Cricondentherm & Cricondenbar Pressures | Gases - xdocs.net
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The Cricondentherm and Cricondenbar Pressures of The Cricondentherm and Cricondenbar Pressures of Multicomponent Hydrocarbon Mixtures Multicomponent Hydrocarbon Mixtures ROBER ROBER T T . GRIEVES . GRIEVES NORTHWESTERN NORTHWESTERN V. V. GEORGE THODOS GEORGE THODOS EVANSTON, EVANSTON, ILL. ILL. ABSTRACT ABSTRACT method is presented f method is presented f r r the accurate the accurate calcu calcu latio latio of the cricondentherm and cricondenbar pressures of the cricondentherm and cricondenbar pressures of multicon~ponent of multicon~ponent hydroca hydrocarbon mixtu rbon mixtu res o res of kno f kno wn wn composi composition. tion. The mixtures may contain The mixtures may contain si si x and x and quite poss quite poss ibly ibly any num any number ber f f compon compon ents including ents including para paraffin ffins, s, isopa isopa mffins mffins , o , olef lefir irzs, acetylene zs, acetylene s, s, napht napht henes and arom henes and aromatics. atics. Th Th e ap e approa proach i ch i s s similur similur to that use to that use d d fo fo r calcula r calcula ting cri ting cri tical pressures tical pressures and and criconde cricondentherm and cric ntherm and cricondenbar tem ondenbar temperatur peratures. es. Th Th cri cri tic tic al al press press ure, ure, th th e e norm normal boil al boiling poi ing poi nt and the nt and the approximate vapor pressure approximate vapor pressure behavior o behavior o f eac f eac component are all that art required. component are all that art required. il il stepuiise stepuiise culculation proc culculation procedu edure re is ne is ne ces ces sar sar y y r r mixtures mixtures containing more than two components. containing more than two components. Frorri an analysis of Frorri an analysis of binary systems and binary systems and 11 11 mixtures, mixtures, the the average average de~iiati de~iiatiorz orz f f calcu calcu luted luted cricondentherm pressures from reported values is cricondentherm pressures from reported values is 2. 2. pvr cent. For nine multicomponent mixtures the pvr cent. For nine multicomponent mixtures the average deviation is average deviation is per cent. Considering per cent. Considering 19 19 binary systems and binary systems and 108 108 mixtur mixtures, es, the average the average dev dev iat iat ion o ion of cal f cal culat culat ed crico ed cricorzde rzdenbar nbar pre pre ssu ssu rts rts fr fr om om reported values is reported values is 1.7 1.7 per cent. For per cent. For 15 15 multi- multi- component mixtures, the average deviation is component mixtures, the average deviation is per cent. per cent. INTRODUCTION INTRODUCTION A knowledge of t A knowledge of t he ph he ph ase behavior in the critic ase behavior in the critic al al region o region o f multicomponent hydrocarbon f multicomponent hydrocarbon mixtures i mixtures i s of s of value both in industrial processing operation value both in industrial processing operation s and s and for for the the opt optim imum operation o um operation o f g f g as as conden conden sate rese sate rese r- r- voirs. Accurate methods of calculating the voirs. Accurate methods of calculating the critical critical te te mper mper at at ur ur es and es and cri cri tic tic al pres al pres sur sur es4 es4 .6~ .6~ 7~ 7~ 8.9 8.9 ~2 ~2 criconden criconden the therm rm and and criconden criconden bar bar temperatur temperatur es6p es6p 10 10 of multicomponent hydrocarbon mixtures are of multicomponent hydrocarbon mixtures are avail avail able i able i n the literamre. n the literamre. f the cri f the cri condentherm and cricondenbar pres condentherm and cricondenbar pres su su res res could be calculated with equal accuracy, the entire could be calculated with equal accuracy, the entire phase diagram of phase diagram of multicomponent hydrocarbon multicomponent hydrocarbon mixture could be w mixture could be w ell approximated. T ell approximated. T he work o he work o Etter and Kay6 i Etter and Kay6 i s limi s limi te te d d to systems to systems containing t containing t he he nor nor mal para mal para ffins and ffins and as not been tested on sys as not been tested on sys tem tem Original manuscript r Original manuscript r eceive eceive d in Society o d in Society of Petroleum f Petroleum Engineers Engineers office Jan office Jan 196 1964. 4. Re Re vis vis ed manusc ed manuscript receiv ript receiv ed ed Jul Jul y 6. 1964. y 6. 1964. *Pres *Pres ent address: Illin ent address: Illin ois ois Institute o Institute of Technology, Chicago. f Technology, Chicago. 4~ 4~ ef ef er er en en ce ce s s iven at en iven at end o d of pap f paper. er. containing a heavier component than heptane. containing a heavier component than heptane. n addition n addition , the d , the d evelopm evelopm ent o ent of their multicomponent f their multicomponent equat equat ions i ions i s based s based up up on on limited number of limited number of mixtures co mixtures co ntain ntain ing f ing f om three to si om three to si x components. x components. Silverman and Silverman and tho do^^^ tho do^^^ have considered systems have considered systems containing containing both both paraff paraff inic an inic an d non-pa d non-pa raf raf fini fini hydrocarbons, but hydrocarbons, but their corr their corr elati elati on on s s limi limi ted to ted to bina bina ry s ry s ys ys tem tem s and is highly inaccurate for met s and is highly inaccurate for met hane hane systems. systems. Eilerts5 has done extensiv Eilerts5 has done extensiv e wo e wo k on the k on the cricondenbar cricondenbar pres pres sure; he has sure; he has produc produc ed an ex ed an ex cellent cellent correl correl ation for bina ation for bina ry sy ry sy stem stem s. However s. However , hi , hi procedure for procedure for multicomponent mixture multicomponent mixture s i s i s chiefly s chiefly useful useful for for highly com highly com plex mixtures requiring a plex mixtures requiring a know know ledge o ledge of the f the vapor-liquid equilibrium beha vapor-liquid equilibrium beha vior vior f f the mixtures; he ha the mixtures; he ha s not considered the criconden- s not considered the criconden- therm pressure. therm pressure. The objectiv The objectiv e e f this study w f this study w as the as the development development f an ac f an ac cu cu rate and rapid method f rate and rapid method f or or the ca the ca lcula lcula tion tion of the of the cri cri conden conden ther ther m a m a nd cricondenbar pressur nd cricondenbar pressur es es of multi of multi componen componen t mixtures contain t mixtures contain ing al ing al l types l types hydrocarbons and having hydrocarbons and having wide volatility range. wide volatility range. The The appr appr oach that was adopted is oach that was adopted is similar similar to that to that used used by G by G rieves and T rieves and T hodos hodos fo for cri r cri conden conden ther ther and cricondenbar temperatures and cricondenbar temperatures and for critical and for critical pressures.9 However pressures.9 However , methane system , methane system s had to be s had to be considered separatel considered separatel y y and a and a modi modi fi fi ed stepw ed stepw ise ise calculation procedure was u calculation procedure was u tilized for t tilized for t he cricond he cricond er- er- therm pressure. therm pressure. Th Th e e correlations correlations were developed in a manner were developed in a manner similar to those for similar to those for critical pressu critical pressu res res and criconden- and criconden- the therm and rm and cricondenbar tempera cricondenbar tempera tures. B tures. B ase ase d upo d upo binar binar y da y da ta repor ta repor ted in ted in the liter the liter ature it w ature it w as ob as ob served served that the ratios of cricondentherm and cricondenbar that the ratios of cricondentherm and cricondenbar pressure pressure to the pseudocritical pressure (mol to the pseudocritical pressure (mol ar ar average), average), pL pL /ppc /ppc /ppc, /ppc, respectively, in two- respectively, in two- componen componen t sy t sy ste ste ms depended upon th ms depended upon th e mole fra e mole fra cti cti on on of the low-boiling component of the low-boiling component and upon th and upon th e diversity e diversity in properties o in properties o f f the two components. the two components. A dimensionless boiling-point parameter A dimensionless boiling-point parameter i, i, was chosen to represent the diversity in properties was chosen to represent the diversity in properties f the components. F f the components. F or a b or a b inar inar y sy y sy ste ste m, m, is the is the molar avera molar avera ge of the ge of the normal normal boiling po boiling po ints o ints o f t f t he he two components involved. For two components involved. For multicomponent multicomponent system system it i it i s either the mol s either the mol ar average o ar average of th f th e nor e nor mal mal boiling p boiling p oints of all o oints of all of the compo f the compo nents invo nents invo lved o lved o the molar average of the normal the molar average of the normal boiling point o boiling point of th f th pure low-boil pure low-boil ing ing component and of the atmospheric component and of the atmospheric boiling point of the low-boiling-free mixture of boiling point of the low-boiling-free mixture of 40 40 SOCIETY O SOCIETY O F F PETROLEUM ENGINEE PETROLEUM ENGINEERS JOURNAI RS JOURNAI
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Transcript of Cricondentherm & Cricondenbar Pressures | Gases - xdocs.net
The Cricondentherm and Cricondenbar Pressures ofThe Cricondentherm and Cricondenbar Pressures of
Multicomponent Hydrocarbon MixturesMulticomponent Hydrocarbon Mixtures
R O B E RR O B E R T T . G R I E V E S. G R I E V E S NORTHWESTERNNORTHWESTERN V.V.
G E O R G E T H O D O SG E O R G E T H O D O S EVANSTON ,EVANSTON , ILL.ILL.
A B S T R A C TA B S T R A C T
method is presented fmethod is presented f r r the accurate the accurate calcucalcu latiolatio
of the cricondentherm and cricondenbar pressuresof the cricondentherm and cricondenbar pressures
of multicon~ponentof multicon~ponenthydrocahydrocarbon mixturbon mixtu res ores of knof kno wnwn
composicomposition. tion. The mixtures may contain The mixtures may contain sisi x andx and
quite possquite poss ibly ibly any numany number ber f f componcompon ents includingents including
paraparaffinffins, s, isopaisopa mffinsmffins , o, oleflefirirzs, acetylenezs, acetylene s,s,
naphtnapht henes and aromhenes and aromatics. atics. ThTh e ape approaproach ich i s s similursimilur
to that useto that use d d fofor calcular calcula ting criting cri tical pressures tical pressures andand
cricondecricondentherm and cricntherm and cricondenbar temondenbar temperaturperatures. es. ThTh
cricri tictic al al presspress ure, ure, thth e e normnormal boilal boiling poiing point and thent and the
approximate vapor pressure approximate vapor pressure behavior obehavior of eacf eac
component are all that art required.component are all that art required. ilil stepuiisestepuiise
culculation procculculation proceduedure re is neis ne cesces sarsar y y r r mixturesmixtures
containing more than two components.containing more than two components.
Frorri an analysis ofFrorri an analysis of binary systems andbinary systems and 1111
mixtures, mixtures, the the average average de~iiatide~iiatiorz orz f f calcucalcu lutedluted
cricondentherm pressures from reported values iscricondentherm pressures from reported values is
2.2. pvr cent. For nine multicomponent mixtures thepvr cent. For nine multicomponent mixtures the
average deviation isaverage deviation is per cent. Consideringper cent. Considering 1919
binary systems andbinary systems and 108108 mixturmixtures, es, the averagethe average
devdev iatiat ion oion of calf cal culatculat ed cricoed cricorzderzdenbar nbar prepre ssussu rts rts frfromom
reported values isreported values is 1.71.7 per cent. Forper cent. For 1515 multi-multi-
component mixtures, the average deviation iscomponent mixtures, the average deviation is
per cent.per cent.
I N T R O D U C T I O NI N T R O D U C T I O N
A k n o w l e d g e o f tA k n o w l e d g e o f th e p hh e p h a s e b e h a v i o r i n t h e c r i t i ca s e b e h a v i o r i n t h e c r i t i c a la l
r e g i o n or e g i o n of m u l t i c o m p o n e n t h y d r o c a r b o n f m u l t i c o m p o n e n t h y d r o c a r b o n m i x t u r e s im i x t u r e s i s o fs o f
v a l u e b o t h i n i n d u s t r i a l p r o c e s s i n g o p e r a t i o nv a l u e b o t h i n i n d u s t r i a l p r o c e s s i n g o p e r a t i o n s a n ds a n d
f o r f o r t h e t h e o p to p ti mi mu m o p e r a t i o n ou m o p e r a t i o n of gf g a s a s c o n d e nc o n d e n s a t e r e s es a t e r e s e r -r -
v o i r s . A c c u r a t e m e t h o d s o f c a l c u l a t i n g t h e v o i r s . A c c u r a t e m e t h o d s o f c a l c u l a t i n g t h e c r i t i c a lc r i t i c a l
t et em p e rm p e ra ta tu ru re s a n d e s a n d c r ic r it i ct i ca l p r e sa l p r e s s u rs u r e s 4e s 4 . 6 ~. 6 ~ 7 ~7 ~ 8 . 98 . 9 ~ 2~ 2
c r i c o n d e n c r i c o n d e n t h et h er m r m a n d a n d c r i c o n d e nc r i c o n d e n b a r b a r t e m p e r a t u rt e m p e r a t u re s 6 pe s 6 p 1010
o f m u l t i c o m p o n e n t h y d r o c a r b o n m i x t u r e s a r eo f m u l t i c o m p o n e n t h y d r o c a r b o n m i x t u r e s a r e
a v a i la v a i l a b l e ia b l e in t h e l i t e r a m r e .n t h e l i t e r a m r e .
f t h e c r if t h e c r ic o n d e n t h e r m a n d c r i c o n d e n b a r p r e sc o n d e n t h e r m a n d c r i c o n d e n b a r p r e s s us u r e sr e s
c o u l d b e c a l c u l a t e d w i t h e q u a l a c c u r a c y , t h e e n t i r ec o u l d b e c a l c u l a t e d w i t h e q u a l a c c u r a c y , t h e e n t i r e
p h a s e d i a g r a m o fp h a s e d i a g r a m o f m u l t i c o m p o n e n t h y d r o c a r b o nm u l t i c o m p o n e n t h y d r o c a r b o n
m i x t u r e c o u l d b e wm i x t u r e c o u l d b e w e l l a p p r o x i m a t e d . Te l l a p p r o x i m a t e d . T h e w o r k oh e w o r k o
E t t e r a n d K a y 6 iE t t e r a n d K a y 6 i s l i m is l i m it et ed d t o s y s t e m s t o s y s t e m s c o n t a i n i n g tc o n t a i n i n g th eh e
n o rn o rm a l p a r am a l p a r af f i n s a n d f f i n s a n d a s n o t b e e n t e s t e d o n s y sa s n o t b e e n t e s t e d o n s y s t e mt e m
Orig ina l manuscr ip t rOr ig ina l manuscr ip t r ece iveece ive d in Soc ie ty od in Soc ie ty of Pe t ro leumf Pe t ro leum
E n g i n e e r s E n g i n e e r s o f f i c e J a no f f i c e J a n 1961964. 4 . ReRe visv is ed manusced manuscr ip t rece ivr ip t rece iv eded
JulJul y 6. 1964.y 6. 1964.*Pres*Pres en t address : I l l inen t address : I l l in o is o i s Ins t i tu te oIns t i tu te of Technology , Chicago .f Technology , Chicago .
4 ~4 ~ e fe f e re r e ne n c ec e s s i v e n a t e ni v e n a t e nd od of p a pf p a pe r .e r .
c o n t a i n i n g a h e a v i e r c o m p o n e n t t h a n h e p t a n e .c o n t a i n i n g a h e a v i e r c o m p o n e n t t h a n h e p t a n e .
n a d d i t i o nn a d d i t i o n , t h e d, t h e d e v e l o p me v e l o p m e n t oe n t of t h e i r m u l t i c o m p o n e n tf t h e i r m u l t i c o m p o n e n t
e q u a te q u a ti o n s ii o n s i s b a s e d s b a s e d u pu po no n l i m i t e d n u m b e r o fl i m i t e d n u m b e r o f
m i x t u r e s c om i x t u r e s c o n t a i nn t a i n i n g fi n g f o m t h r e e t o s io m t h r e e t o s i x c o m p o n e n t s .x c o m p o n e n t s .
S i l v e r m a n a n dS i l v e r m a n a n d tho do^^^tho do^^^ h a v e c o n s i d e r e d s y s t e m sh a v e c o n s i d e r e d s y s t e m s
c o n t a i n i n g c o n t a i n i n g b o t h b o t h p a r a f fp a r a f fi n i c a ni n i c a n d n o n - p ad n o n - p ar a fr a ff i n if i n i
h y d r o c a r b o n s , b u t h y d r o c a r b o n s , b u t t h e i r c o r rt h e i r c o r re l a t ie l a t io n o n s s l i m il i m it e d t ot e d t ob i n ab i n ar y sr y s y sy s t e mt e m s a n d i s h i g h l y i n a c c u r a t e f o r m e ts a n d i s h i g h l y i n a c c u r a t e f o r m e th a n eh a n e
s y s t e m s . s y s t e m s . E i l e r t s 5 h a s d o n e e x t e n s i vE i l e r t s 5 h a s d o n e e x t e n s i v e w oe w o k o n t h ek o n t h e
c r i c o n d e n b a r c r i c o n d e n b a r p r e sp r e s s u r e ; h e h a s s u r e ; h e h a s p r o d u cp r o d u ce d a n e xe d a n e x c e l l e n tc e l l e n t
c o r r e lc o r r e la t i o n f o r b i n aa t i o n f o r b i n ar y s yr y s y s t e ms t e m s . H o w e v e rs . H o w e v e r, h i, h i
p r o c e d u r e f o r p r o c e d u r e f o r m u l t i c o m p o n e n t m i x t u r em u l t i c o m p o n e n t m i x t u r es is i s c h i e f l ys c h i e f l y
u s e f u l u s e f u l f o r f o r h i g h l y c o mh i g h l y c o m p l e x m i x t u r e s r e q u i r i n g ap l e x m i x t u r e s r e q u i r i n g a
k n o wk n o w l e d g e ol e d g e of t h e f t h e v a p o r - l i q u i d e q u i l i b r i u m b e h av a p o r - l i q u i d e q u i l i b r i u m b e h a v i o rv i o r
f f t h e m i x t u r e s ; h e h at h e m i x t u r e s ; h e h a s n o t c o n s i d e r e d t h e c r i c o n d e n -s n o t c o n s i d e r e d t h e c r i c o n d e n -
t h e r m p r e s s u r e .t h e r m p r e s s u r e .
T h e o b j e c t i vT h e o b j e c t i v e e f t h i s s t u d y wf t h i s s t u d y w a s t h e a s t h e d e v e l o p m e n td e v e l o p m e n t
f a n a cf a n a c c uc u r a t e a n d r a p i d m e t h o d fr a t e a n d r a p i d m e t h o d fo r o r t h e c at h e c a l c u l al c u l a t i o nt i o n
o f t h e o f t h e c r ic r ic o n d e nc o n d e nt h e rt h e rm am a n d c r i c o n d e n b a r p r e s s u rn d c r i c o n d e n b a r p r e s s u r e se s
o f m u l t io f m u l t ic o m p o n e nc o m p o n e nt m i x t u r e s c o n t a i nt m i x t u r e s c o n t a i n i n g a li n g a l l t y p e s l t y p e s
h y d r o c a r b o n s a n d h a v i n gh y d r o c a r b o n s a n d h a v i n g w i d e v o l a t i l i t y r a n g e .w i d e v o l a t i l i t y r a n g e .
T h e T h e a p p ra p p ro a c h t h a t w a s a d o p t e d i s o a c h t h a t w a s a d o p t e d i s s i m i l a r s i m i l a r t o t h a tt o t h a t
u s e d u s e d b y Gb y G r i e v e s a n d Tr i e v e s a n d T h o d o s h o d o s f of or c r ir c r ic o n d e nc o n d e nt h e rt h e r
a n d c r i c o n d e n b a r t e m p e r a t u r e sa n d c r i c o n d e n b a r t e m p e r a t u r e s a n d f o r c r i t i c a la n d f o r c r i t i c a l
p r e s s u r e s . 9 H o w e v e rp r e s s u r e s . 9 H o w e v e r, m e t h a n e s y s t e m, m e t h a n e s y s t e m s h a d t o b es h a d t o b e
c o n s i d e r e d s e p a r a t e lc o n s i d e r e d s e p a r a t e ly y a n d a a n d a m o d im o d if if ie d s t e p we d s t e p w i s ei s e
c a l c u l a t i o n p r o c e d u r e w a s uc a l c u l a t i o n p r o c e d u r e w a s u t i l i z e d f o r tt i l i z e d f o r th e c r i c o n dh e c r i c o n d e r -e r -
t h e r m p r e s s u r e .t h e r m p r e s s u r e .
T hT h e e c o r r e l a t i o n s c o r r e l a t i o n s w e r e d e v e l o p e d i n a m a n n e rw e r e d e v e l o p e d i n a m a n n e r
s i m i l a r t o t h o s e f o r s i m i l a r t o t h o s e f o r c r i t i c a l p r e s s uc r i t i c a l p r e s s u r e s r e s a n d c r i c o n d e n -a n d c r i c o n d e n -
t h et h er m a n d r m a n d c r i c o n d e n b a r t e m p e r ac r i c o n d e n b a r t e m p e r at u r e s . Bt u r e s . B a s ea s e d u p od u p o
b i n a rb i n a ry d ay d a t a r e p o rt a r e p o rt e d i n t e d i n t h e l i t e rt h e l i t e ra t u r e i t wa t u r e i t w a s o ba s o b s e r v e ds e r v e d
t h a t t h e r a t i o s o f c r i c o n d e n t h e r m a n d c r i c o n d e n b a rt h a t t h e r a t i o s o f c r i c o n d e n t h e r m a n d c r i c o n d e n b a r
p r e s s u r e p r e s s u r e t o t h e p s e u d o c r i t i c a l p r e s s u r e ( m o lt o t h e p s e u d o c r i t i c a l p r e s s u r e ( m o la ra r
a v e r a g e ) ,a v e r a g e ) , pLpL / ppc/ppc /ppc ,/ppc , r e s p e c t i v e l y , i n t w o -r e s p e c t i v e l y , i n t w o -
c o m p o n e nc o m p o n e nt s yt s y s t es t e m s d e p e n d e d u p o n t hm s d e p e n d e d u p o n t h e m o l e f r ae m o l e f r ac t ic t io no n
o f t h e l o w - b o i l i n g c o m p o n e n t o f t h e l o w - b o i l i n g c o m p o n e n t a n d u p o n t ha n d u p o n t h e d i v e r s i t ye d i v e r s i t yi n p r o p e r t i e s oi n p r o p e r t i e s o f f t h e t w o c o m p o n e n t s .t h e t w o c o m p o n e n t s .
A d i m e n s i o n l e s s b o i l i n g - p o i n t p a r a m e t e rA d i m e n s i o n l e s s b o i l i n g - p o i n t p a r a m e t e r i,i,w a s c h o s e n t o r e p r e s e n t t h e d i v e r s i t y i n p r o p e r t i e sw a s c h o s e n t o r e p r e s e n t t h e d i v e r s i t y i n p r o p e r t i e s
f t h e c o m p o n e n t s . Ff t h e c o m p o n e n t s . F o r a bo r a bi n a ri n a ry s yy s y s t es t e m ,m , i s t h ei s t h e
m o l a r a v e r am o l a r a v e r a g e o f t h e g e o f t h e n o r m a l n o r m a l b o i l i n g p ob o i l i n g p o i n t s oi n t s of tf t h eh e
t w o c o m p o n e n t s i n v o l v e d . F o rt w o c o m p o n e n t s i n v o l v e d . F o r m u l t i c o m p o n e n tm u l t i c o m p o n e n t
s y s t e m s y s t e m i t ii t i s e i t h e r t h e m o ls e i t h e r t h e m o la r a v e r a g e oa r a v e r a g e of t hf t h e n o re n o rm a lm a l
b o i l i n g pb o i l i n g p o i n t s o f a l l oo i n t s o f a l l of t h e c o m p of t h e c o m p o n e n t s i n v on e n t s i n v o l v e d ol v e d o
t h e m o l a r a v e r a g e o f t h e n o r m a l t h e m o l a r a v e r a g e o f t h e n o r m a l b o i l i n g p o i n t ob o i l i n g p o i n t of t hf t h
p u r e l o w - b o i lp u r e l o w - b o i li n g i n g c o m p o n e n t a n d o f t h e a t m o s p h e r i cc o m p o n e n t a n d o f t h e a t m o s p h e r i c
b o i l i n g p o i n t o f t h e l o w - b o i l i n g - f r e e m i x t u r e o fb o i l i n g p o i n t o f t h e l o w - b o i l i n g - f r e e m i x t u r e o f
4040S O C I E T Y OS O C I E T Y O F F P E T R O L E U M E N G I N E EP E T R O L E U M E N G I N E ER S J O U R N A IR S J O U R N A I
the system. Tb s the boiling point of the mixture
at atmospheric pressur e, c alc ulat ed from the
relation,
where s the number of compon ents. Tb s arrive
t by a trial-and-error procedure. s chosen an
the vapor pressures of the components determined;
the vapor pressures and mole fractions are then
subs titu ted into Eq. 1 to s e if the equality holds.
The approximate straight li ne given by a plot of the
logarithm of the vapor press ure f e ac h pure
component vs the reciprocal f the abs olute
temperature is sufficiently accurat e for the evalua-
tion of the critical point, the normal boiling
point and perhaps one additional point are all that
are required. For multicomponent mixtures, a step-
wise calculation procedure s necessary for pt and
reducing all of the high-boiling components to
a s e seudo-component. The procedure i s fully
described and example calculations are included
in the s ec tio ns that follow
BINARY SYSTEMS
CRICONDENTHERM PRESSURE
Based upon data available in the literature for
10 non-methane binary syst ems containing paraffin s,
Tb
FIG. ELATIONSHIP BETWEEN pt /ppc AN
Tb FOR NON-METHANE SYSTEMS.
S E P T E M B E R , 1 9 6 . 1
isoparaff ins and olefins, the relationship betwee
the cricondentherm press ure rati o pt /ppc and the
boiling-point parameter T i , T b s presented a s Fig.
The parameters are the mole fraction of the low-
boiling component in the mixture, and the upper
limit on T i T b s establis hed by the ethane-n
deca ne system. For the 1 0 syst ems and 53 mixtures
the average deviation of cricondentherm pressures
cal cula ted with Fig. 1 from reported values s 1.73
per cent.
A similar relationship for methane sys tems i
presented a s Fig. in which the parameters are
the mole fraction of methane. The limit on Ti , Tb
s est abli shed by the methane-n-heptane system.
For the seven available systems and 35 mixtures
the average deviation of calculated values from
reported value s i s 3.25 per cent.
For syst ems containing an acety lene , a naphthene,
or an aroma tic hydrocarbon a s a component,
correction factor must be applied for use with Figs.
1 and 2. For such sys te ms the behavior of the
cricondentherm press ure r ati o does not vary with
the difference in boiling point properties of the
components in the same manner a s it d oes fo
paraffin and olefin systems. The value of pt/ pP
obtained by the normal procedure from Figs. and
should be multiplied by the factors in Table
to give the correct value to be used in finding pl.
For values of ze outs ide of the ranges indica ted,
no correction is needed. For five systems and 30
mixtures containing acetylenes, naphthenes and
aromatics, the average deviation of calculated
values from reported value s i 2. per cent. The
results for all 2 binary syst ems considered ar
pres ente d a s part of Tabl e 2. The maximum deviation
for each system i s al so included
CRICONDENBAR PRESSURE
Figs. 3 and present the relationships between
the cricondenbar pressure r atio, pp/pp c, and i
FIG. ELATIONSHIP BETWEEN pt/ppc AND
Tb FOR METHANE SYSTEMS.
Tb (from Eq. 1 and vapor pres sure da ta) 397R
0.2 (707.1) 0.8 (494.2) 536.8 psia
Component Rang e of ze Fig. 1 Fig.
cety lene < 0.65 1 1.22n o ~ h t h e n e 0.2 < .z p<0 .9 1 .06 1 .17arornat ic 0. 0.9 1.08 1.2 From Fig s. 1 and 3 at 0.2 and T i
1.289, P c / p p c 1.17; p p / p p c 1.24.
for non-methane and methane sys tems , respecti vely.
The parameters are the mole fractions of the low-
boiling component and of methane, and the upper
limits on i are establ ishe d by the ethane-n-
decane and y the methane-n-heptane sy st em s,
respectively. For acetylene, naphthene, and
aromatic-containing systems, the correction factors
and ranges of presented in the preceding section
again apply. For eight non-methane binary systems
containing paraffins, isoparaffins and olefins, the
average deviation for the 46 mixtures i s 1.73 per
cent. For six methane systems, the average
deviation for 32 mixtures is 1.56 per cent; for five
acetylene, naphthene and aromatic systems and
30 mixtures, 1.92 per.cent The resul ts a re include
s part of Ta ble together with maximu
deviations.
1.17(536.8) 628.1 ps ia ;
1.24(536.8) 665.6 psia.
Reamer, Sage and Lac ey 28 report valu es f 632
and 677 psia for this mixture.
EXAMPLE CALCULATION
Determine the cricondentherm and cricondenbar
pre ssures of a mixture having the following composi-
tion:
Mole Fraction Tb (% (psia)
Ethane 0.502 331.7 707.
Cyclohexane 0.498 637 591.5
0.502(331.7) 0.498(637) 483.7R
(from Eq. 1 and vapor pressu re dat a) 356R
0.502(707.i) 0.498(591.5) 649.6 psia
From Fig s. 1 and ze 0.502 and TL /Tb
1.354, P c / P p c 1.34; pp /ppc 1.79. Using the
correction actors, p, /ppc 1.34(1.06) 1.42;
p p / p p c 1.79 (1.06) 1.9.
EXAMPLE CALCULATION
Determine the cricondentherm and cricondenbar
pressures of a mixture having the following con-
position:
Mole Fraction (OR) (psia)
thane 0.2 331.7 707.1
n-Pentane 0.8 556.6 494.2
1-4 2 (649.6) 922.4 psia;
T A B L E 2 I N A R Y S Y S TE M S I N V E S T I G A T E D A N D C R I C O N D E N T H E R M
A N D C R I C O N D E N B A R P R E S S U RE D E V I A T I O N
Cricondentherrn Pressure
No. of Devi at ion s,
Cr icondenbar Pressure . Pn
No. of Devi at ions
System Mixtures Average Maximu m Mixtures Average Maximu m
Methane-cyclohexane(27)
Ethane-cyclohexone(l6)
Ethane -benzene( l7 )
ca lcu la ted va lve reported value 10reported value
S O C I E T Y O F P E T R O L E U M E N G I N E E R S J O U R N A L
1.9 (649.6) 1234.2 p s i a .
K a y l 6 r e p o r t s v a l u e s o f 50 1,244 p s i a f o r t h i s
m i x t u r e .
M U L T I C O M P O N E N T M I X T L J R E S
CRICONDENTHERM PRESSURE
F i g . m a y a l s o b e u s e d f or t h e c a l c u l a t i o n o
o f a n o n - m e t h a n e h y d r o c a r b o n m i x t u r e c o n t a i n i n
t h r e e o r m o r e c o n s t i t u e n t s . s t e p w i s e c a l c u l a t i o n
p r o c e d u r e m u s t b e a d o p t e d , w h i c h s o m e w h a t
d i f f e r e n t th a n t h a t d e v e l o p e d b y G r i e v e s a n d
T h o d o s 1 0 f o r c r ic o n d e nt h er m a n d c r i c o n d e n b a r
t e m p e r a t u r e s . F o r a t e r n a ry s y s t e m , t h e b i n a r y
p o r t io n c o n s i s t i n g of t h e t w o h ig h - b o i l i n g c o m p o n e n t s
c o n s i d e r e d f i r s t . T h e c r i c o n d e n t h e rm p r e s s u r e o f
t h e b i n a ry i s c a l c u l a t e d u s i n g t h e r e l a t i v e (l o w -
b o i l in g - f r e e b a s i s ) m o l e f r a c t i o n s o f t h e t w o
c o m p o n e n t s t o e s t a b l i s h t h e b i n a r y c o m p o s i t i o n .
T h e n , p p , , T b a n d T i , a r e c a l c u la t e d a n d
d e te r m in e d . N e x t t h e t e r n a ry s c o n s i d e r e d a n d T
s c a l c u l a te d w i t h E q . 1. is c o m pu te d a s t h e
m o l a r a v e r a g e o f t h e n o rm a l b o i l i n g p o i n t of t h e
p u r e l o w - b o i l in g c o m p o n e n t a n d of t h e a t m o s p h e r i c
b o i l in g p o i n t o f t h e h i g h - b o i li n g b i n a r y ( c o m p o s i t i o n
b a s e d on l o w - b o i li n g - f re e b a s i s ) . c a l c u l a t e d
s t h e m o l a r a v e r a g e o f t h e C r i t i c af C p r e s su r e of t h e
p u r e , l o w - b o i li n g c o m p o n e n t a n d of t h e d e t e r m i n e
c r i c o n d e n th e r m p r e s s u r e of t h e h e a v y b i n a r y . F o rs y s t e m s c o n t a i n i n g m or e t h a n t w o c o m p o n e n t s ,
m a y b e te r m e d a p s e u d o c r ic o n d e n t h e r m p r e s s u r e .
T h e c r i c o n d e n t he rm p r e s s u r e i s t h en e s t a b l i s h e d
f r o m F i g . 1.
F o r a f o u r c o m p o n e nt s y s t e m , t h e h e a v i e s t
b i n ar y i s a g a i n c o n s i d e r e d f i r s t , t h en t h e h e a v i e s t
t e r n a ry a n d f i n a l l y t h e q u a t e r n a r y , d e t e r m i n i n g
o f t h e b i n a r y f o r o f t h e te r n a r y , a n of the
t e r n a r y f o r o f t h e q u a t e r n a r y . f or e a c h s t e
is c o m p u te d u s i n g b of t h e h e a v i e s t b in a r y
t e r n a ry , e t c . T h e n e c e s s i t y f a s t e p w i s e p r o c e d u r
s o b v i o u s f ro m F i g . w h e n ze b e c o m e s z e r o ,
p I / p p c b e c o m es un i y ( a s d o e s T i / T b ) , a n d
m u s t b e c o m e t h e a c t u a l c r ic o n d en t h er m p r e s s u r e o
t h e m i x t u re o f t h e r e m a i n i n g h ig h - b o i l in g c o m p o n e n t s .
F o r m u l t i c o m p o n e n t m i x t u r e s c o n t a i n i n g m e t h a n e ,
t h e p r o c e d u re s t h e s a m e a s f o r n o n - m et h an e
s y s t e m s , e x c e p t f o r t h e f i n a l s t e p i n t h e c a l c u l a t i o n .
F i g . u s e d t o c a l c u l a t e t h e c r i c o n d e n t h e r m
p r e s s u r e of t h e h e a v i e s t b i n a ry , t e r n a ry , e t c . ; t h e n ,
f o r t h e c a l c u l a t i o n o f o f t h e r e q u i r e d m i x t u r e ,
F i g . u s e d .
T h e p r o c e d u re h a s b e e n t e s t e d n n i n e s y n t h e ti c
a n d n a t u r a l l y - o c c u r r i n g m i x t u r e s c o n t a i n i n g f r o m
t h r e e t o s i x c o m p o n en t s. T h e a v e r a g e d e v i a ti o n i
0.96 p e r c e n t f o r b o t h r n e t h an e a n d n o n - m e t h a n e
m i x t u r e s. T h e r e s u l t s a r e i n c lu d e d i n T a b l e 3.
CRICONDENBAR PRESSURE
s l i g h t l y m o di fi ed s t e p w i s e p r o ce d u r e s h o u l d
b e e m p l o y e d f o r t h e c o m p u t a t i o n o f f o r m u l t i -
c o m p o n en t m i x t u r e s ; t h e p r o c e d u r e i s i d e n t i c a l t o
t h a t p r e s e n t e d b y G r i e v e s a n d T h o d o s l o f o r
c r i co n d e n t h e r m a n d c r i c o n d e n b a r t e m p e r a t u r e s .
T h e o n l y d i f f e r e n c e f ro m t h a t g i v e n f o r s in t h e
c a l c u la t i o n f . In e a c h s t e p f t h e c a l c u la t i o n ,
i i s e v a l u a te d a s t h e m o la r a v er a g e of t he n or ma l
b o i l in g p o i n t s of a l l t h e c o m p o n e n t s i n v o l v e d .
FIG. ELATIONSHIP BETWEENAND
FIG. ELATIONSHIP BETWEEN p p / p , , AND T,
Tb FOR N O N - M E T H A N E S Y S ~ E ~ S .' I - ~ OR M E T H A N E SYSTEMS.
SEPTEMBER , 196 .124
p p c , a p s e u d o c r i c o n d e n b a r p r e s s u r e , i s c a l c u l a t e d
n t h e s a m e m a n n e r s g i v e n f o r c ri c o n d e n th e r m
p r e s s u r e s , e x c e p t c r ic o n d en b a r p r e s s u r e s a r e u s e d
f or e a c h s t e p f o l lo w i n g t h e bi n ar y . F i g . i s u se d
f o r no n - m e th a n e s y s t e m s , a n d F i g s . fo
m e t h a n e s y s t e m s w it h F i g . u s e d i n t h e l a s t s t e p
f t h e c n l c u l a t i o n . F o r 15 s y n t h e t i c a n d n a t u r al l y -
o c c u r ri n g m u l t i c o m p o n e n t m i x t u r e s t h e a v e r a g
d e v i a t i o n o f c a l c u l a t e d c r i c o n d e n b a r p r e s s u r e s
o m r e p o r t e d v a l u e s i 2.24 p e r c e n t. T h e re s u l t s
a r e g i v en i n T a b l e 3.
E X A M P L E C A L C U L A T I O N
D e t e r m i n e t h e c r i c o n d e n th e r m a n d c r i c o n d e n b a r
p r e s s u r e s o f m i x t u r e h a v i n g t h e f o l l o w i n g
c o m p o s i t i o n :
M o l e F r a c t i o n ?' .(%) P c i ( p s i a )
P r o p a n e 0.486 416.1 617.4
n - B u t a n e 0.332 491.6 550.1
n - P e n t a n e 0.121 556.6 494.2
n - H e x a n e 0.061 61 5.4 433.
A . E s t a b l i s h f t h e n - p e n t a n e - w h e x a n eb i n a r y .
B i n a r y c o m p o s i t i o n :
0.121n - p e n t a n e : 0.665
0.121 0.061
0.061n - h e x a n e : ------ 0.335
0.121 0.061
0.665 (556.6) 0.335 (615.4) 576.3K
T b ( f ro m E q . a n d v a po r p r e s s u r e d a t a ) 570R
0.665 (494.2) 0.335 (433.9) 474.0 p s i a
F r o m F i g s . z~ 0.665 a n d 7 ' ; / T b
1.011, Pt /ppc 1.02; pp / ' ppc 1.03.
1.02(474) 483.5 p s i a ;
,bp 1.03(474) 488.2 p s i a .
B . E s t a b l i s h pp o f t h e n - b u t a n e - n - p e n t a n e -
n - h e x a n e t e r n a ry .
T e r n a r y c o m p o s i t i c n :
0.332n - b u t a n e : 0.6460.332 +0.121 +0.061
S i m i l a r l y , n - p e n t a n e 0.235; n - h e x a n e 0.119
(from Eq. a n d v a p o r p r e s s u r e d a t a ) 508R
0.646 (491.6) (0.235 0.119) (570)
519.4R
( N o t e t h e u s e of T b c a l c u l a t e d i n S e c ti o n A )
0.646(550.1) (0.235 0.119) (483.5)
526.6 p s i a
F r o m F i g . 0.646 a n d T E, 519.4 /508
1.022, p t / p p c 1.04
1.04(526.6) 547.7 p s i a .
0.646 (491.6) 0.235 (556.6) 0.119 (615.4)
521.6R
0.646 (550.1) (0.235 0.119) (488.2)
528.2 p s i a .
F r o m F i g . 0.646 T L / T b 521.6/508
1.027, p p / p p , 1.06.
1.06(528.2) 559.9 p s i a .
C. E s t a b l i s h p, o f t h e r e q u i r e d q u a t e r n a r y
T b ( f ro m E q . a n d v a po r p r e s s u r e d a t a ) 442R
0.486(416.1) (0.332 0.121 0.061)
508 463.3R
T A B L E 3 U L T I C O M P O N E N T S Y S TE M S I N V E S T I G A T E D A N D C R I C O N D E N T H E R M
A N D C R I C O N D E N B A R P R E S S U RE D E V I A T I O N S
System
Methane-ethane-n-butane(3)
Ethane-propane-n-pentane(6)
Propane -n-butane-n-pentane(6)
n-B~tane-n-~entane-n-hexane(6)
Methane-ethane-propane-n-
b u t a n e ( l 8 )Ethane-propane--n-butane -n-
pentane(6 )
Propane-n-butane- n-pentane-
n-hexane(6)
Methane-ethane-propane
n-butane-n-pentane(6,ll)
Methane-ethane-propme
n-pentane-n-hexane(1 1)
Ethane-propane-n-butane-
n-pentane-n-hexane(6)
Cricondentherm Pressu re, pt
Number of Average
Mixtures Dev ia t ion .
2.65
1 0.84
0.55
1.19
Cricondenbar Pressure,
Number of Average
Mixtures Dev ia t ion ,
1 1.44
3.43
3.45
1 0.7
Methane-ethane-propane-
n-butane -n-pentane-
n-hexane(6)
S O C I E T Y P E T R O L E U M E N G I N E E R S J O I J R N A I
( N o t e th e u s e Tb ca l cu l a t ed i n Sec t i on
0.486 (617.4) (0.332 0.121 0.061)
547.7 581.6 p s i a .
From Fig . 0.486 1.048,
/ p p C 1.07
1.07 (581.6) 622.3 p s i a .
p:
0.486(416.1) 0.332(491.6) 0.121 (556.6)
0.061 (615.4) 470.2R
0.486(617.4) (0.332 0.121 0.061)
559.7 587.9 p s i a .
From Fig . 0.486 T i 1.063,
p p / p p c 1.11.
l . l l(587.9) 652.6 p s i a .
E t t e r a n d ~ a ~ repor t va lues of 635 65 p s i afor th is mixture .
EXAMPLE CALCULATION
Determine the cr icondentherm and cr icondenbar
p re s su re s f a mix ture hav ing the fo l l owing com-
pos i t i on :
Mole Frac t ion Tbi('%) pci(psia)
Methane 0.193 200.7 673.1
E t h a n e 0.470 331.7 707.1
n-Bu tane 0.337 491.6 550.1
A. E s t a b l i s h f the ethane-n -buta ne
binary.
Binary composi t ion:
e t h a n e :0.47
0.5820.47 0,337
n-butane 0.418
0.582 (331.7) 0.418 (491.6) 398.4R
351R
p p c = 0.582 (707.1) 0.418 (550.1) 642 p s i a .
F rom F igs . 0.582
1.134, p t / p p c = 1.205; p p / p P c 1-31.
1.205 (642) 773.6 p s i a ;
1.31 (642) 841 p s i a
B . Es t ab l i sh of the requi red te rnary
PP 0.193(673.1) (0.47 0.337) (773.6)
753.9 p s i a
From Fig . zb 0.193 1.316,
/ p p , 1.17
1.17(753.9) 881.1 ps i a .
0.193 (200.7) 0.47(331.7) 0.337 (491.6)
360.3R
0.193 (673.1) (0.47 0.337) (841)
807.3 p s i a
From Fig . z~ 0.193 1.471,
1.35
1.35 (809.3) 1092 p s i a .
Co ta an d Thod os3 repo rt va lue s o f 905 1108
ps i a fo r t h i s mix tu re .
SUMMARY
ra the r accu ra t e me thod has been deve loped
for the predic t ion of the cr icondentherm and cr icon
denbar pressures of mul t icomponent hydrocarbon
mixtures of known compo si t ion . The se mixtures
may conta in normal and i soparaf f ins , o lef ins ,
a c e t y l e n e s , n a p h t h e n e s a n d a r o m a t i c s , a n d t h e i r
c r i conden the rm and c r i condenba r p r e s su re s may be
computed from a knowledge of the pure component
c r i t i c a l p rope r t i e s and vapor p re s su re behav io r .
NOMENCLATURE
pc pseu doc r i t i c a l , - p seudoc r iconden the rm, o r
pseudocr icon denbar pre ssu re f mixture
(method of ca lcula t ion depends on number
f com ponents) , ps ia
c r i t i c a l p r e s su re o f pu re j th componen t , p s i a
vapor press ure of pure jth component , p s ia
c r i condenba r p re s su re o f mix tu re , p s i a
c r i conden the rm p re s s u re f mix tu re, p s i
a tm osph er ic boi l ing point of mixture , OR
molar ave rag e boi l ing point of mixture
(method of ca lcula t ion depends on number
f com ponents and whether orbeing computed) ,
normal boil ing point of pure j th component,
mole fraction of j th component
Z& mole fraction of low-boiling component
t o t a l p r e s s u r e , p s i a .
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