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 .

REFERENCES

1. Amick, E. Johnson, W. and Dodge, B. .:

C h e m . E n g . P r o g + . (Symposium Series ) (1952)

Vol. 6, No. 3, 65.

2. Bloomer, Gami, D. C. and Parent, J. .:

"Phys ical -Chemical Properties of Methane-Ethan

Mixtures", R e s e a r c h B u l l e t i n N o . 22 Institute of-.

Gas T echnol ogy, T echnol ogy Center, Chicago, 1

(July, 1953).

3. Cota, . and Tho dos , Geor ge: J o u r . C h e m . E n g .

D a t a (1962) Vol.

4. Eilerts, ., e l a l . : "Phase Relations of Gas-

Condensate Fluids", M o n o g r a p h N o . U S B M(1957 ) Vol. 1, 101.

SEPTEMBER , 1 9 6 4

5. Eilerts, C. K., cJr a l . : "Pha se Re la t ions of Gas -

Condensa te F lu ids" , Monograph No. USBM

(1957) Vol. 1, 154.

6. Et ter , D. 0. and Kay , W. J o u r . C h e n ~ . E n g .

Datt7 (1961) Vol. 6 , 409.

7. Grieves, B. and Thodos , George: "The Cr i t i ca l

T e m p e r a t u r e s a n d C r i t i c a l P r e s s u r e s Binary

Mixtures o f the F ixed Ga se s and Aliphatic Hydro-

carbons", S o c . P e t . Fug . J o u r . (Sept., 1962) 197.

8 . Gr ieves , R. and Thodos , George : A l C h E J o u r .

(1962) Vol. 8, 550.

9. Grieves, B. and Thorlos, George: A l C h E l o u r .

(1963) Vol. 9, 25.

10 . Gr ieves , R B. and Thodos , George : "The Cr iconden-

therm and Cr icondenb ar Temper atur es of Multi -

component Hydrocarbon Mixtures", Tor . P e l . E n g .

Jotrr . (1963) Vol. 3, 287.

11. Hanson, G. H. an d Brown, G. G.: I n d . E n g . C h e m .

(1945) Vol. 37, 821.

12 Kay, B.: I n d . E n g . C h e m . (1938) Vol. 30, 459.

13. Kay, B. I n d . E n g . C h e m . (1940) Vol. 32, 353.

14. Kay, W. B.: I n d . E n g . C h e m , (1941) Vol. 33, 590.

15. Kay, B. I n d . E n g . C h e m . (1948) Vol. 40, 1459.

16. Kay, W. I n d . E n g . C h e m . (1956) Vol. 48, 422.

17. Kay, W. B. a n d N e v e n s , T. D. C h e m . E n g . P r o g r .

(Symposium Serie s) (1952) Vol 48, No. 3 , 108.

18. Kurata , Fred an d Katz, D. L. T r a n s . , A I C h E

(194 2) Vol. 38, 995.

19. McCurdy, L . and Katz , D. L. O i l G a s J o ur .

(1945) Vol. 43, 102.

20. McKay, R. A., R eame r, H. H. , Sage , B. H. and

L a c e y , N1 N.: l a d . E t r g . C h e m . (1951) Vol. 43, 2112.

21. Nysewander , C. N., Sage, B. H. a n d L a c e y , W. N.:

I n d . E n g . C h e m . (19 40) Vol. 32, 118.

22. Olds, R. H., Sage , B. H. and Lace y , N.: I n d .

E n R . C h e m . (1942) Vol. 34, 1008.

23. Organick, E. I. C h e m . E n g . P r o g r . (Sympcsium

Ser ies ) (1953) Voi. 49, No. 6, 81.

23. Reamer, H. H. and Sage, B. .: ] o u r . Chern . E n g .

D a t a (1962) Vol. 161.

25. Reamer, H., Sage, B. . and Lace y , W. N.:

I n d . E n g . C h e m . (1950) Vol. 42, 534.

26. Ream er, . H., S ag e, B H. a n d L a c e y , W. N.

I n d . E n g . C h e m . (Data Series) (1956) No. 29

27. Reamer, H. , Sage, B. . and Lac ey , N.:

l o u r . C h c r n . E n g . Da t a (19 58) Vol. 3, 240.

28. Reamer, H. ., Sage , B. . and Lac ey , W. N.

] o u r . C h e r n . E n g . D a t a (1960) Vol. 5, 44.

29. Sage , B. H., Hick s, B. L . a n d L a c e y , \V. N.: I n d .

E n g . C h e m . (1940) Vol. 32, 1085.

30. Sage, B. H. a n d L a c e y , W. N.: Ind. Errg. C h e m .

(1940) Vol. 32, 992.

31. Sage, H., Rea mer, H. H., Old s, R. H. a n d L a c e y ,W. N.: I n d . E n g . C h e m . (1942) Vol. 34, 1108.

32. Silverman, E. D. and Thodos, George: I n d . E n g .

C h e m . (Fun dame ntal s) (1962) Vol . 1 , 299

33 Vaughn, W. E . a n d C o l l i n s , F. C.: Itzd. Eng. C h e m .

(1942) Vol. 34, 885.

S OC I E T Y P E T ROL EUM EVCINEEHS JO I I RNA I .