PILE COPY

NBSIR 77-860 DO NOT REMOVE

PROVISIONAL THERMODYNAMIC FUNCTIONS OF PROPANE,

FROM 85 TO 700 K AT PRESSURES TO 700 BAR

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

July 1977

Prepared for:

The American Gas Association

1515 Wilson Boulevard

Arlington, Virginia 22209

Robert D. Goodwin

NBSIR 77-8 6 0

PMVISIOIUI THERMinVIUMIt FUNCTIONS OF PROPtNE,

FROM 85 TO 700 K «T PRESSORES TO 700 BAR

Robert D. Goodwin

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

July 1977

Prepared for:

The American Gas Association

1515 Wilson Boulevard

Arlington, Virginia 22209

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director
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CONTENTS

I Page

PREFACE vii

1. INTRODUCTION 1

2. PHYSICAL PROPERTIES AND THEIR FORMULATION 1

2.1 Fixed-Point Values i

\ 2.2 Melting Line and Vapor Pressures 2

! 2.3 The Orthobaric Densities 3

2. A The Virial Equation 5

I 2.5 The Equation of State 6

j 2.6 The Ideal Gas Functions 10

I 2.7 Specific Heats Along Isobar P, 10

I ^

I 2.8 Specific Heats for Saturated Liquid 11

2.9 The Heats of Vaporization 12

I 3 . COMPUTATIONAL METHODS 13

3.1 The Homogeneous Domain 13

3.2 The Saturated Liquid 14

3.3 The Compressed Liquid 15

! 3.4 The Supercritical Shadow 16

4. TESTS AND COMPARISONS , 17

4.1 The P-p-T Compressibility Data 17

I 4.2 Specific Heats, C^(p,T) 17

4.3 Speeds of Sound, W(p,T) 18

4.4 Enthalpy Differences at 60 bar 18

4.5 Enthalpy Differences at 400 K 18

4.6 Residual Specific Heats at 400 K 19

4.7 Loop Closure for the Saturated Vapor 19

5. TABLES OF PHYSICAL AND THERMODYNAMIC PROPERTIES 22

5.1 Calculated P-p-T Isochores and Isotherms 22

5.2 The Joule-Thomson Inversion Locus 22

5.3 Thermophysical Properties of the Saturated Liquid 22

5.4 Thermophysical Properties along Selected Isobars 22

,6. COMMENTS AND RECOMMENDATIONS 23

I 6.1 Comments on Uncertainties 23

6.2 Recommendations 23

iii
CONTENTS (Continued)

7. ACKNOWLEDGMENTS

8. BIBLIOGRAPHY

APPENDIX A. Symbols and Units

APPENDIX B. Fixed-Point Values for Propane

APPENDIX C. Computer Programs

Page

27

28

34

36

210
LIST OF FIGURES

Figure 1.

jFigure 2.

jFigure 3.

!jFigure 4.

[Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

Figure 12.

Figure 13.

Figure 14.

Figure 15.

Density-temperature diagram of propane

The locus of isochore inflection points

Behavior of the locus 0(p)

Behavior of the function 0(p,T)

Behavior of the function YCp,!)

Behavior of coefficients B(p), C(p) for propane . . . . 2 2 Behavior of 9 P/9T on the critical isotherm

Behavior of C (T) on the critical isochore

V

Paths used to derive heats of vaporization

Deviation plots for densities

Deviations of Ernst specific heats

Deviations of Yesavage specific heats

Comparison of C pc(T) at P/P = 0.813

Comparison of C pc(T) at P/P = 1.626

Deviations of Lacam speeds of sound

Page

37

38

38

39

39

40

41

42

43

44

46

47

48

49

50

LIST OF TABLES

Table 1.

Table 2.

Table 3.

Table 4.

Table 5. Table 6.

Table 7. Table 8.

Table 9.

Table 10.

Table 11.

Table 12.

Table 13.

Vapor pressures of propane

Densities of the saturated liquid

Densities of the saturated vapor

Second virial coefficients of propane . . . . Third virial coefficients of propane

Summary of P-p-T data

Coefficients of the equation of state . . . . Calculated P(p) critical isotherm

Comparisons with P-p-T data

Comparison with data for ideal gas functions .

Interpolated ideal gas functions

Specific heats along isobar P^

Specific heats for the saturated liquid . . .

Page

51

55

57

59

62

63

64

65

67

93

95

96

97

V
LIST OF TABLES (Continued)

Table 14.

Table 15.

Table 16.

Table 17.

Table 18.

Table 19.

Table 20.

Table 21.

Table 22.

Table 23.

Table 24.

Table 25.

Table 26.

Table 27.

Table 28.

Table 29.

Table 30.

The heats of vaporization

Comparison with specific heat data of Ernst

Comparison with specific heat data of Yesavage . . . . Comparisons with speed of sound data

Comparison of enthalpy differences at 60 bar

Comparison of enthalpy differences at 400 K

Comparison of residual specific heats at 400 K . . . . Loop closure for the saturated vapor

Comparison with vapor 'pressures of Tsai

Comparison with heats of vaporization of Tsai

Derived coexistence data (Q, = 18 780 J/mol)

b Derived coexistence data (Q, = 18 864 J/mol)

b

Calculated P(T) isochores

Calculated P(p) isotherms

The Joule-Thomson inversion locus

Thermophysical properties of the saturated liquid . . . Thermophysical properties along isobars

Page

99 :| 102 |! 103

) 104 I 109

‘

110

111

112

113

114

115

118

121

138

152

153

156
PREFACE I

I The Cryogenics Division of the National Bureau of Standards, with support

I from the American Gas Association, is providing experimental data and

! computational methods for the thermophysical properties of both the pure

j components and the mixtures which constitute liquefied natural gas (LNG)

.

I The present report on propane is the third in a series on the pure

I components. The properties of methane were published in NBS Technical Note

1

I 653 (April 1974), and those of ethane in NBS Technical Note 684 (August 1976)

[29].

Our objective in the present report is to discover the availability and

deficiencies of physical properties data needed for computation of the

thermodynamic properties of propane, and at the same time to produce useful

interim results.

In the .range of normal boiling temperatures for LNG, the vapor pressures,

vapor densities, .and heats of vaporization of propane cannot be measured

accurately by any existing experimental techniques. Computational method« for

the thermodynamic network have been devised to circumvent these difficulties

in so far as possible.

The present results, covering the entire range of fluid states of propane,

have become possible by use of recent P-p-T data for the compressed liquid [22],

ideal gas specific heats from spectroscopic data [9], and specific heats C^(T)

over a wide range of conditions [67].

All of the analytical formulations of physical properties data in this

report have been developed for the data on propane, and are new as compared

with our earlier work on ethane.

vii
PROVISIONAL THERMODYNAMIC FUNCTIONS OF PROPANE FROM 85 TO 700 K

AT PRESSURES TO 700 BAR*

Robert D. Goodwin

Thermophysical properties of propane are tabulated at integral

temperatures over the entire range of fluid states from 85 to 700 K

along isobars to 700 bar. A modified form of the nonanalytic

equation of state is employed for the first time. Thermodynamic

functions for the compressed liquid are obtained by use of heats of

vaporization from the boiling point to the critical point, such that

the free energies of saturated liquid and vapor are equal.

Key words: Densities; enthalpies; entropies; equation of state; internal

energies; isobars; isochores; isotherms; Joule-Thomson inversion; latent

heats of vaporization; melting line; orthobaric densities; propane; specific

heats; speeds of sound; vapor pressures.

This work at the National Bureau of Standards was supported by the American

Gas Association, 1515 Wilson Boulevard, Arlington, Virginia 22209.

viii
1. INTRODUCTION

The economic importance of propane, as one of the constituents of LNG, is

well known. Our objective is to produce basic thermodynamic information on

the pure components of LNG, needed both for the pure substances per se, and

for the prediction of properties of mixtures.

I

j The present work on propane provides background on available physical

properties data. The tables of derived thermodynamic functions may serve

engineering needs until such time as new physical data permit a revision of

these tables.

Our computational method differs from that used in previous reports for

compressed liquid states at T < T^. We have estimated the heats of vaporization

from the boiling- to the critical-temperature. Use of these "data" to cross

the "dome" of figure 1 along Isotherms yields a free energy change of zero for

the vapor-liquid equilibrium transition.

Symbols and units for this report are listed in Appendix A.

2. PHYSICAL PROPERTIES AND THEIR FORMULATION

2.1 Fixed-Point Values

These values are listed in Appendix B.

(a) The Triple Point . The temperature is adopted from Das and Eubank [15].

The pressure was selected by trial for the present vapor-pressure equation (2)

.

The liquid density is assigned for consistency with data in equation (3)

.

The

vapor density is from the ideal gas law.

(b) The Boiling Point . The temperature is from vapor-pressure equation (2)

at a pressure of 1 atm = 1.01325 bar. Liquid and vapor densities are from

equations (3) and (4). The heat of vaporization from equation (10) is 0.45%
greater than the experimental (+ 0.1%) value of Kemp and Egan [38], whereas

that from the Clapeyron equation is 0.25% greater.

(c) The Critical Point . The temperature was selected to give a best

"fit" of orthobaric densities data, equations (3) and (4). The pressure is

given by vapor-pressure equation (2). The density was selected by trial to

yield a well-behaved critical isotherm from the equation of state. It is about

1% lower than values reviewed in reference [15].

2.2 Melting Line and Vapor Pressures

(a) The Melting Line . Experimental pressures from about two to ten

kilobars were reported by Reeves, Scott, and Babb [52] as constants for the

Simon equation (1). Their extrapolation to zero pressure gave T^ = 85.3 K.

As their uncertainty in T was at least 1 K, we have used our selected

triple-point temperature,

P = + P^- [(T/T^)^ - 1], (1)

with P^ from Appendix B, T^ = 85.47 K, P^ = 7180 bar, and e = 1.283.

(b) The Vapor Pressures . Data used for adjusting equation (2) appear in

the first part of table 1. Other data appear in the continuation. At pressures

below about 0.01 bar the noise-level is at least 5%. We estimate at least 10%

uncertainty in our selected triple-point pressure. The equation used for

ethane [28,29] gave negative curvature at the critical point with present

propane data, which is wrong. We therefore developed the following, using

arguments—

2

1
x(T) _ (T - T^)/(T^ - T^), u(T) = (1 - T^/T)/(l - T^/T^),

£n(P/P^) = a*u + [b + c‘x + d*x^]*x*(l - x)^.

3.0 • 10 ^ bar

85.47 K

369.80 K

1.30

a = 23.372 2838

b = 5.716 6879

c = - 8.511 7071

d = 3.975 8738

( 2 )

The last column of table 1 gives the experimental residual.

Y(P,T) E (y - u)/[x-(l - x)^] (2a)

where

y(P) E Jln(P/P^)/£n(P^/P^).

It is extremely sensitive to all parameters. When T^, T^, P^, P^, and e have

been selected, a plot of Y vs. x suggests the form of polynomial needed to

complete the vapor-pressure equation. As the "fit” of present data is sensitive

to exponent £ in equation (2), we cannot adjust e for a best "fit" of P-p-T

data via the equation of state, as was performed for ethane [29].

2.3 The Orthobaric Densities

(a) The Saturated Liquid Densities . Data in table 2 include only modern,

consistent measurements. For equation (3) define the variables —

3
x(T) E (T^ - T)/(T^ - T^). y(p) E (d - d^)/(d^ - d^),

when the equation for saturated liquid densities is —

y(p) = ^ ^ r . u 2 ^ 3, X + (x - x)*[a + b*x + c*x ], ( 3 )

85. A7 K

369.80 K

4.96 mol/L

16.62 mol/L

e =

a =

b =

c =

0.35

0.775 3967

-0.167 9130

0.081 1668

The last column of table 2 gives the experimental residual,

Y(P,T) E (y - x)/(x"- - x). (3a)

The polynomial on the right side of equation (3) was selected to describe the

plot of Y vs. X.

(b) The Saturated Vapor Densities . Data in the first part of table 3

were used for adjusting equation (4). For ID = 1, the "data" are from our

vapor-pressure and virial equations. Other data are given in the continuation

of table 3. The triple-point vapor density in equation (4) is from the ideal

gas law, d E P /(R*T ). Define the arguments —

8 t t

x(T) E (T^ - T)/(T^ - T^), u(T) E (T^/T - 1)/(T^/T^ - 1),

4
I and the dependent variable —

|Y(d,T) E £n[d^-T^/(d-T)]/£n[d^-T^/(dg-T^)],

when the equation for saturated vapor densities is

Y = u + (x^ - x) • Z A.*x^,

i=0 ^

(4)

T

t 85.47 K 0.170 5345

T

c 369.80 K

^2

= -0.278 0602

d

c 4.96 mol/L 0.438 9823

£ 0.35 -0.841 0803

^0

= 0.072 4533 0.405 1054

£ The last column of table 3 gives the experimental residual (Y - u)/(x - x)

.

This is extremely sensitive to all parameters. Behavior approaching the

triple-point temperature appears irregular.

2.4 The Virial Equation

This equation of state usually is accurate at densities up to P^/3 when

truncated as follows —

Pv/RT = 1 + B(T)‘p + C(T)*p^ + . . . (5)

The second and third coefficients, B(T), C(T), here are dimensionless through

use of reduced density and temperature, p = d/d^, x = T/T^. Data have been

5
collected in two excellent monographs [21,49]. Tables 4 and 5 compare selected

data with the following fitting functions developed here for propane —

B(T) = “2 /x + B^/x^, (5a)

C(T) = (1 - T

o /T)-[C^/x + (5b)

d

c = 4.96 mol/L »2 = -1.189913

T

c = 369.80 K -0.472695

T

o = 343.375 K 0.214009

= 0.454061 4.836300

In present work, only the second coefficient has been used: to synthesize

P-p-T data for adjusting our equation of state, and to obtain saturated vapor

densities via the vapor-pressure equation.

2.5 The Equation of State

Table 6 summarizes P-p-T data reproduced here. They occur almost entirely

in the single-phase domain of figure 1. Inclusion of the recent, unpublished

data of Ely and Kobayashi [22] provides a dense coverage of the P(p,T) surface

for propane at densities up to 15 mol/L, and temperatures down to 170 K.

The present type of equation of state has been explained in [27,28,29,30].

It is nonanalytic, yielding a maximum in specific heats C^(p,T) at the critical

point, (see figures 2 and 3, taken from [27]) —
( 6 ) |P = P^(p) + p-R**[T - T^(P)] + pVt^*F(p,T),

I

F(p,T) E B(p)-$(p,T) + C(p)*'l'(p,T).

j

I For any density, obtain the coexistence temperature T^(p) by iteration

' from equations (3) or (4) for the orthobaric densities. Place this in the

I vapor pressure equation (2) to obtain P^^(P) = Pj^[T|^(P)]» Densities, p E d/d^,

! are reduced at the critical point. The gas constant for equation (6) therefore

is redefined, R E (0. 0831434) *d , bar/K.

I

; The temperature-dependent functions in equation (6) are shown in figures 4

and 5 —

! <KP,T) E x^^^-£n[T/T^(p)], (6a)

'f(p,T) E 4j(p,T) - ij;^(p), (6b)

where x = T/T , and ip (p) is obtained from i|;(p,T) merely by replacing T with

c o

I„(P),

ijj(p,T) E 6/x + (1 - 5)*[1 - 0) + 0) £n(w)], (6c

o)(p,T) E [1 - 0(p)/T].

The parameter 0 £ 6 ^ 1 in equation (6c) is for relative weighting of the

analytic and nonanalytic parts. The locus of temperatures inside the coexistence

envelope [27] was shown in figure 3 —

7
0(p) = T^(p)«exp[- a*f (p)]. (6d)

f(p) E |p - l|^/(p^ - 1)^

where p^ = ^ constant, and d^ refers to liquid at the triple point.

The parameter a is to be found by trial.

The density-dependent coefficients of equation (6) have been developed

tediously by trial for propane, as shown in figure 6 —

B(p) = + B2*P + B^-p^ + B^-p^, (6e)

C(p) = c *(p - l)’(p - C )*exp(- yp ), i o (6f)

where parameters and y are to be found by trial.

The parameters and coefficients of equation (6) for propane are —

a = 1, y

= 0.06, 6 = 0.75,

0.2256 6372 605

1.0A64 6227 554

B^ = -0.4449 1000 068

0.1270 8270 211

2.0

= -0.5988 3339 489

Figure 2 and table 7 give behavior of coefficients B(p), C(p). We have

adjusted all parameters including d^, T^, not only for a best fit of the

8
orthobaric densities, but also to obtain a well-behaved critical isotherm free

i of negative slopes, as shown in table 8. Figures 7 and 8 show that derived

[specific heats along the critical isochore agree with established experimental

1[behavior very near the critical temperature [27].

j The following, more highly constrained modification of the equation of state

I[for propane has not been used in present work, but may be valuable in future

[investigations. With reference to figure 6, we have removed the possibility for

Ian inflection in B(p), demanding ethane-like behavior [28], and we have removed

I the second root in C(p), forcing it, instead, to diminish strongly toward zero

I at high densities —

B(p) = + B2*exp(3*p)

,

I

I

: 4

C(p) = C^*(p -l)*exp(- Y*P )»

a = 1, 3 = 0.7, Y

= 0.25, 6 = 0.75,

B^ = 0.3400 1917 213

B

2 = 0.3050 4218 746

C = 0.7306 3900 769

i

The "fit" of P-p-T data with above coefficients is not quite as precise at low

densities as with equation (6), due to the restriction on B(p). At densities

well above critical, however, the fit is equally precise.

9
2.6 The Ideal Gas Functions

Chao, et al. used spectroscopic data, and compared results for the specific

heat with other sources [9]. A plot of their C°(T) is linear at low temperatures

changing to the usual sigmoid shape at high temperatures, a behavior we could not

represent analytically. We represent their enthalpies by use of the arguments

1/1

X = T/lOO, u = X ,

(H° - H°)/RT

o

4 + exp(-e/x)* Z A./u^,

i=0

^

where R = 8.31434 J/mol/K, e = 3, and —

A = 24.11012

o

A, = 94.40550

980.124 065

A, = -678.640 94

4

(7)

A^ = -585.32814 170.427 78

Specific heats are C°(T) = dH°/dT, but the entropies require numerical integration

(SUBROUTINE IDEAL, Appendix C)

,

S°(T) = S°(300) + J'

C *dT/T, (7a)

300

where S°(300) = 32.552 J/mol/K. Table 10 presents the data used for adjusting

equation (7), and table 11 gives interpolated results from equation (7).

2.7 Specific Heats Along Isobar

Table 12 compares Yesavage [69] data for Cp(T) at 1500 psi with our fitting

function, equation (8)

.

Deviations from simple functions were systematic over

10
small ranges of T, but irregular when viewed over the full range. We have been

compelled to use a high-order polynomial, valid at temperatures no greater than

405 K. Define the argument x=(T-T)/(T -T) when —

t m t"^

’

C (T) = A + Z A.-x^, J/mol/K,

P i=2 ^ ( 8 )

m

85.47 K

405.00 K

83.700

719.296

-7 767.049

40 574.6955

-118 438.853

205 520.887

-210 152.230

116 726.413

- 27 098.492

2.8 Specific Heats for Saturated Liquid

Table 13 gives sources of data for our fitting function, equation (9).

"Data" at ID = 30 were obtained by starting with Yesavage 0^(1) along isobar

= 1500 psi, and then integrating down to the saturated liquid boundary by

use of our equation of state. Define the argument x = when —

C^(T) = A^-x/(l - x)^ + Z A.-x^ J/mol/K,

i=2

^ a

(9)

where e = 0.8, and -

11
369.80 K 18.313 35

4.201 41

79.737 88

A, = -36.564 45

4

A. = 67.003 23

Deviations are given in table 13.

2.9 The Heats of Vaporization

Table 14 gives the "data," ID = 31, used for adjusting our fitting function!

equation (10). These data were derived by computing around the critical point

I on paths T, , P, , T of figure 9. The continuation of table 14 gives "data,"

b b

ID = 30, obtained from the Clapeyron equation, as well as experimental data. '

A plot of these data shows that, at temperatures from 170 K down to the

triple point, the ID = 31 data diverge upwards, and the ID = 30 data diverge

downwards from a smooth extrapolation of the data at higher temperatures. By

use of the argument x = (T - T)/(T - T ) we at first found a heat of

c c t vaporization at the triple point

Qj.^p by use of data ID = 31 at T ^ 170 K and

extrapolation via the monotonic formula.

= a*x + b*x , (e = 0.42).

Under constraint to this value for Q

= 23.906 kJ/mol, we then adjusted

trp

constants in the equation —

1-e

Q^ap/^trp

^ X + (x - x)‘[a + b*x + c*x]. ( 10 )

12
85.47 K a 0.983 7347

T = 369.80 K

c 0.38

b = 0.417 5844

c = -0.306 7414

3. COMPUTATIONAL METHODS

The numerical values for E and H in this report are on the same absolute

basis as those of Stearns and George [63], obtained by use of E° = H° = 27452.0

j/mol. They obtained 18,589.67 J/mol for enthalpy of liquid at the normal

boiling-point by integrating specific heats of Kemp and Egan [39].

3.1 The Homogeneous Domain

The homogeneous domain of figure 9 includes all regions which can be

attained along isotherms starting at zero density without crossing the vaporliquid "dome," and without passing close to the critical point at T > T^.

We start our computations with ideal gas thermodynamic functions at zero

density, and then integrate along isotherms by use of the equation of state in

the following relations.

AE = y* [P - T- OP/3T)]‘dp/p'

AC^ = - O^P/3T^)‘dp/p^,

( 11 )

( 12 )

AS = R*iln[P°/(pRT)] OP/9T)/p]-dp/p. (13)

Equation (13) is for use with initial entropies in hypothetical ideal gas

at P° = 1 atm. For all other initial states we use -

13
t^S =

- J

OP/aT)*dp/p^.

In each (p,T) state, reached by above

H = E + P‘v,

Cp = + T- OP/8T)^/(3P/ap)/p^,

= C *(3P/3p)/C . P V

(13a;

integrations, we compute —

(14) i

(15)

(16)

3.2 The Saturated Liquid

(a) At temperatures from the boiling point up to the critical point, we

first obtain thermo functions for the saturated vapor via equations (11) through

(14). We then use equation (10) for the heat of vaporization, Q^^p> 1° compute

AH = - Q, AS = AH/T, (17)

such that the free energy of vaporization, AF E AH - T*AS, is zero. Having

obtained H and S for the saturated liquid, we compute E = H - P*v.

The single-phase specific heat, C^(p,T), at the saturated liquid boundary

is obtained via equation (9) for C^(T) and the thermodynamic relation [54],

C^(p,T) = C^(T) + T*OP/8T)*(dp^/dT)/p^, (18)

14
'where is density of the saturated liquid. Values for C^Cp,!) and W(p,T)

on this boundary follow from equations (15) and (16) . For liquid at the

boiling point we have obtained —

231.0707 K,

E = 18 582.17 J/mol,

a

H = 18 589.86 J/mol,

a

’

S = 170.8125 J/mol/K.

(b) At temperatures below the boiling point, down to the triple point, we

I start with E , S for liquid at the boiling point, and then integrate along the

I 3. 3

saturated liquid path down to any temperature, T, by use of equation (9) for

C„(T),

AE = C *dT +

a / (19)

AS = f C *dT/T

a

( 20 )

wherein P (T) is the vapor pressure, and p„ is density of the saturated liquid.

o ^ Values for H, C , C and then are obtained as in paragraph (a) above.

V p

3.3 The Compressed Liquid

Starting with above values for E, S, and on the saturated liquid

boundary, we use equations (11), (12), and (13a) to integrate along isotherms,

and then obtain H, C^, and W via equations (14), (15), and (16).

15
3.4 The Supercritical Shadow

The integration of equation (12) along the critical isotherm of figure 9

2 2

cannot be carried through the critical point, because |8 P/8T | approaches

infinity at densities just below and above p^. The accuracy of other derivative

from the equation of state may be low, very near the critical point.

At temperatures T < T^, therefore, we establish a shadow on figure 9

at densities p > p^. For this region we compute thermo functions along paths

T,no, P, , T. At the point (T, , P, ) we have obtained the values (T, = 405 K,

b b b

P, = 103.42135 bar, d, = 7.3637 mol/L)

,

b b

= 40, 454.53 J/mol,

S, = 236.9352 J/mol/K,

b

i£

1

il 1

i

\ (C ), = 170.71 J/mol/K. ^ p b

5 The "experimental" value of from equation (8) is 168.37 J/mol/K at this point..

From point (T, , P, ) of figure 9 we integrate along isobar P, down to any

b b b

T by use of equation (8), I

AH = yCp*dT, AS = y* Cp*dT/T (21)

At any point (T, P, ), E = H - P*v, and C is obtained via equation (8) and

b V

equation (15). The final path of integration is along any isotherm, T, by use

of equations (11), (12), and (13a). We finally apply equations (14), (15), and

(16).

16
4. TESTS AND COMPARISONS

I 4.1 The P-p-T Compressibility Data

j Detailed deviations appear in table 9. Figure 10 shows relative deviations

I|of experimental densities from the smooth P(p,T) surface of equation (6). In

the critical region, T = T^ + 5%, P = + 50%, small inconsistencies in the

pressure and temperature scales of different laboratories are expected to give

large deviations of density because the derivatives (8p/9T) and (8p/9P) are

approaching infinity at the critical point. At the other extreme, the derivative

(9P/9p) becomes very large for compressed liquid at low temperatures, such that

small relative errors in the experimental densities yield (via any equation of

state) deviations of the calculated pressures greatly exceeding the accuracy of

pressure measurements. In this domain, any equation of state should be used only

to find p(P,T).

4.2 Specific Heats , C^(p,T)

Detailed deviations appear in tables 15 and 16. Figure 11 shows relative

deviations of the data of Ernst, et al. [23] from our calculated specific heats

for gaseous states at subcritical densities. The differences of roughly 0.5%

persist down to zero pressure, table 15, and therefore constitute a difference

from the ideal gas values of Chao, et al. [9].

Figure 12 shows relative deviations of the data of Yesavage [69] from our

calculated specific heats. Except near the critical point, most deviations are

under 1%. Figures 13 and 14 show excellent agreement near the extrema along

isobars just below, and just above the critical pressure.

17
4.3

Speeds of Sound, W(p,T)

The first part of table 17 for the saturated liquid compares speeds of

sound from Rao [50] with our calculated results. He gave only values calculated

by a linear dependence on T, not reported. We reconstituted a linear formula

to regenerate his "data.” These "data” are uniformly about 12% lower than our

results. We believe it unlikely that our results are this far in error.

‘

The second part of table 17 gives speeds of sound measured by Lacam [42].

Figure 15 shows that, with a few exceptions, the deviations are under 2%.

4.4

Enthalpy Differences at 60 Bar

Table 18 compares our enthalpy differences along the 60 bar isobar with

results of Kuloor, et al. [41] along their 60 atm isobar. Differences must be

expected from the different ideal gas functions used, slightly different heats

of vaporization, different equations of state based on different P-p-T data,

and different computational paths and procedures.

This table, therefore, gives a rough indication of uncertainties which

arise from these many sources when computing a thermodynamic network.

Differences of enthalpy between 1 atm and 1 bar, (1 atm = 1.01325 bar) are

insignificant relative to the differences in AH between Kuloor, et al., and

this report.

4.5

Enthalpy Difference at 400 K

Table 19 compares our enthalpy decrease along the 400 K isotherm with

results of Kuloor, et al. [41], and of Eubank, et al. [24]. At pressures below

the critical isochore at 66.756 bar, differences must arise from the different

equations of state used for this computation, assuming that the different

computational procedures in each case are equivalent.

18
Present results up to 44 bar fall between those of Kuloor and of Eubank.

At higher pressures, our decreases are about 1% smaller than Kuloor, and 1.5%

I smaller than Eubank.

j

I At pressures above 66.756 bar, our enthalpies for table 19 were obtained

I

! by computation around the critical point, as shown by figure 9. On this path

j

j we obtained a heat of vaporization at the normal boiling point of 18864 J/mol,

I 0.45% greater than the experimental value, 18780 + 17 J/mol measured by Kemp

and Egan [38]. Eubank, et al. exceed our enthalpy decrease by 262 J/mol at 400 K

up to 100 bar. On the similar path, this would lead to a heat of vaporization

about 1.8% greater than experimental.

4.6 Residual Specific Heats at 400 K

Table 20 compares our derived, residual specific heats, = C^Cp,!) - 0^(1),

along the 400 K isotherm, with results of Kuloor, et al. [41], and of Eubank,

et al. [24]. Agreement is fair for this difficult computation at densities up to

the critical isochore at 66.756 bar, with exception of our smaller value at

P = 1 bar. At higher pressures, present results are near those of Kuloor, et al.

Specific heats of Eubank, et al. are much greater than ours. The experimental

value from Yesavage [69] at T = 399.8 K, P = 103.42 bar, is = 70.5 J/mol/K,

obtained by use of our C° (400) = 93.9 J/mol/K.

4.7 Loop Closure for the Saturated Vapor

Starting with enthalpy and entropy of the saturated liquid at temperatures

below the boiling point [section 3.2(b)], we have used heats of vaporization

from the Clapeyron equation, “ T* (dP^/dT) • (v^ - v^) , to compute H and S

of the saturated vapor.

19
In table 21 these results are compared with H and S computed for the

vapor via ideal gas values and the equation of state. Inconsistencies

increasing to almost 10% of the heat of vaporization at the triple point are

seen in this table. This difficulty is anticipated, considering an uncertainty

of at least 10% in vapor pressures and vapor densities.

When specific heats for ideal gas states and also for the saturated liquid

are known, together with one heat of vaporization, it is possible in principle

to utilize the Clapeyron and virial equations to deduce vapor pressures, as i

described recently by Cheng-Hsiung Tsai [67], following methods of Ziegler,

et al. [73].

In this work, Cheng-Hsiung Tsai was not aware of the specific heats for

saturated liquid, and the heat of vaporization of Kemp and Egan [39]. Ideal gas

specific heats of Chao, et al. [9] appeared later than his work. This noble

enterprise therefore should be repeated with recent data. For reference, however,

we compare results of Tsai with our vapor pressures from equation (2) in table 22,

and with our heats of vaporization from equation (10) in table 23.

In the last column, of the first page of table 29, we give heats of

vaporization at temperatures below the boiling point calculated as the difference

of vapor and liquid enthalpies, Q

= H - , where H was obtained from ideal

gas properties via the equation of state.

After the present report was completed, we derived data for vapor pressures,

densities of the saturated vapor, and for heats of vaporization by similar

methods at temperatures below the normal boiling point. Primary data used are

specific heats for ideal gas states, equation (7), the heat of vaporization,

Q, , at the normal boiling point, T, , [39], specific heats for the saturated

b b

20
I

liquid equation (9), and the virial equation of state (5). Secondary data used are our approximate vapor-pressures, equation (2), and the saturated liquid

densities, equation (3).

At any temperature, T^, there are two unknown variables, the vapor pressure

P, and the heat of vaporization, Q^. Closed—loop computations for enthalpy and

for entropy, yield

+ AH^(a,b) - AHg(a,b)

AS^ = ^S^(a,b) - ASg(a,b)

We iterate P to minimize the free energy change at T = T

AF = Q

- T *AS = 0. a a a a

Well-known relations have been used with the virial equation to compute AH (a,b)

S

and AS^(a,b), and to obtain AH^(a,b), AS^(a,b) via the saturated liquid specific

heats C^(T), all as detailed in PROGRAM ZIEGLER, given at the end of Appendix C.

Table 24 gives results via Q, = 18 780 J/mol of Kemp and Egan. Table 25

b

gives results via Q, = 18 864 J/mol used in the present report. Under the heading

b

P,EQN are given vapor pressures from our equation (2). The heading P,BAR is for

pressures derived by iteration. The heading MOL/L is for saturated vapor

densities via the virial equation (5). The heading Q,EQN is for heats of

vaporization via our equation (10) , whereas heading Q,VAP is for the derived

heats of vaporization.

21
i

5. TABLES OF PHYSICAL AND THERMODYNAMIC PROPERTIES

5.1 I Calculated P-p-T Isochores and Isotherms

I Tables 26 and 27 give a selection of isochores and isotherms computed by I

equation of state (6). These are essential to examine behavior of the P(p,T)

surface. They are a useful supplement to the isobars of table 30 for interpola

P-p-T values and their derivatives.

5.2

The Joule-Thomson Inversion Locus

Table 28 gives the P-p-T locus of the J.-T. inversion, (9T/9P) = 0, obtaii

H

from equation of state (6) under the condition T*(9P/9T) = p*(9P/9p). This tab:

has been computed to temperatures well above those of P-p-T data, to find the^'

^ maximum in P-T coordinates.

5.3

Thermophysical Properties of the Saturated Liquid

Table 29 gives physical and thermodynamic properties of saturated liquid

propane computed by methods of section 3. Column headings are interpreted on

the first page of this table.

5.4

Thermophysical Properties Along Selected Isobars

Table 30 gives physical and thermodynamic properties on isobars, computed |J

by methods of section 3. Explanations for this table are given on the first

page. This table is extrapolated beyond the maximum temperature (600 K) , and

the maximum pressure 400 bar) of most of the P-p-T data used for adjusting

the equation of state.

22
6. COMMENTS AND RECOMMENDATIONS

6.1 Comments on Uncertainties

Kuloor, Mewitt, and Bateman give an excellent discussion of problems in

estimating ''accuracy'' in a thermodynamic network [41].

Densities from the equation of state in most regions of the P(p,T) surface

here are within 0.2% of experimental data, tables 6 and 9. Much of the P-p-T

data of Beattie, Kay, and Kaminsky [2], however, fall in or near the critical

region where any small inconsistencies in the temperature or pressure scales

necessarily give large density deviations, especially with an equation of state

which originates on the coexistence boundary, as discussed in section 4.1. We

estimate uncertainty of densities in table 30 (isobars) to be under 0.2%, except

in the critical region where it increases toward 2% near the critical point.

Heats of vaporization, used to cross the "dome" of figure 9, we estimate

uncertain by under 0.5%, table 14. At the boiling point, this is under

90 J/mol, which then applies to enthalpies in the compressed liquid at 231 K.

Enthalpy differences along Isobars in table 30 in general agree with

experimental specific heats of Yesavage [69] within 3%, which we assess as

uncertainty for AH over small ranges. Enthalpy differences from points in the

compressed liquid at low temperatures have the increased uncertainties discussed

above.

Tables 18, 19, and 20 give an indication of differences among authors using

different data and methods.

6.2 Recommendations

1) The melting line, P^(T) , of Reeves, Scott, and Babb was uncertain by

at least 1 K in temperature [52]. This corresponds to an enormous uncertainty

23
in pressure. Experimental determination of this boundary of the P(p,T) surfacei

is relatively easy in conventional P-p-T apparatus, and is desirable.

2) Vapor-Pressure data for propane are of low precision, table 1. Accur

measurements from a single laboratory on a pure sample of propane from the

lowest possible pressure [e.g., 0.1 bar via the "air dead-weight gage"] to the

critical pressure would be valuable for thermal computations. At very low

temperatures, new experimental techniques are needed for pressures down to

-9

3*10 bar at the triple-point. i

3) Saturated liquid densities from different sources are consistent and

of high precision, table 2. No further measurements are needed. I

4) Saturated vapor densities always are difficult to measure or derive

||j with good accuracy. Table 3 shows available data. For an equation of state (! which originates on the coexistence boundary, higher confidence and accuracy is

needed for the vapor densities, all the way down to the triple point where this

density is about 10 mol/L.

The present equation of state (6) appears to be well suited for obtaining

coexistence densities from sets of P(T) data along Isochores. Assume that

parameters T^, p^, a, y, 6 are known from preliminary work. For data at a

constant density, we need only treat T^(P) as an unknown parameter in equation '

to be found by trial or iterative procedures for a best fit of the data. The ^

coefficients B(p), C(p) may be used as least-squares coefficients, or taken as

constants (at this density) from previous work.

It follows that a complete set of accurate and self-consistent P-p-T data ^

on isochores (or isotherms) , from the lowest possible densities up to at least

the critical density, would be most helpful both for a reanalysis of virial

24
coefficients, and to obtain the saturated vapor densities. The older data of

Beattie, et al. [2] probably need unknown adjustments of the temperature scale.

5) The virial coefficients for propane at low temperatures are important

because the virial and vapor-pressure equations provide a means to estimate

saturated vapor densities at values down to about 10~^*^ mol/L near the triplepoint. Measurable virial coefficients for propane at higher temperatures are

of low precision, tables 4 and 5. Methods for accurate extrapolation to lower

temperatures need to be investigated.

6) The equation of state used here requires accurate and consistent data

for the liquid-vapor coexistence boundary, namely the vapor-pressure equation

and orthobaric densities. Experimental P-p-T data (used to adjust coefficients

in the equation of state) are lacking for propane only in the compressed liquid

at temperatures from 170 K down to the triple point (85 K) . Any new data in

the critical region, we believe, would be useful only if both highly accurate

and consistent with our temperature and pressure scales. With the present,

highly-constrained equation of state, excessive numbers of P-p-T data points

are not needed. Greater absolute accuracy in a smaller number of carefullychosen points would be preferable. Many points along isochores and/or isotherms

nevertheless are needed for any new substance to estimate the coexistence

boundary by classical methods.

7) Specific heats for ideal gas states, estimated from spectroscopic

data [9], might well be modified in future work on propane by inclusion of the

calorimetric data of Ernst, et al. [23].

8) Specific heats Cp(p,T), or C^(p,T) are essential data for computing a

thermodynamic network. Whereas we have obtained reasonably consistent, closed—loop

25
results with data of Yesavage [69], more accurate data would be helpful, because) ji

1 l' small relative uncertainties lead to large absolute uncertainties in tabulated;,- \

enthalpies. For closed-loop computation around the critical point, figure 9, / \ ,(

i specific heats C^Cp,!) at constant pressure are most convenient for entering the q

compressed liquid region, all the way down to the triple-point temperature,

although these measurements are much more difficult experimentally than those

J

for C^(p,T) at constant density. - H

measured only at temperatures below the normal boiling point [39]. Tabl

shows poor precision for the few data at higher temperatures. Data over the

and consistency tests in a thermodynamic network. Determination of these data

from specific heat observations on a liquid-vapor sample at constant volume

requires accurate knowledge of the vapor-pressure and saturated-liquid-density

equations

.

10) Heats of vaporization for propane at temperatures above the normal

boiling point are not highly precise, table 14. Very high relative accuracy is

needed in new experimental data because the large absolute heats of vaporization

lead to large absolute uncertainties in enthalpy for the saturated liquid.

Research similar to that of Ziegler, et al. [73] should be conducted for

consistency of vapor pressures and heats of vaporization at very low temperatures

where adequate experimental methods do not exist. See section 5.3, above.

11) In conclusion, more experimental data are available for propane than

was anticipated at the start of present work. Further computational work could

be performed to make the best possible, self-consistent thermodynamic network

9) Accurate specific heats, C^(T), for the saturated liquid have

full range of the coexistence boundary are valuable for many alternative procedurej

26
' from these, available data. As with all such problems, however, more accurate

data for nearly all physical properties is desirable, because the thermodynamic

properties (enthalpies) in many regions are extremely sensitive to the physical

properties used. A particular, unsolved problem for the higher hydrocarbons is

the long, liquid-vapor range below the normal boiling point, where vapor

pressures, vapor densities, and heats of vaporization cannot be measured accurately

by current, experimental techniques.

7 . ACKNOWLEDGMENTS

The author is indebted to many staff members of the Cryogenic Fluid Properties

Section of this laboratory for discussions and valuable suggestions, and to the

Cryogenic Data Center for bibliographies and reference documents. Robert D.

McCarty provided the essential least-squares program for adjusting the equation

of state and other functions. J. F. Ely and R. Kobayashi of Rice University

very kindly communicated new, prepublication P-p-T data. We express grateful

appreciation for support by the American Gas Association, without which this

work might not have been accomplished.

27
1

1 .

2 .

3.

4.

5.

6 .

7.

8 .

9.

10 .

11 .

12 .

13.

14.

8. BIBLIOGRAPHY

|

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31
56 . Sage, B. H., and Lacey, W. N. , Phase equilibria in hydrocarbon systems IX. ( Specific heats of n-butane and propane, Ind . Eng. Chem. '2J_ (12), 1484 (1935)

t 57. Sage, B. H., Schaafsma, J. H. , and Lacey, W. N. , Phase equilibria in [ hydrocarbon systems. V. Pressure-volume-temperature relations and thermal J properties of propane, Ind. Eng. Chem. 2^ (11), 1218 (Nov 1934).

r 58. Seeman, V. F. W. , and Urban, M. , Die Dichte des flussigen Propans, Erdbl j und Kohle-Erdgas-Petrochemie 1^ (2), 117 (Feb 1963).

/

‘ 59. Seshadri, D. N., and Viswanath, D. S., (Dept. Chem. Engrng., Indian Inst. i Sci., Bangalore 560012, S. India), Thermodynamic properties of propane, ' Fifth Biennial International CODATA Conference, Boulder, Colorado, (Jun * 1976). [International Council of Scientific Unions, 51 Boulevard de

Montmorency, 75016 Paris, France.]

60. Shana'a, M. Y. , and Canfield, F. B. , Liquid density and excess volume of \ light hydrocarbon mixtures at -165 °C and at saturation pressure, AIChE j 61st Nat. Meeting, Houston, Tex. (Feb 19, 1967); Trans. Faraday Soc. 6^, | 2281 (1968).

61. Sliwinski, P., Die Lorentz-Lorenz-Funktion von dampf fbrmigem und fliissigem

athan, propan und butan, Z. Physikal. Chemie, Neuefolge 6^, 263 (1969).

62. Starling, K. E. , and Kwok, Y. C. , Thermo data refined for LPG. Part 4: prop^

Hydrocarbon Processing, p. 116 (Jun 1971).

63. Stearns, W. V., and George, E. J. , Thermodynamic properties of propane, Ind.

Eng. Chem. ^

(5), 602 (May 1943).

64. Strein, V. K. , Lichtenthaler , R. N. , Schramm, B. , and Schafer, Kl.,

Messwerte des zweiten virialkoef f izienten einiger gesattigter kohlenwasserstoffe von 300 - 500 K, Ber. Bunsenges Phys. Chem. 7_5 (12), 1308 (1971).

65. Tickner, A. W. , and Lossing, F. P. , The measurement of low vapor pressures

by means of a mass spectrometer, J. Phys. and Colloid Chem. 733 (1951).

66. Tomlinson, J. R. , Liquid densities of ethane, propane, and ethane-propane

mixtures. Technical Publication TP-1, Natural Gas Processors Assoc., 808

Home Federal Bldg., Tulsa, Okla. 74103 (Feb 1971).

67. Tsai, Cheng-Hsiung, Low temperature phase equilibrium for systems containing

a pure condensed phase. Thesis, Tennessee Technological Univ. , College of

Engineering, Cookeville, Tenn. 38501 (Jun 1971).

68. Van der Vet, A. P., (Dutch-Shell Labs., Amsterdam), Density, compressibility

expansion of light hydrocarbons and of light hydrocarbon blends. Congress

Modial du Petrol. II, 515, Paris (1937).

69. Yesavage, V. F. , The measurement and prediction of the enthalpy of fluid

mixtures under pressure. Dissertation, Dept, of Chemical and Metallurgical

Engineering, Univ. of Michigan (Nov 1968).

32
70. Yesavage, V. F., Katz, D. L., and Powers, J. E. , Thermal properties of

propane, J. Chem. Eng. Data 1^ (2), 197 (Apr 1969).

71. Young, S., On the boiling points of the normal paraffins at different

pressures, Proc. Roy Irish Acad. 38B (4), 65 (1928).

72. Ziegler, W. T., The vapor pressures of some hydrocarbons in the liquid and

solid state at low temperatures, Nat. Bur. Stand. (U.S.), Tech. Note 4

(May 1959), PB 151363.

73. Ziegler, W. T., Kirk, B. S., Mullins, J. C., and Berquist, A. R. , Calculation

of the vapor pressure and heats of vaporization and sublimation of liquids

and solids below one atmosphere pressure. VII. Ethane, Tech. Report No. 2,

Proj . A-764, Eng. Expt. Sta., Georgia Inst. Technology, Atlanta, Georgia

(Dec 1964).

33
APPENDIX A. Symbols and Units

Subscripts c and t refer to critical and liquid triple points.

Subscripts g and £ refer to saturated vapor and liquid.

Subscript a refers to liquid-vapor coexistence (usually the liquid)

.

Superscript o refers to ideal gas states.

a, Y, 6, non-linear constants in the equation of state

B(p), C(p) density-dependent coefficients in the equation of state

B(T), C(T) second and third virial coefficients

C^(p,T) molal heat capacity at constant volume, (J/mol)/K

Cp(p,T) molal heat capacity at constant pressure, (J/mol)/K

C^(T) molal heat capacity for saturated liquid, (J/mol)/K

d density, mol/L

E(p,T) the internal energy, J/mol

E°

n 27, 452.0 J/mol

f(p) used in the definition of 0(p)

F(p,T) definition in the equation of state

H(P,T) the enthalpy, J/mol

J the joule, 1 N-m

L

-3 3 the liter, 10 m

mol 12

44.09721 grams of propane (C = 12 scale)

P

5 2 pressure in bars, 1 bar = 10 N/m , (1 atm = 1.01325 bar)

P^(T) the vapor pressure, bar

P„(P) PqLT^Cp)], vapor pressure as function of density

*(P,T) function in the equation of state

4'(p,T) function in the equation of state

'4ap

Ah , the heat of vaporization, J/mol

vap

34
APPENDIX A. (Continued)

R

P

S(P,T)

T

"b

i„(p)

0(p)

V

w(p,T)

W(p,T)

x(T)

x(T)

x„(P)

the gas constant, 8.31434 (J/mol)/K, 0.0831434 (bar-L/mol) /K

d/d^, density reduced at the critical point

the entropy, (J/mol)/K

temperature, K

405.0 K, (figure 1)

liquid-vapor coexistence temperature, K

defined locus of temperatures

1/d, molal volume, L/mol

[1 - 0(p)/T] for the equation of state

the speed of sound, meters/second

T/T for the equation of state

c variously defined for other equations

T (p)/T , reduced temperature at coexistence, for the equation of a c state.

35
APPENDIX B. Fixed-Point Values for Propane

Triple Point Boiling Point Critical Point

Temperature, K 85.47 231.071 369.80

Pressure, bar 3.0*10"^ 1.01325 42.4204

Density, mol/L 4.96

Vapor 4.22*10"^° 0.05485

Liquid 16.620 13.168

36
PROPANE

OOCO^CNJOeOCO^CMO

;/|o»u AiiSNaa

Figure 1. Density-temperature diagram of propane.

37

TEMPERATURE,
DENSITY

Tc T

Figure 2. The locus of isochore inflection points.

TEMPERATURE

Figure 3. Behavior of the locus 0(p)

•

38
i

0 ^o(p) T —

Figure 4. Behavior of the function $(p,T).

0(p) Tjp)

Figure 5. Behavior of the function 'f(p,T).

39
3

O

Figure 6. Behavior of coefficients B(p), C(p) for propane.

40
41
[a/(oO-^o)]'^

Figure 8. Behavior of C^(T) on the critical isochore.

42
>

CO

LU

O

Figure 9. Paths used to derive heats of vaporization.

43
%'

o'/o'

V

0.1

0

-0.1

0.5

0

-0.5

3

2

10

0.5

0

-0.5

Figure 10. Deviation plots for densities.

1 1 - (9 o

°

o

1 1

1

o o

1

\ Beattie, —

7.994 mol/l _

1 400 500 600

T, K

Beattie,

5.995 mol/l

P O

r~ ^

O —1 1—

Cherney, “

T=323.15 K

O OO

O _ O O

1 O O o

1 1 0.4 0.6 0.8 1.0

DENSITY, mol/l

_l

o o o o

1 o o

o

Beattie, — 3.497 mol/l

_J Q_J 1 1

44
%'

0 -0.2

-0.4 -0.6

0.3

0.2

0.1

0

0.2

0.1

0 - 0.1

0.05

0

0.05

0.05

0

0.05

0.05

-0.05

r- ~ Dittmar, o o o _ 8.617 mol/l

\ l_

o

_ o

o

o“

1 1 °

o o

* Dittmar, * 11.339 mol/l — _ o

1 1 O 0

O

_ o

o o

o o o_

1

) O

o

o1 \

1

Dittmar,

13.226 mol/l - - o

"

0_J L_ 1 1

—

280 320 360 400

1 1 Ely, oo

1

\ O 0 n

|11. 52 mol/l

1 o ^

1 O|o

260 280 300 320

' O Q

' Ely, O 0

|13-17 mol/l 1 0 o

1 1

° Q 0 O 0 1

-

220 240 260 280

1 O ^

1

' Ely,

°,° ° O O O 14.77 mol/r

1 160 170 180

T, K

190 200

Figure 10. Deviation plots for densities (continued)

45
Q.

o

Q.

o

<

0.5

0

0.5

0.5

0

0.5

0.5

0

0.5

~o

I

1

O L

o —

I

P=0.981 bar

O -

-o

L

o

L

o

I P=3.432 bar _ O

1

_o

L_

o

L_

o

\ P=7.845 bar _ O _

\ 300 320 340 360

T, K

Figure 11. Deviations of Ernst specific heats.

46
ACp/

Cp,

1.0

0

-1.0

o oi

-o

P=17.237 bar

O

Liquid

O

X/ O

Vapor

I 3.9%

t 1.7%

T, K

Figure 12. Deviations of Yesavage specific heats.

hi
TEMPERATURE, K

Figure 13. Comparison of Cp(T) at = 0.813.

48
TEMPERATURE, K

Figure 14. Comparison of C^CT) at “ 1.626.

/

49
<

T, K

Figure 15. Deviations of Lacam speeds of sound.

50
Table 1. Vapor pressures of propane

H

I

jlPANE VAPOR PRESSURES, EPP = 1.300

TICKWER, (2)CARRUTH, (3)MAAS, (4)DANA, (6)SAGE, (7)BEATTIE, (9) KEMP, (11) DESCHNER,

DREAMER, (13)CHERNEY, (14ICLEGG, ( 17) HELGESON, (19) GILLILAND, (20)BURREL, (25)0r

IP = 85.470, TCRT = 369.800

\P : .30000E-08, PORT = 42.420437 BAR

1,37228380 5.71668788 -8. 51170714 3.97587379 0.00000000 0. DOOOOOOO

HT T,K> U X P,8AR CALCO PONT OPS/DT RESIO.

.010 94.540 .12478 .03190 .68500E-07 .65470E-07 4.63 .201E-07 .29643

.011 99.780 .18653 .05033 .30650E-06 .30112E-06 1.79 .831E-07 .24280

.012 105.150 .24342 .06922 .12190E-05 .12272E-05 -.66 .304E-06 .21568

.012 105.350 .24543 .06992 .13330E-05 .12895E-05 3.38 .319E-06 .24229

.012 108.250 .27370 .08012 .26660E-05 .25696E-05 2.95 .6Q6E-06 .23382

.012 110.650 .29597 .08856 .43650E-05 .44835E-05 -2.64 .lOOE-05 .19907

.012 112.450 .31205 .09489 .66660E-05 .66618E-05 .06 .144E-05 .21189

.013 115.750 .34024 .10650 .13330E-04 .13324E-04 .04 .272E-05 .20794

.013 117.420 .35389 .11237 .17800E-04 .18636E-04 -4.49 .369E-05 .18540

.013 119.250 .36842 .11881 .26660E-04 .26620E-04 .15 .510E-05 .20437

.014 124.350 .40665 .13674 .66660E-04 .67892E-04 -1.81 .119E-04 . 19104

.015 127.720 .43024 .14859 .11360E-03 .12077E-03 -5.93 .201E-04 .17252

.015 128.350 .43451 .15081 .13330E-03 .13402E-03 -.54 .220E-04 .19164

.015 132.850 .46385 .16664 .26660E-03 .27362E-03 -2.57 .418E-04 .18 017

.016 134.150 .47196 .17121 .31250E-03 .33313E-03 -6.19 .499E-04 . 16684

.016 139.150 .50173 .18879 .66660E-03 .68473E-03 -2.65 .949E-04 .17392

.017 143.740 .52724 .20494 .11960E-02 .12657E-02 -5.50 .164E-03 .16118

.017 144.350 .53051 .20708 .13330E-02 .13690E-02 -2.63 .175E-03 .16903

.019 149.950 .55927 .22678 .26660E-02 .27248E-02 -2.16 .321E-03 .16500

.020 155.720 .58674 .24707 .50660E-02 .52353E-02 -3.23 .568E-03 .15677

.020 158.150 .59771 .25562 .66660E>02 .67858E-02 -1.77 .712E-03 . 15824

.021 162.450 .61631 .27074 .10390E-01 .10517E-01 -1.20 .104E-02 .15558

.022 164.750 .62587 .27883 .13330E-01 .13156E-01 1.32 .126E-02 .15935

.045 166.190 .63171 .28390 .15480E-01 .15084E-01 2.63 .142E-02 . 16095

.049 173.320 .65923 .30897 .29330E-01 .28596E-01 2.57 .245E-02 .15399

.024 173.580 .66019 .30989 .29920E-01 .29238E-01 2.33 .249E-02 .15 323

.026 178.650 .67837 .32772 .45700E-01 .44437E-01 2.84 .355E-02 .14965

.053 179.842 .68249 .33191 .49850E-01 .48844E-01 2.06 .385E-02 .14690

.058 187.347 .70725 .35831 . 87250E-01 .85857E-01 1.62 .616E-02 • X 39 3 T .064 195.131 .73092 .38568 .14803E4-00 .14630E-i-00 1.18 .956E-02 • 13169

.070 202.910 .75276 .41304 .23987E+00 .23788E+00 .84 .142E-01 •12492

.077 209.926 .77107 .43772 .35774E+00 .35595E+00 .50 .197E-01 • 11661

.082 214.982 .78352 .45550 .46884E4^00 .46709E+00 .37 .244E-01 • 11476

.088 220.259 .79591 .47406 .61212E+00 .61086E1-00 .21 .302E-01 • 11061

.094 225.098 . 80676 .49108 .77179E+00 .77144E+00 .05 . 363E-0

1

• 10667

.098 228.806 .81476 .50412 .91484E+00 .91548E+00 -.07 .415E-01 • 10409

.102 231.462 .82034 .51346 .10302E+01 .10309E+01 -.07 .455E-01 • 10 230

.710 258.150 .86999 .60732 .29197E+01 .29207Ef01 -.03 .lOlE^OO • 0660 6

51

"
Table 1 Continued.

•s

PROPANE VAPOR PRESSURES, EPP = 1. 300 1

10 WT T,K U X P .BAR CALCO PCNT OPS/OT RE

25 . 751 263.150 . 87817 .62491 .34549E+01 .34586E4-D1 -.11 .115E4-00 . 0 25 .792 263.150 . 88605 .64249 .40623E+01 .40676E4-01 -.13 .129E+00 . 0 25 .631 273.150 .89364 .66008 .47462E+01 .47533E+01 -.15 .145E+00 . 0 17 . 865 277.594 .90015 . 67571 . 54470E401 .54318E^01 .28 . 160E+00 . 0 25 . 369 278.150 . 90095 .67766 . 55124E+01 .55214E+01 -.16 .162E*00 . 0 17 . 902 283.150 . 908ul . 69525 .6398CE+01 .63781E*C1 .31 .181E+00 . 0 25 .902 283.15

0

. 90801 .69525 .63672E4-01 .63781E+01 -.17 . 181E + 00 . 0 25 .932 288 . 150 .91482 .71283 .73159E+01 .73292E+-01 -.18 .200E4'00 . 0 17 .935 233.706 .91556 . 71479 . 74330E + 01 .74411E+01 -.11 .202E+00 . 0 25 . 956 293.150 .92140 . 73042 . 83650E+01 . 83811E4-01 -.19 .221E+00 . Ol 6 . 192 293.930 .92241 .73316 .86180E+01 .85547E+01 .74 .224E+00 . o; 17 . 961 294.251 .92263 . 73433 . 36180E401 . 86291E + 01 -.13 .226E+00 . 01 25 .974 298.150 . 92776 .74800 . 95202E+01 .95401E+01 -.21 .243E+00 . Ol 17 . 979 299.817 . 92983 .75387 .99350E+01 .99514E+01 -.16 .251E*00 .01

6 .196 301.090 . 93140 .75834 . 10352E4-02 .10274E+C2 .76 .257E4-00 . 0( 11 . 984 301.950 . 93245 .76137 .10536E+02 .10497E402 .38 .261E+00 . 0( 11 . 936 302.950 .93367 . 76489 . 10807E+02 .10760E*02 .44 .265E^00 . 0( 25 . 937 303.150 . 93391 . 76559 . 10739E + 02 .10813E4-02 -.22 .266Et00 .0( 11 .990 304.610 . 93567 .77072 .11248E+02 .11207E402 .37 .273E4-00 .0( 17 . 991 305.372 . 93658 . 77340 .11397E4-02 .11416E+02 -.17 .277E+00 . 0( 11 .h93 306.680 .93813 .77800 . 11829E+02 .11783E+02 .39 .284E400 . 0( 6 .199 307.480 . 93907 .73032 . 12066E+02 .12012E+02 .45 .283E^00 . oe 11 .995 308.350 . 94009 .78388 .12317E4-02 .12264E*02 .43 .292E+00 . oc 17 . 997 510 . 928 . 94308 .79294 . 13010E4Q2 .13034E+02 -.18 . 305E4-00 . OE 11 .997 311.490 .94373 .79492 .13246E+02 .13206E+02 .30 . 308E<-00 . 06 11 . 997 311.490 . 94373 .79492 . 13249E+02 .13206E^02 .32 . 308E+00 . 06 25 . 993 313 . 150 . 94562 .80076 . 13692E + 02 .13725E+02 -.25 .317E+00 . 06 6 . 200 313.320 . 94581 • 8 0 1 3 6 . 13790E+02 .13779E+02 .08 .318E+00 . 06 12 . 996 313.483 . 9460C .30193 . 13790E+02 .13831E4-02 -.30 . 319E+00 . 06 11 . 999 315 .480 .94824 .80895 . 14500E+02 .14479E+02 .14 .330E+00 . 06 17 . 999 316.483 . 94936 . 81248 . 14739E+02 .14813E+02 -.16 .335E+00 . 06 11 1.000 318.150 .95120 .61834 .15471E+02 .15379E+02 .60 .345E+00 . 06 11 l.OOG 318.280 . 95134 .81830 . 15474E+ 0 2 .15424E+02 .32 .345E400 . 06

6 .200 318.590 . 95166 .81989 . 15513E+02 .15532E+02 -.12 .347E+00 . 05 17 1.000 322.039 .95542 .83202 . 16734E+02 .16763E+02 -.17 .367E+00 . 05

7 1.000 323.150 .95661 .63593 . 17122E+02 .17174E+02 -.31 .374E«-00 .05

14 1.000 323.150 . 95661 .63593 .17154E+02 .17174E+02 -.12 .374E+00 . 05

2 5 1.000 323.150 . 95661 . 83593 . 17130E+02 .17174E+02 -.26 .374Ef00 . 05

6 . 200 323.373 .95684 . 8367 0 . 17237E+02 .17257E+02 -.11 .375E+00 . 05 11 1.000 324.940 . 95850 . 84223 . 17798E+02 .17853E402 -.31 .384E+Q0 . 05 17 1.000 327.594 . 96127 .85155 . 18857E*02 . 18894E + 02 -.20 .401E+00 .05

5 . 200 327.930 . 96162 .85274 . 18961E+02 .19029E+02 -.36 .40 3E4-00 .05

11 1.000 330.600 .96436 .86213 .20098E+02 .20127E+02 -.14 .420E4-00 . 05 11 1. 000 330.600 . 96436 . 86213 . 20107E+02 .20127E+02 -.10 .420E+00 . 05

12 1.000 332.039 . 96581 . 86719 . 20684E402 .20737E+02 -.26 .429E4-00 . 05

6 .200 332.090 . 96587 . 66737 .20684E+02 .20759E+02 -.36 .429E+00 . 05

1 4 1 . u 0 0 333.150 . 96693 .87110 . 21197E+02 .21218E+02 -.10 .436E+00 .05

17 1.000 333.150 . 96693 .87110 . 21138E-t-02 .21218E+02 -.14 .436E»00 . 05 25 1.000 333,150 .96693 .87110 . 21164E+02 .21218E+02 -.26 .436E+00 . 05

52
Table 1. Continued

iPANE VAPOR PRESSURES, EPP = 1.300

MT T,K U X P,BAR CALCO PCNT DPS/OT RESIO.

l.GOO 333.960 .96774 .87395 .21596E+02 .21573E+02 .11 .441E400 .05702

• 200 336.090 .96985 .88144 .22400E^02 .22520E4-02 -.53 .4566400 .0516 0 1.000 336.650 .97040 .88341 .22749E+02 .22785E+02 -.16 .459E4Q0 .05439

1.000 338.706 .97240 .89064 .23718E+02 .23744E+02 -.11 .474E400 . 05425-

1.000 339.594 .97326 .89376 .24132E+02 .24167E+02 -.14 .480E400 . 05371

.200 339.870 .97353 .89473 .24132E+02 .24300E>02 -.69 .4826400 .04875

1.000 340.120 .97377 .89561 .24561E»02 .24420E4-02 .58 .484E400 .06005

1.000 340.120 .97377 .89561 .24539E+02 .24420E>02 .49 .4846400 .05925

1.000 343.150 .97665 .90627 .25909E+02 .25918E+02 -.04 .5056400 . 05390

1.000 343.170 .97667 .90634 .25872E+02 .25928E+02 -.22 .5056400 .05204

.200 343.480 .97697 .90743 .25855E4-02 .26085E«02 -.88 .5086400 . 04497

1.000 344.261 .97770 .91018 .26462E4-02 .26484E«02 -.08 .5136400 . 05315

1.000 344.640 .97005 .91151 .26778E+02 .26679E>02 .37 .5166400 . 05803

1.000 346.428 .97972 .91780 .27579E+02 .27614E4^02 -.13 .5306400 .05211

.200 346.930 .98018 .91957 .27579E+02 .27881E4-02 -1.08 .5346400 . 04013

1.000 348.150 •98131 .92386 .28405E^02 .28538E>02 -.18 .5436400 .05090

1.000 348.150 .98131 .92386 .28533E4^02 .28538E«^02 •^.02 .5436400 .05312

1.000 348.150 .98131 .92386 .28486E4^02 .28538E4-02 -.18 .5436400 .05094

1.000 348.240 .90139 .92417 .28709E+02 .28587E«02 .43 .5446400 . 05897

1.000 349.817 .98283 .92972 .29434E>02 .29454E«02 -.07 .5566400 .05208

.200 350.090 .90308 .93068 .29303E4-02 .29606E^02 -1.02 .5586400 . 03782

1.000 351.640 .98448 .93613 .30683E-»02 .30481Ei^02 .66 .5716400 .06356

1.000 352.706 .98543 .93988 .31026E4-02 .31094E4-02 -.22 .5796400 .04875

.200 353.090 .98577 .94123 .31026E*02 .31317E+02 -.93 .5836400 .03564

1.000 353.150 .98583 .94144 .31390E4^02 .31352E^02 .12 .5836400 .05473

1.000 353.150 .98583 .94144 .31308E4-02 .31352E4^02 -.14 .5836400 . 05000

1.000 355.372 .98780 .94926 .32654E-I-02 .32668E^02 -.04 .6026400 . 05122

.200 355.870 .98823 .95101 .32750E^02 .32969E^02 -.67 .6066400 .03696

1.000 358.010 .99010 . 95853 .34289E*02 .34288E«02 .00 .6266400 .05193

1.000 358.150 .99022 .95903 .34400E4-02 .34375E+02 .07 .6276400 . 05384

1.000 358.261 .99032 .95942 .34474E4-02 .34445E>02 .08 .6286400 .05421

.200 358.590 .99060 .96057 .34474E+02 .34652E>02 -.51 .6316400 .03639

1.000 360.928 .99261 .96880 .36184E>02 .3615364^02 .08 .6546400 .05482

1.000 361.120 .99277 .96947 .36292E+02 .36279E4-02 .04 .6566400 .05287

1.000 361.120 .99277 . 96947 .36320E4-02 .36279E+02 .11 .6566400 . 05605

.200 361.260 .99289 .96996 .36197E+02 .36371E+02 -.48 .6576400 . 03124

1.000 363.150 .99450 .97661 .37683E-i^02 .37631E+02 .14 .6776400 .05915

1.000 363.200 .99454 .97679 .37687E*02 .37665E+02 .06 .6776400 .05459

1.000 363.450 .99475 .97767 .37828E+02 .37835E+02 -.02 .6806400 .05008

1.000 363.594 .99487 .97817 .37921E+02 .37933E+02 -.03 .6826400 .04920

.200 363.760 .99501 .97876 .37921E+02 .30 04664^02 -.33 .6836400 .02962

1.000 365.470 . 99644 . 98477 .39048E4-02 .392316402 -.47 .7046400 . 00401

.200 366.260 .99709 .98755 .39645E+02 .39791E402 -.37 .7146400 . 00312

1.000 368.150 .99865 .99420 .41239E*02 .411656402 .18 .7426400 . 11271

1.000 368.372 .99883 .99498 .41369E+02 .413316402 .09 .7466400 . 08956

.200 368.760 .99915 .99634 .41369E*02 .416216402 -.61 .7546400 -.33395

1.000 368.850 .99923 .99666 .41585E+02 .416896402 -.25 .7566400 -.12760

1.000 368.970 .99932 .99708 .41813E>02 .417806402 .08 .7586400 . 11697

= 135, RMSPCT = ,369

53
Table 1 . Continued.

PROPANE VAPOR PRESSURES, EPP = 1,300

ID WT T.K U X P ,8AR CALCD PCNT OPS/OT RES

3 J.OGG 223. 750 . 81676 . 50 744 .11426E+01 .95530E«-00 19.61 .429E-01 . 14

3 0.000 230. 250 .81781 .50920 .11599E401 .97693E+00 18.73 .436E-01 . 13

3 0.000 230.850 .81907 .51131 . 11919E401 . 1 C034E*01 18.79 .446E-01 .13

3 0 . OOC 234.750 .82707 .52502 .13999E+01 .11892Ef01 17.72 .503E-01 . 13

3 O.OGO 242.300 . 34132 .55158 .18236E+01 .16234E401 12.34 .646E-01 . 12

3 0 . OGG 250.050 . 85604 .57883 .26944E4Q1 .21860E+D1 23.26 .810E-01 . 13

4 O.OOC 210 . 330 . 77209 .43914 .36837E+00 .36397E400 1.21 .200E-01 . 11

4 0 . 0 0 0 216.410 .78694 .46052 . 50689E + 00 .50302E+00 .77 .259E-01 . 11

4 O.OGO 216.470 .78708 .46073 .50322E4C0 .50458E400 .72 .260E-01 . 11

4 0.000 221.640 . 79906 .47692 . 65635E400 .65371E+00 .71 .319E-01 . 11

4 0. OOG 227.250 .81144 .49865 .85753E+00 .85268E400 .57 .392E-01 . 10

4 0.000 231.080 . 81955 .51212 . 10181E+01 .10137E401 .43 .449E-01 . 10

4 O.OGO 235.040 . 82765 .52604 . 12050E401 .12040E401 .08 . 513E-01 . 10 4 0.000 235.090 . 32775 .52622 .12082E+01 . 12066E+01 .14 .514E-01 . 10

4 0.000 242, 730 . 84263 .55309 .1652QE+01 .16514E+01 .04 .654E-01 . 09

4 0.000 249.070 . 85429 .57539 .21041E401 .21077E+01 -.17 .788E-01 . 091 4 0.000 256.290 . 86 68 6 .60078 . 27238E+01 .27376E401 -.50 .960E-01 .oai

4 0.000 267.230 . 38470 . 63943 .39303E+01 .39563E+01 -.66 .127E+00 .07'

4 0.000 272.120 .89210 . 65646 .45903E+01 . 46055E + 01 -.33 .142E400 .0 7; 4 O.OGO 275.630 . 89730 .66880 .50529E+01 . 51236E+01 -1.38 .154E400 .07;

4 0.000 282. b70 .90734 .69356 .62542E+01 .62918E+01 -.60 .179E400 . 07:

4 0.000 283.300 . 90822 . 69578 . 63648 E4 0 1 .64052E+01 -.63 . 181E400 . 075

4 O.OOC 291.080 .91371 .72314 . 78607E+01 .79330E401 -.91 . 212E400 . 06)

4 0.000 298.080 . 92767 . 74776 .94352E+01 .95231E401 -.92 .243E+00 . 06<

4 0.000 307.090 . 93862 .77945 .11644E+02 . 11900E+02 -2.15 .286E+00 . 055

4 0.000 315.210 . 94794 .80800 . 14232E+02 .14390E+02 -1.10 . 328E+-00 . 056

4 0.000 323. <+90 . 95697 .83713 . 17023E402 .17302E+02 -1.61 .376E400 . 05C

4 0.000 323 .490 . 95697 .83713 . 17065E4-02 .17302E402 -1.37 .376E400 . 051

i 3 0.000 303,150 . 93391 .76559 .10801E+02 .10813E+02 -.11 .266E400 . 065

1 3 0.000 323 . 15 0 .95661 .83593 . 17154E+02 .17174E+02 -.12 .374E+00 . 056 19 0.000 314.817 . 94750 . 30662 . 14065E4Q2 .14262E+02 -1.38 .326E+00 . 055

19 0.000 330 .372 . 96412 .86133 . 20271E+02 .20031E4-02 1. 20 .418E400 . 064

1 9 O.OOC 3‘*5.372 . 97874 .91409 .27441E+02 .27059E+02 1.41 .522E400 . 069

19 0.000 357.594 . 98974 . 95707 . 34060E+02 .34028E+02 .09 .622E+00 . 054

20 0 . 0 0 0 148.950 . 55429 .22326 .40000E-02 .24196E-02 65.32 .290E-03 . 305

20 0.000 154. 853 .58273 .24401 . 8QOOOE-02 .47605E-02 68.05 .523E-03 .296

20 0.000 163.950 .62258 . 27 60 2 . 20000E-01 .12130E-01 64.20 .118E-02 .274

20 0.000 172. 650 . 65674 . 3 066 2 .40000E-01 .26995E-01 48.17 .233E-02 . 237

20 0.000 17 9 .85 0 .68252 .33194 .66660E-01 . 48874E-01 36.39 .335E-02 .210

20 0.000 190,350 .71661 .36887 . 13332E + 0 0 .10608E+00 25.68 .734E-02 . 181

20 0 . 0 Ol 196.650 .73590 . 39173 . 19998E + 0 0 .16352E400 22.30 .105E-01 . 170

20 0 . 0 C 0 202.050 . 75043 .41002 .26664E4Q0 .22591E+00 18.03 .136E-01 . 158

20 0.000 213.250 . 77189 .43880 . 39997E+00 . 36237E+00 10.38 .199E-01 . 137

20 0.000 215.450 . 78465 .45714 . 53329E+00 .47363E+00 11.42 .249E-01 . 136

20 0 . 0 C 0 219.950 . 79520 .47297 . 66661E+00 .60158E4C0 10.81 .298E-01 .131

20 0 . u 0 0 223. 750 . 80379 .48634 .79993E400 .72372E+00 10.53 .345E-01 . 128' 20 0.000 225.550 . 80775 .•,9267 . 86660E+00 .78798E400 9.98 .369E-01 . 126' 20 0.000 227.050 .81101 .49794 . 93326E+00 . 84436E40 0 10.46 .390E-01 . 126.

20 O.OOC 223 . 050 .81315 . 50146 .97325E+00 .88454E4Q 0 10.03 .404E-01 . 124'

20 0.000 229. C50 .81528 . 50498 . 10133E + 01 .92565E400 9.46 .418E-01 .123;

54
Table 2. Densities of the saturated liquid

PROPANE SATURATED LIQUID DENSITIES, EL = ,350

(l)MAAS, <2)VANOERVET, {3)NGASAA, (V)SAGE, (6)REAMER, »7)CLEGG,

(8)FRANCIS, flDSEEMANN, (12 J HELGESON , (13)KL0SEK, (14ISHANAA, (15)JENSEN,

(16)SLIWINSKI, (17)T0MLINS0N, (18)KAHRE, ( 19) RODOSEVICH , (20)HAYNES, (21) DESCHNER,

(22)0RRIT, (23)MCCLUNE, (25)D0USLIN.

TTRP = 85.470, TCRT = 369 .800, OTRP = 16.620, OCRT = 4.960

• 775396679 -.167912979 ,081166807

ID HT T,K X MOL/L CALCD PONT ODS/OT RESIO.

22 1.000 86.650 .99585 16,607 16,593 .08 -.02266 1.12279

22 1.000 90.100 .98372 16.522 16.515 .04 -.02268 .74573

19 1.000 91.010 .98052 16.485 16,494 -.06 -.02268 .62847

23 1.000 93.150 .97299 16.442 16.446 -.02 -.02269 o67268

22 1.000 96.040 .96282 16.385 16.380 .03 -.02271 .70803

23 1.000 98.150 .95540 16.331 16.332 -.01 -.02272 •69012

19 1.000 100.010 . 94886 16.291 16.290 .01 -.02273 .69704

20 1.000 100.075 .94863 16.307 16.289 .11 -.02273 .74003

22 1.000 100.980 .94545 16.272 16.268 .02 -.02274 .70316

23 1.000 103.150 .93782 16,217 16.219 -.01 -.02275 ,69047

20 1.000 105,075 .93105 16.187 16.175 .08 -.02276 .71929

22 1.000 106.170 .92720 16,152 16.150 .01 -.02277 .69921

14 1.000 108.150 .92023 16.096 16.105 -. 06 -.02278 .68132

19 1.000 108.150 .92023 16.105 16.105 -.00 -.02278 .69609

23 1.000 108.150 .92023 16.101 16.105 -.03 -.02278 .68938

20 1.000 110.075 .91346 16.072 16.061 .07 -.02280 .71397

22 1.000 111.520 .90838 16.028 16.028 .00 -.02281 .69769

23 1.000 113.150 .90265 15.985 15.991 -.04 -.02282 .69012

19 1.000 115.000 . 89614 15.946 15.949 -.01 -.02283 .69614

20 1.000 115.075 .89588 15,956 15.947 .06 -.02283 .71040

22 1.000 116.8^0 . 88960 15.906 15.906 .00 -.02285 .70002

23 l.COO 118.150 .88506 15.870 15.877 -.04 -.02286 .69225

20 1.000 120.075 , 87829 15.841 15.833 .05 -.02287 .71028

22 1.000 122.270 .87057 15.782 15.782 .00 -.02289 .70171

23 1.000 123,150 .86748 15.755 15,762 -.05 -.02290 .69413

20 1.000 125,075 ,86071 15,725 15.718 .04 -.02292 .70943

22 1.000 127.660 .85162 15.660 15.659 .01 -.02294 .70451

23 1.000 128.150 . 84989 15,639 15.648 -.06 -.02295 .69577

20 1.000 130.075 .84312 15.609 15.603 .03 -.02297 .70907

22 1.000 133.130 .83238 15.531 15,533 -.01 -.02300 .70438

23 1.000 133.150 .83231 15.524 15.533 -.06 -.02300 .69866

20 1.000 135.075 ,82554 15.491 15.488 .02 -.02302 .70860

23 1.000 138.150 .81472 15.411 15.418 -.04 -.02306 .70322

22 1.000 138.430 .81374 15.408 15.411 -.02 -.02306 .70560

20 1.000 140.075 .80795 15,375 15,373 .01 -.02308 .70993

23 1.000 143.150 .79714 15.296 15,302 -.04 -.02312 • 70547

22 1.000 143.890 .79453 15.282 15,285 -.02 -.02313 .70770

20 1.000 145.075 .79037 15.259 15.258 . 01 -.02315 .71132

23 1.000 148.150 .77955 15.182 15.186 -.03 -.02319 .70872

22 1.000 149.610 .77442 15.148 15.153 -.03 -.02321 .70985

20 1.000 150.075 .77278 15.140 15.142 -.01 -.02322 .71151

23 1.000 153.150 .76197 15.067 15.070 -.02 -.02327 .71202

22 1.000 155.080 .75518 15.025 15.025 -.00 -.02330 .71429

23 1.000 158,150 .74438 14,951 14,954 -.02 -.02336 .71424

22 1.000 160.540 ,73598 14.898 14.898 .00 -.02340 .71710

23 1.000 163.150 .72680 14,834 14.837 -.02 -.02346 . 71664

22 1.000 165.940 .71698 14.772 14.771 .00 -.02351 .71936

23 1.000 168,150 ,70921 14. 718 14.719 -.01 -.02356 ,71929

22 1.000 171.410 .69775 14.659 14.642 .11 -.02364 .72882

23 1.000 173.150 .69163 14.595 14.601 -.04 -.02368 .71907

55
Table 2. Continued

I

I

PROPANE SATURATED LIQUID OENSITIESt EL = .350

ID WT T,K X MOL/L CALCO PONT DOS/DT RESIO . 22 1.000 182.340 .65930 14.385 14.382 .02 -.02393 .72672

22 1.000 187.800 .64010 14.254 14.251 .02 -.02410 .72890

22 1.000 193.300 .62076 14.120 14.118 .02 -.02429 .73100

22 1.000 198.890 .60110 13.986 13.982 .03 -.02451 .73375

20 1.000 200.000 .59719 13.956 13.954 .01 -.02455 .73336

22 1.000 204.540 .58123 13.847 13.843 .03 -.02475 .73620

22 1.000 210.020 .56195 13. 710 13.706 .03 -.02500 .73818

22 1.000 216.020 .54085 13.559 13.555 .03 -.02531 .74035

22 1.000 222.040 .51968 13.405 13.402 .02 -.02566 .74238

22 1.000 227.360 .50097 13.268 13.264 .02 -.02600 .74437

22 1 . oou 232.910 .48145 13.120 13.119 .01 -.02638 .74581

22 1.000 235.610 .47195 13.051 13.048 .02 -.02658 .74735

22 1.000 238.400 .46214 12.975 12.973 .01 -.02680 .74792

20 1.000 240.000 .45651 12.927 12.930 -.02 -.02693 .74724

22 1.000 241.180 .45236 12.903 12.898 .04 -.02703 .74982

22 1.000 243.980 .44251 12.829 12.822 .05 -.02727 .75125

25 1.000 258.150 .39268 12.415 12.426 -.09 -.02868 .75144

25 1.000 263.150 .37509 12.270 12.282 -.09 -.02927 .75310

25 1.000 268.150 .35751 12.126 12.134 -.06 -.02992 .75574

20 1.000 270.000 .35100 12.073 12.078 -.04 -.03017 .75705

25 1.000 273.150 .33992 11.983 11.982 .01 -.03063 .75937

25 1.000 278.150 .32234 11.829 11.827 .02 -.03141 .76112

20 1.000 280.000 .31583 11.762 11.769 -.06 -.03172 .75961

25 1.000 283.150 .30475 11.671 11.668 .03 -.03228 .76283

16 1.000 283.200 .30458 11.663 11.666 -.03 -.03228 •76128

25 1.000 288.150 .28717 11. 507 11.504 .02 -.03323 .76413

20 1.000 288.706 .28521 11.479 11.486 -.06 -.03335 .76201

25 1.000 293.150 .26958 11.338 11.335 .02 -.03430 .76539

16 1.000 293.190 .26944 11.336 11.334 .02 -.03431 .76532

25 1.000 298.150 .25200 11.165 11.161 .04 -.03549 .76696

16 1.000 303.150 .23441 10.983 10.980 .02 -.03683 .76775

25 1.000 303.150 .23441 10.981 10.980 .01 -.03683 .76738

16 1.000 313.120 .19935 10.600 10.598 .03 -.04009 .76999

25 1.000 313 . 150

' .19924 10.586 10.596 -.10 -.04010 .76697

16 1.000 323.120 .16418 10.176 10.176 .00 -.04447 .77124

25 1.000 323.150 .16407 10.169 10.175 -.05 -.04449 .76994

16 1.000 333.110 .12904 9.714 9.702 .12 -.05072 .77554

25 1.000 333.150 .12890 9.697 9.700 -.03 -.05075 .77197

16 1.000 343.080 .09398 9.157 9.152 .05 -.06052 .77511

25 1.000 343.170 .09366 9.142 9.147 -.05 -.06064 .77283

16 1.000 348.080 .07639 8.838 8.832 .07 -.06807 .77615

25 1.000 348.150 .07614 8.825 8.827 -.02 -.06820 .77397

16 1.000 353.090 .05877 8.469 8.465 .05 -.07917 .77593

25 1.000 353.150 .05856 8.459 8.460 -.01 1 -. 07934 .77455

16 1.000 358.100 . 04115 8.022 8.027 -.06 -.09757 .77377

16 1.000 363.110 .02353 7.459 7.455 .05 -.13645 •77648

16 1.000 368.100 .00598 6.488 6.482 .09 -.31941 .77835

16 1.000 369.100 .00246 6.080 6.071 .14 -.56146 .78170

16 1.000 369.600 .00070 5.669 5.674 -.09 - 1.25597 .76992

NP = 99, RMSPCT = .046

56
i

t

I Table 3. Densities of the saturated vapor.

i

PROPANE SATURATED VAPOR DENSITIES, EG = .350

(1) VIRIAL/V.P.EQNS. » (41SAGE, <6IREAMER, (7)CLEGG, (12) HELGESON, (16) SLIHINSKI,

(2D0ESCHNER, (25)00USLIN.

|TTRP = 85.470, TCRT = 369.800, OGAT = .4221626E-09, DCRT = 4.960

j

j .072453281 .170534468 -.278060163 .438982342 -.841080253 .405105441

ID NT T,K U X MOL/L CALCD PCT DDS/OT RESIO.

1 .122 90.000 .93454 .98407 .20201E-08 .202822-08 -.40 .6672-09 -.01309

1 .135 100.000 .81102 .94890 .38478E-07 .387342-07 -.66 .1022-07 -.01332

1 .149 110.000 .70997 .91373 .42353E-06 .425652-06 -.50 .9242-07 -. 00 987

1 .162 120.000 .625^ .87856 .30778E-05 .308462-05 -.22 .5572-06 -.00409

' 1 .176 130.000 .55449 .84339 .16207E-04 .162022-04 .03 .2472-05 .00312

1 1 .189 140.000 .49342 .80822 .66138E-04 .660102-04 .20 .8552-05 .01112

i 1 .203 150.000 .44048 .77305 .21987E-03 .219292-03 .26 .2442-04 .01946

1 1 .216 160.000 .39416 .73788 .61850E-03 .616992-03 .25 .5932-04 .02782

1 .230 170.000 .35330 .70270 .15165E-02 .151392-02 .17 .1272-03 .03595

1 .243 180.000 .31697 .66753 .33180E-02 .331542-02 .08 .2432-03 .04368

1 .257 190.000 .28446 .63236 .66013E-02 .660242-02 -.02 .4272-03 .05089

1 .270 200.000 .25521 .59719 .12128E-01 .121392-01 -.09 .6962-03 .05748

1 .284 210.000 .22874 .56202 .20840E-01 .208682-01 -.14 .1072-02 .06342

1 .297 220.000 .20468 .52685 .33846E-01 .338962-01 -.15 .1562-02 . 06868

1 .311 230.000 .18271 .49168 .52415E-01 .524862-01 -.14 .2182-02 .07325

1 .324 240.000 .16258 .45651 .77981E-01 .780662-01 -.11 .2962-02 .07716

1 .338 250.000 .14405 .42134 .11217EtOO .112252+00 -.08 .3912-02 .08041

1 .352 260.000 .12695 .38617 .156832^00 .156912+00 -.05 .5062-02 .08305

1 .365 270.000 .11111 .35100 .21419E«00 .214222+00 -.01 .6452-02 .08508

1 .379 280.000 .09641 .31583 .286962-^00 .286862+00 .04 .8132-02 .08653

16 1.000 283.200 .09192 .30458 .3140 8E-i-00 .313852+00 .07 .8742-02 .08687

16 1.000 293.190 .07855 .26944 .41159E1-00 .411762+00 -.04 .1092-01 .08784

16 1.000 303.150 .06609 .23441 .53473E+00 .533632+00 .21 .1362-01 .08798

16 1.000 313.120 .05441 .19935 .68553E-«-00 .686002+00 -.07 .1712-01 .08830

16 1.000 323.120 .04343 .16418 .879872+00 .878282+00 .18 .2162-01 .08770

25 1.000 323.150 .04339 .16407 .87580E+00 .878932+00 -.36 .2162-01 .08829

16 1.000 333.110 .03311 .12904 .11252E+01 .112392+01 .12 .2802-01 .08712

25 1.000 333.150 .03307 .12890 .11219E+01 .112512+01 -.28 .2802-01 .08756

16 1.000 343.080 .02341 .09398 .145272+01 .144802+01 .32 .3792-01 .08582

25 1.000 343.170 .02333 .09366 .14489E+01 .145142+01 -.17 .3802-01 .08639

16 1.000 348.080 .01876 .07639 .165632+01 .165542+01 .05 .4552-01 .08539

25 1.000 348.150 .01869 .07614 .16565E+01 .165862+01 -.13 .4572-01 .08561

16 1.000 353.090 .01423 .05877 .19140E+01 .190972+01 .22 .5682-01 .08420

25 1.000 353.150 .01417 .05856 .191072+01 .191312+01 -.13 .5702-01 .08464

16 1.000 358.100 .00982 .04115 .224502+01 .223642+01 .38 .7542-01 .08259

16 1.000 363.110 .00554 .02353 .269472+01 .269742+01 -.10 .1142+00 . 08121

16 1.000 365.600 .00345 .01477 . 302152+01 .303032+01 -.29 .1582+00 .08000

16 1.000 368.100 .00139 .00598 .353672+01 .355052+01 -.39 .2892+00 .07791

16 1.000 369.100 .00057 .00246 .392662+01 .392482+01 .04 .5132+00 .07506

16 1.000 369.600 .00016 .00070 .431772+01 .428832+01 .69 .1162+01 .07023

NP = 40, RMSPCT = .252

57
PROPANE SATURATED VAPOR DENSITIESt EG 350

10 WT T,K U X MOL/L CALCO PCT DDS/DT RESIO.

« 0.000 293.928 .07759 .26684 .43306E+00 .41990 Ei^OO 3.14 .lllE-01 .08439

4 0.000 301.094 .06859 .24164 .52372E+00 .50622E«'00 3.46 .130E-01 .0 8439

4 0.000 307.483 . 06092 .21917 .61340E4^00 .59568E^00 2.98 .150E-01 . 08503

4 0.000 313.317 .05419 .19865 .70507E+00 .68937E+00 2.26 .171E-01 .08575

4 O.OGO 318.594 .04831 .18009 .80100E-*-00 .78563E+00 1.96 .194E-01 . 08596 4 0.000 323.371 .04316 .16329 .89692E+00 .88372E«^00 1.49 .217E-01 .08625

4 0.000 327.928 .03838 .14727 .99576E+00 . 93864E>00 .72 .244E-01 .08683

4 0.000 332.094 . 03413 .13261 . 11082E+01 .10959E+01 1.12 .272E-01 . 08607

4 0.000 336.094 .03015 .11855 .12218E4’01 .12110E^01 .89 .304E-01 .06597

4 0.000 339.872 .02647 .10526 .13434E+01 .13327E+01 .80 .341E-01 .06566

4 0.000 343.483 .02303 .09256 .14766E+01 .14634E+01 .90 .384E-01 . 08506 4 0.000 346.928 .01982 . 08044 .16202E-^01 .16042E4^01 1.00 .435E-01 .08446

4 0.000 350.094 . 01692 .06931 .17815E+01 .17510E+01 1.74 .495E-01 .08296

4 0.000 353.094 .01422 .05876 .19572E+01 .19099E«^01 2.47 .568E-01 .08131

4 0.000 355.872 .01176 .04899 .21469E+01 .20796E+01 3.24 .658E-01 .07946

4 0.000 358.594 .00939 .03941 .23512E+01 .22743E+01 3.38 .780E-01 . 07820 4 0.000 361.261 .U0711 . 03003 .25910E+01 .25043E+01 3.46 .957E-01 .07670

4 0.000 363.761 .00499 .02124 .28357E+01 .27746E*01 2.20 .123E+00 .07696

4 0.000 366.261 .00290 .01245 .30889E+01 .31411E*01 -1.66 .178E4^00 .08226

4 c.ooc 368.761 .00085 .00365 .34895E+01 .37726E+01 -7.50 .397E+00 .09905

6 0.000 313.480 .05401 .19808 .69556E4-00 .69218E+00 .49 .172E-01 .08766

6 0.000 324.480 . 04198 .15939 . 88590E-^00 .90817E>00 -2.45 .223E-01 .09056

6 0.000 332.040 .03418 .13280 .10997E+01 .10944E4^01 .48 .272E-01 .08679

6 0.000 339.590 .02674 .10625 .13511E+01 .13231E+01 2.11 .338E-01 .08420

6 0.000 346.430 .02028 .08219 .15827E+01 .15827E+01 -.00 .427E-01 .08577

6 0.000 352.710 .01457 .06011 .18713E+01 .18883E+01 -.90 .557E-01 . 06576

6 0.000 358.260 .00968 . 04059 .22167E+01 .22486E4-01 -1.42 .763E-01 .08511

6 0.000 363.590 .00513 . 02184 .26643E+01 .27533E+01 -3.25 .121E+00 .08636

6 0.000 368.370 .00117 .00503 .34203E^01 .36329E+01 -5.85 .323E+00 .09265

7 0.000 323.150 .04339 .16407 .85900E+00 .87893E+00 -2.27 .216E-01 .09043

7 0.000 333.150 .03307 .12890 .11250E+01 .11251E+01 -.00 .280E-01 .08725

7 0.000 343.150 .02335 .09373 .14600E+01 .14507E+01 .64 .380E-01 .08543

7 0.000 348.150 .01869 .07614 .16700E+01 .16586E+01 .66 .457E-01 . 08461

7 0.000 353.150 .01417 . 05856 .19200E+01 .19131E+01 .36 .570E-01 .08401

7 0.000 358.150 .00978 .04097 .22400E+01 .22402E+01 -.01 .757E-01 . 06313

7 0.000 363.150 .00550 .02339 .27Q00E+01 . 27020E+01 -.07 .115E+00 .08115

7 0.000 368.150 .00135 .00580 .35200E+01 .35651E+01 -1.27 .295E+00 . 08010 12 0.000 277.594 .09985 .32429 .26657E+00 .26782E+00 -.47 .770E-02 .06680

12 0.000 283.150 .09199 .30475 .31213E+00 .31341E^00 -.41 .873E-02 . 08741 12 0.000 288.706 . 08444 .28521 .36387E+00 .36510E4-00 -.34 .989E-02 . 08786 12 0.000 294.261 . 07717 .26567 .42258E+00 .42361E+00 -.24 .112E-01 . 08813 12 0.000 299.817 .07017 .24613 .48903E+00 .48981E+00 -.16 .127E-01 .06829

12 0.000 305.372 .06342 .22660 .56432E+00 .56470E+00 -.07 .143E-01 . 08831 12 0.000 310.928 . 05692 .20706 .64959E+00 .64950E+00 .01 .162E-01 .08826

12 0.000 316.483 .05064 .18752 .74621E+00 .74570E+00 .07 .185E-01 . 08806 12 0.000 322.039 .04458 .16798 .85592E+00 .85523E+00 .08 .210E-01 .08786

12 0.000 327.594 .03873 .14844 .98123E+00 .98053E4-00 .07 .242E-01 .08757

12 0.000 333.150 .03307 .12890 .11246E+01 .11251E+01 -.04 .280E-01 . 08729 12 0.000 338.706 , 02760 .10936 .12909E+01 .12936E+01 -.21 .329E-01 .08696

12 0.000 344.261 .02230 .08932 .14851E+01 .14937E+01 -.57 .395E-01 . 08673 12 0.000 349.817 .01717 . 07028 .17175E+01 .17374E+01 -1.14 .489E-01 .08659

12 0.000 355.372 .01220 .05074 . 20058E4-01 .20472E+01 -2.02 .640E-01 . 08666 12 0.000 360.928 .00739 .03120 .23993E+01 .24729E+01 -2.97 .931E-01 .08669

21 0.000 303.150 .06609 .23441 . 45354E+00 .53363E+00 -15.01 .136E-01 .10616

21 0.000 308.150 . 06014 .21683 .56013E+00 .60577E+00 -7.53 .153E-01 .09686 21 O.OGO 313.150 .05438 .19924 .65764E+00 .68652E^00 -4.21 .171E-01 .09296 21 0.000 318.150 .04880 .18166 .77102E+00 .77706E+00 -.78 .192E-01 . 08896 21 0.000 323.150 . 04339 .16407 . 89575E+00 .87893E+00 1.91 .216E-01 . 08581 21 0.000 328.150 .03815 .14648 .10386E+01 .99406E+00 4.48 .245E-01 . 08273 21 0.000 333.150 .03307 .12890 .11792E+01 .11251E+01 4.81 .280E-01 .08196

21 0.000 338.150 .02814 . 11131 .13153E+01 .12755E+01 3.12 .323E-01 .08326

21 0.000 343.150 .02335 .09373 .14853E+01 .14507E+01 2.39 .380E-01 . 08340 21 0.000 348 .150 .01869 .07614 .16441E+01 .16586E+01 -.88 .457E-01 . 08653 21 0.000 353.150 .01417 . 05856 .18367E+01 .19131E+01 -1.38 .570E-01 . 08626 21 0.000 358.150 .00978 .04097 .22224E+01 .22402E+01 -.79 .757E-01 .08429

21 0.000 363.150 .00550 .02339 .26759E4-01 .27020E+01 -.97 .115E+00 . 08263 21 0.000 368.150 .00135 .00580 . 35830E+01 .35651E+01 .50 .295E+00 . 07558

58
Table 4. Second vin'al coefficients of propane

PROPANE SECOND VIRIAL COEFF., M = 3, E = 0.0

(l)MCSLASHAN, (2>KAPALLO, ( 3) OYMONO/SMITH, (4)STREIN, I5)HAHN,

I7)GUNN, (8)BREWER, <9)BEATTIE, (10 ) BOTTOMLEY , (ll)CHERNEY,

(12»0ESCHNER, (13)JESSEN, ( 14) KRETSCHNER, (15)REAMER, ( 16) SAGE

TCRT = 369.80. DCRT = .00496 MOL/CC

.4540611 -1.1899134 -.4726952

10 MT T,K X B* CALC DIF PCT

5 .458 211.300 .5714 -4. 1862 -4.1623 -.0239 -.58

5 .552 231.200 .6252 -3.3728 -3.3835 .0107 .32

2 .597 244.000 .6598 -3.0256 -2.9949 -.0307 -1.03

8 .610 248.150 .6710 -2.8718 -2.8835 .0117 .41

5 .620 251.500 .6801 -2.8123 -2.7982 -.0141 -.50

3 .643 260.000 .7031 -2.6090 -2.5984 -.0105 -.41

3 .667 270.000 .7301 -2.3709 -2.3902 .0193 .81

2 .673 273.000 .7362 -2.3659 -2.3327 -.0333 -1.43

8 .673 273.150 .7386 -2.3213 -2.3298 .0086 .37

13 .673 273.160 .7387 -2.3312 -2.3296 -.0016 -.07

5 .675 273.800 .7404 -2.3362 -2.3177 -.0185 -.80

3 .697 285.000 .7707 -2.1030 -2.1225 .0195 .92

16 0.000 294.270 .7958 -2.0711 -1.9794 -.0917 -4.63

10 .715 295.210 .7983 -2.0232 -1.9657 -.0575 -2.93

1 .715 295.400 .7988 -1.9790 -1.9629 -.0161 -.82

4 .716 296.100 .8007 -1.9642 -1.9528 -.0113 -.58

2 .717 297. COO .8031 -1.9542 -1.9400 -.0 143 -.74

8 .719 298.150 .6062 -1.92.45 -1.9237 -.0007 -.04

3 .722 300.000 .8112 -1.3848 -1.8981 .0133 .70

12 0.000 303.160 .8198 -1.6949 -1.8554 -.0395 -2.13

12 0.000 303.160 .8196 -1.9046 -1.8554 -.0493 -2.66

14 0.000 303.160 .8196 -1.9592 -1.8554 -.1038 -5.60

1 .732 306.500 .8288 -1.8302 -1.8118 -.0184 -1.02

4 .734 308.000 .8329 -1.7881 -1.7928 .0047 .26

7 .738 310.900 .8407 -1.6656 -1.7567 .0912 5.19

15 .738 310.940 .840 6 -1.6640 -1.7563 .0922 5.25

15 .738 310.940 .8406 -1.6368 -1.7563 .1195 6.80

16 0.000 310.940 .8408 -1.8937 -1.7563 -.1375 -7.83

3 .744 315.000 .8516 -1.6914 -1.7077 .0163 .95

1 .747 317.600 .8588 -1.6814 -1.6776 -.0038 -.23

2 .751 321.000 .8680 -1.6864 -1.6395 -.0469 -2.86

11 .754 323.160 .8739 -1.6349 -1.6159 -.0190 -1.18

13 .754 323.160 .8739 -1.6120 -1.6159 .0039 .24

1 .759 327.600 .8659 -1.6070 -1.5690 -.0380 -2.42

15 .759 327.600 .8859 -1.5150 -1.5690 .0541 3.45

15 .759 327.600 .8859 -1.5176 -1.5690 .0513 3.27

16 0.000 327.600 .3859 -1.7531 -1.5690 -.1341 -11.73

3 .762 330.000 .8924 -1.5376 -1.5445 .0069 .45

4 .765 332.900 .9002 -1.5326 -1.5157 -.0169 -1.12

1 .770 337.800 .9135 -1.4830 -1.4687 -.0143 -.97

15 .777 344.270 .9310 -1.3895 -1.4099 .0204 1.45

15 .777 344.270 .9310 -1.3918 -1.4099 .0182 1.29

16 0.000 344.270 .9310 -1.5709 -1.4099 -.1609 -11 .41

7 .777 344.300 .9310 -1.3908 -1.4097 .0189 1.34

1 .781 347.900 .9408 -1.3590 -1.3785 .0194 1.41

12 0.000 343.160 .9415 -1.4341 -1.3762 -.0578 -4.20

12 0.000 343.160 .9415 -1.4533 -1.3762 -.0770 -5.60

3 .783 350.000 .9465 -1.3640 -1.3607 -. 0033 -.24

59
Table 4. Continued

PROPANE SECOND VIRIAL COEFF .* N = 3 « E = 0.0

ID NT T,K X 8

* CALC DIF PCT

4 .786 353.800 .9567 - 1.3452 - 1.3294 -.0157 - 1.18

1 .790 357.900 .9678 - 1.3144 - 1.2968 -.0176 - 1.35

15 .793 360.940 .9760 - 1.2701 - 1.2734 .0034 .26

15 .793 360.940 .9760 - 1.2737 - 1.2734 -.0003 -.02

16 0.000 360.940 .9760 - 1.4074 - 1.2734 -.1339 - 10.52

1 .799 368.200 .9957 - 1.2102 - 1.2199 .0097 .79

9 .800 369.970 1.0005 - 1.2181 - 1.2073 -.0107 -.89

9 .800 369.970 1.0005 - 1.2896 - 1.2073 -.0823 - 6.81

9 .803 373.160 1.0091 - 1.1994 - 1.1852 -.0142 - 1.20

9 .803 373.160 1.0091 - 1.2251 - 1.1852 -.0399 - 3.37

11 .803 373.160 1.0091 - 1.1911 - 1.1852 -.0060 -.50

12 0.000 373.160 1.0091 - 1.2201 - 1.1852 -.0349 - 2.94

12 0.000 373.160 1.0091 - 1.2698 - 1.1852 -.0846 - 7.14

4 .803 373.400 1.0097 - 1.2008 -1.1835 -.0173 - 1.46

3 .804 375.000 1.0141 - 1.1755 - 1.1727 -.0029 -.24

7 .806 377.600 1.0211 - 1.1701 - 1.1553 -.0148 - 1.28

15 .806 377.600 1.0211 - 1.1654 - 1.1553 -.0101 -.87

15 .806 377.600 1.0211 - 1.1636 - 1.1553 -.0083 -.72

16 0.000 377.600 1.0211 - 1.2634 - 1.1553 -.1081 - 9.36

1 .806 377.700 1.0214 - 1.1358 - 1.1546 .0188 1.63

12 0.000 380.960 1.0302 - 1.1169 - 1.1334 .0165 1.45

1 .814 388.500 1.0506 - 1.0565 - 1.0862 .0298 2.74

4 .818 394.000 1.0654 - 1.0600 - 1.0536 -.0064 -.60

9 .820 398.160 1.0767 - 1.0330 - 1.0298 -.0032 -.31

9 .820 398.160 1.0767 - 1.0466 - 1.0298 -.0168 - 1.63

11 .820 398.160 1.0767 - 1.0278 - 1.0298 .0020 .20

12 0.000 398.160 1.0767 - 1.0406 - 1.0298 -.0107 - 1.04

12 0.000 398.160 1.0767 - 1.1110 - 1.0298 -.0812 - 7.89

3 .822 400.000 1.0817 - 1.0218 - 1.0195 -.0022 -.22

1 .822 400.100 1.0819 -.9970 - 1.0190 .0220 2.16

15 .828 410.940 1.1112 -.9874 -.9612 -.0262 - 2.73

15 .828 410.940 1.1112 -.9900 -.9612 -.0288 - 3.00

4 .830 413.300 1.1190 -.9479 -.9467 -.0012 -.12

9 .835 423.160 1.1443 -.9001 -.9013 .0011 .13

9 .835 423.160 1.1443 -.9077 -.9013 -.0064 -.71

12 0.000 423.160 1.1443 -.9293 -.9013 -.0280 - 3.11

12 0.000 423.160 1.1443 -.9771 -.9013 -.0758 - 8.41

3 .839 430.000 1.1628 -.8730 -.8699 -.0030 -.35

4 .841 433.100 1.1712 -.8561 -.8562 .0001 .01

15 .846 444.270 1.2014 -.8329 -.8090 -.0239 - 2.96

15 .846 444.270 1.2014 -.8353 -.8090 -.0263 - 3.25

7 .846 444.300 1.2015 -.8283 -.8089 -.0194 - 2.40

9 .848 448.160 1.2119 -.7901 -.7934 .0032 .41

9 .848 448.160 1.2119 -.7936 -.7934 -.0002 -.03

4 .850 453.500 1.2263 -.7748 -.7725 -.0022 -.29

3 .858 470.000 1.2710 -.7093 -.7124 .0031 .44

9 .859 473.160 1.2795 -.6946 -.7016 .0070 1.00

9 .859 473.160 1.2795 -.6894 -.7016 .0121 1.73

12 0.000 473.160 1.2795 -.7313 -.7016 -.0297 - 4.24

12 0.000 473.160 1.2795 -.7688 -.7016 -.0672 - 9.58

4 .859 474.900 1.2842 -.6944 -.6957 .0013 .19

15 .861 477.600 1.2915 -.7013 -.6867 -.0146 - 2.13

15 .861 477.600 1.2915 -.7043 -.6867 -.0176 - 2.57

4 .866 493.300 1.3340 -.6354 -.6371 .0017 .27

9 .868 498.160 1.3471 -.6074 -.6226 .0153 2.45

9 .868 498.160 1.3471 -.6002 -.6226 .0225 3.61

3 .869 500.000 1.3521 -.6101 -.6172 . 0072 1.16

60
Table 4. Continued

PROPANE SECOND VIRIAL COEFF., N = 3* E = 0.0

ID NT T,K X CALC DIF PCT

7 .872 510.900 1.3816 -.5813 -.5865 .0052 .86

15 .873 510.940 1.3817 -.5862 -.5664 .0001 .03

15 .673 510.940 1.3817 -.5902 -.5864 -.0039 -.66

9 .876 523.160 1.4147 -.5435 -.5540 .0105 1.90

9 .876 523.160 1.4147 -.5406 -.5540 .0133 2.41

12 0.000 526.380 1.4234 -.5491 -.5458 -.0033 -.60

12 0.000 526.380 1.4234 -.5357 -.5458 .0101 1.85

9 .684 548.160 1.4823 -.4638 -.4938 .0100 2.02

9 .884 548.160 1.4823 -.4762 -.4938 .0176 3.57

3 .684 550.000 1.4873 -.4811 -.4897 . 0086 1.75

12 0.000 570.460 1.5426 -.4558 -.4461 -.0097 -2.18

12 0.000 570.460 1.5426 -.4414 -.4461 .0046 1.04

12 0.000 609.320 1.6477 -.4225 -.3738 -.0488 -13.05

NP = 116, HEANOIF = 0174, RHSPCT 1.99
Table 5. Third virial coefficients of propane

PROPANE THIRD VIRIAL COEFF,, M = 5, E = 1.0

(9)BEATTIE, (ll)CHERNEY. (12) DESCHNER. (15)REAMER. (16)SAGE.

TCRT = 369.80. OCRT = .00496 MOL/CC

343.3750000 .2140090 4.8363002

10 MT T.K X C* CALC OIF

16 0.000 294.270 .7958 -.2586 -2.5742 2.3156

12 .291 303.160 .8198 -1.5440 -1.7673 .2233

15 .446 310.940 .8408 -1.3314 -1.2269 -.1046

15 . 446 310.940 .8408 -1.5991 -1.2269 -.3722

16 0.000 310.940 .840 8 .0212 -1.2269 1.2481

11 .593 323.160 .8739 -.5528 -.6089 .0562

15 .629 327.600 .8859 -.5789 -.4385 -.1404

15 .629 327.600 .8859 -.3444 -.4385 .0940

16 0.000 327.600 .8859 1.4690 -.4385 1.9074

15 .722 344.270 .9310 -.0424 .0186 -. 0610

15 .722 344.270 .9310 .0492 .0186 . 0306

16 0.000 344.270 .9310 1.0468 .0186 1.0282

12 .738 348.160 .9415 .7376 .0930 .6446

15 .778 360.940 .9760 .1824 .2764 -.0940

15 .778 360.940 .9760 .3198 .2764 .0435

16 0.000 360.940 .9760 .6957 .2764 .4194

9 .800 369.970 1.0005 .4785 .3622 .1163

9 .807 373.160 1.0091 .3909 .3859 .0050

11 .807 373.160 1.0091 .4704 .3859 .08<*5 12 .807 373.160 1.0091 .4738 .3859 .0879

15 .816 377.600 1.0211 .3058 .4139 -.1081

15 .816 377.600 1.0211 . 2214 .4139 -.1925

16 0.000 377.600 1.0211 .3572 .4139 -.0567

12 .822 380.960 1. 0302 .4500 .4317 .0182

9 .848 398.160 1.0767 .3826 .4872 -.1047

11 .848 398.160 1.0767 .4163 .4872 -.0710

12 .848 398.160 1.0767 .4222 .4872 -.0651

15 .862 410.940 1.1112 .4920 .5009 -.0089

15 .862 410.940 1.1112 .6150 .5009 .1141

9 .874 423.160 1.1443 .3680 .5000 -.1320

12 .874 423.160 1.1443 .4133 .5000 -.0867

15 .890 444.270 1.2014 .4721 .4793 -.0072

15 .890 444.270 1.2014 .5658 .4793 .0865

9 .893 448.160 1.2119 .3594 .4739 -.1144

9 .906 473.160 1.2795 . 3535 .4327 -.0792

12 .906 473.160 1.2795 .3796 .4327 -.0531

15 .908 477.600 1.2915 .4458 .4248 .0209

15 .908 477.600 1.2915 .5166 .4248 .0918

9 .917 498.160 1.3471 . 3220 .3881 -.0661

15 .922 510.940 1.3817 .4026 .3658 .0368

15 .922 510.940 1.3817 .5658 .3658 .2000

9 .926 523.160 1.4147 .3144 .3453 -.0309

12 .927 526.380 1.4234 .3405 .3400 . 0005

9 .932 548.160 1.4823 .3107 .3064 .0043

12 .938 570.460 1.5426 .3085 .2756 . 0329

12 .945 609.320 1.6477 .2306 .2305 . 0001

NP = 46, MEANDIF = .0887, RMSPCT = 0.00

62
TABLE

6.

Summary

of

P-p-T

data

(—1 CN

pH o O Ln 00 00 CN CO <] o• o• • NO CN O o • • • cn drti o o o o 1

1 O 1—

1

<T

CN

<r

ON

CN

6^

CN CN on CN 00 NO vO

T3 O CN r-- on on rH o o on —. • • • • • • • t3 o O o (—

t

o o o o o a

CNI 00 m

CN

NOO

ro

LO

CN O CN

CNCN

NO

ro

ro

00

t—

1

o CN o o 00 LO

1—1 rH On LO CO CN on on rH NO 1—1 o

1 1 1 1

1 1

1 1

t—i

1 a^ o

I O

1 1 1 1

• • « • vO o on rH 1

1 r-H o CN o CM rH CN r-H

O

r'' o

CJN CN

00 00 <JN rH 00 ONj cn o rH CON CN CN rH m

1

LO

1

NO

1

un

1

CO

1

on

1

on

1

1

1 on

1 o1 CO

1

r-H

i CO1 1 NO1 cn o rH CN NO

Cs) on CO on CO O'nI 1—

1

CN

oro

o O to o NO O 00

• • • • • • • • o o C3N on CN CN on

1—

1

rH 1

1 1—1 1—t

CN on CN o o o o o on LO on CD rH o CD CD CD rH

1—

1

1

r NO

'w' 00 1—1 NO r—1

1—I r—

n

I

1 1—1 o 1 1 CO • NO CN 1—

1

I—

1

1—

1

1—

1

u CO 1—

t

1——

1

LO 1—

I

d

j o w 1 1 d 1 1 o

cu CIJ >N CO CN u

•u 1—

1

d -rH d d 0) d CN cd d cd o 4J jd QJ d •H e

<! •rl CO 4-) o e u t—

1

4-) U IS cd CO cO 0) e

4J •H cc) OJ cu CU 42 o rH •H > O PQ O CD H P

CN CO fO <r

CN

NO

(N

63
Table 7. Coefficients of the equation of state

EQUATION OF STATE, COEFFICIENTS

DGAT = .«»22162614E-09

OTRP = 16.6200, TTRP = 85.470, PTRP = .300000000E-08

OCRT = 4.9600, TCRT = 369.800, PCRT = 42.420436922

AL = 1.00, BE = 0.00000, GA = .060, OE = .750, ER = 2.00

.22566372605 1.04646227554 >.44491000068 .12708270211

>.59883339489

MOL/L TSAT THETA PSAT B E .5 300.614 284.253 10.153 .3268 >1.02265

1.0 328.391 315.776 19.216 .4196 >.85973

1.5 344.421 335.538 26.566 .5050 >.70878

2.0 354.619 348.865 32.218 .5836 >.56973

2.5 361.216 357.840 36.342 .6564 >.44259

3.0 365.406 363.674 39.186 .7240 >.32750

3.5 367.919 367.198 40.995 .7872 >.22479

4.0 369.237 369.031 41.984 .8469 >.13487

4.5 369.734 369.711 42.368 .9038 >.05827

5.0 369.800 369.800 42.420 .95 86 .00450

5.5 369.710 369.673 42.349 1.0123 .05306

6.0 369.219 368.957 41.970 1.0655 .08727

6.5 368.044 367.197 41.087 1.1190 .10741

7.0 365.956 364.002 39.575 1.1736 .11428

7.5 362.776 359.046 37.379 1.2301 .10934

8.0 358.370 352.075 34.514 1.2893 .09466

8.5 352.642 342.910 31.057 1.3520 .07293

9.0 345.526 331.449 27.140 1.4189 .04721

9.5 336.982 317.665 22.937 1.4908 .02070

10.0 326.984 301.615 18.651 1.5685 >.00364

10.5 315.525 283.434 14.494 1.6527 >.02344

11.0 302.614 263.343 10.671 1.7444 >.03719

11.5 288.278 241.644 7.355 1.8442 >.04442

12.0 272.569 218.720 4.669 1.9529 >.04563

12.5 255.571 195.018 2.669 2.0713 >.04209

13.0 237.398 171.039 1.330 2.2002 >.03552

13.5 218.199 147.306 .551 2.3404 >.02765

14.0 198.142 124.332 .178 2.4926 -.01992

14.5 177.407 102.590 .040 2.6576 >.01329

15.0 156.167 82.476 .005 2.8363 >.00821

15.5 134.574 64.295 .000 3.0293 >.00469

16.0 112.747 48.247 .000 3.2375 >.00246

16.5 90.764 34.426 .000 3.4617 >.00119

17.0 68.662 22.833 .000 3.7026 >.00053

64
TABLE 8. Calculated P(p) critical isotherm

The following page gives a high-resolution examination of the critical

I isotherm of propane as computed by equation of state (6). Column headings

II

1

I have the following interpretations

D/DC

TS/TC

PS/PC

P/PC

DP /DR

d/d^, density reduced at the critical point.

T^(p)/T^, reduced coexistence temperature.

P_(p)/P , reduced coexistence pressure,

o c P/P^, pressure reduced at the critical point.

8P/9p slope of the critical isothem, bar .

j The last five columns give the density-dependence of functions used in the

I

I equation of state, where R = p = d/d^ is density reduced at the liquid triple

' point

DTS/DR E dT^(p)/dp, K.

DTH/DR E d0(p)/dp, K.

DPS /DR E dP^(p)/dp, bar.

DXB/DR E 9$(p,T)/9p.

DXC/DR E 94'(p,T)/9p.

^ • Note: p E d/d^, density reduced at the liquid triple-point.

65
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6&
TABLE 9. Comparisons with P-p-T data

The following pages compare experimental P-p-T (compressibility) data

with densities and pressures computed by the equation of state (6) . The

first column identifies sources of the data (as in table 6)

:

12. Authors Reference

1 Virial equation This report

2 Dawson and McKetta [16]

3 Beattie, Kay and Kaminsky [2]

4 Deschner and Brown [18]

5 Reamer, Sage and Lacey [50]

13 Cherney, Marchman and York [10]

17 Tomlinson [65]

24 Ely and Kabayashi [22]

26 Dittmar, Schulz and Strese [19]

67
Table 9. Comparisons with P-p-T data

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN.t (2)0AHS0N« (3>BEATTIE«

(4)0ESCHNERt I5)REAMER. I13)CHERNEY, ( 17) TOHL INSON , I24)ELY, (26)D1TTHAR.

10 T,K MOL/L CALCO 0,PCT P,BAR CALCO P,OIF

1 290.000 .3000 .2998 .06 6.339 6.343 -.003

1 300.000 . 3000 .2998 .05 6.624 6.627 -.003

1 310.000 .3000 .2999 .04 6.906 6.908 -.003

1 320.000 . 3000 .2999 .03 7.185 7.187 -.002

1 330.000 .3000 .2999 .02 7.462 7.464 -.001

1 340.000 . 3000 .3000 .01 7.738 7.739 -.001

1 350.000 .3000 .3000 .01 8.012 8.012 -.001

1 360.000 .300 0 .3000 .00 8.284 8.284 -.000

1 370.000 .3000 .3000 .00 8.555 8.555 -.000

1 380.000 .3000 .3000 .00 8.825 8.825 -.000

1 390.000 .3000 .3000 0.00 9.094 9. 094 .000

1 400.000 .3000 .3000 .00 9.362 9.362 -.000

1 410.000 .3000 .3000 .00 9.629 9.629 -.000

1 420.000 .3000 .3000 .00 9.895 9.896 -.000

1 430.000 .3000 .3000 .00 10.161 10.161 -.000

1 440.000 .3000 .3000 .01 10.426 10.427 -.000

1 450.000 .3000 .3000 .01 10.691 10.691 -.001

1 460.000 .3000 .3000 .01 10.955 10.955 -.001

1 470.000 .3000 .3000 .01 11.218 11.219 -.001

1 480.000 .3000 .3000 .01 11.481 11.482 -.001

1 490.000 .3000 .3000 .01 11.744 11.745 -.001

1 500.000 .3000 .3000 .01 12.006 12. 007 -.002

1 510.000 .3000 .3000 .01 12.268 12.269 -.002

1 520.000 .3000 .3000 .01 12.529 12.531 -.002

1 530.000 .3000 .3000 .01 12.791 12.792 -.002

1 540.000 .3000 .3000 .02 13.052 13.054 -.002

1 550.000 . 3000 .3000 .01 13.312 13. 314 -.002

1 560.000 . 3000 .3000 .01 13.573 13.575 -.002

1 570.000 .3000 .3000 .01 13.833 13.835 -.002

1 580.000 .3000 .3000 .01 14.093 14.095 -.002

1 590.000 .3000 .3000 .01 14.353 14.355 -.002

1 600.000 .3000 .3000 .01 14.613 14.614 -.002

1 610.000 .3000 .3000 .01 14.872 14. 874 -.001

1 620.000 .300 0 . 3000 .01 15.132 15.133 -.001

1 630.000 .3000 .3000 .01 15.391 15.392 -.001

1 640.000 . 300 0 .3000 .00 15.650 15.651 -.001

1 650.000 .3000 .3000 .00 15.909 15.909 -.000

1 660.000 .3000 .3000 -.00 16.168 16.168 .000

1 670.000 .3000 .3000 -.00 16.427 16.426 .000

1 680.000 . 3000 .3000 -.01 16.685 16.684 .001

1 690.000 .3000 .3000 -.01 16.944 16.942 .001

1 700.000 .3000 .3000 -.01 17.202 17.200 .002

NP = 42, ONRMSPCT = .017, PMEANDIF = .001
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. CDVIRIAL EQN.» I2)0AWS0N« C3)BEATTIE«

I4)0ESCHNER, (5)REAMERt (13)CHERNEY, (17) TOMLINSONt (24)ELY* (26)0ITTMAR

ID t,k MOL/L CALCO 0,PCT P,BAR CALCO P,OIF

2 243.150 .0451 .0452 -.22 .887 .885 .002

2 243.150 .0596 .0597 -.14 1.161 1.159 .002

2 258.150 .0595 .0596 -.17 1.237 1.235 .002

2 258.150 . 0451 .0452 -.19 .945 .943 .002

2 273.150 .0707 .0708 -.20 1.552 1.549 .003

2 273.150 .0451 .0452 -.25 1.003 1.001 .002

2 273.150 .0596 .0597 -.19 1.316 1.313 .002

2 288.150 .0593 .0594 -.18 1.386 1.383 .002

2 288.150 .0206 .0207 -.28 .490 .489 .001

2 288.150 .0451 .0452 -.21 1.060 1.058 .002

2 288.150 .0707 .0708 -.21 1.643 1.640 .003

2 288.150 .0370 .0371 -.31 .874 .872 .003

2 323.150 .0370 . 0371 -.21 .983 .981 .002

2 323.150 .0700 .0702 -.21 1.838 1.835 .004

2 323.150 .0207 .0207 -.12 .551 .551 .001

2 323.150 .0451 .0452 -.24 1.193 1.190 .003

2 348.150 . 0595 .0596 -.22 1.694 1.690 .004

2 348.150 .0451 .0452 -.31 1.290 1.286 .004

NP = 18, DNRMSPCT - .220, PMEANDIF = .002

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN. , (2)DAWSON, (3)BEATTIE,

(4)0ESCHNER, (5)REAMER, (13)CHERNEY, ( 17 ) TOMLINSON , (24)ELY, (26)DITTMAR

ID T,K MOL/L CALCO 0,PCT P,BAR CALCO P,DIF

13 323.150 .4735 .4738 -.07 10.801 10.795 .006

13 323.150 .4940 .4944 -.07 11.186 11.180 .006

13 323.150 .5325 .5333 -.14 11.896 11.882 .013

13 323.150 .5586 .5584 .04 12.341 12. 345 -.004

13 323.150 .5774 .5782 -.13 12.686 12.673 .013

13 323.150 .6082 .6086 -.06 13.203 13.196 .007

13 323.150 .6307 .6312 -.09 13.578 13.569 .009

13 323.150 .6947 .6955 -.12 14.601 14.588 .013

13 323.150 .7732 .7734 -.03 15.756 15.753 .003

13 323.150 .8718 .8726 -.09 17.094 17.084 .010

13 373.150 . 3833 .3839 -.17 10.832 10.815 .016

13 373.150 .4063 .4071 -.19 11.419 11.400 .0 20 13 373.150 .4617 .4625 -.18 12.797 12.777 .020

13 373.150 .5344 .5350 -.10 14.540 14.528 .013

13 373.150 .6344 .6353 -.14 16.840 16. 821 .019

13 373.150 .7805 .7814 -.12 19.971 19.952 .019

13 373.150 1.0140 1.0138 .01 24.429 24.432 -.002

13 373. 150 1.4466 1.4445 .15 31.127 31.155 -.028

13 373.150 2.5197 2.5281 -.34 40.733 40.689 .0 44

13 398.150 .5354 .5364 -.20 15.847 15.820 .028

13 398.150 .6362 .6372 -.14 18.431 18.408 .023

13 398.150 .7841 .7850 -.11 22.018 21.997 .021

13 398.150 1.0214 1.0214 .00 27.267 27.267 -.000

13 398.150 1.4643 1.4612 .21 35.565 35.616 -.051

13 398.150 2.5805 2.5810 -.02 49.781 49.776 .005

NP = 25, DNRMSPCT = .137, PMEANDIF = .016
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN. * (2)OAWSON« (3) BEATTIE*

I4)UESCHNER« (5)REAHERf <13)CHERNEY« ( 17 ) TOMLINSON * (24)ELY, (26I0ITTMAR.

ID T,K MOL/L CALCO 0,PCT P,BAR CALCO P.OIF

3 369.960 .9992 .9898 .94 23.659 23.826 -.166

3 373.150 .9992 .9947 .46 24.085 24.167 -.082

3 393.150 .9992 .9978 .14 26.770 26. 799 -.029

3 423.150 .9992 .9985 .08 29.354 29.372 -.018

3 443.150 .9992 .9987 .05 31.887 31.900 -.013

3 473.150 .9992 .9995 -.03 34.400 34.392 .008

3 493.150 .9992 1.0003 -.11 36.892 36.856 .0 37

3 523.150 .9992 .9989 .03 39.284 39.295 -.012

3 543.150 .9992 1.0008 -.16 41.776 41.715 .061

3 369.960 1.4988 1.4841 .98 31.087 31.269 -.183

3 373.150 1.4988 1.4893 .64 31.715 31.838 -.123

3 393.150 1.4988 1.4940 .32 36.112 36.192 -.080

3 423.150 1.4988 1.4940 .32 40.317 40.414 -.097

3 448.150 1.4988 1.4946 .28 44.441 44.541 -.100

3 473.150 1.4988 1.4955 .22 48.504 48.594 -.090

3 498.150 1.4988 1.4964 .16 52.517 52.589 -.073

3 523.150 1.4988 1.4937 .34 56.367 56.537 -.170

3 548.150 1.4988 1.4984 .03 60.430 60.444 -.014

3 369.960 1.9984 1.9963 .11 36.295 36.312 -.017

3 373.150 1.9984 1.9874 .55 37.044 37.139 -.095

3 398.150 1.9984 1.9919 .33 43.357 43.440 -.083

3 423.150 1.9984 1.9905 .40 49.386 49.517 -.131

3 443.150 1.9984 1.9911 .37 55.293 55. 442 -.149

3 473.150 1.9984 1.9912 .36 61.079 61.252 -.174

3 498.150 1.9984 1.9927 .29 66.814 66.973 -.159

3 523.150 1.9984 1.9938 .23 72.478 72.621 -.143

3 548.150 1.9984 1.9954 .15 78.101 78.208 -.106

3 373.150 2.4980 2.4993 -.05 40.581 40.574 .007

3 398.150 2.4980 2.4928 .21 48.940 48.991 -.051

3 423.150 2.4980 2.4897 .33 56.975 57.091 -.116

3 448.150 2.4980 2.4886 .38 64.818 64.988 -.170

3 473.150 2.4980 2.4881 .40 72.518 72.737 -.218

3 498.150 2.4980 2.4888 .37 80.128 80.369 -.242

3 523.150 2.4980 2.4903 .31 87.677 87. 908 -.232

3 548.150 2.4980 2.4917 .25 95.154 95.369 -.215

3 369.960 2.9976 3.0204 -.76 41.300 41.244 .056

3 373.150 2.9976 3.0153 -.59 42.708 42.654 .055

3 398.150 2.9976 2.9961 .05 53.287 53.299 -.012

3 423.150 2.9976 2.9871 .35 63.429 63.557 -.127

3 448.150 2.9976 2.9853 .41 73.380 73.583 -.203

3 473.150 2.9976 2.9991 -.05 83.472 83.441 .030

3 493.150 2.9976 2.9860 .39 92.874 93.170 -.295

3 523.150 2.9976 2.9871 .35 102.480 102.793 -.313

3 548.150 2.9976 2.9881 .32 112.005 112.327 -.323

3 373.150 3.4972 3.5298 -.93 43.884 43.829 .054

3 398.150 3.4972 3.4947 .07 56.752 56.768 -.016

3 423.150 3.4972 3.4827 .42 69.144 69.305 -.161

3 448.150 3.4972 3.4815 .45 81.364 81.613 -.249

3 473.150 3.4972 3.4814 .45 93.432 93.756 -.3 24

3 498.150 3.4972 3.4825 .42 105.398 105.771 -.373

3 523.150 3.4972 3.4837 .39 117.274 117.681 -.407

3 548.150 3.4972 3.4848 .36 129.068 129.502 -.434

3 369.960 3.9968 4.1229 -3.15 42.486 42.450 .0 36

3 373.150 3.9968 4.0383 -1.04 44.502 44.464 .038

3 398.150 3.9968 3.9793 .44 59.650 59.750 -.100

70
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN. . (2)OAWSON, <3)BEATTIE,

<4)0ESCHNER. <5)REAMER, (13)CH£RNEY, ( 17) TOMLINSON, (24)ELY, (26)DITTMAR.

10 T,K MOL/L CALCD 0,PCT P,BAR CALCD P,DIF

3 423.150 3.9968 3.9731 .59 74.443 74.697 -.254

3 448.150 3.9968 3.9753 .54 89.115 89.456 -.340

3 473.150 3.9968 3.9767 .50 103.655 104.077 -.422

3 498.150 3.9968 3.9791 .44 118.125 118,590 -.465

3 523.150 3.9968 3.9813 .39 132,523 133.011 -.488

3 548.150 3.9968 3.9856 .28 146.942 147,354 -.412

3 373.150 4.4964 4.4793 .38 44.826 44.837 -.011

3 398.150 4.4964 4.4509 1.01 62.305 62.562 -.257

3 423.150 4.4964 4.4566 .89 79.652 80. 090 -.439

3 448.150 4.4964 4.4658 .68 96.998 97.506 -.508

3 473.150 4.4964 4.4717 .55 114.284 114.836 -.551

3 498.150 4.4964 4.4757 .46 131.510 132. 092 -.562

3 523.150 4.4964 4.4790 .39 148.694 149.283 -.589

3 548.150 4.4964 4.4811 .34 165,808 166.416 -.607

3 373.150 4.9961 4,8441 3.04 45.049 45.143 -.0 94

3 398.150 4.9961 4.9092 1.74 64.959 65,486 -.526

3 423.150 4.9961 4.9375 1.17 85.133 85. 834 -.701

3 448.150 4.9961 4.9556 .81 105.439 106,172 -.733

3 473.150 4.9961 4 . 9663 .60 125.765 126,492 -.727

3 498.150 4.9961 4.9414 1.09 145.108 146.787 -1.680

3 523.150 4.9961 4.9504 .91 165.352 167.054 -1.701

3 548.150 4.9961 4.9825 .27 186,691 187.288 -.597

3 369.960 5.9953 5.9730 .37 42.708 42,721 -.013

3 373.150 5.9953 5.7853 3.50 45.758 46,027 -.269

3 398.150 5.9953 5.8792 1.94 71.657 72.648 -.991

3 423.150 5.9953 5.9309 1.07 98.680 99.730 -1.050

3 448.150 5.9953 5.9595 .60 126.170 127.040 -.870

3 473.150 5.9953 5.9760 .32 153.862 154.488 -.626

3 498.150 5.995 3 5.9852 .17 181.615 182.024 -.409

3 523.150 5.9953 5.9911 .07 209.408 209.613 -.205

3 548.150 5.9953 5.9944 .01 237,162 237.231 -.050

3 369.960 6.9945 6.9294 .93 44.725 45.043 -.319

3 373.150 6.9945 6.9025 1.32 48.910 49,476 -.5 66

3 398.150 6.9945 6.9253 .99 83.826 84.992 -1.166

3 423.150 6.9945 6.9577 .53 120.192 121.212 -1.021

3 448.150 6.9945 6.9798 .21 157.246 157.816 -.570

3 473.150 6.9945 6.9978 -.05 194.828 194.664 .164

3 498.150 6.9945 7.0018 -.10 232.115 231,672 .443

3 523.150 6,9945 7.0056 -.16 269.585 268,783 .802

3 548.150 6.9945 7.0076 -.19 307.045 305,958 1.088

3 369.960 7,9937 7.9485 .56 55.587 56.471 -.8 84

3 373.150 7.9937 7.9429 .63 61.504 62.596 -1.092

3 398.150 7.9937 7.9495 .55 109.472 111.102 -1,630

3 423.150 7.9937 7.9715 .28 159.019 160.177 -1.158

3 448.150 7.9937 7.9857 .10 209.044 209.585 -.542

3 473.150 7.9937 7.9972 -.04 259.493 259,200 .294

3 498.150 7.9937 8.0029 -.11 309.832 308.937 .895

3 369.960 8.9929 8.9666 .29 90.068 91.471 -1.403

3 373.150 8.9929 8.9604 .36 98.123 99.940 -1.817

3 398.150 8.9929 8.9686 .27 164.623 166.491 -1.868

3 423.150 8.9929 8,9781 .16 231.801 233.245 -1.444

3 448.150 8.9929 8.9809 .13 298.676 300.086 -1.410

3 369.960 9.9921 9.9875 .05 173.357 173,890 -.533

3 373.150 9.9921 9.9786 .13 183.824 185.438 -1.614

3 398.150 9. 9921 9.9776 .15 273.699 275.832 -2.133

NP = 110, ONRMSPCT = .763, PMEANDIF = .448
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN.« (2)0AMS0Nt (3)BEATTIE«

(4)0ESCHNER, (5)REAMER« (13)CHERNEY. ( 17) TOMLINSON » (24)ELY« (26>0ITTMAR.

10 T.K MOL/L CALCO O.PCT P,BAR CALCO P.OIF

4 303.150 .0406 .0409 -.82 1.013 1.005 .008

4 348.150 .0352 .0 354 -.73 1.013 1.006 .007

4 373.150 .0327 .0330 -.76 1.013 1.006 .008

4 380.950 .0320 .0323 -.81 1.013 1.005 .008

4 303.150 .0825 . 0831 -.77 2.027 2.011 .015

4 348.150 .0711 .0716 -.73 2.027 2.012 .014

4 303.150 .1258 .1268 -.77 3.040 3.018 .022

4 380.950 .0975 .0984 -.88 3.040 3.014 .0 26

4 303.150 .1707 .1720 -.76 4.053 4.025 .0 28

4 348.150 .1452 .1462 -.67 4.053 4.027 .0 26

4 303.150 .2174 .2190 -.77 5.066 5.031 .0 36

4 373.150 .1696 .1704 -.53 5.066 5.041 .0 25

4 380.950 .1650 .1665 -.90 5.066 5.023 .043

4 398.150 .1575 .1585 -.60 5.066 5.037 .0 29

4 303.150 .2661 .2681 -.74 6.080 6.040 .040

4 348.150 .2227 .2241 -.66 6.080 6.042 .0 37

4 303.150 .3173 .3194 -.64 7.093 7.053 .0 39

4 303.150 .3714 .3733 -.50 8.106 8.072 .0 34

4 348.150 .3038 .3060 -.71 8.106 8.054 .052

4 303.150 .4293 .4302 -.20 9.119 9.104 .015

4 303.150 .4927 .4907 .42 10.133 10.166 -.034

4 343.150 .3893 .3922 -.75 10.133 10.066 .067

4 373.150 .3552 .3567 -.43 10.133 10.093 .039

4 380.950 .3435 .3473 -1.10 10.133 10.031 .101

4 398.150 .3267 .3284 -.50 10.133 10.086 .047

4 348.150 .4801 .4835 -.71 12.159 12.086 .073

4 348.150 .5766 .5807 -.72 14.186 14.102 .0 84

4 373.150 .5619 .5631 -.23 15.199 15.169 .0 30

4 380.950 .5393 .5457 -1.19 15.199 15.043 .156

4 398.150 .5056 .5118 -1.24 15.199 15.033 .166

4 348.150 .6800 .6849 -.72 16.212 16. 121 .0 91

4 348.150 .7919 .7976 -.72 18.239 18.141 .098

4 348.150 .9146 .9209 -.69 20.265 20.166 .099

4 373.150 .7955 .7958 -.04 20.265 20.259 .006

4 380.950 .7582 .7665 -1.09 20.265 20.087 .178

4 398.150 . 7087 .7115 -.40 20.265 20.196 .069

4 348.150 1.0520 1.0582 -.59 22.292 22.206 .0 86

4 348.150 1.2083 1.2145 -.52 24.318 24.242 .076

4 373.150 1.0651 1.0652 -.00 25.331 25.331 .000

4 380.950 1.0057 1.0169 -1.12 25.331 25.119 .212

4 398.150 .9280 .9311 -.34 25.331 25.262 .069

4 348.150 1.3982 1.3997 -.11 26.345 26.329 .015

4 348. 150 1.6167 1.6355 -1.17 28.371 28.231 .140

4 373.150 1.3908 1.3909 -.01 30.398 30.396 .001

4 380.950 1.2924 1.3097 -1.34 30.398 30.122 .2 76

4 398.150 1.1722 1.1762 -.34 30.398 30.320 .0 78

4 373.150 1.8069 1.8176 -.60 35.464 35.356 .108

4 380.950 1.6407 1.6688 -1.71 35.464 35.109 .355

4 398.150 1.4513 1.4552 -.27 35.464 35.397 .067

4 373.150 2.4358 2.4899 -2.22 40.530 40.230 .300

4 380.950 2.0992 2.1475 -2.30 40.530 40. 095 .435

4 398.150 1.7758 1.7816 -.33 40.530 40.447 .083

4 373.150 5.2163 5.6236 -7.81 45.596 45.285 .312

4 380.950 2.7381 2.9045 -6.08 45.596 44.724 .872

4 398.150 2.1608 2.1771 -.76 45.596 45.407 .189
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN., (2)0AMS0N» <3)BEATTIE»

(4) DESCHNER. (5)REAM£R» (13)CHERNEYt ( 17) TOMLINSON* I24IELT. C26)0ITTMAR.

10 T,K MOL/L CALCO

4 373.150 6.6556 6.6336

4 373.150 6. 8813 6.8534

4 373.150 7.0652 7.0204

4 373.150 7.2126 7.1562

4 380.950 4.0759 4.6185

4 398.150 2.6405 2.6779

4 373.150 7.6747 7.6137

4 380.950 6.0778 6.3385

4 398.150 3.2869 3.3377

4 380.950 6.4720 6.6760

4 380.950 6.7741 6.9257

4 373.150 8.0075 7.9084

4 380.950 6.9064 7.0296

4 398.150 4.1339 4.1818

4 373.150 8.2346 8.1310

4 380.950 7.3254 7.4271

4 398.150 5.0440 5.0570

4 373.150 8.4085 8.3120

4 380.950 7.6371 7.7095

4 398.150 5.7737 5.7891

4 373.150 8.5653 8.4657

4 380.950 7.8616 7.9306

4 398.150 6.3197 6.3387

4 373.150 8.6725 8.5998

4 380.950 8.0512 8.1135

4 398.150 6.7336 6.7452

4 373.150 8.8057 8.7193

4 380.950 8.2288 8.2702

4 398.150 7.0839 7.0584

4 373.150 8.9167 8.8273

4 380.950 8.3688 8.4077

4 398.150 7. 3594 7.3109

4 373.150 9.0158 8.9260

4 380.950 8.4911 8.5306

4 398.150 7.5987 7.5218

4 373.150 9.1094 9.0171

4 380.950 8.6018 8.6419

4 398.150 7.7738 7.7029

4 373.150 9.1859 9.1018

4 380.950 8.6977 8.7438

4 398.150 7.9393 7.8617

4 373.150 9.2566 9.1810

4 380.950 8.7868 8.8379

4 398.150 8.0823 8.0031

4 373.150 9.3197 9.2555

4 380.950 8.8762 8.9255

4 398.150 8.2040 8.1308

4 373.150 9.3761 9.3259

4 380.950 8.9598 9.0073

4 398.150 8.3150 8.2473

4 373.150 9.4308 9.3925

4 380.950 9.0381 9.0843

4 398.150 8.4123 8.3545

4 373.150 9.4860 9.4560

4 380.950 9.1196 9.1571

4 398.150 8.5006 8.4539

0,PCT P.BAR CALCO P.DIF

.33 47.623 47.710 -.088

.41 48.636 48.789 -.153

.63 49.649 49.963 -.314

.78 50.663 51.141 -.478

13.31 50.663 49.480 1.183

-1.42 50.663 50.327 .335

.79 55.729 56.642 -.914

-4.29 55.729 54.563 1.166

-1.54 55.729 55.386 .343

-3.15 57.755 56.449 1.306

-2.24 59.782 58.489 1.293

1.24 60.795 62.902 -2.107

-1.78 60.795 59.605 1.190

-1.16 60.795 60.526 .269

1.26 65.861 68.646 -2.785

-1.39 65.861 64.361 1.500

-.26 65.861 65.780 .081

1.15 70.928 74.021 -3.093

-.95 70.928 69.491 1.437

-.27 70.928 70.806 .122

1.16 75.994 79.696 -3.702

-.88 75.994 74.296 1.698

-.30 75.994 75.790 .204

.84 81.060 84.077 -3.017

-.77 81.060 79.238 1.822

-.17 81.060 80.894 .166

.98 86.126 90.143 -4.016

-.50 86.126 84.720 1.407

.36 86.126 86.593 -.467

1.00 91.193 95.764 -4.571

-.46 91.193 89.699 1.494

.66 91.193 92.285 -1.093

1.00 96.259 101.249 -4.990

-.47 96.259 94.571 1.668

1.01 96.259 98.324 -2.065

1.01 101.325 106.864 -5.539

-.47 101.325 99.446 1.879

.91 101.325 103. 511 -2.186

.92 106.391 111.780 -5.389

-.53 106.391 104.048 2.343

.98 106.391 109.104 -2.713

.82 111.458 116.598 -5.140

-.58 111.458 108.658 2.799

.98 111.458 114.541 -3.083

.69 116.524 121.136 -4.612

-.55 116.524 113.631 2.893

.89 116.524 119.652 -3.129

.54 121.590 125.382 -3.792

-.53 121.590 118.608 2.982

.81 121.590 124.739 -3.149

.41 126.656 129.678 -3.022

-.51 126.656 123.576 3.080

.69 126.656 129.558 -2.902

.32 131.723 134.210 -2.488

-.41 131.723 129.078 2.645

.55 131.723 134.234 -2.512

73
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (DVIRIAL EQN., (2)DAWSON, (3) BEATTIE,

<4)0ESCHNER, (5)REAMER, <13)CHERNEY, ( 17 > TOML INSON , J2'»)ELY, (26I0ITTHAR.

10 T,K MOL/L CALCO 0,PCT P,BAR CALCD P,OIF

k 398.150 8.6558 8.6333 .26 141.855 143.220 -1.365

4 423.150 . 0288 .0290 -.75 1.013 1.006 .007

4 473.150 .0257 .0259 -.74 1.013 1.006 .007

4 526.370 .0231 .0232 -.76 1.013 1.006 .008

4 423.150 . 0874 .0880 -.65 3.040 3.020 .019

4 473.150 . 0777 .0783 -.69 3.040 3.019 .0 21

4 526.370 .0696 . 0701 -.77 3.040 3.017 .023

4 423. 150 . 1474 .1482 -.56 5.066 5.039 .0 27

4 473.150 .1306 .1314 -.62 5.066 5.035 .031

4 526.370 .1165 .1174 -.78 5.066 5.028 .0 39

4 423.150 . 3 U SB .3049 -.42 10.133 10.092 .040

4 473.150 .2665 .2678 -.48 10.133 10.086 .0 46

4 526.370 .2361 .2379 -.73 10.133 10.061 .072

4 423.150 .4692 .4712 -.43 15.199 15.139 .060

4 473.150 .4080 .4095 -.35 15.199 15.149 .050

4 526.370 .3588 .3614 -.71 15.199 15.096 .103

4 570.450 . 3278 .3301 -.69 15.199 15.097 .101

4 423.150 . 645 6 .6483 -.42 20.265 20.189 .076

4 473.150 .5554 .5567 -.24 20.265 20.220 .045

4 526.370 .4850 .4879 -.60 20.265 20.150 .115

4 570.450 .4415 .4441 - .60 20.265 20.148 .117

4 423.150 . 8347 .8378 -.37 25.331 25.252 .080

4 473.150 .7085 .7098 -.18 25.331 25.290 .0 41

4 526.370 .6144 .6175 -.51. 25.331 25.209 .122

4 570.450 .5572 .5601 -.51 25.331 25.209 .123

4 423.150 1.0383 1.0418 -.34 30.398 30.314 .084

4 473.150 .8677 .8690 -.15 30.398 30.356 .0 41

4 526.370 .7469 .7502 -.44 30.398 30.273 .124

4 570.450 .6751 .6778 -.41 30.398 30.280 .118

4 423.150 1.2577 1.2629 -.41 35.464 35.350 .113

4 473.150 1.0340 1.0349 -.08 35. 464 35.439 .024

4 526.370 . 8825 .8859 -.38 35.464 35.340 .124

4 570.450 .7952 .7974 -.28 35.464 35.371 .092

4 423.150 1.4981 1.5046 -.43 40.530 40.400 .130

4 473.150 1.2074 1.2078 - .03 40.530 40. 520 .010

4 526.370 1.0215 1.0247 -.31 40.530 40.414 .116

4 570.450 .9171 .9186 -.16 40.530 40.467 .063

4 609.310 . 8460 .8450 .12 40.530 40. 577 -.047

4 423.150 1.7663 1.7714 -.29 45.596 45.503 .093

4 473.150 1.3895 1.3883 .09 45.596 45.630 -.033

4 526.370 1.1635 1.1666 -.27 45.596 45.486 .110

4 570.450 1.0405 1.0415 -.10 45.596 45.554 .042

4 423.150 2. 0642 2.0686 -.21 50.663 50.592 .071

4 473.150 1.5797 1.5768 .18 50.663 50.739 -.076

4 526.370 1.3088 1.3117 -.22 50.663 50.563 .099

4 570.450 1.1653 1.1661 -.07 50.663 50.629 .0 34

4 609.310 1.0698 1.0676 .21 50.663 50.762 -.100

4 423.150 2.3924 2.4017 -.39 55.729 55.595 .133

4 473.150 1. 7769 1.7738 .18 55.729 55.808 -.079

4 526.370 1.4559 1.4599 -.27 55.729 55.595 .134

4 570.450 1.2914 1.2922 -.06 55.729 55.697 .0 32

4 423.150 2.7508 2.7757 -.91 60.795 60.475 .320

4 473.150 1. 9809 1.9794 .08 60.795 60.832 -.037

4 526.370 1.6062 1.6112 -.31 60.795 60.631 .164

4 570.450 1.4182 1.4199 -.11 60.795 60.731 .0 64

4 609.310 1.2968 1.2937 .23 60.795 60.930 -.135

74
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. IDVIRIAL EQN., l2)0AMS0Nt 13IBEATTIE,

(4)0ESCHNER» (5)REAMER. (13)CHERNEY, ( 17 ) TOML INSON , (24)ELY, (26)0ITTMAR.

ID T.K MOL/L CALCO D,PCT PyBAR CALCO P.DIF

4 423.150 3.1495 3.1923 -1.36 65.861 65.363 .4 98

4 473.150 2.1930 2.1938 -.04 65.861 65.842 .019

4 526.370 1.7595 1.7655 -.34 65.861 65.668 .193

4 570.450 1.5468 1.5489 -.14 65.861 65.777 .0 84

4 423.150 3.5957 3.6456 -1.39 70.928 70.384 .543

4 473.150 2.4142 2.4166 -.10 70.928 70.874 .053

4 526.370 1.9156 1.9226 -.36 70.928 70.705 .223

4 570.450 1.6759 1.6793 -.20 70.928 70.795 .132

4 609.310 1.5253 1.5229 .16 70.928 71.036 -.108

4 423.150 4.0764 4.1182 -1.03 75.994 75.547 .447

4 473.150 2.6418 2.6471 -.20 75.994 75.879 .114

4 526.370 2.0741 2.0823 -.39 75.994 75.737 .257

4 570.450 1.8064 1.8109 -.25 75.994 75.822 .172

4 423.150 4.5576 4.5838 -.57 81.060 80.768 .292

4 473.150 2.8761 2.8842 -.28 81.060 80.888 .172

4 526.370 2.2352 2.2443 -.41 81.060 80.777 .283

4 570.450 1.9367 1.9435 -.35 81.060 80.801 .2 59

4 609.310 1.7548 1.7543 .02 81. 060 81.079 -.019

4 423.150 5.0038 5.0202 -.33 86.126 85.928 .199

4 473.150 3.1176 3.1266 -.29 86.126 85.939 .187

4 526.370 2.3991 2.4084 -.39 86.126 85.842 .2 84

4 570.450 2.0695 2.0770 -.36 86.126 85.344 .283

4 423.150 5.3890 5.4187 -.55 91.193 90.797 .396

4 473.150 3.3617 3.3723 -.32 91.193 90.973 .219

4 526.370 2.5661 2.5740 -.31 91.193 90.950 .242

4 570.450 2.2027 2.2112 -.39 91.193 90.870 .323

4 609.310 1.9866 1.9874 -.04 91.193 91.160 .033

4 423.150 5.7401 5.7754 -.62 96.259 95.728 .531

4 473.150 3.6068 3.6192 -.34 96.259 96.005 .253

4 526.370 2.7330 2.7408 -.29 96.259 96.022 .236

4 570.450 2.3344 2.3459 -.49 96.259 95.828 .431

4 423.150 6.0562 6.0898 -.55 101.325 100. 751 .574

4 473.150 3.8538 3.8648 -.23 101.325 101.098 .227

4 526.370 2.9008 2.9083 -.26 101.325 101.099 .226

4 570.450 2.4679 2.4809 -.53 101.325 100.837 .488

4 609.310 2.2179 2.2210 -.14 101.325 101.191 .134

4 423.150 6.3403 6.3649 -.39 106.391 105.910 .482

4 473.150 4.1002 4.1068 -.16 106.391 106.253 .139

4 526.370 3.0679 3.0759 -.26 106.391 106.149 .243

4 570.450 2.6012 2.6159 -.57 106.391 105.840 .552

4 423.150 6.5893 6.6060 -.25 111.458 111.086 .371

4 473.150 4.3465 4.3430 .08 111.458 111.534 -.077

4 526.370 3.2337 3.2432 -.29 111.458 111.169 .288

4 570.450 2.7347 2.7508 -.59 111.458 110.850 .607

4 609.310 2.4479 2.4543 -.26 111.458 111.178 .280

4 423.150 6.8147 6.8187 -.06 116.524 116.423 .101

4 473.150 4.5909 4.5717 .42 116.524 116.956 -.432

4 526.370 3.3998 3.4096 -.29 116.524 116. 224 .300

4 570.450 2.3691 2.8854 -.57 116.524 115.909 .615

4 423.150 7.0166 7.0079 .12 121.590 121.837 -.247

4 473.150 4.8342 4.7918 . 88 121.590 122.590 -1.000

4 526.370 3.5627 3.5746 -.33 121.590 121.222 .368

4 570.450 3.0009 3.0193 -.61 121.590 120.891 .699

4 609.310 2.6764 2.6863 -.37 121.590 121.156 .4 34

4 423.150 7.1842 7.1776 .09 126.656 126.862 -.206

4 473.150 5.0699 5.0028 1.33 126.656 128.319 -1.662

75
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (1

(4)DESCHNER, (5)REAMER, (13)CHERNEY

ID T,K MOL/L CALCO

4 526.370 3.7280 3.7378

4 570.450 3.1344 3.1524

4 423.150 7.3360 7.3313

4 473.150 5.2988 5.2044

4 526.370 3.8897 3.8986

4 570.450 3.2663 3.2845

4 609.310 2.9034 2.9160

4 423.150 7.4680 7.4714

4 473.150 5.5184 5.3967

4 526.370 4.0535 4.0566

4 570.450 3.3980 3.4154

4 423.150 7.5848 7.6002

4 609.310 3.1267 3.1425

NP = 236, DNRHSPCT = 1.333, PNEAND

IVIRIAL EQN., <2)0AHS0N, I3IBEATTIE,

, (17) TOMLINSON, (24)ELY, (26)0ITTHAR.

D,PCT P,BAR CALCO P.DIF

-.26 126.656 126.351 .306

-.58 126.656 125.968 .689

.06 131.723 131.886 -.164

1.78 131.723 134.178 -2.456

-.23 131.723 131.441 .281

-.56 131.723 131.021 .701

-.43 131.723 131.162 .560

-.05 136.789 136.658 .130

2.21 136.789 140.131 -3.342

-.07 136.789 136.690 .0 98

-.51 136.789 136.110 .679

-.20 141.855 141.227 .628

-.50 141.855 141.144 .711

F = .682

7fi
Table 9. Continued

EQUATION OF STATE VS# PVT DATA. (DVIRIAL EQN. * <2)OAWSON» f3»BEATTIE»

(4)0ESCHNER« (5)REAHER» (13ICHERNEY« ( 17) TOMLINSON . (24)ELY« (26)0ITTMAR.

10 T,K MOL/L CALCO O.PCT PtBAR CALCO P.OIF

5 310.928 .0397 • 0396 -.29 1.013 1.010 .003

5 327.594 .0376 .0377 -.26 1.013 1.011 .003

5 344.261 .0358 .0356 -.23 1.013 1.011 .002

5 360.928 .0 341 • 0341 -.21 1.013 1.011 .002

5 377.594 .0325 .0326 -.18 1.013 1.011 .002

5 410.928 • 0298 .0299 -.17 1.013 1.012 .002

5 444.261 .0276 .0276 -.15 1.013 1.012 .002

5 477.594 .0256 .0256 -.14 1.013 1.012 .001

5 510.928 .0239 .0240 -.14 1.013 1.012 .001

5 310.928 .0543 .0545 -.31 1.379 1.375 .004

5 327.594 .0514 .0516 -.27 1.379 1.375 .004

5 344.261 .0488 .0490 -.24 1.379 1.376 .003

5 360.928 .0465 .0466 -.22 1.379 1.376 .003

5 377.594 .0444 .0445 -.20 1.379 1.376 .003

5 410.928 .0407 .0406 -.17 1.379 1.377 .002

5 444.261 . 0376 .0376 -.16 1.379 1.377 .002

5 477.594 .0349 .0350 -.16 1.379 1.377 .002

5 510.928 .0326 .0326 -.16 1.379 1.377 .002

5 310.928 . 0823 .0826 -.33 2.068 2.062 .007

5 327.594 .0778 . 0780 -.29 2.068 2.063 .006

5 344.261 .0738 .0740 -.24 2.068 2.064 .005

5 360.928 .0702 .0703 -.22 2.068 2.064 .005

5 377.594 .0669 .0671 -.23 2.066 2.064 .005

5 410.928 .0613 .0614 -.17 2.068 2.065 .0 04

5 444.261 .0565 .0566 -.17 2.068 2.065 .003

5 477.594 .0525 .0526 -.16 2.068 2.065 .003

5 510.928 .0490 .0491 -.16 2.068 2.065 .003

5 310.928 .1109 .1112 -.34 2.758 2.749 .009

5 327.594 .1046 .1049 -.29 2.758 2.750 .008

5 344.261 .0991 .0993 -.24 2.758 2.752 .006

5 360.928 .0942 .0 944 -.21 2.758 2 . 752 .006

5 377.594 .0897 .0899 -.19 2.758 2.753 .0 05

5 410.928 .0620 .0622 -.16 2.758 2.754 .004

5 444.261 .0756 .0757 -.15 2.758 2.754 .004

5 477.594 . 0701 .0703 -.16 2.758 2.754 .004

5 510.928 .0654 .0655 -.17 2.758 2.753 .005

5 310.926 .1401 .1405 -.34 3.447 3.436 .011

5 327.594 .1319 .1323 -.29 3.447 3.438 .010

5 344.261 .1248 .1251 -.24 3.447 3.439 .008

5 360.928 .1185 .1187 -.20 3.447 3.441 .007

5 377.594 . 1128 .1130 -.17 3.447 3.442 .006

5 410.928 .1030 .1031 -.14 3.447 3.443 .005

5 444.261 .0948 .0950 -.14 3.447 3.443 .005

5 477.594 .0879 .0880 -.15 3.447 3.442 .005

5 510.928 .0819 .0821 -.17 3.447 3.442 .006

5 310.928 .1699 .1705 -.33 4.137 4.124 .013

5 327.594 .1597 .1602 -.29 4.137 4.126 .011

5 344.261 .150 9 .1512 -.22 4.137 4.128 .009

5 360.926 .1431 .1433 -.19 4.137 4. 129 .007

5 377.594 .1361 .1363 -.15 4.137 4.131 .0 06

5 410.928 .1241 .1243 -.13 4.137 4.132 .005

5 444.261 .1141 .1143 -.13 4.137 4.132 .005

5 477.594 .1057 .1059 -.14 4.137 4.131 .0 06

5 510.928 . 0985 .0987 -.17 4.137 4.130 .007

5 310.926 .2319 .2326 -.31 5.516 5.500 .015

77
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (I)VIRIAL EQN.« (2)DAWSONt (3)BEATTIE«

(4)DESCHNER, <5)REAMER, (13>CHERNEYt ( 17) TOMLINSON, (24)ELY, (26)DITTMAR.

ID T,K MOL/L CALCO 0,PCT P,BAR CALCO P.DIF

5 327.594 .2170 .2176 -.28 5.516 5 .50 2 .014

5 344.261 .2044 .2048 -.21 5.516 5.505 .011

5 360.926 .1933 .1936 -.17 5.516 5.507 .009

5 377.594 ,1835 .1636 -.12 5.516 5.509 .006

5 410.926 .1669 .1671 -.10 5.516 5.511 .005

5 444.261 .1532 .1534 -.10 5.516 5.510 .006

5 477.594 , 1417 .1419 -.13 5.516 5.509 .007

5 510.926 . 1319 .1321 -.16 5.516 5.507 .009

5 310.926 .2974 .2981 -.21 6.895 6.882 .013

5 327.594 .2768 .2775 -.25 6.895 6.879 .016

5 344.261 .2597 .2602 -.19 6.895 6.883 .012

5 360.926 .2450 .2453 -.16 6.895 6.884 .010

5 377.594 .2321 .2324 -.11 6.895 6.887 .007

5 410.926 .2104 .2106 -.09 6.895 6.889 .006

5 444.261 .1927 .1929 -.09 6.895 6.889 .006

5 477.594 .1780 .1782 -.11 6.895 6.887 .008

5 510.926 .1655 .1657 -.16 6.895 6.884 .011

5 310.926 .3856 .3855 .04 8.616 8.621 -.003

5 327.594 .3555 .3562 -.21 6.618 8.603 .016

5 344.261 .3318 .3323 -.15 8.616 8.607 .011

5 360.926 .3118 .3122 -.12 6.618 8.609 .010

5 377.594 .2945 .2948 -.08 6.618 8.612 .007

5 410.926 .2659 .2661 -.05 8.616 8.614 .004

5 444.261 .2429 .2431 -.06 8.616 8.613 .005

5 477.594 .2239 .2241 -.09 8.618 8.611 .008

5 510.928 .2078 .2062 -.15 8.616 8.606 .013

5 310.926 .4813 .4604 .18 10.342 10. 357 -.015

5 327.594 .4396 .4400 -.08 10.342 10.335 .007

5 344.261 ,4077 .4060 -.08 10.342 10. 335 .007

5 360.926 .3813 .3816 -.07 10.342 10.336 .006

5 377.594 .3590 .3592 -.05 10.342 10.337 .005

5 410.928 .3227 .3226 -.04 10.342 10.339 .003

5 444.261 .2940 .2941 -.05 10.342 10.338 .004

5 477.594 .2704 .2706 -.10 10.342 10.333 .010

5 510.928 .2506 .2510 -.16 10.342 10.326 .016

5 310.926 10.7105 10.6916 .18 13.790 15.837 -2.048

5 327.594 .6266 .6266 .33 13.790 13.824 -.0 35

5 344.261 .5727 .5720 .12 13.790 13.803 -.014

5 360.928 .5298 .5295 .06 13.790 13.797 -.007

5 377.594 .4950 .4948 .05 13.790 13.795 -.006

5 410.926 .4404 .4403 .02 13.790 13.792 -.003

5 444.261 .3987 .3987 .00 13.790 13.790 -.000

5 *77.594 .3652 .3654 -.07 13.790 13.780 .009

5 510.926 . 3374 .3379 -.16 13.790 13.768 .021

5 310.926 10.7827 10.7540 .27 20.684 23.980 -3.296

5 327.594 10.0181 9.9973 .21 20.684 22.154 -1.470

5 344.261 .9858 .9759 1.01 20.684 20.827 -.143

5 360.926 .8775 .8729 .52 20.684 20.766 -.082

5 377.594 .8014 .7987 .34 20.684 20.741 -.057

5 410.926 .6942 .6934 .13 20.684 20. 707 -.022

5 444.261 .6196 .6191 .09 20.684 20.700 -.016

5 477.594 .5624 .5623 .01 20.684 20.686 -.002

5 510.928 .5161 .5168 -.13 20.684 20.658 .0 26

5 310.926 10. 8301 10.6132 .16 27.579 29.621 -2.042

5 327,594 10. 1148 10.0912 .23 27.579 29.415 -1.836

5 344.261 9.1411 9.1101 .34 27.579 28.736 -1.157

78
Table 9. Continued.

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN.» (Z)OAWSON» (3)8EATTIE» (4)DESCHNER» <5)REAMER» (13)CHERNEY* ( 17) TOMLINSON t (24)ELY» (26)0 ITTm«o,

10 T,K MOL/L CALCO D,PCT P.BAR CALCO P,OIF

5 360.928 1.3416 1.3244 1.28 27.579 27.796 -.217

5 377.594 1. 1733 1.1652 .68 27.579 27. 714 -.135

5 410.928 .9779 .9756 .24 27.579 27.633 -.054

5 444.261 .8575 .8559 .18 27.579 27.623 -.044

5 477.594 . 7702 .7694 .10 27.579 27.604 -.025

5 510.928 .7018 .7024 -.09 27.579 27.557 .0 22

5 310.928 10.8854 10.8694 .15 34.474 36.488 -2.015

5 327.594 10.1984 10.1772 .21 34.474 36.255 -1.781

5 344.261 9.2928 9.2802 .14 34.474 35.038 -.5 64

5 360.928 2.1031 2.0885 .70 34.474 34.557 -.083

5 377.594 1.6584 1.6429 .93 34.474 34.661 -.188

5 410.928 1.3007 1.2960 .36 34.474 34.568 -.094

5 444.261 1. 1149 1.1118 .28 34.474 34.554 -.081

5 477.594 .9896 .9876 .21 34.474 34.538 -.0 64

5 510.928 . 8949 .8950 -.01 34.474 34.471 .003

5 310.928 10.9375 10.9231 .13 41.369 43.262 -1.894

5 327^594 10.2757 10.2568 .18 41.369 43.074 -1.705

5 344.261 9.4335 9.4231 .11 41.369 41.911 -.543

5 360.928 3.1712 8.1276 .53 41.369 42.144 -.776

5 377.594 2.3974 2.3843 .55 41.369 41.457 -.0 88

5 410.928 1.6751 1.6691 .36 41.369 41.470 -.102

5 444.261 1.3948 1.3900 .34 41.369 41.482 -.113

5 477.594 1.2207 1.2177 .25 41.369 41.457 -.089

5 510.928 1.0951 1.0946 .05 41.369 41.386 -.018

5 310.928 11.0317 11.0238 .07 55.158 56.290 -1.132

5 327.594 10.4166 10.4007 .15 55.158 56.797 -1.639

5 344. 261 9.6589 9.6582 .01 55.158 55.205 -.047

5 360.928 3.7315 8.6813 .57 55.158 56.892 -1.734

5 377.594 7.0499 6.9273 1.74 55.158 56.191 -1.033

5 410.928 2.6803 2.6719 .31 55.158 55.251 -.093

5 444.261 2.0399 2. 0305 .46 55.158 55.343 -.185

5 477.594 1.7237 1.7178 .34 55.158 55.312 -.154

5 510.928 1.5189 1.5161 .19 55.158 55.248 -.090

5 310. 928 11.1214 11.1169 .04 68.948 69.646 -.6 98

5 327.594 10.5380 10.5285 . 09 68.948 70.033 -1.085

5 344.261 9.8475 9.8502 -.03 68.948 68.738 .210

5 360.928 9.0630 9.0231 .44 68.948 70.883 -1.935

5 377.594 7.9510 7.9006 .63 68.948 70.119 -1.171

5 410.928 4.2278 4.1832 1.05 68.948 69.313 -.366

5 444.261 2.8165 2.8055 .39 68.948 69.127 -.180

5 477.594 2.2845 2.2754 .40 68.948 69.162 -.214

5 510.928 1.9727 1.9673 .28 68.948 69.109 -.161

5 310.928 11.2244 11.2244 0.00 86.184 86.186 -.002

5 327.594 10.6749 10.6714 . 03 86.184 86.638 -.453

5 344.261 10.0496 10.0517 -.02 86.184 85.989 .196

5 360.928 9.3637 9.3357 .30 86.134 87.974 -1.790

5 377. 594 8.5092 8.4712 .45 86.184 87.686 -1.502

5 410.928 6.0635 5.9740 1.48 86.184 87.335 -1.150

5 444.261 3.9558 3.9309 .63 86.184 86.556 -.372

5 477.594 3.0576 3.0440 .44 86.184 86.478 -.2 94

5 510.928 2.5778 2.5676 .40 86.184 86.470 -.265

5 310.928 11. 3261 11.3237 .02 103.421 103. 853 -.432

5 327.594 10.8049 10.7996 . 05 103.421 104.178 -.756

5 344.261 10.2294 10.2242 .05 103.421 103.984 -.563

5 360.928 9.6021 9.5809 .22 103.421 105.086 -1.664

5 377.594 8.8861 8.8466 .45 103.421 105.576 -2.155

79
Table 9. Continued.

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN., (Z)OAWSONt (3) BEATTIE*

<4)0ESCHNERf (5»REAMER, (13ICHERNEV, (17) TOMLINSON , (24)ELT. (26)DITTMAR.

ID T,K MOL/L CALCO O.PCT PtBAR CALCO P.DIF

5 410.926 7.0606 6.9935 .95 103.421 104 .986 -1.565

5 444.261 5.0693 5.0199 .97 103.421 104.283 -.861

5 477.594 3.6640 3.8477 .42 103.421 103.775 -.354

5 510.926 3.2585 3.1911 2.07 103.421 105.277 -1.856

5 310.926 11.3999 11.4161 -.14 120.658 117.539 3.119

5 327.594 10.9051 10.9163 -.10 120.658 118.946 1.713

5 344.261 10.3746 10.3758 -.01 120.658 120.514 .144

5 360.926 9.7919 9.7850 .07 120.656 121.294 -.636

5 377.594 9.1524 9.1325 .22 120.658 122.009 -1.351

5 410.926 7.6255 7.6038 .28 120.658 121.414 -.755

5 444.261 5.9152 5.9022 .22 120.658 120.950 -.292

5 477.594 4.6360 4.6133 .49 120.658 121.199 -.540

5 510.926 3.8522 3.6110 1.07 120.658 121.826 -1.168

5 310.926 11.4929 11.5027 -.09 137.895 135.880 2.016

5 327.594 11.0150 11.0236 -.08 137.895 136.459 1.436

5 344.261 10.5206 10.5117 .06 137.895 139.090 -1.195

5 360.926 9. 9716 9.9611 .11 137.895 139.006 -1.111

5 377.594 9.3649 9.3661 .20 137.895 139.415 -1.519

5 410.926 8.0717 8.0321 .49 137.895 139.759 -1.864

5 444.261 6.6036 6.5693 .52 137.895 133.931 -1.036

5 477.594 5.3177 5.2897 .53 137.895 138.667 -.772

5 510.926 4.4132 4.3992 .32 137.895 138.323 -.428

5 310.926 11.5573 11.5842 -.23 155.132 149.337 5.795

5 327.594 11.1062 11.1231 -.15 155.132 152.128 3.004

5 344.261 10.6433 10.6351 .08 155.132 156.332 -1.200

5 360.926 10.1141 10.1166 -.02 155.132 154.836 .2 96

5 377.594 9.5684 9.5649 .04 155.132 155.456 -.324

5 410.926 6.3816 8.3628 .22 155.132 156.233 -1.101

5 444.261 7.1060 7.0740 .45 155.132 156.387 -1.255

5 477.594 5.6607 5.8677 .22 155.132 155.556 -.424

5 510.928 4.950 8 4.9368 .26 155.132 155.605 -.473

5 310.928 11.6480 11.6613 -.11 172.369 169.328 3.041

5 327.594 11.2121 11.2160 -.03 172.369 171.622 .747

5 344.261 10.7569 10.7484 .08 172.369 173.725 -1.356

5 360.926 10.2620 10.2563 .06 172.369 173.108 -.739

5 377.594 9.7464 9.7388 .08 172.369 173.169 -.801

5 410.928 8.6576 6.6332 .28 172.369 174.036 -1.717

5 444.261 7.4708 7.4706 .00 172.369 172.330 -.012

5 477.594 6. 3614 6.3521 .46 172.369 173.516 -1.147

5 510.928 5.4309 5.4189 .22 172.369 172.823 -.454

5 310.926 11.7344 11.7344 .00 189.606 189.617 -.011

5 327.594 11.3002 11.3032 -.03 189.606 188.992 .613

5 344.261 10.6713 10.8533 .17 189.606 192.695 -3.089

5 360.926 10.3963 10.3836 .14 189.606 191.710 -2.104

5 377.594 9.9084 9.8938 .15 189.606 191.322 -1.716

5 410.928 6.8868 8.8626 .29 189.606 191.741 -2.136

5 444.261 7.8031 7.7947 .11 139.606 190.101 -.495

5 477.594 6.7745 6.7574 .25 189.606 190.404 -.798

5 510.926 5.8649 5.8470 .30 189.606 190.375 -.769

5 310.926 11.7831 11.8040 -.18 206.843 201. 588 5.255

5 327.594 11.3883 11.3854 .03 206.843 207.459 -.616

5 344.261 10.9436 10.9511 -.07 206.843 205.479 1.364

5 360.926 10.4923 10.5005 -.08 206.843 205.591 1.251

5 377.594 10.0216 10.0340 -.12 206.843 205.249 1.594

5 410.928 9.0639 9.0624 .02 206.843 206.974 -.131

5 444.261 6.0615 6.0681 -.08 206.843 206.399 .443

80
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN., (2)0AMS0N» (3) BEATTIE*

(4)DESCHNER» (5)REAMER« (13}CHERNEY* ( 17) TOMLINSON* (24)ELY* (26)OITTHAR.

10 T,K HOL/L CALCD

5 477.594 7.0906 7.1001

5 510.926 6.2230 6.2242

5 310.926 11.9424 11.9342

5 327.594 11.5326 11.5374

5 344.261 11.1410 11.1293

5 360.926 10.7172 10.7100

5 377.594 10.2812 10.2804

5 410.926 9.3969 9.399f

5 444.261 6.5140 8.5127

5 477.594 7.6525 7.6514

5 510.926 6.8455 6.8497

5 310.928 12.0498 12.0539

5 327.594 11.6620 11.6753

5 344.261 11.2819 11.2686

5 360.926 10.8859 10.8941

5 377.594 10.4749 10.4930

5 410.928 9.6748 9.6788

5 444.261 6.6565 8.8676

5 477.594 8.0765 8.0828

5 510.928 7.3313 7.3450

5 310.926 12.1457 12.1649

5 327.594 11.7683 11.8020

5 344.261 11.4072 11.4332

5 360.926 11.0621 11.0590

5 377.594 10.6490 10.6805

5 410.928 9.8918 9.9180

5 444.261 9.1416 9.1638

5 477.594 8.4166 8.4362

5 510.928 7.7251 7.7498

5 310.928 12.2572 12.2686

5 327.594 11.9061 11.9191

5 344.261 11.5514 11.5656

5 360.928 11.1908 11.2084

5 377.594 10.8276 10.8487

5 410.928 10.1139 10.1280

5 444.261 9.4069 9.4186

5 477.594 8.7283 8.7357

5 510.928 8.0761 8.0904

5 310.928 12.4749 12.4574

5 327.594 12.1499 12.1304

5 344.261 11.8179 11.8016

5 360.926 11.5007 11.4717

5 377.594 11.1447 11.1415

5 410.928 10.4881 10.4847

5 444.261 9.8540 9.8424

5 477.594 9.2476 9.2256

5 510.928 8.6504 8.6418

5 310.928 12.6352 12.6263

5 327.594 12.3149 12.3172

5 344.261 12.0092 12.0081

5 360.928 11.6962 11.6993

5 377.594 11.3853 11.3914

5 410.928 10.7778 10.7821

5 444.261 10.1948 10.1886

5 477.594 9.6351 9.6191

5 510.928 9.0952 9.0794

0*PCT P*BAR CALCD P*DIF

-.13 206.843 206 .325 .517

-.02 206.843 206.784 .058

.07 241.316 243.618 -2.301

-.04 241.316 240.180 1.136

.11 241.316 243.741 -2.424

.07 241.316 242.599 -1.282

.01 241.316 241.435 -.118

-.03 241.316 241.018 .298

.02 241.316 241.432 -.116

.01 241.316 241.392 -.075

-.06 241.316 241.051 .2 65

-.03 275.790 274.561 1.229

-.11 275.790 272.319 3.471

-.06 275.790 274.266 1.525

-.08 275.790 274.155 1.635

-.17 275.790 272.674 3.116

-.04 275.790 275.257 .533

-.13 275.790 274.607 1.184

-.08 275.790 275.228 .563

-.19 275.790 274.728 1.062

-.16 310.264 304.101 6.163

-.29 310.264 300.830 9.434

-.23 310.264 303.836 6.426

.03 310.264 310.945 -.661

-.30 310.264 304.188 6.077

-.27 310.264 306.237 4.027

-.24 310.264 307.430 2.784

-.23 310.264 308.176 2.089

-.32 310.264 307.976 2.288

-.09 344.738 340.840 3.898

-.11 344.738 340.782 3.956

-.12 344.738 340.909 3.829

-.16 344.738 340.502 4.235

-.19 344.738 340.221 4.516

-.14 344.738 342.293 2.445

-.12 344.738 343.050 1.687

-.08 344.738 343. 329 .909

-.18 344.738 343.178 1.560

.14 413.685 420.494 -6.809

.16 413.685 420.548 -6.862

.14 413.685 418. 821 -5.136

.25 413.685 421.967 -8.281

.03 413.685 414.502 -.816

.03 413.685 414. 422 -.736

.12 413.685 415.792 -2.107

.24 413.685 417.199 -3.514

.10 413.685 414. 919 -1.233

.07 482.633 486.457 -3.824

-.02 482.633 481.714 .919

.01 482.633 483.006 -.373

-.03 482.633 481.640 .993

-.05 482.633 480. 832 1.801

-.04 482.633 481.570 1.063

.06 482.633 483. 975 -1.342

.17 482.633 485.727 -3.094

.17 482.633 485.398 -2.765

81
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN. , (2)0AMS0N, {3JBEATTIE,

(i»)OESCHNER» (5)REAMER, (13)CHERNEY, ( 17 ) TOML INSON , <24»ELYt (26)DITTMAR.

ID T,K MOL/L CALCO 0,PCT P.BAR CALCO P,OIF

5 310.926 12.7787 12.7793 -.00 551.581 551.309 .271

5 327.594 12.4753 12.4851 -.08 551.581 547.345 4.236

5 344.261 12.1820 12.1919 -.08 551.581 547.673 3.907

5 360.928 11.8832 11.9000 -.14 551.561 545.486 6.094

5 377.594 11.5956 11.6099 -.12 551.581 546.797 4.784

5 410.926 11.0322 11.0378 -.05 551.581 549.959 1.622

5 444.261 10.4616 10.4820 -.00 551.581 551.494 .087

5 477.594 9.9612 9.9487 .13 551.581 554.423 -2.843

5 510.926 9.4627 9.4426 .21 551.581 555. 737 -4.156

5 310.926 12.9058 12.9193 -.10 620.528 613.634 6.8 94

5 327.594 12.6232 12.6377 -.11 620.528 613.704 6.8 24

5 344.261 12. 3438 12.3579 -.11 620.528 614.438 6.091

5 360.928 12.0567 12.0800 -.19 620.528 611.201 9.327

5 377.594 11.7793 11.6044 -.21 620.528 611.207 9.321

5 410.926 11.2496 11.2625 -.11 620.528 616.332 4.196

5 444.261 10.7243 10.7370 -.12 620.528 616.905 3.623

5 477.594 10.2346 10.2327 .02 620.526 621.008 -.480

5 510.928 9.7710 9.7535 .18 620.528 624.706 -4.178

5 310.928 13.0584 13.0485 .06 689.476 695. 002 -5.526

5 327.594 12.8054 12.7777 .22 689.476 703.784 -14.309

5 344.261 12.5179 12.5092 .07 689.476 693.618 -4.142

5 360.928 12.2479 12.2432 .04 689.476 691. 585 -2.109

5 377.594 11.9696 11.9799 -.09 689.476 685.244 4.232

5 410.928 11.4707 11.4631 .07 689.476 692.215 -2.740

5 444.261 10.9750 10.9627 .11 689.476 693.447 -3.971

5 477.594 10.5055 10.4825 .22 689.476 696.237 -6.761

5 510.928 10. 0543 10.0256 .29 689.476 697.281 -7.805

NP = 306, ONRMSPCT = .320, PMEANOIF = 1.279
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. IDVIRIAL EQN., (2)DAWS0N, I3)BEATTIE,

(4)OESCHNER, (5)REAMER, (13)CHERNEY, (17) TOMLINSON, (24)ELY, (26)DITTMAR,

10 T,K MOL/L CALCO D,PCT P,8AR CALCO P,DIF

17 322.594 10.2592 10.2461 .13 20.774 21.861 -1.087

17 324.817 10.2567 10.2415 .15 29.110 30.409 -1.299

17 327.594 10.2537 10.2378 .16 39.672 41.088 -1.415

17 318.706 10.4385 10.4259 .12 20.864 22.050 -1.187

17 323.150 10.4335 10.4190 .14 38.638 40.078 -1.439

17 327.594 10.4286 10.4140 .14 56.523 58.038 -1.515

17 313.706 10.6195 10.6083 .11 17.382 18.545 -1.163

17 320.928 10.6106 10.5987 .11 48.022 49.358 -1.337

17 327.594 10.6029 10.5916 .11 76.311 77.676 -1.365

17 309.261 10.8163 10.8077 .08 19.140 20.156 -1.016

17 314.817 10.8095 10.7996 .09 44.064 45.294 -1.230

17 320.372 10.8025 10.7935 .08 69.085 70.271 -1.185

17 325.928 10.7959 10.7868 .08 93.913 95.177 -1.264

17 304.261 10.9973 10.9869 .09 17.127 18.473 -1.347

17 313.150 10.9857 10.9763 .09 59.412 60.738 -1.326

17 322.039 10.9746 10.9672 .07 101.567 102.699 -1.132

17 298.150 11.1828 11.1731 .09 11.238 12.606 -1.367

17 305.372 11.1728 11.1648 .07 47.615 48.330 -1.214

17 313.706 11.1619 11.1557 .06 89.370 90.385 -1.015

17 322.039 11.1510 11.1470 .04 130.890 131.594 -.704

17 293.150 11.3642 11.3553 . 08 11.445 12.842 -1.397

17 298.150 11.3570 11.3499 .06 38.100 39.253 -1.152

17 308.150 11.3431 11.3398 .03 91.162 91.758 -.595

17 316.483 11.3318 11.3316 .00 135.096 135.124 -.028

17 298.150 11.5322 11.5278 .04 69.272 70. 101 -.830

17 299.817 11.5465 11.5602 -.12 85.157 82. 501 2.656

17 303.150 11.5252 11.5228 .02 97.195 97.678 -.483

17 308.706 11.5173 11.5173 -.00 128.125 123.120 .005

17 282.594 11.7243 11.7147 .08 11.625 13.449 -1.824

17 284.261 11.7216 11.7127 .08 21.484 23.182 -1.698

17 291.483 11.7098 11.7061 .03 64.383 65.130 -.747

17 298.150 11.7003 11.6994 .01 103.635 103.815 -.180

17 303.150 11.6930 11.6937 -.01 132.765 132.618 .148

17 277.594 11.8799 11.8701 . 08 10.563 12.547 -1.984

17 285.928 11. 8663 11.8628 .03 62.501 63.254 -.753

17 291.483 11. 8572 11.8576 -.00 96.864 96.772 .093

17 298.150 11.8472 11.8509 -.03 137.792 136.910 .882

17 280.372 12.0377 12.0385 -.01 65.769 65.591 .178

17 285.928 12.0287 12.0326 -.03 101.780 100.821 .959

17 291.483 12.0198 12.0277 -.07 137.881 135.871 2.011

NP = 40, ONRMSPCT = .083, PMEANOIF = 1.080

83
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN. , (2)DAHS0N« (3)BEATTIEt

<4)DESCHNER, (5)REAMER, (13»CHERNEY, ( 17) TOMLINSON , (24)ELYt (26)DITTMAR.

ID t,k MOL/L CALCO Of PCT PfBAK CALCO PfOIF

24 288.263 11.5184 11.5159 .02 9.950 10.370 -.420

24 288.981 11.5182 11.5158 .02 14.087 14.487 -.400

24 291.393 11.5180 11.5156 .02 27.986 28.397 -.411

24 293.489 11.5175 11.5155 .02 40.067 40.431 -.364

24 296.555 11.5171 11.5154 .01 57.744 58.054 -.310

24 300.104 11.5164 11.5154 .01 78.212 78.400 -.188

24 303.696 11.5159 11.5155 .00 98.936 99.010 -.074

24 307.131 11.5152 11.5158 -.00 118.760 118.648 .112

24 310.771 11.5148 11.5162 -.01 139.780 139.485 .295

24 314.179 11.5141 11.5167 -.02 159.460 158.918 .542

24 317.799 11.5137 11.5173 -.03 180.380 179.592 .788

24 321.470 11.5130 11.5179 -.04 201.600 200.484 1.116

24 277.973 11.8368 11.8328 .03 5.517 6.303 -.786

24 278.268 11.8368 11.8330 .03 7.419 8.181 -.763

24 280.501 11.8363 11.8339 .02 21.805 22.305 -.500

24 283.701 11.3359 11.8351 .01 42.392 42.563 -.171

24 288.949 11.8348 11.8367 -.02 76.082 75.651 .431

24 294.597 11.8339 11.8382 -.04 112.241 111.255 .986

24 299.983 11.8329 11.8392 -.05 146.620 145.131 1.489

24 308.342 11.8316 11.8402 -.07 199.780 197.589 2.191

24 319.913 11.8295 11.8408 -.09 273.000 269.910 3.090

24 267.752 12.1552 12.1456 .08 4.041 6.258 -2.217

24 268.361 12.1550 12.1459 .07 8.370 10.473 -2.103

24 269.318 12.1550 12.1464 .07 15.169 17.178 -2.009

24 270.036 12.1547 12.1467 .07 20.268 22.154 -1.886

24 271.190 12.1545 12.1473 .06 28.457 30.180 -1.723

24 273.224 12.1541 12.1482 .05 42.877 44.306 -1.429

24 275.321 12.1538 12.1490 .04 57.722 58.916 -1.194

24 277.531 12.1534 12.1498 .03 73.345 74.248 -.903

24 280.521 12.1527 12.1507 .02 94.447 94.954 -.507

24 283.740 12.1522 12.1516 .01 117.120 117.291 -.171

24 287.984 12.1513 12.1525 -.01 146.930 146.618 .312

24 293.573 12.1504 12.1533 -.02 186.070 185.248 .822

24 299.091 12.1493 12.1538 -.04 224.570 223.243 1.327

24 304.757 12.1482 12.1539 -.05 263.950 262.184 1.766

24 312.701 12.1468 12.1536 -.06 318.910 316.717 2.193

24 323.740 12.1448 12.1523 -.06 394.790 392.192 2.598

24 258.574 12.4459 12.4317 .11 7.550 11.314 -3.764

24 260.283 12.4457 12.4330 .10 20.907 24.328 -3.421

24 264.687 12.4448 12.4358 .07 55.231 57.739 -2.508

24 269.204 12.4439 12.4381 .05 90.289 91.954 -1.665

24 273.221 12.4430 12.4397 .03 121.340 122. 303 -.963

24 278.846 12.4418 12.4414 .00 164.630 164.762 -.132

24 283.771 12.4409 12.4423 -.01 202.350 201.890 .460

24 288.215 12.4400 12.4428 -.02 236.230 235.307 .923

24 293.359 12.4391 12.4429 -.03 275.270 273.965 1.305

24 297.819 12.4382 12.4427 -.04 308.960 307. 384 1.576

24 300.501 12.4375 12.4424 -.04 329.150 327.404 1.746

24 305.386 12.4366 12.4417 -.04 365.800 363.937 1.863

24 310.827 12.4355 12.4405 -.04 406.410 404. 504 1.906

24 250.200 12.6886 12.6701 .15 7.767 13.233 -5.466

24 251.067 12.6883 12.6710 .14 15.143 20.310 -5.167

24 251.924 12.6881 12.6719 .13 22.426 27.301 -4.875

24 253.890 12.6877 12.6737 .11 39.104 43.352 -4.248

24 258.311 12.6867 12.6773 .07 76.451 79.435 -2.984

84
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN. . (2)OAWSONt (3)BEATTIEt

(4)0ESCHNERf (5)REAMER, (ISICHERNEY. ( 17) TOMLINSON » (24)ELYt (26)DITTMAR,

10 T,K MOL/L CALCO D.PCT PfBAR CALCO P.DIF

24 263.206 12.6856 12.6804 .04 117.550 119.275 -1.725

24 263.239 12.6856 12.6804 .04 117.830 119.546 -1.716

24 268.014 12.6847 12.6825 .02 157.660 158.402 -.742

24 276.292 12.6829 12.6846 -.01 226.120 225.517 .603

24 263.484 12.6813 12.6848 -.03 284.990 283.649 1.341

24 294.455 12.6790 12.6830 -.03 373.690 372.080 1.610

24 247.621 12.7416 12.7244 .14 2.571 7.758 -5.187

24 247.734 12.7416 12.7245 .13 3.546 8.704 -5.159

24 248.490 12.7416 12.7253 .13 10.065 15.038 -4.973

24 248.673 12.7414 12.7254 .13 11.642 16.501 -4.859

24 249.310 12.7414 12.7260 .12 17.130 21.836 -4.706

24 250.333 12.7412 12.7269 .11 25.934 30.332 -4.398

24 251.088 12.7409 12.7275 .11 32.424 36.582 -4.158

24 252.974 12.7405 12.7290 .09 48.612 52.219 -3.607

24 255.995 12.7398 12.7312 .07 74.466 77.259 -2.793

24 258.548 12.7394 12.7327 .05 96.241 98.436 -2.195

24 263.440 12.7382 12.7351 .02 137.810 138.872 -1.062

24 268.197 12.7373 12.7366 .01 177.930 178.187 -.257

24 273.360 12.7362 12.7376 -.01 221.250 220.725 .525

24 278.376 12.7350 12.7380 -.02 263.070 261.959 1.111

24 283.231 12.7339 12.7378 -.03 303.300 301.779 1.521

24 288.691 12.7328 12.7371 -.03 348.260 346.527 1.733

24 293.107 12.7319 12.7361 -.03 384.390 382.656 1.734

24 297.847 12.7310 12.7346 -.03 422.950 421.397 1.553

24 247.820 12.7731 12.7613 .09 15.453 19.117 -3.664

24 248.646 12.7731 12.7620 .09 22.614 26.102 -3.488

24 250.345 12.7727 12.7632 .07 37.322 40.322 -3.000

24 252.131 12.7722 12.7644 .06 52.754 55.267 -2.513

24 254.247 12.7718 12.7657 .05 70.999 72.986 -1.987

24 256.785 12.7713 12.7671 .03 92.827 94.250 -1.423

24 259.619 12.7706 12.7683 .02 117.130 117.913 -.783

24 262.510 12.7700 12.7694 .00 141.840 142.029 -.189

24 265.495 12.7693 12.7703 -.01 167.280 166.908 .3 72 24 268.171 12.7688 12.7710 -.02 190.010 189.244 .766

24 271.181 12.7682 12.7715 -.03 215.500 214.279 1.221

24 276.240 12.7670 12.7719 -.04 258.150 256.296 1.854

24 281.440 12.7659 12.7718 -.05 301.730 299.410 2.320

24 286.945 12.7648 12.7711 -.05 347.600 344.986 2.614

24 286.968 12.7648 12.7711 -.05 347.790 345.179 2.611

24 291.062 12.7638 12.7704 -.05 381.720 378.985 2.735

24 296.653 12.7627 12.7689 -.05 427.790 425.112 2.678

24 235.542 13.0727 13.0591 .10 4.570 9.317 -4.747

24 236.163 13.0725 13.0598 .10 10.563 15.003 -4.440

24 237.116 13.0723 13.0609 .09 19.745 23.770 -4.025

24 237.986 13.0720 13.0618 .08 28.112 31.763 -3.651

24 239.626 13.0718 13.0634 .06 43.844 46.895 -3.051

24 242.193 13. 0711 13.0655 .04 68. 363 70 .445 -2.082

24 245.592 13. 0704 13.0677 .02 100.630 101.675 -1.045

24 249.203 13. 0695 13.0693 .00 134.660 134.739 -.079

24 252.921 13.0686 13.0704 -.01 169.440 168.744 .696

24 256.518 13.0677 13.0708 -.02 202.830 201.584 1.246

24 260.718 13.0668 13.0705 -.03 241.490 239.933 1.557

24 264.442 13.0659 13.0697 -.03 275.490 273.841 1.649

24 267.990 13.0650 13.0685 -.03 307.630 306.032 1.548

24 232.965 13.1686 13.1475 .16 11.792 19.533 -7.741

24 234.603 13.1684 13.1489 .15 27.885 35.118 -7,233

85
Table 9. Continued.

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN. , (2»DAWS0N, C3)BEATTIE,

I4)DESCHNER, (5)REAMER, (13)CHERNEY, ( 17) TOMLINSON , (24)ELY, (26)0ITTMAR.

10 T,K MOL/L CALCO 0,PCT P.BAR CALCO P.DIF

24 234.672 13.1684 13.1490 .15 28.562 35,778 -7.216

24 236.343 13.1680 13.1503 .13 44.938 51.585 -6.647

24 238.154 13.1675 13.1516 .12 62.641 68.719 -6.078

24 239.793 13.1670 13.1526 .11 78.622 84.198 -5.576

24 242.380 13.1664 13.1540 .09 103,770 108.625 -4.855

24 245.001 13.1659 13.1552 .08 129.150 133.442 -4.292

24 249.556 13.1648 13.1567 .06 173.020 176.374 -3,354

24 254.065 13.1636 13.1575 .05 216.150 218.792 -2.642

24 258.913 13.1625 13.1577 .04 262.210 264.353 -2,143

24 263.566 13.1614 13.1573 .03 306.100 307.981 -1.881

24 268.618 13.1602 13.1562 .03 353.390 355.303 -1.913

24 273.058 13.1591 13.1548 .03 394.660 396.751 -2.091

24 226.866 13. 315.. 13.3040 .08 11.092 15.410 -4.318

24 228.670 13.3147 13.3056 .07 29.726 33. 311 -3.565

24 230.980 13.3142 13.3074 .05 53.514 56.266 -2.752

24 234.058 13.3133 13.3094 .03 85.084 86,699 -1.615

24 237.362 13.3129 13.3111 .01 118.810 119.545 -.735

24 242.108 13. 3115 13.3129 -.01 166.960 166.356 .604

24 247.394 13.3101 13.3140 -.03 220.190 218.456 1.734

24 250.151 13.3095 13.3142 -.04 247.790 245. 601 2.189

24 254.663 13. 3083 13.3141 -.04 292.690 289,951 2.739

24 258.294 13.3074 13.3136 -.05 328.600 325.586 3.014

24 261.963 13.3061 13.3128 -.05 364.690 361.321 3.369

24 265.574 13.3056 13.3118 -.05 400.010 396,879 3.131

24 218.855 13.5163 13.5006 .12 7.779 14, 399 -6.620

24 219.585 13.5160 13.5012 .11 15.821 22.107 -6.286

24 221.230 13.5156 13.5026 .10 33.908 39.494 -5.586

24 223.680 13.5151 13.5044 .08 60.763 65.466 -4.703

24 226.125 13.5145 13.5060 .06 87.463 91.263 -3.800

24 227.750 13.5140 13.5068 . 05 105,150 108.394 -3.244

24 228.861 13.5138 13.5074 .05 117.220 120.138 -2,918

24 229.601 13.5136 13.5077 .04 125.250 127.923 -2.673

24 231.940 13.5129 13.5087 .03 150.560 152,531 -1.971

24 234.664 13.5122 13.5095 .02 179.930 181.214 -1,284

24 238.083 13.5113 13.5102 .01 216.610 217.146 -.536

24 242.385 13.5102 13.5105 -.00 262.480 262.293 .187

24 246.702 13.5090 13.5103 -.01 308.200 307.522 .678

24 251.325 13.5079 13.5096 -.01 356.820 355.911 .909

24 256.596 13.5065 13.5081 -.01 411,820 410.937 .883

24 211.641 13.6959 13.6738 .16 4.075 14.055 -9.981

24 212.694 13.6957 13.6747 .15 16.320 25.887 -9.567

24 214.101 13.6952 13.6758 .14 32.652 41.619 -8.967

24 217.902 13.6941 13.6783 .12 76.602 84.119 -7.517

24 222.089 13.6929 13.6803 .09 124.730 130.918 -6.188

24 225.450 13.6920 13.6315 .08 163.140 168.432 -5.292

24 230.231 13.6907 13.6831 .06 217.740 221.674 -3.934

24 235.520 13.6893 13.6829 .05 277.060 280.530 -3.470

24 241.297 13.6877 13.6824 .04 341.620 344.621 -3.001

24 244. 776 13.6868 13.6817 .04 380.220 383.171 -2.951

24 247.542 13.6859 13.6809 .04 410.760 413.673 -2.913

24 205.755 13. 8569 13. 8486 .06 17.649 21,716 -4.067

24 207.297 13.8564 13.8497 .05 36.606 39.920 -3.314

24 209.435 13.8560 13.8512 .03 62.801 65.230 -2.429

24 212.526 13. 3551 13.8528 .02 100.490 101.662 -1.172

24 216.578 13. 8537 13.8543 -.00 149.560 149.263 .297

24 220.157 13.8528 13.8550 -.02 192.590 191.399 1.191

86
Table 9. Continued.

EQUATION OF STATE VS. PVT DATA. (DVIRIAL EQN., (2JDAWS0N* (3)BEATTIE»

(4)0ESCHNER» (SJREAMER* (13»CHERNEY. ( 17) TOMLINSON . I24)ELY. <26)DITTMAR.

ID T,K MOL/L CALCO 0,PCT P,BAR CALCO P,DIF

24 225.334 13.8512 13.8552 -.03 254.320 252 .094 2.2 26

24 227.547 13.3508 13.8549 -.03 280.520 278.127 2.393

24 230.619 13.8496 13.8543 -.03 319.060 316.310 2.750

24 235.224 13.8485 13.8530 -.03 370.550 367.860 2.690

24 237.320 13.8478 13.8521 -.03 394.890 392.271 2.619

24 199.157 13.9909 13.9853 .04 5.378 8.234 -2.856

24 200.472 13. 9905 13.9864 .03 22.353 24.438 -2.085

24 202.817 13.9898 13.9879 .01 52.383 53.379 -.996

24 206.391 13.9886 13.9898 -.01 97.993 97.388 .605

24 210.980 13.9873 13.9911 -.03 156.020 153.857 2.163

24 216.347 13.9857 13.9917 -.04 223.260 219.771 3.489

24 216.464 13.9855 13.9910 -.04 224.300 221.095 3.205

24 221.205 13.9841 13.9859 -.01 280.310 279.220 1.0 90 24 225.885 13.9827 13.9891 -.05 340.430 336.475 3.955

24 231.094 13. 9812 13.9868 -.04 403.660 400.023 3.637

24 192.615 14.1549 14.1513 .03 9.162 11.105 -1.943

24 193.111 14.1549 14.1517 .02 15.904 17.659 -1.755

24 195.904 14.1540 14.1534 .00 53.735 54.045 -.310

24 197.140 14.1535 14.1540 -.00 70.407 70.105 .302

24 199.390 14.1528 14.1550 -.02 100.650 99.402 1.248

24 202.609 14. 1517 14.1559 -.03 143.660 141.178 2.482

24 205.926 14.1508 14.1563 -.04 187.680 184.324 3.356

24 209.500 14.1496 14.1563 -.05 234.770 230.655 4.115

24 213.137 14.1485 14.1557 -.05 282.320 277.744 4.576

24 215.014 14. 1478 14.1552 -.05 306.720 301.956 4.764

24 217.285 14.1472 14.1545 -.05 336.100 331.315 4.785

24 220.119 14. 1462 14.1533 -.05 372.570 367.875 4.695

24 184.715 14.3397 14.3358 .03 6.163 8.475 -2.312

24 185.973 14.3392 14.3365 .02 24.300 25.918 -1.618

24 187.723 14.3368 14.3267 .08 42.992 50.274 -7.282

24 189.954 14. 3379 14.3383 -.00 81.375 81.102 .273

24 194.865 14.3363 14.3394 -.02 151.110 149.115 1.995

24 198.151 14.3351 14.3395 -.03 197.350 194.501 2.849

24 204.051 14.3331 14.3386 -.0^1 279.550 275.827 3.723

24 208.548 14.3317 14.3370 -.Oi* 341.470 337.807 3.663

24 213.736 14.3299 14.3343 -.03 412.140 408.984 3.156

24 177.351 14.5243 14.5227 .01 13.550 14.535 -.985

24 179.819 14.5234 14.5238 -.00 51.280 51.008 .272

24 181.543 14.5227 14.5243 -.01 77.509 76.433 1.0 76

24 183.330 14.5222 14.5247 -.02 104.590 102.935 1.655

24 187.888 14.5206 14.5249 -.03 173.130 170.162 2.968

24 190.854 14.5195 14.5246 -.04 217.350 213.768 3.582

24 194. 795 14.5182 14.5235 -.04 275.610 271.722 3.888

24 198.915 14.5168 14.5217 -.03 335.930 332.245 3.6 85

24 201.433 14.5159 14.5203 -.03 372.500 369.123 3.377

24 204.616 14.5148 14.5183 -.02 418.440 415.716 2.724

24 166.227 14. 7764 14.7745 .01 7.033 8.424 -1.391

24 167.461 14.7760 14.7749 .01 27.642 28.385 -.743

24 168.747 14.7755 14.7753 .00 49.045 49.192 -.147

24 171.053 14. 7746 14.7758 -.01 87.235 86.406 .829

24 174.434 14. 7733 14.7758 -.02 142.790 140.880 1.910

24 178.373 14. 7717 14.7751 -.02 206.850 204.237 2.613

24 182.557 14.7701 14.7734 -.02 274.110 271.484 2.626

24 187.796 14.7683 14.7702 -.01 357.200 355.643 1.557

24 189. 617 14. 7676 14.7686 -.01 388.920 388.070 .650

NP = 222, DNRMSPCT = .060, PMEANOIF = 2.494

87
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (DVIRIAL EQN. , (2)OAWSONt (3)BEATTIE.

<4)DESCHNER, (5)REAMER, I13ICHERNEY, 1 17) TOMLINSON. (24»ELY, (26)DITTMAR.

ID T.K MOL/L CALCD D.PCT P,BAR CALCO P.OIF

26 373.150 7.2567 7.4795 -3.07 53.937 51.540 2.397

26 383.150 7.2567 7.3794 -1.69 68.647 66.809 1.837

26 393.150 7.2567 7.3627 -1.46 84.337 82.251 2.086

26 403.150 7.2567 7.3476 -1.25 100.028 97.815 2.213

26 413.150 7.2567 7.3341 -1.07 115.718 113.471 2.247

26 363.150 7.7102 7.9057 -2.54 42.169 39. 807 2.361

26 373.150 7.7102 7.8588 -1.93 59.821 57.206 2.615

26 383.150 7.7102 7.8248 -1.49 77.473 74.835 2.637

26 393.150 7.7102 7.8315 -1.57 96.105 92.614 3.492

26 403. 150 7.7102 7.7776 -.87 112.776 110.503 2.274

26 413.150 7.7102 7.7845 -.96 131.409 128.479 2.930

26 363.150 8.1638 8.2843 -1.48 49.033 46.476 2.558

26 373.150 8.1638 8.2346 -.87 68.647 66.711 1.936

26 383.150 8.1638 8.2268 -.77 89.241 87.107 2.133

26 393.150 8.1638 8.2423 -.96 110.815 107.620 3.195

26 403.150 8.1638 8.2316 -.83 131.409 128.223 3.186

26 413.150 8.1638 8.2220 -.71 152.003 148.898 3.105

26 353.150 8.6173 8.6318 -.17 35.304 34.935 .369

26 363.150 3.6173 8.6341 -.20 58.840 58.278 .562

26 373.150 8.6173 8.6321 -.17 82.376 81.768 .608

26 383.150 8.6173 8.6486 -.36 106.892 105.364 1.529

26 393.150 8.6173 8.6592 -.49 131.409 129.038 2.371

26 403.150 8.6173 8.6513 -.39 154.945 152.775 2.170

26 413. 150 8.6173 8.6579 -.47 179.462 176.561 2.901

26 353.150 9.0709 9. 0668 .05 50.014 50.190 -.176

26 363.150 9.0709 9.0928 -.24 78.453 77.307 1.146

26 373.150 9.0709 9.0940 -.26 105.912 104.499 1.413

26 383.150 9.0709 9.0942 -.26 133.370 131.746 1.624

26 393.150 9.0709 9.0939 -.25 160.829 159. 035 1.794

26 403.150 9.0709 9.0932 -.25 188.288 186.355 1.933

26 413.150 9. 0709 9.0925 -.24 215.746 213.696 2.050

26 343.150 9.2976 9.2830 .16 31.381 32.028 -.647

26 353.150 9.2976 9.2914 .07 60.801 61.134 -.333

26 363.150 9.2976 9.3117 -.15 91.202 90.306 .896

26 373.150 9.2976 9.3127 -.16 120.622 119.524 1.097

26 383.150 9.2976 9.3131 -.17 150.042 148.776 1.266

26 393.150 9.2976 9.3132 -.17 179.462 178.049 1.412

26 403. 150 9.2976 9.3131 -.17 208.882 207.338 1.543

26 413.150 9.2976 9.3219 -.26 239.282 236.635 2.647

26 343. 150 9.5244 9.5017 .24 42.169 43.440 -1.272

26 353.150 9.5244 9.5211 .04 74.531 74. 754 -.2 24

26 363.150 9.5244 9.5219 .03 105.912 106.100 -.188

26 373.150 9.5244 9.5224 .02 137.293 137.467 -.174

26 383.150 9.5244 9.5328 -.09 169.655 168.846 .809

26 393.150 9.5244 9.5321 -.08 201.036 200.229 .607

26 403.150 9.5244 9.5314 -.07 232.418 231.612 .606

26 413.150 9.5244 9.5388 -.15 264.780 262.988 1.792

26 343.150 9.7512 9.7521 -.01 57.859 57.798 .061

26 353.150 9.7512 9.7483 .03 91.202 91.439 -.237

26 363.150 9.7512 9.7453 .06 124.544 125.084 -.539

26 373.150 9.7512 9.7526 -.01 158.868 158.727 .141

26 383.150 9.7512 9.7586 -.08 193.191 192.362 .629

26 393.150 9.7512 9.7557 -.05 226.534 225.985 .549

26 403.150 9.7512 9.7533 -.02 259.876 259.591 .286

26 413.150 9. 7512 9.7652 -.14 295.180 293.176 2.004

8
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN. » (2)DAHS0Ni <3)8EATTIE,

(4)DESCHNERy (5)REAMER« (13ICHERNEY* ( 17) TOMLINSON* (24)ELY* <26)0ITTHAR.

ID T.K MOL/L CALCO DtPCT PtBAR CALCO P,DIF

26 333.150 9.9780 9.9755 .02 39.227 39.407 -.180

26 343.150 9.9780 9.9779 .00 75.511 75,517 -.006

26 353.150 9.9780 9.9798 -.02 111.796 111.612 .183

26 363.150 9.9780 9.9725 .05 147.100 147.688 -.589

26 373.150 9.9780 9.9750 .03 183.384 183.742 -.357

26 383.150 9.9780 9.9772 .01 219.669 219.768 -.100

26 393.150 9.9780 9.9723 .06 254.973 255. 766 -.793

26 403.150 9.9780 9.9683 .10 290.277 291.731 - 1.455

26 413.150 9.9780 9.9712 .07 326.561 327.662 - 1.101

26 333.150 10.2047 10.1889 .15 56.879 58.327 - 1.449

26 343.150 10.2047 10.1956 .05 96.105 97.053 -.948

26 353.150 10.2047 10.1927 .12 134.351 135,739 - 1.388

26 363.150 10.2047 10.1906 .14 172.597 174. 386 - 1.789

26 373.150 10.2047 10.1892 .15 210.843 212.991 - 2.148

26 363.150 10.2047 10.1949 .10 250.070 251,552 - 1.482

26 393.150 10.2047 10.1878 .17 287.335 290.068 - 2.733

26 403.150 10.2047 10.1990 .06 327.542 328.536 -.994

26 413.150 10.2047 10.1931 .11 364.807 366.957 - 2.149

26 323.150 10.4315 10.4249 .06 39.227 39.875 -.648

26 333.150 10.4315 10.4313 .00 81.395 81.420 -.024

26 343.150 10.4315 10.4210 .10 121.602 122.903 - 1.301

26 353.150 10.4315 10.4202 .11 162.790 164.328 - 1.538

26 363.150 10.4315 10.4266 .05 204.959 205.694 -.735

26 373.150 10.4315 10.4201 .11 245.166 247.002 - 1,835

26 383.150 10.4315 10.4091 .21 284.393 288.249 - 3.856

26 393.150 10.4315 10.4213 .10 327.542 329.436 - 1.894

26 403.150 10.4315 10.4172 .14 367.749 370.561 - 2.812

26 413.150 10.4315 10.4233 .08 409.918 411.624 - 1.706

26 313.150 10.6583 10.6530 .05 19.613 20.178 -.565

26 323.150 10.6583 10.6500 .08 63,743 64.740 -.997

26 333.150 10.6583 10.6408 .16 106.892 109.219 - 2.326

26 343.150 10.6583 10.6472 .10 152.003 153.617 - 1.614

26 353.150 10.6583 10.6408 .16 195.152 197,939 - 2.787

26 363.150 10.6583 10.6414 .16 239.282 242.186 - 2.904

26 373.150 10.6583 10.6424 .15 283.412 286,357 - 2.945

26 383.150 10.6583 10.6436 .14 327.542 330.454 - 2.911

26 393.150 10.6583 10.6403 .17 370.691 374.475 - 3,784

26 403.150 10.6583 10.6422 .15 414.821 418.421 - 3.600

26 413.150 10.6583 10.6483 .09 459.932 462.292 - 2.360

26 313.150 10.8850 10.8624 .21 44.130 47,055 - 2.925

26 323.150 10.8850 10.8673 .16 92.183 94.735 - 2.552

26 333.150 10.8850 10.8656 .18 139.254 142.315 - 3,061

26 343.150 10.8850 10.8648 .19 186.326 189.800 - 3.473

26 353.150 10.8850 10.8699 .14 234.379 237. 191 - 2.812

26 363.150 10.8850 10.8698 .14 281.451 284.492 - 3,041

26 373.150 10.8850 10.8701 .14 328.523 331.703 - 3.180

26 383.150 10.8850 10.8708 .13 375.595 378,824 - 3.230

26 393.150 10.8850 10.8800 .05 424.628 425.857 - 1.229

26 403.150 10. 8850 10.8769 .08 470.719 472.800 - 2.081

26 413.150 10.8850 10.8781 .06 517,791 519,656 - 1.864

26 303.150 11.1118 11.0840 .25 24.517 28.410 - 3.894

26 313.150 11.1118 11.0923 .18 76.492 79,514 - 3.022

26 323.150 11.1118 11.0999 .11 128.467 130.496 - 2.029

26 333.150 11.1118 11.1016 .09 179.462 181.363 - 1.902

26 343.150 11.1118 11.1035 .07 230.456 232.121 - 1,664

26 353.150 11.1118 11.1057 .06 281.451 282.771 — 1.320

89
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. IDVIRIAL EQN. , I2)0AWS0N, I3JBEATTIE,

I4)0ESCHNER» (5)REAMER, (13)CHERNEY, ( 17) TOML INSON , <24)ELY, (26)0ITTMAR,

ID T,K MOL/L CALCO O.PCT P.BAR CALCD P.OIF

26 363.160 11.1118 11.1038 .07 331.465 333.316 -1.851

26 373.150 11.1118 11.1065 .05 382.459 383.756 -1.297

26 383.150 11.1118 11.1056 .06 432.473 434. 094 -1.621

26 393.150 11.1118 11.1015 .09 481.507 484.329 -2.823

26 403.150 11.1118 11.1050 .06 532.501 534.463 -1.962

26 413.150 11.1118 11.1053 .06 582.515 584.495 -1.980

26 303.150 11.3386 11.3160 .20 59.821 63.623 -3.802

26 313.150 11.3386 11.3196 .17 114.738 118.243 -3.505

26 323.150 11.3386 11.3233 .14 169.655 172.731 -3.076

26 333.150 11.3386 11. 3270 .10 224.572 227. 091 -2.519

26 343.150 11.3386 11.3265 .11 278.509 281.328 -2.619

26 353.150 11. 3386 11.3265 .11 332.445 335.444 -2.998

26 363.150 11.3386 11.3270 .10 386.382 389.440 -3.058

26 373.150 11.3336 11.3314 .06 441.299 443.320 -2.021

26 383.150 11.3386 11.3290 .08 494.255 497.083 -2.628

26 393.150 11.3386 11.3304 .07 548.192 550. 730 -2.538

26 403.150 11.3386 11.3290 . 08 601.148 604.263 -3.115

26 413.150 11.3386 11.3252 .12 653.123 657.681 -4.558

26 293.150 11.4520 11.4246 .24 22.555 27.126 -4.571

26 303.150 11.4520 11.4285 .20 79.434 83.734 -4.300

26 313.150 11.4520 11.4375 .13 137.293 140.196 -2.903

26 323.150 11.4520 11.4412 .09 194.172 196. 520 -2.348

26 333.150 11.4520 11.4407 .10 250.070 252.710 -2.641

26 343.150 11.4520 11.4408 .10 305.967 308.770 -2.803

26 353.150 11.4520 11.4450 .06° 362.846 364.703 -1.857

26 363.150 11.4520 11.4422 .08 417.763 420.511 -2.748

26 373.150 11.4520 11.4435 .07 473.661 476.194 -2.533

26 383.150 11.4520 11.4450 .06 529.559 531. 754 -2.195

26 393.150 11.4520 11.4438 .07 584.476 587.192 -2.716

26 403.150 11.4520 11.4430 .08 639.394 642.509 -3.115

26 413. 150 11.4520 11.4372 .13 692.349 697.705 -5.355

26 293.150 11. 5654 11.5436 .19 43.149 47.136 -3.986

26 303.150 11.5654 11.5520 .12 102.970 105.649 -2.679

26 313.150 11.5654 11.5552 .09 161.810 164. 012 -2.202

26 323.150 11.5654 11.5586 .06 220.650 222.232 -1.582

26 333.150 11. 5654 11.5582 . 06 278.509 280.312 -1.603

26 343.150 11.5654 11.5547 .09 335.387 338.256 -2.868

26 353.150 11. 5654 11.5589 .06 394.227 396.066 -1.838

26 363.150 11.5654 11.5599 .05 452.087 453.743 -1.657

26 373.150 11.5654 11.5581 .06 508.965 511.291 -2.325

26 383.150 11.5654 11.5598 .05 566.824 563.708 -1.884

26 393.150 11.5654 11.5589 .06 623.703 625.997 -2.294

26 403.150 11.5654 11.5557 .08 679.601 683.157 -3.557

26 413.150 11.5654 11.5557 .08 736.479 740.191 -3.712

26 293.150 11.6787 11.6574 .18 64.724 68.992 -4.269

26 303.150 11.6787 11.6651 .12 126.506 129.474 -2.969

26 313.150 11.6787 11.6682 .09 187.307 189.802 -2.495

26 323.150 11.6787 11.6714 .06 248. 108 249.980 -1.872

26 333.150 11.6787 11.6747 .03 308.909 310. 013 -1.103

26 343.150 11.6787 11.6713 .06 367.749 369.903 -2.154

26 353.150 11.6787 11.6751 .03 428.551 429.653 -1.103

26 363.150 11.6787 11.6730 .05 487. 391 489.265 -1.874

26 373.150 11.6787 11.6743 .04 547.211 548.739 -1.528

26 333.150 11.6787 11.6758 .02 607.032 608.077 -1.045

26 393.150 11.6787 11.6750 .03 665.872 667.279 -1.408

26 403.150 11.6787 11.6721 .06 723.731 726.347 -2.616

90
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN., (2)DAWSON» (3JBEATTIE.

(4)0ESCHNER* (5)REAMER. I13)CHERNEY, ( 17) TOMLINSON. C24)ELY. (26)0ITTHAR.

10 T.K MOL/L CALCD O.PCT P,BAR CALCD P.DIF

26 413.150 11.6787 11.6697 .08 781.590 785.281 -3.691

26 263.150 11.7921 11.7689 .20 25.497 30.124 -4.627

26 293.150 11.7921 11.7757 .14 89.241 92.808 -3.567

26 303.150 11.7921 11.7781 .12 152.003 155.325 -3.322

26 313.150 11.7921 11.7845 .06 215.746 217.683 -1.936

26 323. 150 11.7921 11.7871 .04 278.509 279.886 -1.377

26 333.150 11.7921 11.7865 .05 340.291 341.938 -1.647

26 343.150 11.7921 11.7864 .05 402.073 403.841 -1.769

26 353.150 11.7921 11.7898 .02 464.835 465.598 -.763

26 363.150 11.7921 11.7904 .01 526.617 527.209 -.592

26 373.150 11.7921 11.7887 .03 587.418 588.677 -1.258

26 383.150 11.7921 11.7900 .02 649.200 650.001 -.801

26 393.150 11.7921 11.7867 . 05 709.021 711. 183 -2.162

26 403.150 11.7921 11.7864 .05 769.822 772.224 -2.402

26 413.150 11.7921 11.7841 .07 829.643 833.124 -3.481

26 283.150 11.9055 11.8967 .07 51.975 53.906 -1.931

26 293.150 11.9055 11.8971 .07 116.699 118.699 -2.000

26 303.150 11.9055 11.9058 -.00 183.384 183.321 .063

26 313.150 11.9055 11.9067 -.01 243.108 247.779 .329

26 323.150 11.9055 11.9081 -.02 312.832 312.078 .754

26 333.150 11.9055 11.9067 -.01 376.575 376.219 .356

26 343.150 11.9055 11.9068 -.03 441.299 440.205 1.094

26 353.150 11.9055 11.9112 -.05 506.023 504.039 1.905

26 363.150 11.9055 11.9111 -.05 569.766 567.720 2.047

26 373.150 11.9055 11.9113 -.05 633.510 631.250 2.260

26 383.150 11.9055 11.9096 -.03 696.272 694.630 1.642

26 393.150 11.9055 11.9083 -.02 759.035 757.861 1.174

26 403.150 11.9055 11.9052 .00 820.817 820.943 -.127

26 413.150 11.9055 11.9027 .02 882.598 883.879 -1.280

26 273.150 12.0189 12.0058 .11 9.807 12.658 -2.852

26 283.150 12.0189 12.0090 .08 77.473 79.814 -2.342

26 293.150 12.0189 12.0163 .02 146.119 146.790 -.671

26 303.150 12.0189 12.0196 -.01 213.785 213. 592 .193

26 313.150 12.0189 12.0197 -.01 280.470 280.225 .245

26 323.150 12.0189 12.0235 -.04 348. 136 346.692 1.444

26 333.150 12.0189 12.0243 -.05 414.821 412.997 1.825

26 343.150 12.0189 12.0228 -.03 480.526 479.140 1.386

26 353.150 12.0189 12.0219 -.02 546.230 545. 123 1.108

26 363.150 12.0189 12.0214 -.02 611.935 610. 946 .988

26 373.150 12.0189 12.0214 -.02 677.640 676.613 1.027

26 383.150 12.0189 12.0172 .01 741.383 742.122 -.739

26 393.150 12.0189 12.0180 .01 807.087 807.474 -.387

26 403.150 12.0189 12.0150 .03 870.831 872.672 -1.841

26 413.150 12.0189 12.0125 . 05 934.574 937.714 -3.141

26 273.150 12.1323 12.1269 .04 37.265 38.556 -1.291

26 283.150 12.1323 12.1319 .00 107.873 107.977 -.104

26 293.150 12.1323 12.1333 -.01 177.500 177.214 .286

26 303.150 12.1323 12.1351 -.02 247.128 246.274 .853

26 313.150 12.1323 12.1342 -.02 315.774 315.160 .614

26 323.150 12.1323 12.1368 -.04 385.401 383.875 1.527

26 333.150 12.1323 12.1395 -.06 455.029 452.420 2.609

26 343.150 12.1323 12.1398 -.06 523.675 520.797 2.878

26 353.150 12.1323 12.1406 -.07 592.322 589. 007 3.315

26 363.150 12.1323 12.1416 -.08 660.968 657. 051 3.917

26 373.150 12.1323 12.1385 -.05 727.653 724.930 2.724

26 383.150 12.1323 12.1360 -.03 794.339 792.644 1.694
Table 9. Continued

EQUATION OF STATE VS. PVT OATA. (i)VIRIAL EQN.t (2)0AMS0Nt 13)BEATTIE«

<4)0ESCHNER, (5)REAMER, (13)CHERNEY, ( 17 ) TOMLINSON , (24>ELY, (26IDITTMAR.

10 T.K MOL/L CALCO PCT P,BAR CALCO P,DIF

26 393.150 12.1323 12.1340 -.01 861.024 860.195 .829

26 403.150 12.1323 12.1306 .01 926.728 927,583 -.855

26 413.150 12.1323 12.1296 .02 993.414 994.810 -1.396

26 273.150 12.2457 12.2454 .00 66.685 66.761 -.076

26 263.150 12.2457 12.2463 -.02 139.254 138.530 .724

26 293.150 12.2457 12.2513 -.05 211.824 210.113 1.711

26 303.150 12.2457 12.2516 -.05 283.412 281.514 1.899

26 313.150 12.2457 12.2523 -.05 355.001 352,735 2.266

26 323.150 12.2457 12.2534 -.06 426.589 423.779 2.810

26 333.150 12.2457 12.2523 -.05 497.197 494,647 2.551

26 343.150 12.2457 12.2541 -.07 568.786 565.339 3.446

26 353.150 12.2457 12.2517 -.05 638.413 635.858 2.555

26 363.150 12.2457 12.2520 -.05 709.021 706.203 2.817

26 373.150 12.2457 12.2505 -.04 778.648 776, 376 2.272

26 383.150 12.2457 12.2516 -.05 849.256 846,377 2.879

26 393.150 12.2457 12.2490 -.03 917.902 916.206 1.696

26 403.150 12.2457 12.2451 .00 985.568 985.865 -.297

26 273.150 12.3591 12.3614 -.02 98.066 97,414 .652

26 263.150 12.3591 12.3655 -.05 173.578 171. 620 1.957

26 293.150 12.3591 12.3666 -.06 248.108 245. 636 2,472

26 303.150 12.3591 12.3682 -.07 322.639 319.465 3.173

26 313.150 12.3591 12.3700 -.09 397.169 393.109 4.060

26 323.150 12.3591 12.3696 -.09 470.719 466.569 4.150

26 333. 150 12.3591 12.3698 -.09 544.269 539.846 4.423

26 343.150 12.3591 12.3703 -.09 617,819 612.941 4.878

26 353.150 12.3591 12.3668 -.06 689.407 685.853 3.554

26 363.150 12.3591 12.3641 -.04 760.996 758.585 2.411

26 373.150 12.3591 12.3639 -.04 833.565 831.137 2.429

26 363.150 12.3591 12.3622 -.03 905.154 903.508 1.646

26 393.150 12.3591 12.3610 -.02 976.742 975.700 1.042

26 273.150 12.4724 12.4813 -.07 133.370 130.666 2.704

26 263.150 12.4724 12.4859 -.11 211.824 207.403 4.421

26 293.150 12.4724 12.4876 -.12 289.296 283,945 5.351

26 303.150 12.4724 12.4897 -.14 366,769 360.295 6.474

26 313.150 12.4724 12.4895 -.14 443.261 436.453 6.808

26 323.150 12.4724 12.4899 -.14 519.752 512.420 7.332

26 333.150 12.4724 12.4862 -.11 594.283 588,197 6.086

26 343.150 12.4724 12.4875 -.12 670.775 663.784 6,991

26 353.150 12.4724 12.4850 -.10 745.305 739.181 6.124

26 363.150 12.4724 12.4812 -.07 818.855 814.390 4.466

26 373.150 12.4724 12.4781 -.05 892.405 889.409 2.996

26 363.150 12.4724 12.4773 -.04 966.936 964.240 2.696

26 273.150 12.5858 12.6007 -.12 171.616 166.678 4.939

26 263.150 12.5858 12.6027 -.13 252.031 246.044 5,987

26 293.150 12.5858 12.6023 -.13 331.465 325.210 6.255

26 303.150 12.5858 12.6025 -.13 410.899 404.178 6.721

26 313.150 12.5858 12.6031 -.14 490.333 482.947 7.385

26 323.150 12.5858 12.6020 -.13 568.786 561,518 7,267

26 333.150 12.5858 12.6014 -.12 647.239 639. 891 7.348

26 343.150 12.5858 12.5972 -.09 723.731 718.066 5.665

26 353.150 12.5858 12.5939 -.06 800.223 796.042 4.180

26 363.150 12.5858 12.5930 -.06 877.695 873.821 3.874

26 373.150 12.5858 12.5908 -.04 954.187 951.402 2.785

26 383.150 12. 5858 12.5874 -.01 1029.698 1028.787 .912

26 273.150 12.6992 12.7165 -.14 211.824 205.620 6.204

26 283.150 12.6992 12.7161 -.13 294.200 287.720 6.480

92
Table 9. Continued

EQUATION OF STATE VS. PVT DATA. (l)VIRIAL EQN. , (2)0AWS0N, (3) BEATTIE*

C4)DESCHNER» (5)REAMER« (13)CHERNEY* (17) TOMLINSON* (24)ELY* (26)0ITTMAR.

ID T*K MOL/L CALCO D*PCT P*BAR CALCD P*OIF

26 293.150 12.6992 12.7187 -.15 377.556 369.614 7.942

26 303.150 12.6992 12.7191 -.16 459.932 451.302 8.630

26 313.150 12.6992 12.7158 -.13 540.346 532.785 7,562

26 323.150 12.6992 12.7172 -.14 622.722 614.061 8.661

26 333.150 12.6992 12.7131 -.11 702.156 695.131 7.025

26 343.150 12.6992 12.7098 -.08 781.590 775,993 5.597

26 353.150 12.6992 12.7071 -.06 861.024 856.649 4.375

26 363.150 12.6992 12.7033 -.03 939.477 937.098 2.379

26 373.150 12.6992 12.7018 -.02 1018.911 1017.340 1.571

26 273.150 12.8126 12.8314 -.15 254.973 247.677 7.296

26 283.150 12.8126 12.8288 -.13 339.310 332.620 6.690

26 293.150 12.8126 12.8292 -.13 424.628 417.350 7,277

26 303.150 12.8126 12.8279 -.12 508.965 501.868 7.097

26 313.150 12.8126 12.8272 -.11 593.302 586.172 7.131

26 323.150 12.8126 12.8231 -.08 675.678 670.260 5.418

26 333.150 12.8126 12.8199 -.06 758.054 754.133 3.921

26 343.150 12.3126 12.8173 -.04 840.430 837.789 2.641

26 353.150 12.8126 12.8136 -.01 921.825 921.228 .597

26 363.150 12. 8126 12.8106 .02 1003.220 1004.451 -1,231

26 273.150 12.9260 12.9452 -.15 301.064 293.043 8.021

26 283.150 12.9260 12.9426 -.13 388.343 380.946 7.398

26 293.150 12.9260 12.9408 -.11 475.623 468.626 6.994

26 303.150 12. 9260 12.9377 -.09 561.921 556.089 5.832

26 313.150 12.9260 12.9353 -.07 646.220 643,327 4.693

26 323.150 12.9260 12.9318 -.05 733.537 730.340 3.198

26 333.150 12.9260 12.9290 -.02 816.855 817.127 1.728

26 343.150 12.9260 12.9235 .02 902.212 903.688 -1.476

26 353.150 12.9260 12.9204 .04 986.549 990. 022 -3.473

26 273.150 13.0394 13.0575 -.14 350.097 341,929 8.169

26 283.150 13.0394 13.0549 -.12 440.319 432.913 7.406

26 293.150 13.0394 13.0510 -.09 529.559 523.669 5.690

26 303.150 13.0394 13.0462 -.05 617.819 614.193 3.626

26 313.150 13.0394 13.0422 -.02 706.079 704.484 1.594

26 323.150 13.0394 13.0390 .00 794.339 794,540 -.202

26 333.150 13.0394 13.0349 .03 881.618 884. 360 -2.742

26 343.150 13.0394 13.0299 .07 967.916 973.942 -6.026

26 273.150 13.1528 13.1663 -.10 401.092 394,558 6,534

26 283.150 13.1528 13.1616 -.07 493.274 488.752 4.522

26 293.150 13.1528 13.1579 -.04 585.457 582.709 2,748

26 303.150 13.1528 13.1514 .01 675.676 676.423 -.745

26 313.150 13.1528 13.1477 .04 766.860 769.894 -3.014

26 323.150 13.1528 13.1431 .07 857.101 863.117 -6.016

26 333.150 13. 1528 13.1378 .11 946.342 956.093 -9.751

26 343.150 13.1528 13.1318 .16 1034.602 1048. 819 -14.218

26 273.150 13.2661 13.2736 -.06 455.029 451.168 3.660

26 283.150 13.2661 13.2688 -.02 550.153 548,710 1.443

26 293.150 13.2661 13.2632 .02 644.297 646.001 -1.704

26 303.150 13.2661 13.2569 .07 737.460 743.039 -5.579

26 313.150 13.2661 13.2532 .10 831.604 639.821 -8.217

26 323.150 13.2661 13.2472 .14 923.786 936.343 -12.557

26 333.150 13.2661 13.2407 .19 1014,988 1032.605 -17.617

26 273.150 13.3795 13.3740 .04 508.965 512.019 -3.054

26 283.150 13.3795 13.3693 .08 607.032 613.049 -6.018

26 293.150 13.3795 13.3638 .12 704.117 713,817 -9.700

26 303.150 13.3795 13.3592 .15 801.203 814.319 -13.116

26 313.150 13.3795 13.3526 .20 896.328 914.551 -18.223

26 323.150 13.3795 13.3454 .25 990.472 1014.510 -24.036

NP = 336* DNRMSPCT = .360, PMEANOIF = 2.944

S3
Table

10.

Comparison

with

data

for

ideal

gas

functions. roN.

O'

O CO ^ o kD ^ ^ ro CM

A o CM CM ITk CM fO Z o a Cl o ^ O o a o o o o o o o O o O o o o o o a o o o o o o o o o o a o o

a. 1 • 1 1 1 • 1 1 a in ro vO vO CM ^ OO a N. K CM O' vD CM CM o m fo CM CM ^ O' irt .9- o UN U> UN CM 00 CM fs. ro O ON

fO .» vO j’ US (M COn t"O 'H (SJ t4 o CO

u CM UN N> ON CM CM UN CO o ro in « O CM vO CTN CM CM CM CM ro ro ro ro ro j- j- ^ UN UN UN UN UN UN

of ro ro CM ON ON CO CJN CM o CM CO OO ro CM

O K.

V UN ro CM CM O' UN kO UN CM CO ro hN. fO o ON M ro sD .»• N. UN CM CO ro IS. o 4 CM o 00

CM UN N. ON CM CM UN CO o ro UN 00

O CM -i* \D O'

CM CM CM CM ro ro ro ro ro 4* UN UN UN UN UN UN ^ t4 UN fs U) K t4 ro O' U) N. UN ro UN O N. CO Z CM O ^ vD ^ T4 ^ ^ ^ ro -H o 4^0 O t4 O a o o a o o o o o o o a o o o o o O O O o a 1 1 1 • 1 1 1 1 1 1 O ro ^ rs. iO lO h.. UN CM N. O' iO ro lO kD K ro cjN sD o 4 UN ^ UN O ^ U) O CO UN CO UN UN O' K o rw O O' O (Si sO O N, O' CTN O O ^ t4 t4 O CO vO 4* o h- CM o ^ UN UN UN UN <o ON CJ CM CM ro ^ UN UN U> t4 4 4 t4 t4 4 ^ 4 t4

us O' N- 4 CO CO CM CM ^ J- K- 4 o O' 4

0£ •H UN 4* UN

O 4* vO CJN OO U> CO UN UN O' r^

O CO o O'

"SO (SI vO o r^ O' O' O' o t4 t4 t4 O OO U) 4 o CM

rsj 4, 4. 4. 5. 5, UN UN \0 00 CJN

O 4 CM cvi ro 4 UN UN vO

IM t4 t4 4 t4 t4 t4 ^4 4 4 I H* 1 O M a I U) w Z

a:

U)

I- U) O' o ^ O U> UN CJN

O .»O ro

O vO ro 4 <o M> o z CJN o ro O UN 4 « <o N. t4 I'w o UN 4 <o 4 h* 4 o CM J- CM CM CM CM CM O 4 O o t4 O O O o O o CM ro 0. o I I • o< M O<

tooz

u.

to<o<

UJo

UJz<

a.o

0^

a. o 4 N. •t o os ^ r>. r>» O' rs CM j- 00 u> hN. ro CM O' U) u CO CO UN ro CO t4 O' ^ N. fs. ro CJN ON UN O UN 4

-J o (7S CO N. CM CO O' (SI us ^ u> flO CJN (JN CO UN CM CO o 4- UN lb CO «> CO ^ rb UN K CO OS a CM rb 4

'H t4 4 t4 CM CM CM CM CM CM

QC \0 N- OO ro CO CM CM CO CM as o j- 00O »4 ^ 40 o 4

>» O' 40 U> 4 vO UN O' o K 40 ^ O CM UN o 10 IM O O' 00 N. CM 00 flO ro UN 4- tH vO <o o O' CO UN CM N. O 4 4 UN 40 CO CO ro UN CO O' t4 4 CM ro 4 ^ t4 t4 sH CM CM CM CM CM CM o O o o o O O o o o O o o o o o O o O

•» o o o O UN UN o o o o O o o o o o o o o

r- 9 o o o t4 o o o o o o o o o o o o o C3 o o o ro CO o o o o o o o o o CO o o o

UN o UN o rw CJN e o o o o o o o o a o o o 4 CM CM CM ro 4- UN sD h*. CO O' o CM ro 4 UN4 a t4 5t4 »4 4 r4 4 »4 o

Q.tooczMo

Q.

toQC

CLOM

Q.Z

94
Table 10. Continued.

PROPANE IDEAL GAS SPECIFIC HEATS, CPZ/R

(2) API(1952> , (3)8EEK, (4)SAGE,

(5) KISTIAKOWSKY/LACHER, (6) KISTIAK. /RICE,

I7)DAILEY, C8) ERNST, (9)R0SSINI VIA YESAVAGE.

ID T,K CPZ/R CALCO PCNT

2 iOQ.OOO 4.952 4.987 -.72

2 298.150 8.642 8.874 -.36

2 700.000 17.210 17.172 .22

2 1000.000 21.050 20.996 .26

3 273.150 7.770 8.289 -6.68

3 373.150 10.135 10.665 -5.23

3 473.150 12.420 12.947 -4.24

3 573.150 14.433 14.976 -3.78

t* 294.300 8.817 8.783 .39

k 310.900 9.088 9.177 -.97

4 327.600 9.350 9.576 -2.42

4 344.300 9.617 9.976 -3.74

4 360.900 9.893 10.374 -4.85

4 377.600 10.165 10.771 -5.96

4 394.300 10.432 11.164 -7.02

4 410.900 10.704 11.551 -7.91

4 427.600 10.970 11.934 -8.78

4 444.300 11.242 12.311 -9.51

5 148.200 5.883 5.825 .99

5 157.800 6.059 5.983 1.26

5 213.100 7.045 6.986 .85

5 219.000 7.131 7.105 .37

5 258.000 7.926 7.944 -.22

6 272.380 3.037 8.271 -2.92

6 300.370 8.796 8.926 -1.47

6 334.050 9.642 9.731 -.92

6 368.550 10.487 10.556 -.65

7 334.700 9.878 9.746 1.34

7 360.100 10.236 10.354 -1.16

7 387.800 10.875 11.012 -1.26

7 452.600 12.616 12.496 .95

7 521.000 14.035 13.953 .59

7 562.000 14 . 644 14.765 -.83

7 603. 300 15.479 15.537 -.37

7 693.200 16.918 17.065 -.86

8 293.150 8.740 8.755 -.17

8 313.150 9.154 9.230 -.83

8 333.150 9.658 9.709 -.53

8 353.150 10.151 10.188 -.37

9 338.706 9.840 9.842 -.03

9 352.594 10.186 10.175 .11

9 366.483 10.523 10.507 .20

9 380.372 10.869 10.836 .30

9 394.261 11.206 11.163 .38

9 408.150 11.537 11.487 .43

9 422.039 11.857 11.807 .42

95
Table 11 . Interpolated ideal gas functions.

PROPANE IDEAL GAS FUNCTIONS. JOULESI.HOLES. KELVINS

T,K EZ HZ SZ CVZ CPZ

60 2076.0 2741.1 202.599 29.75 38.07

90 2382.1 3130.4 207.182 31.48 39.79

100 2705.3 3536.8 211.461 33.15 41.47

110 3044.8 3959.4 215.488 34.73 43.04

120 3399.6 4397.3 219.297 36.21 44.53

130 3768.9 4849.7 222.918 37.63 45.94

140 4152.0 5316.0 226.373 39.00 47.31

150 4548.8 5796.0 229.683 40.36 48.67

160 4959.3 6289.6 232.868 41.73 50.05

170 5383.5 6797.0 235.944 43.13 51.45

180 5822.1 7318.7 238.925 44.58 52.90

190 6275.3 7855.1 241.825 46.08 54.40

200 6743.9 8406.8 244.654 47 .64 55.95

210 7228.3 8974.3 247.423 49.25 57.57

220 7729.2 9558.3 250.139 50.93 59.24

230 8247.0 10159.3 252.811 52.65 60.97

240 8762.4 10777.8 255.443 54.43 62.74

250 9335.7 11414.3 258.041 56.25 64.56

260 9907.4 12069.1 260.609 58.11 66.42

270 10497.9 12742.8 263.151 60.00 68.31

280 11107.5 13435.5 265.670 61.92 70.23

290 11736.4 14147.5 268.168 63.86 72.18

300 12384.6 14879.1 270.648 65.83 74.14

310 13053.0 15630.4 273.112 67.80 76.12

320 13740.9 16401.5 275.560 69.79 78.11

330 14446.6 17192.5 277.994 71.78 80.10

340 15176.6 18003.5 280.414 73.78 82.09

350 15924.3 18834.4 282.823 75.77 84.08

360 16692.0 19685.1 285.219 77.76 86.07

370 17479.4 20555.7 287. 605 79.74 88.05

380 18286.7 21446.1 289.979 81.71 90.02

390 19113.6 22356.2 292.343 83.67 91.98

400 19960.0 23285.8 294.696 85.62 93.93

410 20825.9 24234.7 297.039 87.55 95.86

420 21710.9 25203.0 299. 372 89.46 97.78

430 22615.1 26190.3 301.695 91.36 99.68

440 23538.1 27196.4 304.008 93.24 101.56

450 24479.9 28221.3 306. 312 95.10 103.42

460 25440.1 29264.7 308. 605 ^96.94 105.26

470 26418.6 30326.4 310.888 98.76 107.07

460 27415.2 31406.1 313. 161 100.56 108.87

490 28429.7 32503.7 315.424 102.33 110.65

500 29461.8 33619.0 317.677 104.09 112.40

510 30511.3 34751.6 319.920 105.82 114.13

520 31578.0 35901.5 322.153 107.52 115.84

530 32661.7 37068.3 324.375 109.21 117.52

540 33762.1 38251.9 326.588 110.87 119.19

550 34879.1 39451.9 328.790 112.51 120.82

560 36012.3 40668.3 330.981 114.13 122.44

570 37161.5 41900.7 333.163 115.72 124.04

580 38326.6 43148.9 335. 334 117.29 125.61

590 39507.3 44412.8 337.494 118.84 127.16

600 40703.4 45692.0 339. 644 120.37 128.68

610 41914.6 46986.3 341.783 121.87 130.19

620 43140.7 48295.6 343.912 123.36 131.67

630 44331.6 49619.7 346.031 124.82 133.13

640 45637.0 50958.2 348.139 126.26 134.57

650 46906.7 52311.0 350.236 127.67 135.99

36
Table 12. Specific heats along isobar

PROPANE CP AT 1500 PSI» CPTRP = 83.70

.719296234E+03 -.776704935E*04 . 40 5746955E+05

118438853E+06 .205520887Ef06 -.210152230E+06

.116726413E+06 270984921E+05 0. T,K J/MOL/K CALCO OIFF PCNT

116.483 86.16 86.11 .05 .06

130.372 86.90 87.06 -.15 -.18

144.261 87.82 87.82 .01 .01

158.150 88.75 88.64 .10 .12

172.039 89.85 89.70 .16 .17

185.928 90.96 91.04 -.08 -.09

199.817 92.44 92.67 -.23 -.25

213.706 94.65 94.55 .10 .11

227.594 96.68 96.69 -.01 -.01

241.483 99.08 99.12 -.04 -.04

255.372 102.03 101.89 .14 .14

269.261 105.17 105.02 .15 .14

283.150 108.49 108.51 -.03 -.02

297.039 111.99 112.35 -.35 -.31

310.928 116. A2 116.48 -.06 -.05

324.817 121.22 120.98 .24 .20

338.706 126.20 126.02 .18 .14

352.594 131.92 132.01 -.09 -.07

366.483 139.30 139.50 -.20 -.14

377.594 146.86 146.87 -.01 -.01

380.372 148.89 148.91 -.02 -.01

383.150 151.11 151.03 . 08 .05

388.706 155.54 155.43 .11 .07

394.261 159.96 159.96 .00 .00

399.817 164.39 164.46 -.06 -.04

405.372 168.64 168.63 .01 .00

NP = 26, RMSPCT = .12

97
Table 13. Specific heats for the saturated liquid.

PROPANE SP. HEAT OF SATO. LIQUID, E = .dOO

IDOANA, (2)KEHP, (8)CUTLER,

(30)ROG VIA YESAVAGE CP, EQNSTATE.

.42014101E<-01 .79737878E»02 .18313347E + 02

-.36564<»48E4^02 .67003225E«^02 0.

ID NT T,K J/MOL/K CALCO PCNT

2 1.000 89.720 84.547 84.259 .34

8 1.000 91.060 83.973 84.328 -.42

8 1.000 93.430 84.224 84.451 -.27

2 1.000 95.530 84.756 84.562 .23

8 1.000 95.760 84.475 84.574 -.12

8 1.000 98.060 84.140 84.698 -.66

8 1.000 100.330 84.057 84.821 -.90

2 1.000 101.960 85.091 84.911 .21

8 1.000 102.570 84.726 84.945 -.26

8 1.000 104.780 85.061 85.070 -.01

2 1.000 108.500 85.426 85.283 .17

2 1.000 115.160 85.803 85.682 .14

2 l.UOO 121.970 86.179 86.113 .08

2 1.000 128.900 86.556 86.580 -.03

2 1.000 135.950 87.226 87.086 .16

2 1.000 142.790 87,435 87.612 -.20

2 1.000 149.740 88.147 88.184 -.04

2 1.000 156.850 88.691 88.811 -.14

2 1.000 164.390 89.360 89.529 -.19

2 1.000 172.020 89.863 90. 313 -.50

2 1.000 179.090 90.742 91.098 -.39

2 1.000 185.900 91.662 91.909 -.27

2 1.000 194.280 92.792 92.989 -.21

2 1.000 200.940 93.839 93.917 -.08

2 1.000 207.090 94.257 94.831 -.61

2 1.000 213.100 95.429 95.783 -.37

2 1.000 219.250 96.266 96.819 -.57

2 1.000 224.960 97.480 97 . 841 -.37

2 1.000 229.810 98.275 98,758 -.49

1 0.000 241.760 99.820 101.221 -1.38

1 0.000 246.880 96.490 102.374 -5.75

1 0.000 252.820 100.550 103. 792 -3.12

1 0.000 255.330 100.740 104.418 -3.52

1 0.000 261.550 105.720 106.045 -.31

1 0.000 264.740 97.790 106.924 -8.54

1 0.000 266.440 106.270 107.405 -1,06

98
Table 13 Continued

PROPANE SP. HEAT OF SATO. LIQUIOt E = .900

(l)OANA, (2>KEHPt (8)CUTLER«

(30)ROG VIA YESAVAGE CP, EQNSTATE.

.<*2014101E + 01 .79737878E+02 , 18313347E + 02

-.36564<*<»6E4^0 2 .67003225E«02 0.

ID NT T,K J/MOL/K CALCO PCNT

1 0.000 269.060 107.200 108.165 -.89

1 0.000 276.430 107.010 110. 428 -3.10

1 0.000 276.790 111.440 110.541 .81

1 0.000 287.550 107.750 114.246 -5.69

1 0.000 291.590 110.890 115.773 -4.22

30 1.000 90.000 84.039 84.273 -.28

30 1.000 100.000 84.960 84.803 .07

30 1.000 110.000 85.848 85.371 .56

30 1.000 120.000 86.716 85.986 .85

30 1.000 130.000 87.424 86.657 .89

30 1.000 140.000 88.041 87.393 .74

30 1.000 150.000 88.665 88.206 .52

30 1.000 160.000 89.379 89.104 .31

30 1.000 170.000 90.237 90.099 .15

30 1.000 180.000 91.263 91.203 .07

30 1.000 190.000 92.461 92.426 .04

30 1.000 200.000 93.825 93.782 .05

30 1.000 210.000 95.351 95.285 .07

30 1.000 220.000 97.044 96.950 .10

30 1.000 230.000 98.916 98.794 .12

30 1.000 240.000 100.994 100.839 .15

30 1.000 250.000 103.307 103.108 .19

30 1.000 260.000 105.887 105.630 .24

30 1.000 270.000 108.767 108.443 .30

30 1.000 280.000 111.979 111. 597 .34

30 1.000 290.000 115.566 115.162 .35

30 1.000 300.000 119.599 119.241 .30

30 1.000 310.000 124.219 123.995 .18

30 1.000 320.000 129.702 129.700 .00

30 1.000 330.000 136.627 136.882 -.19

30 1.000 340.000 146.278 146.709 -.29

30 1.000 350.000 162.174 162.479 -.19

30 1.000 360.000 199.625 199.396 .11

NP = 69, RMSPCT = .36

99
Table 14. The heats of vaporization

PROPANE HEATS OF VAPORIZATION. E = .3800

(l)OANAt (2)KEHP, (3)SAGE» (AtSTAVELY.

(51HELGESON. (&)YESAVAGE» tZlCARROTH.

(30)CLAPEYRON« (31IPATH TB.PB.T.

.98373471E4-00 .41758440E*00 30 674140E^00

10 NT T,K KJ/HOL CALCO PCNT

31 0.000 90.000 24.708 23. 783 3.89

31 0.000 100.000 24.245 23.507 3.14

31 0.000 110.000 23.810 23.224 2.52

31 0.000 120.000 23.391 22.933 2.00

31 0.000 130.000 22.983 22.634 1.54

31 0.000 140.000 22.582 22.325 1.15

31 0.000 150.000 22.185 22.006 .81

31 0.000 160.000 21.791 21.676 .53

31 1.000 170.000 21.398 21.333 .30

31 1.000 180.000 21.002 20.975 .13

31 1.000 190.000 20.601 20.602 -.01

31 1.000 200.000 20.193 20.212 -.09

31 1.000 210.000 19.774 19.802 -.14

31 1.000 220.000 19.341 19.371 -.15

31 1.000 230.000 18.890 18.915 -.14

31 1.000 240.000 18.415 18.433 -.10

31 1.000 250.000 17.912 17.919 -.04

31 1.000 260.000 17.374 17.371 .02

31 1.000 270.000 16.793 16.782 .07

31 1.000 280.000 16.163 16.146 .10

31 1.000 290.000 15.473 15.455 .11

31 1.000 300.000 14.712 14.698 .10

31 1.000 310.000 13.867 13.858 .06

31 1.000 320.000 12.917 12.916 .01

31 1.000 330.000 11.831 11.836 -.05

31 1.000 340.000 10.555 10. 563 -.08

31 1.000 350.000 8.977 8.983 -.07

31 1.000 360.000 6.792 6.794 -.02

NP = 28. RMSPCT = .111

100
Table 14 Continued

PROPANE HEATS OF VAPORIZATION, E = .3800

(l)OANA, (2>KEMP, (3)SAGE, C4ISTAVELY,

(5)HELGES0N, (6)YESAVAGE, (ZICARROTH,

I30)CLAPEYRON, I3DPATH TB,PB,T.

•98373471E+00 .41758440E+00 -.30674140E+00

10 HT T,K KJ/HOL CALCO PCNT

30 0.000 90.000 22.746 23. 783 -4.36

30 0.000 100.000 22.682 23.507 -3.51

30 0.000 110.000 22.659 23.224 -2.43

30 0.000 120.000 22.610 22.933 -1.41

30 0.000 130.000 22.503 22. 634 -.58

30 0.000 140.000 22.331 22.325 .02

30 0.000 150.000 22.094 22.006 .40

30 0.000 160.000 21.803 21.676 .58

30 0.000 170.000 21.465 21.333 .62

30 0.000 180.000 21.091 20.975 .55

30 0.000 190.000 20.689 20.602 .42

30 0.000 200.000 20.264 20.212 .26

30 0.000 210.000 19.821 19.802 .09

30 0.000 220.000 19.359 19.371 -.06

30 0.000 230.000 18.880 18.915 -.19

30 0.000 240.000 18.381 18.433 -.28

30 0.000 250.000 17.858 17.919 -.34

30 0.000 260.000 17.305 17.371 -.38

30 0.000 270.000 16.717 16.782 -.39

30 0.000 280.000 16.085 16.146 — .38

30 0.000 290.000 15.399 15.455 -.36

30 0.000 300.000 14.647 14.698 -.34

30 0.000 310.000 13.813 13.858 -.33

30 0.000 320.000 12.873 12.916 -.33

30 0.000 330.000 11.793 11.836 -.37

30 0.000 340.000 10.515 10.563 -.45

30 0.000 350.000 8.929 8.983 -.60

30 0.000 360.000 6.746 6.794 -.70

1 0.000 234.070 18.441 18.722 -1.50

1 0.000 237.750 17.856 18.544 -3.71

1 0.000 241.830 18.242 18.341 -.54

1 0.000 247.100 17.873 18.072 -1.10

1 0.000 253.740 17.819 17.719 .57

1 0.000 261.210 17.397 17.302 .55

1 0.000 269.100 16.865 16.837 .17

1 0.000 275.420 16.330 16.444 -.69

1 0.000 279.890 16.524 16.153 2.29

1 O.QOO 281.850 15.814 16.023 -1.30

1 0.000 285.530 15.738 15.772 -.21

1 0.000 287.150 15.795 15.658 .87

1 0.000 292.200 15.356 15.295 .40

1 0.000 292.700 15.596 15.258 2.22

2 0.000 231.090 18.780 18.864 -.45

3 0.000 312.817 13.627 13.605 .17

3 0.000 312.983 13.649 13.589 .44

3 0.000 316.206 13.360 13.287 .55

3 0.000 316.372 13.551 13.272 2.11

3 0.000 316.483 13.551 13.261 2.19

101
Table 14. Continued

PROPANE HEATS OF VAPORIZATION* E = .3800

(DOANAt (2)KEHP« (3)SAGE* I4)STAVELY,

(5)HELGES0N. (6)YESAVAGE« (Z)CARRUTH,

<30)CLAPEYRON, (3DPATH TB,PB*T.

.98373471E+

10 NT

3 0.000

3 0.000

3 o.odo

3 0.000

3 0.000

3 0.000

3 0.000

3 0.1)00

3 0.000

3 0.000

3 0.000

4 0.000

4 0.000

5 0.000

5 0.000

5 0.000

5 0.000

6 0.000

6 0.000

6 0.000

6 0.000

6 0.000

6 0.000

6 0.000

6 0.000

6 0.000

6 0.000

6 0.000

6 0.000

6 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

7 0.000

0 .41758440E«^00

T,K KJ/MOL

316.539 13.282

318.928 13.171

320.983 13.127

321.150 13.143

327.983 12.284

328.094 12.224

335.594 11.297

335.650 11.344

345.706 10.205

346.039 10.188

348.150 9.648

135.000 20.690

213.200 19.660

310.928 13.651

322.039 12.592

327.594 11.989

330.372 11.612

231.094 18.778

263.206 17.148

285.928 15.734

301.317 14..617

313.428 13.633

323.428 12.649

331.817 11.624

339.483 10.578

346.206 9.512

352.428 8.405

358.039 7.216

363.372 5.873

367.039 4.449

110.946 23.719

118.342 23.391

125.739 23.068

133.135 22.770

140.532 22.460

147.928 22.182

155.324 21.887

162.721 21.631

170.117 21.326

177.514 20.989

184.910 20.745

192.306 20.459

199.703 20.144

207.099 20.014

214.496 19.504

221.892 19.189

229.288 18.857

236.685 18.500

-.30674140E+00

CALCO PCNT

13.256 .20

13.023 1.14

12.816 2.42

12.799 2.68

12.067 1.79

12.055 1.40

11.153 1.29

11.146 1.78

9.711 5.09

9.657 5.49

9.307 3.66

20.791 -.48

19.666 -.03

13.776 -.91

12.708 -.91

12.111 -1.01

11.793 -1.53

18.864 -.46

17.187 -.23

15.744 -.06

14.592 .17

13.548 .63

12.563 .68

11.622 .02

10.635 -.54

9.630 -1.23

8.528 -1.44

7.304 -1.20

5.749 2.15

4.125 7.85

23.197 2.25

22.982 1.78

22. 763 1.34

22.538 1.03

22.309 .68

22.073 .49

21.832 .25

21. 584 .22

21.328 -.01

21.065 -.36

20.794 -.24

20 . 514 -.27

20.224 -.39

19.923 .46

19.611 -.54

19.286 -.51

18.949 -.48

18.596 -.52

102
Table 15. Comparison with specific heat data of Ernst.

ERNST PROPANE CPITtPI* J/MOL/K* ALONG ISOTHERMS

THE ISOTHERM AT T = 293.15 K PtBAR MOL/L CPIP) CALCO PCNT CP-CPZ CALCO OIFF

0.000 0.000 72.67 72.80 -.17 0.00 0.00 0.00

.490 .020 73.06 73.22 -.22 .39 .43 -.04

.901 .041 73.51 73.66 -.20 .84 .86 -.02

1.961 .083 74.47 74.62 -.20 1.80 1.82 -.02

3.432 .150 76.32 76.34 -.02 3.65 3.54 .11

4.903 .221 78.48 78.47 .01 5.81 5.68 .13

6.374 .297 81.13 81.20 -.09 8.46 8.40 . 06

7.845 .379 84.57 84.85 -.33 11.90 12.06 -. 16

THE ISOTHERM AT T = 313.15 K P*BAR MOL/L CPIP) CALCO PCNT CP-CPZ CALCO OIFF

0.000 0.000 76.11 76.74 — .83 0.00 0.00 0.00

.490 .019 76.53 77.09 -.73 .42 .35 . 07

.981 .038 76.95 77.44 -.63 .84 .69 .15

1.961 .078 77.79 78.18 -.51 1.68 1.44 .24

3.432 .139 79.19 79.46 -.34 3.08 2.72 .36

4.903 .203 80.63 80.96 -.40 4.52 4.21 .31

6.374 .270 82.44 82.72 -.34 6.33 5.98 .35

7.845 .342 84.61 84.82 -.25 8.50 8.08 .42

9.807 .445 88.01 88.37 -.41 11.90 11.63 .27

11.768 .558 93.18 93.24 -.07 17.07 16.50 .57

THE ISOTHERM AT T = 333.15 K PtBAR MOL/L CPIP) CALCO PCNT CP-CPZ CALCO OIFF

0.000 0.000 80.30 80.72 -.53 0.00 0.00 0.00

.490 .018 80.55 81.01 -.57 .25 .29 -. 04

.981 .036 80.93 81.30 -.45 .63 .57 .06

1.961 .073 81.54 81.89 -.43 1.24 1.17 .07

3.432 .129 82.56 82.89 -.39 2.26 2.16 .10

4.903 .188 83.56 84.01 -.53 3.26 3.28 -.02

6.374 .249 85.00 85.27 -.32 4.70 4.55 .15

7.845 .313 86.45 86.71 -.30 6.15 5.99 .16

9.807 .40 3 88.65 88.95 -.34 8.35 8.23 .12

11.768 .499 91.28 91.68 -.43 10.98 10.95 .03

13.729 .603 94.95 95.08 -.14 14.65 14.35 .30

THE ISOTHERM AT T = 353.15 1K PtBAR MOL/L CPIP) CALCO PCNT CP-CPZ CALCO OIFF

0.000 0.000 84.40 84.71 -.37 0.00 0.00 0.00

.490 .017 84.59 84.95 -.43 .19 .24 -. 05

.981 .034 84.79 85.19 -.47 .39 .48 -.09

1.961 .068 85.36 85.68 -.37 .96 .97 -.01

3.432 .121 86.19 86.47 -.33 1.79 1.76 .03

4.903 .175 86.97 87.35 -.43 2.57 2.64 -. 07

6.374 .232 88.01 88.31 -.34 3.61 3.60 .01

7.845 .290 39.02 89.37 -.39 4.62 4. 66 -.04

9.807 .371 90.65 90.96 -.34 6.25 6.25 .00

11.768 .456 92.39 92.78 -.42 7.99 8.07 -. 08

13.729 .545 94.37 94.89 -.55 9.97 10.18 -.21

NP = 40 t AVPCT = .37t AVDIF : OJ •

II

103
Table 16. Comparison with specific heat data of Yesavage

YESAVAGE CP(T) ISOBAR AT P«BAR = 17.237

T,K HOL/L J/MOL/K CALCO PONT

116.483 15.930 85.79 85.71 .10

144.261 15.296 87.64 87.64 •.00

172r039 14.653 89.85 90.18 -.37

199.817 13.992 93.17 93.57 - .42

227.594 13.301 97.79 98.11 - .33

255.372 12.558 104.06 104.28 - .21

283.150 11.726 112.73 113.01 - .25

310.928 10.723 128.41 127.03 1 .08

338.706 .785 101.85 102.04 • .19

366.483 .673 98.89 99.34 - .45

394.261 .599 102.03 101.09 .92

YESAVAGE CP(TI ISOBAR AT P.BAR = 34.474

T,K NOL/L J/HOL/K CALCO PCNT

116.483 15.945 85.98 85.65 .38

144.261 15.316 87.64 87.56 .09

172.039 14.679 89.67 90.05 -.43

199.817 14.025 92.80 93.36 -.60

227.594 13.345 97.60 97.76 -.16

255.372 12.618 103.51 103.65 -.14

283.150 11.814 112.18 111.74 .39

310.928 10.869 124.17 123.76 .33

338.706 9.615 150.37 147.48 1.92

366.483 1.881 157.57 162.12 -2.89

394.261 1.434 122.14 120.64 1.23

422.039 1.225 114.02 115.15 -.99

YESAVAGE CP(T) ISOBAR AT P.BAR = 68.948

T,K MOL/L J/MOL/K CALCO PCNT

116.483 15.975 85.98 85.54 .50

144.261 15.355 87.64 87.40 .28

172.039 14.728 89.48 89.81 -.36

199.817 14.089 92.62 92.97 -.38

227.594 13.428 97.05 97.13 -.08

255.372 12.730 102.77 102.57 .20

283.150 11.973 110.15 109.70 .40

310.928 11.117 118.82 119.28 -.38

338.706 10.089 133.21 133.02 .14

366.483 8.694 159.23 159.15 .05

394.261 6.057 267.53 257.01 3.93

422.039 3.515 176.38 177.81 -.81

104
Table 16. Continued

YESAVAGE CPIT) ISOBAR AT P*BAR = 103.421

T,K MOL/L J/NOL/K CALCD PONT

116.483 16.003 86.16 85.44 .83

144.261 15.392 87.82 87.25 .66

172.039 14.776 89.85 89.58 .30

199.817 14.150 92.44 92.62 -.20

227.594 13.507 96.68 96.58 .11

255.372 12.834 102.03 101.66 .37

283.150 12.115 108.49 100.12 .34

310.928 11.324 116.42 116.28 .12

338.706 10.423 126.20 126.44 -.19

366.483 9.348 139.30 139.50 -.14

394.261 7.991 159.96 159.96 .00

422.039 6.279 177.68 180.02 -1.32

YESAVAGE CP(T> ISOBAR AT PtBAR s 137.895

T,K HOL/L J/NOL/K CALCO PCNT

116.483 16.032 86.16 85.35 .94

144.261 15.428 88.01 87.11 1.02

172.039 14.822 90.22 89.37 .94

199.817 14.208 92.44 92.31 .14

227.594 13.501 96.31 96.09 .23

255.372 12.930 101.29 100.88 .40

283.150 12.243 107.20 106.85 .32

310.928 11.503 113.84 114.10 -.23

338.706 10.686 122.51 122.48 .02

366.483 9.768 131.55 131.75 -.16

394.261 8.723 146.13 143.66 1.69

NP = 58, HEANPCT = .55

Table 17. Comparisons with speed of sound data.

RAO PROPANE SPEED

T,K NOL/L

140.000 15. 3? 5 145.000 15.259

150.000 15.144

155.000 15.027

160.000 14.910

165.000 14.793

170.000 14.676

175.000 14.557

180.000 14.438

185.000 14.319

190.000 14.198

195.000 14.077

200.000 13.954

205.000 13.831

210.000 13.707

215.000 13.581

220.000 13.454

225.000 13.326

230.000 13.196

NP = 19, MEANPCT =

OF SOUND FOR SATO. LIOUIO

H/SEC CALCO PCNT

1528 1727 -12.96

1499 1688 -12.60

1469 1649 -12.29

1439 1612 -12.02

1409 1575 -11.80

1379 1540 -11.62

1350 1505 -11.49

1320 1470 -11.40

1290 1436 -11.35

1260 1403 -11.34

1230 1370 -11.38

120 0 1338 -11.45

1171 1306 -11.57

1141 1275 -11.72

1111 1243 -11.92

1081 1213 -12.16

1051 1182 -12.44

1021 1152 -12.76

992 1122 -13.12

11.97

105
Table 17. Continued.

LACAH PROPANE SPEED OF SOUND AT T.K = 296.15

PtBAR MOL/L H/SEC CALCO PONT

10.133 11.165 724 718 .83

20.265 11.235 742 735 .92

30.396 11.302 758 751 .84

40.530 11.365 774 767 .86

43.570 11.383 778 771 .77

50.663 11.425 790 782 .95

60.795 11.462 804 797 .86

70.926 11.537 819 611 .95

81.060 11.589 833 824 .97

91.193 11.640 847 838 1.04

101.325 11.689 860 851 1.04

126.656 11.803 893 681 1.24

151.968 11.909 924 911 1.40

177.319 12.008 953 938 1.50

202.650 12.100 979 965 1.42

253. 313 12.269 1017 1014 .22

303.975 12.421 1070 1061 .84

354.638 12.560 1110 1104 .49

405.300 12.687 1146 1145 .01

506.625 12.914 1214 1222 -.73

607.950 13.113 1275 1294 -1.50

709.275 13.291 1331 1360 -2.24

810.600 13.451 1384 1423 -2.87

911.925 13.598 1432 1483 -3.61

1013.250 13.732 1482 1540 -3.98

LACAN PROPANE SPEED OF SOUND AT T,K = 323.15

P.BAR HOL/L M/SEC CALCD PCNT

10.133 .439 520 231 55.52

20.265 10.213 552 564 -2.34

30.398 10.332 581 589 -1.51

40.530 10.438 608 612 -.73

43.570 10.468 615 618 -.64

50.663 10.535 632 633 -.23

60.795 10.625 652 653 -.17

70.928 10.709 672 671 .06

81.060 10.787 695 689 .84

91.193 10.860 709 705 .44

101.325 10.930 727 721 .71

126.656 11.089 766 759 .89

151.988 11.232 803 793 1.19

177.319 11.361 834 825 1.05

202.650 11.480 864 855 1.02

253.313 11.692 918 910 .83

303.975 11.878 966 960 .54

354.636 12.044 1011 1007 .35

405.300 12.194 1052 1051 .07

506.625 12.459 1126 1132 -.55

607.950 12.686 1192 1206 -1.18

709.275 12.887 1252 1274 -1.81

810.600 13.067 1308 1339 -2.37

911.925 13.229 1360 1399 -2.94

1013.250 13.378 1408 1458 -3.55

106
Table 17. Continued

LACAH PROPANE SPEED OF SOUND AT T,K = 369.95

PfBAR MOL/L H/SEC CALCO PONT

10.133 .361 254 258 -1.58

20.265 .809 231 235 -2.03

30.39S 1.430 204 207 -1.52

40.530 2.759 165 162 1.80

43.570 6.605 154 193 -25.35

50.663 7.641 264 278 -5.31

60.795 8.187 340 340 -.24

70.928 8.527 387 385 .32

81.060 8.782 425 422 .66

91.193 8.988 457 453 .78

101.325 9.163 487 481 1.22

126.656 9.515 550 539 1.86

151.988 9.791 601 588 2.03

177.319 10.021 643 631 1.76

202.650 10.219 682 670 1.74

253.313 10.551 748 737 1.37

30 3.975 10.824 805 796 1.02

354.638 11.057 855 849 .59

405.300 11.261 902 898 .38

506.625 11.609 995 986 .87

607.950 11.898 1056 1064 -.84

709.275 12.146 1120 1136 -1.49

810.600 12.364 1179 1203 -2.07

911.925 12.559 1234 1266 -2.60

1013.250 12.735 1286 1325 -3.06

LACAH PROPANE SPEED OF SOUND AT T,K = 398.15

PtBAR MOL/L H/SEC CALCO PCNT

10.133 .328 266 271 -1.99

20.265 .712 251 254 -1.47

30.398 1.176 234 236 -.99

40.530 1.782 212 215 -1.52

43.570 2.009 205 208 -1.70

50.663 2.678 192 193 -.71

60.795 4.182 182 185 -1.85

70.928 5.789 223 217 2.62

81.060 6.745 273 264 3.11

91.193 7.311 318 308 3.05

101.325 7.703 356 345 2.83

126.656 8.355 433 421 2.66

151.988 8.792 493 480 2.44

177.319 9.126 542 531 2.03

202.650 9.399 589 574 2.43

253.313 9.832 661 649 1.74

303.975 10.173 723 713 1.34

354.638 10.455 788 769 2.32

405.300 10.698 827 820 .75

506.625 11.102 914 911 .24

607.950 11.432 990 992 -.24

709.275 11.711 1056 1065 -.90

810.600 11.954 1117 1133 -1.45

911.925 12.169 1174 1196 -1.91

1013.250 12.362 1226 1256 -2.46

107
Table 17 Continued

LACAN PROPANE SPEED OF SOUND AT T.K = 423.15

P«BAR HOL/L M/SEC CALCO PCNT

10.133 .305 277 282 -1.81

20.265 .648 265 268 -1.42

30.398 1.042 252 255 -1.23

40.530 1.505 238 240 -1.11

43.570 1.661 233 236 -1.40

50.663 2.069 223 226 -1.48

60.795 2.776 213 214 -.88

70.928 3.646 211 211 -.18

81.060 4.584 218 221 -1.51

91.193 5.419 243 241 .69

101.325 6.090 275 267 2.65

126.656 7.178 352 340 3.28

151.988 7.830 415 404 2.61

177.319 8.290 468 458 2.09

202.650 8.646 515 505 1.91

253.313 9.186 597 584 2.07

303.975 9.595 660 651 1.28

354.638 9.926 716 710 .81

405.300 10.205 757 762 -.78

506.625 10.660 854 855 -.23

607.950 11.027 931 937 -.73

709.275 11.334 1000 1011 -1.17

810.600 11.599 1064 1079 -1.49

911.925 11.832 1124 1143 -1.73

1013.250 12.040 1180 1203 -1.98

LACAN PROPANE SPEED OF SOUND AT T.K = 448.15

P«BAR NOL/L N/SEC CALCD PCNT

10.133 • 285 287 291 -1.74

20.265 .598 275 281 -2.26

30.398 .945 262 270 -3.28

40.530 1.332 250 259 -3.98

43.570 1.458 247 256 -3.96

50.663 1.771 241 249 -3.59

60.795 2.271 236 240 -2.08

70.928 2.839 234 235 -.58

81.060 3.462 235 234 .08

91.193 4.107 238 240 -1.13

101.325 4.722 247 252 -2.32

126.656 5.980 304 296 2.33

151.988 6.839 364 351 3.51

177.319 7.438 417 403 3.20

202.650 7.888 463 451 2.57

253.313 8.545 540 532 1.36

303.975 9.026 608 601 1.09

354.638 9.406 667 661 .84

405.300 9.721 720 715 .68

506.625 10.230 810 809 .06

607.950 10.632 888 892 -.45

709.275 10.967 958 966 -.87

810.600 11.253 1022 1034 -1.24

911.925 11.504 1082 1098 -1.51

1013.250 11.727 1138 1158 -1.78

108
Table 17 Continued

LACAM PROPANE SPEED OF SOUND AT T,K = 473.15

P.BAR MOL/L H/SEC CALCD PCNT

10.133 .268 299 301 -.60

20.265 .557 290 292 -.85

30.398 .869 280 284 -1.44

40.530 1.208 271 275 -1.81

43.570 1.315 269 273 -1.68

50.663 1.577 264 268 -1.59

60.795 1.979 259 261 -.99

70.928 2.417 256 256 -.31

81.060 2.884 255 254 .12

91.193 3.372 256 255 .04

101.325 3.865 261 260 .07

126.656 5.003 291 287 1.30

151.988 5.917 337 324 3.72

177.319 6.615 360 367 3.20

202.650 7.149 424 411 2.94

253.313 7.921 500 491 1.75

303.975 8.472 564 560 .68

354.638 6.902 621 620 .06

405.300 9.253 674 674 -.12

506.625 9.812 767 769 -.36

607.950 10.250 846 652 -.77

709.275 10.611 916 926 -1.18

810.600 10.918 980 995 -1.54

911.925 11.186 1040 1058 -1.78

1013.250 11.423 1096 1116 -2.03

LACAH PROPANE SPEED OF SOUND AT T,K = 496.15

P.BAR HOL/L H/SEC CALCD PCNT

10.133 .253 308 310 -.75

20.265 .522 301 302 -.62

30.398 .808 295 296 -.36

40.530 1.112 288 289 -.59

43.570 1.207 287 287 -.31

50.663 1.435 282 263 -.66

60.795 1.779 276 278 -.29

70.926 2.143 274 275 -.38

81.060 2.525 27 3 272 .01

91.193 2.920 273 272 .00

101.325 3.321 275 275 -.10

126.656 4.300 293 291 .60

151.988 5.161 326 317 2.46

177.319 5.678 360 350 2.68

202.650 6.460 395 386 2.11

253.313 7.325 465 460 1.06

303.975 7.942 529 527 .34

354.638 8.417 586 587 -.20

405.300 8.804 640 641 -.19

506.625 9.411 734 736 -.29

607.950 9.882 814 818 -.57

709.275 10.268 885 692 -.87

810.600 10.595 948 960 -1.32

911.925 10.879 1009 1023 -1.45

1013.250 11.129

NP = 200, MEANPCT =

1065

1.77

1083 -1.69

NP = 200

109
TABLE 18. Comparison of enthalpy differences at 60 bar

Ah, J/mol

Kuloor [41] This Report 9H/9P,

K P = 60 atm P = 60 bar J/mol/bar

230 0 0 4.3

250 1,964 2,011 3.9

300 7,063 7,443 1.4

350 13,440 13,772 - 9.8

400 24,685 23,913 -216.1

500 39,184 39,264 - 50.9

600 52,335 52,490 - 28.8

110
p

0

1

20

40

50

60

100

200

300

400

450

500

TABLE 19. Comparison of enthalpy differences at 400 K

This Report

P in bar

- AH, J/mol

Kuloor [41]

P in atm

0 0

67 63

1,485 1,407

3,507 3,425

4,972 4,999

6,995 7,051

11,018 11,041

12,098 12,251

12,181 12,228

12,018 12,108

11,889

11,739 11,790

Eubank [24] aH/9P

P in atm J/mol/bar

0

71 - 73

1,575 - 84

3,698 -126

5,226 -172

7,318 -216

11,280 - 31

12,301 - 3.2

12,369 + 0.8

12,198 2.3

12,067 2.8

3.2

111
TABLE 20. Comparison of residual specific heats at 400 K

C (P,T) - C°(T), J/mol/K

?

This Report

P in bar

0 0

1 0.2

20 9.6

40 35.1

50 79.7

60 147.2

100 74.3

200 40.5

300 33.8

400 30.7

450 29.6

500 28.8

Kuloor [41]

P in atm

Eubank [24]

P in atm

0 0 / 0.4 0.4

7.5 11.2

30.6 38.2

76.6

151.1

73.3 198.3

39.8 86.0

31.4 63.3

28.1 53.2

50.1

26.4

!

112
LOOP

CLOSURE

FOR

SATURATED

VAPOR*

HLtSL

VIA

PATH

TA

AND

CSAT.

Q«VAP

VIA

CLAPEYRON,

HGtSG

VIA

IDEAL

GAS

AND

EQNSTATE*

JOULES«MOLEStKELVINS

u.

u.

i-t a

<sr>>O'(M4’U\tOc0 tOtOtOtOoeoinCJ \o vo ^ (vj o <r> 4 O' vD O <T< T* ro >o 4- in CO 'T^ K ro w^in^orooa)

toro<i>-^coa>tOT4

o^Hcviwroforofo

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KinHco*»^0'oiniooco^^a>\00>iX>ce.^h^r«(Or>..roinKT4^oHfo

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CNJ 00 N> N. « O rvi in O' (Si vx> o in O ITS o in o U3 (Vi CO o r^ ro O \D ro O' in in N. o> •H ro lo eo o CM in Is. o (SI in N. o (Si in I'* O (Si in OO a ro iD «0 tH ro a a a a ^ ^ «c4 (Si csj (sj (Si ro ro ro ro lA m tA lA lO iO \D r^ fN.. h* w i*> ro lo fo fo ro ro ro ro fo ro ro ro fo ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro

or 4 ivj >2 .0 lO CSJ o in 4 (SJ ^ O ^ >0 .1 >1 in ^ (Si CO ^ vO .3 cn o .8 ,7 rw .6

-J vO 4 o in 4 (vj CO O' in vo ^ 00 *H ro 'O •H O ro o 4 r^ CO o o ^ (Si ro r^ X ro ro ro 4 in in ro o iO o ro ^ in (SJ O N. ro O' in o in o vO r-« vO <o ro vo O ^ «o (SI vD O 4 CO 'H in CO 'T^ 4 r^ o ro in CO o ro lO eo ro vO CO ro 4

oo oo (?' O' O' O O ^ -H (SI (SJ (SJ ro ro ro ^ 4 4 4 in in in in vO vO vO ^ N. N.

(M (SJ (SJ (SI (M ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro

Q. « ^ CO N. (VJ 4 CO .6 >3 .3 ,7 4 CO in CO .9 >9 o o oo o r4 in in .1 .3 4 (SJ .8 > (SJ \0 (SJ O O' O (n 4 ro in o o 4 •t (si CO 4 4 ro CO O' 4 4 o (SJ O' (SJ o

•> (SJ 4 o eo h- in 4

> o \0 Q CSJ ro CSJ O' in o ro OO O' (JS eo rw \D 4 (SJ (T» in (SJ CO (Si C2f CO K N. vO \0 \D vO in in 4 ro (SJ o (Ji OO vO 4 CSJ o CO \0 4 (Si o CO in ro CD CO

CSJ (VJ (VJ (SI (VJ (M (VI (SJ (SJ (SJ (M (M (SI (Si •H -H a o o o o O' O' <T> O' oO (M (SJ CSJ (SI CSJ (SJ (SJ (VJ (SI (SI (M (SI (SI (SI (SJ CSI CSI CSJ (SI (SI (SJ (SI (SJ (Si (SJ t4 t4 t4 4 w4

CO ro sD CO C'J \0 K o vO CO in lO O' CSI CSI ro CSI 4 ro in CO rw (SJ ro in (SJ ro ro

CO (SI rs. ro r<- CSJ O CO in 4 CSJ (JS in in rw (SI o (SJ CO O' in (SJ 4 ro eo O O' in t4

vO cn in CO o O' n. 4 O' ro \0 (O CO r^ in ro o «4 vO in O' (SI in o 4 ro CO

CSJ \0 t4 in o ro r^ 4 «0 •H 4 o ro kO ^ (SI ^ N. O' CSJ 4 vD O' ro \0 o O

<0 CO O' O' o o e (M (VJ (VI ro ro ro ro 4 4 4 4 in in in in ^0 vO N. r^ 4 t4 H H •H t4 4 t4 t4 H <v4 4 t4

kD CO (SJ .9 >0 .6 CO in O' T* 1-1 o (SI in .3 .6 .5 .2 .8 .6 lD (SJ in .7 .3 in «0 O'

CO O' O' \o ro (SJ ro in a 4 4 \0 o r^ vO <D ro a «4 in ro 4 O' eo (SJ o ro O' o CO ^ ro in «o »i 4 !'• O 4 N- 1-t in <n CO ro « 4 a vD (SJ O' 10 ro ^ o O' « CO in eo ro N. ^ in o 4* « ro K <H \0 o ^ O' ro CO (SJ (SJ vO t4 in o in o in (JT' in in in vO vO n- h. « CO CO O' O' O O •4 (SI CSJ ro ro 4 4 in in lO lO N. eo ce 4 T4 f4 4 ^ t4 H ^ t4 ^ t4 -4

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4 4 4 in in in in vO vD n- rw «> CO O' O' o o •H t4 (Si ro ro 4* in 10 10 r^ O' CO CO CO CO <o CO CD 9 CO CO CO 00 4> CO O' O' O' O' (^ O' (n O' O' O' O' O' O' cn

rw o e» o e o o o o o o o o o O O O o O O o O o o o o O Q o o r«»

«k ^ o o o ea o o o o o o o o a o o o a O o o o o o o o o o o a o

LA a in o in o in o in o in o in o in o in o in o in o in o in o in o in o

o 1-1 1-1 (VJ (VJ lO w 4 4 in in tO vO r^ K CO CO O' (T' o o 4 (SJ (SJ ro ro 4 ^ ^ t4 H «4 H *4 t4 t4 4 4 (SJ (SI (Si (SI eg eg CM CM

113
Table 22 Comparison with vapor pressure of Tsai

PROPANE VAPOR PRE

T.K P»BAR

85.47 .4917E-08

86.00 .6000E-08

88.00 .1245E-07

90.00 .2493E-07

95.0 0 .1243E-06

100.00 .5226E-06

105.00 .1907E-05

110.00 .6119E-05

115.00 .1760E-04

120.00 .4640E-04

125.00 .1121E-03

130.00 .2520E-03

135.00 .5306E-03

140.00 .1057E-02

145.00 .2000E-02

150.00 .3533E-02

155.00 .6146E-02

160.00 .1027E-01

165.00 .1653E-01

170.00 .2586E-01

175.00 .3933E-01

180.00 .5826E-01

185.00 .8399E-01

190.00 .1187E*00

195.00 .164064^00

200.00 .2226E*00

205.00 .2960E+00

210.00 .3866E4-00

215.00 .4986E>00

220.00 .6319E+00

225.00 .7893E>00

230.00 .9719E+00

231.00 .lOllE+01

SSURES OF TSAI

CALCO PCNT

.3000E-08 63.90

.3657E-08 64.07

.7555E-08 64.83

.1512E-07 64.93

.7536E-07 64.88

.3199E-06 63.36

.1182E-05 61.26

.3873E-05 57.98

.1142E-04 54.06

.3071E-04 51.09

.7606E-04 47.41

.1752E-03 43.85

.3780E-03 40.36

.7697E-03 37.35

.1487E-02 34 . 46

.2741E-02 28.90

.4840E-02 27.00

.8220E-02 24.90

.1347E-01 22.69

.2139E-01 20.92

. 3297E-01 19.31

.4945E-01 17.81

.7238E-01 16.05

. 1035E4-00 14.60

.1451E+00 13.05

.1993E*00 11.69

.2691E+00 9.98

.3574E+00 8.18

.4675E+00 6.65

.6031E4-00 4.79

.7679E+00 2.78

.9661E4-00 .61

. lOlOE-t-01 .05

114
Table 23. Comparison with heats of vaporization of Tsai.

PROPANE HEATS OF VAPORIZATION OF TfK KJ/MOL

85.47 23.002

66.00 22.988

88.00 22.938

90.00 22.887

95.0 0 22.759

100.00 22.630

105.00 22.499

110.00 22.366

115.00 22.232

120.00 22.097

125.00 21.960

130.00 21. 821

135.00 21.681

140.00 21.539

145.00 21.396

150.00 21.252

155.00 21.106

160.00 20.958

165.00 20.808

170.00 20.658

175.00 20.506

180.00 20.352

185.00 20.197

190.00 20.042

195.00 19.885

200.00 19.741

205.00 19.578

210.00 19.417

215.00 19.259

220.00 19.105

225.00 18.954

230.00 18.809

231.00 18.730

CALCO PCNT

23.906 -3.78

23.692 -3.78

23.837 -3.77

23.783 -3.77

23.646 -3.75

23.507 -3.73

23.366 -3.71

23.224 -3.69

23.080 -3.67

22.933 -3.65

22.785 -3.62

22.634 -3.59

22.461 -3.56

22.325 -3.52

22.167 -3.48

22.006 -3.43

21.843 -3.37

21.676 -3.31

21.506 -3.24

21.333 -3.16

21.156 -3.07

20.975 -2.97

20.791 -2.85

20.602 -2.72

20.409 -2.57

20.212 -2.33

20.009 -2.15

19.802 -1.94

19.589 -1.69

19.371 -1.37

19.146 -1.00

18.915 -.56

18.868 -.47

TSAI

115
Table 24. Derived coexistence data (Q|^ = 18 780 J/mol).

PROPANE ESTIH. V.P.tBAR, ANO QVAP, KJ/HOL.

TB = 231.07070 , PB = 1.01325* OB = . 054791

EZB = 8303.5* EGB = 8139. 7* HZB = 10224.7* HGB = 9989.0

SZB = 253.0943 * SGB = 252 .3795* QB = 18780.0

T,K 100/T P*EQN P*BAR LN(P) MOL/L Q*EQN Q* VAP

85.47 1.17000 .30000E-08 •16566E-08 -20.21853 .23311E-09 23.906 24.824

86.00 1.16279 .36567E-08 •20543E-08 -20.00333 .28730E-09 23.892 24.800

87.00 1.14943 .52778E-08 .30594E-08 -19.60504 .42295E-09 23.865 24.755

88.00 1.13636 .75547E-08 .45121E-08 -19.21650 .61670E-09 23.837 24.711

89.00 1.12360 . 10728E-07 .65922E-08 -18.83738 . 89087E-09 23.810 24.666

90.00 1.11111 .15116E-07 .95443E-08 -18.46732 .12755E-08 23.783 24.622

91.00 1.09890 .21140E-07 .13697E-07 -18.10606 . 18104E-08 23.756 24.577

92.00 1.08696 .29350E-07 .19491E-07 -17.75331 . 25481E-08 23.728 24.533

93.00 1.07527 .40463E-07 .27509E-07 -17.40874 .35577E-D8 23.701 24.489

94.00 1.06383 .55404E-07 •38518E-07 -17.07214 .49284E-C8 23.673 24.445

95.00 1.05263 .75363E-07 .53521E-07 -16.74320 .67759E-08 23.646 24.401

96.00 1.04167 .10186E-06 .73818E-07 -16.42167 .92483E-08 23.618 24.357

97.00 1.03093 .13681E-06 •10108E-06 -16.10739 . 12533E-07 23.590 24.313

98.00 1.02041 .18264E-06 .13745E-06 -15.80004 . 16869E-07 23.563 24.269

99.00 1.01010 . 24241E-06 .18564E-06 -15.49944 .22554E-07 23.535 24.226

100.00 1.00000 .31992E-06 .24910E-06 -15.20539 .29961E-07 23.507 24.183

101.00 .99010 .41987E-06 .33216E-06 -14.91765 . 39555E-07 23.479 24.139

102.00 .98039 .54809E-06 .44017E-06 -14.63610 .51903E-07 23.451 24.096

103.00 .97087 .71175E-06 .57986E-06 -14.36048 .67711E-07 23.423 24.053

104.00 .96154 .91958E-06 .75945E-06 -14.09067 .87830E-07 23.395 24.010

105.00 .95238 .11823E-05 .98912E-06 -13.82645 .11330E-06 23.366 23.967

106.00 .94340 .15127E-05 .12813E-05 -13.56767 .14538E-06 23.338 23.924

107.00 .93458 .19264E-05 .16509E-05 -13.31421 . 18557E-D6 23.310 23.682

108.00 .92593 .24422E-05 .21162E-05 -13.06587 .23568E-06 23.281 23.839

109.00 .91743 .30823E-05 .26993E-05 -12.82253 . 29785E-06 23.252 23.797

110.00 .90909 .38735E-05 .34263E-05 -12.58403 .37463E-06 23.224 23.754

111.00 .90090 .48474E-05 .43287E-05 -12.35024 . 46904E-06 23.195 23.712

112.00 .89286 .60413E-05 .54438E-05 -12.12104 . 58460E-06 23.166 23.670

113.00 .83496 .74993E-05 .68157E-05 -11.89628 .72545E-06 23.137 23.626

114.00 .87719 .92731E-05 .84963E-05 -11.67588 . 89639E-06 23.109 23.566

115.00 .86957 .11423E-04 .10547E-04 -11.45970 . 11030E-05 23.060 23.544

116.00 .86207 .14020E-G4 .13038E-04 -11.24761 .13519E-05 23.050 23.502

117.00 .85470 .17144E-04 .16054E-04 -11.03953 .16504E-05 23.021 23.460

118.00 .84746 .20892E-04 .19692E-04 -10.83531 . 20071E-05 22.992 23.419

119.00 .84034 .25371E-04 .24061E-04 -10.63491 . 24319E-05 22.963 23.377

120.00 .83333 .3070 8E-04 .29292E-04 -10.43820 . 29359E-05 22.933 23.335

121.00 .82645 .37046E-04 .35532E-04 -10.24507 . 35320E-05 22.904 23.294

122.00 .81967 .44550E-04 .42951E-04 -10.05545 .42344E-05 22.674 23.253

123.00 .81301 .53407E-04 .51743E-04 -9.86923 . 50597E-05 22.844 23.211

124.00 .80645 .63830E-04 .62125E-04 -9.68635 .60260E-05 22.615 23.170

125.00 .80000 .76061E-04 . 74352E-04 -9.50670 .71543E-05 22.785 23.129

126.00 .79365 .90372E-04 .88700E-04 -9.33025 . 84672E-05 22.755 23.066

127.00 .78740 .10707E-03 .10550E-03 -9.15684 .99912E-05 22.725 23.047

128.00 .78125 .12650E-03 .12509E-03 -8.98647 .11755E-04 22.695 23. 006

129.00 .77519 .14906E-03 .14789E-03 -8.81904 . 13789E-04 22.664 22.965

130.00 .76923 .17517E-03 .17435E-03 -8.65446 . 16131E-04 22.634 22.925

131.00 .76336 .20532E-03 .20496E-03 -8.49270 . 18819E-04 22.604 22.864

132.00 .75758 .24005E-03 .24029E-03 -8.33367 . 21896E-04 22.573 22.843

133.00 .75188 .27996E-03 .28096E-03 -8.17731 .25409E-04 22.542 22.803

116
Table 24. Continued

PROPANE ESTIM. V.P.,8AR, AND QVAP, KJ/MOL.

TB = 231.07070 f PB = 1. 01325* DB = . 054791

EZB = 8303.5. EGB = 8139. 7, HZB = 10224.7, HGB = 9989.0

SZB = 253.0943 « SGB = 252 .3795, QP = 18780.0

T,K 100/T P»EQN P,BAR LN(P) MOL/L Q.EQN Q,VAP

13^.00 .74627 .32572E-03 .32766E-03 -8.02354 . 29412E-04 22.512 22.762

135.00 .74074 .37805E-03 .38114E-03 -7.87234 .33960E-04 22.461 22.722

136.00 .73529 .43777E-03 .44227E-03 -7.72359 .39117E-04 22.450 22.681

137.00 .72993 .50577E-03 .51194E-03 -7.57730 .44949E-04 22.419 22.641

138.00 .72464 . 58303E-03 .59120E-03 -7.43336 .51532E-04 22.388 22.601

139.00 .71942 .67063E-03 .68113E-03 -7.29176 .58945E-04 22.357 22.560

140.00 .71429 .76974E-03 .78294E-03 -7.15245 .67273E-04 22.325 22.520

141.00 .70922 .88165E-03 .89801E*03 -7.01533 .76614E-04 22.294 22.480

142.00 .70423 .10078E^2 .10278E-02 -6.88037 . 87068E-04 22.262 22.440

143.00 .69930 .11496E-02 ,11738E-02 -6.74755 .98743E-04 22.231 22.400

144.00 .69444 .13088E-02 .13377E-02 -6.61682 . 11176E-03 22.199 22.360

145.00 .68966 . 14873E-02 .15214E-02 -6.48810 .12623E-03 22.167 22.320

146.00 .68493 .16868E-02 .17270E-02 -6.36136 . 14231E-03 22.135 22.260

147.00 .68027 .19096E-02 .19566E-02 -6.23657 . 16014E-03 22.103 22.240

148.00 .67568 .21579E-02 .22123E-02 -6.11371 . 17985E-03 22.071 22.200

149.00 .67114 .24341E-02 .24970E-02 -5.99266 .20164E-03 22.039 22.161

150.00 .66667 .27409E-02 .28131E-02 -5.87347 .22566E-03 22.006 22.121

151.00 .66225 .30811E-02 .31636E-02 -5.75605 .25210E-03 21.974 22.061

152.00 .65789 .34577E-02 .35514E-02 -5.64040 . 28116E-03 21.941 22.042

153.00 .65359 .38740E-02 .39802E-02 -5.52643 . 31306E-03 21.908 22.002

154.00 .64935 .43334E-02 .44531E-02 -5.41416 .34800E-03 21.876 21.962

155.00 .64516 .48396E-02 .49740E-02 -5*. 30353 .38623E-03 21.643 21.923

156.00 .64103 .53966E-02 .55471E-02 -5.19448 .42799E-03 21.809 21.683

157.00 .63694 .60084E-02 .61762E-02 -5.08705 .47353E-03 21.776 21.644

158.00 .63291 .66797E-02 .68662E-02 -4.98114 .52314E-03 21.743 21.804

159.00 .62893 .74151E-02 .76219E-02 -4.87673 .57711E-03 21.709 21.765

160.00 .62500 .82195E-02 .84481E-02 -4.77382 .63571E-03 21.676 21.725

161.00 .62112 .90984E-02 .93500E-02 -4.67238 .69928E-03 21.642 21.686

162.00 .61728 .10057E-01 .10334E-01 -4.57233 .76816E-03 21.608 21.646

163.00 .61350 .11102E-01 .11405E-01 -4.47370 . 84267E-03 21.574 21.607

164.00 .60976 .12239E-01 .12570E-01 -4.37643 .92318E-03 21.540 21.567

165.00 .60606 .13475E-01 .13836E-01 -4.28051 . lOlOlE-02 21.506 21.526

166.00 .60241 . 14816E-01 .15208E-01 -4.18591 . 11037E-02 21.471 21.488

167.00 .59880 .16271E-01 .16696E-01 -4.09261 . 12046E-02 21.437 21.449

168.00 .59524 .17846E-01 .18305E-01 -4.00057 .13130E-02 21.402 21.410

169.00 .59172 . 19549E-01 .20045E-01 -3.90976 .14295E-02 21.367 21.370

170.00 .58824 .21389E-01 .21924E-01 -3.82018 .15545E-02 21.333 21.331

171.00 .58480 . 23375E-01 .23950E-01 -3.73181 .16885E-02 21.297 21.291

172.00 .58140 .25516E-01 .26132E-01 -3.64459 .18319E-02 21.262 21.252

173.00 .57803 .27821E-01 .28480E-01 -3.55854 .19854E-02 21.227 21.212

174.00 .57471 .30301E-01 .31005E-01 -3.47361 . 21493E-02 21.191 21.173

175.00 .57143 .32966E-01 .33715E-01 -3.38981 .23243E-02 21.156 21.133

176.00 .56818 .35826E-01 .36623E-01 -3.30708 .25109E-02 21.120 21.094

177.00 .56497 .38893E-01 .39739E-01 -3.22542 .27097E-02 21.084 21.054

178.00 .56180 .42178E-01 .43074E-01 -3.14483 .29213E-02 21.048 21.014

179.00 .55866 .45695E-01 .46642E-01 -3.06526 . 31463E-02 21.012 20.975

180.00 .55556 .49454E-01 .50454E-01 -2.98670 . 33853E-02 20.975 20.935

181.00 .55249 .53470E-01 .54523E-01 -2.90913 .36391E-02 20.939 20.895

182.00 .54945 .57756E-01 .58862E-01 -2.63257 .39081E-02 20.902 20.656

117
Table 24. Continued.

PROPANE ESTIM. V.P.,BAR, AND QVAP, KJ/MOL.

T8 = 231.07070 , PB = 1.01325, 08 = . 054791

EZ8 = 8303.5, EG8 = 8139. 7, HZB = 10224.7, HG8 = 9989.0

SZ8 = 253.0943 , SGB = 252 .3795, QB = 18780.0

T,K 100/T P,EQN P,BAR LN(P) MOL/L Q,EQN Q,VAP

183.00 .54645 .62326E-01 .63487E-01 -2.75693 .41933E-02 20.865 20.816

164.00 .54348 .67195E-01 .68409E-01 -2.68226 .44951E-02 20.828 20.776

135.00 .54054 .72376E-01 .73646E-01 -2.60848 .48146E-02 20.791 20.736

186.00 .53763 .77886E-01 .79210E-01 -2.53565 .51521E-02 20.753 20.696

187.00 .53476 .83741E-01 .85121E-01 -2.46368 .55088E-02 20.716 20.656

186.00 .53191 .89957E-01 .91390E-01 -2.39262 .58850E-02 20.678 20.616

189.00 .52910 .96551E-01 .98039E-01 -2.32239 .62620E-02 20.640 20.576

190.00 .52632 .10354E+00 .10506E400 -2.25301 .67003E-02 20.602 20.536

191.00 .52356 .11094E+00 .11253E400 -2.18450 .71406E-02 20.564 20.495

192.00 .52083 .11878E+00 .12042E400 -2.11679 .76041E-02 20.525 20.455

193.00 .51813 .12706E+00 .12875E400 -2.04988 . 80915E-02 20.487 20.415

194.00 .51546 .13581E4-00 .13755E+00 -1.98374 . 86039E-02 20.448 20.374

195.00 .51262 .1450664^00 .14684E400 -1.91841 .91417E-02 20.409 20.334

196.00 .51020 .15481E400 . 15664E+ 0 0 -1.85382 .97063E-02 20.370 20.293

197.00 .50761 .16509E400 . 16696E400 -1.78999 . 10298E-01 20.331 20.252

196.00 .50505 . 17593E400 .17783E+00 -1.72690 . 10919E-01 20.291 20.211

199.00 .50251 .18734E+00 .18928E400 -1.66455 .11569E-01 20.252 20.170

200.00 .50000 .19934E+00 .20131E400 -1.60289 . 12250E-01 20.212 20.129

201.00 .49751 .21197E+00 .21396E400 -1.54195 .12962E-01 20.172 20.088

202.00 .49505 .22523E+00 .22725E+00 -1.48170 . 13706E-01 20.131 20.047

203.00 .49261 .23916E+00 .24120E400 -1.42213 . 14484E-01 20.091 20.005

204.00 .49020 .25378E+00 .25584E400 -1.36322 .15297E-01 20.050 19.964

205.00 .48760 . 26912E400 .27118E400 -1.30497 . 16145E-01 20.009 19.922

206.00 .48544 .28519E+00 .28727E400 -1.24735 . 17030E-01 19.968 19.880

207.00 .48309 .30203E400 .30410E400 -1.19040 .17953E-01 19.927 19.838

208.00 .48077 .31967E+00 .32173E400 -1.13406 . 18915E-01 19.886 19.796

209.00 .47847 .33812E+00 .34017E+00 -1.07831 .19917E-01 19.844 19.754

210.00 .47619 .35741E+00 .35944E400 -1.02321 . 20960E-01 19.802 19.712

211.00 .47393 .37758E400 .37958E400 -.96868 . 22046E-01 19.760 19.669

212.00 .47170 . 39865E4Q0 .40062E400 -.91475 .23175E-01 19.718 19.627

213.00 .46948 .42064E400 .42258E+00 -.86138 .24350E-01 19.675 19.584

214.00 .46729 .44359E+00 .44549E400 -.80858 . 25570E-01 19.632 19.541

215.00 .46512 .46753E+00 .46937E400 -.75636 .26838E-01 19.589 19.498

216.00 .46296 .49249E400 .49426E400 -.70466 . 28155E-01 19.546 19.455

217.00 .46083 .51849E400 .52021E+00 -.65352 .29521E-01 19.502 19.411

218.00 .45872 .54557E400 .54721E400 -.60291 .30938E-01 19.459 19.368

219.00 .45662 .57375E400 .57531E400 -.55285 .32407E-01 19.415 19.324

220.00 .45455 .60307E+00 .60455E400 -.50328 .33931E-01 19.371 19.280

221.00 .45249 .63357E400 .63494E+00 -.45423 . 35509E-01 19.326 19.236

222.00 .45045 .66526E400 .66654E + 0 0 -.40565 .37144E-01 19.282 19.192

223.00 .44643 .69819E400 .69936E400 -.35758 . 38837E-01 19.237 19.147

224.00 .44643 .73239E+00 .73344E400 -.31001 .40589E-01 19.192 19.102

225.00 .44444 .76789E+00 .76680E400 -.26292 .42401E-01 19.146 19.057

226.00 .44248 .80472E400 .80550E400 -.21629 .44276E-01 19.101 19.012

227.00 .44053 .84292E400 .84356E400 -.17012 .46215E-01 19.055 18.967

228.00 .43660 .88252E400 .86303E400 -.12440 .48219E-01 19.008 18.921

229.00 .43668 .92356E400 .92389E400 -.07916 .50287E-01 18.962 18.876

230.00 .43478 . 96607E400 .96624E400 -.03434 . 52425E-01 18.915 18.830

231.00 .43290 . 10101E4Q1 .10101E401 .01003 . 54632E-01 18.868 18.783

118
Table 25. Derived coexistence data

(Qj^ = 18 864 J/mol)

PROPANE ESTIM. V.P..BAR, AND QVAP, KJ/MOL.

T8 = 231.07070t P8 = 1.01325, DB = .054791

EZB = 8303.5, EGB = 8139.7, HZB = 10224.7, HGB = 9989.0

SZB = 253.0943, SGB = 252.3795, QB = 18864.0

T,K 100/T P,EQN P,BAR

85.47 1.17000 .30000E-08 .15376E-08

86.00 1.16279 .36567E-08 .19082E-08

87.00 1.14943 .52778E-08 .28457E-08

88.00 1.13636 .75547E-08 .42025E-08

89.00 1.12360 .10728E-07 .61480E-08

90.00 1.11111 .15116E-07 .89123E-08

91.00 1.09890 •21140E-07 .12806E-07

92.00 1.03696 .29350E-07 .18244E-07

93.00 1.07527 .40463E-07 .25781E-07

94.00 1.06383 .55404E-07 .36139E-07

95.00 1.05263 .75363E-07 .50273E-07

96.00 1.04167 .10186E-06 .69413E-07

97.00 1.03093 .13681E-06 .95152E-07

98.00 1.02041 .18264E-06 .12953E-06

99.00 1.01010 .24241E-06 .17512E-06

100.00 1.00000 .31992E-06 .23523E-06

101.00 .99010 .41987E-06 .31397E-06

102.00 .98039 .54809E-06 .41649E-06

103.00 .97087 .71175E-06 .54917E-06

104.00 .96154 .91958E-06 .71994E-06

105.00 .95238 .11823E-05 .93854E-06

106.00 .94340 .15127E-05 .12168E-05

107.00 .93458 .19264E-05 .15693E-05

108.00 .92593 .24422E-05 .20134E-05

109.00 .91743 .30823E-05 .25703E-05

110.00 .90909 .38735E-05 .32653E-05

111.00 .90090 .48474E-05 .41287E-05

112.00 .89286 .60413E-05 .51965E-05

113.00 .88496 .74993E-05 .65113E-05

114.00 .87719 .92731E-05 .81233E-05

115.00 .86957 .11423E-04 .10091E-04

116.00 .86207 .14020E-04 .12485E-04

117.00 .85470 .17144E-04 .15385E-04

118.00 .84746 .20892E-04 .18883E-04

119.00 .84034 .25371E-04 .23091E-04

120.00 .83333 .30708E-04 .28131E-04

121.00 .82645 .37046E-04 .34147E-04

122.00 .81967 .44550E-04 .41305E-04

123.00 .81301 .53407E-04 .49793E-04

124.00 .80645 .63830E-04 .59825E-04

125.00 .80000 .76061E-04 .71643E-04

126.00 .79365 .90372E-04 .85526E-04

127.00 .78740 . 10707E-03 .10178E-03

128.00 .78125 .12650E-03 .12076E-03

129.00 .77519 .14906E-03 .14286E-03

130.00 .76923 .17517E-03 .16852E-03

131.00 .76336 .20532E-03 .19822E-03

132.00 .75758 .24005E-03 .23253E-03

133.00 .75188 .27996E-03 .27204E-03

LN(P) MOL/L Q.EQN Q,VAP

-20.29302 . 21638E-09 23.906 24.906

-20.07709 . 26687E-09 23.892 24.664

-19.67746 .39340E-09 23.865 24.639

-19.28759 .57438E-09 23.837 24.795

-18.90715 . 83083E-09 23.810 24.750

-18.53583 . 11910E-08 23.763 24.706

-18.17337 . 16925E-08 23.756 24.661

-17.81942 .23851E-08 23.728 24.617

-17.47364 .33341E-08 23.701 24.573

-17.13589 .46241E-08 23.673 24.529

-16.80579 . 63648E-08 23.646 24.465

-16.48319 .86964E-08 23.618 24.441

-16.16779 .11798E-07 23.590 24.397

-15.85939 .15896E-07 23.563 24.353

-15.55778 . 21275E-07 23.535 24.310

-15.26270 .28292E-07 23.507 24.267

-14.97398 .37388E-07 23.479 24.223

-14.69141 .49111E-07 23.451 24.180

-14.41486 .64127E-07 23.423 24.137

-14.14410 . 83260E-07 23.395 24.094

-13.87894 . 10751E-06 23.366 24.051

-13.61927 .13807E-06 23.338 24.008

-13.36491 .17639E-06 23.310 23.966

-13.11569 .22422E-06 23.261 23.923

-12.87148 . 28362E-06 23.252 23.861

-12.63216 .35703E-06 23.224 23.838

-12.39754 .44737E-06 23.195 23.796

-12.16752 .55805E-06 23.166 23.754

-11.94197 .69305E-06 23.137 23.712

-11.72077 . 85704E-06 23.109 23.670

-11.50383 . 10554E-05 23.060 23.628

-11.29100 . 12945E-05 23.050 23.586

-11.08214 . 15815E-05 23.021 23.544

-10.87723 .19247E-05 22.992 23.503

-10.67607 . 23338E-05 22.963 23.461

-10.47864 . 28195E-05 22.933 23.419

-10.28483 . 33943E-05 22.904 23.378

-10.09454 .40721E-05 22.874 23.337

-9.90763 .48691E-05 22.844 23.295

-9.72409 .58028E-05 22.815 23.254

-9.54381 .68936E-05 22.785 23.213

-9.36669 . 81641E-05 22.755 23.172

-9.19269 .96393E-05 22.725 23.131

-9.02168 . 11348E-04 22.695 23. 090

-8.85365 . 13320E-04 22.664 23.049

-8.68348 . 15591E-04 22.634 23.009

-8.52612 .18200E-04 22.604 22.968

-8.36649 .21189E-04 22.573 22.927

-8.20955 .24603E-04 22.542 22.887

113
Table 25. Continued.

PROPANE ESTIM. V.P.tBAR, AND QVAP, KJ/MOL.

TB = 231.07070 , PB = 1.01325, OB - . 054791

EZB = 6303.5, EGB = 8139.7 , HZB = 10224.7, HGB = 9989.0

SZB = 253.0943 , SGB = 252. 3795, QB = 18864.

0

T,K 100/T P,EQN P,BAR LNCP) M0L7L Q,EaN Q, VAP

134.00 .74627 .32572E-03 .31744E-03 -8.05523 . 28494E-04 22.512 22.846

135.00 .74074 .37805E-03 .36947E-03 -7.90345 . 32919E-04 22.481 22.806

136.00 .73529 .43777E-03 .42895E-03 -7.75417 . 37939E-04 22.450 22.765

137.00 .72993 .50577E-03 .49680E-03 -7.60732 .43619E-04 22.419 22.725

136.00 .72464 .58303E-03 .57401E-03 -7.46287 .50034E-04 22.388 22.685

139.00 .71942 .67063E-03 .66166E-03 -7,32075 .57260E-04 22.357 22.644

140.00 .71429 .76974E-03 .76100E-03 -7.18088 .65388E-04 22.325 22.604

141.00 .70922 .88165E-03 .87329E-03 -7.04325 .74504E-04 22.294 22,564

142.00 .70423 .10078E-02 .99996E-03 -6.90780 . 84712E-04 22.262 22.524

143.00 .69930 .11496E-02 .11426E-02 -6.77448 .96118E-04 22.231 22.484

144.00 .69444 .13088E-02 .13028E-02 -6.64326 . 10884E-03 22.199 22.444

145.00 .68966 .14873E-02 .14825E-02 -6.51406 .12300E-03 22.167 22.404

146.00 .68493 .16868E-02 .16836E-02 -6.38684 .13873E-03 22.135 22.364

147.00 .68027 .19096E-02 .19082E-02 -6.26160 .15618E-03 22.103 22.324

146.00 .67568 .21579E-02 .21587E-02 -6.13823 .17549E-03 22.071 22.284

149.00 .67114 .24341E-02 .24375E-02 -6.01677 . 19683E-03 22.039 22.245

150.00 .66667 .27409E-02 .27474E-02 -5,89712 .22038E-03 22.006 22.205

151.00 .66225 .30811E-02 .30910E-02 -5.77927 .24632E-03 21.974 22.165

152.00 .65789 .34577E-02 .34716E-02 -5.66315 .27484E-03 21.941 22.126

153.00 .65359 .38740E-02 .38923E-02 -5.54875 . 30615E-03 21.908 22.086

154.00 .64935 .43334E-02 .43567E-02 -5.43605 .34047E-03 21.876 22.046

155.00 .64516 .48396E-02 .48684E-02 -5.32499 .37802E-03 21.843 22.007

156.00 .64103 .53966E-02 .54315E-02 -5,21555 .41907E-03 21.809 21.967

157.00 .63694 .60084E-02 .60501E-02 -5.10769 .46385E-03 21,776 21.928

158.00 ,63291 .66797E-02 .67288E-02 -5.00135 . 51266E-03 21.743 21.888

159.00 .62893 .74151E-02 .74721E-02 -4.89658 .56575E-03 21.709 21.849

160.00 .62500 .82195E-02 .82853E-02 -4.79328 .62345E-03 21.676 21. 809

161.00 .62112 .90984E-02 .91737E-02 -4.69142 .68607E-03 21.642 21.770

162.00 .61728 .10057E-01 .10143E-01 -4.59100 .75393E-03 21.608 21.730

163.00 .61350 .11102E-01 .11198E-01 -4.49198 . 82738E-03 21.574 21.691

164.00 .60976 .12239E-01 .12347E-01 -4.39433 .90678E-03 21.540 21.651

165.00 .60606 .13475E-01 .13595E-01 -4.29805 .99248E-03 21.506 21.612

166.00 .60241 .14816E-01 .14949E-01 -4.20309 . 10849E-02 21.471 21.573

167.00 .59880 .16271E-01 .16418E-01 -4.10940 . 11845E-02 21.437 21.533

168.00 .59524 .17846E-01 .18007E-01 -4,01701 . 12916E-02 21.402 21.494

169.00 .59172 .19549E-01 .19726E-01 -3.92584 .14067E-02 21.367 21.454

170.00 .58824 .21389E-01 .21581E-01 -3.83593 . 15302E-02 21,333 21.415

171.00 .53480 .23375E-01 .23584E-01 -3.74720 . 16626E-02 21.297 21.375

172.00 .58140 .25516E-01 .25741E-01 -3.65966 . 18045E-02 21.262 21.336

173.00 .57803 .27821E-01 .28064E-01 -3.57326 .19563E-02 21.227 21.296

174.00 .57471 . 30301E-01 .30562E-01 -3.48800 . 21185E-02 21.191 21.257

175.00 .57143 .32966E-01 .33244E-01 -3.40387 .22917E-02 21.156 21.217

176.00 .56818 . 35826E-01 .36123E-01 -3.32082 . 24765E-02 21.120 21.178

177.00 .56497 . 38893E-01 .39210E-01 -3.23883 . 26735E-02 21.084 21.138

178,00 .56180 .42178E-01 .42514E-01 -3,15791 . 28832E-02 21.048 21.099

179.00 .55866 .45695E-01 .46050E-01 -3.07802 . 31062E-02 21.012 21.059

180.00 .55556 .49454E-01 .49829E-01 -2.99916 .33432E-C2 20.975 21.019

181.00 .55249 .53470E-01 .53864E-01 -2.92130 .35949E-02 20.939 20.980

162.00 . 54945 .57756E-01 .58169E-01 -2.84440 . 38619E-02 20.902 20.940

12 0
Table 25. Continued

PROPANE ESTIM. V,P.,BAR, AND QVAP, KJ/MOL.

T8 = 231.07070 t PB = 1.01325. OB = . 054791

EZB = 8303.5. EGB = 8139. 7, HZB = 10224.7, HGB = 9989.0

SZB = 253.0943 t SGB = 252 .3795, QB = 18864.0

T,K 100/T P.EQN P.BAR LNIPI MOL/L Q,EQN Q, VAP

183.00 .54645 .62326E-01 .62758E-01 -2.76847 .41450E-02 20.865 20.900

184.00 .54348 .67195E-01 .67644E-01 -2.69350 .44446E-02 20.828 20.060

185.00 .54054 .72376E-01 .72844E-01 -2.61943 .47619E-02 20.791 20.020

186.00 .53763 .77886E-01 .78371E-01 -2,54630 .50972E-02 20.753 20.780

187.00 .53476 .83741E-01 .84242E-01 -2.47406 .54516E-02 20.716 20.740

188.00 .53191 .89957E-01 .90473E-01 -2.40270 .58256E-02 20.678 20.700

189.00 .52910 .96551E-01 .97082E-01 -2.33220 .62202E-02 20.640 20.660

190.00 .52632 .10354E4^00 .10408E400 -2.26256 .66362E-02 20.602 20.620

191.00 .52356 . 11094E+00 .11150E400 -2.19372 .70746E-02 20.564 20.580

192.00 .52083 .11878E+00 .11935E400 -2.12574 . 75358E-02 20.525 20.539

193.00 .51813 .12706EVQ0 .12764E400 -2.05856 .80210E-02 20.487 20.499

194.00 .51546 .13581E4-00 .13640E400 -1.99218 .85309E-02 20.448 20.459

195.00 .51282 .14506E4-00 .14565E400 -1.92658 .90666E-02 20.409 20.418

196.00 .51020 .15481E4-00 .15540E400 -1.86172 .96291E-02 20.370 20.377

197.00 .50761 .16509E^00 .16569E400 -1.79762 .10219E-01 20.331 20.337

198.00 .50505 .17593E+00 .17652E400 -1.73430 .10838E-01 20.291 20.296

199.00 .50251 .18734E+00 .18793E400 -1.67168 . 11486E-01 20.252 20.255

200.00 .50000 .19934E*00 .19993E400 -1.60978 .12165E-01 20.212 20.214

201.00 .49751 .21197E+00 .21255E400 -1.54856 .12875E-01 20.172 20.172

202.00 .49505 .22523E+00 .22581E400 -1.48807 .13618E-01 20.131 20.131

203.00 .49261 .23916E4^00 .23973E400 -1.42824 .14395E-01 20.091 20.090

204.00 .49020 .25378E+00 .25433E400 -1.36911 .15206E-01 20.050 20.048

205.00 .48780 .26912E4-00 .26965E400 -1.31062 .16053E-01 20.009 20.007

206.00 .48544 .28519E4-00 .28572E400 -1..25276 .16937E-01 19.968 19.965

207.00 .48309 .30203E*00 .30253E400 -1.19557 .17859E-01 19.927 19.923

208.00 .48077 .31967E+00 .32014E400 -1.13898 .18820E-01 19.886 19.881

209.00 .47847 .33812E«^00 .33857E+00 -1.08302 .19822E-01 19.844 19.839

210.00 .47619 .35741E+00 .35784E+00 -1.02768 . 20865E-01 19.802 19.796

211.00 .47 393 .37758E+00 .37798E+00 -.97291 .21951E-01 19.760 19.754

212.00 .47170 .39865E+00 .39901E400 -.91877 .23081E-01 19.718 19.711

213.00 .46948 .42064E1-00 .42099E400 -.86515 .24256E-01 19.675 19.669

214.00 .46729 .44359E+00 .44390E400 -.81215 .25478E-01 19.632 19.626

215.00 .46512 .46753E+00 .46780E400 -.75971 .26746E-01 19.589 19.583

216.00 .46296 .49249E+00 .49273E400 -.70780 . 28064E-01 19.546 19.539

217.00 .46083 .51849E+00 .51869E400 -.65644 .29433E-01 19.502 19.496

218.00 .45872 .54557E+00 . 54575E+- 0 0 -.60560 . 30853E-01 19.459 19.452

219.00 .45662 .57375E+00 .57389E400 -.55532 .32325E-01 19.415 19.408

220.00 .45455 .60307E4-00 .60318E400 -.50553 . 33852E-01 19.371 19.364

221.00 .45249 .63357E+00 .63364E400 -.45627 . 35434E-01 19.326 19.320

222.00 .45045 .665262 4^00 .66532E400 -.40748 .37074E-01 19.282 19.276

223.00 .44843 .69819E400 .69821E400 -.35923 . 38772E-01 19.237 19.231

224.00 .44643 .73239E400 .73239E400 -.31144 .40529E-01 19.192 19.187

225.00 .44444 .76789E400 .76786E<n0 -.26414 .42348E-01 19.146 19.142

226.00 .44248 .80472E+00 .80469E400 -.21729 .44230E-01 19.101 19.096

227.00 .44053 .84292E400 .84289E400 -.17092 .46177E-01 19.055 19.051

228.00 .43860 .88252E4Q0 .68249E400 -.12501 .48188E-01 19.000 19. 005

229.00 .43668 .92356E+00 .92353E+00 -.07955 .50267E-01 10.962 18.960

230.00 .43478 .96607E400 .96604E400 -.03455 .52413E-01 18.915 18.914

231.00 .43290 .10101E401 .10101E401 .01003 .54632E-01 18.068 18.867

121
TABLE 26. Calculated P(T) isochores

The following pages give P(T) along isochores, as computed by the equation

of state. The third column DP/DD is the isotherm slope (9P/9p) in units of the

bar and mol/L. The last two columns give the isochore slopes and curvatures

9P/9T, 9^T/9T^, in units of the bar and K.

These tables show that the isochore curvatures are qualitatively consistent

with a maximum in the specific heat C^(p,T) at the critical point.

I

Ir

!

)

\

122
Table 26. Calculated P(T) isochores.

THE ISOCHORE AT 1.00 MOL/L

T,K P,8AR DP/DD OP/OT D2P/DT2

334.0 19.866 12.573 . 1148 -.00034

342.0 20.774 13.758 . 1125 -.00025

350.0 21.667 14.893 .1107 -.00021

358.0 22.546 15.995 .1092 -.00017

366.0 23.414 17.070 .1079 -.00015

374.0 24.272 18.124 .1068 -.00013

382.0 25.122 19.160 .1058 -.00012

390.0 25.965 20.180 .1049 -.00010

398.0 26.800 21.187 . 1041 -.00009

406.0 27.630 22.182 .1034 -.00009

414.0 23.455 23.165 . 1027 -.00008

422.0 29.274 24.139 .1021 -.00007

430.0 30.089 25.104 . 1016 -.00007

438.0 30.899 26.061 . 1010 -.00006

446.0 31.705 27.011 . 1006 -.00006

454.0 32.508 27.953 . 1001 -.00005

462.0 33.307 28.889 . 0997 -.00005

470.0 34.103 29.820 .0993 -.00005

478.0 34.896 30.744 . 0990 -.00004

486.0 35.687 31.664 . 0986 -.00004

494.0 36.474 32.579 .0983 -.00004

502.0 37.259 33.489 .0980 -.00004

510.0 38.042 34.395 .0977 -.00003

518.0 38.822 35.296 . 0974 -.00003

526.0 39.601 36.194 .0972 -.00003

534.0 40 .377 37.089 .0969 -.00003

542.0 41.152 37.980 . 0967 -.00003

550.0 41.924 38.368 .0965 -.00003

558.0 42.695 39.752 .0963 -.00003

566.0 43 .464 40.634 .0961 -.00002

574.0 44.232 41.513 . 0959 -.00002

582.0 44.998 42.389 . 0957 -.00002

590.0 45.763 43.263 .0955 -.00002

598.0 46.527 44.134 .0953 -.00002

1 2 3
Table 26 Continued

THE ISOCHORE AT 2.00 MOL/L

T,K P.BAR OP/00 OP/DT 02P/0T2

358.0 33.146 5.653 .2721 -.00139

366.0 35.286 7.320 .2637 -.00063

374.0 37.372 8.700 .2580 -.00061

362.0 39.418 10.035 .2537 -.00048

390.0 41.434 11.338 .2502 -.00040

398.0 43.423 12.619 .2472 -.00035

406.0 45.390 13.881 .2446 -.00030

414.0 47.337 15.127 .2423 -.00027

422.0 49.267 16.361 .240 2 -.00024

430.0 51.181 17.583 .2384 -.00022

438.0 53.061 18.795 .2367 -.00020

446.0 54.969 19.998 .2351 -.00019

454.0 56.644 21.192 .2337 -.00017

462.0 58.708 22.380 .2324 -.00016

470.0 60.563 23.560 .2312 -.00015

476.0 62.408 24.734 .2300 -.00014

486.0 64.244 25.903 .2290 -.00013

494.0 66.072 27.066 .2280 -.00012

502.0 67.892 28.223 .2271 -.00011

510.0 69.705 29.377 .2262 -.00011

518.0 71.511 30.525 .2254 -.00010

526.0 73.311 31.670 .2246 -.00010

534.0 75.104 32.811 .2236 -.00009

542.0 76.892 33.947 .2231 -.00009

550.0 78.674 35.081 .2225 -.00008

558.0 60.452 36.211 .2216 -.00006

566.0 82.224 37.337 .2212 -.00007

574.0 83.991 36.461 .2207 -.00007

562.0 85.754 39.582 .2201 -.00007

590.0 87.513 40.700 .2196 -.00006

598.0 89.268 41.815 .2191 -.00006

124
Table 26 Continued

THE ISOCHORE AT 3.00 MOL/L

T,K P,BAR OP/00 OP/OT 02P/0T2

366.0 39.461 1.694 .4599 -.00585

374.0 43.034 3.273 .4382 -.00154

382.0 46.498 4.744 .4286 -.00096

390.0 49.899 6.190 .4220 -.00071

398.0 53.254 7.624 .4169 -.00057

406.0 56.572 9.050 .4127 -.00048

414.0 59.859 10.472 .4091 -.00042

422.0 63.119 11.890 .4060 -.00037

430.0 66.355 13.305 .4032 -.00033

438.0 69.570 14.717 . 4007 -.00030

446.0 72.766 16.128 .3984 -.00027

454 .

0

75.945 17.537 .3963 -.00025

462.0 79.107 18.944 .3944 -.00023

470.0 82.255 20.350 .3926 -.00021

478.0 35.390 21.755 . 3910 -.00020

486.0 88.511 23.158 .3894 -.00019

494.0 91.621 24.560 .3880 -.00017

502.0 94.720 25.960 .3867 -.00016

510.0 97.808 27.360 .3854 -.00015

518.0 100.886 28.758 .3842 -.00015

526.0 103.955 30.155 .3831 -.00014

534.0 107.015 31.551 .3820 -.00013

542.0 110.067 32.946 .3810 -.00012

550.0 113.111 34.340 .3800 -.00012

558.0 116.147 35.733 .3791 -.00011

566.0 119.176 37.125 .3782 -.00011

574.0 122.198 38.515 .3773 -.00010

582.0 125.214 39.905 .3765 -.00010

590.0 128.223 41.293 .3757 -.00010

598.0 131.226 42.681 .3750 -.00009

125
Table 26 Continued

THE ISOCHORE AT 4.00 MOL/L

T,K P.BAR OP/DO DP/OT D2P/0T2

374.0 44.999 1.082 .6245 -.00210

382.0 49.947 2.578 .6139 -.00092

390.0 54.832 4.10 9 .6079 -.00062

398.0 59.677 5.665 .6036 -.00048

406.0 64.492 7.242 .6001 -.00040

414.0 69.280 8.835 .5972 -.00034

422.0 74.047 10.442 .5946 -.00030

430.0 78.795 12.062 .5924 -.00027

438kP 83.526 13.691 .5903 -.00024

446.0 38.241 15.331 .5885 -.00022

454.0 92.942 16.978 .5868 -.00020

462.0 97.630 18.633 . 5852 -.00019

470.0 102.305 20.295 .5837 -.00018

478.0 106.970 21.962 .5824 -.00017

486.0 111.623 23.635 .5811 -.00016

494.0 116.267 25.313 .5799 -.00015

502.0 120 .901 26.995 .5787 -.00014

510.0 125.526 28.681 .5776 -.00013

518.0 130.143 30.371 .5765 -.00013

526.0 134.751 32.064 .5755 -.00012

534.0 139.351 33.760 .5746 -.00012

542.0 143.944 35.459 .5736 -.00011

550.0 148.529 37.160 .5727 -.00011

558.0 153.108 38.863 .5719 -.00011

566.0 157.679 40.568 .5710 -.00010

574.0 162.244 42.275 .5702 -.00010

582.0 166.803 43.984 .5694 -.00010

590.0 171.355 45.694 . 5687 -.00009

598.0 175.902 47.406 .5679 -.00009

12 S
Table 26. Continued

THE ISOCHORE AT 4.96 MOL/L

T,K P.BAR OP/ 00 OP/OT 02P / 0 T 2 374.0 45.805 .790 .8 059 -.00000

302.0 52.253 2.465 .8059 -.00001

390.0 58.699 4.225 .8058 -.00001

398.0 65.145 6.038 .8057 -.00002

406.0 71.590 7.890 .8 055 -.00002

414.0 78.034 9.774 .8053 -.00003

422.0 84.475 11.685 .8051 -.00003

430.0 90.915 13.618 .8 049 -.00003

438.0 97.353 15.571 .8046 -.00003

446.0 103.789 17.541 .8 043 -.00004

454.0 110.222 19.527 .8040 -.00004

462.0 116.653 21.527 .6037 -.00004

470.0 123.081 23.539 .8033 -.00004

478.0 129.506 25.562 .6030 -.00005

486.0 135.928 27.595 .8026 -.00005

494.0 142.347 29.638 .8022 -.00005

502.0 148.763 31.688 .8016 -.00005

510.0 155.176 33.747 .8 014 -.00005

518.0 161.585 35.312 . 8009 -.00005

526.0 167.991 37.884 .8005 -.00006

534.0 174.393 39.961 .8001 -.00006

542.0 180.792 42.044 .7996 -.00006

550.0 187.187 44.131 .7991 -.00006

558.0 193.578 46.223 .7987 -.00006

566.0 199.965 48.319 .7982 -.00006

574.0 206.349 50.419 .7977 -.00006

582.0 212.729 52.522 .7972 -.00006

590.0 219.104 54.628 .7967 -.00006

598.0 225.476 56.737 .7962 -.00006

127
Table 26 Continued

THE ISOCHORE AT 6.00 MOL/L

T,K P.BAR DP/DD OP/DT D2P/DT2

374.0 46.924 1.729 1.0484 .00301

382.0 55.381 4.015 1.0636 .00131

390.0 63.926 6.371 1.0721 .00087

398.0 72.528 8.777 1.0781 .00065

406.0 81.172 11.221 1.0828 .00052

414.0 89.850 13.697 1.0865 .00043

422.0 98.555 16.199 1.0897 .00036

430.0 107.284 18.724 1.0924 .00031

438.0 116.032 21.269 1.0947 .00026

446.0 124.797 23.832 1.0966 .00023

454.0 133.577 26.410 1.0983 .00020

462.0 142.370 29.002 1.0998 .00017

470.0 151.173 31.606 1.1010 .00015

478.0 159.986 34.222 1.1021 .00013

486.0 168.607 36.847 1.1031 .00011

494.0 177.635 39.482 1.1039 .00009

502.0 186.469 42.125 1.1046 .00008

510.0 195.306 44.775 1. 1051 .00006

518.0 204.151 47.432 1.1056 .00005

526.0 212.997 50.095 1.1060 .00004

534.0 221.847 52.763 1.1063 .00003

542.0 230.698 55.437 1.1065 .00002

550.0 239.551 58.114 1.1067 .00002

558.0 246.404 60.796 1.1068 .00001

566.0 257.259 63.481 1.1068 .00000

574.0 266.113 66.170 1.1068 -.00001

582.0 274.967 68.861 1.1067 -.00001

590.0 283.620 71.555 1.1066 -.00002

598.0 292.673 74.252 1.1064 -.00002

12 8
Table 26 Continued

THE ISOCHORE AT 7.00 MOL/L

T.K P.BAR OP/DD OP/DT 02P/0T2

366.0 39.634 3.392 1.3563 .01280

374.0 50.702 6.978 1.4003 .00299

382.0 61.984 10.428 1.4187 .00181

390.0 73.385 13.869 1.4310 .00132

398.0 84.872 17.313 1.4404 .00104

406.0 96.426 20.765 1.4479 .00085

414.0 108.035 24.225 1.4541 .00072

422.0 119.689 27.692 1.4594 .00061

430.0 131.383 31.165 1.4639 .00053

438.0 143.111 34.645 1.4679 .00046

446.0 154.868 38.130 1.4713 .00040

454.0 166.650 41.619 1.4743 .00035

462.0 178.455 45.112 1.4769 .00030

470.0 190.279 48.609 1.4792 .00027

478.0 202.121 52.108 1.4812 .00023

486.0 213.977 55.610 1.4829 .00020

494.0 225.847 59.114 1.4844 .00018

502.0 237.727 62.619 1.4857 .00015

510.0 249.618 66.125 1.4869 .00013

518.0 261.517 69.632 1.4878 .00011

526.0 273.422 73.140 1.4386 .00009

534.0 285.334 76.648 1.4893 .00008

542.0 297.251 80.155 1.4899 .00006

550.0 309.172 83.663 1.4903 .00005

558.0 321.096 87.169 1.4906 .00004

566.0 333.022 90.675 1.4909 .00002

574.0 344.949 94.181 1.4910 .00001

582.0 356.878 97.684 1.4911 .00000

590.0 368.806 101.187 1.4911 -.00001

598.0 380.734 104.688 1.4910 -.00001

129
Table 26 Continued

THE ISOCHORE AT 8.00 MOL/L

T,K P.BAR OP/DO DP/OT 02P/0T2

366.0 49.009 17.715 1.9117 .00255

37^.0 64.374 22.783 1.9284 .00173

362.0 79.652 27.766 1.9405 .00132

390.0 95.415 32.700 1.9499 .00106

396.0 111.046 37.598 1.9576 .00087

406.0 126.732 42.470 1.9639 .00073

414.0 142.466 47.319 1.9693 .00062

422.0 156.240 52.150 1.9739 .00053

430.0 174.047 56.964 1.9779 .00046

436.0 169.664 61.763 1.9813 .00039

446.0 205.746 66.549 1.9842 .00034

454 .

0

221.630 71.321 1.9867 .00029

462.0 237.532 76.062 1.9888 .00024

470.0 253.450 60.831 1.9906 .00021

476.0 269.361 85.570 1.9921 .00017

466.0 285.323 90.298 1.9934 .00014

494.0 301.274 95.016 1.9944 .00011

502.0 317.232 99.724 1.9952 .00009

510.0 333.197 104.423 1.9958 .00007

516.0 349.165 109.112 1.9963 .00005

526.0 365.137 113.793 1.9966 .00003

534.0 361. 110 118.465 1.9967 .00001

542.0 397.084 123.126 1.9966 -.00001

550.0 413.058 127.782 1.9967 -.00002

556.0 429.031 132.428 . 1.9964 -.00003

566.0 445.001 137.066 1.9961 -.00005

574.0 460.968 141.696 1.9957 -.00006

562.0 476.932 146.316 1.9952 -.00007

590.0 492.892 150.932 1.9947 -.00006

596.0 508.847 155.538 1.9940 -.00009

130
Table 26 Continued

THE ISOCHORE AT 9.00 MOL/L

T,K P,BAR OP/00 DP/DT 02P/DT2

350.0 38.937 37.009 2.6405 .00138

358.0 60.101 43.993 2.6498 .00100

366.0 81.329 50.865 2.6568 .00077

374.0 102.606 57.655 2.6623 .00061

382.0 123.922 64.380 2.6666 .00048

390.0 145.269 71.051 2.6701 .00039

398.0 166.642 77.675 2.6729 .00031

406.0 188.034 84.257 2.6751 .00024

414.0 209.442 90.802 2.6768 .00019

422.0 230.862 97.311 2.6781 .00014

430.0 252.290 103.790 2.6790 .00009

438.0 273.725 110.238 2.6796 .00006

446.0 295.163 116.659 2.6799 .00002

454.0 316.603 123.053 2.6800 -.00001

462.0 333.042 129.422 2.6798 -.00004

470.0 359.479 135.768 2.6794 -.00006

478.0 380.912 142.091 2.6788 -.00008

436.0 402.340 148.393 2.6781 -.00010

494.0 423. 761 154.673 2.6771 -.00012

502.0 445.174 160.933 2.6761 -.00014

510.0 466.578 167.174 2.6749 -.00016

513.0 437.972 173.396 2.6736 -.00017

526.0 509.355 179.600 2.6722 -.00018

534.0 530.727 185.786 2.6707 -.00019

542.0 552.086 191.955 2.6691 -.00021

550.0 573.432 198.107 2.6674 -.00022

558.0 594.764 204.243 2.6657 -.00022

566.0 616.082 210.362 2.6638 -.00023

574.0 637.385 216.466 2.6619 -.00024

582.0 658.673 222.555 2.6600 -.00025

590.0 679.945 228.628 2.6580 -.00025

131
Table 26 Continued

THE ISOCHORE AT 10.00 MOL/L

t,k P.BAR OP/DO OP/DT 02P/0T2

330.0 29.621 72.974 3.6370 -.00013

334.0 44.168 77.521 3.6365 -.00014

338.0 58.713 82.047 3.6359 -.00016

342.0 73.255 86.553 3.6352 -.00017

346.0 87.795 91.042 3.6345 -.00019

350.0 102.331 95.513 3.6337 -.00020

354.0 116.864 99.969 3.6329 -.00022

358.0 131.394 104.409 3.6320 -.00023

362.0 145.921 108.834 3.6311 -.00024

366.0 160.443 113.246 3.6301 -.00026

370.0 174.961 117.644 3.6290 -.00027

374.0 189.475 122.029 3.6279 -.00028

378.0 203.984 126.402 3.6267 -.00030

382.0 218.489 130.763 3.6255 -.00031

386.0 232.988 135.112 3.6243 -.00032

390.0 247.483 139.450 3.6230 -.00033

394.0 261.972 143.777 3.6217 -.00034

398.0 276.456 148.094 3.6203 -.00035

402.0 290.935 152.400 3.6189 -.00036

406.0 305.407 156.697 3.6174 -.00037

410.0 319.374 160.984 3.6159 -.00038

414.0 334.335 165.261 3.6144 -.00038

418.0 348.789 169.529 3.6129 -.00039

422.0 363.237 173.788 3.6113 -.00040

426.0 377.679 178.038 3.6097 -.00041

430.0 392.115 182.279 3.6080 -.00041

434.0 406.543 186.512 3.6063 -.00042

438.0 420.965 190.736 3.6047 -.00043

442.0 435.381 194.953 3.6029 -.00043

446.0 449.789 199.161 3.6012 -.00044

450.0 464.190 203.361 3.5994 -.00044

454.0 478.584 207.554 3.5976 -.00045

458.0 492.971 211.739 3.5958 -.00045

462.0 507.351 215.917 3.5940 -.00046

466.0 521.723 220.087 3.5921 -.00046

470.0 536.088 224.250 3.5903 -.00047

474.0 550 . 445 228.406 3.5884 -.00047

478.0 564.795 232.555 3.5865 -.00048

482.0 579.137 236.697 3.5846 -.00048

486.0 593.472 240.832 3.5827 -.00048

490.0 607.798 244.961 3.5807 -.00049

494.0 622.117 249.083 3.5788 -.00049

498.0 636.428 253.198 3.5768 -.00049

502.0 650.732 257.307 3.5748 -.00050

506.0 665.027 261.410 3.5728 -.00050

510.0 679.314 265.506 3.5708 -.00050

514.0 693.594 269.596 3.5688 -.00050

13 2
Table 26 Continued

THE ISOCHORE AT 11.00 MOL/L

T,K P,BAR DP/OD OP/DT 02P/OT2

306.0 27.429 132.742 4.9470 -.00122

310.0 47.208 138.590 4.9422 -.00118

314.0 66.967 144.430 4.9376 -.00114

318.0 86.709 150.260 4.9331 -.00111

322.0 106.433 156.080 4.9288 -.00108

326.0 126.139 161.890 4.9245 -.00106

330.0 145.828 167.690 4.9203 -.00104

334.0 165.501 173.480 4.9161 -.00103

338.0 185.158 179.260 4.9121 -.00101

342.0 204.798 185.029 4.9080 -.00100

346.0 224.422 190.788 4.9040 -.00100

360.0 244.030 196.537 4.9000 -.00099

354.0 263.622 202.276 4.8961 -.00098

358.0 283.199 208.005 4.8922 -.00098

362.0 302.760 213.723 4.8883 -.00097

366.0 322.305 219.432 4.8844 -.00097

370.0 341.835 225.131 4.8805 -.00097

374.0 361.349 230.820 4.8767 -.00096

378.0 380.848 236.499 4.8728 -.00096

382.0 400.332 242.169 4.8690 -.00096

386.0 419.800 247.830 4.8652 -.00096

390.0 439.253 253.481 4. 8613 -.00096

394.0 458.691 259.122 4.8575 -.00095

398.0 478.113 264.754 4.8537 -.00095

402.0 497.521 270.378 4.8499 -.00095

406.0 516.913 275.992 4.8461 -.00095

410.0 536.289 281.597 4.8423 -.00095

414.0 555.651 287.193 4.8385 -.00095

418.0 574.997 292.780 4.8347 -.00095

422.0 594.329 298.359 4.8309 -.00095

426.0 613.645 303.929 4.8271 -.00095

430.0 632.946 309.490 4.8234 -.00095

434.0 652.232 315.043 4.8196 -.00094

438.0 671.50 2 320.587 4.8158 -.00094

442.0 690.758 326.123 4.8120 -.00094

133
Table 26 Continued

THE

T,K

274.0

276.0

278.0

280.0

282.0

284.0

286.0

288.0

290.0

292.0

294.0

296.0

298.0

300.0

302.0

304.0

306.0

308.0

310.0

312.0

314.0

316.0

318.0

320.0

322.0

324.0

326.0

328.0

330.0

332.0

334.0

336. 0 338.0

340.0

342.0

344.0

346.0

348.0

350.0

352.0

354.0

356.0

358.0

360.0

362.0

364.0

366.0

368.0

370.0

372.0

374.0

376.0

ISOCHORE AT 12.00 HOL/L

P.BAR OP/OD

14.240 217.100

27.609 221.001

40.971 224.902

54.325 228.802

67.672 232.701

81.011 236.600

94.343 240.498

107.669 244.395

120.987 248.291

134.298 252.185

1^7.602 256.079

160.900 259.971

174.190 263.861

187.474 267.750

200.751 271.637

214.021 275.522

227.285 279.406

240.541 283.288

253.792 287.168

267.035 291.046

280.272 294.922

293.503 298.796

306.727 302.668

319.944 306.538

333.155 310.406

346.359 314.271

359.557 318.135

372.748 321.996

385.933 325.855

399.112 329.712

412.284 333.566

425.449 337.418

438.609 341.268

451.762 345.115

464.908 348.960

478.048 352.803

491.182 356.643

504.310 360.481

517.431 364.317

530.546 368.150

543.654 371.980

556.756 375.808

569.852 379.634

582.942 383.457

596.025 387.278

609.102 391.096

622.173 394.912

635.238 398.725

648.296 402.536

661.348 406.344

674.394 410.150

687.433 413.953

OP/DT D2P/DT2

6.6864 -.00190

6.6826 -.00187

6.6789 -.00185

6.6752 -.00183

6.6716 -.00181

6.6680 -.00179

6.6644 -.00178

6.6609 -.00176

6.6573 -.00175

6.6539 -.00173

6.6504 -.00172

6.6470 -.00171

6.6436 -.00170

6.6402 -.00169

6.6368 -.00168

6.6334 -.00168

6.6301 -.00167

6.6268 -.00166

6.6234 -.00165

6.6201 -.00165

6.6168 -.00164

6.6136 -.00164

6.6103 -.00163

.6.6070 -.00163

6.6038 -.00162

6.6005 -.00162

6.5973 -.00162

6.5941 -.00161

6.5909 -.00161

6.5877 -.00160

6.5844 -.00160

6.5812 -.00160

6.5780 -.00160

6.5749 -.00159

6.5717 -.00159

6.5685 -.00159

6.5653 -.00159

6.5622 -.00158

6.5590 -.00158

6.5558 -.00158

6.5527 -.00158

6.5495 -.00157

6.5464 -.00157

6.5432 -.00157

6.5401 -.00157

6.5370 -.00157

6.5338 -.00156

6.5307 -.00156

6.5276 -.00156

6.5245 -.00156

6.5213 -.00156

6.5182 -.00156

134
Table 26 Continued

THE

T.K

23 a *0 240.0

242.0

244.0

246.0

248.0

250.0

252.0

254.0

256.0

258.0

260.0

262.0

264.0

266.0

268.0

270.0

272.0

274.0

276.0

278.0

280.0

282.0

284.0

286.0

288.0

290.0

292.0

294.0

296.0

298.0

300.0

302.0

304.0

306.0

308.0

310.0

312.0

314.0

ISOCHORE AT 13.00 MOL/L

P.BAR DP/DO

6.792 339.378

24.943 344.886

43.086 350.394

61.221 355.901

79.346 361.407

97.463 366.912

115.572 372.415

133.672 377.917

151.763 383.417

169.845 388.916

187.919 394.412

205.983 399.907

224.039 405.399

242.087 410.889

260.125 416.376

278.155 421.861

296.176 427.344

314.188 432.823

332.191 438.300

350.185 443.774

368.170 449.245

386.146 454.713

404.113 460.179

422.071 465.640

440.021 471.099

457.961 476.555

475.892 482.007

493.814 487.456

511.727 492.902

529.630 498.344

547.525 503.782

565.410 509.218

583.287 514.649

601.154 520.077

619.012 525.502

636.860 530.923

654.700 536.340

672.530 541.753

690.351 547.163

OP/DT 02P / DT 2 9.0779 -.00215

9.0736 -.00215

9.0693 -.00216

9.0650 -.00216

9.0607 -.00216

9.0564 -.00216

9.0520 -.00217

9.0477 -.00217

9.0434 -.00218

9.0390 -.00218

9. 0346 -.00219

9.0302 -.00219

9.0258 -.00220

9.0214 -.00220

9. 0170 -.00221

9.0126 -.00221

9. 0082 -.00222

9.0037 -.00223

8.9993 -.00223

8.9948 -.00224

8.9903 -.00224

8.9858 -.00225

8.9813 -.00225

8.9768 -.00226

8.9723 -.00226

8.9678 -.00227

8.9633 -.00227

8.9587 -.00228

8.9542 -.00228

8.9496 -.00228

8.9450 -.00229

8.9404 -.00229

8.9359 -.00230

8.9313 -.00230

8.9267 -.00230

8.9220 -.00231

8.9174 -.00231

8.9128 -.00231

8.9082 -.00232

135
Table 26 Continued

THE ISOCHORE AT 14.00 MOL/L

T,K PtBAR

200.0 23.481

202.0 48.552

204.0 73.615

206.0 98.668

208.0 123.712

210.0 148.746

212.0 173.770

214.0 198.784

216.0 223.788

218.0 248.782

220.0 273.764

222.0 298.736

224.0 323.697

226.0 348.646

228.0 373.584

230.0 398.510

232.0 423.424

234.0 448.327

236.0 473.217

238.0 498.095

240.0 522.960

242.0 547.813

244.0 572.654

246.0 597.481

248.0 622.296

250.0 647.097

252.0 671.886

254.0 696.661

OP/00 OP/DT

519.563 12.5377

527.809 12.5334

536.051 12.5289

544.286 12.5243

552.515 12.5195

560.738 12.5146

568.955 12.5097

577.166 12.5046

585.370 12.4993

593.567 12.4940

601.757 12.4886

609.940 12.4831

618.116 12.4775

626.285 12.4718

634.447 12.4660

642.602 12.4601

650.749 12.4542

658.888 12.4482

667.020 12.4421

675.144 12.4359

683.260 12.4296

691.369 12.4233

699.470 12.4170

707.563 12.4105

715.648 12.4040

723.725 12.3975

731.794 12.3909

739.856 12.3842

02P/0T2

-.00215

-.00221

-.00228

-.00234

-.00241

-.00246

-.00252

-.00258

-.00263

-.00268

-.00273

-.00278

-.00283

-.00287

-.00291

-.00296

-.00299

-.00303

-.00307

-.00310

-.00314

-.00317

-.00320

-.00323

-.00326

-.00329

-.00331

-.00334

136
Table 26 Continued

THE ISOCHORE i t,k PfBAR

157.0 14.870

158.0 32.714

159.0 50.555

160.0 68.394

161.0 86.231

162.0 104.065

163.0 121.897

164.0 139.726

165.0 157.552

166.0 175.376

167.0 193.196

168.0 211.014

169.0 228.828

170.0 246.639

171.0 264.446

172.0 232.251

173.0 300.051

174.0 317.848

175.0 335.641

176.0 353.431

177.0 371.216

178.0 388.998

179.0 406.775

180.0 424.548

181.0 442.318

182.0 460.083

183.0 477.843

184.0 495.599

185.0 513.351

186.0 531.098

187.0 548.841

188.0 566.578

189.0 584.312

190.0 602.040

191.0 619.763

192.0 637.482

193.0 655.196

194.0 672.904

195.0 690.608

15.00 MOL/L

OP/00 DP/DT

770.630 17.8443

777.183 17.8423

783.730 17.8402

790.273 17.8379

796.809 17.8356

803.341 17.8331

809.867 17.8305

816.387 17. 8278

822.902 17.8249

829.412 17.8220

335.916 17.8190

842.414 17.8158

848.908 17.8126

855.395 17.8093

861.877 17.8059

868.354 17.8024

874.825 17.7988

881.291 17.7951

887.751 17.7913

394.206 17.7875

900.655 17.7835

907.099 17.7795

913.537 17.7754

919.970 17.7713

926.398 17.7670

932.819 17.7627

939.236 17.7584

945.647 17.7539

952.052 17.7494

958.452 17.7448

964.847 17.7402

971.236 17.7355

977.619 17.7308

983.998 17.7259

990.370 17.7211

996.738 17.7161

1003.100 17.7112

1009.456 17.7061

1015.807 17.7010

02P/0T2

-.00194

-.00207

-.00219

-.00231

-.00243

-.00255

-.00266

-.00277

-.00287

-.00298

-.00308

-.00318

-.00328

-.00337

-.00346

-.00355

-.00364

-.00373

-.00381

-.00389

-.00397

-.00405

-.00412

-.00420

-.00427

-.00434

-.00441

-.00447

-.00454

-.00460

-.00467

-.00473

-.00478

-.00484

-.00490

-.00495

-.00501

-.00506

-.00511

137
Table 26 Continued

THE ISOCHORE AT 16.00 MOL/L

t,k P,BAR OP/DO OP/OT 02P/DT2

113.0 6.718 1167.797 26.5782 -.00169

114.0 33.295 1179.147 26.5763 -.00213

115.0 59.870 1190.478 26.5739 -.00255

116.0 86.443 1201.790 26. 5712 -.00296

117.0 113.012 1213.082 26.5680 -.00336

118.0 139.579 1224.356 26.5645 -.00374

119.0 166.141 1235.610 26.5605 -.00411

120.0 192.700 1246.845 26.5562 -.00447

121.0 219.254 1258.061 26.5516 -.00481

122.0 245.803 1269.258 26.5466 -.00515

123.0 27^2.347 1280.437 26.5413 -.00547

124.0 298.885 1291.597 26.5357 -.00578

125.0 325.418 1302.739 26.5297 -.00608

126.0 351.945 1313.863 26.5235 -.00637

127.0 378.465 1324.968 26.5170 -.00665

128.0 404.978 1336. 055 26.5102 -.00692

129.0 431.485 1347.123 26.5032 -.00718

130.0 457.985 1358.174 26.4959 -.00744

131.0 484.477 1369.207 26.4883 -.00768

132.0 510.961 1380.223 26.4805 -.00792

133.0 537.438 1391.220 26.4725 -.00815

134.0 563.906 1402.201 26.4642 -.00837

135.0 590.366 1413.163 26.4557 -.00858

136.0 616.818 1424.108 '26.4471 -.00879

137.0 643.260 1435.036 26.4382 -.00898

138.0 669.694 1445.947 26.4291 -.00918

139.0 696.118 1456.841 26.4198 -.00936

THE ISOCHORE AT 16.62 MOL/L

T,K P,9AR OP/00 OP/DT 02P/DT2

86.0 18.724 1568.820 35. 3280 -.00211

87.0 54.051 1586.139 35.3254 -.00316

88.0 89.374 1603.409 35.3217 -.00417

89.0 124.694 1620.632 35.3170 -.00513

90.0 160.008 1637.807 35.3114 -.00605

91.0 195.317 1654.936 35.3050 -.00692

92.0 230.618 1672.019 35.2976 -.00776

93.0 265.911 1689.056 35.2894 -.00856

94.0 301.197 1706. 048 35.2805 -.00932

95.0 336.472 1722.995 35.2708 -.01005

96.0 371.738 1739.896 35.2604 -.01075

97.0 406.993 1756.756 35.2493 -.01142

98.0 442.236 1773.572 35.2376 -.01206

99.0 477.468 1790.345 35.2252 -.01267

100.0 512.687 1807.075 35.2123 -.01325

101.0 547.892 1823.763 35.1987 -.01381

102.0 583.084 1840.409 35.1847 -.01434

103.0 618.261 1857.013 35.1701 -.01485

104.0 653.424 1873.577 35.1550 -.01534

105.0 688.571 1390.100 35.1394 -.01580

138
j TABLE 27. Calculated P(p) isotherms

J

i The following pages give P(p) isotherms, as computed by the equation of

i

I state (6). The third column DP/DD is the isotherm slope (3P/8p) in units of

j the bar and mol/L. The last two columns give the isochore slopes and

! curvatures, DP/DT = (3P/3T), D2P/DT2 E (9^P/9t^) in units of the bar and

! kelvins.

i

j

These tables show that 9P/9p is non-negative, and that it increases

j monotonically with density to pressures about twice those used for adjusting

i

; the equation of state.

i

I

I

139
Table 27. Calculated P(p) isotherms

THE ISOTHERM AT 90.00 OEG. K MOL/L PtBAR OP/00 OP/OT 02P/DT2

16.55 49.191 1529.744 34.1370 -.002909

16.60 127.570 1606.099 34.9706 -.005126

16.65 209.871 1686.680 35.8310 -.007470

16.70 296.313 1771.810 36.7195 -.009947

16.75 387.132 1861.846 37.6374 -.012565

16.80 482.587 1957.190 38.5863 -.015332

THE ISOTHERM1 AT 95.00 OEG. K MOL/L PtBAR DP/00 OP/OT 02P/0T2

16.45 66.121 1465.221 32.5406 -.003180

16.50 141.146 1536.356 33.3141 -.005070

16.55 219.821 1611.263 34.1117 -.007068

16.60 302.341 1690.215 34.9344 -.009177

16.65 388.916 1773.512 35.7834 -.011404

16.70 479.770 1861.486 36.6599 -.013754

16.75 575.146 1954.503 37.5651 -.016235

16.80 675.312 2052.976 38.5005 -.018852

THE ISOTHERM1 AT 100.00 DEG. K MOL/L PtBAR OP/00 OP/OT 02P/0T2

16.30 12.966 1341.361 30.3547 -.001823

16.35 81.604 1404.648 31.0539 -.003357

16.40 153.484 1471.107 31.7739 -.004979

16.45 228.769 1540.952 32.5156 -.006691

16.50 307.639 1614.417 33.2799 -.008498

16.55 390.277 1691.756 34.0677 -.010404

16.60 476.884 1773.247 34.8802 -.012414

16.65 567.676 1859.200 35.7183 -.014533

16.70 662.884 1949.954 36.5833 -.016767

THE ISOTHERM AT 110.00 DEG. K MOL/L PtBAR OP/DO OP/OT 02P/0T2

16.10 45 . 464 1238.049 27.7549 -.002380

16.15 103.772 1293.887 28.3664 -.003526

16.20 174.916 1352.336 28.9952 -.004737

16.25 244.052 1413.554 29.6418 -.006015

16.30 316.321 1477.715 30.3069 -.007362

16.35 391.875 1545.006 30.9914 -.008782

16.40 470.877 1615.631 31.6958 -.010277

16.45 553.495 1689.811 32.4211 -.011850

16.50 639.920 1767,796 33.1681 -.013507

16.55 730.344 1849.648 33.9377 -.015249

140
Table 27. Continued

THE ISOTHERM AT 120.00 DEG. K MOL/L P.BAR

15.85 17.094

15.90 73.163

15.95 131.663

16.00 192.700

16.05 256.386

16.10 322.840

16.15 392.186

16.20 464.559

16.25 540.098

16.30 618.953

16.35 701.283

OP/DD DP/OT

1097.746 24.9376

1145,339 25.4630

1195.001 26.0024

1246.845 26.5562

1300.993 27.1251

1357.578 27.7094

1416.741 28.3099

1478.636 28.9269

1543.429 29.5612

1611.301 30.2134

1682.448 30.8841

D2P/0T2

-.001857

-.002680

-.003550

-.004469

-.005439

-.006461

-.007537

-.008670

-.009861

-.011113

-.012429

THE ISOTHERM AT 140.00 DEG. K MOL/L PyBAR OP/00 OP/DT 02P/0T2

15.40 22.555 909.995 20.7852 -.001945

15.45 68.975 947.075 21.1928 -.002406

15.50 117.287 985.602 21.6104 -.002895

15.55 167.561 1025.641 22.0384 -.003414

15.60 219.877 1067.265 22.4770 -.003962

15.65 274.316 1110.552 22.9266 -.004541

15.70 330.961 1155.583 23.3875 -.005152

15.75 389.904 1202.444 23.8600 -.005795

15.80 451.238 1251.230 24.3446 -.006473

15.85 515.061 1302.040 24.8414 -.007185

15.90 581.477 1354.980 25.3511 -.007933

15.95 650.596 1410.165 25.8739 -.008719

16.00 722.533 1467.718 26.4104 -.009543

THE ISOTHERM AT 160.00 OEG. K MOL/L PtBAR OP/OD OP/OT D2P/0T2

14.95 29.625 760.664 17,5147 -.002050

15.00 68.394 790.273 17,8379 -.002312

15.05 108.670 820.940 18.1687 -.002592

15.10 150.506 852.712 18.5072 -.002690

15.15 193.960 885.632 18.8536 -.003208

15.20 239.090 919.751 19.2081 -.003545

15.25 285.955 955.119 19.5709 -.003902

15.30 334.623 991.792 19.9424 -.004260

15,35 385.158 1029.827 20.3226 -.004678

15.40 437.629 1069.283 20.7118 -.005099

15.45 492.110 1110.227 21.1103 -.005541

15.50 548.678 1152.726 21.5184 -.006007

15.55 607.411 1196.853 21.9363 -.006496

15.60 668.392 1242.685 22.3643 -.007009

15.65 731.709 1290.304 22.8027 -.007548

141
Table 27. Continued

THE ISOTHERM AT 180.00 DEG, K MOL/L PfBAR DP/DD DP/DT 02P/0T2

14.45 7.283 615.906 14.6331 -.002013

14.50 38.658 639.202 14.8880 -.002148

14.55 71.216 663.272 15.1486 -.002295

14.60 104.998 688.145 15.4149 -.002454

14.65 140.044 713.850 15.6872 -.002625

14.70 176.398 740.421 15.9655 -.002809

14.75 214.102 767.888 16.2500 -.003007

14.80 253.202 796.289 16.5409 -.003217

14.85 293.747 825.658 16.8383 -.003441

14.90 335.785 856.034 17.1424 -.003679

14.95 379.367 887.458 17.4533 -.003931

15.00 424.548 919.970 17.7713 -.004198

15.05 471.383 953.616 18.0964 -.004479

15.10 519.930 988.442 18.4289 -.004776

15.15 570.243 1024.498 18.7690 -.005089

15.20 622.401 1061.834 19.1168 -.005417

15.25 676.453 1100.505 19.4727 -.005762

15.30 732.475 1140.570 19.8367 -.006125

THE: ISOTHERM AT 200.00 OEG. K MOL/L P.BAR OP/00 DP/OT O2P/0T2

14.00 23.481 519.563 12.5377 -.002145

14.05 49.938 538.797 12. 7462 -.002216

14.10 77.371 558.633 12.9590 -.002295

14.15 105.811 579.092 13.1763 -.002383

14.20 135.291 600.196 13.3983 -.002480

14.25 165.842 621.967 13.6250 -.002585

14.30 197.499 644.430 13.8565 -.002699

14.35 230.297 667.608 14.0930 -. 002822

14.40 264.272 691.528 14. 3345 -.002955

14.45 299.463 716.216 14.5812 -.003097

14.50 335.907 741.701 14.8333 -.003248

14.55 373.646 768.011 15.0907 -.003409

14.60 412. 722 795.177 15.3538 -.003581

14.65 453.179 823.231 15.6225 -.003762

14.70 495.061 852.206 15.8970 -.003954

14.75 538.415 882.137 16.1775 -.004157

14.80 583.291 913.062 16.4641 -.004371

14.85 629.739 945.017 16.7570 -.004597

14. 90 677.811 978.044 17.0564 -.004834

14.95 727.562 1012.184 17. 3623 -. 005083

14 2
Table 27. Continued

THE ISOTHERM AT 220.00 OEG. K MOL/L P»BAR DP/OD DP/DT 02P/DT2

13.50 19.712 423.236 10.6356 -.002172

13.55 41.261 438.818 10.8046 -.002201

13.60 63.601 454.860 10.9770 -.002236

13.65 86.755 471.380 11.1529 -.002277

13.70 110.748 488.392 11. 3324 -.002324

13. 75 135.603 505.912 11.5155 -.002377

13.80 161.348 523.958 11.7023 -.002435

13.85 188.008 542.547 11.8930 -.002500

13.90 215.612 561.697 12.0875 -.002571

13.95 244.187 581.427 12.2860 -.002649

14.00 273.764 601.757 12.4866 -.002733

14.05 304.373 622.707 12.6954 -.002823

14.10 336.046 644.299 12.9064 -.002920

14.15 368.^4 666.553 13.1218 -.003025

14.20 402.712 689.494 13.3417 -.003136

14.25 437.775 713.145 13.5661 -.003254

14.30 474.039 737.531 13.7952 -.003380

14.35 511. 541 762.677 14.0291 -.003513

14.40 550.320 788.611 14.2679 -.003654

14.45 590.416 815.361 14.5117 -.003803

14.50 631.870 842.955 14.7607 -.003961

14.55 674.726 871.425 15.0148 -.004126

14.60 719.028 900.803 15.2744 -.004300

THE ISOTHERM AT 240.00 OEG, K MOL/L P.BAR OP/DD DP/DT D2P/DT2

.05 .965 18.692 . 0043 -.000002

12.95 8.010 332.484 8.9372 -.002149

13. 00 24.943 344.886 9.0736 -.002154

13.05 42.505 357.638 9.2126 -.002163

13.10 60.713 370.749 9.3543 -.002176

13.15 79.586 384.232 9.4986 -.002193

13.20 99.142 398.097 9.6456 -.002214

13.25 119.402 412.357 9.7955 -.002238

13.30 140.385 427.025 9. 9483 -.002267

13.35 162.111 442.113 10.1040 -.002300

13.40 164.603 457.634 10.2627 -.002337

13.45 207.882 473.603 10.4246 -.002379

13.50 231.971 490.033 10.5895 -.002424

13.55 256.894 506.940 10.7577 -.002474

13.60 282.674 524.339 10.9292 -.002529

13.65 309.336 542.245 11.1041 -.002588

13. 70 336.907 560.675 11.2825 -.002651

13.75 365.413 579.647 11.4643 -.002720

13.80 394.881 599.177 11.6498 -.002793

13. 85 425.340 619.284 11.8390 -.002872

13.90 456.819 639.937 12.0320 -.002955

13.95 489.349 661.306 12.2288 -.003044

14.00 522.960 683.260 12.4296 -.003138

14.05 557.686 7 05.873 12.6345 -.003238

14.10 593.559 729.165 12.8435 -. 003344

14.15 630.614 753.159 13.0567 -.003455

14.20 668.887 777.879 13.2743 -.003573

14.25 708.415 803.351 13.4963 -.003697

14.30 749.235 829.600 13.7229 -.003827

143
Table 27. Continued

THE ISOTHERM AT 260.00 OEG. K MOL/L PtBAR DP/OD OP/OT

.05 1.051 20.458 . 0043

.10 2.046 19.363 .0088

.15 2.986 18.239 .0136

12.40 10.046 260.716 7.5468

12.45 23.330 270.680 7.6589

12.50 37.118 280.912 7.7729

12.55 51.425 291.421 7.8889

12.60 66.265 302.214 8.0070

12.65 81.652 313.302 8.1271

12.70 97.600 324.691 8.2493

12.75 114.126 336.392 8.3737

12.80 131.245 348.414 8.5003

12.85 148.973 360.766 8.6293

12.90 167.327 373.459 8.7605

12.95 186.325 386.502 8.8942

13.00 205.983 399.907 9.0302

13.05 226.322 413.684 9.1688

13.10 247.358 427.845 9.3100

13.15 269.113 442.402 9.4538

13.20 291.605 457.367 9.6002

13.25 314.856 472.752 9.7495

13.30 338.887 488.570 9.9015

13.35 363.721 504.836 10.0564

13.40 389.379 521.562 10.2142

13.45 415.885 538.763 10.3751

13.50 443.263 556.455 10.5390

13.55 471. 539 574.651 10.7061

13.60 500.737 593.369 10.8764

13.65 530.885 612.625 11.0500

13.70 562.009 632.436 11.2270

13.75 594.138 652.819 11.4074

13.80 627.301 673.793 11.5913

13.85 661.527 695.377 11.7789

13.90 696.849 717.591 11.9701

13.95 733.297 740.455 12.1651

02P/DT2

-.000001

-.000005

-.000015

-.002047

-.002046

-.002047

-.002050

-.002056

-.002064

-.002075

-.002088

-.002104

-.002122

-.002143

-.002167

-.002193

-.002222

-.002253

-.002288

-.002325

-.002366

-.002410

-.002457

-.002507

-.002561

-.002618

-.002679

-.002743

-.002812

-.002884

-.002961

-.003042

-.003127

-.003217

-.003311

144
Table 27. Continued

THE ISOTHERM AT 280,00 OEG. K MOL/L P.BAR OP/DD OP/DT D2P/DT2

. 05 1.136 22.206 .0043 -.000001

.10 2.221 21.208 . 0067 -.000003

.15 3.256 20.194 .0134 -.000008

.20 4.240 19.170 .0183 -.000017

.25 5.173 18.141 .0235 -.000032

11.60 11.882 196.185 6.2970 -.001811

11.85 21.887 204.027 6.3894 -.001814

11.90 32.288 212.072 6.4632 -.001818

11.95 43.097 220.329 6.5785 -.001823

12.00 54.325 228.802 6.6752 -.001630

12.05 65.981 237.497 6,7735 -.001837

12.10 78.078 246.421 6.8733 -.001846

12.15 90.627 255.581 6.9747 -.001856

12.20 103.640 264.982 7.0778 -.001868

12.25 117.130 274.632 7.1825 -.001860

12.30 131.108 284.538 7.2890 -.001894

12.35 145,588 294.708 7.3973 -.001909

12.40 160.583 305.149 7.5073 -.001925

12.45 176.108 315.869 7.6192 -.001943

12.50 192.175 326.676 7.7330 -.001962

12.55 208.800 338.178 7.8487 -.001983

12.60 225.998 349.784 7.9665 -.002005

12.65 243.784 361.703 8.0862 -.002029

12.70 262.173 373.945 6.2081 -.002054

12.75 261.184 386.518 6.3321 -.002082

12.80 300.831 399.432 8.4582 -.002111

12.85 321.133 412.699 8.5866 -.002142

12.90 342.107 426.327 8.7174 -.002174

12.95 363.772 440.328 8.6504 -.002209

13.00 386.146 454.713 8.9858 -.002247

13.05 409.250 469.494 9.1237 -.002286

13.10 433. 102 484.682 9.2642 -.002328

13.15 457.725 500.290 9.4071 -.002372

13.20 483.136 516.329 9.5528 -.002418

13.25 509.365 532.814 9.7011 -.002467

13.30 536.427 549.758 9.8521 -.002519

13.35 564.349 567.174 10.0060 -.002574

13.40 593. 153 585.078 10.1626 -.002631

13.45 622.865 603.464 10. 3225 -.002692

13.50 653.510 622.407 10.4852 -.002755

13.55 685.114 641.864 10.6510 -.002822

13.60 717.705 661.870 10.8199 -.002692

14 5
Table 27. Continued

THE ISOTHERM AT 300.00 DEG. K

MOL/L P.BAR OP/OD OP/OT D2P/0T2

.10 2.395 23.021 . 0007 -.000002

.20 4.604 21.160 .0100 -.000011

.30 6.627 19.303 .0203 -.000030

.40 8.465 17.468 .0394 -.000064

11.10 10.660 135.257 5.1031 -.001357

11.20 24.796 147.152 5.2555 -.001394

11.30 40.131 159.671 5.4119 -.001431

11.40 56.752 172.846 5.5727 -.001467

11.50 74.724 186.711 5.7379 -.001503

11.60 94.118 201.302 5.9079 -.001539

11.70 115.010 216.658 6.0029 -.001576

11.80 137.477 232.822 6.2631 -.001614

11.90 161.602 249.836 6.4407 -.001652

12.00 187.474 267.750 6.6402 -.001692

12.10 215.184 286.612 6.8376 -.001735

12.20 244.630 306.478 7.0414 -.001779

12.30 276.515 327.405 7. 2519 -.001827

12.40 310.343 349.452 7.4693 -.001878

12.50 346.445 372.686 7.6941 -.001934

12.60 384.927 397.174 7.9265 -.001993

12.70 425.924 422.992 0.1670 -.002059

12.60 469.572 450.215 8.4158 -.002130

12.90 516.017 478.928 8.6735 -.002207

13.00 565.410 509.218 8.9404 -.002292

13.10 617.916 541.179 9.2170 -.002384

13.20 673.705 574.911 9.5037 -.002485

13.30 732.960 610.522 9. 8009 -.002595

THE ISOTHERM AT 320.00 DEG. K MOL/L P.BAR OP/00 DP/OT 02P/DT2

.10 2.567 24.814 .0086 -.000002

.20 4.963 23.095 .0179 -.000008

.30 7.187 21.393 .0278 -.000020

.40 9.243 19.727 .0304 -.000040

.50 11.134 18.097 .0498 -.000069

.60 12.863 16.500 .0620 -.000113

.70 14.434 14.930 .0751 -.000180

.80 15. 850 13.376 . 0892 -.000290

10.40 23.619 92.486 4.1199 -.000632

10.50 33.506 101.329 4.2471 -.000726

10.60 44.101 110.650 4.3773 -.000811

10.70 55.653 120.471 4.5106 -.000889

10.80 63.213 130.815 4.6472 -.000962

10.90 81.834 141.706 4.7873 -.001029

11.00 96.573 153.171 4.9309 -. 001093

11.10 112.483 165.237 5.0783 -.001153

11.20 129.641 177.935 5.2297 -.001210

11. 30 148.097 191.295 5.3852 -.001265

11.40 167.924 205.352 5.5450 -.001319

11.50 189.192 220.143 5.7094 -.001371

11.60 211. 978 235.705 5.8784 -.001422

11.70 236.360 252.080 6.0525 -.001473

11. 80 262.422 269.312 6.2318 -.001524

11.90 290.253 287.448 6.4166 -.001575

12.00 319.944 306.538 6.6070 -.001628

12. 10 351.594 326.634 6. 8035 -.001682

12.20 365.306 347.794 7.0063 -.001738

12.30 421.190 370.076 7.2157 -.001796

12.40 459.361 393.545 7.4320 -.001858

12.50 499.941 418.268 7.6555 -.001923

12.60 543.059 444.317 7.8867 -.001993

12.70 588.851 471.769 8.1257 -.002067

12. 80 637.462 500.703 8. 3731 -.002146

12.90 689.044 531.206 8.6291 -.002231

13.00 743.759 563.370 8.8943 -.002323

146
Table 27. Continued

THE ISOTHERM AT 340.00 DEG. K MOL/L PtBAR OP/00 OP/OT D2P/OT2

.10 2.739 26.590 . 0086 -.000001

.20 5.318 24.993 .0177 -.000006

.30 7.739 23.419 .0274 -.000015

.40 10.004 21.885 .0377 -.000029

.50 12.117 20.394 .0467 -.000047

.60 14.084 18.942 . 0602 -.000072

.70 15.907 17.526 .0724 -.000105

.80 17.590 16.142 .0852 -.000147

.90 19.136 14.790 .0988 -.000201

1. 00 20.549 13.467 .1130 -.000271

1.10 21.^31 12.172 .1280 -.000367

1.20 22.984 10.905 .1439 -.000503

1.30 24.013 9.663 .1607 -.000711

9.40 27.376 46.571 3.0032 .000839

9.50 32.300 51.977 3.1029 .000608

9.60 37.782 57.716 3.2048 . 000413

9.70 43.855 63.804 3.3089 .000243

9.80 50.555 70.254 3.4153 .030093

9.90 57.918 77.082 3.5242 -.000041

10.00 65.984 84.302 3.6356 -.000163

10.10 74.793 91.931 3.7495 -.000276

10.20 84.385 99.986 3.8662 -.000379

10.30 94.805 108.484 3.9857 -.000475

10.40 106.097 117.445 4.1081 -.000565

10.50 118.310 126.888 4.2335 -.000649

10.60 131.492 136.836 4.3621 -.000729

10.70 145.694 147.310 4.4938 -.000804

10.80 160.972 158.335 4.6290 -.000876

10.90 177.381 169.938 4.7677 -.000944

11.00 194.980 182.146 4.9100 -.001010

11.10 213.831 194.988 5. 0562 -.001072

11.20 234.000 208.497 5.2064 -.001133

11. 30 255.554 222.706 5.3607 -.001193

11.40 278.565 237.652 5.5194 -.001251

11.50 303.110 253.371 5.6826 -.001303

11.60 329.267 269.907 5.8506 -.001364

11.70 357.120 287.301 6.0236 -.001421

11.80 386.757 305.601 6.2018 -.001477

11.90 418.272 324.855 6.3855 -.001534

12.00 451.762 345.115 6.5749 -.001593

12.10 487.330 366.438 6.7702 -.001653

12.20 525.087 388.882 6.9718 -.001715

12.30 565.146 412.509 7.1800 -.001779

12.40 607.630 437.387 7.3950 -.001346

12.50 652.667 463.584 7.6171 -.001917

12.60 700.393 491.175 7.8468 -.001992

14 7
Table 27. Continued.

THE ISOTHERM AT 360.00 DEG. K

MOL/L PtBAR OP/ DO OP/OT 02P/DT2

.20 5.671 26.865 .0176 -.000005

.40 10.753 23.979 .0372 -.000022

.60 15.275 21.266 .0590 -.000053

.80 19.269 18.701 .0828 -.000100

1.00 22.764 16.266 .1088 -.000166

1.20 25.784 13.959 .1369 -.000257

1.40 28.357 11.790 .1670 -.000380

1.60 30.510 9.771 .1991 -.000550

1.80 32.276 7.916 .2333 -.000795

2.00 33.688 6.233 .2695 -.001179

2.20 34.780 4.719 . 3082 -.001874

8.00 37.592 13.798 1.8925 .004130

8.20 40.799 18.395 2.0293 .002964

8.40 45.004 23.802 2.1730 .002221

8.60 50.379 30.104 2.3243 .001686

8.80 57.111 37.381 2.4838 .001270

9. 00 65.402 45.720 2.6518 .000928

9.20 75.475 55.208 2.8286 .000637

9.40 87.569 65.939 3.0146 .000382

9.60 101.940 78.011 3.2102 .000155

9.30 113.870 91.533 3.4157 -.000050

10.00 138.653 106.623 3.6315 -.000237

10.20 161.632 123.415 3.8584 -.000408

10.40 188.147 142.055 4.0969 -.000565

10.60 218.589 162.713 4.3477 -.000711

10.80 253.379 185.578 4.6118 -.000847

11.00 292.981 210.865 4.8902 -.000975

11.20 337.903 238.821 5.1841 -.001097

11.40 388.706 269.722 5.4948 -.001215

11.60 446.009 303.884 5.8237 -.001332

11.80 510.500 341.663 6.1726 -.001449

12.00 582.942 383.457 6.5432 -.001570

12.20 664.181 429.719 6.9377 -.001698

THE ISOTHERM AT 369.80 OEG. K MOL/L P,BAR OP/DO OP/DT 02P/DT2

.40 11.117 24.987 . 0370 -.000020

.80 20.076 19.909 .0819 -.000086

1.20 27.114 15.362 .1346 -.000209

1.60 32.438 11.355 .1945 -.000405

2.00 36.283 7.983 .2608 -.000702

2.40 38.916 5.295 . 3322 -.001156

2.80 40.607 3.265 .40 75 -.001882

3.20 41.605 1.818 .4853 -.003153

3.60 42.126 .862 .5642 -.005708

4.00 42.343 .306 .6427 -.012157

4.40 42.413 .058 .7188 -.037355

4.80 42.420 .001 .7873 -.451909

5.20 42.421 .006 .8379 .239433

5.60 42.439 .121 .9193 . 039082

6.00 42.560 .561 1.0229 .016198

6^ no 42.969 1.612 1.1489 .009040

6.80 43.979 3.634 1.2994 . 005818

7.20 46. 063 7.059 1.4768 .004035

7.60 49.879 12.379 1.6832 .002895

8.00 56.291 20.136 1.9205 .002078

8.40 66.390 30.913 2.1903 .001442

8.80 81.506 45.325 2.4943 .000916

9.20 103.223 64.036 2.8340 . 000466

9.60 133.406 87.784 3.2113 .000074

10.00 174.235 117.424 3.6291 -.000270

10.40 228.269 154.001 4. 0913 -.000572

10.80 298.535 198.829 4.6036 -.000841

11.20 388.655 253.592 5.1734 -.001086

11.60 503.018 320.449 5.8107 -.001320

12.00 646.990 402.155 6.5279 -.001562

148
Table 27. Continued

THE ISOTHERH AT 380.00 DEG. K MOL/L PtBAR DP/00 OP/OT 02P/DT2

.40 11.493 26.026 .0368 -.000018

.30 20.908 21.144 .0811 -.000075

1.20 28.477 16.783 .1327 -.000175

1.60 34.403 12.940 .1909 -.000321

2.00 38.910 9.704 .2547 -.000509

2.40 42.253 7.119 .3230 -.000729

2.80 44.688 5.153 .3942 -.000953

3.20 46.443 3.732 .4673 -.001131

3.60 47.735 2.771 .5412 -.001187

4.00 48.717 2.200 .6159 -.001056

4.40 49.539 1.960 .6923 -.000722

4.80 50.320 1.980 .7723 -.000232

5.20 51.143 2.157 .8584 .000350

5.60 52.076 2.565 .9533 .000964

6.00 53.256 3.436 1.0603 .001510

6.40 54.922 5.039 1.1856 .001880

6.80 57.429 7.708 1.3322 .002017

7.20 61.285 11.853 1.5044 .001940

7.60 67.171 17.948 1.7055 . 001714

8.00 75.974 26.526 1.9378 .001401

8.40 88.799 38.160 2.2029 .001050

8.80 106.991 53.467 2.5024 . 000690

9.20 132.152 73.117 2.8380 .000339

9.60 166.164 97.862 3. 2117 .000006

10.00 211.237 128.584 3.6261 -.000301

10.40 269.970 166.362 4.0854 -.000582

10.80 345.447 212.557 4.5950 -.000838

11.20 441.367 268.905 5.1624 -.001078

11.60 562.219 337.629 5.7973 -.001311

12.00 713.494 421.552 6.5120 -.001553

THE ISOTHERM AT 400.00 DEG. K MOL/L P,BAR OP/DD P/DT D2P/DT2

.40 12.227 28.035 . 0365 -.000014

.30 22.516 23.503 .0798 -.000059

1.20 31.098 19.479 • 1296 -.000132

1.60 38.163 15.930 .1855 -.000228

2.00 43.916 12.936 .2465 -.000336

2.40 43.591 10.535 .3118 -. 000441

2.30 52.421 3.702 . 3804 -.000523

3.20 55.621 7.379 .4518 -.000562

3.60 58.384 6.509 .5257 -.000541

4.00 60.884 6.058 .6026 -.000455

4.40 63.233 6.003 .6834 -.000307

4.80 65.733 6.301 .7694 -.000108

5.20 63.353 6.864 .8624 .000124

5.60 71.274 7.802 .9648 .000374

6.00 74.685 9.384 1.0794 .000615

6.40 73.906 11.902 1.2096 . 000817

6.80 84.376 15.688 1.3592 .000951

7.20 91.677 21.130 1.5318 . 000999

7.60 101.560 28.674 1.7309 .000956

8.00 114.963 33.318 1.9593 . 000833

8.40 133.035 52.117 2.2194 .000646

8.80 157.157 69.176 2.5132 .000417

9. 20 188.967 90.674 2.8429 .000164

9.60 230. 391 117.388 3.2107 -.000096

10.00 283.696 150.248 3.6196 -.000354

10.40 351.561 190.400 4.0736 -.000601

10.80 437. 179 239.289 4.5782 -.000837

11.20 544.400 298.756 5.1410 -.001066

11.60 677.904 371.139 5.7713 -.001294

149
Table 27. Continued

THE ISOTHERM AT 420.00 DEG. K

MOL/L P.BAR OP/00 OP/DT 02P/DT2

.40 12.954 30.015 .0363 -.000012

.80 24.101 25.811 .0787 -.000048

1.20 33.666 22.089 .1273 -.000104

1.60 41.831 18.813 .1815 -.000175

2.00 48.786 16.054 .2407 -.000250

2.40 54.748 13.848 .3043 -.000318

2.80 59.936 12.181 .3717 -.000367

3.20 64.559 11.009 .4426 -.000385

3.60 68.805 10.298 .5169 -.000366

4.00 72.857 10.039 .5952 -.000307

4.40 76. 897 10.233 .6783 -.000211

4.80 81.101 10.355 .7675 -.000085

5. 20 85.627 11.832 .8642 . 000063

5.60 90.633 13.305 .9705 .000222

6.00 96.377 15.571 1.0890 . 000377

6.40 103.237 18.941 1.2225 .000511

6.30 111.722 23.756 1.3743 .000606

7.20 122.485 30.401 1.5479 .000649

7.60 136.343 39.304 1.7464 .000631

8.00 154.293 50.944 1.9729 .000552

8.40 177. 534 65.856 2.2299 .000421

8.30 207.493 84.637 2.5198 .000247

9.20 245.850 107.969 2.8450 .000045

9.60 294.581 136.653 3.2080 -.000172

10.00 356. 014 171.659 3.6121 -.000396

10.40 432.911 214.196 4. 0614 -.000619

10.80 528.577 265.790 4.5615 -.000838

11.20 647.007 328.380 5.1197 -.001056

THE ISOTHERM AT 450.00 DEG. K MOL/L P.BAR OP/OD OP/DT D2P/DT2

.40 14. 037 32.941 .0359 -.000009

.80 26.442 29.181 .0775 -.000036

1.20 37.442 25.885 .1246 -.000078

1.60 47.205 23.002 .1770 -.000127

2.00 55.908 20.596 .2344 -.000178

2.40 63.751 13.708 .2964 -.000222

2.80 70.943 17.334 . 3626 -.000252

3.20 77.684 16.452 .4331 -.000262

3.60 84.169 16.053 .5079 -.000249

4.00 90.593 16.153 .5876 -.000212

4.40 97.162 16.782 .6730 -.000153

4. 80 IOh. 089 17.938 .7651 -.000074

5.20 111.574 19.567 .8654 .000017

5.60 119.830 21.850 .9754 .000116

6.00 129.186 25.119 1.0975 .000212

6.40 140.102 29.711 1.2342 .000295

6. 80 153.179 35.986 1.3883 .000355

7.20 169.166 44.329 1.5629 .000381

7.60 188.973 55.158 1.7610 .000367

8. 00 213.686 68.936 1.9855 . 000311

8.40 244.584 86.180 2.2391 .000214

8. 80 283.170 107.479 2.5245 .000082

9.20 331. 199 133.521 2.8444 -.000077

9.60 390.730 165.140 3. 2015 -.000255

10.00 464. 190 203.361 3.5994 -.000445

10.40 554. 470 249.481 4.0425 -.000640

10.80 665 . 044 305.137 4.5363 -.000839

150
Table 27. Continued

THE ISOTHERM AT 500.00 OEG. K MOL/L P .BAR DP/DO DP/OT 02P/DT2

.40 15. 624 37.727 . 0355 -.000006

.80 30.276 34.629 .0760 -.000025

1.20 43.587 31.989 .1214 -.000052

1.60 55.919 29.739 .1719 -.000083

2.00 67.437 27.934 .2273 -.000115

2.40 78.332 26.625 .2875 -.000142

2.80 68.805 25.822 .3526 -.000161

3.20 99.058 25.527 .4226 -.000168

3.60 109.297 25.761 .4979 -.000162

4.00 119.744 26.574 .5790 -.000143

4.40 130.642 28.027 .6665 -.000112

4.80 142.255 30.149 .7615 -.000070

5.20 154.845 32.914 .8652 -.000021

5.60 168.704 36.559 .9788 .000031

6.00 184.260 41.463 1.1044 .000082

6.40 202.093 48.006 1.2441 . 000124

6.80 222.935 56.574 1.4003 .000152

7.20 247.676 67.568 1.5757 . 000159

7.60 277.369 81.408 1.7730 .000141

8.00 313.242 98.548 1.9950 . 000096

6.40 356.714 119.494 2.2445 .000022

8.80 409.423 144.835 2.5243 -.000077

9.20 473.263 175.232 2.8372 -.000200

9.60 550.446 211.716 3.1864 -.000340

10.00 643.581 255.253 3.5758 -.000495

THE ISOTHERM AT 550.00 OEG. K MOL/L P.BAR OP/DD OP/DT 02P/OT2

.40 17.594 42.432 . 0353 -.000005

.80 34.046 39.930 . 0749 -.000018

1.20 49.600 37.903 .1192 -.000037

1.60 64.420 36.269 .1684 -.000059

2.00 78.674 35.081 .2225 -.000081

2.40 92.552 34.391 .2816 -.000100

2.80 106.257 34.223 . 3459 -.000114

3.20 120.002 34.596 .4155 -.000121

3.60 134.011 35.550 .4910 -.000120

4.00 143.529 37.160 .5727 -.000110

4.40 163.838 39.512 .6615 -.000093

4.80 180.245 42.657 .7581 -.000069

5.20 198.067 46.593 . 8636 -.000041

5.60 217.663 51.606 .9792 -.000012

6.00 239.551 58.114 1.1067 .000015

6.40 264.410 66.535 1.2479 . 000037

6.80 293.089 77.284 1.4050 . 000047

7.20 326.604 90.782 1.5805 .000044

7.60 366.139 107.462 1.7768 .000022

8.00 413.058 127.782 1.9967 -.000020

8.40 468.918 152.256 2.2428 -.000083

8. 80 535.497 181.485 2.5180 -.000166

9.20 614.838 216.208 2.8253 -.000268

9.60 709.319 257.359 3.1681 -.000387

151
Table 27. Continued

THE ISOTHERM AT 600.00 OEG. K MOL/L P.BAR P/00 P/OT 02P/0T2

.40 19.352 47.079 .0351 -.000004

.80 37. 771 45.125 .0741 -.000013

1.20 55.519 43.683 .1176 -.000028

1.60 72.772 42.656 .1658 -.000044

2.00 89.706 42.093 .2190 -.000061

2.40 106.516 42.051 .2772 -.000076

2. 80 123.419 42.558 .3409 -.000087

3.20 140.640 43.647 .4102 -.000093

3.60 158.422 45.375 .4857 -.000095

4.00 177.038 47.834 .5678 -.000090

4.40 196.801 51.130 .6571 -.000081

4.80 213.063 55.332 .7546 -.000068

5.20 241.187 60.459 .8612 -.000053

5.60 266.597 66.838 .9779 -.000037

6.00 294.886 74.926 1.1064 -.000023

6.40 326.826 85.172 1.2433 -.000014

6.80 363.371 98.023 1.4057 -.000013

7.20 405.650 113.921 1.5808 -.000024

7.60 454.974 133.318 1.7760 -.000048

8.00 512.834 156.688 1.9938 -.000088

8.40 580.924 184.557 2.2370 -.000145

8.80 661.163 217.549 2.5082 -.000218

152
Table 28. The Joule-Thomson inversion locus.

THE JOULE-THOMSON INVERSION LOCUS FOR PROPANE

T.K P,8AR MOL/L T.K P.BAR MOL/L

300 14.8 11.13 560 456.7 8.17

310 43.3 11.01 570 464.0 6.08

320 79.9 10.89 580 471.0 7.99

330 109.5 10.76 590 477.6 7.90

340 137.2 10.64 600 463.9 7.81

350 163.3 10.52 610 489.9 7.72

360 187.7 10.40 620 495.6 7.64

370 210.5 10.27 630 500.9 7.55

360 231.8 10.15 640 506.0 7.47

390 251.8 10.03 650 510.7 7.38

400 270.5 9.91 660 515.1 7.30

410 237.9 9.79 670 519.2 7.22

420 304.3 9,67 680 523.0 7.14

430 319.6 9,55 690 526.4 7.06

440 334.0 9.43 700 529.5 6.98

450 347.6 9.32 710 532,3 6.90

460 360.3 9.20 720 534.7 6.82

470 372.3 9.09 730 536.7 6.74

480 383.7 8.98 740 538.5 6.66

490 394,5 8.87 750 539.8 6.58

500 404.7 8.77 760 540.8 6.50

510 414.5 8.66 770 541.4 6.42

520 423.7 6.56 780 541.6 6.34

530 432.6 8.46 790 541.4 6.26

540 441.0 8.36 800 540.8 6.18

550 449.0 8.27 610 539.8 6.09

153
TABLE 29. Thermophysical properties of the saturated liquid

This table was computed along paths described in section 3.0.

headings have the following interpretations

Column!

DPS/DT

DDL/DT

DP/DT

DP/DD

Q,VAP

CV

CS

CP

W

dP^/dT, vapor pressure,

dp^/dT, saturated liquid,

(9P/9T), single phase,

(9P/9p), single phase,

AH , heat of vaporization,

vap

C^(P,T),

C (T), aCp(P,T),

speed of sound
Table 29. Thermophysical properties of the saturated liquid

PROPERTIES OF SATURATED LIQUID PROPANE

T P DEN V.LIQ V.GAS

DEG K BAR MOL/L L/HOL L/MOL

85. 4/D .3000E-08 16.620 .06017 .23692+10

90.000 .1512E-07 16.517 .06054 .49302+09

95.000 .7536E-07 16.404 .06096 .10422+09

100.000 .3199E-06 16.290 .06139 .25822+08

105.000 .1182E-05 16.177 .06182 .73392+07

110.000 .3873E-05 16.063 .06226 .23492+07

115.000 .ll^*2E-04 15.949 .06270 .83402+06

120.000 .3071E-04 15.834 .06315 .32422+06

125.000 .7606E-04 15.720 .06361 .13652+06

130.000 .1752E-03 15.605 .06408 .61722+05

135.000 •3780E-03 15.490 .06456 .29732+05

140.000 .7697E-03 15.375 .06504 .15152+05

145.000 .1A87E-02 15.259 .06553 .81232+04

150.000 .2741E-02 15.144 .06603 .45602+04

155.000 .4840E-02 15.027 .06655 .26682+04

160.000 .8220E-02 14.910 .06707 .16212+04

165.000 .1347E-01 14.793 .06760 .10192+04

170.000 .2139E-01 14.676 .06814 .66062+03

175.000 .3297E-01 14.557 .06869 .44062+03

180.000 .4945E-01 14.438 .06926 . 30162+03

185.000 .7238E-01 14.319 .06984 .21142+03

190.000 .1035E^00 14.198 .07043 .15152+03

195.000 .1451E^00 14.077 .07104 .11072+03

200.000 .1993E«00 13.954 .07166 .82382+02

205.000 .2691E4^00 13.831 .07230 .62352+02

210.000 .3574E>00 13.707 .07296 .47922+02

215.000 .4675E+00 13.581 .07363 .37362+02

220.000 .6031E+00 13.454 .07433 .29502+02

225.000 .7679E>00 13.326 .07504 .23582+02

231.071 .101324^01 13.168 .07594 .18232+02

235.000 .1202E>01 13.064 ,07655 .15552+02

240.000 .1480E+01 12.930 .07734 .12812+02

245.000 .1805E«^01 12.795 .07816 ,10642+02

250.000 .218224-01 12.657 .07901 .89092+01

255.000 .26162^01 12.^!^16 .07990 .75112+01

260.000 .31122^01 12.373 .08082 .63732+01

265.000 .367524-01 12.227 .08179 .54402+01

270.000 .4312E4-01 12. 078 .08280 .46682+01

275.000 .502624-01 11.925 .08386 .40252+01

280.000 .562824-01 11.769 .08497 .34862+01

285.000 .6719E+01 11.606 .08615 .30312+01

290.000 .77062+01 11.442 .08739 .26452+01

295.000 .87972+01 11.272 .08872 .23152+01

300.000 .9997E+01 11.095 .09013 .20322+01

305.000 .11312+02 10.912 .09165 .17882+01

310.000 .1275E+02 10. 721 .09328 .15762 + 01

315.000 .14322+02 10.521 .09504 .13912+01

320.000 .1603E+02 10.312 .09697 .12292+01

325.000 .17882+02 10.091 .09910 .10872+01

330.000 .19882+02 9.85 7 .10145 .96112+00

335.000 .22042+02 9.605 .10411 .84872+00

340.000 .24362+02 9.333 .10715 ,74792+00

345.000 .26872+02 9.033 .11070 .65652+00

350.000 .29562+02 8.697 .11498 .57262+00

355.000 .32442+02 8.308 .12036 .49422+00

360.000 .35552+02 7. 831 .12769 .41852+00

365.000 .38902+02 7.171 .13945 .34022+00

369.800 .42422+02 4.960 .20161 .20162+00

DPS/DT ODL/DT DP/OT DP/DO Q. VAP BAR/K M0L7L/K BAR/K BAR-L/MOL J/MOL .11272-08 -.02265 35.329 .15602+04 24919 .51262-08 -.02268 33.606 .14822+04 24694

.22942-07 -.02270 31.846 .14032+04 24458

.87862-07 -.02273 30.221 .13292+04 24231

.29422-06 -.02276 26.713 .12612+04 24011

.87682-06 -.02280 27.309 .11982+04 23798

.23612-05 -.02283 26.000 .11392+04 23590

.58122-05 -.02287 24.776 .10832+04 23385

.13222-04 -.02292 23.629 .10312+04 23164

.28052-04 -.02296 22.552 .98202+03 22985

.55882-04 -.02302 21.539 .93572+03 22787

.10532-03 -.02306 20.585 .89202+03 22591

.18862-03 -.02315 19.684 .85052+03 22395

.32302-03 -.02322 16.833 .81112+03 22200

.53092-03 -.02330 16.028 .77362+03 22005

.84082-03 -.02339 17.264 .73802+03 21809

.12872-02 -.02349 16.540 .70402+03 21614

.19122-02 -.02361 15.852 .67142+03 21418

.27602-02 -.02373 15.197 .64032+03 21221

.38662-02 -.02386 14.574 .61052+03 21023

.53432-02 -.02401 13.979 .58192+03 20823

.71932-02 -.02418 13.412 . 55442 + 03 20622

.94942-02 -.02436 12.870 .52802+03 20420

.12312-01 -.02455 12.352 .50252+03 20215

.15702-01 -.02477 11.855 .47802+03 20007

.19732-01 -.02500 11.379 . 45432+0 3 19796

.24442-01 -.02526 10.922 .43142+03 19582

.29902-01 -.02554 10.483 .40932+03 19364

.36162-01 -.02584 10.061 .38792+03 19141

.44892-01 -.02625 9.569 .36292+03 16864

.51242-01 -.02654 9.262 .34712+03 18677

.60152-01 -.02693 8.864 .32772+03 18432

.70032-01 -.02736 8.518 .30882+03 18180

.80902-01 -.02763 8.164 .29052+03 17919

.92802-01 -.02834 7. 821 .27272+03 17649

.10582+00 -.02889 7.487 .25552+03 17370

.11982+00 -.02950 7.163 .23672+03 17081

.13502+00 -.03017 6.848 .22252+03 16781

.15142+00 -.03091 6.540 .20672+03 16470

.16892+00 -.03172 6.240 .19142+03 16146

.18762+00 -.03262 5. 946 .17652+03 15808

.20762+00 -. 03361 5.658 .16212+03 15455

.22892+00 -. 03472 5.374 .14622+03 15085

.25142+00 -.03597 5.096 .13472+03 14697

.27532+00 -.03736 4.820 .12162+03 14289

.30052+00 -.03698 4.548 .10902+03 13858

.32722+00 -.04062 4.279 .96812+02 13401

.35522+00 -.04295 4.011 .85102+02 12915

.38472+00 -.04547 3.743 .73862+02 12396

.41572+00 -.04850 3.476 .63102+02 11836

.44832+00 -.05222 3.208 .52842+02 11229

.48272+00 -.05693 2.937 .43122+02 10 563

.51892+00 -.06313 2.663 .33962+02 9822

.55752+00 -.07178 2.382 .25422+02 8983

.59892+00 -.08497 2.091 .17562+02 8001

.64452+00 -.10841 1.781 .10492+02 6793

.69782+00 -.16715 1.432 .43942+01 5124

n .80592+00 0.00000 .806 0 . u

155
Table 29. Continued.

PROPERTIES OF SATURATED LIQUID PROPANE

T P E H S CV CS CP W DEG K BAR J/HOL J/NOL J/HOL/K J/HOL/K J/NDL/K J/MOL/K H/SEC

85.470 .3000E-08 5508.6 5508.6 82.628 59.28 84.04 84.04 2239

90.000 .1512E-07 5889.8 5889.8 86.973 59.13 84.27 84.27 2188

95.000 .7536E-07 6311.8 6311.8 91.536 59.01 84.53 84.53 2134

100.000 .3199E-06 6735.2 6735.2 95.878 58.92 84.80 84.80 2083

105.000 .1182E-05 7159.9 7159.9 100.022 58.86 85.08 85.08 2033

110.000 .3873E-05 7586.0 7586.0 103.986 58.83 85.37 85.37 1985

115.000 .1142E-04 8013.6 8013.6 107.787 58.83 85.67 85.67 1939

120.000 .3071E-04 8442.8 8442.8 111.440 58.86 85.99 85.99 1894

125.000 .7606E-04 8873.5 8873.5 114.956 58.92 86.31 86.31 1850

130.000 .1752E-03 9305.9 9305.9 118.348 59.01 86.66 86.66 1808

135.000 .3780E-03 9r40.1 9740.1 121.625 59.12 87.02 87.02 1767

140.000 .7697E-03 10176.1 10176.1 124.796 59.26 87.39 87.39 1727

145.000 .1487E-02 10614.0 10614.1 127.869 59.42 87.79 87.79 1688

150.000 .2741E-02 11054.0 11054.0 130.852 59.60 88.21 88.21 1649

155.000 .4840E-02 11496.1 11496.2 133.752 59.81 88.64 88.64 1612

160.000 .8220E-02 11940.5 11940.5 136.573 60.04 89.10 89.11 1575

165.000 .1347E-01 12387.2 12387.3 139.322 60.29 89.59 89.59 1540

170.000 .2139E-01 12836.4 12836.6 142.004 60.56 90.10 90.10 1505

175.000 .3297E-01 13288.2 13288.5 144.623 60.86 90.64 90.64 1470

180.000 .4945E-01 13742.8 13743.2 147.185 61.17 91.20 91.21 1436

185.000 .7238E-01 14200.3 14200.8 149.691 61.51 91.80 91.81 1403

190.000 .1035E«00 14660.8 14661.6 152.148 61.86 92.43 92.44 1370

195.000 .1451E4-00 15124.6 15125.6 154.557 62.24 93.09 93.11 1338

200.000 .1993E«^00 15591.7 15593.2 156.922 62.63 93.78 93.81 1306

205.000 .2691E«^00 16062.4 16064.4 159.247 63.05 94.51 94.56 1275

210.000 .3574E+00 16536.9 16539.5 161.533 63.48 95.28 95.34 1243

215.000 .4675E4-00 17015.3 17018.7 163.785 63.94 96.10 96.17 1213

220.000 .6031E*^00 17497.9 17502.3 166.004 64.41 96.95 97.04 1182

225.000 .7679E4^00 17984.8 17990.5 168.192 64.90 97.85 97.97 1152

231.071 .1013E4-01 18582.2 18589.9 170.813 65.53 99.00 99.16 1115

235.000 .1202E«01 18976.0 18985.2 172.508 65.95 99.79 99.98 1092

240.000 .1480E«01 19482.5 19494.0 174.648 66.50 100.84 101.07 1062

245.000 .1805E4-01 19995.0 20009.1 176.769 67.07 101.94 102.23 1033

250.000 .2182E-^01 20513.8 20531.0 178.872 67.65 103.11 103.46 1003

255.000 .2616E«^01 21038.3 21059.2 180.957 68.26 104.33 104.77 974

260.000 .311264^01 21569.3 21594.4 183.026 68.89 105.63 106.16 944

265.000 .3675E+01 22106.3 22136.4 185.079 69.53 107.00 107.63 915

270.000 .4312E4^01 22650.0 22685.7 187.118 70.20 108.44 109.21 885

275.000 .5028Ef01 23200.3 23242.4 189.144 70.88 109.97 110.90 856

280.000 .5828E4^01 23757.6 23807.1 191.159 71.58 111.60 112.71 826

285.000 .6719E*01 24322.2 24380.1 193.164 72.30 113.32 114.66 796

290.000 .7706E^01 24894.5 24961.9 195.162 73.04 115.16 116.77 766

295.000 .8797E+01 25475.1 25553.1 197.154 73.80 117.13 119.06 736

300.000 .9997E+01 26064.5 26154.6 199.142 74.57 119.24 121.56 705

305.000 .1131E«-02 26663.6 26767.3 201.131 75.37 121.52 124.32 674

310.000 .1275E+02 27273.3 27392.2 203.122 76.18 123.99 127.38 642

315.000 .1432E>02 27894.7 28030.8 205.121 77.01 126.70 130.82 610

320.000 .1603£>02 28529.2 28684.6 207.131 77.86 129.70 134.74 577

325.000 .1788E«02 29178.5 29355.7 209.157 78.73 133.06 139.28 544

330.000 .1988E«02 29845.0 30046.6 211.208 79.61 136.88 144.66 509

335.000 .2204E4’02 30531.2 30760.6 213.290 80.52 141.34 151.23 474

340.000 .2436E4^02 31241.1 31502.2 215.416 81.44 146.71 159.54 437

345.000 .2687E+02 31980.0 32277.4 217.602 82.38 153.45 170.65 399

350.000 .2956E«02 32756.2 33096.0 219.872 83.37 162.48 186.65 359

355.000 .3244E«02 33583.9 33974.4 222.270 84.47 175.84 212.52 316

360.000 .3555E»02 34494.8 34948.7 224.873 86.26 199.62 263.89 269

365.000 .3890E«02 35569.1 36111.6 227.957 89.42 259.35 420.78 216

369.800 .4242E»02 38102.3 38957.5 235.536 0.00 0.00 0.00 0

15g
TABLE 30. Thermophysical properties along isobars

The following pages give physical and thermodynamic properties along

selected isobars, as computed by methods of section 3 of the text.

The first line of each table refers to freezing liquid on the P(T)

melting line.

Each table at P < P contains a blank line for the transition from

c

saturated liquid to vapor, as seen by the abrupt decrease of density.

Table headings for partial derivatives have the following interpretations

DP/DT E 9P/3T,

DP/DD = 9P/ap.

The specific heat interpretations are

CV E C^(p,T),

CP E C (p,T).

P

"k j

These tables are extrapolated beyond the range of some of the P-p-T data used

for adjusting the equation of state. Small discontinuities may be detected at

T = 405 K along isobars at P > P^ = 42.4 bar, due to change in the paths of

computation, section 3 and figure 1.

157
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208
Appendix C. Computer Programs

C

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PROGRAM PTHERM5 (INPUT,OUTPUT)

PROPANE THERHOFUNCTIONS, STARTING OCTOBER 1> 1976.

PTHERM5 REVISED JAN. 25, 1977. PATH FOR COMPii.LIQ. AT T L.T. B.P. NOTE USE OF QVAP ,DATA, TO CROSS THE ,OOME,.

NOTE USE OF CSAT ,DATA, FOR SPECIFIC HEATS IN COMPRESSED LIQUID.

COMMON GKtGKK. B1,B2,B3,B4, E1,ER

C0MM0N/1/AL,BE,6A,0E, OCRT,TCRT,PCRT , OGAT, DTRP,TTRP,PTRP

COMMON/3/OPOT,D2POT2,DPSOT,OPMDT,OPOD,OPDR,DTSDR,OTHDR

COMMON/4/ XB1,XB2, XE1,XE2, OXBOR, OXEDR

COMMON/5/ DOSOT

COMMON/6/ TSAT, THETA, PSAT

C0MM0N/7/TA,T8,PB, EA,HA,SA, HB,SB, TY1,TY2, OYH,OYS

COMMON/8/ IN, IK, P,T,OEN, E,H,S, CV, CP, CSAT, H,WK

CONMON/9/ ONG,EG,HG,SG, CVG,CPG,HG, OPGOT,OPGDO

COMMON/IO/ DY<40) ,HY<40) ,EY(40) , SY(40) ,CPY<40) ,CVY (40)

COMMON/11/ OK(4>lyEK(40) , SK(4Q} ,CVK (40)

COMMON/12/ DELS, OELCV

COMMON/99/ TI,EZZ, EZ,SZ,CVZ, HZ,CPZ

DIMENSION PP<99)

1 FORMATdS, 2F10.0)

2 FORMATdS, 3F10.0)

5 FORMAT(IX)

9

FORMAT(8F10.0)

10 FORMATdHl 9X *PROPANE FUNCTIONS AT POINT (TB,PB) * //

1 lOX 3HT =F8.3, 5H, P =F10.5, 7H, OEN =F8.4//

2 lOX 4HEZ =F11.3, 5H, E =F11.3//

3 lOX 4HHZ =F11.3, 5H, H =F11.3//

4 lOX 4HSZ =F11.5, 5H, S =F11.5//

5 lOX 5HCVZ =F10.3, 6H, CV =F10.3// . 6 lOX 5HCPZ =F10.3, 6H, CP =F10.3//

7 lOX 21HYESAVAGE VALUE, CP =F10.3)

11 FORMATilHO / 12X *FOR SAT.LIQ. AT THE BOILING POINT* //

1

12X4HTA =F10.5/ 12X4HEA =F10.3/ 12X4HHA =F10.3/ 12X4HSA =F10.5)

12 FORMATdHl IIX *LOOP CLOSURE FOR SATURATED VAPOR, * /

1 12X *HL,SL VIA PATH TA AND CSAT. Q, VAP VIA CLAPEYRON, / 2 12X *HG,SG VIA IDEAL GAS AND EQNSTATE, JOULES, MOLES, KELVINS.*//

3 12X 3HT,K 6X4HCSAT 8X2HHL 8X2HSL 5X5HQ.VAP 6X4HHL+Q

4 8X2HHG 6X4HDIFF 4X6HSL+Q/T 8X2HSG 6X4H0IFF ) 13 FORMAT(5X 2F10.2, FlO.l, F10.3, 4F10.1, 3F10.3)

14 FORMATdHl 18X *PROPANE ISOBAR AT P =* F8.5, 4H BAR /)

15 FORMATdHl 18X *PROPANE ISOBAR AT P =* 14, 4H BAR /)

16 FORMAT(19X IHT 6X3H0EN 6X3HV0L 5X5HDP/DT 5X5HDP/00

2 8X1ME 8X1HH 8X1HS 6X2HCV 6X2HCP 5X1HW / 3 15X 5H0EG K 4X5HM0L/L 4X5HL/M0L 5X5HBAR/K 1X9HBAR- L/MOL 4X5HJ/MOL

4 4X5HJ/M0L 2X7HJ/M0L/K 1X7HJ/MOL/K 1X7HJ/MOL/K 1X5HM/SEC ) 17 FORMATCIOX F10.3, F9.3, F9.5, F10.4, F10.3, 2F9. 1 ,F9. 3 ,2F8 .2 , 16

)

18 FORMATdOX F10.3, F9.5, F9.3, F10.6, F10.3, 2F9. 1 ,F9. 3 ,2F8 . 2 , 16)

CONSTANTS, EQNSTATE MARK-II, DEC. 12, 1976.

NOTE EZZ ESTIM. FROM STEARNS AND GEORGE.

29 Q = 1.01325 $ TB = 405.0 $ PB = 103.42135

30 MM = 44.09721 $ HK = 100000/WM $ GKK = 0.0831434

31 TTRP = 85.47 $ OTRP = 16.62 J PTRP = 3.0E-9

32 TCRT = 369.8 S DCRT = 4.960 $ PCRT = PSATF(TCRT)

33 OGAT = PTRP/GKK/TTRP $ GK = GKK*OCRT $ EZZ = 27452.0

34 AL=i.O S BE=0 $ GA=0.06 $ OE=0.75 $ ER=2.0

35 B1 = 0.22566372605 $ B2 = 1.04646227554 $ B3 = -0.44491000068

203
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Appendix C. Continued

36 = 0.12708270211 $ Li = -0.59883339489

37 CALL PEEK S CALL ISt’HRM $ CALL DEBUGIT

INTEGRATE ON ISOTHERM TB UP TO POINT (TB.PB), THEN - COMPARE YESAVAGE CP. PRINT HB« SB. AND ALL VALUES FOR TEST.

40 T = TB $ P = PB S CALL GENEOUS $ CPX = CPXFITI

41 OB = OEN S EB=E $ HB=H S SB=S

46 PRINT 10, T,PB,OB, EZ,E, HZ.HB, SZ,SB, CVZ,CV, CPZ,CP,CPX

49 CALL MEMOBAR S CALL MEMOSAT

ESTABLISH TA,EA,HA,SA FOR LIQUID AT THE BOILING POINT.

58 TA = T = FINOTSF(Q> $ CALL COEXIST $ EA=E $ HA=H $ SA=S

59 PRINT 11, TA, EA,HA,SA

60 CALL CVTEST S CALL JTLOCUS

LOOP-CLOSURE EXAM. FOR SATURATED VAPOR,

70 PRINT 12 $ OO 79 J=l,31 $ IFIJ.EQ.l) 71,72

71 T = TTRP S GO TO 75

72 IF(J.EQ.31) 73,74

73 T = TA $ GO TO 75

74 T = 80 5*J

75 CALL COHABIT I CS = CSAT $ HL = H $ SL = S 76 OG=OENGASF(T) S OL=OENLIQF (T) $ PS=PSATF(T)

77 QV = 100*T»OPSOT*<1/OG - 1/OL)

78 HQ=HL+QV S OH=HQ-HG $ SQ=SL+QV/T $ OS=SQ-SG

79 PRINT 13, T,CS, HL,SL,QV, HQ,HG,OH, SQ,SG,OS

80 CALL PRINTIT $ CALL TABLIQ

COMPUTE THERMOFUNCTIONS ON ISOBARS. START ON THE MELTING LINE.

ADD 5 YESAVAGE PRESSURES TO DATA DECK, FOR PLOT.

ISOBARS AT P UNDER PCRT TRAVERSE THE DOME.

NOTE USE OF CSAT ,OATA, FOR SP. HEATS OF THE COMPR. LIQUID.

90 IN = 1 $ NI = 51 S READ 9, ( PP ( I ) ,1 = 1 , NI

91 OO 300 I=IN,NI S IK=I $ IP=P= PP(I)

92 IF(P-IP) 93,94

93 PRINT 14, P S GO TO 95

94 PRINT 15, IP

95 PRINT 16

100 T = FINOTMF(P) $ CALL COMLIQ S V=l/OEN S IH=W

101 PRINT 17, T,OEN,V,DPOT,DPOO, E , H , S ,C V ,CP , I

102 IT = T/10 S IFIP.LT.PCRT) 110,180

CASES FOR P LESS THAN PCRT,

110 TS = FINOTSF<P) S TX=TS+10 $ K=L=0

111 OO 150 J=l,99 $ T = JT = 10*(IT+J)

112 IF(T.LT.TS) 113,117

113 IF(T.LT.TA) 114,115

114 CALL COMLIQ S V=l/OEN $ IW=W $ GO TO 116

115 CALL COMPRLQ S V=l/OEN S IW=W

116 PRINT 17, T,DEN,V,DPDT,OPOO, E , H , S , C V , CP, I H $ GO TO 150

117 IF(T.LT.TX) 120,130

C CASE FOR SATURATED LIQUID AND VAPOR,

120 T = TS $ IF<T.LT.TA) 121,122

121 CALL COHABIT $ GO TO 123

122 CALL COEXIST

123 V=l/OEN S VG=l/ONG S IH=H S IWG=HG

124 PRINT 17, T,OEN,V,OPOT,DPDD, E , H , S , C V ,CP , I W S PRINT 5 125 IF(P,LT.22» 126,127

210
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Appendix C. Continued.

126 PRINT 18, T,ONG,VG,OPGOT,OPGOO, EG,HG,SG,CV5,CPG,IWG S GOTO 128

127 PRINT 17, T,0NG,VG,0PG0T,0PGDD, EG,HG,SG,CVG,CPG,IHG

128 T = JT C CASES FOR THE HOMOGENEOUS DOMAIN.

130 IF(JT.GT.500) 131,132

131 K = K*1 S T s JT = JT 10*K $ IF(JT.GT. 700) 300,132

132 CALL GENIUS S V = 1/OEN S IM = H 133 IF1P.lt. 22) 134,135

134 PRINT 18, T,OEN,V,OPDT,DPDO, E,H,S, CV,CP,IH $ GO TO 150

135 PRINT 17, T,OEN,V,OPOT,OPDD, E,H,S, CV,CP,IW

150 CONTINUE

C

C CASES FOR P GREATER THAN PCRT. THREE SUBCASES - 180 K=L=0 S DO 250 J=l,99 $ T = JT = 10*<IT+J)

181 IF(T.LT.TCRT) 190,182

182 IFIT.LT.TB) 200,210

C CASE A FOR T LESS THAN TCRT.

190 IF(T.LT.TA) 191,192

191 CALL COMLIQ S V=1/DEN $ IH=M S GO TO 193

192 CALL COMPRLQ S V=l/OEN $ IW=W

193 PRINT 17, T,OEN,V,DPOT,DPDO, E,H,S,CV,CP,IW $ GO TO 250

C CASE B FOR T.GT. TCRT, AND. T.LT. TB.

C USE YESAVAGE AT OEN ABOVE DCRT, USE GENIUS AT DEN UNDER OCRT.

200 PX = PVTF(T,OCRT,0) $ IF(P.GT.PX) 201,220

201 CALL LIQTHRM S V=l/OEN $ IW=M

202 PRINT 17, T,OEN,V,OPOT,OPDO, E,H,S,CV,CP,IH S GO TO 250

C CASE C FOR T GREATER THAN TB, THE HOMOGENEOUS DOMAIN.

210 IF( JT.GT.500) 211,220

211 K = K+1 $ T = JT = JT 10*K $ IF ( JT, GT, 70 0 ) 300,220

220 CALL GENIUS S V = 1/DEN S IH = N 221 PRINT 17, T,OEN,V,DPOT,DPDD, E , H, S ,C V ,CP, IH 250 CONTINUE

300 CONTINUE

310 CALL JTLOCUS S CALL ERNST $ CALL YESAVA5

311 CALL RAO $ CALL LACAM

999 STOP $ END

SUBROUTINE COHABIT

GIVEN T AT COEXISTENCE, GET VAPOR+LIOUID PROPERTIES AT T.LT.B.P.

FOR VAPOR, GET ONG,EG,HG,SG, CVG,CPG,HG, OPGDT,DPGOO,

FOR LIQUID, GET OEN,E,H,S, CV,CP,H.

COMMON/l/AL,BE,GA,OE, DCRT, TCRT , PCRT , DGAT, DTRP ,TTRP,PTRP

COMMON/3/OPDT,02POT2,DPSDT,DPMOT,OPOD,DPOR,DTSDR,OTHOR

COMMON/8/ IN, IK, P,T,DEN, E,H,S, CV,CP,CSAT, W,WK

C0MM0N/9/DNG,EG,HG,SG, CVG,CPG,MG, 0PGDT,0P3DD

COMMON/12/ DELS, OELCW

COMMON/99/ TI,EZZ, EZ,SZ,CVZ, HZ,CPZ

DATA (0=1.01325) , (G = 0. 0831434)

1 PS = PSATF(T) $ ONG = DB = OENGASF(T)

2 TI = T S CALL IDEAL $ N = DB*20 10

3 EG = EZZ «• EZ EOELF(1,N,T,0,OB) $ HG = EG 100*PS/OB

4 SG = SZ DELS - 100*G*ALOG (G*T*OB/Q)

5 CVG = CVZ OELCV $ PX = PVTF(T,OB,l) $ OPGDT=DPOT $ OPGDD=OPOO

6 CPG = CVG 100*T/OPDD*(OPOT/DB)**2 $ WG = SQRT (HK*CPG*OPOO/CVG)

9 CALL CSATSUM S RETURN $ END

211
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Appendix C. Continued

SUBROUTINE COEXIST

GIVEN T AT COEXISTENCE, GET BOTH VAPOR AND LIQUID FUNCTIONS.

FOR VAPOR, GET ONG , EG ,HG , SG , CVG,CPG,HG, OPGOT,OPGOO, • FOR LIQUID, GET OEN,E,H,S, CV,CP,CSAT ,M.

COEXIST CALLED BY COMPRLQ. P NOT USED, MUST NOT CHANGE.

COMMON/l/AL,BE,GA,OE, OCRT,TCRT ,PCRT , DGAT, DTRP,TTRP,PTRP

COMMON/3/OPDT,02POT2,DPSOT,OPMOT,OPOD,DPOR,OTSDR,DTHDR

COMMON/5/ OOSOT

COHMON/8/ IN, IK, P,T,OEN, E,H,S, CV,CP,CSAT, W,WK

C0MM0N/9/DNG,EG,HG,SG, CVG,CPG,MG, OPGDT,OPGDD

COMMON/12/ DELS, DELCV

COMMON/99/ TI,EZZ, EZ,SZ,CVZ, HZ,CPZ

DATA (0=1.01325) , (G=0. 0831434)

1 FORMATdHO 9X *1 EXCEEDS TCRT IN COEXIST. / ) 2 IF(T.GT.TCRT) 3,4

3 PRINT 1 $ STOP

4 PS = PSATF(T) S DNG = DB = DENGASF(T)

5 TI = T $ CALL IDEAL $ N = DB*20 10

6 EG = EZZ EZ EDELF (1,N,T,0,DB) $ HG = EG 100*PS/DB

7 SG = SZ DELS - 100*G*ALOG (G*T*DB/Q)

8 IF(T.EO.TCRT) 9,11

9 PX = PVTF(T,DB,1) $ DPGDT = DPDT $ DPGDO = DPDD

10 CPG = CVG = MG = 0 S GO TO 15

11 CVG = CVZ DELCV $ PX = PVTF<T,DB,1)

12 CPG = CVG 100*T/DPDD*(DPDT/DB)**2 $ MG = SORT ( WK*CPG*DPDD/C VG

13 DPGDT = DPDT $ DPGDD = OPOD

C NOW TRAVERSE THE ,OOME, USING QVAP ,OATA,.

15 DEN = OL = OENLIQF(T) $ DOLDT = DOSOT $ OV = QVAPXF(T)

16 H = HG - QV S S = SG - QV/T $ E = H - 100*PS/DL

17 IF(T.EQ.TCRT) 18,19

18 PX = PVTF(T,OL,l) $ CP=CV=CSAT=W=0 $ RETURN

19 CSAT = CSATXF(T) J PX = PVTF(T,OL,l)

20 CV = CSAT 100*T*OPDT*DDLOT/DL/DL

21 CP = CV 100*T/DPOO* (DPDT/0L)**2

22 W = SORT (WK*CP*OPOO/CV) $ RETURN $ END

SUBROUTINE COMLIQ

C GIVEN P,T FOR COMPRESSED LIQUID, GET DEN ETC, AT T.LT.B.P.

C FIRST INTEGRATE VIA CSATSUM FROM TA DOWN TO T,

C THEN INTEGRATE ALONG ISOTHERM T FROM SATLIQ JP TO P. COMMON/3/ DPDT,D2PDT2,DPSDT,DPMDT, OPOD, DPDR, 3 TSOR,OTHDR

COMMON/8/ IN, IK, P,T,OEN, E,H,S, CV, CP, CSAT, W,WK

COMMON/12/ DELS, DELCV

1 CALL CSATSUM $ DA = DEN $ DEN = DB = FINDENF(T,P)

2 OX = OB-OA S IF(OX) 9,9,3

3 N = DX*10 +5 S E = E EDELF ( 0 , N , T ,DA , OB)

4 H = E + 100*P/DB $ S = S DELS $ CV = CV DELCV

5 PX = PVTF(T,DB,1) $ CP = CV 10 0*T/DPDO* 4 DPDT/DB ) **2

6 W = SQRT(HK*CP*OPOD/CV)

9 RETURN $ END

212
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Appendix C. Continued.

SUBROUTINE COMPRLQ

C GIVEN P.T FOR COMPRESSED LIQUID AT T.LT.TC, GET DEN, FUNCTIONS.

C IF T = MULTIPL. 10 K, START WITH DK,EK,SK,CVK ON SATOLIQ.,

C OTHERWISE, USE COEXIST FOR START ON THE SATDLIQ., AND -

C FINALLY, INTEGRATE ALONG ISOTHERM T FROM SATLIQ. TO POINT (P,T).

COMHON/3/OPOT,02POT2,OPSOT,OPMOT,OPOO,DPDR,DTSDR,OTHDR

COMMON/5/ ODSDT

COMMON/8/ IN, IK, P,T,DEN, E,H,S, CV,CP,CSAT, H,WK

COMHON/11/ DK(<»0) ,EK(40) , SK(40) ,CVK(40)

COMMON/12/ DELS, DELCV

DATA (TCRT = 369.8)

1 FORMATdHO 9X *1 NOT UNDER TCRT IN COMPRLQ. • / ) 2 IF(T.LT.TCRT) 4,3

3 PRINT 1 $ STOP 41= T/10 $ IF(T-10*I) 5,6

5 CALL COEXIST $ DA = DEN $ GO TO 10

6 DA=DK(I) $ E=EK(I) S S=SK(I) $ CV=CVK(I)

C NOW INTEGRATE ALQNG ISOTHERM T UP TO POINT (T,P).

10 DEN = 08 = FINO^F<T,P) $ DX = OB-DA $ IF(DX) 13,13,11

11 N = OX*10 5 $ E = E EDELF<0,N,T,DA,DB)

12 S = S DELS $ CV = CV + DELCV

13 H = E 100*P/OB $ PX = PVTF(T,OB,l)

14 CP = CV 100*T/OPOD* (DP0T/DB)**2

15 W = SQRT (WK*CP*DPOO/CV) $ RETURN $ END

SUBROUTINE CPSUMIT

USE YESAVAGE CPXF(T) ALONG ISOBAR PB = 103.42135 BAR.

INTEGRATE FROM TYl TO TY2. YIELDS DELTA-H, DELTA-S.

COMMON/7/TA,TB,PB, EA,HA,SA, HB,SB, TY1,TY2, DYH,OYS

1 TR = TY2 - TYl $ OYH = OYS = 0 $ IF(TR) 2,6

2 N = A8S(TR)/2 +2 $ OT = TR/N

3 DO 5 J=1,N $ TJ = TYl (J-0.5)*OT $ C = CPXF(TJ)

4 DYH = OYH C*OT $ OYS = DYS C*OT/TJ

5 CONTINUE $ RETURN

6 RETURN $ END

FUNCTION CPXF(T)

C PROPANE CPtT), J/MOL/K, YES AVAGE < 15 0 0 PSD, 103.42135 BAR.

C VIA PROGRAM SAVAGE, SEPT. 27, 1976 AT 9.44.

C DEFINE X = (T-TT)/(TM-TT) , WHEN THE EQUATION IS - C CP = A1 A2*X2 A3*X3 + . . . A7*X7.

DIMENSION A(9)

DATA ITT=85.47) ,ITM=405.0) , CTN=319.53»

OATA(A = 83.7, 719.296, -7767.049, 40574.6955, -118438.853,

1 205520.887, -210152.230, 116726.413, -27098.492)

1 FORMATdHO 9X *T EXCEEDS TB IN CPXF(T).*/ ) 2 IF(T.GT.TM) 3,4

3 PRINT 1 $ STOP

4 X = (T-TTI/TN $ S = A<1) $ DO 5 J=2,9

5 S = S A(J)*X**J $ CPXF = S $ RETURN $ END

213
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Appendix C. Continued.

SUBROUTINE CSATSUM

C FOR SATLIQ START WITH EA,SA AT TAt INTEGRATE FROM TA TO T.

C YIELDS OENtEfH,S»CV»CP»CSAT,W AT T FOR THE SATOLIQUIO.

C0MM0N/3/0P0T,02PDT2,DPS0Tf OPMOT,OPOD»OPOR,OTSDR,DTHDO

COMMON/5/ DDSOT

C0MM0N/7/TA,TB,PB, EA.HA.SA, HB,SB, TYl,TlT2, OYH.DYS

COMMON/8/ INtIKt PfT.OEN, E,H,S, CV»CP»CSAT, M,WK

1E=EA $ S=SA S TR=T-TA $ IF(TR) 2,9

2 N = ABS(TR»/4 * Z $ OT = TR/N

3 00 8 J=1,N S TJ = TA (J-0.5)*OT

4 C = CSATXF(TJ» $ S = S C*OT/TJ $ PS = PSATF(TJ)

50= OENLIOF(TJ) $ 00 = OOSOT*OT

6 E = E C*OT 100*PS*00/0/0

8 COtTINUE

9 CSAT = CSATXF(T) % DEN = OL = OENLIQF(T) S DOLDT = DDSOT

10 PS = PVTF<T,OLfl) $ H = E 100*PS/DL

11 CY = CSAT 100*T*OPOT*OOLOT/OL/DL

12 CP = CV 100»T/DPOO* (DPDT/0L)**2

15 H = SQRT(HK*CP*OPOD/CV) $ RETURN $ END

FUNCTION CSATXF(T)

VIA PROGRAM CSAT-C3, DEC. 15, 1976, AT 11,18, USING - DATA FROM PTHERM4, DEC. 13, 1976, AT 10.31.

CS = A*X/«1-X)**EP B C*X D*X2 E*X3, X = T/TCRT.

OATA(EP = 0.8) ,<TCRT = 369.8) ,( A=4. 20141 0 ) , (0=79.737878)

,

1

(C=18. 313347) ,(0=-36. 564448) , (E=67. 003225)

1 IF(T.LT.TCRT) 2,9

2 X = T/TCRT $ X2 = X*X $ Q = (1-X)**EP

3 CSATXF = A*X/Q B C*X 0*X2 E*X*X2 S RETURN

9

CSATXF =0 $ RETURN $ END

FUNCTION CUBERT(X)

C CUBE ROOT MISSING FROM 6600 COMPUTER LIBRARY.

1 E = 1.0/3. 0 S IF(X) 2,3,4

2 CUBERT = -ABS<X)*»E $ RETURN

3 CUBERT = 0.0 $ RETURN

4 CUBERT = X**E $ RETURN $ END

SUBROUTINE CVTEST

C EXAMINE CV(T) ALONG THE CRITICAL ISOCHORE.

C DEFINE X = (T/TC-1), Y = (CV-CVZ)/R.

COMMON/12/ DELS, DELCV

C0MM0N/99/TI,EZZ, EZ,SZ,CVZ, HZ,CPZ

DATA (0CRT=4.96) , (TCRT=369,8) ,(R=8,31434)

1 FORMATdHl IIX *CV(T), J/MOL/K, ALONG THE CRITICAL ISOCHORE //

1 12X 3HT,K 7X3HCVZ 8X2HCV 9X1HX 9X1HY 5X5HLN(X) 5X5HLN(Y) ) 2 F0RMAT(5X 7F10.3)

10 PRINT 1 S DO 20 J=l,51 $ IFCJ.EO.l) 11,12

11 TI = T = 370,5 $ GO TO 13

12 TI = T = 369 J 13 X = T/TCRT - 1 $ N = 10 0*EXP ( -7. 44365*X)

14 CALL IDEAL S E = EZZ EZ EOELF ( 0 ,N , T , 0 , DC RT

15 CV = CVZ DELCV $ Y = DELCV/R

16 XL = ALOG(X) $ YL = ALOG(Y)

20 PRINT 2, T, CVZ,CV, X,Y, XL,YL $ RETURN $ END

214
Appendix C. Continued.

SUBROUTINE OEBUGIT

C EXAMINE DP/DO FROM PVTF ALONG ISOTHERMS, ESPEC. AT DCRT.

COMMON/l/AL,BE,GA,DE, DCRT, TCRT, PORT , DGAT, DTRP , TTRP , PTRP

COMMON/3/DPOT,02POT2,OPSDT,DPMOT,OPOD,OPDR,OTSDR,DTHDR

COMMON/4/ XB1*XB2, XE1,XE2, OXBOR, OXEOR

CONMON/6/ TSATf THETA, PSAT

COMMON/20/ B,60, E,EO, XB, XE, FI

1 FORMATdHl 4X *DEBUG ISOTHERM AT T,K =* F8.3/

1 5X6HTTRP =F6.2, 8H, TCRT =F7.2, 8H, DTRP =F6.2, 8H, DCRT =F5.2//

2 4X3H0EN 6X2HTS 2X5HDTSDR 6X2HTH 2X5HDTHDR 5X2HPS 2X5HDPSDT

3 6X1HB 5X2HBD 6X1HE 5X2HED SX2HX8 2X5HDXBDR

4 5X2HXE 2X5H0XE0R 5X2HF1 3X5HP,BAR 2X5HDP/DD ) 2 F0RMAT(2XF5.2f F8.3, F7.3, F8.3, F7.3, F8.3, F7.5,

1

9F7.4, F8.3, F7.3)

5 00 20 1=1,8 $ IF(I.EQ.l) 6,7

6 T = TCRT $ GO TO 8

7 T = 360 5*1

8 PRINT 1, T, TTRP, TCRT, DTRP, DCRT

10 DO 20 J=l,25 $ DN = 2.88 * 0.16*J $ P = PVTF(T,DN,1)

15 PRINT 2, ON, TSAT,DTSDR, THETA, OTHOR, PSAT,DPSDT,

1 B,BO, E,EO, XB, OXBOR, XE, OXEOR, FI, P, OPOD

20 CONTINUE S RETURN S END

FUNCTION OELTAF(T,D)

C GET (T*DP/OT - D*DP/OD) FOR THE J-T INVERSION CURVE.

COMMON/l/AL,BE,GA,OE, DCRT, TCRT, PCRT, DGAT, DTRP, TTRP, PTRP

COM M0N/3/DPDT,02PDT2,0PSDT,0PM0T, OPOD, OPOR,OTSOR,DTHDR

1 IF(T-TCRTI 2,4,4

2 OL = DENLIQFIT) $ IF(D-DL) 3,3,4

3 OELTAF = l.OE+100 $ RETURN

4 P = PVTF(T,0,1I

5 OEi TAF = ABS <T*OPOT-D*DPDO) S RETURN $ END

FUNCTION OENGASF(T)

C PROPANE SATURATED VAPOR DENSITIES, MOL/LITER.

C DEN = (DC*TC/T)*EXP(-YNG*Y) , YNG i LN(DC*T3/DGAT/TTRP»

C X = ITC-T)/(TC-TT) , U = (TC/T-1)/ ITC/TT-1) . C Y = U * (XE-X>*(A1 A2*X/XE + A3*X . . A6*X4)

COMMON/5/ DOSOT

DIMENSION A(6)

DATA (DCRT=4.96) , ( TTRP=85 .47) , ( TCRT=369 . 8) DATA (E=0.35) ,(DGAT=4.22162614E-10) , (YNG=24. 65183315)

OATA(A = 0.072453281, 0.170534468, -0.278060163,

1 0.436982342, -0.841080253, 0.405105441)

1 FORMATdHO 9X *T EXCEEDS TCRT IN OENGASPIT). * / ) 2 IF<TCRT-T) 3,4,5

3 PRINT 1 $ STOP

4 OENGASF = DCRT $ DOSOT = 1.0£*10 $ RETURN

5 OCT = DCRT*TCRT $ XN=TCRT-TTRP $ X=ITCRT-T)/XN S X1T=-1.0/XN

6 UN = TCRT/TTRP * 1 S U = ( TCRT/T-1 ) /UN $ UlT = -TCRT/UN/T/T

7 XE = X**E $ V=XE-X $ VI = E*XE/X - 1 8 H = Ad) A(2)*X/XE $ W1 = A (2) * ( 1-E ) /XE

9 00 10 K=3,6 $ L = K-2 $ XL = X**L $ W = W A(K)*XL

10 HI = HI A(K)*L*XL/X

11 Y = U V*H S YIT = UlT (V*W1 V1*H)*X1T

12 OENGASF = OCT/T*EXP (-YNG*Y)

15 DOSOT = -(YNG*Y1T 1/T)*DENGASF $ RETURN S END

215
o

o

o

Appendix C. Continued

FUNCTION OENLI(JF(T)

PROPANE SATURATED LIQUID DENSITIES, MOL/LITER.

DEN = OCRT YNL*(X (XE-X)*Y), YNL = OTRP-DCRT,

Y = A B*X2 C*X3, X i ( TC-T» / ( TC-TT )

COHHON/5/ OOSOT

DATA (TTRP=85.47) , ( TCRT= 369, 6 ) , « DCRT=4. 96) , ( DTRP=16.62)

DATA (E=0.35) , (A=0. 775396679) ,( 8=- 0 . 167912979) ,(0=0.081166807)

1 FORMATdHO 9X *T EXCEEDS TCRT IN OENLIQF(T), * / ) 2 IF(TCRT-T) 3,4,5

3 PRINT 1 $ STOP

4 DENLIQF = DCRT S OOSOT = -l.OE+10 S RETJRN

5 XN = TCRT-TTRP $ X = (TCRT-T)/XN $ X2 = X*X S XIT = -1,0/XN

6 XE = X**E $ V = XE-X $ VI = E*XE/X - 1 $ YNL = OTRP-DCRT

7 Y = A B*X2 C*X*X2 $ Y1 = 2*B*X * 3*C*K2

8 DENLIQF = DCRT YNL* (X V*Y)

9 OOSOT = YNL*(1 * V*Y1 + V1*Y)*X1T $ RETURN S END

FUNCTION EOELF(L,N,T,OA,OB)

C GET CHANGE OF E,S,CV WITH DENSITY ALONG ISOTHERMS.

C GET EOELF, DELS, OELCV FROM DA TO OB ALONG ISOTHERM T,

COMMON/3/OPOT,O2POT2,OPSOT,OPMDT,DPOO,DPDR,0TSDR,OTHOR

COHMON/12/ DELS, OELCV

DATA (G = 0.0831434)

1

OX = (OB-OA)/N S IF(OX) 2,10 2E=S=CV=0 S DO 9 J=1,N $ ON = OA (J-fl,5)*0X

3 OXN = OX/ON/ON $ P = PVTF(T,DN,0)

4 E = E (P-T*OPOT)*OXN $ CV = CV - 02PDT2*0XN

5 IF(L.EQ.O) 6,7

6 S = S - OPOT*OXN S GO TO 9

7 S = S * (G-OPOT/ON)*OX/DN

9 CO.TINUE $ EDELF=100*E $ DELS=100*S S DELCV=100*T*C V $ RETURN

10 EOELF = DELS = OELCV =0 $ RETURN $ ENO

ALONG ISOTHERMS

K /

SUBROUTINE ERNST

G.ERNST/J.8UESSER, J. CHEM. THERMOOYN. 2, 787 (1970).

COMMON/8/ IN, IK, P,T,OEN, E,H,S, CV,CP,CSAT, W,WK

COMMON/99/ TI,EZZ, EZ,SZ,CVZ, HZ,CPZ

DIMENSION TC(4), PK(ll), C(4,ll)

DATA (TZ=273. 15) , (Q=0. 980665)

1 FORMATdOX 4F10.0)

2 FORMAT (5F10. 0)

3 F0RMAT(1H19X*ERNST PROPANE CP(T,P), J/MOL/K,

4 FORMATdHO 9X *THE ISOTHERM AT T =* F7.2, 2H

1 10X5HP,BAR 2X5HM0L/L 2X5HCP(P) 2X5HCALCO 2X4HPCNT

2 2X6HCP-CPZ 2X5HCALCD 3X4H0IFF I 5 F0RMAT(8X 2F7.3, 2F7.2, F6.2, F8.2, 2F7.2)

6 FORMATdHO 8X 4HNP =13, 9H, AVPCT =F4.2, 9H, AVDIF =F4.2)

INDEX I FOR ISOTHERMS. INDEX J FOR PRESSURES.

8 READ 1, (TC(I) ,1=1,4) S DO 9 J=l,ll

9 READ 2, PK(J) , (C(I,J) ,1=1,4) S PRINT 3 S SO = SS = NP = 0

10

00 30 1=1,4 $ T = TZ TC(I) S PRINT 4, T $

12 00 20 J=l,ll $ P = Q*PK(J) S CPX = C(I,J) $

13 NP = NP+1 $ CALL GENEOUS $ CPC = CP

14 PCT = 100*(CPX/CPC-1) $ SS = SS + ABS(PCT)

15 DCPX = CPX - CPXZ S DCPC = CPC - CPZ

16 OIF = OCPX - OCPC $ SO = SO ABS(DIF)

19 PRINT 5, P,OEN, CPX, CPC, PCT, OCPX , DCPC, 01

20 CONTINUE

30 CONTINUE $ SS = SS/NP $ SO = SO/NP

31 PRINT 6, NP, SS, SO $ RETURN $ END

CPXZ = C(I,1)

IF(CPX) 13,20

216
Appendix C. Continued

FUNCTION FINOENFCTtP)

C ON ISOTHERM T, FIND DEN, MOL/L, TO MINIMIZE <P-PC) VIA EQNSTATE.

COMMON/l/AL,BE,GA,OE. DCRT,TCRT .PORT , DGAT, DTRP,TTRP,PTRP

COMMON/3/OPOT,02POT2,OPSOT,DPMOT,OPOD,OPOR,OTSOR,OTHOR

DATA (0M=17.2) , (GKK=0.083143G)

41 FORMATdHO 9X *FINOENF = 0, FAILS TO CONVERGE. • / ) 42 FORMATdHO 9X *FINOENF = OCRT, DP/DR ZERO OR NEG. * / ) 43 FORMATdHO 9X *FINOENF = 0, DOUBLE-VALUED AT P = PSAT. * / ) IF(P.GT.O) 1,35

1 IF(T-TCRT) 2,5,8

2 OG=OENGASF(T) S OL=DENLIQF (T) S PS=PSATF(T) $ IF(P-PS) 3,32,4 30= OG/2 $ GO TO 11

4 0= (0L4-0TRP)/2 $ GO TO 11

5 DG=OL=OCRT $ PS=PCRT $ IF(P-PS) 6,33,7 60= OCRT/2 S \G0 TO 11

70= 2*0CRT S CT TO 11

8 IFIT.LT. 400.0) 9,10

9 PC = PVTFIT,DCRT,0) S IFIP-PC) 6,33,7

10 0 = OCRT

11 00 30 J=l,50 $ 0P=P-PVTF(T,0,1) S IFiABS (0?/P) -l.OE-61 31,31,12

12 IFfOPOO.GT.O) 13,34

13 00 = OP/OPOO $ IFIABS (00/0) -l.OE-6) 31,31,14

14 0 = 0 00 $ IF(O.GT.O.O) 16,15

15 0 = P/GKK/T $ GO TO 30

16 IF(O.GT.OM) 17,18

17 0 = OM S GO TO 30

18 IF(T-TCRT) 19,24,30

19 IF(P.LT.PS) 20,22

20 IF(O.GT.OG) 21,30

21 0 = OG S GO TO 30

22 IF(O.LT.OL) 23,30

23 0 = OL $ GO TO 30

24 IFCP.LT.PCRT) 25,27

25 IF(O.LT.OCRT) 30,26

26 0 = OCRT - 0.02 S GO TO 30

27 IF(O.GT.DCRT) 30,28

28 0 = OCRT 4^ 0.02

30 CONTINUE $ PRINT 41 $ STOP

31 FINOENF =0 S RETURN

32 PRINT 43 $ STOP

33 FINOENF = OCRT S RETURN

34 FINOENF = OCRT S PRINT 42 $ RETURN

35 FINDENF=OPOT=O2POT2=0 $ OPOO=GKK»T $ DPDR=OPOO*OTRP

36 RETURN S END

FUNCTION FINOTMFCP)

C GIVEN P ON THE MELTING LINE, FIND T. C0MM0N/1/AL,BE,GA,0E, OCRT, TCRT, PORT , DGAT, DTRP,TTRP,PTRP

DATA (A=7180.0) , (E=1.283)

1 X = (P-PTRP)/A 1 $ FINDTMF = TTRP*X**d. 0/E» $ RETURN $ END

217
o

o

o

o

Appendix C. Continued

FUNCTION FINOTSFIP)

C GIVEN VAPOR PRESSURE Pt ITERATE T TO MINIMIZE (P-PC).

COHHON/l/AL,BE,GA,OEt OCRT , TCRT , PCRT , DGAT, DTRP , TTRP , PTRP

C0MH0N/3/0P0T,D2PDT2,0PSDT,DPM0T,0P00,0PDR,DTSDR,0TH0R

1 FORHATIIHO 9X *FINDTSF = 0, FAILS TO CONVERGE. * / ) 2 FORHATUHO 9X FINOTSF = 0, P EXCEEDS PCRT. * / ) 3 IF(P-PCRT) 4,11,12

4 T = 250 $ DO 9 J=l,50 $ OP = P - PSATF(T) $ AOP = A8S (DPI

5 IF(AOP/P-1.0E-6) 10,6,6

6 IF(AOP/DPSDT/T-1.0E-6) 10,7,7

7 T = T DP/OPSDT $ IF(T-TCRT) 9,9,8

8 T = TCRT

9 CONTINUE $ PRINT 1 $ STOP

10 FINOTSF = T S RETURN

11 FINOTSF = TCRT S RETURN

12 PRINT 2 S STOP $ END

SUBROUTINE GENEOUS

C GIVEN P,T FOR THE HOMOGENEOUS DOMAIN - C GET DEN AND FUNCTIONS AT ANY TEMPERATURE.

COHHON/3/OPDT,O2POT2,OPSDT,OPMOT,OPaO,OPDR,0TSDR,DTHOR

COHNON/8/ IN, IK, P,T,OEN, E,H,S, CV,CP,CSAT, H,WK

COMHON/12/ DELS, OELCV

COHHON/99/ TI,EZZ, EZ,SZ,CVZ, HZ,CPZ

DATA (0=1.01325), (G=0. 0831434)

3 TI = T S CALL IDEAL $ IF(P.GT.O) 4,10

4 OEN = OB = FINOENF(T,P) S N = OB*20 10

5 E = EZZ EZ EOELF (1,N,T,0,DB) $ H = E f 100*P/DB

6 S = SZ DELS - 100*G*ALOG(G*T*D8/0)

7 CV = CVZ DELCV $ PX = PVTF(T,DB,1)

8 CP = CV 100*T/OPOO*(DPOT/DB)**2

9 H = SQRT(WK*CP»DPOO/CV) $ RETURN

10

OEN=S=0 % E = EZZ EZ $ H = E 100*G*T $ CV=CVZ S CP=CPZ

12 H = SQRT(HK*CP»G*T/CV) $ RETURN $ END

SUBROUTINE GENIUS

GENIUS SAVES IDEAL GAS VALUES ALONG ISOBARS.

SAVE EZK(T), SZK(T), CVZK(T) FROM THE FIRST ISOBAR.

GIVEN P,T FOR HOMOGENEOUS DOMAIN, GET OEN AND FUNCTIONS.

VALID ONLY AT INTEGER MULTIPLES OF 10 K. COMHON/3/OPOT,D2POT2,OPSOT,OPMOT,OPOD,OPOR,DTSOR,OTHOR

COHMON/8/ IN, IK, P,T,OEN, E,H,S, CV,CP,CSAT, M,WK

COMMON/12/ DELS, OELCV

CONMON/99/ TI,EZZ, EZ,SZ,CVZ, HZ,CPZ

DIMENSION EZK(99), SZK(99), CVZK(99)

DATA (0=1. 01325), (G=0. 0831434)

1 FORMATdHO 9X *T NOT INTEGRAL IN GENIUS. * / ) 2 J = T/10 S IF(T-10*J) 3,4

3 PRINT 1 $ STOP

4 IF(IK.EO.IN) 5,10

5 CALL GENEOUS $ EZK(J) = EZZ EZ

6 SZK(J) = SZ $ CVZK(J) = CVZ $ RETURN

10 OEN = OB = F1NDENF(T,P) S N = OB«20 * 10

11 E = EZK(J) EOELF(1,N,T,0,OB) $ H = E 100»P/OB

12 S = SZK(J) DELS - 100*G»ALOG(G*T*OB/O)

13 CV = CVZK(J) DELCV $ PX = PVTF(T,DB,1)

14 CP = CV 100*T/OPOO* (DP0T/0B)**2

15 M = SORT(HK*CP*DPOD/CV) $ RETURN S END

218
Appendix C. Continued.

SUBROUTINE IDEAL

C PROPANE IDEAL GAS (1 ATM) THERMOFUNCTIONS VIA CHAO (1973).

C (HZ-HZZ)/RT = 4.0 (A B/Q C/02 D/X) *EXP ( -E/X) , WHERE - C X = T/lOO* Q = CUBERT(X).

COMNON/99/ TI« EZZ, EZ,SZ»CVZ. HZ.CPZ

DIMENSION A(6)

DATA (E=3.0) «(R=8. 31434) , (SI=32.552)

OATA(A = 24.11012. 94.40550. -535.32814.

1

980.124065. -678.64094. 170.42778)

1 X=TI/100 S 0=CUBERT(X) $ OOOX=0/3/X $ XP=EXP(-E/X)

2 H = 4.0 S SUN = SNl =0 S 00 7 K=l«6

3 M = H AIK)*XP*Q**(1-K) $ L = 4-K $ OL = 0**L

4 SUM = SUM A<K)*QL $ SMI = SMI A (K) *L*0L*DQ0X/Q

7 CONTINUE $ CP = 4.0 (E*SUM/X/X * SM1)*XP

C S = S(300) INTEGRAL (CP/X)*DX FROM T=300 UP TO TI.

10 N = ABS(TI-300)/4 4 S OX = (X-3)/N S S = SI 12 00 20 J=1.N S X = 3.0 4^ (J-0.5)*OX $ 0 = CUBERT(X)

14 DQOX = Q/3/X $ XP = EXP(-E/X) $ SUM = SMI = 0 15 00 19 K=1.6 $ L=4-K $ OL= 0**L

16 SUM = SUM 4 A<K)*QL $ SMI = SMI 4 A (K) *L*QL»DOOX/Q

19 CONTINUE S CPX = 4.0 4 (E*SUM/X/X 4 SMD^XP

20 S X S 4 CPX*OX/X

C CONVERT TO OINENSIONEO RESULTS. JOULES. HOLES. KELVINS.

22 CPZ = R^CP $ SZ = R*S $ HZ = R*TI*H

23 CVZ = CPZ - R S EZ = HZ - R»TI $ RETURN S END

SUBROUTINE ISOTHRM

C PRINTOUT THE CRITICAL ISOTHERM.

COMNON/l/AL. BE.GA. de. DCRT.TCRT.PCRT . DGAT. DTRP. TT RP. PTRP

COMNON/3/OPOT.02POT2.DPSOT.OPMDT.OPOO.OPOR.DTSDR.DTHOR

CONNON/4/ X81.XB2. XE1.XE2. OXBOR. OXEOR

COMMON/6/ TSAT. THETA. PSAT

1 FORMATCIHI 14X »THE CRITICAL ISOTHERM* //

1 6X4HTC =F7.2. 6H. DC =F5.2. 6H. PC =F11.7.

2 . AT THE C.P., DPS/DT = F8.5. 9H. DP/DT =F8.5//

3 6X4H0/0C 9X5HTS/TC 9X5HPS/PC 10X4HP/PC 9X5HDP/DR 4X6H0TS/DR

4 4X6H0TH/0R 4X6H0PS/0R 4X6HDXB/DR 4X6HDXC/0R ) 2 F0RMAT(2X F8.2. 3F14.10. F14.9. 5F10.5)

3 PC = PVTF(TCRT.OCRT.O)

4 PRINT 1. TCRT.DCRT.PCRT. DPSOT.DPDT $ DO 8 J=1.51

5 OR X 0.74 4 0.01*J $ ON X OR’OCRT

6 PR X PVTF<TCRT.DN.1)/PCRT S OPSOR = DPSDT*OTSOR

7 TSN X TSAT/TCRT $ PSN = PSAT/PCRT

8 PRINT 2. OR. TSN. PSN. PR.DPDR. OTSOR.DTHDR. DPSOR. DXBOR.DXEOR

9 RETURN $ END

213
Appendix C. Continued

2

5

6

7 10

1112

14

15

16

17

IS19

20

23

25

26

29

30

SUBROUTINE JTLOCUS

DERIVE THE J-T INVERSION CURVE. USE ROUTINE DELT AF ( T , 01)

COHMON/l/AL.BE,GA,OE» DCRT , TC RT , PCRT , DGAT, OTRP , TTRP , PTRP

OIHENSION TT<99) tPP(99) .DN(99)

DATA ( A=2. 77755 ), (B=0. 60 625) , (TZ=500.0)

FORNATdHl 16X *THE JOULE-THOHSON INVERSION LOCUS FOR PROPANE*//

1 17X3HT,K 5X5HP.BAR 5X5HM0L/L 7X3HT,K 5X5H3,BAR 5X5HM0L/L)

FORMAT<10X IlOt F10.lt F10.2t IlOt FlO.l. F10.2)

TA = 290 $ NP = 52

PRINT 1 J DO 25 1=1, NP $ OX = 1.6

T = TA 10*1 $ U = T/TZ S 01 = EXP<A-B*U)

IF(T-TCRT) 11,12,12

DL = OENLIQF<T) $ IF(OI-OL) 25,12,12

00 20 IT=1,18

S 0=DI+0X $ SP=DELTAF(T,0)

SS = DELTAF(T,OI)

0=0I-0X % SL=0ELTAF(T,0)

IF(SS-SL) 16,16,16

IFCSP-SL) 19,17,17

SS = SL S 01 = 01 - OX $ GO TO 20

IF(SS-SP) 20,20,19

SS = SP S 01 = 01 ox OX = ox/2

TT(I) = T S ON<I) = 01

CONTINUE $ N = NP/2 $ IT = TT(J) S ITT = TT(J+N)

PRINT 2, IT,PP(J) ,0N( J) , ITT.PPCJfN) ,DN(J+N)

RETURN i END

$ PP(I) = PVTF<T,DI,0)

00 29 J=1,N

SUBROUTINE LACAH

C PROPANE SPEED OF SOUND, LACAM,A.,

C JOURNAL OES RESCHERCHES DU CNRS 34, 25 (MARCH, 1956). (PARIS).

C0MM0N/1/AL,BE,GA,0E, DCRT , TCRT , PCRT , DGAT, DT RP , TT RP , PTRP

COHHON/8/ IN, IK, P,T,0EN, E,H,S, CV,CP,CSAT, N,HK

OIHENSION TC(8) ,IPA(25) ,IWX(6,25)

DATA (Q=l. 01325) , (TZ=273.15) , (TB=405.0)

1 F0RMAT(8X 6F8.0)

2 F0RHAT(9I8)

3 FORMATdHO// 15X *LACAM PROPANE SPEED OF SOUND AT T,K =* F7.2//

1 15X 5HP,BAR 5X5HM0L/L 5X5HM/SEC 5X5HCALC0 6X4HPCNT ) 4 FORHATdOX 2F10.3, 2110, F10.2)

5 FORMAT (IHl)

6 FORMATdHO 14X 4HNP = 14, IIH, MEANPCT = F6.2)

C INDEX I FOR ISOTHERMS. INDEX J FOR PRESSURES.

8 READ 1, (TC(I) ,1=1,8) S 00 9 J=l,25

9 READ 2, IPA(J), (IHX ( I , J) , 1=1 , 8) $ SS = NP = 0 $ PRINT 5 C NON COMPARE KITH MY RESULTS ALONG ISOTHERMS.

10 00 90 1=1,8 $ T = TZ TC(I) $ PRINT 3, T 11 IF(T.LT.TCRT) 12,30

C CASES FOR T LESS THAN TCRT.

12 PS = PSATF(T)

13 00 25 J=l,25 $ P = Q*IPA(J) $ WX = JH = IHX(I,J)

14 IF(P-PS) 18,25,15

15 IF(T.LT.361) 16,17

16 CALL COMPRLQ S GO TO 19

17 CALL LIQTHRM $ GO TO 19

18 CALL GENEOUS

19 OIF=HX-H $ PCT=100*OIF/WX $ IW=W $ NP=NP-d $ SS=SS*ABS (PCT

20 PRINT 4, PtOEN, JM,IW, PCT

25 CONTINUE $ GO TO 90 C CASES FOR T GREATER THAN TCRT.

30 00 40 J=l,25 $ P = Q*IPA(J) S wX = JW = IWX(I,J)

31 IF(T.LT.TB) 32,34

32 PX = PVTF(T,DCRT,0) $ IF(P.GT.PX) 33,34

33 CALL LIQTHRM S GO TO 35

34 CALL GENEOUS

35 OIF=WX-H $ PCT=100*DIF/WX $ IM=W $ NP=NP+1 $ SS=SS+ABS (PCT)

40 PRINT 4, P,DEN, JH,IM, PCT

90 CONTINUE $ SS = SS/NP S PRINT 6, NP, SS

99 RETURN S END

220
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Appendix C. Continued

SUBROUTINE LIQTHRM

FOR OEN ABOVE OCRT, AND T UNDER TB = 405 K. GIVEN P»T, GET DEN AND FUNCTIONS.

IF T = MULTIPL. 10 K, START WITH OY.EY.SY.CVT ON ISOBAR PB,

OTHERWISE, INTEGRATE VIA CPSUMIT ALONG PB TO T, THEN - FINALLY, INTEGRATE ALONG ISOTHERM T TO POINT (P,T).

COMMON/3/OPOT,D2PDT2,OPSDT,DPMOT,DPOO,DPOR,OTSDR,OTHDR

C0MH0N/7/TA,TB,PB, £A,HA,SA, HB,SB, TY1,TY2, DYH.OYS

COMMON/8/ IN, IK, P,T,DEN, E,H,S, CV,CP,CSAT, W,WK

COMMON/10/ OY(40) ,HY(40) ,EY(40> , SY(40) ,CPY(40I ,CVY(40»

COMMON/12/ DELS, OELCV

1 FORMAH1H0 9X *T EXCEEDS TB IN LIOTHRM. / ) 2 IF(T.GT.TB) 3,4

3 PRINT 1 S STOP 41= T/10 $ IF<T-10*I) 10,5

5 OA=OY(I) $ E=EY(>T $ S=SY(I) S CV=CVY(I> $ GO TO 20

10 IF(I-23) 11,12,12

11 K = I+l $ GO TO 13

12 K = I 13 TYl = 10*K 1 TY2 = T $ CALL CPSUMIT

14 H = HY(K» OYH $ S = SY(K) * OYS $ CP = CPXF(T)

15 DA = FINOENF<T,PB) S E = H * 100*PB/DA

16 CV = CP - 10O*T/OPOO*(DPDT/OA)**2

NOW INTEGRATE ALONG T FROM ISOBAR PB TO POINT (P,T).

20 OEN = OB = FINOENF(T,P) $ N = ABS(DB-DA)*5 5 21 E = E EOELF (0,N,T,OA,DB) $ H = E + 100*P/DB

22 S = S DELS $ CV = CV DELCV

23 PX = PVTF(T,OB,l) $ CP = CV 100»T/DPDD*( DPDT/DB) **2

25 W = SQRT(WK*CP*DPDO/CV» $ RETURN- $ END

SUBROUTINE MEMOBAR

MEMORIZE FUNCTIONS ALONG ISOBAR PB = 103.42135 BAR. STORE OY ,HY,EY,SY,CPY ,CVY EVERY 10 K FROM 90 THRU 400 K,

START AT TB = 405 K WITH VALUES HB, SB, THEN - USE CPSUMIT FOR DYH, DYS FROM TYl TO TY2.

COMMON/3/OPDT,02POT2,DPSDT,OPMOT,OPOD,OPDR,DTSDR,OTHOR

C0MM0N/7/TA,T8,PB, EA,HA,SA, HB,SB, TY1.TY2, DYH.OYS

COMMON/10/ OYI40) ,HY<40) ,EYC40) , SY I 40) ,CPY< 40) , CVY <40»

C FIRST, GET VALUES AT 400 K.

1 TYl = TB $ J = 40 S TY2 = TT = 10*J

2 CALL CPSUMIT S OY(J) = ON = FINOENF <TT,PB)

3 HY(J) = HB OYH $ SY(J) = SB OYS

4 EY(J) = HY(J) - 100*PB/ON $ CPY(J) = CPXF(TT»

5 CVY(J) = CPYTJ) - 100»TT/DPOO*(OPDT/ON)**2

C NOW INTEGRATE FROM 400 K DOWN TO 90 K IN STEPS OF 10 K.

10 DO 20 J=l,31 $ K=41-J $ L=40-J

11 TYl = lfl»K $ TY2 = TT = 10*L $ CALL CPSUMIT

12 OY(L) = ON = FINDENF(TT,P8)

13 HY(L) = HYCKI OYH $ SYIL) = SY(K) DYS

14 EY(L) = HY(L» - 100*PB/ON $ CPY<L) = CPXF(TT)

15 CVY(L) = CPYCLI - 100*TT/DPOD*<OPOT/DN) **2

20 CONTINUE $ RETURN $ END

221
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Appendix C. Continued.

SUBROUTINE MEHOSAT

MEMORIZE FUNCTIONS ON THE SATURATED LIQUID BOUNDARY.

STORE OK.EKtSK.CVK EVERY 10 K FROM 90 THRU 360 K. COMMON/a/ IN, IK. P,T,DEN, E,H,S, CV,CP,CSAT, H,HK

COMMON/11/ DK(40) ,EK(40) , SK( 40) ,CVK (40

1 00 3 J=9,36 $ T = 10*J S CALL COEXIST

2 OK(J)=OEN $ EK(J)=E t SK(J)=S $ CVK(J)=CV

3 CONTINUE S RETURN S END

SUBROUTINE PEEK

EXAMINE BEHAVIOR OF EQNSTATE COEFFICIENTS.

B(R) = B1 B2*R B3*R2 B4*R3,

E(R) = E1»(R-1)*(R-ER)*EXP(-GA*R4).

COMMON GKfGKK, B1,B2,B3,B4, E1,ER

C0MM0N/1/AL,8E,GA,0E, OCRT,TCRT,PCRT , DGAT, DTRP , TTRP , PTRP

COMMON/6/ TSAT, THETA, PSAT

4 FORMATdHl 14X *EQUATION OF STATE, COEFFICIENTS* //

1 15X 6HDGAT =E15.9/

2 15X 6HDTRP =F8.4, 8H, TTRP =F8.3, 8H, PTRP =E16.9/

3 15X 6H0CRT =F8.4, 8H, TCRT =F8.3, 8H, PCRT =F13.9//

4 15X 4HAL =FS.2, 6H, BE =F5.2, 6H, GA =F6.3, 6H, OE =F6.3,

5 6H, ER =F5.2// 13X 4F16.11/ 13X F16.ll/ ) 5 F0RMAT(15X 5HM0L/L 6X4HTSAT 5X5HTHETA 6X4HPSAT 9X1HB 9X1HC ) 6 FORMATdOX FlO.l, 3F10.3, F10.4, F10.5)

70 PRINT 4, DGAT, DTRP , T TRP , PTRP , DCRT, TCRi ,PCRT,

1 AL,BE,GA,DE,ER, B1,B2,63,B4, El

71 PRINT 5 $ DO 77 J=l,34 $ ON = 0.5*J S R = S = ON/OCRT

72 R2 = R*R $ R3 = R*R2 $ SN = S-1 $ SR = S-ER

73 B = B1 B2*R B3*R2 B4*R3 S E = E1*SN*SR*EXP(-GA*R2*R2)

76 TS=TSAT=TSATF(ON) S T H=THET AF ( ON) S PS=PSATF(TS)

77 PRINT 6, ON, TS,TH,PS, B,E S RETURN S END

FUNCTION PMELTF(T)

PROPANE MELTING LINE, BAR, VIA REEVES, SCOTT, AND BABB(JR),

J. CHEM. PHYS. 40(12), 3662 (1964).

C0MM0N/1/AL,8E,GA,DE, DCRT , TCRT , PCRT , DGAT, DTRP , TTRP, PTRP

COMHON/3/OPDT,02POT2,OPSOT,OPMOT,OPOD,DPDR,DTSOR,OTHOR

DATA (A = 7180.0),(E = 1.283)

1 X = T/TTRP $ XE = X**E S PMELTF = PTRP * A*(XE-1)

2 OPMDT = A*E*XE/X/TTRP $ RETURN $ END

222
AoDendix C. Continued.

SUBROUTINE PRINTIT

C PRINTOUT ISOCHORES AND ISOTHERMS.

COMMON/1/AL,BE,GA,OE, DCRT.TCRT ,PCRT , DGAT, DTRP.TTRP.PTRP

COMMON/3/OPOT,02POT2tOPSOT,OPMOT»DPOD,OPOR,OTSOR,OTHOR

1 FORMATdB. 2F10.0)

6 FORMATCIHI 16X *THE ISOCHORE AT* F6.2. * MOL/L* //

1 17X 3HT.K 5X5HP.BAR 5X5H0P/0D 5X5HOP/DT lX^H02P/0T2)

7 FORHATdOX FlO.l* 2F10.3. F10.<f, F11.5)

8 FORMATdHl 14X *THE ISOTHERM AT* F7.2t * DEG. K* //

1 lOX 5HM0L/L 5X5HP.BAR 5X5HOP/DO 5X5HDP/DT 5X7H02P/0T2 ) 9 FORMATI5X F10.2, 2F10.3, F10.4, F12.6)

C PRINTOUT THE ISOCHORES.

30 00 60 I=itl7 $ IF(I.EQ.B) 31.32

31 ON = OCRT S GO TO 38

32 IF(I.EQ.17) 33.34

33 ON = OTRP S GO TO 38

34 ON = I 38 PRINT 6. ON

39 IF(ON-OTRP) 40.41.41

40 TS = TSATF(ON) S GO TO 42

41 TS = TTRP*(DN/DTRP»**4

42 IF(I>9) 43.43.44

43 IT = 8 S GO TO 50

44 IFd'll) 45.45.46

45 IT = 4 S GO TO 50

46 IF(I-14) 47,47.48

47 IT = 2 $ GO TO 50

48 IT = 1 50 00 59 J=86.600,IT $ TT = J $ IF(TT-TS) 59,52,52

52 PP = PVTF<TT,ON,l) $ IF (PP.GT. 700) 60 ,58

58 PRINT 7. TT.PP. OPDD, DPOT. 02P0T2

59 CONTINUE

60 CONTINUE

C PRINTOUT THE ISOTHERMS.

100 DO 130 1=1.99 $ READ 1. lOD, TT.DX $ IF(IDD) 101.999

101 PRINT 8. TT S PM = PMELTF(TT)

102 IF(TT-TCRT) 103.103,104

103 DG = OENGASF(TT) $ OL = DENLIQF(TT)

104 IF(I.LT.14) 105.106

105 OS =0.05 $ GO TO 113

106 IF(I.LT.17) 107.108

107 OS = 0.10 S GO TO 113

108 IF(I.EQ.17) 109,110

109 OS = 0.20 $ GO TO 113

110 OS = 0.40

113 00 120 N=1.500 $ ON = N*DS S IFITT-TCRT) 114.115,115

114 IF(ON.GT.DG.ANO.ON.LT.OL) 120.115

115 PP = PVTF (TT ,ON.l) $ IF (PP.GT. PM. OR, PP.GT. 750) 130.119

119 PRINT 9, ON.PP, OPOO, DPDT, D2P0T2

120 CONTINUE

130 CONTINUE

999 RETURN S ENO

223
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Appendix C. Continued.

FUNCTION PSATF(T)

PROPANE VAPOR PRESSURES. BAR.

LN(P/PT) = A*X IB*U C*U2 0*U3) * ll-U) *»E.

ARGS.t U = (T-TT»/aC-TT) , X = (1-TT/T ) / ( 1-TT/TC) . COHHON/3/OPDT«D2POT2f OPSOTtOPHOT.OPOOt OPOR. DTSOR. OTHOR

DATA IE=i.3l « <PTRP=3.0E-9) , <TTRP=85.47) , <TCRT = 369.8 0)

OATA(A=23.37228380I • 18=5.71668738) , f C=>8. 51170 714) » <0=3.97587379)

1 FORMATCIHO 9X ^T EXCEEDS TCRT IN PSATF(T). • / ) 2 UN = TCRT-TTRP $ U = (T-TTRP)/UN $ U2 = U*U S UlT = 1.0/UN

3 XN » 1-TTRP/TCRT S X * (1-T TRP/T ) / XN $ XlT = TTRP/XN/T/T

4 V = 1.0 - U S IF(V) 5,6,7

5 PRINT 1 $ STOP

6 Z = Z1 = 0 S GO TO 8

7 Z = V**E $ Z1 = -E*Z/V

8 M = B*U C*U2 0*U*U2 $ HI = B 2»C*U 3*0*U2

9 F = A*X H*Z S FIT = A*X1T (H*Z1 H1*Z)*U1T

10

PSATF = PTRP*EXPCF) S DPSOT = F1T*PSATF S RETURN S END

FUNCTION PVTF(T,0,H)

C THE EQUATION OF STATE FOR PROPANE.

C PWTF = P,BAR. M=0 YIELDS DP/OT, 02P/DT2. M=1 YIELDS ALSO DP/OO.

C EQNSTATE, P-PSAT = S*GK* (T-TSAT) S*S*GK*TCRT*F (R, T ) , WHERE -

C F(R,T) i B<S)*XBF(R,T) E<S)*XEF(R,T) , AND -

C BIR) = B1 B2*R B3*R2 B4*R3,

C E(R) = E1*(R-1)*<R-ER)»EXP(-GA*R4)

COMMON GK,GKK, B1,B2,B3,B4, E1,ER

COMMON/l/AL,BE,GA,OE, DCRT,TCRT,PCRT , OGAT, OTRP , TT RP , PTRP

COMN0N/3/0P0T,02P0T2, DPSOT, OPMOT,OPOO,OPOR,DTSDR,OTHOR

COMMON/4/ XB1,XB2, XE1,XE2, OXBOR, OXEOR

COMMON/6/ TSAT, THETA, PSAT

COMMON/20/ B,BO, E,EO, XB, XE, FI

IF(O.GT.O) 1,29

1 R = S = O/OCRT $ R2 = R*R S R3 = R*R2 $ R4 = R2*R2 2SN=S-1 S SR=S-ER S TC= TCRT

3 RG = R»GK % GKT = GK*TC $ OSDR = DTRP/03RT

5 TS=TSAT=TSATF(0) S PS=PSAT=PSATF (TS) $ THETA=THETAF(D)

6 XB = XBF(T,0) $ XE = XEF(T,0)

7 B = <B1 B2*R B3*R2 B4*R3) *R2

8 XP = EXP<-GA*R4) $ SM = SN*R2*SR $ E = E1*SM*XP

10 F = B*XB E*XE $ FI = B*XB1 E*XE1

11 F2 = B*XB2 E*XE2 S PVTF = PS RG*(T-TS) GKT*F

14 DPOT = RG GK*F1 $ 02P0T2 = GK*F2/TC $ IF(M) 15,30

15 BD = (2*B1*R 3*B2*R2 4*B3*R3 5*B4*R4) *OSDR

16 XPl = -4*GA*R3 $ SMI = SN*R2 C3*R-2)*R*SR

17 ED = CSM^XPl SM1)*E1*XP*DS0R

20 FI = B*OXBOR BO»XB E*OXEOR ED*XE

26 OPOR = (OPSOT-RG)*OTSOR (T-TS) GK*DSDR GKT*F1

27 OPOD = OPOR/OTRP S RETURN

29 PVTF = DPOT = 02P0T2 =0 S OPOD = GKK*T $ DPOR = DPOD^OTRP

30 RETURN S END

224
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Appendix C. Continued

FUNCTION OVAPXFm

C PROPANE HEATS OF VAPORIZATION, J/MOL. - C VIA PROGRAM QVAP-C3, DEC. 15, 1976 AT 14.31, USING - C DATA FROM PTHERH4, DEC. 13, 1976 AT 10.31.

C QVAP/QTRP X X (XE-X)*(A B*X/XE C*X), WHERE - C X = (TC-T) /(TC*TT) , XE = X**E.

DATA (E=0.38) , CQTx23.906)

DATA (TTRPX85.47) , (TCRT=369.8) , (XNx284.33)

DATA (AxQ. 98373471) ,< B=0 . 41758440) , (Cx> 0.30 674140)

1 IF(T.LT.TCRT) 2,5

2 X X |TCRT-T)/XN $ XE = X**E t S x A B*X/XE C*X

3 QVAPXF X QT*1000*CX (XE-X)*S) % RETURN

5 QVAPXF X 0 { RETURN S END

SUBROUTINE RAO

C SPEED OF SOUND FOR SATLIQ PROPANE AT 143T0 228 K. C INDIAN J. PURE/APPLIED PHYS. 9, 169 tMARCH, 1371).

C HIS FORMULA, M x 2364 - 5.9647*T, METERS/SEC.

COMMON/ 8 / IN, IK, P,T,OEN, E,H,S, CV,CP,CSAT, H,WK

DATA (A=2364.0) ,(Bx5.9647)

3 FORMATdHl 16X *RAO PROPANE SPEED OF SOUND FOR SATO. LIQUID*//

1 17X 3HT,K 5X5HM0L/L 5X5HM/SEC 5X5HCALC0 6X4HPCNT ) 4 FORMATCIOX 2F10.3, 2110, F10.2)

6 FORMATdHO 14X 4HNP x 14 , hh, MEANPCT = F6.2)

10 PRINT 3 S SS X 0 s NP X 19 S DO 15 J=1,NP

11 T X 135 5*J $ IHX = MX X A - B*T

12 CALL CSATSUM S IH x w 13 OIFxHX-M S PCT=100*DIF/HX $ SS=SS*ABS(PCT)

14 PRINT 4, T,OEN, IHX, IN, PCT

15 CONTINUE $ SS X SS/NP $ PRINT 6, NP, SS

30 RETURN S END

1

2

34

5 10

SUBROUTINE SATLQTR

GIVEN P,T, FOR SATLIQ, GET DEN AND FUNCTIONS.

START WITH DY,EY,SY,CVY ON ISOBAR PB AT MULTIPLES OF 10 K. IF T X MULTIPLE OF 10 K, INTEGRATE ON ISOTHERM T DOWN TO SATLIQ.

OTHERWISE, FIRST INTEGRATE ALONG PB VIA CPSUMIT.

COMMON/ 3/0P0T,02P0T2,0PS0T,DPM0T,QP00,0P0R,DTS0R,0TH0R

COMMON/5/ OOSDT

COMMON/7/TA,TB,PB, EA,HA,SA, HB,SB, TY1,TY2, OYH,OYS

COMMON/ 8 / IN, IK, P,T,DEN, E,H,S, CV,CP,CSAT, H,WK

COMMON/10/ DY*40),HY(40),EYI40),

COMMON/12/ DELS, OELCV

DATA (TCRT x 369.80)

FORMATdHO 9X *T EXCEEDS TCRT IN SATLQTR.

IFtT.GT.TCRT) 3,4

SY<40) ,CPYI40) ,CVY<40)

/ )

PRINT 1

I X T/10

OAxOY(I)

K X Id

S STOP

% IF(T-10*I) 10,5

$ ExEY(I) $ SxSY(I) $ CVxCVY(I)

S TYl X 10*K $ TY2 X T $

$ GO TO 20 CALL CPSUMIT

= CPXF(T) 11 H X HY(K) OYH S S x SY(K) DYS $ CP

12 DA X FINOENF (T,PB) $ E x h - 100 *PB/OA

13 CV X CP - 100 *T/OPOO* (DPDT/DA)**2

NOW INTEGRATE ALONG ISOTHERM T DOWN TO THE SATLIQ.

20 DEN X OB X OENLIQF(T) $ DOLOT x OOSDT $ N = 5*ABS(DB-0A)

E X E EOELF(0,N,T,DA,DB) S H x E 100*=»/DB

DELS $ IF(T.LT.TCRT) 24,23

W X 0 $ RETURN

$ PX X PVTF<T,DB,1)

25 CP X CV 100 *T/OPDO* (DP0T/0B)**2

26 CSAT X CV - 100 *T*OPDT*DOLDT/DB/DB

30 H X SQRT (HK*CP*DPOD/CV) $ RETURN $ END

5 21

22 S X s 23 CP X CV X CSAT X 24 CV X CV * OELCV

225
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Appendix C. Continued

SUBROUTINE TABLIQ

C TABULATE THE PROPANE SATURATED LIQUID FUNCTIONS.

COMHON/1/AL,BE,GA,OE, DCRT , TCRT , PCRT , DGAT, OTRP , TTRP , PTRP

COHHON/3/OPDT,02POT2,OPSOT,DPMOT,OPOO,DPOR,DTSDR,OTHDR

COMMON/5/ OOSOT

COMMON/7/TA,TB,PB, EA.HA.SA, HB.SB, TY1,TY2, DYH.OYS

COMMON/8/ INtIKt P.T.OEN, E.H,S« CV.CP.CSAT. HyWK

C0NM0N/9/0NG,EGtHG«SG« CVG.CPG.MG. OPGOT.OPGDD

DIMENSION TSA(60), PSA(60)

4 FORMATdHl 13X PROPERTIES OF SATURATED LIQUID PROPANE* //

1 14X1HT lOXlHP 5X3HDEN 3X5HV.LIQ 6X5HV.GAS 5X6HOPS/OT 3X6HDDL/DT

2 4X5H0P/DT 6X5H0P/0D 2X5HQ.VAP /

3 lOX 5HDEG K 8X3HBAR 3X5HMOL/L 3X5HL/MOL 6X5HL/MOL 6X5HBAR/K

4 2X7HM0L/L/K 4X5HBAR/K 2 X9HBAR-L/M0L 2X5HJ/M0L ) 5 FORMAT(5XF10.3. Ell. 4, F8.3, F8.5, 2E11.4, F9.5, F9.3, Ell. 4, 17) 11 FORMATdHl 13X *PROPERTIES OF SATURATED LIQUID PROPANE* //

1 14X1HT IIXIHP 9X1HE 9X1HH 9X1HS

2 6X2HCV 6X2HCS 6X2HCP 6X1HW /

3 10X5HOEG K 9X3HBAR 5X5HJ/MOL 5X5HJ/M0L 3X7HJ/MOL/K

4 1X7HJ/M0L/K 1X7HJ/M0L/K 1X7HJ/MOL/K 2X5HM/SEC ) 12 F0RMAT(5X F10.3, E12.4, 2F10.1, F10.3, 3F8.2, 17)

FOR PAGE ONE OF TABLIQ.

REPLACE T = 230 BY BOILING-POINT AT J = 30.

130 PRINT 4 $ NP = 58

131 DO 150 J=1,NP $ IF<J.EQ.l) 132,133

132 T = TTRP S GO TO 139

133 IF(J.EQ.30) 134,135

134 T = FINOTSFCI. 01325) $ GO TO 139

135 IF(J.EQ.NP) 136,138

136 T = TCRT S OG = OL = DCRT S DDLDT = 0 137 VG = VL = 1.0/DCRT S GO TO 141

138 T = 80 5*J

139 OL = DENLIQF(T) S OOLOT = DDSDT

140 OG = OENGASFTT) $ VG = 1/OG $ VL = 1/OL

141 TSA(J) = T S PSA(J) = PS = PSATF(T) $ OPXOT = OPSOT

145 IF(T.LT.TA) 146,147

146 CALL COHABIT S IQX = HG - H i GO TO 150

147 PX = PVTF(T,OL,l) S IQX = QVAPXF(T)

150 PRINT 5, T,PS,OL,WL,VG, DPXDT, OOLOT, OPDT,OPDO, IQX

C FOR PAGE TWO OF TABLIQ.

C USE COEXIST AT T UNDER 360 K, USE SATLQTR AT T > 360 K. 160 PRINT 11 S DO 170 J=1,NP $ P = PSA(J) S T = TSA<J)

161 IF(T.LT.360) 162,165

162 IF(T.LT.TA) 163,164

163 CALL CSATSUM S GO TO 166

164 CALL COEXIST S GO TO 166

165 CALL SATLQTR

166 IN = H 170 PRINT 12, T,P, E,H,S, CV,CSAT,CP, IW 999 RETURN $ END
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Appendix C. Continued.

FUNCTION THETAFCOEN)

THETA = TSAT»EXP(UtS) )

LET Q = (S-U/<ST-1>, WHERE ST = OTRP/DCRT, THEN - IF S < 1» U = AL»Q**3t IF S > 1, U = -AL*Q**3,

COHHON/l/AL,BE,GA,OE, DCRT , T CRT , PCRT , OGAT, OTRP , TTRP , PTRP

C0MM0N/3/0P0T»02P0T2f DPSOT,DPMDT»OPODtDPDR,OTSOR,OTHOR

COHHON/6/ TSAT, THETA, PSAT

1 S = OEN/DCRT i OSOR = OTRP/DCRT $ C = OSDR-1

2 Q = (S-D/C $ Q2 = Q^Q $ U = AL*Q*Q2

3 U1 = AL*3*Q2*0SDR/C $ IF<Q) 5,9,4

4 U = -U $ U1 = -U1

5 XP = EXP(U) $ THETAF = TSAT*XP

6 DTHOR = (TSAT*U1 OTSOR)»XP S RETURN

9

THETAF = TCRT $ DTHOR =0 $ RETURN $ END

SUBROUTINE TSAI

C COMPARE VAPOR-PRESSURE AND QVAP DATA OF CHEN3-HSIUNG TSAI, THESIS,

C TENN. TECH. INST., COOKEVILLE, TENN., (JUNE, 1971).

DATA (PA=760.0) , (QP= 1.01 325) , (QK = 4.184) , ( HM= 44. 0 9721

1 F0RMAT(I5, FIO.O, E15.0)

2 F0RMAT(I5, 2F10.0)

3 FORMATCIHI 16X *PROPANE VAPOR PRESSURES OF TSAI * //

1 17X 3HT,K 7X5HP,BAR 7X5HCALC0 6X4HPCNT ) 4 FORMATdOX F10.2, 2E12.4, F10.2)

5 FORMATdHl 16X *PROPANE HEATS OF VAPORIZATION OF TSAI //

1 17X 3HT,K 4X6HKJ/H0L 5X5HCALCD 6X4HPCNT ) 6 FORMATdOX F10.2, 2F10.3, F10.2)

10 PRINT 3 $ 00 15 J=l,99

11 READ 1, ID, T, P S IF(IO) 12,20

12 P = P*QP/PA 1 PC = PSATF(T) S PCT = 100*(P/PC-1)

15 PRINT 4, T, P, PC, PCT

20 PRINT 5 S DO 25 J=l,99

21 READ 2, ID, T, QV S IF(IO) 22,30

22 QV = QV*QK*HM/44095 $ QC=QVAPXF (T) /lOOO $ PCT = 10 0 • ( QV/QC-1

25 PRINT 6, T, QV, QC, PCT

30 RETURN $ END

FOR SAT.LIQ. AT THE BOILING POINT

TA = 231.07066

EA = 16582.169

HA = 16589.864

SA = 170.81253

227
Appendix C. Continued

FUNCTION TSATF(OEN)

C ITERATE T TO MINIMIZE <OEN-OCALCI VIA OENGASF(T), OENLIQF<T».

COMMON/l/AL,BEtGA,OE, OCRT,TCRT ,PCRT , DGAT, DTRP , TT RP, PTRP

COMMON/3/OPOT»02POT2,OPSDT,DPMOT,OPDD,OPDR,OTSDR,DTHOR

COMMON/5/ DOSOT

DATA (Q=2. 01 « (FN=6. 38905611

C NOTE, FN = EXP(Q) - 1.0.

1 FORMATdHO 9X *TSATF FAILS TO CONVERGE. * / ) 2 S = DEN/OCRT $ YN = TCRT/TTRP - 1 S IF(OEN-OCRT) 3,30,4

3 ST=OGAT/DCRT $ F=ALOG (S) /ALOG (ST) * ( ( 1-S ) / ( 1-ST ) ) **2 $ GO TO 5 4 ST=OTRP/OCRT $ U= ( (S-1) / ( ST-1) ) •S S F= (EXP ( Q*U) -1 ) /FN

5 T = TCRT/d YN*F)

6 00 15 J=l,50 S IF(OEN-OCRT) 7,30,8

7 DO = OEN - OENGASF(T) $ GO TO 9

8 00 = OEN - OENLIQF(T)

9 IF(ABS(DO/OEN) .LT.l.OE-7) 16,10

10 OT = OO/DOSOT % IF(ABS(OT/T» .LT.l.OE-7) 16,11

11 T = T DT S IF(T) 12,12,13

12 T = TTRP S GO TO 15

13 IF(T.LT.TCRT) 15,14

14 T = TCRT - 0.10

15 CONTINUE $ PRINT 1 $ STOP

16 TSATF = T $ OTSOR = DTRP/OOSOT S RETURN

30 TSATF = TCRT S OTSOR =0 S RETURN $ ENO

FUNCTION XBF(T,0)

C XBF = SQRT(T/TC)*LN(T/TS) = Q(T)*Z(R,T),

COMMON/l/AL,BE,GA,OE, OCRT , TCRT , PORT , DGAT, DT RP , TT RP , PTRP

COMMON/3/OPOT,02POT2,DPSOT,DPMDT,DPOO,DPDR,DTSOR,OTHDR

COMHON/4/ X81,XB2, XE1,XE2, OXBOR, OXEOR

COMMON/6/ TSAT, THETA, PSAT

1 TC = TCRT i TS = TSAT $ X = T/TC

2 U = T/TS $ UIX = TC/TS $ UlR = -U*DTSDR/TS

3 Z = ALOG(U) $ Z1R=U1R/U $ Z1X=U1X/U $ Z2X=-Z1X*Z1X

4 Q = SQRT(X) $ Q1 = 0.5/Q $ Q2 = -Q1/2/X

5 XBF = $ OXBOR = Q*Z1R $ X81 = 0*Z1X ai*Z

6 XB2 = 0»Z2X Q1*2*Z1X Q2*Z $ RETURN S ENO

function XEF(T,0)

C XEF(T,0) = PSI(T,0) - PSISAT(O), WHERE - C PSI = DE/X (l-OE)*(l - W W*LN(W)), W E (1-TH/T).

C0MM0N/1/AL,8E,GA,DE, OCRT , TCRT , PORT , DGAT, DTRP , TT RP , PTRP

C0MM0N/3/0P0T,02P0T2 ,DPSOT,OPMOT, DP00,0P0R, OTSOR, OTHOR

COMMON/4/ XB1,XB2, XE1,XE2, OXBOR, OXEOR

COMMON/6/ TSAT, THETA, PSAT

2 A = OE S B = 1-A S TC = TCRT $ TH = THETA $ TS = TSAT

3 X = T/TC $ X2 = X*X $ XS = TS/TC $ XSl = OTSOR/TC

4 M = 1.0 - TH/T S IF(H) 30,30,5

5 HIR = -OTHOR/T S HIX = TH/T/X S W2X = -2*H1X/X

6 G=ALOG(W) S G1R=N1R/H $ G1X=W1X/H $ G2X = W2X/H - GIX^^GIX

10 P = A/X B*(W*G - W 1) $ PIR = B*(W*G1R W1R*G - HIR)

11 XEl = -A/X2 B*(H*G1X W1X*G - WIX)

12 XE2 = 2*A/X/X2 B*(W*G2X 2*W1X*G1X H2X»G - H2X)

19 HS = 1.0 - TH/TS $ IF(HS) 20,20,21

20 PS = 1 S PSI =0 S GO TO 25

21 GS = ALOG(WS) $ PS = A/XS B*(HS*GS - HS 1)

22 PSI = -A*XS1/XS/XS B*(TH*0TS0R/TS - DTHOR)*GS/TS

25 XEF = P - PS $ OXEOR = PIR - PSI $ RETURN

30 XEF = XEl = XE2 = OXEOR =0 $ RETURN $ ENO

228
Appendix C. Continued.

SUBROUTINE YESAVAG

C READ AND COMPARE YESAVAGE SP. HEATS CP(T) ALONG ISOBARS.

COMMON/l/AL,BE»GA,OE, OCRT , TCRT , PCRT , DGAT, OTRP , TT RP , PTRP C0MM0N/7/TA,TB,PB. EA,HA,SA, HB,SB, TY1,TY2, DYH.DYS

COMMON/8/ IN, IK, P,T,OEN, E,H,S, CV,CP,CSAT, H.MK

DIMENSION PSIC5) ,TF(12) ,CPB(5,12)

DATA (TCRT=369.8) , (TB=405.0)

DATA (0=1. 01325) , (QP= 14.69595 ) , ( CPK= 184 . 50 2 7

1 FORMATdOX 5F10.0)

2 FORMAT(6F10.0)

3 FORMATdHO// 17X *YESAVAGE CP(TI ISOBAR AT »,BAR =» F8.3//

1 17X 3HT,K 5X5HH0L/L 3X7HJ/M0L/K 5X5HCALC0 4X4HPCNT ) 4 FORMATdOX 2F10.3, 2F10.2, F8.2)

6 FORMATdHO 14X 4HNP = 14, IIH, MEANPCT = F6.2)

10 READ 1, (PSI(I) ,1=1,5) $ DO 11 J=l,12

11 READ 2, TFd), (CPB ( I , J) , 1=1 , 5) S SS = NP = 0 C COMPARE WITH MY RESULTS ALONG HIS ISOBARS.

20 DO 90 1 = 1,5 $ P = Q^PSKD/QP $ PRINT 3, P 21 IF(P.LT.PCRT) 22,50

22 TS = FINOTSF(P) S DO 40 J=l,12

23 T = (TF (J)-32)/1.8 + 273.15 $ CPY=CPK*CPB ( I, J) $ IF(CPY) 24,40

24 IF(T.LT.TS) 25,31

25 IFIT.LT.TA) 26,27

26 CALL COMLIQ $ GO TO 32

27 CALL COMPRLQ $ GO TO 32

31 CALL GENEOUS

32 DIF=CPY-CP $ PCT=100*DIF/CPY $ NP=NP+1 S SS=SS+ ABS ( PCT

33 PRINT 4, T,DEN,CPY, CP,PCT

40 CONTINUE S GO TO 90

C CASES FOR P GREATER THAN PCRT.

50 DO 70 J=l,12 $ T = (TF( J) -32) /1.8 273.15

52 CPY = CPK*CPB(I,J) $ IF(CPY) 53,70

53 IF(T.LT.361) 55,54

54 IF(T.LT.TB) 56,58

C CASE FOR T LESS THAN TCRT.

55 CALL COMPRLQ $ GO TO 60

C CASES FOR T.GT.TC. AND. T.LT.TB.

56 OX = FINOENF(T,P) $ IF ( OX .GT . OCRT) 57,58

57 CALL LIQTHRM $ GO TO 60

58 CALL GENEOUS

60 OIF=CPY-CP $ PCT=100*OIF/CPY $ NP=NP-fl $ SS=SS + ABS (PCT)

61 PRINT 4, T, DEN, CPY, CP, PCT

70 CONTINUE

90 CONTINUE S SS = SS/NP $ PRINT 6, NP, SS

99 RETURN $ END

PROPANE FUNCTIONS AT POINT (TB,I

T = 405.000, P = 103 .42135, OEN

EZ = 20390.536, E = 39050.050

HZ = 23757.844, H = 40454. 530

SZ = 295.36896, S = 236.93524

CVZ = 86.584, cv = 96.926

CPZ = 94.899, CP = 170.706

YESAVAGE VALUE, CP = 168.368
o

o

Appendix C. Continued

PROGRAM ZIEGLER (OUTPUT)

PROPANE, ESTIM. V.P. AND QVAP FROM TRIPLE- TO BOILING-POINTS,

USING ENTHALPY AND ENTROPY CLOSED LOOPS.

COMMON/1/ TA,TB,PB,QB, DELH,OELS

COMMON/2/ EZA,HZA,SZA, HGB,SGB, OHLAB.DSLAB

C0MM0N/3/0P0T,02P0T2,DPS0T,0PM0T,0PD0,DP0R,0TSDR,0TH0R

COMMON/9/ PZIP, BZ, DBZOT, DPZOT, OZDD

COMMON/99/ TI,EZZ, EZ,SZ,CVZ, HZ,CPZ

DIMENSION QK(2) ,TK( 150) ,OK(1SO) ,PIK( 150) ,PK(150I ,QJ (150)

3 FORMATdHl IIX »PROPANE ESTIM. V.P. , BAR, AND QVAP, KJ/MOL. • //

1 12X 4HTB =F10.5, 6H, PB =F8.5, 6H, OB =F9.6/

2 12X5HEZB =F7.1, 7H, EGB =F7.1, 7H, HZB =F8.1, 7H, HGB =F8.1/

3 12X 5HSZB =F9.4, 7H, SGB =F9.4, 6H, QB =F8.1/ ) 4 FORMAK7X 3HT,K 8X2HPI 6X5HP,BAR 5X5HMOL/L 6X3HHZA 6X3HHGA

1 6X3HSZA 6X3HSGA 4X5H0HGAB 4X5H0HLAB 4X5H0SGAB 4X5H0SLAB

2 5X3HQAH 5X3HQAS ) 5 F0RMAT(2XF8.2, El 0 . 4 , Ell . 5 , El 0 . 4 , 2F9.1.2F9.3, 2F9.1.2F9.3, 2F8.3)

6 FORMAT(12X 3HT,K 4X5H100/T 7X5HP.EQN 7X5HP,BAR 6X5HLN(P)

1 7X5HM0L/L 3X5HQ,EQN 3X5HQ.VAP ) 7 F0RMAT(5X F10.2, F9.5, 2E12.5, F11.5, E12.5, 2F8.3)

8 TTRP = 85.47 $

' TB = 231.0707 $ PB = 1.01325

9 QK(1) = 18780.0 $ QK(2) = 13864.0

C GET HGB, SGB FOR SATVAPOR AT THE BOILING POINT,

10 TI = TB $ CALL IDEAL $ EZB=EZ $ HZB=HZ $ SZB=SZ

11 ONB = FINOENF(TB,PB) $ EGB = EZ EDELF ( T B , DNB)

12 SGB = SZ DELS $ HGB = EGB 100*PB/ONB

C USE BOTH KEMP, EGAN QK(1), AND R.O.G. QK(2).

14 DO 99 1=1,2 $ QB = QK(I)

15 PRINT 3, TB,PB,ONB, EZB,EGB, HZB, HGB, SZB,SGB, QB £ PRINT 4

C DO TEMPERATURES FROM TRIPLE- TO BOILING-POINTS - 20 DO 50 J=l,147 $ IF(J.EQ.l) 21,22

21 TA = T = TTRP $ GO TO 23

22 TA = T = 84 J

C GET EZA, HZA, SZA AT T = TA.

23 TI = TA £ CALL IDEAL £ EZA=EZ £ HZA=HZ £ SZA=SZ

C GET OHLAB, DSLAB FOR THE SATOLIQUIO FROM TA TO TB.

24 CALL CSATSUM £ DHLAB = OELH £ DSLAB = DELS

C NOW ITERATE P (T=TA) TO MINIMIZE (QAH - QAS)

30 P = PI = PSATF(T) £ DP = P/2 £ SS = OELTAF(T,P)

31 DO 40 IT=1,15 £ PL = P-DP £ SL = DELTAF(T,PL)

32 PF = P+DP £ SP = DELTAF(T,PP)

35 IF(SL-SS) 36,36,38

36 IF(SL-SP) 37,37,39

37 SS = SL £ P = P - OP £ GO TO 40

38 IF(SP-SS) 39,40,40

39 SS = SP £ P = P DP

40 DP = OP/2 £ ONA = FINDENF(T,P)

C USE FINAL P TO GET ONA, HGA,SGA, OHGAB,OSGAB,

C AND THEN, VIA LOOP, GET QAH, QAS.

42 EGA = EZA EDELF(T,ONA) £ SGA = SZA DELS

43 HGA = EGA 100*P/DNA £ DHGAB=HGB- HGA £ DSGA8=SGB-SGA

44 QAH = QB OHLAB - OHGAB £ QAS = TA*(QB/TB DSLAB - OSGAB)

45 QAH = QAH/1000 £ QAS = QAS/1000 £ PIK(J) = PI

46 TK(J)=TA £ OK(J)=ONA £ PK(J)=P £ QJ(J) = (QAH+QAS)/2

50 PRINT 5, TA,PI,P,DNA, HZA, HGA, SZA, SGA, OHGAB, DHLAB,

1 OSGAB, DSLAB, QAH, QAS

C PRINT T,l/T, PEQN,P,LN (P) , ONA, QEQN,Q, FOR PUBLICATION.

61 PRINT 3, TB,PB,0NB, EZB,EGB, HZB, HGB, SZB,SGB, QB £ PRINT 6 65 00 99 J=l,147 £ IF(J.EQ.50 tOR«J*EQ« 99) 67,70

67 PRINT 3, TB,PB,0NB, EZB.EGB, HZB.HGBf SZBfSGBt QB £ PRINT 6

70 T = TK(J) £ AT = 100/T £ P = PK(J) £ GP = ALOG(P)

71 QE = QVAPXF(T)/1000

75 PRINT 7, T,AT, PIK(J),P,GP, OK(J), QE ,QJ( J) 99 CONTINUE £ STOP £ END

230
n

OOOO

OOO

Appendix C. Continued.

SUBROUTINE CSATSUH

C GET OELH, DELS ALONG SATOLIO FROM TA TO T0.

COMMQN/1/ TA.TB.PB.QB, DELH.OELS

COMHON/3/OPOT.D2PO.T2»OPSOT,OPMOT,OPOD,OPDR,DTSOR,DTHOR 1E = H= S = 0 2 TR = TB - TA S N..= A8S(TR)/2 *2 $ QT = TR/N

3 DO a J=ltN S TJ i TA IJ-0.5I»OT

4 CS = CSATXF(TJ) t PS = PSATF4TJ) S PS = DENLIQF4TJ)

5 H = H CS*OT iaO*DPSOT*OT/OS % S = S CS*0T'/TJ

8 CONTINUE

9 OELH = H S DELS = S S RETURN $ END

FPNCTIOH OELTAFIT.PI

GET 0NA,EL6A,HGA,SGA FOR SATDVAPOR AT T,P, (ToTA),

GET 0H6AB = HGB-HGA* OSGAB z SGB-SGA,

GET QAH, QAS VIA CLOSED LOOPS, THEN, OELTAF = ABSCQAH-QASI

COMNON/1/ TA,TB,PB,OB, OELH, DELS

COHHON/2/ EZA,HZA,S2A, HGB.SGB, OHLAB,DSLAB

COHMON/99/ TI.EZZ, EZ,SZ,CVZ, HZ,CP7

1 IF(P.GT.Q) 2,9

2 ONA = FINOENf(T,P) S EGA = EZA EDELF(T,DNA)

3 SGA = SZA DELS HGA = EGA 100*P/ONA

5 OHGA8 = HGB • HGA S OSGAB = SGB > SGA

6 QAH = QB OHLAB - OHGAB $ QAS = T*(QB/TB DSLAB - OSGABJ

8 OELTAF = ABS(QAH-QAS) $ RETURN

9 OELTAF = 1.0E*100 S RETURN $ ENO

FUNCTION E0ELF(T,0)

CHANGE OF.E,S ON ISOTHERM T FROM OEN = 0 TO DEN = D,

USE VIRIAL EQNSTATE. NOTE DCZ =5.0 MOL/L.

OELE = EOELF = -R*(0/0C2)*T*T*DB.<T)/0T,

DELS = -R*LN<0*R*T/PU - R*<D/DCZJ * ( B <T» T*OB<T)/OT).

COMHON/1/ TA,TB,PB,QB, OELH, DELS

COMMO.N/9/ PZIP, BZ, OBZOT, OPZOT, OZOO

DATA {Q=i.01325) ,(R=0.0831434) , (DCZ=4.96)

1 Z = ZIPF<T,OI S EOELF = -100»R*(O/DCZ)*T*T*OBZOT

2 DELS = AL0G(0*R*T/Q) (D/OCZ)*4BZ T*OBZDT)

9 DELS = -100*R»OELS S RETURN S ENO

FUNCTION FINOENFIT,P)

GIVEN P,T IN VIRIAL EQN., SOLVE QUADRATIC FOR DEN, MOL/L.

DATA IOCRT=4.96),|TCRT=369.80I, IR=0.0831434)

DATA (B1=0.45406U) , 4 B2=-1.1899134) , 4 B3=-0 . 4726952

1 X = T/TCRT S B = B1 B2/X B3/X/X/X

2 Q = SQRT41.0 4*P*B/R/T/OCRT)

3 FINDENF = DCRT* 4Q-1 ) /2/B $ RETURN $ ENO

FUNCTION ZIPF4T,0)

PROPANE VIRIAL EQUATION, R.O.G., MAY 6, 1976.

Z4T,0) = 1 B4X)*S, X = T/TCRT, S

= HEN/OCRT,

B4X) = B1 -1^ B2/X B3/X3. OEN IN MOL/L.

COMHON/9/ PZIP, 8Z, OBZOT, OPZOT, OZOO

DATA 40CRT=4.96) , 4TCRT=369.80) , 4R=0. 083I4S4)

DATA 4B1=0.4540611» , 4 B2 = -l. 1899134) , 4B7=-0. 4726952)

1 S = O/OCRT $ X = T/TCRT $ X2 = X*X S X3 = X*X2

2 BZ = B = B1 B2/X B3/X3

3 ZIPF^ = 1.0 B*S t PZIP = D*R*T^ZIPF

4 OBZOT = -IB2/X2 3»B3/X/X3» /TCRT S OZOO = B/OCRT

5 OPZOT = 0*R» 4S*T*O0ZOT ZIPF) $ RETURN $ END

231
U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. iniHLK ATION OR KI-MOKT NO.

NBSIR 77-860

2. Gov't Accfs.sion No.

3. Rec ipicnt Vs Acccs.sion No.

4, TITU-; AND SUHTITUPROVISIONAL THERMODYNAMIC FUNCTIONS OF PROPANE, FROM 85 TO

700 K AT PRESSURES TO 700 BAR

S. Publication Date July 1977

6. Performing Organisation Co4( 275.02

7. AUHIOR(S) 8. Performing Organ. Report No.

,D. Goodwin

9. PKRPOR.MINCi ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No 2750574

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

The American Gas Association

1515 Wilson Boulevard

Arlington, Virginia 22209

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most sigpificartt informatiort. If document includes a significant

bibliography or literature survey, mention it here.)

Thermophysical properties of propane are tabulated at integral temperatures over the

entire range of fluid states from 85 to 700 K along isobars to 700 bar. A modified

form of the nonanalytic equation of state is employed for the first time. Thermodynaaij

functions for the compressed liquid are obtained by use of heats of vaporization fron

the boiling point to the critical point, such that the free energies of saturated

liquid and vapor are equal.

17. KEY VORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Densities; enthalpies; entropies; equation of state; internal

energies; isobars; isochores; isotherms; Joule-Thomson inversion; latent heats of

vaporization; melting line; orthobaric densities; propane; specific heats; speeds of

sound; vapor pressures.

18. AVAILABILITY |X Unlimited 19. SECURITY CLASS

(THIS REPORT)

21.

1 For Official Distribution. Do Not Release to NTIS

UNCL ASSIFIED

r Order From Sup. of Doc., U.S. Government Printing Office Washington, D.C. 20402. SD Cat. No. C13

20. SECURITY CLASS

(THIS PAGE)

22.

1 X ' Order From National Technical Information Service (NTIS)

Springfield, Virginia 22I5I UNCLASSIFIED

21. NO. OF PAGES

239

$ 8.00

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