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New pilot plant technique for designing gas absorbers with chemical reactions Tontiwachwuthikul, Paitoon 1990

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N E W P I L O T P L A N T T E C H N I Q U E F O R D E S I G N I N G G A S A B S O R B E R S W I T H C H E M I C A L R E A C T I O N S by P A I T O O N T O N T I W A C H W U T H I K U L B.Eng.(Hons.), King Mongkut's Institute of Technology, Thailand, 1983 B.A.(Political Science), Ramkhamhaeng University, Thailand, 1983 M.Eng.(Chemical Engineering), The University of British Columbia, 1986 A THESIS S U B M I T T E D IN PARTIAL F U L F I L M E N T O F T H E R E Q U I R E M E N T S FOR T H E D E G R E E O F D O C T O R OF PHILOSOPHY in T H E F A C U L T Y O F G R A D U A T E STUDIES D E P A R T M E N T O F C H E M I C A L E N G I N E E R I N G We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A December 1990 (c) Paitoon Tontiwachwuthikul, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at The University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Chemical Engineering The University of British Columbia 2075 Wesbrook Mall Vancouver, B.C., Canada V6T 1Z3 Date: December 1990 i i ABSTRACT Gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n i s an i m p o r t a n t u n i t o p e r a t i o n i n the c h e m i c a l and pe t r o l e u m i n d u s t r i e s f o r the s e l e c t i v e removal of components from i n d u s t r i a l gas str e a m s . A p a r t from c h o o s i n g a b s o r p t i o n media, the most d i f f i c u l t problems f a c i n g the d e s i g n e n g i n e e r a r e the s i z i n g and performance p r e d i c t i o n of t h e a b s o r p t i o n tower due t o the s c a r c i t y of fundamental d e s i g n d a t a , e s p e c i a l l y when n o v e l a b s o r p t i o n media and/or p a c k i n g s a re used. The s o l u b i l i t y of carbon d i o x i d e i n 2 and 3 M s o l u t i o n s of 2-amino-2-methyl-1-propanol (AMP), which i s a newly i n t r o d u c e d a b s o r b e n t , was de t e r m i n e d a t 20, 40, 60 and 80 ° C and f o r C O 2 p a r t i a l p r e s s u r e s r a n g i n g from a p p r o x i m a t e l y 1 t o 100 kPa. The r e s u l t s were i n t e r p r e t e d w i t h a m o d i f i e d K e n t - E i s e n b e r g model . which p r e d i c t e d the p r e s e n t and p r e v i o u s e x p e r i m e n t a l r e s u l t s w e l l . The a b s o r p t i o n c a p a c i t i e s of AMP and monoethanolamine (MEA) s o l u t i o n s were a l s o compared. D e t a i l e d c o n c e n t r a t i o n and temperature measurements were r e p o r t e d f o r the a b s o r p t i o n of carbon d i o x i d e from a i r i n t o NaOH, MEA and AMP s o l u t i o n s . A f u l l - l e n g t h a b s o r b e r (0.1 m ID, packed w i t h 12.7 mm B e r l Saddles up t o h e i g h t s of 6.55 m) was used. I t was o p e r a t e d i n c o u n t e r c u r r e n t mode and a t 30 t o 75 % f l o o d i n g v e l o c i t i e s which a r e t y p i c a l f o r gas a b s o r b e r o p e r a t i o n s . The f o l l o w i n g ranges of o p e r a t i n g c o n d i t i o n s were employed: s u p e r f i c i a l gas f l o w r a t e 11.1 t o 14.8 mol/m 2 s; s u p e r f i c i a l l i q u i d f l o w r a t e 9.5 t o 13.5 m^/m2 h; f e e d C O 2 c o n c e n t r a t i o n 11.5 t o 19.8 %; t o t a l a b s o r b e n t c o n c e n t r a t i o n 1.2 t o 3.8 kmol/m^; l i q u i d f e e d t e m p e r a t u r e 14 t o 20 °C; t o t a l p r e s s u r e 103 kPa. The measurements f o r the CC>2-NaOH and CC^-MEA systems were compared w i t h p r e d i c t i o n s from a p r e v i o u s l y d e v e l o p e d m a t h e m a t i c a l model. G e n e r a l l y good agreement was o b t a i n e d e x cept a t h i g h C O 2 l o a d i n g s of MEA s o l u t i o n s . Compared w i t h MEA, AMP was found t o have s u p e r i o r C O 2 a b s o r p t i o n c a p a c i t i e s and i n f e r i o r mass t r a n s f e r r a t e s . A new p r o c e d u r e , c a l l e d the P i l o t P l a n t Technique (PPT), f o r d e s i g n i n g gas a b s o r b e r s w i t h c h e m i c a l r e a c t i o n s has been d e v e l o p e d . The PPT i s p r i m a r i l y i n t e n d e d f o r d e s i g n i n g a b s o r b e r s f o r which fundamental d e s i g n i n f o r m a t i o n i s l a c k i n g . I t i s based on the premise t h a t f u l l - l e n g t h a b s o r p t i o n columns can be s i z e d by making a minimum number of t e s t s u s i n g a s m a l l - s c a l e p i l o t p l a n t . Two s p e c i a l f e a t u r e s of the PPT a r e ( i ) the d e t a i l s of hydrodynamic pa r a m e t e r s ( i . e . mass t r a n s f e r c o e f f i c i e n t s , e f f e c t i v e i n t e r f a c i a l a r ea and l i q u i d hold-up) and the p h y s i c o -c h e m i c a l i n f o r m a t i o n of the system (e . g . r e a c t i o n mechanism, r e a c t i o n r a t e c o n s t a n t s ) need not be known and ( i i ) complex c a l c u l a t i o n s are a v o i d e d . U s i n g the PPT t o s i z e the h e i g h t or t o p r e d i c t the performance of a g i v e n f u l l - l e n g t h a b s o r b e r , the s p e c i f i c a b s o r p t i o n r a t e , which i s the e s s e n t i a l i n f o r m a t i o n , can be measured d i r e c t l y u s i n g the p i l o t p l a n t model (PPM) column i f b o t h columns have the same hydrodynamic c o n d i t i o n s . T h i s can be a c h i e v e d by u s i n g the same type and s i z e of p a c k i n g i n t he PPM and the f u l l - l e n g t h columns and e n s u r i n g t h a t the end and w a l l e f f e c t s a r e n e g l i g i b l e . The PPM column must a l s o be o p e r a t e d a t t h e same s u p e r f i c i a l f l u i d v e l o c i t i e s as th o s e of the f u l l - l e n g t h column. The s p e c i f i c a b s o r p t i o n r a t e was then o b t a i n e d from the g r a d i e n t of the f l u i d c o m p o s i t i o n p r o f i l e a l o n g the PPM column. The v a l i d i t y of the PPT was demonstrated by d e t e r m i n i n g the h e i g h t and p r e d i c t i n g the performance of the f u l l - l e n g t h column i n which c a r b o n d i o x i d e was absorbed from a i r by aqueous s o l u t i o n s of NaOH and AMP a t v a r i o u s o p e r a t i n g c o n d i t i o n s ; good agreement was o b t a i n e d . V TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES i x LIST OF FIGURES x i ACKNOWLEDGEMENTS ' x x i 1. INTRODUCTION 1 1.1 ACID GAS ABSORPTION BY CHEMICAL SOLVENTS 9 1.2 DESIGN OF CHEMICAL GAS ABSORPTION COLUMNS 13 1.3 RESEARCH OBJECTIVES 17 2. LITERATURE REVIEW 21 2.1 GAS ABSORPTION WITH CHEMICAL REACTION 21 2.2 REACTION OF C 0 2 IN CAUSTIC AND AMINE SOLUTIONS 28 2.2.1 REACTION CHEMISTRY OF THE CAUSTIC - C 0 2 SYSTEM 28 2.2.2 REACTION CHEMISTRY OF C 0 2 ~ AMINE SYSTEM 30 2.3 DESIGN OF PACKED ABSORBERS WITH CHEMICAL REACTION ...32 2.3.1 EMPIRICAL DESIGN METHOD 43 2.3.2 THEORETICAL DESIGN METHOD 48 2.3.2.1 INFORMATION REQUIRED IN THEORETICAL CALCULATIONS 59 2.3.2.2 WEAK POINTS OF THEORETICAL DESIGN METHOD 69 2.3.3 DESIGN METHODS BASED ON LABORATORY MODELS 70 2.3.3.1 WEAK POINTS OF LABORATORY MODELS 82 THEORY 83 3.1 MATHEMATICAL MODEL 83 3.1.1 MODEL FORMULATION 85 3.1.2 COMPUTATIONAL PROCEDURE 91 3.2 PROPOSED PILOT PLANT TECHNIQUE FOR DESIGNING GAS ABSORBERS WITH CHEMICAL REACTION 97 3.2.1 THE PILOT PLANT TECHNIQUE 97 3.2.2 A SHORT-CUT PROCEDURE FOR PPT 108 3.2.3 VERIFICATION OF PPT 112 SOLUBILITY OF C 0 2 IN 2-AMINO-2-METHYL-1-PROPANOL SOLUTIONS 113 4.1 BACKGROUND INFORMATION 113 4.2 EXPERIMENTAL APPARATUS AND PROCEDURE 115 4.3 PREDICTIVE MODEL FOR C 0 2 SOLUBILITY IN AMP SOLUTIONS 115 4.4 RESULTS AND DISCUSSION 120 PILOT PLANT AND EXPERIMENTAL PROCEDURE 131 5.1 THE PILOT PLANT ABSORPTION COLUMN 131 5.2 PILOT PLANT MODEL (PPM) COLUMN 143 5.3 REGENERATION COLUMN 148 5.4 AUXILIARY EQUIPMENT 153 v i i 5.5 PROCEDURE FOR ABSORPTION EXPERIMENTS USING THE FULL-LENGTH AND PPM COLUMNS 155 5.6 ANALYSIS OF SAMPLES 159 5.7 COLUMN TESTING 161 6. RESULTS AND DISCUSSION: COMPARISON BETWEEN FULL-LENGTH ABSORBER PERFORMANCE AND THEORETICAL PREDICTIONS 168 6.1 FULL-LENGTH ABSORBER PERFORMANCE 169 6.1.1 EFFECT OF OPERATING CONDITIONS 175 6.2 COMPARISON BETWEEN FULL-LENGTH ABSORBER PERFORMANCE AND THEORETICAL PREDICTIONS 183 6.2.1 SOURCES OF BASIC INFORMATION 183 6.2.2 COMPARISON OF RESULTS 190 7. RESULTS AND DISCUSSIONS: COMPARISON BETWEEN FULL-LENGTH ABSORBER PERFORMANCE AND PREDICTIONS BASED ON PPT 210 7.1 VERIFICATION USING R y-CONCENTRATION DIAGRAM 210 7.2 VERIFICATION USING PPT SHORT-CUT PROCEDURE 220 7.2.1 NaOH-C0 2 SYSTEM 220 7.2.2 C0 2"AMP SYSTEM 231 7.3 DISCUSSION OF THE VERIFICATION RESULTS 253 7.4 LIMITATIONS OF PPT 258 7.5 PRACTICAL IMPLICATIONS OF THE PPT 260 8. SUMMARY OF RESULTS AND CONCLUSIONS 264 9. RECOMMENDATIONS FOR FURTHER WORK 267 viii NOMENCLATURE 270 R E F E R E N C E S 273 A P P E N D I C E S A . A N A L Y S I S OF L I Q U I D SAMPLES 286 B . ERROR A N A L Y S I S 294 C . COMPUTER PROGRAM L I S T I N G S 299 LIST OF TABLES T a b l e 1.1: Major i n d u s t r i a l p r o c e s s e s r e q u i r i n g a c i d gas t r e a t i n g 2 Ta b l e 1.2: T y p i c a l c o m p o s i t i o n of Canadian, T h a i and American n a t u r a l gases (dry b a s i s , mole %) 3 Ta b l e 1.3: T y p i c a l c o m p o s i t i o n of p r o d u c t gas from n a t u r a l gas steam r e f o r m i n g p r o c e s s 4 T a b l e 1.4: T y p i c a l c o m p o s i t i o n of p r o d u c t gas from a c o a l g a s i f i c a t i o n p r o c e s s , F l e x i c o k e r 4 Ta b l e 1.5: C a p i t a l c o s t breakdown f o r a commercial s c a l e p l a n t p r o d u c i n g s y n t h e s i s gas (N 2+3H 2) from steam r e f o r m i n g f o r making ammonia 8 Ta b l e 1.6: Common a l k a l i n e r e a g e n t s used as c h e m i c a l s o l v e n t s 10 Ta b l e 2.1: Comparison r e s u l t s between a c t u a l and p r e d i c t e d h e i g h t from t h e P o i n t model by Danckwerts and A l p e r 74 Ta b l e 2.2: Comparison r e s u l t s between a c t u a l and p r e d i c t e d h e i g h t from t h e P o i n t model by La u r e n t 75 Ta b l e 4.1: E x p e r i m e n t a l S o l u b i l i t y of C 0 2 i n 2 M AMP S o l u t i o n 121 Ta b l e 4.2: E x p e r i m e n t a l S o l u b i l i t y of C 0 2 i n 3 M AMP S o l u t i o n 122 Ta b l e 4.3: Comparison of p r e s e n t and p r e v i o u s l y r e p o r t e d pK 1 v a l u e s ....126 T a b l e 5.1: "Proper" D e s i g n C r i t e r i a of Packed Columns ...140 T a b l e 5.2: Systems s t u d i e d and number of e x p e r i m e n t a l runs 157 Ta b l e 5.3: O p e r a t i n g C o n d i t i o n s 158 Ta b l e 5.4: Gas and l i q u i d f l o w r a t e s a t f l o o d i n g p o i n t . . . 165 T a b l e 6.1: E x p e r i m e n t a l r e s u l t s f o r C0 2-NaOH system 171 X T a b l e 6.2: E x p e r i m e n t a l r e s u l t s f o r C0 2-MEA system 173 Ta b l e 6.3: L i s t of o p e r a t i n g c o n d i t i o n s and parameters f o r Run T9 (C0 2-NaOH system) 185 Ta b l e 6.4: L i s t of o p e r a t i n g c o n d i t i o n s and parameters f o r Run T22 (C0 2-MEA system) 186 Ta b l e 6.5: Comparison between the c a l c u l a t i o n r e s u l t s from p r e v i o u s r e p o r t s and from t h i s work 191 Ta b l e 6.6: Comparison of enhancement f a c t o r v a l u e s o b t a i n e d from Merchuk et a l . [ l 4 2 ] , Onda e t a l . [ 143] and Run T9 196 Ta b l e 6.7: E f f e c t of mass b a l a n c e on the h e i g h t p r e d i c t i o n f o r Run T9 (NaOH-C0 2 system). O p e r a t i n g C o n d i t i o n s : gas r a t e = 1545 kg/m 2 h; l i q u i d r a t e = 13.5 m3/m2 h; NaOH cone. = 0.413 t o 2.0 kmol/m 3; C 0 2 cone. = 1.0 t o 18.45 %; Column tem p e r a t u r e = 15.0 t o 35.0 °C 206 Ta b l e 6.8: E f f e c t s of major parameters on the h e i g h t p r e d i c t i o n f o r Run T9 (NaOH - C O o ) . O p e r a t i n g C o n d i t i o n s : gas r a t e = 1545 kg/m 2 h; l i q u i d r a t e = 13.5 m3/m2 h; NaOH cone. = 0.413 t o 2.0 kmol/m 3; C 0 2 cone. = 1.0 to 18.45 %; Column temperature = 15.0 t o 35.0 °C 209 Ta b l e 7.1: A c t u a l and p r e d i c t e d h e i g h t s f o r an a b s o r p t i o n tower removing C 0 2 from a i r by c o n t a c t w i t h an aqueous NaOH s o l u t i o n 217 Ta b l e 7.2: V e r i f i c a t i o n r e s u l t s f o r the PPT s h o r t - c u t p r o c e d u r e u s i n g the NaOH-C0 2 system 221 Ta b l e 7.3: E x p e r i m e n t a l r e s u l t s f o r C0 2~AMP system 232 Ta b l e 7.4: V e r i f i c a t i o n r e s u l t s f o r PPT s h o r t - c u t p r o c e d u r e u s i n g t h e AMP-C0 2 system 239 Ta b l e 7.5: E f f e c t of u n c e r t a i n t y a s s o c i a t e d w i t h Ry on the p r e d i c t e d h e i g h t u s i n g o p e r a t i n g c o n d i t i o n s of Run T9 (NaOH - C O o ) . O p e r a t i n g c o n d i t i o n : gas f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w rate= 9.5 m3/m2 h r ; _ i n l e t C 0 2 c o n c e n t r a t i o n = 18.4%; i n l e t [OH ] =2.0 kmol/m 3 257 Ta b l e 7.6: Some of h i g h - e f f i c i e n c y s o l v e n t s 262 XI LIST OF FIGURES F i g u r e 1.1: T y p i c a l f l o w s h e e t f o r gas sweetening by c h e m i c a l r e a c t i o n 11 F i g u r e 1.2: C o n c e n t r a t i o n and temperature p r o f i l e s of a t y p i c a l i n d u s t r i a l a b s o r b e r 16 F i g u r e 2.1: Schematic of gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n system 22 F i g u r e 2.2: I n t e r f a c e b e h a v i o r f o r gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n 24 F i g u r e 2.3: Packed a b s o r b e r 33 F i g u r e 2.4: Major d e s i g n p r o c e d u r e s f o r gas a b s o r b e r s w i t h c h e m i c a l r e a c t i o n 34 F i g u r e 2.5: T y p i c a l v a p o r - l i q u i d e q u i l i b r i u m c u r v e s a t 40 °C of C 0 2 - C h e m i c a l s o l v e n t s 38 F i g u r e 2.6: Schematic of a packed a b s o r b e r 39 F i g u r e 2.7: K G a v v a l u e s of C0 2-K 2C03 system [65] 47 F i g u r e 2.8: A t y p i c a l p l o t of I as f u n c t i o n s of I j and M parameters [70] 56 F i g u r e 2.9: V a r i a t i o n of the enhancement f a c t o r f o r C0 2-MEA system o b t a i n e d from l a b o r a t o r y a b s o r b e r s 57 F i g u r e 2.10: G a s - s i d e mass t r a n s f e r c o e f f i c i e n t , k G, as a f u n c t i o n of gas f l o w r a t e 61 F i g u r e 2.11: H i g h - e f f i c i e n c y random p a c k i n g 62 F i g u r e 2.12: S t r u c t u r e d p a c k i n g 63 F i g u r e 2.13: Apparent r a t e c o n s t a n t of C 0 2 - DEA system r e p o r t e d by v a r i o u s r e s e a r c h e r s 66 F i g u r e 2.14: Schematic r e p r e s e n t a t i o n of the P o i n t model 71 F i g u r e 2.15: Schematic r e p r e s e n t a t i o n of Complete m o d e l l i n g 77 xii F i g u r e 2.16: Sphere column 78 F i g u r e 2.17: Procedure f o r u s i n g the complete m o d e l l i n g 81 F i g u r e 3.1: Schematic diagram of a d i a b a t i c packed a b s o r b e r s 86 F i g u r e 3.2: D i f f e r e n t i a l s e c t i o n of packed a b s o r b e r s 87 F i g u r e 3.3: S i m p l i f i e d f l o w c h a r t of the major c a l c u l a t i o n s t e p s used i n the p r e s e n t computer models 96 F i g u r e 3.4: Schematic of the P i l o t P l a n t Technique 99 F i g u r e 3.5: Main d e s i g n p r o c e d u r e s f o r gas a b s o r b e r s w i t h c h e m i c a l r e a c t i o n 105 F i g u r e 3.6: Schematic r e p r e s e n t a t i o n t o s i m u l a t e i n d u s t r i a l a b s o r b e r s u s i n g t h e PPT s h o r t - c u t p r o c e d u r e 110 F i g u r e 4.1: S o l u b i l i t y of C 0 2 i n a 2 M AMP s o l u t i o n a t 40 °C. ( S o l i d c i r c l e s - p r e s e n t e x p e r i m e n t a l d a t a ; open c i r c l e s - R o b e r t s and Mather [ 9 5 ] ; s o l i d l i n e s - p r e s e n t model) 123 F i g u r e 4.2: S o l u b i l i t y of C 0 2 i n a 3 M AMP s o l u t i o n a t 40 °C. ( S o l i d c i r c l e s - p r e s e n t e x p e r i m e n t a l d a t a ; open c i r c l e s - R o b e r t s and Mather [ 9 5 ] ; squares - S a r t o r i and Savage [ 7 1 ] ; s o l i d l i n e s - p r e s e n t model) 124 F i g u r e 4.3: S o l u b i l i t y of C 0 2 i n a 2 M AMP s o l u t i o n a t v a r i o u s t e m p e r a t u r e s . (Open c i r c l e s - 20 °C; s o l i d c i r c l e s - 40 °C; s quares - 60 °C; t r i a n g l e s - 80 °C; s o l i d l i n e s - p r e s e n t model) 128 F i g u r e 4.4: S o l u b i l i t y of C 0 2 i n a 3 M AMP s o l u t i o n a t v a r i o u s t e m p e r a t u r e s . (Open c i r c l e s - 20 °C; s o l i d c i r c l e s - 40 °C; squares - 60 °C; t r i a n g l e s - 80 °C; s o l i d l i n e s - p r e s e n t model) 129 F i g u r e 4.5: S o l u b i l i t y of C 0 2 i n 2.5 M AMP and MEA s o l u t i o n s X l l l a t v a r i o u s t e m p e r a t u r e s . ( D o t t e d , dashed and c h a i n d o t t e d l i n e s a r e the model p r e d i c t i o n s f o r the C0 2~AMP system a t 40, 60 and 80 °C, r e s p e c t i v e l y . S o l i d l i n e s a r e from the K e n t - E i s e n b e r g model [97] f o r the C0 2-MEA system.) 130 F i g u r e 5.1: Schematic of the p i l o t p l a n t 132 F i g u r e 5.2: P i c t u r e showing how the p i l o t p l a n t equipment f i t t e d i n t o the C h e m i c a l E n g i n e e r i n g B u i l d i n g 133 F i g u r e 5.3: Schematic of the a b s o r p t i o n column ...134 F i g u r e 5.4: Drawing of a column s e c t i o n 135 F i g u r e 5.5: Schematic of the r e d i s t r i b u t o r s 136 F i g u r e 5.6: Drawing of the j o i n t between two s e c t i o n s ...137 F i g u r e 5.7: P i c t u r e of the s a m p l i n g system and the j o i n t between two s e c t i o n s 141 F i g u r e 5.8: Schematic of the s a m p l i n g system 142 F i g u r e 5.9: Drawing of the PPM column .....144 F i g u r e 5.10: Diagram showing the gas sam p l i n g p o s i t i o n . . . 145 F i g u r e 5.11: P i c t u r e of the PPM column 146 F i g u r e 5.12: P i c t u r e of s a m p l i n g probes a l o n g t h e PPM column 1 47 F i g u r e 5.13: Schematic of the r e g e n e r a t o r 149 F i g u r e 5.14: P i c t u r e of the r e g e n e r a t o r .150 F i g u r e 5.15: P i c t u r e of the t o p p a r t of the r e g e n e r a t o r .151 F i g u r e 5.16: P i c t u r e of the bottom p a r t of the r e g e n e r a t o r 152 F i g u r e 5.17: P r e s s u r e drops as f u n c t i o n s of gas and l i q u i d f l o w r a t e . ( L i q u i d f l o w r a t e (kg/m 2 s ) : s o l i d squares -2.802; open squares - 4.160; open c i r c l e s - 6.740; s o l i d c i r c l e s - 8.112) ....164 XIV F i g u r e 5.18: G e n e r a l i z e d c o r r e l a t i o n f o r p r e s s u r e drop and f l o o d i n g c a l c u l a t i o n s suggested by T r e y b a l 166 F i g u r e 5.19: Measured and p r e d i c t e d p r e s s u r e drops 167 F i g u r e 6.1 E f f e c t of C 0 2 l o a d i n g . The i n l e t C 0 2 l o a d i n g was i n c r e a s e d from 0.0 (Run T13 - s o l i d c i r c l e s ) t o 0.118 (Run T14 - open squares) mol C 0 2 per mol MEA. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h; t o t a l MEA c o n c e n t r a t i o n = 2.0 kmol/m 3; i n l e t gas C 0 2 c o n c e n t r a t i o n = 15.5% 177 F i g u r e 6.2: E f f e c t of gas C 0 2 c o n c e n t r a t i o n . The i n l e t C 0 2 c o n c e n t r a t i o n was i n c r e a s e d from 15.6 % (Run T16 - open squares) t o 19.1 % (Run T18 - s o l i d c i r c l e s ) . O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h; t o t a l MEA c o n c e n t r a t i o n = 2.0 kmol/m 3; i n l e t C 0 2 l o a d i n g = 0.0 mol C 0 2 / mol MEA ...178 F i g u r e 6.3: F i g u r e 6.4; E f f e c t of l i q u i d f l o w r a t e . The l i q u i d f l o w r a t e was i n c r e a s e d from 9.5 (Run T18 - s o l i d c i r c l e s ) t o 13.5 (Run T15 - open squares) m3/m2 s. Op e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 mol/m 2 s; t o t a l MEA c o n c e n t r a t i o n = 2.0 kmol/m 3; i n l e t C 0 2 l o a d i n g = 0.0 mol C 0 2 / mol MEA; i n l e t gas C 0 2 c o n c e n t r a t i o n = 19.5% .• ...179 E f f e c t of absorbent c o n c e n t r a t i o n . The t o t a l MEA c o n c e n t r a t i o n was i n c r e a s e d from 2.0 (Run T18 -s o l i d c i r c l e s ) t o 2.55 (Run T20 - open squares) kmol/m 3. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h; i n l e t C 0 2 l o a d i n g = 0.0 mol C 0 2 / mol MEA; i n l e t gas C02 c o n c e n t r a t i o n = 19.1% 180 F i g u r e 6.5; F i g u r e 6.6; E f f e c t of gas f l o w r a t e . The gas f l o w r a t e was i n c r e a s e d from 11.1 (Run T21 - open squares) t o 14.8 (Run T18 - s o l i d c i r c l e s ) mol/m 2 s. Op e r a t i n g c o n d i t i o n s : l i q u i d f l o w r a t e = 9.5 m3/m2 h; i n l e t C 0 2 l o a d i n g = 0.0 mol C 0 2 / mol MEA; i n l e t gas C 0 2 c o n c e n t r a t i o n = 19.1%; t o t a l MEA c o n c e n t r a t i o n = 2.0 kmol/m 3 181 E f f e c t of absorbent t y p e . The s o l v e n t type was changed from NaOH (Run T11 - s o l i d c i r c l e s ) t o MEA (Run T14 - open s q u a r e s ) . O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h; t o t a l a b sorbent XV c o n c e n t r a t i o n = 2.0 kmol/m 3; i n l e t gas C02 c o n c e n t r a t i o n = 15.5% 182 F i g u r e 6.7 F i g u r e 6.8: P r e d i c t e d ( l i n e s ) and e x p e r i m e n t a l ( p o i n t s ) r e s u l t s f o r the C 0 2 - NaOH system (Run T 9 ) : [a] Temperature p r o f i l e s f o r the l i q u i d ( s o l i d l i n e ) and gas phases ( d o t t e d l i n e ) , Open squares a r e the e x p e r i m e n t a l measurements of the l i q u i d t e m p e r a t u r e ; [b] c o n c e n t r a t i o n p r o f i l e s of C 0 2 (open c i r c l e ) and NaOH ( s o l i d c i r c l e ) ; [ c ] Enhancement f a c t o r 192 P r e d i c t e d ( l i n e s ) and e x p e r i m e n t a l ( p o i n t s ) r e s u l t s f o r the C 0 2 - MEA system (Run T22): [a] Temperature p r o f i l e s f o r the l i q u i d ( s o l i d l i n e ) and gas phases ( d o t t e d l i n e ) , Open squares a r e the e x p e r i m e n t a l measurements of the l i q u i d t e m p e r a t u r e ; [b] c o n c e n t r a t i o n p r o f i l e s of C 0 2 (open c i r c l e ) and l o a d i n g ( s o l i d c i r c l e ) ; [ c ] Enhancement f a c t o r 193 F i g u r e 6.9: C o n c e n t r a t i o n of C 0 2 i n the gas phase f o r Run T16. Open c i r c l e s r e p r e s e n t e x p e r i m e n t a l measurements; the s o l i d l i n e and d o t t e d l i n e s denote the p r e d i c t e d v a l u e s u s i n g a column co m p r i s e d of s i x and f i v e s e c t i o n s , r e s p e c t i v e l y . ( O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 m3/m2 h; l i q u i d f l o w r a t e = 9.5 m3/m2 h; i n l e t C 0 2 l o a d i n g = 0.0 mol C 0 2 / mol MEA; i n l e t gas C02 c o n c e n t r a t i o n = 15.5%; t o t a l MEA c o n c e n t r a t i o n = 2.0 kmol/m 3.) 198 F i g u r e 6.10: C r o s s p l o t of p r e d i c t e d and measured C 0 2 c o n c e n t r a t i o n s i n the gas phase ...202 F i g u r e 6.11: C r o s s p l o t of p r e d i c t e d and measured NaOH c o n c e n t r a t i o n s i n the l i q u i d phase 203 F i g u r e 6.12: C r o s s p l o t of p r e d i c t e d and measured C 0 2 l o a d i n g i n t h e MEA s o l u t i o n 204 F i g u r e 6.13: C r o s s p l o t of p r e d i c t e d and measured t e m p e r a t u r e s i n the l i q u i d phase 205 F i g u r e 7.1: A t y p i c a l p l o t of C 0 2 mole r a t i o i n the gas phase as a f u n c t i o n of h e i g h t i n the PPM column, Run S5. P o i n t s denote e x p e r i m e n t a l d a t a and t h e s o l i d l i n e i n d i c a t e s the bes t f i t u s i n g a t h i r d o r d e r p o l y n o m i a l e q u a t i o n . ( E x p e r i m e n t a l c o n d i t i o n s : L i q u i d f l o w r a t e = 13.5 m3/m2 h r ; a i r f l o w r a t e = 14.8 mol/m 2 s; temperature = 293 XVI K; t o t a l p r e s s u r e = 101.3 kPa; [ N a + ] = 1.20 kmol/m 3; [OH ] = 0.75 t o 0.56 kmol/m 3; CO2 c o n c e n t r a t i o n = 4.1 t o 2.0%.) 211 F i g u r e 7.2: Comparison of R v v a l u e s o b t a i n e d e x p e r i m e n t a l l y from model column t e s t s and from f i r s t p r i n c i p l e s . ( E x p e r i m e n t a l c o n d i t i o n s : L i q u i d f l o w r a t e = 13.5 m3/m2 h r ; a i r f l o w r a t e = 14.8 mol/m 2 s; temperature = 293 K; t o t a l p r e s s u r e = 101.3 kPa; [ N a + ] = 1.20 kmol/m 3.) 213 F i g u r e 7.3: S p e c i f i c a b s o r p t i o n r a t e ( R v ) as a f u n c t i o n of CO2 c o n c e n t r a t i o n i n the gas phase and OH c o n c e n t r a t i o n . The p o i n t s and s o l i d l i n e s a r e o b t a i n e d from e x p e r i m e n t s and t h e o r e t i c a l c a l c u l a t i o n s , r e s p e c t i v e l y . The d o t t e d l i n e denotes t y p i c a l R v v a l u e s a l o n g the column f o r Run T2. ( E x p e r i m e n t a l c o n d i t i o n s : L i q u i d f l o w r a t e = 13.5 m3/m2 h r ; a i r f l o w r a t e = 14.8 mol/m 2 s; temperature = 293 K; t o t a l p r e s s u r e = 101.3 kPa; [ N a + ] = 1 .20 kmol/m 3.) 215 F i g u r e 7.4: A c t u a l ( p o i n t s ) and p r e d i c t e d ( s o l i d l i n e s ) of CO2 and NaOH c o n c e n t r a t i o n s i n the f u l l - l e n g t h a b s o r b e r f o r Run T2. ( E x p e r i m e n t a l c o n d i t i o n s : L i q u i d f l o w r a t e = 13.5 m3/m2 h r ; a i r f l o w r a t e = 14.8 mol/m 2 s; temperature = 293 K; t o t a l p r e s s u r e = 101.3 kPa; [ N a + ] = 1 .20 kmol/m 3. ) 218 F i g u r e 7.5: A c t u a l ( p o i n t s ) and PPT p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and NaOH ( d o t t e d l i n e ) c o n c e n t r a t i o n s i n the f u l l - l e n g t h a b s o r b e r f o r Run T7* O p e r a t i n g c o n d i t i o n s : a i r f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; CO2 c o n c e n t r a t i o n = 1.25%(top) and 15.45%(bottom); [OH~] = 2.0(top) and 0.14(bottom) kmol/m 3 223 F i g u r e 7.6: A c t u a l ( p o i n t s ) and PPT p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and NaOH ( d o t t e d l i n e ) c o n c e n t r a t i o n s i n the f u l l - l e n g t h a b s o r b e r f o r Run T8. O p e r a t i n g c o n d i t i o n s : a i r f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; C 0 2 c o n c e n t r a t i o n = 1.7%(top) and 18.6% (bottom); [OH ] = 2.5(top) and 0.18 (bottom) kmol/m 3 224 F i g u r e 7.7: A c t u a l ( p o i n t s ) and PPT p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and NaOH ( d o t t e d l i n e ) XVll c o n c e n t r a t i o n s i n the f u l l - l e n g t h a b s o r b e r f o r Run T9. O p e r a t i n g c o n d i t i o n s : a i r f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h r ; C0 2 c o n c e n t r a t i o n =_1.0%(top) and 18.45%(bottom); [OH ] = 2.0(top) and 0.37(bottom) kmol/m 3 225 F i g u r e 7.8: A c t u a l ( p o i n t s ) and PPT p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and NaOH ( d o t t e d l i n e ) c o n c e n t r a t i o n s i n the f u l l - l e n g t h a b s o r b e r f o r Run T10. O p e r a t i n g c o n d i t i o n s : a i r f l o w c a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h r ; C 0 2 c o n c e n t r a t i o n = 1.75%(top) and 15.2%(bottom); [OH -] = 1.5(top) and 0.24 (bottom) kmol/m 3 226 F i g u r e 7.9: Column tem p e r a t u r e measured from the f u l l - l e n g t h ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T7. O p e r a t i n g c o n d i t i o n s : a i r f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; C 0 2 c o n c e n t r a t i o n = 1.25% (t o p ) and 15.45% (bottom); [OH ] = 2.0(top) and 0.14 (bottom) kmol/m 3 227 F i g u r e 7.10: Column tem p e r a t u r e measured from the f u l l -l e n g t h ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T8. O p e r a t i n g c o n d i t i o n s : a i r f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; C 0 2 c o n c e n t r a t i o n = 1 . 7 % ( t o p ) and 18.6% (bo t t o m ) ; [OH ] = 2.5 (top) and 0.18 (bottom) kmol/m 3 228 F i g u r e 7.11:. Column tem p e r a t u r e measured from the f u l l -l e n g t h ( s o l i d c i r c l e s ) and PPM column (open s q u a r e s ) f o r Run T9. O p e r a t i n g c o n d i t i o n s : a i r f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h r ; C 0 2 c o n c e n t r a t i o n = 1.0%(top) and 18.45% (bottom); [OH ] = 2.0(top) and 0.37 (bottom) kmol/m 3 229 F i g u r e 7.12: Column t e m p e r a t u r e measured from the f u l l -l e n g t h ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T10. O p e r a t i n g c o n d i t i o n s : a i r f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h r ; C 0 2 c o n c e n t r a t i o n = 1.75%(top) and 15.2% (bo t t o m ) ; [OH~] = 1.5(top) and 0.24(bottom) kmol/m 3 230 F i g u r e 7.13: Column performance a t low l o a d i n g . MEA (Run T21 - open s q u a r e s ) vs AMP (Run T27 - s o l i d c i r c l e s ) . O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = XVlll 11.1 mol/m^  s; liquid flow rate =9.5 m-Vm hr; total amine concentration = 2.0 kmol/m2; inlet gas C 0 2 concentration = 19.0%; inlet C 0 2 loading = 0.02 moles of C 0 2 / mole of amine 234 F i g u r e 7.14: Column performance a t h i g h l o a d i n g . AMP (Run T28 - s o l i d c i r c l e s ) v s MEA (Run T18 - open s q u a r e s ) . O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l amine c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 19.15%; o u t l e t C 0 2 l o a d i n g = 0.583 moles of C 0 2 / mole of amine 235 F i g u r e 7.15: C 0 2 c o n c e n t r a t i o n p r o f i l e of Run #S70 without a n t i f o a m i n g agent (open c i r c l e s ) and Run #S94 with a n t i f o a m i n g agent ( s t a r s ) . O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e =14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l amine c o n c e n t r a t i o n = 2.0 kmol/m 2 238 F i g u r e 7.16: A c t u a l ( p o i n t s ) and p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and l i q u i d l o a d i n g ( d o t t e d l i n e ) i n t he f u l l - l e n g t h a b s o r b e r f o r Run T23. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e =14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 15.5%; i n l e t l i q u i d l o a d i n g = 0 mol C0 2/mol AMP 241 F i g u r e 7.17: A c t u a l ( p o i n t s ) and p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and l i q u i d l o a d i n g ( d o t t e d l i n e ) i n t he f u l l - l e n g t h a b s o r b e r f o r Run T24. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e =14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9 . 5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 15.5%.; i n l e t l i q u i d l o a d i n g = 0.147 mol C0 2/mol AMP 242 F i g u r e 7.18: A c t u a l ( p o i n t s ) and p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and l i q u i d l o a d i n g ( d o t t e d l i n e ) i n t he f u l l - l e n g t h a b s o r b e r f o r Run T25. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e =14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 18.9%; i n l e t l i q u i d l o a d i n g = 0.152 mol C0 2/mol AMP 243 F i g u r e 7.19: A c t u a l ( p o i n t s ) and p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and l i q u i d l o a d i n g ( d o t t e d l i n e ) XIX i n the f u l l - l e n g t h a b s o r b e r f o r Run T26. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e =14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas CO2 c o n c e n t r a t i o n = 18.65%; i n l e t l i q u i d l o a d i n g = 0.022 mol C0 2/mol AMP 244 F i g u r e 7.20: A c t u a l ( p o i n t s ) and p r e d i c t e d v a l u e s of CO2 ( s o l i d l i n e ) and l i q u i d l o a d i n g ( d o t t e d l i n e ) i n the f u l l - l e n g t h a b s o r b e r f o r Run T27. • O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e =11.1 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas CO2 c o n c e n t r a t i o n = 19.0%; i n l e t l i q u i d l o a d i n g = 0.021 mol C0 2/mol AMP 245 F i g u r e 7.21: A c t u a l ( p o i n t s ) and p r e d i c t e d v a l u e s of CO2 ( s o l i d l i n e ) and l i q u i d l o a d i n g ( d o t t e d l i n e ) i n the f u l l - l e n g t h a b s o r b e r f o r Run T30. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 11-1 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n =2.0 kmol/m 2; i n l e t gas CO2 c o n c e n t r a t i o n = 19.0%; i n l e t l i q u i d l o a d i n g = 0.29 mol C0 2/mol AMP ......246 F i g u r e 7.22: Column tem p e r a t u r e measured from the f u l l -l e n g t h ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T23. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e =14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas CO2 c o n c e n t r a t i o n = 15.5%; i n l e t l i q u i d l o a d i n g = 0 mol C0 2/mol AMP^ 247 F i g u r e 7*23: Column t e m p e r a t u r e measured from the f u l l -l e n g t h ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T24. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 15.5%; i n l e t l i q u i d l o a d i n g = 0.147 mol C0 2/mol AMP 248 F i g u r e 7.24: Column t e m p e r a t u r e measured from the f u l l -l e n g t h ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T25. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 18.9%; i n l e t l i q u i d l o a d i n g = 0.152 mol C0 2/mol AMP 249 XX F i g u r e 7 .25 : Column temperature measured from the f u l l -l e n g t h ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T26. O p e r a t i n g c o n d i t i o n s : gas flow r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 18.65%; i n l e t l i q u i d l o a d i n g = 0.022 mol C0 2/mol AMP 250 F i g u r e 7.26: Column temperature measured from the f u l l -l e n g t h ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T27. O p e r a t i n g c o n d i t i o n s : gas fl o w r a t e = 11.1 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m*2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 19.0%; i n l e t l i q u i d l o a d i n g = 0.021 mol C0 2/mol AMP 251 F i g u r e 7.27: Column temperature measured from the f u l l -l e n g t h ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T30. O p e r a t i n g c o n d i t i o n s : gas fl o w r a t e = 11.1 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 19.0%; i n l e t l i q u i d l o a d i n g = 0.29 mol C0 2/mol AMP 252 XXI ACKNOWLEDGEMENTS The c o m p l e t i o n of t h i s t h e s i s owes d e e p l y t o the e f f o r t s of many i n d i v i d u a l s . I would l i k e t o thank them as f o l l o w s : * Dean A x e l Meisen and Dr. C. J i m Lim f o r t h e i r s u p e r v i s i o n , c o n t i n u o u s g u i d a n c e , wise s u g g e s t i o n s and encouragement; * The f a c u l t y members and s u p p o r t i n g s t a f f a t the Chemical E n g i n e e r i n g Department, UBC, f o r t h e i r a s s i s t a n c e i n many ways over the d u r a t i o n when t h i s work was b e i n g completed; * My p a r e n t s , b r o t h e r s and s i s t e r s f o r t h e i r c o n t i n u o u s l o v e and encouragement. The f i n a n c i a l s u p p o r t p r o v i d e d by the N a t u r a l S c i e n c e and E n g i n e e r i n g Research C o u n c i l of Canada i s g r a t e f u l l y acknowledged. F i n a l l y , I want t o thank my w i f e C h r i s t i n e f o r her l o v e and u n d e r s t a n d i n g over the p a s t few y e a r s . Her c o n t i n u o u s encouragement and c o n f i d e n c e i n me a r e more than v i t a l t o the s u c c e s s of t h i s t h e s i s . 1 CHAPTER 1  INTRODUCTION Most n a t u r a l gas p r o c e s s i n g p l a n t s , p e t r o l e u m r e f i n e r i e s , and many c h e m i c a l p r o d u c t i o n p l a n t s use gas a b s o r p t i o n p r o c e s s e s f o r removing a c i d gases (such as C 0 2 , H 2S) from t h e i r streams [ 1 - 1 2 ] . Some major i n d u s t r i a l p r o c e s s e s t h a t need a c i d gas t r e a t i n g are l i s t e d i n Table 1.1 [12] and t y p i c a l c o m p o s i t i o n s of some c o r r e s p o n d i n g gas streams a r e shown i n T a b l e s 1.2 t o 1.4. As can be seen from t h e s e t a b l e s , s u b s t a n t i a l amounts of a c i d gases have t o be removed b e f o r e the streams can be u t i l i z e d or marketed. In the case of n a t u r a l gas, which i s one of the w o r l d ' s most e x t e n s i v e and c l e a n e s t energy s o u r c e s , the m a j o r i t y of raw gases c o n t a i n s i g n i f i c a n t amounts of C 0 2 and H 2S. A c c o r d i n g t o s t a t i s t i c s p u b l i s h e d i n 1990 i n the O i l & Gas J o u r n a l [121, 122], more than 0.14 t r i l l i o n m 3 (5.04 t r i l l i o n f t 3 ) and 2.0 t r i l l i o n m 3 (70.0 t r i l l i o n f t 3 ) of n a t u r a l gas a r e b e i n g produced a n n u a l l y i n Canada and w o r l d w i d e , r e s p e c t i v e l y . (The proven n a t u r a l gas r e s e r v e s worldwide ( e x c l u d i n g communist c o u n t r i e s ) and of Canada are T a b l e 1 . 1 : Major i n d u s t r i a l p r o c e s s e s r e q u i r i n g a c i d gas t r e a t i n g [ 1 2 ] . Process Acid gases to treating* Common cleanup targets (% acid gas) Hydrogen manufacture Petroleum desulfurization Coal liquefaction Chemicals Ammonia manufacture ( H 2 / N 2 mixture) Natural gas purification Pipeline gas LNG feedstock Syn gas for chemicals (H 2/CO) Coal gasification SNG (high Btu gas) Intermediate Bin gas Low Um gas Oil desulfurization Refinery fuel gas treating Ethylene manufacture (steam cracker gas treating) Flue gas desulfurization Utilities (electric) Refineries, etc. COj C 0 2 + H 2 S + COS COj C 0 2 +HjS + COS H 2 S , C 0 2 l COS, RSH, etc. COj , H : S , COS ll,S HjS, C O j , COS H 2 S, C 0 2 SO, <0.1%CO 2 10 ppm H 2 S < 16 ppm C 0 2 + CO 0.01 ppm H 2 S <4 ppm H 2 S ; < 1% C 0 2 1-2 ppm HjS; <50 ppm C 0 2 <500 ppmCO 2 ;<0 .01 ppm H 2 S 500 ppm CO 2 ;0 .01 ppm H 2 S 100 ppm I12S 100 ppm l l 2 S 100ppmH 2 S ~1 ppm H 2 S , 1 ppm C 0 2 90% removal 3 Table 1.2: T y p i c a l composition of Canadian, Thai and American n a t u r a l gases (dry b a s i s , mole % ) . Canada T h a i l a n d US Compound F t . S t. John East C a l g a r y Erawan "B" S t r u c t u r e Wyoming 85.34 54.40 63.34 65.60 71.15 c 2 4.50 0.35 10.61 5.82 2.01 c 3 1 .50 0.12 5.17 2.87 0.49 ic 4 0.25 0.01 1 .07 0.65 0.07 c 5 0.48 0.04 0.89 0.64 0.23 0.83 0.00 0.81 0.54 0.25 co2 2.41 13.77 17.20 23.06 17.56 H2S 4.37 29.12 0.00 0.00 3.76 N 2 0.32 2.13 0.90 0.81 4.20 H 2 0.00 0.00 0.00 0.00 0.28 * from Younger [149] ** from Meisen [3] *** from A s t a r i t a et a l . [12] 4 T a b l e 1.3: T y p i c a l c o m p o s i t i o n of pr o d u c t gas from n a t u r a l gas steam r e f o r m i n g p r o c e s s [ 1 2 ] . Component Mole % ( d r y b a s i s ) H 2 58.3 N 2 18.3 co 2 20.4 CO 1.0 CH 4 1 .7 Ar 0.3 Tab l e 1.4: T y p i c a l c o m p o s i t i o n of p r o d u c t gas from a c o a l g a s i f i c a t i o n p r o c e s s , F l e x i c o k e r [ 1 2 ] . Component Mole % ( d r y b a s i s ) H 2 18.2 N 2 50.0 C 0 2 11.4 CO 17.9 CH 4 1 .4 H 2 S 1.0 COS 0.02 NH 3 0.06 5 2.7 and 68.6 t r i l l i o n m 3, r e s p e c t i v e l y [ 1 2 1 , 122].) For a t y p i c a l gas p r o c e s s i n g p l a n t which p r o c e s s e s n a t u r a l gas c o n t a i n i n g 10 t o 20 % of a c i d g ases, the c a p i t a l and o p e r a t i n g c o s t s of a c i d gas removal can be as h i g h as one q u a r t e r t o one h a l f of t h e t o t a l c o s t [ 1 4 7 ] . In the manufacture of hydrogen, v e r y l a r g e volumes of C 0 2 must be removed from the p r o d u c t stream b e f o r e i t can be marketed or used as a f e e d s t o c k f o r o t h e r c h e m i c a l s such as ammonia. The C 0 2 removal r e q u i r e m e n t s depend l a r g e l y on the p r o c e s s used and the p l a n t f e e d s t o c k s which a r e m o s t l y l i g h t or heavy hydrocarbons or c o a l . For example, i n the p r o d u c t i o n of s y n t h e s i s gas (a m i x t u r e of H 2 and N 2 f o r p r o d u c i n g N H 3 ) , the C 0 2 removal requirement ranges from 1.22 t o n s C 0 2 / t o n of s y n t h e s i s gas produced from steam r e f o r m i n g of n a t u r a l gas t o 2.49 t o n s C 0 2 / ton of s y n t h e s i s gas made by the p a r t i a l o x i d a t i o n of heavy f u e l o i l . The amounts of C 0 2 t o be removed a r e s i g n i f i c a n t , r a n g i n g up t o over 20,000 t o n s / day f o r l a r g e p l a n t s [ 1 9 ] . A c c o r d i n g t o Weinberg e t a l . [ 1 0 0 ] , worldwide a n n u a l p r o d u c t i o n of H 2 and N H 3 a r e w e l l over 160 b i l l i o n m 3 and 100 m i l l i o n t o n s , r e s p e c t i v e l y . F u r t h e r m o r e , t h e i r p r o d u c t i o n r a t e s a r e s t i l l g rowing a t more than 10 % per y e a r . S t r a t t o n and Teper [148] have e s t i m a t e d the c a p i t a l c o s t a s s o c i a t e d w i t h the C 0 2 6 s e p a r a t i o n u n i t f o r commercial s y n t h e s i s gas p l a n t s t o be up t o 40 % of the t o t a l c o s t ( c . f . T a b l e 1.5). As can be seen from t h e s e f i g u r e s , a s i g n i f i c a n t p o r t i o n of the p r o c e s s i n g e f f o r t s i s d i r e c t l y a s s o c i a t e d w i t h C O 2 s e p a r a t i o n i n p r o d u c i n g b a s i c c h e m i c a l p r o d u c t s . For c o a l g a s i f i c a t i o n p l a n t s p r o d u c i n g h i g h - B t u s y n t h e t i c n a t u r a l gas, a c i d gas removal systems a l s o account f o r a s i z e a b l e p e r c e n t a g e of the t o t a l p l a n t i n v e s t m e n t . A c c o r d i n g t o Penner e t a l . [ 8 3 ] , about 30 % of the p l a n t i n v e s t m e n t i s a l l o c a t e d t o p u r i f i c a t i o n p r o c e s s e s ; the g a s i f i c a t i o n s e c t i o n r e q u i r e s o n l y 10 t o 15 %. F u r t h e r m o r e , the o p e r a t i n g c o s t s f o r the p u r i f i c a t i o n p r o c e s s e s a r e s u b s t a n t i a l . I t i s t h e r e f o r e c l e a r t h a t a c i d gas s e p a r a t i o n i s one of the most im p o r t a n t p r o c e s s i n g s t e p s i n the p r o d u c t i o n s of a v a r i e t y of b a s i c c h e m i c a l s . To summarize the importance of gas t r e a t i n g , the statement by A s t a r i t a , Savage and B i s i o [12] may be quoted: "...The major traditional uses of gas treating for CO2 and removal in hydrogen manufacture, ammonia production, petroleum refining, and natural gas purification are expected to experience significant growth in I the coming decades. The importance of gas treating will grow faster than industrial activity as a whole, owning to the growing use of heavier more sulfurous petroleum, coal, shale, and tar sands as feedstocks and fuels. Large quantities of acid gases will have to be removed from these new energy sources. Moreover, the complexity of gas treating will increase since the acid gases will contain large quantities of CO2, significant amounts of H2S, and troublesome levels of other sulfur contaminants such as COS. These changes will require improved energy-efficient treating technology for both simultaneous and selective gas treating. In the case of natural gas, new gas finds are expected to be at greater depths and in more remote locations than was the case in the past. New natural gas is expected to be more highly contaminated with and CO2. These gases will require extensive treating to make them suitable for pipelining or conversion to LNG, methanol, or gasoline. Remote production of gas (e.g. offshore or on permafrost) will require improved technology with emphasis on small size units of light weight and high reliability." 8 Table 1.5: C a p i t a l cost breakdown f o r a commercial s c a l e plant producing synthesis gas (N 2+3H 2) from steam reforming f o r making ammonia [148]. Plant s e c t i o n C a p i t a l cost as % of the t o t a l Primary and secondary reforming 51.4 % S h i f t and Methanation 8.6 % C0 2 removal 40.0 % 9 1.1 ACID GAS ABSORPTION BY CHEMICAL SOLVENTS Even though many a c i d gas removal p r o c e s s e s a r e a v a i l a b l e , over 90% of e x i s t i n g p l a n t s use c h e m i c a l a b s o r p t i o n [ 3 , 4, 6, 10, 11]. I t s p o p u l a r i t y stems from h i g h s e p a r a t i o n r a t e s and c a p a c i t i e s which l e a d t o r e l a t i v e l y low o v e r a l l c o s t s [ 8 ] . The most commonly used c h e m i c a l s o l v e n t s a r e l i s t e d i n Table 1.6 [ 1 2 ] . Amine s o l u t i o n s a r e employed i n more than 60% of the e x i s t i n g p l a n t s , e s p e c i a l l y i n n a t u r a l gas p r o c e s s i n g p l a n t s . The second major group i s based on aqueous p o t a s s i u m c a r b o n a t e s o l u t i o n s w i t h i n o r g a n i c or o r g a n i c a d d i t i v e s [ 1 1 ] . Sodium h y d r o x i d e s o l u t i o n s a r e g e n e r a l l y o n l y used as a f i n a l t r e a t m e n t s t e p [ 1 2 ] . A t y p i c a l f l o w sheet of an i n d u s t r i a l a c i d gas removal system u t i l i z i n g a c h e m i c a l a b s o r b e n t i s shown i n F i g u r e 1.1. The sour gas, which e n t e r s the u n i t t h r o u g h an i n l e t s e p a r a t o r where e n t r a i n e d l i q u i d and s o l i d p a r t i c u l a t e s a r e removed, f l o w s from the bottom of the a b s o r b e r upwards a g a i n s t a c o u n t e r - c u r r e n t stream of the l e a n s o l u t i o n . The a c i d gases a r e absorbed and t h e t r e a t e d (or "sweet") gas l e a v e s the t o p of the a b s o r b e r . 10 Table 1.6: Common a l k a l i n e reagents used as chemical s o l v e n t s [12]. ^ c — c — O H Monoethanolamine N — H (MEA) \ H yC—C—OH Diethanolamine Nr—H (DEA) (DIPA) C — C — O H OH yQ—C—OH Diisopropanolamine Nr—H ^ C — C — C I OH yZ—C—O— C — C — O H P, fi' Hydroxyaminoethylether Nr—H (DGA) \ H Potassium carbonate K 2 C 0 3 (with promoters) / C - c / Potassium glycinate Nr—H OK ^ H Caustic NaOH F i g u r e 1.1: T y p i c a l f l o w s h e e t f o r gas sweetening by c h e m i c a l r e a c t i o n [ 1 3 ] . 12 The a c i d gas l o a d e d ( " r i c h " ) s o l u t i o n f l o w s from the bottom of the a b s o r b e r and passes t h r o u g h the l e a n - r i c h heat exchanger where i t i s heated by the h o t , r e c y c l e d l e a n s o l u t i o n . I t then e n t e r s the t o p of the s t r i p p e r column. In some c a s e s , a f l a s h tank i s i n s t a l l e d upstream of the heat exchanger t o desorb d i s s o l v e d h ydrocarbons and some of the a c i d gases by l e t t i n g down the p r e s s u r e of the r i c h s tream. Upon e n t r y i n t o t h e s t r i p p e r , some of the absorbed a c i d gases a r e f l a s h e d . The s o l u t i o n then f l o w s downward a g a i n s t a c o u n t e r - c u r r e n t f l o w of water vapor g e n e r a t e d i n the r e b o i l e r . The s t r i p p i n g vapor removes most of the r e m a i n i n g a c i d gases from the r i c h stream. The overhead m i x t u r e l e a v e s the s t r i p p e r t h r o u g h a condenser where most of the water vapor i s condensed and r e t u r n e d t o the s t r i p p e r as r e f l u x . The l e a n s o l u t i o n , which l e a v e s the bottom of t h e s t r i p p e r , exchanges heat w i t h the r i c h s o l u t i o n i n the l e a n - r i c h heat exchanger and then passes through a c o o l e r b e f o r e b e i n g pumped t o the a b s o r b e r . 13 1.2 DESIGN OF CHEMICAL GAS ABSORPTION COLUMNS In g e n e r a l , the most i m p o r t a n t d e s i g n problem of a gas a b s o r p t i o n p r o c e s s i s posed by the a b s o r p t i o n column because i t has the g r e a t e s t e f f e c t on the c a p i t a l and o p e r a t i n g c o s t of the p r o c e s s . A l t h o u g h many d i f f e r e n t t y p e s of g a s - l i q u i d c o n t a c t o r s have been d e v e l o p e d , o n l y packed and t r a y columns have found s i g n i f i c a n t i n d u s t r i a l use as gas a b s o r b e r s . More r e c e n t l y , packed towers a r e g a i n i n g an i n c r e a s i n g share of the market due t o the development of h i g h - c a p a c i t y , h i g h -e f f i c i e n c y p a c k i n g s [ 1 9 ] . These new p a c k i n g a r e a l s o used t o r e t r o f i t e x i s t i n g u n i t s i n o r d e r t o improve column c a p a c i t i e s . I n d u s t r i a l d e s i g n methods f o r s i z i n g packed a b s o r p t i o n towers a r e g i v e n by the NGPSA E n g i n e e r i n g Data Book [ 1 3 ] , Maddox [ 4 ] , and K o h l and R i e s e n f e l d [ 1 5 ] . In a d d i t i o n , the l a t e s t d a t a and methods f o r the s e l e c t i o n and d e s i g n of i n d u s t r i a l gas t r e a t i n g p r o c e s s e s have been c o m p i l e d by Newman [ 1 6 ] . T h e o r e t i c a l d e s i g n approaches a r e p r e s e n t e d by A s t a r i t a [17] and Danckwerts [ 1 8 ] . R e c e n t l y , b o t h the i n d u s t r i a l and t h e o r e t i c a l d e s i g n approaches were combined by A s t a r i t a , Savage and B i s i o [ 1 9 ] . 14 Nevertheless, the design of many gas absorbers using, for example, amines or activated hot potassium carbonate i s s t i l l largely based on experience or "rules of thumb" [14, 22, 124] despite the fact that absorption with chemical reaction has been studied for over sixty years. (Hatta's work [23] was f i r s t published in 1928.) The main reason for t h i s i s the lack of fundamental design data, i . e . mass transfer c o e f f i c i e n t s , i n t e r f a c i a l areas, reaction k i n e t i c s , and physico-chemical properties. Another reason i s the lack of confidence in the t h e o r e t i c a l design procedures [15,24] which are often complex or based on doubtful assumptions [4,22]. For instance, using the t h e o r e t i c a l method recommended by Danckwerts [18] and the data given by Beddome [21], DeCoursey showed that the height of absorbers would be overestimated by as much as a factor of four [20]. This indicates that considerable discrepancies, may exist between th e o r e t i c a l predictions and actual requirements [25]. To quote from Maddox [4], "Fixing the number of trays, either theoretical or actual, in the absorber is not a simple task. As a matter of fact, many authors feel that computation of the number of trays required is an exercise in futility. The calculation of rates and efficiencies of a simple absorption process is complicated enough. In the case of absorption followed by chemical reaction, the calculations 15 become exceedingly difficult". A s i m i l a r statement a l s o a p p l i e d t o d e s i g n i n g packed t o w e r s . E v i d e n c e s u p p o r t i n g t h i s o b s e r v a t i o n i s p r o v i d e d i n F i g u r e 1.2 which i s based on t y p i c a l i n d u s t r i a l d a t a [ 1 5 ] . As can be seen, most of the a b s o r b e r ( a p p r o x i m a t e l y 60 %) does not p e r f o r m a u s e f u l duty and r e p r e s e n t s an over d e s i g n of the column. 16 F i g u r e 1.2: C o n c e n t r a t i o n and temperature p r o f i l e s of a t y p i c a l i n d u s t r i a l a b s o r b e r [ 1 5 ] . 17 1.3 RESEARCH OBJECTIVES I n t h e p a s t f e w y e a r s , m u c h p r o g r e s s h a s b e e n m a d e i n t h e b a s i c u n d e r s t a n d i n g o f c h e m i c a l a b s o r p t i o n p r o c e s s e s [ 2 2 , 8 4 ] . F o r s o m e s y s t e m s l i k e C 0 2 - N a O H a n d C 0 2 -c o n v e n t i o n a l a m i n e s , a c c u r a t e , s t e a d y s t a t e s i m u l a t i o n o f g a s a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n h a s b e c o m e p o s s i b l e p r o v i d e d t h e f u n d a m e n t a l d e s i g n d a t a ( i . e m a s s t r a n s f e r c o e f f i c i e n t s , r e a c t i o n k i n e t i c s , p h y s i c o - c h e m i c a l p r o p e r t i e s , e t c . ) a r e a v a i l a b l e . U n f o r t u n a t e l y , c o m p r e h e n s i v e d a t a o n a b s o r b e r p e r f o r m a n c e u n d e r i n d u s t r i a l c o n d i t i o n s a r e r a r e l y p u b l i s h e d i n t h e o p e n l i t e r a t u r e . M o s t o f t h e p u b l i s h e d d a t a a r e i n c o m p l e t e o r i n s u f f i c i e n t t o p e r m i t s o u n d c o m p a r i s o n s w i t h t h e o r e t i c a l p r e d i c t i o n s [ 1 5 , 1 2 3 ] . T h e r e f o r e , g o o d f u l l - l e n g t h a b s o r b e r d a t a a r e r e q u i r e d t o v a l i d a t e t h e t h e o r e t i c a l p r e d i c t i o n s a n d t o g i v e c o n f i d e n c e t o i n d u s t r i a l d e s i g n . F u r t h e r m o r e , i m p r o v e m e n t s i n c h e m i c a l a b s o r p t i o n p r o c e s s e s a r e s t i l l p r o g r e s s i n g a t a f a i r l y f a s t r a t e . New a n d h i g h e r c a p a c i t y c h e m i c a l s o l v e n t s ( e . g . m i x t u r e o f a m i n e s , s t e r i c a l l y h i n d e r e d a m i n e s ) a n d h i g h - e f f i c i e n c y m a s s t r a n s f e r e q u i p m e n t ( e . g . s t r u c t u r e d p a c k i n g s ) a r e i n t r o d u c e d e v e r y y e a r . E n o r m o u s a m o u n t s o f f u n d a m e n t a l d e s i g n d a t a 18 would be needed t o p e r m i t the complete s i m u l a t i o n of such a b s o r b e r s . The p r i n c i p a l o b j e c t i v e of t h i s t h e s i s i s t o d e v e l o p a new d e s i g n concept f o r i n d u s t r i a l a b s o r b e r s w i t h c h e m i c a l r e a c t i o n . T h i s new d e s i g n c o n c e p t i s s u b s e q u e n t l y c a l l e d the " P i l o t P l a n t Technique" or PPT. The concept depends o n l y on l a b o r a t o r y - s c a l e , p i l o t p l a n t e x p e r i m e n t s and r e q u i r e s a minimum knowledge of the a b s o r p t i o n system. T h i s new d e s i g n c o n c e p t i s s u b s e q u e n t l y v a l i d a t e d by a p p l y i n g i t t o a f u l l -l e n g t h a b s o r b e r (6.6 m h i g h ) i n which C 0 2 was removed from a i r u s i n g aqueous s o l u t i o n s of sodium h y d r o x i d e and 2-amino-2-methy l - 1 - p r o p a n o l (AMP), which i s a s t e r i c a l l y h i n d e r e d amine. These a b s o r p t i o n systems were s e l e c t e d because they a r e i n d u s t r i a l l y i m p o r t a n t and used e x t e n s i v e l y [17, 18, 7 6 ] . To narrow the scope of the s t u d y , the r e s e a r c h was r e s t r i c t e d o n l y t o packed columns. T h i s d i s s e r t a t i o n a l s o r e p o r t s e x t e n s i v e e x p e r i m e n t a l d a t a on gas and l i q u i d c o n c e n t r a t i o n s as w e l l as temperature p r o f i l e s f o r C 0 2 - NaOH, C 0 2 - MEA and C 0 2 - AMP a b s o r b e r s of v a r i o u s h e i g h t s . In a d d i t i o n , comparisons between the e x p e r i m e n t a l d a t a and t h e o r e t i c a l p r e d i c t i o n s a r e p r e s e n t e d 1 9 f o r the C 0 2 _NaOH and C0 2-MEA systems because t h e i r fundamental d e s i g n d a t a are a v a i l a b l e . S i n c e the C0 2~AMP system i s one of the systems used t o v a l i d a t e the PPT c o n c e p t , the s o l u b i l i t y of C 0 2 i n AMP s o l u t i o n s had t o be d e t e r m i n e d . P r e v i o u s l y r e p o r t e d s o l u b i l i t y d a t a were t o o l i m i t e d and d i d not c o v e r the t y p i c a l o p e r a t i n g ranges of a b s o r b e r s . T h i s t h e s i s i s d i v i d e d i n t o n i n e c h a p t e r s . Chapter 2 i s a g e n e r a l l i t e r a t u r e r e v i e w of s u b j e c t s r e l a t e d t o gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n . The d e t a i l s of the t h e o r e t i c a l a b s o r b e r d e s i g n p r o c e d u r e , which i s based on p r e v i o u s l y p u b l i s h e d work, and the development of the P i l o t P l a n t Technique a r e g i v e n i n Chapter 3 . Chapter 4 i s a s e l f c o n t a i n e d c h a p t e r and r e p o r t s t h e s t u d y of C 0 2 s o l u b i l i t y i n AMP s o l u t i o n s . Chapter 5 p r e s e n t s the d e t a i l s of the e x p e r i m e n t a l equipment and the r e l a t e d o p e r a t i n g p r o c e d u r e s . In Chapter 6 the r e s u l t s , which were o b t a i n e d from the f u l l -l e n g t h a b s o r b e r and the t h e o r e t i c a l d e s i g n p r o c e d u r e g i v e n i n Chapter 3 , a r e d i s c u s s e d . Chapter 7 p r e s e n t s the v e r i f i c a t i o n r e s u l t s of t h e P i l o t P l a n t T e c h nique. C o n c l u s i o n s drawn from t h i s r e s e a r c h p r o j e c t a r e summarized i n C h a p t e r 8 . The t h e s i s t e r m i n a t e s w i t h a summary s u g g e s t i o n s f o r f u t u r e work i n C h a p t e r 9 . 21 CHAPTER 2 LITERATURE REVIEW The c o n t e n t s i n t h i s c h a p t e r a r e g e n e r a l r e v i e w s of the s u b j e c t s r e l a t e d t o t h e d e s i g n a s p e c t s of gas a b s o r b e r s w i t h c h e m i c a l r e a c t i o n . I n the l a t e r c h a p t e r s , more s p e c i f i c r e v i e w s a r e a l s o g i v e n where n e c e s s a r y . 2.1 GAS ABSORPTION WITH CHEMICAL REACTION Gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n o c c u r s when a r e a c t a n t i n t h e gas phase and a n o t h e r r e a c t a n t i n the l i q u i d phase a r e brought i n t o c o n t a c t . L e t A denote a r e a c t a n t from the gas phase and B denote a r e a c t a n t i n the l i q u i d phase. A c c o r d i n g t o A s t a r i t a [17] and Danckwerts [ 1 8 ] , the f o l l o w i n g major s t e p s o c c u r d u r i n g a b s o r p t i o n ( a l s o see F i g u r e 2.1): ( i ) T r a n s f e r of A from the gas phase by d i f f u s i o n t o the g a s / l i q u i d i n t e r f a c e and d i s s o l u t i o n i n t o the l i q u i d f i l m . ( i i ) S i m u l t a n e o u s d i f f u s i o n and c h e m i c a l r e a c t i o n i n the l i q u i d phase. 22 Gas Absorption with CheMical Reaction Liquid reaction products / c A B / Mass transfer \ i n t t r f « o < F i g u r e 2 . 1 : Schematic of gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n system. 23 ( i i i ) D i f f u s i o n of a l l components i n the l i q u i d due t o c o n c e n t r a t i o n g r a d i e n t s . ( i v ) Heat t r a n s f e r from the l i q u i d phase t o the gas phase due t o the temperature g r a d i e n t which i s caused by the h e a t s of s o l u t i o n and r e a c t i o n . S t e p s ( i i ) t o ( i v ) t a k e p l a c e s i m u l t a n e o u s l y a f t e r s t e p ( i ) . The o v e r a l l a b s o r p t i o n r a t e i s s i g n i f i c a n t l y a f f e c t e d by the c h e m i c a l r e a c t i o n s i n c e the r e a c t a n t a c t s as a s i n k f o r the s o l u t e A. As a r e s u l t , c h e m i c a l a b s o r p t i o n p r o c e s s e s have much h i g h e r r a t e s and c a p a c i t i e s than p h y s i c a l a b s o r p t i o n p r o c e s s e s . In g e n e r a l , the c h e m i c a l r e a c t i o n i n the l i q u i d f i l m can be s i m p l i f i e d by r e c o g n i z i n g c h a r a c t e r i s t i c r e a c t i o n regimes [ 1 , 17-19, 20, 23, 2 6 ] . These regimes, which are d e s c r i b e d i n d e t a i l by L e v e n s p i e l [30,31] and Godfrey [ 3 2 ] , a r e summarized below. S t a r t i n g from th e i n s t a n t a n e o u s c h e m i c a l r e a c t i o n regime and p r o c e e d i n g t o the e x t r e m e l y slow r e a c t i o n regime, t h e i r c o r r e s p o n d i n g c o n c e n t r a t i o n p r o f i l e s are p r e s e n t e d i n F i g u r e 2.2. 24 | Gas film Liquid I film I Reaction plane 1 Gas Liquid | s i film i film LL l 1 ^Reaction! I N . 1 > plane J Reaction zone ® j^ High and constant ® Reaction only in film Phase inteffaceV r \ i f Any value 1 i f 1 1 ) ! \ 1 1 1 — Gas Liquid — In film and main body Reaction only in main body oi liquid F i g u r e 2 . 2 : I n t e r f a c e b e h a v i o r f o r gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n [ 3 0 ] , 25 Regimes A and B. When the r e a c t i o n i s i n s t a n t a n e o u s or v e r y f a s t , the r e a c t i o n p l a n e l i e s e i t h e r w i t h i n the l i q u i d f i l m i f t he c o n c e n t r a t i o n of B, C B, i s not t o o h i g h (regime A ) , or a t the gas l i q u i d i n t e r f a c e i f C B i s h i g h enough (regime B ) . The a b s o r p t i o n r a t e i s d e t e r m i n e d p r i m a r i l y by the r a t e of d i f f u s i o n of components A and B f o r the regime A. For the regime B, the d i f f u s i o n of A t h r o u g h the gas f i l m c o n t r o l s the o v e r a l l a b s o r p t i o n r a t e . Regimes C and D. When the r e a c t i o n i s not e x t r e m e l y f a s t , but i s f a s t enough so t h a t r e a c t a n t A i s c o m p l e t e l y consumed w i t h i n the l i q u i d f i l m , the r e a c t i o n zone o c c u r s e i t h e r w i t h i n t h e l i q u i d f i l m i n case of low C B v a l u e s or near the gas l i q u i d i n t e r f a c e i n case of h i g h C B v a l u e s . Regime E and F. In t h e s e c a s e s the r e a c t i o n and mass t r a n s f e r r a t e s a r e of the same magnitude. The r e a c t i o n zone exte n d s from the g a s - l i q u i d i n t e r f a c e t o w i t h i n t h e b u l k of the l i q u i d . Regime G. The r e a c t i o n i s slow and t h e amount of d i s s o l v e d gas h e l d up i n the f i l m i s s m a l l . The mass t r a n s f e r r a t e of A i n the f i l m i s s t i l l i m p o r t a n t but the o v e r a l l p r o c e s s i s such t h a t i t can be v i s u a l i z e d as one of p h y s i c a l a b s o r p t i o n 26 f o l l o w e d by c h e m i c a l r e a c t i o n w i t h i n the b u l k of the l i q u i d phase. Regime H. The r e a c t i o n i s e x t r e m e l y slow i n t h i s c a s e . The mass t r a n s f e r r e s i s t a n c e s i n the f l u i d f i l m a r e n e g l i g i b l e due t o a low consumption r a t e of A by the r e a c t i o n i n the l i q u i d phase. As a r e s u l t , the e n t i r e l i q u i d phase becomes u n i f o r m i n c o n c e n t r a t i o n of A a t the c o n c e n t r a t i o n c o r r e s p o n d i n g t o the p a r t i a l p r e s s u r e above the l i q u i d . The r a t e of a b s o r p t i o n i s s i m p l y e q u a l t o the r a t e of r e a c t i o n w i t h i n the bu l k l i q u i d . For a g i v e n system and s e t of o p e r a t i n g c o n d i t i o n s , the f a s t e r the r e a c t i o n r a t e , the s h o r t e r the d i s t a n c e between the i n t e r f a c e and the r e a c t i o n p l a n e (or the h i g h e r the l i q u i d mass t r a n s f e r c o e f f i c i e n t ) . I n a c h e m i c a l a b s o r p t i o n column, the r e a c t i o n regime can change s i g n i f i c a n t l y a l o n g the column from i n s t a n t a n e o u s r e a c t i o n a t the t o p t o slow r e a c t i o n a t the bottom because of the v a r i a t i o n of r e a c t a n t c o m p o s i t i o n i n b o t h phases. T h i s causes the e f f e c t i v e mass t r a n s f e r c o e f f i c i e n t of the l i q u i d f i l m t o change s i g n i f i c a n t l y a l o n g the column and t h e r e f o r e makes c h e m i c a l a b s o r p t i o n more complex than p h y s i c a l a b s o r p t i o n . The e f f e c t of r e a c t i o n i n the l i q u i d f i l m on the o v e r a l l a b s o r p t i o n 2 7 r a t e i s o f t e n p r e s e n t e d i n t h e term of an "enhancement factor" w h i c h i s d e f i n e d as t h e r a t i o of t h e l i q u i d f i l m c o e f f i c i e n t f o r a b s o r p t i o n with c h e m i c a l r e a c t i o n t o t h e l i q u i d f i l m c o e f f i c i e n t f o r t h e p u r e l y p h y s i c a l a b s o r p t i o n [ 1 8 ] . 2 8 2 .2 REACTION OF CQ 2 IN CAUSTIC AND AMINE SOLUTIONS S i n c e the a b s o r p t i o n of carbon d i o x i d e i n t o c a u s t i c and amine s o l u t i o n s i s of major i n d u s t r i a l i m p o r t a n c e , the s u b j e c t has been e x t e n s i v e l y reviewed [ 1 8 ] , [ 1 9 ] , The i n d u s t r i a l a s p e c t s of t h e s e p r o c e s s e s are d i s c u s s e d by K o h l and R i e s e n f e l d [ 1 5 ] . S i n c e t h e s e two systems w i l l be used i n the p r e s e n t t h e s i s , t h e i r r e a c t i o n k i n e t i c s a r e b r i e f l y d e s c r i b e d i n the f o l l o w i n g s e c t i o n . 2 . 2 . 1 REACTION CHEMISTRY OF THE CAUSTIC - CQ 2 SYSTEM A b s o r p t i o n of carbon d i o x i d e i n t o aqueous s o l u t i o n s of c a u s t i c i s p r o b a b l y the most w i d e l y s t u d i e d system. B e f o r e the r e a c t i o n o c c u r s , C 0 2 i s p h y s i c a l l y d i s s o l v e d i n the s o l u t i o n and OH - i o n s a r e from the d i s s o c i a t i o n of the c a u s t i c . Once C 0 2 e n t e r s the s o l u t i o n , two r e a c t i o n s t e p s can o c c u r : C 0 2 + OH" => HC0 3" (a) HCO3" + OH" => C 0 3 = + H 20 (b) A c c o r d i n g t o A s t a r i t a [ 1 7 ] , r e a c t i o n (b) may be r e g a r d e d as i n s t a n t a n e o u s , whereas r e a c t i o n (a) proceeds a t a f i n i t e 29 r a t e . When a s u b s t a n t i a l amount of f r e e h y d r o x i d e i s p r e s e n t , the r e a c t i o n e q u i l i b r i u m l i e s f a r t o the r i g h t s i n c e the e q u i l i b r i u m c o n s t a n t of r e a c t i o n (b) i s l a r g e ( 5 . 9 X 1 0 + 3 m 3/kmol a t 20 °C). The b i c a r b o n a t e c o n c e n t r a t i o n may be assumed t o be z e r o whenever the h y d r o x i d e c o n c e n t r a t i o n exceeds 10~ 2 kmol/m 3 [ 1 7 ] , The o v e r a l l r e a c t i o n which t a k e s p l a c e may t h e r e f o r e be w r i t t e n a s : C 0 2 + 20H" => C 0 3 = + H 20 (c) the r a t e of which i s g i v e n by r a t e = k 2 [C0 2][OH~] Pohoreck and Moniuk [111] r e c e n t l y r e p o r t e d new r a t e c o n s t a n t d a t a f o r t h i s system. They a l s o r e v i e w e d the d a t a p r e v i o u s l y p u b l i s h e d i n the open l i t e r a t u r e . They found t h a t t h e r a t e c o n s t a n t i s not o n l y a f u n c t i o n of the a c t i v a t i o n e n e rgy, but -also the c o n c e n t r a t i o n of the i o n i c s p e c i e s i n s o l u t i o n . 30 2.2.2 REACTION CHEMISTRY OF CQ 2 - AMINE SYSTEM A c c o r d i n g t o A s t a r i t a e t a l . [19] as w e l l as o t h e r r e s e a r c h e r s , the r e a c t i o n s g o v e r n i n g the C0 2-aqueous amine system a re remarkably complex and a r e not f u l l y u n d e r s t o o d even though they have been s t u d i e d f o r more than h a l f a c e n t u r y . I t i s b e l i e v e d t h a t t h e r e a r e t h r e e p r i n c i p a l s t e p s g o v e r n i n g the system: Carbamate f o r m a t i o n : C 0 2 + 2RRNH = RRNCOO" + RRNH 2 + (d) B i c a r b o n a t e f o r m a t i o n : C 0 2 + RRNH + H 20 = HC0 3~ + RRNH 2 + (e) Carbamate r e v e r s i o n : RRNCOO" + H 20 = HC0 3~ + RRNH ( f ) where R stands f o r -C 2H 4OH and R denotes -H and -C 2H 4OH f o r p r i m a r y and secondary amines, r e s p e c t i v e l y . For p r i m a r y amines, Danckwerts [18] and A s t a r i t a e t a l . [19] s u g g e s t e d t h a t the carbamate f o r m a t i o n r e a c t i o n predominates when the C 0 2 l o a d i n g i s l e s s than about 0.5 moles of C 0 2 / mole of amine. On the o t h e r hand, the carbamate r e v e r s i o n predominates when the C 0 2 l o a d i n g exceeds about 0.5 moles of 31 CC>2 p e r m o l e o f a m i n e . T h e r e l a t i v e i m p o r t a n c e o f t h e b i c a r b o n a t e f o r m a t i o n d e p e n d s o n t h e s t a b i l i t y o f t h e c a r b a m a t e ; t h e i m p o r t a n c e o f b i c a r b o n a t e f o r m a t i o n i s i n v e r s e l y p r o p o r t i o n a l t o t h e s t a b i l i t y o f c a r b a m a t e . F o r t h e CC>2 - MEA s y s t e m , t h e r a t e o f b i c a r b o n a t e f o r m a t i o n i s r e l a t i v e l y u n i m p o r t a n t s i n c e t h e MEA c a r b a m a t e i s q u i t e s t a b l e [ 7 l ] . D a n c k w e r t s [ 1 8 ] a s w e l l a s o t h e r r e s e a r c h e r s c o n c l u d e d f r o m t h e i r e x p e r i m e n t a l r e s u l t s t h a t t h e o v e r a l l r a t e o f r e a c t i o n c a n b e a p p r o x i m a t e d a s f i r s t o r d e r w i t h r e s p e c t t o b o t h C O 2 a n d a m i n e w h e n t h e l o a d i n g i s l e s s t h a n 0 . 5 m o l e s o f C O 2 p e r m o l e o f a m i n e , i . e . r a t e a [ C 0 2 ] [ R N H 2 ] F o r o t h e r s y s t e m s s u c h a s s e c o n d a r y a m i n e s a n d s t e r i c a l l y * h i n d e r e d a m i n e s , t h e r e a c t i o n m e c h a n i s m s a r e m o r e c o m p l e x . T h e i r c a r b a m a t e s t a b i l i t y v a r i e s f r o m m o d e r a t e t o l o w b y c o m p a r i s o n w i t h t h a t o f M E A . T h e r e f o r e , t h e o v e r a l l r e a c t i o n r a t e d e p e n d s o n a l l t h r e e r e a c t i o n s . T h e u n d e r s t a n d i n g o f t h e e f f e c t o f e a c h r e a c t i o n o n t h e o v e r a l l r e a c t i o n r a t e s f o r t h e s e s y s t e m s i s s t i l l u n c l e a r w i t h r e s p e c t t o t h e * A s t e r i c a l l y h i n d e r e d a m i n e i s d e f i n e d a s a p r i m a r y a m i n e i n w h i c h t h e a m i n o g r o u p i s a t t a c h e d t o a t e r t i a r y c a r b o n a t o m , o r a s e c o n d a r y a m i n e i n w h i c h t h e a m i n o g r o u p i s a t t a c h e d t o a s e c o n d a r y o r a t e r t i a r y c a r b o n a t o m [ 7 1 ] . 32 r e a c t i o n mechanisms and r a t e c o n s t a n t s [19, 43, 120, 145]. For more d e t a i l s on the r e a c t i o n c h e m i s t r y of the s e systems, R e f e r e n c e s [ 1 8 ] , [19] and [87] s h o u l d be c o n s u l t e d . 2 . 3 D E S I G N OF PACKED ABSORBERS WITH CHEMICAL R E A C T I O N Packed a b s o r b e r s a re v e r t i c a l columns f i l l e d w i t h p a c k i n g s of l a r g e s u r f a c e a r e a s ( F i g u r e 2.3). The o p e r a t i o n may be e i t h e r c o - c u r r e n t or c o u n t e r - c u r r e n t . However, most packed a b s o r b e r s a r e o p e r a t e d c o u n t e r - c u r r e n t l y t o o b t a i n maximum c o n c e n t r a t i o n d r i v i n g f o r c e s . In c o u n t e r - c u r r e n t packed a b s o r b e r s , the absorbent i s d i s t r i b u t e d over and t r i c k l e s down th r o u g h the p a c k i n g s t h e r e b y c r e a t i n g a l a r g e s u r f a c e f o r c o n t a c t i n g w i t h the gas. The main d e s i g n o b j e c t i v e s a r e t o f i n d t h e d i a m e t e r and h e i g h t of the tower. The main s t e p s f o r d e s i g n i n g gas a b s o r b e r s w i t h c h e m i c a l r e a c t i o n a r e shown s c h e m a t i c a l l y i n F i g u r e 2.4. Routes 1, 2 and 3 i n F i g u r e 2.4 r e f e r t o E m p i r i c a l d e s i g n method, T h e o r e t i c a l d e s i g n method and d e s i g n methods based on l a b o r a t o r y models, r e s p e c t i v e l y . F i g u r e 2 . 3 : P a c k e d a b s o r b e r [86] 34 DEFINITION OF PROCESS CONDITIONS - T o t a l flow r a t e s of gas and l i q u i d - I n l e t and o u t l e t c o n d i t i o n s SPECIFY GAS-LIQUID CONTACTING SYSTEM - Type and d e t a i l s of packings OBTAIN PHYSICAL INFORMATION - D e n s i t i e s and v i s c o s i t i e s - G a s - l i q u i d e q u i l i b r i u m data DETERMINATION OF SUPERFICIAL VELOCITIES - L i q u i d s i d e - Gas side OBTAIN PHYSICAL GAS ABSORPTION PARAMETERS - Mass t r a n s f e r c o e f f i c i e n t s - I n t e r f a c i a l area - L i q u i d hold-up  OBTAIN ADDITIONAL INFORMATION D i f f u s i v i t i e s S o l u b i l i t i e s Reaction k i n e t i c s DETERMINATION OF ENHANCEMENT FACTOR DETERMINATION OF ( K ^ y ) ave DETERMINATION OF ABSORPTION RATE * . DETERMINATION OF COLUMN HEIGHT Fi g u r e 2.4: Major design procedures f o r gas absorbers with chemical r e a c t i o n . 35 The d e t a i l s of each method w i l l be d e s c r i b e d i n S e c t i o n s 2.3.1 t o 2.3.3. Once the s p e c i f i c d e s i g n problem i s d e f i n e d i n terms of the t o t a l f l o w r a t e of each phase, i n l e t and o u t l e t c o n d i t i o n s , a s u i t a b l e g a s - l i q u i d c o n t a c t i n g system can be s e l e c t e d . In g e n e r a l , t h e r e i s no s p e c i f i c c r i t e r i o n f o r s e l e c t i n g the p a c k i n g type and s i z e . However, T r e y b a l [86] suggested t h a t good p a c k i n g s s h o u l d have the f o l l o w i n g c h a r a c t e r i s t i c s : 1. Large e f f e c t i v e g a s - l i q u i d c o n t a c t i n g a r e a . 2. Large v o i d a g e . 3. C h e m i c a l l y i n e r t n e s s . 4. S t r u c t u r a l s t r e n g t h t o p e r m i t easy h a n d l i n g and i n s t a l l a t i o n . 5. Low c o s t . The next d e s i g n s t e p i s t o o b t a i n p h y s i c a l i n f o r m a t i o n such as d e n s i t y and v i s c o s i t y of both phases i n o r d e r t o determine t h e i r s u p e r f i c i a l v e l o c i t i e s and the column d i a m e t e r ; t h i s i s n o r m a l l y based on p r e s s u r e drop or f l o o d i n g c o n d i t i o n s . These c a l c u l a t i o n s can be p e r formed 36 u s i n g t e c h n i q u e s suggested by F a i r [85] or T r e y b a l [ 8 6 ] . The t e c h n i q u e s w i l l be d e s c r i b e d i n some d e t a i l i n Chapter 5. B e f o r e the d e t a i l e d c a l c u l a t i o n of the a b s o r b e r h e i g h t can be undertaken, i t i s n e c e s s a r y t o know the v a p o r - l i q u i d e q u i l i b r i u m d ata of the system. The e q u i l i b r i u m i n f o r m a t i o n i s needed t o determine i f t h e r e i s a pinch (or e q u i l i b r i u m ) c o n d i t i o n i n the column. I f such a c o n d i t i o n e x i s t s , the column w i l l not be a b l e t o p e r f o r m as e x p e c t e d . T h e r e f o r e , a d j u s t m e n t s of the p r o c e s s c o n d i t i o n s ( e.g. f l o w r a t e s , c o m p o s i t i o n s of gas and l i q u i d e t c . ) a r e n e c e s s a r y . The e q u i l i b r i u m i n f o r m a t i o n i s a l s o need t o determine the c o n c e n t r a t i o n d r i v i n g f o r c e i n o r d e r t o c a l c u l a t e the a b s o r b e r h e i g h t . E x t e n s i v e e q u i l i b r i u m d a t a have been r e p o r t e d f o r the CO2 - amine systems. P a r t i c u l a r l y noteworthy i s the work conducted a t the U n i v e r s i t y of A l b e r t a by O t t o , Mather and t h e i r co-workers. Among t h e i r many s t u d i e s on s o l u b i l i t y , some of these d a t a a r e i n R e f e r e n c e s [ 9 5 ] , [96] and [ 1 0 1 ] . These d a t a as w e l l as the d a t a p r e v i o u s l y p u b l i s h e d by o t h e r r e s e a r c h e r s were w e l l summarized i n K o h l and R i e s e n f e l d ' s book, "Gas P u r i f i c a t i o n " [ 1 5 ] . R e c e n t l y , Austgen e t a l . [88] and C h a k r a v a r t y [119] have proposed r i g o r o u s m a t h e m a t i c a l 37 models t o p r e d i c t the e q u i l i b r i u m b e h a v i o r of a c i d gases i n amine s o l u t i o n s . However, the d e v i a t i o n s between t h e i r model p r e d i c t e d s o l u b i l i t y and p r e v i o u s l y r e p o r t e d e x p e r i m e n t a l r e s u l t s can be as h i g h as ± 60 %. Austgen e t a l . [88] and C h a k r a v a r t y • [ 1 1 9 ] suggested t h a t the wide v a r i a t i o n i n the s o l u b i l i t y d a t a r e p o r t e d by d i f f e r e n t r e s e a r c h groups i s one of the causes of the d e v i a t i o n . F i g u r e 2.5 shows t y p i c a l v a p o r - l i q u i d e q u i l i b r i u m c u r v e s f o r CO2 a b s o r p t i o n i n t o commonly used s o l v e n t s [138] The next d e s i g n s t e p i s t o d e t e r m i n e the column h e i g h t . F i g u r e 2.6 shows a s c h e m a t i c diagram of a packed column t o g e t h e r w i t h the nomenclature t h a t w i l l be used i n d e v e l o p i n g the d e s i g n e q u a t i o n s . A c c o r d i n g t o Sherwood et a l . [ 2 6 ] , the mass f l u x of A a t s t e a d y s t a t e may be e x p r e s s e d i n terms of the mass t r a n s f e r c o e f f i c i e n t s and d r i v i n g f o r c e s f o r each phase: N A = kG P<YA " YA,i> (2.1) N A = k L < C A , i " C A*) (2.2) where N A = mass t r a n s f e r f l u x of the absorbed component A kg = g a s - s i d e mass t r a n s f e r c o e f f i c i e n t 38 F i g u r e 2.5: T y p i c a l v a p o r - l i q u i d e q u i l i b r i u m c u r v e s a t 40 °C of CC^-Chemical s o l v e n t s [ 1 3 8 ] . Liquid 39 Packed Absorber dZ y A , out T" c B,out »ft,in Gas F i g u r e 2 .6 : Schematic of a packed absorber . 40 P = t o t a l p r e s s u r e y A = mole f r a c t i o n of A i n the b u l k gas y A i = mole f r a c t i o n of A on t h e g a s - s i d e of the gas-l i q u i d i n t e r f a c e k L = e f f e c t i v e l i q u i d - s i d e mass t r a n s f e r c o e f f i c i e n t C A = c o n c e n t r a t i o n of A i n t h e b u l k l i q u i d = c o n c e n t r a t i o n of A on t h e l i q u i d - s i d e of the g a s - l i q u i d i n t e r f a c e . The r e l a t i o n s h i p a t the g a s - l i q u i d i n t e r f a c e i s assumed t o obey Henry's law: C A , i = H P YA,i ^2.3) where H denotes Henry's c o n s t a n t . A l t h o u g h the above assumption may not be a p p l i e d f o r n o n i d e a l systems, the e f f e c t s of system n o n i d e a l i t i e s can however be lumped i n t o the v a l u e s of H as d e t a i l e d i n S e c t i o n 6.2.1. The mass f l u x can a l s o be w r i t t e n i n terms of the o v e r a l l mass t r a n s f e r c o e f f i c i e n t , K Q , and the o v e r a l l d r i v i n g f o r c e by r e a r r a n g i n g E q u a t i o n s 2.1 and 2.2: N A - K G p < y A - y A * ) (2.4) 4 1 K Q i s g i v e n by 1 / K G = l / k G + l / ( H k L ) = l / k G + l/(HIk L°) where I denotes the enhancement f a c t o r I = k L/k L° k L° denotes the l i q u i d - s i d e mass t r a n s f e r c o e f f i c i e n t without c h e m i c a l r e a c t i o n . The mass b a l a n c e f o r an element of column w i t h h e i g h t dZ can be w r i t t e n a s : N A a v d Z = G T d [ y A / ( 1 - y A ) ] ( 2 . 5 ) = K G a v P ( y A - y A * ) d Z ( 2 . 6 ) where Gj i s the i n e r t gas molar f l o w r a t e , a v i s the e f f e c t i v e i n t e r f a c i a l a r e a per u n i t volume of p a c k i n g , and y A i s the vapor-phase mole f r a c t i o n of component A which i s i n e q u i l i b r i u m w i t h the c o n c e n t r a t i o n i n the l i q u i d phase. R e a r r a n g i n g and i n t e g r a t i n g E q u a t i o n s 2 . 5 and 2 . 6 g i v e s yA,out z t = G i { d y A / f K G a v P < i - y A ) 2 ^ A - y A * ) ] YA, i n ( 2 . 7 ) 4 2 In the t r a d i t i o n a l d e s i g n method f o r packed columns, E q u a t i o n 2.5 i s sometimes r e a r r a n g e d as the p r o d u c t of the " h e i g h t of a t r a n s f e r u n i t (HTU)" and the "number of t r a n s f e r u n i t (NTU)", i . e (HTU)*(NTU) where HTU = [ G T / ( K G a v P ) ] and NTU YA,out / d y A / [ ( i - y A ) 2 ( y A - y A * ) ] YA, i n The HTU i s an i n v e r s e measure of the p a c k i n g e f f i c i e n c y ; the lower i t s v a l u e , the more e f f i c i e n t the p a c k i n g . The NTU r e p r e s e n t s the t o t a l number of t h e t r a n s f e r u n i t s r e q u i r e d f o r a g i v e n a b s o r p t i o n d u t y . I t s h o u l d be noted t h a t t h e s e d e f i n i t i o n s a re o n l y v a l i d p r o v i d e d K Q , a v and P a r e c o n s t a n t . A c c o r d i n g t o Danckwerts [ 1 8 ] , E q u a t i o n 2.7 can a l s o be w r i t t e n as 43 Z t = Gj yA,out d y A / [ R a a v ( 1 - y A ) 2 ] Y A r i n (2.8) where R a i s d e f i n e d as the s p e c i f i c r a t e of a b s o r p t i o n per u n i t i n t e r f a c i a l a r e a . (The d e t a i l e d e x p r e s s i o n of R a w i l l d e r i v e d i n S e c t i o n 2.3.2.) S o l v i n g E q u a t i o n s 2.7 or 2.8 i s u s u a l l y d i f f i c u l t because I i s a complex f u n c t i o n of the column hydrodynamics, f l u i d p r o p e r t i e s and c o n c e n t r a t i o n s , which can v a r y s i g n i f i c a n t l y a l o n g the column. The d e t a i l s of t h e o r e t i c a l c a l c u l a t i o n s of the enhancement f a c t o r w i l l be e x p l a i n e d on page 50 t o 57. The f o l l o w i n g s e c t i o n s a r e r e v i e w s of t h r e e d i f f e r e n t approaches f o r d e t e r m i n i n g the column h e i g h t . 2.3.1 EMPIRICAL DESIGN METHOD E m p i r i c a l d e s i g n approach (see Route# 1 of F i g u r e 2.4) i s based on the c o n c e p t s d e v e l o p e d f o r the d e s i g n of d i s t i l l a t i o n and p h y s i c a l a b s o r p t i o n columns. By u s i n g t h i s 44 approach, the o v e r a l l v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t ( K g a v ) i s assumed t o be c o n s t a n t a l o n g the packed column and has t o be o b t a i n e d e x p e r i m e n t a l l y u s i n g a column which i s f i l l e d w i t h the same p a c k i n g as the f u l l - l e n g t h column t o be d e s i g n e d . The e x p e r i m e n t a l d a t a a r e u s u a l l y c o l l e c t e d i n the form of the average K G a v v a l u e s on the b a s i s of a l o g -mean d r i v i n g f o r c e : ( K G a v ) a v e = G T [ y A f B / ( l - y A f B ) - y A , T / ( 1 - y A f T ) ] / t z e p <YA " YA*>lm] where Z e i s the h e i g h t of the e x p e r i m e n t a l column and ( y ^ -y A ) ^ m denotes the l o g mean d r i v i n g f o r c e , <yA-YA*>lm = t ( Y A - Y A * ) B - ( Y A - y A * ) T V l n [ ( y A - y A * ) B / ( y A - y A * ) T ] S u b s c r i p t B and T r e p r e s e n t the bottom and t o p c o n d i t i o n s , r e s p e c t i v e l y . The v a l u e s of (KQ av^ave o b t a i n e d t h i s way a r e u s u a l l y c o r r e l a t e d as e m p i r i c a l f u n c t i o n s of the o p e r a t i n g parameters (such as f l o w r a t e s ) . The h e i g h t of an a b s o r b e r can then be c a l c u l a t e d by u s i n g E q u a t i o n 2.7. Numerous s t u d i e s u s i n g t h i s approach have been re v i e w e d by K o h l and R i e s e n f e l d [15] and Edwards [ 2 4 ] . 4 5 A l t h o u g h the e m p i r i c a l approach has been used e x t e n s i v e l y f o r the d e s i g n of d i s t i l l a t i o n and p h y s i c a l a b s o r p t i o n columns, i t u s u a l l y l e a d s t o problems i n the case of a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n . When the e x t e n t of c h e m i c a l r e a c t i o n i s h i g h , which i s u s u a l l y the c a s e , the enhancement f a c t o r and t h e r e f o r e ( K G a v ) change a p p r e c i a b l y a l o n g the column. A s t a r i t a e t a l . [19] and J o s h i e t a l . [65] r e c e n t l y p o i n t e d out t h i s problem. To quote from A s t a r i t a e t a l . [ 1 9 ] , " the assumptions that the mass transfer is constant and independent of fluid concentrations are certainly not justified in the case of chemical absorption. It follows that the values of (KQay)ave. obtained in this way will strongly depend on all operating parameters in rather unpredictable ways and cannot be extrapolated to conditions different from the ones for which they have been obtained ". In s u p p o r t i n g t h i s s t a t e m e n t , A s t a r i t a e t a l . [19] f u r t h e r showed t h a t u s i n g t h i s e m p i r i c a l approach would l e a d t o l a r g e e r r o r s i n p r e d i c t i n g column h e i g h t s . As i l l u s t r a t e d by F i g u r e 2.7, the ( K G a v ) a v e v a l u e s of the K2CO3-CO2 system r e p o r t e d by Benson e t a l . [139] v a r y by more than an o r d e r of magnitude. S i n c e the c a l c u l a t e d h e i g h t ( c f . E q u a t i o n 46 2 . 7 ) depends d i r e c t l y on the v a l u e s of K G a v , the u n c e r t a i n t y a s s o c i a t e d w i t h the h e i g h t p r e d i c t i o n i s s i m i l a r t o t h a t a s s o c i a t e d w i t h the K G a v v a l u e s . As a r e s u l t , a " s a f e t y f a c t o r " of 1 . 5 t o 2 . 5 i s commonly a p p l i e d t o t h i s d e s i g n method i n o r d e r t o overcome the u n c e r t a i n t y a s s o c i a t e d w i t h t h e ( K G a v ) ave d a t a [ 1 2 4 , 1 2 5 ] . T h i s may l e a d t o e x c e s s i v e l y o v e r s i z e d columns r e s u l t i n g i n unnecessary e x p e n d i t u r e s of c a p i t a l and o p e r a t i n g c o s t s . I t i s t h e r e f o r e d i f f i c u l t t o have c o n f i d e n c e i n the e m p i r i c a l d e s i g n approach f o r gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n systems. F i g u r e 2.7: K G a v v a l u e s of C0 2-K 2C03 system [ 6 5 ] . 4 8 2.3.2 THEORETICAL DESIGN METHOD The h e i g h t of an a b s o r b e r w i t h c h e m i c a l r e a c t i o n may a l s o be c a l c u l a t e d by u s i n g E q u a t i o n 2.8 p r o v i d e d t h a t the v a l u e s of the s p e c i f i c a b s o r p t i o n r a t e , R a, a l o n g the a b s o r b e r a r e known. However, t o e v a l u a t e t h e s e v a l u e s t h e o r e t i c a l l y , i n f o r m a t i o n r e g a r d i n g the column hydrodynamics and p h y s i c o - c h e m i c a l p r o p e r t i e s of the system ( d i f f u s i v i t i e s , s o l u b i l i t i e s and r e a c t i o n k i n e t i c s ) must be known (see Route# 2 i n F i g u r e 2.4). THEORETICAL DETERMINATION OF RQ Even though some of the f o l l o w i n g e q u a t i o n s were p r e s e n t e d b e f o r e , they a r e r e p e a t e d here f o r c o n v e n i e n c e sake. The mass t r a n s f e r r a t e of A a t any p o i n t of the a b s o r b e r may be w r i t t e n a s : R a a v d Z = k G P ( y A - y A f i ) a v d Z = I kL°< cA,i " C A * ) a v d Z (2.9) (2.10) E q u a t i o n s 2.9 and 2.10 can be r e a r r a n g e d a s : 49 k G p ( y A - y A f i> = I k L 0 ( c A f i - cA*) (2.11) S u b s t i t u t i n g = H P y A ^ i n t o E q u a t i o n 2.11 and r e a r r a n g i n g g i v e s ; Y A , i ( l k L ° H P + k G p ) = + I k L ° C A * < 2- 1 2> YA, i = < kG pYA + IkL°0 / d k L ° H P + k Q P ) (2.13) From E q u a t i o n 2.9, the c o n c e n t r a t i o n of A a t the i n t e r f a c e can a l s o be w r i t t e n a s : Yk,i = Yk ~ * a/< P kG> < 2- 1 4> S u b s t i t u t i n g E q u a t i o n 2.13 i n t o E q u a t i o n 2.14 and r e a r r a n g i n g g i v e s R a = kG PYA " * k G P £< kG PYA + IkL°0 / (lkL°HP + kG P> H . . . (2 .15) R a = {(k GPy A)(Ik L°H) + ( k G P y A ) ( k G ) - ( k G ) ( k G P y A ) - (k G)(Ik L°C A*)} / (lk L°H + k G ) ] } (2.16) T h e r e f o r e , 50 R a = {lk L°(HPy A - C A * ) / [ 1 + I H ( k L ° A G ) ] } (2.17) To f i n d R a, an i t e r a t i v e method must be used s i n c e the enhancement f a c t o r depends on the c o n c e n t r a t i o n s a t the i n t e r f a c e which a r e not known and cannot be measured. As a r e s u l t , E q u a t i o n s 2.14 and 2.17 are c o u p l e d and need t o be s o l v e d s i m u l t a n e o u s l y . For example, y A f i = y A may be t a k e n as a f i r s t a p p r o x i m a t i o n . C A ^ and the enhancement f a c t o r a r e then c a l c u l a t e d . E q u a t i o n 2.17 i s then used t o e v a l u a t e R a. The second a p p r o x i m a t i o n f o r y A ^ i i s then o b t a i n e d from E q u a t i o n 2.14. The c a l c u l a t i o n s a re r e p e a t e d u n t i l Yh,i °^ the c u r r e n t i t e r a t i o n c l o s e l y a p p r o x i m a t e s t h a t of t h e p r e v i o u s i t e r a t i o n . ENHANCEMENT FACTOR CALCULATION One of the most i m p o r t a n t c a l c u l a t i o n s t e p s i s t o dete r m i n e the enhancement f a c t o r , I , which i s a f u n c t i o n of the p h y s i c a l and c h e m i c a l p r o p e r t i e s of a l l components i n the l i q u i d f i l m . To c a l c u l a t e the enhancement f a c t o r i n g e n e r a l , a s e t of p a r t i a l d i f f e r e n t i a l e q u a t i o n s which r e p r e s e n t s i m u l t a n e o u s d i f f u s i o n a l mass t r a n s f e r and 51 c h e m i c a l r e a c t i o n a l o n g the l i q u i d f i l m , need t o be s o l v e d . A c c o r d i n g t o A s t a r i t a [ 1 7 ] , the d i f f u s i o n e q u a t i o n s which r e p r e s e n t these phenomena w i t h i n the l i q u i d phase may be w r i t t e n i n the f o l l o w i n g form: D j V 2 C j = uVCj + a C j / 3t + r j (2.18) ( m o l e c u l a r = ( c o n v e c t i v e + ( a c c u m u l a t i o n ) + ( f o r m a t i o n by t r a n s p o r t ) t r a n s p o r t ) c h e m i c a l r e a c t i o n ) r j denotes the r e a c t i o n r a t e of s p e c i e s j i n s i d e the l i q u i d f i l m . In g e n e r a l , the r e a c t i o n r a t e depends on the l o c a l c o n c e n t r a t i o n s of the r e a c t a n t s and the r e a c t i o n p r o d u c t s . To o b t a i n the enhancement f a c t o r , the d i f f u s i o n e q u a t i o n s f o r a l l s p e c i e s i n the l i q u i d have t o be s o l v e d . The type of c h e m i c a l a b s o r p t i o n system which has r e c e i v e d the most a t t e n t i o n i n the l i t e r a t u r e i s the one i n which component A from th e gas phase r e a c t s w i t h component B i n the l i q u i d by an i r r e v e r s i b l e second-order r e a c t i o n . T h i s system w i l l be used t o i l l u s t r a t e the enhancement f a c t o r c a l c u l a t i o n . The r e a c t i o n i s r e p r e s e n t e d by A + »>ABB = C and the r a t e e x p r e s s i o n i s g i v e n by: rAB = k 2 C A C B 52 I t must be noted t h a t t h e r e i s not n e c e s s a r i l y any r e l a t i o n s h i p between the s t o i c h i o m e t r i c c o e f f i c i e n t , t » A B , of the r e a c t i o n and the o r d e r of the r e a c t i o n [ 1 8 ] . A c c o r d i n g t o A s t a r i t a [ 1 7 ] , E q u a t i o n 2.18 can be s i m p l i f i e d by making the f o l l o w i n g a s s u m p t i o n s : ( i ) the g a s - l i q u i d i n t e r f a c e i s p l a n e , ( i i ) the f i l m t h e o r y i s v a l i d , which means the s u r f a c e element behaves r i g i d l y d u r i n g i t s l i f e (u=0), ( i i i ) s t e a d y s t a t e c o n d i t i o n s p r e v a i l i n the l i q u i d f i l m . The mass t r a n s f e r phenomena a c r o s s a g a s - l i q u i d i n t e r f a c e c o u l d a l s o be d e s c r i b e d by the p e n e t r a t i o n and s u r f a c e renewal t h e o r y . However, a l l t h r e e t h e o r i e s g i v e v i r t u a l l y the same r e s u l t s as f a r as t h e n u m e r i c a l r e s u l t s a r e concerned [ 2 6 ] . S i n c e the f i l m t h e o r y i s r e l a t i v e l y easy t o u n d e r s t a n d , i t has been more w i d e l y used and w i l l be used i n the f o l l o w i n g d i s c u s s i o n . The e f f e c t of the r e a c t i o n p r o d u c t , C, on the p h y s i c a l and c h e m i c a l p r o p e r t i e s of components A and B a r e assumed t o be i n s i g n i f i c a n t . T h e r e f o r e , the d i f f e r e n t i a l e q u a t i o n s f o r components A and B can be r e w r i t t e n a s : D A ( 3 2 C A / a x 2 ) - k 2 C A C B = 0 D B( 3 2 C B / 9 x 2 ) - * A B k 2 C A C B = 0 (2.19) (2.20) 53 where x i s the d i s t a n c e i n the l i q u i d f i l m from the i n t e r f a c e . The boundary c o n d i t i o n s f o r E q u a t i o n s 2.19 and 2.20 a r e : At x = 0 C A = c A , i 3C B/3x = 0 At x = 6 where 6 denotes the l i q u i d f i l m t h i c k n e s s . The enhancement f a c t o r i s e q u a l t o the r a t i o of the a c t u a l i n t e r f a c e c o n c e n t r a t i o n g r a d i e n t of A t o the g r a d i e n t which would be e s t a b l i s h e d i n p u r e l y p h y s i c a l a b s o r p t i o n : I = { - < 3 C A / 9 x ) x = 0 } / ( C A f i / 6 ) At the p r e s e n t t i m e , t h e r e i s no e x a c t a n a l y t i c a l s o l u t i o n f o r t h i s s e t of e q u a t i o n s [18, 5 9 ] . However Van K e v e l e n and H o f t i j z e r [44, 67] p r o v i d e d an a p p r o x i m a t e a n a l y t i c a l s o l u t i o n which r e l a t e s the a c t u a l enhancement 54 f a c t o r , I , t o the enhancement f a c t o r f o r the i n s t a n t a n e o u s r e a c t i o n , Ia,z I = [M{(I c c-I)/(I 0 0-1)}]°- 5/tanh[M{(I 0 6 - l)/(I 0 0 - l ) } ] ° - 5 (2.21) where M = ( D A k 2 C B * ) / ( k L ° ) 2 and I . = 1 + ( D B C B * ) / U A B D A C A f i ) However, t h i s e q u a t i o n i s i m p l i c i t and can be s o l v e d o n l y by an i t e r a t i v e method. To improve the c o m p u t a t i o n a l e f f i c i e n c y , s e v e r a l e x p l i c i t e q u a t i o n s have been p r o p o s e d . P o r t e r [ 6 8 ] : I = 1 + (loo ~ D O ~ exp[-(v/M - D / d . - D ] } (2.22) K i s h i n e v s k i i [ 6 9 ] : 1 = 1 + WM/p){l - exp(-O.65 /M0)} (2.23) where 0 = \/U/(Ia-)) + exp{ (0.68/v/M) - (0.45/M/(I.-1 )) } DeCoursey [ 9 0 ] : I = [ ( M 2 / ( 4 ( I 0 0 - 1 ) 2 ) ) + I o . M / d . - l ) +1]°- 5 - [ M / d d . - l ) ) ] (2.24) 55 W e l l e k et a l . [ 8 9 ] : I = 1 + {1 + [ ( I B - D / d j - 1 ) ] 1 -35} ( 1/1 .35) ( 2.25) where 1 1 = »/M/tanhv/M A l p e r [70] and Wellek e t a l . [ 8 9 ] a l s o made a comprehensive comparison of these e q u a t i o n s w i t h p r e c i s e n u m e r i c a l s o l u t i o n s over wide ranges of c o n d i t i o n s . They found t h a t the maximum d i f f e r e n c e s among the r e s u l t s were l e s s than 10 %. The above e q u a t i o n s can t h e r e f o r e be used t o e s t i m a t e the enhancement f a c t o r f o r slow t o i n s t a n t a n e o u s r e a c t i o n (I 1 t o I ^ IooK In l a b o r a t o r y equipment ( i . e . s t i r r e d c e l l s , sphere columns, e t c . ) which has a w e l l - d e f i n e d g a s - l i q u i d c o n t a c t i n g a r e a , the p r e c i s e p r e d i c t i o n of the e x p e r i m e n t a l r e s u l t s can be o b t a i n e d from t h e s e e q u a t i o n s p r o v i d e d a l l fundamental d a t a a r e a v a i l a b l e . Some of t h e s e r e s u l t s were summarized by Danckwerts [ 1 8 ] . A l p e r [70] gave a t y p i c a l p l o t of I as f u n c t i o n s of I j and \/M ( F i g u r e 2.8). Some t y p i c a l v a l u e s of I o b t a i n e d from w e l l - d e f i n e d a b s o r b e r s f o r the CO2-MEA system a r e shown i n F i g u r e 2.9 [ 1 3 1 ] . For systems i n which one or more components i n the gas phase r e a c t r e v e r s i b l y w i t h one or more l i q u i d r e a c t a n t s , the enhancement f a c t o r c a l c u l a t i o n i s even more complex. 56 5 7 F i g u r e 2.9: V a r i a t i o n of the enhancement f a c t o r f o r C O o - M E A system o b t a i n e d from l a b o r a t o r y a b s o r b e r s [ 1 3 1 ] . ( P o i n t s were from e x p e r i m e n t a l measurements and l i n e s were from t h e o r e t i c a l p r e d i c t i o n s . ) 58 DETERMINATION OF COLUMN HEIGHT A f t e r the v a l u e s of R a a r e d e t e r m i n e d t h e o r e t i c a l l y a t v a r i o u s p o i n t s a l o n g the column, t h e column h e i g h t can be o b t a i n e d by i n t e g r a t i n g E q u a t i o n 2.8 n u m e r i c a l l y or g r a p h i c a l l y . S u r p r i s i n g l y , no d e t a i l e d c omparisons have been p u b l i s h e d on the c o n c e n t r a t i o n and t e m p e r a t u r e p r o f i l e s o b t a i n e d from t h e o r e t i c a l p r e d i c t i o n s and p i l o t p l a n t measurements. T h e r e f o r e , such d e t a i l e d c o m p a r i s o n s a r e made f o r the C0 2 _NaOH and C0 2-MEA systems i n Ch a p t e r 6. 59 2.3.2.1 INFORMATION REQUIRED IN THEORETICAL CALCULATIONS As can be seen from the p r e v i o u s s e c t i o n , s e v e r a l k i n d s of i n f o r m a t i o n a r e r e q u i r e d b e f o r e the s p e c i f i c a b s o r p t i o n r a t e , and t h e r e f o r e the tower h e i g h t , can be d e t e r m i n e d t h e o r e t i c a l l y . PHYSICAL GAS ABSORPTION PARAMETERS For the p h y s i c a l gas a b s o r p t i o n e x t e n s i v e e x p e r i m e n t a l r e s u l t s have been r e p o r t e d on k G , k L°and a v i n the 1950's and 1960's f o r c o n v e n t i o n a l p a c k i n g s l i k e c e ramic R a s c h i g r i n g s and B e r l S a d d l e s . These d a t a were c o r r e l a t e d i n terms of d i m e n s i o n l e s s parameters such as Reynolds number (Re ) , Schmidt number ( S c ) . These d a t a and t h e i r c o r r e l a t i o n s a r e w e l l documented i n P e r r y ' s C h e m i c a l E n g i n e e r s ' Handbook [ 8 5 ] , However, the u n c e r t a i n t i e s ( e r r o r s ) a s s o c i a t e d w i t h t h e s e d a t a and c o r r e l a t i o n s a r e s u b s t a n t i a l as p o i n t e d out by many r e s e a r c h e r s i n c l u d i n g Hudgins and R e i l l y [ 1 2 6 ] . For example, F i g u r e 2.10, r e p r o d u c e d from P e r r y ' s Handbook, shows t h a t the g a s - s i d e mass t r a n s f e r c o e f f i c i e n t has a two-t o t h r e e - f o l d v a r i a t i o n a t a g i v e n gas f l o w r a t e [ 1 2 6 ] , T h i s t y p e of u n c e r t a i n t y has a l s o been obser v e d f o r the case of 60 l i q u i d - s i d e mass t r a n s f e r c o e f f i c i e n t s and e f f e c t i v e i n t e r f a c i a l a r e a s [ 3 6 ] . A major reason f o r the u n c e r t a i n t i e s i s t h a t the f l o w b e h a v i o r and mass t r a n s f e r phenomena i n packed a b s o r b e r s a r e complex and cannot be a c c u r a t e l y p r e d i c t e d by s i m p l y u s i n g c o r r e l a t i o n s of d i m e n s i o n l e s s p a r a m e t e r s . To quote from Sherwood e t a l . [ 2 6 ] , " .... it seems doubtful that the complicated phenomena involved in flow in packings will ever be satisfactorily correlated by using classical dimensionless parameters such as Re, Sc For the newer, h i g h - e f f i c i e n c y p a c k i n g s , which a r e f a v o u r e d by i n d u s t r y [ 3 7 ] , v e r y l i t t l e i n f o r m a t i o n i s a v a i l a b l e i n the l i t e r a t u r e r e g a r d i n g t h e i r mass t r a n s f e r c o e f f i c i e n t s and e f f e c t i v e i n t e r f a c i a l a r e a . F i g u r e s 2.11 and 2.12 show some of the h i g h - e f f i c i e n c y random and s t r u c t u r e d p a c k i n g s , r e s p e c t i v e l y . The c l a s s i c a l c o r r e l a t i o n s o b t a i n e d f o r the c o n v e n t i o n a l p a c k i n g s s h o u l d not be used t o p r e d i c t t h e p h y s i c a l gas a b s o r p t i o n p r o p e r t i e s of h i g h - e f f i c i e n c y p a c k i n g s s i n c e the l a t t e r 61 Gas f l o w r a t e ( r e l a t i v e u n i t s ) F i g u r e 2.10: G a s - s i d e mass t r a n s f e r c o e f f i c i e n t , k G , as a f u n c t i o n of gas f l o w r a t e [ 1 2 6 ] , 62 Poll Ring M e t a l (ntalox F i g u r e 2.11: H i g h - e f f i c i e n c y random p a c k i n g [ 1 9 ] . F i g u r e 2 . 1 2 : S t r u c t u r e d p a c k i n g [ 3 8 ] . 64 p a c k i n g s have much more complex c o n f i g u r a t i o n r e s u l t i n g i n d i f f e r e n t f l o w and mass t r a n s f e r phenomena. The h i g h -e f f i c i e n c y p a c k i n g s u s u a l l y have much h i g h e r e f f e c t i v e i n t e r f a c i a l a r e a s and l o w e r p r e s s u r e d r o p s compared w i t h c o n v e n t i o n a l o n e s . 65 PHYSICO-CHEMICAL PROPERTIES For the case of a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n , p h y s i c o - c h e m i c a l d a t a such as s o l u b i l i t y , d i f f u s i v i t y and r e a c t i o n r a t e c o n s t a n t s a r e needed i n o r d e r t o c a l c u l a t e the enhancement f a c t o r . These d a t a a r e h i g h l y s p e c i f i c and have t o be o b t a i n e d f o r each system a t t h e p r e s c r i b e d c o n d i t i o n s . The r e a c t i o n k i n e t i c s of a g i v e n r e a c t i o n system can o n l y be o b t a i n e d by p e r f o r m i n g e x p e r i m e n t s which a r e o f t e n d i f f i c u l t , time-consuming and i n a c c u r a t e . For the case of C O 2 a b s o r p t i o n i n t o amine s o l u t i o n s o t h e r than MEA, the u n d e r s t a n d i n g of the r e a c t i o n k i n e t i c s i s s t i l l i n adequate [40-51, 87] a l t h o u g h i t has been s t u d i e d f o r more than h a l f a c e n t u r y . F o r i n s t a n c e , t h e r e i s no g e n e r a l agreement on the r e a c t i o n mechanism f o r t h e C O 2 a b s o r p t i o n i n t o d i e t h a n o l a m i n e (DEA) which i s a secondary a l k a n o l a m i n e . A l t h o u g h prominent r e s e a r c h e r s i n the f i e l d a gree on the r e a c t i o n mechanism t o be second o r d e r r e a c t i o n , t h ey found t h a t the r a t e c o n s t a n t s , under c e r t a i n c o n d i t i o n s , d i f f e r by as much as a f a c t o r of f o u r [52] (see F i g u r e 2.13). F i g u r e 2 . 1 3 : Apparent r a t e c o n s t a n t of C O 2 - DEA system r e p o r t e d by v a r i o u s r e s e a r c h e r s [ 4 3 ] . 67 For the new, h i g h - c a p a c i t y s o l v e n t s such as s t e r i c a l l y h i n d e r e d amines, v e r y l i t t l e i n f o r m a t i o n i s a v a i l a b l e on t h e i r r e a c t i o n mechanism and r a t e c o n s t a n t s . To measure d i f f u s i v i t i e s and p h y s i c a l s o l u b i l i t i e s f o r gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n systems a l s o p r e s e n t s f u r t h e r d i f f i c u l t i e s due t o the s i m u l t a n e o u s d i f f u s i o n and r e a c t i o n which take p l a c e i n the l i q u i d phase. I t i s not p o s s i b l e t o o b t a i n t h e s e p r o p e r t i e s d i r e c t l y and i n d i r e c t methods must t h e r e f o r e be used. A commonly used method i s t o deduce th e s e data from c o r r e s p o n d i n g , but n o n r e a c t i n g systems. In view of i t s s i m i l a r c o n f i g u r a t i o n , m o l e c u l a r volume, and e l e c t r o n i c s t r u c t u r e , N 20 i s o f t e n used as the n o n r e a c t i n g gas t o e s t i m a t e the d i f f u s i v i t y and p h y s i c a l s o l u b i l i t y of C 0 2 i n amine s o l u t i o n s . Laddha e t a l . [127] and V e r s t e e g and Swaaij [128] i n v e s t i g a t e d the s o l u b i l i t y of N 20 and C 0 2 i n aqueous s o l u t i o n s of amines and o t h e r o r g a n i c compounds. They found t h a t the r a t i o of the s o l u b i l i t i e s of N 20 and C 0 2 was c o n s t a n t . T h e r e f o r e , the "N 20 a n a l o g y " may be a p p l i e d t o e s t i m a t e the p h y s i c a l s o l u b i l i t y of C 0 2 i n aqueous a l k a n o l a m i n e s o l u t i o n s a c c o r d i n g t o : 68 ( P h y s i c a l s o l u b i l i t y of C O 2 i n amine) = C ; ( N 2 0 S o l u b i l i t y i n amine) where Cj = ( C O 2 s o l u b i l i t y i n w a t e r ) / ( N 2 0 s o l u b i l i t y i n water) V e r s t e e g and S w a a i j [128] and V e r s t e e g e t a l . [129] a l s o used t h i s approach t o e s t i m a t e C O 2 d i f f u s i v i t i e s i n aqueous a l k a n o l a m i n e s o l u t i o n s . T h e i r e x p e r i m e n t a l r e s u l t s c o v e r i n g i n d u s t r i a l o p e r a t i n g c o n d i t i o n s have been p u b l i s h e d r e c e n t l y [128, 129]. They found t h a t t h e i r r e s u l t s agree w e l l w i t h the p r e v i o u s l y r e p o r t e d f i n d i n g s . E s t i m a t i o n methods f o r s o l u b i l i t i e s and d i f f u s i v i t i e s of gases i n l i q u i d s f o r both r e a c t i n g and n o n r e a c t i n g systems have r e c e n t l y been reviewed and summarized by M o r s i and C h a r p e n t i e r [ 3 9 ] , V e r s t e e g and S w a a i j [128] and V e r s t e e g e t a l . [ 1 2 9 ] . 69 2.3.2.2 WEAK POINTS OF THEORETICAL DESIGN METHOD As have been shown above, t h e r e a r e two major d i f f i c u l t i e s i n p r e d i c t i n g t he h e i g h t of a gas a b s o r b e r w i t h c h e m i c a l r e a c t i o n u s i n g the t h e o r e t i c a l approach. F i r s t l y , i t i n v o l v e s complex c a l c u l a t i o n s . S e c o n d l y , i t needs d e t a i l e d i n f o r m a t i o n r e g a r d i n g the hydrodynamic p r o p e r t i e s of the ab s o r b e r and the p h y s i c o - c h e m i c a l p r o p e r t i e s of the system. I t i s t h e r e f o r e v e r y i m p o r t a n t t o d e v e l o p a l t e r n a t i v e d e s i g n p r o c e d u r e s which a r e f r e e of th e s e two major r e s t r i c t i o n s . 70 2.3.3 DESIGN METHODS BASED ON LABORATORY MODELS S i n c e many d i f f i c u l t i e s a r e enc o u n t e r e d i n the p r o c e s s of o b t a i n i n g the p h y s i c o - c h e m i c a l i n f o r m a t i o n and i n computing the enhancement f a c t o r s as mentioned i n the p r e v i o u s s e c t i o n , Danckwerts and A l p e r [18, 36, 55, 56] and C h a r p e n t i e r and L a u r e n t [58-60] proposed two l a b o r a t o r y models f o r d e s i g n i n g gas a b s o r b e r s w i t h c h e m i c a l r e a c t i o n . The l a b o r a t o r y models (see Route# 3 of F i g u r e 2.4) a r e based on the assumption t h a t the r a t e of a b s o r p t i o n per u n i t i n t e r f a c i a l a r e a , R a, depends o n l y on t h e a b s o r b e r hydrodynamics and the r e a c t a n t c o n c e n t r a t i o n s i n b o t h phases [18, 36, 54-63]. The R a v a l u e s can be d e t e r m i n e d from l a b o r a t o r y a b s o r b e r s r a t h e r than t h e o r y . I n d o i n g t h i s , the hydrodynamic parameters i n the l a b o r a t o r y a b s o r b e r must be known p r e c i s e l y and can be matched w i t h t h o s e of the f u l l -s c a l e column. POINT MODEL The f i r s t model i s c a l l e d t h e Point model [18, 55, 57-59, 61-64]. A sc h e m a t i c r e p r e s e n t a t i o n of the p r i n c i p l e of " P o i n t m o d e l l i n g " i s shown i n F i g u r e 2.14. ( D e t a i l s a r e Figure 2.14: Schematic re p r e s e n t a t i o n of Point model [55]. 72 g i v e n by Danckwerts and A l p e r [ 5 5 ] . ) The a b s o r p t i o n - r e a c t i o n i n t e r a c t i o n s are measured i n a s m a l l s t i r r e d c e l l , which i s a g a s - l i q u i d c o n t a c t o r o p e r a t i n g a t steady s t a t e . There a r e two s t i r r e r s i n the c e l l t o keep the b u l k gas and l i q u i d c o n c e n t r a t i o n s u n i f o r m . In o r d e r t o use t h i s model f o r s i m u l a t i n g a b s o r p t i o n , the s t i r r e d c e l l has t o be o p e r a t e d i n such a way t h a t i t s kg and k L° v a l u e s a r e the same as t h o s e i n the f u l l - s c a l e a b s o r b e r . Danckwerts and A l p e r [55] showed t h a t the d e s i r e d v a l u e s of k G and k L ° , which c o r r e s p o n d t o p u r e l y p h y s i c a l a b s o r p t i o n , can be o b t a i n e d by v a r y i n g the s t i r r e r speeds. Once the s e c o n d i t i o n s a r e met, t h e a b s o r p t i o n r a t e per u n i t i n t e r f a c i a l a r e a i n the c e l l can be measured f o r v a r i o u s b u l k gas and b u l k l i q u i d c o m p o s i t i o n s . The r e s u l t i n g R a v a l u e s a r e then s u b s t i t u t e d i n t o E q u a t i o n 2.8 t o y i e l d the r e q u i r e d column h e i g h t . I t i s shown t h a t t h i s method e l i m i n a t e s the need f o r o b t a i n i n g the r e a c t i o n k i n e t i c s and p h y s i c o - c h e m i c a l parameters e x p l i c i t l y . Danckwerts and A l p e r [55] t e s t e d the P o i n t model by p r e d i c t i n g the performance of a C 0 2 a b s o r b e r (0.1 m ID) packed w i t h 12.7 mm c eramic R a s c h i g r i n g s t o v a r i o u s h e i g h t s . Aqueous NaOH was used as the a b s o r p t i o n medium. T a b l e 2.1 shows t h a t the p r e d i c t e d and a c t u a l h e i g h t s 73 d i f f e r e d by l e s s than 9% i n a l l c a s e s . F u r t h e r t e s t i n g of t h i s model was performed by L a u r e n t [130] w i t h the same system. However, the p r e d i c t e d r e s u l t s were not as good and d i s c r e p a n c i e s of up t o ± 20% o c c u r r e d . No reason was g i v e n f o r the l a r g e r d i s c r e p a n c i e s i n t h i s c a s e . I t s h o u l d be noted t h a t t h e P o i n t model i s o n l y a p p l i c a b l e t o systems where the r e a c t i o n s a re f a s t enough t o t a k e p l a c e i n the l i q u i d f i l m near the i n t e r f a c e so t h a t t h e r e i s no r e a c t i o n i n the b u l k of the l i q u i d . T h i s l i m i t a t i o n a r i s e s because the l i q u i d h o l d up per u n i t volume of the s t i r r e d c e l l i s much l a r g e r than t h a t of the packed column. 74 Table 2 . 1 : Comparison r e s u l t s between a c t u a l and p r e d i c t e d height from P o i n t model by Danckwerts and A l p e r [ 55 ] . CBO = (mol 1 Inlet C O H " - 1 ) -Outlet PCO, (atm) Inlet x 101 Outlet out r d(CBo)h ) * in zaZ = (s c m - 1 ) WL Packing height (cm) Predicted height (cm) Difference (%) Error in material balance (%) 0.39 0.29 4.6 3.8 430 48.0 46.3 +3.5 8.4 0.52 0.42 4.1 3.3 410 48.0 44.1 +8.1 4.2 0.58 0.46 4.6 3.6 430 48.0 46.3 +3.5 3.6 0.28 0.10 5.2 3.6 970 108.0 104.0 +3.7 3.5 0.62 0.19 7.6 4.0 1430 163.0 154.0 +5.5 0.5 0.60 0.08 10.3 6.2 1430 163.0 154.0 +5.5 0.8 0.55 0.19 6.0 3.1 1420 163.0 153.0 +6.1 7.0 0.52 0.20 5.0 2.2 1430 163.0 154.0 +5.5 0.0 0.55 0.08 10.6 7.0 1320 143.0 142.0 +0.7 5.3 0.46 0.10 7.8 5.0 1310 143.0 141.0 + 1.4 6.7 0.46 0.13 7.8 5.2 1120 123.0 121.0 + 1.6 5.4 0.58 0.13 10.2 6.7 1130 123.0 122.0 +0.8 2.6 0.53 0.26 5.3 3.0 1120 123.0 121.0 +1.6 6.0 75 T a b l e 2.2: Comparison r e s u l t s between a c t u a l and p r e d i c t e d h e i g h t from P o i n t model by Lau r e n t [ 1 3 0 ] . Error Pcoi x 102 C B 0 — C 0 n f 0 U T dcjo in (aim) (mollir 1 ) JIN <t>m Predicted materal "G "L // height Difference balance (cms"1] Inlet Outlet (cms"1) Inlet Outlet (scrn"1) (m) (m) <%) (%> 7.5 6.2 0.4 0.5 0.60 0.52 654 1.72 10.4 9.9 7.5 3.2 0.01 0.5 0.60 0.55 578 1.52 20.8 25 6.9 2.9 0.05 0.23 0.59 0.52 1120 1.84 4.2 4 6.9 5.5 0.6 0.23 0.59 0.47 1102 1.81 5.7 3.5 6.9 7.3 0.75 0.23 0.59 0.42 1144 1.88 2.1 2.4 7.6 2.5 0.4 0.5 0.30 0.27 673 1.92 1.77 7.8 11.9 7.5 2.8 0.45 0.23 0.30 0.24 1096 1.80 6.2 6.7 10.9 2.0 0.5 0.23 0.30 0.24 1145 1.88 2.1 0 7.5 2.6 0.3 0.5 0.28 0.25 692 1.82 5.2 4 7.4 4.2 0.4 0.5 0.28 0.23 722 1.90 1.0 5.9 76 COMPLETE MODEL The second, p r e v i o u s l y p u b l i s h e d method of a b s o r b e r m o d e l l i n g i s based on s o - c a l l e d Complete modelling, which i s shown i n F i g u r e 2.15. ( F u l l d e t a i l s of"Complete m o d e l l i n g u s i n g sphere columns a r e g i v e n i n R e f e r e n c e s 55 and 60.) The f u l l - s c a l e a b s o r b e r can be r e p r e s e n t e d by a model column c o n s i s t i n g of spheres and a c y l i n d r i c a l s h e l l (see F i g u r e 2.16). The spheres a r e connected by a r o d . On t h e t o p of each s p h e r e , t h e r e i s a l i q u i d p o o l . In o r d e r t o s i m u l a t e the packed column, t h e v a l u e s of o k C k L ' ( L / G ) , ( a v Z / L ) and (av/f) i n the l a b o r a t o r y a b s o r b e r must be the same as t h o s e i n the f u l l - s c a l e column. 7 r e p r e s e n t s the h o l d - u p of the a b s o r b e r . The above c o n d i t i o n s can be a c h i e v e d by s e l e c t i n g the r i g h t d i m e n s i o n s f o r the column ( i . e sphere d i a m e t e r , p o o l d i m e n s i o n and s h e l l c y l i n d e r d i a m e t e r ) . The d e s i r e d " s c a l i n g r a t i o " ( Z t / Z m ) s h o u l d be about 5-10 ( a s , suggested by A l p e r and Danckwerts [56, 62]) where the Z t and Z m denote the h e i g h t of the f u l l - s c a l e column and model column, r e s p e c t i v e l y . F i g u r e 2 . 1 5 : S c h e m a t i c r e p r e s e n t a t i o n of Complete model Ii ng [ 5 6 ] . 78 Liquid inlet 0 3 cm dio. stainless" steel rod 8x0-3 cm dia. holes 70 cm Liquid outlet F i g u r e 2 . 1 6 : Sphere co lumn [ 5 6 ] . 79 This scaling r a t i o makes the value of the wetting rate ( L m / a v m) for the laboratory absorber small since i t can be shown that Z t/Z m = ( L / a v ) / ( L m / a V f m ) (2.26) Since L/G i s fixed, the gas flow rate in the model column i s also small. If there are reactions in the bulk l i q u i d , the mean residence time of l i q u i d in both columns must be the same. The mean residence time can be written as: t = 7 Z t / L = 7 m Z m / L m (2.27) Rearranging Equations 2.26 and 2.27, one obtains a V/7 = a V , A <2-2 8> This identity of the i n t e r f a c i a l area per unit volume of l i q u i d (a v/7) means that the residence times of the l i q u i d in both columns are the same. This condition must be met in order to provide the same environment for the reactions which occur in the bulk of the l i q u i d . When a l l of the afore-mentioned parameters are matched, the f u l l - s c a l e column can be simulated by the model column without any 80 assumption about the t r a n s f e r mechanism or r e a c t i o n k i n e t i c s . F u r thermore, no p h y s i c o - c h e m i c a l i n f o r m a t i o n i s needed. The procedure f o r - u s i n g t h i s model t o s i m u l a t e an i n d u s t r i a l packed column i s o u t l i n e d i n F i g u r e 2.17 [ 6 0 ] . A good i l l u s t r a t i o n of t h i s t e c h n i q u e was p r e s e n t e d by A l p e r and Danckwerts [56] who s i m u l a t e d a 0.1 m ID column packed w i t h 12.7 mm ceramic R a s c h i g r i n g s (0.49 t o 1.58 m h i g h ) by a s t r i n g of 10 s p h e r e s , 0.49 m i n h e i g h t . The e x p e r i m e n t s were c a r r i e d out w i t h v a r i o u s r e a c t i o n systems where the r e a c t i o n s o c c u r r e d i n the b u l k of the l i q u i d phase. In each c a s e , the d i f f e r e n c e between the p r e d i c t e d and measured t o t a l a b s o r p t i o n r a t e s was w i t h i n ± 7 %. However, the s c a l e r a t i o i n these e x p e r i m e n t s was o n l y about 1 t o 2. There i s no i n f o r m a t i o n on u s i n g the complete model f o r h i g h e r s c a l e r a t i o s . Another weakness of t h i s model i s t h a t the h e i g h t of t h e f u l l - s c a l e column i s assumed t o be known a p r i o r i , w h i c h i s not u s u a l l y the case i n d e s i g n problems. 81 INDUSTRIAL PACKED COLUMN SPECIFY Packing material Z. L, (G/L) DETERMINE by experiments - & < •- S X JP - ^&.-',\t.-'~<,-~ CHOOSE APPROPRIATE SIZED SPHERES o -•-' . - u . , - ' N NO- ;\-, \ IS fT CONVENIENTLY SIZED ? sYES- . COMPLETE MODEL OF THE PACKED COLUMN CHOOSE 1^  To match k ) by experiments GAS FLOW RATE = L M(G7L) DETERMINE CONFINING TUBE DIAMETER (To match k G ) DETERMINE POOL DIMENSIONS (To match a^  bp DETERMINE m V L / a v / F i g u r e 2.17: Procedure f o r u s i n g Complete m o d e l l i n g [ 6 0 ] . 82 2 . 3 . 3 . 1 WEAK P O I N T S O F L A B O R A T O R Y M O D E L S A l t h o u g h t h e t w o m o d e l s d e s c r i b e d a b o v e h a v e b e e n t e s t e d w i t h p i l o t p l a n t a b s o r b e r s , t h e y s t i l l s u f f e r f r o m s o m e i m p o r t a n t d e f i c i e n c i e s . F i r s t , t h e p h y s i c a l g a s a b s o r p t i o n p r o p e r t i e s ( k G , k L ° , a v , 7) o f t h e f u l l - s c a l e a b s o r p t i o n c o l u m n m u s t b e p r e c i s e l y k n o w n . S e c o n d , e x p e r i m e n t s h a v e t o b e p e r f o r m e d o n t h e l a b o r a t o r y a b s o r b e r s t o o b t a i n t h e d e s i r e d v a l u e s o f t h e p h y s i c a l g a s a b s o r p t i o n p r o p e r t i e s , w h i c h a r e i d e n t i c a l t o t h o s e o f t h e f u l l - s c a l e c o l u m n . T h i r d , i n s o m e c a s e s , t h e d e s i r e d v a l u e s o f t h e p h y s i c a l g a s a b s o r p t i o n p r o p e r t i e s may n o t b e m a t c h e d b y t h e l a b o r a t o r y a b s o r b e r s d u e t o ~ t h e i r l i m i t e d c a p a b i l i t i e s . A n e x a m p l e f o r t h e c a s e o f Point modelling, t h e l i m i t a t i o n o f a s t i r r e d c e l l i s i t s m a x i m u m s t i r s p e e d . I f i t i s o p e r a t e d a t a h i g h e r s p e e d , t h e g a s - l i q u i d i n t e r f a c e a r e a b e c o m e s u n k n o w n d u e t o r i p p l e s a t t h e g a s / l i q u i d c o n t a c t i n g s u r f a c e . I t i s t h e r e f o r e d e s i r a b l e t o d e v e l o p a new d e s i g n p r o c e d u r e f o r f u l l - s c a l e a b s o r b e r s w i t h c h e m i c a l r e a c t i o n w h i c h i s f r e e o f t h e a b o v e r e s t r i c t i o n s . 83 CHAPTER 3  THEORY T h i s c h a p t e r p r e s e n t s the t h e o r e t i c a l frame work f o r r i g o r o u s m a t h e m a t i c a l m o d e l l i n g and the proposed p i l o t p l a n t t e c h n i q u e f o r s i z i n g gas a b s o r b e r s w i t h c h e m i c a l r e a c t i o n . 3 . 1 MATHEMATICAL MODEL Packed a b s o r b e r d e s i g n p r o c e d u r e s based on f i r s t p r i n c i p l e s have improved s u b s t a n t i a l l y i n r e c e n t y e a r s . T r e y b a l [105] f i r s t d e v e l o p e d a method f o r s t e a d y s t a t e , a d i a b a t i c a b s o r p t i o n and s t r i p p i n g i n v o l v i n g s i n g l e s o l u t e systems. The proc e d u r e p r o p e r l y a c c o u n t s f o r the h e a t s of a b s o r p t i o n , s o l v e n t e v a p o r a t i o n and c o n d e n s a t i o n as w e l l as heat and mass t r a n s f e r r e s i s t a n c e s i n b o t h phases. The method was s u c c e s s f u l l y t e s t e d by R a a l and Khurana [106] u s i n g the air-ammonia-water system. F e i n t u c h and T r e y b a l [75] s u b s e q u e n t l y extended the work t o multicomponent systems. E x p e r i m e n t a l v e r i f i c a t i o n was p r o v i d e d by K e l l y e t a l . [106] f o r the p h y s i c a l a b s o r p t i o n of a c i d gases from c o a l gas u s i n g methanol as the a b s o r b e n t . R i g o r o u s t h e o r i e s f o r a b s o r p t i o n with c h e m i c a l r e a c t i o n were w e l l documented by A s t a r i t a [17] and Danckwerts [ 1 8 ] . The p r e v i o u s e f f o r t s were p r i m a r i l y d i r e c t e d towards 84 d e v e l o p i n g e x p r e s s i o n s f o r the l o c a l mass t r a n s f e r c o e f f i c i e n t s . By c o n t r a s t , l i t t l e emphasis was p l a c e d on d e v i s i n g d e s i g n methods. A new s e t of d e s i g n e q u a t i o n s f o r i s o t h e r m a l gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n was r e c e n t l y d e v e l o p e d by J o s h i e t a l . [ 6 5 ] . However, assuming a d i a b a t i c c o n d i t i o n s would have been more r e a l i s t i c because heat l o s s e s a r e g e n e r a l l y s m a l l i n i n d u s t r i a l a b s o r b e r s as su g g e s t e d by T r e y b a l [104] and Pandya [ 5 4 ] . A r i g o r o u s d e s i g n p r o c e d u r e f o r a d i a b a t i c gas a b s o r b e r s with chemical reaction was f i r s t d e s c r i b e d by Pandya [ 5 4 ] . The p r o c e d u r e was based on T r e y b a l ' s c o n c e p t s [104] f o r a d i a b a t i c , p h y s i c a l gas a b s o r p t i o n and Danckwerts' work [18] on i s o t h e r m a l gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n . Pandya's p r o c e d u r e a c c o u n t e d f o r t h e h e a t s of a b s o r p t i o n and r e a c t i o n , s o l v e n t e v a p o r a t i o n and c o n d e n s a t i o n , c h e m i c a l r e a c t i o n s i n the l i q u i d phase as w e l l as heat and mass t r a n s f e r r e s i s t a n c e s i n both phases. DeLeye and Froment [107] used a s i m i l a r p r o c e d u r e and p r e s e n t e d some n u m e r i c a l r e s u l t s f o r commercial p r o c e s s e s ; comparisons w i t h i n d u s t r i a l d a t a were however not g i v e n . R e c e n t l y , S a n y a l e t a l . [108] used a s i m i l a r approach t o model B e n f i e l d a b s o r b e r s i n which carbon d i o x i d e i s removed w i t h hot c a r b o n a t e s o l u t i o n s . A l t h o u g h good agreement between the p r e d i c t i o n s and f i e l d d a t a was c l a i m e d , o n l y two s e t s of a b s o r b e r i n l e t and o u t l e t d a t a were p r e s e n t e d . 85 3.1.1 MODEL FORMULATION The m a t h e m a t i c a l model p r e s e n t e d here i s based on the a l g o r i t h m proposed by Pandya [54] s i n c e i t i s r i g o r o u s and based on the w i d e l y a c c e p t e d c o n c e p t s proposed by T r e y b a l [104] and Danckwerts [ 1 8 ] . F i g u r e s 3.1 and 3.2 a r e sc h e m a t i c diagrams of an a d i a b a t i c , packed a b s o r b e r and a d i f f e r e n t i a l packed s e c t i o n , r e s p e c t i v e l y . A five-component system i s c o n s i d e r e d which i s comprised of an i n e r t c a r r i e r gas ( I ) , an a c i d gas ( A ) , an i n e r t l i q u i d s o l v e n t ( S ) , a r e a c t a n t (B) i n t h e l i q u i d and a r e a c t i o n p r o d u c t ( C ) . The o v e r a l l c h e m i c a l r e a c t i o n i n the l i q u i d phase i s g i v e n by A + vkBB = C (3.1.1) The major assumptions of the p r e s e n t model a r e : the r e a c t i o n i s f a s t and t a k e s p l a c e o n l y i n t h e l i q u i d f i l m ; heat and mass t r a n s f e r r e s i s t a n c e s f o r t h e i n e r t s o l v e n t (S) i n the l i q u i d phase a r e n e g l i g i b l e ; t h e i n t e r f a c i a l a r e a i s the same f o r heat and mass t r a n s f e r ; a x i a l d i s p e r s i o n i s n e g l i g i b l e ; the ab s o r b e r o p e r a t e s a d i a b a t i c a l l y . dz I Y A,out Y S , o u t T G.out A Y S - H i Y s C B T G + d T G T r A Y S -B,in T L , in Y C B + d C B T , + d T L 86 f A , i n YS,in r G , i n T: -B,out L,out F i g u r e 3 . 1 : S c h e m a t i c d i a g r a m of a d i a b a t i c p a c k e d a b s o r b e r s . Y A + d Y , Y s + d Y s T r : + dTr Interface Gas Phase A,i 'S.i R a,A' R a,S 4G 'A,i : s,i Liquid Phase C B + d C B T T +dT T Figure 3.2: D i f f e r e n t i a l section of packed absorbers. 88 S i n c e no r e a c t i o n o c c u r s i n the gas phase, the t r a n s f e r of b o th s o l u t e A and vapor of s o l v e n t S w i t h i n the gas f i l m can be w r i t t e n as f o l l o w s : Ra,A a v d z = kG,A p <YA " YA, i ^  a v d z = G : d Y A (3.1.2) R a , s a v d z = kG,s p ( Y s " y s , i J a v d z = G T dY s* (3.1.3) The heat t r a n s f e r between gas and l i q u i d i s g i v e n by : q G a v dZ = h G ( T G - T L ) a v dZ (3.1.4) S i n c e the r e a c t i o n i s assumed t o be f a s t and t a k i n g p l a c e o n l y i n the l i q u i d f i l m , the c o n c e n t r a t i o n of the d i s s o l v e d gas i n the b u l k l i q u i d w i l l be n e a r l y t h a t which i s a t e q u i l i b r i u m w i t h i n t h e b u l k of the l i q u i d phase. T h e r e f o r e , the mass t r a n s f e r of A i n the l i q u i d f i l m i s : Ra,A a v d z = kL°,A I <C A f i " C A*) a v dZ (3.1.5) where I i s the enhancement f a c t o r and C A i s the e q u i l i b r i u m c o n c e n t r a t i o n of the d i s s o l v e d gas A i n the l i q u i d b u l k . As e x p l a i n e d i n Chapter 2, t h e enhancement f a c t o r i s a complex f u n c t i o n of hydrodynamic p r o p e r t i e s , r e a c t i o n k i n e t i c s , and 89 c o n c e n t r a t i o n s of b o t h phases. T h i s f u n c t i o n must be d e t e r m i n e d f o r the s p e c i f i c r e a c t i o n t a k i n g p l a c e i n the l i q u i d f i l m . For example, f o r a s i m p l e i n s t a n t a n e o u s second o r d e r i r r e v e r s i b l e r e a c t i o n where C A i s n e g l i g i b l e , the enhancement f a c t o r based on t h e t w o - f i l m t h e o r y can be w r i t t e n as [ 5 4 ] : I = (1 + [ ( C B * D B ) / U A B C A f i D A ) ] } where C B i s a b u l k c o n c e n t r a t i o n of r e a c t a n t B. D A and D B a r e the d i f f u s i v i t i e s of A and B i n t h e l i q u i d f i l m , r e s p e c t i v e l y . For the case of second-order f a s t r e a c t i o n s , the enhancement f a c t o r c a l c u l a t i o n s have been e x p l a i n e d i n Chapter 2. For o t h e r c a s e s , t h e works by Danckwerts [18] and A s t a r i t a e t a l . [19] s h o u l d be c o n s u l t e d . The change i n c o n c e n t r a t i o n of r e a c t a n t (B) and r e a c t i o n p r o d u c t (C) can be w r i t t e n as : L d C B = f A B R 3 f A a v dZ • (3.1.6) and L d C c " Ra,A a v d z (3.1.7) 90 T h e r e f o r e , the o v e r a l l m a t e r i a l b a l a n c e f o r a component over the d i f f e r e n t i a l h e i g h t can be o b t a i n e d by r e a r r a n g i n g E q u a t i o n s 3.1.2 and 3.1.6: d Y A = (L / i > A B ) d C B (3.1.8) The o v e r a l l heat b a l a n c e over dZ can be w r i t t e n a s : G T ( I ( Y j C P f j ) ) d T G (heat change i n the gas phase) = L C P f L d T L (heat change i n the l i q u i d phase) + Gj. H R d Y A ( h e a t s of a b s o r p t i o n and r e a c t i o n ) + G x H s d Y s (3.1.9) ( h e a t s of e v a p o r a t i o n ) where j denotes component A,S, and I A l s o , the r a t e of heat t r a n s f e r between the gas and l i q u i d phases i s g i v e n by: G T ( Z ( Y j C P f j ) ) d T G = h Q a v ( T Q - T L) dZ (3.1.10) (heat change i n (heat t r a n s f e r between the gas phase) gas and l i q u i d ) 91 The i n t e r f a c i a l c o n c e n t r a t i o n of the s o l u t e gas A i s o b t a i n e d by combining of E q u a t i o n s 3.1.2 and 3.1.5: Y A , i = YA - Ra,A/< p kG> (3.1.11) where R a = *I K L ° < H P YA ~ C A * ^ 1 + I H ( k L ° A G ) ]} (3.1.12) and H denotes Henry's c o n s t a n t . S i n c e I depends on and Y A , i ' E q u a t i o n s 3.1.11 and 3.1.12 need t o be s o l v e d s i m u l t a n e o u s l y . 3.1.2 COMPUTATIONAL PROCEDURE At the s t a r t -of the c a l c u l a t i o n s , the f o l l o w i n g parameters are known: the f l o w r a t e s , temperature and c o m p o s i t i o n s of the i n l e t gas and l i q u i d phases; the t o t a l p r e s s u r e of the a b s o r b e r ; the t y p e and s i z e of the p a c k i n g . The c o n c e n t r a t i o n of A i n t h e e x i t gas i s t y p i c a l l y s p e c i f i e d . I f the temperature and the c o n c e n t r a t i o n of the s o l v e n t vapor i n the e x i t gas a r e known, t h e r e i s s u f f i c i e n t i n f o r m a t i o n t o determine p a c k i n g h e i g h t by the f o l l o w i n g c o m p u t a t i o n a l s t e p s : 92 1. A s s u m e t h e t e m p e r a t u r e o f a n d t h e s o l v e n t v a p o r c o n c e n t r a t i o n ( Y S ) i n t h e o u t l e t g a s . T h e s e v a l u e s a r e s u b j e c t t o l a t e r v e r i f i c a t i o n . ( G o o d i n i t i a l a p p r o x i m a t i o n o f T Q a n d Y S v a l u e s a t t h e c o l u m n t o p a r e t h e e q u i l i b r i u m v a l u e s w i t h t h e e n t e r i n g l e a n s o l v e n t . ) 2 . C o m p u t e t h e l i q u i d t e m p e r a t u r e a n d c o m p o s i t i o n o f t h e l i q u i d l e a v i n g t h e a b s o r b e r b y u t i l i z i n g o v e r a l l m a s s a n d e n e r g y b a l a n c e s : c B , o u t = c B , i n ~ * G I < Y A , i n " Y A , o u t ^ /(L /i> A B )} ( 3 . 1 . 1 3 ) T h e e x i t t e m p e r a t u r e o f t h e l i q u i d i s g i v e n b y : T L , o u t = T L , i n + C [ G I ( L T j C P f j ) ) * ( T G f i n - T G f 0 u t ) + G j H R ( Y A F I N - Y A F Q U T ) + G I H S < Y S , i n " Y S , o u t ) V ( L C P f L ) } ( 3 . 1 . 1 4 ) N o w , b e g i n t h e s t e p - b y - s t e p c o m p u t a t i o n o f h e a t a n d m a s s t r a n s f e r i n a d i f f e r e n t i a l h e i g h t , d Z , s t a r t i n g f r o m t h e b o t t o m o f t h e c o l u m n . 9 3 3. O b t a i n a l l the n e c e s s a r y p h y s i c a l and c h e m i c a l p r o p e r t i e s of both phases ( i . e . s o l u b i l i t y , d i f f u s i v i t y , r e a c t i o n r a t e c o n s t a n t e t c . ) . 4. E s t i m a t e k G ^ A , k 0 L f A , kg^g, hg, a v from d a t a bases or c o r r e l a t i o n s . 5. Assume y A f i and then d e t e r m i n e CA,i which i s e q u a l t o {H P y A f i i and the enhancement f a c t o r , I . The a b s o r p t i o n r a t e , R a, i s then c a l c u l a t e d from E q u a t i o n 3.1.12. 6. C a l c u l a t e Yh,i f r o m E q u a t i o n 3.1.11. Repeat s t e p s 5 and 6 u n t i l the v a l u e s of y A f i from b o t h s t e p s a r e a p p r o x i m a t e l y e q u a l . 7. Compute the f o l l o w i n g g r a d i e n t s over t h e d i f f e r e n t i a l h e i g h t : dY A/dZ = R 3 f A a v / G : (3.1.15) dY s/dZ = R a S av/Gj (3.1.16) dT G/dZ dT L/dZ (3.1.17) 94 + G T H R ( d Y A / d Z ) + Gj H s ( d Y s / d Z ) } / { L C P f L } (3.1.18) 8. S e l e c t a r e a s o n a b l y s m a l l v a l u e of AY A, an increment of gas c o m p o s i t i o n , so t h a t the above-mentioned g r a d i e n t s do not change s i g n i f i c a n t l y . The l e v e l of p a c k i n g a t which the next c o m p u t a t i o n w i l l be made i s : z n e x t = Z + AZ (3.1.19) where Z=0 f o r the bottom of t h e tower and AZ = AY A / ( d Y A / d Z ) (3.1.20) 9. Compute the c o m p o s i t i o n s and t e m p e r a t u r e s a t Z n e x t : Y A , n e x t = Y A + A* A (3.1.21) Y S , n e x t = Y S + AZ(dY s/dZ) (3.1.22) T G , n e x t = T G + AZ(dT G/dZ) (3.1.23) T L , n e x t = T L + AZ(dT L/dZ) (3.1.24) c B , n e x t = C B + A z (»< AB Ra, A av> (3.1.25) c C , n e x t = C C + A z ^ R a , A a v ) (3.1.26) 10. Repeat s t e p s 3 t o 9 u n t i l t h e d e s i r e d Y A f o r the o u t l e t gas i s reached. 9 5 11. Compare T Q and Y S v a l u e s t h o s e assumed f o r s t e p 1. s t e p s 1 t o 9 u n t i l these e q u a l . However, f u r t h e r because the s o l u t i o n i s i n s e n s i t i v e t o the v a l u e s Pandya [54]. o b t a i n e d from s t e p 10 w i t h I f they do not match, r e p e a t two v a l u e s a r e a p p r o x i m a t e l y i t e r a t i o n may not be needed i n most c a s e s found t o be of T G and Y S as su g g e s t e d by -Computer programs w r i t t e n i n FORTRAN were d e v e l o p e d based on the above c o m p u t a t i o n a l p r o c e d u r e . A s i m p l i f i e d f l o w c h a r t of th e s e programs i s shown i n F i g u r e 3.3. The p r e d i c t i v e a b i l i t y of the computer models was t e s t e d by comparing t h e i r r e s u l t s w i t h t h e e x p e r i m e n t a l p i l o t p l a n t d a t a . The comparisons a r e r e p o r t e d i n Chapter 6. 96 Start calculations at the bottom of absorber Assume i n t e r f a c i a l conditions Compute enhancement factor, I Compute heat and mass transfer I Assume new i n t e r f a c i a l conditions I yes Composition meets absorber e x i t conditions + yes END Recalculate and check No assumed i n t e r f a c i a l conditions No Go to next higher section of tower Figure 3.3: S i m p l i f i e d flow chart of the major c a l c u l a t i o n steps used in the present computer models. 9 7 3.2 PROPOSED PILOT PLANT TECHNIQUE FOR DESIGNING  GAS ABSORBERS WITH CHEMICAL REACTION A l t h o u g h t h e r e a r e a few p r o c e d u r e s a v a i l a b l e f o r d e s i g n i n g gas a b s o r b e r s w i t h c h e m i c a l r e a c t i o n , they s t i l l s u f f e r from the d e f i c i e n c i e s d e s c r i b e d i n Chapter 2. The o b j e c t i v e of t h i s s e c t i o n i s t h e r e f o r e t o d e v e l o p a new d e s i g n c o n c e p t , which i n v o l v e s s m a l l - s c a l e l a b o r a t o r y e x p e r i m e n t s and r e q u i r e s o n l y m i n i m a l knowledge of the a b s o r p t i o n - r e a c t i o n system. In p a r t i c u l a r , i t i s not n e c e s s a r y t o know the c h e m i c a l r e a c t i o n mechanism, r e a c t i o n r a t e c o n s t a n t s , mass t r a n s f e r c o e f f i c i e n t s and i n t e r f a c i a l a r e a . 3.2.1 THE PILOT PLANT TECHNIQUE* The proposed p r o c e d u r e , s u b s e q u e n t l y c a l l e d the P i l o t P l a n t Technique (PPT), i s based on measurements performed on p i l o t columns and i s p r i m a r i l y i n t e n d e d f o r a b s o r b e r s i z i n g when b a s i c d e s i g n d a t a a r e u n a v a i l a b l e . The fundamental i d e a i s t o use a s m a l l column, s u b s e q u e n t l y c a l l e d t h e " p i l o t p l a n t model or PPM column", t o s i m u l a t e the f u l l - s c a l e * I n i t i a l work on the PPT has been p r e s e n t e d a t the Symposium on S c a l e - u p of I n d u s t r i a l C h e m i c a l P r o c e s s e s ( T o r o n t o , 1988) and has been p u b l i s h e d i n the Canadian J o u r n a l of Che m i c a l E n g i n e e r i n g , 6 7(4), 602-607(1989). 98 ( i n d u s t r i a l s i z e ) a b s o r p t i o n tower. The sche m a t i c diagram of the proposed p r o c e d u r e i s shown i n F i g u r e 3 . 4 . An e s s e n t i a l c o n d i t i o n of the PPT i s t h a t the model column must have the same hydrodynamic c o n d i t i o n s as the f u l l - s c a l e column. C o n s i d e r t h a t s t e a d y - s t a t e c o n d i t i o n s p r e v a i l i n the packed column and t h a t o n l y one component, A, i s ab s o r b e d by the l i q u i d . The dominant c h e m i c a l r e a c t i o n i n the l i q u i d i s denoted by: A + vkBB = C At any p o i n t i n the column, the t r a n s f e r of A (or t h e change of B) per u n i t volume of p a c k i n g f o r a d i f f e r e n t i a l element dZ i s g i v e n by O v e r a l l a b s o r p t i o n r a t e = (A l o s t by gas phase) = (A g a i n e d by l i q u i d phase) + (A removed by the r e a c t i o n ) where (A removed by the r e a c t i o n ) = j»Ag(B consumed by the r e a c t i o n ) F i g u r e 3 . 4 Schematic of the P i l o t P l a n t T e c h nique. 100 The o v e r a l l a b s o r p t i o n r a t e can be e x p r e s s e d a s : R v , A = f*PA' C B ' kG' k L ° ' a v 1> rAB* and R V f k dZ = G j d Y A (3.2.1) = L d C A + 7 r A B d Z (3.2.2) where rAB = f * c A ' CB> T> and the change of component B i s g i v e n by: p A B 7 r A B dZ = -LdC B (3.2.3) R v , A * s t n e o v e r a l l a b s o r p t i o n r a t e of A per u n i t volume of p a c k i n g , p A i s the p a r t i a l p r e s s u r e of A i n the b u l k gas, 7 i s t he volume of l i q u i d per u n i t volume of p a c k i n g , C A i s the c o n c e n t r a t i o n of phys i c a l l y d i s s o l v e d A, and r A B i s the r e a c t i o n r a t e between A and B per volume of l i q u i d and dependent of the r e a c t i o n k i n e t i c s of the r e a c t i o n between A and B i n the l i q u i d phase. A m a t e r i a l b a l a n c e around the t o p s e c t i o n of the column can be w r i t t e n a s : G I t Y A , o u t " yA , z 3 = " L t c A , i n " c A , z l + < L / v A B ) [ C B r i n - C B f Z ] (3.2.4) where L i s the s u p e r f i c i a l l i q u i d f l o w r a t e . I t s h o u l d be 101 noted t h a t t h e r e i s o n l y one p a i r of f l u i d c o n c e n t r a t i o n s a t h e i g h t Z t h a t s a t i s f i e s E q u a t i o n 3.2.4 f o r a g i v e n s e t of to p and bottom c o n d i t i o n s . For some gas t r e a t i n g p r o c e s s e s , e s p e c i a l l y amine p r o c e s s e s , the l i q u i d c o m p o s i t i o n i s u s u a l l y e x p r e s s e d i n terms of the l i q u i d l o a d i n g , a, which i s d e f i n e d as moles of s o l u b l e gas ( p h y s i c a l l y and c h e m i c a l l y absorbed) per mole of t o t a l r e a c t a n t i n the l i q u i d . c h e m i c a l l y absorbed i n the l i q u i d phase and C A ^ denotes the c o n c e n t r a t i o n of the c h e m i c a l s i n k f o r the component A. The l o a d i n g of component A i n the l i q u i d i s g i v e n by: (3.2.5) where C A t i s the t o t a l c o n c e n t r a t i o n of A p h y s i c a l l y and a A = C A , t / C B , t = ( C A +  ch,$)/ cB,t (3.2.6) where CA,<: = <Vi»AB><CB,t - CB> (3.2.7) T h e r e f o r e , d a A = <1/C B, t> ( d C A + <3CA,c) (3.2.8) and d c A f C = - O A A B ) d c B (3.2.9) 1 02 The mass b a l a n c e over the top p a r t of t h e column can be w r i t t e n i n terms of l o a d i n g a s : G l t Y A , o u t " Y A , z J = L C B , t t a A f i n " aA,Z> (3.2.10) The above e q u a t i o n s can be r e a r r a n g e d and i n t e g r a t e d t o o b t a i n t h e t o t a l h e i g h t , Z t, of the column : VA, i n z t = Gj J d y A / [ R V f A d - y A ) 2 ] (3.2.11) v A , o u t (from E q u a t i o n 3.2.1) or c A , o u t c B , o u t Z t = L |dC A/R V / A - L | d C B / ( ^ A B R V / A ) (3.2.12) c A , i n c B , i n (from E q u a t i o n s 3.2.1 and 3.2.3) or aA, i n z t = L C B , t | d a A / R v , A (3.2.13) aA,OUt (from E q u a t i o n s 3.2.2, 3.2.3, 3.2.8 and 3.2.9) 103 In o r d e r t o e v a l u a t e the i n t e g r a l , R V f A m u s t D e known as a f u n c t i o n of gas and l i q u i d c o m p o s i t i o n s . For any h e i g h t Z, the s e c o n c e n t r a t i o n s can be o b t a i n e d from mass b a l a n c e e q u a t i o n s , p r o v i d e d the c o r r e s p o n d i n g v a l u e s a t the t o p (or the bottom) of the column a r e g i v e n , as i s u s u a l l y the c a s e . A l t h o u g h t h e r e a r e a few methods t o de t e r m i n e R V,A v a l u e s , they cannot be a p p l i e d t o the systems where fundamental d e s i g n d a t a a r e not known. The weaknesses of the a f o r e m e n t i o n e d methods have been d e s c r i b e d i n Chapter 2. By u s i n g the PPT, the R V f A v a l u e s a l o n g the f u l l s c a l e column can be measured d i r e c t l y from a model column i f b o t h columns have the same hydrodynamic c o n d i t i o n s which i n c l u d e mass t r a n s f e r c o e f f i c i e n t s , i n t e r f a c i a l a r e a and l i q u i d h o l d - u p . S i m i l a r hydrodynamics can be a c h i e v e d by p a c k i n g the PPM column w i t h the same t y p e and s i z e of p a c k i n g s as the f u l l -s c a l e column. The PPM column must a l s o be o p e r a t e d a t the same s u p e r f i c i a l gas and l i q u i d v e l o c i t i e s as t h o s e of the f u l l - s c a l e column. T h i s means t h a t the PPM column can be much s m a l l e r than the f u l l - s c a l e column i n b o t h d i a m e t e r and h e i g h t as l o n g as the gas and l i q u i d f l o w r a t e per u n i t c r o s s - s e c t i o n a l a r e a of the PPM column are t h e same as tho s e i n the f u l l - s c a l e column. Under t h e s e c o n d i t i o n s , the f l o w b e h a v i o r of gas and l i q u i d i n both columns s h o u l d be s i m i l a r . T h e r e f o r e , the p h y s i c a l gas a b s o r p t i o n d a t a f o r bot h columns s h o u l d be i d e n t i c a l p r o v i d e d w a l l e f f e c t s a r e 104 n e g l i g i b l e . The s p e c i f i c a b s o r p t i o n r a t e per u n i t volume of p a c k i n g , which now depends o n l y on the bu l k c o n c e n t r a t i o n s of r e a c t a n t s i n the gas and l i q u i d phases, can be measured f o r v a r i o u s gas and l i q u i d c o m p o s i t i o n s . Once the b u l k c o m p o s i t i o n s and temperature of the gas and l i q u i d phases a t l e v e l Z m i n t h e PPM column a r e a r r a n g e d t o be the same as those a t l e v e l Z i n the f u l l - s c a l e column, then R v A ( a t Z and Z m) must be s i m i l a r i n the PPM and f u l l -s c a l e columns. Hence R V f A can be det e r m i n e d e x p e r i m e n t a l l y as a f u n c t i o n of the f l u i d c o n c e n t r a t i o n s by u s i n g the PPM column. The h e i g h t of the f u l l - s c a l e a b s o r p t i o n tower i s then r e a d i l y found by n u m e r i c a l i n t e g r a t i o n of E q u a t i o n s 3.2.11, 3.2.12 or 3.2.13. ( A l t e r n a t i v e l y , i f the f u l l - s c a l e tower h e i g h t i s g i v e n , i t s a b s o r p t i o n c a p a c i t y can be p r e d i c t e d . ) I t i s c l e a r t h a t the PPT does not r e q u i r e knowledge of the hydrodynamic and p h y s i c o - c h e m i c a l p a r a m e t e r s . C o n s e q u e n t l y , the weak p o i n t s of t h e p r e v i o u s models a r e overcome (see Route # 4 i n F i g u r e 3.5). S i n c e e x p e r i m e n t a l v a l u e s a r e o b t a i n e d f o r R V f A from the PPM column which has the same hydrodynamic c h a r a c t e r i s t i c s as the f u l l - s c a l e tower, the PPT procedure i s a p p l i c a b l e t o a l l c a s e s r e g a r d l e s s of whether the o v e r a l l r a t e of a b s o r p t i o n i s DEFINITION OF PROCESS CONDITIONS - T o t a l flow rates of gas and l i q u i d - I n l e t and o u t l e t c o n d i t i o n s r SPECIFY GAS-LIQUID CONTACTING SYSTEM - Type and d e t a i l s of packings r OBTAIN PHYSICAL INFORMATION - D e n s i t i e s and v i s c o s i t i e s - G a s - l i q u i d e q u i l i b r i u m data 1 r 105 DETERMINATION OF SUPERFICIAL VELOCITIES L i q u i d s i d e Gas side OBTAIN PHYSICAL GAS ABSORPTION PARAMETERS - Mass t r a n s f e r c o e f f i c i e n t s - I n t e r f a c i a l area - L i q u i d hold-up OBTAIN ADDITIONAL INFORMATION - D i f f u s i v i t i e s - S o l u b i l i t i e s - Reaction k i n e t i c s DETERMINATION OF ENHANCEMENT FACTOR DETERMINATION OF ( K G a v ) a v e ® DETERMINATION OF ABSORPTION RATE ± DETERMINATION OF COLUMN HEIGHT Figu r e 3 . 5 : Main design procedures f o r gas absorbers with chemical r e a c t i o n 106 p r i m a r i l y d e t e r m i n e d by the r e a c t i o n i n the l i q u i d f i l m , i n the b u l k or i n b o t h . T h i s i m p l i e s t h a t the PPT may be a p p l i e d t o systems w i t h a l l r e a c t i o n regimes r a n g i n g from i n s t a n t a n e o u s t o slow r e a c t i o n ( a l s o see S e c t i o n 2.1 and F i g u r e 2.2) p r o v i d e d t h a t t h e w a l l and end e f f e c t s a r e n e g l i g i b l e . The model column may have w a l l and end e f f e c t s which a r e d i f f e r e n t ( t y p i c a l l y g r e a t e r ) than t h o s e of the f u l l -s c a l e column. F o r t u n a t e l y , t h e s e e f f e c t s may be m i n i m i z e d by proper d e s i g n of t h e packed column. In g e n e r a l , such a d e s i g n can be a c h i e v e d i f the f o l l o w i n g c r i t e r i a a r e s a t i s f i e d : 1. Good i n i t i a l and i n t e r m e d i a t e f l u i d d i s t r i b u t i o n i n the packed bed. A c c o r d i n g t o F a i r [ 8 5 ] , the number of l i q u i d streams per u n i t c r o s s s e c t i o n a l a r e a of the column s h o u l d be a t l e a s t 340 per m^. As was suggested by T r e y b a l [ 8 6 ] , the good l i q u i d d i s t r i b u t i o n can be m a i n t a i n e d by h a v i n g a r e d i s t r i b u t i o n p l a t e i n s i d e the column e v e r y 6 t o 10 column d i a m e t e r s or e v e r y 6 t o 7 m of p a c k i n g h e i g h t . 2. Large r a t i o of column diameter t o p a c k i n g s i z e . A c c o r d i n g t o F a i r [ 1 3 4 ] , the r a t i o of the 107 column ID t o p a c k i n g s i z e must be a t l e a s t 8 f o r c o n v e n t i o n a l p a c k i n g s i n o r d e r t o m i n i m i z e w a l l f l o w ( w a l l e f f e c t ) . However, t h i s r a t i o may be reduced t o 6 f o r h i g h e f f i c i e n c y random p a c k i n g s as r e p o r t e d by B i l l e t [ 1 3 2 ] . For s t r u c t u r e d p a c k i n g s , the column d i a m e t e r may be as s m a l l as 0.03 m w i t h o u t any s i g n i f i c a n t w a l l e f f e c t s [ 1 3 3 ] . More d e t a i l s on t h e proper column d e s i g n c r i t e r i a a r e p r e s e n t e d i n Chapter 5. DETERMINATION OF Rv A To o b t a i n t h e s p e c i f i c a b s o r p t i o n r a t e from PPM column t e s t s , t he c o n c e n t r a t i o n p r o f i l e i n the column i s measured and R V f A i s c a l c u l a t e d from t h e s l o p e of the p r o f i l e s , i . e . R v , A = G I clY A/dZ (3.2.14) where the mole r a t i o , Y A, i s g i v e n by Y A = YA /< 1 - V A " Ys> (3.2.15) The s p e c i f i c a b s o r p t i o n r a t e can a l s o be o b t a i n e d from the p r o f i l e of the l i q u i d c o m p o s i t i o n , i . e . R V f A = L dC A/dZ - (L/*> A B)dC B/dZ (3.2.16) 1 0 8 or R V f A = LCBft da A/dZ (3.2.17) S i n c e the R V > A v a l u e s a r e d e t e r m i n e d from the s l o p e of the c o n c e n t r a t i o n p r o f i l e s , t h e r e i s no need t o assume t h a t the o v e r a l l mass t r a n s f e r c o e f f i c i e n t s a r e c o n s t a n t as i m p l i e d by the e m p i r i c a l d e s i g n method (see s e c t i o n 2.3.1). The e x p e r i m e n t a l p r o c e d u r e s of o b t a i n i n g the R V,A v a l u e s w i l l be d e s c r i b e d i n S e c t i o n s 5.5 and 7.1. 3.2.2 A SHORT-CUT PROCEDURE FOR PPT I f t he c o n c e n t r a t i o n of t h e l i q u i d r e a c t a n t and the degree of c o n v e r s i o n a r e h i g h , t h e l i q u i d t e m p e r a t u r e may r i s e s i g n i f i c a n t l y due t o t h e h e a t s of a b s o r p t i o n and r e a c t i o n . Once the o p e r a t i o n becomes n o n - i s o t h e r m a l , the temperature a l o n g the column changes a p p r e c i a b l y and, s i n c e the c h e m i c a l r e a c t i o n r a t e s , s o l u b i l i t y and d i f f u s i v i t y a l l depend on tem p e r a t u r e , R V,A m a Y b e a f f e c t e d . To a p p l y the PPT t o n o n - i s o t h e r m a l s i t u a t i o n s , R V,A v a l u e s have t o be dete r m i n e d as f u n c t i o n s of gas and l i q u i d c o n c e n t r a t i o n s as w e l l as tempe r a t u r e . The t o t a l h e i g h t ( o r a b s o r p t i o n c a p a c i t y ) of the column can s t i l l be found by u s i n g E q u a t i o n 109 3.2.11. I t i s c o n v e n i e n t , and i n most c a s e s v a l i d , t o assume t h a t the temperature of the gas and l i q u i d a t any p o i n t of the column a r e a p p r o x i m a t e l y the same s i n c e the heat c a p a c i t y of the l i q u i d phase i s much l a r g e r than t h a t of the gas phase. To reduce the e x p e r i m e n t a l work i n h e r e n t i n the PPT, i t i s not n e c e s s a r y t o determine the s p e c i f i c a b s o r p t i o n r a t e f o r the e n t i r e range of gas and l i q u i d c o m p o s i t i o n s . To s i m u l a t e a b s o r p t i o n - r e a c t i o n b e h a v i o r i n the f u l l - s c a l e column f o r a g i v e n s e t of o p e r a t i n g c o n d i t i o n s - , o n l y R V,A v a l u e s t h a t c o r r e s p o n d t o the c o n c e n t r a t i o n s a l o n g the column a r e r e a l l y needed; a t i m e - s a v i n g p r o c e d u r e t h e r e f o r e s u g g e s t s i t s e l f . The f u l l - s c a l e column i s n o t i o n a l l y d i v i d e d i n t o m s e c t i o n s (see F i g u r e 3 . 6 ) . The model column (equipped w i t h n s a m p l i n g p o i n t s ) i s used t o s i m u l a t e the f u l l - s c a l e column s e c t i o n by s e c t i o n , s t a r t i n g from s e c t i o n 1 a t the t o p . The l i q u i d f e e d c o m p o s i t i o n ( C B ( 1 , 1 ) } i s known and the t r e a t e d gas c o m p o s i t i o n ( y A ( 1 , 1 ) 1 , which i s s p e c i f i e d , can be o b t a i n e d by v a r y i n g the gas c o m p o s i t i o n ( y A ( 1 , n ) } e n t e r i n g the base of the PPM column. In the case of n o n - i s o t h e r m a l o p e r a t i o n , the i n l e t t e m p e r a t u r e of the l i q u i d of the model column i s a l s o a d j u s t e d t o be the same as t h a t of the f u l l - s c a l e column. S i n c e the heat c a p a c i t y of the gas phase i s much s m a l l e r than t h a t of t h e l i q u i d , the 110 L G CB.in | j Vput S E C T I 0 N (1) S E C T I 0 N (2) S E C T I 0 N <m-l) S E C T I 0 N (m) C B,out~{ f Y A , i n FULL COLUMN A t s E C T I 0 * N * (2) I—T C0(2.n) , (2,n| Cfl(m-1,1) 1 1 s E C T I * 0 * • N « (n.) rA(m,n-t) 1 F MODEL COLUMN Cf l(m,n| F i g u r e 3.6 Schematic r e p r e s e n t a t i o n t o s i m u l a t e i n d u s t r i a l a b s o r b e r s u s i n g the PPT s h o r t - c u t p r o c e d u r e . I l l t e m p e r a t u r e of gas e n t e r i n g the model column may be a d j u s t e d t o be the same as t h a t of the l i q u i d . When thes e c o n d i t i o n s a r e met, the model column behaves l i k e s e c t i o n 1 of the f u l l - s c a l e column; c o n s e q u e n t l y the o u t l e t c o n c e n t r a t i o n of the l i q u i d {C B ( 1,n)} and the tem p e r a t u r e a t the model column bottom can be measured. Then, the c o n c e n t r a t i o n p r o f i l e s a l o n g the model column {e.g. C B ( 1 , 1 ) t o C B ( l , n ) and y A ( l , l ) t o y ^ ( l , n ) } can be measured and R V,A v a l u e s can be de t e r m i n e d . For s e c t i o n 2, i t s t o p c o n c e n t r a t i o n s C B ( 2 , 1 ) and y A ( 2 , 1 ) a r e made e q u a l t o the c o n c e n t r a t i o n s a t t h e bottom of t he s e c t i o n 1 { C B d , n ) and y A ( l , n ) , r e s p e c t i v e l y } . I f i t i s n e c e s s a r y f o r the tem p e r a t u r e t o be matched f o r the case of n o n - i s o t h e r m a l o p e r a t i o n , the tempe r a t u r e of t h e l i q u i d e n t e r i n g the model column i s a l s o s e t t o be the same as t h a t of the e x i t stream l e a v i n g s e c t i o n 1. The model column can then be used t o s i m u l a t e t h i s s e c t i o n i n t h e same way as the s e c t i o n 1 . The p r o c e d u r e i s r e p e a t e d u n t i l the bottom c o n d i t i o n s of the f u l l - s c a l e column a r e r e a c h e d . R V,A v a l u e s a l o n g the f u l l - s c a l e column can thus be o b t a i n e d . The number of ex p e r i m e n t s r e q u i r e d t o s i m u l a t e t h e f u l l - s c a l e column i s of the o r d e r of m. When R V f A does not change r a p i d l y , t h i s number can be f u r t h e r reduced by p e r f o r m i n g e x p e r i m e n t s o n l y 1 1 2 on some s e l e c t e d s e c t i o n s ( e . g . s e c t i o n 1, 3, 5,... or 1, 4, 8 , . . .) 3.2.3 VERIFICATION OF PPT A l t h o u g h the PPT concept d e v e l o p e d i n t h i s t h e s i s i s b e l i e v e d t o have g e n e r a l v a l i d i t y , i t s f e a s i b i l i t y and u s e f u l n e s s were t e s t e d w i t h f u l l - l e n g t h a b s o r p t i o n towers i n which carbon d i o x i d e i s a b s o r b e d from a i r by aqueous s o l u t i o n s of sodium h y d r o x i d e and 2-amino-2-methyl-1-p r o p a n o l (AMP) which i s a s t e r i c a l l y h i n d e r e d amine. The v e r i f i c a t i o n w i l l be p r e s e n t e d i n Chapter 7. The carbon d i o x i d e - sodium h y d r o x i d e system was chosen because i t has been s t u d i e d e x t e n s i v e l y p r e v i o u s l y , i s r e l a t i v e l y easy t o examine e x p e r i m e n t a l l y and p e r m i t s e v a l u a t i o n of a b s o r b e r performances based on f i r s t p r i n c i p l e s . By c o n t r a s t , the c a r b o n d i o x i d e - AMP system was chosen because i t i s a r e l a t i v e l y new system, h a v i n g been i n t r o d u c e d t o i n d u s t r y i n the e a r l y 1980's and v e r y l i t t l e i n f o r m a t i o n on t h i s system i s c u r r e n t l y a v a i l a b l e . C o n s e q u e n t l y , p r e d i c t i o n of column performance f o r t h i s system based on f i r s t p r i n c i p l e s i s not p o s s i b l e . 1 1 3 CHAPTER 4 SOLUBILITY OF CQ 2 IN 2-AMINQ-2-METHYL-1-PROPANOL SOLUTIONS* Very l i t t l e i n f o r m a t i o n on the C0 2-AMP system has been r e p o r t e d i n the open l i t e r a t u r e and even the s o l u b i l i t y c h a r a c t e r i s t i c s a r e m i s s i n g . T h i s c h a p t e r , which i s s e l f c o n t a i n e d , i s t h e r e f o r e p r e s e n t e d t o p r o v i d e comprehensive s o l u b i l i t y d a t a on the C 0 2 - AMP system. 4 .1 BACKGROUND INFORMATION S t e r i c a l l y h i n d e r e d amines have been i n t r o d u c e d r e c e n t l y and a r e c l a i m e d t o e x c e l over c o n v e n t i o n a l amines i n terms of C 0 2 a b s o r p t i o n c a p a c i t y , d e g r a d a t i o n r e s i s t a n c e and s e l e c t i v i t y [ 71, 100]. Very l i t t l e i n f o r m a t i o n has been r e p o r t e d i n t h e open l i t e r a t u r e even f o r 2-amino - 2-methyl-1-p r o p a n o l , or "AMP", which i s one of t h e more.widely used s t e r i c a l l y h i n d e r e d amines. The s t r u c t u r a l f o r m u l a of AMP i s : * T h i s c h a p t e r has been p u b l i s h e d i n the J o u r n a l of Chemical and E n g i n e e r i n g Data, 3 6 ( 1 ) , 130-133 (1991). 1 1 4 H 0 - C H 9 - C - N H o I C H 3 S a r t o r i and Savage [71] r e p o r t e d the CO2 s o l u b i l i t y - i n 3 M AMP s o l u t i o n s a t 40 and 120 ° C . R o b e r t s and Mather [95] p r o v i d e d C 0 2 and H 2 S s o l u b i l i t y d a t a f o r 2 M AMP s o l u t i o n s a t 40 and 100 ° C and, more r e c e n t l y , Teng and Mather [96] have examined the d i s s o l u t i o n of t h e same gases i n 3.43 M AMP s o l u t i o n s a t 50 ° C . The p r i n c i p a l o b j e c t i v e of t h i s c h a p t e r i s t o a c q u i r e s o l u b i l i t y d a t a f o r C 0 2 i n 2 and 3 M AMP s o l u t i o n s a t t e m p e r a t u r e s r a n g i n g from 20 t o 80 ° C s i n c e these v a l u e s c o v e r the t y p i c a l o p e r a t i n g ranges of a b s o r b e r s and have not been r e p o r t e d . The p r e s e n t and p r e v i o u s d a t a a r e s u b s e q u e n t l y i n t e r p r e t e d w i t h a m o d i f i e d K e n t - E i s e n b e r g model [ 9 7 ] . The performance of AMP i s a l s o compared w i t h t h a t of monoethanolamine. 1 1 5 4.2 EXPERIMENTAL APPARATUS AND PROCEDURE The a p p a r a t u s and p r o c e d u r e s used i n t h i s s tudy were s i m i l a r t o those d e s c r i b e d by Muhlbauer and Monaghan [98]. Gas m i x t u r e s of the d e s i r e d c o n c e n t r a t i o n were formed by m e t e r i n g streams of pure C 0 2 and N 2 t h r o u g h p r e c i s i o n r o t a m e t e r s . The m i x t u r e was then bubbled ( a t a f l o w r a t e of a p p r o x i m a t e l y 500 mL/min) th r o u g h a gas d i s p e r s e r i n t o a v e s s e l f i l l e d w i t h 50 mL of a NaCl s o l u t i o n , which had a water vapor p r e s s u r e i d e n t i c a l t o t h a t of the AMP s o l u t i o n under e x a m i n a t i o n . The gas m i x t u r e was then d i s p e r s e d i n t o an e q u i l i b r i u m v e s s e l c o n t a i n i n g 50 mL of aqueous AMP s o l u t i o n . Both v e s s e l s were p l a c e d i n a c o n s t a n t t e m p e r a t u r e bath c o n t r o l l e d t o w i t h i n ±0.5 °C. The C 0 2 d i s s o l u t i o n was f o l l o w e d by t a k i n g s m a l l samples of t h e AMP s o l u t i o n p e r i o d i c a l l y ; 4 t o 8 hours were u s u a l l y r e q u i r e d t o r e a c h e q u i l i b r i u m . Three AMP samples were then t a k e n and a n a l y z e d f o r t h e i r amine c o n c e n t r a t i o n and C 0 2 l o a d i n g u s i n g t h e methods d e s c r i b e d i n s e c t i o n 5.6. 4 . 3 P R E D I C T I V E MODEL FOR C 0 2 S O L U B I L I T Y IN AMP S O L U T I O N S A model" of the type proposed by Kent and E i s e n b e r g [97] was chosen because i t i s based on the fundamental t h e o r y of Danckwerts and M c N e i l [99] and because i t had g i v e n good 116 performance f o r p r e d i c t i n g a c i d gas s o l u b i l i t i e s i n a l k a n o l a m i n e s o l u t i o n s [101,118]. The c h e m i c a l e q u i l i b r i u m i n systems c o m p r i s e d of C O 2 , p r i m a r y amines and water i s governed by the f o l l o w i n g e q u a t i o n s : RNH 3 + = H + + RNH 2 4.1 RNHCOO" + H 20 = RNH 2 + H C O 3 " 4.2 H 2 0 + C 0 2 = H + + H C 0 3 ~ 4.3 H 20 = H + + OH~ 4.4 H C 0 3 ~ = H + + C 0 3 = 4.5 E q u a t i o n s 4.1 and 4.2 r e p r e s e n t t h e amine p r o t o n a t i o n and the amine carbamate h y d r o l y s i s , r e s p e c t i v e l y [ 1 0 0 ] . E q u a t i o n s 4.3 t o 4.5 a r e the t y p i c a l i o n i z a t i o n r e a c t i o n s f o r aqueous systems c o n t a i n i n g C 0 2 . S i n c e AMP has a t e r t i a r y c arbon atom a t t a c h e d t o the amino group, i t s carbamate i o n i s h i g h l y u n s t a b l e and e a s i l y r e v e r t s t o amine and b i c a r b o n a t e ; t h i s was f i r s t d i s c o v e r e d by S a r t o r i and Savage [ 7 1 ] . C h a k r a b o r t y e t a l . [72] r e c e n t l y r e p o r t e d t h a t carbamate i o n s c o u l d not be d e t e c t e d i n C 0 2 b e a r i n g - AMP s o l u t i o n s and they c o n c l u d e d t h a t the b i c a r b o n a t e and c a r b o n a t e i o n s a r e the o n l y major c h e m i c a l s i n k s f o r C 0 2 . 117 The e q u i l i b r i u m c o n s t a n t s r e p r e s e n t i n g the i m p o r t a n t r e a c t i o n s i n the C0 2~AMP-H 20 system, i n which water i s p r e s e n t i n e x c e s s , a r e g i v e n by: K i = [ H + ] [ R N H 2 ] / [ R N H 3 + ] 4.6 K 3 = [ H + ] [ H C 0 3 ~ ] / [ C 0 2 ] 4.7 K 4 = [H +][OH~] 4.8 K 5 = [ H + ] [ C 0 3 = ] / [ H C 0 3 ~ ] 4.9 A l t h o u g h some v a l u e s of K i (or pK 1 where pK 1 = - l o g K ^ have been r e p o r t e d , they u s u a l l y o n l y a p p l y t o i n f i n i t e l y d i l u t e s o l u t i o n s a t 25 and 40 °C. D e t a i l e d i n f o r m a t i o n on pK 1 as a f u n c t i o n of s o l u t i o n c o n c e n t r a t i o n and te m p e r a t u r e i s s t i l l l a c k i n g . In a d d i t i o n t o the above e q u i l i b r i u m e q u a t i o n s , o v e r a l l m a t e r i a l and charge b a l a n c e s must a l s o be s a t i s f i e d : [AMP] = [RNH 2] + [RNH 3 +] 4.10 a[AMP] = [ C 0 2 ] + [HC0 3~] + [ C 0 3 = ] 4.11 [RNH 3 +] + [ H + ] = [OH -] + [ H C 0 3 _ ] + 2 [ C 0 3 = ] 4.12 where [AMP] and a denote the t o t a l AMP c o n c e n t r a t i o n and the C 0 2 l o a d i n g of the AMP s o l u t i o n , r e s p e c t i v e l y . 118 The p h y s i c a l s o l u b i l i t y of C 0 2 i n the l i q u i d phase i s governed by Henry's law: PC02 = HC02 t C 0 2 ] 4 - 1 3 where P Q O 2 a n o - HC02 denote the p a r t i a l p r e s s u r e of carbon d i o x i d e i n the gas phase and Henry's c o n s t a n t , r e s p e c t i v e l y . E q u a t i o n s 4.6 t o 4.13 may be used t o f i n d the c o n c e n t r a t i o n s of seven s p e c i e s ( i . e . [RNH 2], [ H + ] , [ R N H 3 + ] , [ H C 0 3 " ] , [ C 0 2 ] , [ O H - ] , [ C 0 3 = ] ) and K, p r o v i d e d [AMP], a, p C 0 2 ' H C 0 2 ' K 3 ' K 4 a n d K 5 a r e g i v e n . The f i r s t t h r e e parameters a r e measured e x p e r i m e n t a l l y . The l a t t e r f o u r p arameters may be taken from the c o r r e l a t i o n s d e r i v e d by Kent and E i s e n b e r g [97] s i n c e t h e y were s u c c e s s f u l i n r e p r e s e n t i n g C 0 2 e q u i l i b r i a i n aqueous s o l u t i o n s of c o n v e n t i o n a l amines [102,103]. These c o r r e l a t i o n s were l a t e r c o n v e r t e d i n t o SI u n i t s by Chakma and Meisen [ 1 1 8 ] : K 3 = exp{-241.8l8 + 298.253x10 3T" 1 - 148.528x10 6T~ 2 + 3 3 2 . 6 4 8 X 1 0 8 T - 3 - 282.394x10 1°T" 4} (4.14) K 4 = exp{39.5554 - 9 8 7 . 9 X 1 0 2 T " 1 + 5 6 8 . 8 2 8 x 1 0 5 T - 2 - 1 4 6 . 4 5 1 X 1 0 8 T - 3 + 1 3 6 . 1 4 6 X 1 0 1 0 T " 4 } (4.15) 119 K 5 = exp{-294.74 + 364.385x10-% 1 - l 8 4 . l 5 8 x l O B T ^ + 4 1 5 . 7 9 3 x l 0 8 T ~ 3 - 3 5 4 . 2 9 1 x 1 0 1 ° T ~ 4 } (4.16) HC02 = exp{22.28l9 - 138.306x10 2T~ 1 + 6 9 1 . 3 4 6 x 1 0 4 T ~ 2 - 1 5 5 . 8 9 5 X 1 0 7 T ~ 3 + 120.037x10 9T" 4}/7.50061 (4.17) A n o n l i n e a r e q u a t i o n s o l v e r c a l l e d NDINVT, which i s based on the g e n e r a l i z e d s e c a n t method and which i s a v a i l a b l e from The U n i v e r s i t y of B r i t i s h Columbia Computing C e n t r e , was used t o s o l v e t h e e q u a t i o n s n u m e r i c a l l y . I n i t i a l e s t i m a t e s of the c o n c e n t r a t i o n s and K 1 had t o be p r o v i d e d f o r the i t e r a t i v e c a l c u l a t i o n s . These i n i t i a l v a l u e s c o u l d be o b t a i n e d from t h e approximate e q u i l i b r i u m r e a c t i o n e q u a t i o n of the C0 2-AMP system suggested by C h a k r a b o r t y e t a l . [ 7 2 ] : C 0 2 + RNH 2 + H 20 = HC0 3" + RNH 3 + The f r e e amine, [RNH 2], i s a p p r o x i m a t e l y e q u a l t o [AMP](1 a) and the c h e m i c a l s i n k C 0 2 , a[AMP], i s a p p r o x i m a t e l y e q u a l t o [HC0 3~] and [ R N H 3 + ] . S i n c e t h e pH of t h e s o l u t i o n i s u s u a l l y i n the o r d e r of 9 t o 11 and the v a l u e of K5 i s n o r m a l l y i n the o r d e r of 1 0 - 1 ^ kmol-ions/m 3, t h e v a l u e s of [ H + ] and [ C 0 3 = ] were a s s i g n e d t o be 1 0 ~ 1 0 and 1 0 - 8 , r e s p e c t i v e l y . The i n i t i a l v a l u e s a r e summarized below: 120 [RNH 2] = [AMP ] O.0-a) [ H + ] [HC0 3~] = a[AMP] [ C 0 2 ] [ C 0 3 = ] = 10~ 8 Kj 10 -10 [ RNH 3 +] = a[AMP] [OH~] = K 4 / [ H + ] PC02/ HC02 10 ~ 8 . S i n c e the v a l u e s of the unknown parameters range over s e v e r a l o r d e r s of magnitude, f a l s e convergence may o c c u r . To ensure t h i s does not happen, back c a l c u l a t i o n s were pe r f o r m e d by u s i n g a d i f f e r e n t n o n l i n e a r r o u t i n e c a l l e d QNEWT which i s based on a quasi-Newton method. By t a k i n g t h e K 1 v a l u e s computed w i t h NDINVT, P Q O 2 o r a v a l u e s were r e c a l c u l a t e d and compared w i t h t h e e x p e r i m e n t a l r e s u l t s . The comparisons were always e x c e l l e n t and pr o v e d t h a t f a l s e c o nvergence had not a r i s e n . 4.4 RESULTS AND DISCUSSION The C 0 2 s o l u b i l i t y d a t a and the pK^ v a l u e s a r e summarized i n T a b l e s 4.1 and 4.2. To a s s e s s t h e v a l i d i t y of the r e s u l t s , the C 0 2 s o l u b i l i t i e s i n 2 and 3 M AMP s o l u t i o n s a t 40 °C were compared w i t h t h o s e r e p o r t e d p r e v i o u s l y [ 7 1 , 9 6 ] . As shown by F i g u r e s 4.1 and 4.2, the agreement i s v e r y good t h e r e b y v a l i d a t i n g the p r e s e n t e x p e r i m e n t a l p r o c e d u r e . T a b l e 4.1: E x p e r i m e n t a l S o l u b i l i t y of C 0 2 i n 2 M AMP S o l u t i o n . Temp. C 0 2 P a r t i a l C 0 2 S o l u b i l i t y p l ^ K P r e s s u r e , kPa mol C0 2/mol AMP 293 98.93 0.960 9.343 293 49.88 0.900 9.316 293 19.28 0.880 9.704 293 8.39 0.815 9.842 293 3.23 0.781 10.242 31 3 94.00 0.940 9.339 313 47.05 0.841 9.167 313 18.01 0.768 9.373 313 7.94 0.704 9.576 313 2.70 0.620 9.864 333 82.66 0.830 8.994 333 41.14 0.735 9.015 333 16.46 0.600 9.066 333 8.00 0.476 9.059 333 1 .90 0.375 9.410 353 53.33 0.618 8.720 353 25.84 0.463 8.638 353 10.40 0.291 8.507 353 4.99 0.212 8.504 353 1 .59 0.154 8.692 T a b l e 4.2: E x p e r i m e n t a l S o l u b i l i t y of C 0 2 i n 3 M AMP S o l u t i o n . Temp. C 0 2 P a r t i a l C 0 2 S o l u b i l i t y pK} K P r e s s u r e , kPa .mol C0 2/mol AMP 293 98 .93 0 .898 9.161 293 49 .88 0 .846 9 .272 293 19.28 0 .830 9 .680 293 8 .39 0 .763 9 .854 293 3 .23 0 .747 10.342 313 94 .00 0 .875 9 . 170 313 47 .05 0 .815 9 .267 313 18.01 0 .714 9 .399 313 7 .94 0 .643 9 .589 313 2 .70 0 .582 9 .949 333 82 .66 0 .809 9 .116 333 41 .14 0 .683 9 .056 333 16.46 0 .546 9 . 107 333 8 .00 0 .427 9 . 104 333 1 .90 0.321 9 .405 353 53 .33 0 .524 8 .658 353 25 .84 0 .394 8.621 353 10.40 0 .247 8 .514 353 4 . 9 9 0 . 169 8 .458 353 1 .59 0 . 126 8 .673 123 F i g u r e 4.1: S o l u b i l i t y of C 0 2 i n a 2 M AMP s o l u t i o n a t 40 °C. ( S o l i d c i r c l e s - p r e s e n t e x p e r i m e n t a l d a t a ; open c i r c l e s - R o b e r t s and Mather [ 9 5 ] ; s o l i d l i n e s - p r e s e n t model.) 124 F i g u r e 4.2: S o l u b i l i t y of C0 2 i n a 3 M AMP s o l u t i o n a t 40 °C. ( S o l i d c i r c l e s - present e x p e r i m e n t a l d a t a ; open c i r c l e s - Roberts and Mather [ 9 5 ] ; squares - S a r t o r i and Savage [ 7 1 ] ; s o l i d l i n e s -present model.) 125 The v a l u e s of K 1 r e p o r t e d here are a p p a r e n t e q u i l i b r i u m c o n s t a n t s s i n c e the e f f e c t s of system n o n i d e a l i t i e s were not e x p l i c i t l y a c counted f o r i n the model, but lumped i n t o the K 1 v a l u e s . The l a t t e r were t h e r e f o r e e x p r e s s e d as a f u n c t i o n of T, [ C 0 2 ] and [AMP]. U s i n g [ C 0 2 ] i s p r e f e r a b l e t o a s i n c e t h e former can be c a l c u l a t e d d i r e c t l y from P Q O 2 a n o - HC02 a s s u g g e s t e d by Chakma and Meisen [ 1 1 8 ] . The f o l l o w i n g c o r r e l a t i o n was found t o be o p t i m a l : pR} = 2309.1 + 0.49828 T - 70850. 1/T - 388.03 l n T - 6.3899 [ C 0 2 ] - 0.095221 l n [ C 0 2 ] + 0.038508 [AMP] (4.18) T a b l e 4.3 p r o v i d e s a comparison between t h e pK 1 v a l u e s found i n t h i s work and t h o s e r e p o r t e d e a r l i e r . The r e s u l t s p r e d i c t e d by E q u a t i o n 4.18 agree w e l l w i t h t h e d a t a r e p o r t e d by S a r t o r i and Savage [71] and Teng and Mather [ 9 6 ] , but they a r e somewhat h i g h e r than t h o s e of C h a k r a b o r t y e t a l . [ 7 2 ] . When E q u a t i o n 4.18 i s used t o f i n d K 1, t h e n E q u a t i o n s 4.6 t o 4.13 may be e v a l u a t e d t o o b t a i n the c o n c e n t r a t i o n s of a l l s p e c i e s f o r a g i v e n s e t of T, [ C 0 2 ] and [AMP]. As a r e s u l t , t h e t o t a l C 0 2 s o l u b i l i t y , a, may be d e t e r m i n e d . 126 T a b l e 4.3: Comparison of p r e s e n t and p r e v i o u s l y r e p o r t e d pKi v a l u e s . Source Temp. AMP Cone. C O 2 P a r t i a l pR-| (°C) (M) P r e s . , (kPa) S a r t o r i and Savage [71] 40 3 0.7-305 9.70 C h a k r a b o r t y e t a l . [72] 40 1-3 0. -100 8.50 T h i s work (Eq. 4.18) 40 3 10.0 9.67 Teng and Mather [96] 50 3.43 4-5650 9.11 T h i s work (Eq. 4.18) 50 3.43 100 9.16 127 The QNEWT r o u t i n e was employed f o r t h i s purpose w i t h the i n i t i a l e s t i m a t e s of a f a l l i n g i n t o the range of 0.5 t o 1.0 mol CC^/mol AMP. As can be seen from F i g u r e s 4.1 t o 4.4, good agreement was found between the p r e d i c t e d and measured r e s u l t s ; the mean square d e v i a t i o n was 6.0 % f o r the p r e s e n t e x p e r i m e n t a l r e s u l t s . I t s h o u l d be noted t h a t the s o l u b i l i t y of C 0 2 i n AMP s o l u t i o n i s a f a i r l y weak f u n c t i o n of temperature between 20 and 40 °C, but i t becomes a s t r o n g f u n c t i o n i n the range of 60 t o 80 °C. The C 0 2 s o l u b i l i t i e s i n 2.5 M AMP and MEA s o l u t i o n s a r e shown i n F i g u r e 4.5. I t i s i n t e r e s t i n g t o note t h a t the s o l u b i l i t i e s i n AMP s o l u t i o n s a r e h i g h e r than those i n MEA s o l u t i o n s a t 40 °C. At 80 °C the o p p o s i t e i s t r u e and a c r o s s - o v e r i s seen a t 60 °C. From the p o i n t of s o l u b i l i t y , AMP s o l u t i o n s are t h e r e f o r e s u p e r i o r t o MEA s o l u t i o n s f o r t h e r e g e n e r a t i v e s e p a r a t i o n of C 0 2 s i n c e a b s o r b e r s o p e r a t e a t low temperatures where a i s l a r g e and r e g e n e r a t o r s o p e r a t e a t e l e v a t e d t e m p e r a t u r e s where a i s low. However, t h e r e are i n d i c a t i o n s t h a t the r e a c t i o n and mass t r a n s f e r r a t e s are lower f o r the C0 2-AMP system than the C0 2 _MEA system [ 1 0 3 ] . F u r t h e r r e s e a r c h i s t h e r e f o r e w a r r a n t e d on AMP r e a c t i o n k i n e t i c s , mass t r a n s f e r r a t e s and s t a b i l i t y . Some of the p i l o t p l a n t a b s o r p t i o n d a t a of t h e s e two systems w i l l a l s o be compared and d i s c u s s e d i n Chapter 7. 128 P-. o - 6 I l l l 11 1 1 I I I I l 11 ' ' • • i i i 11 5*10_110° id 1 10* C0 2 Partial Pressure (kPa) F i g u r e 4.3: S o l u b i l i t y of C 0 2 i n a 2 M AMP s o l u t i o n at v a r i o u s t e m p e r a t u r e s . (Open c i r c l e s - 20 °C; s o l i d c i r c l e s - 40 °C; squares - 60 °C; t r i a n g l e s - 80 °C; s o l i d l i n e s - pr e s e n t model.) 129 F i g u r e 4.4: S o l u b i l i t y of C 0 2 i n a 3 M AMP s o l u t i o n a t v a r i o u s t e m p e r a t u r e s . (Open c i r c l e s - 20 °C; s o l i d c i r c l e s - 40 °C; squares - 60 °C; t r i a n g l e s - 80 °C; s o l i d l i n e s - p r e s e n t model.) 130 5*io_1 io° io1 io 2 C0 2 Partial Pressure (kPa) F i g u r e 4.5: S o l u b i l i t y of C 0 2 i n 2.5 M AMP and MEA s o l u t i o n s a t v a r i o u s t e m p e r a t u r e s . ( D o t t e d , dashed and c h a i n d o t t e d l i n e s a r e the model p r e d i c t i o n s f o r the C0 2-AMP system a t 40, 60 and 80 °C, r e s p e c t i v e l y . S o l i d l i n e s a r e from the Kent-E i s e n b e r g model [97] f o r the C0 2-MEA system.) 131 CHAPTER 5 PILOT PLANT AND EXPERIMENTAL PROCEDURE The p i l o t p l a n t shown i n F i g u r e 5.1 was used t o p e r f o r m th e p r e s e n t a b s o r p t i o n s t u d i e s . F i g u r e 5.2 shows the way i n whic h the p i l o t p l a n t f i t t e d i n t o the e x i s t i n g l a b o r a t o r y of the C h e m i c a l E n g i n e e r i n g Department, UBC. The equipment d e t a i l s a r e d e s c r i b e d i n the f o l l o w i n g s e c t i o n s . 5.1 THE FULL-LENGTH ABSORPTION COLUMN The f u l l - l e n g t h a b s o r p t i o n column (7.2 m h i g h , 0.1 m ID) was made of a c r y l i c p l a s t i c and was packed w i t h 12.7 mm (1/2") ceramic B e r l S a d d l e s ( p r o v i d e d by Koch E n g i n e e r i n g Co. of C a l g a r y , A l b e r t a ) . These dimensions were s e l e c t e d s i n c e they c o u l d be r e a d i l y accommodated i n the e x i s t i n g l a b o r a t o r y and p r o v i d e d r e a l i s t i c e x p e r i m e n t a l d a t a . F i g u r e 5.3 shows the d e t a i l e d d i m e n s i o n s of the a b s o r b e r . The f u l l - l e n g t h column was comprised of s i x s e c t i o n s (each 1.2 m h i g h ) w i t h r e d i s t r i b u t o r s i n s e r t e d between s e c t i o n s . The drawings of the column s e c t i o n and r e d i s t r i b u t o r s a r e shown i n F i g u r e s 5.4 and 5.5, r e s p e c t i v e l y . F i g u r e 5.6 a l s o shows how two s e c t i o n s a r e j o i n e d t o g e t h e r . Condenter Regeneration Column Figure 5 . 1 : Schematic of the p i l o t plant Abjorpllon Column Storage Tink F i g u r e 5.2: P i c t u r e showing how the p i l o t p l a n t equipment f i t t e d i n t o the Chemical E n g i n e e r i n g B u i l d i n g C i s Sample Point Liquid Simple Point Thermocouple F i g u r e 5 . 3 : Schematic the a b s o r p t i o n column 136 F i g u r e 5.5: Schemat ic of the r e d i s t r i b u t o r s 137 F i g u r e 5 . 6 : Drawing of the j o i n t between two s e c t i o n s 138 The dimensions s e l e c t e d for t h i s absorber were c a r e f u l l y checked by comparing them with the "proper" design c r i t e r i a suggested p r e v i o u s l y . The comparisons are shown i n Table 5.1. To pack a column s e c t i o n , approximately 500 mL o f -packing elements were dumped i n t o the empty s e c t i o n and planed. (This way of packing i s commonly used i n i n d u s t r y [38, 137].) The process was repeated u n t i l a packing height of approximately 1.1 m was reached. In order to vary the e f f e c t i v e packing height over which absorption occurred i n the f u l l - l e n g t h column, the gas could be introduced at d i f f e r e n t p o s i t i o n s between s e c t i o n s as shown i n Figure 5.7. The gas and l i q u i d phases c o u l d be sampled at each s e c t i o n i n l e t and o u t l e t to determine t h e i r composition. To measure the column temperature p r o f i l e , a thermocouple ( J type, Omega Engineering) was i n s e r t e d j u s t below the r e d i s t r i b u t o r of each s e c t i o n . The diagram of the sampling system i s shown i n Figure 5.8. The f l u i d sampling probes c o n s i s t e d of 100 mm long, 18-gauge needles f i t t e d w i t h s p e c i a l l y made 9 mm O.D. and 9 mm high T e f l o n cups at t h e i r t i p s . To sample the gas phase, the cups were p o s i t i o n e d i n such a way that t h e i r open ends faced i n t o the d i r e c t i o n of 139 the gas flow. The needle o u t l e t s were connected to an i n f r a r e d gas a n a l y z e r by nylon tubes. The gas sampling r a t e was c o n t r o l l e d by polycarbonate clamps (Canlab, Vancouver, B.C.). For l i q u i d sampling, the open ends of the cups p o i n t e d i n t o the d i r e c t i o n of the l i q u i d flow and the needles were connected to 50 mL s y r i n g e s . The p o s i t i o n s of both cups can be changed along the column r a d i u s . A p i c t u r e of the sampling system i s shown i n F i g u r e 5.7 . 140 T a b l e 5.1: "Proper" Design C r i t e r i a of Packed Columns. C r i t e r i o n P r e s e n t column Column ID ^ 0.10 m 0.10m ( F a i r [ 1 3 4 ] , Rase [33]) P a c k i n g s i z e £ 12.7 mm 12.7 mm ( F a i r [ 1 3 4 ] , Rase [33]) Column ID t o p a c k i n g s i z e r a t i o £ 6 t o 8 8 ( B i l l e t e t a l . [ 1 3 2 ] , F a i r [134]) L i q u i d d i s t r i b u t i o n : No. of stream > 340 per m 2 2546 per m 2 ( F a i r [ 85]) R e d i s t r i b u t i o n : e v e r y 6 t o 10 column ID's or 6 t o 7 m e v e r y 1.10 m ( T r e y b a l [86]) 9.53 mm, NPT 100 mm l o n g , 18 gauge SS needle F i g u r e 5.8: Schematic of the s a m p l i n g system t o 143 5.2 PILOT PLANT MODEL (PPM) COLUMN For the sake of c o n v e n i e n c e , the t o p s e c t i o n of the f u l l - l e n g t h a b s o r b e r was used as the PPM column (see F i g u r e 5.3). The drawing of t h i s s e c t i o n i s shown i n F i g u r e 5.9. In o r d e r t o e v a l u a t e the R V,A v a l u e s , the gas or l i q u i d c o n c e n t r a t i o n p r o f i l e i s needed (see E q u a t i o n s 3.2.14 t o 3.2.17). The l i q u i d c o m p o s i t i o n s may be measured u s i n g on-l i n e i n s t r u m e n t s such as pH meters or i o n i c s p e c i f i c e l e c t r o d e s . However, they a re not v e r y r e l i a b l e u n l e s s they a r e p r o p e r l y c a l i b r a t e d . I n t h e p r e s e n t s t u d y , i t was d e c i d e d t o measure the CO2 c o n c e n t r a t i o n p r o f i l e i n t h e gas phase u s i n g i n f r a r e d s p e c t r o s c o p y , which i s r e l i a b l e , r e a d i l y a v a i l a b l e and easy t o use. The d e t a i l s of the gas c o m p o s i t i o n a n a l y z e r w i l l be g i v e n i n S e c t i o n 5.6. The PPM column was d e s i g n e d i n such a way t h a t t h e gas phase c o u l d be sampled e v e r y 0.1 m a l o n g t h e s e c t i o n . T h i s was a c h i e v e d by c a r e f u l l y p l a c i n g gas sa m p l i n g probes w i t h i n the p a c k i n g a l o n g the column. F i g u r e 5.10 shows the p o s i t i o n of the gas sampl i n g p r o b e s i n s i d e the column. The p i c t u r e s of t h e PPM column i s shown i n F i g u r e s 5.11 and 5.12. H 1 1 0 0 mm F i g u r e 5 . 9 : D r a w i n g o f t h e PPM c o l u m n 145 F i g u r e 5.10: Diagram showing the gas s a m p l i n g p o s i t i o n F i g u r e 5.11: P i c t u r e of the PPM column F i g u r e 5 .12 : P i c t u r e of sampling probes a l o n g the PPM column 148 5.3 REGENERATION COLUMN In the case of amine s o l u t i o n s , the C 0 2 - r i c h s o l u t i o n was r e g e n e r a t e d i n a s e p a r a t e u n i t . The diagram of the r e g e n e r a t o r i s shown i n F i g u r e 5.13. The column had a dia m e t e r of 0.1 m ID, was made of QVF g l a s s and packed w i t h 12.7 mm ceramic R a s c h i g r i n g s t o a h e i g h t of 1.4 m. The r e b o i l e r was made from a s t a i n l e s s s t e e l drum (0.7 m ID x 0.7 m h i g h ) . A steam c o i l (15.88 mm OD x 12 m) w i t h 1.93 m 2 h e a t i n g a r e a was used as the h e a t i n g element. The condenser a t the r e g e n e r a t o r t o p was a s t a i n l e s s s t e e l d ouble tube j a c k e t . A water c o o l i n g c o i l (9.53 mm OD x 6 m lo n g ) was a l s o f i t t e d i n s i d e t h e condenser. The t o t a l c o o l i n g s u r f a c e i s about 0.325 m2. F i g u r e s 5.14 t o 5.16 show the p i c t u r e s of the r e g e n e r a t o r . F i g u r e 5 .14 : P i c t u r e of the r e g e n e r a t o r F i g u r e 5.15: P i c t u r e of the top part of the regenerator F i g u r e 5 .16 : P i c t u r e of the bottom par t of the r e g e n e r a t o r 153 5.4 AUXILIARY EQUIPMENT T h i s s e c t i o n d e s c r i b e s the d e t a i l e d s p e c i f i c a t i o n s of the a u x i l i a r y equipment used i n the a b s o r p t i o n s t u d i e s ( a l s o see F i g u r e 5.1). The l i q u i d f e e d and s t o r a g e t a n k s were made of 45 g a l l o n p o l y e t h y l e n e drums. The c a p a c i t y of each tank was about 0.2 m3. and p e r m i t t e d e x p e r i m e n t a l runs l a s t i n g a t l e a s t 90 minut e s . The c o n s t a n t temperature bath was used t o c o n t r o l the f l u i d t e m p e r a t u r e s . I t was made of a 45 g a l l o n s t a i n l e s s s t e e l drum equipped w i t h a 6 kW immersion h e a t e r (Model MT 360, Chromalox Canada). Water, which was a g i t a t e d by a s t i r r e r i n o r d e r t o keep the bath temperature u n i f o r m , was used as the h e a t i n g medium. The ba t h temperature was c o n t r o l l e d ( w i t h i n ±1 °C) by a p r o p o r t i o n a l c o n t r o l l e r (Model 49, Omega E n g i n e e r i n g I n c . , S t a m f o r d , CT). A magnetic d r i v e pump made of p o l y p r o p y l e n e and powered by a 1/3 Hp motor (Fabco, Model MDR-60t-t03) was used t o f e e d the s o l u t i o n t o t h e column. The maximum o p e r a t i n g p r e s s u r e and f l o w r a t e were 190 kPa and 3.8 m 3/hr, r e s p e c t i v e l y . A s t a i n l e s s s t e e l gear pump (Arco Instrument Co., Model 211-513) was used t o pump the C 0 2 r i c h s o l u t i o n 154 back to the feed tank or to the regenerator. Its maximum operating pressure and flow rate were 1374.0 kPa and 0.34 m3/hr, respectively. A cali b r a t e d rotameter from Omega Engineering Inc. (Model FL-73C) was used to measure the a i r flow rate.- Its operating range was 0 to 255 (std) L/min. Since the physical properties of solutions change with concentration and solvent type, the l i q u i d rotameter (Model FL-73M, Omega Engineering Inc.) was calibr a t e d before each run using a precision measuring cylinder and stop watch. The maximum measurable flow rate of the l i q u i d rotameter was about 4.0 L/min. The rotameter for measuring C0 2 flow rates was obtained from Brooks Instrument, Markham, Ontario (Model R-8M-25-2[tube] and 8-RV-8[float]). Its maximum measurable flow rate i s about 91 (std) L/min. 155 5.5 PROCEDURE FOR ABSORPTION EXPERIMENTS USING  THE FULL-LENGTH AND PPM COLUMNS The f e e d s o l u t i o n s were p r e p a r e d i n advance w i t h the d e s i r e d c o m p o s i t i o n s . (The e x a c t c o m p o s i t i o n s of the s o l u t i o n s were d e t e r m i n e d by methods d e s c r i b e d i n S e c t i o n 5.6.) A l l s o l u t i o n c h e m i c a l s were of commercial grade p r o v i d e d by Van Water and Rogers Co., Vancouver, BC. For the f u l l - l e n g t h column e x p e r i m e n t s , the l i q u i d , a i r and CO2 f l o w r a t e s were' measured- by the r o t a m e t e r s . The a i r and CO2 were then premixed and f l o w e d i n t h e same gas l i n e . A l l f l u i d s were p r e h e a t e d i n the c o n s t a n t temperature b a t h . A f t e r t h e f l o w r a t e and c o n c e n t r a t i o n of t h e f e e d gas were s e t t o t h e d e s i r e d v a l u e s , the gas m i x t u r e was i n t r o d u c e d i n t o the column and f l o w e d upwards and c o u n t e r - c u r r e n t l y t o the l i q u i d s o l u t i o n which was i n t r o d u c e d i n t o the t o p of t h e tower. The e x i t gas l e f t a t the t o p of t h e a b s o r b e r . The CO2 r i c h s o l u t i o n l e a v i n g the a b s o r b e r bottom was c o l l e c t e d i n the s t o r a g e t a n k s . Steady s t a t e was u s u a l l y r e a c h e d w i t h i n 15 t o 20 minutes f o r the PPM column runs and 30 t o 40 minutes f o r t h e f u l l - l e n g t h column r u n s . Steady s t a t e was i n d i c a t e d by c o n s t a n t temperature r e a d i n g s a l o n g the column and c o n s t a n t c o n c e n t r a t i o n of the e x i t gas. A f t e r r e a c h i n g steady s t a t e , 156 the gas c o n c e n t r a t i o n and temperature p r o f i l e s a l o n g the column were measured and r e c o r d e d . The gas s a m p l i n g r a t e was about 20 mL/min. A p p r o x i m a t e l y 40 mL of l i q u i d sample were a l s o withdrawn a t each s a m p l i n g l o c a t i o n d u r i n g the run u s i n g the samp l i n g s y r i n g e . The c o m p o s i t i o n s of the l i q u i d samples were d e t e r m i n e d upon c o m p l e t i o n of a run and u s i n g methods d e s c r i b e d i n the next s e c t i o n . For e x p e r i m e n t a l runs conducted w i t h the PPM column, the gas m i x t u r e was f e d i n t o the column j u s t below the r e d i s t r i b u t i o n p l a t e of the t o p s e c t i o n . The e x p e r i m e n t a l p r o c e d u r e was then the same as t h a t of the f u l l - l e n g t h column. The systems and o p e r a t i n g c o n d i t i o n s used i n the s e s t u d i e s a r e summarized i n T a b l e s 5.2 and 5.3 157 T a b l e 5.2 : Systems s t u d i e d and number of e x p e r i m e n t a l r u n s . System Absorbent No. of Runs Purpose Comments Cone. (kmol/m3) F u l l - l e n g t h PPM Column Column C0 2-NaOH 1.2 6 17 t o v e r i f y w e l l PPT and known t o t e s t system t h e o r e t i c a l model C0 2-MEA up t o 3.8 10 - t o t e s t m o d e r a t e l y t h e o r e t i c a l w e l l model known system C0 2-NaOH up t o 2.5 6 24 t o v e r i f y w e l l PPT and known t o t e s t system t h e o r e t i c a l model C0 2-AMP 2.0 8 24 . t o v e r i f y new PPT system no. of runs 30 + 65 = 95 ( t o t a l ) Table 5.3: O p e r a t i n g C o n d i t i o n s Gas f l o w r a t e 11.1 t o 14.8 mol/m-* hr C 0 2 c o n c e n t r a t i o n up t o 20 % L i q u i d f l o w r a t e 9.5 t o 13.5 m3/m2 hr T o t a l a b s o r b e n t c o n c e n t r a t i o n 1.2 t o 3.8 kmol/m 3 Column temperature 14 t o 57 °C Column p r e s s u r e 101 kPa F l o o d i n g c o n d i t i o n 30 t o 70 % P a c k i n g h e i g h t 3.25 t o 6.55 m 159 5.6 ANALYSIS OF SAMPLES The c o n c e n t r a t i o n of C 0 2 i n the gas phase was measured by an i n f r a r e d gas a n a l y z e r (Model 300D, Nova A n a l y t i c a l Systems, H a m i l t o n , O n t a r i o ) . The r e a d i n g range was 0.0 t o 20.0 % of C 0 2 by volume. B e f o r e each r u n , the a n a l y z e r was c a l i b r a t e d w i t h s t a n d a r d gas m i x t u r e s of C 0 2 i n n i t r o g e n p r o v i d e d by Matheson, Vancouver, BC. The a c c u r a c y of the a n a l y z e r was w i t h i n ± 2 % of the f u l l s c a l e r e a d i n g . No i n t e r f e r e n c e of water vapor on the measurements was found. In t h e case of t h e NaOH s o l u t i o n s , the s t a n d a r d method d e s c r i b e d by B a s s e t e t a l . [73] was used t o d e t e r m i n e t h e i r c o m p o s i t i o n s . The t o t a l a l k a l i c o n t e n t ( c a r b o n a t e and h y d r o x i d e ) was found by t i t r a t i o n w i t h s t a n d a r d 1.0 N HCl s o l u t i o n s u s i n g m e t h y l orange as t h e i n d i c a t o r ; - To determine the h y d r o x i d e c o n t e n t , the c a r b o n a t e i o n s were f i r s t p r e c i p i t a t e d by a d d i n g e x c e s s barium c h l o r i d e s o l u t i o n . The s o l u t i o n was then t i t r a t e d w i t h 1 N HCl u s i n g p h e n o l p h t h a l e i n as the i n d i c a t o r . The l a t t e r t i t r a t i o n gave the sodium h y d r o x i d e c o n t e n t ; the sodium c a r b o n a t e c o n t e n t was then o b t a i n e d by d i f f e r e n c e . In t h e case of the amine s o l u t i o n s , the t o t a l amine c o n c e n t r a t i o n was d e t e r m i n e d by t i t r a t i o n w i t h s t a n d a r d 1 N HCl s o l u t i o n s t o the methyl orange end p o i n t . The C 0 2 160 c o n t e n t i n the l i q u i d sample was d e t e r m i n e d by the s t a n d a r d method g i v e n by the A s s o c i a t i o n of O f f i c i a l A n a l y t i c a l C hemists (AOAC) [ 1 1 5 ] . The l a t t e r i n v o l v e d a c i d i f y i n g a p r e c i s e l y measured q u a n t i t y of t h e sample by a d d i n g e x c e s s 2 N HCl s o l u t i o n . The C 0 2 gas was r e l e a s e d and then c o l l e c t e d i n a p r e c i s i o n gas b u r e t t e and used t o c a l c u l a t e the C 0 2 l o a d i n g i n the s o l u t i o n . The d e t a i l s of t h e gas a p p a r a t u s and the p r o c e d u r e a r e g i v e n i n Appendix A. Sample c a l c u l a t i o n s of the l i q u i d c o m p o s i t i o n a n a l y s e s a r e found i n Appendix A. 161 5.7 COLUMN T E S T I N G A c c o r d i n g t o F a i r [ 9 5 ] , t h e r e a r e t h r e e m a j o r c o n s i d e r a t i o n s i n t e s t i n g p a c k e d c o l u m n s : 1) C a p a c i t y o r f l o o d p o i n t 2) P r e s s u r e d r o p 3) M a s s t r a n s f e r I n o r d e r t o e n s u r e t h a t t h e p a c k e d c o l u m n u s e d i n t h i s r e s e a r c h w o r k was p r o p e r l y i n s t a l l e d , t h e a f o r e - m e n t i o n e d c o n s i d e r a t i o n s w e r e a p p l i e d . T h e r e s u l t s o f f l o o d i n g a n d p r e s s u r e d r o p m e a s u r e m e n t s a r e r e p o r t e d i n t h i s s e c t i o n . T h e m a s s t r a n s f e r e v a l u a t i o n i s p r o v i d e d i n C h a p t e r 6. A t o w e r c o n t a i n i n g a g i v e n t y p e a n d s i z e o f p a c k i n g a n d b e i n g f e d w i t h a g i v e n d e s c e n d i n g l i q u i d f l o w e x h i b i t s a n u p p e r l i m i t o f t h e g a s f l o w r a t e a t w h i c h f l o o d i n g o c c u r s . I f t h e g a s f l o w i s i n c r e a s e d b e y o n d t h e f l o o d i n g v e l o c i t y , t h e l i q u i d c e a s e s t o d e s c e n d a n d t h e c o l u m n b e c o m e i n o p e r a b l e . T h e f l o o d i n g p o i n t c a n b e f o u n d f r o m t h e p r e s s u r e d r o p a n d t h e g a s f l o w r a t e r e l a t i o n s h i p T o d e t e r m i n e t h e f l o o d i n g v e l o c i t y o f t h e a b s o r b e r , e a c h s e c t i o n w a s e q u i p p e d w i t h a w a t e r - f i l l e d m a n o m e t e r t o m e a s u r e t h e p r e s s u r e d i f f e r e n c e b e t w e e n t h e i n l e t a n d 162 o u t l e t . Water and a i r were used as the l i q u i d and gas phase, r e s p e c t i v e l y . The water f l o w r a t e was s e t t o a p r e d e t e r m i n e d v a l u e and the gas was then a d j u s t e d t o t h e d e s i r e d f l o w r a t e . The p r e s s u r e drop of each s e c t i o n was then measured a f t e r s t e a d y s t a t e was reached ( a p p r o x i m a t e l y 10 t o 15 minutes a f t e r the gas f l o w r a t e was s e t ) . The p r e s s u r e drops were found t o be v i r t u a l l y the same f o r each s e c t i o n which i n d i c a t i n g u n i f o r m p a c k i n g , l i q u i d and gas f l o w r a t e s . The average p r e s s u r e drops from 6 s e c t i o n s were p l o t t e d a g a i n s t the gas and l i q u i d f l o w r a t e s as shown i n F i g u r e 5.17. To determine the gas v e l o c i t y a t f l o o d i n g f o r a g i v e n l i q u i d f l o w r a t e , the c r i t e r i o n suggested by F a i r [95] was used, i . e . f l o o d i n g o c c u r r e d when the p r e s s u r e drop reached 2.04 kPa/m of p a c k i n g (2.5" of w a t e r / f t ) . The r e s u l t s a r e shown i n Ta b l e 5.4 To p r e d i c t p r e s s u r e drop and f l o o d i n g , t h e g e n e r a l i z e d c o r r e l a t i o n of F i g u r e 5.18 suggested by T r e y b a l [86] was used. The a b s c i s s a i s the d i m e n s i o n l e s s f l o w parameter, FP, d e f i n e d as FP = ( L ' / G ' ) / ( p G / p L ) 0 - 5 (5.1) where L' and G' are the s u p e r f i c i a l mass f l o w r a t e s . The o r d i n a t e i s the c a p a c i t y parameter: 163 CP = ( G ' 2 C f M L ° - 1 J ) / ( p G ( ' ? L " ' 0 G ) g c ) ( 5 - 2 ) To use F i g u r e 5.18, the v a l u e s of FP and CP a r e c a l c u l a t e d from E q u a t i o n s 5.1 and 5.2 and t h e p r e s s u r e drop i s read from t h e graph. I n o r d e r t o use t h i s c o r r e l a t i o n , the p a c k i n g f a c t o r , C f , must be s u p p l i e d . U n f o r t u n a t e l y , i n v e s t i g a t o r s have r e p o r t e d wide d i s c r e p a n c i e s i n Cf v a l u e s . Lobo et a l . [ 9 2 ] , C l a y e t a l . [ 9 3 ] , and E c k e r t [94] r e p o r t e d the Cf v a l u e s of 12.7 mm (1/2") B e r l S a d d l e s as 450, 380 and 240, r e s p e c t i v e l y . T h i s d i s c r e p a n c y was a l s o mentioned by T r e y b a l [ 8 6 ] , A c c o r d i n g t o the e x p e r i m e n t a l r e s u l t s o b t a i n e d i n the p r e s e n t s t u d y , a Cf v a l u e of 380 gave the b e s t p r e d i c t i o n s f o r f l o o d i n g (see T a b l e 5.4). When t h i s number was used t o c a l c u l a t e the p r e s s u r e d r o p s , a c c u r a t e p r e d i c t i o n s were a l s o o b t a i n e d as shown i n F i g u r e 5.19. 164 F i g u r e 5.17: P r e s s u r e drops as f u n c t i o n s of gas and l i q u i d f l o w r a t e . ( L i q u i d f l o w r a t e (kg/m 2 s ) : s o l i d s quares -2.802; open squares - 4.160; open c i r c l e s - 6.740; s o l i d c i r c l e s - 8.112) 165 T a b l e 5.4: Gas and l i q u i d f l o w r a t e s a t f l o o d i n g p o i n t E x p e r i m e n t a l E x p e r i m e n t a l L. f l o w r a t e Gas f l o w r a t e kg/m2 s kg/m2 s P r e d i c t e d P r e d i c t e d Gas f l o w r a t e Gas f l o w r a t e kg/m2 s kg/m2 s (Cf=240) (Cf=380) 2.808 1.02 1.35 1.08 4.160 0.89 1.16 0.93 6.740 0.75 0.98 0.79 8.112 0.64 0.86 0.67 166 G' = gas mass v e l o c i t y , kg/m 2.s L' = l i q u i d mass v e l o c i t y , kg/m .s Cf = p a c k i n g f a c t o r ML = l i q u i d v i s c o s i t y , mPa ( c e n t i p o i s e s ) PG = 9 a s d e n s i t y , kg/m 3 p L = L i q u i d d e n s i t y , kg/m 3 g c = 1.0 J =1.0 F i g u r e 5.18: G e n e r a l i z e d c o r r e l a t i o n f o r p r e s s u r e d r o p and f l o o d i n g c a l c u l a t i o n s suggested by T r e y b a l [ 8 6 ] . Figure 5.19: Measured and predicted pressure drops. 168 C H A P T E R 6 R E S U L T S AND D I S C U S S I O N : C O M P A R I S O N B E T W E E N  F U L L - L E N G T H A B S O R B E R P E R F O R M A N C E A N D T H E O R E T I C A L P R E D I C T I O N S T h e p r i m a r y o b j e c t i v e o f t h i s c h a p t e r i s t o p r o v i d e c o m p r e h e n s i v e e x p e r i m e n t a l d a t a ( i . e . g a s a n d l i q u i d c o n c e n t r a t i o n s a n d t e m p e r a t u r e p r o f i l e s a l o n g t h e c o l u m n ) f o r C 0 2 a b s o r p t i o n i n t o a q u e o u s s o d i u m h y d r o x i d e ( N a O H ) a n d m o n o e t h a n o l a m i n e ( M E A ) s o l u t i o n s . A s m e n t i o n e d i n C h a p t e r 2 , n o c o m p r e h e n s i v e c o m p a r i s o n s b e t w e e n e x p e r i m e n t a l r e s u l t s a n d t h e o r e t i c a l p r e d i c t i o n s h a v e b e e n r e p o r t e d i n t h e o p e n l i t e r a t u r e . T h e s e c o n d o b j e c t i v e o f t h i s c h a p t e r i s t h e r e f o r e t o p r o v i d e c o m p a r i s o n s o f t h e s e e x p e r i m e n t a l r e s u l t s w i t h t h e p r e d i c t i o n s f r o m t h e m a t h e m a t i c a l m o d e l d e s c r i b e d i n S e c t i o n 3 . 1 . A t t h e p r e s e n t t i m e , o n l y t h e C O 2 -N a O H a n d C O 2 - M E A s y s t e m s c o u l d b e m o d e l l e d e x a c t l y s i n c e t h e n e c e s s a r y f u n d a m e n t a l d a t a a r e a v a i l a b l e i n t h e o p e n l i t e r a t u r e . R i g o r o u s m o d e l l i n g o f t h e C O 2 - A M P s y s t e m w a s n o t p o s s i b l e s i n c e i n s u f f i c i e n t f u n d a m e n t a l d a t a h a v e b e e n r e p o r t e d . 169 6 . 1 FULL-LENGTH ABSORBER PERFORMANCE To emphasize the importance of d e t a i l e d f u l l - l e n g t h column performance w i t h c o n c e n t r a t i o n and temperature p r o f i l e s , a statement i n the paper by Kr i s h n a m u r t h y and T a y l o r [ 1 4 0 ] , a s k i n g f o r comprehensive and d e t a i l e d e x p e r i m e n t a l d a t a i n o r d e r t o v e r i f y t h e i r n o n e q u i l i b r i u m s t a g e model, i s quoted as f o l l o w s : " ....For this (testing the model), we need data, preferably taken on industrial scale columns. Composition and temperature profiles (along the tower) are highly desirable. Details of the equipment used are also necessary The authors would greatly appreciate correspondence with any of our readers who have information of this kind "' In the p r e s e n t a b s o r p t i o n s t u d i e s , the r e s u l t s from 22 e x p e r i m e n t a l runs a r e summarized i n T a b l e s 6.1 and 6.2. They - -• -i n c l u d e 378 measured d a t a p o i n t s : 131 p o i n t s of C 0 2 c o n c e n t r a t i o n ; 116 p o i n t s of l i q u i d c o m p o s i t i o n ; 131 p o i n t s of t e m p e r a t u r e . The column was o p e r a t e d a t 30 t o 75 % f l o o d i n g v e l o c i t i e s which i s t y p i c a l f o r gas ab s o r b e r o p e r a t i o n s . The f o l l o w i n g ranges of o p e r a t i n g c o n d i t i o n s were used: s u p e r f i c i a l gas f l o w r a t e 11.1 t o 14.8 mol/m 3s; s u p e r f i c i a l l i q u i d f l o w r a t e 9.5 t o 13.5 m3/m2h; fe e d C 0 2 c o n c e n t r a t i o n 11.5 t o 19.8 %; t o t a l a b s o r b e n t c o n c e n t r a t i o n 1.2 t o 3.8 kmol/m 3; C 0 2 l o a d i n g i n the l i q u i d f e e d 0.00 t o 170 0.237 mol C02/mol a b s o r b e n t ; l i q u i d feed temperature 14 t o 20 °C; t o t a l p r e s s u r e 103.15 kPa. The d a t a i n T a b l e s 6.1 t o 6.2 a r e s i g n i f i c a n t l y d i f f e r e n t from the measurements r e p o r t e d by o t h e r r e s e a r c h e r s because t h e l a t t e r g e n e r a l l y used s h o r t e r columns ( t y p i c a l l y 1 t o 2 m h i g h ) and r e c o r d e d o n l y i n l e t and o u t l e t c o n d i t i o n s . By c o n t r a s t , the d a t a i n T a b l e s 6.1 and 6.2 were o b t a i n e d from f a i r l y t a l l columns (up t o 6.55 m of p a c k i n g h e i g h t ) and p r o v i d e e x t e n s i v e c o n c e n t r a t i o n and temp e r a t u r e measurements a l o n g t h e column. The p r e s e n t d a t a a r e t h e r e f o r e w e l l s u i t e d t o t e s t the performance of t h e o r e t i c a l models. The p r e s e n t o v e r a l l c o n c e n t r a t i o n and temp e r a t u r e changes a r e a l s o c o n s i d e r a b l e . The C 0 2 c o n c e n t r a t i o n i n the gas phase ranged from 19.1 t o 0.0 %, the C 0 2 l o a d i n g i n t h e l i q u i d v a r i e s from 0.0 t o 0.583 moles of C0 2/mole of a b s o r b e n t and temperature changed from 15 t o 48 °C. 171 T a b l e 6.1: E x p e r i m e n t a l r e s u l t s f o r the C0 2-NaOH system. Run (#) T l T2 T3 T4 T5 T6 A i r Flow Rate 14. .8 14. .8 14. .8 14. .8 14. .8 14. .8 (mol/m 2 s) L i q u i d Flow Rate (m 3/m 2 h) 13. .5 13. .5 13. .5 13. .5 13. .5 13. .5 Absorbent Feed 1 . 2 1 . 2 1 . 2 1 . 2 1 . 2 1 . 2 Cone, (kmol/m 3) Gas C 0 2 Cone.(%) i h e i g h t from t o p : 0.00 m 2. .3 4. .4 7. .7 1 . 0 2. .9 1 . 9 1 .05 m 4. .0 7. .8 12. .3 2. .2 5. .3 3, .7 2.15m 6. .3 1 1 . .8 16. .5 4. .2 8. .5 6, .7 3.25 m 8. .9 14, .6 18. .2 6. .8 1 1 . .2 10, . 1 4.35 m i » i > i » 9. . 1 12. .3 12, .5 5.45 m i i » » i * » 6.55 m i * » » • « * C 0 2 removal (%) 75. .6 73. . 1 62, .2 89. .4 78, .4 86, .8 OH Cone, (kmol/m 3) ©height from t o p : 0.00 m 0.750 1.000 1.020 0.800 0.860 1.030 1.05m 0.610 0.690 0.590 0.710 0.660 0.880 2.15m 0.420 0.310 0.190 0.550 0.390 0.620 3.25m 0.180 0.050 0.010 0.320 0.130 0.300 4.35 m -.- -.- -.- 0.100 0.010 0.070 5.45 m -.- -.- -.- -.- -.-6.55 m -.- -.- -.- -.- -.-Mass B a l . E r r o r (%) +1.54 -0.37 +1.91 +3.06 -1.24 -3.76 L i q . Temp (°C) @height from t o p : 0.00 m 15.0 16.0 16.0 18.0 16.5 16.0 1.05m 17.0 20.0 21.5 19.0 19.0 18.0 2.15m 20.0 25.0 26.5 20.5 23.0 21.0 3.25 m 23.0 29.0 29.0 24.0 26.5 26.0 4.35 m -.- -.- -.- 26.0 27.0 27.5 5.45 m -.- -.- -.- -.- -.-6.55 m -.- -.- -.- -.- - -Note: For run T1 t o t 6 , the column was not i n s u l a t e d . 172 T a b l e 6 . 1 ( c o n ' t ) : E x p e r i m e n t a l r e s u l t s f o r the C02-NaOH system. Run (#) T7 T8 T9 T1 0 T1 1 T12 A i r Flow Rate (mol/m 2 s) L i q u i d Flow Rate (m 3/m 2 h) Absorbent Feed Cone, (kmol/m 3) Gas C 0 2 ©height 0.00 m 05 15 25 35 Cone.(%) from t o p : 1, 2 3-, 4 5.45 6.55 m m m m m m C 0 2 removal (%) OH~ Cone, (kmol/m 3) ©height from t o p : 0.00 m 1 .05 m 2.15m 3.25 m 4.35m 5.45 m 6.55 m 14.8 14.8 14 .8 14 .8 14.8 14.8 9.5 9.5 1 3 .5 13 .5 13.5 13.5 2.0 2.5 2 .0 2 .0 2.0 2.0 1 .25 1 .70 1 .00 1 .75 0.0 0.0 2.95 3.50 2 .65 3 .60 0.5 0.0 6.15 7.05 5 .80 6 .65 1.2 0.5 1 1 .20 12.85 1 1 .55 10 .90 3.1 1 .4 1 5.45 18.60 18 .45 15 .20 7.0 3.7 • • • • 12.0 8.2 • • • • 15.5 15.4 93.0 92.5 ' 95 .5 90 .0 100.0 100.0 2.000 1 .800 1 .425 0.720 0. 137 2.500 2.275 1 .800 0.950 0.180 2.000 1 .900 1 .625 1 .075 0.370 1.500 1.530 1.350 (1.480) 1.060 1.475 0.625 (1.270) 0.243 0.930 -.- 0.470 0.080 900 900 900 750 600 150 0.480 Mass B a l . E r r o r (%)• -1 .78 -2.23 -5.69 + 1 .50 + 1 .20 + 1 .4; L i q . Temp (°C) ©height from t o p : 0.00 m 14.5 14.0 15.0 15.0 20.0 21 .0 1.05 m 17.0 17.0 17.0 17.0 20.0 21 .0 2.15m 23.0 23.5 22.0 20.0 21 .0 22.0 3.25 m 35.0 39.0 29.0 26.0 23.5 23.0 4.35m 37.0 42.0 35.0 30.0 28.0 26.0 5.45 m • • • • 35.0 33.0 6.55 m • • • • 37.5 39.0 Note: The v a l u e s i n ( ) a r e c a l c u l a t e d from mass b a l a n c e . T a b l e 6.2: E x p e r i m e n t a l r e s u l t s f o r the C0 2-MEA system. Run (#) T1 3 T1 4 T1 5 T16 T17 A i r Flow Rate (mol/m 2 s) 14.8 14.8 14.8 14.8 14.8 L i q u i d Flow Rate (m 3/m 2 h) Absorbent Feed Cone, (kmol/m 3) Gas C 0 2 Cone.(%) ©height from t o p : 13.5 2.00 13.5 2.00 13.5 2.03 9.5 2.08 13.5 3.8 0.00 m 0.0 0.0 0.0 0.0 0.0 1 .05 m 0.0 0.6 0.0 0.5 0.0 2.15m 0.4 1 .4 0.6 1 .3 0.8 3.25 m 1.0 4.0 2.1 3.9 2.0 4.35 m 3.3 8.4 6.5 8.9 5.3 5.45 m 8.3 12.8 13.6 13.8 10.2 6.55 m 15.3 15.6 19.5 15.5 15.6 C 0 2 removal (%) 100.0 100.0 100.0 100.0 100.0 C 0 2 l o a d i n g (mol C0 2/mol MEA) @height from t o p : 0.00 m 0. 000 0. 1 18 0. 000 0. 000 0. 237 1.05m (0. 000) (0. 125) (0. 000) (0. 000) (0. 237) 2.15m (0. 012) 0. 140 0. 013 0. 038 0. 243 3.25 m 0. 025 (0. 198) (0. 040) 0. 090 0. 255 4.35 m 0. 078 0. 295 0. 140 0. 255 0. 296 5.45 m 0. 200 0. 400 0. 302 0. 425 0. 350 6.55 m 0. 362 0. 480 0. 475 0. 500 0. 428 Mass B a l . E r r o r (%) +2. 36 +0. 09 -0. 34 -2. 31 +0. 89 L i q . Temp (°C) @height from t o p : 0.00 m 19. 0 19. 0 19. 0 19. 0 20. 0 1 .05 m 19. 0 20. 0 19. 0 19. 0 20. 0 2.15m 19. 5 21 . 0 19. 0 20. 0 21 . 0 3.25 m 20. 0 22. 0 21 . 0 26. 0 22. 0 4.35 m 23. 0 28. 0 25. 0 33. 0 . 26. 0 5.45 m 29. 0 33. 0 35. 0 41 . 0 32. 0 6.55 m 34. 0 34. 0 37. 5 39. 0 36. 0 Note: The v a l u e s i n ( ) a r e c a l c u l a t e d from mass b a l a n c e . 1 7 4 T a b l e 6 . 2 ( c o n ' t ) : E x p e r i m e n t a l r e s u l t s f o r the C02-MEA system. Run (#) T18 T19 T20 T21 T22 A i r Flow Rate 14.8 14.8 14.8 11.1 14.8 (mol/m2 s) L i q u i d Flow Rate 9.5 13.5 9.5 9.5 9.5 (m-Vm2 h) Absorbent Feed 2.00 2.00 2.55 2.00 3.00 Cone, (kmol/m 3) Gas C 0 2 Cone.(%) ©height from t o p : 0.00 m 3.3 0.0 0. 0 0. 0 0. 0 1 .05 m 7.9 0.0 0. 6 0. 0 0. 0 2.15m 14.0 0.1 2. 8 0. 1 0. 1 3.25 m 17.2 0.2 7. 7 1 . 2 1 . 2 4.35 m 18.4 1 .4 14. 2 6. 0 5. 3 5.45 m 18.8 4.8 17. 7 13. 2 12. 8 6.55 m 19.1 11.5 19. 2 19. 1 19. 1 CO2 removal (%) 85.4 100.0 100. 0 100. 0 100. 0 C 0 2 l o a d i n g (mol C0 2/mol MEA) ©height from t o p : 0.00 m 0.000 0.000 0. 000 0. 000 0. 000 1 .05 m 0. 150 (0.000) 0. 010 (0. 000) 0. 000 2.15m 0.362 (0.002) 0. 070 0. 000 0. 000 3.25 m 0.482 0.005 0. 190 0. 030 0. 033 4.35 m (0.530) 0.032 (0. 366) 0. 142 0. 125 5. 45 m 0.538 0.108 0. 474 0. 325 0. 292 6.55 m 0.558 0.265 0. 514 0. 488 0. 443 Mass B a l . E r r o r (%) -0.94 +4,58 -3. 14 -1 . 19 + 0. 92 L i q . Temp (°C) ©height from t o p : 0.00 m 20.0 19.0 19. 0 19. 0 19. 0 1 .05 m 27.0 19.0 20. 0 19. 0 19. 0 2.15m 36.0 19.0 22. 0 19. 0 19. 0 3.25 m 43.0 19.0 32. 0 21 . 0 21 . 0 4.35m 42.0 20.0 47. 0 26. 0 29. 0 -5.45 m 41.0 24.0 57. 0 33. 5 45. 0 6.55 m 36.0 30.0 48. 0 37. 5 47. 0 Note: The v a l u e s i n ( ) a r e c a l c u l a t e d from mass b a l a n c e . 175 6 . 1 . 1 EFFECT OF OPERATING CONDITIONS To show the e f f e c t of v a r i o u s o p e r a t i n g v a r i a b l e s on column performance, the C 0 2 c o n c e n t r a t i o n p r o f i l e s a r e p l o t t e d a g a i n s t the column h e i g h t i n F i g u r e s 6.1 t o 6.6. The e f f e c t of CO2- l o a d i n g on the p r o f i l e i s shown i n F i g u r e 6.1 (Run T13 vs T14). When the l o a d i n g i s i n c r e a s e d from 0.0 t o 0.118 w h i l e keeping a l l o t h e r c o n d i t i o n s a p p r o x i m a t e l y the same, the p a c k i n g h e i g h t r e q u i r e d f o r n e a r l y complete removal i n c r e a s e d from about 5.45 t o 6.55 m. T h i s i n c r e a s e i s , of c o u r s e , due t o the reduced a v a i l a b i l i t y of f r e e absorbent f o r r e a c t i n g w i t h the absorbed c a r b o n d i o x i d e . F i g u r e 6.2 (Run T16 vs T18) shows the e f f e c t of C 0 2 c o n c e n t r a t i o n i n the i n l e t gas. The removal of C 0 2 f a l l s from a p p r o x i m a t e l y 100% t o 81% when the C 0 2 i n l e t c o n c e n t r a t i o n i s r a i s e d from about 15% t o 19%. The e f f e c t of l i q u i d f l o w r a t e i s shown i n F i g u r e 6.3 (Run T15 vs T 1 8 ) . When t h e l i q u i d f l o w r a t e i s i n c r e a s e d , t h e a b s o r p t i o n r a t e and c a p a c i t y of the column a re i n c r e a s e d due t o : ( i ) h i g h e r k L° and a v v a l u e s and ( i i ) h i g h e r c o n c e n t r a t i o n s of f r e e a b s o r b e n t . The i n c r e a s e i n f r e e absorbent a l s o enhances t h e e f f e c t i v e mass t r a n s f e r c o e f f i c i e n t of the l i q u i d phase. 1 7 6 For a b s o r b e r s u s i n g p h y s i c a l s o l v e n t s ( a b s o r p t i o n without c h e m i c a l r e a c t i o n ) , the p r i m a r y way t o i n c r e a s e the a b s o r p t i o n c a p a c i t y i s t o i n c r e a s e the s o l u t i o n f l o w r a t e . By c o n t r a s t , f o r gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n , the c a p a c i t y can be enhanced by j u s t i n c r e a s i n g the ab s o r b e n t c o n c e n t r a t i o n as shown by F i g u r e 6.4 (Run T18 vs T20). As e x p e c t e d , r e d u c i n g the gas f e e d r a t e i n c r e a s e s the degree of removal (see F i g u r e 6.5 - Run T18 vs T21). The e f f e c t of s o l v e n t type on the a b s o r p t i o n r a t e i s demonstrated by F i g u r e 6.6. There i s almost no d i f f e r e n c e i n the column performance when u s i n g NaOH or MEA under the c o n d i t i o n s of Runs T11 and T14 (see F i g u r e 6.6). I t may be i n f e r r e d t h a t t h e r e i s no s i g n i f i c a n t d i f f e r e n c e i n a b s o r p t i o n c a p a c i t y when e i t h e r one of t h e s e s o l v e n t s i s used under the p r e s e n t o p e r a t i n g c o n d i t i o n s . 177 0.0 6.0 12.0 18.0 C 0 2 Cone. (%) F i g u r e 6.1: E f f e c t of C 0 2 l o a d i n g . The i n l e t C 0 2 l o a d i n g was i n c r e a s e d from 0.0 (Run T13 - s o l i d c i r c l e s ) t o 0.118 (Run T14 - open squares) mol C 0 2 per-mol MEA. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h; t o t a l MEA c o n c e n t r a t i o n = 2.0 kmol/m 3; i n l e t gas C 0 2 c o n c e n t r a t i o n = 15.5%. 178 C0 2 Cone. (%) F i g u r e 6.2: E f f e c t of gas C 0 2 c o n c e n t r a t i o n . The i n l e t C 0 2 c o n c e n t r a t i o n was i n c r e a s e d from 15.6 % (Run T16 - open s q u a r e s ) t o 19.1 % (Run T18 - s o l i d c i r c l e s ) . O p e r a t i n g c o n d i t i o n s : g a s . f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9 . 5 m3/m2 h; t o t a l MEA c o n c e n t r a t i o n = 2.0 kmol/m 3; i n l e t C 0 2 l o a d i n g = 0.0 mol C 0 2 / mol MEA. 179 0 . 0 6.0 12.0 18.0 C 0 2 Cone. (%) F i g u r e 6.3: E f f e c t of l i q u i d f l o w r a t e . The l i q u i d f l o w r a t e was i n c r e a s e d from 9.5 ( R u n T t 8 - s o l i d c i r c l e s ) t o 13.5 (Run T15 - open s q u a r e s ) m3/m2 s. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 mol/m 2 s; t o t a l MEA c o n c e n t r a t i o n = 2.0 kmol/m 3; i n l e t C 0 2 l o a d i n g = 0.0 mol C 0 2 / mol MEA; i n l e t g a s C 0 2 c o n c e n t r a t i o n = 19.5%. 180 0.0 6.0 12.0 18.0 C0 2 Cone. (%) ure 6 .4 : E f f e c t of a b s o r b e n t c o n c e n t r a t i o n . The t o t a l MEA c o n c e n t r a t i o n was i n c r e a s e d from 2 .0 (Run T18 -s o l i d c i r c l e s ) t o 2 . 55 (Run T20 - open squares) kmol/m 3. O p e r a t i n g c o n d i t i o n s : gas flo w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9 . 5 m3/m2 h; i n l e t CO2 l o a d i n g = 0.0 mol C 0 2 / mol MEA; i n l e t gas C02 c o n c e n t r a t i o n = 19.1%. 1 8 1 0.0 6.0 12.0 18.0 C0 2 Cone. (%) Figure 6.5: E f f e c t of gas flow r a t e . The gas flow rate was increased from 11.1 (Run T21 - open squares) to 14.8 (Run T18 - s o l i d c i r c l e s ) mol/m2 s. Operating c o n d i t i o n s : l i q u i d flow rate = 9.5 mVm h; i n l e t C0 2 loading = 0.0 mol C0 2 / mol M E A ; i n l e t gas C02 concentration = 19.1%; total M E A concentration = 2.0 kmol/m3. 1 8 2 I 0.0 6.0 12.0 C0 2 C o n e . (%) F i g u r e 6.6: E f f e c t of abso r b e n t t y p e . The s o l v e n t type was changed from NaOH (Run T11 - s o l i d c i r c l e s ) t o MEA (Run T14 - open s q u a r e s ) . O p e r a t i n g c o n d i t i o n s : gas fl o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h; t o t a l a b s o r b e n t c o n c e n t r a t i o n = 2.0 kmol/m 3; i n l e t gas C02 c o n c e n t r a t i o n = 15.5%. 183 6.2 COMPARISON BETWEEN FULL-LENGTH ABSORBER PERFORMANCE AND  THEORETICAL PREDICTIONS* Computer programs, which were dev e l o p e d based on the a l g o r i t h m and computation p r o c e d u r e s d e s c r i b e d i n S e c t i o n 3.2, were used t o p r e d i c t the f u l l - l e n g t h a b s o r b e r performance f o r the C02-NaOH and CO2-MEA systems. 6.2.1 SOURCES OF BASIC INFORMATION B e f o r e the model e q u a t i o n s can be e v a l u a t e d , v a r i o u s p a rameters (e.g. mass t r a n s f e r c o e f f i c i e n t s , s o l u b i l i t y , r e a c t i o n r a t e c o n s t a n t , e t c . ) a r e needed. These parameters may be o b t a i n e d from e x p e r i m e n t a l measurements or c o r r e l a t i o n s . Great c a u t i o n has t o be e x e r c i s e d because t h e r e a r e c o n s i d e r a b l e d i s c r e p a n c i e s between the p r e v i o u s l y r e c o r d e d d a t a as r e p o r t e d by K e l l y e t a l . [ l 0 6 ] and R a a l and Khurana, [105] and t h e s e d i s c r e p a n c i e s can s t r o n g l y a f f e c t the p r e d i c t i o n r e s u l t s . * Some e x p l o r a t o r y r e s u l t s on the comparison between a b s o r b e r performance and t h e o r e t i c a l p r e d i c t i o n s were p r e s e n t e d a t 38th Canadian Chemical E n g i n e e r i n g C o n f e r e n c e (Edmonton, Oct. 2-5, 1988) and were p u b l i s h e d i n "Gas S e p a r a t i o n Technology" e d i t e d by Vansant and D e w o l f s , E l s e v i e r , p. 38-90, 1990. 1 8 4 Some t y p i c a l v a l u e s of these b a s i c parameters used i n the computer models a r e l i s t e d i n Ta b l e 6.3 f o r CC>2-NaOH system (Run T9) and T a b l e 6.4 f o r C0 2-MEA system (Run T22). A l t h o u g h s e v e r a l c o r r e l a t i o n s a r e a v a i l a b l e f o r e s t i m a t i n g k G and a v , t h e e x p r e s s i o n s proposed by Onda_ e t a l . [ 3 5 ] were chosen because they were found t o be s a t i s f a c t o r y f o r c o n v e n t i o n a l p a c k i n g s by K e l l y e t a l . [106] and S a n y a l e t a l . [ 1 0 8 ] . A new s e t of d a t a f o r the l i q u i d mass t r a n s f e r i n B e r l S a d d l e s p a c k i n g r e c e n t l y r e p o r t e d by C h o f l l O ] was used i n t h i s model. The heat t r a n s f e r c o e f f i c i e n t was c a l c u l a t e d by u s i n g t h e c o r r e l a t i o n s u g g e sted by Pandya [ 5 4 ] . The v a l u e s f o r the t o t a l heat of a b s o r p t i o n , which i s the sum of the heat of s o l u t i o n and the heat of r e a c t i o n , were t a k e n from Danckwerts [18] and K o h l and R i e s e n f e l d [5] f o r the C0 2-NaOH and C0 2-MEA systems, r e s p e c t i v e l y . One of the most i m p o r t a n t p a r t s of gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n m o d e l l i n g i s the enhancement f a c t o r c a l c u l a t i o n . U n l i k e p h y s i c a l gas a b s o r p t i o n , the k L and I v a l u e s i n the c h e m i c a l a b s o r b e r s change s i g n i f i c a n t l y from the bottom t o t h e t o p due t o the e f f e c t of the c h e m i c a l r e a c t i o n as p r e v i o u s l y mentioned i n S e c t i o n 2.3.2. T h i s e f f e c t w i l l a l s o be demonstrated i n the f o l l o w i n g s e c t i o n . 185 T a b l e 6.3: L i s t of o p e r a t i n g c o n d i t i o n s and parameters f o r Run T9 (C0 2-NaOH s y s t e m ) . P r o p e r t y Column t o p Column bottom Source L (m 3/m 2 h) C B (kmol/m 3) Gj (mol/m 2 s) V C 0 2 Temp. (°C) D A (m 2/s) D B (m 2/s) k G (kmol/m 2 s kPa) k L° (m/s) a v (m 2/m 3) H (kmol/m 3 kPa) h G ( k j / s m 2 °K) k 2 (m 3/kmol s) H R (kJ/kmol) I 13.5 2.0 14.8 0.1 15.0 1.518x10 -9 0.893X10" 9 3.168x10" 6 150. 2.274x10" 4 0.099 1 .025X10 + 4 1.021x10 90.6 + 5 13.5 0.413 14.8 0. 185 35.0 1 .803x10" 9 1 .060X10" 9 3.168x1O" 6 Experiment Danckwerts and Sharma [1] Danckwerts and A l p e r [5] Onda e t a l . [35] 6 . 2 8 3 x 1 0 - 5 6 . 8 4 6 X 1 0 " 5 Cho [1103 150. 1 . 0 7 6 X 1 0 " 4 0.099 4 . 5 7 4X 1 0 + 4 1 . 0 2 1 X 1 0 + 5 48.7 Onda e t a l . [35] P o h o r e c k i and Monuik [111] Pandya [54] P o h o r e c k i and Monuik [111] Danckwerts!18] W e l l e c k e t a l . [89]; 186 T a b l e 6.4: L i s t of o p e r a t i n g c o n d i t i o n s and parameters f o r Run T22 (C0 2-MEA s y s t e m ) . P r o p e r t y Column t o p Column bottom Source L (m 3/m 2 h) T o t a l MEA (kmol/m 3) L o a d i n g (mol C0 2/mol MEA) Gj (mol/m 2 s) y c o 2 Temp. (°C) D A (m 2/s) D B (m 2/s) k L° (m/s) a v (m 2/m 3) H (kmol/m 3 kPa) h G ( k J / s m 2 °K) k 2 (m 3/kmol s) H R (kJ/kmol) I— • 9.5 3.0 0.0 14.8 0.0 19.0 1 . 2 0 9 X 1 0 " 9 0.756x10 -9 k G (kmol/m 2 s kPa) 3.168x10 6 5 . 3 8 7 x l 0 - 5 135. 6 . 2 2 0 x l 0 ~ 4 0.099 0 . 4 0 1 X 1 0 + 4 0 . 9 3 7 x l 0 + 5 70.9 9.5 3.0 0.443 14.8 0.191 47.0 1.558x10~ 9 0.974x10~ 9 3. 168X10~ 6 Experiment Thomas and F u r z e r [112] Thomas and F u r z e r [112] Onda e t a l . [35] 6.115x10~ 5 Cho [110] 135. 2.049X10" 4 0.099 1.854X10 + 4 0 . 9 3 7 X 1 0 + 5 24. 13 Onda e t a l . [35] P o h o r e c k i and Monuik [111] Pandya [54] Blauwhoff e t a l . [43] Danckwerts[18] W e l l e c k e t a l . [89] 187 For the r e a c t i o n of C0 2-NaOH and C0 2-MEA systems, the second-order r e a c t i o n can be assumed [ 1 , 17, 18, 5 4 ] . To a v o i d complex n u m e r i c a l c a l c u l a t i o n , t h e r e a r e a few e q u a t i o n s a v a i l a b l e f o r the approximate s o l u t i o n s (see S e c t i o n 2.3.2). The e x p l i c i t e q u a t i o n p r e s e n t e d by W e l l e c k et a l . [89] was used (see E q u a t i o n 2.25). However, the i n f o r m a t i o n r e g a r d i n g the r a t e c o n s t a n t and p h y s i c o - c h e m i c a l p r o p e r t i e s of the system must be known b e f o r e the enhancement f a c t o r can be e v a l u a t e d . The r a t e c o n s t a n t of C0 2-NaOH r e a c t i o n , i n the temperature range and a t the i o n i c s t r e n g t h of p r a c t i c a l i n t e r e s t , has been r e c e n t l y c o r r e l a t e d by P o h o r e c k i and Moniuk [111] as where I c i s the i o n i c s t r e n g t h of the s o l u t i o n . For C0 2-MEA system, Blauwhoff et a l . [43] c o r r e l a t e d i t s second-order r a t e c o n s t a n t as l o 9 k2,NaOH = 11.895 - 2382/T + 0.221I C - 0 . 0 1 6 ( I C ) 2 (6.1 ) l o 9 k2,MEA = 1 0 - 9 9 _ 2152/T (6.2) 188 The Henry's c o n s t a n t f o r CO2 s o l u b i l i t y i n NaOH s o l u t i o n i s e s t i m a t e d u s i n g the f o l l o w i n g e x p r e s s i o n : l o g ( H / H w ) = - K S I C (6.3) where K s i s the sum of the c o n t r i b u t i o n s due t o i o n s i n the l i q u i d phase and r e p o r t e d by Danckwerts [ 1 8 ] , H w denotes the Henry's c o n s t a n t of C 0 2 i n water: l o g ( H w ) = 9.1229 - 5 . 9 0 4 4X 1 0 ~ 2 T + 7.8857x10~ 5T 2 (6.4) T h i s c o r r e l a t i o n was taken from P o h o r e c k i and Moniuk [ 1 1 1 ] , For the C0 2-MEA system, H i k i t a e t a l . [49] found a s a l t i n g - i n e f f e c t c o r r e l a t e d by l o g ( H / H w ) = 0.3[MEA]/(1 - K [ M E A ] ) - K S I C (6.5) where K = 1./(1.2850 - 0.001(T - 314.5513) 2) The d i f f u s i v i t y d a t a f o r C0 2-NaOH and C0 2-MEA systems were r e p o r t e d by Danckwerts and Sharma [1] and Thomas and F u r z e r [ 1 1 2 ] . The e f f e c t of te m p e r a t u r e on d i f f u s i v i t y i s c a l c u l a t e d u s i n g an e q u a t i o n s u g g e s t e d by R e i d e t a1.[113 ]: Dab< T2>/ Dab< T1> = ( ( T c - T ^ / f T c - T ; , ) ) ' 1 (6.6) 189 where T c i s the c r i t i c a l t e m perature of the s o l v e n t . The in d e x n i s r e l a t e d t o the heat of v a p o r i z a t i o n of the s o l v e n t . I n our c a s e , n i s e q u a l t o 3. The d a t a f o r o t h e r p arameters such as d e n s i t y , v i s c o s i t y , s p e c i f i c h e a t , e t c . were taken from P e r r y ' s Handbook, Gas P u r i f i c a t i o n by K o h l and R i e s e n f e l d [ 1 5 ] , and Gas C o n d i t i o n i n g F a c t Book by Dow Che m i c a l Company [ 7 4 ] . I t s h o u l d be noted t h a t the i n f o r m a t i o n on some parameters have been r e p o r t e d q u i t e r e c e n t l y even though the CC>2-NaOH and C0 2 _MEA systems have been s t u d i e d f o r a l o n g p e r i o d of t i m e . T h i s shows t h a t a c q u i r i n g the fundamental d a t a f o r d e s i g n i n g gas a b s o r b e r s w i t h c h e m i c a l r e a c t i o n i s v e r y d i f f i c u l t and time-consuming. 190 6.2.2 COMPARISON OF RESULTS The computer models p r e d i c t i o n s were f i r s t t e s t e d a g a i n s t some c a l c u l a t e d r e s u l t s r e p o r t e d p r e v i o u s l y t o ensure t h a t the programs worked p r o p e r l y . As can be seen i n T a b l e 6.5, the p r e d i c t i o n s and p r e v i o u s r e s u l t s a r e v i r t u a l l y i d e n t i c a l t h e r e b y c o n f i r m i n g the v a l i d i t y of the p r e s e n t programs. T y p i c a l p l o t s of e x p e r i m e n t a l ( p o i n t s ) and p r e d i c t e d ( s o l i d l i n e s ) gas c o n c e n t r a t i o n s , l i q u i d c o m p o s i t i o n s and te m p e r a t u r e s a l o n g the column a r e shown i n F i g u r e s 6.7 (Run T9) and 6.8 (Run T22) f o r the C0 2-NaOH and C0 2-MEA systems, r e s p e c t i v e l y . The l i s t s of b a s i c parameters and o p e r a t i n g c o n d i t i o n s f o r Run T9 and Run T22 a r e g i v e n i n T a b l e s 6.3 and 6.4, r e s p e c t i v e l y . The agreement between the r e s u l t s i s g e n e r a l l y v e r y good t h e r e b y a g a i n c o n f i r m i n g the v a l i d i t y of the m a t h e m a t i c a l model. A d d i t i o n a l e v i d e n c e f o r the good agreement i s p r o v i d e d by F i g u r e s 6.10 t o 6.13. As seen from F i g u r e s 6.7a and 6.8a, the gas and l i q u i d t e m p e r a t u r e p r o f i l e s d i f f e r s i g n i f i c a n t l y near the column bottom where the e n t e r i n g gas i s r a p i d l y heated by the 191 T a b l e 6.5: Comparison between the c a l c u l a t i o n r e s u l t s from p r e v i o u s r e p o r t s and from t h i s work. Source and C o n d i t i o n s Computed H e i g h t T h i s work Pandya [54] C0 2-MEA system Column: 0.1m ID, 12.7mm R a s c h i g r i n g s O p e r a t i n g C o n d i t i o n s : gas r a t e = 1573 kg/m 2 h l i q u i d r a t e = 13.68 m3/m2 s T o t a l MEA cone. = 2.5 kmol/m 3 l o a d i n g = 0.15 (top ) and 0.4 (bottom) YCQ2 = 0.01?6(top) and 0.176 (bottom) Column temp. = 46 °C Column P r e s s u r e = 2020 kPa. 0.84 m 0.84 m Danckwerts and Sharma [1] C0 2 _MEA system Column: 2.27m, 38.1mm R a s c h i g r i n g s O p e r a t i n g C o n d i t i o n s : gas r a t e = 2628 kg/m 2 h l i q u i d r a t e = 60.84 m3/m2 s T o t a l MEA cone. = 2.5 kmol/m 3 l o a d i n g = 0.15 (top) and 0.4 (bottom) YC02 = 0.025(top) and 0.25 (bottom) Column temp. = 30 °C Column P r e s s u r e = 2020 kPa. 1 .42 m 1.51 m A l p e r [56] 1.54 m C0 2-NaOH system Column: 0.1m ID, 12.7mm R a s c h i g r i n g s O p e r a t i n g C o n d i t i o n s : gas r a t e = 1831 kg/m 2 h l i q u i d r a t e = 10.08 m3/m2 s [N a + ] cone. = 1.2 kmol/m 3 [OH~] = 0.6(top) and 0.08(bottom) kmol/m 3 YCQ2 = 0.066(top) and 0.115 (bottom) Column temp. = 25 °C Column P r e s s u r e = 101 kPa. 1 .48 m 192 F i g u r e 6.7: P r e d i c t e d ( l i n e s ) and e x p e r i m e n t a l ( p o i n t s ) r e s u l t s f o r the C 0 2 - NaOH system (Run T9 ) : [a] Temperature p r o f i l e s f o r the l i q u i d ( s o l i d l i n e ) and gas phases ( d o t t e d l i n e ) , Open squares a r e the e x p e r i m e n t a l measurements of the l i q u i d t e m p e r a t u r e ; [b] c o n c e n t r a t i o n p r o f i l e s of C 0 2 (open c i r c l e ) and NaOH ( s o l i d c i r c l e ) ; [ c ] Enhancement f a c t o r . 193 o 0.0 3.0 6.0 Distance from the bottom (m) F i g u r e 6 . 8 : P r e d i c t e d ( l i n e s ) and e x p e r i m e n t a l ( p o i n t s ) r e s u l t s f o r the C 0 2 - MEA system (Run T22): [a] Temperature p r o f i l e s f o r the l i q u i d ( s o l i d l i n e ) and gas phases ( d o t t e d l i n e ) , Open squares a r e the e x p e r i m e n t a l measurements of the l i q u i d .. t e m p e r a t u r e ; [b] c o n c e n t r a t i o n p r o f i l e s of C 0 2 (open c i r c l e ) and l o a d i n g ( s o l i d c i r c l e ) ; [ c ] Enhancement f a c t o r . 194 descending l i q u i d . Higher up in the column, the gas and l i q u i d temperatures reach a maximum and then become very similar resulting from the facts that the heat capacity and the mass flow rate of the l i q u i d are higher than those of the gas phase. This evidence also confirms the assumption stated in Section 3.2.2 that-the temperatures of the gas and l i q u i d phases along the column are approximately the same. Figures 6.7b-c and 6.8b-c show r e l a t i v e l y steeper gradients of gas and l i q u i d composition p r o f i l e s at the bottom part of the column. These are due to higher d r i v i n g -force between the phases resulting in higher absorption rate. Since the enhancement factor depends strongly on the concentration of both gas and l i q u i d , i t varies considerably along the column with the greater changes occurring in the lower section as shown in Figures 6.7c and 6.8c. The assumption of a constant enhancement i s therefore not generally j u s t i f i a b l e . For instance, in the case of Run T9 (see Figure 6.7), the enhancement factor increases from about 48 at the column bottom to about 90 at the column top. This means that the absorption rate with chemical reaction is 48 to 90 times higher than without chemical reaction. Near the top of the column, the reactant concentration is r e l a t i v e l y high and, therefore, most of C O 2 i s consumed right after being dissolved at the interface. As a result, 195 the r e a c t i o n zone i s l o c a t e d c l o s e t o the g a s - l i q u i d i n t e r f a c e r e s u l t i n g i n h i g h e r v a l u e s of the enhancement f a c t o r . On the o t h e r hand, near the bottom of the column, the c o n c e n t r a t i o n of the l i q u i d r e a c t a n t i s much lower but the C O 2 c o n c e n t r a t i o n a t the i n t e r f a c e i s c o n s i d e r a b l y h i g h e r by comparison w i t h t h a t a t the t o p of the column. The C O 2 can then d i f f u s e d e e p l y i n t o the l i q u i d f i l m b e f o r e r e a c t i n g w i t h the l i q u i d r e a c t a n t . As a r e s u l t , the r e a c t i o n zone i s l o c a t e d f u r t h e r away from the i n t e r f a c e r e s u l t i n g i n reduced enhancement f a c t o r s . S i n c e the enhancement f a c t o r i s a complex f u n c t i o n of the hydrodynamic c o n d i t i o n s of the a b s o r b e r as w e l l as the. p h y s i c o - c h e m i c a l p r o p e r t i e s of the system, i t i s d i f f i c u l t t o make d i r e c t c o m p a r i s o n s between t h e r e s u l t s from t h i s and o t h e r s t u d i e s . To our knowledge, only- 2 s e t s of e x p e r i m e n t a l v a l u e s of the enhancement f a c t o r f o r C 0 2-NaOH a b s o r p t i o n i n packed columns have been e x p l i c i t l y r e p o r t e d by Merchuk e t a l . [ 1 4 2 ] and Onda e t a l . [ l 4 3 ] . As can be seen from T a b l e 6.6, the enhancement f a c t o r s o b t a i n e d i n t h i s s t u d y a r e of the same order as t h o s e r e p o r t e d by the a f o r e - m e n t i o n e d a u t h o r s . 196 T a b l e 6.6: Comparison of enhancement f a c t o r v a l u e s o b t a i n e d from Merchuk e t a l . [ l 4 2 ] , Onda e t a l . [ l 4 3 ] and Run T9. Source Enhancement f a c t o r Merchuk e t a l . [ 1 42] 6 t o 60 Column: 0.25m ID, 0.335m h i g h 25.4mm carbon R a s c h i g r i n g s C o n d i t i o n s : gas r a t e = 2800 t o 3000 kg/m 2 h l i q u i d r a t e = 3.0 t o 10.0 m3/m2 h NaOH cone. = 0.5 t o 1.0 kmol/m 3 CO? cone. = 8.0 t o 90.0 % Column temperature = 29.0 t o 32 °C Onda e t a l . [143] 10 t o 150 Column: 0.076m ID, 0.4m h i g h 6.0mm ceramic R a s c h i g r i n g s C o n d i t i o n s : l i q u i d r a t e = 6.37 t o 39.25 m3/m2 h NaOH cone. = 0.5 t o 3.0 kmol/m 3 C 0 2 cone. = 1 0 0 % Column temperature = 15 t o 45 °C T h i s work - Run T9 Column: 0.10m ID, 4.35m h i g h 12.7mm ceramic B e r l s a d d l e s C o n d i t i o n s : gas r a t e = 1545 kg/m 2 h l i q u i d r a t e = 13.5 m3/m2 h NaOH cone. = 0.413 t o 2.0 kmol/m 3 C 0 2 cone. = 1.0 t o 18.45 % Column temperature = 15.0 t o 35.0 °C 48 t o 90 197 COMPARI SON AT HIGH LOADING When the CO2 loading at the column bottom reached 0.5 moles of CO2 per mole of amine fo r the CC^-MEA system, the d i f f e r e n c e between the r e s u l t s and p r e d i c t i o n are s i g n i f i c a n t as shown by Figure 6.9 (Run T16). I f only t e r m i n a l c o n d i t i o n s are considered, good agreement would be deduced. Nevertheless, the discrepancy between the two p r o f i l e s i s larg e (see s o l i d l i n e and p o i n t s ) . This shows that a comparison of model p r e d i c t i o n s and experimental r e s u l t s at the absorber i n l e t and o u t l e t are i n s u f f i c i e n t to v a l i d a t e models. One reason f o r the discrepancy i n t h i s case may be due to bicarbonate formation, which becomes important as the CO2 l o a d i n g approaches 0.5 moles of CO2 per mole of MEA; the bicarbonate formation was not taken i n t o account i n the present model. Another reason may be because the r e a c t i o n r a t e i s a f f e c t e d by the i o n i c concentration which was not included i n the rate constant (Equation 6.2). The loading increases with the i o n i c strength but there i s no information on v a r i a t i o n i n rat e constant f o r CO2-MEA r e a c t i o n with i o n i c strength. The e f f e c t of the i o n i c s t r e n g t h on the rate constant i s w e l l known and has been stu d i e d e x t e n s i v e l y for the C02-NaOH system. For example, Pohorecki and Moniuk [111 ] reported that the value of 0.0 3.0 Distance from the bottom (m) s.o F i g u r e 6.9: C o n c e n t r a t i o n of C 0 2 i n the gas phase f o r Run T16. Open c i r c l e s r e p r e s e n t e x p e r i m e n t a l measurements; the s o l i d l i n e and d o t t e d l i n e s denote the p r e d i c t e d v a l u e s u s i n g a column comprised of s i x and f i v e s e c t i o n s , r e s p e c t i v e l y . ( O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 m3/m2 h; l i q u i d f l o w r a t e = 9.5 m3/m2 h; i n l e t C 0 2 l o a d i n g = 0.0 mol C 0 2 / mol MEA; i n l e t gas C02 c o n c e n t r a t i o n = 15.5%; t o t a l MEA c o n c e n t r a t i o n = 2.0 kmol/m 3.) 1 9 9 k 2 NaOH i n c r e a s e s by more than 4 times when the i o n i c s t r e n g t h was i n c r e a s e d from 0.0 to 3.8 kmol/m 3. T h i s e f f e c t s h o u l d be f u r t h e r s t u d i e d f o r C 0 2 - a m i n e systems. S i n c e both the r e a c t i o n mechanism and the r a t e c o n s t a n t i n f l u e n c e the enhancement f a c t o r , i t i s not s u r p r i s i n g t h a t good agreement was not o b t a i n e d a t the h i g h C O 2 l o a d i n g s . To c o n f i r m t h i s , the c a l c u l a t i o n s were r e p e a t e d f o r j u s t the t o p f i v e s e c t i o n s of the a b s o r b e r and u s i n g the e x p e r i m e n t a l l y d e t e r m i n e d c o m p o s i t i o n s of the l i q u i d and gas phases l e a v i n g and e n t e r i n g the bottom of the l o w e s t s e c t i o n , r e s p e c t i v e l y . Under the s e c o n d i t i o n s , the s o l u t i o n l o a d i n g ranged from 0.00 t o 0.425 moles C O 2 per mole of MEA. As shown by the d o t t e d l i n e i n F i g u r e 6.9, the agreement between the p r e d i c t e d and e x p e r i m e n t a l v a l u e s becomes once a g a i n v e r y good. 200 OVERALL COMPARISON Due t o the l a r g e amount of e x p e r i m e n t a l d a t a , i t i s d i f f i c u l t t o i l l u s t r a t e the comparison i n t a b u l a r form. T h e r e f o r e , the comparisons between r e s u l t s and p r e d i c t i o n s of CO2 c o n c e n t r a t i o n , NaOH c o n c e n t r a t i o n , C 0 2 l o a d i n g and l i q u i d t emperature f o r a l l runs a r e shown i n F i g u r e s 6.10, 6.11, 6.12 and 6.13, r e s p e c t i v e l y . S i n c e the p r e d i c t i o n s when C 0 2 l o a d i n g approaches 0.5 moles of C 0 2 per mole of amine f o r the C0 2-MEA system a re not a c c u r a t e , the r e s u l t s of the bottom s e c t i o n s of runs T15, T16, T18, T20 and T21 a r e not i n c l u d e d i n the c o m p a r i s o n s . As can be seen from t h o s e f i g u r e s , good agreements between e x p e r i m e n t a l r e s u l t s and p r e d i c t i o n s a r e o b t a i n e d . The d i s c r e p a n c i e s between t h e two a r e , on the a v e r a g e , about 12%. I t was a l s o found t h a t the model appears t o be q u i t e s e n s i t i v e t o the mass b a l a n c e . In some c a s e s , d e v i a t i o n s of a few p e r c e n t i n the i n p u t d a t a ( c o n c e n t r a t i o n s ) can r e s u l t i n l a r g e d i f f e r e n c e s i n the p r e d i c t e d h e i g h t . Some sample c a l c u l a t i o n s a r e shown i n Ta b l e 6.7 (Run T 9 ) . I f the l i q u i d c o n c e n t r a t i o n a t the column bottom i s reduced by 0.2 kmol/m 3 (10% of the t o t a l c o n c e n t r a t i o n ) , the h e i g h t p r e d i c t i o n d e v i a t e s by 13.9%. However, i f the c o n c e n t r a t i o n i s f u r t h e r reduced by 15%, the d e v i a t i o n i s e x p o n e n t i a l l y i n c r e a s e d t o about 26%. The e f f e c t of c o n c e n t r a t i o n on the a b s o r b e r 201 height p r e d i c t i o n i s even l a r g e r when s a t u r a t i o n i s approached. This i s not s u r p r i s i n g s i n c e the enhancement f a c t o r and the s p e c i f i c a b s o r p t i o n r a t e are s t r o n g l y dependent on the f l u i d c o n c e n t r a t i o n s . T h e r e f o r e , o b t a i n i n g good experimental data f o r v e r i f y i n g mathematical models should be as important as d e v e l o p i n g more r i g o r o u s t h e o r e t i c a l models. 202 F i g u r e 6.10: Cross p l o t of p r e d i c t e d and measured C O 2 c o n c e n t r a t i o n s i n the gas phase. 203 F i g u r e 6 . 1 1 : C r o s s p l o t o f p r e d i c t e d a n d m e a s u r e d N a O H c o n c e n t r a t i o n s i n t h e l i q u i d p h a s e . 204 o 0.00 0.25 0.50 C02 Loading, exp. F i g u r e 6.12: C r o s s p l o t of p r e d i c t e d and measured C 0 2 l o a d i n g i n the MEA s o l u t i o n . 205 Figure 6.13: Cross plot of predicted and measured temperatures in the l i q u i d phase. 206 T a b l e 6.7: E f f e c t of mass bal a n c e on the h e i g h t p r e d i c t i o n f o r Run T9 (NaOH-C0 2 s y s t e m ) . O p e r a t i n g C o n d i t i o n s : gas r a t e = 1545 kg/m 2 h; l i q u i d r a t e = 13.5 m3/m2 h; NaOH cone. = 0.413 t o 2.0 kmol/m 3; C 0 2 cone. = 1.0 t o 18.45 %; Column temperature = 15.0 t o 35.0 °C P r e d i c t e d D e v i a t i o n h e i g h t 4.40 m 0.0% 5.01 m 13.9% 5.56 m 26.4% Mass b a l a n c e a t Column bottom C B - 0.% of 2.0 kmol/m 3 ( a t 0.37 kmol/m 3) C B - 10% of 2.0 kmol/m 3 ( a t 0.17 kmol/m 3) C B - 15% of 2.0 kmol/m 3 ( a t 0.07 kmol/m 3) 207 EFFECT OF BASIC PARAMETERS S i n c e the u n c e r t a i n t i e s a s s o c i a t e d w i t h the d a t a or c o r r e l a t i o n s a v a i l a b l e i n the open l i t e r a t u r e a r e h i g h , i t i s u s e f u l t o know the degree of importance of t h e s e p arameters on t h e _ p r e d i c t e d r e s u l t s . The c o n d i t i o n s of Run-T9 a r e used t o i l l u s t r a t e t h e d e v i a t i o n i n t h e p r e d i c t e d r e s u l t s when v a l u e s of kg, k L ° , a v , H, and I i n the computer model a r e f o r c e d t o i n c r e a s e or d e c r e a s e by 20%; t h e s e a r e t y p i c a l ranges of u n c e r t a i n t y a s s o c i a t e d f o r th e s e p a r a m e t e r s . The c a l c u l a t e d r e s u l t s a r e summarized i n T a b l e 6.8. As can be seen, the impact of the i n t e r f a c i a l a r e a and the enhancement f a c t o r a r e as h i g h as 26.1% and 20.4%, r e s p e c t i v e l y . On t h e o t h e r hand, t h e impact of the p h y s i c a l mass t r a n s f e r c o e f f i c i e n t s i s r a t h e r s m a l l w h i l e t h a t of Henry's c o n s t a n t , H, i s moderate. - -To i d e n t i f y whether r e a c t i o n i n the l i q u i d phase i s f a s t or slow, L e v e n s p i e l [ 30, 141] su g g e s t e d t h a t a measurement of the s o - c a l l e d f i l m c o n v e r s i o n parameter be used: maximum p o s s i b l e c o n v e r s i o n i n l i q u i d f i l m M = 7 ——~ maximum d i f f u s i o n t r a n s p o r t t h r o u g h the f i l m = <k2 C A f i C B* 5 ) / { ( D A / 8 ) C A f i } = k 2 C B* D A / ( k L ° ) 2 2 0 8 I f t he v a l u e of M i s much g r e a t e r than 1 , a l l r e a c t i o n o c c u r s i n the l i q u i d f i l m , and e f f e c t i v e c o n t a c t i n g a r e a i s the c o n t r o l l i n g r a t e . On the o t h e r hand, no r e a c t i o n t a k e s p l a c e i n the f i l m , and b u l k volume of the l i q u i d phase becomes the c o n t r o l l i n g f a c t o r when M « 1 . I n the case of Run T 9 as w e l l as o t h e r r u n s , the v a l u e s of M a l o n g the column a r e w e l l over 1 0 0 . I t i s not s u r p r i s i n g t h a t the e f f e c t s of the i n t e r f a c i a l a r e a and the enhancement f a c t o r on the h e i g h t p r e d i c t i o n a r e t h e r e f o r e v e r y h i g h . 209 T a b l e 6.8: E f f e c t s of major parameters on the h e i g h t p r e d i c t i o n f o r Run T9 (NaOH - C O o ) . O p e r a t i n g C o n d i t i o n s : gas r a t e = 1545 kg/m 2 h; l i q u i d r a t e = 13.5 m3/m2 h; NaOH cone. = 0.413 t o 2.0 kmol/m 3; C 0 2 cone. = 1.0 t o 18.45 %; Column temperature = 15.0 t o 35.0 °C The normal p r e d i c t e d h e i g h t = 4.40 m Parameter P r e d i c t e d h e i g h t D e v i a t i o n k G + 20% 4.28 m 2.7 % 20% 4.69 m 6.4 % 20% 4.36 m 0.9 % 20% 4.56 m 3.6 % a v + 20% 3.70 m 15.9 % — 20% 5.55 m 26. 1 % H + 20% 3.94 m 10.4 % — 20% 5.19 m 17.9 % I + 20% 3.86 m 12.3 % - 20% 5.30 m 20.4 % 210 CHAPTER 7 RESULTS AND DISCUSSIONS: COMPARISON BETWEEN FULL-LENGTH  ABSORBER PERFORMANCE AND PREDICTIONS BASED ON PPT The o b j e c t i v e of t h i s c h a p t e r i s t o t e s t and v e r i f y the r e s u l t s of the PPT d e s i g n p r o c e d u r e proposed i n Chapter 3. The v a l i d a t i o n i s based on u s i n g R v ~ c o n c e n t r a t i o n diagrams and a PPT s h o r t - c u t p r o c e d u r e . 7 .1 VERIFICATION USING R y-CONCENTRATION DIAGRAM The a b s o r p t i o n of C 0 2 i n t o NaOH s o l u t i o n s was u s e d t o demonstrate the performance of PPT. The t e m p e r a t u r e changes i n the PPM and f u l l - l e n g t h columns were w i t h i n ±3 and ±8 °C, r e s p e c t i v e l y . These changes a r e s u f f i c i e n t l y s m a l l t o assume t h a t b oth columns o p e r a t e d i s o t h e r m a l l y . F i g u r e 7 .1 shows a t y p i c a l p l o t of Y c o 2 v s Z. The d a t a p o i n t s v a r y s y s t e m a t i c a l l y and do not f a l l on a s t r a i g h t l i n e even f o r t h i s s h o r t PPM column. T h i s i m p l i e s t h a t the o v e r a l l mass t r a n s f e r c o e f f i c i e n t was not c o n s t a n t and demonstrates the importance of measuring the c o n c e n t r a t i o n p r o f i l e s r a t h e r than j u s t the . t e r m i n a l c o n d i t i o n s . As d i s c u s s e d i n S e c t i o n 6.2.2, the v a l u e of the enhancement 211 q o o o 0.00 0.25 0.50 0.75 1.00 Distance from Column Botom (m) F i g u r e 7.1: A t y p i c a l p l o t of C 0 2 mole r a t i o i n the gas phase as a f u n c t i o n of h e i g h t i n the PPM column, Run S5. P o i n t s denote e x p e r i m e n t a l d a t a and the s o l i d l i n e i n d i c a t e s the be s t f i t u s i n g a t h i r d o r d e r p o l y n o m i a l e q u a t i o n . ( E x p e r i m e n t a l c o n d i t i o n s : L i q u i d f l o w r a t e = 13.5 m3/m2 h r ; a i r f l o w r a t e = 14.8 mol/m 2 s; temperature = 293 K ; t o t a l p r e s s u r e = 101.3 kPa; [Na*] = 1.20 kmol/m 3; [OH ] = 0.75 t o 0.56 kmol/m 3; C 0 2 c o n c e n t r a t i o n = 4.1 t o 2.0%.) 2 1 2 f a c t o r can change by as much as a f a c t o r of 2 over the column h e i g h t . For each e x p e r i m e n t a l run w i t h the PPM column, the c o n c e n t r a t i o n measurements were f i t t e d by means of a t h i r d o r d e r p o l y n o m i a l e q u a t i o n . The c o r r e l a t i o n c o e f f i c i e n t s f o r the f i t s g e n e r a l l y exceeded 0.99. The p o l y n o m i a l s were then d i f f e r e n t i a t e d a n a l y t i c a l l y . The v a l u e s of R v were o b t a i n e d from the p r o d u c t of the d i f f e r e n t i a t e d r e s u l t s and Gj ( a l s o see E q u a t i o n 3.2.14). In the case of the CC^-NaOH system, a l l fundamental parameters a r e known and R v, which i s the p r o d u c t of R a and a v , c o u l d a l s o be c a l c u l a t e d based on f i r s t p r i n c i p l e s as d e s c r i b e d p r e v i o u s l y i n Chapter 2. The d e v i a t i o n s between the e x p e r i m e n t a l and c a l c u l a t e d R v v a l u e s were, on the a v e r a g e , 5.5% (maximum 12%) and due t o e x p e r i m e n t a l and n u m e r i c a l u n c e r t a i n t i e s . The fundamental parameters r e q u i r e d i n t h e s e c a l c u l a t i o n s a r e taken from the same so u r c e s as the computer model ( a l s o see S e c t i o n 6.2.1). The q u a l i t y of the agreement i s good as shown by F i g u r e 7.2 because: ( i ) the CC^-NaOH system has been s t u d i e d e x t e n s i v e l y and i t s k i n e t i c s model i s w e l l u n d e r s t o o d , ( i i ) the r e a c t i o n i s s i m p l e and i r r e v e r s i b l e , which improves the a c c u r a c y of the ^ 1 <J F i g u r e 7.2: Comparison of R v v a l u e s o b t a i n e d e x p e r i m e n t a l l y from model column t e s t s and from f i r s t p r i n c i p l e s . ( E x p e r i m e n t a l c o n d i t i o n s : L i q u i d f l o w r a t e = 13.5 m3/m2 h r ; a i r f l o w r a t e = 14.8 mol/m 2 s; temperature = 293 K; t o t a l p r e s s u r e = 101.3 kPa; [ N a + ] = 1.20 kmol/m 3.) 214 enhancement f a c t o r c a l c u l a t i o n , and ( i i i ) a l most a l l k L , k G and a v v a l u e s , which a r e r e p o r t e d i n the l i t e r a t u r e , have been d e r i v e d f o r the CC^-NaOH system. The R v - c o n c e n t r a t i o n diagram i s p r e s e n t e d i n F i g u r e 7.3. The diagram shows the r e l a t i o n s h i p between the s p e c i f i c a b s o r p t i o n r a t e and the f l u i d c o m p o s i t i o n s . The c o n t i n u o u s l i n e s show the c a l c u l a t e d v a l u e s of R v f o r d i f f e r e n t f l u i d c o m p o s i t i o n s . As can be seen, the computed R v v a l u e s agree v e r y w e l l w i t h the e x p e r i m e n t a l r e s u l t s , showing t h a t i t i s p o s s i b l e t o d e s i g n packed a b s o r b e r s w i t h c h e m i c a l r e a c t i o n based on f i r s t p r i n c i p l e s p r o v i d e d t h a t the fundamental d a t a (mass t r a n s f e r c o e f f i c i e n t s , p h y s i c o -c h e m i c a l p r o p e r t i e s , e t c . ) a r e reliably known. The R v v a l u e s o b t a i n e d from model column t e s t s can then be used t o e v a l u a t e the i n t e g r a l i n E q u a t i o n 3.2.11 u s i n g e i t h e r g r a p h i c a l o r n u m e r i c a l methods. In o r d e r t o p e r f o r m t h i s i n t e g r a t i o n , the R v must be a v a i l a b l e as a f u n c t i o n of f l u i d c o m p o s i t i o n s or i n t h e from of R v - c o n c e n t r a t i o n diagrams such as shown i n F i g u r e 7.3. In the p r e s e n t c a s e , 56 d a t a p o i n t s from 14 PPM column runs were e n t e r e d i n t o a d a t a base. The R v v a l u e s c o r r e s p o n d i n g t o any d e s i r e d p a i r of gas and l i q u i d c o n c e n t r a t i o n s were r e t r i e v e d from t h e 215 Figure 7.3: Specific absorption rate (R v) as a function of C O 2 concentration in the gas phase and OH" concentration. The points and s o l i d lines are obtained from experiments and theoretical calculations, respectively. The dotted line denotes t y p i c a l Rv values along the column for Run T2. (Experimental conditions: Liquid flow rate = 13.5 m3/m2 hr; a i r flow rate = 14.8 mol/m2 s; temperature = 293 K; t o t a l pressure = 101.3 kPa; [Na +] = 1.20 kmol/m3.) 216 d a t a b a s e b y u s i n g a n i n t e r p o l a t i o n p a c k a g e c a l l e d D F I N 3 D , w h i c h i s b a s e d o n a w e i g h t e d l e a s t s q u a r e s i n t e r p o l a t i o n m e t h o d a n d w h i c h i s a v a i l a b l e f r o m t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a C o m p u t i n g C e n t r e . T h e d o t t e d l i n e i n F i g u r e 7 . 3 s h o w s t y p i c a l R v v a l u e s a l o n g t h e f u l l - l e n g t h c o l u m n f o r R u n T 2 . A s c a n b e s e e n , t h e s p e c i f i c a b s o r p t i o n r a t e c h a n g e s s i g n i f i c a n t l y a l o n g t h e a b s o r b e r d u e t o t h e v a r i a t i o n s o f t h e f l u i d c o n c e n t r a t i o n s . T h e r e s u l t s o f s i x e x p e r i m e n t a l r u n s c o n d u c t e d w i t h t h e f u l l - l e n g t h c o l u m n f o r a v a r i e t y o f C O 2 a n d h y d r o x i d e c o n c e n t r a t i o n s a r e s h o w n i n T a b l e 7 . 1 . T h e d i f f e r e n c e b e t w e e n t h e a c t u a l a n d p r e d i c t e d h e i g h t s i s a l w a y s l e s s t h a n 8% t h e r e b y p r o v i d i n g s t r o n g s u p p o r t f o r t h e v a l i d i t y o f t h e P P T . T h e g o o d a g r e e m e n t c o u l d b e e x p e c t e d b e c a u s e : ( i ) t h e h y d r o d y n a m i c s o f t h e f u l l - l e n g t h a n d m o d e l c o l u m n s w e r e t h e s a m e a n d ( i i ) t h e e f f e c t o f c o n c e n t r a t i o n o n t h e s p e c i f i c a b s o r p t i o n r a t e a n d e n h a n c e m e n t f a c t o r w a s f u l l y t a k e n i n t o a c c o u n t . F i g u r e 7 . 4 a l s o s h o w s e x c e l l e n t a g r e e m e n t b e t w e e n p r e d i c t e d ( s o l i d l i n e s w h i c h a r e f r o m t h e i n t e g r a t i o n o f E q u a t i o n 3 . 2 . 1 1 ) a n d e x p e r i m e n t a l v a l u e s ( p o i n t s ) w h e n t h e m o d e l r e s u l t s a r e u s e d t o p r e d i c t t h e c o n c e n t r a t i o n p r o f i l e s i n t h e f u l l - l e n g t h c o l u m n . 217 Table 7 . 1 : A c t u a l and p r e d i c t e d heights f o r the a b s o r p t i o n tower removing CO2 from a i r by contact with an aqueous NaOH s o l u t i o n . (Experimental c o n d i t i o n s : L i q u i d flow r a t e = 13.5 m^ /m^  hr; a i r flow r a t e = 14.8 mol/m^ s; temperature = 293 K; t o t a l p r e s s u r e = 101.3 kPa; [Na +] = 1.20 kmol/m 3.) Run [OH~] Cone. C 0 2 Cone. Mass Bal Tower Height # (kmol/m 3) (% ) E r r o r A c t u a l P r e d i c t e d E r r o r i n out i n out (%) (m) (m) (%) T1 0.75 0.18 8.90 2.30 +3.06 3.25 3.01 7.38 T2 1 .00 0.05 14.60 4.40 -1 .24 3.25 3.30 1 .54 T3 1 .02 0.01 18.20 7.75 -3.76 3.25 3.36 3.38 T4 0.80 0.10 9.10 1 .05 + 1 .54 4.35 4.40 1.15 T5 0.86 0.00 12.35 2.95 -0.37 4.35 4.01 7.82 T6 1 .03 0.07 12.50 1 .90 + 1.91 4.35 4.19 3.68 For the d e t a i l s of the f u l l - l e n g t h column p r o f i l e s , see Table 6.1. 218 0.0 1.0 2.0 3.0 Distance from Column Top (m) F i g u r e 7 .4 : A c t u a l ( p o i n t s ) and p r e d i c t e d ( s o l i d l i n e s ) of C 0 2 and NaOH c o n c e n t r a t i o n s i n the f u l l - s c a l e a b s o r b e r f o r Run T 2 . ( E x p e r i m e n t a l c o n d i t i o n s : L i q u i d f low r a t e = 13.5 m 3 / m 2 h r ; a i r f low r a t e = 14.8 m o l / m 2 s ; temperature = 293 K; t o t a l p r e s s u r e = 101.3 kPa ; [ N a + ] = 1.20 k m o l / m 5 . ) 219 7.2 VERIFICATION USING THE PPT SHORT-CUT PROCEDURE As can be seen from F i g u r e 7.3, o n l y the R v v a l u e s t h a t c o r r e s p o n d t o the c o n c e n t r a t i o n s a l o n g the column f o r a g i v e n s e t of o p e r a t i n g c o n d i t i o n s are r e a l l y needed. When the gas and l i q u i d f l o w r a t e s are changed, the R v-c o n c e n t r a t i o n diagram must be c o n s t r u c t e d as a f u n c t i o n of the f l u i d f l o w r a t e as w e l l . In d o i n g t h i s , i t i s n e c e s s a r y t o p e r f o r m a l a r g e number of e x p e r i m e n t s w i t h the PPM column. T h e r e f o r e , u s i n g the PPT s h o r t - c u t procedure as e x p l a i n e d i n S e c t i o n 3.2.2 would be p r a c t i c a l under such c i r c u m s t a n c e s . The a p p r o x i m a t i o n of a d i a b a t i c o p e r a t i o n would a l s o be more r e a l i s t i c s i n c e t h e r e i s v e r y l i t t l e heat exchange between the column and s u r r o u n d i n g s [54, 1.05]. To ensure a d i a b a t i c c o n d i t i o n , t h e column was i n s u l a t e d w i t h 3/4" f i b e r g l a s s . The R v v a l u e s thus depend on the f l u i d c o n c e n t r a t i o n s and the t e m p e r a t u r e . The v e r i f i c a t i o n was p erformed u s i n g NaOH-C0 2 and AMP-C0 2 systems o p e r a t e d under a v a r i e t y of f l u i d c o n c e n t r a t i o n s . 7.2.1 NaOH-C0 2 SYSTEM O r i g i n a l l y i t had been i n t e n d e d t o use the C0 2~MEA system f o r the s h o r t - c u t v e r i f i c a t i o n . However, the a b s o r p t i o n of C 0 2 i n t o h i g h l y c o n c e n t r a t e d (2.0 - 2.5 M) 220 NaOH s o l u t i o n s was s e l e c t e d i n s t e a d , s i n c e e x p l o r a t o r y e x p e r i m e n t s showed t h a t both have s i m i l a r a b s o r p t i o n -r e a c t i o n c h a r a c t e r i s t i c s (see Chapter 6 and F i g u r e 6.6). The reason s f o r f a v o r i n g the C02 _NaOH system were t h a t i t t a k e s l e s s time and r e s o u r c e s t o run ex p e r i m e n t s and the a n a l y s i s of the - l i q u i d sample i s more d i r e c t and r e l i a b l e . The r e s u l t s of 4 s e t s of exp e r i m e n t s (4 f u l l - l e n g t h runs and 16 s e c t i o n runs u s i n g the model column) a r e shown i n T a b l e 7.2. Due t o the f a c t t h a t h i g h l y c o n c e n t r a t e d NaOH s o l u t i o n s were used and h i g h c o n v e r s i o n (up t o more than 90%) o c c u r r e d , the temperature i n c r e a s e s i n the f u l l - l e n g t h a b s o r b e r ranged from 14 up t o 42 °C. To v e r i f y the a b i l i t y of the PPT t o d e s i g n f u l l - l e n g t h a b s o r b e r s o p e r a t i n g under n o n - i s o t h e r m a l c o n d i t i o n s , e x p e r i m e n t s were performed w i t h the PPM column by matching t h e - f l u i d c o n c e n t r a t i o n s as w e l l as temperatures s e c t i o n by s e c t i o n s t a r t i n g from the t o p of the a b s o r b e r ( a l s o see s e c t i o n 3.2.2). As can be noted from T a b l e 7.2, the d i f f e r e n c e s between the a c t u a l and p r e d i c t e d h e i g h t s a re always l e s s than 7%. F i g u r e s 7.5 t o 7.8 a l s o show good agreement between e x p e r i m e n t a l measurements and PPT p r e d i c t e d r e s u l t s f o r the c o n c e n t r a t i o n p r o f i l e a l o n g the f u l l - l e n g t h columns. 221 T a b l e 7 . 2 : V e r i f i c a t i o n r e s u l t s f o r the PPT s h o r t - c u t p r o c e d u r e u s i n g the NaOH-CC^ s y s t e m . Run # T7 T8 T9 T1 0 L i q u i d f low r a t e ( m 3 / m 2 h) 9 .5 9 .5 13.5 13.5 Gas f low r a t e ( m o l / m 2 s) 14.8 14.8 14.8 14.8 [ N a + ] t o t a l cone, (kmol /m 3 ) 2.0 2 .5 2.0 2.0 [OH ] cone. (kmol /m 3 ) i n out 2.00 0.09 2.50 0.18 2.00 0.37 1 .50 0.24 C 0 2 c o n e . (%) i n out 15.45 1 .25 18.60 1 .70 18.45 1 .00 15.20 1 .75 L i q u i d temp. ( ° C ) i n out 14.5 37.0 14.0 42.0 15.0 35.0 15.0 30.0 Mass B a l a n c e E r r o r (%) •1 .79 - 2 . 2 3 - 5 . 6 9 + 1 .51 A c t u a l h e i g h t (m) 4.35 4 .35 4.35 4.35 PPT p r e d i c t e d h e i g h t (m) 4.40 4.53 4.65 4.62 E r r o r (%) 1.2 4. 1 6.9 6.2 For d e t a i l s of the column p r o f i l e s , see T a b l e 6 . 1 . 222 However, the temperature measurements p r e d i c t e d by the s h o r t - c u t procedure u s i n g the model column were a l i t t l e l o wer ( 2 t o 5 °C) than the a c t u a l measurements as shown by F i g u r e s 7.9 t o 7.12. The reason f o r t h i s may be t h a t u n s a t u r a t e d a i r was used as the i n e r t gas. As a r e s u l t , water v a p o r i z a t i o n o c c u r r e d and consumed some heat which caused the temperature measured by the PPT s h o r t - c u t p r o c e d u r e t o be lower than the a c t u a l v a l u e s . S i n c e the r e a c t i o n r a t e i s an i n c r e a s i n g f u n c t i o n of t e m p e r a t u r e , the reduced t e m p e r a t u r e s r e s u l t e d i n lower enhancement f a c t o r s and s p e c i f i c a b s o r p t i o n r a t e s . To c o n f i r m the e f f e c t of t e m p e r a t u r e , the computer model d e s c r i b e d i n Chapter 6 was f o r c e d t o lower the l i q u i d t emperature by 3 °C. The p r e d i c t e d a b s o r b e r h e i g h t was found t o be 4.52 m compared w i t h 4.39 m under the normal c o n d i t i o n . The d i f f e r e n c e between the two i s a p p r o x i m a t e l y 3%. For t h i s r e a s o n , the PPT p r e d i c t e d h e i g h t s shown i n T a b l e 7.2 a r e up t o about 7% g r e a t e r than the a c t u a l h e i g h t s . D e v i a t i o n s of 7% i n the p r e d i c t i o n of column h e i g h t s a r e however v e r y s m a l l compared w i t h i n d u s t r i a l d e s i g n approaches t h a t u t i l i z e s a f e t y f a c t o r of 1.5 t o 2.5 (50% t o 150%). 223 0.0 2.0 4.0 Distance from Column Top (m) Figure 7.5: Actual (points) and PPT predicted values of C0 2 ( s o l i d l i n e ) and NaOH (dotted l i n e ) concentrations in the f u l l - s c a l e absorber for Run T7. Operating conditions: a i r flow rate = 14.8 mol/m2 s; l i q u i d flow rate = 9.5 m3/m2 hr; C0 2 concentration = 1.25%(top) and 15.45%(bottom); [OH ] = 2.0(top) and 0.14(bottom) kmol/m3. 224 0.0 2.0 4.0 Distance from Column Top (m) F i g u r e 7.6: A c t u a l ( p o i n t s ) and PPT p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and NaOH (d o t t e d l i n e ) c o n c e n t r a t i o n s i n the f u l l - s c a l e absorber f o r Run T8. Operating c o n d i t i o n s : a i r flow r a t e = 14.8 mol/m 2 s; l i q u i d flow r a t e = 9.5 m3/m2 h r ; C 0 2 _ c o n c e n t r a t i o n = 1.7%(top) and 18.6%(bottom); [OH ] = 2.5(top) and O.!8(bottom) kmol/m 3. 225 0.0 2.0 4.0 Distance from Column Top (m) F i g u r e 7.7: A c t u a l ( p o i n t s ) and PPT p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and NaOH ( d o t t e d l i n e ) c o n c e n t r a t i o n s i n the f u l l - s c a l e a b s o r b e r f o r Run T9. O p e r a t i n g c o n d i t i o n s : a i r f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h r ; C 0 2 c o n c e n t r a t i o n =_1.0%(top) and l 8 . 4 5 % ( b o t t o m ) ; [OH ] = 2.0(top) and 0.37(bottom) kmol/m 3. 2 2 6 o O 6 o o o o 0.0 F i g u r e 7.8 q d 2.0 4.0 Distance from Column Top (m) A c t u a l ( p o i n t s ) and PPT p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and NaOH ( d o t t e d l i n e ) c o n c e n t r a t i o n s i n the f u l l - s c a l e a b s o r b e r f o r Run T10. O p e r a t i n g c o n d i t i o n s : a i r f low r a t e = 14.8 m o l / m 2 s ; l i q u i d f low ra te = 13.5 m 3 / m 2 h r ; C 0 2 c o n c e n t r a t i o n = 1.75%(top) and 15.2%(bottom); [OH ] = l . 5 ( t o p ) and 0 .24(bottom) k m o l / m 3 . 227 0.0 2.0 4.0 Distance from Column Top (m) F i g u r e 7.9: Column tem p e r a t u r e measured from the f u l l - l e n g t h column ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T7. O p e r a t i n g c o n d i t i o n s : a i r fl o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; C 0 2 c o n c e n t r a t i o n = 1.25% (top) and 15.45%(bottom); [OH~] = 2.0(top) and 0.14(bottom) kmol/m 3. 2 2 8 F i g u r e 7.10: Column temperature measured from the f u l l -l e n g t h column ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T8. O p e r a t i n g c o n d i t i o n s : a i r f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; COo c o n c e n t r a t i o n = 1.7%(top) and 18.6%fbottom); [OH ] = 2.5(top) and 0.!8(bottom) kmol/m 3. 229 F i g u r e 7.11: Column t e m p e r a t u r e measured from the f u l l -l e n g t h column ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T9. O p e r a t i n g c o n d i t i o n s : a i r f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h r ; CO? c o n c e n t r a t i o n = 1.0%(top) and 18.45%(bottom); [0H~] = 2.0(top) and 0.37(bottom) kmol/m 3. 230 q d co F i g u r e 7.12: Column temperature measured from the f u l l -l e n g t h column ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T10. O p e r a t i n g c o n d i t i o n s : a i r f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h r ; C 0 2 c o n c e n t r a t i o n = 1.75%(top) and 15.2%(bottom); [OH ] = 1.5(top) and 0.24(bottom) kmol/m 3. 231 7.2.2 CO2-AMP SYSTEM F u r t h e r v e r i f i c a t i o n of the PPT i s performed u s i n g the a b s o r p t i o n of C O 2 by 2 M AMP s o l u t i o n s . The v e r i f i c a t i o n p r ocedure f o r t h i s system i s the same as t h a t used f o r the NaOH -C02 system d e s c r i b e d i n the p r e v i o u s s e c t i o n . However, b e f o r e d e a l i n g w i t h the v e r i f i c a t i o n i t i s n e c e s s a r y t o make some g e n e r a l o b s e r v a t i o n s . GENERAL OBSERVATIONS S i n c e no comprehensive e x p e r i m e n t a l d a t a have been r e p o r t e d r e g a r d i n g columns u s i n g the CO2-AMP system, the temperature and c o m p o s i t i o n p r o f i l e s a l o n g the f u l l - l e n g t h a b s o r b e r a r e p r e s e n t e d , for the f i r s t time, i n T a b l e 7.3. S i n c e the e x p e r i m e n t a l d a t a f o r C O 2 a b s o r p t i o n i n t o the s o l u t i o n of MEA i n the same packed column a r e a v a i l a b l e , t he column performance i s t h e r e f o r e compared by p l o t t i n g the C O 2 c o n c e n t r a t i o n p r o f i l e a l o n g the column h e i g h t as shown i n F i g u r e s 7.13 and 7.14. I t i s i n t e r e s t i n g t o see t h a t the a b s o r p t i o n r a t e u s i n g MEA i s much h i g h e r than f o r AMP when the l o a d i n g i s below a p p r o x i m a t e l y 0.5 moles of C O 2 per mole of amine as shown i n F i g u r e 7.13 (Runs T21 and T27). T h i s may be due l a r g e l y t o the f a c t t h a t the r e a c t i o n r a t e of C0 2-AMP system i s slowe r than t h a t of C0 2"MEA [72, 145]. 232 T a b l e 7.3: E x p e r i m e n t a l r e s u l t s f o r the C02 -AMP system. Run (#) T23 T24 T25 T26 A i r Flow Rate 14. ,8 14. ,8 14. ,8 14. ,8 (mol/m 2 s) L i q u i d Flow Rate (m 3/m 2 h) 9. ,5 9. .5 9. .5 9. ,5 Absorbent Feed 2. .0 2. .0 2. .0 2. .0 Cone, (kmol/m 3) Gas C 0 2 Conc.(%) ©height from t o p : 0.00 m 6. .80 8, .90 10. .10 7. .70 1 .05 m 8. .60 10, .50 1 1 . .80 9, .55 2.15m 10. .70 12, .20 13, .40 1 1 , .55 3.25 m 13. .30 13, .85 15, .15 13, .70 4.35 m 15. .25 15, .45 16, .70 15, .70 5.45 m » > 17, .80 17, .35 6.55 m < —, > 18, .90 18, .65 C 0 2 removal (%) 60, .4 46, .6 51 , .8 63, .6 C 0 2 l o a d i n g (mol C0 2/mol AMP) ©height from t o p : 0.00 m 0.000 0. 147 0.1 52 0.022 1 .05 m 0.058 0.202 0.215 0.083 2.15 m 0.131 0.258 0.277 0. 149 3.25 m 0.212 0.317 0.341 0.223 4.35 m 0.285 0.387 0.396 0.303 5.45 m • • 0.442 0.358 6.55 m • • 0.464 0.411 Mass b a l a n c e e r r o r (%) -4.24 +1.52 -7.53 -4.31 L i q . Temp (°C) ©height from t o p : 0.00 m 15.0 15.0 15.0 15.0 1 .05 m 16.0 17.0 17.0 17.0 2.15 m 17.0 19.0 18.0 20.0 3.25 m 19.0 21 .0 21 .0 23.0 4.35 m 23.0 21 .0 23.0 26.5 5.45 m • • 24.5 28.0 6.55 m • • 24.5 29.0 Note: The v a l u e s i n ( ) a r e c a l c u l a t e d from mass b a l a n c e . Table 7 . 3 ( c o n ' t ) : E x p e r i m e n t a l r e s u l t s f o r the CO2-AMP system. Run (#) A i r Flow Rate (mol/m 2 s) L i q u i d Flow Rate <m3/m2 h) Absorbent Feed Cone, (kmol/m 3) Gas C 0 2 Cone.(%) ©height from t o p : 0.00 m 1.05m 2.15m 3.25 m 4.35 m 5.45 m 6.55 m T27 T28 T29 T30 11. 1 14.8 14.8 1 1 . 19. 5 9.5 13.5 13. 5 2. 0 2.0 2.0 2. 0 4. 25 13.25 5.95 2. 65 6. 15 14.55 7.65 4. 00 8. 40 15.65 9.50 6. 00 1 1 . 20 16.75 1 1 .70 8. 70 14. 1 5 17.75 1 4.70 12. 25 16. 95 18.40 17.05 15. 85 19. 00 19.15 19.00 19. 00 81 . 1 35.5 73.0 88. 4 C 0 2 removal (%) C 0 2 l o a d i n g (mol C0 2/mol ©height from t o p : 0.00 m 0.021 1.05 m 0.058 2.15m 0.113 3.25 m 0.174 4.35 m 0.254 5.45 m 0.323 6.55 m 0.383 Mass b a l a n c e e r r o r (%) -9.31 L i q . Temp (°C) ©height from t o p : 0.00 m 15.0 1.05 m 16.5 2.15m 19.0 3.25 m 21.0 4.35 m 24.5 5.45 m 26.0 6.55 m 28.0 AMP) 0. 371 0. 038 0. 029 0. 417 (0. 079) 0. 045 0. 449 (0. 1 19) 0. 078 0. 484 (0. 173) 0. 1 22 0. 536 (0. 251 ) 0. 182 0. 550 (0. 316) 0. 233 0. 583 0. 385 0. 300 9. 67 + 3. 61 - 1 1 . 60 15.0 14.0 15.0 16.0 16.0 16.0 18.0 18.0 17.0 19.0 20.0 19.0 20.0 22.5 21 .0 21 .0 24.0 23.0 21 .0 26.0 25.0 Note: The v a l u e s i n ( ) a r e c a l c u l a t e d from mass b a l a n c e . 2 3 4 0.0 6.0 12.0 18.0 C 0 2 C o n e . (%) F i g u r e 7.13: Column performance a t low l o a d i n g . MEA (Run T21 - open squares) vs AMP (Run T27 - s o l i d c i r c l e s ) . O p e r a t i n g c o n d i t i o n s : gas fl o w r a t e = 11.1 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l amine c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 19.0%; i n l e t C 0 2 l o a d i n g = 0.02 moles of C 0 2 / mole of amine. 235 F i g u r e 7.14: Column performance at high l o a d i n g . AMP (Run T28 - s o l i d c i r c l e s ) vs MEA (Run T18 - open squares). Operating c o n d i t i o n s : gas flow rate = 14.8 mol/m 2 s; l i q u i d flow r a t e = 9.5 m3/m2 hr; t o t a l amine c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C0 2 c o n c e n t r a t i o n = 19.15%; o u t l e t C0 2 l o a d i n g = 0.583 moles of C0 2 / mole of amine. The l i n e s represent smoothed experimental values. 236 On the o t h e r hand, the o p p o s i t e i s t r u e and a c r o s s - o v e r can be seen when the l o a d i n g exceeds 0.5 moles of CO2 per mole of amine as shown i n F i g u r e 7.14 (Run T18 vs T28). The reason f o r t h i s i s t h a t when the l o a d i n g i s l a r g e r than 0.5 moles of CO2 per mole of amine, the f r e e amine c o n c e n t r a t i o n i n MEA s o l u t i o n s i s . v i r t u a l l y n i l . By c o n t r a s t , the f r e e amine c o n c e n t r a t i o n i n AMP s o l u t i o n s f o r the same s i t u a t i o n i s a p p r o x i m a t e l y h a l f of the t o t a l amine c o n c e n t r a t i o n due t o the h i n d e r e d e f f e c t which causes i n s t a b i l i t y f o r the AMP carbamate. As a r e s u l t , the carbamate i s e a s i l y r e v e r s e d t o f r e e AMP ( a l s o see S e c t i o n s 2.2 and 4.3). I t - s h o u l d be noted t h a t the s o l i d l i n e s i n F i g u r e s 7.13 and 7.14 a r e drawn from smoothed v a l u e s of the c o r r e s p o n d i n g d a t a . A f t e r the AMP s o l u t i o n had been used f o r a p p r o x i m a t e l y 8 r u n s , a tendency t o f l o o d d i d occur due- t o foaming problems a l t h o u g h the a b s o r b e r was d e s i g n e d and o p e r a t e d below the f l o o d i n g v e l o c i t y . The problem i s b e l i e v e d t o be caused by the foaming n a t u r e of the s o l u t i o n , which was f u r t h e r a g g r a v a t e d by f i n e p a r t i c u l a t e m a t t e r from the p a c k i n g and the a i r . I t was a l s o n o t i c e d t h a t f l o o d i n g was more s e r i o u s i n the a b s o r b e r than i n the r e g e n e r a t o r . The problem was reduced c o m p l e t e l y by a d d i t i o n of a few ppm of the a n t i f o a m i n g agent, A n t i f o a m B ( t r a d e name) manufactured by Dow C o r n i n g Corp. and marketed i n Canada by BDH I n c . of T o r o n t o , Ont. In s p i t e of the a d d i t i o n of the a n t i f o a m i n g 2 3 7 a g e n t , the problem would reappear a f t e r s o l u t i o n r e g e n e r a t i o n . The f l o o d i n g reappearance may be due t o the e v a p o r a t i o n and/or d e g r a d a t i o n of the a n t i f o a m i n g agent caused by the h i g h temperature i n the r e b o i l e r . 5 t o 10 ppm of the a n t i f o a m i n g agent were t h e r e f o r e t y p i c a l l y added t o the s o l u t i o n a f t e r each r e g e n e r a t i o n r u n . To ensure t h a t t h e r e i s no s i g n i f i c a n t e f f e c t of the a n t i f o a m on the o v e r a l l a b s o r p t i o n , comparison runs were performed as shown i n F i g u r e 7.15 . The s o l u t i o n used f o r run S70 c o n t a i n e d no a n t i f o a m agent. On the o t h e r hand, run S94 was c o n d u c t e d w i t h a n t i f o a m added and had been used f o r more than 40 a b s o r p t i o n and r e g e n e r a t i o n e x p e r i m e n t s . Both r u n s , S70 and S94, were performed under the same c o n d i t i o n s . F i g u r e 7.15 shows t h a t the C 0 2 c o n c e n t r a t i o n , p r o f i l e from b o t h runs a r e v i r t u a l l y i d e n t i c a l . COMPARISON RESULTS The r e s u l t s of 6 e x p e r i m e n t a l runs p r e d i c t e d by the s h o r t - c u t p r o c e d u r e u s i n g 24 PPM column runs a r e summarized i n T a b l e 7.4. As can be seen from T a b l e 7.4, good agreement was o b t a i n e d . The d i f f e r e n c e between the a c t u a l and PPT p r e d i c t e d r e s u l t s was always l e s s than 12%. S l i g h t l y l e s s a c c u r a t e r e s u l t s were o b t a i n e d w i t h the C0 2-AMP system than 2 3 8 O O 0.00 0.25 0.50 0.75 1.00 Distance from Column Botom (m) F i g u r e 7.15: C O 2 c o n c e n t r a t i o n p r o f i l e of Run #S70 without a n t i f o a m i n g agent (open c i r c l e s ) and Run #S94 with a n t i f o a m i n g agent ( s t a r s ) . O p e r a t i n g c o n d i t i o n s : gas fl o w r a t e =14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l amine c o n c e n t r a t i o n = 2.0 kmol/m 2. 2 3 9 T a b l e 7 .4 : V e r i f i c a t i o n r e s u l t s f o r the PPT s h o r t - c u t procedure u s i n g the AMP-CO2 sys tem. Run # T23 T24 T25 T26 T27 T30 L i q u i d f low r a t e ( m 3 / m 2 h) 9.5 9.5 9.5 9.5 9.5 13.5 Gas f low r a t e ( m o l / m 2 s) 14.8 14.8 14.8 14.8 11.1 11.1 T o t a l c o n e , of AMP (kmol /m 3 ) 2.0 2.0 2.0 2.0 2.0 2.0 C 0 2 l o a d i n g i n 0.000 0.147 0.152 0.022 0.021 0.29 (mol C 0 2 / out 0.285 0.387 0.464 0.411 0.383 0.300 mol C02) C 0 2 c o n e . i n 15.25 15.45 18.90 18.65 19.00 19.00 (%) out 6.80 8.90 10.10 7.70 4.25 2.65 L i q u i d temp, i n 15.0 15.0 15.0 15.0 15.0 15.0 ( ° C ) out 23.0 21.0 24.0 29.0 28.0 25.0 Mass Balance E r r o r (%) -4 .24 +1.52 - 7 . 5 3 -4 .31 -9 .31 - 1 1 . 6 A c t u a l h e i g h t (m) 4.35 4.35 6.55 6.55 6.55 6.55 PPT p r e d i c t e d h e i g h t (m) 4.85 4.75 6.37 6.15 6.68 6.88 E r r o r (%) 11.5 9.0 2 .7 6.1 2.0 5.0 For more d e t a i l s on the column p r o f i l e s , see T a b l e 7 .3 . 240 the C02 -NaOH system. The reason f o r t h i s may be due t o the f a c t t h a t the a n a l y s i s of l i q u i d samples f o r the former system i s i n d i r e c t and t h e r e f o r e l e s s p r e c i s e than t h a t f o r the l a t t e r . For a g i v e n sample s i z e and c o n c e n t r a t i o n , the a c c u r a c y of c o m p o s i t i o n a n a l y s i s of N a + and OH - i s w i t h i n ± 2 % as compared w i t h ± 3.3 % f o r t h e C 0 2 l o a d i n g i n t h e AMP s o l u t i o n ( a l s o see Appendix A ) . S i n c e the v a l u e s of R v c o u l d be a f f e c t e d by the f l u i d c o m p o s i t i o n , the u n c e r t a i n t y i n v o l v e d i n p r e d i c t i n g the column h e i g h t i n t h i s case i s l a r g e r than t h a t f o r the C02 -NaOH system. By comparison w i t h i n d u s t r i a l d e s i g n p r a c t i c e which t y p i c a l l y a l l o w s f o r s a f e t y f a c t o r s of 1.5 t o 2.5 (50 t o 150%), the 12 % a c c u r a c y f o r the PPT p r e d i c t i o n s i s v e r y good. F i g u r e s 7.16 t o 7.27 a l s o show good agreement between the e x p e r i m e n t a l and PPT r e s u l t s f o r the column p r o f i l e s . I t s h o u l d be noted t h a t the p r e c i s e p r e d i c t i o n of the o v e r a l l a b s o r p t i o n r a t e i n , o r the performance o f , the column u s i n g the AMP-CO2 system based on f i r s t p r i n c i p l e s i s p r a c t i c a l l y i m p o s s i b l e because the r e a c t i o n mechanism i n v o l v e d i s not w e l l u n d e r s t o o d and i n s u f f i c i e n t fundamental d a t a r e g a r d i n g i t s p h y s i c o - c h e m i c a l p r o p e r t i e s have been r e p o r t e d . d 1 1 L_ 0.0 2.0 4.0 6.0 Distance from Column Top (m) F i g u r e 7.16: A c t u a l ( p o i n t s ) and p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and l i q u i d l o a d i n g ( d o t t e d l i n e ) i n the f u l l - s c a l e absorber f o r Run T23. Operating c o n d i t i o n s : gas flow r a t e = 14.8 mol/m 2 s; l i q u i d flow r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n - 2.0 kmol/m 2; i n l e t -gas C0 2 c o n c e n t r a t i o n = 15.5%; i n l e t l i q u i d l o a d i n g = 0 mol C0 2/mol AMP. 2 4 2 F i g u r e 7.17: A c t u a l ( p o i n t s ) and p r e d i c t e d v a l u e s of C O 2 ( s o l i d l i n e ) and l i q u i d l o a d i n g ( d o t t e d l i n e ) i n the f u l l - s c a l e absorber f o r Run T 2 4 . Operating c o n d i t i o n s : gas flow r a t e - 14.8 mol/m 2 s; l i q u i d flow r a t e = 9 . 5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2 .0 kmol/m 2; i n l e t gas CO2 c o n c e n t r a t i o n = 15 .5%. ; i n l e t l i q u i d l o a d i n g = 0 .147 mol C0 2/mol AMP. 2 4 3 0.0 2.0 4.0 6.0 Distance from Column Top (m) F i g u r e 7 . 1 8 : A c t u a l ( p o i n t s ) and p r e d i c t e d values of C 0 2 ( s o l i d l i n e ) and l i q u i d l o a d i n g ( d o t t e d l i n e ) i n the f u l l - s c a l e absorber f o r Run T 2 5 . Operating c o n d i t i o n s : gas flow r a t e = 1 4 . 8 mol/m 2 s; l i q u i d flow r a t e = 9 . 5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2 . 0 kmol/m 2; i n l e t -gas C 0 2 c o n c e n t r a t i o n = 1 8 . 9 % ; i n l e t l i q u i d l o a d i n g = 0 . 1 5 2 mol C 0 2/mol AMP. 244 0.0 2.0 4.0 6.0 Distance from Column Top (m) F i g u r e 7.19: A c t u a l (points ) and p r e d i c t e d values of CO2 ( s o l i d l i n e ) and l i q u i d l o a d i n g (dotted l i n e ) in the f u l l - s c a l e absorber f o r Run T26. Operat ing c o n d i t i o n s : gas flow rate = 14.8 " mol /m 2 s; l i q u i d flow rate = 9.5 m 3 / m 2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 k m o l / m 2 ; i n l e t gas C 0 2 concentra t ion = 18.65%; i n l e t l i q u i d l o a d i n g = 0.022 mol C 0 2 / m o l AMP. 245 F i g u r e 7.20: A c t u a l ( p o i n t s ) and p r e d i c t e d v a l u e s of C 0 2 ( s o l i d l i n e ) and l i q u i d l o a d i n g ( d o t t e d l i n e ) i n the f u l l - s c a l e absorber f o r Run T27. O p erating c o n d i t i o n s : gas flow r a t e = 11.1 mol/m 2 s; l i q u i d flow r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n — 2.0 kmol/m 2; i n l e t gas C0 2 c o n c e n t r a t i o n = 19.0%; i n l e t l i q u i d l o a d i n g = 0.021 mol C0 2/mol AMP. 2 4 6 Distance from Column Top (m) F i g u r e 7.21: A c t u a l ( p o i n t s ) and p r e d i c t e d v a l u e s of C0 2 ( s o l i d l i n e ) and l i q u i d l o a d i n g ( d o t t e d l i n e ) i n the f u l l - s c a l e absorber f o r Run T30. Operating c o n d i t i o n s : gas flow r a t e = 11.1 mol/m 2 s; l i q u i d flow r a t e = 13.5 m3/m2 h r ; -t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 19.0%; i n l e t l i q u i d l o a d i n g = 0.29 mol C0 2/mol AMP. o CM CO o o CO o d CO CM -• -o : — 1 i i 0.0 2.0 4.0 6.0 Distance from Column Top (m) F i g u r e 7 . 2 2 : Column temperature measured from the f u l l -l e n g t h column ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T 2 3 . Operating c o n d i t i o n s : gas flow r a t e = 14.8 mol/m 2 s; l i q u i d flow r a t e =9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2 . 0 kmol/m 2; i n l e t gas C0 2 c o n c e n t r a t i o n = 15.5%; i n l e t l i q u i d l o a d i n g mol C0 2/mol AMP. 2 4 8 q d CM CO ft o o CO O O o co CM 0.0 2.0 4 .0 6.0 Distance from Column Top (m) F i g u r e 7.23: Column temperature measured from the f u l l -l e n g t h column ( s o l i d c i r c l e s ) and PPM column (open squares) f o r Run T24. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e =14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 15.5%; i n l e t l i q u i d l o a d i n g = 0.147 mol C0 2/mol AMP. 249 o cv CO PH o o CO o d CO 0.0 2.0 4 .0 6.0 Distance f rom Column Top (m) F i g u r e 7.24: Column temperature measured from the f u l l -l e n g t h column ( s o l i d c i r c l e s ) and PPM column-(open s q u a r e s ) f o r Run T 2 5 . O p e r a t i n g c o n d i t i o n s : gas fl o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n ^ 18.9%; i n l e t l i q u i d l o a d i n g = 0.152 mol C0 2/mol AMP. o d CM CO ft d I • • o - • m & m*"*' O d 03 CM 0.0 2.0 4.0 6.0 Distance from Column Top (m) F i g u r e 7.25: Column temperature measured from the f u l l -l e n g t h column ( s o l i d c i r c l e s ) and PPM column, (open squares) f o r Run T26. O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C O o c o n c e n t r a t i o n = 18.65%; i n l e t l i q u i d l o a d i n g 0.022 mol C0 2/mol AMP 251 0.0 2.0 4.0 6.0 D i s t a n c e f r o m C o l u m n Top (m) F i g u r e 7.26: Column temperature measured from the f u l l -l e n g t h column ( s o l i d c i r c l e s ) and PPM column" (open squares) f o r Run T27. O p e r a t i n g c o n d i t i o n s : gas flow r a t e =11.1 mol/m 2 s; l i q u i d flow r a t e = 9.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 19.0%; i n l e t l i q u i d l o a d i n g = 0.021 mol C0 2/mol AMP. 252 0.0 2.0 4.0 6.0 Distance from Column Top (m) F i g u r e 7.27 Column temperature measured from the f u l l -l e n g t h column ( s o l i d c i r c l e s ) and PPM column (open squares) f o r R u n T 3 0 . O p e r a t i n g c o n d i t i o n s : gas f l o w r a t e = 11.1 mol/m 2 s; l i q u i d f l o w r a t e = 13.5 m3/m2 h r ; t o t a l AMP c o n c e n t r a t i o n = 2.0 kmol/m 2; i n l e t gas C 0 2 c o n c e n t r a t i o n = 19.0%; i n l e t l i q u i d l o a d i n g = 0.29 mol C0 2/mol AMP. 253 7.3 DISCUSSION OF THE VERIFICATION RESULTS The v a l i d i t y of the PPT d e s i g n p r o c e d u r e has been t e s t e d under a v a r i e t y of o p e r a t i n g c o n d i t i o n s w i t h two d i s t i n c t systems: the C02-NaOH system which i s w e l l known and t h e CO2-AMP system which i s new. As can be seen from T a b l e s 7.1-7.2 and 7.4, the maximum d i f f e r e n c e between the a c t u a l and p r e d i c t e d h e i g h t s i s always l e s s than ± 12 % f o r both systems. From t h e s e r e s u l t s , i t can be c o n c l u d e d t h a t the PPT d e s i g n procedure proposed i n Chapter 3 i s sound. I t must be noted t h a t no assumption has been made r e g a r d i n g t h e r e a c t i o n k i n e t i c s and mechanism. T h e r e f o r e , t h e PPT can be a p p l i e d t o a l l r e a c t i o n regimes shown i n F i g u r e 2.2 which were suggested by L e v e n s p i e l [30, 3 1 ] . Fu r t h e r m o r e , no assu m p t i o n s were made r e g a r d i n g the g a s - l i q u i d mass t r a n s f e r mechanism and f l u i d f l o w i n p a c k i n g s . T h i s means t h a t t h e i n f l u e n c e of the hydrodynamics on the s p e c i f i c a b s o r p t i o n r a t e i s f u l l y taken i n t o account i n the PPT p r o c e d u r e . " Very r e c e n t l y (May 1990), Bosch e t a l . [120] have r e p o r t e d a study on the r e a c t i o n k i n e t i c s of CO2 i n aqueous AMP s o l u t i o n . They have suggested t h a t the o v e r a l l r e a c t i o n c o n s i s t s of two p a r a l l e l and h i g h l y r e v e r s i b l e r e a c t i o n s : C0 2 + 2 RNH 2 = RNHCOO" + RNH 3 + (g) and C O OH" = HCO-254 (h) The h y d r o x y l i o n i s d e r i v e d from AMP: RNH- HoO = RNH- OH" ( i ) I f t h i s h y p o t h e s i s i s i n d e e d c o r r e c t , t h e e v a l u a t i o n of the enhancement f a c t o r would be v e r y c o m p l i c a t e d . F i r s t of a l l , f i n d i n g s o l u t i o n s of p a r t i a l d i f f e r e n t i a l e q u a t i o n s w hich r e p r e s e n t s i m u l t a n e o u s d i f f u s i o n a l mass t r a n s f e r and c h e m i c a l r e a c t i o n i n the l i q u i d phase i s u n a v o i d a b l e . S e c o n d l y , the e q u i l i b r i u m and r e a c t i o n r a t e c o n s t a n t s of b o t h r e a c t i o n s as w e l l as a l l o t h e r p h y s i c o - c h e m i c a l parameters must be p r e c i s e l y known. I t s h o u l d be kept i n mind t h a t t h e s e parameters n o r m a l l y c o u l d not be measured d i r e c t l y . I n d i r e c t methods, which a r e u s u a l l y a p p l i e d , would i n c r e a s e the u n c e r t a i n t y i n parameter e s t i m a t i o n . By a p p l y i n g the PPT method f o r column d e s i g n u s i n g t h i s system or s i m i l a r systems, t h e above-mentioned problems would be e l i m i n a t e d . To e v a l u a t e t h e u n c e r t a i n t i e s ( e r r o r s ) a s s o c i a t e d w i t h R v d e t e r m i n a t i o n based on the t h e o r e t i c a l c a l c u l a t i o n s , 2 5 5 l a b o r a t o r y models and the P i l o t P l a n t Technique, an e r r o r a n a l y s i s of the type suggested by M i c k l y e t e l . [ 1 4 4 ] was made. The d e t a i l s of t h i s e r r o r a n a l y s i s a r e g i v e n i n Appendix B and the r e s u l t s a r e summarized i n T a b l e B.2. As can be seen from Appendix B-; the potential e r r o r s a s s o c i a t e d w i t h the R v d e t e r m i n a t i o n based on t h e o r e t i c a l c a l c u l a t i o n s , l a b o r a t o r y models and the P i l o t P l a n t Technique a r e i n the o r d e r of 95%, 40% and 20%, r e s p e c t i v e l y . The u n c e r t a i n t y a s s o c i a t e d w i t h R v v a l u e s o b t a i n e d from the t h e o r e t i c a l c a l c u l a t i o n i s the l a r g e s t s i n c e t hey a r e a f u n c t i o n of many parameters i n c l u d i n g t h e mass t r a n s f e r c o e f f i c i e n t s , i n t e r f a c i a l a r e a and t h e enhancement f a c t o r . As mentioned i n Chapter 2, t h e u n c e r t a i n t i e s a s s o c i a t e d w i t h t h e i r e s t i m a t i o n a r e , i n g e n e r a l , i n the o r d e r of ±25%. By c o n t r a s t , the a c c u r a c y of R v d e t e r m i n e d by t h e PPT depends o n l y on the measurements of the f l u i d f l o w r a t e and c o m p o s i t i o n p r o f i l e s . The p r e c i s e measurement of t h e s e two q u a n t i t i e s c o u l d be a c h i e v e d w i t h minimum u n c e r t a i n t y u s i n g t h e c u r r e n t l y a v a i l a b l e i n s t r u m e n t s . I f we use the o p e r a t i n g c o n d i t i o n s of Run T9 t o i l l u s t r a t e the e f f e c t of u n c e r t a i n t y a s s o c i a t e d w i t h R v v a l u e s on the h e i g h t p r e d i c t i o n , the r e s u l t s can be seen i n 256 T a b l e 7.5. The p r e d i c t e d h e i g h t i s v a r i e d from 4.65 t o 2.32 m when the e r r o r r e l a t e d t o R v i s i n c r e a s e d t o about 1 0 0 % . T a b l e 7.5 a l s o shows the r a t i o of the h e i g h t p r e d i c t e d w i t h a g i v e n u n c e r t a i n t y t o t h a t under normal c o n d i t i o n s . T h i s r a t i o can be c o n s i d e r e d as a minimum s a f e t y f a c t o r , F s , r e q u i r e d i n o r d e r t o ensure t h a t the d e s i g n e d a b s o r b e r p e r f o r m s as ex p e c t e d or t o a v o i d the chance of f a i l u r e . As can be seen, the d e s i g n based on the PPT approach needs o n l y a f a c t o r of 1.2 by comparison w i t h 1.4 f o r the l a b o r a t o r y models and about 2.0 f o r the t h e o r e t i c a l d e s i g n approach. I t i s thus not s u r p r i s i n g t h a t a s a f e t y f a c t o r of 1.5 t o 2.5 i s commonly a p p l i e d i n i n d u s t r i a l d e s i g n p r a c t i c e f o r gas a b s o r b e r s w i t h c h e m i c a l r e a c t i o n . I t i s a l s o i n t e r e s t i n g t o know t h a t a s a f e t y f a c t o r of about 1.7 i s u s u a l l y needed f o r s i z i n g packed d i s t i l l a t i o n towers and p h y s i c a l gas a b s o r b e r s a c c o r d i n g t o B o l l e s and F a i r [ 1 4 6 ] . I t s h o u l d be n o t e d t h a t t h e s e two a r e j u s t d i f f u s i o n a l mass t r a n s f e r o p e r a t i o n s without c h e m i c a l r e a c t i o n . When r e a c t i o n s t a k e p l a c e i n the f l u i d , t h e s i t u a t i o n becomes more complex and the u n c e r t a i n t y i n c r e a s e s c o n s i d e r a b l y . As a r e s u l t , the r e q u i r e d s a f e t y f a c t o r i s h i g h e r f o r the case of gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n . 257 T a b l e 7.5: E f f e c t of u n c e r t a i n t y a s s o c i a t e d w i t h R v on the p r e d i c t e d h e i g h t u s i n g o p e r a t i n g c o n d i t i o n s of Run T9 (NaOH - C O o ) . O p e r a t i n g c o n d i t i o n : gas f l o w r a t e = 14.8 mol/m 2 s; l i q u i d f l o w rate= 9.5 m3/m h r ; i n l e t C 0 2 c o n c e n t r a t i o n = 18.4%; i n l e t [OH ] =2.0 kmol/m 3. U n c e r t a i n t y P r e d i c t e d H e i g h t F s R v + 0% 4.65 m 1 .0 R v + 20% 3.87 m 1.2 R v + 40% 3.32 m 1 .4 Rv + 80% 2.58 m 1 .8 Rv + 100% 2.32 m 2.0 F s i s d e f i n e d as the r a t i o of the h e i g h t p r e d i c t e d w i t h u n c e r t a i n t y t o t h a t a t the normal c o n d i t i o n . For example, i f a g i v e n u n c e r t a i n t y a s s o c i a t e d w i t h R v i s 100% f o r t h e c a s e , F s would be e q u a l t o 2.0 (4.65/2.32). 258 7.4 LIMITATIONS OF PPT There a r e p r a c t i c a l and fundamental l i m i t a t i o n s of t h e PPT. Both t y p e s of l i m i t a t i o n s r e l a t e t o the a b i l i t y of measuring the s p e c i f i c a b s o r p t i o n r a t e , R v. P r a c t i c a l Limitations: * The PPM column must be c o n s t r u c t e d of m a t e r i a l s c o m p a t i b l e w i t h t h e a b s o r p t i o n system and i t s o p e r a t i n g c o n d i t i o n s ( p a r t i c u l a r l y temperature and p r e s s u r e ) . * The d i a m e t e r of t h e PPM column cannot be s m a l l e r t h a n 6 t o 10 t i m e s the diameter of the random p a c k i n g t o ensure t h a t the w a l l e f f e c t i s n e g l i g i b l e . * O n - l i n e and/or o f f - l i n e s e n s o r s must be a v a i l a b l e t o measure the c o n c e n t r a t i o n s i n the l i q u i d and gas phases r e l i a b l y . * An adequate s u p p l y of c h e m i c a l a b s o r b e n t and gas m i x t u r e must be a v a i l a b l e ; when e x p e n s i v e c h e m i c a l s a r e i n v o l v e d , a r e g e n e r a t o r may be r e q u i r e d . 259 Fundamental Limitations: * For the PPM column t o r e p r e s e n t t h e c o n d i t i o n s i n s e c t i o n of the f u l l - s c a l e column, t h e b u l k of the l i q u i d and gas phases must be w e l l mixed. ( T h i s c o n d i t i o n may not be met f o r h i g h l y v i s c o u s l i q u i d s ) . * For multicomponent systems the number of c o n c e n t r a t i o n measurements may become p r o h i b i t a t i v e l y l a r g e and the i n t e r a c t i o n between the a b s o r p t i o n r a t e s may not be e a s i l y d e t e r m i n e d . * For multicomponent systems, the i n l e t and o u t l e t c o n d i t i o n s f o r f u l l - s c a l e i n d u s t r i a l columns a r e not u s u a l l y g i v e n and i t i s t h e r e f o r e d i f f i c u l t t o s p e c i f y the t e r m i n a l , c o n d i t i o n s f o r the PPM column as w e l l . I t e r a t i v e p r o c e d u r e s may be r e q u i r e d t o overcome t h i s p roblem. * I f t h e a x i a l d i s p e r s i o n i n the f u l l - l e n g t h column i s s i g n i f i c a n t , the PPM column has t o be d e s i g n e d i n such a way t h a t s i m i l a r d i s p e r s i o n o c c u r s . 260 7.5 PRACTICAL IMPLICATIONS OF THE PPT The f o l l o w i n g s e c t i o n d i s c u s s e s v a r i o u s ways i n which the PPT c o n c e p t may be a p p l i e d i n i n d u s t r i a l s i t u a t i o n s . In g e n e r a l , the s i z e of a b s o r b e r s used i n i n d u s t r y i s i n the o r d e r of a few meters i n d i a m e t e r and s e v e r a l meters i n h e i g h t . The p a c k i n g s i z e i s u s u a l l y about 37.5 t o 62.5 mm (1.5" t o 2.5") f o r random p a c k i n g . For a s p e c i f i c example, the s i z e of a c h e m i c a l gas a b s o r b e r removing C O 2 from n a t u r a l gas a t the Rayong N a t u r a l Gas S e p a r a t i o n P l a n t ( P e t r o l e u m A u t h o r i t y of T h a i l a n d ) i s 3.75 m O.D. x 14.0 m i n h e i g h t . The a b s o r b e r i s packed w i t h 50.0 mm P a l l r i n g s . I f we want t o s i m u l a t e t h e a b s o r p t i o n r a t e o c c u r r i n g i n t h i s column u s i n g the P i l o t P l a n t Technique, a PPM column of 0.5 m ID x 1.0 - 2.0 m h i g h c o u l d be used. The column of t h i s s i z e i s s m a l l enough t o be h a n d l e d i n l a b o r a t o r y environment and the column i s s t i l l a b l e t o d u p l i c a t e t h e hydrodynamic p r o p e r t i e s of the i n d u s t r i a l column. The R v v a l u e s would then be measured as f u n c t i o n s of the f l u i d c o n c e n t r a t i o n s and used t o c o n s t r u c t the R v - c o n c e n t r a t i o n d i a g r a m l i k e t he one i n F i g u r e 7.3 f o r the d e s i r e d ranges of o p e r a t i n g c o n d i t i o n s . T h i s diagram c o u l d then be employed t o p r e d i c t the a b s o r p t i o n c a p a c i t y of the i n d u s t r i a l column by a p p l y i n g t h e p r o p o s e d P i l o t P l a n t Technique. A l t e r n a t i v e l y , the model column can be used t o s i m u l a t e t h i s i n d u s t r i a l s i z e column 261 s e c t i o n by s e c t i o n u s i n g the PPT s h o r t - c u t p r o c e d u r e . As can be seen from t h i s example, the s c a l i n g f a c t o r f o r t h i s case would be i n the o r d e r of one hundred. I f s t r u c t u r e d p a c k i n g s a r e used i n i n d u s t r i a l a b s o r b e r s , the PPM column di a m e t e r c o u l d be reduced t o the 0.03 t o 0.10 m range and t h e r e f o r e t h e s c a l i n g f a c t o r would i n c r e a s e c o n s i d e r a b l y . The above s u g g e s t i o n can a l s o be used f o r d e s i g n i n g new a b s o r b e r s . The d e s i g n s t e p s up t o the d e t e r m i n a t i o n of a b s o r b e r d i a m e t e r a r e a l r e a d y g i v e n i n S e c t i o n 2.3. At t h i s p o i n t , t h e f o l l o w i n g items a r e s e l e c t e d or d e t e r m i n e d : p a c k i n g t y p e and s i z e ; column d i a m e t e r ; f l u i d s u p e r f i c i a l v e l o c i t i e s . The dimensions of the PPM column can t h e n be s i z e d based on proper d e s i g n c r i t e r i o n g i v e n i n T a b l e 5.1. T h i s PPM column i s then used t o o b t a i n t h e v a l u e s of R v f o r the d e s i r e d range of f l u i d c o m p o s i t i o n s , i n o r d e r t o p r e d i c t the f u l l - s c a l e a b s o r b e r h e i g h t . As d i s c u s s e d p r e v i o u s l y , the P i l o t P l a n t Technique does not r e q u i r e knowledge of the hydrodynamic and p h y s i c o -c h e m i c a l p a r a m e t e r s . The PPT method would be s u i t a b l e f o r h e l p i n g d e s i g n e n g i n e e r s t o d e s i g n new c h e m i c a l a b s o r b e r s or p r o c e s s e n g i n e e r s t o r e t r o f i t the e x i s t i n g columns. T h i s t e c h n i q u e s h o u l d be v e r y u s e f u l when i t i s a p p l i e d t o 262 systems t h a t use h i g h - e f f i c i e n c y p a c k i n g s and s o l v e n t s which a r e f a v o u r e d by i n d u s t r y . Some of t h e s e p a c k i n g s were a l r e a d y shown i n F i g u r e s 2.11 and 2.12. Some of the h i g h -c a p a c i t y s o l v e n t s a r e l i s t e d i n T a b l e 7.6. To d e s i g n and s i m u l a t e t h e s e systems based on f i r s t p r i n c i p l e s would be e i t h e r t o o c o m p l i c a t e d - i f inde e d p o s s i b l e - or would l e a d t o l a r g e e r r o r s due t o the u n c e r t a i n t y i n parameter e s t i m a t i o n s . T a b l e 7.6: Some of h i g h - c a p a c i t y s o l v e n t s . S o l v e n t R e f e r e n c e s S t e r i c a l l y h i n d e r e d amines [ 7 1 , 101] H i g h c o n c e n t r a t i o n a l k a n o l a m i n e s [10, 11] A l k a n o l a m i n e s i n nonaqueous s o l v e n t s [116, 117] A l k a n o l a m i n e s i n a m i x t u r e of nonaqueous and aqueous s o l v e n t s [10, 11] M i x t u r e of amines [10, 11] In some i n d u s t r i a l s i t u a t i o n s , t h e presence of i m p u r i t i e s a r e u n a v o i d a b l e and can be a major problem. To 263 quote from B i s i o [ 8 0 ] , " .... One of the most serious and frustrating problems that can be encountered in a commercial operation is the presence of impurities that were not considered or studied in the smaller scale laboratory or pilot plant studies Moreover, once a commercial installation has been built without giving adequate consideration to the removal of impurities from process streams, modification can be made only with great difficulty and at significant expense " In gas t r e a t i n g w i t h c h e m i c a l s o l v e n t s , a good example i s the a c c u m u l a t i o n of the d e g r a d a t i o n p r o d u c t s i n the s o l u t i o n when i t has been used f o r an extended p e r i o d of t i m e . R e c e n t l y , Kennard and Meisen [117] and Chakma and Meisen [118] have r e p o r t e d t h a t t h e s e d e g r a d a t i o n compounds c o u l d s i g n i f i c a n t l y a f f e c t both a b s o r p t i o n r a t e and c a p a c i t y of the s o l u t i o n . To i n t e g r a t e these f a c t o r s i n t o the pr o c e d u r e s f o r d e s i g n i n g new a b s o r b e r s or s i m u l a t i n g e x i s t i n g u n i t s based o n l y on f i r s t p r i n c i p l e s would be v e r y c o m p l i c a t e d , i f i t i s in d e e d f e a s i b l e . The PPT method would p r o v i d e a more r e a l i s t i c way t o d e a l w i t h the above-mentioned problems. By a p p l y i n g the PPT method t o thes e s i t u a t i o n s , the PPM column must be o p e r a t e d w i t h the s o l u t i o n s c o n t a i n i n g the same or s i m i l a r c o m p o s i t i o n s as those i n the i n d u s t r i a l p l a n t s . The e f f e c t i v e v a l u e s of R v o b t a i n e d t h i s way can then be used t o p r e d i c t t h e c a p a c i t y or h e i g h t of a b s o r b e r u s i n g such s o l u t i o n s . T h i s i s an a p p l i c a t i o n of the PPT method t h a t a w a i t s f u r t h e r r e s e a r c h . 264 CHAPTER 8  SUMMARY OF RESULTS AND CONCLUSIONS The results and p r i n c i p a l conclusions drawn from the research studies may be summarized as follows: SOLUBILITY OF CO2 IN AMP SOLUTIONS * S i g n i f i c a n t l y extended results from the previous works are reported. These s o l u b i l i t y data cover the t y p i c a l operating ranges of absorbers. * The modified Kent-Eisenberg model represents the experimental data quite accurately and i s well suited for use in the design of regenerative AMP separation processes. * The s o l u b i l i t y of C0 2 in AMP solution was found, by comparison with that of C0 2 in MEA solution, to be higher at low temperatures ( < 60 °C ) and lower at high temperatures ( >60 °C ). 265 EXPERIMENTAL AND SIMULATION RESULTS OF FULL SCALE ABSORBERS * Comprehensive p i l o t plant data i n c l u d i n g gas and l i q u i d concentrations and temperature p r o f i l e s along the p i l o t p l a n t absorber f o r the CO2 absorption i n t o NaOH and MEA - s o l u t i o n s were reported. * Good agreement was found between the experimental measurements and model p r e d i c t i o n s f o r the C02-NaOH and CO2-MEA systems except at loadings approaching 0.5 moles of CO2 per mole of MEA. * T h e o r e t i c a l model v e r i f i c a t i o n should be based on concentration and temperature p r o f i l e s and not j u s t on the c o n d i t i o n s at the absorber top and bottom. * The enhancement f a c t o r v a r i e s s i g n i f i c a n t l y along the absorption column and must be a c c u r a t e l y known f o r r e l i a b l e modelling. THE PILOT PLANT TECHNIQUE (PPT) * A new method, c a l l e d the " P i l o t Plant Technique" has been proposed f o r s i z i n g gas-absorption towers w i t h chemical r e a c t i o n . This new design technique does not 266 r e q u i r e e x p l i c i t knowledge of hydrodynamics and p h y s i c o - c h e m i c a l p a r a m e t e r s . The r e s u l t s o b t a i n e d w i t h the C0 2-NaOH and C 0 2 _ A M P systems show t h a t the PPT can be used f o r p r e c i s e s i z i n g of a b s o r b e r s ; the a c c u r a c y f a l l s t y p i c a l l y w i t h i n ± 1 2 %. S i n c e t h e a c c u r a c y of R v v a l u e s o b t a i n e d from the PPT depends o n l y on the measurements of the f l u i d f l o w r a t e s and c o m p o s i t i o n s , the u n c e r t a i n t y a s s o c i a t e d w i t h i t s d e t e r m i n a t i o n i s r e l a t i v e l y low compared w i t h t h a t o b t a i n e d from f i r s t p r i n c i p l e s and l a b o r a t o r y models. P o t e n t i a l l y , the PPT may be a p p l i e d t o o t h e r c o n t i n u o u s c o n t a c t i n g o p e r a t i o n s i n v o l v i n g mass t r a n s f e r w i t h c h e m i c a l r e a c t i o n ( e . g . packed bed r e a c t o r s , e x t r a c t i o n columns, r e a c t i v e d i s t i l l a t i o n c o l u m n s ) . The p r i m a r y drawback of the PPT i s t h a t the v a l u e s , of R v must be o b t a i n e d e x p e r i m e n t a l l y i n the PPM column which has t o be s p e c i a l l y c o n s t r u c t e d and o p e r a t e d . The PPT may not be p r a c t i c a l f o r multicomponent systems. 267 CHAPTER 9  RECOMMENDATIONS FOR FURTHER WORK SOLUBILITY STUDIES C o n s i d e r a b l e work has been done on the CO2 s o l u b i l i t y i n aqueous s o l u t i o n s of s i n g l e amines. However, no s u b s t a n t i a l work has been r e p o r t e d on CO2 s o l u b i l i t y i n m i x t u r e s of amines. I t would t h e r e f o r e be w o r t h w h i l e t o conduct such e x p e r i m e n t s s i n c e t h e r e a r e some s u g g e s t i o n s i n the l i t e r a t u r e t h a t t h e s e s o l u t i o n s may have h i g h e r a b s o r p t i o n c a p a c i t y as w e l l as mass t r a n s f e r r a t e . COMPUTER MODELLING ...... As d i s c u s s e d i n Chapter 6, the p r e d i c t i o n of a b s o r b e r performance i s s t i l l not a c c u r a t e when the l i q u i d l o a d i n g approaches 0.5 moles of CO2 per mole of amine. F u r t h e r e x p e r i m e n t a l and m o d e l l i n g work s h o u l d be co n d u c t e d t o st u d y t h e s e a s p e c t s . The p h y s i c o - c h e m i c a l p r o p e r t i e s and r e a c t i o n k i n e t i c s of p a r t i a l l y l o a d e d s o l u t i o n s s h o u l d be f u r t h e r i n v e s t i g a t e d , e s p e c i a l l y a t h i g h l o a d i n g s ( i . e . - a t 0.4 t o 1.0 moles of C 0 2 / mole of amine). 268 THE PILOT PLANT TECHNIQUE In t h i s t h e s i s , the PPT d e s i g n approach has been s u c c e s s f u l l y t e s t e d w i t h two d i f f e r e n t systems under a v a r i e t y of c o n d i t i o n s . I t would t h e r e f o r e be w o r t h w h i l e t o conduct f u r t h e r t e s t s on -the PPT w i t h i n d u s t r i a l a b s o r b e r s and under p l a n t c o n d i t i o n s . The i d e a l s i t u a t i o n i s t o o b t a i n a complete d a t a s e t of an e x i s t i n g i n d u s t r i a l a b s o r b e r which i n c l u d e the temperature and c o m p o s i t i o n p r o f i l e s as w e l l as the d e t a i l s of the a b s o r b e r . The PPT can then be used t o p r e d i c t the tower h e i g h t o r i t s a b s o r p t i o n c a p a c i t y . I t would a l s o be w o r t h w h i l e t o conduct f u r t h e r t e s t s on the PPT i n o t h e r i n d u s t r i a l s i t u a t i o n s such as s i m u l t a n e o u s a b s o r p t i o n of more than one gas s p e c i e s and t r a y a b s o r p t i o n t o w e r s . As d i s c u s s e d e a r l i e r , the R v v a l u e s can be computed from f i r s t p r i n c i p l e s f o r well-known systems such as C 0 2 ~ NaOH. However, f o r new systems l i k e CO2-AMP, the R v v a l u e s can o n l y be o b t a i n e d e x p e r i m e n t a l l y . F u n d a m e n t a l l y , e x p e r i m e n t a l v a l u e s of R v o b t a i n e d i n the model column c o u l d be used f o r b a c k - c a l c u l a t i o n s i n o r d e r t o e s t i m a t e the hydrodynamics and p h y s i c o - c h e m i c a l p a r a m e t e r s , p r o v i d e d the k i n e t i c model of the system i s known. R e s u l t s from some e x p l o r a t o r y works have s u g g e s t e d t h a t such parameter 269 e s t i m a t i o n may be f e a s i b l e [150]. T h e o r e t i c a l l y , •optimization techniques c o u l d be employed to determine the set of unknown parameters which would g i v e the minimum e r r o r between the computed and experimental a b s o r p t i o n r a t e s . In many cases when the r a t e constant and/or mass t r a n s f e r c o e f f i c i e n t s are not known, t h i s technique can be applie'd to e x t r a c t the unknown parameters. The parameter e s t i m a t i o n approach suggested here may be used f o r gas a b s o r p t i o n with chemical r e a c t i o n systems i n v o l v i n g new packings and/or h i g h - e f f i c i e n c y absorbents. 270 NOMENCLATURE a v i n t e r f a c i a l a r e a per u n i t volume of p a c k i n g , m2/m 3 Cf p a c k i n g f a c t o r CJ c o n c e n t r a t i o n of component j i n the l i q u i d , kmol/m3 C P , j heat c a p a c i t y of component j i n the gas, kJ/kmol. °K C P , L heat c a p a c i t y of s o l u t i o n , kJ/m 3.°K DJ d i f f u s i v i t y of component j , m2/s F S s a f e t y f a c t o r (see Table 7.5) G' gas mass v e l o c i t y , kg/m 2.s Gl molar gas flow r a t e of component I , kmol/m 2.s H Henry's law c o n s t a n t , kmol/m 3.kPa h G heat t r a n s f e r c o e f f i c i e n t , kJ/s.m 2.°K HR heat of a b s o r p t i o n and r e a c t i o n , kJ/kmol H S heat of v a p o r i z a t i o n of s o l v e n t S, kJ/kmol I enhancement f a c t o r *C i o n i c s t r e n g t h , kmol/m 3 K e q u i l i b r i u m c o n s t a n t KG o v e r a l l gas mass t r a n s f e r c o e f f i c i e n t , kmol/m 2.s. kPa) k 2 r e a c t i o n r a t e c o n s t a n t , m 3/kmol.s kG p h y s i c a l gas mass t r a n s f e r c o e f f i c i e n t , kmol/m 2.s .kPa) o k L p h y s i c a l l i q u i d mass t r a n s f e r c o e f f i c i e n t , m/s L l i q u i d f l o w r a t e , m3/m2.s L' l i q u i d mass v e l o c i t y , kg/m 2.s M f i l m c o n v e r s i o n parameter N j mass t r a n s f e r f l u x of component j , kmol/m 2 s 271 t o t a l p r e s s u r e , kPa s p e c i f i c r a t e of a b s o r p t i o n per u n i t i n t e r f a c i a l a r e a of p a c k i n g , kmol/m 2 s s p e c i f i c r a t e of a b s o r p t i o n per u n i t volume of p a c k i n g , kmol/m 2 s r a t e of r e a c t i o n i n the l i q u i d phase, kmol/m 3 s t e m p e r a t u r e , °K t i m e , s mole r a t i o of component j , kmol j/kmol I mole f r a c t i o n of component j , kmol j/mol p a c k i n g h e i g h t , m Superscripts * e q u i l i b r i u m Subscripts A absorbed compound B r e a g e n t i n l i q u i d G gas I i n e r t c a r r i e r gas i i n t e r f a c e j g e n e r a l i z e d component j L l i q u i d m model S i n e r t l i q u i d s o l v e n t t t o t a l P R a Rv r T t y j z 272 w w a t e r Greek Letters v s t o i c h i o m e t r i c c o e f f i c i e n t p d e n s i t y , k g / m 3 7 l i q u i d h o l d - u p , m 3 o f l i q u i d / m 3 o f p a c k i n g CO2 l o a d i n g , m o l e s o f C C ^ / m o l e o f a m i n e 8 l i q u i d f i l m t h i c k n e s s , mm u v i s c o s i t y , mPa s ( c e n t i p o i s e ) 273 REFERENCES 1. 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The f i r s t t i t r a t i o n i s to determine the t o t a l a l k a l i ( carbonate + h y d r o x i d e ) by t i t r a t i o n w i t h s t a n d a r d 1 N H C l , u s i n g methyl orange as i n d i c a t o r . In a second sample of the s o l u t i o n , the c a r b o n a t e i s p r e c i p i t a t e d w i t h a s l i g h t excess of barium c h l o r i d e s o l u t i o n : N a 2 C 0 3 + B a C l 2 = B a C 0 3 ( i n s o l u b l e ) + 2NaCl The s o l u t i o n i s then t i t r a t e d w i t h s t a n d a r d 1 N H C l u s i n g p h e n o l p h t h a l e i n as i n d i c a t o r . The l a t t e r t i t r a t i o n g i v e s the h y d r o x i d e c o n t e n t , and by s u b t r a c t i n g t h i s from" the f i r s t t i t r a t i o n , the volume of a c i d r e q u i r e d f o r the carbonate i s o b t a i n e d . Sample Calculation I f the sample s i z e = 5.0 ml and the a c i d r e q u i r e d f o r the f i r s t and second t i t r a t i o n s are 10.0 and 5.0 m l , r e s p e c t i v e l y . 287 T h e r e f o r e , [ N a + ] = t o t a l a l k a l i = (10.0/5.0)x1.0 = 2.0 N [OH -] = h y d r o x i d e c o n t e n t = (5./5.)x1.0 = 1.0 N [ C 0 3 = ] = c a r b o n a t e c o n t e n t = ( 1 0 . - 5 . ) / ( 5 . x 2 . ) = 0.5 N The major c o n t r i b u t i o n t o the e r r o r i s the volume measurement of HCl which i s a c c u r a t e w i t h i n ± 0.1 ml. T h e r e f o r e , the u n c e r t a i n t y a s s o c i a t e d w i t h the d e t e r m i n a t i o n of [ N a + ] and [OH~] i s w i t h i n ± 1.0X10~ 4 moles per 5 ml sample ( 5 . 0 x 1 0 ~ 3 m o l e s ) . For the above sample c a l c u l a t i o n , the e r r o r i n o b t a i n i n g [OH -] i s 2.0 %. 288 A.2 DETERMINATION OF CARBON DIOXIDE LIQUID LOADING The f o l l o w i n g d e t a i l s a r e taken from R e f e r e n c e [ 1 1 4 ] . Gas measuring apparatus. F i g u r e A.1. Connect d e c o m p o s i t i o n f l a s k , A, by g l a s s T-tube, B, p r o v i d e d w i t h s t o p c o c k , C, t o g r a d u a t e d gas-measuring t u b e , D, connected i n t u r n w i t h l e v e l i n g b u l b , E. For f l a s k A, use 250 ml Pyrex f l a s k f i t t e d w i t h 2-hole rubber s t o p p e r , through one h o l e of which passes extended t i p of 25 ml b u r e t , F, and t h r o u g h o t h e r , t h e g l a s s tube of same d i a m e t e r as c o n n e c t i n g T-tube. Use b u r e t g r a d u t e d i n ml, numbered a t 1 ml i n t e r v a l s , and f i t t e d w i t h e x t r a - l o n g t i p bent t o pass t h r o u g h rubber s t o p p e r . Connect g l a s s t u b e l e a d i n g from d e c o m p o s i t i o n f l a s k t o T-tube w i t h rubber t u b i n g t o p e r m i t r o t a t i o n of f l a s k . Use gas-measuring tube g r a d u a t e d i n ml w i t h 0 mark a t p o i n t 25 ml below t o p marking t o a l l o w f o r g r a d u a t i n g upward from 0 t o 25 ml and downward from 0 t o 200 m l . Connect gas-measuring tube t o 300 ml l e v e l i n g b u l b , E, w i t h l o n g rubber tube. Displacement s o l u t i o n . D i s s o l v e 100 g NaCI i n 350 ml of d i s t i l l e d w a t e r . Add 1 g of NaHC03 and 2 ml M e t h y l orange t o make j u s t a c i d ( d e c i d e d p i n k ) . S t i r u n t i l a l l C 0 2 i s removed. T h i s s o l u t i o n i s used i n gas measuring tube and l e v e l i n g b u l b F i g u r e A . 1 : Gas measuring a p p a r a t u s [114] . 290 Determination. P i p e t t e 5 ml of l i q u i d sample i n t o f l a s k A, and connect f l a s k w i t h a p p a r a t u s , see F i g u r e A . 1 . Open s t o p c o c k C, and u s i n g l e v e l i n g b u l b E, b r i n g d i s p l a c e m e n t s o l u t i o n t o 1.0 ml g r a d u a t i o n above 0 mark. ( T h i s 10 ml i s p r a c t i c a l l y e q u a l t o volume of a c i d t o be used i n d e c o m p o s i t i o n . ) L e t a p p a r a t u s s t a n d 1 t o 2 minute f o r t e m p e r a t u r e and p r e s s u r e w i t h i n a p p a r a t u s t o come t o room c o n d i t i o n s . C l o s e s t o p c o c k , lower l e v e l i n g b u l b somewhat t o reduce p r e s s u r e w i t h i n a p p a r a t u s , and s l o w l y add 10 ml of 2 M HCl t o decompose the sample i n the f l a s k A from b u r e t F. To p r e v e n t escape of l i b e r a t e d C 0 2 t h r o u g h a c i d b u r e t i n t o a i r , a t a l l t i m e s d u r i n g d e c o m p o s i t i o n keep d i s p l a c e m e n t s o l u t i o n a t l e v e l lower i n l e v e l i n g b u l b than t h a t i n gas-measuring t u b e . R o t a t e and then v i g o r o u s l y a g i t a t e f l a s k t o mix c o n t e n t s i n t i m a t e l y . L e t s t a n d 5 min t o s e c u r e e q u i l i b r i u m . E q u a l i z e p r e s s u r e i n measuring t u b e , u s i n g l e v e l i n g b u l b , and r e a d volume of gas i n the t u b e . Observe te m p e r a t u r e of a i r s u r r o u n d i n g and a l s o b a r o m e t r i c p r e s s u r e . The t o t a l amine can be d e t e r m i n e d by t i t r a t i o n w i t h s t a n d a r d 1N HCl t o m e t h y l orange e n d - p o i n t . Calculation of CO 2 loading. M u l t i p l y ml of e v o l v e d gas by f a c t o r , f Q , which i s g i v e n i n T a b l e A . 1 , f o r the g i v e n 291 t e m p e r a t u r e and p r e s s u r e . The c o r r e c t e d r e ading/10 g i v e s %CC>2 c o n t e n t by wt. of sample s i z e of 1.7 g. T h i s can be c o n v e r t e d t o moles of C 0 2 by ((ml of e v o l v e d g a s ) * f g / l 0 ) / l 0 0 ) * ( 1 . 7 / 4 0 ) Sample c a l c u l a t i o n . sample s i z e = 5.0 ml ml of 1 N HCI = 10 ml e v o l v e d gas = 55 ml Temp. = 16 °C, P r e s s u r e = 758.5 mmHg, f g = 1.07 T h e r e f o r e , t o t a l amine = (10/5)*1.0 = 2.0 ml moles of C 0 2 = 55*1.07*1.7/(10*100*40) = 2 . 5X 1 0 ~ 3 moles of C 0 2 C 0 2 l o a d i n g = 2 . 5 x 1 0 " 3 / ( 2 * 5 / l 0 0 0 ) = 0.25 moles of C0 2/mole of amine The major e r r o r s a s s o c i a t e d i n t h i s a n a l y s i s a r e as f o l l o w s : * measurement of e v o l v e d gas ± 1.0 ml ( a f f e c t t h e C02 c o n t e n t by 1.8 %) * measurement of room te m p e r a t u r e ± 1.0 °C ( a f f e c t f g by 0.5 %) * measurement of HCI ± 0.1 ml ( a f f e c t t h e t o t a l amine ± 1.0 %) / T h e r e f o r e , the e r r o r i n C 0 2 l o a d i n g i s i n the o r d e r of 3.3 % which i s a p p r o x i m a t e l y 40 % more than the [OH-] d e t e r m i n a t i o n . 292 T a b l e A.1: The v a l u e s of f q f o r a v a r i e t y of t e m p e r a t u r e and p r e s s u r e [ 1 1 4 ] . ( B a s e d o n s a m p l e w e i g h i n g 1.7000 g) ( M u l t i p l y n u m b e r of m l gas e v o l v e d f r o m 1.7000 g s a m p l e by factor tha t c o r r e s p o n d s w i t h e x i s t i n g a t m o s p h e r i c c o n d i t i o n s a n d d i v i d e by 10 to o b t a i n % C O j by wt i n s a m p l e . ) 15.0°C S3.VT 15.5°C S9.9T 16.0°C 60.8-F 16.S-C 6I.7°F 17.0-C 62.6°F 17.5-C K3.5»F 18.0°C 64.-*°F 18.5°C 65.3°F I9.0°C 66.2°F 19.5-C 67.1»F Inches 700 702 704 70S 708 710 712 71< 716 718 720 722 724 726 728 730 732 734 736 738 740 742 744 746 748 750 752 754 756 758 760 762 764 766 768 770 0.99194 0.99494 0.99794 1.00Q94 1.00394 1.00694 1.00994 1.01294 1.01594 1.01894 1.02194 1.02482 1.02771 1.03059 1.03347 1.03635 1.03924 1.04218 1.04506 1.04794 1.05082 1.05371 1.05659 1.05947 1.06235 1.06524 1.06818 1.07106 1.07394 1.07682 1.07971 1.08259 1.08547 1.08841 1.09129 1.09418 0.99006 0.99300 0.99544 0.99886 1.00183 1.00477 1.00767 1.01061 1.01356 1.01650 1.01949 1.02232 1.02521 1.02809 1.03097 1.03385 1.03674 1.03915 1.042S3 1.04541 1.04829 1.05118 1.05403 1.05691 1.05929 1.06218 1.06512 1.06847 1.07135 1.07423 1.07712 1.08050 1.08288 1.08580 1.08868 1.09156 0.98818 0.99106 0.99394 0.99682 0.99971 1.00259 1.00541 1.00829 1.01118 1.01406 1.01694 1.01982 1.02271 1.02S59 1.02847 1.03135 1.03424 1.03712 1.04000 1.04288 1.04576 1.0486S 1.05147 1.05435 1.05724 1.06012 1.06306 1.06588 1.06876 1.07165 1.07453 1.07741 1.08029 1.08318 1.08606 1.0 0.98573 0.98862 0.99147 0.99435 0.99723 1.00012 1.00294 1.00582 1.00871 1.01156 1.01444 1.01732 1.02021 1.02306 1.02594 1.02882 1.03171 1.03459 1.03744 1.04037 1.04321 1.04609 1.04991 1.05180 1.05418 1.05748 1.06047 1.06330 1.06618 1.06906 1.07191 1.07480 1.07768 1.08056 1.08344 1.08630 0.98329 0.98618 0.98900 0.99188 0.99476 0.99765 1.00047 1.00335 1.00624 1.00906 1.01194 1.01482 1.01771 1.02053 1.02341 1.02629 1.02918 1.03206 1.03488 1.03776 1.04065 1.04353 1.04635 1.04924 1.05212 1.05494 1.05788 1.06071 1.06359 1.06647 1.06929 1.07218 1.07506 1.07794 1.08082 1.08365 0.98082 0.98368 0.98653 0.98941 0.99226 0.99512 0.99795 1.00080 1.00368 1.00653 1.00941 1.01229 1.01518 1.01800 1.02088 1.02374 1.02662 1.02950 1.03232 1.03521 1.03806 1.04094 1.04377 1.04665 1.049S3 1.05235 1.05527 1.05812 1.06197 1.06386 1.06668 1.06956 1.07244 I.O7S30 1.07818 1.08100 0.9783S 0.98118 0.98406 0.98694 0.98976 0.99259 0.99541 1.99824 1.00112 1.00400 1.00688 1.00976 1.01265 1.01574 1.01835 1.02118 1.02406 1.02694 1.02976 1.03265 1.03547 1.03835 1.04118 1.04406 1.04694 1.04976 1.05265 1.05553 1.05835 1.06124 1.06406 1.06694 1.06982 1.07265 1.07553 1.07835 0.9758S 0.97868 0.98156 0.98406 0.98726 0.99009 0.99291 0.99576 0.99861 1.00150 -1.00435 1.00720 1.01009 1.01291 1.01580 1.01862 1.02147 1.02435 1.02718 1.03006 1.03288 1.03577 1.03859 1.04147 1.04433 1.04715 1.05003 1.05289 1.05571 1.05859 1.06141 1.06430 1.06715 1.06997 1.07285 1.07567 0.97335 0.97618 0.97906 0.98188 0.98476 0.98759 0.99041 0.99329 0.99612 0.99900 1.00182 1.00465 1.00753 1.01035 1.01324 1.01606 1.01888 1.02176 1.02459 1.02747 1.03029 1.03318 1.03600 1.03888 1.04171 1.04453 1.04741 1.05024 1.05306 1.05594 1.05876 1.06165 1.06447 1.06729 1.07018 1.07300 0.97085 0.97368 0.97653 0.97938 0.98224 0.98506 0.98788 0.99073 0.99358 0.99644 0.9992S 1.00209 1.00497 1.00779 1.01065 1.01347 1.01629 1.01919 1.02200 1.02486 1.02768 1.03056 1.03338 1.03624 1.03906 1.04189 1.04477 1.04759 1.05041 1.05330 1.05612 1.05897 1.06179 1.06462 1.06750 1.07032 27.56 27.64 27.72 27.80 27.87 27.95 28.03 28.11 28.19 28.27 28.35 28.43 28.50 28.58 28.66 28.74 28.82 28.90 28.98 29.06 29.13 29.21 29.29 29.37 29.45 29.53 29.61 29.69 29.76 29.84 29.92 30.00 30.08 30.16 30.24 30.31 20.0'C 68.0*F 6S.9°F 21.VC 69.PF 21.50C 22.0°C 22.50C 23.0°C 23.5°C 24.0«C 24.5°C 70.7T 71.e"F 72.5-F 73.4"F 74J°F 7S.rF 76.1»F Inches 0.96023 0.95753 0.95509 0.95265 0.95020 0.94776 0.94508 27.56 0.96311 0.96041 0.95794 0.95547 0.95303 0.95059 0.94788 27. 64 0.96S97 0.96329 0.96082 0.95835 0.95585 0.95335 0. 95067 27. 72 0.96888 0.96624 0.96371 0.96118 0.95865 0.9S612 0. ,95344 27. 80 0.97173 0.96912 0.96656 0.96400 0.96147 0.95894 0. .95626 . 27. 87 0.97459 0.97195 0.96938 0.96682 0.96429 0.96176 0. .95905 27. 95 0.97747 0.97483 0.97227 0.96971 0.96712 0.96453 0. .96182 28. 03 0.98032 0.97771 0.97512 0.97253 0.96991 0.96729 0. .96461 - 28. 11 0.98323 0.98065 0.97800 0.97535 0.97273 0.97012 0. .96741 28. ,19 0.98606 0.98348 0.98083 0.97818 0.97556 0.97294 0. ,97023 28. 27 0.98894 0.98636 0.98371 0.98106 0.97838 0.97571 0. .97300 28. 35 0.99176 0.98918 0.98653 0.98388 0.98120 0.97853 0. .97582 28. 43 0.99462 0.99200 0.98932 0.98665 0.98397 0.98129 0. .97858 28. so 0.99746 0.99483 0.99215 0.98947 0.98679 0.98412 0. .98141 28. 58 1.00027 0.99765 0.99497 0.99229 0.98961 0.98694 0. .98420 28. ,66 1.00306 1.00041 0.99781 0.99512 0.99241 0.98971 0. .98697 28. 74 1.00588 1.00324 1.00056 0.99788 0.99517 0.99247 0. .98973 28. .82 1.00870 1.00606 1.00338 1.00071 0.99799 0.99529 0. .99255 28. 90 1.01153 1.00888 1.00620 1.00353 1.00083 0.99812 0. .99538 28. 98 1.01435 1.01171 1.00900 1.00629 1.00359 1.00088 0. .99815 29. .06 1.01717 1.01453 1.01182 1.00912 1.00643 1.00371 1. .00095 29. 13 1.02000 1.01735 1.01464 1.01194 1.00923 1.00653 1. .00377 29. 21 1.02279 1.02212 1.01752 1.01471 1.01200 1.00929 1. .00643 29. .29 1.02561 1.02294 1.02024 1.01753 1.01482 1.01212 .00936 29. ,37 1.02844 1.02576 1.02306 1.02035 1.01762 1.01488 1 .01212 29. .45 1.03126 1.02859 1.02589 1.02318 1.02045 1.01771 1. .01492 29. ,53 1.03408 1.03141 1.02868 1.02594 1.02321 1.02047 1. .01771 29. .61 1.03691 1.03424 1.03150 1.02876 1.02603 1.02329 1. .02050 29. .69 1.03973 1.03706 1.03433 1.03159 1.02883 1.02606 1 .02326 29. .76 1.04259 1.03988 1.03715 1.03441 1.03165 1.02888 1. .02608 29. .84 1.04539 1.04265 1.03992 1.03718 1.03442 1.03165 1 .02886 29. .92 1.04821 1.04S47 1.04274 1.04000 1.03724 1.03447 1 .03164 30. 00 1.05103 1.04829 1.04556 1.04282 1.04003 1.03723 1 .03444 30. .08 1.05386 1.05112 1.04839 I.0456S 1.04285 1.04005 1 .03723 30. 16 1.05668 1.05394 • 1.05118 1.04841 1.04562 1.04282 1 .04003 30. .24 1.05950 1.05676 1.05400 1.05123 1.04844 1.04564 .04282 30. .31. 700 702 704 706 708 710 712 714 716 718 720 722 724 726 728 730 732 734 736 738 740 742 744 746 748 750 752 754 756 758 760 762 764 766 768 770 0.96835 0.97118 0.97400 0.97688 0.97971 0.98253 0.98535 0.98818 0.99106 0.99388 0.99671 0. 99953 1.00241 1.00524 1.00806 1.01088 1.01371 1.01659 1. -01941 1.02224 1.02506 1.02794 1.03076 1.03359 1.03641 1.03924 1.04212 1.04494 1.04776 1.05065 1.05347 1.05629 1.05912 1.06194 1.06482 1.06765 0.96564 0.96850 0.97132 0.97420 0.97703 0.97988 0.98273 0.98556 0.98844 0.99126 0.99412 0.99694 0.99982 1.00265 1.00547 1.00829 1.01112 1.01497 1.01679 1.01962 1.02244 I.02S29 1.02811 1.03094 1.03376 1.03659 1.03944 1.04226 1.04508 1.04797 1.O5079 1.05361 1.05644 1.05926 1.06212 1.06424 0.96294 0.96582 0.96865 0.97153 0.97435 0.97724 0.98012 0.98294 0.98582 0.98865 0.991S3 0.9943S 0.99724 1.00006 1.00288 1.00571 1.00853 1.01135 1.01418 1.01700 1.01982 1.0226S 1.02547 1.02829 1.03112 1.03394 1.03676 1.03959 1.04241 1.04529 1.04812 1.05094 1.05376 1.05659 ' 1.05941 1.06224 (Continued) ' C a l c d f r o m 1.976 - wt 1 L C O j at 0*C. 760 m m p r e s s u r e , a n d 41* l a t i t u d e . F o r m u l a g iven by W P a r r J. Am. Chem. S o c . 31. 237(1909). Table A.l (Con't): The values of f q for a v a r i e t ; temperature and pressure [1T4 ] . 52.007 Correction factors for gasometric determination of carbon d i o x i d e 0 — C o n c l u d e d . (Based on sample weighing 1.7000 g) (Multiply number of ml gas evolved from 1.7000 g sample by factor that corresponds with existing atmospheric conditions and divide by 10 to obtain % COj by wt in sample.) 25.0°C 25.5°C 26.0°C 265°C 27.0°C 27.5°C 28.0°C 28.5°C 29.0°C 29.5°C mm 77.0»F 77.9°F 78.8°F 79.7^  W-fff 81.5°F 82.4°F 83.3°F 84.2">F 85.1°F Inches 700 0.94241 0.93373 0.93706 0.93432 0.93159 0.92885 0.92612 0.92332 0.92053 0.91773 27.56 702 0.94518 0.94250 0.93982 0.93708 0.93435 0.92161 0.92888 0.92608 0.92329 0.92047 27.64 704 0.94800 0.94532 0.94256 0.93988 0.93712 0.93438 0.93165 0.92882 0.92600 0.92320 27.72 706 0.95076 0.94808 0.94541 0.94267 0.93994. 0.93717 0.93441 0.93158 0.92876 0.92594 27.80 708 0.95359 0.95088 0.94818 0.94544 0.94271 0.93994 0.93718 0.93435 0.93153 0.92870 27.87 710 0.9563S 0.95364 0.95094 0.94820 0.94547 0.94267 0.93988 0.93706 0.93424 0.93141 27.95 712 0.95812 0.95644 0.95376 0.95100 0.94824 0.94544 0.94265 0.93982 0.93700 0.93414 28.03 714 0.96194 0.95923 0.95653 0.95376 0.95100 0.94820 0.94541 0.94258 0.93976 0.93691 28.11 716 0.96471 0.96200 0.95929 0.95655 0.9S382 0.95100 0.94818 0.9453S 0.94253 0.93964 28.19 718 0.96753 0.96482 0.96212 0.9593S 0.95659 0.95376 0.95094 0.94809 0.94524 0.94238 28.27 720 0.97029 0.96758 0.96488 0.96213 0.95939 0.95655 0.95371 0.95085 0.94800 0.94512 28.35 722 0.97312 0.97038 0.96765 0.69488 0.96212 0.95929 0.95647 0.95361 0.95076 0.94788 28.43 724 0.97588 0.97314 0.97041 0.96764 0.96488 0.96206 0.95924 0.95638 0.95353 0.95062 28.50 726 0.97871 0.97594 0.97318 0.97041 0.96765 0.96482 0.96200 0.95912 0.95624 0.95332 28.58 728 0.98147 0.97870 0.97594 0.97319 0.97041 0.96758 0.96476 0.96188 0.95900 0.95609 28.66 730 0.98424 0.98147 0.97871 0.97594 0.97318 0.97036 0.96753 0.96464 0.96176 0.95885 28.74 732 0.98700 0.98423 0.98147 0.97871 0.97594 0.97309 0.97024 0.96735 0.96447 0.961S6 28.82 734 0.98982 0.98705 0.98429 0.98165 0.97871 0.97585 0.97300 0.97012 0.96724 0.96429 28.90 736 0.99265 0.98985 0.98706 0.98426 0.98147 0.97861 0.97576 0.97288 0.97000 0.96706 28.98 738 0.99541 0.99261 0.98982 0.98703 0.98424 0.98138 0.97835 0.97564 0.97276 0.96982 29.06 740 0.99818 0.99538 0.99259 0.98976 0.98694 0.98409 0.98124 0.97835 0.97547 0.97253 29.13 742 1.00100 0.99820 0.99541 0.992SS 0.98976 0.98691 0.98406 0.93115 0.97824 0.97529 29.21 744 1.00376 1.00097 0.99818 0.99535 0.99253 0.98967 0.98682 0.98391 0.98100 0.97806 29.29 746 1.00659 1.00376 1.00094 0.99809 0.99529 0.99241 0.98953 0.98662 0.98371 0.98076 29.37 748 1.00935 1.006S3 1.00371 1.00088 0.99806 0.99517 0.99229 0.98938 0.98647 0.98353 29.45 750 1.01212 1.00936 1.00659 1.00370 1.00082 0.99796 0.99506 0.99215 0.98924 0.98626 29.53 752 1.01494 1.01211 1.00929 1.00644 1.00359 1.00071 0.99782 0.99491 0.99200 0.98903 29.61 754 1.01771 1.01483 1.01206 1.00921 1.00635 1.00342 1.00059 0.99738 0.99471 0.99173 29.69 756 1.02047 1.01764 1.01482 1.01197 1.00912 1.00624 1.00335 1.00041 0.99747 0.99450 29.76 758 1.02329 1.02047 1.01765 1.01477 1.01188 1.00900 1.00612 1.00318 1.00024 0.99724 29.84 760 1.02606 1.02323 1.02041 1.01753 1.01465 1.01174 1.00882 1.00588 1.00294 0.99995 29.92 762 1.02882 1.02600 1.02318 1.02030 1.01741 1.01450 1.01159 1.00865 1.00571 1.00274 30.00 764 1.03165 1.02880 1.02594 1.02306 1.02018 1.01727 1.01435 1.01141 1.00847 1.00547 30.08 766 1.03441 1.03156 1.02871 1.02583 1.02294 1.02003 1.01712 1.01418 1.01124 1.00824 30.16 768 1.03724 1.03435 1.03147 1.028S9 1.02571 1.02280 1.01988 1.01611 1.01394 1.01094 30.24 770 1.04000 1.03712 1.03424 1.03136 1.02847 1.02556 1.02265 1.01968 1.01671 1.01371 30.31 ; 1 ;  30.0X 305°C 31.0°C 3I5°C 32.0°C 325°C 33.0°C 3ZS°C 34.0°C 34.5°C 3S.0°C mm 86.0°F 86.9T 87.PF 88.7-F 89.6°F 90.5°F 91.4T 925°F 93.2°F 94.1°F 9S.0°F Inches 700 . 0.91494 0.91203 0.90912 0.90620 0.90329 0.90082 0.89735 0.89432 0.89129 0.88821 0.88512 27.56 702 0.91765 0.91476 051188 0.90894 0.90600 0.90303 0.90006 0.89703 0.89400 0.89091 0.88782 27.64 704 0.92041 0.91750 0.91459 0.91165 0.90871 0.90576 0.90282 0.89976 0.89671 0.89362 0.89053 27.72 706 0.92312 052024 0.91735 051441 0.91147 0.90847 0.90547 0.90241 0.89935 0.89627 0.89318 27 JO 708 0.92588 052297 0.92006 051712 051418 0.91118 0.90818 0.90512 0.90206 0.89897 0.89588 27.87 710 0.92859 052567 052276 051982 051688 051388 051088 0.90782 0.90476 0.90168 0.89859 2755 712 0.93129 0.92841 0.92553 0.92256 0.91959 051659 051359 0.91053 0.90747 0.90438 050129 28.03 714 0.93406 0.93115 052824 052S29 052235 0.91932 051629 0.91323 051018 0.90706 0.90394 . 28.11 716 0.93676 0.93388 0.93100 052803 052506 0.92203 051900 051594 0.91288 0.90976 0.90665 28.19 718 0.93953 0.93662 053371 053078 052776 0.92474 052171 051865 0.91559 0.91247 0.90935 28.27 720 0.94224 053932 0.93641 053344 0.93047 052744 0.92441 0.92135 051829 051517 051206 28.35 722 054500 054209 053918 053618 053318 0.93015 052712 052412 052100 051785 051471 28.43 724 0.94771 0.94479 0.94188 0.93897 053606 053294 0.92982 0.92676 052371 052056 0.91741 2850 726 0.95041 0.94750 0.94459 054159 053859 053556 053253 052944 . 0.92635 0.92323 052012 2858 728 0.95318 055026 054735 05443S 054135 0.93830 0.93544 053215 052906 0.92591 052276 28.66 730 0.95594 055300 055006 054706 054406 0.94103 053800 053488 053176 052861 052547 2874 732 04S865 055578 055282 054979 0.94676 054373 0.94071 053759 0.93447 053132 052818 2842 734 0.96I3S 0.95844 0.95553 0.95250 0.94947 054644 0.94341 0.94034 053718 053403 053088 2850 736 0.96412 0.96118 055824 0.95521 055218 0.94915 054612 0.94300 053988 053670 053353 2858 738 0.96688 0.96394 0.96100 055797 055494 0.95188 054882 0.94570 054259 053941 053624 . 29.06 740 056959 056665 0.96371 056068 055765 055459 055153 054841 054529 054211 0.93894 29.13 742 0.9723S 0.96941 0.96647 056341 0.96035 0.95730 055424 0.95112 0.94800 0.94482 0.94165 29.21 744 057512 057215 056918 05661S 056312 0.96003 055694 055382 0.95071 054750 0.94429 29-H 746 0.97782 057485 0.97188 0.9688S 0.96582 0.96273 0.95965 0.95653 0.95341 0.95020 0.94700 2947 748 0.98059 057762 0.97465 057159 056853 0.96544 0.96235 0.95925 0.95606 0.95288 0.94971 29.45 750 0.98329 0.98032 0.97735 057429 057124 0.96815 0.96506 0.96191 . 0.95876 0.95558 0.94251 2943 752 0.98606 0.98306 0.98006 057703 057400 0.97088 0.96776 0.96461 0.96147 0.95826 0.95506 29.61 754 058876 0.98579 0.98282 057976 0.97671 0.97359 0.97047 0.96732 0.96418 0.96097 055776 29.69 756 0.99153 0.98853 0.98553 0.98247 057941 0.97629 0.97318 057003 0.96688 0.96367 0.96047 29.76 758 059429 0.99129 0.98829 0.98521 0.98212 0.97900 0.97588 0.97273 0.96959 0.96638 056318 2944 760 059700 0.99400 059100 0.98794 0.98488 0.98176 057865 0.97547 0.97229 0.96908 0.96588 2952 762 0.99976 059673 0.99371 0.99065 0.98759 0.98443 058135 0.97817 057500 0.97176 0.968S3 30.00 764 1.00247 0.99948 059647 0.99338 . 0.99029 058717 0.98406 0.98088 057771 057447 0.97124 30.08 766 1.00524 1.00221 0.99918 0.99609 0.99300 0.98988 0.98676 0.98356 0.98053 0.97714 057394 30.16 768 1.00794 1.00491 1.00188 0.99880 0.99571 0.99259 0.98947 0.98629 0.98312 0.97986 0.97659 30.24 770 1.01071 1.00768 1.00465 1.00156 0.99847 0.99532 0.99218 0.98897 0.98576 0.98252 0.97929 3051 294 APPENDIX B ERROR ANALYSIS The f o l l o w i n g e r r o r a n a l y s i s i s d e r i v e d from M i c k l e y e t a l . [ l 4 4 ] . C o n s i d e r a q u a n t i t y Q which i s a f u n c t i o n of t h e independent v a r i a b l e s x 1 f x 2 , X 3 , . . . , x n Q = f ( X], x 2 , x 3 , . . . , x n ) ( b . 1 ) When t h e r e a r e s m a l l f i n i t e i n c r e m e n t s x 1 , x 2 , . . . , x n , the c o r r e s p o n d i n g e r r o r i n Q i s Q +AQ = f ( x , + A x 1 f x 2 +Ax 2, , x n + A x n ) (b .2) By T a y l o r ' s 'ser i e s e x p a n s i o n Q + AQ = f ( x 1 r x 2 , x 3 , x n ) + ( 3 f / 9 x 1)Ax 1 + ( 3 f / 9 x 2 ) A x 2 ...+ ( 9 f / 9 x n ) A x n + (d2t/dx-l 2 ) ( A x 1 2 ) + . . ( h i g h e r o r d e r terms) (b . 3 ) When A x l f A x 2 , A X 3 , A x n a r e s u f f i c i e n t l y s m a l l , the h i g h e r o r d e r terms a r e n e g l i g i b l e . The f o l l o w i n g e q u a t i o n would r e s u l t i n a good a p p r o x i m a t i o n 2 9 5 AQ = (bt/dx])Ax] + ( 3 f / 3 x 2 ) A x 2 ...+ O f / 3 x n ) A x n t h a t i s , AQ = ( e r r o r caused by Ax«) + ( e r r o r caused by A x 2 ) +...+ ( e r r o r caused by A x n ) I t s h o u l d be n o t e d t h a t E q u a t i o n (b .4) may o v e r e s t i m a t e the e r r o r i n v o l v e d i n the c a l c u l a t i o n , because i t c o n s i d e r s o n l y the s i m u l t a n e o u s o c c u r r e n c e of the e r r o r s and does not t a k e i n t o account the p o s s i b i l i t y of compensating e f f e c t s . N o n e t h e l e s s , e r r o r e s t i m a t e s i n e n g i n e e r i n g a n a l y s i s a r e o f t e n c a l c u l a t e d by t h e above proce d u r e because they a r e known t o be conservati ve and hence, a l l o w f o r an a d d i t i o n a l 'margin-of-safety'. The above mentioned p r o c e d u r e i s used t o a n a l y z e u n c e r t a i n t y a s s o c i a t e d w i t h the R v v a l u e d e t e r m i n a t i o n . The o p e r a t i n g c o n d i t i o n s of Run T9 a r e used as an example. R v from f i r s t p r i n c i p l e s can be w r i t t e n a s : R v = {lk L°a v(HPy A - C A*)/[l+IH(k L°/k G)]} 296 The u n c e r t a i n t i e s a s s o c i a t e d w i t h the e s t i m a t e s of kg, a v , H and I a r e g e n e r a l l y i n the o r d e r of ±25 % [85] (see Chapter 2 ) . Assuming t h a t the a c c u r a c y of the measurements of the gas c o m p o s i t i o n and p r e s s u r e a r e w i t h i n ±2.5%. For C0 2-NaOH system, the f r e e C 0 2 i n the l i q u i d phase i s v i r t u a l l y z e r o . S i n c e R v i s a f u n c t i o n of many pa r a m e t e r s , i t i s d i f f i c u l t t o determine the g r a d i e n t s a n a l y t i c a l l y . T h e r e f o r e , the monitor program NLMON, which i s a v a i l a b l e a t UBC Computing C e n t e r , i s used t o p r o v i d e the v a l u e of 3f/3x£ f o r each parameter. These v a l u e s of g r a d i e n t s a r e then used t o d e t e r m i n e u n c e r t a i n t y i n R v by means E q u a t i o n b.4. The r e s u l t s a r e shown i n T a b l e B.1. T a b l e B.1: P r o p a g a t i o n of E r r o r s f o r Run T9. U n c e r t a i n t y i n v a r i a b l e U n c e r t a i n t y i n R v U s i n g Eq. b.4 k G±25%; k L°±25%; a v±25%; R v±95% H±25%; I±25%; P±25%; y A±25% 2 9 7 As can be seen from T a b l e -B.1, the u n c e r t a i n t y a s s o c i a t e d w i t h the computed v a l u e d of R v from e q u a t i o n b.4 c o u l d be as h i g h as 95% because a number of parameters a r e i n v o l v e d . For the case of u s i n g l a b o r a t o r y models, R v can be a c q u i r e d from the p r o d u c t of R a and a v . B e f o r e R v can be. d e t e r m i n e d from e x p e r i m e n t a l t e s t i n g , k G and k L 0 of t h e system must be matched. A c c o r d i n g t o A l p e r [62] and L a u r e n t [ 1 3 0 ] , the a c c u r a c y of o b t a i n i n g R a i s w i t h i n ±10% t o 20%. For comparison p u r p o s e s , the average v a l u e of ±15% i s a s s i g n e d . S i n c e R v i s d e t e r m i n e d by d i r e c t m u l t i p l i c a t i o n of R a and a v , t h e e r r o r f o r t h i s case i s the sum of the e r r o r s a s s o c i a t e d w i t h R a and a v , which i s ±40 %. For the case of u s i n g the PPT, the a c c u r a c y i n o b t a i n i n g R v depends o n l y on the a c c u r a c y i n measuring- th e i n e r t gas f l o w r a t e , G j , and the gas c o m p o s i t i o n , Y A. The e r r o r i n measuring the d i s t a n c e a l o n g the column a x i a l may be n e g l e c t e d . The a c c u r a c y i n measuring the gas f l o w r a t e u s i n g a rotameter i s about 5 %. To measure the C 0 2 c o m p o s i t i o n u s i n g i n f r a r e d a n a l y z e r , the a c c u r a c y would be i n the o r d e r of ±2 %. However, the e r r o r i n mass b a l a n c e as w e l l as the l i q u i d c o m p o s i t i o n measurements c o u l d i n c r e a s e the u n c e r t a i n t y . I f we adopt a worst case s c e n a r i o and s e t 298 the u n c e r t a i n t y of the former and l a t t e r p a rameters t o ±5 % and ±15% r e s p e c t i v e l y , the maximum e r r o r t h a t c o u l d o c c u r f o r t h i s case i s ±20 %. A summary of the p o t e n t i a l maximum u n c e r t a i n t i e s i n d e t e r m i n i n g the R v p r o v i d e d by T a b l e B.2. Ta b l e B.2: E s t i m a t e s of p o t e n t i a l u n c e r t a i n t i e s i n R v D e t e r m i n a t i o n of P o t e n t i a l max. e r r o r s p e c i f i c a b s o r p t i o n r a t e F i r s t p r i n c i p l e s L a b o r a t o r y models PPT 95 % 40 % 20 % APPENDIX C COMPUTER PROGRAM LISTINGS C l . PROGRAM FOR P R E D I C T I N G C Q 2 ~ A M P S O L U B I L I T Y C PRIDICT LOADING *******riew fitted for pKl C MODIFIED FROM SOL9/5 (PRIDICTION OF PC02) C SOLUBILITY CALCULATION FOR C02 - AMP SYSTEM C >>>> C A L C U L A T E ======= ********* Q ******************************* IMPLICIT REAL*8(A-H,0-Z) DIMENSION X(10),F(10),AJINV(10,10),W(500),IPERM(20) COMMON CK1,CK3,CK4,CK5,CK6 COMMON AMP,T,PC02,ALFA D A T A AAl,ABl/-2.3091D+3,-4.9828D-01/ D A T A ACl,ADl/7.0850E+4,3.8803D+2/ D A T A AEl,AFl/6.3899D+00,9.5221D-2/ D A T A AG1/-3.8508D-2/ DATA A3,B3,C3/-241.818D0, 298.253D3, -148.528D6/ DATA D3.E3/332.648D8, -282.394D10/ D A T A A4,B4,C4/39.5554D0, -987.9D2, 568.828D5/ D A T A D4.E4/-146.451D8, 136.146D10/ DATA A5,B5,C5/-294.74D0, 364.385D3, -184.158D6/ DATA D5.E5/415.793D8, -354.291D10/. D A T A A6,B6,C6/22.2819D0, -138.306D2, 691.346D4/ D A T A D6.E6/-155.895D7, 120.037D9/ AVE=0. NP=60 C ** READ DATA FROM Kl -DATA/5 NE =8 DO 5 I=1,NP READ (5,10) AMP,T,ALFA,PC02,CK1 10 F O R M A T (5D12.4) C WRITE (6,12) CK1 C 12 FORMAT (' DATA OF K l = \D12.4) C C C A L C U L A T E CONSTANTS ~ CK3 = DEXP(A3 + B3/T +(C3/(T**2)) +(D3/(T**3)) +(E3/(T**4))) CK4 = DEXP(A4 + B4/T +(C4/(T**2)) +(D4/(T**3)) +(E4/(T**4))) CK5 = DEXP(A5 + B5/T +(C5/(T**2)) +(D5/(T**3)) +(E5/(T**4))) CK6 = DEXP(A6 + B6/T +(C6/(T**2)) +(D6/(T**3)) +(E6/(T**4))) CK6 = CK6/(760./101.15) C02=PC02/CK6 CK1 =AA1 + AB1*T + (AC1/(T**1)) + (ADl*DLOG(T)) >+ AE1*(C02) +(AF1*DL0G(C02)) +AG1*(AMP) CK1 = 10.**CK1 C WRITE (6,11) CK1 C 11 . FORMAT(' FITTED KI = \D12.4) C SET INITIAL VALUE C X(1)=H+, X(2)=RRNH, X(3)=RRNH2+, X(4)=HC03-C X(5)= C02, X(6)=OH-, X(7)=C03-, X(8)=ALFA (CAL) C X A L F A = 0.75 IF(T.GT.(273.+60.)) XALFA=.75 IF(T.GT.373.) XALFA=.20 X(l)= l.D-8 X(2)= AMP*(1.-XALFA) X(3)= AMP*XALFA X(4)= AMP*XALFA X(5)= X(1)*X(4)/CK3 X(6)= CK4/X(1) X(7)= l.D-5 X(8)= XALFA C X(l)= l.D-8 C X(5)= PC02/CK6 C X(4)= CK3*X(5)/X(1) C X(6)= CK4/X(1) C X(7)= l.D-4 C X(3)= X(4) C X(2)= CK1*X(3)/X(1) C X(8)= (X(5)+X(4)+X(7))/AMP C C WRITE (6,50) X(1),X(2),X(3),X(4),X(5),X(6),X(7),X(8) C 50 FORMAT (/'INIT= '/.8D9.2) C SET INPUT FOR NDINVT C DSTEP=l.D-7 DMAX = 10. A C C = l.D-20 MAXFUN = 15000 LOG = 00 EXTERNAL FCN C CALL QNEWT CALL QNEWT(NE,X,F,NE,AJINV,DSTEP,DMAX,ACC,MAXFUN,LOG,W,IPERM, > FCN.&70) C C PRINT XI TO X9 C EER = (ALFA-X(8))*100/ALFA WRITE (6,52) AMP,T,PC02,ALFA,X(8),EER A V E = A V E +DABS(EER) 52 FORMAT (6D12.4) 5 CONTINUE WRITE (6,75) 75 FORMAT ( ,AMP',9X,'TEMP',9X,'PC02',9X, ,ALFA',8X,'CAL.PC02') A V E = A V E / N P WRITE (6,85) A V E 85 FORMAT (/' A V E ERR = ',F9.3) STOP 70 WRITE (7,100) 100 FORMAT ('?? ERR FORM NDINVT') STOP 1 END C C SUBROUTINE FCN C SUBROUTINE FCN(X.F) IMPLICIT REAL*8(A-H.O-Z) DIMENSION X(1),F(1) COMMON CK1,CK3,CK4,CK5,CK6 COMMON AMP,T,PC02,ALFA _ C DO 3 IJ = 1,8 C3 IF (X(IJ).LT.l.D-20) X(IJ)=l.D-20 X(3) + X(l) - X(6) - X(4) - 2 *X(7) X(8)*AMP - X(5) - X(4) - X(7) AMP - X(2) - X(3) PC02 - (CK6)*X(5) CK5 - (X(1)*X(7)/X(4)) CK4 - (X(1)*X(6)) CK3 - (X(1)*X(4)/X(5)) CK1 - (X(1)*X(2)/X(3)) F(l) = F(2) = F(3) = F(4) = F(5) = F(6) = F(7) = F(8) = RETURN END C 2 . PROGRAM FOR P R E D I C T I N G COLUMN PERFORMANCE FOR RUN T 9 ( N a O H - C Q 2 ) C RUN-T9 (RUN44) C FULL SCALE RUN ********** C IMPLICIT REAL*8(A-H,J-M,0-Z) DIMENSION PYA(900),PYS(900),PCR(900),T(900),HT(900) DIMENSION PTG(900),PEG( 15),PEC( 15),PET( 15),PHT(20) C WRITE(6,321) 321 FORMAT(/ ' **** RUN # (T9) 44 ****'/ > •===================./) C WRITE(7,323) 323 FORMAT(/ ' **** RUN # (T9) 44 ****'/ > . = = = = = = = = _ = = = _ = = = - = = = . ) C c C CALCULATION OF C02 - AMINE SYSTEM. C C 1. ASSUME THE TEMP. AND SOLVENT VAPOR CONCENTRATION (YS) C OF T H E OUTLET GAS . C TG(C), TGK(K), YS(MOLE FRACTION) C T G O U T = 15.0 YSOUT = 0.031 C C - 2. COMPUTE THE ENTHALPIES OF THE ENTERING STREAMS C AND T H E OUTLET GAS . BY THE MATERIAL AND ENTHALPY C BALANCES FOR THE ENTIRE TOWER, COMPUTE THE OUTLET C LIQUID RATE, COMPOSITION AND T E M P E R A T U R E . C NDUM=0 C ? C C P = T O T A L PRESSURE. P = 1.0 C CONC. IN LIQUID = G-MOL/CC. C CRIN = 2.00 CPIN = (2.00-CRIN)/2. LMIN= (1.00)*(1820./(60*80)) TLIN = 15.0 GB =1.475E-3 SYAIN = 18.45/100. YAIN = SYAIN/(1.-SYAIN) YBIN = 1.0 YSIN = 0.001 TGIN =15. CROUT = 0.37 CPOUT = (2.0-CROUT)/2. C T L O U T IS ASSUMED FROM OVERALL ENERGY BALANCE. T L O U T = 35.0 SYAOUT = 1.00/100 Y A O U T = SYAOUT/(l .-SYAOUT) YBOUT = 1. C YSOUT AND TGOUT ARE ASSUME AS A B O V E C C STEP BY STEP CALCULATIONS NOW BEGIN FROM THE BOTTOM C OF THE TOWER . CR = CROUT CP = CPOUT T L = TLOUT LM = LMIN+0.0005 Y A = YAIN YB = YBIN YS = YSIN T G = TGIN Z = 0. C GBin and G'Bout are the same. C . . C - 3. OBTAIN ALL THE NECESSARY PHYSICAL AND CHEMICAL PROPERTIES C OF THE GAS AND LIQUID . C EG. VISCOSITY, DENSITY, HEAT CAPACITY, THERMAL CONDUCTIVITY, C • DIFFUSIVITIES, VAPOR PRESSURE OF SOLVENT S , C CHEMICAL EQUILIBRIUM CONSTANT Kc , C FORWARD REACTION RATE CONSTANT K2 . C C SEE T A B L E I P.356 C N = 1 NOUT = 1 NSET = 900 C ???? C 300 STOI = 2. CPA = 8.8 CPS = 8.1 CPB = 7.0 HLH20 = 10761 CL = 1.0 PL = 1.0 HR = -24400. TLK = TL+273.15 DA = (1.65D-5)*(((647.3-298.)/(647.3-TLK))**3) DR = DA/1.7 C C THE REACTION RATE CONSTANT K2. C ASI = CR + (((2.*CP)+(CP*4.))/2) ALK2 = 11.895 - (2382/TLK) +(0.221*ASI)-(.016*(ASI**2)) K2 = 10 **(ALK2) C K2 = L / G - M OL.SEC. C C THE SOLUBILITY OF GAS IN SOLUTION. C ( SEE COMMENTS ON P.356 ) C HW= 10 **(9.1229-(.059044*TLK)+(7.8857D-5*(TLK**2))) AHG = 0.124515-(.00047*(TLK)) SHI=(CR*(.091+.066+AHG))+(((2.*CP-l-CP*4.)/2)*(.09H-.066-|-AHG)) H = HW*(10.**(-SHI)) C WRITE (7,221) DA,ASI,K2,HW,H C221 FORMAT (/5D10.3) C C 4. ESTIMATE KLA, KGA, KGS, HGA FROM T H E AVAIBLE CORRELATIONS. C SEE T A B L E II P.356 C A = 1.500 KLA = (2.6*DA)**(.5) KGA = 3.2 D-5 KGS = 3.2 D-5 HGA = 2.478 D-3 C C STORE D A T A PYA(N)=YA PYS(N)=YS PCR(N)=CR T(N) = T L PTG(N) = T G HT(N) = Z C C 5. ASSUME PAI = PA C PA = P*(YA/(YA+YS+YB)) PAI =PA CAI = H*PAI C REAL*8 M,M2 C 200 IF(CR.LT.0.0005) E=l. IF(CR.LT.0.0005) GOTO201 M2 = K2*CR*DA/(KLA**2) E l = DSQRT(M2)/DTANH(DSQRT(M2)) C EI = 1. + ((CR*DR)/(2.*CAI*DA)) EI = (DSQRT(DA/DR))+(CR/(2.*CAI))*(DSQRT(DR/DA)) C C ASSUME LIQUID HOLD UP = 5% OF T O T A L V A L U E . C C HU = 0.05 C XXX = HU*K2*CR/(KLA*A) C C IF (XXX.LT.20.) GO TO 550 C EA = l./((EI-l.)**1.35) EB = l./((El-l.)**1.35) E=1.+(1./((EA+EB)**(1./1.35))) 201 CONTINUE C C550 WRITE (6,555) C555 FORMAT (IX,' !!! E OUT OFF RANGE.') C GOTO 900 CC C560 WRITE (6,565) C565 FORMAT (/' !! E » 1. ???'/) C C CHACK E VALUE? C WRITE (6,566) C566 FORMAT (/' CHACK E CALCULATION. '/) C WRITE (6,567)M2,M,SRM C567 FORMAT (' '.F15.4/F15.4/F15.4/) C WRITE (6,568)Q,QM,XXX,E C568 FORMAT (' ',F15.4/F15.4/F15.4/,' . . » E',F15.4/) C C GO TO 900 C C C 6. ASSUME CAE = 0.0 C R = (E*KLA*PA*H*l.D-3)/(l.+((E*KLA*H)*I.D-3)/(KGA)) CAINEW = (PA*H)-(R*H/KGA) PAIN = CAI/H C IF (DABS(CAINEW-CAI).LE.DABS(0.00010*(CAINEW+CAI))) GOTO 700 C CAI=CAINEW GO TO 200 C C 7. COMPUTE DYA/DZ, DYS/DZ, DTG/DZ, AND C DTG/DZ FROM THE EQ.S 30,31,32,..29) C 700 PSI = 0.90*( 2.7182818**(16.5362-(3985.44/(TLK-38.9974))))/ > 101.13 YSI = PSI/(P-PAIN-PSI) YAI = PAIN/(P-PAIN-PSI) PS =P*(YS/(YA+YB+YS)) DYADZ = -KGA*A*(PA-PAIN)/GB DYSDZ = -KGS*A*(PS-PSI)/GB HDGA= (-l.*GB)*(CPA*DYADZ + CPS*DYSDZ)/ > (1-DEXP(GB*(CPA*DYADZ + CPS*DYSDZ)/HGA)) DTGDZ = -HDGA*(TG-TL)/(GB*(CPB+YA*CPA+YS*CPS )) C C REF. TEMP. TO = 25 C. TO = 25. DTLDZ = (l./(LM*CL))*((GB*(CPB+YA*CPA+YS*CPS)*DTGDZ) > + (GB*(CPS*(TG-T0) + HLH20 )*DYSDZ) > + (GB*(CPA*(TG-T0) - HR)*DYADZ)) C C 8. CHOOSE A SUITABLY SMALL VALUE OF DYA , C AN INCREMENT OF GAS COMPOSITION, SO T H A T THE C GRADIENTS DYA/DZ,DYS/DZ,DTG/DZ, AND DTL/DZ C WILL NOT CHANGE TOO GREATIY . C DELYA = -0.00025*4. DELZ = DELYA/DYADZ C C WRITE(6,10) CR,PA,PAIN,PSI,Z,DELZ,E C10 FORMAT(' ',F10.6,'(CR)',F10.6,,(PA)',F10.6,,(PAI)*, C > F12.4,'(PSI)\F12.4,'(DZ)',F12.4,'(Z),,F12.4,,(E),) C C WHERE Z=0. FOR T H E B OTTOM OF T H E TOWER . C Z= Z+ DELZ C C 9. COMPUTE T H E CIRCUMSTANCES A T Z-NEXT . C Y A = Y A + DELYA YS = YS + DELZ*DYSDZ T G = T G + DELZ*DTGDZ TL = T L + DELZ*DTLDZ LMOLD = LM LM = LM + GB*DELZ*(DYADZ+DYSDZ)*29. C CR=(((LMOLD*CR/1000.) - STOI*GB*DELYA)/LM)*1000. CP=(((LMOLD*CP/1000.) + GB*DELYA)/LM)*1000. C C PRINT SOME RESULTS C NIN = N/50 IF(NIN.GE.NOUT) CALL CHACK (NIN,CR,CP,LM,TL, > YA,YB,YS,TG,Z,NOUT) IF(NDUM.EQ.0.AND.Z.GT.110.) CALL CKOUT(Z,CR,YA,TL,N,NDUM) IF(Z.GT.110..AND.Z.LT.220.) GOTO 850 IF(NDUM.EQ.1.AND.Z.GT.220.) CALL CKOUT(Z,CR,YA,TL,N,NDUM) IF(Z.GT.220..AND.Z.LT.330) GOTO 850 IF(NDUM.EQ.2.AND.Z.GT.330.) CALL CKOUT(Z,CR,YA,TL,N,NDUM) IF(Z.GT.330.AND.Z.LT.435.) GOTO 850 IF(NDUM.EQ.3.AND.Z.GT.435.) CALL CKOUT(Z,CR,YA,TL,N,NDUM) IF(Z.GT.440..AND.Z.LT.550) GOTO 850 IF(NDUM.EQ.4AND.Z.GT.550.) CALL CKOUT(Z,CR,YA,TL,N,NDUM) IF(Z.GT.550..AND.Z.LT.650) GOTO 850 850 CONTINUE IF(YA.LT.YAOUT) CALL CKOUT(Z,CR 1YA,TL,N,NDUM) C C 10. REPEAT STEP 3 TO 9 UNTIL Y A FOR THE OUTLET GAS C IS REACHED . C IF(YA.LT.YAOUT) GO TO 900 N=N+1 IF(N.GT.NSET) GO TO 900 C WRITE(8,1111) Z,PA,CR,TL,TG,E 1111 FORMAT(6F11.6) C GOTO 300 C C C 11. CHECK THE ASSUMPTION OF STEP" 1. C IF NOT MATCHED, IT MAY BE APPROPRIATE GUESS FOR . C THE NEXT ITERATION . HOWEVER, IF THE SOLUTION IS FOUND C TO BE INSENSITIVE TO THE ASSUMED VALUES OF T G AND YS C (THROUGH THE BACK CALCULATION OF OUTLET LIQUID TEMP. C FROM AN OVERALL ENTHALPY BALANCE) FURTHER ITERATION C WILL NOT BE REQUIRED . C C C 900 WRITE(6,905) 905 FORMAT(/ ' ***** THE END CONDITION *****'/) WRITE(6,910) CRIN 910 FORMAT(/ ' INLET CONCN. OF MEA \F10.5,' G-MOL/L') WPJTE(6,915) CPIN 915 FORMATC INLET CONCN. OF PROD. \F10.5,* G-MOL/L') WRITE(6,920) LMIN 920 FORMATC INLET L. MOLAR VEL. ',F10.5,' G-MOL/SEC.CM2') WRITE(6,925) TLIN 925 FORMATC INLET LIQUID TEMP. \F10.5,' C ) WRITE(6,930) CROUT 930 FORMAT(/ ' OUTLET CONCN. OF MEA \F10.5,' G-MOL/L') WRITE(6,935) CPOUT 935 FORMATC OUTLET CONCN. OF PROD. \F10.5,' G-MOL/L') WRITE(6,945) TLOUT 945 FORMATC OUTLET LIQUID TEMP. \F10.5,' C ) WRITE(6,950) GB 950 FORMAT(/ ' INLET AIR MOL. VEL. ',F10.5,'G-MOL/SEC.CM2') WRITE(6,955) YAIN 955 FORMATC INLET MOL FRAC. OF C02 \F10.5) WRITE(6,960) YBIN 960 FORMATC INLET MOL FRAC. OF AIR \F10.5) WRITE(6,965) TGIN 965 FORMATC INLET GAS TEMP. \F10.5,' C ) WRITE(6,970) YAOUT 970 FORMAT(/ ' OUTLET MOL FRAC. OF C02 '.F10.5) WRITE(6,975) YBOUT 975 FORMATC OUTLET MOL FRAC. OF AIR \F10.5) WRITE(6,980) YSOUT 980 FORMATC OUTLET MOL FRAC. OF H20 \F10.5) WRITE(6,985) TGOUT 985 FORMATC OUTLET GAS TEMP. \F10.5,' C ) WPJTE(6,990) 990 FORMAT(/ ' *** >> CALCULATION RESULTS') WRITE(6,991) CR 991 FORMAT(/ ' INLET CONCN. OF MEA \F10.5,' G-MOL/L') WRITE(6,992) CP 992 FORMATC INLET CONCN. OF PROD. \F10.5,' G-MOL/L') WRITE(6,993) LM 993 FORMATC INLET L. MOLAR VEL. \F10.5,' G-MOL/SEC.CM2') WRTTE(6,994) TL 994 FORMAT(' INLET LIQUID TEMP. \F10.5,' C ) WRITE(6,995) YA 995 FORMAT(/ ' OUTLET MOL FRAC. OF C02 '.F10.5) WRTTE(6,996) YB 996 FORMATC OUTLET MOL FRAC. OF AIR '.F10.5) WRJTE(6,997) YS 997 FORMAT(' OUTLET MOL FRAC. OF H20 \F10.5) WRITE(6,998) T G 998 F O R M A T f OUTLET GAS TEMP. \F10.5,' C ) WRITE(6,999) Z 999 FORMATC THE T O T A L HEIGHT ',F10.5,' CM.'/) C SCALING DO 1 I=1,N HT(I) = 2. + (HT(I)/(1.*100.)) PMIX = l.+PYS(I) +PYA(I) PMLXX = 1. + PYA(I) PYA(I) = 1. +((PYA(I)/(PMIXX))/0.03) PYS(I) = 1. +((PYS(I)/(PMIX))/0.03) PCR(I) = 1. + (PCR(I)/.6) T(I) = 1. + (T(I)*5./50.) PTG(I) = 1. + (PTG(I)*5./50.) 1 CONTINUE C PLOTTING CALL AXIS(1.,.5,'P. CO2',-6,7.,0.,0.,0.03) CALL AXIS(1.,1.,'P. H2O',-6,7.,0.,0.,0.03) C A L L AXIS(1.,1.5,'MEA (MOL/L)',-11,7.,0.,0.,0.6) CALL AXIS(1,2.,'TEMP. (C)',-9,7.,0.10.,10.) CALL AXIS(1,2.,'HEIGTH (M)',10,7.,90,0.,l.) CALL PLOT(l.,2.,3) CALL PLOT(2,2.,2) CALL PLOT(2.,9.,2) CALL PLOT(3.,9.,2) CALL PLOT(3.,2.,2) CALL PLOT(4.,2.,2) CALL PLOT(4.,9.,2) CALL PLOT(5.,9.,2] CALL PLOT(5.,2.,2) CALL PLOT('6.,2.,2; CALL PLOT(6.,9.,2; CALL PLOT(7.,9.,2; CALL PLOT(7.,2.,2; CALL PLOT(8.,2.,2; CALL PLOT(8.,9.,2; CALL PLOT(7.,9,2; CALL PLOT(8.,3.,3; CALL PLOT(l.,3.,2; CALL PLOT(l.,4.,2; CALL PLOT(8.,4.,2^ CALL PLOT(8.,5.,2^ CALL PLOT(l.,5.,2 CALL PLOT(l.,6.,2 310 CALL PLOT(8.,6.,2) CALL PLOT(8.,7.,2) CALL PLOT(l.,7.,2) CALL PLOT(l.,8.,2) CALL PLOT(8.,8.,2) CALL PLOT(8.,9.,2) CALL PLOT(l.,9.,2) CALL PLOT(l.,2.,3) DO 2 I=1,N CALL SYMBOL(PYA(I),HT(I)1.010,0,0.,-2) 2 CONTINUE CALL PLOT(l.,2.,3) DO 3 I=1,N CALL SYMBOL(PYS(I),HT(I),.010,l,0.,-2) 3 CONTINUE CALL PLOT(l.,2.,3) DO 4 I=1,N CALL SYMBOL(PCR(I),HT(I),.010,2,0.r2) 4 CONTINUE CALL PLOT(l.,2.,3) DO 5 I=1,N CALLSYMBOL(T(I),HT(I),.010,ll,0.,-2) 5 CONTINUE CALL PLOT(l.,2.,3) DO 6 1=1,N CALL SYMBOL(PTG(I),HT(I),0.01,5,0.,-2) 6 CONTINUE CALL SYMBOL(2.0,10.0,0.08,0,0.,-1) CALL SYMBOL(2.2,10.0,0.08,'P-CO2 (ATM)',0.,11) CALL SYMBOL(3.5,10.,0.08,1,0.,-1) CALL SYMBOL(3.7,10.,0.08,'P-H2O (ATM)',0.,11) CALL SYMBOL(5.0,10.0,0.08,2,0.,-1) CALL SYMBOL(5.2,10.0,0.08,*NAOH (MOL/L)',0.,12) C A L L SYMBOL(2.0,9.7,0.08,11,0.,-1) CALL SYMBOL(2.2,9.7,0.08,'LIQUID TEMP. (C)',0.,16) CALL S Y M B O L l s . S ^ J . O . O S . S . O . , - ! ) CALL SYMBOL(3.7,9.7,0.08,'GAS TEMP. (C)',0.,13) CALL PDATA(PEG,PEC,PET,PHT,NEX) DO 10011=1,NEX EG = 1.+ (PEG(I)/0.03) EC = 1. + (PEC(I)/.6) E T = l.+(PET(I)/10.) EH = 2.+(PHT(I)/100.) CALL SYMBOL(EG,EH,.12,0,0.,-1) CALL SYMBOL(EC,EH,.12,2,0.,-1) CALL SYMBOL(ET,EH,.12,11,0.,-1) 1001 CONTINUE CALL SYMBOL(4,9.25,.25,'RUN# T09',0.,8) CALL PLOTND STOP END Q ********************************************** C SUBROUTINE CHACK(NIN,CR,CP,LM,TL,YA,YB,YS,TG,Z,NOUT) C IMPLICIT REAL*8(A-M.O-Z) C WRITE(6,990) 990 FORMAT(/ ' :::: INTERMEDIAD CALCULATION RESULTS') WRITE(6,991) CR 991 FORMAT(/ ' CONCN. OF MEA \F10.5,' G-MOL/L') WRITE(6,992) CP 992 FORMATC CONCN. OF PROD. ',F10.5,' G-MOL/L') WRITE(6,993) LM 993 FORMATC LIQUID MOLAR VEL. \F10.5,' G-MOL/SEC.CM2') WRITE(6,994) TL 994 FORMATC LIQUID TEMP. ',F10.5,' C ) WRITE(6,995) YA 995 FORMAT(/ ' MOL FRAC. OF C02 \F10.5) WRITE(6,996) YB 996 FORMATC MOL FRAC. OF AIR \F10.5) WRITE(6,997) YS 997 FORMATC MOL FRAC. OF H20 \F10.5) WRITE(6,998) T G 998 FORMATC GAS TEMP. \F10.5,' C ) WRITE(6,999) Z 999 FORMATC THE HEIGHT \F10.5,' CM.'/) NOUT = NOUT + 1 c R E T U R N E N D Q ************************************************* C SUBROUTINE CKOUT(Z,CR,YA,TL,N,NDUM) C IMPLICIT REAL*8(A-M,0-Z) C WRITE(7,990) 990 F O R M A T ( / ' :::: INTERMEDIAL CALCULATION RESULTS') WRITE(7,999) Z 999 F O R M A T ( / ' THE HEIGHT ',F10.5,' CM.'/) PYA = 100.*YA/(1.+YA) WRITE( 7,995) PYA 995 FORMAT(' C02 CONC. (%) '.F10.5) WRITE(7,991) CR 991 FORMAT(' CONCN. OF NAOH ',F10.5,' G-MOL/L') WRITE(7,994) T L 994 FORMAT(' LIQUID TEMP. ',F10.5,' C ) C NDUM=NDUM+1 RETURN END Q ************************************************** SUBROUTINE PDATA(EG,EC,ET,EH,NEX) IMPLICIT REAL*8(A-H.O-Z) DIMENSION EG(20),EC(20),ET(20),EH(20),G(20),C(20),T(20),H(20) NEX=5 DATA H/0.000,110.,220.,330.,435./ DATA G/.1845,.1155,.0580,.0265,.0100/ DATA C/.41,1.08,1.625,1.900,2.00/ DATA T/35.0,29.0,22.0,17.0,15.0/ DO 10 1=1,NEX EH(I)=H(I) EG(I)=G(I) EC(I)=C(I) 10 ET(I)=T(I) RETURN END 313 C3. PROGRAM FOR P R E D I C T I N G COLUMN PERFORMANCE FOR RUN T22  ( M E A - C Q 2 ) C C RUN-T22(RUN41) C FULL SCALE RUN ********** C IMPLICIT REAL*8(A-H,J-M,0-Z) DIMENSION PYA( 1900),PYS( 1900),PALF( 1900),T( 1900),HT( 1900) DIMENSION PTG(1900),PEG(15),PEC(15),PET(15),PHT(20) C WRITE(6,321) 321 FORMAT(/ ' ***** RUN # (T22)41 ****'/ > •-===================7) C WRITE(7,323) 323 F O R M A T ( / ' **** RUN # (T22)41 ****7 > '===================•) C C C CALCULATION OF C02 - AMINE SYSTEM. C C 1. ASSUME THE TEMP. AND SOLVENT VAPOR CONCENTRATION (YS) C OF T H E OUTLET GAS . C TG(C), TGK(K), YS(MOLE FRACTION) C T G O U T = 19.0 YSOUT = 0.031 C C 2. COMPUTE THE ENTHALPIES OF THE ENTERING STREAMS C AND THE OUTLET GAS . BY THE MATERIAL AND ENTHALPY C BALANCES FOR THE ENTIRE TOWER, COMPUTE THE O U T L E T C LIQUID RATE, COMPOSITION AND TEMPERATURE. C NDUM=0 C ? C C P = T O T A L PRESSURE. P = 1.0 C CONC. IN LIQUID = G-MOL/CC. C CTOT = 3:00 ALFIN= .000 LMIN= (1.00)*(1270y(60*80)) TLIN = 19.0 GB =1.475E-3 SYAIN = 19.10/100. YAIN = SYAIN/(1.-SYAIN) YBIN = 1.0 YSIN = 0.001 TGIN =15. ALFOUT = 0.443 C T L O U T IS ASSUMED FROM OVERALL ENERGY BALANCE. TLOUT = 47.0 SYAOUT = 0.05/100 Y A O U T = SYAOUT/(l.-SYAOUT) YBOUT = 1. C YSOUT AND TGOUT ARE ASSUME AS ABOVE C C STEP BY STEP CALCULATIONS NOW BEGIN FROM THE BOTTOM C OF THE TOWER . ALF = ALFOUT TL = TLOUT LM = LMIN+0.0005 Y A = YAIN YB = YBIN YS = YSIN T G = TGIN Z = 0. C GBin and GBout are the same. C C 3. OBTAIN ALL THE NECESSARY PHYSICAL AND CHEMICAL PROPERTIES C OF THE GAS AND LIQUID . C EG. VISCOSITY, DENSITY, HEAT CAPACITY, THERMAL CONDUCTIVITY, C DIFFUSIVITIES, VAPOR PRESSURE OF SOLVENT S , C CHEMICAL EQUILIBRIUM CONSTANT Kc , C FORWARD REACTION RATE CONSTANT K2 . C C SEE T A B L E I P.356 C N = 1 . NOUT = 1 NSET = 1900 C ???? C 300 STOI = 2. CPA = 8.8 CPS = 8.1 CPB = 7.0 HLH20 = 10761 CL = 1.0 PL = 1.0 HR = -20166. T L K = T L + 2 7 3 . 1 5 DA = (0.64)*(2.0D-5)*(((647.3-298.)/(647.3-TLK))**3) DR = (0.80D-5)*(((647.3-298.)/(647.3-TLK))**3) C C T H E REACTION RATE CONSTANT K2. C ASI=ALF*CTOT IF(ALF.GE.0.5) ASI=0.5*CTOT ALK2 = 11.069 - (2142.34/TLK) K2 = 10.**(ALK2) C K2 = L / G - M OL.SEC. C C T H E SOLUBILITY OF GAS IN SOLUTION. C ( SEE COMMENTS ON P.356 ) C HW= 10.**(9.1229-(.059044*TLK)+(7.8857D-5*(TLK**2))) A H G = 0.124515-(.00047*(TLK)) SHI=(.031+.021+.021+AHG)*ASI H = HW*(10 **(-SHI)) C CAL. FREE AMINE CALL SOL(TLK,CTOT,ALF,PEC02) CAB=H*PEC02 CR = CTOT-(2 *CTOT*ALF)+CAB C WRITE (7,221) DA,ASI,K2,HW,H C221 FORMAT (/5D10.3) C C 4. ESTIMATE KLA, KGA, KGS, HGA FROM THE AVAIBLE CORRELATIONS. C SEE TABLE II P.356 C A = 1.350 KLA = (2.4*DA)**(.5) K G A = 3.2 D-5 KGS = 3.2 D-5 HGA = 2.478 D-3 C C STORE DATA PYA(N)=YA PYS(N)=YS PALF(N)=ALF T(N) = TL PTG(N) = T G HT(N) = Z C C 5. ASSUME PAI = PA PA : PAI P*(YA/(YA+YS+YB)) PA CAI H*PAI C REAL*8 M,M2 C 200 IF(CR.LT.0.00005) E=l. IF(CR.LT.0.00005) GOTO201 M2 = K2*CR*DA/(KLA**2) E l = DSQRT(M2)/DTANH(DSQRT(M2)) C EI = 1. + ((CR*DR)/(2.*CAI*DA)) EI = (DSQRT(DA/DR))+(CR/(2.*CAI))*(DSQRT(DR/DA)) C C ASSUME LIQUID HOLD UP = 5% OF T O T A L VALUE . C C HU = 0.05 C XXX = HU*K2*CR/(KLA*A) C C IF (XXX.LT.20.) GO TO 550 C EA = l./((EI-l.)**1.35) EB = l./((El-l.)**1.35) EIR=1.+(1./((EA+EB)**(1./1.35))) E=EIR*(CAI-CAB)/CAI IF(E.LT.l.O) WRITE(6,565) 565 F O R M A T (/' !! E < 1. ???'/) C IF(E.LT.l.O) E=l. 201 CONTINUE C C550 WRITE (6,555) C555 F O R M A T (IX,' !!! E OUT OFF RANGE.') C GOTO 900 CC C560 WRITE (6,565) C565 FORMAT (/' !! E < 1. ???'/) C C CHACK E VALUE? C WRITE (6,566) C566 F O R M A T (/' CHACK E CALCULATION. '/) C WRITE (6,567)M2,M,SRM C567 F O R M A T (' '.F15.4/F15.4/F15.4/) C WRITE (6,568)Q,QM,XXX,E C568 FORMAT (' '.F15.4/F15.4/F15.4/,' . . » E',F15.4/) C C GO TO 900 C C 6. CAL. ABSORPTION RATE C R = ((E*KLA*l.D-3)*(H*PA-CAB))/(l.+((E*KLA*H)*l.D-3)/(KGA)) CAINEW = (PA*H)-(R*H/KGA) PAIN = CAI/H C IF (DABS(CAINEW-CAI).LE.DABS(0.00010*(CAINEW+CAI))) GOTO 700 C CAI=CAINEW GO TO 200 C C 7. COMPUTE DYA/DZ, DYS/DZ, DTG/DZ, AND C DTG/DZ FROM THE EQ.S 30,31,32,..29) C 700 PSI = 0.90*( 2.7182818**(16.5362-(3985.44/(TLK-38.9974))))/ > 101.13 YSI = PSI/(P-PAIN-PSI) YAI = PAIN/(P-PAIN-PSI) PS =P*(YS/(YA+YB+YS)) DYADZ = -KGA*A*(PA-PAIN)/GB DYSDZ = -KGS*A*(PS-PSI)/GB HDGA= (-1 *GB)*(CPA*DYADZ + CPS*DYSDZ)/ > (1-DEXP(GB*(CPA*DYADZ + CPS*DYSDZ)/HGA)) DTGDZ = -HDGA*(TG-TL)/(GB*(CPB+YA*CPA+YS*CPS )) C C REF. TEMP. TO = 25 C. TO = 25. DTLDZ = (l./(LM*CL))*((GB*(CPB+YA*CPA+YS*CPS)*DTGDZ) > + (GB*(CPS*(TG-T0) + HLH20 )*DYSDZ) > + (GB*(CPA*(TG-T0) - HR)*DYADZ)) C C 8. CHOOSE A SUITABLY SMALL V A L U E OF DYA , C AN INCREMENT OF GAS COMPOSITION, SO T H A T T H E C GRADIENTS DYA/DZ,DYS/DZ,DTG/DZ, AND DTL/DZ C WILL NOT CHANGE TOO GREATIY . C DELYA = -0.00025*2. IF(ALF.GT.0.4) DELYA = -0.00005*2. DELZ = DELYA/DYADZ C C WRITE(6,10) ALF,PA,PAIN,PSI,Z,DELZ,E C10 FORMATC ,,F10.6,'(ALF)',F10.6,'(PA)',F10.6,,(PAI)', C > F12.41,(PSI)',F12.41,(DZ),1F12.41,(Z)',F12.4,,(E)') C C WHERE Z=0. FOR T H E BOTTOM OF T H E TOWER . C Z= Z+ DELZ C C 9. COMPUTE THE CIRCUMSTANCES A T Z-NEXT . C Y A = Y A + DELYA YS = YS + DELZ*DYSDZ T G = T G + DELZ*DTGDZ T L = TL + DELZ*DTLDZ LMOLD = LM LM = LM + GB*DELZ*(DYADZ+DYSDZ)*29. CR=(((LMOLD*CR/1000.) - STOI*GB*DELYA)/LM)*1000. C CP=(((LMOLD*CP/1000.) + GB*DELYA)/LM)*1000. ALF=(CTOT-CR+CAB)/(CTOT*2.) C C PRINT SOME RESULTS C NIN = N/100 IF(NIN.GE.NOUT) CALL CHACK (NIN,ALF,LM,TL, > YA,YB,YS,TG,Z,NOUT) IF(NDUM.EQ.0.AND.Z.GT.110.) CALL CKOUT(Z,ALF,YA,TL,N,NDUM) IF(Z.GT.110..AND.Z.LT.220.) GOTO 850 IF(NDUM.EQ.1.AND.Z.GT.220.) CALL CKOUT(Z,ALF,YA,TL,N,NDUM) IF(Z.GT.220..AND.Z.LT.33O) GOTO 850 IF(NDUM.EQ.2.AND.Z.GT.330.) CALL CKOUT(Z,ALF,YA,TL,N,NDUM) IF(Z.GT.330..AND.Z.LT.440.) GOTO 850 IF(NDUM.EQ.3.AND.Z.GT.440.) CALL CKOUT(Z,ALF,YA,TL,N,NDUM) IF(Z.GT.440..AND.Z.LT.550) GOTO 850 IF(NDUM.EQ.4.AND.Z.GT.550.) CALL CKOUT(Z,ALF,YA,TL,N,NDUM) IF(Z.GT.550..AND.Z.LT.650) GOTO 850 IF(NDUM.EQ.5.AND.Z.GT.655.) CALL CKOUT(Z,ALF,YA,TL,N,NDUM) IF(Z.GT.655.) GOTO 850 850 CONTINUE IF(YA.LT.YAOUT) CALL CKOUT(Z,ALF,YA,TL,N,NDUM) C C 10. REPEAT STEP 3 TO 9 UNTIL Y A FOR T H E OUTLET GAS C IS REACHED . C IF(YA.LT.YAOUT) GO TO 900 N=N+1 IF(N.GT.NSET) GO TO 900 WRITE(8,1111) Z,PA,ALF,TL,TG,E 1111 FORMAT(6F11.6) GOTO 300 C C C 11. CHECK THE ASSUMPTION OF STEP 1. C IF NOT MATCHED, IT M A Y BE APPROPRIATE GUESS FOR C THE NEXT ITERATION . HOWEVER, IF THE SOLUTION IS FOUND C TO BE INSENSITIVE T O T H E ASSUMED VALUES OF T G AND YS C (THROUGH THE BACK CALCULATION OF OUTLET LIQUID TEMP. C FROM AN OVERALL ENTHALPY BALANCE) FURTHER ITERATION C WILL NOT BE REQUIRED . C C C 900 WRITE(6,905) 905 FORMAT(/ ' ***** THE END CONDITION *****'/) WRITE(6,910) CTOT 910 FORMAT(/ ' TOTAL CONCN. OF MEA \F10.5,' G-MOL/L') WRJTE(6,915) ALFIN 915 FORMAT(' C02 LOADING (IN) \F10.5,' ') WRITE(6,920) LMIN 920 F O R M A T ^ INLET L. MOLAR VEL. \F10.5,' G-MOL/SEC.CM2') WRITE(6,925) TLIN 925 FORMATC INLET LIQUID TEMP. \F10.5,' C ) WRITE(6,930) ALFOUT 930 FORMAT(/ ' C02 LOADING (OUT) \F10.5,' ') WRITE(6,945) TLOUT 945 FORMAT(' OUTLET LIQUID TEMP. ',F10.5,' C ) WRITE(6,950) GB 950 FORMAT(/ ' INLET AIR MOL. VEL. ',F10.5,'G-MOL/SEC.CM2') WRITE(6,955) YAIN 955 FORMATC INLET MOL FRAC. OF C02 '.F10.5) WRITE(6,960) YBIN 960 FORMATC INLET MOL FRAC. OF AIR \F10.5) WRITE(6,965) TGIN 965 FORMATC INLET GAS TEMP. *,F10.5,' C ) WRITE(6,970) Y A O U T 970 FORMAT(/ ' OUTLET MOL FRAC. OF C02 \F10.5) WRITE(6,975) YBOUT 975 FORMATC OUTLET MOL FRAC. OF AIR \F10.5) WRITE(6,980) YSOUT 980 FORMATC OUTLET MOL FRAC. OF H20 \F10.5) WRITE(6,985) TGOUT 985 FORMATC OUTLET GAS TEMP. \F10.5,' C ) WRITE(6,990) 990 FORMAT(/ ' ***>> CALCULATION RESULTS') WRITE(6,991) ALF 991 FORMAT(/ ' C02 LOADING (IN) CAL. ',F10.5,7L') WRITE( 6,993) LM 993 FORMAT(' INLET L. MOLAR VEL. \F10.5,' G-MOL/SEC.CM2') WRITE(6,994) TL 994 FORMATC INLET LIQUID TEMP. \F10.5,' C ) WRITE(6,995) YA 995 FORMAT(/ ' OUTLET MOL FRAC. OF C02 ',F10.5) WRITE(6,996) YB 996 FORMAT(' OUTLET MOL FRAC. OF AIR \F10.5) WRITE(6,997) YS 997 FORMAT(' OUTLET MOL FRAC. OF H20 \F10.5) WRITE(6,998) T G 998 FORMATC OUTLET GAS TEMP. ',F10.5,' C ) WRITE(6,999) Z 999 FORMATC THE T O T A L HEIGHT \F10.5,' CM.'/) C SCALING DO 1 1=1,N HT(I) = 2. + (HT(I)/(1.*100.)) PMIX = l.+PYS(I) +PYA(I) PMIXX = 1. + PYA(I) PYA(I) = 1. +((PYA(I)/(PMLXX))/0.03) PYS(I) = 1. +((PYS(I)/(PMLK))/0.03) PALF(I) = 1. + (PALF(I)/.l) T(I) = 1. + (T(I)*5./50.) PTG(I) = 1. + (PTG(I)*5./50.) 1 CONTINUE C PLOTTING CALL AXIS(1.,.5,'P. CO2',-6,7.,0.,0.,0.03) CALL AXIS(1.,1.,'P. H2O',-6,7.,0.,0.,0.03) CALL AXIS(1.,1.5,'C02 LOADING',-11,7.,0.,0.,0.6) CALL AXIS(1.,2.,'TEMP. (C)',-9,7.,0.,0,10.) CALL AXIS(1.,2.,'HEIGTH (M)',10,7.,90.,0.,l.) CALL PLOT(l.,2.,3) CALL PLOT(2.,2.,2) CALL PLOT(2.,9.,2) CALL PLOT(3.,9.,2) CALL PLOT(3.,2.,2) CALL PLOT(4.,2.,2) CALL PLOT(4.,9.,2) CALL PLOT(5.,9.,2) CALL PLOT(5.,2.,2) CALL PLOT(6.,2.,2) CALL PLOT(6.,9.,2) CALL PLOT(7.,9.,2) CALL PLOT(7.,2.,2) CALL PLOT(8.,2.,2) CALL PLOT(8.,9.,2) CALL PLOT(7.,9.,2) CALL PLOT(8.,3.,3) 321 C A L L PLOT(l.,3.,2) C A L L PLOT(l.,4.,2) C A L L PLOT(S.,4.,2)' C A L L PLOT(8.,5.,2) C A L L PLOT(l.,5.,2) C A L L PLOT(l.,6.,2) C A L L PLOT(8.,6.,2) C A L L PLOT(8.,7.,2) C A L L PLOT(l.,7.,2) C A L L PLOT(l.,8.,2) C A L L PLOT(8.,8.,2) C A L L PLOT(8.,9.,2) C A L L PLOT(l.,9.,2) C A L L PLOT(l.,2.,3) D O 2 1=1,N C A L L SYMBOL(PYA(I),HT(I),.010,0,0.-2) 2 C O N T I N U E C A L L PLOT(l.,2.,3) D O 3 I=1,N C A L L SYMBOL(PYS(I),HT(I),.010,l,0.,-2) 3 C O N T I N U E C A L L PLOT(l.,2.,3) D O 4I=1,N C A L L SYMBOL(PALF(I),HT(I),.010,2,0.,-2) 4 C O N T I N U E C A L L PLOT(l.,2.,3) D O 5 1=1 ,N C A L L SYMBOL(T(I),HT(I),.010,11,0.-2) 5 C O N T I N U E C A L L PLOT(l.,2.,3) D O 6 I=1,N C A L L SYMBOL(PTG(I),HT(I),0.01,5,0.,-2) 6 C O N T I N U E C A L L SYMBOL(2.0,10.0,0.08,0,0.,-1) C A L L SYMBOL(2.2,10.0,0.08,'P-CO2 (ATM)',0.,11) C A L L SYMBOL(3.5,10.,0.08,1,0.,-1) . C A L L SYMBOL(3.7,10.,0.08,'P-H2O (ATM)',0.,11) C A L L SYMBOL(5.0,10.0,0.08,2,0.,-1) C A L L SYMBOL(5.2,10.0,0.08,'CO2 LOADING)',0.,11) CALL SYMBOL(2.0,9.7,0.08,11,0.,-1) CALL SYMBOL(2.2,9.7,0.08,'LIQUID TEMP. (C)',0.,16) CALL SYMBOL(3.5,9.7,0.08,5,0.,-1) CALL SYMBOL(3.7,9.7,0.08,'GAS TEMP. (C)',0.,13) CALL PDATA(PEG,PEC,PET,PHT,NEX) DO 1001 I=1,NEX EG = 1.+ (PEG(I)/0.03) EC = 1. + (PEC(I)/.l) ET = l.+(PET(I)/10.) EH = 2.+(PHT(I)/100.) CALL SYMBOL(EG,EH,.12,0,0.-1) CALL SYMBOL(EC,EH,.12,2,0.-1) CALL SYMBOL(ET,EH,.12,11,0.,-1) 1001 CONTINUE CALL SYMBOL(4.,9.25,.25,'RUN# T22',0,8) CALL PLOTND STOP END Q ************************************ c SUBROUTINE CHACK(NIN,ALF,LM,TL,YA,YB,YS,TG,Z,NOUT) C IMPLICIT REAL*8(A-M.O-Z) C WRITE(6,990) 990 FORMAT(/' :::: INTERMEDIAD CALCULATION RESULTS') WRITE(6,991) ALF 991 FORMAT(/' C02 LOADING ',F10.5,' ') WRITE(6,993) LM 993 FORMATC LIQUID MOLAR VEL. ',F10.5,' G-MOL/SEC.CM2') WRITE(6,994) TL 994 FORMATC LIQUID TEMP. ',F10.5,' C) WRITE(6,995) YA 995 FORMAT(/' MOL FRAC. OF C02 \F10.5) WRITE(6,996) YB 996 FORMATC MOL FRAC. OF AIR \F10.5) WRITE(6,997) YS 997 FORMAT(' M 0 L FRAC. OF H20 ',F10.5) WRITE(6,998) TG 998 FORMATC GAS TEMP. \F10.5,' C) WRITE(6,999) Z 999 FORMATC THE HEIGHT \F10.5,' CM.'/) NOUT = NOUT + 1 C RETURN END Q ********************************************** c SUBROUTINE CKOUT(Z,ALF,YA,TL,N,NDUM) C IMPLICIT REAL*8(A-M,0-Z) C WRITE(7,990) 990 FORMAT(/ ' :::: INTERMEDIAD CALCULATION RESULTS') WRITE(7,999) Z 999 FORMAT(/ ' THE HEIGHT ',F10.5,' CM.'/) PYA = 100 *YA/(1.+YA) WRITE(7,995) PYA 995 FORMAT(' C02 CONC. (%) '.F10.5) WRITE(7,991) ALF 991 FORMATC C02 LOADING \F10.5,' ') WRITE(7,994) TL 994 FORMATC LIQUID TEMP. \F10.5,' C ) C NDUM=NDUM+1 RETURN END Q ************************************************** SUBROUTINE PDATA(EG,EC,ET,EH,NEX) IMPLICIT REAL*8(A-H,0-Z) DIMENSION EG(20),EC(20),ET(20),EH(20),G(20),C(20),T(20),H(20) NEX=7 D A T A H/0.000,110.,220.,330.,440.,550.,655./ DATA G/.1910,.1280,.0530,.0120,.0010,.000,-0/ C C = C02 LOADING DATA C/.443,.292,.1250,:0330,0000,.0000,.0000/ D A T A T/47.0,45.0,29.0,21.0,19.0,19.,19./ DO 10 I=1,NEX EH(I)=H(I) EG(I)=G(I) EC(I)=C(I) 10 ET(I)=T(I) RETURN END Q ************************************************ SUBROUTINE SOL(TLK,CTOT,ALF,PEC02) IMPLICIT REAL*8(A-H,0-Z) C CAL PC02 A T EQUILIBRIUM IF(ALF.LE.0.3) PECO2=0.0 IF(ALF.LE.0.3) GOTO 100 DX1 = 2.9410 + (1.5940D+01)*(ALF) - (6.3439D-00)*(ALF**2) DX2=(2.6218D-01)*(1./ALF)+7.2388D-1*CTOT-(7.881D-02)*(CTOT**2) DX3 = -(8.9512D-02)*(TLK) + (1.8524D-04)*(TLK**2) PEC02 = (DXl+DX2+DX3)/760. 100 CONTINUE RETURN END 

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