x . I t a l s o can be used i n h a z a r d o u s a r e a s and does no t l i m i t t h e d e s i g n g e o m e t r y . H o w e v e r , i t has a l i m i t e d t e m p e r a t u r e range w h i c h depends on t h e v a p o u r used and a c c u r a t e c o n t r o l o f c o n d e n s i n g v a p o u r h e a t i n g i s d i f f i c u l t t o a t t a i n . A l s o , i t may be d i f f i c u l t t o p r e d i c t c o n d e n s i n g f i l m c o e f f i c i e n t s . Knudsen (47 ) s t a t e s t h a t t h e h i g h v a r i a b i l i t y o f t h e c o n d e n s i n g c o e f f i c i e n t w i t h l o c a t i o n and i t s h i g h s u s c e p t i b i l i t y t o r e d u c t i o n by t h e p r e s e n c e o f n o n - c o n d e n s i b l e g a s e s , makes c o n d e n s i n g v a p o u r h e a t i n g t h e l e a s t d e s i r a b l e mode o f h e a t i n g t h e f o u l i n g f l u i d . 37 S e n s i b l e f l u i d h e a t i n g i s e x c e l l e n t f o r comp lex g e o m e t r i e s . I t g i v e s b e t t e r t h e r m a l c o n t r o l t h a n e l e c t r i c a l h e a t i n g and c o n d e n s i n g v a p o u r h e a t i n g b u t i s l i m i t e d t o l o w e r h e a t f l u x e s and t e m p e r a t u r e s . L i k e c o n d e n s i n g v a p o u r h e a t i n g , i t can be used i n h a z a r d o u s a r e a s ( 2 1 ) . S e n s i b l e f l u i d h e a t i n g p r o v i d e s l ow h e a t f l u x e s no t p o s s i b l e w i t h most c o n d e n s i n g v a p o u r s , bu t w i t h t h e added d i s a d v a n t a g e o f i n c r e a s e d p i p i n g and f l o w r e q u i r e m e n t s ( 7 ) . T a b l e 2 - 2 comes f r o m Knudsen ( 4 7 ) . The t a b l e l i s t s v a r i o u s f e a t u r e s o f f o u l i n g t e s t d e v i c e s and i n d i c a t e s t o w h i c h d e v i c e s t h e s e f e a t u r e s a p p l y . 2 . 6 . PFRU AND UOP M o n i r e x F o u l i n g P r o b e s - D e t a i l s o f  C o n s t r u c t i o n , H y d r o d y n a m i c s , and Hea t T r a n s f e r The two f o u l i n g p r o b e s w h i c h a r e t h e s u b j e c t o f t h i s t h e s i s a r e t h e P o r t a b l e F o u l i n g R e s e a r c h U n i t o f HTRI ( 2 1 ) , and a h o t w i r e p robe b a s e d on t h e UOP M o n i r e x F o u l i n g T e s t ( 1 7 ) , b o t h o f w h i c h have a l r e a d y been d e s c r i b e d b r i e f l y . 2 . 6 . 1 . PFRU F o u l i n g P r o b e The PFRU uses i n d i r e c t e l e c t r i c a l h e a t i n g and measures l o c a l f o u l i n g r e s i s t a n c e . From t h e p o i n t o f v i e w o f o v e r a l l a d v a n t a g e s v e r s u s o v e r a l l d i s a d v a n t a g e s , i t i s p r o b a b l y t h e most d e s i r a b l e f o u l i n g p r o b e . . . 38 FEATURE TEST Device 1 2a 2b 2c 3 T 4 A T H 5 c H A c 6 T A 7 6 Visual observation possible )( during run X X X x Must be destroyed (or dis-assembled) to observe deposit X X X X X X X X X Local heat flux easily deter- V mined X X rk Local heat f lu* easily deter-mined but losses to envir-onment must be accounted for X X X X X Local heat flux usually cannot be determined X X X X X X X* Wall temperature can be determined X. X X X X X X X X X X X X X X Surface temperature can ]( be determined K X X X X X X Can be made from a wide var- X X iety of materials A * X X X X X X X X Can be made fro" a limited X number of materials X X Can determine local fouling factor X X X X X X X x Can determine only average X fouling factor X X X X X Results can be extrapolated X X •) to circular tube conditions X X X X X X X X X X Results can be extrapolated to conplex geometries 7 > 7 7 7 7 ? 7 7 7 ? 7 » X Easy to control X K X X X X X X X X Diff icult to control X X X X 7 Stable operation during t fouling test X X X X X X X X X X X Retains calibration X X 7 7 7 X X X X X X X X X X Low power requirement X X X High power requirement X X X X X • X X X X X X X T - fouling fluid flows 1n circular tube A - Fouling fluid flows 1n Annular duct "H - Heating fouling fluid C - Cooling fouling f luid 1. - Annular geometry,, indirect electric heatino ?a. - Thin-walled tube, indirect electric heatm-i ?b. - Thici-waHed tube, indirect e lectru heat mo «?c. - Thick-wdl led tub*, transient technique 3. - Circular tube geometry, therr»oe lec tr Ilc *eat'nj or cjoHng 4. - Annular or circular tube geometry, direct electric heating ti. - Annular or circular tube geometry, sensible.heat of fluids 6. - Annular or circular tube geometry, condensing vapor 7. - Complex geometries 8. - Electrically heated wires and coils T a b l e 2 - 2 . C l a s s i f i c a t i o n o f F o u l i n g Measurement T e c h n i q u e s ( t a k e n f rom Knudsen ( 4 7 ) ) 39 The e n t r a n c e l e n g t h i s a b o u t 8 . 5 i n c h e s . The h e a t e r o u t s i d e d i a m e t e r i s a b o u t 0 . 4 2 5 i n . , and t h e i n s i d e d i a m e t e r o f t h e s u r r o u n d i n g tube i s 3 / 4 i n . ( 7 7 ) . The s u r r o u n d i n g t u b e can be t r a n s p a r e n t f o r v i s u a l o b s e r v a t i o n . Thus t h e e q u i v a l e n t d i a m e t e r i s 0 . 3 2 5 i n . ( D ^ ^ = D 0 - D 1 - ) , and t h e e n t r a n c e l e n g t h i s 2 6 . 2 e q u i v a l e n t d i a m e t e r s . The d a t a o f O l s o n and S p a r r o w (78) a p p e a r t o show e n t r y l e n g t h s o f l e s s t h a n 50 d i a m e t e r s , w i t h 30 d i a m e t e r s s u f f i c i e n t f o r a c l o s e a p p r o a c h t o f u l l y d e v e l o p e d t u r b u l e n t f l o w i n an a n n u l u s . T h u s , t h e t u r b u l e n t v e l o c i t y p r o f i l e f o r t he PFRU a s s e m b l y s h o u l d be a l m o s t f u l l y d e v e l o p e d as i t e n t e r s t h e h e a t e d s e c t i o n . The r o d i s i n t e r n a l l y h e a t e d by a N ich rome e l e c t r i c a l r e s i s t a n c e c o i l , packed i n magnesium o x i d e i n s i d e t h e t u b e , w i t h t h e a s s e m b l y swaged t o g e t h e r . T h i s p r o v i d e s a u n i f o r m l y h e a t e d l e n g t h o f a b o u t 4 i n c h e s . The h e a t e r e l e m e n t r e s i s t a n c e i s a b o u t 32 Q and t he maximum power i n p u t i s 1000 W. The p robe has an uppe r t e m p e r a t u r e l i m i t o f 650°F beyond w h i c h t he h e a t e r e l e m e n t i s p r o n e t o damage. E x c e p t f o r c o p p e r r o d s , a x i a l h e a t l o s s i s n e g l i g i b l e ( 2 1 ) . F o u r t h e r m o c o u p l e s a r e imbedded i n t he t ube w a l l a t 9 0 ° i n t e r v a l s , a t a p o s i t i o n a b o u t 3 i n . downst ream f r o m the b e g i n n i n g o f the h e a t e d s e c t i o n . T h e r m o c o u p l e h o l e s a r e d r i l l e d by e l e c t r i c a l d i s c h a r g e m a c h i n i n g t h r o u g h t he o u t s i d e o f t he t ube w a l l , w i t h o u t p e n e t r a t i n g t h e i n s i d e w a l l . T h e r m o c o u p l e s i n s i d e 0 . 0 2 0 i n . d i a m e t e r s h e a t h s , a r e i n s e r t e d i n t h e d r i l l e d h o l e s , l a i d i n g r o o v e s t o t he downst ream end o f t h e t e s t s e c t i o n and s o l d e r e d i n p l a c e ( 2 1 ) . The t h e r m o c o u p l e m a t e r i a l i s c h r o m e l - c o n s t a n t a n . Knudsen (47) s t a t e s t h a t t h e 40 imbedded t h e r m o c o u p l e s s h o u l d be l o c a t e d 8 t o 10 e q u i v a l e n t d i a m e t e r s f r o m t h e u p s t r e a m end o f t h e h e a t e d s e c t i o n . A t t h i s l o c a t i o n , t he t h e r m a l bounda ry l a y e r w i l l no t be f u l l y d e v e l o p e d bu t 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 s h o u l d be a l m o s t c o n s t a n t i n t he f l o w d i r e c t i o n . Knudsen s u p p o r t s t h i s s t a t e m e n t w i t h F i g u r e 2 - 1 , w h i c h shows t h a t t he t e m p e r a -t u r e d i f f e r e n c e T - T ^ , and hence 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 , i s a l m o s t c o n s t a n t i n t h e f l o w d i r e c t i o n . T a b l e 2 - 3 t a k e n f r o m Rohsenow and H a r t n e t t ( 7 9 ) , w h i c h i s t h e t h e r m a l e n t r y l e n g t h s o l u t i o n f o r t u r b u l e n t f l o w be tween p a r a l l e l p l a n e s , one s i d e a t c o n s t a n t h e a t r a t e and t h e o t h e r i n s u l a t e d , shows t h a t N u s s e l t number and hence h e a t t r a n s f e r c o e f f i c i e n t change v e r y l i t t l e beyond 10 e q u i v a l e n t d i a m e t e r s o f h e a t e d l e n g t h . The b e h a v i o u r and p e r f o r m a n c e o f p a r a l l e l p l a n e s d i f f e r s l i t t l e •A- n f r om t h a t o f an a n n u l u s w i t h r (= i / D Q ) down t o a t l e a s t 0 . 5 0 ( 7 9 ) . The t h e r m o c o u p l e s i n t he PFRU a r e l o c a t e d 9 . 2 e q u i v a l e n t d i a m e t e r s i n t o t h e t h e r m a l e n t r y r e g i o n , w h i c h i s w i t h i n t h e a f o r e m e n t i o n e d s p e c i f i c a t i o n s . Knudsen and K a t z (80) recommend the f o l l o w i n g e q u a t i o n f o r r m a x , t h e r a d i u s a t w h i c h t h e t u r b u l e n t v e l o c i t y p r o f i l e ( as w e l l ~ a s t h e l a m i n a r v e l o c i t y p r o f i l e ) i n t h e a n n u l u s i s a t a maximum ( i . e . a t r = r u = u ) : max, max 7 r max ( r o 2 " r i 2 ) 7 2 1 n ( ^ ) ( 2 , 1 5 ) 4,1 CM 8 0 6 0 4 0 o ° o o o o o o 0 ° 2 0 o TEMPERATURE SENSOR 6 INCHES COIL-FLOW TUBE = 7 - HEATER CARTRIDGE F i g u r e 2 - 1 . W a l l T e m p e r a t u r e P r o f i l e i n t h e  V i c i n i t y o f T e m p e r a t u r e S e n s o r ( t a k e n f r om Knudsen ( 4 7 ) ) 42 Pr - 0.01 Re 7104 73712 495164 x/D, N » M «; N«„ »; Nu,, 1 8.33 0.233 23.5 0.076 60.2 0.058 3 6.52 0.378 16.1 0.133 45.1 0.063 10 6.11 0.417 11.3 0.284 32.0 0.131 30 6.10 0.417 9.36 0.39'J 24.8 0.265 100 6.10 0.417 9.13 0.414 21.9 0.349 300 6.10 0.417 9.13 0.414 21.8 0.353 Pr = 0.1 Re 7096 73612 494576 x/De N u u Nu„ *; Nu„ 1 19.7 0.056 75.2 0.018 241 0.005 3 14.3 0.122 56.2 0.016 194 0.023 10 10.7 0.267 42.4 0.1 IS 155 0.062 30 9.44 0.352 34.8 0.233 132 0.147 100 9.34 0.359 32.1 0.290 120 0.219 300 9.34 0.359 32.1 0.291 120 0.219 Pr = IJO Re 7096 73612 494576 x/D, N u n N u M N u n I 47J 0.013 234 0.005 940 0.000 3 37.9 0.033 203 0.018 851 0.009 10 31.5 0.089 177 0.049 761 0.030 30 28.0 0.173 160 0.114 697 0.077 100 27.1 0.200 152 0.155 661 0.123 Pr = 10.0 Re 7096 73612 494576 x/De Nu,, Nu,, «t Nu„ 1 102 0.004 602 0.004 2925 0.000 3 88.6 0.012 575 0.008 2829 0.003 10 81.9 0.027 550 0.018 2724 0.010 30 78.6 0.057 S32 0.041 2640 0.027 100 . 77.5 0.070 522 0.057 2590 0.045 T a b l e 2 - 3 . N u s s e l t Numbers and I n f l u e n c e C o e f f i c i e n t s - , T u r b u l e n t  F low between P a r a l l e l P l a n e s , One S i d e a t C o n s t a n t  Heat R a t e , t h e O t h e r I n s u l a t e d , Thermal E n t r y  L e n g t h S o l u t i o n ( t a k e n f rom Rohsenow and H a r t n e t t ( 7 9 ) ) ' 43 E x p e r i m e n t a l l y i t was f o u n d t h a t U b / u m a v = 0 . 8 7 6 ± . 1 . 8 % ( 8 0 ) . Thus t h e o u t e r v e l o c i t y p r o f i l e , a c c o r d i n g t o Knudsen and K a t z ( 8 0 ) , i s : - r 0 , 1 4 2 u = 1 . 1 4 u . ( ^ _ - ) ( 2 - 1 6 ) o max and t h e i n n e r v e l o c i t y p r o f i l e i s : 0 : 1 4 2 ( 2 - 1 7 ) max " ' i An e n t h a l p y b a l a n c e on an e l e m e n t o f f l u i d , dx i n l e n g t h y i e l d s : ( Q / A W D i d x + W C p T b = ^ l o s s 7 ^ * + W C p ( T b + d J b ] ( 2 " 1 8 ) H e n c e , ( Q / A J r o d . D i - ( Q / A ) l o s s , D 0 dx = W C p d T b ( 2 - 1 9 ) I n t e g r a t i n g f r om 0 t o x and f r om T^. e n t t o T b y i e l d s : T b = ° r o d " ^ l o s s WC. I ' b . e n t ( 2 - 2 0 ) H e n c e , b u l k t e m p e r a t u r e v a r i e s l i n e a r l y w i t h a x i a l d i s t a n c e . F o r t u r b u l e n t f l o w i n an a n n u l u s w h i c h i s f u l l y d e v e l o p e d h y d r o d y n a m i c a l l y and t h e r m a l l y , t h e f o l l o w i n g e q u a t i o n s can be used t o p r e d i c t 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 under c l e a n c o n d i t i o n s : R e f e r e n c e h = 0 . 0 1 4 3 ( £ ) R e ° ' 8 5 P r 0 - 5  u e q h = 0 . 0 2 3 ( j i ) R e ° - 8 P r 0 - 4 ( ^ i - ) 0 . 4 5 eq ( 2 - 2 1 ) ( 2 - 2 2 ) W (82) 44 0 53 HQ i/ i D 9 ' R e f e r e n c e h = 0.020(1 ) R e U - B P r l / J ( ^ - ) ( 2 - 2 3 ) [ 8 3 ] ~ eq 1 Howeve r , t h e t h e r m a l bounda ry l a y e r i s no t f u l l y d e v e l o p e d , so T a b l e 2 - 3 s h o u l d be used w i t h t h e a p p r o p r i a t e i n t e r p o l a t i o n s . Under c l e a n c o n d i t i o n s , t h e t o t a l h e a t t r a n s f e r r e s i s t a n c e i s a sum o f t h e w a l l r e s i s t a n c e and f l u i d r e s i s t a n c e , o r : i x w i l j c n " T b IJ = T ^ - + r- = n / fl c 1 e a n c o n d i t i o n s ( 2 - 2 4 ) u o K wo n o g / A a t t i m e z e r o 1 X W n , 1 ^TC ^b . , . „ „ / o o r - \ u = R f + F = — w ~ a t t i m e 0 ! ( 2 _ 2 5 ) S u b t r a c t i n g ( 2 - 2 4 ) f r om ( 2 - 2 5 ) , on t he a s s u m p t i o n s t h a t t he a f o r e m e n t i o n e d d e p o s i t i o n r o u g h n e s s / s u r f a c e e f f e c t s and t h e b l o c k a g e e f f e c t do n o t change t h e f l u i d h e a t t r a n s f e r c o e f f i c i e n t ; t h a t t he t h e r m a l c o n d u c t i v i t y o f t h e m e t a l s u r f a c e i s a weak f u n c t i o n o f t e m p e r a t u r e ; and t h a t t he d e p o s i t does n o t s i g n i f i c a n t l y i n c r e a s e t he h e a t t r a n s f e r s u r f a c e a r e a , y i e l d s t h e f o l l o w i n g : V - V R F " ' Q/A. < 2 ' 2 6 ) Howeve r , k w has a modera te dependence on t e m p e r a t u r e , so f o r l a r g e changes i n m e t a l t e m p e r a t u r e , i t wouTd be more a c c u r a t e t o c a l c u l a t e u s i n g w a l l t e m p e r a t u r e ( g i v e n an a c c u r a t e v a l u e f o r xw ) ; R F - ^ > ( 2 - 2 7 ) 45 where T = T T „ - r^h~ ( 2 - 2 8 ) w " e L w TIC k /X v 7 w w To d e t e r m i n e t h e v a l u e o f x w / k w a g r a p h i c a l t e c h n i q u e d e v e l o p e d by W i l s o n i s emp loyed ( 4 7 ) . The W i l s o n p l o t c o n s i s t s o f d e t e r m i n i n g 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 a t v a r i o u s f l o w r a t e s . F o r a g i v e n T ^ , T ^ a n d Q / A , 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 can be c a l c u l a t e d as f o l l o w s : U = S / A ( 2 - 2 9 a ) 'TC " ' b bu t 1 • - ( 2 - 2 9 b ) w F o r c o n s t a n t b u l k and s u r f a c e t e m p e r a t u r e , h = ( c 4 ) ( u b ) . n ( 2 - 3 0 a ) and k = c o n s t a n t ( 2 - 3 0 b ) w J - - T T + TS& ( 2 - 3 1 ) w ( u . ) and a p l o t o f rr v e r s u s n w i l l be a s t r a i g h t l i n e w i t h a s l o p e o f c 5 and i n t e r c e p t o f - p a t j 1 - . n e q u a l t o z e r o ( i . e . when u b = i n f i n i t y ) 1 1 To m a i n t a i n c o n s t a n t b u l k and s u r f a c e t e m p e r a t u r e , i t wou ld be n e c e s s a r y t o a d j u s t t h e h e a t f l u x p r o p o r t i o n a l l y t o t h e change i n 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 u s e d by t he change i n f l o w v e l o c i t y ) . A p r o b l e m w i t h t h e W i l s o n p l o t i s t h a t t h e e x p o n e n t n i s a 46 f u n c t i o n o f R e y n o l d s number and hence v e l o c i t y . F i g u r e 2 - 2 t a k e n f r om Rohsenow and H a r t n e t t (79) c l e a r l y shows t h a t as R e y n o l d s number i n c r e a s e s , n i n c r e a s e s . T h i s means t h a t t h e e x p o n e n t used i n a W i l s o n p l o t based on a range o f mode ra te v e l o c i t i e s wou ld be t o o l ow s i n c e i t s v a l u e i s c o n s t a n t and n o t i n c r e a s i n g w i t h i n c r e a s i n g v e l o c i t y . However , t h e l i t e r a t u r e does n o t s u g g e s t any b e t t e r me thod . 2 . 6 . 2 . UOP M o n i r e x F o u l i n g T e s t The UOP M o n i r e x F o u l i n g T e s t uses d i r e c t c u r r e n t e l e c t r i c a l r e s i s t a n c e h e a t i n g and measures t he o v e r a l l f o u l i n g r e s i s t a n c e o f t h e c o i l e d w i r e . F i g u r e 2 - 3 , t a k e n f r om H a u s l e r and T h a l m a y e r (17) shows t h e c o n f i g u r a t i o n o f t h e i r t e s t c e l l . F l u i d f l o w s p e r p e n d i c u l a r t o a c o i l e d w i r e unde r l a m i n a r f l o w c o n d i t i o n s , t h r o u g h a d u c t o f r e c t a n g u l a r c r o s s - s e c t i o n . From e x a m i n a t i o n o f p h o t o g r a p h s and t h e i r r e s p e c t i v e m a g n i f i c a t i o n s , i t was p o s s i b l e t o deduce t h a t t h e d r a w i n g o f t h e t e s t c e l l i n H a u s l e r and T h a l m a y e r (17) was p r o b a b l y t o s c a l e . T h u s , t h e c r o s s - s e c t i o n i s a b o u t 4 cm x 1.2 cm and t h e e n t r a n c e l e n g t h i s a b o u t 4 . 9 cm. The c o i l e d w i r e i s made o f c a r b o n s t e e l f o r c o r r o s i o n s t u d y p u r p o s e s . The w i r e i s c o n n e c t e d t o two b u s b a r s t h a t a r e e l e c t r i c a l l y i n s u l a t e d f r om t h e t e s t c e l l w a l l , and t h a t a r e c o n n e c t e d t o an e l e c t r i c a l power s o u r c e . The f l u i d i s p r e h e a t e d i n a h e a t e r s i m i l a r t o t h e one used i n t h e E r d c o c o k e r t e s t . I t r e q u i r e s a 2 g a l l o n samp le o f t h e p r o c e s s s t r e a m f o r use i n a r e c i r c u l a t i n g f l o w s y s t e m ( 8 4 ) . Conax c o n n e c t o r s a r e used f o r 1 /16 i n . t h e r m o c o u p l e s t h a t a r e immersed i n t h e f l u i d b e l o w and above t h e h o t w i r e . They a r e used t o a d j u s t t h e t e m p e r a t u r e o f t h e f l u i d t o a c o n s t a n t l e v e l and 47 F i g u r e 2 - 2 . N u . ^ . f o r F u l l y D e v e l o p e d T u r b u l e n t F low t h r o u g h an Annulus~~ ( t a k e n f r om Rohsenow and H a r t n e t t ( 7 9 ) ) 48 U O P F O U L I N G P R O B E FB F l o w Section 'A' -'A' F i g u r e 2 - 3 . UOP M o n i r e x F o u l i n g T e s t P robe ( t a k e n f r om H a u s l e r and T h a l m a y e r ( 1 7 ) ) 49 i n d i c a t e t h e amount o f h e a t t r a n s f e r r e d t o t he f l u i d f r om t h e ho t w i r e ( 1 7 ) . A f t e r a r u n , t h e t e s t c e l l , w h i c h i s a c t u a l l y two s e c t i o n s c o n n e c t e d by a f l a n g e , can be s e p a r a t e d a t t he f l a n g e f o r v i s u a l o b s e r v a t i o n and p h o t o g r a p h i n g o f t he w i r e d e p o s i t and f o r c l e a n i n g p u r p o e s . The u s u a l mode o f r u n n i n g an e x p e r i m e n t was t o o b s e r v e t he f o u l i n g b e h a v i o u r o f a h y d r o c a r b o n f l u i d f o r a c e r t a i n l e n g t h o f t i m e and a t a c e r t a i n b u l k t e m p e r a t u r e . Then t he b u l k f l u i d t e m p e r a t u r e w o u l d be i n c r e a s e d , and t h e f o u l i n g b e h a v i o u r w o u l d a g a i n be o b s e r v e d f o r a c e r t a i n l e n g t h o f t i m e . T h i s p r o c e d u r e can be r e p e a t e d s e v e r a l t i m e s . F i g u r e 2 - 4 , t a k e n f rom H a u s l e r e t a l . ( 1 7 ) , g r a p h i c a l l y shows t h e r e s u l t s o f t h i s p r o c e d u r e . They s t a t e t h a t t he i n c r e a s e i n h e a t t r a n s f e r c o e f f i c i e n t c o n c o m i t a n t w i t h t h e i n c r e a s e i n b u l k f l u i d t e m p e r a t u r e i s due t o a c e r t a i n amount o f b o i l i n g t a k i n g p l a c e on t he w i r e . The e x t e n t o f c o r r o s i o n o f t h e h o t w i r e i s d e t e r m i n e d a f t e r each f o u l i n g p e r i o d and i s assumed t o p r o g r e s s a t a c o n s t a n t r a t e d u r i n g t he p e r i o d i n q u e s t i o n ( 1 7 ) . From Drummer ( 8 5 ) , R = R Q (1 + cTT) ( 2 - 3 2 ) and R = JT = ^ p A / U D 2 / 4 ) ( 2 - 3 3 ) c s A t t h e b e g i n n i n g o f t h e p e r i o d ( t i m e = z e r o ) , R b e g = V 1 + a V = V 2 [ 1 + a T b ] ( 2 " 3 4 ) 50 FOULING R U N 5 8 A 74-2341 W/10T DXY PLT 2 7 D Q UJ CJ t z UJ ™ O n LU h en -j DC I 10 20 30 40 TIME, HOURS F i g u r e 2 - 4 . G r a p h i c a l R e s u l t s o f UOP M o n i r e x F o u l i n g T e s t ( t a k e n f r om H a u s l e r and T h a l m a y e r ( 1 7 ) ) 51 A t t h e end o f t h e p e r i o d ( t i m e = 0 ) , Thus R e n d W - . V R b e g 1 / D 0 2 D f 2 ( 2 - 3 6 ) Hence R, : ' h , beg , D - D f K e n d C o r r o s i o n r a t e = - — = — ( 2 - 3 7 ) 0 9 U . S . P a t e n t s # 3 , 7 3 1 , 1 8 7 and 3 , 8 1 0 , 0 0 9 , w r i t t e n by H a u s l e r and Sampson ( 8 6 , 8 7 ) , d e s c r i b e a t e m p e r a t u r e c o n t r o l s ys tem where a v o l t a g e o u t p u t i . e . a t h e r m o c o u p l e , l o c a t e d p r o x i m a t e t o t h e t e s t spec imen i . e . t h e e l e c t r i c a l l y h e a t e d c o i l e d w i r e , i s a t t he same t e m p e r a t u r e as t he medium i n w h i c h t h e t e s t spec imen r e s i d e s . I t a d j u s t s e i t h e r t h e c u r r e n t v a l u e o r v o l t a g e v a l u e t o n e g a t e t h e e f f e c t s o f v a r y i n g t e m p e r a t u r e o f t h e medium on t h e o t h e r v a l u e a c r o s s t he t e s t s p e c i m e n . F i g u r e 2 - 5 , t a k e n f rom u \ S . P a t e n t # 3 , 7 3 1 , 1 8 7 , g i v e s a d i a g r a m o f t h i s t e m p e r a t u r e - c o m p e n s a t i n g c i r c u i t . The p a t e n t s a l s o d e s c r i b e how t o d e t e r m i n e 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 : h = V I 2 a e R e / [ ( V - I R £ ) F ] ( 2 - 3 8 ) where R Q = r e s i s t a n c e o f p robe a t r e f e r e n c e t e m p e r a t u r e a = t e m p e r a t u r e c o e f f i c i e n t o f r e s i s t i v i t y d e f i n e d a t t h e r e f e r e n c e t e m p e r a t u r e . F i g u r e 2 - 5 . UOP M o n i r e x F o u l i n g T e s t Tempera tu re C o m p e n s a t i n g C i r c u i t ( t a k e n f rom U . S . P a t e n t # 3 , 7 3 1 , 1 8 7 ) 53 From H a u s l e r and T h a l m a y e r ( 1 7 ) , w b ( 2 - 3 9 ) From E q . ( 2 - 3 2 ) R -. R R - R a - o _ e e e ( 2 - 4 0 ) F o r l o a d s e n e r g i z e d by 'D.VC. c u r r e n t , t h e power f a c t o r e q u a l s 1 .00 and Q e q u a l s V I . H e n c e , V I / F h - R - R R, - R ( 2" 4 1 a) e b e a R a R e e e e a R V I / F e e . _ . R- Rb But R = j , But R. = R b e ( 2 - 4 1 b ) a R VI 2-h = (v - IR b)F ( 2 " 4 1 C ) *• h ' = - e R e V I ^ C V - IR e)F] ' ( 2" 4 1 d> The f u l l y d e v e l o p e d v e l o c i t y d i s t r i b u t i o n f o r a r e c t a n g u l a r d u c t o f c r o s s - s e c t i o n a l d i m e n s i o n s 2a and 2b i s g i v e n by Lundgren e t a l . (88) a s : 54 n N n J c o s h N n a n where N p = (2n+l ) i r /2b ( 2 - 4 2 b ) _ / d _ _ _ 4 _ _ V ( 2 - 4 2 c ) ,, Hv 4 3 8 v - 5 ^ ' a x ^ a b J - J z'N t a n h N a 3 b n n and t h e o r i g i n o f t h e c o o r d i n a t e s i s a t t he c e n t e r o f t h e d u c t . A s i m p l e r e q u a t i o n f o r t he v e l o c i t y d i s t r i b u t i o n f r om Shah and London (89) i s : jr M l - ( £ ) " ] [1 - ( f M ( 2 - 4 3 ) u max b a f o r . a =•_-* ; ( ) .5 ( f o r UOP M o n i r e x , a = 0 . 3 ) a N a t a r a j a n and Lakshmanan (90) s u g g e s t t he f o l l o w i n g v a l u e s f o r m and n : m = 1.7 + 0 . 5 ( a * ) " 1 , 4 ( 2 - 4 4 a ) n = 2 ( f o r a* * 1 /3) ( 2 - 4 4 b ) From t h e d a t a o f H a r t n e t t e t a l . ( 9 1 ) , t h e h y d r o d y n a m i c e n t r a n c e l e n g t h f o r l a m i n a r f l o w i n a r e c t a n g u l a r d u c t i s : J = c 6 , Re ( 2 - 4 5 ) eq Where Cg = 0.051 f o r an a s p e c t r a t i o o f 3 . 3 3 . 55 ' 2ci b The e q u i v a l e n t d i a m e t e r f o r a r e c t a n g u l a r c h a n n e l i s . y ^ - . T h u s , t h e e q u i v a l e n t d i a m e t e r f o r t h e UOP M o n i r e x i s abou t 1 .85 cm, w h i c h means t h e e n t r a n c e l e n g t h i s 2 . 6 5 e q u i v a l e n t d i a m e t e r s . T h u s , f o r R e y n o l d s number g r e a t e r t h a n 5 2 , t h e l am ina r f l o w i s no t f u l l y d e v e l o p e d . A p r o b l e m w i t h t h e t e m p e r a t u r e c o m p e n s a t i n g method o f H a u s l e r and Sampson (86) wou ld be t h a t t h e t h e r m o c o u p l e i s m e a s u r i n g a p o i n t t e m p e r a t u r e w h i l e t h e c o i l e d w i r e i s e x p e r i e n c i n g a d i s t r i b u t i o n o f t e m p e r a t u r e s a c r o s s t h e r e c t a n g u l a r d u c t . The t h e r m o c o u p l e t e m p e r a t u r e wou ld n o t be t h e same as t he a v e r a g e f l u i d t e m p e r a t u r e e x p e r i e n c e d by t h e w i r e , bu t a change i n t h e t h e r m o c o u p l e t e m p e r a t u r e may be o f t h e same m a g n i t u d e as a change i n t h e a v e r a g e f l u i d t e m p e r a t u r e . From Shah and London ( 8 9 ) , f o r a f u l l y d e v e l o p e d v e l o c i t y p r o f i l e , * L t h , H l = L t h / D e q R . e P r = . ° ' 0 4 6 . ( 2 - 4 6 ) where L ^ = . t he rma l e n t r y l e n g t h S i m i l a r l y , f o r s i m u l t a n e o u s l y d e v e l o p i n g f l o w , * L t h , H l = L t h / D R e P r V 0 ' 1 5 6 ( 2 " 4 7 ) eq The HI r e f e r s t o t h e t h e r m a l boundary c o n d i t i o n o f c o n s t a n t a x i a l w a l l h e a t f l u x w i t h c o n s t a n t p e r i p h e r a l w a l l t e m p e r a t u r e . T h u s , f o r s i m u l t a n e o u s l y d e v e l o p i n g f l o w , w h i c h a p p e a r s t o be t h e c a s e f o r t h e UOP M o n i r e x f o u l i n g p r o b e , t h e t h e r m a l boundary l a y e r w i l l be f u l l y d e v e l o p e d o n l y f o r RePr l e s s t h a n a b o u t 17 . 56 The t e m p e r a t u r e d i s t r i b u t i o n s / p r o f i l e s i n l a m i n a r f l o w o f an i n c o m p r e s s i b l e f l u i d i n a r e c t a n g u l a r c h a n n e l have been a n a l y t i c a l l y d e t e r m i n e d by I k r y a n n i k o v ( 9 2 , 9 3 ) and S a v i n o and S i e g e l (94) f o r d i f f e r e n t s e t s o f c o n d i t i o n s . S a v i n o and S i e g e l (94) were c o n s t r a i n e d t o f u l l y d e v e l o p e d l a m i n a r h e a t t r a n s f e r and unequa l h e a t a d d i t i o n on a d j a c e n t s i d e s . I k r y a n n i k o v (92) c o n s i d e r e d t h e c a s e o f l a m i n a r f l o w o f a l i q u i d i n an i n f i n i t e l y l o n g c h a n n e l w i t h c o n s t a n t w a l l t e m p e r a t u r e , and a l l o w i n g f o r e n e r g y d i s s i p a t i o n . He a l s o c o n s i d e r e d t he c a s e when t h e h e a t f l u x t o t he w a l l s i s a f u n c t i o n o f the c h a n n e l c o o r d i n a t e s ( 9 2 ) . The s o l u t i o n s a r e e x t r e m e l y l o n g and cumbersome. I k r y a n n i k o v (93) p r e s e n t s a g raph o f m i d - p l a n e t e m p e r a t u r e d i s t r i b u t i o n f o r a s q u a r e c h a n n e l , w h i c h shows t h a t t he t e m p e r a t u r e p r o f i l e i s p a r a b o l i c w i t h t he c e n t r a l s e c t i o n f l a t t e n e d . To d e t e r m i n e b u l k t e m p e r a t u r e , g i v e n t he v e l o c i t y and t e m p e r a t u r e p r o f i l e s , one w o u l d use t h e f o l l o w i n g ( 8 9 ) : T =1 ' b ab r - r b M T . d x d y ( 2 - 4 8 ) o To d e t e r m i n e t h e t h e o r e t i c a l h e a t t r a n s f e r c o e f f i c i e n t s . H a u s l e r and T h a l m a y e r (17) use the f o l l o w i n g e q u a t i o n s f r om K r e i t h (95) w h i c h a p p l y t o f l o w norma l t o a h o r i z o n t a l c y l i n d e r : c -w _ l i l c ( l W ) P r 0 .31 ( 2 _ 4 g ) k f " ' - ' ^ u f ' " f Where Cy and n depend on t h e Re range a n d , h . D , u.D ° - 5 0 .31 = [0 .35 + 0 . 5 6 ( 4 ^ ) - ] P r f ( 2 - 5 0 ) K f v f 57 I t s h o u l d be n o t e d t h a t t h e s e c o n d e q u a t i o n o r i g i n a l l y came f r om McAdams ( 9 6 ) , who used s l i g h t l y d i f f e r e n t e x p o n e n t s , i . e . 0 . 5 2 i n s t e a d o f . 0 . 5 and 0 . 3 i n s t e a d o f 0 . 3 1 . Fand (97) s u g g e s t s t h e use o f a s l i g h t l y d i f f e r e n t e q u a t i o n w h i c h has t h e v i r t u e o f r e p r e s e n t i n g t h e s e p a r a t e c o n t r i b u t i o n s t o Nu.p by t h e l e a d i n g and t r a i l i n g p o r t i o n s o f t h e c y l i n d e r : N u f = =• [ 0 . 3 5 + 0 . 3 4 R e f P ' - - r , 0 . 1 5 R e f ° - 5 8 ] P r f 0 - 3 0 ( 2 - 5 1 ) H a u s l e r and T h a l m a y e r (17) e x p l a i n e d t h e d i s c r e p a n c y between t h e i r e x p e r i m e n t a l r e s u l t s and t h e o r e t i c a l v a l u e s by s u g g e s t i n g t h a t some n a t u r a l c o n v e c t i o n i s s u p e r i m p o s e d on t h e f o r c e d c o n v e c t i o n . o Fand and Keswani (98) i d e n t i f i e d f o u r z o n e s . In zone 1 , G r ^ / R e ^ i s l e s s t h a n 0 . 5 and t h e p r e d o m i n a n t h e a t t r a n s f e r mechan ism i s f o r c e d c o n v e c t i o n . In zone 2 , G r f / R e f i s between 0 . 5 and 2 . 0 , and n a t u r a l c o n v e c t i o n a f f e c t 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 by as much as 10%. In zone 3 , n a t u r a l and f o r c e d c o n v e c t i o n e f f e c t s a r e o f t h e same o r d e r and m a g n i t u d e . In zone 4 , n a t u r a l c o n v e c t i o n p r e d o m i n a t e s . Zone 1: N u f = [ 0 . 2 5 5 + 0 . 6 9 9 R e f 0 - 5 ] P r f 0 ' 2 9 ( 2 - 5 2 ) S r _ ° - 3 0 0 . 2 5 0 . 2 9 Zone 2 : N u f = [ 0 . 2 5 5 + 0 . 6 9 9 R e f u , D + 0 . 0 3 3 0 ( - ^ T ) .. G r f - . ] P r • R e ^ ( 2 - 5 3 ) From t h e r e s u l t s o f H a u s l e r and T h a l m a y e r ( 1 7 ) , i t a p p e a r s t h a t a h o r i z o n t a l c y l i n d e r does a p p r o x i m a t e a c o i l e d w i r e , i n t e rms 58 o f h e a t t r a n s f e r c o e f f i c i e n t s . Howeve r , a c o i l s h o u l d be b e t t e r a p p r o x i m a t e d by a c o m b i n a t i o n o f f l o w p a r a l l e l and normal t o a c y l i n d e r . h , . = f h + ( 1 . - f ) 'h ( 2 T 5 4 ) t o t p a r ' norm where 0 $ f $ 1 To d e t e r m i n e a v a l u e f o r h , p a r a l l e l f l o w p a s t a c y l i n d e r p a r r r J can be f u r t h e r a p p r o x i m a t e d by a n n u l a r f l o w ( f u l l y d e v e l o p e d l a m i n a r v e l o c i t y p r o f i l e and u n d e v e l o p e d t e m p e r a t u r e p r o f i l e ) , w h i c h a l l o w s use o f T a b l e 19 on p . 7 - 7 6 o f Rohsenow and H a r t n e t t ( 7 9 ) . Hot w i r e p r o b e s t h a t a r e t h e r m a l l y m o n i t o r e d s h o u l d have t h e i r w i r e ' s c r i t i c a l r a d i u s d e t e r m i n e d . Be low t h i s c r i t i c a l r a d i u s , t h e a c t o f i n s u l a t i n g i n c r e a s e s h e a t l o s s , s i n c e t h e e f f e c t o f t h e added s u r f a c e more t h a n o f f s e t s t h e i n c r e a s e d t h e r m a l r e s i s t a n c e o f t h e low t h e r m a l c o n d u c t i v i t y i n s u l a t i o n . McAdams (96) goes t h r o u g h t h e d e r i v a t i o n o f r? , t h e c r i t i c a l r a d i u s , w h i c h e q u a l s t h e r a t i o o f i n s u -l a t i o n t h e r m a l c o n d u c t i v i t y t o t h e s u r f a c e c o e f f i c i e n t . Howeve r , t h i s assumes t h a t t h e s u r f a c e 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 no t a f u n c t i o n o f r a d i u s , w h i c h i s n o t n e c e s s a r i l y c o r r e c t . F o r l a m i n a r f l o w f o r c e d c o n v e c t i o n , t h e g e n e r a l f o rm o f 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 c o r r e l a t i o n i s : , 2 r u . „ h c = f r [ a + b ( — ^ ] P r m ( 2 - 5 5 a ) = K' (1) + K " n n _ 1 ( 2 - 5 5 b ) 59 U s i n g McAdams' (96) d e r i v a t i o n p r o c e d u r e : . l n ( i 7 r , ) and x 2 T T L R s = 1 / ( h c 2 1 r r ) ( 2 - 5 6 ) ( 2 - 5 7 ) d ( R x + R s L 0 1 n K V " " 1 d r 2Trk m r 2^ n 2 m ( K ' + K " r n ) ( 2 - 5 8 ) As r i n c r e a s e s , t h e d e p o s i t and f i l m t e m p e r a t u r e s c h a n g e , so k m and t h e t r a n s p o r t p r o p e r t i e s i n 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 c o r r e l a t i o n a r e i n d i r e c t l y f u n c t i o n s o f r . H o w e v e r , t h e y a r e weak f u n c t i o n s o f t e m p e r a t u r e and t h i s e f f e c t can p r o b a b l y be i g n o r e d . The f i n a l s o l u t i o n i s : 1 K" where K' nk K' ± n k m ( nk m m v 4 K1 ) - r r l / n akP r 1 m h k P r m , 2 u h n and K" = ^ f - ( - r ^ ) ( 2 - 5 9 a ) ( 2 - 5 9 b ) ( 2 - 5 9 c ) I f t h e w i r e r a d i u s i s l e s s t han t h e c r i t i c a l r a d i u s , t h e n d u r i n g t h e i n i t i a l s t a g e s o f f o u l i n g , t h e r e may be n e g a t i v e f o u l i n g r e s i s t a n c e s . From H a u s l e r and T h a l m a y e r ( 1 7 ) , R 1 1 t o ( 2 - 6 0 ) where h = an 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 . 60 H e n c e , u s i n g E q . ( 2 - 3 9 - J , T... T Tr w wo Q/F ^vt'~'^wo Q/F Q/F (2-61 a) ( 2 - 6 1 b ) T h i s d e r i v a t i o n assumes i n s i g n i f i c a n t s u r f a c e a r e a change and f i l m t r a n s f e r c o e f f i c i e n t c h a n g e , w h i c h f o r a t h i n w i r e i s g r o s s l y i n c o r r e c t . A c t u a l l y , T - T W wo + 1 h o A w i r e hA; Mm ( 2 - 6 2 a ) where • : -A 1 _ • = I - 2 i r L ( r 2 - r 1 ) / l n ( r 2 / r - | ) ( 2 - 6 2 b ) The dependence o f f l u i d h e a t t r a n s f e r c o e f f i c i e n t on d i a m e t e r must be known f o r t h i s k i n d o f a n a l y s i s . 2 . 7 F o u l i n g M o d e l s F o u l i n g mode ls were r e v i e w e d by Tabo rek e t a l . ( 7 ) , S u i t o r e t a l . ( .16), and E p s t e i n ( 9 ) . Kern and S e a t o n (6) i n t r o d u c e d t h e i d e a t h a t n e t measured f o u l i n g was t h e d i f f e r e n c e between two s i m u l t a n e o u s p r o c e s s e s , a d e p o s i t i o n p r o c e s s and a remova l p r o c e s s , w h i c h e x p l a i n s t h e phenomenon o f a s y m p t o t i c f o u l i n g . The n e t f o u l i n g r a t e can t h u s be e x p r e s s e d as 61 t he d i f f e r e n c e between t h e g r o s s d e p o s i t i o n f l u x , n ^ , and t h e r e - e n t r a i n m e n t f l u x , m r ( 9 ) : U = * = ™ d - \ ( 2 - 6 3 ) rhj i s c o n s i d e r e d t o r e m a i n c o n s t a n t w i t h t i m e bu t m^ i s c o n s i d e r e d t o be p r o p o r t i o n a l t o m and hence i n c r e a s e s w i t h t i m e . Hence. m = m d - bm ( 2 - 6 4 ) I n t e g r a t i n g E q . ( 2 - 6 4 ) w i t h t h e i n i t i a l c o n d i t i o n m=0, e - 0 ( a f t e r t h e i n d u c t i o n p e r i o d ) , » - 5 g _ < l - . - b ( > - . * < ! ( 2 - 6 5 ) * where m i s t h e a s y m p t o t i c v a l u e o f m, t h e t i m e c o n s t a n t e c e q u a l s 1 / b , m d e q u a l s m * / e c , and m r e q u a l s m d ( l - e " 6 7 6 c ) . The t i m e c o n s t a n t e r e p r e s e n t s t h e a v e r a g e r e s i d e n c e t i m e o f an e l e m e n t o f f o u l i n g d e p o s i t on t h e w a l l ( 9 ) . A s s u m i n g r e - e n t r a i n m e n t by t u r b u l e n t b u r s t s as p r o p o s e d by C l e a v e r and Y a t e s ( 9 9 , 1 0 0 ) , t h e n f o r a r e - e n t r a i n m e n t e f f i c i e n c y o f 100%, e = A v e r a g e t i m e between b u r s t s 00 V x s c F r a c t i o n o f s u r f a c e c o v e r e d by b u r s t s ~ g U - o o ; a t any i n s t a n t where 3 s 0 . 0 0 5 Howeve r , r e - e n t r a i n m e n t e f f i c i e n c y i s c o n s i d e r a b l y l e s s t h a n 100% s i n c e o n l y t h e most w e a k l y a d h e r i n g d e p o s i t s can be 100% removed by a 62 t u r b u l e n t b u r s t ( 1 0 1 ) . E q . ( 2 - 6 5 ) i s e q u i v a l e n t t o t h e K e r n - S e a t o n e q u a t i o n : R f = R f * ( . l - e " 6 / 9 c ) ( 2 - 6 7 ) E p s t e i n (101) s u g g e s t s t he use o f a d i m e n s i o n l e s s c r i t e r i o n , u , f o r p r e d i c t i n g w h e t h e r o r n o t r e - e n t r a i n m e n t o c c u r s , w h i c h can be e x p r e s s e d a s : Hyd rodynamic f o r c e s t e n d i n g t o d i s r u p t t h e d e p o s i t ^ 53) v A d h e s i v e / c o h e s i v e f o r c e o f d e p o s i t v " ' He s t a t e s t h a t t h e n u m e r a t o r w o u l d l i k e l y be a f u n c t i o n o f t h e f r i c t i o n v e l o c i t y u* (.= ( x s / p ) 2 = u b ( f / 2 ) 2 ) , w h i l e t h e d e n o m i n a t o r wou ld be t h e s m a l l e r o f t h e two f o r c e s i n v o l v e d . T h u s , above some c r i t i c a l v a l u e o f T T , r e - e n t r a i n m e n t wou ld o c c u r . E p s t e i n f u r t h e r s t a t e s t h a t f o r some p r o c e s s e s t h e c r i t i c a l v a l u e o f TT i s no t e x c e e d e d f o r a l o n g t i m e , d u r i n g w h i c h t i m e t he d e p o s i t i s g r a d u a l l y b e i n g weakened by some i n t e r n a l mechan i sm. When t h e a d h e s i v e a n d / o r c o h e s i v e f o r c e s have d i m i n i s h e d s u f f i c i e n t l y , t h e c r i t i c a l ir v a l u e i s e x c e e d e d , and v i g o r o u s r e - e n t r a i n -ment o c c u r s . Such b e h a v i o u r was o b s e r v e d by R i t t e r and S u i t o r (102) f o r s e a w a t e r f o u l i n g o f c o p p e r . a l l o y . A model n o t c o v e r e d i n t h e summary t a b l e s o f E p s t e i n (9) i s t h a t o f C r i t t e n d e n and K o l a c z k o w s k i (12) whose d e p o s i t i o n f l u x i s e x p r e s s e d a s : 63 where t h e f i r s t t e r m i s themass f l u x o f f o u l a n t p r e c u r s o r t o t h e r e a c t i o n zone a t t h e s u r f a c e / f l u i d i n t e r f a c e and t he s e c o n d t e rm i s t h e f o u l a n t mass f l u x away f r om t h e z o n e . T h i s e q u a t i o n assumes a f i r s t - o r d e r r e a c t i o n . C r i t t e n d e n ' s d e p o s i t remova l t e rm i s : ' r IJJ m = - 4 - ( 2 - 7 0 ) where i> i s a f u n c t i o n o f d e p o s i t s t r u c t u r e . T h i s e x p r e s s i o n i s s i m i l a r t o t h a t o f Tabo rek e t a l . ( 7 ) . F o r E q . ( 2 - 6 9 ) , C r i t t e n d e n and K o l a c z k o w s k i (12) a p p l y t h e C h i l t o n - C o b u r n a n a l o g y f o r mass t r a n s f e r : S t = = I s c , _ 2 / 3 ( 2 - 7 1 a ) u b c i b u t { = j ^ R e " 0 ' 2 ( 2 - 7 1 b ) where X-| i s a f u n c t i o n o f s u r f a c e r o u g h n e s s H e n c e , K i = T H 7 ^ p t e a , 8 ( S c i > " 2 / 3 ( 2 - 7 2 ) The r e a c t i o n v e l o c i t y c o n s t a n t can be e x p r e s s e d by t h e A r r h e n i u s e q u a t i o n : k = A e x p ( - E / R T ) ( 2 - 7 3 ) where E i s t h e a c t i v a t i o n e n e r g y and A i s t h e p r e - e x p o n e n t i a l f a c t o r . F o r E q . ( 2 - 7 0 ) , T s c a n be e x p r e s s e d a s : \ - <•%% < 2 - 7 4 > F o r r e l a t i v e l y low t e m p e r a t u r e , s m a l l d i a m e t e r t u b e s , and 64 h i g h mass f l o w r a t e s , d e p o s i t i o n i s l i k e l y t o be c o n t r o l l e d by r e a c t i o n k i n e t i c s i . e . k << K . A t h i g h e r t e m p e r a t u r e , d e p o s i t i o n may be c o n t r o l l e d by d i f f u s i o n i . e . Kp<< k. Hasson and Z a h a v i (103) d e v e l o p e d an e x p r e s s i o n ( b a s e d on t h e i r a n a l y t i c a l model d e s c r i b i n g t h e p r o p a g a t i o n o f a n u c l e a t i o n f r o n t a l o n g a t u b e s u r f a c e ) f o r t h e t h i c k n e s s p r o f i l e o f a s c a l e l a y e r a l o n g a h e a t e d annu l u s , a t t i m e e ^ : l o g ( l - ~ ) = l o g f - - B ( x - | 1 ) (2.-75) y f o e , f B x o r . * f = y f o i i o -B ^ - F ^ ( 2 - 7 6 ) where B i s a s t e a d y - s t a t e n u c l e a t i o n c o e f f i c i e n t , D i s an u n s t e a d y - s t a t e n u c l e a t i o n c o e f f i c i e n t and K is . a n u c l e a t i o n - k i n e t i c s c o e f f i c i e n t . They o b s e r v e d t h a t t h e d e p o s i t i o n p r o c e s s f s a t w o - s t a g e phenomenon: ( i ) i n i t i a l i n d u c t i o n s t a g e c o n s i s t s o f t h e d e p o s i t i o n o f n u c l e a t e s , w h i c h r e s u l t s i n a p r i m a r y c r y s t a l l a y e r on t h e m e t a l s u r f a c e . ( i i ) a d d i t i o n a l l a y e r s c r y s t a l l i z e on t h e p r i m a r y d e p o s i t i n t h e s e c o n d s t a g e . The PFRU h e a t e d s e c t i o n s h o u l d a l s o d e v e l o p a x i a l l y n o n -u n i f o r m d e p o s i t s , p o s s i b l y i n t h e same manner as t h e h e a t e d s e c t i o n s o f Hasson and Z a h a v i . 65 2 . 8 P o l y m e r i z a t i o n K i n e t i c s Braun and H a u s l e r ( 2 2 ) s t a t e t h a t p e t r o l e u m p r o c e s s f o u l i n g i n v o l v e s t h e d e p o s i t i o n o f b l a c k and brown i n s o l u b l e p o l y m e r i c m a t e r i a l w i t h a h i g h d e g r e e o f u n s a t u r a t i o n . A u t o x i d a t i o n ^ ( w h i c h was d e s c r i b e d e a r l i e r ) i s c o n s i d e r e d t h e b a s i s o f t h e f o u l i n g mechan i sm. F o r c h e m i c a l r e a c t i o n c o n t r o l l e d f o u l i n g , , t h e k i n e t i c s o f t h e p o l y m e r i z a t i o n r e a c t i o n must be known. R a d i c a l c h a i n p o l y m e r i z a t i o n c o n s i s t s o f a sequence o f t h r e e s t e p s - i n i t i a t i o n , p r o p a g a t i o n , and t e r m i n a t i o n . I n i t i a t i o n i n v o l v e s two r e a c t i o n s . The f i r s t i s t he p r o d u c t i o n o f f r e e r a d i c a l s by a v a r i e t y o f t h e r m a l , p h o t o c h e m i c a l and r e d o x m e t h o d s . Od ian (104) s t a t e s t h a t t h e u s u a l method i s t h e t h e r m a l , h o m o l y t i c d i s s o c i a t i o n o f a c a t a l y s t o r i n i t i a t o r t o y i e l d a p a i r o f r a d i c a l s : I 2R: ( 2 - 7 7 ) where k_ i s t h e r a t e c o n s t a n t f o r t h e c a t a l y s t d i s s o c i a t i o n . O n l y s t y r e n e and me thy l m e t h a c r y l a t e have been o b s e r v e d t o undergo a p u r e l y t h e r m a l , s e l f - i n i t i a t e d p o l y m e r i z a t i o n , bu t a t r a t e s much l e s s t h a n t h o s e u s i n g i n i t i a t o r s . The s e c o n d p a r t o f t h e i n i t i a t i o n i n v o l v e s t he a d d i t i o n o f t h e r a d i c a l t o a monomer t o p r o d u c e t h e c h a i n i n i t i a t i n g s p e c i e s M-j: : k i R v + M — ! - > M 1 ••• ( 2 - 7 8 ) where k. i s t h e r a t e c o n s t a n t f o r t h e i n i t i a t i o n s t e p . 66 P r o p a g a t i o n i s shown b y : k M n - + M _ H - » M n ; i ( 2 - 7 9 ) where k- i s t h e r a t e c o n s t a n t f o r p r o p a g a t i o n . T e r m i n a t i o n o c c u r s by b i m o l e c u l a r r e a c t i o n between r a d i c a l s . The two r a d i c a l s r e a c t w i t h each o t h e r by c o m b i n a t i o n : M • + M • - ^ - > M x ( 2 - 8 0 ) n m n+m where k t c i s t h e r a t e c o n s t a n t f o r c o u p l i n g , o r by d i s p r o p o r t i o n a t e i n w h i c h a hyd rogen r a d i c a l t h a t i s b e t a t o one r a d i c a l c e n t e r i s t r a n s f e r r e d t o a n o t h e r r a d i c a l c e n t e r t o f o rm two p o l y m e r m o l e c u l e s - one s a t u r a t e d and one u n s a t u r a t e d : k . , M • + M • z > M + M m ( 2 - 8 1 ) n m 7 n m v ' where k ^ i s t h e r a t e c o n s t a n t f o r d i s p r o p o r t i o n a t e . T e r m i n a t i o n can a l s o o c c u r t h r o u g h c h a i n t r a n s f e r , t h e r e a c t i o n o f a p o l y m e r c h a i n w i t h a m o l e c u l e o f s o l v e n t , monomer o r o t h e r l ow m o l e c u l a r w e i g h t s p e c i e s : V + R X * M n X + R * ( 2 " 8 2 ^ The r a t e o f monomer d i s a p p e a r a n c e , i . e . r a t e o f p o l y m e r i z a t i o n , i s g i v e n b y : - h + R P < 2 - 8 3 > Bu t R p>> R n - , h e n c e , 67 - R P ( 2 - 8 4 ) The r a t e o f p o l y m e r i z a t i o n i s t h e sum o f many i n d i v i d u a l p r o p a g a t i o n s t o p s , a l l h a v i n g t h e same r a t e c o n s t a n t . T h u s , one can e x p r e s s p o l y m e r i z a t i o n r a t e b y : R p = k p [ M - ] [ M ] ( 2 - 8 5 1 where [M«] i s t h e t o t a l c o n c e n t r a t i o n o f a l l c h a i n r a d i c a l s . Assuming t h e r a t e s o f i n i t i a t i o n and t e r m i n a t i o n a r e e q u a l : R i = 2 k t [ M - ] 2 ( 2 - 8 6 ) S u b s t i t u t i n g E q . X 2 - 8 6 ) i n t o E q . ( 2 . 8 5 ) y i e l d s : ; R p = M M ^ % (2-87> The r a t e o f t h e r m a l h o m o l y s i s o f an i n i t i a t o r , R^ , i s g i v e n b y : R d = 2 f k d [ I ] ( 2 - 8 8 ) The i n i t i a t o r e f f i c i e n c y , f , i s d e f i n e d as t h e f r a c t i o n o f r a d i c a l s p r o d u c e d i n t he h o m o l y s i s r e a c t i o n w h i c h i n i t i a t e p o l y m e r c h a i n s ( 1 0 4 ) . H o m o l y s i s i s t h e . r a t e d e t e r m i n i n g s t e p i n i n i t i a t i o n . H e n c e , R^ i s g i v e n b y : Rn- = 2 f k d [ I ] ( 2 - 8 9 ) S u b s t i t u t i n g E q . ( 2 - 8 9 ) i n t o E q . ( 2 - 8 7 ) y i e l d s : f k d [ t ] h 68 2 . 9 . B o i l i n g A c c o r d i n g t o Tabo rek e t a l . ( 7 ) . f o u l i n g d u r i n g b o i l i n g under n a t u r a l c o n v e c t i o n o r f o r c e d f l o w has n e v e r been i n v e s t i g a t e d q u a n t i t a t i v e l y . They s t a t e t h a t i n t he c a s e o f n u c l e a t e b o i l i n g , t h e e f f e c t o f t h e f o u l i n g l a y e r r e s i s t a n c e must be comb ined w i t h t h e e f f e c t o f n u c l e a t i o n s i t e s . They f u r t h e r s t a t e t h a t b o i l i n g a f f e c t s t h e e f f e c t i v e s u r f a c e . t e m p e r a t u r e w h i c h i s a v e r y i m p o r t a n t f a c t o r i n c h e m i c a l r e a c t i o n f o u l i n g . P a l e n and Wes twa te r (105) s t u d i e d h e a t t r a n s f e r and f o u l i n g r a t e s d u r i n g t h e poo l b o i l i n g o f c a l c i u m s u l p h a t e s o l u t i o n s , and a t o l u e n e - s t y r e n e s o l u t i o n . They f o u n d t h a t t h e s c a l e f o r m a t i o n was l i n e a r w i t h t i m e and p r o p o r t i o n a l t o t h e s q u a r e o f t h e h e a t f l u x . As s c a l e fo rmed i n i t i a l l y , t h e f o u l i n g r e s i s t a n c e i n c r e a s e d . Then b o i l i n g n u c l e a t i o n s i t e s a p p e a r e d i n t h e d e p o s i t , soon c a u s i n g a d e c r e a s e i n f o u l i n g r e s i s t a n c e . A f t e r a minimum was r e a c h e d , f o u l i n g r e s i s t a n c e a g a i n i n c r e a s e d l i n e a r l y w i t h t i m e . F o r t h e t o l u e n e - s t y r e n e s o l u t i o n , f o u l i n g r e s i s t a n c e was n e g l i g i b l e a t f i r s t and t h e n i n c r e a s e d i n a l m o s t a s t e p w i s e f a s h i o n , a f t e r w h i c h i t began o s c i l l a t i n g . The i n d u c t i o n t i m e was c o r r e l a t e d as a f u n c t i o n o f h e a t f l u x and s t y r e n e c o n c e n t r a -t i o n t o g i v e : 2 6 . n d = 1.67 x 1 0 8 q " 2 ( ^ ) . ( 2 - 9 1 ) They p r o p o s e d t h e f o l l o w i n g p h y s i c a l e x p l a n a t i o n f o r t h e f o u l i n g b e h a v i o u r o f c a l c i u m s u l p h a t e s o l u t i o n s . I n i t i a l l y t h e f o u l i n g d e p o s i t i s v e r y p o r o u s , has a low t h e r m a l c o n d u c t i v i t y , and t h e i n c r e a s e i n 69 ATS» i . e . i n f o u l i n g r e s i s t a n c e , : i s v e r y r a p i d . As t h e d e p o s i t g r o w s , me ta l t e m p e r a t u r e i n c r e a s e s , and v a p o u r i s f o r c e d f r om c a v i t i e s i n t h e me ta l i n t o new c a v i t i e s i n t h e p o r o u s d e p o s i t , w h i c h become b u b b l e -p r o d u c i n g s i t e s . As t h e number o f n u c l e a t i o n s i t e s i n c r e a s e s , t h e n u c l e a t e b o i l i n g h e a t t r a n s f e r c o e f f i c i e n t i n c r e a s e s , c a u s i n g a d e c r e a s e i n ATG. E v e n t u a l l y , t h e f o u l i n g d e p o s i t t h i c k n e s s i n c r e a s e s t o such an e x t e n t t h a t t h e t e m p e r a t u r e d r o p a c r o s s t h e b o i l i n g f i l m i s i n s i g n i f i c a n t compared t o t h a t a c r o s s t h e f o u l i n g d e p o s i t , a t w h i c h t i m e f u r t h e r d e p o s i t i o n c a u s e s an i n c r e a s e i n AT$. E p s t e i n (9) s t a t e s t h a t b o i l i n g c a u s e s h i g h e r r a t e s o f s c a l i n g t h a n s e n s i b l e h e a t i n g b e c a u s e o f t h e h i g h e r t e m p e r a t u r e s and h e a t f l u x e s u s u a l l y i n v o l v e d , t h e c o n c e n t r a t i o n e f f e c t due t o e v a p o r a t i o n , and t h e h i g h e r mass f l u x e s o f l i q u i d t o t h e h e a t t r a n s f e r s u r f a c e , e s p e c i a l l y i n n u c l e a t e b o i l i n g . C o l l i e r (106) d e f i n e s t h e r e g i o n s o f d e v e l o p i n g t w o - p h a s e f l o w i n a h e a t e d t u b e . They a r e s i n g l e phase l i q u i d , b u b b l y f l o w , s l u g f l o w , a n n u l a r f l o w , d r o p f l o w , and s i n g l e phase v a p o u r . The PFRU h e a t e d s e c t i o n wou ld be i n t h e f i r s t two o r t h r e e r e g i o n s , where v a p o u r q u a l i t y i s l o w and s u b c o o l e d o r l o c a l b o i l i n g t a k e s p l a c e . The UOP M o n i r e x ho t w i r e wou ld p r o b a b l y e x p e r i e n c e n u c l e a t e b o i l i n g , a l t h o u g h f i l m b o i l i n g wou ld o c c u r f o r h i g h enough s u r f a c e t e m p e r a t u r e s . In t h e l i t e r a t u r e , a few e q u a t i o n s have been f o u n d w h i c h can be used t o p r e d i c 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 f o r t h e PFRU unde r b o i l i n g c o n d i t i o n s . Chen ( 1 0 7 ) , f o r a n n u l a r f l o w , recommends t h i s f o r c e d c o n v e c t i o n e v a p o r a t i o n c o r r e l a t i o n ( i n BES u n i t s ) : 70 . 0 . 7 9 r 0 . 4 5 0 . 4 9 n 0 . 2 5 U n n m o o 1 ^ P l P 1 J C 2 4 , ^ 0 . 7 5 c , , r h = 0 . 0 0 1 2 2 Q.5 , 0 . 2 9 . 0 . 2 4 0 . 2 4 ( a T ) ( A p ) S + h L P F  a y l h f g p u ( 2 - 9 2 a ) ( A T ) h f where Ap = 1 5 ( 2 - 9 2 b ) ' s a t u f g g c = 3 2 . 2 ( 3 6 0 0 ) 2 ( 2 - 9 2 c ) h L p = 0 . 0 2 3 k l u b ( J - x )D 0 . 8 P r ^ ' 4 ( 2 - 9 2 d ) S and F a r e g i v e n i n two g r a p h s i n Rohsenow and H a r t n e t t ( 7 9 ) . S i m p l e r e q u a t i o n s have been d e v e l o p e d f o r t h e e x t e n s i v e l y s t u d i e d wa te r , s y s t e m . F o r e x a m p l e , Thorn e t a l . (108) s u g g e s t e d t h e f o l l o w i n g e q u a t i o n f o r low q u a l i t y and s u b c o o l e d f o r c e d c o n v e c t i o n o f w a t e r ( i n BES u n i t s ) : 7 2 ( S - M ( 2 - 9 3 ) w ' s a t e p / 1 2 6 0 v 1 0 6 F o r f o r c e d c o n v e c t i o n l o c a l b o i l i n g o f w a t e r i n s i d e v e r t i c a l t u b e s , J a k o b (109) recommends ( i n SI u n i t s ) : h = 2 .54 (AT J 3 e p / 1 ' 5 5 1 ( 2 - 9 4 ) No c o r r e l a t i o n s c o u l d be f o u n d f o r f o r c e d c o n v e c t i o n n u c l e a t e b o i l i n g a c r o s s a w i r e o r c y l i n d e r , w h i c h c o u l d have been used t o p r e d i c 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 f o r t h e UOP M o n i r e x F o u l i n g P robe unde r n u c l e a t e b o i l i n g c o n d i t i o n s . 71 H o w e v e r , f o r t u r b u l e n t f l o w , f o r c e d c o n v e c t i o n f i l m b o i l i n g o v e r s m a l l h o r i z o n t a l c y l i n d e r s and w i r e s , B r o m l e y (110) s u g g e s t s ( i n BES u n i t s ) : where h b = 2 . 7 V. k P -y b v v D AT . w s a t h f g { 1 + 0 .4AT C ' f g ( 2 - 9 5 a ) ( 2 - 9 5 b ) F o r f l o w t h a t i s n o t f u l l y d e v e l o p e d t u r b u l e n t f l o w , h^ can be e v a l u a t e d f rom a g r a p h i n B r o m l e y ( 1 1 0 ) . 72 3 . SCOPE AND METHOD OF PRESENT WORK T h e r e have been a few p a p e r s t h a t have r e v i e w e d , a n a l y z e d , d i s c u s s e d a n d / o r compared v a r i o u s f o u l i n g measurement t e c h n i q u e s , such as F i s c h e r e t a l . ( 2 1 ) , S u i t o r e t a l . ( 1 6 ) , B raun and H a u s l e r ( 2 2 ) , E p s t e i n ( 9 ) , and Knudsen ( 4 7 ) . The a d v a n t a g e s and d i s a d v a n t a g e s o f t h e v a r i o u s t e c h n i q u e s were a n a l y z e d . The t e c h n i q u e s were c l a s s i f i e d and c a t e g o r i z e d a c c o r d i n g t o geomet ry o f f o u l i n g s u r f a c e , t y p e o f h e a t i n g a n d / o r method o f m o n i t o r i n g t h e d e p o s i t . Howeve r , i n none o f t h e s e p a p e r s , d i d t h e a u t h o r s a c t u a l l y d u p l i c a t e t h e o p e r a t i n g c o n d i t i o n s ( e x p e r i m e n t a l l y o r t h e o r e t i c a l l y ) , e . g . b u l k t e m p e r a t u r e , s u r f a c e t e m p e r a t u r e , f l o w r a t e , h e a t f l u x , oxygen c o n t e n t , f l u i d c o m p o s i t i o n , e t c , , u s e d i n a f o u l i n g run by f o u l i n g measurement t e c h n i q u e A , f o r a f o u l i n g run measured by t e c h n i q u e B. T h e r e i s a p o s s i b i l i t y t h a t under t h e same o p e r a t i n g c o n d i t i o n s , f o u l i n g measurement t e c h n i q u e B may n o t even d e t e c t - - a n y f o u l i n g . Of c o u r s e s u c h a c o m p a r i s o n i s no t a l w a y s p o s s i b l e . Mos t f o u l i n g measurement t e c h n i q u e s were d e s i g n e d f o r s p e c i f i c t y p e s o f f o u l i n g . F o r e x a m p l e , a t e c h n i q u e d e s i g n e d t o m o n i t o r b i o f o u l i n g a t t e m p e r a t u r e s l e s s t h a n 100°F w o u l d o n l y r e q u i r e s e n s i b l e f l u i d h e a t i n g . T h i s b i o f o u l i n g t e c h n i q u e c o u l d no t be used f o r c h e m i c a l r e a c t i o n f o u l i n g w h i c h r e q u i r e s s u r f a c e t e m p e r a t u r e s t h a t s e n s i b l e f l u i d h e a t i n g , u s i n g common f l u i d s , i s i n c a p a b l e o f a c h i e v i n g . F u r t h e r m o r e , a t e c h n i q u e w h i c h emp loys s t r i c t l y one k i n d o f m o n i t o r i n g , s u c h as v i s u a l o r p r e s s u r e d r o p , i s d i f f i c u l t t o compare q u a n t i t a t i v e l y t o a t e c h n i q u e w h i c h emp loys a n o t h e r k i n d o f m o n i t o r i n g such as t h e r m a l . 73 A l s o , a t e c h n i q u e w h i c h emp loys q u a l i t a t i v e m o n i t o r i n g i s d i f f i c u l t t o compare t o a t e c h n i q u e w h i c h emp loys q u a n t i t a t i v e m o n i t o r i n g . T h u s , f o r a q u a n t i t a t i v e c o m p a r i s o n between two f o u l i n g measurement t e c h n i q u e s , t h e two t e c h n i q u e s s h o u l d employ s i m i l a r methods o f m o n i t o r i n g t h e d e p o s i t q u a n t i t a t i v e l y and s h o u l d be c a p a b l e o f g e n e r a t i n g s i m i l a r o p e r a t i n g c o n d i t i o n s , such as s u r f a c e t e m p e r a t u r e and h e a t f l u x . Such a q u a n t i t a t i v e c o m p a r i s o n s h o u l d answer t h e f o l l o w i n g q u e s t i o n s : (1) Which t e c h n i q u e i s t h e more s e n s i t i v e t o changes i n o p e r a t i n g c o n d i t i o n s ? (2 ) Does one t e c h n i q u e c o n s i s t e n t l y g i v e h i g h e r f o u l i n g r a t e s a n d / o r f o u l i n g r e s i s t a n c e s t h a n t h e o t h e r ? (3) Which t e c h n i q u e g i v e s t h e more r e p r o d u c i b l e r e s u l t s ? (4 ) Which t e c h n i q u e g i v e s t h e f e w e r p r o b l e m s ? I t was d e c i d e d t o compare t h e P o r t a b l e F o u l i n g R e s e a r c h U n i t , w h i c h emp loys t h e c o n v e n t i o n a l a n n u l a r geomet r y and t u r b u l e n t f l o w r a t e s p r e s e n t i n many i n d u s t r i a l h e a t e x c h a n g e r s , t o t h e UOP M o n i r e x F o u l i n g T e s t , w h i c h emp loys a w i r e c o i l geomet ry and l a m i n a r f l o w r a t e s no t as commonly p r e s e n t i n i n d u s t r i a l h e a t e x c h a n g e r s . Bo th p r o b e s w i l l soon be c o m m e r c i a l l y a v a i l a b l e , w h i c h i n c r e a s e s t h e s i g n i f i c a n c e o f t h i s c o m p a r i s o n , s i n c e p o t e n t i a l i n d u s t r i a l u s e r s o f f o u l i n g p r o b e s wou ld w i s h t o know w h i c h p robe i s s u p e r i o r . A t p r e s e n t , t h e PFRU i s p e r h a p s t h e more w i d e l y a c c e p t e d p robe b e c a u s e o f t h e s u p p o r t o f h e a t e x c h a n g e r m a n u f a c t u r e r s and u s e r s o f H T R I , t h e p r o b e ' s d e v e l o p e r s . W a t k i n s o n (111) s t a t e s t h a t i n most i n d u s t r i a l s h e l 1 - a n d - t u b e h e a t e x c h a n g e r s , t h e 74 f o u l i n g s t r e a m s a r e pumped t h r o u g h t h e t u b e s i f p o s s i b l e , t o f a c i l i t a t e c l e a n i n g . T h u s , f o u l i n g d e p o s i t s w o u l d most l i k e l y a c c u m u l a t e on t h e i n s i d e s u r f a c e o f a t u b e r a t h e r t h a n o u t s i d e . Howeve r , a c c o r d i n g t o Knudsen ( 4 7 ) , t h e f o u l i n g r a t e s and f o u l i n g f a c t o r s o b t a i n e d on t h e i n n e r c o r e o f an a n n u l a r d u c t can be e x t r a p o l a t e d t o c o n d i t i o n s o f f l o w i n a c i r c u l a r t u b e . Knudsen (47) comments on t h e a p p a r e n t d i f f i c u l t y o f a c c u r a t e l y e x t r a p o l a t i n g f o u l i n g r e s u l t s f r o m w i r e c o i l g e o m e t r i e s t o a c t u a l c o n f i g u r a t i o n s used i n i n d u s t r y . He f u r t h e r s t a t e s t h a t t h e a p p a r a t u s wou ld a p p e a r t o be u n s u i t a b l e f o r o b t a i n i n g d a t a on w h i c h t o base r e l i a b l e m e c h a n i s t i c m o d e l s . Howeve r , B raun and H a u s l e r (22) c l a i m t h a t t h e p robe g i v e s r e p r o d u c i b l e r e s u l t s w h i c h a r e r e p r e s e n t a t i v e o f p e t r o l e u m r e f i n e r y f i e l d c o n d i t i o n s . S i n c e i t i s a c k n o w l e d g e d t h a t t he PFRU f o u l i n g r e s u l t s can be e x t r a p o l a t e d t o a c t u a l h e a t e x c h a n g e r c o n f i g u r a t i o n s , t h e n a f a v o r a b l e c o m p a r i s o n s h o u l d c o n f i r m t h e c l a i m o f B raun and H a u s l e r ( 2 2 ) . B e s i d e s f l o w c o n d i t i o n s and g e o m e t r y , t h e two methods a l s o d i f f e r i n method o f h e a t i n g - UOP M o n i r e x uses d i r e c t e l e c t r i c a l r e s i s t a n c e h e a t i n g w h i l e t h e PFRU uses i n d i r e c t e l e c t r i c a l h e a t i n g ; method o f m e a s u r i n g s u r f a c e t e m p e r a t u r e - UOP M o n i r e x uses t h e change i n w i r e r e s i s t a n c e w h i l e t h e PFRU uses imbedded t h e r m o c o u p l e s ; and t y p e o f f o u l i n g f a c t o r d e t e r m i n e d - t he UOP f o u l i n g f a c t o r i s an a v e r a g e v a l u e o v e r t h e l e n g t h o f t he w i r e w h i l e t h e PFRU f o u l i n g f a c t o r i s a l o c a l f o u l i n g f a c t o r . 75 The two t e c h n i q u e s s h a r e s e v e r a l f e a t u r e s such a s : (a) b o t h t e c h n i q u e s can m o n i t o r d e p o s i t v i s u a l l y ( d u r i n g a r u n , p o s s i b l y ) , t h e r m a l l y and by w e i g h t / t h i c k n e s s m e a s u r e m e n t s ; (b) b o t h t e c h n i q u e s can d e t e r m i n e h e a t f l u x e a s i l y ; ( c ) b o t h t e c h n i q u e s can d e t e r m i n e w a l l t e m p e r a t u r e ; (d) b o t h t e c h n i q u e s can be e a s i l y c o n t r o l l e d ; (e ) b o t h t e c h n i q u e s can o p e r a t e s t a b l y d u r i n g a f o u l i n g t e s t ; ( f ) bo th t e c h n i q u e s can r e t a i n c a l i b r a t i o n . The UOP M o n i r e x as a v a l i d and r e l i a b l e f o u l i n g measurement t e c h n i q u e i s f u r t h e r hampered .by c o n s i d e r a t i o n s o f c r i t i c a l r a d i u s and t h e o p p o s i n g e f f e c t s o f d e p o s i t i o n on s u r f a c e a r e a and f l u i d / s u r f a c 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 u r t h e r m o r e , t h e UOP M o n i r e x must be m o d i f i e d by i n c r e a s i n g t h e e n t r a n c e l e n g t h i n o r d e r t o e s t a b l i s h w e l l - d e v e l o p e d t e m p e r a t u r e and v e l o c i t y p r o f i l e s . The method o f c o m p a r i s o n i s t o c o n n e c t t h e two f o u l i n g p r o b e s i n p a r a l l e l , i n a r e c i r c u l a t i n g , c l o s e d l o o p . The two f o u l i n g p r o b e s a r e t h e n e x p o s e d t o t h e same f l u i d c o m p o s i t i o n and b u l k t e m p e r a t u r e . C o n d i t i o n s can be c h o s e n so t h a t t h e two p r o b e s w i l l have s i m i l a r s u r f a c e t e m p e r a t u r e s ( c l e a n , i n i t i a l ) , h e a t f l u x e s , and t h u s s i m i l a r i n i t i a l h e a t t r a n s f e r c o e f f i c i e n t s under s u c h c o n d i t i o n s . The f l o w r a t e s w i l l r e m a i n v a s t l y d i f f e r e n t (PFRU - t u r b u l e n t , UOP M o n i r e x - l a m i n a r ) s i n c e t h e p r o b e s were d e s i g n e d t o p e r f o r m most e f f i c i e n t l y w i t h i n t h e i r r e s p e c t i v e f l o w r e g i m e s . Howeve r , t h e t i m e w i t h w h i c h an e l e m e n t o f f l u i d i s i n c o n t a c t w i t h t h e h e a t e d s e c t i o n o f a p robe w i l l be o f t h e same o r d e r o f m a g n i t u d e . 76 The c o m p a r i s o n w i l l be based on such f a c t o r s as r a t e s o f f o u l i n g , a s y m p t o t i c f o u l i n g r e s i s t a n c e s , d e p o s i t w e i g h t p e r u n i t s u r f a c e a r e a , a p p e a r a n c e o f d e p o s i t , e l e m e n t a l a n a l y s i s o f d e p o s i t , i n d u c t i o n t i m e , and s e n s i t i v i t y t o changes i n c o n d i t i o n s . 77 4 . SELECTION OF WORKING FLUID 4 . 1 . B a c k g r o u n d The f i r s t f l u i d c o n s i d e r e d f o r use i n t h e e x p e r i m e n t s as a s o u r c e o f f o u l a n t was a heavy a t m o s p h e r i c gas o i l ( 3 3 - 3 4 ° API g r a v i t y ) p r o -d u c e d by a l o c a l r e f i n e r y . However , t h e HAGO was r e j e c t e d as a c a n d i d a t e f o r t e s t f l u i d i n f a v o u r o f a c h e m i c a l l y p u r e and s i m p l e s y s t e m . I t was s u g g e s t e d i n a p r i v a t e c o m m u n i c a t i o n f r om J . Tabo rek o f Heat T r a n s f e r R e s e a r c h I n c . t h a t a s o l u t i o n o f 10 wt.% 1 , 3 - b u t a d i e n e i n n - p e n t a n e o r some o t h e r l i g h t h y d r o c a r b o n , be u s e d . T h e r e a r e a t l e a s t f i v e a d v a n t a g e s o f u s i n g a c h e m i c a l l y pu re s o l u t i o n as t h e t e s t f l u i d i n s t e a d o f an a c t u a l p r o c e s s f l u i d : (1) I m p u r i t i e s such as s u l p h u r compound, n i t r o g e n compounds , u n s a t u r a t e d h y d r o c a r b o n s a n d / o r t r a c e m e t a l s , w h i c h i n c r e a s e t h e number o f f o u l i n g v a r i a b l e s t h a t a r e no t s t r i c t l y c o n t r o l l e d , a r e m i n i m i z e d . (2 ) The t e s t f l u i d can be r e p r o d u c e d i n te rms o f components and t h e i r r e s p e c t i v e c o n c e n t r a t i o n s . (3) F o u l i n g due t o a s i m p l i f i e d s e t o f c h e m i c a l r e a c t i o n s i . e . p o l y m e r i z a t i o n , o c c u r r i n g i n t h e b u l k f l u i d and a t t h e f l u i d / s u r f a c e i n t e r f a c e , can be s t u d i e d . (4) A d e p o s i t o f known c o m p o s i t i o n and h e n c e , a l s o o f known d e n s i t y and t h e r m a l c o n d u c t i v i t y , s h o u l d be p r o d u c e d . (5) T r a n s p o r t p r o p e r t i e s f o r t h e s y s t e m can be f o u n d i n t h e l i t e r a t u r e o r can be a c c u r a t e l y e s t i m a t e d , w h i c h s i m p l i f i e s and i m p r o v e s equ ipmen t d e s i g n . 78 The v a p o u r p r e s s u r e s f o r t e m p e r a t u r e s f r om 2 5 5 . 3 8 K t o 4 2 2 . 0 5 ° K were c a l c u l a t e d f o r 10 wt % b u t a d i e n e i n n - p e n t a n e , n - h e x a n e , n - h e p t a n e , n - o c t a n e , n - n o n a n e , and n - d e c a n e . A n t o i n e e q u a t i o n c o n s t a n t s were t a k e n f r om R e i d e t a l . (112) f o r each component t o d e t e r m i n e d t h e pu re component v a p o u r p r e s s u r e , and R a o u l t ' s Law was used t o c a l c u l a t e t h e s o l u t i o n v a p o u r p r e s s u r e . : K = • •RA°\ + P B ° X B ( 4 " 1 ) T a b o r e k had s t a t e d t h a t t h e b u t a d i e n e wou ld p o l y m e r i z e a t 2 2 0 - 2 3 0 ° F . Which s o l u t i o n gave t h e minimum t o t a l v a p o u r p r e s s u r e a t 230°F and t h u s r e q u i r e d t h e minimum p r e s s u r i z a t i o n t o p r e v e n t b o i l i n g a t t h e s u r f a c e o f t h e p r o b e s ? B o i l i n g was no t d e s i r e d s i n c e i t wou ld i n t r o d u c e a n o t h e r u n c o n t r o l l e d f o u l i n g v a r i a b l e ; s i n c e i t wou ld p r e v e n t c o m p a r i s o n s w i t h e a r l i e r s t u d i e s w h i c h were m o s t l y done under n o n -b o i l i n g c o n d i t i o n s ; and s i n c e i t wou ld p r e v e n t u s i n g w e l l - k n o w n f o r c e d c o n v e c t i o n h e a t t r a n s f e r c o r r e l a t i o n s and any o t h e r n o n - b o i l i n g f l u i d f l o w and h e a t t r a n s f e r e q u a t i o n s . I t was f o u n d t h a t a t 110°C , t h e o c t a n e / b u t a d i e n e s o l u t i o n g i v e s t h e l o w e s t t o t a l v a p o u r p r e s s u r e . Howeve r , h e p t a n e , nonane and decane s o l u t i o n s were a l l w i t h i n 5 p s i a o f 5 3 . 5 2 p s i a , t h e o c t a n e / b u t a d i e n e s o l u t i o n v a p o u r p r e s s u r e . S i n c e Tabo rek s t r e s s e d " l i g h t " h y d r o c a r b o n , i t was. d e c i d e d t o use t h e l o w e s t m o l e c u l a r w e i g h t h y d r o c a r b o n t h a t s t i l l g i v e s a r e a s o n a b l y l ow s o l u t i o n v a p o u r p r e s s u r e , w h i c h was n - h e p t a n e . T h u s , i t was d e c i d e d t o use a s o l u t i o n o f 10 wt % 1 , 3 - b u t a d i e n e i n n - h e p t a n e as t h e w o r k i n g f l u i d . 79 U n f o r t u n a t e l y , a l l a t t e m p t s t o p o l y m e r i z e 1 , 3 - b u t a d i e n e t o fo rm p o l y b u t a d i e n e by p u r e l y t h e r m a l s e l f - i n i t i a t i o n , f a i l e d m i s e r a b l y . S a t u r a t i n g t h e s o l u t i o n w i t h oxygen o r a d d i n g a r a d i c a l - f o r m i n g i n i t i a t o r s u c h as b e n z o y l p e r o x i d e , wou ld p r o b a b l y c a u s e t h e b u t a d i e n e t o p o l y m e r i z e , bu t t h i s w o u l d add a n o t h e r f o u l i n g v a r i a b l e w h i c h was u n d e s i r a b l e . A l s o , c h e m i c a l b y - p r o d u c t s f r om a u t o x i d a t i o n r e a c t i o n s a n d / o r f r o m t h e i n i t i a t o r r e a c t i n g w i t h b u t a d i e n e and n - h e p t a n e wou ld a l s o c o m p l i c a t e m a t t e r s . m e t h a c r y l a t e undergo p u r e l y t h e r m a l s e l f - i n i t i a t i o n , unde r d e o x y g e n a t e d c o n d i t i o n s . S i n c e s t y r e n e ' s r a t e o f p o l y m e r i z a t i o n i s much h i g h e r t h a n t h a t o f me thy l m e t h a c r y l a t e , i t was d e c i d e d t o use a s o l u t i o n o f s t y r e n e i n n - h e p t a n e ( p r o b a b l y 10 wt %) as t h e w o r k i n g f l u i d . a s u r f a c e t e m p e r a t u r e g r e a t e r t h a n 422 K t o i n i t i a t e f o u l i n g . The c o n c e n t r a t i o n s i n t h e t e s t s r a n g e d f r o m 3 . 0 8 t o 1 1 . 7 9 w t . %. U s i n g l i t e r a t u r e v a l u e s f o r pu re component v a l u e s ( P e r r y and C h i l t o n (83) f o r n - h e p t a n e and Boundy and B o y e r (113) f o r s t y r e n e ) and R a o u l t ' s Law f o r t h e s o l u t i o n v a p o u r p r e s s u r e , t h e f o l l o w i n g was d e t e r m i n e d : T a b l e 4 - 1 . Vapour P r e s s u r e o f S t y r e n e / n - H e p t a n e S o l u t i o n T e m p e r a t u r e Vapou r P r e s s u r e ( 3 . 0 8 wt %) V a p o u r P r e s s u r e ( 1 1 . 7 9 wt %) As s t a t e d i n t h e l i t e r a t u r e r e v i e w , o n l y s t y r e n e and me thy l The s t y r e n e / n - h e p t a n e s o l u t i o n p r o d u c e d f o u l i n g , bu t r e q u i r e d ( p s i g ) ( p s i g ) 250 1 2 . 0 1 0 . 4 300 3 6 . 9 3 3 . 8 350 7 5 . 9 7 0 . 8 80 T h u s , t h e s y s t e m t h e o r e t i c a l l y s h o u l d be p r e s s u r i z e d t o 80 p s i g t o p r e v e n t b o i l i n g . 4 . 2 P r o p e r t i e s o f S t y r e n e and n -Hep tane T a b l e 4 - 2 g i v e s some p r o p e r t i e s o f s t y r e n e monomer as a f u n c t i o n o f t e m p e r a t u r e ( f r o m Boundy and B o y e r ( 1 1 4 ) ) . U s i n g methods d e s c r i b e d i n t he " E x p e r i m e n t a l P r o c e d u r e " , t h e k i n e m a t i c v i s c o s i t y and d e n s i t y o f s t y r e n e / h e p t a n e s o l u t i o n s were d e t e r -mined as a f u n c t i o n o f t e m p e r a t u r e and s t y r e n e c o n c e n t r a t i o n . T a b l e 4 - 3 . K i n e m a t i c V i s c o s i t y and D e n s i t y o f S t y r e n e / n - H e p t a n e S o l u t i o n s as a F u n c t i o n o f T e m p e r a t u r e ( i n - ° F ) and C o n c e n t r a t i o n ( i n wt %)  C o n c e n t r a t i o n (wt %) K i n e m a t i c V i s c o s i t y ( c e n t i s t o k e s ) D e n s i t y ( g / m i ) 2 4 . 9 8 0 . ,5763-•5 . 4 5 5 x l 0 " 3 ( T - 7 7 . 0 ) 0 ' .7783 0 . ,7581 - 5 . 1 3 0 8 x 1 0 ~ 4 T 2 0 . 0 0 0 . 5720-•5 . 2 8 3 x l 0 " 3 ( T - 7 7 . 0 ) 0 , .7832 0 . ,7649 - 4 . 9 7 6 1 x l O " 4 T 1 6 . 0 0 0 . 5708-•5 . 4 0 2 x l O " 3 ( T - 7 7 . 0 ) ° - .7778 0 . 7476. - 4 . 9 2 8 7 x l O " 4 T 1 2 . 0 0 0 . 5 7 0 1 - 5 . 3 5 3 x l 0 " 3 ( T - 7 7 . 0 ) ° - ,7796 0 . 7443-- 4 . 9 3 1 2 x l O " 4 T 1 0 . 0 0 0 . 5690 - 5 . 3 2 7 x l 0 " 3 ( T - 7 7 . 0 ) 0 ' 7792 0 . 7457-- 5 , 3 7 3 0 x l O " 4 T 8 . 0 0 0 . 5 7 0 1 - 5 . 5 0 6 x l 0 " 3 ( T - 7 7 . 0 ) ° - 7735 0 . 7352-- 4 . 9 6 6 7 x 1 0 ~ 4 T 4 . 0 0 0 . 5 7 0 1 - 5, . 3 2 7 x l 0 " 3 ( T - 7 7 . 0 ) ° - 7800 0 . 7303-- 5 . 2 3 6 4 x 1 0 " 4 T 0 . 0 0 4 . 7 0 0 - 3 . 2 4 5 9 T 0 - 0 5 5 5 o; 7170-- 4 . 8 7 7 x 1 0 " 4 T Based on l i t e r a t u r e v a l u e s f r om P e r r y and C h i l t o n ( 8 3 ) , t h e e q u a t i o n f o r t h e h e a t c a p a c i t y o f n - h e p t a n e i s : C p = 0 . 4 5 1 9 + 7 . 8 6 2 x l O " 4 T B T U / ( l b ) ( ° F ) ( 4 - 2 ) Denaity (f/mI) TC Liquid Vapor (C«lo.) 0.0 0 .0238 0.00000819 10.0 .9150 .0000150 20.0 .9063 .0000283 25.0 .9019 .0000374 30.0 .8975 .0000489 40.0 .8887 .0000812 50.0 .8800 .000129 60.0 .8712 .000200 70.0 ( .8624) .000300 80.0 ( .8535) .000438 90.0 ( .8446) .000622 100.0 ( .8356) .000871 110.0 ( .8265) .00119 120.0 ( .8174) .00160 130.0 ( .8081) .00211 140.0 ( .7988) .00276 145 2 ( .7939) .00311 150.0 ( .7893) .00346 Values in parentheses are exti Specific Vol. in ml/l Vwo.ily Litiuid Vapor {C+\c.) (cp) 1.0824 122,0110 0.976 1.0928 63,7(K> -877 1.1033 35,200 .781 1.1087 26,700 .730 1.1142 20,400 .694 1.1252 12,300 .621 1.1363 7,750 .552 1.1478 5,0110 .49(1 (1.1595) 3,330 (.438) (1.1716) 2,280 (.392) (1.1839) 1,610 (.348) (1.1907) 1,150 (.312) (1.2099) 840 (.278) (1.2234) 625 (.24R) (1.2374) 474 (.221) (1.2518) 362 (.196) (1.2590) 321 (.181) (1.2669) 289 (.174) polated. Burfkce Vepor lleatnf Tennion PreMure VaporiulHin lynfln/cm) (mm Hf) (cal/mule) 34.5 1.13 11,210 33.4 2.34 11,010 32 3 4.53 10,790 31.7 6.17 10,690 31.2 8.31 10,590 30.0 14.51 10,410 28 0 24.28 10,230 27.8 39.07 10,070 (26.7) 60.78 9,920 (25.6) 91.74 9,770 (21.6) 134.7 9,630 (23.5) 192.9 0,490 (22.5) 270.2 9,350 (21.5) 370.7 9,220 (20.4) 500.4 9,080 (19.4) 660.9 8,940 (18.9) 700.0 8,870 (18.4) 861.5 8,800 T a b l e 4 - 2 . P r o p e r t i e s o f S t y r e n e Monomer as a  F u n c t i on o f T e m p e r a t u r e 1 ( t a k e n f r om Boundy and B o y e r ( 1 1 3 ) ) 82 Based on l i t e r a t u r e v a l u e s f r om Yaws (114) and Boundy and B o y e r ( 1 1 3 ) , t h e e q u a t i o n f o r t h e h e a t c a p a c i t y o f s t y r e n e i s : C p = 0 . 3 8 6 7 + 4 . 6 1 1 x l O " 4 T B T U / ( l b ) ( ° F ) ( 4 - 3 ) Based on l i t e r a t u r e v a l u e s f r om P e r r y and C h i l t o n ( 8 3 ) , t h e e q u a t i o n f o r t h e t h e r m a l c o n d u c t i v i t y o f n - h e p t a n e i s : k = 0 . 0 8 4 2 - 3 . 7 0 0 x l O " 5 T B T U / ( h r ) ( f t ) ( ° F ) ( 4 - 4 ) Based on l i t e r a t u r e v a l u e s f r om Yaws ( 1 1 4 ) , t h e e q u a t i o n f o r t h e t h e r m a l c o n d u c t i v i t y o f s t y r e n e i s : k. = 0 . 1 0 6 5 - 1 . 0 5 0 x l 0 " 5 T B T U / ( h r ) ( f t ) ( ° F ) ( 4 - 5 ) From R e i d e t a l . ( 1 1 2 ) , t h e e q u a t i o n s f o r t h e p r o p e r t i e s o f a m i x t u r e o f two p u r e components a r e : cP m= x S C P S + X H C P H ( 4 - 6 ) and k = (x > 3 / 2 ( k - - k ') + k" ( 4 - 7 ) Km l x S j [KS ••'••V H where x i s mo le f r a c t i o n . T a b l e 4 - 4 t a k e n f r o m Boundy and B o y e r (113) l i s t s a l l t h e e s s e n t i a l p h y s i c a l p r o p e r t i e s o f s t y r e n e . T a b l e 4 - 5 i s a l i s t o f p r o p e r t i e s o f n - h e p t a n e t a k e n f r om B o l z and Tuve ( 1 1 5 ) . Formula. . . CJIt Molecular wt 104.14 Density at 25°C (g/ml) 0.9019 Pounds l>cr gal nt 25°C 7.5 Iti'frnclivo index ill 2.r>°('. 1.5139 Viscosity ill 25"C (rctitipnise) 0.730 Surface tension nt 25"C (dynes/cm) 31.7 Cocflicient of expansion lit 25"C (rr/°C) 0.0009719 Hoiling point (°C) 145.2 Heal of vaporization nt 25°C (cal/g) 102.65 Freezing point in iiir at 1 aim (°C) —30.628 Heat of fusion (rul/g) 25.4 Specific licit :il 25"C (cal/g/°C) 0.416 Heal of combustion at 25°C (Kra!/g) 10.086 Critical temperature (°C) .". 373. Critical pressure in aim 40.0 Critical density (is/ml) 0.30 Flash print. ("(') 31 Fire point (°C) 34 Explosive limits, vol. % in air 1.1 to 6.1 Heat of polymerization (cnl/g) 160.2 Volume id i r inknge on |Milymcrizi i l ion (%) 17 T a b l e 4 - 4 . P h y s i c a l P r o p e r t i e s o f Pu re S t y r e n e ( t a k e n f rom Boundy and B o y e r ( 1 1 3 ) ) 84 T a b l e 4 - 5 . P h y s i c a l P r o p e r t i e s o f n - H e p t a n e ( 1 . 0 atm p r e s s u r e , 25 C) F o r m u l a Cy H^g M o l e c u l a r We igh t 1 0 0 . 2 0 8 S p e c i f i c G r a v i t y 0 .681 V i s c o s i t y , cp 0 .376 Sound V e l o c i t y , m / s e c 1138 S u r f a c e T e n s i o n , d y n e s / c m 1 9 . 9 D i e l e c t r i c C o n s t a n t 1 .92 R e f r a c t i v e Index 1 .38 S p e c i f i c Heat 0 . 5 3 6 Thermal C o n d u c t i v i t y , B T U / ( h r ) ( f t ) ( ° F ) 0 . 0 7 4 F r e e z i n g P o i n t , °F - 1 3 1 . 1 L a t e n t Heat o f F u s i o n , B T U / l b 6 0 . 2 B o i l i n g P o i n t , ° F 209.1 L a t e n t Heat o f E v a p o r a t i o n , B T U / l b 137 T a b l e 4 - 6 i s a l i s t o f p r o p e r t i e s and e q u a t i o n c o n s t a n t s f o r s t y r e n e and n - h e p t a n e , t a k e n f r om R e i d e t a l . ( 1 1 2 ) . 85 T a b l e 4 - 6 . P r o p e r t i e s and E q u a t i o n C o n s t a n t s f o r n -Hep tane and S t y r e n e S t y r e n e n - H e p t a n e C r i t i c a l t e m p e r a t u r e , °K 647 5 4 0 . 2 C r i t i c a l p r e s s u r e , atm 3 9 . 4 2 7 . 0 C r i t i c a l v o l u m e , cm / g - m o l e - 432 C r i t i c a l c o m p r e s s i b i l i t y - 0 . 2 6 3 P i t z e r ' s a c e n t r i c f a c t o r 0 . 2 5 7 0.351 D i p o l e moment 0.1 0 . 0 A n t o i n e E q u a t i o n : ANTA 1 6 . 0 1 9 3 15 .8737 ANTB 3 3 2 8 . 5 7 2 9 1 1 . 3 2 ANTC - 6 3 . 7 2 - 5 6 . 5 1 A method t o d e t e r m i n e t h e s t y r e n e c o n c e n t r a t i o n d u r i n g and a f t e r a r un i s based on t h e e x p e r i m e n t a l l y d e r i v e d e q u a t i o n o f s o l u t i o n d e n s i t y as a f u n c t i o n o f s t y r e n e c o n c e n t r a t i o n a t a r e f e r e n c e t e m p e r a t u r e o f 25°C : p = 0 . 6 8 2 2 + 1 . 7 9 4 x l O " 3 C ( 4 - 8 ) where p i s i n g /ml and C i s i n wt % s t y r e n e . 4 . 3 . S o l v e n t E f f e c t s From B r a n d r u p and Immergut (116) and Boundy and B o y e r ( 1 1 3 ) , i t has been d i s c o v e r e d t h a t n - h e p t a n e i s a good s o l v e n t f o r s t y r e n e bu t a n o n - s o l v e n t f o r p o l y s t y r e n e . T h u s , any p o l y s t y r e n e fo rmed on t h e p r o b e s c a n n o t be d i s s o l v e d by t h e n - h e p t a n e bu t c o u l d p o s s i b l y be d i s s o l v e d by t h e s o l u t i o n ' s s t y r e n e component w h i c h i s a s o l v e n t f o r 86 p o l y s t y r e n e . The same a p p l i e s f o r any b u l k p o l y m e r i z e d p o l y s t y r e n e . I f " p a r t i c l e s " o f p o l y s t y r e n e e x i s t i n t h e b u l k f l u i d , t h e n t h e f o u l i n g mechan ism may be a c o m b i n a t i o n o f c h e m i c a l r e a c t i o n and p a r t i c u l a t e f o u l i n g , w h i c h t h e n can be d e s c r i b e d by t h e f o u l i n g model o f W a t k i n s o n and E p s t e i n ( 1 8 ) . F o r c l e a n i n g p u r p o s e s , t o l u e n e can be used s i n c e i t i s an e x c e l l e n t s o l v e n t f o r s t y r e n e , p o l y s t y r e n e and n - h e p t a n e . 4 . 4 . P r o p e r t i e s o f P o l y s t y r e n e T a b l e 4 - 7 , t a k e n f r om Boundy and B o y e r ( 1 1 3 ) , g i v e s t h e g e n e r a l p h y s i c a l p r o p e r t i e s o f p o l y s t y r e n e . T a b l e 4 - 8 , t a k e n f r o m B r a n d r u p and Immergut ( 1 1 6 ) , g i v e s more f u n d a m e n t a l p h y s i c a l p r o p e r t i e s o f p o l y s t y r e n e . U s i n g v a l u e s f r om B r a n d r u p and Immergut (116) and Boundy and B o y e r ( 1 1 3 ) , t h e f o l l o w i n g e q u a t i o n s were d e t e r m i n e d : p o l y s t y r e n e = 7 . 3 9 1 x l O - 5 T + 5 . 8 3 0 x l 0 - 2 B T U / ( h r ) ( f t ) ( ° F ) ( 4 - 9 ) " p o l y s t y r e n e ^ f o r T > G l a s s t e m p e r a t u r e ) = 1 .036 i 6 . 0 5 x 1 0 " % - 9 0 ) g / m l ( 4 - 1 0 ) where T i s i n °C 4 . 5 . S t y r e n e P o l y m e r i z a t i o n T a b l e 4 - 9 , t a k e n f r om Boundy and B o y e r ( 1 1 3 ) , shows how the i n i t i a l r a t e o f p o l y m e r i z a t i o n , v i s c o s i t y , and w e i g h t a v e r a g e m o l e c u l a r w e i g h t v a r y w i t h p o l y m e r i z a t i o n t e m p e r a t u r e . I t i s c l e a r l y e v i d e n t t h a t as p o l y m e r i z a t i o n t e m p e r a t u r e i n c r e a s e s , t h e i n i t i a l r a t e o f 87 D392-38 D569-44T D792-44T D672-44T D672-44T 1)512-12 DC96-42T C177-45 D648-4ST D63S-44 D570-42 Property A6TM Tut BtetW Fabrication Bulk factor Flow or mobility range (*F) Injection molding temp. (*F) " " pressure (psi) " " mold slirink. (in/in) Compres. molding temp. (*K) " " pressure (psi) " " mold slirink. (in/in) Extruding temp. (°F) Ifiictllaneou* Tat Value* Specific gravity Haze (crystal) (%) Luminous transinitlnnco (Dcjicnilnnt ujM>n color) (%) Refractive index (nj) Thermal coefficient of exper. linear (max/°C) Thermal eonductivity (eal/sq cm/sec/'C/cm) Specific beat (Cal/g) Ifeat distortion, 204 psi (*F) Flammahility (in/min) Water absorption 24 hrs (%) Durability Effect of light Heat resistance (max recommended for continuous serv-ice) (°F) Electrical Value* Dielectric atr., short time (1* v/mil) " " stcp-by-step (I* v/mil) Volume resistivity (Ohm-cm) Dielectric constant, 60 eps " " 1000 r|w " " 10« cps Dissipation factor, 60 cps " 10C cps " " 10* cps Loss factor, 60 eps " " 1000 eps " •« 10* eps Arc Resistance, arc Mechanical Tetl Value* Impnct sir., Isod notched 77°K (ft. Ibs./in.) Compres. atr., stress at yield (up|>cr), (psi) strain " " " (%) Deformation under lond ntS0°C 4000 psi (rigid mnterials) (%) Flexure, stress at fracture (|*i) " strain at fracture (in) (%) Tension, stress al fracture (|mi) " strain at fracture (%) Modulus of elasticity (Apparent) flexure (psi) compression (psi) tension (psi) 6hcar strength (psi) Rockwell Hardness D149-44T D149-44T D257-46 D150-46T D150-46T D150-46T D150-46T D150-46T D150-46T D150-46T D150-46T D150-46T D495-42 D256-45T D605-44T D695-44T DC2I-45T 1)050-42T D650-42T D038-46T D038-40T D650-42T D695-44T DC38H6T Vain* 1.9-2.3 240-280 325-550 10,000-30,000 0.003-0.006 265-350 1,000-10,000 0.002-0.005 375-550 1.052-1.065 10 0-93 1.69-1.60 6-8 X 10-' .2.4-3.3 X 10"* 0.32 180-190 0.6-1.0 0.03-0.04 Slight 150-1M 600-700 400-600 10"-10'» 2.45-2.65 2.45-2.65 2.45-2.65 10-30 X 10-' 10-30 10-40 25-70 25-70 25-70 io-» lO" 10-' io-» 10-' 70-135 0.25-0.40 11,500-18,000 4.5-5.5 1.0 8,000-19,000 0.10-0.20 6,000-8,600 1.0-3.6 4.0-6.0 X 10* 8.<W.6 X 10* 4.0-*.0 X W 6,000-8,000 M65-M90 T a b l e 4 - 7 . G e n e r a l P h y s i c a l P r o p e r t i e s o f P o l y s t y r e n e ( t a k e n f rom Boundy and B o y e r ( 1 1 3 ) ) Property Birefringence dispersion 6n(70 An(5461 A") Coefficient of expenslon l i ( l inear) (volume) Compressibility Compressive modulus [deg"1] tber ' 1 ] tdynes cm"2) Cryatallographlc Data Density, p eiDorphous crys ta l l ine dp/dt, [g cm"J] [g cm"3deg"1] Dielect r ic constant amorphous crys ta l l ine Dissipation factor amorphous crys ta l l ine Class transit ion temperature, T t-**g: 8 Heat of combustion Heat of fusion crys ta l l ine [keel/monomer unit] [kcal/monomer unit] Heat of polymerisation (keel/monomer unit] Heat of solution [kcal/monomer unit] Melting point , T B [deg] Value A + T T * T T XT + TS Remarks A - 0.8905 B - 1.869 x 10" 9 A 2 C - -6.685 x 10" 1 9 A4 -5 (6 to 8) x l O " ' «Tg (unorlented) (1.7 to 2.1) x 10" 4 <T„ (5.1 to 6.0) x 10 2.2 x 10" 5 3.0 x 1 0 1 0 see Unit Cel l -4 »T_ 1.04-1.065 1.111 1.12 -4 -2.65 x 10 -6.05 x 10" 2.49 to 2.55 2.61 15 x 10 3 x 10 80 90 (100) -1.034 * 10, -1.036 x l O 3 2.00 i 0.02 2.15 -16.1 -16.7 -0.86 240 (250) (Unorlented) 8 1000 c (flat to 10 c) T *>373-10 /M (fractions) to solid polymer to solid polymer Property Melt vlscoslty-moleculsr weight relationship log nj . 3.4 log M - k Remarks Type atactic lsotactlc Optical dispersion, n^-n c Polsson's ra t io Refractive lnder, n n dnD/dt (deg"1) M Range 217 281 1.92 x 10 > 38,000 100.000 --600,000 13.40 14.42 4861.3 4 (F) 6562.8 A (C) 5892.6 A (D) Resist ivi ty [ohm-cmj Solvents Specific heat, [cal g ] C P dC /dt [cal g" 1 deg"1] P Stress-optical coefficient [hrewstersj Tensile modulus [dynes cm" ] Thermal conductivity [cal sec'^cm" 1 deg"1] Unit c e l l [A) Velocity of sound [m sec**J 0.325 0.33 1.59-1.60 -1.42 x 10 see tables on "Solvents-Monsolvents" in this Handbook. 0.283 (0.272) 0.300 (0.333) 0.439 (0.435) 9.65 x 10 -4 0'C 50 *C 100'C 50'C 10 .1 9 .5 8 .3, 8.7 3 .2 x 1 0 " 3 .4 x 1 0 1 0 2, .51 x 10"' 2 .78 x 10"' 3 .06 x 10-' 21 .90 22, .08 21 .90 22 .08 6. .65 6. ,626 2. .1 x 10 3 monofilament extruded sheet compr, molding unorlented 0#C 50 °C 100 *C rhombohedrel T a b l e 4 - 8 . P h y s i c a l C o n s t a n t s o f P o l y s t y r e n e ( t aken f rom B r a n d r u p and Immergut ( 116 ) ) CO 89 (Uiicfttnlyicd Polymcriintion) Vapor Pressure of Polymerization Temp. C O Initial Rate of Polymerization O^/Hr) 10% Solution Viscosity in Toluene (cps) Wt. Averaje Mol. Wt. Styrene Monomer at Indicated Temp, mm Ha 60 .089 3000 2,250,000 40 70 .21 IS 1400 1,400,000 61 80 .462 650 880,000 92 90 1.02 360 610,000 134 100 2.15 200 420,000 192 110 4.25 120 310,000 270 120 8.5 75 230,000 380 130 16.2 48 175,000 490 140 28.4 30 130,000 650 160 — 14 83,000 1100 T a b l e 4 - 9 . P o l y m e r i z a t i o n Ra te and M o l e c u l a r ^ We igh t f o r S t y r e n e a t S e v e r a l T e m p e r a t u r e s  o f P o l y m e r i z a t i o n ( t a k e n f r om Boundy and B o y e r ( 1 1 3 ) ) 90 p o l y m e r i z a t i o n i n c r e a s e s , bu t t h e v i s c o s i t y and m o l e c u l a r w e i g h t d e c r e a s e . F i g u r e 4 - 1 , t a k e n f r om Boundy and B o y e r ( 1 1 3 ) , i s a s e r i e s o f t h r e e g r a p h s w h i c h g i v e t h e r m a l p o l y m e r i z a t i o n r a t e d a t a a t v a r i o u s t e m p e r a t u r e s and c o n v e r s i o n s . 5 The o v e r a l l r a t e o f p o l y m e r i z a t i o n i s ^ o r d e r i n s t y r e n e ( 1 1 7 ) . From E q . ( 2 - 8 7 ) , t h i s s u g g e s t s t h a t t h e i n i t i a t i o n i s t h i r d o r d e r , i . e . i n i t i a t i o n f o l l o w s a t e r m o l e c u l a r mechan i sm. S i n c e t e r m o l e c u l a r r e a c t i o n s i n s o l u t i o n a r e r a r e , i t was s u g g e s t e d by Geo rge (118 ) t h a t i n i t i a t i o n i s a t w o - s t e p p r o c e s s - t h e r e v e r s i b l e , i n e f f i c i e n t b i m o l e c u l a r f o r m a t i o n o f a d i r a d i c a l f o l l o w e d by a r a p i d t r a n s f e r r e a c t i o n w i t h a monomer. Mayo (119) p o s t u l a t e d t h a t t h e s e c o n d s t e p o f t h e t h e r m a l i n i t i a t i o n i n v o l v e d a r e a c t i o n between s t y r e n e and a c y c l i s i z e d fo rm o f t h e d i r a d i c a l p r o d u c e d i n t h e f i r s t s t e p : + C 6 H 5 C H C H B r i g h t o n e t a l . (117:) s t a t e t h a t r e g a r d l e s s o f t h e s t r u c t u r e HOURS « COMVtMIM F i g u r e 4 - 1 . Thermal P o l y m e r i z a t i o n Da ta f o r V a r i o u s T e m p e r a t u r e s and C o n v e r s i o n s ( t a k e n f rom Boundy and B o y e r ( 1 1 3 ) ) 92 o f t h e i n i t i a l r a d i c a l , once g e n e r a t e d i t w i l l r e a c t w i t h a s t y r e n e m o l e c u l e i n t h e f o r m a l i n i t i a t i o n s t e p : t he u s u a l scheme o f p r o p a g a t i o n and t e r m i n a t i o n . C a l c u l a t i o n s f rom a c t i v a t i o n e n e r g i e s f o r t h e i n d i v i d u a l s t e p s i n s t y r e n e p o l y m e r i z a t i o n -i n i t i a t i o n , g r o w t h , and t e r m i n a t i o n - p l a c e t h e a p p a r e n t o v e r a l l a c t i v a t i o n e n e r g y a t 2 3 . 6 K c a l / m o l e , w h i c h i s s u p p o r t e d by e x p e r i m e n t a l l y d e r i v e d v a l u e s ( 1 1 3 ) . 4 . 6 . T e r t i a r y B u t y l C a t e c h o l p o l y m e r i z a t i o n i n h i b i t o r and a n t i o x i d a n t f o r t h e s t o r a g e o f s t y r e n e ( 1 1 7 ) . The l e v e l o f TBC i n t h e t e s t s t y r e n e i s 100 ppm, a l t h o u g h t h e l e v e l can range between 10 and 100 ppm. C o u l t e r e t a l . (120) show t h a t i n h i b i t i o n w i t h TBC i s g r e a t e s t when u s i n g a i r , bu t u s i n g a i r w i t h no TBC i n h i b i t i o n c a u s e s s i g n i f i c a n t l y l a r g e r q u a n t i t i e s o f bo th p o l y m e r and a l d e h y d e t o f o r m . C o u l t e r e t a l . (120) s t a t e t h a t u n i n h i b i t e d p o l y m e r i z a t i o n o f s t y r e n e i n t h e p r e s e n c e o f oxygen p r o d u c e s a c o p o l y m e r o f s t y r e n e and o x y g e n , s t y r e n e p o l y p e r o x i d e : ( 4 - 1 2 ) A f t e r t h e i n i t i a t i o n , t h e p o l y m e r i z a t i o n o f s t y r e n e f o l l o w s P - t e r t i a r y - b u t y l c a t e c h o l (TBC) i s used e x t e n s i v e l y as a 93 w h i c h s u b s e q u e n t l y decomposes t o g i v e r a d i c a l s . The e f f e c t i v e n e s s o f TBC as an i n h i b i t o r i s a t t r i b u t e d t o i t s r e a c t i o n w i t h p e r o x y r a t h e r t h a n w i t h a l k y l r a d i c a l s , w h i c h a l s o e x p l a i n s i t s dependence on oxygen ( 1 2 0 ) . C ( C H 3 ) C ( C H 3 ) 3 C ( C H 3 ) 3 C ( C H 3 ) 3 + + R00H R00H ( 4 - 1 4 ) Too much oxygen wou ld l e a d t o e x c e s s i v e o x i d a t i o n . Too l i t t l e oxygen wou ld d i m i n i s h t h e e f f e c t i v e n e s s o f TBC as an i n h i b i t o r . C o u l t e r e t a l . (120) s u g g e s t t h a t a mole r a t i o o f oxygen t o TBC o f 10:1 wou ld be a p p r o p r i a t e . A p r o b l e m w i t h TBC i n h i b i t i o n i s t h a t t h e TBC c o n c e n -t r a t i o n i s c o n t i n u a l l y b e i n g d i m i n i s h e d as i t i s c o n v e r t e d t o q u i n o n e f rom i t s r e a c t i o n w i t h p e r o x y r a d i c a l s . The minimum TBC c o n c e n t r a t i o n n e c e s s a r y f o r i n h i b i t i o n p u r p o s e s i s 6 t o 8 ppm. TBC can be removed f r om t h e s t y r e n e t o g i v e u n i n h i b i t e d s t y r e n e by w a s h i n g w i t h sod ium h y d r o x i d e s o l u t i o n f o l l o w e d by d r y i n g o v e r c a l c i u m c h l o r i d e , by t r e a t i n g w i t h w h i t e " D r i e r i t e " , o r by vacuum d i s t i l l a t i o n ( b o i l i n g p o i n t o f TBC a t 5 mm Hg i s 1 4 9 ° C ) . However , C o u l t e r e t a l . (120) s t a t e t h a t normal p o l y m e r i z a t i o n o f t h e monomer does no t r e q u i r e t h e remova l o f t h e i n h i b i t o r . T h i s can be e x p l a i n e d f rom Boundy and B o y e r ( 1 1 3 ) , who s t a t e t h a t . i n h i b i t o r s a r e s u b s t a n c e s w h i c h e x t e n d o r p r o t r a c t t h e i n d u c t i o n p e r i o d p r i o r t o 94 p o l y m e r i z a t i o n , a p p a r e n t l y by d e s t r o y i n g t he a c t i v e c e n t e r s fo rmed d u r i n g i n i t i a t i o n . T h u s , once s t y r e n e i s e x p o s e d t o c o n d i t i o n s beyond norma l s t o r a g e c o n d i t i o n s , such as h i g h t e m p e r a t u r e s o r r a d i c a l c a t a l y s t s / i n i t i a t o r s , o r when t h e TBC has been c o m p l e t e l y c o n s u m e d , t h e n t h e p o l y m e r i z a t i o n w i l l p r o p a g a t e w i t h no e f f e c t f r om t h e TBC. F i g u r e 4 - 2 , t a k e n f r o m Boundy and B o y e r , i l l u s t r a t e s t h i s c o n c e p t . 4 . 7 R o l e o f Oxygen Oxygen has t h e d u a l r o l e o f bo th b e i n g a c a t a l y s t and an i n h i b i t o r i n v i n y l t y p e p o l y m e r i z a t i o n s s u c h as s t y r e n e p o l y m e r i z a t i o n . Oxygen r e a d i l y r e a c t s w i t h e t h y l e n i c compounds t o f o rm p e r o x i d e s , w h i c h w i l l i n i t i a t e p o l y m e r i z a t i o n . I f s u f f i c i e n t amounts o f oxygen a r e p r e s e n t , p e r o x i d e f o r m a t i o n t a k e s p r e c e d e n c e o v e r p o l y m e r i z a t i o n and f r e e r a d i c a l s w h i c h wou ld n o r m a l l y i n i t i a t e c h a i n s r e a c t w i t h oxygen i n s t e a d ( 1 2 0 ) , w h i c h i s a f o rm o f i n h i b i t i o n . O d i a n (104) s t a t e s t h a t m o l e c u l a r oxygen r e a c t s w i t h c h a i n r a d i c a l s t o f o r m a r e l a t i v e l y u n r e a c t i v e p e r o x y r a d i c a l . Howeve r , i n i t i a t i o n o c c u r s by t he t h e r m a l d e c o m p o s i t i o n o f t h i s p e r o x y r a d i c a l . S t a u d i n g e r (121) assumes t h a t t h e r e a c t i o n o f oxygen and monomer p r o d u c e s an a c t i v e p e r o x i d e w h i c h i n i t i a t e s p o l y m e r i z a t i o n and i s f o rmed a t h i g h t e m p e r -a t u r e s , and a " m o l o x i d e " w h i c h i s i n a c t i v e as a p o l y m e r i z a t i o n c a t a l y s t and i s f o u n d a t l ow t e m p e r a t u r e s . 95 TIMt u r e 4 - 2 . F u n c t i o n a l D e f i n i t i o n s o f t h e Terms I n d u c t i o n P e r i o d , I n h i b i t i o n and R e t a r d a t i o n ( t a k e n f r om Boundy and B o y e r ( 1 1 3 ) ) 96 5 . EXPERIMENTAL APPARATUS 5 . 1 . F low Loop F i g u r e 5-1 i s t h e f l o w d i a g r a m o f t h e a p p a r a t u s . The t e s t f l u i d i s pumped a r o u n d t h e c l o s e d l o o p by a S iemen and H i n s c h Type CAD Model 3102 s t a i n l e s s s t e e l t w o - s t a g e s e l f - p r i m i n g c e n t r i f u g a l pump d r i v e n by a 3 HP m o t o r . The f l u i d i s pumped f r om the s u p p l y t ank t h r o u g h a 1 i n . Neptune b a l l v a l u e i n t o t h e pump v i a . l i n . S c h e d u l e 40 s t a i n l e s s s t e e l 316 p i p e . A 1 i n . f l e x i b l e me ta l hose i s l o c a t e d i n t he 1 i n . p i p e l i n e , above t h e pump i n l e t , as a means o f a l i g n i n g t h e f l a n g e s w h i c h c o n n e c t t h e p i p e t o t h e pump. The f l a n g e s a r e s e a l e d by 1/8 i n . t h i c k neop rene r u b b e r g a s k e t s . The pump s h a f t s e a l i n g s y s t e m was m o d i f i e d by r e p l a c i n g t h e s h a f t p a c k i n g w i t h m e c h a n i c a l s e a l s ( J o h n C rane Type 9T s h a f t s e a l s ) , w h i c h e n t a i l e d b o r i n g ou t t he s t u f f i n g b o x ; t u r n i n g down t h e m e t r i c s h a f t so i t c o u l d accommodate a BES ( B r i t i s h E n g i n e e r i n g Sys tem) s e a l ; c o n s t r u c t i n g g l a n d p l a t e s w h i c h house the s t a t i o n a r y c e r a m i c i n s e r t ; and s l e e v i n g o f t h e new b e a r i n g s . The f l u i d e x i t s t h e pump v i a 1/2 i n . S c h e d u l e 40 s t a i n l e s s s t e e l 316 p i p e . I f t h e p r e s s u r e i n t h e s y s t e m e x c e e d s 150 p s i g , a b r o n z e 1/2 i n . F u l f l o s p r i n g - l o a d e d b y p a s s v a l v e i s opened w h i c h r e c i r c u l a t e s t he f l u i d t o t he 1 i n . p i p e o f t h e pump i n l e t . O t h e r w i s e , t h e f l u i d i s pumped t h r o u g h t h e 1/2 i n . p i p e , w i t h p a r t o f t h e f l o w r e c y c l e d t o t h e s u p p l y t ank and c o n t r o l l e d by a 1/2 i n . J e n k i n s 200 F i g . 1308 g l o b e v a l v e . T h e . r e m a i n d e r o f t h e f l u i d i s b r a n c h e d o u t be tween t h e two t e s t SEWER SUPPLY TANK DIFFERENTIAL PRESSURE MANOMETER PFRU SURFACE THERMOCOUPLES THERMOCOUPLE PRESSURE RELIEF VALVE IMMERSION HEATER SM STIRRER MOTOR MC MIXING CHAMBER HT HEATING TAPE (P) PRESSURE GAGE F i g u r e 5 - 1 . F low D iagram o f A p p a r a t u s 98 s e c t i o n s . t T h e . f l o w i s m e t e r e d u s i n g two c a l i b r a t e d s t a i n l e s s s t e e l s h a r p - e d g e d o r i f i c e p l a t e s {$•= 0 . 5 0 2 4 f o r t h e PFRU t e s t s e c t i o n and 8 = 0 . 0 7 4 8 f o r t h e HWP t e s t s e c t i o n ) s u p p o r t e d by o r i f i c e f l a n g e s w i t h c o r n e r t a p s ( s e e F i g u r e 5 - 2 ) . The p r e s s u r e d i f f e r e n t i a l s a c r o s s t h e o r i f i c e p l a t e s a r e measured by two Mer iam d i f f e r e n t i a l manometers (Model 10AA25WM, 36 i n . r a n g e , U - t y p e ) . Each manometer has two s h u t - o f f v a l v e s ( W h i t e y 1VS4) and two b l e e d v a l v e s ( G o u l d 1/4 i n . b r a s s n e e d l e v a l v e s ) . The f l o w r a t e i s c o n t r o l l e d m a n u a l l y by c o n t r o l v a l v e s l o c a t e d downst ream o f t h e o r i f i c e m e t e r s . I n i t i a l l y , t h e c o n t r o l v a l v e s were 1/2 i n . P o w e l l 200 CF8M A 3392 s t a i n l e s s s t e e l g l o b e v a l v e s w i t h T e f l o n p a c k i n g . Howeve r , f o r b e t t e r c o n t r o l , t h e y were r e p l a c e d w i t h a W h i t e y 8RF8 r e g u l a t i n g v a l v e f o r t h e PFRU s t r e a m and a W h i t e y 31RF4 r e g u l a t i n g v a l v e f o r t h e HWP s t r e a m . Beyond t h e c o n t r o l v a l v e s , t he 1/2 i n . p i p i n g i s r e p l a c e d w i t h 1/2 i n . 18 gage s t a i n l e s s s t e e l 304 t u b i n g . The l e n g t h o f p i p i n g / t u b i n g be tween t h e b r a n c h i n g - o u t p o i n t and t h e HWP t e s t s e c t i o n i s wrapped w i t h a 615 W E l e c t r o t h e r m a l ' h e a t i n g t a p e w h i c h i s c o n t r o l l e d by a S t a c o I n c . V a r i a b l e A u t o t r a n s f o r m e r Type 3PN 1 0 1 0 . I m m e d i a t e l y b e f o r e and a f t e r t h e PFRU t e s t s e c t i o n , two m i x i n g chambers a r e l o c a t e d . 1 They were made f r om 2 i n . S c h e d u l e 40 s t a i n l e s s s t e e l 316 p i p e . S t a i n l e s s s t e e l 316 p l a t e o f 0 . 3 2 cm t h i c k n e s s was w e l d e d t o t h e t o p and bo t tom o f t h e p i p e , p r o d u c i n g a t o t a l l e n g t h o f 5 . 0 0 cm. A 1/2 i n . n i p p l e was w e l d e d t o t h e c e n t e r o f t h e top p l a t e . A 1/2 i n . n i p p l e was a l s o w e l d e d t o the m i d d l e o f t he p i p e , be tween t h e two p l a t e s . F l u i d e n t e r s t h e chamber t h r o u g h t h i s n i p p l e . A 1/4 i n . n i p p l e was w e l d e d on t h e p i p e 9 0 ° f r om the 1/2 i n . n i p p l e and 1.50 cm f r o m the top p l a t e . 1/2 i n . t o 1/2 i n . ma le c o n n e c t o r s were fc- 0-875 #»0-7M •25 —H f*pT5i| ARGON WELO TO SCHED- 40 STAINLESS STEEL PIPE DLL 8 TAP 1/8* MPT A 0173 8 0-012 8 HOLES EQUALLY SPACED DRILL tt TAP I/4-20NC-2 MATERIAL-si" STAINLESS STEEL BAR STdCK DRILL c - 0 . 3 1 2 5 and : x = 0 . 0 4 6 5 •0291-001 MATERIAL—STAINLESS STEEL TWO REQUIRED WITH DIMENSIONS " C * ABOVE ORIFICE PLATES ORIFICE PLATE FLANGE F i g u r e 5 - 2 . O r i f i c e P l a t e s and F l a n g e s 100 s c r e w e d i n t o t h e 1/2 i n . n i p p l e s and were c o n n e c t e d t o 1/2 i n . t u b i n g . A 1/4 i n . t o 1/4 i n . ma le t h e r m o c o u p l e c o n n e c t o r was s c r e w e d i n t o t he 1/4 i n . n i p p l e . A 1/4 i n . ch rome l c o n s t a n t a n t h e r m o c o u p l e was c o m p r e s s i o n f i t t e d by t h i s c o n n e c t o r . . A b l e e d v a l v e ( W h i t e y 3VS4) i s c o n n e c t e d t o a ' 1 / 2 i n . t e e i n t h e t u b i n g c o n n e c t i n g t h e two t e s t s e c t i o n s (downs t ream o f t h e t e s t s e c t i o n s ) . The two f l o w s t r e a m s a r e r e c o n n e c t e d and r e t u r n e d t o t h e s u p p l y t ank v i a a W h i t e y 63F8 b a l l v a l v e . A s a m p l i n g l i n e w i t h a W h i t e y 1VF4 v a l v e was c o n n e c t e d t o t h e s u p p l y t ank v i a t h e r e t u r n l i n e . 5 . 2 . S u p p l y Tank The s u p p l y t ank i s c o n s t r u c t e d f r om 8 i n . S c h e d u l e 40 s t a i n l e s s s t e e l 316 p i p e . The t a n k has a d e p t h o f 2 9 . 2 0 cm and i n t e r n a l d i a m e t e r o f 2 0 . 3 cm. A 0 . 6 4 cm t h i c k p l a t e i s w e l d e d t o t h e bo t tom o f t h e p i p e and a 1.20. cm t h i c k r i n g (bo t t om f l a n g e ) o f 2 0 . 3 cm I . D . and 2 9 . 5 cm O . D . , w i t h 12 e q u a l l y s p a c e d b l o t h o l e s , i s w e l d e d t o t h e top o f t h e p i p e . A 1 .20 cm t h i c k p l a t e ( t o p f l a n g e ) w i t h a d i a m e t e r o f 2 9 . 5 0 cm, an 0 - r i n g , and 12 e q u a l l y s p a c e d b o l t h o l e s i s b o l t e d t o t he bo t t om f l a n g e w i t h t h e 0 - r i . n g p r o v i d i n g t h e s e a l . Two h o l e s a r e d r i l l e d and t a p p e d t o 1/2 i n . NPT and 1 i n . NPT r e s p e c t i v e l y , i n t h e bo t tom o f t h e s u p p l y t a n k . The 1/2 i n . NPT h o l e i s c o n n e c t e d t o a W h i t e y 63F8 b a l l v a l v e w h i c h i s used as a d r a i n . The 1 i n . NPT h o l e i s c o n n e c t e d t o t h e 1 i n . p i p e l e a d i n g t o t h e pump. Two 1/2 i n . NPT n i p p l e s were w e l d e d t o t h e s i d e o f t h e t a n k , t h e l o w e r one c o n n e c t e d t o t he r e c y c l e l i n e and t h e uppe r c o n n e c t e d t o t h e r e t u r n l i n e . A 1 /8 i n . 101 c h r o m e l - a l u m e l t h e r m o c o u p l e \ s compress , ion f i t t e d t o a 1/4 i n . t o 1 /8 i n . ma le t h e r m o c o u p l e c o n n e c t o r , w h i c h i s s c r e w e d i n t o a 1/4 i n , n i p p l e w e l d e d o n t o t h e s u p p l y t ank o p p o s i t e t h e 1/2 i n . n i p p l e s , Fou r b a f f l e s , 2 . 5 4 cm i n w i d t h , and s p a c e d a t 90° i n t e r v a l s , a r e w e l d e d t o t h e i n s i d e o f t h e t a n k . A s i x - b l a d e , f l a t - b l a d e d t u r b i n e i m p e l l e r i s a t t a c h e d t o a 1 0 . 0 0 mm. s t a i n l e s s s t e e l 316 s t i r r e r s h a f t w h i c h i s a t t a c h e d t o a d i s c - s h a p e d magne t , housed i n a t h i n - w a l l e d g l a n d p l a t e (w i t h , b e a r i n g s ) w h i c h i s s c r e w e d o n t o t h e t o p f l a n g e p l a t e . An 0 - r i n g s e a l s t h e g l a n d p l a t e - t o p f l a n g e c o n n e c t i o n . An o u t s i d e d r i v e magne t , w h i c h encompasses t h e t o p p a r t o f t h e g l a n d p l a t e and t h u s a l s o t h e s h a f t magne t , i s a t t a c h e d t o a G . K . H e l l e r E l e c t r o n i c C o n t r o l l e d GT 21 L a b o r a t o r y s t i r r e r w h i c h i s c o n t r o l l e d by a GT 21 M o t o r C o n t r o l l e r . A J - s h a p e d 1/4 i n . s t a i n l e s s s t e e l 304 t u b e , used f o r gas s p a r g i n g , i s c o m p r e s s i o n f i t t e d by a 1/4 i n . t o 1/4 i n . ma le c o n n e c t o r s c r e w e d i n t o t h e t o p f l a n g e , and i s f u r t h e r c o n n e c t e d t o a W h i t e y 42S4 b a l l v a l v e . The end o f t h e J - s h a p e d t ube i s l o c a t e d 2 . 0 0 cm d i r e c t l y be low t h e t u r b i n e i m p e l l e r , 1/4 i n . t u b i n g i s a t t a c h e d t o t h e o t h e r end o f t h e 42S4 b a l l v a l v e and b r a n c h e s o u t t o two G i l m o n t ( 1 / 8 i n . b a l l - s i z e No. 2) f l o w m e t e r s , one f o r n i t r o g e n , t h e o t h e r f o r o x y g e n . F o r n i t r o g e n , f l o w i s c o n t r o l l e d by a W h i t e y 31RS4 r e g u l a t i n g v a l v e - f o r o x y g e n , a 2RS4 r e g u l a t i n g v a l v e . These v a l v e s a r e a t t a c h e d , v i a 1/4 i n . t u b i n g , t o t h e i r r e s p e c t i v e p r e s s u r e r e g u l a t o r s and gas c y l i n d e r s . A c o o l i n g c o i l , made f r om 3 / 8 i n . x 0 . 0 3 5 i n . s t a i n l e s s s t e e l 316 t u b e , i s f i t t e d i n t o t h e t ank and c o m p r e s s i o n f i t t e d by two d r i l l e d o u t 3 / 8 i n . t o 3 / 8 i n , ma le c o n n e c t o r s s c r e w e d i n t o t he t o p f l a n g e . A t h i c k - w a l l e d , f i b e r - r e i n f o r c e d r u b b e r t ube i s a t t a c h e d t o t h e ends o f t h e c o o l i n g 102 c o i l ( u s i n g hose c l a m p s ) . One t u b e i s s e w e r e d , w h i l e t h e o t h e r i s a t t a c h e d t o a W h i t e y 1RS4 r e g u l a t i n g v a l v e w h i c h i s c o n n e c t e d t o t h e w a t e r o u t l e t . A W h i t e y 1RS6 r e g u l a t i n g v a l v e i s a t t a c h e d t o t h e t o p f l a n g e t o a c t as a r e l i e f v a l v e . A Marsh M a s t e r g a u g e Type 1 0 0 - 3 ( 0 - 1 6 0 p s i g ) p r e s s u r e gage i s a l s o a t t a c h e d t o t h e t o p f l a n g e . A 500 W V u l c a n L6 i m m e r s i o n h e a t e r ( 8 . 5 0 mm d i a m e t e r ) i s a l s o f i t t e d i n t o t h e t ank and c o m p r e s s i o n -f i t t e d by two d r i l l e d o u t 3 / 8 i n . t o 3 / 8 i n . ma le c o n n e c t o r s s c r e w e d i n t o t h e t o p f l a n g e . A s m a l l e r , m o d i f i e d f e r r u l e was used i n t h e s e ma le c o n n e c t o r s . Coppe r w i r e l e a d s , s c r e w c o n n e c t e d t o t h e ends o f t h e i m m e r s i o n h e a t e r , were a t t a c h e d t o a T h e r m o e l e c t r i c 100 Mode l 32106 -02 t e m p e r a t u r e c o n t r o l l e r . The t a n k ' s c h r o m e l - a l u m e l t h e r m o c o u p l e was e l e c t r i c a l l y c o n n e c t e d t o t h e t e m p e r a t u r e c o n t r o l l e r and a B a l l a n t i n e L a b o r a t o r i e s I n c . Model 8310 B D i g i t a l P a n e l M i l l i v o l t m e t e r . An 1100 W E l e c t r o t h e r m a l h e a t i n g t a p e was wrapped a r o u n d t h e o u t s i d e o f t h e s u p p l y t ank and was c o n t r o l l e d by a S u p e r i o r E l e c t r i c C o . P o w e r s t a t Model 3PN 1168 ( s e e F i g u r e 5 - 3 ) . 5 . 3 . PFRU T e s t S e c t i o n The PFRU t e s t s e c t i o n i t s e l f c o n s i s t s e s s e n t i a l l y o f two p a r t s - t h e PFRU and t h e o u t e r t u b e a s s e m b l y ( s e e F i g u r e s 5 -4 and 5 - 5 ) . The b a s i c d e s i g n o f t h e PFRU was c o v e r e d i n t h e L i t e r a t u r e R e v i e w . The i m p o r t a n t p h y s i c a l d i m e n s i o n s a r e an e n t r a n c e l e n g t h o f 2 1 . 6 0 cm, a h e a t e d l e n g t h o f 1 0 . 2 0 cm, a r o d d i a m e t e r o f 1 0 . 7 4 mm t o 1 0 . 9 2 mm, and a t h r o a t d i a m e t e r o f 1 9 . 0 5 mm ( 3 / 4 i n . ) . The r o d m a t e r i a l i s s t a i n l e s s s t e e l 3 0 4 . The 0 . 0 2 0 i n . s h e a t h e d , c h r o m e l - c o n s t a n t a n t h e r m o c o u p l e w i r e s a r e a t t a c h e d t o " s p e c i a l " t u b u l a r c o n n e c t o r s w h i c h F i g u r e 5 - 3 . I n t e r n a l s and E x t e r n a l s o f S u p p l y Tank 104 DIMENSIONS IN mm. MATERIAL: SS 304 F i g u r e 5 - 4 . PFRU A s s e m b l y 105 (b) Figure 5 - 5 . P h o t o g r a p h s o f PFRU A s s e m b l y (a ) PFRU o u t e r t ube a s s e m b l y (b ) PFRU h e a t e r r o d 106 c o n n e c t t h e h i g h gage w i r e i n t h e 0 . 0 2 0 i n . sheaths , t o t h e r e l a t i v e l y low gage w i r e o f t h e t h e r m o c o u p l e j a c k s . The s h e a t h e d t h e r m o c o u p l e w i r e s between t h e t u b u l a r c o n n e c t o r s and t h e t h r o a t a r e n o t i m m o b i l i z e d and t h u s a r e s u s c e p t i b l e t o b r e a k a g e . The o u t e r t u b e a s s e m b l y i s c o n s t r u c t e d t o 7 / 8 i n . 18 gage s t a i n l e s s s t e e l 304 t u b e , 1/2 i n . n i p p l e s w e l d e d on e i t h e r end o f t h e t u b e , 3 / 4 i n . 18 gage s t a i n l e s s s t e e l 304 t ube w e l d e d t o t h e s i d e o f 7 / 8 i n . t ube a t an a n g l e o f 30° f r o m t h e v e r t i c a l , a 1 /8 i n . n i p p l e l o c a t e d be low t h e 3 / 4 i n . t ube w e l d , and t h r e e 1/8 i n . n i p p l e s ( a t 120° i n t e r v a l s t o each o t h e r ) l o c a t e d above t h e bo t tom 1/2 i n . n i p p l e . A 1/2 i n . t o 3 / 4 i n . ma le c o n n e c t o r , used f o r c o m p r e s s i o n f i t t i n g t h e PFRU r o d (by i t s t h r o a t ) t o t h e o u t e r t ube a s s e m b l y , was s c r e w e d i n t o t h e t o p 1/2 i n . n i p p l e . A 1/2 i n . t o 1/2 i n . ma le c o n n e c t o r , used f o r c o n n e c t i n g t h e o u t e r t ube a s s e m b l y t o t h e 1/2 i n . t u b i n g , was s c r e w e d i n t o t he bo t tom 1/2 i n . n i p p l e . 1 /8 i n . t o 1/8 i n . ma le c o n n e c t o r s w i t h T e f l o n f e r r u l e s were s c r e w e d i n t o t h e t h r e e 1 /8 i n . n i p p l e s . 1 /8 i n . r o d s were pushed t h r o u g h t h e c o n n e c t o r s a n d , f o r a few r u n s , were used t o c e n t e r t he PFRU r o d w i t h r e s p e c t t o t h e o u t e r t u b e . A 1 /8 i n . t o 1/2 i n . ma le c o n n e c t o r , w h i c h c o n n e c t e d t h e p r e s s u r e t a p t o a Ma rsh M a s t e r g a u g e Type 1 0 0 - 3 p r e s s u r e gage (0 t o 200 p s i g ) , was s c r e w e d i n t o t h e o t h e r 1 /8 i n . n i p p l e . When t h e PFRU r o d i s c o n n e c t e d t o t h e o u t e r t ube a s s e m b l y , t h e p r e s s u r e t a p i s 1 9 . 3 0 cm f rom t h e t o p o f t h e t h r o a t o r 1 .10 cm be low t h e end o f t h e h e a t e d s e c t i o n . A 3 / 4 i n . t o 1/2 i n . u n i o n was used t o c o n n e c t t h e a r m - l i k e 3 / 4 i n . t ube t o t h e 1/2 i n . t u b i n g . I t s h o u l d be n o t e d t h a t t h e I .D . o f t h e o u t e r t u b e i s 0 . 7 7 7 i n ( 1 9 . 7 4 mm) i n s t e a d o f t h e l i t e r a t u r e v a l u e o f 0 . 7 5 i n . ( 1 9 . 0 5 mm). The power i n p u t t o t h e 107 32 ft N i ch rome w i r e r e s i s t a n c e h e a t e r c o i l was c o n t r o l l e d by a S u p e r i o r E l e c t r i c C o . P o w e r s t a t Model 236 and was measured by a S e n s i t i v e R e s e a r c h . V o l t - A m p W a t t m e t e r . 5 . 4 . HWP T e s t S e c t i o n The HWP t e s t s e c t i o n c o n s i s t s e s s e n t i a l l y o f t h r e e p l a t e s ( see F i g u r e s 5 - 6 , 5 - 7 , and 5 - 8 ) . The m i d d l e p l a t e was m i l l e d o u t t o a w i d t h o f 4 . 0 0 cm and l e n g t h o f 6 1 . 6 8 cm, w i t h t h e c o r n e r s s l i g h t l y r o u n d e d . An e l l i p t i c a l h o l e , 1 5 . 5 4 mm x 7 .77 mm, was d r i l l e d o u t a t each end o f t h e m i d d l e p l a t e . A 1/2 i n . f l a t t e n e d t u b e was s i l v e r s o l d e r e d t o t h e o u t s i d e o f each, e l l i p s e . 4 5 . 4 4 cm f rom t h e end o f t h e p l a t e , a h o l e was d r i l l e d and t a p p e d t o 1/8 i n . NPT on each s i d e o f t h e p l a t e . T e f l o n 1/8 i n . t o 1/4 i n . ma le c o n n e c t o r s ( d r i l l e d o u t t o an i n s i d e d i a m e t e r s l i g h t l y g r e a t e r t h a n 1/4 i n . i n o r d e r t o accommodate t he 1/4 i n . b u s b a r s ) were s c r e w e d i n t o t h e s e h o l e s . 36 b o l t h o l e s were d r i l l e d i n each p l a t e . Two 1/2 i n . t e f l o n g a s k e t s were c u t and d r i l l e d t o c o n f o r m w i t h t h e m i d d l e p l a t e s u r f a c e and t h e b o l t h o l e s . The t h r e e p l a t e s and t e f l o n g a s k e t s were b o l t e d t o g e t h e r t o p r o d u c e a d u c t o f r e c t a n g u l a r c r o s s - s e c t i o n , 4 . 0 0 cm x 1 .30 cm, w h i c h means t h e g a s k e t s were c o m p r e s s e d t o t h i c k n e s s e s o f 0 . 0 5 cm. In t h e t o p p l a t e , a h o l e was d r i l l e d and t a p p e d t o 1 3 / 8 i n . NF a t a d i s t a n c e o f 4 5 . 4 4 cm f rom t h e end o f t h e p l a t e . The s c r e w cap o f F i g u r e 5 -8 i s s c r e w e d i n t o t h i s t h r e a d e d h o l e a f t e r t h e c o i l e d w i r e i s s e t i n p o s i t i o n . The c o i l e d w i r e i s c o n n e c t d t o t h e b u s b a r s by p i n c e r a c t i o n . The u n c o i l e d l e n g t h o f t h e w i r e , between t h e p o i n t s o f c o n t a c t on t h e b u s b a r s , was a b o u t 11 cm. The s t a i n l e s s s t e e l 304 w i r e had a d i a m e t e r o f 0 . 1 4 mm. The w i r e was c o i l e d a b o u t 25 t i m e s w i t h a c o i l d i a m e t e r o f a b o u t 1 .45 mm. Two h o l e s F i g u r e 5 - 6 . Hot W i r e P robe A s s e m b l y 109 (b) F i g u r e 5 - 7 , p h o t o g r a p h s o f D i s a s s e m b l e d Hot W i r e P r o b e ( a ) Top v i e w (b) S i d e