A Computer Model for Calculating Physical and Thermodynamic

14 A Computer Model for Calculating Physical and Thermodynamic Properties of Synthetic Gas Process

Downloaded by NANYANG TECHNOLOGICAL UNIV on June 10, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0060.ch014

Streams GRANT M. WILSON and MARK D. WEINER Brigham Young University, Provo, UT 84602

This paper describes our progress to date on development of a computer model based on a thermodynamically-consistent correlation that will accurately and reliably predict enthalpies, entropies, densities and ultimately K-values for synthetic gas systems over the range of typical synthetic gas processing conditions. A review of various gasification processes is given in Table 1. This table shows that process operating temperatures range from 550º to 3000ºF. The gasification of liquid hydrocarbons is done at temperatures ranging from 550ºF to 1000ºF, while coal gasification processes operate at temperatures from 500ºF to 3000ºF. Gasification pressures range from ambient to 1500 psia, and may be extended to 4000 psia. The principal chemical reactions of these processes can be characterized by the following equations. C Η + H O -> H + CO

(1)

CO + H 0 -> H + C0

(2)

x

y

2

2

CO +

2

2

3H

2

2

->

CH

4

+

HO 2

(3)

In some cases hydrogen is produced by reactions 1 and 2, and then the feedstock is hydrogenated to produce gas and oil. High operating temperatures are achieved either by pre-heating the reactants or by partial combustion using oxygen or air. Reactor products and by-products therefore consist of the following compounds. Hydrogen Carbon monoxide Carbon dioxide

Argon Hydrogen sulfide Carbonyl sulfide 256

Storvick and Sandler; Phase Equilibria and Fluid Properties in the Chemical Industry ACS Symposium Series; American Chemical Society: Washington, DC, 1977.


1700-3000 500-1870

l i q u i d hyd.

l i q u i d hyd.

l i q u i d hyd.

coal

coal

coal

coal

coal

coal

c o a l o r coke

c o a l or coke

coal

coal

Gasynthan

JGC MethaneR i c h Gas (MRG)

Shell Gasification

Agglomerating Gasification

Bi-Gas

CO^ Acceptor

Coal S o l u t i o n Gasification

Hydrane

Lurgi-SNG/Coal

Molten S a l t C o a l Gasification

Koppers-Totzek

U-Gas

Winkler G a s i f i c a t i o n

Burner

l i q u i d hyd.

CRG Hydrogasification

2000

700-1900

2900

1700

600-1850

1450-1800

not given

1600-2100

not given

not given

550-750

600-1000

Feedstock

Process (5) Temp. °F

not given

300-350

not given

1200

1500

1000

not g i v e n

150

1000-1500

100-400

not given

not g i v e n

300-500

375

Pressure, p s i a

Table 1, Process C o n d i t i o n s of Various G a s i f i c a t i o n Methods

Product

3

3

4

H /CO

2

H /C0

2

H /C0

SNG, 950 B t u / f t

3

SNG, 950 + B t u / f t

95% CH

3

SNG, 1000 + B t u / f t

SNG, 950 + B t u / f t

SNG, 900 B t u / f t

2

H /C0

2

98% CH. 4 50% H , 45% CO

97% CH. 4 98% CH. 4


3

1

I—

S3

to

s 9°

ο

Co

Ο a

S"

(S

S*

CO

M

w

α

>

F ο

nix

258

P H A S E EQUILIBRIA A N D


Water Methane Nitrogen Oxygen

F L U I D PROPERTIES IN

C H E M I C A L INDUSTRY

Ammonia Light hydrocarbons Heavy hydrocarbons

The prediction and correlation of energy requirements, heat exchanger duty, chemical equilibria, and separation equilibria requires a knowledge of the enthalpy, compressibility, fugacity, and vapor-liquid equilibrium properties of these compounds and their mixtures. Existing prediction methods apply primarily to hydrocarbon mixtures at relatively low temperatures and their application to mixtures containing significant concentrations of water, CO , H S, and COS at high temperatures is questionable. Thus, accurate prediction methods are needed either by modification of existing methods or by development of new methods. A discussion of various alternatives for development of a new prediction method is given in the next section of this report. 2

2

Possibilities for New Prediction Methods Equation-of-state methods appear to be the most likely candidates for reliable accurate data. They are capable of predicting enthalpy, entropy, density, fugacity, vapor-liquid, and liquid-liquid data from one equation in regions where both low and high densities are encountered. Rapid computation requires that the equation be simple yet accurate without computational difficulties in areas surrounding the c r i t i c a l point. Possible candidates for this purpose are the following. 1. Modify existing correlations based on the Redlich-Kwong equation of state. a) Mark V (P-V-T, Inc., Houston, Texas) b) Soave (1) method 2. Adapt the BWR equation 3. Develop new equations of state Correlations based on the Redlich-Kwong equation of state have a "built i n " volume-dependence limitation. The equation has the right form for non-polar compounds but not for polar compounds. For example, i f one correlates the solubility of CO2 in water at 77 F; then one would expect that the correlation should also predict the solubility of water in CO2. This is not the case, since the predicted solubility of water in CO2 at liquid-liquid saturation i s 2.1 mole percent instead of the measured value of 0.25 mole percent (2). This represents a factor-of-eight prediction error. No amount of change of the temperature parameters w i l l correct this error because i t is related to the volume dependence of the equation. Since water is a principal component of synthetic gas processes, an accurate prediction of this mixture seems essential. The BWR equation has not been adequately tested for predicting


14.

WILSON

AND

Synthetic Gas Process Streams

WEINER

259


the p r o p e r t i e s of p o l a r and non-polar compounds. The author has some doubts whether i t would be s u i t a b l e . A second disadvantage i s t h a t the BWR equation has so many constants t h a t i t takes about f i v e times the computer time r e q u i r e d by the Redlich-Kwong equation. What i s needed then i s a new equation comparable i n comput a t i o n speed to e x i s t i n g Redlich-Kwong c o r r e l a t i o n s , but w i t h the c a p a b i l i t y of c o r r e l a t i n g the p r o p e r t i e s of both p o l a r and nonp o l a r mixtures. A new m o d i f i e d Van der Waals equation which meets these requirements i s d e s c r i b e d i n the next s e c t i o n of t h i s r e p o r t . A New M o d i f i e d Van der Waals Equation f o r Both P o l a r and Non-Polar Compounds and T h e i r M i x t u r e s Van Laar (3>4) used the Van der Waals equation to d e r i v e the now w i d e l y used Van Laar equation f o r c a l c u l a t i n g a c t i v i t y c o e f f i c i e n t s i n n o n - i d e a l mixtures. His d e r i v e d equation i s as f o l l o w s .

ln

Y

£ n

l

b l

2

+

(

^2 = x

V

x b/

(

= x.

2

Tx b/ V

l b l

2

where b = Van der Waals b

a

a

= 1_ RT

1

a

l' 2

=

V

a

_^1 _ 2 2 b b

k

;

1

a

n

2

^

e rW a a

^

s

a

As d e r i v e d , the equation gave only approximate r e s u l t s ; but i t was found that by making the b s and a s e m p i r i c a l parameters a l a r g e number of mixtures could be a c c u r a t e l y c o r r e l a t e d . Of course, by t h i s method the parameters l o s e t h e i r p h y s i c a l s i g n i f i c a n c e as parameters i n the Van der Waals equation. N e v e r t h e l e s s , the equat i o n has proved to be a very u s e f u l equation, and i s now more a p p r o p r i a t e l y w r i t t e n i n the f o l l o w i n g form. T

T

x S l n

l n

Y

Y

(

l- x

2 -

I x s / 1 12 S

l S l

(x

B

2

T x s / 2 12 S

l S l

B

2

where S, B = e m p i r i c a l

3

4

parameters.



260

P H A S E EQUILIBRIA

A N D F L U I D PROPERTIES

IN C H E M I C A L INDUSTRY

I f the o r i g i n a l Van Laar equation came from the Van der Waals equation, then what equation of s t a t e corresponds to the e m p i r i c a l Van Laar equation? I f t h i s equation of s t a t e were known, one would have an equation of s t a t e w i t h e m p i r i c a l parameters to a d j u s t f o r a s s y m e t r i c n o n - i d e a l behavior i n mixtures. The authors b e l i e v e t h a t such an equation i s d e r i v a b l e by assuming t h a t v o i d spaces i n a f l u i d can be considered as a d d i t i o n a l component of a mixture. When t h i s method i s used w i t h the e m p i r i c a l Van Laar equation, then the f o l l o w i n g m o d i f i e d Van der Waals (M-VDW) equation i s produced. (See the appendix for details.) S x S (A

V Z Z x .1 k

PV _ _ V

3

V - b

/RT) 3

J

K

(V + S-b)

where b = molecular-volume parameter analogous to Van der Waals b A j k = energy parameter analogous to Van der Waals jk S = symmetry parameter from the e m p i r i c a l Van Laar equation B = Zxibi i S = ExiSi i A

This equation reduces to the form of the Van der Waals equation when S equals b. Thus the model i s i n agreement w i t h the o r i g i n a l Van Laar equation when S = b; t h i s confirms the method by which i t was d e r i v e d . The parameters Sj and Ajj/RT have been assumed to be temperature dependent as f o l l o w s . Tc. £

n

(

=

yv

C

(

j ~T

1 )

( 6 )

Tc. S

A

j j j

/

R

T

=

A

+

3

("T ) 1

Tc. +

Y

("T ) 1

+

Tc. 6

(

"T

1

)

+

Tc. . A

( 7 )

00

Equation (6) i s s i g n i f i c a n t because i t shows that as T -> then Sj b j . T h i s means that the equation approaches the Van der Waals form a t h i g h temperatures. The parameter S can be considered to be the e f f e c t i v e volume of a molecule r e s u l t i n g from i n t e r a c t i o n f o r c e s between the molecules. The t r a j e c t o r y of a molecule passing a c e n t r a l molecule i s changed as a r e s u l t of molecular i n t e r a c t i o n s , and passing molecules thus c o l l i d e more f r e q u e n t l y w i t h the c e n t r a l molecule than would otherwise be expected. When t h i s happens, the e f f e c t i v e s i z e of the molecule i s l a r g e r than i t s a c t u a l s i z e . At h i g h temperatures, the molecular i n t e r a c t i o n s



14.

WILSON

AND

WEINER


261

become s m a l l compared to the k i n e t i c energy of the molecules and the t r a j e c t o r y of a molecule i s n e g l i g i b l y a l t e r e d . When t h i s happens, the e f f e c t i v e s i z e of a molecule i s the same as the a c t u a l s i z e of the molecule. The parameter A j j has the u n i t s of energy per u n i t volume and i s analogous to the square of the s o l u b i l i t y parameter i n the Scatchard-Hildebrand equation. Numerous t e s t s of the ScatchardH i l d e r b r a n d equation have shown that there i s s i g n i f i c a n c e to the s o l u b i l i t y parameter. P r e v i o u s l y , there has been no way to i n t e r p r e t t h i s type of parameter from an equation of s t a t e . This new M-VDW equation could provide t h i s opportunity. P r e l i m i n a r y s t u d i e s show that the M-VDW equation can be adjusted to a c c u r a t e l y p r e d i c t the p h y s i c a l p r o p e r t i e s of water, hydrogen, carbon d i o x i d e and methane. Comparisons w i t h e x p e r i mental data are given i n Tables 2 to 21. Tables 2 to 5 give comparisons between experimental and p r e d i c t e d l i q u i d molar volume, vapor pressure, and saturated vapor c o m p r e s s i b i l i t y f a c t o r data f o r these compounds. These are p r e l i m i n a r y r e s u l t s , nevert h e l e s s the agreement between experimental and p r e d i c t e d data from the M-VDW equation are q u i t e good. With some exceptions, l i q u i d molar volumes are p r e d i c t e d w i t h i n about ±2%. This could be improved by assuming a s m a l l temperature dependence of the b parameter. Vapor pressure data appear to be p r e d i c t e d to b e t t e r than ±1%, and saturated vapor c o m p r e s s i b i l i t y f a c t o r s are accur a t e l y p r e d i c t e d except at c o n d i t i o n s c l o s e to the c r i t i c a l temperature where t h i s property changes q u i t e d r a s t i c a l l y w i t h only s m a l l changes i n temperature. The p r e d i c t i o n of these p r o p e r t i e s presumably can be improved by a d j u s t i n g e i t h e r the A or S parameters. One important c o n c l u s i o n from these comparisons i s that water p r o p e r t i e s can be p r e d i c t e d w i t h accuracy comparable to other non-polar compounds. This r e s u l t i s important i n d e t e r mining the s u i t a b i l i t y of the M-VDW f o r c o r r e l a t i n g and p r e d i c t i n g the p r o p e r t i e s of mixtures c o n t a i n i n g p o l a r and non-polar compounds. Tables 2 to 5 compare p r o p e r t i e s at temperatures below the c r i t i c a l temperature of the compounds. Tables 6 to 9 extend the comparisons to temperatures above the c r i t i c a l temperatures. The t a b l e s compare experimental and p r e d i c t e d c o m p r e s s i b i l i t y f a c t o r data. D e v i a t i o n s between experimental and p r e d i c t e d data are s m a l l except i n regions near the c r i t i c a l p o i n t . A l l equations of s t a t e tend to d e v i a t e i n t h i s r e g i o n , and the authors b e l i e v e the accuracy i s comparable to p r e d i c t i o n s from other equations of state. From past experience, the authors have found that i f other p h y s i c a l p r o p e r t i e s such as vapor pressure and c o m p r e s s i b i l i t y f a c t o r are a c c u r a t e l y p r e d i c t e d ; then enthalpy w i l l be a c c u r a t e l y p r e d i c t e d . This was found to be so i n t h i s case as i s shown i n Tables 10 to 15. Tables 20, 11, and 12 compare published and c a l c u l a t e d enthalpy data i n the s a t u r a t i o n regions f o r water, CO2



.4231

.4252

600

-0.49

1543

680.8

.3623

.3675

500

-1.41

.3280

.3358

400

67.01 247.3

-1.97

.3082

.3144

300

11.53

.949

Exp^

-2.32

-0.23

.2993

.3000

200

%Diff

4.13

M-VDW

.3026

.2906

100°F

Temperature

P

Ex

L i q u i d Molar Volume f t 3 / l b --mole

0.29 1.66

.9012 .8143 .6914

.8986 .8010 .6468

1.12 0.80 -0.32

250.07 686.26

6.90

-0.01 .9573 .9574

0.67

67.46

1538.07

-0.09

.9872

.9881

-0.30

11.50

%Diff

-0.09

M-VDW

.9978

Exp

.9987

%Diff

Saturated Vapor C o m p r e s s i b i l i t y Factor

-0.11

.948

M-VDW

Vapor Pressure psia

Table 2, WATER, Comparison of P r e d i c t e d and Experimental L i q u i d Molar Volume, Vapor Pressure, and Saturated Vapor C o m p r e s s i b i l i t y Factor


3

I—I

a >

g

O X W

W H W

§

a

S

1

*i r

a

> >

S

F

w

W

to to


.4059

.4326

.4727

.5400

.6902

.4278

.4521

.4876

.5454

.6920

-430.87°F

-423.67

-416.47

-409.27

-402.07

smperature

M-VDW

3

-0.26

-0.99

-3.06

-4.31

-5.12

%Diff

L i q u i d Molar Volume ft /lb-mole

160.67

83.69

37.41

13.07

2.966

P

Ex ^

161.45

84.36

37.50

13.04

2.966

M-VDW

0.00

%Diff

0.49

0.80

0.24

-0.23

Vapor Pressure psia

1.23 5.52

.7164 .5446

.7077 .5161

0.31

.8304

.8278

-0.04

-0.17

%Diff

.9124

.9662

M-VDW

.9128

.9678

Exp^

Saturated Vapor Compressibility Factor

Table 3, NORMAL HYDROGEN, Comparison of P r e d i c t e d and Experimental L i q u i d Molar Volume, Vapor P r e s s u r e , and Saturated Vapor C o m p r e s s i b i l i t y Factor


3

85

3

o o Co

C/3

w

s

o

>

O

I—I


.5985

.6324

.6914

.7860

-40

0

40

(8)

-69.6°F

Temperature

EX£

.7949

.6916

.6253

.5887

M-VDW

3

1.13

0.03

-1.12

-.164

%Diff

L i q u i d Molar Volume ft /lb-mole (8)

567.3

305.8

145.87

75.15

Exp

561.9

308.2

147.2

74.7

M-VDW

%Diff

-0.95

0.78

0.91

-0.60

Vapor Pressure psia

.6714

.7923

.8713

.9142

Exp,

(8)

.6796

.7865

.8698

.9175

M-VDW

1.,22

-0,.73

-0.,17

0..36

%Diff

Saturated Vapor Compressibility Factor

Table 4, CARBON DIOXIDE, Comparison of P r e d i c t e d and Experimental L i q u i d Molar Volume, Vapor Pressure,and Saturated C o m p r e s s i b i l i t y F a c t o r


Hi

§ o >

— ii

I—I

c

w

to


-0.56 -0.61 -0.70 0.36

.8933 .8142 .7082 .5564

.898 .819 .713 .554

0.23 1.22 1.65 1.43

151.83 301.91 534.54

150.0 297.0

0.52 2.65 5.37

.7144

.8135

1.0142

.7107

.7925

.9625

-190

-160

-130

527.0

64.65

64.5

-0.56

.6524

0.21 .9483

.946

0.20

%Diff

-0.69

21.56

.6561

21.71

-220

-250

M-VDW

.9817

0.00

-1.01

.5839

-280°F

ExpW

Saturated Vapor C o m p r e s s i b i l i t y Factor

.980

%Diff

4.90

M-VDW

.6098

4.90

ExpW

.6160

%Diff

-0.75

M-VDW

Vapor Pressure psia

.5795

nperature

Exp®

3

L i q u i d Molar Volume ft /lb-mole

Table 5, METHANE, Comparison of P r e d i c t e d and Experimental L i q u i d Molar Volume, Vapor P r e s s u r e , and Saturated Vapor C o m p r e s s i b i l i t y F a c t o r


ss

o

a

C/3

3

B

a

>

i

3 p

266



I N C H E M I C A L INDUSTRY

Table 6, WATER, Comparison of P r e d i c t e d and Experimental C o m p r e s s i b i l i t y Data i n Super Heat Region Data Obtained From (6)

700°F

1200°F

)

EXP

M-VDW

%DIFF

500

.9866

.9865

-0.01

-0.09

1000

.9727

.9733

0.06

.7969

0.68

1600

.9560

.9561

0.01

.7207

.7341

1.86

2000

.9445

.9452

0.07

2500

.6103

.6400

4.87

2500

.9302

.9315

0.14

3000

.4274

.5000

16.99

3000

.9159

.9179

0.22

4000

.1662

.1582

-4.81

4000

.8870

.8910

0.45

5000

.1940

.1834

-5.46

5000

.8579

.8644

0.76

PSIA Downloaded by NANYANG TECHNOLOGICAL UNIV on June 10, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0060.ch014

a

EXP

M-VDW

%DIFF

PSIA

500

.9443

.9422

-0.22

1000

.8809

.8801

1600

.7915

2000

1600°F

900°F PSIA

EXP

M-VDW

%DIFF

500

.9953

.9946

-0.07

-0.09

1000

.9901

.9894

-0.07

.8996

0.00

1600

.9841

.9832

-0.09

.8723

.8732

0.10

2000

.9800

.9792

-0.08

2500

.8366

.8395

0.35

2500

.9750

.9743

-0.07

3000

.7998

.8035

0.46

3000

.9699

.9695

-0.04

4000

.7221

.7289

0.94

4000

.9596

.9587

-0.09

5000

.6397

.6488

1.42

5000

.9493

.9492

-0.01

EXP

M-VDW

%DIFF

PSIA

500

.9703

.9704

0.01

1000

.9390

.9382

1600

.8996

2000

a)

T h i s i s s l i g h t l y below the c r i t i c a l temperature of 706 F.


14.

WILSON

267


AND WEINER

Table 7, NORMAL HYDROGEN, Comparison of P r e d i c t e d and Experimental C o m p r e s s i b i l i t y Data i n Super Heat Region Data Obtained From (7)

-398 .47°F

-351 .67°F

)

PSIA

EXP

M-VDW

%DIFF

0.22

19.24

.9941

.9948

0.07

.7056

2.53

183.11

.9462

.9514

0.55

.2890

.2784

-3.67

454.69

.8808

.8913

1.19

443.52

.3913

.3872

-1.05

876.18

.8488

.8582

1.11

833.26

.6512

.6302

-3.22

1540.14

.9552

.9582

0.31

PSIA Downloaded by NANYANG TECHNOLOGICAL UNIV on June 10, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0060.ch014

a

EXP

M-VDW

%DIFF

17.75

.9708

.9729

150.93

.6882

221.91

-189 .67°F

-391 .27°F PSIA

EXP

M-VDW

%DIFF

EXP

M-VDW

%DIFF

19.94

.9757

.9777

0.20

80.90

1.003

1.0028

-0.02

159.45

.7803

.7935

1.69

1385.83

1.074

1.0668

-0.67

235.87

.6415

.6635

3.43

2192.64

1.132

1.1221

-0.87

368.28

.4292

.4360

1.58

3640.20

1.254

1.2398

-1.13

612.24

.5167

.5122

-0.87

5894.57

1.462

1.4552

-0.47

PSIA

80 .33°F

-380 ,47°F PSIA

M-VDW

%DIFF

1.007

1.0059

-0.11

3311.01

1.140

1.1325

-0.66

2.44

6126.76

1.266

1.2596

-0.51

.63.26

2.46

9005.71

1.396

1.3989

0.21

.6347

0.51 12526.87

1.553

1.5748

1.40

EXP

M-VDW

%DIFF

14.04

.9887

.9897

163.27

.8623

310.38

PSIA

EXP

0.10

162.39

.8726

1.19

.7287

.7465

467.33

.6174

747.00

.6315

a)

T h i s i s s l i g h t l y above the c r i t i c a l p o i n t a t -399.93°F.


268

P H A S E EQUILIBRIA A N D F L U I D PROPERTIES IN C H E M I C A L

INDUSTRY

Table 8, CARBON DIOXIDE, Comparison of P r e d i c t e d and Experimental C o m p r e s s i b i l i t y Data i n Super Heat Region Data Obtained From (8)

400°F

100


PSIA

EXP

M-VDW

%DIFF

200

.9885

.9886

0.01

2.90

400

.9763

.9775

0.12

.7961

4.96

600

.9647

.9658

0.11

.6695

.7080

5.75

800

.9534

.9547

0.14

.5789

.5921

2.28

1000

.9427

.9439

0.13

EXP

M-VDW

%DIFF

PSIA

200

.9260

.9386

1.36

400

.8471

.8717

600

.7585

800 1000

600°F

140 °F PSIA

EXP

M-VDW

%DIFF

200

.9955

.9966

0.11

3.31

400

.9912

.9934

0.22

.8477

5.40

600

.9865

.9904

0.40

.7337

.7882

7.43

800

.9822

.9875

0.54

.6853

.7230

5.50

1000

.9777

.9848

0.73

EXP

M-VDW

%DIFF

PSIA

200

.9406

.9522

1.23

400

.8727

.9016

600

.8043

800 1000

1000°F

240 °F PSIA

M-VDW

%DIFF

200

.9992 1.0020

0.28

0.23

400

.9986 1.0042

0.56

.9175

0.33

600

.9979 1.0063

0.84

.8859

.8891

0.36

800

.9972 1.0085

1.13

.8564

.8605

0.48

1000

.9964 1.0108

1.45

EXP

M-VDW

%DIFF

PSIA

200

.9718

.9737

0.20

400

.9433

.9455

600

.9145

800 1000

a)

EXP

This i s s l i g h t l y above the c r i t i c a l temperature at 88°F.


14.

WILSON

AND WEINER

Synthetic

Gas Process

269

Streams

Table 9, METHANE, Comparison of P r e d i c t e d and Experimental C o m p r e s s i b i l i t y Data i n Super Heat Region Data O b t a ined From (9) -100°F


PSIA

500°F EXP

M-VDW

%DIFF

100

1.0016

1.0000

-0.16

0.37

300

1.0023

1.0030

0.07

.6820

1.44

600

1.0047

1.0064

0.17

.3217

.3045

-5.35

1000

1.0095

1.0115

0.20

2000

.4646

.4350

-6.37

2000

1.0252

1.0275

0.22

PSIA

EXP

M-VDW

%DIFF

PSIA

EXP

M-VDW

100

.9694

.9706

0.12

100

1.0016

1.0021

0.05

300

.9026

.9061

0.39

300

1.0062

1.0065

0.03

600

.7924

.8009

1.07

600

1.0126

1.0131

0.05

1000

.6250

.6378

2.05

1000

1.0215

1.0222

0.07

2000

.5206

.4931

-5.28

2000

1.0440

1.0438

-0.02

EXP

M-VDW

100

.9567

.9567

300

.8588

.8620

600

.6723

1000

%DIFF

PSIA

60°F

1000°F %DIFF

1500°F PSIA

EXP

M-VDW

%DIFF

PSIA

EXP

M-VDW

%DIFF -0.05

100

.9808

.9818

0.10

100

1.0023

1.0018

300

.9405

.9439

0.36

300

1.0062

1.0056

-0.06

600

.8788

.8867

0.90

600

1.0124

1.0112

-0.12

1000

.7974

.8097

1.54

1000

1.0206

1.0188

-0.18

2000

.6777

.6696

-1.20

2000

1.0420

1.0371

-0.47

100°F PSIA 100

2000°F

EXP

M-VDW

%DIFF

PSIA

.9906

.9915

0.09

100

M-VDW

%DIFF

1.0022

1.0012

-0.10 -0.19

EXP

300

.9711

.9752

0.42

300

1.0057

1.0038

600

.9440

.9502

0.66

600

1.0115

1.0076

-0.39

1000

.9108

.9200

1.01

1000

1.0192

1.0192

-0.64

2000

.8584

.8639

0.64

2000

1.0378

1.0260

-1.14


270




Table 10 Comparison of C a l c u l a t e d Water Enthalpy Data w i t h L i t e r a t u r e Data i n theS a t u r a t i o n Region (10)


Temp °F

Pressure PSIA

Enthalpy, BTU/LB

Calc 32.02 213.03

.089 a

40.8

LIQUID Diff Lit 0

40.8

VAPOR Calc

Lit

Diff

1080.5

1075.5

5.0

1156.6

1150.9

5.7

15.0

181.2

181.2

320.28

90.0

292.2

290.7

1.5

1191.8

1185.3

6.5

377.53

190.0

354.7

350.9

3.8

1204.9

1197.6

7.3

414.25

290.0

395.9

390.6

5.3

1210.8

1202.6

8.2

444.60

400.0

430.6

424.2

6.4

1213.8

1204.6

9.2

503.08

700.0

500.0

491.6

8.4

1214.4

1201.8

12.6

567.19

1200.0

581.4

571.9

9.5

1205.3

1184.8

20.5

613.13

1700.0

645.1

636.5

8.6

1190.5

1158.6

31.9

662.11

2400.00

722.0

719.0

3.0

1163.2

1103.7

59.5

a)

Enthalpy base adjusted to f i t the l i q u i d enthalpy a t 213.03 F


14.

WILSON

AND WEINER

271


Table 11 Comparison of C a l c u l a t e d Carbon D i o x i d e Enthalpy Data w i t h Literature"'" Data i n the S a t u r a t i o n Region (11) Temp °

Pressure


F

P

S

I

„ , ., , , Enthalpy, BTU/LB T

A

mTT/TT

Calc

LIQUID Lit Diff

Calc

VAPOR Lit

Diff

-69.9

75.1

-19.9

-13. 7 -6.2

138.2

136.0

2.2

-50.0

118.3

-6.4

-4. 6 -1.8

139.6

137.3

2.3

145.9

0.0

0.0

—

140.1

137.9

2.2

-20.0

215.0

12.2

9. 2

3.0

140.8

138.7

2.1

0.0

305.8

23.8

18. 8

5.0

140.9

138.9

2.0

20.0

421.8

35.3

29. 6

5.7

140.2

138.5

1.7

40.0

567.3

47.0

41. 8

5.2

138.5

136.8

1.7

60.0

747.4

59.5

55. 7

3.8

135.5

132.2

3.3

80.0

969.3

73.9

74. 0 -0.1

129.8

119.0

10.8

-40.0

a

a)

Enthalpy base adjusted to f i t the l i q u i d enthalpy a t -40°F.


272




Table 12 Comparison of C a l c u l a t e d Methane Enthalpy Data w i t h L i t e r a t u r e Data i n the S a t u r a t i o n Region (9)


Temp o/

Pressure p

s

i

„ , , „ Enthalpy, BTU/LB n m T / T

A

LIQUID Diff Lit

VAPOR Calc

Lit

Diff

—

-1706.1

-1705. 8

-0.3

13. 8

-1918. 1 -1917.4 -0.7

-1697.9

-1697. 6

-0.3

14. 7

-1917. 0 -1917.0

—

-1697.4

-1697. 5

0.1

-235

39. 0

-1897. 4 -1896.4 -1.0

-1689.2

-1689. 2

—

-210

87. 6

-1875. 6 -1875.2 -0.4

-1682.8

-1683. 0

0.2

-185

169. 7

-1852. 2 -1851.2 -1.0

-1679.5

-1679. 2

-0.3

-160

297. 0

-1825. 9 -1826.2

0.3

-1680.3

-1679. 2

-1.1

-135

482. 0

-1797. 0 -1795.3

1.3

-1688.3

-1686. 8

-1.5

673. 1

-1760. 1 -1730.0--30.1

-1708.6

-1730. 0

21.4

Calc -280

4. 90

-260 -258.,68

-116.,5

b

a

-1934. 0 -1934.0

a)

Enthalpy base a d j u s t e d to f i t the l i q u i d enthalpy at -258.68°F.

b)

C r i t i c a l p o i n t of methane.


14.

WILSON

A N D WEINER


273

Table 13 Comparison of C a l c u l a t e d Water Enthalpy Data w i t h L i t e r a t u r e Data i n the Superheat Region (10) Temp °F Downloaded by NANYANG TECHNOLOGICAL UNIV on June 10, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0060.ch014

750

a

1500

a)

Pressure PSIA

Calc

1000

1361.8

1358.7

3.1

1500

1332.4

1328.0

4.4

2000

1299.6

1292.6

7.0

2500

1262.6

1250.6

12.0

3000

1218.1

1197.9

20.2

3500

1158.9

1127.1

31.8

4000

933.8

1007.4

-73.6

6000

819.4

822.9

-3.5

8000

796.1

796.6

-0.5

10000

783.8

783.8

—

15000

769.6

769.7

0.1

250

1806.4

1800.2

6.2

500

1803.2

1796.9

6.3

Enthalpy, BTU/LB Lit

Diff

750

1799.9

1793.6

6.3

1000

1796.7

1790.3

6.4

1500

1790.2

1783.7

6.5

2000

1783.8

1777.1

6.7

2500

1777.1

1770.4

6.7

3000

1770.6

1763.8

6.8

3500

1764.1

1757.2

6.9

4000

1757.6

1750.6

7.0

6000

1731.8

1724.2

7.6

8000

1706.4

1698.1

8.3

10000

1681.7

1672.8

8.9

15000

1624.6

1615.9

8.7

b

S l i g h t l y above c r i t i c a l temperature of water at 706 F.

b) The e r r o r of 6 BTU/lb i s an e r r o r i n the i d e a l gas enthalpy at 1500 F r e f e r r e d t o the l i q u i d a t 213 F. This e r r o r i s caused by a s m a l l e r r o r i n the i d e a l gas heat c a p a c i t y of water. This problem w i l l be c o r r e c t e d . Storvick and Sandler; Phase Equilibria and Fluid Properties in the Chemical Industry ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

274


INDUSTRY

Table 14 Comprison of C a l c u l a t e d Carbon Dioxide Enthalpy w i t h L i t e r a t u r e Data i n the Superheat Region ( i i )


Temp °F •20

300

1000

Pressure PSIA

Calc


Diff

1.0

152.5

151.5

1.0

10.0

152.1

151.1

1.0

25.0

151.4

150.4

1.0

50.0

150.2

149.0

1.2

100.0

147.6

146.0

1.6

200.0

141.9

139.9

2.0

1.0

219.6

218.8

0.8

10.0

219.5

218.8

0.7

25.0

219.3

218.7

0.6

50.0

218.9

218.4

0.5

100.0

218.3

217.8

0.5

200.0

216.9

216.4

0.5

400.0

214.2

214.0

0.2

600.0

211.4

211.4

0

1000.0

205.7

205.9

-0.2

1.0

399.9

399.0

0.9

10.0

399.9

399.0

0.9

25.0

399.8

399.0

0.8

50.0

399.8

398.9

0.9

100.0

399.6

398.9

0.7

200.0

399.3

398.8

0.5

400.0

398.7

398.4

0.3

600.0

398.1

398.0

0.1

397.0

397.2

-0.2

1000.0


14.

WILSON

A N D WEINER


275

Table 15 Comparison of C a l c u l a t e d Methane Enthalpy Data .th L i t e r a t u r e Data i n theSuperheat Region


Temp

-60

700

2200

Pressure PSIA

Calc


Diff

1.0

-1595.7

-1595.6

-0.1

25.0

-1596.9

-1596.8

-0.1

50.0

-1598.2

-1597.9

-0.3

100.0

-1600.7

-1600.4

-0.3

200.0

-1606.0

-1605.7

-0.3

400.0

-1617.3

-1617.0

-0.3

600.0

-1630.0

-1629.8

-0.2

1000.0

-1662.0

-1661.9

-0.1

2000.0

-1727.3

-1720.8

-6.5

1.0

-1110.0

-1107.8

-2.2

25.0

-1110.1

-1107.9

-2.2

50.0

-1110.3

-1108.0

-2.3

100.0

-1110.4

-1108.3

-2.1

200.0

-1110.8

-1108.9

-1.9

400.0

-1111.5

-1109.8

-1.7

600.0

-1112.3

-1110.3

-2.0

1000.0

-1113.7

-1112.6

-1.1

2000.0

-1117.0

-1116.3

-0.7

1.0

518.5

518.6

-0.1

50.0

518.4

518.6

-0.2

100.0

518.7

518.8

-0.1

200.0

518.8

519.2

-0.4

400.0

519.0

519.8

-0.8

600.0

519.2

520.4

-1.2

1000.0

519.7

521.8

-2.1

2000.0

521.2

525.3

-4.1


276


INDUSTRY

Table 16, WATER, Comparison of P r e d i c t e d and Experimental Second V i r i a l C o e f f i c i e n t s


T°K

M-VDW

G. S. K e l l

(12) Literature — M. P. V u k a l o v i c h

353.16

-561.4

-844.4

373.16

-465.75

-453.6

423.16

-308.59

-326

-283.3

473.16

-217.35

-209

-196.1

523.16

-160.18

-152.5

-145.4

573.16

-122.2

-117.1

-112.9

623.16

-95.67

-92.38

-90.2

673.16

-76.53

-73.26

-72.4

723.16

-62.24

-59.36

-60.6

773.16

-51.29

-50.4

823.16

-42.72

-42.0

923.16

-30.33

-29.4

1073.16

-18.75

-17.0

1173.16

-13.68

-11.6



-316.61 -296.24 -223.46 -174.05 -151.70 -100.80 -69.99 -58.74 -49.35 -34.54 -14.64 -1.82 7.15 13.81 21.10

1. 2. 3. 4. 5. 6. 7.

E. R. K. A. K. M. B.

-46.3 -29.1

-147.4 -100.7 -69.5

1*

G. Butcher (12) S. Dadson (12, 13) E. MacCormack (L2, 13) Perez Masia (12, 13) Schafer (12, 13) P. V u k a l o v i c h (12_, 13) L. T u r l i n g t o n (12)

Primary Data Source:

203.83 209.03 233.34 258.15 273.15 323.15 373.15 398.15 423.15 473.15 573.15 673.15 773.15 873.15 1023.15

M-VDW

-70..2 -58,.4

-147. ,4

2

-50.59 -34.08 -13.58 -1.58 6.05 12.11

4

-142 -104, .3 -73,.9 -59..4 -52,.6

Literature

-156.36 -102.63 -71.85

3 -330 -302 -210

5

Table 17, CARBON DIOXIDE, Comparison of P r e d i c t e d and Experimental Second V i r i a l

-103.1 -73.1 -61.7 -52.5 -36.8 -15.9 -3.4 4.0 10.4 15.8

6

Coefficients


-173. ,5 -149. ,3 -104. ,5

7

278

P H A S E EQUILIBRIA A N D F L U I D PROPERTIES IN C H E M I C A L INDUSTRY


Table 18, HYDROGEN, Comparison of P r e d i c t e d and Curve F i t Experimental Second V i r i a l C o e f f i c i e n t s

T^K

M-VDW

15 25 50 100 200 300 400

-239.2 -106.0 -30.3 -1.6 9.7 13.0 14.5

Literature

(12) —

±5 ±3 ±2 ±1 ±0.5 ±0.5 ±0.5

-230 -111 -35 -1.9 11.3 14.8 15.2

Table 19, METHANE, Comparison of P r e d i c t e d and Curve F i t Experimental Second V i r i a l C o e f f i c i e n t s

T^K

M-VDW

110 150 200 250 300 400 500 600

-415.5 -204.8 -107.3 -62.7 -37.7 -11.1 2.6 11.0

(12) Literature— -344 -191 -107 -67 -42 -15.5 -0.5 8.5

±10 ±6 ±2 ±1 ±1 ±1 ±1 ±1

Table 20, P r e d i c t e d S o l u b i l i t y of Water i n Carbon Dioxide a t L i q u i d - L i q u i d S a t u r a t i o n from the M-VDW and Mark V Equations of State a t 25 C Solubility Mole % Measured (2)

Error %

0.25

Predicted

b

M-VDW

0.20

Predicted

b

Mark V

2.1

20 840

b) The CO2-H2O i n t e r a c t i o n c o e f f i c i e n t was adjusted t o f i t the measured s o l u b i l i t y of CO2 i n H2O which i s 2.55 mole % as reported by F r a n c i s . Storvick and Sandler; Phase Equilibria and Fluid Properties in the Chemical Industry ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

14.

WILSON

>^

vO

O O

ON

d

rH rH

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00

rH vO 00 00 00

A Computer Model for Calculating Physical and Thermodynamic

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