Equations of State

Abbott, Michael M. Adachi, Y. Barrufet, Maria A. Blum, Lesser. Brainard, A. J . BurCham ... Esper, Gunter J . Eubank, Philip T. Georgeton, Gus K. Gree...
1 downloads 0 Views 2MB Size
Download PDF
Equations of State Downloaded from pubs.acs.org by 5.101.220.137 on 12/04/18. For personal use only.

Author Index A b b o t t , M i c h a e l M. Adachi, Y. B a r r u f e t , M a r i a A. Blum, L e s s e r B r a i n a r d , A. J . BurCham, Andy F . Calado, J . C . G. Celmins, Ilga Chabak, J o s e p h J . Chang, R . F . Chao, K . C . C h o r n g , H. Twu Chung, F . T . H . Copeman , Thomas W. D e i t e r s , U l r i c h Κ. Donahue, Marc D. E l y , James F . E n i c k , R. M . E r i c k s o n , D a l e D. E s p e r , Gunter J . Eubank, P h i l i p T . G e o r g e t o n , Gus K . G r e e n k o r n , R. A. G r e n k o , J . A. H a l l , C . K. H a l l , K e n n e t h R. Han, S. J . H a s e l o w , J . S. Heidemarm, R o b e r t A. H e n d e r s o n , Douglas H o l d e r , G. D. H o l s t e , James C . Honnell, K.G. Kanchanakpan, S . B . K i m , H. Lee, K . - H .

Lee. L . L . Lee, R . J . L e i a n d , Thomas W. Levelt Sengers, J.M.H. L i , M.H. Lu, B.C.-Y. Majeed, A l i I. M a n l e y , D a v i d B. Mansoori, G. A l i M a t h i a s , Paul M . M o r r i s , R a n d a l l W. Morrison, G. Nass, Kathryn K. P a l e n c h a r , Robert M . P a n a g i o t o p o u l o s , A. Z. P o l i n g , Bruce E . Reid, R.C. R i j k e r s , M a r i nus P.W. Rowlinson, John S. Rubio, R.G. Sandler, S.I. Smith, Richard Lee, J r . So, C . - K . Starling, K.E. S t r e e t t , W.B. S t r y j e k , R. T a n i , Alessandro T e j a , Am yη S . Trampe, Mark D. T u r e k , Edward A. Vera, J . H . V i m a l c h a n d , P. Wagner, Jan W i l s o n , Grant M. Yu, J . - M .

Subject Index A c i d g a s - o i l system phase d i s t r i b u t i o n s f o r San Andres o i l s t u d y , 432f s a t u r a t i o n pressure l o c i , 428f,429f A c t i v i t y c o e f f i c i e n t , d e f i n i t i o n , 21 A c t i v i t y c o e f f i c i e n t model a p p l i c a t i o n s , 352 F l o r y - H u g g i ns mode1, 195 Adhesive i n t e r m o l e c u l a r p o t e n t i a l , l o c a l compositions for m i x t u r e s , 356

A

Accelerated Successive S u b s t i t u t i o n (ACSS) c o n v e r g e n c e b e h a v i o r of a m i x t u r e , 484 COSS c o m p a r i s o n , 484 f l a s h c a l c u l a t i o n s , 484,486f K v a l u e s u p d a t e d , 480-481 s o l u t i o n r e g i o n f o r a m i x t u r e , 486f

583

584

EQUATIONS OF STATE: THEORIES AND

A l k a n e m o d e l , Monte C a r l o s i m u l a t i o n o f l o c a l f l u i d s t r u c t u r e , 202-203 Alkanes properties cubic equations performance s t u d i e d , 539-542 percent d e v i a t i o n s i n c u b i c e q u a t i o n s s t u d y , 541t predictive a b i l i t y of cubic e q u a t i o n s compared, 541-542 t r e a t m e n t i n Monte C a r l o s i m u l a t i o n o f f l u i d s , 204 A r g o n , m o l e c u l a r volume, C a r n a h a n - S t a r l i n g and R a c k e t t e q u a t i o n s compared, 53Of Average p o t e n t i a l model (APM), m i x t u r e radial distribution f u n c t i o n s , 322 - 323 A z e o t r o p e s , p r e d i c t i o n by t h e p e r t ur be d - a n i s ot r o p i c - c h a i n t h e o r y , 305

Β Bead-bead i n t e r m o l e c u l a r r a d i a l distribution function a l k a n e c o m p a r i s o n s , 208f bead d i a m e t e r e f f e c t , 207,208f butane c o m p a r i s o n i n f l u i d s t r u c t u r e s t u d y , 206f c h a i n l e n g t h e f f e c t , 207 c h a i n l e n g t h i n c r e a s e , 205 e q u a t i o n , 204-205 l o c a l c o r r e l a t i o n s of h a r d - s p h e r e monatomi c s , 20 6f Monte C a r l o s i m u l a t i o n c a l c u l a t i o n f o r f l u i d s , 204 Monte C a r l o s i m u l a t i o n p r e d i c t i o n f o r b u t a n e , 206f range i n f l u i d s t r u c t u r e s t u d y , 209-212 RISM and Monte C a r l o c o m p a r i s o n f o r butane,

21 Of

RISM and Monte C a r l o c o m p a r i s o n f o r o c t a n e , 21 Of temperature e f f e c t , 207,208f Binary c r i t i c a l l o c i d e f i n i n g e q u a t i o n s , 133-134 d i f f i c u l t i e s of p r o p e r t y p r e d i c t i o n , 132 m a t h e m a t i c a l approach used i n p r e d i c t i o n , 136 p r e d i c t i o n error for cubic equations of s t a t e , I48t p r e d i c t i v e a b i l i t y of cubic equations of s t a t e , 132-154 r e s u l t s i n p r e d i c t i o n s t u d y , 137-138 systems s e l e c t e d f o r s t u d y , 136-137

APPLICATIONS

Binary c r i t i c a l l o c i — C o n t i n u e d u n i i k e - p a i r parameters e n h a n c i n g p r e d i c t a b i l i t y , 150 van der Waals q u a l i t a t i v e p r e d i c t i o n , 133 van Konyenburg and S c o t t c l a s s i f i c a t i o n , 139-141 B i n a r y f l u i d m i x t u r e , thermodynamic c o n d i t i o n s of phase e q u i l i b r i u m , 375 B i n a r y i n t e r a c t i o n parameters d e f i n i t i o n and p u r p o s e , 572 new l o c a l c o m p o s i t i o n model u s e , 262 o n e - f l u i d m i x i n g r u l e s i m p r o v e d , 353 p e r t ur be d - a n i s o t r o p i c - c h a i n t h e o r y a p p l i c a t i o n , 305, 306t second i n t e r a c t i o n parameter i n t r o d u c e d , 572 Binary mixtures c r i c o n d e n t h e r m l o c a t i o n , 48 e q u a t i o n - o f - s t a t e mixing r u l e s s t u d i e d , 366t l o c a l compositions defined f o r f l u i d s , 252 phase e q u i l i b r i u m s t u d y r e s u l t s , 378-380 phase e q u i l i b r i u m p r e d i c t e d , 378-380 van der Waal s o n e - f l u i d t h e o r y , 256 van d e r Waals t h r e e - f l u i d t h e o r y , 255 van der Waals t w o - f l u i d t h e o r y , 255-256 vapor-liquid equilibrium calculations from m i x i n g r u l e s , 263-26 8t B i n a r y p a r a m e t e r s , a p p l i c a t i o n t o phase e q u i l i b r i u m c a l c u l a t i o n s , 378 B o i l i n g p o i n t s , e n t r o p y d e v i a t i o n , 521 B o u b l i k - A l d e r - C h e n - K r e g l e w s k i (BACK) equation accuracy for nonspherical m o l e c u l e s , 244 model b a s i s , 228 t e t r a f l u o r o m e t h a n e a p p l i c a t i o n , 76-78 Bring-back correction factors, four-phase f l a s h calculations u s e , 504 Bubble-point pressures , p r e d i c t i o n f r o m PFGC e q u a t i o n f o r s y n t h e t i c o i l , 469f B u t a n e , c a l c u l a t e d volume e r r o r u s i n g R e d l i c h - K w o n g p a r a m e t e r s , 400t

C

Carbon d i o x i d e " a " parameter equation, " b " parameter equation,

f o r Redlich-Kwong 391f f o r Redlich-Kwong 391f

585

INDEX Carbon

dioxide—Continued

Conformai s o l u t i o n a p p r o x i m a t i o n (CSA) mixture r a d i a l d i s t r i b u t i o n f u n c t i o n s , 320 R e d l i c h - K w o n g parameters , 398t See a l s o M u l t i f l u i d c o n f o r m a i m o l a r volume e r r o r f o r R e d l i c h - K w o n g s o l u t i o n approximation equation Conformai s o l u t i o n m i x i n g r u l e s new p a r a m e t e r s , 396f Soave p a r a m e t e r s , 393f compared w i t h new l o c a l c o m p o s i t i o n s t a n d a r d parameters , 392f m o d e l s , 262 Y a r b o r o u ^ i p a r a m e t e r s , 394t density calculations for binary vapor p r e s s u r e e r r o r f o r m i x t u r e s , 269t Conventional Successive S u b s t i t u t i o n R e d l i c h - K w o n g e q u a t i o n , 397f (COSS) Carbon d i o x i d e - o i l system ACSS c o m p a r i s o n , 484 s a t u r a t i o n l o c i comparison of convergence b e h a v i o r of a p r e d i c t e d and compared v a l u e s , 41 8t m i x t u r e , 487 s a t u r a t i o n l o c u s i n t e r s e c t i o n , 426f Κ v a l u e s u p d a t e d , 479 Carnahan-Starling equation s o l u t i o n r e g i o n f o r a m i x t u r e , 485f c o m p r e s s i b i l i t y f a c t o r , 526 Convergence, speed w i t h f l a s h c o n t a c t v a l u e s f o r f l u i d s , 256 c a l c u l a t i o n s , 488-492 Chemical p o t e n t i a l s , b i n a r y f l u i d C o o r d i n a t i o n number l o c a l c o m p o s i t i o n model f o r b i n a r y m i x t u r e , 375 m i x t u r e s , 252 C l a s s i c a l behavior predictions for square-well f l u i d m i x t u r e s , 115-116 f l u i d s , I86f i m p l i c a t i o n s , 115 C o o r d i n a t i o n number models s c a l e d behavior c r o s s o v e r , 113-115 square-well f l u i d C l a s s i c a l e q u a t i o n s , d i s a d v a n t a g e s , 119 comparison, 183-I85t Classical fluids van der Waals p a r t i t i o n f u n c t i o n , 184 d e f i n i t i o n , 111 Correlation hole, explanation i n f l u i d s t r o n g divergences i n behavior s t r u c t u r e e x p e r i m e n t , 20 5 o b t a i n e d , 111 C o s t a i d c o r r e l a t i o n , s p e c i f i c volume C l a s s i c a l s o l u t i o n thermodynamics, p r e d i c t i o n , 93 independent v a r i a b l e s , 2 Cricondentherm, c o l l i n e a r isochores for Combining r u l e s e m p i r i c a l m o d i f i c a t i o n , 572 v a r i o u s s y s t e m s , 51 e x p r e s s i o n , 572 C r i t i c a l l i n e , i n i t i a l slope e x p r e s s i o n , 126 new l o c a l c o m p o s i t i o n m o d e l s , 261 C r i t i c a l point C o m p r e s s i b i l i t y equation, mixing r u l e thermodynamics, 133-134 d e v i a t i o n f o r f l u i d s , 317-318 See a l s o M i x t u r e c r i t i c a l p o i n t Compressibility factor C r i t i c a l s t a t e s , d e s c r i b e d by e q u a t i o n s d e v i a t i o n contours f o r c u b i c of s t a t e , 109-178 equations, 555f,556f C r i t i c a l volume, c u b i c e q u a t i o n s hard spheres predictive a b i l i t y i n binary C a r n a h a n - S t a r l i n g e q u a t i o n , 528f m i x t u r e s , 151 d i s r u p t e d by m i x i n g r u l e s , 335-336 C r o s s o v e r f u n c t i o n , d e f i n i t i o n , 113 m i x t u r e h a r d - s p h e r e e r r o r , 339f C r y o g e n i c m i x t u r e s , f l u i d - f l u i d and mixtures of Lennard-Jones s o l i d - f l u i d e q u i l i b r i a , 371-385 m o l e c u l e s , 259t Cubic Chain of Rotators equation predictions for square-well d e s c r i p t i o n of binary f l u i d s , I88f s u p e r c r i t i c a l p r o p e r t i e s , 171 p r o p a n e - p r o p a d i e n e system r e s u l t s , s o l u b i l i t y of a c r i d i n e i n 98 t r i f l u o r o c h l or cm e t h a n e , 1 76f van der Waals m i x i n g r u l e s compared s o l u b i l i t y o f phenol i n c a r b o n w i t h new, 337 d i o x i d e , 1 76f Computer s i m u l a t i o n , l o c a l c o m p o s i t i o n supercritical solubility f o r m u l a t i o n s c o m p a r i s o n , 357-358 d e s c r i p t i o n , 164 Conf i g u r a t i o n a l e n e r g i e s , d e f i n e d f o r C u b i c e q u a t i o n s of s t a t e van der Waals p a r t i t i o n f u n c t i o n , 191 binary system's c r i t i c a l l o c i Conformai p a r a m e t e r s , d e f i n i t i o n , 315 p r e d i c t e d , 153-154 Conformai s o l u t i o n design, 542-546 d e f i n i t i o n , 315 d i s a d v a n t a g e s of two m i x i n g r u l e s , 31 7 t em per at ur e - de pen dent p o l a r f l u i d t r e a t m e n t d i f f i c u l t y , 316 parameters, 546-548 calculated

volume e r r o r

using

586 Cubic equations

EQUATIONS OF STATE: THEORIES AND APPLICATIONS of

state—Continued

e q u a t i o n s examined i n d e s i g n s t u d y , 538-539 e v a l u a t i o n , 538-539 e x p r e s s i o n , 537 f e a t u r e s , 540t g e n e r a l , c h o i c e s of c o n s t a n t s , 436t g e n e r a l f o r m , 434,571 mixing rules a p p l i c a t i o n s , 324 p o l a r , asymmetric systems d e r i v e d , 571-582 g e n e r a l i z e d , 314-328 m i x t u r e a p p l i c a t i o n s , 314 parameter v a l u e s i n b i n a r y c r i t i c a l l o c i s t u d y , I48t parameters , 572 Peng-Robinson e q u a t i o n m o d i f i e d t o low r e d u c e d t e m p e r a t u r e s , 560 -56 9 p o l a r f l u i d s a p p l i c a t i o n , 434-451 p r e d i c t i n g binary c r i t i c a l l o c i , 132-154 quadratic temperature f u n c t i o n u s e d , 435 s e l e c t i o n and d e s i g n , 537-538 t em per at ur e - de pen dent par am et e r s , 43 5, 53 9 van d e r Waals m i x i n g r u l e s a p p l i c a t i o n , 361-362 r e s u l t s , 331

D

D e i t e r ' s equation a p p l i e d t o t et r a f l u o r cm e t h a n e , 71-73 d i s a d v a n t a g e s , 82 m i x i n g r u l e s , 374 D e v i a t i o n entropy a r g o n , l i q u i d s a t u r a t i o n c u r v e , 527f hard-sphere equation-of-state p r o p e r t y c o r r e l a t i o n , 520-521 heats of v a p o r i z a t i o n o b t a i n e d , 520 i d e a l gas h y d r o c a r b o n s w i t h r a r e g a s e s , 523f l i g h t g a s e s , h a l o g e n s , and a m i n e s , 523f v a r i o u s compounds, 521f, 524f liquid-volume variation with t e m p e r a t u r e , 52 5 Deviation functions d e f i n i t i o n , 3-4 rationale, 3 Dew-bubble p o i n t curve (DBC), m i x t u r e c r i t i c a l p o i n t l o c a t i o n , 42-44 D i e l e c t r i c continuum m o d e l , i o n i c f l u i d s , 281 Diffusional s t a b i l i t y homogeneous phase c r i t e r i a , 481

Diffusional stability—Continued l i m i t evaluated i n s i n g l e - s t a g e c a l c u l a t i o n s t u d y , 483 D i l u t e m i x t u r e s , c l a s s i c a l and non c l a s s i c a l t r e a t m e n t , 125 D i l u t e n e a r - c r i t i c a l mixtures d i v e r g i n g p a r t i a l m o l a r volumes t h e s o l u t e , 121 non c l a s s i c a l a n a l y s i s , 122-125 o s m o t i c s u s c e p t i b i l i t y , 124

flash

of

Ε

E f f e c t i v e carbon number (ECN) d e f i n i t i o n , 443 P a t e l - T e j a e q u a t i o n , parameters o b t a i n e d , 443 E n e r g y — S e e G i b b s energy — S e e Helmholtz f r e e energy Energy e q u a t i o n , m i x i n g r u l e d e v i a t i o n f o r f l u i d s , 317-318 E n e r g y o f i n t e r a c t i o n , van der Waals p a r t i t i o n f u n c t i o n , 181 Entropy c a l c u l a t i o n f o r m e t h a n e - c a r bon s y s t e m , 55t See a l s o D e v i a t i o n e n t r o p y E q u a t i o n s of s t a t e Adachi e q u a t i o n , 135 a p p l i c a t i o n s , 352 c l a s s i c a l s o l u t i o n thermodynamics c o n n e c t i o n , 1-40 c o m b i n i n g r u l e s f o r new l o c a l c o m p o s i t i o n m o d e l s , 261 c o m p a r i s o n of e q u a t i o n s a p p l i e d t o t et r a f l u o r cm e t h a n e , 81-82 composition mixing rules studied for b i n a r y s y s t e m s , 366t d a t a , phenomena, and c r i t i q u e , 41-107 D e i t e r ' s e q u a t i o n i n phase e q u i l i b r i a s t u d y , 372 d e n s i t y dependence o f a t t r a c t i v e terra, 363f d e s c r i p t i o n f o r San Andres o i l s d e v e l o p e d , 407-408 d i s t r i b u t i o n function theory basis for nonspherical m o l e c u l e s , 227-244 examined f o r b i n a r y c r i t i c a l l o c i p r e d i c t i o n , 134-135 f l u i d m i x t u r e s , 259 f l u i d - f l u i d and s o l i d - f l u i d e q u i l i b r i a , 371-385 formalism concepts r e l a t i n g t o s o l u t i o n the rm o d y na m i c s, 35 g e n e r a l i z e d van der Waals p a r t i t i o n f u n c t i o n , 180-200 h a r d - s p h e r e a p p l i c a t i o n , 521

587

INDEX Equations of

state—Continued

hard-sphere mixtures f o r f l u i d r e p r e s e n t a t i o n , 255-258 i n i t i a l l o c a l composition i m p o r t a n c e , 354 l i q u i d - m i x t u r e p r o p e r t i e s , 10 l o c a l composition a c t i v i t y c o e f f i c i e n t model a s s i m i l a t i o n , 251 m i x i n g r u l e s development, 3 53-355 parameter c o n s t r a i n t s , 58 P e n g - R o b i n s o n e q u a t i o n , 135 p e r t u r b a t i o n t h e o r y , 64-70 perturbed-anisotropic-chain theory e q u a t i o n , 299 phase e q u i l i b r i u m c a l c u l a t i o n b a s i s , 371 quantum c o r r e c t i o n o f van der Waals t y p e , 373 quantum e f f e c t s contributions a v e r a g e d , 374 radial-distribution function a p p l i c a t i o n , 361 R e d l i c h - K w o n g e q u a t i o n , 134 selected i n supercritical extraction s t u d y , 157-159b Soave e q u a t i o n , 134 s o l u b i l i t y data deviations for binary m i x t u r e s , 166-16 9t supercritical extraction calculation summary, 170t,171 supercritical solubility calculation u s e , 157-159,171 T e j a e q u a t i o n , 135 volume r o o t s , 476 See a l s o C u b i c e q u a t i o n s of s t a t e E t h a n e , c a l c u l a t e d volume e r r o r u s i n g R e d l i c h - K w o n g parameters , 399t Excess f r e e energy, l o c a l c o m p o s i t i o n model a p p l i c a t i o n s , 250 Excess f u n c t i o n s c a l c u l a t i o n o f van der W a a l s , 25 definition, 6 r e s i d u a l Helmholtz energy r e l a t i o n s h i p , 1 4t E x c e s s volumes , s i m u l a t e d and c a l c u l a t e d compared, 344f Expansion c o e f f i c i e n t s , l i q u i d - l i q u i d m i x t u r e s , 119-120

F

F i e l d - d e n s i t y space , c r i t i c a l exponents p a t h , 112f F i e l d - f i e l d s p a c e , c r i t i c a l exponents p a t h , 112f First-contact studies, d e f i n i t i o n , 406-407

Flash calculations c h a r a c t e r i s t i c p r o b l e m s , 495 flow diagram of c o m p u t a t i o n a l a l g o r i t h m , 508f m u l t i phase c o m p u t a t i o n a l a l g o r i t h m , 496 -504 d i s t r i b u t i o n d e t e r m i n e d , 500-501 f o u r - p h a s e s y s t e m r e s u l t s , 494-51 5 o v e r v i e w , 495 s o l u t i o n s e a r c h s t r a t e g y , 505f water a d d i t i o n e f f e c t s t o f o u r - p h a s e s y s t e m , 515 w a t e r - f r e e d e s c r i p t i o n , 504 - 507 s i n g l e stage convergence b e h a v i o r , 476-492 COSS r e s u l t s , 4 8 4 , 4 8 7 f slow convergence p r o b l e m s , 488 two phase e q u i l i b r i u m c o n s t a n t s d e f i n e d , 497 Κ v a l u e i n i t i a t i o n , 498 water e f f e c t on phase distribution, 512f-514f Flory-Huggins model, a c t i v i t y c o e f f i c i e n t m o d e l , 195 Fluid descriptions development f o r o i l - c a r b o n d i o x i d e s y s t e m s , 415-42 5 o v e r v i e w , 407-408 See a l s o F l u i d - f l u i d e q u i l i b r i a Fluid-fluid equilibria e q u a t i o n - o f - s t a t e a p p l i c a t i o n to c r y o g e n i c m i x t u r e s , 371-385 thermodynamic c o n d i t i o n s , 375-376 See a l s o F l u i d d e s c r i p t i o n s F l u i d mixtures c l a s s i c a l c r i t i c a l behavior, 115-116 n o n c l a s s i c a l b e h a v i o r e v i d e n c e , 119 nonclassical c r i t i c a l behavior, 116-119 See a l s o F l u i d s Fluids a t t r a c t i v e and r e p u l s i v e f o r c e s i n m o d e l s , 228 c r i t i c a l b e h a v i o r of p u r e , 110-113 l o c a l s t r u c t u r e v i a Monte C a r l o s i m u l a t i o n , 201-213 t e s t e d by t h e per t ur be d - a n i sot r ο p i c - c h a i η t h e o r y , 301-302 See a l s o F l u i d m i x t u r e s See a l s o R e a l f l u i d s Free energy expression derived for i o n i c f l u i d s , 292-295 W h i t i n g - P r a u s n i t z e x p r e s s i o n , 253-254 See a l s o G i b b s energy See a l s o H e l m h o l t z f r e e e n e r g y F u g a c i t y , mixture behavior, 21-25 Fugacity coefficient activity coefficient c o n v e r s i o n , 21-22 d e f i n i t i o n , 21,479

EQUATIONS OF STATE: THEORIES AND

588

Fugacity coefficient—Continued d e r i v e d from new c u b i c e q u a t i o n m i x i n g r u l e , 573 e v a l u a t i o n at i n f i n i t e d i l u t i o n , 23 e x p r e s s i o n f o r PRSV e q u a t i o n , 563 e x p r e s s i o n f o r use i n p r o p a n e - p r o p a d i e n e s y s t e m , 97 e x p r e s s i o n from van d e r Waals e q u a t i o n , 34 P e n g - R o b i n s o n e q u a t i o n , 354 PFGC e q u a t i o n d e r i v a t i o n , 456 p r e s s u r e - e x p l i c i t e q u a t i o n - o f - s t ate e x p r e s s i o n , 19

G

G a s e s , quantum e f f e c t s a t l o w t e m p e r a t u r e , 372-373 Gibbs-Duhem e q u a t i o n , d i f f e r i n g f o r p a r t i a l p r o p e r t i e s , 18 G i b b s energy b i n a r y f l u i d m i x t u r e , 375 c a l c u l a t i o n f o r pure s u b s t a n c e s , 379f i n f i n i t e pressure excess f u n c t i o n d e r i v e d , 567 m u l t i p h a s e e f f e c t s , 506 s i m u l a t e d and c a l c u l a t e d v a l u e s compared, 346f Goodwin e q u a t i o n parameter p r e c i s i o n i n pro p a n e - p r o pa d i en e s y s t e m , 93 propane and p r o p a d i en e c o n s t a n t s , 911 pro p a n e - p r o pa d i en e system a p p l i c a t i o n , 89

H

Haar

and K o h l e r e q u a t i o n , a p p l i e d t o t e t r a f l u o r cm e t h a n e , 70-71 Han-Cox-Bono-Kwok-Starling equation s o l u b i l i t y of b e n z o i c a c i d i n c a r b o n d i o x i d e , 175f s o l u b i l i t y of f l u o r i n e i n e t h y l e n e , 175f supercritical solubility d e s c r i p t i o n , 164 Hard-sphere e q u a t i o n , property c a l c u l a t i o n at h i g h d e n s i t i e s , 526 H a r d - s p h e r e e x p a n s i o n (HSE) approximation m e a n - d e n s i t y a p p r o x i m a t i o n , 332 mixture r a d i a l d i s t r i b u t i o n f u n c t i o n s , 321 Hard spheres conformai s o l u t i o n m i x i n g r u l e s , 335-337

APPLICATIONS

Hard s p h e r e s — C o n t i n u e d e q u a t i o n s of s t a t e f o r f l u i d s , 255-258 Harmen-Knapp e q u a t i o n , s u p e r c r i t i c a l s o l u b i l i t y d e s c r i p t i o n , 164 Heats of v a p o r i z a t i o n e n t r o p y d e v i a t i o n s used f o r e s t i m a t i o n , 520 e n t r o p y e f f e c t s used f o r e s t i m a t i n g , 52 5 Heavy h y d r o c a r b o n d i s t r i b u t i o n s , f l u i d s from San Andres o i l s , 412f Helmholtz f r e e energy e q u a t i o n , 453 m i x t u r e e r r o r , 34Of p e r t u r b a t i o n t h e o r y d e s c r i p t i o n , 282 PFGC e q u a t i o n - o f - s t a t e f o r m u l a t i o n , 453 van d e r Waals m i x i n g r u l e s compared w i t h new, 337 W h i t i n g - P r a u s n i t z e x p r e s s i o n used f o r f l u i d m i x t u r e s , 260 See a l s o R e s i d u a l H e l m h o l t z energy Henry's constants, mixing rules a s s e s s e d f o r e q u a t i o n s of s t a t e , 35 H e n r y ' s law a c t i v i t y c o e f f i c i e n t , d e f i n i t i o n , 22 Heyen e q u a t i o n s o l u b i l i t y of benzoic a c i d i n carbon d i o x i d e , 1 73f s o l u b i l i t y of fluorine i n e t h y l e n e , 173f Hydrocarbon systems water a d d i t i o n t o s i n g l e - p h a s e s y s t e m , 507, 508t water a d d i t i o n t o t h r e e - p h a s e s y s t e m , 509 water a d d i t i o n t o t w o - p h a s e s y s t e m , 509 Hydro c a r bon-water system A CSS t e c h n i q u e d e r i v e d , 502-503 d i v e r g e n c e problems p r e v e n t e d , 502 i n i t i a l e s t i m a t e o f Κ v a l u e s , 502 m u l t i component system des c r i b e d , 511 multiphase flash c a l c u l a t i o n s , 504 -50 7 Hydrocarbons m o l e c u l a r f l e x i b i l i t y i n c r e a s e as c h a i n l e n g t h i n c r e a s e s , 522 See a l s o L i g j i t h y d r o c a r b o n systems Hydrogen s u l f i d e , c a l c u l a t e d volume error u s i n g Redlich-Kwong p a r a m e t e r s , 400t

I

I n f l e c t i o n l o c u s , i s o c h o r i c , 58 I n t e r a c t i o n e n e r g y , PFGC e q u a t i o n ,

455

589

INDEX I n t e r a c t i o n parameters c a r b o n d i o x i d e , d e s c r i b e d by R e d l i c h - K w o n g e q u a t i o n , 410 determined f o r propane-propadiene system, 93-95 h y d r o c a r b o n - w a t e r s y s t e m , 51 0t R e d l i c h - K w o n g e q u a t i o n f o r San Andres F o r m a t i o n o i l s , 41 It I n t e r n a l energy l o c a l c o m p o s i t i o n model of b i n a r y m i x t u r e , 2 53 s i m p l e f l u i d , 534f Ionic fluids d i e l e c t r i c continuum m o d e l , 281 e q u a t i o n of s t a t e , 2 8 1 - 2 9 5 f r e e energy e x p r e s s i o n d e r i v e d , 292-295 model a p p r o x i m a t i o n s used i n p e r t u r b a t i o n e x p a n s i o n , 287 models u s e d , 281 p e r t u r b a t i o n t h e o r y a d v a n t a g e s , 282 I s e n t r o p e s , c o l l i n e a r i t y at c r i c o n d e n b a r , 51-53 I s o b u t a n e , c a l c u l a t e d volume e r r o r using Redlich-Kwong p a r a m e t e r s , 399t Isochores c o l l i n e a r i t y f o r f l u i d s , 42-59 c o l l i n e a r i t y p r o o f of G r i f f i t h s , 48-51 I s o p l e t h — S e e Dew-bubble p o i n t c u r v e (DBC) I s o t h e r m a l m e l t i n g , d i a g r a m , 383f I t e r a t i o n counts ACSS a p p l i e d t o m i x t u r e , 490f ,491f COSS a p p l i e d t o m i x t u r e , 490f Newton-Raphson p r o c e d u r e a p p l i e d t o m i x t u r e , 491f

Κ

Ko h i e r e q u a t i o n , d i s a d v a n t a g e s , 82 Kubic equation, s u p e r c r i t i c a l s o l u b i l i t y d e s c r i p t i o n , 164

L

L a t t i c e f l u i d t h e o r i e s , approximations f o r s h o r t - c h a i n m o l e c u l e s , 202 L a t t i c e gas model c o o r d i n a t i o n number model d e r i v e d , 184 n o n c l a s s i o a l model a p p l i c a t i o n , 118 See a l s o L a t t i c e models Lattice models, a p p l i e d t o tetrafluoromethane, 78

L a t t i c e t h e o r i e s , l o c a l composition m i x i n g r u l e s d e r i v e d , 355-356 Lennard-Jones mixtures compressibility factor for binary m i x t u r e s , 259t c o n f o r m a i s o l u t i o n c a l c u l a t i o n s , 342 e q u a t i o n s of s t a t e f o r b i n a r y m i x t u r e s , 258 l o c a l c o m p o s i t i o n compared w i t h s q u a r e - w e l l f l u i d s , 22Ot new m i x i n g r u l e s t e s t e d , 342 compressibility factor for binary m i x t u r e s , 259t Lennard-Jones p o t e n t i a l a p p r o x i m a t i o n by s q u a r e - w e l l p o t e n t i a l , 230 six-step square-well potential a p p r o x i m a t i o n , 23Of Leung-Griffiths equation, gas-liquid m i x t u r e s m o d e l i n g , 118 Lewis-Randall standard s t a t e s , a c t i v i t y c o e f f i c i e n t d e f i n i t i o n , 21 L i g h t h y d r o c a r b o n s y s t e m s , PFGC e q u a t i o n a p p l i c a t i o n , 462-469 L i q u i d d e n s i t i e s , P e n g - R o b i n s o n and P a t e l - T e j a compared, 442t Li quid-liquid equilibrium m e t h a n o l - h e p t a n e s y s t e m , 449f l i q u i d - l i q u i d mixtures, divergence p r e d i c t e d f o r s p e c i f i c h e a t , 119 L i quid-vapor e q u i l i b r i u m , compositions f o r San Andres o i l - a c i d gas m i x t u r e , 42Ot Local composition adhesive i n t e r molecular p o t e n t i a l for m i x t u r e s , 356 b u l k c o m p o s i t i o n d i f f e r e n c e s , 214 bulk composition e f f e c t s i n s q u a r e - w e l l m o l e c u l e s s t u d y , 217 d e f i n i t i o n for binary f l u i d s y s t e m s , 252 density effects i n square-well m o l e c u l e s s t u d y , 217 d e t e r m i n a t i o n , 214 f o r m u l a t i o n c o m p a r i s o n t o computer s i m u l a t i o n , 357-358 equations f o r s q u a r e - w e l l m o l e c u l e s , 215 e x t e n t i n s q u a r e - w e l l m i x t u r e , 198f G i e r y c z and N a k a n i s h i e q u a t i o n , 218 H u , L u d e c k e , and P r a u s n i t z e q u a t i o n , 21 8 mixing r u l e s , density calculations f o r b i n a r y m i x t u r e s , 269t model c o m p a r i s o n f o r s q u a r e - w e l l m o l e c u l e s , 219 o r i g i n , 354 s q u a r e - w e l l m o l e c u l e s by Monte C a r l o s i m u l a t i o n , 214-225 s t a t i s t i c a l mechanical d e f i n i t i o n f o r f l u i d s , 251-252

590 Local

EQUATIONS OF STATE: THEORIES AND

composition—Continued

temperature e f f e c t s i n s q u a r e - w e l l m o l e c u l e s s t u d y , 217 L o c a l c o m p o s i t i o n models c o m b i n i n g r u l e s f o r f l u i d s , 261 c o m p a r i s o n among d e n s i t y de p e n d e n t , 196-199 comparison with conformai s o l u t i o n m i x i n g r u l e s , 262 c o m p o s i t i o n dependence of m o d e l , 199 c o o r d i n a t i o n number f o r b i n a r y m i x t u r e s , 252 d e n s i t y - d e pendent model d i s c u s s i o n , 196 e r r o r s , 358 W h i t i n g and P r a u s n i t z , 195-199 e q u a t i o n of s t a t e f o r m i x t u r e s , 260 e x c e s s f r e e energy a p p l i c a t i o n s , 250 i n t e r n a l energy of binary m i x t u r e , 253 mixing r u l e f o r low-density m i x t u r e , 360 summary and c o m p a r i s o n , 197t See a l s o L o c a l c o m p o s i t i o n L o c a l c o o r d i n a t i o n numbers , d i f f e r e n t models l e a d i n g t o d i f f e r e n t e q u a t i o n s of s t a t e , 191-192

M

Mean-density approximation (MDA) compared t o m o d i f i e d m e a n - d e n s i t y approximation for argon-krypton m i x t u r e , 334f Lennard-Jones molecules s t u d i e d f o r f l u i d s , 258-259 van der W a a l s , 332 See a l s o M o d i f i e d m e a n - d e n s i t y a p p r o x i m a t i o n (MMDA) Mean s p h e r i c a l a p p r o x i m a t i o n (MSA) , expansion of i o n i c f l u i d m o d e l i n g , 290-291 M e c h a n i c a l s t a b i l i t y , homogeneous phase c r i t e r i a , 481 M e t h a n e , c a l c u l a t e d volume e r r o r f o r R e d l i c h - K w o n g p a r a m e t e r s , 398t Mixing rules a t t r a c t i v e e n e r g i e s e f f e c t on b i n a r y f l u i d s , 258-259 binary c r i t i c a l l o c i prediction u s e d , 136 conformai s o l u t i o n s d e r i v a t i o n , 332-335 c o n f o r m a i s o l u t i o n s e q u a t i o n s , 335 d e f i n i t i o n , 314 d e n s i t y d e p e n d e n t , 195-196 d e n s i t y - d e pen dent l o c a l c o m p o s i t i o n , 354

Mixing

APPLICATIONS

rules—Continued

e q u a t i o n - o f - s t ate composition dependence, 254-255 e q u a t i o n - o f - s t ate a p p l i c a t i o n s , 324 i n d u s t r i a l p e r s p e c t i v e , 352- 3 67 L e n n a r d - J o n e s m i x t u r e s t e s t e d , 342 l o c a l c o m p o s i t i o n d e r i v a t i o n , 355-357 l o c a l composition e f f e c t , 358-360 l o c a l c o m p o s i t i o n model a p p l i e d t o l o w - d e n s i t y m i x t u r e , 360 l o c a l c o m p o s i t i o n r u l e s and c o n f o r m a i s o l u t i o n r u l e s compared, 262-272 van d e r Waals o n e - f l u i d , m a c h i n e - s i m u l a t i o n r e s u l t s , 360 molecular size effects, 255-258 Monte C a r l o s i m u l a t i o n used t o t e s t L e n n a r d - J o n e s f l u i d s , 342 m u l t i f l u i d hard-sphere e x p a n s i o n , 323 - 324 m u l t i f l u i d t h e o r y , 322 new l o c a l c o m p o s i t i o n r u l e a p p l i e d t o t e r n a r y s y s t e m s , 272 o n e - f l u i d conformai s o l u t i o n s i m p r o v e d , 331-349 o n e - f l u i d d i a m e t e r s c a l c u l a t e d , 337 o n e - f l u i d t h e o r y , 318-319 P a t e l - T e j a e q u a t i o n , 446 Peng-Robinson e q u a t i o n , 326-329t PRSV e q u a t i o n , 565-566 r e c e n t d e v e l o p m e n t s , 331 R e d l i c h - K w o n g e q u a t i o n , 326, 329t s t a t i s t i c a l mechanical t h e o r y , 317-318 s u p e r c r i t i c a l extraction study a p p l i c a t i o n s , 157 systems s t u d i e d by l o c a l c o m p o s i t i o n , 355 van der Waals and random m i x i n g compared, 359-360 van der Waals compared w i t h MMDA, 337 van d e r Waals e q u a t i o n , 324-326 van der Waals one f l u i d a s s u m p t i o n s , 359-360 i m p r o v e d , 353 m a c h i n e - s i m u l a t i o n r e s u l t s , 360 p r e d i c t i v e power, 360 r a d i a l d i s t r i b u t i o n f u n c t i o n , 359 summary, 353 See a l s o C o n f o r m a i s o l u t i o n m i x i n g rules See a l s o van der Waals o n e - f l u i d mixing rules Mixture c r i t i c a l point, r e l a t i o n s h i p to t h e c r i con den bar and c r i c o n d e n t h e r m , 42-44 M i x t u r e p r o p e r t i e s , two major formalisms, 2 Mixture r a d i a l d i s t r i b u t i o n functions c o n f o r m a i s o l u t i o n a p p r o x i m a t i o n , 320 d e n s i t y expansion a p p r o x i m a t i o n , 321-322

591

INDEX Mixture r a d i a l d i s t r i b u t i o n f u n c t i o n s —Continued hard-sphere expansion a p p r o x i m a t i o n , 321 m u l t i f l u i d conformai s o l u t i o n a p p r o x i m a t i o n s , 323 random m i x i n g a p p r o x i m a t i o n s , 319-320 See a l s o R a d i a l d i s t r i b u t i o n function Mixtures c r i t i c a l exponents p a t h , 117f e q u a t i o n of s t a t e f r o m l o c a l c o m p o s i t i o n m o d e l s , 260 equations of s t a t e f o r f l u i d s , 259-260 i m p u r i t y e f f e c t s on e x t e n s i v e p r o p e r t i e s , 128 non c l a s s i c a l b e h a v i o r n e a r a c r i t i c a l p o i n t , 123f perturbed-anisotropic-chain theory d i s c u s s e d , 300-301 t e s t e d f o r f l u i d s , 302-306 van d e r Waals p a r t i t i o n f u n c t i o n e q u a t i o n , 189 See a l s o B i n a r y m i x t u r e s See a l s o M u l t i c o m p o n e n t m i x t u r e s Models characteristics, 3 phase e q u i l i b r i u m d e s c r i p t i o n , 352 Modified mean-density approximation (MMDA) argon-krypton mixture a p p l i c a t i o n , 333 c o m p a r i s o n w i t h van der Waals o n e - f l u i d p r e d i c t i o n s , 347t e q u a t i o n , 333 h a r d - s p h e r e diameter comparison, 34Of,341f h a r d - s p h e r e diameter r a t i o , 338f,339f Lennard-Jones mixtures r e s u l t s , 344t-345t phase e q u i l i b r i a a p p l i c a t i o n , 377-378 phase e q u i l i b r i a c a l c u l a t i o n f o r b i n a r y s y s t e m s , 380 s i m u l a t i o n r e s u l t s compared, 348t van der Waals compared f o r b i n a r y s y s t e m s , 380 M o l a r heat of v a p o r i z a t i o n , d e t e r m i n e d from an e q u a t i o n of s t a t e , 26 M o l a r volumes d i v e r g e n c e s i n m i x t u r e s , 213f PFGC e q u a t i o n , 457 p r e d i c t i o n e r r o r s f o r e q u a t i o n s of state, 46lt p r e d i c t i o n e r r o r s f o r PFGC e q u a t i o n , 462 p r e d i c t i o n from PFGC e q u a t i o n f o r i s o p e n t a n e , 463f M o l e f r a c t i o n s — S e e Phase m o l e fractions M o l e c u l a r dynamics s i m u l a t i o n , m o l e c u l a r model e x a m i n a t i o n , 202

Molecules—See Nonspherical molecules Monte C a r l o program d e s c r i p t i o n , 203 m o l e c u l a r movements, 203 r e l i a b i l i t y t e s t s , 204 Monte C a r l o s i m u l a t i o n f l u i d s t r u c t u r e c a l c u l a t i o n , 204-205 mixing r u l e s t e s t e d f o r Lennard-Jones m i x t u r e s , 342 models h i s t o r y , 202 procedure i n s q u a r e - w e l l molecules s t u d y , 216 r e s u l t s compared w i t h RISM, 209 results i n fluid structure e x p e r i m e n t , 212 r e s u l t s i n square-well molecules s t u d y , 216-217 M u l t i component m i x t u r e s , i s o c h o r i c and i s e n t r o p i c c o l l i n e a r i t y , 58 M u l t i f l u i d conformai s o l u t i o n approximation, mixture r a d i a l d i s t r i b u t i o n f u n c t i o n s , 323 M u l t i f l u i d density expansion, mixing r u l e s , 324 M u l t i f l u i d hard-sphere expansion, m i x i n g r u l e s , 323-324 M u l t i f l u i d t h e o r y , m i x i n g r u l e s , 322 Multiphase e q u i l i b r i u m , governing e q u a t i o n s , 500 Multiphase s o l u t i o n s , search s t r a t e g y , 504

Ν

N - f l u i d t h e o r i e s , compared, 256-258 Near-critical fluids d e s c r i p t i o n o f i m p u r e , 125-129 i m p u r i t y e f f e c t s c a l c u l a t e d , 126 i m p u r i t y e f f e c t s on d e n s i t y , 126 See a l s o N e a r - c r i t i c a l m i x t u r e s N e a r - c r i t i c a l mixtures c l a s s i c a l a n a l y s i s , 120-122 non c l a s s i c a l d e s c r i p t i o n , 110-131 p a r t i a l molar p r o p e r t i e s behavior, 120-121 See a l s o N e a r - c r i t i c a l f l u i d s Near-critical region ACSS d e f i n e d and u s e d , 499 Κ v a l u e e s t i m a t i o n by e v a p o r a t i o n t e c h n i q u e , 499 N e a r - c r i t i c a l s t a t e s , d e s c r i b e d by e q u a t i o n s of s t a t e , 109-178 N e a r e s t n e i g h b o r s , d e f i n i t i o n , 356-357 Newton-Raphson p r o c e d u r e d e f i n e d , 481 Κ v a l u e s u p d a t e d , 481 N i t r o g e n , c a l c u l a t e d volume e r r o r f o r R e d l i c h - K w o n g parameters , 398t

592

EQUATIONS OF STATE: THEORIES AND APPLICATIONS

N o n c l a s s i c a l f l u i d s , d i s c u s s i o n , 111 Ν on p o l a r f l u i d s , l o c a l c o m p o s i t i o n model a p p l i c a t i o n , 2 5 0 - 2 7 5 Nonspherical molecules a c c u r a c y of e q u a t i o n of s t a t e f o r h y d r o c a r b o n s , 240-244 equation-of-state a p p l i c a t i o n to p o l a r f l u i d s , 244 e q u a t i o n s of s t a t e based o n t h e distribution function t h e o r i e s , 227-244 e q u a t i o n s of s t a t e compared, 240-244 parameter r e d u c t i o n i n e q u a t i o n s of s t a t e , 239-240

0 O n e - f l u i d conformai s o l u t i o n , m i x i n g r u l e s i m p r o v e d , 331-349 O n e - f l u i d t h e o r y , d e f i n i t i o n , 23 One-step square-well potential a n g l e - d e pendent G a u s s i a n o v e r l a p e q u a t i o n , 235-238 c o n t a c t v a l u e s of c o r r e l a t e d f u n c t i o n s , 236-237t i n d e x v a r i a t i o n w i t h i n t e n s i t y , 234f p r e s s u r e p r e d i c t i o n , 237t Osmotic s u s c e p t i b i l i t y d i v e r g e n c e i n m i x t u r e s , 115,116 n e a r - c r i t i c a l m i x t u r e s , 124

Ρ

P a r a f f i n s , h a r d - c o r e volume v a r i a t i o n w i t h c r i t i c a l volume, 243f Parameters c o r r e c t i o n parameter c o r r e l a t e d f o r P a t e l - T e j a e q u a t i o n , 445f correlation for Patel-Teja e q u a t i o n , 444f degrees of freedom v s . b v a l u e o f paraffins, 532f development f o r San Andres F o r m a t i o n o i l s , 410-413 no η p o l a r f l u i d s t e s t e d f o r p e r t ur be d - a n i s o t r o p i c - c h a i η t h e o r y , 302 Pen g-R o b i ns o n - S t r yj ek-V er a e q u a t i o n , 562t P e n g - R o b i n s o n and P a t e l - T e j a compared, 437f Redlich-Kwong equation carbon d i o x i d e , 402-403 c r i t i c a l t e m p e r a t u r e s and r a n g e s f i t , 204t d e f i n e d , 390 d e t e r m i n a t i o n , 390

in

Redlich-Kwong e q u a t i o n — C o n t i n u e d v a r i o u s s u b s t a n c e s , 403-404 v o l u m e t r i c e r r o r comparison f o r c a r b o n d i o x i d e , 398t v o l u m e t r i c e r r o r comparison f o r e t h a n e , 399t v o l u m e t r i c e r r o r comparison f o r hydrogen s u l f i d e , 400t v o l u m e t r i c e r r o r comparison f o r i s o b u t a n e , 399t v o l u m e t r i c e r r o r comparison f o r methane, 398t v o l u m e t r i c e r r o r comparison f o r n i t r o g e n , 398t t em per at ur e - de pen dent c u b i c e q u a t i o n s , 539 f o r t h e Redlich-Kwong e q u a t i o n , 389-400 two t e m p e r a t u r e - d e p e n d e n t , d e v i a t i o n curves o b t a i n e d from c u b i c e q u a t i o n s , 547f See a l s o C o n f o r m a i parameters See a l s o I n t e r a c t i o n parameters Parameters from group c o n t r i b u t i o n s (PFGC) e q u a t i o n b a s i s , 453 b i n a r y i n t e r a c t i o n c o e f f i c i e n t s , 457 des c r i p t i o n , 4 52 d i f f i c u l t i e s , 462 g r o u p parameters o b t a i n e d , 456-4 57 l i m i t a t i o n , 457 p a r a m e t e r s , 455 phase e q u i l i b r i a , 452-470 w r i t t e n i n t e r m s of c o m p r e s s i b i l i t y f a c t o r , 4 54 Partial equation-of-state parameters determination, 23-24 van der Waals e q u a t i o n e x a m p l e , 2 4 - 2 5 P a r t i a l properties d e f i n i t i o n o f g e n e r a l i z e d , 16 e q u a t i o n - o f - s t ate p r o p e r t i e s , conversion of laboratory pro p e r t i e s , 18-19 d e f i n i t i o n , 17 l a b o r a t o r y p r o p e r t i e s , d e f i n i t i o n , 17 l i s t , 15b r a t i o n a l e and d e f i n i t i o n s , 13-20 r e l a t i o n s h i p of d i f f e r e n t t y p e s , 17-20 s u m m a b i l i t y f e a t u r e , 15 Patel-Teja equation c o n s t a n t s o b t a i n e d from the c r i t i c a l p o i n t , 438 c r i t i c a l l o c i p r e d i c t i o n s , 448 m i x i n g r u l e s , 446 p o l a r m o l e c u l e vapor p r e s s u r e s , 439 r e d u c t i o n t o Peng-Robinson e q u a t i o n , 438 vapor-liquid equilibria results c o m p a r e d , 446-448 Peng-Robinson equation accuracy for nonspherical m o l e c u l e s , 244

593

INDEX Peng-Robinson e q u a t i o n — C o n t i n u e d c r i t i c a l l o c i p r e d i c t i o n s , 448 e x p r e s s i o n , 561 f u g a c i t y c o e f f i c i e n t s , 354 m i x i n g r u l e s , 326 - 3 2 9 t , 4 96 - 4 97t parameter i n f l u e n c e o n s a t u r a t e d l i q u i d volume p r e d i c t i o n , 550 - 5 5 2 f parameter v a r i a t i o n f o r n - h e x a n e , 54 9f p o l a r m o l e c u l e vapor p r e s s u r e s , 439 solubility benzoic a c i d i n carbon d i o x i d e , 1 74f f l u o r i n e i n e t h y l e n e , 174f s u p e r c r i t i c a l d e s c r i p t i o n , 164 Peng-Ro b i n s o n - S t r y j e k - V e r a e q u a t i o n f u g a c i t y c o e f f i c i e n t e x p r e s s i o n , 563t r e s u l t s compared, 563t P e r t u r b a t i o n expansion i o n i c f l u i d modeling approximations u s e d , 287 mean s p h e r i c a l a p p r o x i m a t i o n s (MSA) result obtained f o r i o n i c f l u i d s , 287 Perturbation theory a d v a n t a g e s , 64 applied to tetrafluoromethane, 79-81 integral evaluation for ionic f l u i d s , 287-290 i o n i c f l u i d m o d e l i n g a d v a n t a g e s , 282 mixture equation-of-state development, 3 53 - 3 54 Perturbed-anisotropic-chain theory a c c u r a c y , 302 anisotropic multipolar interactions c a l c u l a t e d , 300 a z e o t r o p e p r e d i c t i o n i n m i x t u r e s , 305 binary i n t e r a c t i o n p a r a m e t e r s , 305, 306t c a n o n i c a l ensemble p a r t i t i o n f u n c t i o n , 298 e q u a t i o n of s t a t e , 299 f l u i d m i x t u r e s , 302-306 fluid-mixture properties c a l c u l a t e d , 303-305 h a r d - c h a i n r e p u l s i o n c a l c u l a t i o n , 299 h i g h e r o r d e r terms i n p e r t u r b a t i o n e x p a n s i o n , 300 isotropic interactions c a l c u l a t i o n , 299 Κ factors c o m p a r i s o n f o r hydrogen s u l f i d e - p e n t a n e s y s t e m , 308f comparison f o r methyl i o d i d e - a c e t o n e s y s t e m , 309f comparison f o r s u l f u r d i o x i d e - a c e t o n e s y s t e m , 307f Lennard-Jones i s o t r o p i c i n t e r a c t i o n s c a l c u l a t e d , 299 m i x t u r e p r o p e r t y p r e d i c t i o n from pure-component p a r a m e t e r s , 305

Perturbed-anisotropic-chain

theory

—Continued parameters f o r no η p o l a r f l u i d s , 302 phase e q u i l i b r i a c o m p a r i s o n f o r a cet o n e - c y c l o h e x a n e s y s t e m , 31 Of pure f l u i d s t e s t e d , 3 0 1 - 3 0 2 pure-component f l u i d parameters o b t a i n e d , 301t pure-component p a r t i t i o n f u n c t i o n e x t e n s i o n , 300-301 s a t u r a t e d l i q u i d m o l a r volume c o m p a r i s o n , 304f thermodynamics of m u l t i p o l a r m o l e c u l e s , 297-311 vapor p r e s s u r e c o m p a r i s o n of d i p o l a r f l u i d s , 303f Perturbed-hard-chain theory approximations for s h o r t - c h a i n m o l e c u l e s , 202 e q u a t i o n - o f - s t a t e model b a s i s , 228 p r o p e r t y p r e d i c t i v e a b i l i t i e s , 298 Perturbed-soft-chain theory, d i f f e r e n c e s from h a r d - c h a i n t h e o r y , 298 Petroleum r e s e r v o i r s , water i n c l u s i o n i n phase b e h a v i o r s t u d i e s , 494 Phase b e h a v i o r , p r e d i c t e d by PFGC e q u a t i o n , 462 Phase diagram a r g o n - w a t e r s y s t e m at c r i t i c a l r e g i o n , 450f e t h e n e - n a p h t h a l e n e s y s t e m , 384f t e t r a f luorom ethane-alkane s y s t e m , 386f Phase d i s t r i b u t i o n c o e f f i c i e n t s c o m p u t a t i o n of f e e d m i x t u r e s e p a r a t i o n i n t o two p h a s e s , 478 d e f i n i t i o n , 477 i n i t i a l values v a r i e d f o r mixtures i n f l a s h c a l c u l a t i o n s t u d y , 483 Newton-Raphson a l g o r i t h m employed, 489 single-stage flash calculations u p d a t e d , 479 t r i v i a l s o l u t i o n convergence a f t e r i n i t i a t i o n , 492 Phase e q u i l i b r i a behavior new m i x i n g r u l e a p p l i e d t o b i n a r y system, 575f,577f p r e d i c t e d behavior f o r b i n a r y s y s t e m u s i n g new m i x i n g r u l e , 578f,579f t e r n a r y phase b e h a v i o r u s i n g new m i x i n g r u l e , 58lf c a l c u l a t i o n d i f f i c u l t i e s at h i g h p r e s s u r e s , 371 data, s c a r c i t y for high molecular w e i g h t h y d r o c a r b o n s , 297 e q u a t i o n - o f - s t a t e c a l c u l a t i o n , 371 PFGC e q u a t i o n r e p r e s e n t a t i o n , 452-470

EQUATIONS OF STATE: THEORIES AND APPLICATIONS

594 Phase e q u i l i b r i u m — C o n t i n u e d

p r o p e r t i e s , algorithm developed f o r c u b i c e q u a t i o n s , 573-574 t h e o r i e s , f a i l u r e f o r high molecular w e i # i t h y d r o c a r b o n s , 297 Phase mole f r a c t i o n s , d e t e r m i n a t i o n f o r single-stage flash c a l c u l a t i o n s , 478 Polar f l u i d s cubic equation-of-state a p p l i c a t i o n , 434-451 equation-of-state application to n o n s p h e r i c a l m o l e c u l e s , 244 l o c a l c o m p o s i t i o n model a p p l i c a t i o n , 250-275 Polar s u p e r c r i t i c a l f l u i d properties c o n v e n t i o n a l method i n a d e q u a c i e s , 574 l o w - p r e s s u r e range e x a m i n e d , 574 new m i x i n g r u l e a p p l i e d , 574 P r e s s u r e c o m p o s i t i o n diagram h y d r o g e n - c a r bo η monoxide s y s t e m , 382f h y d r o gen-methane s y s t e m , 379f t et r a f l u o r cm et h a n e - b u t a n e s y s t e m , 386f Pressure composition l o c i , c a l c u l a t e d f o r San Andres Formation o i l s , 417,425 Près sure-temperature diagram, h y d r o gen-met hane s y s t e m , 3 8 l f P r o p a d i en e a n a l y s i s i n v a r i o u s compounds, 89t p r o p e r t i e s i n pro p a n e - p r o pa d i en e e x p e r i m e n t , 94t vapor p r e s s u r e v a l u e s i n propane-propadiene experiment compared, 94f Propane c a l c u l a t e d volume e r r o r u s i n g R e d l i c h - K w o n g p a r a m e t e r s , 399t relative volatilities i n p r o p a d i ene, 1 04t vapor pressure values i n pro pan e - pro pa d i ene e xperim ent c o m p a r e d , 91 f Pro p a n e - p r o p a d i ene s y s t e m b i n a r y i n t e r a c t i o n p a r a m e t e r s , 99t c e l l and t r a n s d u c e r u s e d , 88f e q u a t i o n s u s e d , 87 e x p e r i m e n t a l c o n d i t i o n s , 87-89 f u g a c i t y c o e f f i c i e n t e x p r e s s i o n , 97 i n t e r a c t i o n p a r a m e t e r s , 96f liquid compressibility factors i n e x p e r i m e n t , 98 n o n l i n e a r b e h a v i o r of r e l a t i v e v o l a t i l i t i e s , 98 phase e q u i l i b r i a , 86-105 p r e s s u r e d a t a , 90t p r e s s u r e measurements used t o d e t e r m i n e p a r a m e t e r s , 89-93 relative volatilities compared, 102f-104f

Pure f l u i d s , van d e r Waals p a r t i t i o n f u n c t i o n u s e d , 181-189

Q

Quantum c o r r e c t i o n , van der W a a l s - t y p e e q u a t i o n of s t a t e , 372-373 Quantum c o r r e c t i o n f u n c t i o n , e x p a n s i o n c o e f f i c i e n t , 373t

R

Radial d i s t r i b u t i o n functions, s o f t - s p h e r e m i x t u r e , 334f Random m i x i n g a p p r o x i m a t i o n (RMA) , mixture r a d i a l d i s t r i b u t i o n f u n c t i o n s , 319-320 Raoul t ' s l a w , Κ v a l u e s i n i t i a t e d , 477 Real f l u i d s h a r d s p h e r e s as model b a s i s , 227 P - V - T b e h a v i o r , 238-244 Redlich-Kwong e q u a t i o n a t t r a c t i o n parameter, 374 b i n a r y system r e s u l t s , 378 c a l c u l a t e d volume e r r o r from parameters f o r c a r b o n d i o x i d e , 398t description of binary s u p e r c r i t i c a l p r o p e r t i e s , 171 d i s a d v a n t a g e , 380 g e n e r a l i z e d , component p r o p e r t i e s f o r San Andres o i l s , 409t m i x i n g r u l e s , 326,327t,374 m i x t u r e phase b e h a v i o r o f San Andres F o r m a t i o n o i l s , 406-433 parameters d e f i n e d , 134, 390, 408 pro p a n e - p r o p a d i ene s y s t e m , 95-98 Soave m o d i f i c a t i o n , 390 t em per at u r e - d e pen d e n t , 390 t e m p e r a t u r e s above c r i t i c a l , 390-3 9 5 used i n San Andres o i l s s t u d y , 408 P e n g - R o b i n s o n e q u a t i o n compared, 533 phase e q u i l i b r i a e q u a t i o n , 372 solubility b e n z o i c a c i d i n carbon d i o x i d e , 1 72f f l u o r i n e i n e t h y l e n e , 172f three-phase e q u i l i b r i a d e s c r i p t i o n of San Andres o i l s , 419 van d e r Waals e q u a t i o n c o m p a r i s o n , 81 Relative v o l a t i l i t i e s , nonlinear b e h a v i o r of pro p a n e - p r o p a d i ene s y s t e m , 98

INDEX Residual functions definition, 4 H e l m h o l t z e n e r g y d e r i v a t i o n , 9t pressure-explicit equation-of-state d e r i v a t i o n , 7t r e l a t i o n s h i p t o excess f u n c t i o n s , 12 volume-explicit equation-of-state d e r i v a t i o n , 8t Residual Helmholtz energy, r o l e i n e q u a t i o n - o f - s t a t e thermodynamics, 5

595

S o l i d volume, d a t a and s o u r c e s f o r v a r i o u s compounds, 1 63t S o l u b i l i t y , deviations for binary m i x t u r e s from e q u a t i o n s of state, 166-I69t Solute saturated vapor, e q u a t i o n - o f - s t a t e c a l c u l a t i o n , 161 S o l u t i o n thermodynamics, p a r t i a l - p r o pert y c o n c e p t , 13 Square-well fluids c o o r d i n a t i o n number models compared, 183-184 c o o r d i n a t i o n number models f o r S v a r i o u s e q u a t i o n s of s t a t e , I85t deviation in compressibility f a c t o r , I87t San Andres F o r m a t i o n o i l s l o c a l c o m p o s i t i o n s compared w i t h a c i d g a s - o i l mixture L e n n a r d - J o n e s f l u i d s , 220t d e s c r i p t i o n , 425-43 0 p r e s s u r e c a l c u l a t i o n e q u a t i o n , 235 c a l c u l a t e d and e x p e r i m e n t a l r e s u l t s S q u a r e - w e l l m i x t u r e s , s i m u l a t e d number compared, 41 7t of n e a r e s t n e i g h b o r s , 2211 c o m p a r i s o n i n s o u r gas s t u d i e s , 427t Square-well molecules c o m p o s i t i o n data p r e p a r a t i o n f o r b u l k c o m p o s i t i o n e f f e c t on l o c a l R e d l i c h - K w o n g a p p l i c a t i o n , 410 c o m p o s i t i o n , 219 equation-of-state parameters l o c a l composition a d j u s t e d , 41 4t changing with bulk f l u i d c o m p o s i t i o n s compared, 413t c o m p o s i t i o n , 223f Redlich-Kwong equation a p p l i e d t o f u n c t i o n of d e n s i t y , 22Of phase b e h a v i o r , 406-433 f u n c t i o n o f t e m p e r a t u r e , 222f Saturated l i q u i d d e n s i t i e s , Monte C a r l o s i m u l a t i o n , 2 1 4 - 2 2 5 P e n g - R o b i n s o n and P a t e l - T e j a model c o m p a r i s o n at v a r i o u s c o m p a r e d , 442t d e n s i t i e s , 224 S a t u r a t e d l i q u i d volume, d e v i a t i o n Monte C a r l o s i m u l a t i o n contours for cubic com p a r i s o n , 218-219 e q u a t i o n s , 553f, 554f new l o c a l c o m p o s i t i o n model Scaled p a r t i c l e theory, r i g i d p r o p o s e d , 224 n o n s p h e r i c a l m o l e c u l e s , 228 t e m p e r a t u r e e f f e c t on l o c a l S c a l i n g l a w s , pure f l u i d s a p p l i e d t o c o m p o s i t i o n , 219 f l u i d m i x t u r e s , 116-118 u n l i k e - e n e r g y f a c t o r e f f e c t on l o c a l S c a l i n g v a r i a b l e s , one-component c o m p o s i t i o n , 219 f l u i d , 1l4f Square-well potential Schmidt-Wenzel e q u a t i o n , s u p e r c r i t i c a l c o n t a c t v a l u e , 232 s o l u b i l i t y d e s c r i p t i o n , 164 c o n t a c t v a l u e s of c o r r e l a t e d Second v i r i a l c o e f f i c e n t , p r e d i c t e d v s . f u n c t i o n s , 232-23 8 c o m p o s i t i o n f o r b i n a r y s y s t e m , 577f d e f i n i t i o n , 229 Soave-Redlich-Kwong equation e q u a t i o n , 215 mixture pressure d e v i a t i o n s f o r Gaussian o v e r l a p f o r a n i s o t r o p i c o n e - p a r a m e t e r f i t , 96f m o l e c u l e s , 23Of mixture pressure d e v i a t i o n s f o r G a u s s i a n o v e r l a p m o d e l , 230 two-parameter f i t , 99f See a l s o O n e - s t e p s q u a r e - w e l l parameter i n f l u e n c e o n s a t u r a t e d potential l i q u i d volume See a l s o T w o - s t e p s q u a r e - w e l l p r e d i c t i o n , 550-552f potential parameter v a l u e s , 134 S t a b i l i t y l i m i t s , mixtures i n f l a s h supercritical solubility c a l c u l a t i o n s t u d y , 482f d e s c r i p t i o n , 164 S t a t i s t i c a l mechanics Solid-fluid equilibria d i f f i c u l t i e s i n equation-of-state b i n a r y systems s t u d i e d , 380 a p p l i c a t i o n s , 201-202 d i s c u s s e d f o r b i n a r y m i x t u r e , 376-377 f l u i d m o d e l i n g , 180 equation-of-state application to h i s t o r y of equation-of-state c r y o g e n i c m i x t u r e s , 371-385 a p p l i c a t i o n s , 201

596

EQUATIONS OF STATE: THEORIES AND

S t a t i s t i c a l mechanics—Continued m i x i n g r u l e s , 31 7-31 8 Strobridge equation c o e f f i c i e n t s and t h e i r e r r o r s , 65t form used i n t e t r a f l u o r omet hane e x p e r i m e n t , 63 Successive s u b s t i t u t i o n algorithms, convergence t o t r i v i a l s o l u t i o n , 489 Supercritical extraction a p p l i c a t i o n s , 156,352 c a l c u l a t i o n summary f o r v a r i o u s e q u a t i o n s of s t a t e , 170t c r i t i c a l p r o p e r t i e s used i n s t u d y , 1 60t e q u a t i o n s of s t a t e e v a l u a t e d , 156-180 e q u a t i o n s of s t a t e s e l e c t e d , 157 r e s u l t s i n b i n a r y m i x t u r e s s t u d y , 164 Supercritical solubility c a l c u l a t i o n , 161-164 data sources for various compounds, I65t e q u a t i o n - o f - s t ate u s e f u l n e s s , 157 S u p e r c r i t i c a l s t a t e s , d e s c r i b e d by e q u a t i o n s of s t a t e , 109-178

Τ

T e r n a r y s y s t e m s , new m i x i n g r u l e performance d e s c r i p t i o n , 576-580 T et r a f l u o r omet hane a p p a r a t u s used i n e x p e r i m e n t , 63 density values from Strobridge e q u a t i o n , 67t e q u a t i o n of s t a t e , 60-82 i s o t h e r m s s t u d i e d , 61 PVT p r o p e r t i e s , 61 thermodynamic b e h a v i o r , 60-61 Thermodynamic m o d e l i n g a p p l i c a t i o n r e q u i r e m e n t s , 182 a p p r o a c h e s , 180 T h r e e - p h a s e s y s t e m , water a d d i t i o n t o h y d r o c a r b o n s y s t e m , 509 T r i v i a l solution convergence i n f l a s h c a l c u l a t i o n s t u d y , 483 m i x t u r e s o c c u r r e n c e , 476 T r o u t o n ' s law c o r r e c t i o n f o r d i f f e r e n c e s i n vapor m o l a r volume, 521 i n t e r p r e t a t i o n s , 52 0-53 3 Two-phase e q u i l i b r i u m g o v e r n i n g e q u a t i o n s , 497 p r e d i c t i o n by i n i t i a l f l a s h c a l c u l at i ons , 50 6 Two-phase f l a s h c a l c u l a t i o n s , p r o c e d u r e , 497 -500 Two-phase s y s t e m , w a t e r a d d i t i o n t o h y d r o c a r b o n s y s t e m , 50 9

APPLICATIONS

Two-step square-well p o t e n t i a l a n g l e - d e pendent G a u s s i a n o v e r l a p , e q u a t i o n , 238 a n g l e - d e pen dent p a r a m e t e r s , 234f n o n s p h e r i c a l m o l e c u l e s , 230

U

Unlike-interaction potential p a r a m e t e r s , e x p r e s s i o n s , 317 Unlike-pair coefficients a p p l i c a t i o n t o projected binary c r i t i c a l l o c i , 138 o b t a i n e d f o r Soave e q u a t i o n f o r b i n a r y m i x t u r e s , 152 obtained for Teja equation for binary m i x t u r e s , 152

V

van d e r Waals e q u a t i o n d i s a d v a n t a g e , 81 l i q u i d d e n s i t y e x p r e s s i o n at z e r o p r e s s u r e , 28 m i x i n g r u l e s , 324, 32 5t p o l a r asymmetric s y s t e m d e s c r i p t i o n , 355 terms d i s c u s s e d , 533 van der Waals o n e - f l u i d m i x i n g r u l e s a p p l i e d t o a l l d e n s i t i e s , 192 compared w i t h m o d i f i e d m e a n - d e n s i t y a p p r o x i m a t i o n , 347t compared w i t h random m i x i n g , 3 5 9 - 3 6 0 Lennard-Jones mixture r e s u l t s , 344t-345t p r e d i c t i v e and c o r r e l a t i v e power, 360 square-well configuration p r e d i c t i o n , 362f van d e r Waals p a r t i t i o n f u n c t i o n accuracy for square-well f l u i d s , 187-189 advantages i n e q u a t i o n - o f - s t a t e d e v e l o p m e n t , 189 c o n f i g u r a t i o n a l e n e r g i e s d e f i n e d , 191 c o o r d i n a t i o n number model u s e d , 184 e q u a t i o n , 1 81 fundamental e q u a t i o n o f s t a t e o b t a i n e d , 182 m i x t u r e s e q u a t i o n , 189 v o l u m e t r i c e q u a t i o n of s t a t e o b t a i n e d , 182 van d e r Waals t h e o r i e s — S e e N - f l u i d theories Vapor-liquid equilibrium c y c l ο he xan e - he x a n o l s y s t e m ,

44 7f

597

INDEX Vapor-liquid equilibrium—Continued l o c a l composition mixing r u l e s a p p l i e d to various s y s t e m s , 270-271f , 2 7 3 - 2 7 4 f l o w - p r e s s u r e r e g i o n s t u d i e d f o r new a p p l i c a t i o n , 576 p r e d i c t e d by PFGC e q u a t i o n , 462 p r e d i c t i o n from l i q u i d - l i q u i d phase s e p a r a t i o n s , 385 p r o p a n e - p r o p a d i e n e system values, 100t,102t t o l u e n e - p e n t a n o l s y s t e m , 447f v a l u e s o b t a i n e d from c u b i c e q u a t i o n s o f s t a t e , 537 vapor-pressure representation i n c u b i c e q u a t i o n s s t u d y , 540 Vapor p r e s s u r e s A n t o i n e e q u a t i o n used f o r es t i m a t i n g , 52 5 compared f o r two e q u a t i o n s of s t a t e , 460t data sources for various compounds, 1 62t e f f e c t of a l p h a c o n s t a n t on c u b i c e q u a t i o n s of s t a t e , 436t P e n g - R o b i n s o n e q u a t i o n f a i l u r e , 561 PFGC e q u a t i o n , 457 p r e d i c t i o n s from PFGC e q u a t i o n f o r isopentane, 46lf Variational inequality minimization t h e o r y — S e e VIM t h e o r y

VIM t h e o r y , a p p l i e d t o t et r a f l u o r omet hane, 79 V i r i a l c o e f f i c i e n t — S e e Second v i r i a l coefficient V i r i a l equation a n i s o t r o p i c m o l e c u l e s , 230-232 mixing r u l e d e v i a t i o n for f l u i d s , 317-318 V o l u m e — S e e Excess volumes Volumetric properties c u b i c e q u a t i o n s r e p r e s e n t a t i o n , 538 hydrogen-methane s y s t e m , 3 8 l - 3 8 2 f new m i x i n g r u l e p e r f o r m a n c e , 576

W Water a d d i t i o n t o two-phase hydrocarbon s y s t e m , 509 a d d i t i o n t o s i n g l e - p h a s e hydrocarbon s y s t e m , 507, 50Qt Whiting-Prausnitz expression, free e n e r g y model f o r pure f l u i d s , 2 54 Wilson equation, l a t t i c e theory d e r i v a t i o n r e s u l t s , 356 Wilson formula comparison t o e v a p o r a t i o n t e c h n i q u e , 504 Κ v a l u e e s t i m a t e s , 498

Production and indexing by Keith B. Belton Jacket design by Pamela Lewis Elements typeset by Hot Type Ltd., Washington, D.C. Printed and bound by Maple Press Co., York, Pa.