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Prediction Of Enthalpy Of Saturated Paraffin Hydrocarbon Mixtures
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Prediction Of Enthalpy Of Saturated Paraffin Hydrocarbon Mixtures

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Content PREDICTION OF ENTHALPY OF SATURATED PARAFFIN HYDROCARBON MIXTURES by Edward L o n g s tr e th G horm ley A D i s s e r t a t i o n P r e s e n te d t o t h e FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In P a r t i a l F u lf illm e n t o f th e R eq u irem en ts f o r t h e D egree DOCTOR OF PHILOSOPHY (C h em ical E n g in e e r in g ) Jan u ary 1971 71 - 21,457 GHORMLEY, Edward L o n g s tr e t h , 19 2 3 - PREDICTION OF ENTHALPY OF SATURATED PARAFFIN HYDROCARBON MIXTURES. U n iv e r s it y o f S o u th e rn C a l i f o r n i a , Ph.D., 1971 E n g in e e r in g , c h e m ic a l University Microfilms, A XERO X Com pany, Ann Arbor, M ichigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED UNIVERSITY O F SO UTH ERN CALIFORNIA TH E GRADUATE SCH O O L UNIVERSITY PARK LOS A N G ELES, C A LIFO R N IA 9 0 0 0 7 This dissertation, written by Edward L o n g s tr e th G horm ley under the direction of //is.... Dissertation Com­ mittee, and approved by all its members, has been presented to and accepted by The Gradu­ ate School, in partial fulfillment of require­ ments of the degree of D O C T O R O F P H I L O S O P H Y I'Tti O Dean Date.J33^3F.Z.2921. DISSERTATION COMMITTEE . & L - Chairman _fr?. ............ ACKNOWLEDGMENTS The a u th o r t a k e s t h i s o p p o r tu n ity t o th a n k t h o s e p e r s o n s who w ere p a r t i c u l a r l y h e l p f u l in th e c o m p le tio n o f t h i s w ork . I f i r s t w ou ld l i k e t o th a n k t h e f a c u l t y and :s t a f f a t U .S .C . f o r t h e i r c o o p e r a t io n in m aking i t p o s s i b l e !f o r me t o do t h i s r e s e a r c h w ork in a com p lex s t r u c t u r e o f j s c h e d u le s and com m itm en ts. ! D r. J . M. L e n o ir h a s b e e n p a r t i c u l a r l y h e l p f u l in ; h is g u id a n c e and en cou ragem en t in t h e d ev elo p m en t o f t h i s p a p e r . D r. C. J . R e b e rt h a s added t o t h e c l a r i f i c a t i o n o f t h e p r e s e n t a t io n by s u g g e s te d s i m p l i f i c a t i o n s o f some o f t h e c o n c e p ts w h ich a r e d e v e lo p e d . P r o f e s s o r E . K. S p r in g e r h a s p r o v id e d a d d i t io n a l h e lp and en cou ragem en t tow ard th e |s u c c e s s f u l c o m p le tio n o f t h i s p a p e r . I a l s o w ant t o th a n k th e members o f my fa m ily fo r t h e i r en cou ragem en t and su p p o r t d u r in g t h i s p e r io d o f a c - i c e l e r a t e d a c t i v i t y . In p a r t i c u l a r , I w ant t o a ck n o w led g e t h e l o y a l su p p o r t o f my w if e o v e r t h e e n t i r e p e r io d le a d ­ in g t o t h e p r e p a r a tio n o f t h i s d ocu m en t. I A d d it io n a l m en tio n s h o u ld b e made o f th e ( S ig n if ic a n t c o n t r ib u t io n made b y t h e N o rth A m erican Rock­ w e l l C o r p o r a tio n tow ard t h e c o m p le tio n o f t h i s w ork . I . u t TABLE OF CONTENTS Page ACKNOWLEDGMENTS.............................. 11 INDEX OF F IG U R E S ........................................................................................ v l LIST OF T A B L E S ................................................................................................ v i l i I . THE PRO BLEM .................................................................................. 1 I I . PREVIOUS W O R K ............................................................................. 6 A . S o u r c e s o f E n th a lp y D a ta ......................... 6 B . H eat C a p a c ity D a t a ................................................. 8 C. H eat o f V a p o r iz a tio n . . . . . . . . . . . 9 D. E n th a lp y o f M ixed H yd rocarb on s .................... 10 E . The C r ic o n d e n th e r m ................................................. 13 I I I . THE ENTHALPY E N V E L O PE ................................................. 17 The Mean E n th a lp y C u r v e ................................... 17 B . S a tu r a te d Vapor and L iq u id E n th a lp ie s . . 22 C. S lo p e o f th e S a tu r a te d E n th a lp y C u rves . . 26 D. E n th a lp y P r e d i c t i o n o f P ure H yd rocarb on s . 27 IV . PREDICTION METHODS FOR BINARY MIXTURES . . . . 32 A . S p e c i a l P r o p e r t ie s o f M i x t u r e s ................... 32 B. P r e d ic t io n o f t h e C r ic o n d e n th e r m .............. 39 C. E n th a lp y P r e d ic t io n o f M eth an e-P rop an e M i x t u r e s ........................................................................... 43 iv P age D. E n th a lp y P r e d ic t io n o f P en ta n e -H e x a d e ca n e M i x t u r e s .................................................................................. 43 E . E n th a lp y P r e d ic t io n o f a P ro p a n e- Z so p en ta n e M ix tu re .................................................... 51 V. ACCURACY OP CALCULATED E N T H A L P IE S........................... 53 V I. CONCLUSIONS.................................................................................... 58 V I I . REFERENCES......................................................................................... 60 APPENDICES....................................................................................................... 63 A. N o m e n c la t u r e ........................................................................ 64 B. C a lc u la te d E n th a lp y V a lu e s o f Pure B u t a n e ........................................................ 66 C. C a lc u la te d E n th a lp y V a lu e s o f a M ethane- P rop ane M ix tu re .............................................................. 68 INDEX OF FIGURES I Figure No. 1 Mean E n th a lp y C u rves o f t h e A l i p h a t ic H yd rocarb on s ........................................................................ 2 C o r r e la t io n o f % w it h M o le c u la r W eigh t 3 S a tu r a te d E n th a lp y Boundary f o r P rop ane | 4 S a tu r a te d E n th a lp y Boundary fo r B u tan e . . 5 S a tu r a te d E n th a lp y Boundary f o r H exane . . 6 S a tu r a te d E n th a lp y Boundary f o r O ctan e . . 7 Mean E n th a lp y C u rves fo r M ix tu r e s o f M ethane in P rop an e ......................................................... 8 C o r r e la t io n o f C m /C h c w ith . . . . 9 V a r ia tio n o f Tc c /T gc w ith C o m p o sitio n . . 10 C o r r e la t io n o f (b + c ) w it h € ............................ 11 S a tu r a te d E n th a lp y Boundary f o r a M ix tu re C o n ta in in g 95% M ethane in P rop ane . . . . 12 s a t u r a t e d E n th a lp y Boundary f o r a M ix tu re C o n ta in in g 49.4% M ethane in P ropane . . . 13 S a tu r a te d E n th a lp y B oundary f o r a M ix tu re C o n ta in in g 23.4% M ethane i n P rop ane • . . 14 Mean E n th a lp y C u rves f o r M ix tu r e s o f P en ta n e in H exad ecane ............................................... 15 S a tu r a te d E n th a lp y B oundary fo r a M ix tu re C o n ta in in g 58.7% P en ta n e i n H exad ecan e . . i i j I vi Page 19 25 28 29 30 31 34 37 38 42 44 45 46 4 8 49 | F ig u r e N o. P age i 16 S a tu r a te d E n th a lp y Boundary f o r a M ix tu re C o n ta in in g 79.4% P en ta n e in H exad ecan e . . 50 17 S a tu r a te d E n th a lp y Boundary f o r a M ix tu re ! C o n ta in in g 43% P ropane in I s o p e n ta n e . . . 52 vii :Table j i i i h i i v i l i LIST OF TABLES Page S o u r c e s o f E n th a lp y D a t a .............................................. 7 D e v ia t io n o f C a lc u la te d P ure Component E n t h a l p i e s ........................................................................................ 56 D e v ia tio n o f C a lc u la t e d E n th a lp ie s o f B in a r y M i x t u r e s ......................................................................... 57 I i [ 1 1 j I I . THE PROBLEM i The e n g in e e r in g d e s ig n o f modern c h e m ic a l p r o c e s s i sy s te m s r e q u ir e s p r e c i s e k n o w led g e o f t h e e n th a lp y o f t h e m a t e r ia ls u se d in th e p r o c e s s . H ydrocarbon p r o c e s s in g u s u ­ a l l y i s c o n c e r n e d w it h th e v a p o r iz a t io n o r c o n d e n s a tio n o f I s a t u r a t e d f l u i d s . Such p r o c e s s e s r e q u ir e a c c u r a te e n th a lp y i I d a ta a lo n g th e lo c u s o f t h e s a t u r a t e d vap or and l i q u i d . I V a p o r iz a tio n o c c u r s when th e t r a n s l a t i o n a l e n e r g y o f t h e m o le c u le e x c e e d s t h e f o r c e s o f a t t r a c t i o n b etw een m o le­ c u l e s . The l a t e n t h e a t o f v a p o r iz a t io n o f a m a t e r ia l i s th e h e a t r e q u ir e d t o v a p o r iz e a s p e c i f i e d amount o f th e l i q u i d u n der s p e c i f i c c o n d it io n s o f te m p e r a tu r e and p r e s ­ s u r e . The l a t e n t h e a t o f v a p o r iz a t io n o f a g iv e n f l u i d i s |a c h a r a c t e r i s t i c p r o p e r ty o f t h a t m a t e r ia l. The p r e d i c t i o n !o f th e e n th a lp y or h e a t o f v a p o r iz a t io n o f a p u re compound r e q u ir e s k n ow led ge o f how f a c t o r s su ch a s te m p e r a tu r e , p r e s s u r e , m o le c u la r w e ig h t , and c h e m ic a l s p e c i e s a f f e c t it h e e n t h a lp y o f th e m a t e r ia l. j j Therm al p r o p e r t ie s o f m ix tu r e s a r e more d i f f i c u l t j i t o p r e d ic t b e c a u s e o f th e i n t e r a c t i o n b e tw e en m o le c u le s , j E n t h a lp ie s o f m ix tu r e s h a v e b e e n c a lc u l a t e d f o r many y e a r s 1 " " I 2 ! u s in g t h e rn olal a v e r a g e o f t h e p u re com ponent e n t h a l p i e s . T h is p r o c e d u r e i s q u i t e a c c u r a t e a t low p r e s s u r e s and te m p e r a tu r e s , s i n c e a t v e r y low p r e s s u r e s a l l g a s e s b eh ave i d e a l l y , and t h e h e a t o f m ix in g o f t h e g a s e o u s m o le c u le s i s z e r o . H ow ever, a s th e te m p e r a tu r e and p r e s s u r e i n ­ c r e a s e , g a s e s c e a s e t o be i d e a l , and th e u s e o f p u re compo­ n e n t e n t h a l p ie s becom es i n c r e a s i n g l y in a c c u r a t e . The method o f p r e d i c t i o n d e v e lo p e d in t h i s t h e s i s t r e a t s t h e m ix tu r e s a s an e n t i t y , arid th u s a v o id s th e n e c e s s i t y o f i n d i v i d u a l l y d e f i n i n g t h e e f f e c t s o f m ix in g on th e m ix tu r e e n t h a lp y . The p rob lem o f d e f in in g th e e n th a lp y o f a h y d r o c a r ­ bon m ix tu r e i s f u r t h e r c o m p lic a te d b y th e i r r e g u l a r i t y o f th e v a p o r - liq u id e n v e lo p e . The maximum vap or p r e s s u r e o f a b in a r y m ix tu r e o f a l i p h a t i c h y d ro ca rb o n s can e x c e e d th e c r i t i c a l p r e s s u r e o f e i t h e r o f th e p u re com p on en ts b y a c o n s id e r a b le am ount. S i m i l a r l y , th e maximum l i q u i d tem p er­ a tu r e o f a m ix tu r e o r c r ic o n d e n th e r m ca n e x c e e d t h e c r i t i c a l te m p e r a tu r e o f t h e m ix tu r e . The "tim e h on ored" p r a c t i c e o f p r e d i c t i n g c r i t i c a l p r o p e r t i e s o f m ix tu r e s u s in g m o la l a v e r a g e p r o p e r t i e s can in tr o d u c e c o n s id e r a b le e r r o r i n t o th e r m a l c a l c u l a t i o n s i n v o lv in g m ix t u r e s . In t h e c r i t i c a l r e g io n th e e n th a lp y o f t h e l iq u i d 3 j a p p r o a c h e s t h a t o f t h e v a p o r , and t h e h e a t o f v a p o r iz a t io n o f th e l i q u i d a p p r o a c h e s z e r o . One or more o f th e m ix tu r e com p on en ts may e x i s t in a l iq u i d s t a t e t h a t e x c e e d s t h e I ;c r i t i c a l c o n d it io n s o f th e p u re com p on en t. M ethods o f p r e ­ d i c t i n g th e e n th a lp y o f a m ix tu r e o f h y d r o c a r b o n s u n d er j t h e s e c o n d it io n s a r e s e v e r e l y lim i t e d in b o th ra n g e and a c - c u r a c y . ! F u r th e r p ro b lem s d e v e lo p when an a tte m p t i s made t o p r e d ic t t h e s a t u r a t e d e n th a lp y e n v e lo p e o f a s u b s ta n c e a s ;a f u n c t io n o f te m p e r a tu r e . In a p l o t o f e n t h a lp y v e r s u s te m p e r a tu r e fo r a p u re com p on en t, th e e n th a lp y o f th e |v a p o r a p p r o a c h e s a Maximum a t a p o in t o f t h e c u r v e n ea r t h e c r i t i c a l te m p e r a tu r e and th e n d e c r e a s e s in v a lu e . T h is ty p e o f v a r i a t i o n p r e c lu d e s t h e p r e d i c t i o n o f e n th a lp y in -th e c r i t i c a l r e g io n u s in g sta n d a r d h e a t c a p a c it y d a ta a l o n e . A g r e a t d e a l o f e f f o r t h a s b een a p p lie d in th e p a s t j a tt e m p tin g t o p r e d ic t e n th a lp y u s in g th e C la p ey ro n e q u a tio n com bined w it h an e q u a tio n o f s t a t e . A u n iq u e f e a t u r e o f t h i s t h e s i s i s t h a t d a ta a r e d e f in e d fo r t h e s a t u r a t e d c o n ­ d i t i o n o n ly , and t h e m ethod o f p r e d i c t i o n d e l i b e r a t e l y |a v o id s t h e u s e o f an e q u a tio n o f s t a t e . 4 An a c c u r a te m ethod o f p r e d i c t i n g th e s a t u r a t e d e n - i t h a lp y e n v e lo p e o f p u re and m ixed h y d ro ca rb o n s w i l l p r o v id e a u s e f u l t o o l f o r t e s t i n g th e c o n s is t e n c y o f e x p e r im e n ta l j d a t a . F r e q u e n tly e x p e r im e n ta l th e r m a l d a ta a r e r e s t r i c t e d in s c o p e by th e m e c h a n ic a l l i m i t s o f t h e t e s t f a c i l i t y . The m ethod o f p r e d i c t i o n o u t lin e d in t h i s p ap er w i l l make i isu ch d a ta more v a lu a b le by m aking i t p o s s i b l e t o e x tr a p o - j la t e e x p e r im e n ta l d a ta up t o t h e c r i t i c a l te m p e r a tu r e . An e f f e c t i v e m ethod o f p r e d i c t i n g th e is o th e r m a l jheat o f v a p o r iz a t io n o f p u re com p onents and b in a r y m ix tu r e s I o f h y d r o c a r b o n s up t o th e c r i t i c a l r e g io n i s p r e s e n t e d . iP ro ced u res a r e o u t lin e d fo r th e p r e d i c t i o n o f th e c r i c o n ­ dentherm o f a l i p h a t i c h y d ro ca rb o n m ix tu r e s . A m ethod o f p r e d i c t i n g th e s a t u r a t e d e n th a lp y e n v e lo p e o f p u re and im ixed h y d r o c a r b o n s i s p r e s e n t e d . In a d d i t i o n , e q u a tio n s I a r e d e v e lo p e d f o r th e p r e d i c t i o n o f th e e n th a lp y ch a n g e a s a f u n c t io n o f te m p e r a tu r e fo r a s a t u r a t e d v a p o r and a jbubble p o in t l i q u i d . .. .. The m ethod o f c a l c u l a t i o n o u t lin e d in t h i s p a p er i s I s u i t a b l e fo r e i t h e r m anual or c o m p u te r iz e d o p e r a t io n , js in c e th e m ethod i s a n a l y t i c a l and r e q u ir e s no s t o r a g e o f jla r g e ta b u la r f u n c t i o n s , a com puter may b e e a s i l y 5 programmed fo r c a l c u l a t i o n o f eo m p lex d i s t i l l a t i o n and a b - |s o r p t i o n f u n c t i o n s . The m ethod o f c a l c u l a t i o n i s s im p le in j c o n c e p t s o t h a t m anual c h e c k s can be made a t any p h a se in |t h e c a l c u l a t i o n p r o c e d u r e . The m ethod w i l l p r o v id e a h ig h |d e g r e e o f a c c u r a c y when u sed t o p r e d ic t e n th a lp y v a l u e s . j I I t a l s o e x te n d s t h e r a n g e o f e x i s t i n g th e r m a l d a ta w e l l I jbeyond p r e s e n t l i m i t s o f a p p l i c a t i o n . I I . PREVIOUS W O R K j |A . S o u r c e s o f E n th a lp y D ata | Much w ork h a s b een exp en d ed in th e e x p e r im e n ta l i j I m easurem ent o f e n th a lp y o f c h e m ic a l com pounds. M ost o f th e I I w ork h a s b e e n a p p lie d t o t h e d ev elo p m en t o f e n th a lp y d a ta i j fo r p u re s u b s t a n c e s . The A m erican P e tr o le u m I n s t i t u t e h a s i jsu p p o r te d r e s e a r c h in t h i s f i e l d f o r many y e a r s , and h a s p u b lis h e d c o m p r e h e n siv e t a b l e s o f e n th a lp y d a ta f o r t h e p u re h y d ro ca rb o n compounds ( 1 ) . O n ly a lim i t e d amount o f d a ta i s a v a i l a b l e w h ich a c c u r a t e ly d e f i n e s t h e e n t h a lp y o f a m ix tu r e o f tw o or more s u b s t a n c e s . W ith ou t a tte m p tin g t o l i s t a l l t h e c o n t r ib u - ! t o r s in th e f i e l d , c e r t a i n i n v e s t i g a t o r s sh o u ld b e m en- | i t io n e d b e c a u s e o f t h e i r s i g n i f i c a n t c o n t r ib u t io n s o f e n - |t h a l p y d a ta fo r m ix t u r e s . L e n o ir ( 1 5 ,1 6 ,1 7 ,1 8 ,1 9 ) and ! P ow ers ( 2 ,4 3 ,4 4 ) h a v e s t u d ie d t h e e n th a lp y o f v a r io u s h y - I | d ro ca rb o n m ix tu r e s e x t e n s i v e l y , and S m ith (2 1 ,3 9 ) h a s m ea- ! su r e d t h e e n th a lp y o f v a r io u s m ix tu r e s o f p o la r and n o n - i i p o la r com pounds. T a b le I su m m arizes t h e e n th a lp y d a ta | | s o u r c e s t h a t w ere u se d in t h e p r e p a r a tio n o f t h i s d i s s e r t a - ! t i o n . i j i 6 TABLE I SOURCES OF ENTHALPY DATA Heavy Component L ig h t Comp. C1 c 2 C3 c 4 i c 5 C5 C6 c 7 C8 C16 C1 (1) (2 ,2 0 ,4 0 ) C2 (1) e 3 (1,40) (15) c 4 (1) i$ 5 (1) c 5 (1) (19) (17) C6 (1) C7 (1) C8 (1,19) c 16 (17) N o te: Components a r e I d e n t i f i e d by s u b s c r ip t w h ich i n d ic a t e s th e number o f carbon.-atom s in a m o le c u le . A p r e f i x o f ( i ) i d e n t i f i e s th e iso m e r . -4 3 [ I B . H eat C a p a c ity D ata 1 r The v a r i a t i o n o f e n th a lp y o f h y d ro c a r b o n f l u i d s ca n b e p r e d ic t e d u s in g t a b u la t e d h e a t c a p a c it y d a t a . C o n v e n i- ! | e n t t a b l e s fo r g a s e s a t low p r e s s u r e h a v e b e e n p u b lis h e d ! b y Kobe (1 4 ) and b y t h e A m erican P e tr o le u m I n s t i t u t e ( 1 ) . ; H eat c a p a c it y e q u a t io n s fo r a v a r i e t y o f s u b s t a n c e s a r e i j sum m arized b y H ougen, W atson , and R agatz (1 0 ) and b y S h er­ wood and R eid ( 3 1 ) . Shaw (34) h a s o u t lin e d a m ethod o f p r e d i c t i n g h e a t | c a p a c i t i e s o f l i q u i d s a t room te m p e r a tu r e and a m b ien t p r e s - ! s u r e u s in g a d d i t i v e c o n s t a n t s w h ich a r e grou p ed b y m ole­ c u la r s t r u c t u r e . Hadden h a s d e v e lo p e d e m p ir ic a l e q u a t io n s ' d e s c r ib in g th e h e a t c a p a c it y o f s p e c i f i c h om ologou s s e r i e s ; I l i q u i d h y d r o c a r b o n s up t o t h e norm al b o i l i n g p o in t o f t h e l i q u i d ( 9 ) . D ata o f t h i s ty p e a r e l i m i t e d t o u s e a t low p r e s s u r e c o n d i t i o n s . At h ig h p r e s s u r e g a s e o u s e n t h a l p ie s c a l c u l a t e d from low p r e s s u r e h e a t c a p a c i t i e s m ust b e c o r r e c t e d f o r p r e s - I s u r e . L iq u id e n t h a l p ie s a r e l e s s s e n s i t i v e t o p r e s s u r e i e f f e c t s , b u t f o r a c c u r a t e w ork i t i s n e c e s s a r y t o a p p ly a I | p r e s s u r e c o r r e c t io n t o l i q u i d e n t h a l p ie s c a lc u l a t e d from i h e a t c a p a c it y d a t a . E q u a tio n s f o r p r e d i c t i n g t h e e f f e c t j o f p r e s s u r e on e n t h a lp y , a r e a v a i l a b l e i n sta n d a r d th erm o - idynam ics t e x t s (5). ! I jC. H eat o f V a p o r iz a tio n ! A m ethod o f p r e d i c t i n g t h e h e a t o f v a p o r iz a t io n o f |p u re com pounds was f i r s t d e s c r ib e d by T K iesen in 1897 (40) . jH is c o r r e l a t i o n i s shown in e q u a tio n ( 1 ) . S u b s e q u e n tly , | o th e r a u th o r s h a v e i n v e s t i g a t e d t h i s c o r r e l a t i o n and f u r - ■ther d e f in e d th e c o n s t a n t s w h ic h h e f i r s t p r e d ic t e d . A = K{TC - T)** (1) w h ere K and e* = c o n s t a n t s , T = a b s o lu t e te m p e r a tu r e , Tc - c r i t i c a l te m p e r a tu r e , A = ^e a t o f v a p o r iz a t io n o f t h e m a t e r ia l a t te m p e r a tu r e T . The c o n s ta n t c* h a s b e e n shown t o h a v e a v a lu e o f abou t 0 .3 8 fo r m ost h y d r o c a r b o n s (3). F or o th e r m a t e r ia ls i t can v a r y from a b o u t 0.3 t o 0.4 (35). ! A 0 r e p r e s e n t s th e h e a t o f v a p o r iz a t io n o f t h e m a t e r ia l a t T = 0 a s shown in t h e f o l lo w in g e q u a t io n . j A 0 = K(Tc )°< (2) 10 ; D iv id in g e q u a tio n (1) b y e q u a tio n (2) e li m in a t e s K ! and e x p r e s s e s te m p e r a tu r e a s a g e n e r a liz e d red u ced tem pera* ! jtu r e , Tr , th u s i / \ = A 0 <1 - Tr )°^ (3) whfere Tr r e p r e s e n t s th e r a t i o T /T c . : T h is e q u a tio n may be u se d t o p r e d i c t t h e h e a t o f ; v a p o r iz a t io n o f a compound a s a f u n c t io n o f te m p e r a tu r e ju sin g a known h e a t o f v a p o r iz a t io n a t some c o n v e n ie n t tern- ! ip e r a tu r e su ch a s th e a tm o sp h e r ic b o i l i n g p o i n t . D iv id in g e q u a tio n (3) by i t s e l f f o r tw o s e t s o f c o n d it io n s g iv e s .3 8 T h is e q u a tio n i s f r e q u e n t ly r e f e r r e d t o a s th e W atson C or- i r e l a t i o n ( 4 1 ) . D. E n th a lp y o f M ixed H ydrocarbon s ! S t e i n and M artin (3 7 ) h a v e o u t lin e d a s i m p l i f i e d p r o c e d u r e t o p r e d ic t t h e i s o b a r i c h e a t o f v a p o r iz a t io n o f i I a m ix tu r e by a s t e p w is e su m m ation . The com p on en ts o f th e j m ix tu r e a r e t r e a t e d i n d i v i d u a l l y . The is o th e r m a l h e a t o f v a p o r iz a t io n f o r e a c h com ponent i s s e l e c t e d a t a low r I _________________________________________ _____________________________________________ 11 p r e s s u r e w h ere A i s known. N e x t, v a p o r s a r e t r e a t e d a s 1 i p e r f e c t s g a s e s , and t h e g a se o u s m ix tu r e i s h e a te d from t o T2 . I f t h e p r e s s u r e a t T2 i s lo w , no fu r t h e r c o r r e c t io n s ja r e s u g g e s t e d . H ow ever, i f th e p r e s s u r e a t T2 i s h ig h , a 1 ;p r e s s u r e c o r r e c t io n i s recomm ended t o in c lu d e t h i s e n th a lp y d i f f e r e n c e in t h e c a l c u l a t i o n . To make t h i s c o r r e c t io n i t | i s n e c e s s a r y t h a t th e dew p o in t e n v e lo p e be f u l l y d e f in e d , 1 and t h a t t h e P-V -T p r o p e r t i e s o f t h e m ix tu r e b e known. I S te v e n s and Thodos (38) h a v e e s t im a t e d t h e s a t u r a t e d e n th a lp y o f h y d ro ca rb o n m ix tu r e s b y f i r s t c a l c u l a t i n g th e j v a p o r e n th a lp y a t z e r o p r e s s u r e u s in g th e m o la l a v e r a g e o f th e e n t h a l p ie s o f th e p u re co m p o n en ts. An e n th a lp y c o r r e c ­ t i o n t o th e sta n d a r d va p o r s t a t e w as th e n c a lc u l a t e d from t h e eq u a t io n i H* - H = Tc (mTr + K )1 /P (5) i j The e n th a lp y c o r r e c t io n t o th e s a t u r a t e d l i q u i d s t a t e was c a l c u l a t e d from th e f o l lo w in g e q u a tio n : 1 r H* O h + 1QTC(a - bTr ) 1 / r (6 ) | w h ere H* = t h e e n th a lp y o f an i d e a l g a s , H = th e s a t u r a t e d v a p o r e n t h a lp y , 1 i h = t h e s a t u r a t e d l i q u i d e n t h a lp y . 12 m ,p ,T c ,a ,b , and r = f u n c t io n s o f th e c r i t i c a l c o m p r e s s ib il­ i t y o f th e m ix tu r e . E q u a tio n s (5) and (6 ) w ere d e r iv e d from H ougen, W atson , and R a g a tz 1 (1 0 ) G e n e r a liz e d T a b le s o f th e P ro p er­ t i e s o f S a tu r a te d P ure V apors and L iq u id s . The r ed u c ed !te m p e r a tu r e and c o m p r e s s i b i l i t y o f th e m ix tu r e w ere c a lc u - i |l a t d d u s in g m o la l a v e r a g e p r o p e r t i e s o f t h e co m p o n en ts. 3 ;The a u th o r s show ed t h a t th e m ethod c o u ld b e u sed t o p r e d ic t ;t h e e n th a lp y o f s e v e r a l h y d ro ca rb o n m ix tu r e s w ith an e r r o r i o f from tw o t o f i v e p e r c e n t . O r e n t lic h e r and P r a u s n it z (2 4 ) u t i l i z e d s t a t i s t i c a l therm od ynam ic th e o r y t o p r e d i c t th e e n th a lp y o f s im p le d e n se f l u i d m ix t u r e s . The e n t h a lp y i s t h e sum o f t h r e e . term s H - E + U + RTz (7) w h ere E = th e i d e a l g a s e n th a lp y o b ta in e d from lo w p r e s s u r e h e a t c a p a c it y d a t a , U = th e p o t e n t i a l e n e r g y c o n t r ib u t io n o r r e s i d u a l e n e r g y d e f in e d b y t h e f o l lo w in g e q u a tio n p o ° u ~ / ° y J 0i j (r)g±j (r)4 T T r 2dr (8) | o i i _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ i r = in t e r m o le c u la r d i s t a n c e , R = th e g a s law c o n s t a n t , T = te m p e r a tu r e , g^j = p a ir d i s t r i b u t i o n f u n c t io n fo r an i j p a i r , # i j = p o t e n t i a l f u n c t io n f o r an i j p a i r , z = c o m p r e s s i b i l i t y . M ixed h y d ro c a r b o n e n t h a l p ie s f o r b o th l iq u i d s and ;v a p o r s w ere c a l c u l a t e d u s in g a com puter program d e v e lo p e d j I b y O r e n t lic h e r . The m ethod i s r e p o r te d t o g i v e an e r r o r o f ; l e s s th a n 10%. I t d o e s n o t d e f in e th e s a t u r a t e d or m ixed p h a se r e g io n . E d m iste r (6 ) u sed t h e e q u ilib r iu m (K) c h a r ts t o e v a lu a t e h e a t s o f v a p o r iz a t io n o f i n d iv i d u a l com ponents w it h an e q u a t io n d e r iv e d b y Dodge (5) f o r i d e a l s o l u t i o n s I w h ere A H i s in d e p e n d e n t o f te m p e r a tu r e . T h ese a ssu m p tio n s p r e c lu d e u s e o f t h e e q u a tio n in th e c r i t i c a l r e g io n w h ere & H i s o b v io u s ly n o t in d e p e n d e n t o f te m p e r a tu r e , s i n c e i t i ! r a p id ly a p p r o a c h e s z e r o a t t h e c r i t i c a l te m p e r a tu r e . i | E . The C rico n d en th erm i I The maximum te m p e r a tu r e o f th e v a p o r - liq u id 14 je n th a lp y e n v e lo p e o f a m ix tu re o f h y d ro c a r b o n s i s c a ll e d ■the c r ic o n d e n th e r m . P r e d ic t io n o f e n th a lp y a lo n g th e I !v a p o r - liq u id b ou nd ary r e q u ir e s a p r e c i s e k n o w led g e o f t h i s i !te m p e r a tu r e . The c r ic o n d e n th e r m and th e c r i t i c a l tem p era­ tu r e o f a p u re com ponent are i d e n t i c a l , but w it h m ixed com p on en ts t h e c r ic o n d e n th e r m c a n e x c e e d t h e c r i t i c a l tem - i p e r a tu r e s i g n i f i c a n t l y . Many d i f f e r e n t m eth od s h a v e b een d e v is e d t o p r e d ic t t h e c r i t i c a l te m p e r a tu r e s o f m ix tu r e s , ibut t h e r e a r e r e l a t i v e l y few p r o c e d u r e s fo r p r e d i c t i n g t h e |c r ic o n d e n th e r m . i M ix tu r e s o f a l i p h a t i c h y d ro c a r b o n s a r e s i m i la r in c h e m ic a l s t r u c t u r e , and in t h e i r th e r m a l p r o p e r t i e s . The c r ic o n d e n th e r m o f s u c h m ix tu r e s c a n ex ceed t h e p u re com­ p o n en t c r i t i c a l te m p e r a tu r e s b y a f a c t o r t h a t may be a s la r g e a s 2 , b u t su ch m ix tu r e s a r e c o n s i s t e n t i n t h e i r b e - j h a v io r , and may b e c o r r e la t e d u s i n g th e p r o c e d u r e s o u t lin e d in t h i s s t u d y . E t t e r and Kay (7 ) have d e v e lo p e d e m p ir ic a l e q u a tio n s |t o p r e d i c t t h e c r ic o n d e n th e r m o f a m ix tu r e o f a l i p h a t i c i [h y d r o c a r b o n s. D i f f e r e n t e q u a t io n s a r e p r e s e n t e d f o r v a r i - I jous m ix tu r e s o f l i g h t h y d r o c a r b o n s . Each e q u a t io n i s 1 j l i m i t e d t o a s p e c i f i c sy s te m , and i s n o t a p p l i c a b l e t o o th e r s y s t e m s . 15 S ilv e r m a n and T hodos (3 6 ) h a v e d e v e lo p e d an e m p ir i- | l e a l m ethod o f c a l c u l a t i n g t h e c r ic o n d e n th e r m o f b in a r y | i f ■hydrocarbon m ix t u r e s . T h ese a u th o r s u sed s t a t i s t i c a l t e c h - jn iq u e s t o c o r r e l a t e t h e c h a r a c t e r i s t i c p r o p e r t ie s o f t h e :s y s t e m s . The r e s u l t i n g c o r r e l a t i o n i s a com p lex p o ly n o m ia l !in w h ich t h e c o e f f i c i e n t s m ust b e c a lc u l a t e d from o th e r I T p o ly n o m ia l e q u a tio n s i n v o lv in g t h e r a t i o o f a tm o p p h eric i b o i l i n g p o i n t s o f t h e c o n s t i t u e n t s . i G r ie v e s and Thodos (8) p r e s e n t a group o f e m p ir ic a l e q u a tio n s f o r c a l c u l a t i n g t h e maximum te m p e r a tu r e and m axi­ mum p r e s s u r e o f h y d ro ca rb o n m ix t u r e s . The m ethod r e q u ir e s a k n ow led ge o f t h e m o la l a v e r a g e b o i l i n g p o i n t , t h e m o la l | a v e r a g e c r i t i c a l te m p e r a tu r e , t h e a tm o sp h e r ic b o i l i n g p o i n t , and t h e m ole f r a c t i o n o f t h e l i g h t com p on en t. Where m u ltico m p o n en t m ix tu r e s a r e t o b e i n v e s t i g a t e d , a s te p w is e i c a l c u l a t i o n p r o c e d u r e i s recomm ended t o o b t a in th e maximum i Item p era tu re and p r e s s u r e o f t h e l i q u i d m ix tu r e . The a c ­ c u r a c y o f th e p r o c e d u r e i s c o n s id e r a b ly red u c ed f o r m u lt i- com ponent m ix tu r e s . M ix tu r e s o f compounds from d i f f e r e n t c h e m ic a l fa m i- l i e s a r e much more ir r e g u la r and u n p r e d ic t a b le . Such m ix - i t u r e s d i f f e r from i d e a l s o l u t i o n b e h a v io r , and t h e v a r ia t i o n 16 o f th e c r i t i c a l te m p e r a tu r e and th e c r ic o n d e n th e r m i s e r ­ r a t i c . B in a r y m ix tu r e s o f a l i p h a t i c h y d ro ca rb o n s and c y - c ld h e x a n e e x h ib it t h e same in c r e a s e o f c r i t i c a l te m p e r a tu r e |a s th e a l i p h a t i c h y d r o c a r b o n s i f th e c r i t i c a l te m p e r a tu r e s j |o f th e com ponents a r e w id e ly d i s s i m i l a r . H ow ever, b in a r y j jmixfcfcnes w ith s i m i l a r c r i t i c a l te m p e r a tu r e s may c l o s e l y i ■approach t h e m o la l a v e r a g e c r i t i c a l te m p e r a tu r e or may ev en ! |h ave a s l i g h t r e d u c t io n in t h e c r i t i c a l te m p e r a tu r e b e lo w th e m o la l a v e r a g e . T h ese m ix tu r e s h a v e su ch a narrow b o i l ­ in g r a n g e th a t t h e c r ic o n d e n th e r m and th e c r i t i c a l tem p er a - tu r e a r e i n d i s t i n g u i s h a b l e . U n sa tu r a te d compounds su ch a s a c e t y l e n e or b e n z e n e when m ixed w ith a l i p h a t i c or n a p h th e n ic h y d ro c a r b o n s d i s ­ p la y e v e n more u n p r e d ic t a b le b e h a v io r . M ix tu res o f t h e s e ;d i s s i m i l a r c h e m ic a ls can e x h i b i t a d e f i n i t e r e d u c tio n o f |th e c r i t i c a l te m p e r a tu r e b e lo w th e m o la l a v e r a g e . No c o r ­ r e l a t i o n i s y e t a v a i l a b l e t h a t w i l l p r e d i c t t h i s t y p e o f I v a r ia t io n a c c u r a t e l y . I I I . THE ENTHALPY ENVELOPE IA. The Mean E n th a lp y Curve In 1886 C a i l l e t e t and M a th ia s (4 ) h y p o th e s iz e d t h a t i Ith e mean o f t h e v a p o r and l i q u i d d e n s i t i e s o f a compound i I c o u ld b e c o r r e l a t e d w ith te m p e r a tu r e a s a l i n e a r f u n c t io n . S u b seq u en t i n v e s t i g a t i o n s h a v e shown t h a t th e mean d e n s i t y | i s more a c c u r a t e l y r e p r e s e n te d by a q u a d r a tic e q u a tio n o f i :th e form : + / ° i ) — A + BT + CT2 (9) i w h ere g - d e n s i t y o f vap or ~ d e n s i t y o f l iq u i d T = te m p e r a tu r e A,B,C = s c o n s t a n t s ;T h is c o r r e l a t i o n p r o v id e s an a c c u r a t e m ethod o f p r e d i c t i n g i Ith e mean v a p o r - liq u id d e n s i t y up t o t h e c r i t i c a l tem p er a - | :t u r e . | | When t h e s a t u r a t e d v a p o r and l i q u i d e n t h a l p ie s o f a i |c h e m ic a l s u b s ta n c e a r e p l o t t e d a s a fu n c t io n o f te m p e r a tu r e , | i l 'an e n v e lo p e s i m i l a r t o t h e d e n s i t y e n v e lo p e i s fo rm ed . A I c o r r e l a t i o n o f e n t h a lp y w it h te m p e r a tu r e can b e o b ta in e d 18 by p l o t t i n g ^(H y + H^) v e r s u s te m p e r a tu r e . T h is c o r r e l a ­ t i o n r e p r e s e n t s t h e a v e r a g e o f t h e s a t u r a t e d vapor and l i q u i d e n t h a l p ie s up t o t h e c r i t i c a l te m p e r a tu r e . I t w i l l b e r e f e r r e d t o a s th e "mean" e n th a lp y o f t h e h yd rocarb on in th e rem a in d er o f t h i s d i s c u s s i o n . F ig u r e 1 show s th e v a r ia t i o n o f t h e mean e n th a lp y a s a f u n c t io n o f tem p era­ t u r e fo r s e v e r a l l i g h t h y d r o c a r b o n s. The mean e n th a lp y o f e a c h h y d ro ca rb o n can b e d e s c r ib e d b y a q u a d r a tic e q u a tio n o f t h e ty p e : J*(HV Hx ) = A + BT + CT2 (1 0 a ) w h ere Hy » e n th a lp y o f th e s a t u r a t e d v a p o r , = e n th a lp y o f th e b u b b le p o in t l i q u i d , A, B , and C a r e p o ly n o m ia l c o e f f i c i e n t s . The a b s o lu t e e n th a lp y o f a s u b s ta n c e i s h o t hnown. T h e r e fo r e , an a r b it r a r y te m p e r a tu r e i s u s u a l l y s e l e c t e d a t w h ich th e e n th a lp y o f th e l i q u i d i s assum ed t o be z e r o , and th e e n t h a lp ie s o f b o th th e v a p o r and t h e l iq u i d a r e m easured from t h i s p o i n t . The v a lu e o f t h e c o n s ta n t A i s d ep en d en t on t h e te m p e r a tu r e a t w h ich t h e l i q u i d e n th a lp y i s assum ed t o b e z e r o . The c o n s t a n t A r e p r e s e n t s t h e v a lu e o f + H^) when T e q u a ls z e r o . E x p e r im e n ta l d a ta 19 500 OCTANE HEXANE 400- BUTANE 4 - 1 300- PROPAN] ETHANE 200 100 600 300 400 500 700 800 900 1000 TEMPERATURE °R F ig u r e 1 Mean E n th a lp y C urves o f t h e A lip h a t ic H ydrocarbons 20 a r e n o t a v a i l a b l e in t h i s r e g i o n , and v a lu e s o f A d e r iv e d from e x t r a p o la t e d d a ta a r e e x tr e m e ly in a c c u r a t e . i I f th e c o n s t a n t A i s e lim in a t e d , a more a c c u r a te m ethod o f d e te r m in in g th e c o n s t a n t s o f t h e e q u a tio n r e ­ s u l t s . T h is m o d if ic a t io n can b e a c c o m p lish e d b y s u b s t i - j j t u t in g i n e q u a tio n ( 10a) a known v a lu e o f e n th a lp y ta k e n a t I ja c o n v e n ie n t te m p e r a tu r e , and s u b t r a c t in g t h i s e q u a tio n I :from e q u a tio n ( 1 0 a ) . The c o n s t a n t A i s e lim in a t e d in t h e ;s u b t r a c t i o n . E n th a lp y v a lu e s ta k e n from th e API T e c h n ic a l D ata j Book h a v e an e n t h a lp y b a se a t 260°R . At t h i s b a se te m p e r a - j t u r e - 0 and th e v a lu e o f (Hy + H^) i s e q u a l t o t h e h e a t o f v a p o r iz a t io n o f t h e m a t e r i a l. E n th a lp y v a lu e s from t h e API T e c h n ic a l D ata Book can b e s u b s t it u t e d in e q u a tio n j ( 10a ) t o g iv e : i j H >v260 = A + B (2 6 ° ) + C < 2 6 0 )2 ( 10b) | i 'S u b t r a c t in g t h i s e q u a tio n from (1 0 a ) g i v e s : I Jgdiy + Hx) « ^ > 2 6 0 + B(T " 260) + c ( t 2 “ 26° 2) j ( 10 c ) | T h is e q u a tio n i s e q u iv a le n t t o e q u a tio n ( 1 0 a ) , b u t t h e 21 \q u e s t io n a b le c o n s ta n t A h a s b e e n r e p la c e d b y ah e n th a lp y \v a lu e t h a t i s c h o se n in th e r a n g e o f e x p e r im e n ta l d a ta . I V a lu e s o f X 260 f o r s t r a ^9lllt c h a in a l i p h a t i c | h y d r o c a r b o n s cafi b e c o r r e la t e d w it h m o le c u la r w e ig h t by i ! Ith e f o llo w in g e q u a tio n : | ^ 2 6 0 = 2 3 5 / M ° * 2 t 1 1 ) j D i f f e r e n t i a t i o n o f e q u a tio n (1 0 a ) w ith r e s p e c t t o tem p era­ t u r e g i v e s : i d J s t H v + H j . ) , % | * -= B + 2CT (12) ; dT T h is e q u a t io n d e f in e s t h e h e a t c a p a c it y o f an e q u i-m o la l m ix tu r e o f va p o r and l i q u i d o f a p u re co m p o n en t. The !c u r v e s o f F ig u r e 1 a r e e s s e n t i a l l y p a r a l l e l t o ea ch o th e r ' from 260 R t o th e c r i t i c a l te m p e r a tu r e o f e a c h m a t e r ia l. | iT h is f a c t p e r m its t h e c o n c lu s io n t h a t e q u i- m o la l v a p o r - l i q u i d m ix tu r e s o f t h e a l i p h a t i c h y d ro c a r b o n s h a v e th e !sam e h e a t c a p a c it y , v a lu e s o f B and C u sed t o d e s c r ib e lo n e c u r v e can b e u s e d f o r t h e e n t i r e fa m ily o f c u r v e s . The i c o n s t a n t s B and C can b e e v a lu a t e d u s in g tw o o r more e x - ! i I p e r im e n ta l p o in t s from th e mean e n th a lp y -te m p e r a tu r e d i a - \gram f o r t h e m a t e r ia l. A more p r e c i s e m ethod o f o b ta in in g ! 22 ! t h e s e v a lu e s i s t o d e te r m in e th e p o ly n o m ia l c o e f f i c i e n t s by a l e a s t sq u a r e f i t o f a group o f e x p e r im e n ta l d a ta p o i n t s . The f o llo w in g v a l u e s o f B and C h a v e b e e n u sed t o I d e s c r ib e t h e mean e n t h a lp y c u r v e s o f th e a l i p h a t i c h y d ro ­ c a rb o n s from e th a n e t o h e x a d e c a n e . j B = 0 .2 2 1 (12) C = 2 .1 6 x 1 0“4 (13) i i The o r d in a t e o f e a ch c u r v e a t 260°R i s th e v a lu e o f h A 250 !from e q u a t io n ( 1 1 ) . The mean e n t h a lp y cu rv e f o r an y a l i ­ p h a t ic h y d ro ca rb o n can b e d e s c r ib e d b y u s in g t h e above c o n s t a n t s B and C and a v a lu e o f % ^ 2 6 0 ^rom t ^ ie AP* T ech­ n i c a l D a ta B ook. B . S a tu r a te d Vapor and L iq u id E n th a lp ie s j The is o th e r m a l h e a t o f v a p o r iz a t io n o f a s u b s ta n c e i s d e fin e d a s a f u n c t io n o f te m p e r a tu r e b y e q u a t io n ( 3 ) . T h is e q u a t io n p r e d i c t s t h e h e a t o f v a p o r iz a t io n o f a hydro- i .carb on q u i t e a c c u r a t e l y , i f th e c o r r e c t c r i t i c a l tem p er a - |tu r e i s u s e d . I f an e r r o r o c c u r s in t h e s e l e c t i o n o f Tc , i \a s i g n i f i c a n t e r r o r can o c c u r in t h e v i c i n i t y o f t h e c r i ­ t i c a l p o i n t . I f t h e Tc s e l e c t e d i s lo w er th a n t h e t r u e c r i t i c a l te m p e r a tu r e , a grap h o f e q u a tio n (3) w i l l c u r v e 23 upward in t h e r e g io n a p p r o a c h in g th e c r i t i c a l te m p e r a tu r e , jwhere (1 - Tr ) i s s m a ll. I f Tc i s g r e a t e r th a n t h e t r u e c r i t i c a l tem p er a tu r e* th e grap h w i l l c u r v e downward in t h e I same r e g i o n . E q u a tio n (3 ) m ust be d iv id e d by 2 t o malce i t s e n ­ th a lp y v a l u e s c o n s i s t e n t w ith t h o s e in e q u a tio n ( 1 0 c ) . By c o m b in in g e q u a tio n s (1 0 c ) w ith % o f e q u a tio n ( 3 ) , we o b - i i t a i n e x p l i c i t e q u a t io n s d e f i n i n g term s Ey and H^. A d d itio n r o f th e e q u a tio n s g i v e s an e x p r e s s io n w h ich p r e d i c t s t h e ;e n th a lp y o f th e s a t u r a t e d va p o r c u r v e up t o t h e c r i t i c a l p o i n t . I I I j H v = ^ -* 2 6 0 + B<T " 260) + C^ 2 " 26° 2) * % ^ o ( l * Tt >0f ! (1 4 ) By s u b t r a c t in g h o f e q u a tio n (3 ) from e q u a tio n (1 0 c) a :r e l a t i o n s h i p i s o b ta in e d fo r t h e l iq u i d e n th a lp y b o u n d a ry . H1 = * * 5 ^ 2 6 0 + B(T “ 260) + C (t2 ~ 26° 2) _ ^ o 11 " Tr ,0< | (1 5 ) f [ I T h is e q u a tio n d e s c r i b e s th e e n t h a lp y o f th e s a t u r a t e d ! liq u i d up t o th e c r i t i c a l p o i n t . E v a lu a tio n o f e q u a tio n s [( 1 4 ) and ( i 5 ) p r o v id e s c o m p le te d e f i n i t i o n o f t h e s a t u r a t e d v a p o r and l i q u i d e n th a lp y c u r v e s up t o t h e c r i ­ t i c a l te m p e r a tu r e . To a p p ly e q u a tio n s (1 4 ) and (1 5 ) t o a s p e c i f i c a l i ­ p h a t ic h y d ro ca rb o n th e c o n s t a n t s Tc , and < = < m ust be know n. The c r i t i c a l te m p e r a tu r e can b e o b ta in e d d i r e c t l y from t h e API T e c h n ic a l D ata Book fo r p u re h y d r o c a r b o n s . A v a lu e o f 0 .3 8 sh o u ld b e u sed f o r oC fo r t h e a l p h a t i c h y ­ d r o c a r b o n s o th e r th a n m eth a n e. M ethane c a n n o t be c o r r e ­ l a t e d w it h t h e o th e r h y d ro c a r b o n s and m ust be c o n s id e r e d s e p a r a t e l y . The h e a t o f v a p o r iz a t io n d a ta f o r m eth ane can b e c o r r e l a t e d u s in g a v a lu e o f 0 .3 5 fo r The v a lu e o f X Q c a n b e o b ta in e d b y e x p e r im e n t a lly m ea su r in g X a t s e v e r a l d i f f e r e n t te m p e r a tu r e s , and p l o t ­ t i n g t h e v a lu e s o f A a s a fu n c t io n o f (1 - Tr ) on l o g - l o g p a p e r . The v a lu e o f A Q i s o b ta in e d b y e x t r a p o l a t i n g t h i s c o r r e l a t i o n t o T « 0 (w here (1 - Tr ) = 1 ) . F ig u r e 2 shows t h e v a r i a t i o n o f h X Q a s a f u n c tio n o f m o le c u la r w e ig h t b a se d on th e r m a l d a ta from th e API T e c h n ic a l D ata B ook . V a lu e s o f X Q fo r t h e s t r a i g h t - c h a i n a l i p h a t i c h y d r o c a r b o n s| i from e th a n e th r o u g h ? h e x a d e ca n e can b e p r e d ic t e d b y t h e j e q u a tio n lOOOj 100 - - < 100 MOLECULAR WEIGHT F ig u r e 2 C o r r e la t io n o f *sAv0 w it h M o le c u la r W eigh t 26 i w h ere M i s t h e m o le c u la r w e ig h t o f th e h y d r o ­ carb on . 'E q u a tio n s (1 1 ) th r o u g h (1 6 ) p e r m it th e p r e d i c t i o n o f th e is a t u r a t e d va p o r and l i q u i d e n t h a l p ie s io f th e s t r a i g h t c h a in p a r a f f i n i c h y d r o c a r b o n s k n ow ing o n ly t h e m o le c u la r w e ig h t |and t h e c r i t i c a l te m p e r a tu r e s o f th e m a t e r i a l. Iso m er s |s u c h a s is o b u ta n e and is o p e n ta n e a r e n o t c o r r e la t e d w ith i !e q u a tio n s (11) and ( 1 6 ) . For su ch m a t e r ia ls th e v a lu e o f ^ 2 6 0 can be o b ta in e d from t h e API D a ta B ook, and t h e lv a lu e s o f c a n b e c a lc u l a t e d u s in g e q u a tio n ( 3 ) . i C. S lo p e o f t h e S a tu r a te d E n th a lp y C u rves H aving d e f in e d t h e e n th a lp y o f th e s a t u r a t e d vap or and l i q u i d c u r v e s , i t i s now a s im p le m a tte r t o d i f f e r e n t i ­ a t e e q u a tio n s (1 4 ) and (1 5 ) w it h r e s p e c t t o te m p e r a tu r e t o i o b t a in e x p r e s s io n s f o r t h e s lo p e o f t h e s a t u r a t e d v a p o r e n th a lp y c u r v e , dHy/dT = B + 2CT - h [ ^ - r ] (Tc “ T) 5 * * 1 (17) iand fo r th e l i q u i d a t i t s b u b b le p o in t : | dH^/dT = B + 2CT + H h “ “p r l - T) * " 1 (18) j L c J i I iT h e se e q u a tio n s d e s c r ib e t h e v a r i a t i o n o f th e e n th a lp y o f 27 th e dew p o in t vap or and t h e b u b b le p o in t l iq u i d a s a fu n c­ t i o n o f te m p e r a tu r e . T h ese h e a t c a p a c i t i e s a r e n o t con ­ s t a n t p r e s s u r e , or c o n s t a n t volum e p r o p e r t i e s . T hey s p e c i - i f i c a l l y d e s c r ib e th e ch a n g e o f t h e f l u i d e n th a lp y w ith i te m p e r a tu r e a lo n g th e lo c u s o f th e v a p o r - liq u id e n th a lp y l |e n v e lo p e . i j |D . P r e d ic t io n o f E n th a lp y o f Pure H ydrocarbon s The p r o c e d u r e s o u t l i n e d h e r e h a v e been u s e d t o p r e ­ d i c t t h e e n t h a l p ie s o f a number o f a l i p h a t i c h y d r o c a r b o n s. j The compounds p r o p a n e , b u t a n e , h e x a n e , and o c ta n e h a v e r j b e e n e v a lu a t e d . The r e s u l t s o f t h e s e c a l c u l a t i o n s a r e p l o t t e d in F ig u r e s 3 , 4 , 5 , and 6 . V a lu e s ta k e n from th e i i API T e c h n ic a l D ata Book h a v e b een su p erim p o sed on t h e s e .c a lc u l a t e d c u r v e s t o d e m o n str a te t h e a c c u r a c y o f t h e m eth­ o d . The a v e r a g e d e v i a t io n and th e sta n d a r d d e v i a t i o n o f I e a c h c a lc u l a t e d sy ste m from t h e r e p o r te d d a ta h a v e been c a lc u la t e d and t a b u la t e d i n S e c t io n V. SATURATED ENTHALPY, Btu/lb 28 300 * 200 100 500 600 700 TEMPERATURE °R F ig u r e 3 Saturated Enthalpy Boundary for Propane SATURATED ENTHALPY, Btu/lb. 29 300 200 LOO 600 700 800 TEMPERATURE.°R F ig u r e 4 Saturated Enthalpy Boundary for Butane 30 400 C O 300 200 800 700 900 T E M P E R A T U R E °R F ig u r e 5 Saturated Enthalpy Boundary for Hexane SATURATED ENTHALPY, Btu/lb. 31 500 400 300 900 1000 TEMPERATURE °R F ig u r e 6 Saturated Enthalpy Boundary for Octane j IV. PREDICTION METHODS FOR BINARY MIXTURES I A. S p e c ia l P r o p e r t ie s o f M ix tu re s i The e n th a lp y e n v e lo p e o f a b in a r y m ix tu r e o f h y d r o - I ic a r b o n s on a H-T d iagram a p p r o x im a te s in i t s g e n e r a l sh ap e ith e o u t l i n e o f a p u re com ponent e n v e lo p e . The e n v e lo p e j c o n s i s t s o f a dew p o in t c u r v e , and a b u b b le p o in t c u r v e j w h ic h r e a c h a maximum te m p e r a tu r e a t t h e c r ic o n d e n th e r m . The c o n c e n t r a t io n s o f t h e com ponents rem ain c o n s ta n t a lo n g t h e e n t i r e c u r v e . C o n s e q u e n tly , i t i s n o t p o s s i b l e t o i h e a t a b o i l i n g l i q u i d sa m p le o f a b in a r y m ix tu r e i s o t h e r - i m a lly from a g iv e n p o in t on th e l i q u i d c u r v e t o a p o in t a t t h e same te m p e r a tu r e on t h e dew p o in t c u r v e . The m eth od s o f p r e d i c t i n g th e e n th a lp y e n v e lo p e s o f p u r e a l i p h a t i c h y d r o c a r b o n s w h ich h a v e b een d e s c r ib e d can b e a p p lie d w it h a h ig h d e g r e e o f a c c u r a c y t o b in a r y m ix - i it u r e s o f h y d r o c a r b o n s . H ow ever, i t i s n e c e s s a r y t o u s e th e p r o p e r c o n s t a n t s in t h e e q u a t io n s . The h e a t o f v a p o r iz a t io n o f a h y d ro ca rb o n m ix tu r e i jean b e p r e d ic t e d by e q u a tio n (3 ) i f t h e p r o p e r c r i t i c a l |te m p e r a tu r e i s u s e d , and t h e v a lu e o f i s a d ju s te d t o |c o n fo r m . To c o r r e l a t e t h e is o th e r m a l h e a t o f v a p o r iz a t io n 33 o f a b in a r y m ix tu r e , i t i s n e c e s s a r y t o u s e a s t h e c r i t i c a l | temperature the cricondentherm (Tc c ) , at which A becomes i | z e r o . The v& lue o f A Q must b e red u c ed t o co m p en sa te f o r j the increase in the absolute value of Xl - Tr * ) , where Tr ' i ! = T/Tc c . T h us, e q u a tio n (3) m ust be m o d ifie d in a c c o r d a n c e i i i w it h t h e f o llo w in g e q u a tio n : ^ . T °* o< , A = A q ' (1 - = T c c< |^ t ccJ (Tcc - T) (19) ] The term A 0 ‘ i s r e l a t e d t o t h e m o la l a v e r a g e v a lu e o f A 0 by t h e e x p r e s s io n = E V i ( 2 0 ) C C _J V a lu e s o f A fox t h e m ix tu r e can th e n b e c a lc u la t e d ik sin g t h e c o r r e c t e d A 0 ' in e q u a tio n ( 3 ) . E n th a lp y d a ta fa r s e v e r a l b in a r y m ix tu r e s o f m ethane j in p ro p a n e h ave b e e n r e p o r te d ( 2 , 1 7 , 3 7 ) . F ig u r e 7 shows ; th e s l o p e o f ^(Hy + H1 ) a s a f u n c t io n o f te m p e r a tu r e fo r t h e s e m ix t u r e s . The m ore v o l a t i l e m ix tu r e s show a p r o - j nounced in c r e a s e o f s l o p e in t h e h ig h te m p e r a tu r e or c r i - ! t i c a l r e g i o n . I f t h e a v e r a g e m o le c u la r w e ig h t o f th e m ix­ t u r e v a r i e s s i g n i f i c a n t l y from t h e m o le c u la r w e ig h t o f t h e h e a v y com p on en t, t h e s lo p e o f t h e mean e n th a lp y c u r v e o f 34 400 300 23.4% C « 8 9% C 4 J « PROPANE 200 100 400 300 500 600 700 TEMPERATURE °R F ig u r e 7 Mean E n th a lp y C urves fo r M ix tu r e s o f M ethane in P ropane 35 t h e m ix tu r e w i l l be s t e e p e r th a n t h a t e x h ib it e d b y p u re At low te m p e r a tu r e s and p r e s s u r e s th e e n th a lp y o f im ixed h y d ro ca rb o n g a s e s and l i q u i d s can b e c l o s e l y a p p r o x i­ m a ted by u s in g t h e m o la l a v e r a g e o f th e e n th a lp y o f p u re t h a lp y o f h y d ro ca rb o n m ix tu r e s d iv e r g e s i n c r e a s i n g l y from I !t h e e n th a lp y o f t h e pu re co m p o n en ts. The s lo p e o f t h e mean | e n t h a lp y cu rv e f o r a m ix tu r e m ust v a r y a c c o r d in g ly . The v a lu e o f (B + 2CT) fo r a m ix tu r e m ust c l o s e l y a p p ro x im a te th e e n th a lp y o f t h e pure com p on en ts a t low te m p e r a tu r e , b u t i t m ust in c r e a s e more r a p i d l y th a n t h e e n th a lp y o f th e p u re com p on en ts a s te m p e r a tu r e i n c r e a s e s . C o n s e q u e n tly , th e v a lu e o f B u s e d fo r m ix tu r e s o f a l i p h a t i c h y d r o c a r b o n s can b e t h e same a s t h a t u sed f o r p u re co m p o n en ts, b u t th e v a lu e o f C m ust be c o r r e c t e d t o co m p en sa te fo r th e in c r e a s e d s l o p e o f th e c u r v e . ;to t h e v a lu e o f C fo r t h e h e a v y com ponent by th e f o llo w in g ie q u a tio n : a l i p h a t i c h yd ro ca rb o n s a t t h e same te m p e r a tu r e jcom p on en ts. As te m p e r a tu r e and p r e s s u r e i n c r e a s e , th e e n - The v a lu e o f C f o r a v o l a t i l e m ix tu r e can b e r e l a t e d ^ ( H y - % ) „ - Bm < 3 * 5 <Hy + - Bfic (21) 36 ! | V a lu e s o f Cm /C h c w ere e v a lu a te d f o r e a c h o f th e I m eth a n e-p ro p a n e m ix tu r e s a t s e v e r a l te m p e r a tu r e s , V a lu e s o f Cm /C h c f o r e a ch m ix tu r e w ere c o n s t a n t a c r o s s t h e f u l l r a n g e o f th e d a ta , in d e p e n d e n t o f te m p e r a tu r e . The r a t i o o f C f o r t h e m ix tu r e t o C f o r t h e h e a v y com ponent i s a i c o n s ta n t f o r e a ch b in a r y m ix tu r e w h ic h v a r ie s w it h th e com­ p o s i t i o n o f t h e m ix tu r e . I t can b e c o r r e la t e d w it h th e r a t i o o f t h e m o le c u la r w e ig h t o f t h e h e a v y com ponent t o th e m o le c u la r w e ig h t o f th e m ix tu r e a s shown in F ig u r e 8 . The v a lu e o f Cm /C hc f o r a s p e c i f i c m ix tu r e can be p r e d ic t e d by it h e r e l a t i o n C^c = ^2 2 ^ F ig u r e 9 show s t h a t Cm /C ^c h a s a v a lu e o f 1 when t h e :m o le c u la r w e ig h t r a t i o h a s a v a lu e o f 1 ,0 6 i n d i c a t i n g t h a t ' m ix tu r e s c o n t a in in g ab ou t 95 p e r c e n t o r more o f t h e h e a v y l | |com p onent e x h i b i t no d iv e r g e n c e from t h e norm al s lo p e o f | ' t h e mean e n th a lp y c u r v e . i | V a lu e s o f Cjn/Chc o th e r h y d ro ca rb o n m ix tu r e s a r e I | a l s o shown in F ig u r e 9 . Each m ix tu r e h a s a d e f i n i t e s lo p e |w it h a c o r r e s p o n d in g v a lu e o f /3 • T h e se e x p o n e n ts can b e c o r r e la t e d a s a f u n c t io n o f th e m o le c u la r w e ig h t o f th e SYMBOL MIXTURE COMPONENTS METHANE-PROPANE PROPANE-ISOPENTANE PENTANE-HEXADECANE O o 8 4 2 3 5 Figure 8 Correlation of Cn/C^ with sc 38 2.0 1.8 - CURVE COMPOSITION REFERENCE 1 C1"C 10 26 2 C1~C7 29 3 C1“C 6 25 4 Ci-C5 33 5 C1-C4 32 6 Cl“iC4 23 7 C1_C3 30 8 c2"c7 12 9 C3"C10 28 10 C4_C10 27 11 c2-c4 13 12 C4-C7 11 13 C3"C4 22 o u E -t 1.4 - 0.2 0.8 MOL FRACTION LIGHT COMPONENT F ig u r e 9 V a r ia t io n o f Tc c /T s c w ith C o m p o sitio n 39 h e a v y c o m p o n e n t. T he f o l l o w i n g e q u a t io n d e s c r i b e s t h i s \ ■ r e l a t i o n s h i p . / 3 = 4 6 0 0 (Mh c ) " 2 ,1 (2 3 ) ; The e q u a t io n s f o r t h e s a t u r a t e d v a p o r and l i q u i d e n t h a lp y : o f m ix t u r e s th e n b eco m e: I | Hv = *5*26 0 + B(T - 2 6 0 ) + C (T2 - 2 6 0 2 ) + *$*0 ' (1 - T j ' ) ^ (2 4 ) j and I j = * 5 * 2 6 0 * B ( T “ 2 6 0 ) + C < t 2 “ 2 6 ° 2 ) " ^ o * ( 1 " Tr ' ^ ! (2 5 ) T h e s e e q u a t io n s a r e s i m i l a r in form t o e q u a t io n s ; (1 4 ) and (1 5 ) p r e v i o u s l y show n f o r p u r e c o m p o n e n ts . E q u a- ; t i o n s (2 4 ) and (2 5 ) p e r m it t h e p r e d i c t i o n o f t h e e n t h a lp y j e n v e lo p e o f a m ix tu r e o f h y d r o c a r b o n s up t o t h e c r i c o n d e n - | th e rm te m p e r a tu r e o f t h e m ix t u r e . The e q u a t io n s a r e s p e c i - 1 f i c f o r b in a r y m ix t u r e s and s h o u ld b e a p p l i c a b l e f o r m u l t i - | com p on en t s y s t e m s . I B . P r e d i c t i o n o f t h e C r ic o n d e n th e r m A s t u d y o f t h e v a r i a t i o n o f t h e c r ic o n d e n th e r m w it h ! c o m p o s it io n f o r b in a r y m ix t u r e s sh ow s t h a t t h i s f u n c t i o n 40 m a x im izes fo r p a r a f f i n i c m ix tu r e s a t a c o m p o s itio n b e tw e e n 70 and 95 m ol p e r c e n t o f t h e l i g h t com p on en t. The r a t i o o f th e c r ic o n d e n th e r m (Tc c ) t o t h e p seu d o c r i t i c a l te m p e r a tu r e (Ts c ) can b e r e l a t e d t o th e m ix tu r e c o m p o s itio n a s shown in F ig u r e 9 fa r a v a r i e t y o f b in a r y m ix tu r e s . The maximum tem p er a tu r e o f ea ch c u r v e h a s b e e n c o r ­ r e l a t e d w ith t h e r a t i o o f c r i t i c a l te m p e r a tu r e s o f p u re i I com ponent s su c h t h a t 6 ~ L Ts c ] "ax. 1.2 4 3 - .2 4 3 r l s i l (2 6 ) w here TC2 > TCl The c o m p o s itio n w h ere t h i s maximum o c c u r s i s o b ta in e d b y th e r e l a t i o n Xg. = 0 .5 9 + .1 1 I | (2 7 ) te] The c u r v e s o f F ig u r e 9 can b e d e s c r ib e d by a g e n e r a l eq u a ­ t i o n o f th e form = 1 + bX + cX2 - dX v (2 8 ) i s c w h ere d = (b + c ) when X = * 1 and X = m ol f r a c t i o n o f t h e l i g h t co m p o n en t. [ 41 I f ^ i s a la r g e num ber, th e n t h e fo u r th ter m o f th e e q u a tio n d is a p p e a r s when X i s s m a l l , and th e i n i t i a l s e c t i o n o f t h e cu rv e i s d e s c r ib e d b y 7 = ^ = 1 + bX + cX“ (29) As c D i f f e r e n t i a t i n g e q u a tio n (2 9 ) g iv e s d [ H LTs c J = b + 2 cX (30) dX When X = 0 .5 t h e f u n c t io n (b + c) c a n b e c o r r e la t e d w ith by t h e e q u a t io n b + c = 1 . 25 ( € - 1) (31) a s shown in F ig u r e 1 0 . For v a lu e s o f €. b e lo w 1 .5 , t h e c u r v e s a r e l i n e a r , ian d C * 0 . F or v a lu e s o f £ g r e a t e r th a n 1 .5 th e c u r v e i s I n o t l i n e a r . The v a lu e o f C can b e o b ta in e d from e q u a tio n (3 1 ) u s in g a c o n s ta n t v a l u e o f b = 0 . 4 5 . The a ssu m p tio n t h a t tS i s a l a r g e number c a n now be | p ro v ed b y d i f f e r e n t i a t i n g e q u a tio n (2 8 ) and e v a lu a t in g j | a t t h e maximum p o in t w h er e X = X g a s d e f in e d by e q u a tio n | (27). V a lu e s o f ^ w ere fou n d t o v a r y a s a f u n c t io n o f £ in a c c o r d a n c e w ith th e e q u a tio n 42 X.5 1.0 m © X X J < T > 4 1 0* a iH 0 ) o + 0.5 0 1.0 2.0 6 F ig u r e 10 C o r r e la t io n o f (b + c ) w ith € I 2 T = 6 .7 6 2,5 (32) I i E q u a tio n s (26) th r o u g h (32) c o m p le t e ly d e f i n e th e ; v a r i a t i o n o f t h e c r ic o n d e n th e r m o f a b in a r y m ix tu r e o f | | a l i p h a t i c h y d r o c a r b o n s , u s in g o n ly t h e m o le c u la r c o m p o si- | t i o n and th e c r i t i c a l te m p e r a tu r e s o f t h e co m p o n en ts. i | C. E n th a lp y P r e d ic t io n o f M eth an e-P rop an e M ix tu r e s | i The p r o c e d u r e s o u t l i n e d p e r m it t h e r ea d y c a l c u l a t i o n o f e n t h a l p ie s o f m ix tu r e s o f m ethane w it h o th e r a l i p h a t i c h y d r o c a r b o n s . To d e m o n str a te th e e f f e c t i v e n e s s o f t h i s m ethod o f c a l c u l a t i o n , t h r e e ex a m p les o f m ethane m ixed w ith 5%, 51% and 76% p rop an e h a v e b een c a lc u l a t e d and p l o t t e d in F ig u r e s 1 1 , 12 and 1 3 . E x p e r im e n ta l d a ta p o in t s a r e su p e r ­ im posed on t h e c u r v e s t o d e m o n str a te t h e a c c u r a c y o f th e p r o c e d u r e . A d e t a i l e d c a l c u l a t i o n f o r t h i s p r o c e d u r e i s j ; t a b u la t e d in A p p en d ix C. ID. E n th a lp y P r e d ic t io n o f P en ta n e -H e x a d e ca n e M ix tu r e s The e n t h a l p i e s of- s e v e r a l m ix tu r e s o f p e n ta n e and jh e x a d e c a n e h a v e b e e n r e p o r te d (17). The e n th a lp y d a ta fo r ] |t h e s e a l i p h a t i c h y d ro ca rb o n m ix tu r e s h a v e b een i n v e s t i ­ g a te d f o r co m p a riso n w ith o t h e r h y d ro ca rb o n s y s t e m s . The SATURATED ENTHALPY, Btu/lb. 44 200 100 400 300 260 TEMPERATURE °R F ig u r e 11 Saturated Enthalpy Boundary for a Mixture Containing 95% Methane in Propane 45 300 * .a H P U P5 200 < ! m 100 400 500 600 TEMPERATURE °R F igu re 12 Saturated Enthalpy Boundary for a Mixture Containing 49.4% Methane in Propane 46 300 200 a 100 500 600 TEMPERATURE °R Figure 13 Saturated Enthalpy Boundary for a Mixture Containing 23.4% Methane in Propane mean e n th a lp y c u r v e s fo r t h e s e m ix tu r e s , p l o t t e d in F ig u re 1 4 , show a d iv e r g e n c e o f th e more v o l a t i l e hyd rocarbon m ix tu r e s s im ila r t o t h a t found in th e m eth ane-propan e m ix­ tu r e s * V a lu es o f C fo r t h e s e m ix tu r e s can b e p r e d ic t e d in th e same way a s t h a t o u t lin e d fo r m ethane-propane m ix tu r es u s in g e q u a tio n (21) . To d em o n stra te th e e f f e c t i v e n e s s o f t h i s c a l c u l a t i o n p r o c e d u r e , th e e n th a lp y e n v e lo p e s o f tw o b in a r y m ix tu r e s o f p en ta n e and h exad ecan e w ere c a l c u l a t e d . The m ix tu r e s con­ ta in e d 0 .5 8 7 and 0 .7 9 4 mol f r a c t i o n p e n ta n e . The r e s u l t s o f t h e s e c a l c u l a t i o n s a r e p l o t t e d in F ig u r e s 15 and 16. E x p e r im e n ta lly m easured e n th a lp y p o i n t s a r e p l o t t e d on th e c u r v e s t o show how c l o s e l y th e c a lc u l a t e d cu rve a p p r o x i­ m ates th e a c t u a l d a ta . I t i s app arent t h a t two o f t h e e x p e r im e n ta l e n t h a l­ py v a lu e s do n ot matjcJh t h e c a lc u l a t e d dew p o in t cu rv e in F ig u re 1 6 . The w id e b o i l i n g range o f t h i s sy stem made th e d e te r m in a tio n o f t h e dew p o in t lo c u s d i f f i c u l t . I t i s p o s ­ s i b l e t h a t t h e s e tw o p o in t s a r e p o in t s o f i n f l e c t i o n o f t h e i s o b a r i c e n th a lp y c u r v e s . S in c e th e o th e r d a ta p o in t s c l o s e l y m atch th e c a lc u l a t e d c u r v e , fu r th e r e x p e r im e n ta l s tu d y o f t h e dew p o in t e n th a lp y seem s w arran ted f o r t h e M E A N ENTHALPY, B t u / l b 48 600 0.587 C 0.794 C5 500 « HEXADECANE 300 900 1000 1100 TEMPERATURE °R F igu re 14 Mean E n th a lp y Curves fo r M ixtures o f Pentane in H exadecane SATURATED ENTHALPY, B t u / l b 600 49 500 400 320 960 1000 1100 TEMPERATURE °R F ig u re 15 S a tu r a te d E n th alp y Boundary fo r a M ixtu re C o n ta in in g 58.7% P entane in H exadecane 50 500 3 400 300 900 1000 1100 TEMPERATURE °R Figure 16 Saturated Enthalpy Boundary for a Mixture Containing 79.4% Pentane in Hexadecane 51 i j j p a r t i c u la r c a s e o f t h e 7 9 .4 mol p e r c e n t p en ta n e in h e x a d e - |c a n e s y s te m . i i i i E. E n th a lp y P r e d ic t io n o f a P r o p a n e -Iso p e n ta n e M ixtu re i | E n th alp y d a ta have b een r e p o r te d fo r a s i n g l e m ix- | I ;t u r e o f propane and iso p e n ta n e ( 1 5 ) . The m ixtu re c o n ta in e d I ; 0 .4 3 mol f r a c t i o n p rop an e. The e n th a lp y d a ta showed th e same ty p e o f d iv e r g e n c e e x h i b i t e d by th e p r e v io u s ex a m p les. |The v a lu e o f C fo r t h e m ixtu re was c a l c u l a t e d u s in g eq u a - i t i o n ( 1 0 c ) . B ecau se o n ly one v a lu e o f C was a v a i l a b l e , i t I was n e c e s s a r y t o assum e th a t C = 1 when = 1 .0 6 , a s i shown in F ig u re 8 , i n order t o e s t a b l i s h t h e v a lu e o f i n e q u a tio n (22 ) fo r t h i s b in a r y sy ste m . The c a l c u l a t e d e n th a lp y e n v e lo p e f o r t h i s m ix tu r e i s shown in F ig u r e 1 7 . E x p e r im e n ta lly d eterm in ed e n th a lp y p o in t s a r e p l o t t e d on th e graph fo r com p arison . The a r i t h ­ m e tic and sta n d a rd d e v ia t io n f o r t h i s sy s te m a re ta b u la te d i in S e c t io n V. i i | i i i r r i \ \ I i ___________________________________________________________________________________________ SATURATED ENTHALPY, Btu/lb 52 300 200 100 700 800 600 TEMPERATURE °R Figure 17 Saturated Enthalpy Boundary for a Mixture Containing 43% Propane in Isopentane V. ACCURACY OF CALCULATED ENTHALPIES ; A p roced ure h a s been d e v e lo p ed t o p r e d ic t t h e v a p o r - ! l i q u i d e n th a lp y e n v e lo p e fo r a pu re hyd rocarbon compound, ; or a b in a r y m ix tu re o f h y d ro c a r b o n s. To d e m o n stra te t h e : a c c u r a c y o f th e p r o c e d u r e , i t i s n e c e s s a r y t o d e ter m in e th e I d i s p e r s i o n or d e v i a t io n o f th e m ethod. The d e v i a t i o n , e , i I i s d e fin e d by th e e q u a tio n e = (Hc - H) (33) where H ^ , = th e c a lc u l a t e d e n th a lp y v a lu e , H = th e mean e n th a lp y v a lu e e s t a b l i s h e d by e x p e r im e n ta l m easurem ent. V a lu es o f H o b ta in e d from l i t e r a t u r e s o u r c e s and ; c o r r e l a t e d d a ta r e p r e s e n t th e b e s t a v era g e v a lu e o f t h e ; param eter a t any g iv e n p o i n t . I n d iv id u a l e x p e r im e n ta l e r - I r o r s Which may v a r y up t o 10% a r e averaged in th e c o r r e ­ l a t e d v a l u e . Based on r e p o r te d measurement a c c u r a c ie s , th e ; c o r r e l a t e d d a ta may b e assumed t o have an a v e r a g e a c c u r a c y o f ± 1.5%. These r e p o r te d d a ta v a lu e s have b een u sed t o e s t a b l i s h th e d e v i a t i o n o f th e c a lc u l a t e d e n th a lp y v a l u e s . i One measure o f th e a c c u r a c y o f th e p ro ced u re i s t h e a r it h m e t ic av era g e o f t h e e r r o r o f a number o f p o in t s 53 54 ta k e n a lo n g t h e same c u r v e . The a r it h m e t ic mean e r r o r o f th e p ro ced u re can be o b ta in e d by d i v i d i n g th e sum o f th e e r r o r s by t h e number o f r e a d in g s . 2 e (34) n A more u s e f u l way o f r e p r e s e n t in g th e d a ta i s by i t h e u s e o f t h e stan d ard d e v i a t i o n , or th e r o o t mean sq u are i ! i j d e v ia t io n ( S ) . i (35) The u n i t s o f t h i s d e v i a t io n a r e t h e same a s fo r t h e i n d i ­ v id u a l m easurem ents. H owever, th e v a lu e o f S i s th e sta n d ­ ard d e v i a t i o n o f t h e e n t i r e p o p u la t io n o f d a ta p o i n t s . A h ig h d e g r ee o f a c cu ra c y was a c h ie v e d in th e c a l - j . c u l a t i o n o f th e e n th a lp y b o u n d a rie s o f pure a l i p h a t i c com- ; p o n e n ts. V a lu e s w ere ta k e n a t t e n d e g r e e i n t e r v a l s i n th e ; c r i t i c a l tem p era tu re r e g io n and a t 50 d e g r ee i n t e r v a l s a t i | low er tem p er a tu r es down t o a tem p era tu re a p p r o x im a te ly i ! 200°R b e lo w t h e c r i t i c a l p o i n t . T a b le I I sum m arizes th e a c cu ra c y o f t h e s e c a l c u l a t i o n s . The a v era g e d iv e r g e n c e o f a l l th e c a l c u l a t i o n s was l e s s th an 0.5% w hich i s w it h in t h e a c c u r a c y o f th e o r i g i n a l m easurem ents. 55 TABLE II DEVIATION OF CALCULATED PURE COMPONENT ENTHALPIES A verage D e v ia tio n A r ith m e tic Standard P ercenl Component D e v ia tio n D e v ia tio n E rror Propane 2 .1 4 2 .7 0 .8 5 Butane 1 .5 0 1 .7 5 0 .5 1 Hexane 1 .1 1 1 .5 2 0 .3 0 O ctane 1 .3 9 1 .7 1 0 .3 2 A verage 1 .5 4 0 .4 9 56 j I The a c c u r a c y o f th e p ro ced u re fo r b in a r y m ix tu r e s I h a s b een e v a lu a te d in th e same manner a s fo r pu re compo­ n e n t s . T ab le I I I shows th e a r it h m e t ic d e v i a t io n and th e sta n d a rd d e v i a t io n fo r ea ch o f th e m ix tu r e s s t u d i e d , and th e a v e ra g e d e v i a t io n fo r a l l th e c a s e s . The p e r c e n t : e r r o r based on th e a v e ra g e e n th a lp y o f each sy stem i s | shown a lo n g w ith t h e a v e ra g e p e r c e n t e r r o r fo r a l l th e i | c a s e s . The a v e ra g e p e r c e n t e r r o r fo r t h e s e exam p les i s I 0 . 8% w h ich r e p r e s e n t s a s i g n i f i c a n t improvement o v er a v a i l ­ a b le m ethods o f e n th a lp y p r e d i c t i o n . 57 TABLE III DEVIATION OF CALCULATED ENTHALPIES OF BINARY MIXTURES A v e ra g e D e v i a t i o n A r i t h m e t i c S t a n d a r d P e r c e n t M o l a l C o m p o s itio n ______________ D e v i a t i o n D e v i a t i o n E r r o r 0 .9 5 M ethane, 0 .0 5 Propane 1 .9 5 2 .7 1 .1 7 0 .4 9 M ethane, 0 .5 1 Propane 2 .3 4 2 .8 7 1 .0 3 0 .2 4 M ethane, 0 .7 6 Propane 2 .6 6 3 .3 6 1 .1 4 0 .7 9 4 P en tane , 0 .2 0 6 H exadecane 1 .6 2 1 .9 0 0 .3 7 0 .5 8 7 P en tane , 0 .4 1 3 H exadecane 1 .1 7 .1 .3 0 0 .2 5 0 .4 3 P rop ane, 0 .5 7 P en tane 2 .2 3 2 .7 3 0 .7 4 A verage 1 .9 8 0 .8 VI. CONCLUSIONS The tw o p h ase e n th a lp y b o u n d a rie s o f th e a l i p h a t i c hy­ d rocarb on s can b e c o r r e l a t e d by a p o ly n o m ia l e q u a tio n o f th e form Jjdiy + H]^) = A + 9T + CT2 The mean e n th a lp y c u r v e s o f t h e a l i p h a t i c h yd rocarbons a re p a r a l l e l t o ea ch o t h e r . The change o f e n th a lp y o f t h e s e c u r v e s a s a f u n c t io n o f tem p era tu re i s p r e d ic te d by t h e e q u a tio n dJgtl^ + Hx ) / dT a B + 2CT F ixed v a lu e s o f th e c o n s t a n ts B and C can be u sed t o d e s c r ib e th e mean e n th a lp y c u r v e s o f a l l th e a l i p h a t i c h yd rocarb on s from eth a n e th rou gh h e x a d e c a n e . The d i f f e r e n c e betw een t h e mean e n th a lp y c u r v e s fo r v a r io u s h yd rocarb on s i s e s t a b l i s h e d by th e d i f f e r e n c e in th e h e a t o f v a p o r iz a t io n o f th e i n d iv id u a l h yd roca r­ bons a t th e tem p era tu re o f th e e n th a lp y b a s e . The two p h ase e n th a lp y boundary o f pure a l i p h a t i c h y­ d rocarb on s can b e p r e d ic t e d u s in g o n ly th e c r i t i c a l 58 59 te m p e r a tu r e , th e m o le c u la r w e ig h t , and t h e h e a t o f v a p o r iz a t io n o f th e su b s ta n c e a t th e e n th a lp y b a s e . Mixed h yd rocarb on s e x h i b i t a mean e n th a lp y curve w ith a s lo p e w h ich te n d s t o be g r e a t e r than th e s lo p e o f th e pu re co m p on en ts, -and w hich in c r e a s e s w ith t h e p e r ­ c e n ta g e o f l i g h t component in th e m ix tu r e . The s lo p e for a m ix tu r e can b e r e l a t e d t o t h e s lo p e o f th e pure com ponents u s in g t h e r a t i o Cm /C ^ c . The crico n d en th erm o f a b in a r y m ixtu re o f h yd rocarbons can be p r e d ic t e d u s in g o n ly t h e c r i t i c a l tem p er a tu r es and th e m o le c u la r c o m p o sitio n o f th e m ix tu r e . The two p h a se e n th a lp y boundary o f b in a r y m ix tu r e s o f a l i p h a t i c h y d rocarb on s can be p r e d ic te d u s i n g o n ly t h e pure component c r i t i c a l te m p e r a tu r e s , th e m o lec u la r w e ig h t s , and th e h e a t s o f v a p o r iz a t io n o f th e com­ p on en ts a t th e e n th a lp y b a s e . X. REFERENCES 1 . Am erican P etro leu m I n s t i t u t e , T e c h n ic a l Data Book - P etro leu m R e f in in g , P ort C ity P r e s s , B a ltim o r e , Md. (1 9 6 6 ). 2. B h iru d , V. L. and P ow ers, J . E .,P h .D . T h e s is , U n iv e r ­ s i t y o f M ich igan , August 19 69. 3. 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Chem., .59, 35 (1 9 6 7 ). i I I j i A P P E N D I C E S 63 APPENDIX A NOMENCLATURE i a , b , c , d C o n sta n ts in cricon d en th erm e q u a tio n A,B,C C o n sta n ts in mean e n th a lp y e q u a tio n c s l Heat c a p a c it y o f s a t u r a t e d l i q u i d c sv Heat c a p a c it y o f s a t u r a t e d vapor H1 E n th alpy o f s a tu r a te d l iq u i d ( B t u /lb ) E n th alp y o f s a tu r a t e d vapor ( B t u /lb ) k C on stan t i n e q u a tio n (22) K C on stan t i n T h ie s e n 's e q u a tio n M M o lecu lar w e ig h t o f hyd rocarbon T Tem perature (°R ankine) T C C r i t i c a l tem p era tu re (°R ankine) Tc c C ricondentherm tem p eratu re (°R ankine) Tc l C r i t i c a l te m p e r a tu r e , component 1 t c 2 C r i t i c a l te m p e r a tu r e , component 2 Tc i C r i t i c a l tem p eratu re o f component (i) Tr Reduced tem p eratu re = T/Tc T ' ■ L r Reduced tem p eratu re b a sed on crico n d e n th er m T/Tc c T ±ac Pseudo c r i t i c a l tem p era tu re = ( S x ^ 1 C£) 64 X Mol f r a c t i o n X g Mol f r a c t i o n o f l i g h t e r component o f b in a r y Where crico n d e n th er m m axim izes c* Exponent in T h ie s e n 's e q u a tio n /3 Exponent i n e q u a tio n (22) " S ' Exponent in crico n d en th erm e q u a tio n (28) £ Maximum r a t i o o f c rico n d en th erm tem p eratu re t o pseudo c r i t i c a l tem p era tu re * Heat o f v a p o r iz a t io n (B tu /lb ) ?V Q ' L aten t h e a t o f v a p o r iz a t io n o f m ixtu re when T = 0°R D e n s ity o f vapor D e n s ity o f l iq u i d S u b s c r i o t s : m B inary m ix tu re h e Heavy component i i^fc component APPENDIX B ! CALCULATED ENTHALPY VALUES OF PURE BUTANE I The e n th a lp y e n v e lo p e o f bu tane i s c a lc u l a t e d t o j d em o n stra te t h e a p p l i c a t i o n o f th e e q u a tio n s in t h e p r e d i c - | t i o n o f th e s a tu r a t e d e n th a lp y lo c u s o f a pure h y d ro ca rb o n . The c o n s t a n t s u se d in th e c a l c u l a t i o n a r e a s f o llo w s : M o lecu la r W eight - 5 8 .0 C r i t i c a l Tem perature « 7 6 5 .6°R O 2 3 35X 0 = 3 8 4 /( 5 8 .0 } = 123 (E q u ation 16) is X 260 = 2 3 5 / ( 5 8 . 0 ) ° * 2 » 1 0 4 .5 (E q u ation 11 ) °R ^ 2 6 0 .221(1-260) 2.16x10”4(T2-2602) h(Uv+ H x) 600 1 0 4 .5 7 5 .2 6 3 .1 2 4 2 .8 650 1 0 4 .5 8 6 .3 7 6 .5 2 6 7 .3 700 1 0 4 .5 9 7 .4 9 1 .3 2 9 3 .2 740 1 0 4 .5 1 0 6 .2 1 0 3 .9 3 1 4 .6 750 1 0 4 .5 1 0 8 .6 1 0 6 .8 3 1 9 .9 760 1 0 4 .5 110.6 110.2 3 2 5 .3 66 1 1 1 : °R Tr U -V <1-Tr ) ‘ 38 % 'A 0(1-Tr)*38 H v H1 r r 600 0 . 7 8 4 0 . 2 1 6 0 . 5 5 9 6 8 . 6 3 1 1 .4 1 7 4 . 2 ! 650 ! 0 . 8 4 9 0 . 1 5 1 0 . 4 8 8 6 0 . 6 3 2 7 .9 2 0 6 . 7 7 0 0 0 . 9 1 5 0 . 0 8 5 0 . 3 9 2 4 8 . 2 3 4 1 .4 2 4 5 . 0 740 0 . 9 6 7 0 . 0 3 3 0 . 2 7 4 3 3 . 7 3 4 8 .3 2 8 0 . 9 750 i 0 . 9 8 0 0 . 0 2 0 0 . 2 2 5 2 7 . 7 3 4 7 .6 2 9 2 . 2 760 0 . 9 9 4 0 . 0 0 6 0 . 1 4 3 1 7 . 6 3 4 2 .9 3 0 7 . 7 i I i i i I ! APPENDIX C j CALCULATED ENTHALPY VALUES OF A METHANE-PROPANE MIXTURE | j To dem onstrate th e a p p lic a t io n o f th e e q u a tio n s p r e ­ s e n t e d in t h i s stu d y for th e p r e d ic t io n o f th e e n th a lp y o f !a b in a r y m ix tu re, the e n th a lp y en v elo p e o f a m ixtu re con­ t a i n i n g 95% methane in propane has been c a lc u l a t e d . The j ! c o n s t a n t s used in t h i s c a l c u l a t i o n are as f o llo w s : C r i t i c a l Components Mol F r a c tio n Mol Weight Tem perature, R Methane 0 .9 4 8 1 6 .0 4 3 4 4 .3 Propane 0 .0 5 2 4 4 .0 9 6 6 6 .4 M o la l Average C r i t i c a l Tem perature ( 0 .9 4 8 ) ( 3 4 4 .3 ) = 3 2 6 .4 ( 0 .0 5 2 ) ( 6 6 6 .4 ) = 3 4 .6 Ts c = 3 6 1 .0 M o la l Average Mol Weight ( 0 .9 4 8 ) ( 1 6 .0 4 ) = 1 5 .1 9 ( 0 .0 5 2 ) ( 4 4 .0 9 ) « 2 .2 9 17.48 63 Critical Temperature Ratio ' L c J L = 66 6 .4 - 1 .9 3 5 TC1 3 4 4 .3 Maximum C ricondentherm R a tio (E q u ation 26) 1 .2 4 3 - ( 0 .2 4 3 ) ( 1 .9 3 5 ) = 1 .2 9 Mol F r a c tio n o f L ig h t Component a t 6 (E qu ation 27) X€ = 0 .5 9 + 0 .1 1 ( 1 .9 3 5 ) - 0 .8 0 3 Cr icon d en th erm (b + c) = 1 . 2 5 ( € - 1) (E q u ation 31) = ( 1 .2 5 ( 1 .2 9 - 1) = 0 .3 6 2 S in c e < i s l e s s th an 1 . 5 , th e cu rve i s l i n e a r . T h e r e fo r e , c = 0 b = 0 .3 6 2 y « 6 .7 € 2 ‘ 5 (E q u ation 32) X = 6 .7 ( 1 . 2 9 ) 2 *5 = 1 2 .7 When X = 0 .9 4 8 Z ee s i + bx + c x 2 - d x ^ (E qu ation 28) Ts c 12 7 = 1 + ( .3 6 2 ) ( .9 4 8 ) - ( 0 .3 6 2 ) ( .9 4 8 ) = 1 .1 6 1 Tc c = ( 1 .1 6 1 ) ( 3 6 1 ) « 421°R C a lc u la t io n o f h for m ethane = ( .9 4 8 ) ( 1 5 0 ) = 1 4 2 .1 H fo r propane = ( .0 5 2 ) ( 1 3 3 ) = 6 .9 T o ta l = 1 4 9 .0 h ^o ' = 1 4 9 1 - —7 7 7 | = 140 (E q u ation 20) C a lc u la t io n o f % /N ^ 2 6 0 “ 1 4 0 C a lc u la t io n o f / 3 [ r f e ] 260 , 38 1 " 421 I = 9 7 *5 1 9 > / 3 = 4600 (M^q) (E q u ation 23) = 4600 ( 4 4 .0 9 ) - 2 *1 - 1 .6 4 C a lc u la t io n o f Cn / Ch c When Cm /Ch c = 1 = 1 . 0 6 S a _ = 1 = K d . 0 6 ) 1 *64 (E q u ation 22) Che 71 Cm = ( 4 . 1 6 ) ( 2 , 1 6 x 10~4 ) = 9 x 10~4 B = 0 .2 2 1 I R T a b u la ted E n th a lp y C a lc u la t io n °R ^*260 Bm(T~260) (T^SO2)^ H(lyf %) 260 9 7 .5 0 0 9 7 .5 300 9 7 .5 8 .8 2 0 .2 1 2 6 .5 320 9 7 .5 1 3 .3 3 1 .5 1 4 2 .3 340 9 7 .5 1 7 .7 4 3 .3 1 5 8 .5 360 9 7 .5 2 2 .1 5 5 .8 1 7 5 .4 380 9 7 .5 2 6 .6 6 9 .1 1 9 3 .2 400 9 7 .5 3 1 .0 8 2 .8 2 1 1 .3 420 9 7 .5 3 5 .4 98 2 3 0 .9 °R T ’ A r (1“V ) (1-Tr ')°*38 h X H v H 1 260 0 .6 1 8 0 .3 8 2 0 .6 9 4 9 7 .5 1 9 5 .0 0 300 0 .7 1 3 0 .2 8 7 0 .6 2 2 8 7 .0 2 1 3 .5 3 9 .5 320 0 .7 6 0 0 .2 4 0 .5 8 0 8 1 .2 2 2 3 .5 6 1 .1 340 0 .8 0 9 0 .1 9 1 0 .5 3 4 7 4 .7 2 3 3 .2 8 3 .8 360 0 .8 5 6 0 .1 4 4 0 .4 8 0 6 7 .1 2 4 2 .5 1 0 8 .3 380 0 .9 0 3 0 .0 9 9 0 .4 1 2 5 7 .6 2 5 0 .8 1 3 5 .6 400 0 .9 5 1 0 .0 4 9 0 .3 1 7 4 4 .4 2 5 5 .7 1 6 6 .9 420 0 .9 9 8 0 .0 0 2 0 .0 9 5 1 3 .2 2 4 4 .1 2 1 7 .7 
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Creator Ghormley, Edward Longstreth (author) 
Core Title Prediction Of Enthalpy Of Saturated Paraffin Hydrocarbon Mixtures 
Degree Doctor of Philosophy 
Degree Program Chemical Engineering 
Publisher University of Southern California (original), University of Southern California. Libraries (digital) 
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Advisor Lenoir, John M. (committee chair), Rebert, Charles J. (committee member), Springer, E. Kent (committee member) 
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