Parameters from Group Contributions Equation and Phase Equilibria

22 Parameters from Group Contributions Equation and Phase Equilibria in Light Hydrocarbon Systems 1

2

Ali I. Majeed and Jan Wagner Downloaded by OHIO STATE UNIV LIBRARIES on September 18, 2013 | http://pubs.acs.org Publication Date: March 24, 1986 | doi: 10.1021/bk-1986-0300.ch022

1

Nawazish International, Wetumka, OK 74883 School of Chemical Engineering, Oklahoma State University, Stillwater, OK 74078

2

The Parameters From Group Contribution equation of state is applied to pure fluids and mixtures with emphasis on the representation of phase equilibria. Group parameters and group-interaction parameters were derived from published pure component data using a nonlinear, multiproperty fitting program. Comparisons of calculated and experimental vapor-liquid equilibrium phase compositions, volumetric properties, and enthalpy departures demonstrated the applicability of the PFGC equation to systems of hydrocarbons and hydrocarbons with water. Phase behavior of mixtures of light hydrocarbons with acid gases is also described over a fairly wide range of temperature and pressure. The use of e q u a t i o n s of s t a t e t o d e s c r i b e t h e phase b e h a v i o r and thermodynamic p r o p e r t i e s of l i g h t hydrocarbon systems i s w e l l e s t a b l i s h e d . Among t h e more w i d e l y used c o r r e l a t i o n s are t h e Soave-Redlich-Kwong (1), Peng-Robinson (2), and S t a r l i n g - B e n e d i c t Webb-Rubin (3) e q u a t i o n s . These e q u a t i o n s were developed t o d e s c r i b e t h e b e h a v i o r of nonpolar o r weakly p o l a r s u b s t a n c e s . When r e s t r i c t e d t o t h e s e types of systems a l l t h r e e e q u a t i o n s y i e l d phase b e h a v i o r p r e d i c t i o n s s u i t a b l e f o r many a p p l i c a t i o n s i n process design. At l e a s t two o f t h e s e e q u a t i o n s , t h e SoaveRedlich-Kwong and t h e Peng-Robinson e q u a t i o n s , have been extended t o hydrocarbon-water systems i n an e f f o r t t o d e s c r i b e v a p o r l i q u i d - l i q u i d phase b e h a v i o r . Many problems encountered i n t h e gas p r o c e s s i n g i n d u s t r y i n v o l v e nonideal l i q u i d s o l u t i o n s . F o r example, d e h y d r a t i o n and h y d r a t e i n h i b i t i o n processes may i n v o l v e m i x t u r e s of l i g h t hydrocarbons w i t h aqueous methanol or g l y c o l s o l u t i o n s . The Parameters From Group C o n t r i b u t i o n s , o r PFGC, e q u a t i o n i s an e q u a t i o n of s t a t e analogy t o an a c t i v i t y c o e f f i c i e n t e q u a t i o n which i s c a p a b l e of d e s c r i b i n g v a p o r - l i q u i d - l i q u i d e q u i l i b r i u m i n systems e x h i b i t i n g nonideal l i q u i d b e h a v i o r . As t h e name i m p l i e s , t h e parameters i n t h i s e q u a t i o n a r e d e r i v e d from group c o n t r i b u t i o n t e c h n i q u e s r a t h e r than c o r r e l a t i o n s w i t h c r i t i c a l p r o p e r t i e s . T h i s approach a l s o o f f e r s p o t e n t i a l advantages i n 0097-6156/B6/0300-0452$06.50/0 © 1986 American Chemical Society

In Equations of State; Chao, K., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1986.

Downloaded by OHIO STATE UNIV LIBRARIES on September 18, 2013 | http://pubs.acs.org Publication Date: March 24, 1986 | doi: 10.1021/bk-1986-0300.ch022

22.

M A J E E D A N D WAGNER

453

Parameters from Group Contributions Equation

a p p l i c a t i o n s t o systems i n v o l v i n g undefined m i x t u r e s of petroleum and s y n t h e t i c l i q u i d s . The f u n c t i o n a l groups i n these types of m i x t u r e s can be i d e n t i f i e d by modern a n a l y t i c a l t e c h n i q u e s such as NMR s p e c t r o s c o p y . Reduced r e l i a n c e on c r i t i c a l p r o p e r t i e s c o r r e l a t i o n s i n terms of s p e c i f i c g r a v i t y , average b o i l i n g p o i n t , c h a r a c t e r i z a t i o n parameters, e t c . , should l e a d t o improved p r e d i c t i o n s of thermodynamic p r o p e r t i e s of s y n t h e t i c and n a t u r a l hydrocarbon systems. In t h i s paper we would l i k e t o share some of our e x p e r i e n c e s and r e s u l t s i n d e v e l o p i n g and e v a l u a t i n g the PF6C e q u a t i o n f o r l i g h t hydrocarbon systems. Our primary emphasis has been on the p r e d i c t i o n of phase b e h a v i o r v i a e q u a t i o n s of s t a t e f o r a p p l i c a t i o n s t o process d e s i g n . The PFGC Equation of S t a t e The 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 of s t a t e was i n t r o d u c e d by Cunningham and Wilson (4) i n 1974. The d e t a i l s of the model f o r m u l a t i o n and d e r i v a t i o n s of the e q u a t i o n are g i v e n by Cunningham ( 5 ) . A b r i e f summary i s i n c l u d e d here f o r convenience. The b a s i s f o r the PFGC e q u a t i o n of s t a t e l i e s i n the assumption t h a t the form of e m p i r i c a l r e l a t i o n s h i p s which have s u c c e s s f u l l y d e s c r i b e d the excess Gibbs f r e e energy of m i x i n g can a l s o be used as the b a s i s f o r modeling the Helmholtz f r e e energy. In a d d i t i o n , the v o i d spaces between molecules i n a m i x t u r e are assumed t o be i d e n t i f i a b l e as an a d d i t i o n a l component d e s i g n a t e d as " h o l e s " . The volume i s e v a l u a t e d as the m o l e c u l a r volume occupied by the component d i v i d e d by the t o t a l volume. I n c l u d i n g an a r b i t r a r y parameter f o r one mole of h o l e s , volume f r a c t i o n s can be converted t o mole f r a c t i o n s . Using these r e l a t i o n s h i p s f o r mole f r a c t i o n s permits the Helmholtz f r e e energy of m i x i n g t o be expressed as a f u n c t i o n of c o m p o s i t i o n and volume. The Helmholtz f r e e energy of mixing i s composed of two contributions: 1.

A m o d i f i e d F l o r y - H u g g i n s e q u a t i o n t o account f o r entropy e f f e c t s due t o d i f f e r e n c e s i n m o l e c u l a r s i z e , and A m o d i f i e d Wilson e q u a t i o n which r e p r e s e n t s the i n d i v i d u a l groups i n a m i x t u r e .

2.

Molecular a c t i v i t y c o e f f i c i e n t s corrected for differences in m o l e c u l a r s i z e are c a l c u l a t e d as the sum of group a c t i v i t y c o e f f i c i e n t s w h i c h , i n t u r n , are determined by group c o m p o s i t i o n r a t h e r than by m o l e c u l a r c o m p o s i t i o n . The Helmholtz f r e e energy i s w r i t t e n as

A

n

ΤΓΓ-

J

N

I

T

b

T

I n - T

1

1

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.

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In

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(1)

EQUATIONS O F STATE: THEORIES A N D APPLICATIONS

454

where upper case s u b s c r i p t s r e f e r t o m o l e c u l a r p r o p e r t i e s , lower case s u b s c r i p t s r e f e r t o group p r o p e r t i e s , and η = total

number of moles

b = total

m o l e c u l a r volume =

^ Xj bj

b j = volume of one mole of molecules of type I =

| mj^ b^

b-j = volume of one mole of groups of type i


mj.j = number of groups of type i i n molecule b^ = volume of one mole of V = total

I

holes

volume

C = a universal

constant

i n the m o d i f i e d Wilson

s = I Xj Sj = e x t e r n a l degrees I mixture

equation

of freedom parameter f o r the

s j = £ mj.j s.j = e x t e r n a l degrees of freedom parameter f o r ι molecules of type I Sj = e x t e r n a l degrees type i

of freedom parameter f o r groups o f

E^j = i n t e r a c t i o n energy between groups i and j λ ·,· = EXP(-Ε ·j/kT) and j Ί

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x

ψ.,· =

i

m

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b

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i

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The PFGC e q u a t i o n of s t a t e f o l l o w s d i r e c t l y from the e x p r e s s i o n f o r the Helmholtz f r e e energy of m i x i n g by using f o l l o w i n g thermodynamic r e l a t i o n s h i p :

7ΓΓ

=

" W

the

^ Τ , η

Thus, i n terms of c o m p r e s s i b i l i t y f a c t o r , the PFGC e q u a t i o n of s t a t e can be w r i t t e n as


( 2 )

22.

MAJEED AND WAGNER


455

(3)

where ν i s the molar volume. T a k i n g c / b as a " u n i v e r s a l " c o n s t a n t , t h e r e are t h r e e b a s i c parameters i n the PFGC e q u a t i o n :


H

(1) (2) (3)

Ε ·,·, the i n t e r a c t i o n energy between groups b j , the volume of one mole of groups of type i S j , a parameter p r o p o r t i o n a l t o the e x t e r n a l degrees freedom per group i Ί

of

Note t h a t t h r e e parameters must be known f o r groups i n s t e a d of m o l e c u l e s . The i n t e r a c t i o n energy i s e v a l u a t e d as

where a^,- i s an i n t e r a c t i o n c o e f f i c i e n t . When a^- i s u n i t y , the m i x t u r e p r o p e r t i e s are n e a r l y i d e a l . If a-jj i s l e s s than one, d e v i a t i o n s from i d e a l i t y are i n t h e p o s i t i v e d i r e c t i o n ; f o r a^j g r e a t e r than one, d e v i a t i o n s from i d e a l i t y are i n the n e g a t i v e direction. The group i n t e r a c t i o n energy i s s l i g h t l y temperature dependent. For c o n v e n i e n c e , the f o l l o w i n g form i s used (6)

(5) Thus, t h e PFGC e q u a t i o n of s t a t e i n . i t s f i n a l form has f i v e a d j u s t a b l e parameters: S j , b j , E j j ( ° ' , E j j ' ' , and E j ^ ' . In a d d i t i o n , t h e r e i s one 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 f o r each p a i r of groups. A p p l i c a t i o n of the e q u a t i o n of s t a t e t o t h e p r e d i c t i o n of thermodynamic p r o p e r t i e s i s s t r a i g h t - f o r w a r d once a p p r o p r i a t e group parameters are a v a i l a b l e . The PFGC e q u a t i o n of s t a t e w r i t t e n i n terms of compressibility factor e x h i b i t s cubic-type behavior. Several i t e r a t i v e schemes can be a p p l i e d t o f i n d the l i q u i d - l i k e and/or v a p o r - l i k e r o o t s of E q u a t i o n 3. Moshfeghian, et a l . (6) used a d i r e c t s u b s t i t u t i o n method. However, a t h i r d - o r d e r i t e r a t i o n method u s i n g a Richmond convergence scheme has been found t o improve both the speed and r e l i a b i l i t y of the c a l c u l a t i o n s . The b a s i c a l g o r i t h m i s given by Lapidus (7) as 1

2f(Xj)

2

fix,)

(6) 2Cf

(Xi ) ]

2

-

f ( X j )

f t x j )

S e t t i n g χ = b/v, E q u a t i o n 3 can be w r i t t e n as


456

E Q U A T I O N S O F STATE: T H E O R I E S A N D A P P L I C A T I O N S

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J

The f i r s t and second d e r i v a t i v e s f (x) = 1 + s

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Σ «. [ * Ρ - 1] i (1 - χ + χ I * j ^ j )

b


are

1

(8)

2

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and ς f"(x)

=

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=C=

>C-

12.

13.

14.

15.

16.

17. 23.

24.

2

-.0046 -61.1222 -18.4444 92.0556 -65.7222

-.2419

.01940

-C=

11.

2

-62.3567

10.

17.2222 32.4755 -107.6667 -142.8333 -174.0336

.3471 .2272

.01610 .01634

9.

2

-320.1728

-94.5814

0.07422 3.6022

1.6667

0.1697

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>CH *CH=C
C
CH-

4.2153 -32.5201

5.

.4956

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-176.5500

4.

3

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E(2) Κ

κ

E(D

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1.9780

(0) Κ

3.

1.8982

E

4

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m^/kg-mo le

CH

Group

2.

No

TABLE I. TYPICAL GROUP PARAMETERS FOR THE PFGC EQUATION




22.


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460

E Q U A T I O N S O F STATE: T H E O R I E S A N D A P P L I C A T I O N S


TABLE I I .

COMPARISON OF VAPOR PRESSURE PREDICTIONS

Average A b s o l u t e P e r c e n t E r r o r Component

Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane n-Hexane n-Heptane n-Octane n-Nonane n-Decane n-Tetradecane n-Pentadecane n-Hexadecane n-Heptadecane 2-Methylpentane 3-Methylpentane 2,3-Dimethylbutane Nitrogen Carbon D i o x i d e Hydrogen S u l f i d e

PFGC

SRK

No. of Points

Ref,

2.38 3.60 5.32 1.89 5.66 1.16 6.46 1.95 4.47 3.45 3.72 2.15 5.78 7.86 9.90 13.16 14.80 6.43 13.10

1.50 1.59 1.06 .86 1.62 1.13 1.55 1.33 1.05 1.22 1.16 1.15 2.31 2.94 2.29 4.07 1.07 1.40 1.13

21 38 45 25 52 38 55 44 61 62 27 27 27 27 27 27 58 58 59

10 10 10 11 10 12 10 11 10 10 13 13 13 13 13

1.86 6.94 0.94

0.78 .47 .91

60 48 30

14 15 16


10 10 13

22. M A J E E D A N D WAGNER


461

61 LU

ce D CO CO 4I LU *| LU £

Ο PFGG • SRK

S* Η

Ο

LU < ϋ

>


^LU Ζ-

...

2

. C

1

ο •••φ

Ο , Ρ 0

< >

···

LU Ο

0.5

0.6

Figure 1 Deviations pentane ( 1 6 ) .

TABLE I I I .

Component Methane Ethane iso-Pentane n-Hexane Ethylene Propylene 1-Butene Benzene Toluene Nitrogen Carbon Monoxide Carbon D i o x i d e Hydrogen S u l f i d e Sulfur Dioxide

0.7 0.8 0.9 REDUCED TEMPERATURE

1.0

i n vapor p r e s s u r e p r e d i c t i o n s f o r

iso-

AVERAGE ABSOLUTE PERCENT ERRORS IN MOLAR VOLUMES

PFGC 7.11 3.25 14.14 2.86 3.81 1.76 2.48 6.55 16.05 1.77 17.40 12.20 4.86 7.83

Liquid SRK No. P t s . 4.51 6.59 12.42 19.44 8.11 8.60 12.96 14.16 16.98 3.91 4.67 15.08 6.85 19.54

62 58 38 44 63 63 27 48 61 81 25 60 27 34

PFGC

3.79 4.94 6.19 8.40 9.50 4.72 27.50 12.33 5.04 9.32 6.31 13.30 4.95 14.2

SRK

2.19 3.01 7.48 3.02 3.22 2.56 3.19 1.85 1.74 1.30 2.36 4.05 5.24 7.61

Vapor No. P t s . R e f . 95 77 83 69 108 64 27 48 61 116 67 71 66 64


18 19 12 11 20 21 11 11 10 14 11 15 16 11


462


F i g u r e 2 i l l u s t r a t e s the performance of the two e q u a t i o n s f o r p r e d i c t i n g the molar volumes of s a t u r a t e d i s o p e n t a n e . The SRK e q u a t i o n p r e d i c t s l i q u i d volumes t h a t are t o o h i g h , e s p e c i a l l y near the c r i t i c a l p o i n t . In c o n t r a s t , the PFGC e q u a t i o n p r e d i c t s molar l i q u i d volumes t h a t are t o o low. In g e n e r a l , a b s o l u t e e r r o r s i n l i q u i d volumes are about the same f o r the two e q u a t i o n s . E r r o r s i n p r e d i c t e d vapor volumes are of t h e same o r d e r of magnitude f o r the two e q u a t i o n s . P r e d i c t i o n s of molar volumes can be improved somewhat, but o n l y at t h e expense of vapor p r e s s u r e or phase b e h a v i o r p r e d i c t i o n s . In f i t t i n g group parameters we have t r i e d t o m i n i m i z e e r r o r s i n vapor p r e s s u r e p r e d i c t i o n s w h i l e m a i n t a i n i n g reasonable accuracy of v o l u m e t r i c p r e d i c t i o n s . V a p o r - L i q u i d E q u i l i b r i u m . The c a p a b i l i t i e s of the PFGC e q u a t i o n of s t a t e i n p r e d i c t i n g the phase b e h a v i o r and phase c o m p o s i t i o n s has been e v a l u a t e d f o r a v a r i e t y of systems, i n c l u d i n g t h o s e c o n t a i n i n g both hydrocarbon and nonhydrocarbon components. Examples of e r r o r s i n p r e d i c t e d K-values and l i q u i d volume f r a c t i o n s are presented i n Tables IV and V. I n s p e c t i o n of t h e s e t a b l e s shows a f a i r l y good agreement between e x p e r i m e n t a l and c a l c u l a t e d phase b e h a v i o r f o r both hydrocarbon-hydrocarbon and hydrocarbon-non-hydrocarbon b i n a r y systems. One of the d i f f i c u l t i e s i n u s i n g the group c o n t r i b u t i o n t e c h n i q u e i n v o l v e s the use of t h e same group 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 f o r both pure components and m i x t u r e s . For example, t h e 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 between the -CH3 and =CH2 groups i n t o l u e n e was o p t i m i z e d u s i n g vapor p r e s s u r e data f o r t o l u e n e . However, t h e same i n t e r a c t i o n c o e f f i c i e n t i s a key v a r i a b l e i n o b t a i n i n g good p r e d i c t i o n s of t o l u e n e K-values i n m i x t u r e s of p a r a f f i n s . T h i s problem i s c h a r a c t e r i s t i c of a group c o n t r i b u t i o n t e c h n i q u e where the number of groups are much s m a l l e r t h a n the number of components. The group parameters and t h e 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 r e p r e s e n t a d e l i c a t e balance between t h e a b i l i t y t o p r e d i c t pure component thermodynamic p r o p e r t i e s and the r e p r e s e n t a t i o n of multicomponent v a p o r - l i q u i d equilibria. The performance of the PFGC e q u a t i o n i n p r e d i c t i n g the phase b e h a v i o r and v o l u m e t r i c of multicomponent n a t u r a l gas and r e t r o g r a d e condensate types of systems has been d i s c u s s e d by Wagner et a l . ( 5 9 ) . For h e a v i e r m i x t u r e s , the phase b e h a v i o r of a s y n t h e t i c o i l w i t h high carbon d i o x i d e c o n t e n t s r e p r e s e n t s an extreme t e s t of the PFGC e q u a t i o n . Using group i n t e r a c t i o n c o e f f i c i e n t s d e r i v e d from carbon d i o x i d e - hydrocarbon b i n a r y systems, t h e PFGC e q u a t i o n p r e d i c t e d reasonably w e l l t h e s a t u r a t i o n p r e s s u r e s of the m i x t u r e w i t h carbon d i o x i d e c o n t e n t s up t o 97 mole percent (69) as shown i n F i g u r e 3. Aqueous L i g h t Hydrocarbon Systems For a p p l i c a t i o n s of the PFGC e q u a t i o n t o aqueous systems, two group i n t e r a c t i o n c o e f f i c i e n t s were d e f i n e d f o r the v a r i o u s phases p r e s e n t . One b i n a r y group i n t e r a c t i o n c o e f f i c i e n t i s used f o r both the vapor and h y d r o c a r b o n - r i c h l i q u i d phases; a second group i n t e r a c t i o n c o e f f i c i e n t i s used f o r t h e aqueous l i q u i d phase.





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REDUCED TEMPERATURE Figure 2 Deviations i s o - p e n t a n e (16)

i n s a t u r a t e d molar volume p r e d i c t i o n s f o r


In Equations of State; Chao, K., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1986. 460.0 200.0

-> -*·

79.0

100.0

0.0

150.0

CH (]D - n C H ( 2 )

C H ( ]D " n C H ( 2 )

C H ( ]D " n C H ( 2 )

2 2

1 8

1 4

2

6

CH

->»

150.0

D - nC H (2)

1 2

·*·

5

1 0

40.0

H

6

nC H (2)

C

2

4

8

2 6< D -

3

- C H (2)

1 0

8

6

1 2

nC H (2)

H

2 6< D

4

4

4

5

C H ( D -

C

-131.24 -• 32.0 302.0

-140.0

4

1 0

25.0 100.0

460.0

50.0 ->

21.99 5.22 6.18

7.92

1715.0

1146.0

13.16 22.66

7.94 14.53

39 112

68

955.0

33

32

31

30 5.56

19

805.0

16.93 4.07

3.30

•¥

509.0

29

9.24 2.78

2.11 78

752.0

•>

100.0

28 10.89

25.42 157

5000.0

9.13

27

8.76 12.51

26

25

24

23

22

Reference No.

11.50

11.02

18.14

8.44

9.16

11.60

17.63

22.42

17.80

9.98

32.05

6.42

8.33

7.32

4.21

2

P e r c e n t Abs. Avg. E r r o r K L/F

7.44

105

64

105

81

118

40.0

2675.0

2200.0

1822.0

1450.0

748.0

35

·>

·>

•¥

•>

-•

-*·

No. of Points

3865.0

146.9

19.9

50.0

20.1

50.0

28.0

Pressure Range ( p s i a )

350.0

340.0

250.0

50.0

40.0

32.0

CH (1D - n C H ( 2 )

4

8

-200.0

4

3

-99.8

CH (]D - n C H ( 2 )

4

·>

-176.0

6

CH (1D - C H ( 2 )

2

-225.0

4

Temperature Range (°F)

DEVIATIONS IN K-VALUE PREDICTIONS FOR HYDROCARBON-HYDROCARBON BINARIES

CH (1D - C H ( 2 )

System

TABLE IV.




£ co

^ co

co

LO

00

CT>

CVJ

CO

CVJ rH

i—1 ι—1

ο

i—1

o

CVJ r—1

LO

ΙΟ CVJ

00

P-. CVJ

CVJ

^ co

oo oo

Ο


LO

er> oo

co

CVJ

co co

ο

uo co

CVJ

oo

co

CO

VO CO

r—

σ> O r-H

•

00 CVJ

Γ

er>

CVJ CO

CO CVJ

Ο rr H H

CT>

00 LO

ι—1 P-

p-

00 i-H

cvj oo

·

i—·

r-H 00

Ο

c o c o ^ a -

•

CO

00

oo

CO

CVJ VO LO

CO 00 i-H

LO P-

CVJ

00 CVJ

P-

CVJ CVJ

00 i-H

CO P-

P-

rH

oo

CVJ

·

*

ο

•

UO CVJ

ι—

«3-

4-

ο Ο LO

·

4-

ρ-

p-

ρ-

«3r—I

«3i-H

f—I

Ο

00

Ο Ο VO

LO LO Ρ-

Ο

^

*

·

CVJ

Ο

CVJ

^

LO

4·

4-

4-

•

•

4-

LO

P-

• ο

LO 00

CO CVJ

i—1 CO

rH

ο

ο

00 00 CVJ

ο

ο

•

_ ο CVJ

•

o

•

CVJ CVJ

o

I—«

i-H

+

4·

ο

Ο

ο

Ο

LO

ο

CO

LO

ο ο

4-

·

LO ι—I

4-

Ο

·

• rH LO CO

ο

•

4-

ο

4·

LO

.

4-

Ο

Ο

r**

·

ι—1

ο

LO

rH

Ο Ο CVJ

CVJ CVJ 00 CT> CVJ

LO CO 4-

o ο ο

ι—I

Ο ο ο

^j-

4-

ο ο

4-

ο ο 4-

Ο

ο

Ο ο

ο ο

rH

rH I

^ ^ CVJ ^ w

cvj 31

ο «-< ο C

• ^ «—< v

co 31

co ο

CVJ CVJ I

ο *—I

ο c

I Ο r Ο

ι ,— ^ >>CVJ χι ^ 4->

>> ο

eu eu χ c rcs

I

^

rH Ο rH

•= LO

ο c

I CVJ

^

—^

I

^

4->

CU

rH Q .

=c eu

ΖΠ >>

LOX:

ο

CVJr— ,—ICJ LOU

ο c

χ: cvj +->

I

1

>>

>>

SZ eu ε

eu

Σ.

eu c Π3

c

i-H Ο) — - C CVJitJ H X

ο c

ι r—

1

C V J ^ CVJ

CVJ CVJ »

χ: 4->

eu E co -—^ CVJ

χ

O)

i-HX: — CVJ— H U

ο

ΠΖ

LOO

ο c

—ι—I eu

t-H C — - fCJ 004-> r-HC

^

•c eu Ο

ο00

00 C L

c

CVJ

ο c

ο

1

I

I

rH

rH

rH

ο

eu

C ' (O 00+J H C •= φ

c

rH

00 CO

CL

eu c eu

Ν c

eu

CÛ

eu c eu

Ν c

eu

0Û

eu eu =5

'ο

h-



60.0 33.0

100.0 + 280.0

40.1 + 220.0

nC H (2)

nC H (2)

nC H (2)

-

-

-

co (i;

C0 (1)

co (i]

3 4

- Toluene (2)

2

co (i;

2

-

2

N (2)

2

C0 (1) - H S(2)

2

co (i;

2

C 0 ( 1 ) - Benzene (2)

1 6

nC H (2)

2 2

1 4

1 2

1 0

-

2

co (i;

2

1 0

6

5

4

8

nC H (2)

3

C0 (1] -

2

2

2

2

6

4-

194.0

-67.0 + 32.0

-2.34

100.6 + 399.0

77.0 •> 104.0

372.9 • 735.08

40.0 + 460.0

255.0

293.9

48.4

129.6

284.5

50.0

113.0

100.0

40.0+ 160.0

C H (2)

-

co (i]

2

104.0 4- 248.0

90.0

-58.0 + 68.0

2

- CH (2)

C0 (1 1 - C H (2)

co (i;

4»

4·

•>

·>

•>

-»•

4-

4·

4·

4-

1907.0

1175.7

2218.0

1124.1

749.5

2732.0

1682.0

1397.0

1150.0

950.0

914.0

1146.0

Pressure Range ( p s i a )

161.0

4


30

85

34

17

31

88

40

47

54

67

54

45

No. of Points

4.34

3.53

10.63

17.87

8.30

19.20

24.82

12.21

11.21 2.07

20.80

15.90

12.20

7.07

5.95

19.80

4.89

2

11.32

9.48

8.98

7.45

4.49

3.01

8.51

χ

12.43

21.42

11.76

7.77

8.16

7.78

5.94

6.31

9.11

9.90

20.41

9.61

P e r c e n t Abs. Avg. E r r o r Κ K L/F

SYSTEM DEVIATIONS IN K-VALUE PREDICTIONS FOR NONHYDROCARBON-HYDRQCARBON BINARIES

-100.0 • 29.0

2

System

TABLE V.


52

51

50

49

48

47

46

45

44

43

42

41

Reference No.


4

6

1 0

13.34 16.02 5.29 21.66

4.68 6.62 6.04 28.82

2.08 3.21 4.66 8.96

-

-

-

D

:D

H S(

HS

2

2

1 0

2 2

1 2

nC H (2)

5

1 0

nC H (2)

4

nC H (2)

6

D

2

2

H S(

2

C H (2)

-

D

H S(

40.0 + 340.0

40.0 4- 340.0

100.0 • 250.0

-99.80 4. 50.0

20.0 4- 1935.0

20.0 4- 1302.0

69.4 • 1150.0

9.45 + 442.0

50

60

77

45

7.49

1600.0

12.46

200.0

5.08

-120.0 + 200.0

59

- CH (2)

2

D

2

H S(

2

4

12.43

4.34

17.87

30

255.0 + 1907.0

- 6 7 . 0 +• 32.0

N (]D - C0 (2)

2

57

56

55

54

53

52

58 6.07

10.10

10.60

17

900.86 + 4454.4

167.0 4- 257.0

N ( ] D - Benzene (2)

2 2

57

1 0

12.96

2

18.58

56

55

54

53

27.62

13.24

17.25

10.19

11.03

92

26.14

13.61

13.74

6.19

80.0 4- 5000.0

1 0

22.05

14.23

13.70

4.74

21

28

31

101

350.8 + 4506.5

236.0 + 3402.0

152.7 + 1913.7

40.5 • 710.0

100.0 4- 280.0

5

-200.0 + 0.0

100.0 •> 280.0

-99.67 + 62.33

-240.0 + 130.0

N ( ] L) " n C H ( 2 )

2

N ( lD - n C H ( 2 )

2

2

- C H (2)

4

N ( l L) " n C H ( 2 )

2

N 0D

2

N (]D - CH (2)


S' 3

-Ci

S' S

S

Ci

ο

î

Ο Ζ m

0

> Ζ D

2 >


468


F i g u r e 3 E x p e r i m e n t a l and p r e d i c t e d bubble p o i n t p r e s s u r e s f o r a s y n t h e t i c o i l w i t h v a r y i n g carbon d i o x i d e content (140)



22.



469

Data f o r m i x t u r e s of water w i t h l i g h t h y d r o c a r b o n s , carbon d i o x i d e , hydrogen s u l f i d e , n i t r o g e n , and carbon monoxide were used t o d e r i v e b i n a r y group i n t e r a c t i o n c o e f f i c i e n t s f o r the aqueous phase. These i n t e r a c t i o n c o e f f i c i e n t s were f i t t o m i n i m i z e t h e average a b s o l u t e e r r o r s i n t h e c o m p o s i t i o n of each phase. Some of the nonhydrocarbon-water group i n t e r a c t i o n c o e f f i c i e n t s were found t o be l i n e a r l y dependent on a b s o l u t e t e m p e r a t u r e . T a b l e VI summarizes the e r r o r s i n p r e d i c t e d phase c o m p o s i t i o n s f o r s e v e r a l b i n a r y w a t e r - h y d r o c a r b o n and w a t e r nonhydrocarbon systems. For p a r a f f i n s and o l e f i n s , t h e PFGC e q u a t i o n g i v e s e x c e l l e n t p r e d i c t i o n s of t h e vapor, hydrocarbon l i q u i d , and aqueous l i q u i d phases up t o a p p r o x i m a t e l y 9000 p s i a . V a p o r - l i q u i d - l i q u i d p r e d i c t i o n s f o r t h e b i n a r y systems of water w i t h carbon d i o x i d e and hydrogen s u l f i d e are good up t o 3000 psia. The a b i l i t y of the PFGC e q u a t i o n t o handle t h e s e nonideal aqueous m i x t u r e s i s a r e s u l t of u s i n g an a c t i v i t y c o e f f i c i e n t model as a t h e o r e t i c a l b a s i s f o r the e q u a t i o n of s t a t e .

Other A p p l i c a t i o n s We have r e c e n t l y l i n k e d the PFGC e q u a t i o n of s t a t e w i t h P a r r i s h and P r a u s n i t z (68) hydrate model as m o d i f i e d by Menton, P a r r i s h and Sloan ( 6 9 ) . The p r e l i m i n a r y r e s u l t s of t h i s e f f o r t are very p r o m i s i n g ( 5 9 ) , and we are c o n t i n u i n g our e v a l u a t i o n of the p r e d i c t i o n of h y d r a t e f o r m a t i o n c o n d i t i o n s below the i c e p o i n t . Procedures are a l s o being developed t o extend the PFGC e q u a t i o n t o m i x t u r e s of u n d e f i n e d components i n n a t u r a l gas condensates and crude o i l s . Summary The PFGC e q u a t i o n of s t a t e has the c a p a b i l i t y t o p r e d i c t v a p o r l i q u i d e q u i l i b r i u m and v o l u m e t r i c p r o p e r t i e s f o r a v a r i e t y of l i g h t hydrocarbon and hydrocarbon-water systems. In g e n e r a l , the q u a l i t y of the p r e d i c t i o n s i s q u i t e good c o n s i d e r i n g the s m a l l number of group parameters a v a i l a b l e t o d e s c r i b e a l a r g e number of components. In more p r a c t i c a l t e r m s , the PFGC e q u a t i o n i s s u i t a b l e f o r process d e s i g n / s i m u l a t i o n c a l c u l a t i o n s f o r many l i g h t hydrocarbon systems. Although the Soave-Redlich-Kwong and PengRobinson e q u a t i o n s of s t a t e are more r e l i a b l e f o r " n o r m a l " hydrocarbon systems, the PFGC e q u a t i o n has an advantage i n aqueous systems w i t h both hydrocarbons and nonhydrocarbons. Acknowledgment The authors a p p r e c i a t e t h e f i n a n c i a l support of t h e Mobil Foundation and the School of Chemical E n g i n e e r i n g , Oklahoma S t a t e U n i v e r s i t y , which made t h i s work p o s s i b l e .


In Equations of State; Chao, K., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1986. 65 65

16.6 18.67

68

984.8 1305.4 1446.0 50759.0 2000.0 2000.0 200.0

413.4 301.7 264.0 2900.0 50.0 50.0 50.0

473.0 536.0 564.8 662.0 600.0 600.0 600.0

H 0(1) - n C H ( 2 ) 392.0

H 0(1) - n C H ( 2 ) 392.0

H 0(1) - n C H ( 2 ) 392.0

122.0

100.0

100.0

100.0

H 0(1) - C0 (2)

H 0(1) - H S(2)

H 0(1] - N (2)

H 0(1) - C0(2)

2

2

2

2

2

2

2

2

2

2

10

9

7

6

22

20

16

14

67 65 65 65

3.55 3.81 14.90

12.01 7.84 9.68

18 16 18

65 24.52

21.43

18.50

12.46

7

5

65

24.2

3

789.0

536.6

437.0

2

12

66

H 0(1) - n C H ( 2 ) 392.0

5

10

31.66

9.81

32

3000.0

120.0

600.0

2

4

65

100.0

H 0(1) - n C H ( 2 )

2

4

21.80

115

934.7

52.2

280.0

100.0

H 0(1) - n C H ( 2 )

64 11.21

6.60

6.98

7

491.6

52.2

280.0

99.9

2

10

H 0(1) - n C H ( 2 )

63 10.51

12.90

7.16

240

3000.0

72.0

310.0

8

42.3

2

3

H 0(1) - C H (2)

62

4.71

711.3 130

460.0

100.0

2

6

H 0(21D - C H (2)

2

680.0

302.0

4

H 0(1) - CH (2) 10000.0

Reference No.

200.0

Percent Abs. Avg. Error i n Smaller Component Cone. Vapor Hydrocarbon Water Phase Liquid 61

No. of Points

7.33

Pressure Range (psia)

45


14226.0

2

System

2

TABLE VI. H 0 BINARY SYSTEMS DEVIATIONS IN PHASE CONCENTRATION PREDICTIONS


22.

MAJEED AND WAGNER

Parameters from Group Contributions Equation 47

Literature Cited 1. 2. 3. 4.


5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

18. 19. 20. 21.

Soave, G., Chem. Eng. Sci., 1972, Vol. 27, 1197 Peng, D. Y. and Robinson, D. B. Canadian Jour. Chem. Engr., 1976, Vol. 54, December, 595. Starling, Κ. E. and Han, M. S. Hydrocarbon Processing, 1972, Vol. 51, No. 5, 129. Cunningham, J. R. and Wilson, G. M. Paper presented at GPA Meeting, Tech. Section F, Denver, Colorado, March 25, 1974. Cunningham, J. R., M.S. Thesis, Brigham Young University, Provo, Utah, 1974. Moshfeghian, M., Shariat, Α., and Erbar, J. Η., Paper presented at the AIChE National Meeting, Houston, Texas, April 1-5, 1979. Lapidus, L . , "Digital Computation for Chemical Engineers", McGraw-Hill, New York, 1962. Moshfeghian, Μ., Shariat, Α., and Erbar, J. H. Paper presented at NBS/NSF Symp. on Thermo. of Aqueous Sys., Airlie House, Virginia, 1979. Moshfeghian, M., Shariat, Α., and Erbar, J . H. ACS Symposium Series 113. Engineering Sciences Data Unit, Chemical Engineering Series, Physical Data, Volume 5, 251-259 Regent Street, London WIR 7AD, August, 1975. Canjar, L. and Manning, F. "Thermodynamic Properties and Reduced Correlations for Gases," Gulf Publishing Corporation, Houston, Texas, 1966. Arnold, E. W., Liou, D. W., and Eldridge, J. W., J. Chem. Eng. Data, 1965, Vol. 10, No. 2, 88. Selected Values of Properties of Hydrocarbons and Related Compounds, API Research Project 44, Texas A&M University, Updated, 1979. Strobridge, T. R., "The Thermodynamic Properties of Nitrogen from 64 to 300 Κ between 0.1 and 200 Atmospheres", Nat. Bur. Stand., Tech. Note 129, 1962. IUPAC "International Thermodynamic Tables of the Fluid State", Chem. Data Series No. 7, Carbon Dioxide, Pergamon Press, London, 1980. West, J. R., Chem. Engr. Prog., 1948, 44(4), 287. Videl, J., Proceedings of the Third International Conference on Fluid Properties and Phase Equilibria for Process Design, Callaway Gardens, Georgia, April 10-15, 1983. Goodwin, R. D., "The Thermophysical Properties of Methane from 90 to 500 Κ at Pressures 700 Bar", Nat. Bur. Stand. (U.S.), Tech. Note 653, 1974. Goodwin, R. D., "The Thermophysical Properties of Ethane from 90 to 600 Κ at Pressures 700 Bar", Nat. Bur. Stand. (U.S.), Tech. Note 684, 1976. ASHRAE Handbook, Fundamentals 1981, American Society of Heating, Refrigerating and Air Conditioning Engineers, Third Printing, 1982, 17. IUPAC "International Thermodynamic Tables of the Fluid State", Chem. Data Series No. 25, Propylene, Pergamon Press, London, 1980.


472 22. 23. 24. 25. 26.


27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

EQUATIONS OF STATE: THEORIES AND APPLICATIONS Wichterle, I. and Kobayashi, R. J. Chem. Eng. Data, 1972, 17(1), 9. Akers, W. W., Burns, J. F, and Fairchild, W. R. Ind. Eng. Chem., 46(12), 1954, 2531. Douglas, G. E., Chen, R. J. J., Chappelear P. S., and Kobayashi, R. J. Chem. Eng. Data, 1974. 19(1), 71. Kahre, L. C., J. Chem. Eng. Data, 1975, 20(4), 363. Lin, Y. Ν., Chen, R. R. J., Chappelear, P. S., and R. Kobayashi, J. Chem. Eng. Data, 1977, 22(4), 402. Kohn, J. P. and Bradish, W. F., J. Chem. Eng. Data, 1964, 9(1), 5. Reamer, Η. Η., Olds, R. H., Sage, Β. H., and Lacey, W. N. Ind. Eng. Chem., 1942, 34(12), 1526. Matschke, D. E. and Thodos, G. J. Chem. Eng. Data, 1962, 7(2), 232. Thodos, G. and Mehra, V. S. J. Chem. Eng. Data, 1965, 10(4), 307. Reamer, H. H., Sage, Β. Η., and Lacey, W. N. Ind. Eng. Chem., 1940, 5(1), 44. Zais, E. J. and Silberberg, I. L. J. Chem. Eng. Data, 1970, 15(2), 253. Reamer, H. H. and Sage, B. H. J. Chem. Eng. Data, 1962, 7(2), 161. Sage, Β. H. and Lacey, W. N. Ind. Eng. Chem., 1940, 32(7), 992. Reamer, H. H. and Sage, B. H., J. Chem. Eng. Data, 1966, 11(1), 17. Reamer, H. H. and Sage, B. H., J. Chem. Eng. Data, 1964 9(1), 24. Myers, H. S., Petroleum Refinery, 1957, 36(3), 175. Liu, Ε. K. and Davison, R. R., J. Chem. Eng. Data, 1981, 26(1), 85. Lin, H., Sebastion, H. M., Simnick, J. J., and Chao, K. C. J. Chem. Eng. Data, 1979, 24(2), 146. Glanville, J. W., Sage, Β. H., and Lacey, W. N. Ind. Eng. Chem., 1950, 42(3), 508. Chang, H. L. and Kobayashi, R. J. Chem. Eng. Data, 1967, 12(4), 517. Donnelly, H. G. and Katz, D.L. Ind. Eng. Chem., 1954, 46(3), 511. Fredenslund, A. and Mollerup, J. J. Chem. Soc., Faraday Transactions I, 1974, 70, 1653. Reamer, H. H. and Sage, Β. H. Ind. Eng. Chem., 1951, 43(11), 2515. Besserer, G. J. and Robinson, D. B. J. Chem. Eng. Data, 1973, 18(3), 298. Besserer, G. J. and Robinson, D. B. J. Chem. Eng. Data, 1975, 20(1), 93. Robinson, D. B., Kalra, H., Ng, H. J., and Kubota, H. J. Chem. Eng. Data, 1978, 23(4), 317. Sage, Β. H. and Reamer, H. H. J. Chem. Eng. Data, 1963, 8(4), 508. Yorizane, M., Yoshimura S., and Masuoka, H. Kagaku Kogaku, 1966, 30(12), 1093. Katayama, T. and Ohgaki, K. J. Chem. Eng. Data, 1976, 21(1), 53. In Equations of State; Chao, K., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1986.

22.

51. 52. 53. 54. 55. 56. Downloaded by OHIO STATE UNIV LIBRARIES on September 18, 2013 | http://pubs.acs.org Publication Date: March 24, 1986 | doi: 10.1021/bk-1986-0300.ch022

57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67.

MAJEED AND WAGNER


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Parameters from Group Contributions Equation and Phase Equilibria

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