Equations of State in Engineering and Research - American Chemical

13

An Equation of State for Polar Mixtures: Calculation of High-Pressure Vapor-Liquid Equilibria of Trace Polar Solutes in

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Hydrocarbon Mixtures K. W. WON and C. K. WALKER Fluor Engineers and Constructors, Inc., Irvine, CA 92730

A modification of the Soave equation of state

has been used to calculate vapor-liquid phase equilibria for water, methanol, and mercaptans when these compounds are present in small amounts in hydrocarbon streams. The results of these calculations are compared with experimental data with encouraging results. The equation-of-state method for solving such problems offers advantages over the normal activity coefficient approach.

Tn

energy a n d environmental-related technology

i t is often

necessary

to r e m o v e trace a m o u n t s of n o n h y d r o c a r b o n p o l a r solutes s u c h as w a t e r a n d m e r c a p t a n s f r o m h y d r o c a r b o n streams.

W h i l e equations o f

state h a v e p l a y e d a v e r y i m p o r t a n t r o l e i n the c o r r e l a t i o n of equilibrium

phase

( K - r a t i o s ) of nonpolar a n d slightly polar mixtures, m u c h

less a t t e n t i o n has b e e n g i v e n t o a n e q u a t i o n o f state f o r t h e m o r e difficult p r o b l e m of p o l a r m i x t u r e s . It has b e e n c u s t o m a r y to a p p l y a n a c t i v i t y coefficient m e t h o d to a i d i n the p r e d i c t i o n of v a p o r - l i q u i d equilibria of polar mixtures. A t h i g h pressures a p p r o a c h i n g t h e c r i t i c a l state of t h e fluid m i x t u r e , t h e a c t i v i t y coefficient

m e t h o d r e q u i r e s s u c h t h e r m o d y n a m i c p r o p e r t i e s as p a r t i a l

m o l a r v o l u m e s o r p a r t i a l m o l a r heats of s o l u t i o n t h a t a r e v e r y difficult, 0-8412-0500-0/79/33-182-235$05.00/l © 1979 American Chemical Society

In Equations of State in Engineering and Research; Chao, K., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1979.

236

EQUATIONS O F S T A T E

i f n o t i m p o s s i b l e , t o o b t a i n . W h e n t h e f l u i d m i x t u r e consists m a i n l y of h y d r o c a r b o n s w i t h trace a m o u n t s of p o l a r c h e m i c a l s , the s i n g l e - e q u a t i o n of-state a p p r o a c h appears to b e advantageous. T h i s c h a p t e r illustrates t h e u s e o f a n e q u a t i o n o f state p r e v i o u s l y suggested

a n d shows i t s a p p l i c a t i o n to several i m p o r t a n t

industrial

problems.

Vapor—Liquid

Equilibrium

K-Ratio

F o r any component i i n a mixture, the equilibrium vapor concentra Downloaded by CORNELL UNIV on December 6, 2012 | http://pubs.acs.org Publication Date: December 1, 1979 | doi: 10.1021/ba-1979-0182.ch013

t i o n t/i a n d l i q u i d c o n c e n t r a t i o n Xi are g o v e r n e d b y t h e r e l a t i o n s : fi = f i v

(1)

L

V - V * ? *

(2)

tf-a^P

(3)

w h e r e U a n d φ are the f u g a c i t y a n d f u g a c i t y coefficient of c o m p o n e n t i, {

Ρ is t h e t o t a l pressure, a n d t h e superscripts L a n d V i n d i c a t e t h e l i q u i d o r v a p o r phase. U s i n g these relations, the v a p o r - l i q u i d e q u i l i b r i u m ( V L E ) K - r a t i o is determined b y

Κ , - ^ - ^

(4)

T h e v a p o r - l i q u i d e q u i l i b r i u m K - r a t i o c a n b e c a l c u l a t e d v i a the f u g a c i t y coefficients

f r o m a n e q u a t i o n o f state as a f u n c t i o n o f t e m p e r a t u r e ,

pressure, a n d c o m p o s i t i o n s of l i q u i d a n d v a p o r m i x t u r e s .

Polar

Equation

of

State

T h e e q u a t i o n o f state u s e d here i s a f u r t h e r m o d i f i c a t i o n o f t h e e q u a t i o n g i v e n b y Soave ( J ) . T h i s m o d i f i c a t i o n w a s p r o p o s e d b y W o n (2)

f o r gases i n a p r e v i o u s p a p e r , b u t i t is a p p l i e d t o b o t h gases a n d

l i q u i d s i n this c h a p t e r . I t c a n b e w r i t t e n a s : ,

RT V —b

Aa{T)+Ap(T) V(V + b)

w h e r e the n o n p o l a r a n d p o l a r c o n t r i b u t i o n s are separated.


w

13.

WON AND WALKER

An Equation

of State for Volar Mixtures

237

F o r a polar component,

ΑΛΤ)

=

[A(T )

-

C

A (T )][1 V

ΑΛΤ)

+ a(l

C

C

2V- )] 5

(6)

2

t

3

(7)

= 0 . 4 2 7 8 ^ ^

(8)

= A (T )/T P

-

subject to A(T )

=A (T )

C

a

+ A (T )

c

P

C


where b = 0.0867 RT /P C

(9)

e

a n d a is t r e a t e d as a n independent p a r a m e t e r . F o r a nonpolar component (10)

A (T )=0 p

a =

c

0.48 + 1.57

ω

-

0.176ω

(11)

2

F o r mixtures, = ZZy y A (T)

A(T)

i

i

(12)

ij

and b = Σ

(13)

Vibi

where Α»{Τ)

=

V

A (T )A ,(T ) Dl

c

D

c

[1 + α,(1 -

[1 + «,(1 - TV*) ] +

V

Γ

Γ ί

0

· )] 5

\wlfii

(Tc)

14

S u b s t i t u t i o n of E q u a t i o n s 5, 12, a n d 13 i n t o t h e t h e r m o d y n a m i c d e f i n i t i o n of φ ( 3 ) gives

in * = in

+

^

5 ^

~


238

EQUATIONS OF

STATE

T h e m o l a r v o l u m e V of e a c h e q u i l i b r i u m p h a s e is c a l c u l a t e d

by

s o l v i n g E q u a t i o n 5. A t a g i v e n t e m p e r a t u r e , pressure, a n d c o m p o s i t i o n of the m i x t u r e , three values for V w i l l be o b t a i n e d , the largest of w h i c h is the v a p o r m o l a r v o l u m e a n d the smallest the l i q u i d m o l a r v o l u m e . A l t h o u g h the c a l c u l a t e d l i q u i d m o l a r v o l u m e , V , does not a c c u r a t e l y L

r e p r o d u c e e x p e r i m e n t a l d a t a o n m o l a r v o l u m e , the f u g a c i t y coefficients, y v


= vapor-liquid equilibrium K-ratio = pressure, a t m o s p h e r e

Greek Letter a=

defined b y E q u a t i o n 6

γ = a c t i v i t y coefficient φ = f u g a c i t y coefficient ω = a c e n t r i c factor Superscript and Subscript c = critical property i, / = c o m p o n e n t s i n m i x t u r e L , V = l i q u i d a n d v a p o r phases η, ρ = n o n p o l a r a n d p o l a r c o n t r i b u t i o n r = reduced property S = s a t u r a t e d state oo = state at infinite d i l u t i o n

Literature Cited 1. Soave, G. Chem. Eng. Sci. 1972, 27, 1197. 2. Won, K. W. 69th Annual A.I.Ch.E. Meeting 1976, Tech. Paper 54A. 3. Prausnitz, J. M . "Molecular Thermodynamics of Fluid-Phase Equilibria;" Prentice-Hall: Englewood Cliffs, NJ 1969, 94, 99. 4. Rachford, H . H.; Rice, J. D. J. Pet. Technol. 1952, 4, 10, Sec. 1, 19, Sec. 2, 3. 5. Keenan, J. H.; Keyes, F. G.; Hill, P.G.;Moore, J. G. "Steam Tables;" Wiley Interscience: New York, 1969. 6. Coan, C. R.; King, A. D. J. Am. Chem. Soc. 1971, 93, 1857. 7. "Technical Data Book, Petroleum Refining," 2nd ed.; American Petroleum Institute: Washington, DC, 1971; Chapter 9, p. 9. 8. McKetta, J. J.; Katz, D. L. Ind. Eng. Chem. 1948, 40, 853. 9. Leland, T. W.; McKetta, J. J.; Kobe, K. A. Ind. Eng. Chem. 1955, 47, 1265. 10. Wehe, A. H.; McKetta, J. J. J. Chem. Eng. Data 1961, 6, 167. 11. Thompson, W. H.; Snyder, J. R. J. Chem. Eng. Data 1964, 9, 516. 12. Ramsay; Young. In Intern. Critical Tables, 1928, 3, 436. 13. Hemmaplardh, B.; King, A. D. J. Phys. Chem. 1972, 76, 2170. 14. Storvick, T. S.; Smith, J. M . J. Chem. Eng. Data 1960, 5, 133.


13. WON AND WALKER An Equation of State for Polar Mixtures 251

15. Won, K. W. Adv. Cryog. Eng. 1978, 23, 544. 16. Wolff, H.; Hoppel, Η. E. Ber. Bunsenges. Phys. Chem. 1968, 72, 710. 17. Zudkevitch, D.; Wilson, G. M . Proc. 53rd Ann. Conv. GPA 1974, Tech. Sec. C, 101. 18. Hankinson, R. W.; Wilson, G. M. Proc. 53rd Ann. Conv. GPA 1974, Tech. Sec. C, 98. August 10, 1978.


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Equations of State in Engineering and Research - American Chemical

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