Phase Equilibria Experimental at High Pressure

(1)

Phase Equilibria Experimental at

High Pressure

Principle Investigator: Yan-Ping Chen

Research Worker: Kong - Wei Cheng

Department of Chemical Engineering

National Taiwan University

(2)

Research Topic

Vapor - Liquid Equilibria of Esters in Carbon

dioxide at Elevated Pressure

Solubilities in Supercritical Carbon dioxide

Ternary Systems in Supercritical Carbon

dioxide

(3)

Apparatus in Literature

(1) Analytical Method

(a) Static Type Apparatus

(b) Flow Type Apparatus

(2) Synthetic Method

(a) Visual Synthetic Method

(4)

Experimental Apparatus for VLE

in This Study

to vac.

to vent

2 3 5 9 1 8 6 7 4 11 12 10 needle valve metering valve back-pressure regulator 13 14 1 .C O ₂ c y l i n d e r 5 .t h e r m o m e t e r 9 .h i g h p r e s s u r e p u m p 1 3 .w a t e r c o l u m n 2 .p r e s a t u r a t o r 6 .p r e h e a t e r 1 0 .l i q u i d p u m p 1 4 .b a c k - p r e s s u r e r e g u l a t o r 3 .e q u i l i b r i u m c e l l 7 .t h e r m o s t a t e d b a t h 1 1 .i c e b a t h 4 .p r e s s u r e t r a n s d u c e r 8 .c o o l e r 1 2 .w e t t e s t m e t e r F i g . 1 S c h e m a t i c d i a g r a m o f t h e e x p e r i m e n t a l a p p a r a t u s f o r V L E

(5)

Correlation for Experimental

Data

(a) Krichevsky – Ilinskaya (KI) Equation

(b) Equation of State with Mixing Rules

RT

P

V

RT

x

A

H

x

f

(

1 )

(

sat

)

ln

1

2

2 *

2 ,

1

1 











(6)

Equation of State Using in This

Study

(1) Peng – Robinson (PR) EOS

(2) Soave-Redlich-Kwong (SRK) EOS

)

(

)

(

v

b

v

b

v

a

b

v

RT

P









)

(

v

b

v

a

b

v

RT

P







(7)

Mixing Rules Using in This

Study

(a) van der Waals one-fluid mixing rules

(b) VDW2 mixing rule

(c) Panagiotopoulos – Reid mixing rule

(d) Huron – Vidal mixing rule

(8)

Parameters of the KI equation for three binary systems

Systems (1)/(2) T(K) H

*1,2

(bar) A(J mol

-1

) V

1

(cm

3

mol

-1

) AAD

a

(%)

CO

2

/diethyl oxalate

308.15 71.72 909.53 45.98

2.65 318.15 80.97 844.87 47.21

3.01 328.15 92.61 916.32 48.62

3.22 CO

2

/ethyl laurate

308.15 68.47 616.23 57.33

2.76 318.15 74.70 477.99

58.39

2.61

328.15 86.27 614.17

59.62

2.17 CO

2

/dibutyl phthalate

308.15 85.41 1010.37 56.42

1.90 318.15 97.92 1051.07 57.20

1.30

328.15 108.06 1030.46 58.11

2.74

a

_{AAD(%) =}

k n k cal x x x n



_ _       1 1exp 1 exp 1 100

(9)

Correlated results of experimental VLE data of three binary

mixtures using various and EOS mixing rules

Peng-Robinson EOS Soave-Redlich-Kwong EOS Mixing rule k12 k21 m12 AADP(%) AAD y1(%) k12 k21 m12 AADP(%) AADy1(%)

CO2(1) + diethyl oxalate(2) VDW1 0.012 1.580 0.037 0.010 1.617 0.049 VDW2 0.008 -0.007 1.115 0.039 0.005 -0.007 1.137 0.050 Panagiotopoulos-Reid 0.025 0.011 1.126 0.039 0.023 0.008 1.144 0.050 CO2(1) + ethyl laurate(2) VDW1 0.055 1.763 0.011 0.062 1.814 0.014 VDW2 0.061 0.006 1.022 0.009 0.069 0.006 1.036 0.012 Panagiotopoulos-Ried 0.040 0.057 1.028 0.009 0.044 0.067 1.042 0.012 CO2(1) +dibutyl phthalate(2) VDW1 0.055 2.280 0.032 0.057 2.081 0.037 VDW2 0.051 -0.004 1.360 0.036 0.053 -0.004 1.354 0.039 Panagiotopoulos-Reid 0.069 0.052 1.359 0.036 0.070 0.054 1.351 0.039









n i i i cal

P

n

AADP

1 exp exp

100 (%)

_，









n i i i cal

y

n

AADy

1 1exp, 1 exp 1 1

100 (%)

(10)

VLE results of the binary mixture of CO

₂₂

(1) + diethyl oxalate (2)

0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

x

₁

, y

₁

0 . 0 0 2 . 0 0 4 . 0 0 6 . 0 0 8 . 0 0 1 0 . 0 0 1 2 . 0 0

P(

M

Pa

)

C O 2 ( 1 ) + d i e t h y l o x a l a t e ( 2 ) 3 0 8 . 1 5 K 3 1 8 . 1 5 K 3 2 8 . 1 5 K P e n g - R o b i n s o n E O S , V D W 2 m i x i n g r u l e s

(11)

Solubilities of CO

₂

in various ester compounds at

328.15 K

0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0 x 1 0 . 0 0 2 . 0 0 4 . 0 0 6 . 0 0 8 . 0 0 1 0 . 0 0 1 2 . 0 0 1 4 . 0 0 P( M Pa ) T = 3 2 8 . 1 5 K C O 2 ( 1 ) + d i e t h y l o x a l a t e ( 2 ) C O 2 ( 1 ) + e t h y l la u r a t e ( 2 ) C O 2 ( 1 ) + d ib u t y l p h th a l a t e ( 2 ) P e n g - R o b i n s o n E O S , V D W 2 m i x i n g r u l e s

(12)

Solubilities of various ester compounds in supercritical CO

₂₂

at 328.15 K

0 . 1 0 1 . 0 0 P r 0 . 0 0 0 0 . 0 0 3 0 . 0 0 6 0 . 0 0 9 0 . 0 1 2 y 2 T = 3 2 8 . 1 5 K C O 2 ( 1 ) + d i e t h y l o x a l a t e ( 2 ) C O 2 ( 1 ) + e t h y l l a u r a t e ( 2 ) C O 2 ( 1 ) + d i b u t y l p h t h a l a t e ( 2 ) P e n g - R o b i n s o n E O S , V D W 2 m i x i n g r u l e s

(13)

Apparatus for Solubility in

Literature

Semi-Flow type apparatus

(a) weighting method

(b) on-line analysis

(c) washing and analysis

Recycle type apparatus

(a) on line analysis

(14)

Schematic diagram of the experimental apparatus for

solubility in supercritical fluids in this study

to vent

1 needle valve back-pressure regulator 2 3 4 5 6 6 7 8 9 12 13 10 11 14

1. CO2 cylinder

2. Cooler

3. HPLC Pump

4. Pre-heater

5. Equilibrium Cell

6. Filter

7. Pressure transducer

8. Thermometer

9. Ice bath

10. Saturater

11. Wet test meter

12. Mini punp

13. Solvent Reservior

14. Heating Tape

(15)

Comparison of the solubility data of phenanthrene in

supercritical carbon dioxide at 308.15 K

8 . 0 1 2 . 0 1 6 . 0 2 0 . 0

P ( M P a )

1 E - 4 1 E - 3 1 E - 2

y

₂

C O 2 ( 1 ) + p h e n a n t h r e n e ( 2 ) T h i s w o r k D o b b s e t a l ( 1 9 8 6 ) B a r t l e e t a l ( 1 9 9 0 ) T = 3 0 8 . 1 5 K

(16)

Equilibrium Criterion

(a)Use the mass transfer method to ensure the

equilibrium

(b)Find the optimal operation condition

(c)Find the min time to reach the phase

equilibrium

(17)

Fluid - solid mass transfer

Two type of mixing states will be considered

for the fluid flowing in the equilibrium cell

(a) Mixing - flow case

(18)

Plug flow case



_{For plug flow case}

)

(

C

a

k

z

C

u

t

C

sat

s

g













0

0 







t

any

C

z

any

C

t

(19)

Solution of plug flow case

u

L

a

k

St

L

z

t

u

L

C

X

g

s

sat













)

exp(

1

0 ))

exp(

1 ))(

exp(

1 (







St

X

St

X

St













(20)

Parameter Identification

)

1990

(

)

(

309 .

0 S

G

1 /

4 Lim

et

al

Sh



_c

_r

D

Sc

g

d

G

D

d

k

Sh

f

eq

r

eq

g













:

2

(21)

Thermodynamic and mass transport data for CO

₂₂

(1) + Benzoin (2)

at different operating conditions

T (K ) P(M Pa ) sc f (k g/m3) 105_ (Pa s ) 108D12 (m2/s ) Sc R e S t’ C /Csa t 30 8. 15 1 2. 16 72 4.69 7.03 1. 26 7.69 2. 13 -6. 41 77 .2-2 28 .8 0.9 999 1 3. 47 75 6.89 7.58 1. 16 8.64 1. 98 -5. 95 73 .2-2 16 .8 0.9 999 1 5. 40 79 4.63 8.31 1. 05 1 0. 03 1. 81 -5. 43 68 .3-2 02 .5 0 .9997 1 7. 54 82 8.14 9.07 0. 95 11.50 1. 66 -4. 97 63 .9-1 89 .4 0.9 993 2 0. 44 86 4.97 1 0. 07 0. 86 1 3. 58 1. 49 -4. 48 59 .0-1 74 .6 0.9 984 2 3. 61 89 7.99 11. 16 0. 78 1 5. 97 1. 35 -4. 04 54 .4-1 61 .1 0.9 968 31 8. 15 11. 13 55 4.73 4.89 2. 03 4.43 3. 07 -9. 21 98 .5-2 92 .0 0 .9999 1 3. 54 66 1.92 6.16 1. 53 6.07 2. 44 -7. 32 86 .5-2 56 .5 0.9 999 1 5. 27 70 9.62 6.84 1. 35 7.12 2. 20 -6. 59 80 .7-2 39 .4 0.9 999 1 8. 99 78 1.61 8.09 1. 12 9.26 1. 86 -5. 57 71 .5-2 12 .0 0.9 998 1 9. 88 79 5.29 8.37 1. 08 9.78 1. 79 -5. 39 69 .7-2 06 .7 0.9 997 2 1. 81 2 4. 19 821 . 65 84 9.68 8.96 9.68 1. 00 0. 92 1 0. 90 1 2. 33 1. 68 -5. 03 1. 55 -4. 65 66 .2-1 96 .1 62 .4-1 84 .8 0.9 995 0.9 990 32 8. 15 11. 48 43 3.42 3.75 2. 92 2.97 3. 99-11.99 112 .0-3 32 .0 0.9 999 1 4. 23 58 0.62 5.22 1. 96 4.60 2. 87 -8. 63 97 .7-2 89 .8 0.9 999 1 6. 85 66 2.12 6.21 1.58 5.93 2. 42 -7. 26 88 .3-2 61 .9 0.9 999 1 9. 61 72 1.55 7.07 1. 35 7.24 2. 13 -6. 38 81 .0-2 40 .0 0.9 999 2 1. 95 76 0.76 7.74 1. 22 8.34 1. 94 -5. 83 75 .9-2 24 .9 0.9 999 2 4. 43 79 5.16 8.41 1. 10 9.53 1. 79 -5. 36 71 .3-2 11 .2 0.9 998

(22)

Equation of State Using in This Study

(a) Peng –Robinsion (PR) EOS

(b) Soave-Redlich-Kwong (SRK) EOS

)

(

)

(

v

b

v

b

v

a

b

v

RT

P









)

(

v

b

v

a

b

v

RT

P







(23)

Mixing Rules Using in This

Study

(a) van der Waals one-fluid mixing rules

(b) VDW2 mixing rule

(24)

Correlated results of solubility data in supercritical

carbon dioxide using various EOS mixing rules

Mixing rule Peng-Robinson EOS Soave-Redlic h-Kw ong EOS

k12 l12 y2 (%) k12 l12 y2 (%) CO2 (1) + benzoin (2) ) ( 97 . 13160 38 . 36 ) ( ln K T Pa Psat _ _ V DW 1 0.09 5.52 0.10 6.39 V DW 2 0.08 -0.02 5.40 0.11 0.02 6.15

CO2 (1) + propy l 4-h ydroxybenz oate (2)

) ( 69 . 14209 15 . 41 ) ( ln K T P a Ps at _ _ V DW 1 0.12 14.25 0.13 15.62 V DW 2 0.17 0.13 8.97 0.20 0.19 9.66 CO2 (1) + mandelic acid (2) ) ( 62 . 17256 83 . 49 ) ( ln K T Pa Psat _ _ VDW 1 0.09 25.63 0.10 27.11 V DW 2 0.20 0.31 6.81 0.21 0.32 7.13



    n i i c al i i y y y n y 1 2,exp , 2 exp , 2 2 100 (%)

(25)

Correlated results of the experimental solubility data

in supercritical carbon dioxide by the Huron-Vidal

mixing rules

E OS NRTL liquid model UNIQUAC liquid model

A12 (J mol-1) A21 (J mol-1)  y2(% ) A12(J mol-1) A21(J mol-1) y2 (% )

CO2 (1) +benzoin (2)

PR 10 440.08 1 943.07 0.2 6.95 3 545.93 -171.40 5.64 SRK 10 661.03 1 984.41 0.2 9.77 3 536.35 -139.30 6.48

CO2 (1 ) + propy l 4-hydroxyb enz oate (2)

PR 12 165.35 2 264.56 0.2 14.24 1 326.56 7 122.12 14.50 SRK 12 729.86 2 370.73 0.2 16.14 1 446.92 7 774.27 16.52 CO2 (1) + m and elic ac id (2) PR 6 060.34 11069.44 0.2 26.20 2 250.70 1 348.67 25.67 SRK 7 031.53 10 908.49 0.2 27.89 2 314.94 1 688.93 27.14



    n i i cal i i y y y n y 1 2,exp , 2 exp , 2 2 100 (%)

(26)

Data Correlation

Empirical model

(a) Chrastil (1982)

(b) Teja method (1999)

b

K

T

a

gl

n

gl

S









)

(

)

(

ln

)

(

ln

1 

₁

1 CT

B

A

P

y

T

ln(

₂

)







₁



(27)

Correlated results of the experimental solubility data

in supercritical carbon dioxide by the empirical

model

Model n C1 C2 C3 y2 (%) CO2 (1) + benzo in (2) Chrastil 4.84 -4730.67 -17.44 5.86 Santiago -Teja -9111.06 2.68 16.69 6.01

CO2(1) + propyl 4-hydroxybenzoate(2)

Chrastil 6.20 -7087.26 -19.04 9.49 Santiago -Teja -11952.26 3.24 24.46 4.79

CO2 (1) + mandelic acid (2)

Chrastil 9.07 -10432.59 -26.53 12.23 Santiago-Teja -16148.23 4.50 35.80 6.05



    n i _i cal i i y y y n y 1 ₂_,exp , 2 exp , 2 2 100 (%)

(28)

Solubility data for benzoin in supercritical carbon dioxide

8 . 0 0 1 2 . 0 0 1 6 . 0 0 2 0 . 0 0 2 4 . 0 0 2 8 . 0 0

P ( M P a )

1 E - 5 1 E - 4 1 E - 3

y 2

C O 2 (1 ) + B e n z o in ( 2 ) 3 0 8 . 1 5 K 3 1 8 . 1 5 K 3 2 8 . 1 5 K T e j a m e t h o d

(29)

Solubility data of various compounds in supercritical

CO

₂

at 328.15 K

8 . 0 0 1 2 . 0 0 1 6 . 0 0 2 0 . 0 0 2 4 . 0 0 2 8 . 0 0 P ( M P a ) 1 E - 5 1 E - 4 1 E - 3 1 E - 2 y 2 T = 3 2 8 . 1 5 K C O 2 ( 1 ) + b e n z o i n ( 2 ) C O 2 ( 1 ) + p r o p y l 4 - h y d r o x y b e n z o a te ( 2 ) C O 2 ( 1 ) + m a n d e lic a c i d ( 2 )